Properties

Label 2736.2.cg.a.1151.2
Level $2736$
Weight $2$
Character 2736.1151
Analytic conductor $21.847$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,2,Mod(1151,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.cg (of order \(6\), degree \(2\), minimal)

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: no
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.2
Character \(\chi\) \(=\) 2736.1151
Dual form 2736.2.cg.a.2591.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.27729 - 1.31480i) q^{5} +3.01718i q^{7} +O(q^{10})\) \(q+(-2.27729 - 1.31480i) q^{5} +3.01718i q^{7} -0.730663 q^{11} +(2.20198 + 3.81393i) q^{13} +(-5.35027 - 3.08898i) q^{17} +(2.91110 + 3.24430i) q^{19} +(2.23308 + 3.86781i) q^{23} +(0.957376 + 1.65822i) q^{25} +(4.85101 - 2.80073i) q^{29} -6.37863i q^{31} +(3.96698 - 6.87101i) q^{35} -1.48920 q^{37} +(-3.54789 - 2.04837i) q^{41} +(-6.82401 - 3.93984i) q^{43} +(-1.28368 - 2.22340i) q^{47} -2.10340 q^{49} +(-9.22041 + 5.32341i) q^{53} +(1.66393 + 0.960673i) q^{55} +(-1.08092 + 1.87221i) q^{59} +(-4.26794 - 7.39228i) q^{61} -11.5806i q^{65} +(-8.40407 + 4.85209i) q^{67} +(5.00887 - 8.67561i) q^{71} +(-5.72788 + 9.92098i) q^{73} -2.20455i q^{77} +(1.78342 + 1.02966i) q^{79} +7.34096 q^{83} +(8.12276 + 14.0690i) q^{85} +(-2.22085 + 1.28221i) q^{89} +(-11.5073 + 6.64376i) q^{91} +(-2.36384 - 11.2157i) q^{95} +(-2.80967 + 4.86649i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{13} - 12 q^{19} + 8 q^{25} + 16 q^{37} - 12 q^{43} + 16 q^{49} + 12 q^{55} - 60 q^{67} + 8 q^{73} + 12 q^{79} + 16 q^{85} - 12 q^{91} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.27729 1.31480i −1.01844 0.587995i −0.104786 0.994495i \(-0.533416\pi\)
−0.913651 + 0.406500i \(0.866749\pi\)
\(6\) 0 0
\(7\) 3.01718i 1.14039i 0.821510 + 0.570194i \(0.193132\pi\)
−0.821510 + 0.570194i \(0.806868\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.730663 −0.220303 −0.110152 0.993915i \(-0.535134\pi\)
−0.110152 + 0.993915i \(0.535134\pi\)
\(12\) 0 0
\(13\) 2.20198 + 3.81393i 0.610718 + 1.05779i 0.991120 + 0.132973i \(0.0424525\pi\)
−0.380401 + 0.924821i \(0.624214\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.35027 3.08898i −1.29763 0.749188i −0.317637 0.948213i \(-0.602889\pi\)
−0.979994 + 0.199025i \(0.936223\pi\)
\(18\) 0 0
\(19\) 2.91110 + 3.24430i 0.667852 + 0.744294i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.23308 + 3.86781i 0.465630 + 0.806494i 0.999230 0.0392426i \(-0.0124945\pi\)
−0.533600 + 0.845737i \(0.679161\pi\)
\(24\) 0 0
\(25\) 0.957376 + 1.65822i 0.191475 + 0.331645i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.85101 2.80073i 0.900811 0.520083i 0.0233476 0.999727i \(-0.492568\pi\)
0.877463 + 0.479644i \(0.159234\pi\)
\(30\) 0 0
\(31\) 6.37863i 1.14564i −0.819682 0.572818i \(-0.805850\pi\)
0.819682 0.572818i \(-0.194150\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.96698 6.87101i 0.670542 1.16141i
\(36\) 0 0
\(37\) −1.48920 −0.244823 −0.122411 0.992479i \(-0.539063\pi\)
−0.122411 + 0.992479i \(0.539063\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.54789 2.04837i −0.554087 0.319902i 0.196682 0.980467i \(-0.436983\pi\)
−0.750769 + 0.660565i \(0.770317\pi\)
\(42\) 0 0
\(43\) −6.82401 3.93984i −1.04065 0.600820i −0.120634 0.992697i \(-0.538493\pi\)
−0.920018 + 0.391877i \(0.871826\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.28368 2.22340i −0.187244 0.324316i 0.757087 0.653315i \(-0.226622\pi\)
−0.944330 + 0.328999i \(0.893289\pi\)
\(48\) 0 0
\(49\) −2.10340 −0.300485
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.22041 + 5.32341i −1.26652 + 0.731226i −0.974328 0.225134i \(-0.927718\pi\)
