Properties

Label 1305.2.a.p.1.3
Level $1305$
Weight $2$
Character 1305.1
Self dual yes
Analytic conductor $10.420$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1305,2,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1305.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1305.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(10.4204774638\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.48119 q^{2} +0.193937 q^{4} -1.00000 q^{5} +1.19394 q^{7} -2.67513 q^{8} +O(q^{10})\) \(q+1.48119 q^{2} +0.193937 q^{4} -1.00000 q^{5} +1.19394 q^{7} -2.67513 q^{8} -1.48119 q^{10} -4.15633 q^{11} +2.96239 q^{13} +1.76845 q^{14} -4.35026 q^{16} -5.50659 q^{17} -3.19394 q^{19} -0.193937 q^{20} -6.15633 q^{22} -1.84367 q^{23} +1.00000 q^{25} +4.38787 q^{26} +0.231548 q^{28} +1.00000 q^{29} -4.80606 q^{31} -1.09332 q^{32} -8.15633 q^{34} -1.19394 q^{35} -9.50659 q^{37} -4.73084 q^{38} +2.67513 q^{40} +11.2750 q^{41} -0.0303172 q^{43} -0.806063 q^{44} -2.73084 q^{46} -4.80606 q^{47} -5.57452 q^{49} +1.48119 q^{50} +0.574515 q^{52} +1.35026 q^{53} +4.15633 q^{55} -3.19394 q^{56} +1.48119 q^{58} -13.2750 q^{59} +8.88717 q^{61} -7.11871 q^{62} +7.08110 q^{64} -2.96239 q^{65} +5.84367 q^{67} -1.06793 q^{68} -1.76845 q^{70} +1.27504 q^{71} -15.2447 q^{73} -14.0811 q^{74} -0.619421 q^{76} -4.96239 q^{77} -4.93207 q^{79} +4.35026 q^{80} +16.7005 q^{82} -4.41819 q^{83} +5.50659 q^{85} -0.0449056 q^{86} +11.1187 q^{88} +3.61213 q^{89} +3.53690 q^{91} -0.357556 q^{92} -7.11871 q^{94} +3.19394 q^{95} -1.38058 q^{97} -8.25694 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} + q^{4} - 3 q^{5} + 4 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} + q^{4} - 3 q^{5} + 4 q^{7} - 3 q^{8} + q^{10} - 2 q^{11} - 2 q^{13} - 6 q^{14} - 3 q^{16} + 4 q^{17} - 10 q^{19} - q^{20} - 8 q^{22} - 16 q^{23} + 3 q^{25} + 14 q^{26} + 12 q^{28} + 3 q^{29} - 14 q^{31} + 3 q^{32} - 14 q^{34} - 4 q^{35} - 8 q^{37} + 8 q^{38} + 3 q^{40} + 2 q^{41} + 2 q^{43} - 2 q^{44} + 14 q^{46} - 14 q^{47} - 5 q^{49} - q^{50} - 10 q^{52} - 6 q^{53} + 2 q^{55} - 10 q^{56} - q^{58} - 8 q^{59} - 6 q^{61} - 11 q^{64} + 2 q^{65} + 28 q^{67} - 12 q^{68} + 6 q^{70} - 28 q^{71} - 16 q^{73} - 10 q^{74} - 14 q^{76} - 4 q^{77} - 6 q^{79} + 3 q^{80} + 30 q^{82} - 12 q^{83} - 4 q^{85} - 24 q^{86} + 12 q^{88} + 10 q^{89} - 12 q^{91} - 4 q^{92} + 10 q^{95} + 8 q^{97} - 21 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48119 1.04736 0.523681 0.851914i \(-0.324558\pi\)
0.523681 + 0.851914i \(0.324558\pi\)
\(3\) 0 0
\(4\) 0.193937 0.0969683
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.19394 0.451266 0.225633 0.974212i \(-0.427555\pi\)
0.225633 + 0.974212i \(0.427555\pi\)
\(8\) −2.67513 −0.945802
\(9\) 0 0
\(10\) −1.48119 −0.468395
\(11\) −4.15633 −1.25318 −0.626590 0.779349i \(-0.715550\pi\)
−0.626590 + 0.779349i \(0.715550\pi\)
\(12\) 0 0
\(13\) 2.96239 0.821619 0.410809 0.911721i \(-0.365246\pi\)
0.410809 + 0.911721i \(0.365246\pi\)
\(14\) 1.76845 0.472639
\(15\) 0 0
\(16\) −4.35026 −1.08757
\(17\) −5.50659 −1.33554 −0.667772 0.744366i \(-0.732752\pi\)
−0.667772 + 0.744366i \(0.732752\pi\)
\(18\) 0 0
\(19\) −3.19394 −0.732739 −0.366370 0.930469i \(-0.619399\pi\)
−0.366370 + 0.930469i \(0.619399\pi\)
\(20\) −0.193937 −0.0433655
\(21\) 0 0
\(22\) −6.15633 −1.31253
\(23\) −1.84367 −0.384433 −0.192216 0.981353i \(-0.561568\pi\)
−0.192216 + 0.981353i \(0.561568\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 4.38787 0.860533
\(27\) 0 0
\(28\) 0.231548 0.0437585
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −4.80606 −0.863194 −0.431597 0.902066i \(-0.642050\pi\)
−0.431597 + 0.902066i \(0.642050\pi\)
\(32\) −1.09332 −0.193274
\(33\) 0 0
\(34\) −8.15633 −1.39880
\(35\) −1.19394 −0.201812
\(36\) 0 0
\(37\) −9.50659 −1.56287 −0.781437 0.623985i \(-0.785513\pi\)
−0.781437 + 0.623985i \(0.785513\pi\)
\(38\) −4.73084 −0.767444
\(39\) 0 0
\(40\) 2.67513 0.422975
\(41\) 11.2750 1.76087 0.880433 0.474171i \(-0.157252\pi\)
0.880433 + 0.474171i \(0.157252\pi\)
\(42\) 0 0
\(43\) −0.0303172 −0.00462332 −0.00231166 0.999997i \(-0.500736\pi\)
−0.00231166 + 0.999997i \(0.500736\pi\)
\(44\) −0.806063 −0.121519
\(45\) 0 0
\(46\) −2.73084 −0.402640
\(47\) −4.80606 −0.701036 −0.350518 0.936556i \(-0.613995\pi\)
−0.350518 + 0.936556i \(0.613995\pi\)
\(48\) 0 0
\(49\) −5.57452 −0.796359
\(50\) 1.48119 0.209473
\(51\) 0 0
\(52\) 0.574515 0.0796710
\(53\) 1.35026 0.185473 0.0927364 0.995691i \(-0.470439\pi\)
0.0927364 + 0.995691i \(0.470439\pi\)
\(54\) 0 0
\(55\) 4.15633 0.560439
\(56\) −3.19394 −0.426808
\(57\) 0 0
\(58\) 1.48119 0.194490
\(59\) −13.2750 −1.72826 −0.864131 0.503266i \(-0.832132\pi\)
−0.864131 + 0.503266i \(0.832132\pi\)
\(60\) 0 0
\(61\) 8.88717 1.13788 0.568942 0.822377i \(-0.307353\pi\)
0.568942 + 0.822377i \(0.307353\pi\)
\(62\) −7.11871 −0.904078
\(63\) 0 0
\(64\) 7.08110 0.885138
\(65\) −2.96239 −0.367439
\(66\) 0 0
\(67\) 5.84367 0.713919 0.356959 0.934120i \(-0.383813\pi\)
0.356959 + 0.934120i \(0.383813\pi\)
\(68\) −1.06793 −0.129505
\(69\) 0 0
\(70\) −1.76845 −0.211370
\(71\) 1.27504 0.151319 0.0756596 0.997134i \(-0.475894\pi\)
0.0756596 + 0.997134i \(0.475894\pi\)
\(72\) 0 0
\(73\) −15.2447 −1.78426 −0.892130 0.451779i \(-0.850790\pi\)
−0.892130 + 0.451779i \(0.850790\pi\)
\(74\) −14.0811 −1.63689
\(75\) 0 0
\(76\) −0.619421 −0.0710525
\(77\) −4.96239 −0.565517
\(78\) 0 0
\(79\) −4.93207 −0.554901 −0.277451 0.960740i \(-0.589490\pi\)
−0.277451 + 0.960740i \(0.589490\pi\)
\(80\) 4.35026 0.486374
\(81\) 0 0
\(82\) 16.7005 1.84426
\(83\) −4.41819 −0.484959 −0.242480 0.970156i \(-0.577961\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(84\) 0 0
\(85\) 5.50659 0.597273
\(86\) −0.0449056 −0.00484230
\(87\) 0 0
\(88\) 11.1187 1.18526
\(89\) 3.61213 0.382885 0.191442 0.981504i \(-0.438684\pi\)
0.191442 + 0.981504i \(0.438684\pi\)
\(90\) 0 0
\(91\) 3.53690 0.370768
\(92\) −0.357556 −0.0372778
\(93\) 0 0
\(94\) −7.11871 −0.734239
\(95\) 3.19394 0.327691
\(96\) 0 0
\(97\) −1.38058 −0.140177 −0.0700883 0.997541i \(-0.522328\pi\)
−0.0700883 + 0.997541i \(0.522328\pi\)
\(98\) −8.25694 −0.834077
\(99\) 0 0
\(100\) 0.193937 0.0193937
\(101\) 13.0132 1.29486 0.647430 0.762125i \(-0.275844\pi\)
0.647430 + 0.762125i \(0.275844\pi\)
\(102\) 0 0
\(103\) 5.31994 0.524190 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(104\) −7.92478 −0.777088
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 13.8192 1.33596 0.667978 0.744181i \(-0.267160\pi\)
0.667978 + 0.744181i \(0.267160\pi\)
\(108\) 0 0
\(109\) −1.87399 −0.179496 −0.0897479 0.995965i \(-0.528606\pi\)
−0.0897479 + 0.995965i \(0.528606\pi\)
\(110\) 6.15633 0.586983
\(111\) 0 0
\(112\) −5.19394 −0.490781
\(113\) 11.7685 1.10708 0.553541 0.832822i \(-0.313276\pi\)
0.553541 + 0.832822i \(0.313276\pi\)
\(114\) 0 0
\(115\) 1.84367 0.171924
\(116\) 0.193937 0.0180066
\(117\) 0 0
\(118\) −19.6629 −1.81012
\(119\) −6.57452 −0.602685
\(120\) 0 0
\(121\) 6.27504 0.570458
\(122\) 13.1636 1.19178
\(123\) 0 0
\(124\) −0.932071 −0.0837025
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.2677 1.26606 0.633029 0.774128i \(-0.281811\pi\)
0.633029 + 0.774128i \(0.281811\pi\)
\(128\) 12.6751 1.12033
\(129\) 0 0
\(130\) −4.38787 −0.384842
\(131\) −5.89446 −0.515001 −0.257501 0.966278i \(-0.582899\pi\)
−0.257501 + 0.966278i \(0.582899\pi\)
\(132\) 0 0
\(133\) −3.81336 −0.330660
\(134\) 8.65562 0.747731
\(135\) 0 0
\(136\) 14.7308 1.26316
\(137\) −18.2823 −1.56197 −0.780983 0.624553i \(-0.785281\pi\)
−0.780983 + 0.624553i \(0.785281\pi\)
\(138\) 0 0
\(139\) −11.5369 −0.978547 −0.489274 0.872130i \(-0.662738\pi\)
−0.489274 + 0.872130i \(0.662738\pi\)
\(140\) −0.231548 −0.0195694
\(141\) 0 0
\(142\) 1.88858 0.158486
\(143\) −12.3127 −1.02964
\(144\) 0 0
\(145\) −1.00000 −0.0830455
\(146\) −22.5804 −1.86877
\(147\) 0 0
\(148\) −1.84367 −0.151549
\(149\) −2.77575 −0.227398 −0.113699 0.993515i \(-0.536270\pi\)
−0.113699 + 0.993515i \(0.536270\pi\)
\(150\) 0 0
\(151\) 1.79877 0.146382 0.0731909 0.997318i \(-0.476682\pi\)
0.0731909 + 0.997318i \(0.476682\pi\)
\(152\) 8.54420 0.693026
\(153\) 0 0
\(154\) −7.35026 −0.592301
\(155\) 4.80606 0.386032
\(156\) 0 0
\(157\) 3.76845 0.300755 0.150378 0.988629i \(-0.451951\pi\)
0.150378 + 0.988629i \(0.451951\pi\)
\(158\) −7.30536 −0.581183
\(159\) 0 0
\(160\) 1.09332 0.0864346
\(161\) −2.20123 −0.173481
\(162\) 0 0
\(163\) 1.64244 0.128646 0.0643231 0.997929i \(-0.479511\pi\)
0.0643231 + 0.997929i \(0.479511\pi\)
\(164\) 2.18664 0.170748
\(165\) 0 0
\(166\) −6.54420 −0.507928
\(167\) −8.08110 −0.625334 −0.312667 0.949863i \(-0.601222\pi\)
−0.312667 + 0.949863i \(0.601222\pi\)
\(168\) 0 0
\(169\) −4.22425 −0.324943
\(170\) 8.15633 0.625562
\(171\) 0 0
\(172\) −0.00587961 −0.000448316 0
\(173\) 7.73813 0.588320 0.294160 0.955756i \(-0.404960\pi\)
0.294160 + 0.955756i \(0.404960\pi\)
\(174\) 0 0
\(175\) 1.19394 0.0902531
\(176\) 18.0811 1.36291
\(177\) 0 0
\(178\) 5.35026 0.401019
\(179\) 21.4010 1.59959 0.799795 0.600274i \(-0.204942\pi\)
0.799795 + 0.600274i \(0.204942\pi\)
\(180\) 0 0
\(181\) 15.2750 1.13538 0.567692 0.823241i \(-0.307836\pi\)
0.567692 + 0.823241i \(0.307836\pi\)
\(182\) 5.23884 0.388329
\(183\) 0 0
\(184\) 4.93207 0.363597
\(185\) 9.50659 0.698938