−0.292193 + 0.956359i \(0.594385\pi\)
\(54\) 0 0
\(55\) 1.66393 + 0.960673i 0.224365 + 0.129537i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.08092 + 1.87221i −0.140724 + 0.243741i −0.927770 0.373154i \(-0.878276\pi\)
0.787045 + 0.616895i \(0.211610\pi\)
\(60\) 0 0
\(61\) −4.26794 7.39228i −0.546453 0.946485i −0.998514 0.0544976i \(-0.982644\pi\)
0.452061 0.891987i \(-0.350689\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.5806i 1.43640i
\(66\) 0 0
\(67\) −8.40407 + 4.85209i −1.02672 + 0.592777i −0.916043 0.401079i \(-0.868635\pi\)
−0.110677 + 0.993856i \(0.535302\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00887 8.67561i 0.594443 1.02961i −0.399182 0.916872i \(-0.630706\pi\)
0.993625 0.112734i \(-0.0359608\pi\)
\(72\) 0 0
\(73\) −5.72788 + 9.92098i −0.670398 + 1.16116i 0.307394 + 0.951582i \(0.400543\pi\)
−0.977791 + 0.209580i \(0.932790\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.20455i 0.251231i
\(78\) 0 0
\(79\) 1.78342 + 1.02966i 0.200650 + 0.115845i 0.596959 0.802272i \(-0.296376\pi\)
−0.396309 + 0.918117i \(0.629709\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.34096 0.805775 0.402888 0.915249i \(-0.368007\pi\)
0.402888 + 0.915249i \(0.368007\pi\)
\(84\) 0 0
\(85\) 8.12276 + 14.0690i 0.881037 + 1.52600i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.22085 + 1.28221i −0.235410 + 0.135914i −0.613065 0.790032i \(-0.710064\pi\)
0.377655 + 0.925946i \(0.376730\pi\)
\(90\) 0 0
\(91\) −11.5073 + 6.64376i −1.20630 + 0.696456i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.36384 11.2157i −0.242525 1.15071i
\(96\) 0 0
\(97\) −2.80967 + 4.86649i −0.285278 + 0.494117i −0.972677 0.232164i \(-0.925419\pi\)
0.687398 + 0.726281i \(0.258753\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −16.8914 + 9.75226i −1.68076 + 0.970387i −0.719601 + 0.694388i \(0.755675\pi\)
−0.961158 + 0.275999i \(0.910991\pi\)
\(102\) 0 0
\(103\) 19.6453i 1.93571i −0.251503 0.967857i \(-0.580925\pi\)
0.251503 0.967857i \(-0.419075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −14.6114 −1.41253 −0.706267 0.707946i \(-0.749622\pi\)
−0.706267 + 0.707946i \(0.749622\pi\)
\(108\) 0 0
\(109\) 2.80401 4.85669i 0.268576 0.465187i −0.699918 0.714223i \(-0.746780\pi\)
0.968494 + 0.249036i \(0.0801137\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.55408i 0.522484i −0.965273 0.261242i \(-0.915868\pi\)
0.965273 0.261242i \(-0.0841320\pi\)
\(114\) 0 0
\(115\) 11.7442i 1.09515i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 9.32002 16.1427i 0.854365 1.47980i
\(120\) 0 0
\(121\) −10.4661 −0.951466
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.11294i 0.725644i
\(126\) 0 0
\(127\) 1.99683 1.15287i 0.177190 0.102301i −0.408782 0.912632i \(-0.634046\pi\)
0.585972 + 0.810331i \(0.300713\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.24465 7.35196i 0.370857 0.642343i −0.618840 0.785517i \(-0.712397\pi\)
0.989698 + 0.143173i \(0.0457306\pi\)
\(132\) 0 0
\(133\) −9.78865 + 8.78333i −0.848784 + 0.761611i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.68866 + 3.86170i −0.571450 + 0.329927i −0.757728 0.652570i \(-0.773691\pi\)
0.186278 + 0.982497i \(0.440357\pi\)
\(138\) 0 0
\(139\) −8.66344 + 5.00184i −0.734824 + 0.424251i −0.820184 0.572099i \(-0.806129\pi\)
0.0853606 + 0.996350i \(0.472796\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.60890 2.78670i −0.134543 0.233036i
\(144\) 0 0
\(145\) −14.7296 −1.22322
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.897686 + 0.518279i 0.0735413 + 0.0424591i 0.536320 0.844015i \(-0.319814\pi\)
−0.462778 + 0.886474i \(0.653147\pi\)
\(150\) 0 0