\(186\) 0 0
\(187\) 22.8872 1.67368
\(188\) −0.932071 −0.0679783
\(189\) 0 0
\(190\) 4.73084 0.343211
\(191\) −3.31994 −0.240223 −0.120111 0.992760i \(-0.538325\pi\)
−0.120111 + 0.992760i \(0.538325\pi\)
\(192\) 0 0
\(193\) −4.88129 −0.351363 −0.175681 0.984447i \(-0.556213\pi\)
−0.175681 + 0.984447i \(0.556213\pi\)
\(194\) −2.04491 −0.146816
\(195\) 0 0
\(196\) −1.08110 −0.0772216
\(197\) 24.2374 1.72685 0.863423 0.504481i \(-0.168316\pi\)
0.863423 + 0.504481i \(0.168316\pi\)
\(198\) 0 0
\(199\) 16.7513 1.18747 0.593734 0.804661i \(-0.297653\pi\)
0.593734 + 0.804661i \(0.297653\pi\)
\(200\) −2.67513 −0.189160
\(201\) 0 0
\(202\) 19.2750 1.35619
\(203\) 1.19394 0.0837979
\(204\) 0 0
\(205\) −11.2750 −0.787483
\(206\) 7.87987 0.549017
\(207\) 0 0
\(208\) −12.8872 −0.893564
\(209\) 13.2750 0.918254
\(210\) 0 0
\(211\) −25.3054 −1.74209 −0.871046 0.491201i \(-0.836558\pi\)
−0.871046 + 0.491201i \(0.836558\pi\)
\(212\) 0.261865 0.0179850
\(213\) 0 0
\(214\) 20.4690 1.39923
\(215\) 0.0303172 0.00206761
\(216\) 0 0
\(217\) −5.73813 −0.389530
\(218\) −2.77575 −0.187997
\(219\) 0 0
\(220\) 0.806063 0.0543448
\(221\) −16.3127 −1.09731
\(222\) 0 0
\(223\) 17.6932 1.18483 0.592413 0.805634i \(-0.298175\pi\)
0.592413 + 0.805634i \(0.298175\pi\)
\(224\) −1.30536 −0.0872178
\(225\) 0 0
\(226\) 17.4314 1.15952
\(227\) −26.8423 −1.78158 −0.890792 0.454412i \(-0.849849\pi\)
−0.890792 + 0.454412i \(0.849849\pi\)
\(228\) 0 0
\(229\) −17.2243 −1.13821 −0.569105 0.822265i \(-0.692710\pi\)
−0.569105 + 0.822265i \(0.692710\pi\)
\(230\) 2.73084 0.180066
\(231\) 0 0
\(232\) −2.67513 −0.175631
\(233\) 9.07381 0.594445 0.297222 0.954808i \(-0.403940\pi\)
0.297222 + 0.954808i \(0.403940\pi\)
\(234\) 0 0
\(235\) 4.80606 0.313513
\(236\) −2.57452 −0.167587
\(237\) 0 0
\(238\) −9.73813 −0.631230
\(239\) −20.4993 −1.32599 −0.662995 0.748624i \(-0.730715\pi\)
−0.662995 + 0.748624i \(0.730715\pi\)
\(240\) 0 0
\(241\) 5.47627 0.352758 0.176379 0.984322i \(-0.443562\pi\)
0.176379 + 0.984322i \(0.443562\pi\)
\(242\) 9.29455 0.597476
\(243\) 0 0
\(244\) 1.72355 0.110339
\(245\) 5.57452 0.356143
\(246\) 0 0
\(247\) −9.46168 −0.602032
\(248\) 12.8568 0.816411
\(249\) 0 0
\(250\) −1.48119 −0.0936790
\(251\) 29.6180 1.86947 0.934736 0.355343i \(-0.115636\pi\)
0.934736 + 0.355343i \(0.115636\pi\)
\(252\) 0 0
\(253\) 7.66291 0.481763
\(254\) 21.1333 1.32602
\(255\) 0 0
\(256\) 4.61213 0.288258
\(257\) −17.6629 −1.10178 −0.550891 0.834577i \(-0.685712\pi\)
−0.550891 + 0.834577i \(0.685712\pi\)
\(258\) 0 0
\(259\) −11.3503 −0.705271
\(260\) −0.574515 −0.0356299
\(261\) 0 0
\(262\) −8.73084 −0.539393
\(263\) −27.3561 −1.68685 −0.843426 0.537245i \(-0.819465\pi\)
−0.843426 + 0.537245i \(0.819465\pi\)
\(264\) 0 0
\(265\) −1.35026 −0.0829459
\(266\) −5.64832 −0.346321
\(267\) 0 0
\(268\) 1.13330 0.0692275
\(269\) −10.4993 −0.640153 −0.320077 0.947392i \(-0.603709\pi\)
−0.320077 + 0.947392i \(0.603709\pi\)
\(270\) 0 0
\(271\) −9.61801 −0.584252 −0.292126 0.956380i \(-0.594363\pi\)
−0.292126 + 0.956380i \(0.594363\pi\)
\(272\) 23.9551 1.45249
\(273\) 0 0
\(274\) −27.0797 −1.63594
\(275\) −4.15633 −0.250636
\(276\) 0 0
\(277\) 13.3503 0.802139 0.401070 0.916048i \(-0.368638\pi\)
0.401070 + 0.916048i \(0.368638\pi\)
\(278\) −17.0884 −1.02489
\(279\) 0 0
\(280\) 3.19394 0.190874
\(281\) −20.4241 −1.21840 −0.609199 0.793017i \(-0.708509\pi\)
−0.609199 + 0.793017i \(0.708509\pi\)
\(282\) 0 0
\(283\) −8.02047 −0.476767 −0.238384 0.971171i \(-0.576618\pi\)
−0.238384 + 0.971171i \(0.576618\pi\)
\(284\) 0.247277 0.0146732
\(285\) 0 0
\(286\) −18.2374 −1.07840
\(287\) 13.4617 0.794618
\(288\) 0 0
\(289\) 13.3225 0.783676
\(290\) −1.48119 −0.0869787
\(291\) 0 0
\(292\) −2.95651 −0.173017
\(293\) 23.3054 1.36151 0.680757 0.732510i \(-0.261651\pi\)
0.680757 + 0.732510i \(0.261651\pi\)
\(294\) 0 0
\(295\) 13.2750 0.772903
\(296\) 25.4314 1.47817
\(297\) 0 0
\(298\) −4.11142 −0.238168
\(299\) −5.46168 −0.315857
\(300\) 0 0
\(301\) −0.0361968 −0.00208635
\(302\) 2.66433 0.153315
\(303\) 0 0
\(304\) 13.8945 0.796902
\(305\) −8.88717 −0.508878
\(306\) 0 0
\(307\) −6.73084 −0.384149 −0.192075 0.981380i \(-0.561522\pi\)
−0.192075 + 0.981380i \(0.561522\pi\)
\(308\) −0.962389 −0.0548372
\(309\) 0 0
\(310\) 7.11871 0.404316
\(311\) 22.0567 1.25072 0.625359 0.780337i \(-0.284952\pi\)
0.625359 + 0.780337i \(0.284952\pi\)
\(312\) 0 0
\(313\) 5.03761 0.284743 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(314\) 5.58181 0.315000
\(315\) 0 0
\(316\) −0.956509 −0.0538078
\(317\) −34.2941 −1.92615 −0.963074 0.269237i \(-0.913229\pi\)
−0.963074 + 0.269237i \(0.913229\pi\)
\(318\) 0 0
\(319\) −4.15633 −0.232710
\(320\) −7.08110 −0.395846
\(321\) 0 0
\(322\) −3.26045 −0.181698
\(323\) 17.5877 0.978605
\(324\) 0 0
\(325\) 2.96239 0.164324
\(326\) 2.43278 0.134739
\(327\) 0 0
\(328\) −30.1622 −1.66543
\(329\) −5.73813 −0.316354
\(330\) 0 0
\(331\) −34.8324 −1.91456 −0.957281 0.289159i \(-0.906625\pi\)
−0.957281 + 0.289159i \(0.906625\pi\)
\(332\) −0.856849 −0.0470257
\(333\) 0 0
\(334\) −11.9697 −0.654952
\(335\) −5.84367 −0.319274
\(336\) 0 0
\(337\) −17.6326 −0.960509 −0.480254 0.877129i \(-0.659456\pi\)
−0.480254 + 0.877129i \(0.659456\pi\)
\(338\) −6.25694 −0.340333
\(339\) 0 0
\(340\) 1.06793 0.0579166
\(341\) 19.9756 1.08174
\(342\) 0 0
\(343\) −15.0132 −0.810635
\(344\) 0.0811024 0.00437275
\(345\) 0 0
\(346\) 11.4617 0.616184
\(347\) 3.11871 0.167421 0.0837107 0.996490i \(-0.473323\pi\)
0.0837107 + 0.996490i \(0.473323\pi\)
\(348\) 0 0
\(349\) −13.0738 −0.699825 −0.349912 0.936782i \(-0.613789\pi\)
−0.349912 + 0.936782i \(0.613789\pi\)
\(350\) 1.76845 0.0945277
\(351\) 0 0
\(352\) 4.54420 0.242207
\(353\) −5.19982 −0.276758 −0.138379 0.990379i \(-0.544189\pi\)
−0.138379 + 0.990379i \(0.544189\pi\)
\(354\) 0 0
\(355\) −1.27504 −0.0676720
\(356\) 0.700523 0.0371277
\(357\) 0 0
\(358\) 31.6991 1.67535
\(359\) −30.4182 −1.60541 −0.802705 0.596376i \(-0.796607\pi\)
−0.802705 + 0.596376i \(0.796607\pi\)
\(360\) 0 0
\(361\) −8.79877 −0.463093
\(362\) 22.6253 1.18916
\(363\) 0 0
\(364\) 0.685935 0.0359528
\(365\) 15.2447 0.797945
\(366\) 0 0
\(367\) 20.6556 1.07821 0.539107 0.842237i \(-0.318762\pi\)
0.539107 + 0.842237i \(0.318762\pi\)
\(368\) 8.02047 0.418096
\(369\) 0 0
\(370\) 14.0811 0.732042
\(371\) 1.61213 0.0836975
\(372\) 0 0
\(373\) 11.0884 0.574135 0.287068 0.957910i \(-0.407320\pi\)
0.287068 + 0.957910i \(0.407320\pi\)
\(374\) 33.9003 1.75294
\(375\) 0 0
\(376\) 12.8568 0.663041
\(377\) 2.96239 0.152571
\(378\) 0 0
\(379\) 10.0811 0.517831 0.258916 0.965900i \(-0.416635\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(380\) 0.619421 0.0317756
\(381\) 0 0
\(382\) −4.91748 −0.251600
\(383\) −16.3576 −0.835832 −0.417916 0.908486i \(-0.637239\pi\)
−0.417916 + 0.908486i \(0.637239\pi\)
\(384\) 0 0
\(385\) 4.96239 0.252907
\(386\) −7.23013 −0.368004
\(387\) 0 0
\(388\) −0.267745 −0.0135927
\(389\) −31.9003 −1.61741 −0.808706 0.588213i \(-0.799831\pi\)
−0.808706 + 0.588213i \(0.799831\pi\)
\(390\) 0 0
\(391\) 10.1524 0.513427
\(392\) 14.9126 0.753198
\(393\) 0 0
\(394\) 35.9003 1.80863
\(395\) 4.93207 0.248159
\(396\) 0 0
\(397\) 2.98683 0.149905 0.0749523 0.997187i \(-0.476120\pi\)
0.0749523 + 0.997187i \(0.476120\pi\)
\(398\) 24.8119 1.24371
\(399\) 0 0
\(400\) −4.35026 −0.217513
\(401\) 21.9756 1.09741 0.548704 0.836017i \(-0.315122\pi\)
0.548704 + 0.836017i \(0.315122\pi\)
\(402\) 0 0
\(403\) −14.2374 −0.709217
\(404\) 2.52373 0.125560
\(405\) 0 0
\(406\) 1.76845 0.0877668
\(407\) 39.5125 1.95856
\(408\) 0 0
\(409\) −22.4387 −1.10952 −0.554760 0.832010i \(-0.687190\pi\)
−0.554760 + 0.832010i \(0.687190\pi\)
\(410\) −16.7005 −0.824780
\(411\) 0 0
\(412\) 1.03173 0.0508298
\(413\) −15.8496 −0.779906
\(414\) 0 0
\(415\) 4.41819 0.216880
\(416\) −3.23884 −0.158797
\(417\) 0 0
\(418\) 19.6629 0.961744
\(419\) −10.3634 −0.506287 −0.253143 0.967429i \(-0.581464\pi\)
−0.253143 + 0.967429i \(0.581464\pi\)
\(420\) 0 0
\(421\) 34.0362 1.65882 0.829411 0.558638i \(-0.188676\pi\)
0.829411 + 0.558638i \(0.188676\pi\)
\(422\) −37.4821 −1.82460
\(423\) 0 0
\(424\) −3.61213 −0.175420
\(425\) −5.50659 −0.267109
\(426\) 0 0
\(427\) 10.6107 0.513488
\(428\) 2.68006 0.129545
\(429\) 0 0
\(430\) 0.0449056 0.00216554
\(431\) −25.7743 −1.24151 −0.620753 0.784006i \(-0.713173\pi\)
−0.620753 + 0.784006i \(0.713173\pi\)
\(432\) 0 0
\(433\) 2.18076 0.104801 0.0524004 0.998626i \(-0.483313\pi\)
0.0524004 + 0.998626i \(0.483313\pi\)
\(434\) −8.49929 −0.407979
\(435\) 0 0
\(436\) −0.363436 −0.0174054
\(437\) 5.88858 0.281689
\(438\) 0 0
\(439\) −35.5125 −1.69492 −0.847459 0.530861i \(-0.821869\pi\)
−0.847459 + 0.530861i \(0.821869\pi\)
\(440\) −11.1187 −0.530064
\(441\) 0 0
\(442\) −24.1622 −1.14928
\(443\) 4.34297 0.206341 0.103170 0.994664i \(-0.467101\pi\)
0.103170 + 0.994664i \(0.467101\pi\)
\(444\) 0 0
\(445\) −3.61213 −0.171231
\(446\) 26.2071 1.24094
\(447\) 0 0
\(448\) 8.45439 0.399432
\(449\) −31.3357 −1.47882 −0.739411 0.673254i \(-0.764896\pi\)
−0.739411 + 0.673254i \(0.764896\pi\)
\(450\) 0 0
\(451\) −46.8627 −2.20668
\(452\) 2.28233 0.107352
\(453\) 0 0
\(454\) −39.7586 −1.86596
\(455\) −3.53690 −0.165813
\(456\) 0 0
\(457\) 34.3488 1.60677 0.803386 0.595459i \(-0.203030\pi\)