\(151\) 21.5740i 1.75567i −0.478965 0.877834i \(-0.658988\pi\)
0.478965 0.877834i \(-0.341012\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.38660 + 14.5260i −0.673628 + 1.16676i
\(156\) 0 0
\(157\) −7.79444 + 13.5004i −0.622064 + 1.07745i 0.367036 + 0.930207i \(0.380372\pi\)
−0.989101 + 0.147240i \(0.952961\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −11.6699 + 6.73762i −0.919717 + 0.530999i
\(162\) 0 0
\(163\) 18.2536i 1.42973i 0.699261 + 0.714867i \(0.253513\pi\)
−0.699261 + 0.714867i \(0.746487\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.74585 + 3.02390i 0.135098 + 0.233997i 0.925635 0.378418i \(-0.123532\pi\)
−0.790537 + 0.612414i \(0.790198\pi\)
\(168\) 0 0
\(169\) −3.19739 + 5.53805i −0.245953 + 0.426004i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.9620 6.32893i −0.833428 0.481180i 0.0215969 0.999767i \(-0.493125\pi\)
−0.855025 + 0.518587i \(0.826458\pi\)
\(174\) 0 0
\(175\) −5.00317 + 2.88858i −0.378204 + 0.218356i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.95556 0.146165 0.0730826 0.997326i \(-0.476716\pi\)
0.0730826 + 0.997326i \(0.476716\pi\)
\(180\) 0 0
\(181\) −3.90914 6.77082i −0.290564 0.503271i 0.683379 0.730064i \(-0.260510\pi\)
−0.973943 + 0.226792i \(0.927176\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.39134 + 1.95799i 0.249336 + 0.143954i
\(186\) 0 0
\(187\) 3.90925 + 2.25700i 0.285872 + 0.165048i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.37771 0.0996879 0.0498439 0.998757i \(-0.484128\pi\)
0.0498439 + 0.998757i \(0.484128\pi\)
\(192\) 0 0
\(193\) 2.67422 4.63188i 0.192494 0.333410i −0.753582 0.657354i \(-0.771676\pi\)
0.946076 + 0.323944i \(0.105009\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.1527i 1.50707i −0.657409 0.753534i \(-0.728348\pi\)
0.657409 0.753534i \(-0.271652\pi\)
\(198\) 0 0
\(199\) 8.22547 4.74898i 0.583088 0.336646i −0.179272 0.983800i \(-0.557374\pi\)
0.762360 + 0.647154i \(0.224041\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.45033 + 14.6364i 0.593097 + 1.02727i
\(204\) 0 0
\(205\) 5.38639 + 9.32950i 0.376202 + 0.651601i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.12703 2.37049i −0.147130 0.163970i
\(210\) 0 0
\(211\) 24.6313 + 14.2209i 1.69569 + 0.979006i 0.949759 + 0.312981i \(0.101328\pi\)
0.745929 + 0.666025i \(0.232006\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.3602 + 17.9444i 0.706558 + 1.22379i
\(216\) 0 0
\(217\) 19.2455 1.30647
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 27.2074i 1.83017i
\(222\) 0 0
\(223\) −15.0576 8.69352i −1.00833 0.582161i −0.0976300 0.995223i \(-0.531126\pi\)
−0.910703 + 0.413061i \(0.864459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −26.9603 −1.78942 −0.894708 0.446652i \(-0.852616\pi\)
−0.894708 + 0.446652i \(0.852616\pi\)
\(228\) 0 0
\(229\) −0.645395 −0.0426489 −0.0213245 0.999773i \(-0.506788\pi\)
−0.0213245 + 0.999773i \(0.506788\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −19.3758 11.1866i −1.26935 0.732862i −0.294488 0.955655i \(-0.595149\pi\)
−0.974866 + 0.222794i \(0.928482\pi\)
\(234\) 0 0
\(235\) 6.75110i 0.440393i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5.37564 0.347721 0.173861 0.984770i \(-0.444376\pi\)
0.173861 + 0.984770i \(0.444376\pi\)
\(240\) 0 0
\(241\) −0.0588490 0.101929i −0.00379080 0.00656585i 0.864124 0.503279i \(-0.167873\pi\)
−0.867915 + 0.496713i \(0.834540\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.79005 + 2.76554i 0.306025 + 0.176684i
\(246\) 0 0
\(247\) −5.96338 + 18.2466i −0.379441 + 1.16100i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.16780 8.95089i −0.326188 0.564975i 0.655564 0.755140i \(-0.272431\pi\)