0.803386 + 0.595459i \(0.203030\pi\)
\(458\) −25.5125 −1.19212
\(459\) 0 0
\(460\) 0.357556 0.0166711
\(461\) −11.8641 −0.552568 −0.276284 0.961076i \(-0.589103\pi\)
−0.276284 + 0.961076i \(0.589103\pi\)
\(462\) 0 0
\(463\) 40.4953 1.88198 0.940989 0.338438i \(-0.109899\pi\)
0.940989 + 0.338438i \(0.109899\pi\)
\(464\) −4.35026 −0.201956
\(465\) 0 0
\(466\) 13.4401 0.622599
\(467\) 30.2071 1.39782 0.698909 0.715210i \(-0.253669\pi\)
0.698909 + 0.715210i \(0.253669\pi\)
\(468\) 0 0
\(469\) 6.97698 0.322167
\(470\) 7.11871 0.328362
\(471\) 0 0
\(472\) 35.5125 1.63459
\(473\) 0.126008 0.00579385
\(474\) 0 0
\(475\) −3.19394 −0.146548
\(476\) −1.27504 −0.0584413
\(477\) 0 0
\(478\) −30.3634 −1.38879
\(479\) −0.0547547 −0.00250181 −0.00125090 0.999999i \(-0.500398\pi\)
−0.00125090 + 0.999999i \(0.500398\pi\)
\(480\) 0 0
\(481\) −28.1622 −1.28409
\(482\) 8.11142 0.369465
\(483\) 0 0
\(484\) 1.21696 0.0553163
\(485\) 1.38058 0.0626889
\(486\) 0 0
\(487\) −0.881286 −0.0399349 −0.0199674 0.999801i \(-0.506356\pi\)
−0.0199674 + 0.999801i \(0.506356\pi\)
\(488\) −23.7743 −1.07621
\(489\) 0 0
\(490\) 8.25694 0.373011
\(491\) −41.0698 −1.85346 −0.926728 0.375733i \(-0.877391\pi\)
−0.926728 + 0.375733i \(0.877391\pi\)
\(492\) 0 0
\(493\) −5.50659 −0.248004
\(494\) −14.0146 −0.630546
\(495\) 0 0
\(496\) 20.9076 0.938780
\(497\) 1.52232 0.0682852
\(498\) 0 0
\(499\) 12.3733 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(500\) −0.193937 −0.00867311
\(501\) 0 0
\(502\) 43.8700 1.95801
\(503\) 2.26774 0.101114 0.0505569 0.998721i \(-0.483900\pi\)
0.0505569 + 0.998721i \(0.483900\pi\)
\(504\) 0 0
\(505\) −13.0132 −0.579079
\(506\) 11.3503 0.504581
\(507\) 0 0
\(508\) 2.76704 0.122767
\(509\) 10.9018 0.483212 0.241606 0.970374i \(-0.422326\pi\)
0.241606 + 0.970374i \(0.422326\pi\)
\(510\) 0 0
\(511\) −18.2012 −0.805175
\(512\) −18.5188 −0.818423
\(513\) 0 0
\(514\) −26.1622 −1.15397
\(515\) −5.31994 −0.234425
\(516\) 0 0
\(517\) 19.9756 0.878524
\(518\) −16.8119 −0.738674
\(519\) 0 0
\(520\) 7.92478 0.347524
\(521\) 4.72496 0.207004 0.103502 0.994629i \(-0.466995\pi\)
0.103502 + 0.994629i \(0.466995\pi\)
\(522\) 0 0
\(523\) −1.06793 −0.0466973 −0.0233486 0.999727i \(-0.507433\pi\)
−0.0233486 + 0.999727i \(0.507433\pi\)
\(524\) −1.14315 −0.0499388
\(525\) 0 0
\(526\) −40.5198 −1.76675
\(527\) 26.4650 1.15283
\(528\) 0 0
\(529\) −19.6009 −0.852211
\(530\) −2.00000 −0.0868744
\(531\) 0 0
\(532\) −0.739549 −0.0320635
\(533\) 33.4010 1.44676
\(534\) 0 0
\(535\) −13.8192 −0.597458
\(536\) −15.6326 −0.675225
\(537\) 0 0
\(538\) −15.5515 −0.670472
\(539\) 23.1695 0.997981
\(540\) 0 0
\(541\) −7.46168 −0.320803 −0.160401 0.987052i \(-0.551279\pi\)
−0.160401 + 0.987052i \(0.551279\pi\)
\(542\) −14.2461 −0.611924
\(543\) 0 0
\(544\) 6.02047 0.258125
\(545\) 1.87399 0.0802730
\(546\) 0 0
\(547\) −38.9683 −1.66616 −0.833081 0.553150i \(-0.813425\pi\)
−0.833081 + 0.553150i \(0.813425\pi\)
\(548\) −3.54561 −0.151461
\(549\) 0 0
\(550\) −6.15633 −0.262507
\(551\) −3.19394 −0.136066
\(552\) 0 0
\(553\) −5.88858 −0.250408
\(554\) 19.7743 0.840131
\(555\) 0 0
\(556\) −2.23743 −0.0948881
\(557\) 22.9986 0.974481 0.487241 0.873268i \(-0.338003\pi\)
0.487241 + 0.873268i \(0.338003\pi\)
\(558\) 0 0
\(559\) −0.0898112 −0.00379861
\(560\) 5.19394 0.219484
\(561\) 0 0
\(562\) −30.2520 −1.27610
\(563\) −11.6688 −0.491781 −0.245890 0.969298i \(-0.579080\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(564\) 0 0
\(565\) −11.7685 −0.495102
\(566\) −11.8799 −0.499348
\(567\) 0 0
\(568\) −3.41090 −0.143118
\(569\) −11.3357 −0.475216 −0.237608 0.971361i \(-0.576363\pi\)
−0.237608 + 0.971361i \(0.576363\pi\)
\(570\) 0 0
\(571\) 27.1754 1.13725 0.568627 0.822595i \(-0.307475\pi\)
0.568627 + 0.822595i \(0.307475\pi\)
\(572\) −2.38787 −0.0998420
\(573\) 0 0
\(574\) 19.9394 0.832253
\(575\) −1.84367 −0.0768866
\(576\) 0 0
\(577\) 22.5950 0.940641 0.470321 0.882496i \(-0.344138\pi\)
0.470321 + 0.882496i \(0.344138\pi\)
\(578\) 19.7332 0.820793
\(579\) 0 0
\(580\) −0.193937 −0.00805278
\(581\) −5.27504 −0.218845
\(582\) 0 0
\(583\) −5.61213 −0.232431
\(584\) 40.7816 1.68756
\(585\) 0 0
\(586\) 34.5198 1.42600
\(587\) −9.31994 −0.384675 −0.192338 0.981329i \(-0.561607\pi\)
−0.192338 + 0.981329i \(0.561607\pi\)
\(588\) 0 0
\(589\) 15.3503 0.632497
\(590\) 19.6629 0.809509
\(591\) 0 0
\(592\) 41.3561 1.69973
\(593\) 15.1246 0.621093 0.310546 0.950558i \(-0.399488\pi\)
0.310546 + 0.950558i \(0.399488\pi\)
\(594\) 0 0
\(595\) 6.57452 0.269529
\(596\) −0.538319 −0.0220504
\(597\) 0 0
\(598\) −8.08981 −0.330817
\(599\) −4.09569 −0.167345 −0.0836727 0.996493i \(-0.526665\pi\)
−0.0836727 + 0.996493i \(0.526665\pi\)
\(600\) 0 0
\(601\) 22.2276 0.906682 0.453341 0.891337i \(-0.350232\pi\)
0.453341 + 0.891337i \(0.350232\pi\)
\(602\) −0.0536145 −0.00218516
\(603\) 0 0
\(604\) 0.348847 0.0141944
\(605\) −6.27504 −0.255117
\(606\) 0 0
\(607\) −48.2941 −1.96020 −0.980098 0.198512i \(-0.936389\pi\)
−0.980098 + 0.198512i \(0.936389\pi\)
\(608\) 3.49200 0.141619
\(609\) 0 0
\(610\) −13.1636 −0.532979
\(611\) −14.2374 −0.575985
\(612\) 0 0
\(613\) −9.74798 −0.393717 −0.196859 0.980432i \(-0.563074\pi\)
−0.196859 + 0.980432i \(0.563074\pi\)
\(614\) −9.96968 −0.402344
\(615\) 0 0
\(616\) 13.2750 0.534867
\(617\) −18.2170 −0.733387 −0.366694 0.930342i \(-0.619510\pi\)
−0.366694 + 0.930342i \(0.619510\pi\)
\(618\) 0 0
\(619\) 25.0943 1.00862 0.504312 0.863521i \(-0.331746\pi\)
0.504312 + 0.863521i \(0.331746\pi\)
\(620\) 0.932071 0.0374329
\(621\) 0 0
\(622\) 32.6702 1.30996
\(623\) 4.31265 0.172783
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 7.46168 0.298229
\(627\) 0 0
\(628\) 0.730841 0.0291637
\(629\) 52.3488 2.08729
\(630\) 0 0
\(631\) 21.4617 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(632\) 13.1939 0.524827
\(633\) 0 0
\(634\) −50.7962 −2.01738
\(635\) −14.2677 −0.566198
\(636\) 0 0
\(637\) −16.5139 −0.654304
\(638\) −6.15633 −0.243731
\(639\) 0 0
\(640\) −12.6751 −0.501029
\(641\) −3.17347 −0.125344 −0.0626722 0.998034i \(-0.519962\pi\)
−0.0626722 + 0.998034i \(0.519962\pi\)
\(642\) 0 0
\(643\) −2.74069 −0.108082 −0.0540411 0.998539i \(-0.517210\pi\)
−0.0540411 + 0.998539i \(0.517210\pi\)
\(644\) −0.426899 −0.0168222
\(645\) 0 0
\(646\) 26.0508 1.02495
\(647\) −6.34297 −0.249368 −0.124684 0.992197i \(-0.539792\pi\)
−0.124684 + 0.992197i \(0.539792\pi\)
\(648\) 0 0
\(649\) 55.1754 2.16582
\(650\) 4.38787 0.172107
\(651\) 0 0
\(652\) 0.318530 0.0124746
\(653\) −4.08110 −0.159706 −0.0798529 0.996807i \(-0.525445\pi\)
−0.0798529 + 0.996807i \(0.525445\pi\)
\(654\) 0 0
\(655\) 5.89446 0.230316
\(656\) −49.0494 −1.91506
\(657\) 0 0
\(658\) −8.49929 −0.331337
\(659\) −9.58181 −0.373254 −0.186627 0.982431i \(-0.559756\pi\)
−0.186627 + 0.982431i \(0.559756\pi\)
\(660\) 0 0
\(661\) −27.5271 −1.07068 −0.535339 0.844637i \(-0.679816\pi\)
−0.535339 + 0.844637i \(0.679816\pi\)
\(662\) −51.5936 −2.00524
\(663\) 0 0
\(664\) 11.8192 0.458675
\(665\) 3.81336 0.147876
\(666\) 0 0
\(667\) −1.84367 −0.0713874
\(668\) −1.56722 −0.0606376
\(669\) 0 0
\(670\) −8.65562 −0.334396
\(671\) −36.9380 −1.42597
\(672\) 0 0
\(673\) 3.13727 0.120933 0.0604665 0.998170i \(-0.480741\pi\)
0.0604665 + 0.998170i \(0.480741\pi\)
\(674\) −26.1173 −1.00600
\(675\) 0 0
\(676\) −0.819237 −0.0315091
\(677\) 46.2579 1.77784 0.888918 0.458067i \(-0.151458\pi\)
0.888918 + 0.458067i \(0.151458\pi\)
\(678\) 0 0
\(679\) −1.64832 −0.0632569
\(680\) −14.7308 −0.564902
\(681\) 0 0
\(682\) 29.5877 1.13297
\(683\) 9.01905 0.345104 0.172552 0.985000i \(-0.444799\pi\)
0.172552 + 0.985000i \(0.444799\pi\)
\(684\) 0 0
\(685\) 18.2823 0.698532
\(686\) −22.2374 −0.849029
\(687\) 0 0
\(688\) 0.131888 0.00502817
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) −50.0625 −1.90447 −0.952234 0.305368i \(-0.901221\pi\)
−0.952234 + 0.305368i \(0.901221\pi\)
\(692\) 1.50071 0.0570483
\(693\) 0 0
\(694\) 4.61942 0.175351
\(695\) 11.5369 0.437620
\(696\) 0 0
\(697\) −62.0870 −2.35171
\(698\) −19.3649 −0.732970
\(699\) 0 0
\(700\) 0.231548 0.00875169
\(701\) −45.3014 −1.71101 −0.855505 0.517795i \(-0.826753\pi\)
−0.855505 + 0.517795i \(0.826753\pi\)
\(702\) 0 0
\(703\) 30.3634 1.14518
\(704\) −29.4314 −1.10924
\(705\) 0 0
\(706\) −7.70194 −0.289866
\(707\) 15.5369 0.584325
\(708\) 0 0
\(709\) −3.27504 −0.122997 −0.0614983 0.998107i \(-0.519588\pi\)
−0.0614983 + 0.998107i \(0.519588\pi\)
\(710\) −1.88858 −0.0708772
\(711\) 0 0
\(712\) −9.66291 −0.362133
\(713\) 8.86082 0.331840
\(714\) 0 0
\(715\) 12.3127 0.460467
\(716\) 4.15045 0.155109
\(717\) 0 0
\(718\) −45.0553 −1.68145
\(719\) −27.7235 −1.03391 −0.516957 0.856011i \(-0.672935\pi\)
−0.516957 + 0.856011i \(0.672935\pi\)
\(720\) 0 0
\(721\) 6.35168 0.236549
\(722\) −13.0327 −0.485026
\(723\) 0 0
\(724\) 2.96239 0.110096
\(725\) 1.00000 0.0371391
\(726\) 0 0
\(727\) −26.8930 −0.997408 −0.498704 0.866772i \(-0.666190\pi\)
−0.498704 + 0.866772i \(0.666190\pi\)
\(728\) −9.46168 −0.350673
\(729\) 0 0
\(730\) 22.5804 0.835738
\(731\) 0.166944 0.00617465
\(732\) 0 0
\(733\) 3.17935 0.117432 0.0587160 0.998275i \(-0.481299\pi\)
0.0587160 + 0.998275i \(0.481299\pi\)
\(734\) 30.5950 1.12928
\(735\) 0 0
\(736\) 2.01573 0.0743007
\(737\) −24.2882 −0.894668