−0.981752 + 0.190165i \(0.939098\pi\)
\(252\) 0 0
\(253\) −1.63163 2.82607i −0.102580 0.177673i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.7958 10.8518i 1.17245 0.676914i 0.218194 0.975905i \(-0.429983\pi\)
0.954256 + 0.298991i \(0.0966501\pi\)
\(258\) 0 0
\(259\) 4.49319i 0.279193i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13.5325 23.4391i 0.834453 1.44531i −0.0600228 0.998197i \(-0.519117\pi\)
0.894475 0.447117i \(-0.147549\pi\)
\(264\) 0 0
\(265\) 27.9968 1.71983
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.93328 + 2.84823i 0.300787 + 0.173660i 0.642796 0.766037i \(-0.277774\pi\)
−0.342009 + 0.939697i \(0.611107\pi\)
\(270\) 0 0
\(271\) −2.59990 1.50105i −0.157933 0.0911824i 0.418951 0.908009i \(-0.362398\pi\)
−0.576883 + 0.816827i \(0.695731\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.699519 1.21160i −0.0421826 0.0730624i
\(276\) 0 0
\(277\) 1.08132 0.0649703 0.0324851 0.999472i \(-0.489658\pi\)
0.0324851 + 0.999472i \(0.489658\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.6773 + 9.05127i −0.935227 + 0.539954i −0.888461 0.458952i \(-0.848225\pi\)
−0.0467662 + 0.998906i \(0.514892\pi\)
\(282\) 0 0
\(283\) 1.62115 + 0.935971i 0.0963674 + 0.0556377i 0.547409 0.836865i \(-0.315614\pi\)
−0.451042 + 0.892503i \(0.648947\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.18032 10.7046i 0.364813 0.631875i
\(288\) 0 0
\(289\) 10.5836 + 18.3313i 0.622564 + 1.07831i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.51284i 0.0883812i 0.999023 + 0.0441906i \(0.0140709\pi\)
−0.999023 + 0.0441906i \(0.985929\pi\)
\(294\) 0 0
\(295\) 4.92316 2.84239i 0.286637 0.165490i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.83438 + 17.0337i −0.568737 + 0.985082i
\(300\) 0 0
\(301\) 11.8872 20.5893i 0.685169 1.18675i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 22.4459i 1.28525i
\(306\) 0 0
\(307\) 0.715534 + 0.413114i 0.0408377 + 0.0235776i 0.520280 0.853996i \(-0.325828\pi\)
−0.479442 + 0.877573i \(0.659161\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 26.4749 1.50126 0.750628 0.660725i \(-0.229751\pi\)
0.750628 + 0.660725i \(0.229751\pi\)
\(312\) 0 0
\(313\) −5.36483 9.29215i −0.303238 0.525223i 0.673630 0.739069i \(-0.264734\pi\)
−0.976867 + 0.213846i \(0.931401\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.5225 + 8.96192i −0.871830 + 0.503351i −0.867956 0.496641i \(-0.834567\pi\)
−0.00387421 + 0.999992i \(0.501233\pi\)
\(318\) 0 0
\(319\) −3.54446 + 2.04639i −0.198452 + 0.114576i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.55360 26.3502i −0.309010 1.46617i
\(324\) 0 0
\(325\) −4.21624 + 7.30274i −0.233875 + 0.405083i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.70839 3.87309i 0.369846 0.213531i
\(330\) 0 0
\(331\) 17.6283i 0.968936i −0.874809 0.484468i \(-0.839013\pi\)
0.874809 0.484468i \(-0.160987\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 25.5180 1.39420
\(336\) 0 0
\(337\) 11.5924 20.0786i 0.631477 1.09375i −0.355773 0.934572i \(-0.615782\pi\)
0.987250 0.159178i \(-0.0508843\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.66063i 0.252387i
\(342\) 0 0
\(343\) 14.7739i 0.797718i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.11621 1.93333i 0.0599211 0.103786i −0.834509 0.550995i \(-0.814248\pi\)
0.894430 + 0.447208i \(0.147582\pi\)
\(348\) 0 0
\(349\) −31.8456 −1.70466 −0.852329 0.523007i \(-0.824810\pi\)
−0.852329 + 0.523007i \(0.824810\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.5384i 0.560901i 0.959868 + 0.280451i \(0.0904839\pi\)
−0.959868 + 0.280451i \(0.909516\pi\)
\(354\) 0 0