\(738\) 0 0
\(739\) −29.7440 −1.09415 −0.547076 0.837083i \(-0.684259\pi\)
−0.547076 + 0.837083i \(0.684259\pi\)
\(740\) 1.84367 0.0677748
\(741\) 0 0
\(742\) 2.38787 0.0876616
\(743\) 4.34297 0.159328 0.0796640 0.996822i \(-0.474615\pi\)
0.0796640 + 0.996822i \(0.474615\pi\)
\(744\) 0 0
\(745\) 2.77575 0.101695
\(746\) 16.4241 0.601328
\(747\) 0 0
\(748\) 4.43866 0.162293
\(749\) 16.4993 0.602871
\(750\) 0 0
\(751\) 22.5804 0.823970 0.411985 0.911191i \(-0.364836\pi\)
0.411985 + 0.911191i \(0.364836\pi\)
\(752\) 20.9076 0.762423
\(753\) 0 0
\(754\) 4.38787 0.159797
\(755\) −1.79877 −0.0654639
\(756\) 0 0
\(757\) 9.88461 0.359262 0.179631 0.983734i \(-0.442510\pi\)
0.179631 + 0.983734i \(0.442510\pi\)
\(758\) 14.9321 0.542357
\(759\) 0 0
\(760\) −8.54420 −0.309931
\(761\) −13.6991 −0.496592 −0.248296 0.968684i \(-0.579871\pi\)
−0.248296 + 0.968684i \(0.579871\pi\)
\(762\) 0 0
\(763\) −2.23743 −0.0810003
\(764\) −0.643859 −0.0232940
\(765\) 0 0
\(766\) −24.2287 −0.875419
\(767\) −39.3258 −1.41997
\(768\) 0 0
\(769\) 25.0132 0.901998 0.450999 0.892524i \(-0.351068\pi\)
0.450999 + 0.892524i \(0.351068\pi\)
\(770\) 7.35026 0.264885
\(771\) 0 0
\(772\) −0.946660 −0.0340710
\(773\) 35.9062 1.29146 0.645728 0.763567i \(-0.276554\pi\)
0.645728 + 0.763567i \(0.276554\pi\)
\(774\) 0 0
\(775\) −4.80606 −0.172639
\(776\) 3.69323 0.132579
\(777\) 0 0
\(778\) −47.2506 −1.69402
\(779\) −36.0118 −1.29026
\(780\) 0 0
\(781\) −5.29948 −0.189630
\(782\) 15.0376 0.537744
\(783\) 0 0
\(784\) 24.2506 0.866093
\(785\) −3.76845 −0.134502
\(786\) 0 0
\(787\) 50.3839 1.79599 0.897996 0.440003i \(-0.145023\pi\)
0.897996 + 0.440003i \(0.145023\pi\)
\(788\) 4.70052 0.167449
\(789\) 0 0
\(790\) 7.30536 0.259913
\(791\) 14.0508 0.499588
\(792\) 0 0
\(793\) 26.3272 0.934908
\(794\) 4.42407 0.157004
\(795\) 0 0
\(796\) 3.24869 0.115147
\(797\) 5.69323 0.201665 0.100832 0.994903i \(-0.467849\pi\)
0.100832 + 0.994903i \(0.467849\pi\)
\(798\) 0 0
\(799\) 26.4650 0.936265
\(800\) −1.09332 −0.0386547
\(801\) 0 0
\(802\) 32.5501 1.14938
\(803\) 63.3620 2.23600
\(804\) 0 0
\(805\) 2.20123 0.0775832
\(806\) −21.0884 −0.742807
\(807\) 0 0
\(808\) −34.8119 −1.22468
\(809\) 7.76257 0.272918 0.136459 0.990646i \(-0.456428\pi\)
0.136459 + 0.990646i \(0.456428\pi\)
\(810\) 0 0
\(811\) −26.4894 −0.930170 −0.465085 0.885266i \(-0.653976\pi\)
−0.465085 + 0.885266i \(0.653976\pi\)
\(812\) 0.231548 0.00812574
\(813\) 0 0
\(814\) 58.5256 2.05132
\(815\) −1.64244 −0.0575323
\(816\) 0 0
\(817\) 0.0968311 0.00338769
\(818\) −33.2360 −1.16207
\(819\) 0 0
\(820\) −2.18664 −0.0763609
\(821\) −25.4763 −0.889128 −0.444564 0.895747i \(-0.646641\pi\)
−0.444564 + 0.895747i \(0.646641\pi\)
\(822\) 0 0
\(823\) −9.22028 −0.321399 −0.160699 0.987003i \(-0.551375\pi\)
−0.160699 + 0.987003i \(0.551375\pi\)
\(824\) −14.2315 −0.495779
\(825\) 0 0
\(826\) −23.4763 −0.816844
\(827\) −24.5343 −0.853143 −0.426571 0.904454i \(-0.640279\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(828\) 0 0
\(829\) 0.201231 0.00698903 0.00349452 0.999994i \(-0.498888\pi\)
0.00349452 + 0.999994i \(0.498888\pi\)
\(830\) 6.54420 0.227152
\(831\) 0 0
\(832\) 20.9770 0.727246
\(833\) 30.6966 1.06357
\(834\) 0 0
\(835\) 8.08110 0.279658
\(836\) 2.57452 0.0890415
\(837\) 0 0
\(838\) −15.3503 −0.530266
\(839\) −1.45580 −0.0502599 −0.0251299 0.999684i \(-0.508000\pi\)
−0.0251299 + 0.999684i \(0.508000\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 50.4142 1.73739
\(843\) 0 0
\(844\) −4.90763 −0.168928
\(845\) 4.22425 0.145319
\(846\) 0 0
\(847\) 7.49200 0.257428
\(848\) −5.87399 −0.201714
\(849\) 0 0
\(850\) −8.15633 −0.279760
\(851\) 17.5271 0.600820
\(852\) 0 0
\(853\) 43.1793 1.47843 0.739216 0.673468i \(-0.235196\pi\)
0.739216 + 0.673468i \(0.235196\pi\)
\(854\) 15.7165 0.537808
\(855\) 0 0
\(856\) −36.9683 −1.26355
\(857\) 20.9887 0.716962 0.358481 0.933537i \(-0.383295\pi\)
0.358481 + 0.933537i \(0.383295\pi\)
\(858\) 0 0
\(859\) −49.4069 −1.68574 −0.842871 0.538115i \(-0.819137\pi\)
−0.842871 + 0.538115i \(0.819137\pi\)
\(860\) 0.00587961 0.000200493 0
\(861\) 0 0
\(862\) −38.1768 −1.30031
\(863\) −56.6820 −1.92948 −0.964738 0.263211i \(-0.915218\pi\)
−0.964738 + 0.263211i \(0.915218\pi\)
\(864\) 0 0
\(865\) −7.73813 −0.263104
\(866\) 3.23013 0.109764
\(867\) 0 0
\(868\) −1.11283 −0.0377721
\(869\) 20.4993 0.695391
\(870\) 0 0
\(871\) 17.3112 0.586569
\(872\) 5.01317 0.169767
\(873\) 0 0
\(874\) 8.72213 0.295031
\(875\) −1.19394 −0.0403624
\(876\) 0 0
\(877\) −13.1998 −0.445726 −0.222863 0.974850i \(-0.571540\pi\)
−0.222863 + 0.974850i \(0.571540\pi\)
\(878\) −52.6009 −1.77519
\(879\) 0 0
\(880\) −18.0811 −0.609514
\(881\) −6.37802 −0.214881 −0.107441 0.994212i \(-0.534266\pi\)
−0.107441 + 0.994212i \(0.534266\pi\)
\(882\) 0 0
\(883\) 48.6213 1.63624 0.818119 0.575049i \(-0.195017\pi\)
0.818119 + 0.575049i \(0.195017\pi\)
\(884\) −3.16362 −0.106404
\(885\) 0 0
\(886\) 6.43278 0.216113
\(887\) 15.0317 0.504716 0.252358 0.967634i \(-0.418794\pi\)
0.252358 + 0.967634i \(0.418794\pi\)
\(888\) 0 0
\(889\) 17.0348 0.571328
\(890\) −5.35026 −0.179341
\(891\) 0 0
\(892\) 3.43136 0.114891
\(893\) 15.3503 0.513677
\(894\) 0 0
\(895\) −21.4010 −0.715358
\(896\) 15.1333 0.505568
\(897\) 0 0
\(898\) −46.4142 −1.54886
\(899\) −4.80606 −0.160291
\(900\) 0 0
\(901\) −7.43533 −0.247707
\(902\) −69.4128 −2.31119
\(903\) 0 0
\(904\) −31.4821 −1.04708
\(905\) −15.2750 −0.507759
\(906\) 0 0
\(907\) −0.342968 −0.0113880 −0.00569402 0.999984i \(-0.501812\pi\)
−0.00569402 + 0.999984i \(0.501812\pi\)
\(908\) −5.20570 −0.172757
\(909\) 0 0
\(910\) −5.23884 −0.173666
\(911\) −20.9076 −0.692701 −0.346350 0.938105i \(-0.612579\pi\)
−0.346350 + 0.938105i \(0.612579\pi\)
\(912\) 0 0
\(913\) 18.3634 0.607741
\(914\) 50.8773 1.68287
\(915\) 0 0
\(916\) −3.34041 −0.110370
\(917\) −7.03761 −0.232402
\(918\) 0 0
\(919\) −1.90034 −0.0626864 −0.0313432 0.999509i \(-0.509978\pi\)
−0.0313432 + 0.999509i \(0.509978\pi\)
\(920\) −4.93207 −0.162606
\(921\) 0 0
\(922\) −17.5731 −0.578739
\(923\) 3.77716 0.124327
\(924\) 0 0
\(925\) −9.50659 −0.312575
\(926\) 59.9814 1.97111
\(927\) 0 0
\(928\) −1.09332 −0.0358900
\(929\) −39.3522 −1.29110 −0.645551 0.763717i \(-0.723372\pi\)
−0.645551 + 0.763717i \(0.723372\pi\)
\(930\) 0 0
\(931\) 17.8046 0.583524
\(932\) 1.75974 0.0576423
\(933\) 0 0
\(934\) 44.7426 1.46402
\(935\) −22.8872 −0.748490
\(936\) 0 0
\(937\) −6.37802 −0.208361 −0.104180 0.994558i \(-0.533222\pi\)
−0.104180 + 0.994558i \(0.533222\pi\)
\(938\) 10.3343 0.337426
\(939\) 0 0
\(940\) 0.932071 0.0304008
\(941\) 26.6253 0.867960 0.433980 0.900923i \(-0.357109\pi\)
0.433980 + 0.900923i \(0.357109\pi\)
\(942\) 0 0
\(943\) −20.7875 −0.676934
\(944\) 57.7499 1.87960
\(945\) 0 0
\(946\) 0.186642 0.00606827
\(947\) 12.2823 0.399122 0.199561 0.979885i \(-0.436048\pi\)
0.199561 + 0.979885i \(0.436048\pi\)
\(948\) 0 0
\(949\) −45.1608 −1.46598
\(950\) −4.73084 −0.153489
\(951\) 0 0
\(952\) 17.5877 0.570020
\(953\) −0.821792 −0.0266205 −0.0133102 0.999911i \(-0.504237\pi\)
−0.0133102 + 0.999911i \(0.504237\pi\)
\(954\) 0 0
\(955\) 3.31994 0.107431
\(956\) −3.97556 −0.128579
\(957\) 0 0
\(958\) −0.0811024 −0.00262030
\(959\) −21.8279 −0.704861
\(960\) 0 0
\(961\) −7.90175 −0.254895
\(962\) −41.7137 −1.34490
\(963\) 0 0
\(964\) 1.06205 0.0342063
\(965\) 4.88129 0.157134
\(966\) 0 0
\(967\) −37.4314 −1.20371 −0.601856 0.798605i \(-0.705572\pi\)
−0.601856 + 0.798605i \(0.705572\pi\)
\(968\) −16.7866 −0.539540
\(969\) 0 0
\(970\) 2.04491 0.0656580
\(971\) 8.71625 0.279718 0.139859 0.990171i \(-0.455335\pi\)
0.139859 + 0.990171i \(0.455335\pi\)
\(972\) 0 0
\(973\) −13.7743 −0.441585
\(974\) −1.30536 −0.0418263
\(975\) 0 0
\(976\) −38.6615 −1.23752
\(977\) 33.7645 1.08022 0.540111 0.841594i \(-0.318382\pi\)
0.540111 + 0.841594i \(0.318382\pi\)
\(978\) 0 0
\(979\) −15.0132 −0.479823
\(980\) 1.08110 0.0345345
\(981\) 0 0
\(982\) −60.8324 −1.94124
\(983\) −43.6082 −1.39088 −0.695442 0.718582i \(-0.744791\pi\)
−0.695442 + 0.718582i \(0.744791\pi\)
\(984\) 0 0
\(985\) −24.2374 −0.772269
\(986\) −8.15633 −0.259750
\(987\) 0 0
\(988\) −1.83497 −0.0583780
\(989\) 0.0558950 0.00177736
\(990\) 0 0
\(991\) −52.9741 −1.68278 −0.841390 0.540429i \(-0.818262\pi\)
−0.841390 + 0.540429i \(0.818262\pi\)
\(992\) 5.25457 0.166833
\(993\) 0 0
\(994\) 2.25485 0.0715193
\(995\) −16.7513 −0.531052
\(996\) 0 0
\(997\) 13.6326 0.431749 0.215874 0.976421i \(-0.430740\pi\)
0.215874 + 0.976421i \(0.430740\pi\)
\(998\) 18.3272 0.580139
\(999\) 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 1305.2.a.p.1.3 3
3.2 odd 2 145.2.a.c.1.1 3
5.4 even 2 6525.2.a.be.1.1 3
12.11 even 2 2320.2.a.n.1.2 3
15.2 even 4 725.2.b.e.349.2 6
15.8 even 4 725.2.b.e.349.5 6
15.14 odd 2 725.2.a.e.1.3 3
21.20 even 2 7105.2.a.o.1.1 3
24.5 odd 2 9280.2.a.bj.1.2 3
24.11 even 2 9280.2.a.br.1.2 3
87.86 odd 2 4205.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.c.1.1 3 3.2 odd 2
725.2.a.e.1.3 3 15.14 odd 2
725.2.b.e.349.2 6 15.2 even 4
725.2.b.e.349.5 6 15.8 even 4
1305.2.a.p.1.3 3 1.1 even 1 trivial
2320.2.a.n.1.2 3 12.11 even 2
4205.2.a.f.1.3 3 87.86 odd 2
6525.2.a.be.1.1 3 5.4 even 2
7105.2.a.o.1.1 3 21.20 even 2
9280.2.a.bj.1.2 3 24.5 odd 2
9280.2.a.br.1.2 3 24.11 even 2