\(355\) −22.8133 + 13.1713i −1.21080 + 0.699059i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −17.3642 + 30.0756i −0.916446 + 1.58733i −0.111677 + 0.993745i \(0.535622\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(360\) 0 0
\(361\) −2.05098 + 18.8890i −0.107946 + 0.994157i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 26.0881 15.0620i 1.36551 0.788380i
\(366\) 0 0
\(367\) −13.0717 + 7.54694i −0.682337 + 0.393947i −0.800735 0.599019i \(-0.795557\pi\)
0.118398 + 0.992966i \(0.462224\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −16.0617 27.8197i −0.833882 1.44433i
\(372\) 0 0
\(373\) 31.2927 1.62027 0.810136 0.586242i \(-0.199393\pi\)
0.810136 + 0.586242i \(0.199393\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 21.3636 + 12.3343i 1.10028 + 0.635249i
\(378\) 0 0
\(379\) 13.6109i 0.699146i 0.936909 + 0.349573i \(0.113673\pi\)
−0.936909 + 0.349573i \(0.886327\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.2735 + 24.7223i −0.729339 + 1.26325i 0.227824 + 0.973702i \(0.426839\pi\)
−0.957163 + 0.289550i \(0.906494\pi\)
\(384\) 0 0
\(385\) −2.89853 + 5.02040i −0.147723 + 0.255863i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.3036 6.52612i 0.573114 0.330887i −0.185278 0.982686i \(-0.559319\pi\)
0.758392 + 0.651799i \(0.225985\pi\)
\(390\) 0 0
\(391\) 27.5918i 1.39538i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.70757 4.68965i −0.136233 0.235962i
\(396\) 0 0
\(397\) 3.22502 5.58590i 0.161859 0.280348i −0.773676 0.633581i \(-0.781584\pi\)
0.935535 + 0.353233i \(0.114918\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 27.8231 + 16.0637i 1.38942 + 0.802181i 0.993250 0.115996i \(-0.0370061\pi\)
0.396169 + 0.918178i \(0.370339\pi\)
\(402\) 0 0
\(403\) 24.3277 14.0456i 1.21185 0.699661i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.08810 0.0539353
\(408\) 0 0
\(409\) −13.7369 23.7930i −0.679247 1.17649i −0.975208 0.221290i \(-0.928973\pi\)
0.295961 0.955200i \(-0.404360\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5.64881 3.26134i −0.277960 0.160480i
\(414\) 0 0
\(415\) −16.7175 9.65186i −0.820631 0.473791i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16.7384 −0.817723 −0.408861 0.912597i \(-0.634074\pi\)
−0.408861 + 0.912597i \(0.634074\pi\)
\(420\) 0 0
\(421\) 5.37905 9.31679i 0.262159 0.454072i −0.704657 0.709549i \(-0.748899\pi\)
0.966815 + 0.255476i \(0.0822322\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.8293i 0.573803i
\(426\) 0 0
\(427\) 22.3039 12.8771i 1.07936 0.623169i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.9070 + 18.8915i 0.525373 + 0.909972i 0.999563 + 0.0295500i \(0.00940743\pi\)
−0.474191 + 0.880422i \(0.657259\pi\)
\(432\) 0 0
\(433\) −12.6446 21.9010i −0.607659 1.05250i −0.991625 0.129149i \(-0.958776\pi\)
0.383967 0.923347i \(-0.374558\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.04762 + 18.5044i −0.289297 + 0.885185i
\(438\) 0 0
\(439\) 27.0701 + 15.6289i 1.29198 + 0.745927i 0.979006 0.203833i \(-0.0653401\pi\)
0.312978 + 0.949760i \(0.398673\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.86303 10.1551i −0.278561 0.482482i 0.692466 0.721450i \(-0.256524\pi\)
−0.971027 + 0.238968i \(0.923191\pi\)
\(444\) 0 0
\(445\) 6.74337 0.319667
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.3531i 0.913329i −0.889639 0.456664i \(-0.849044\pi\)
0.889639 0.456664i \(-0.150956\pi\)
\(450\) 0 0
\(451\) 2.59231 + 1.49667i 0.122067 + 0.0704755i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 34.9408 1.63805
\(456\) 0 0
\(457\) −7.43069 −0.347593 −0.173796 0.984782i \(-0.555603\pi\)
−0.173796 + 0.984782i \(0.555603\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0829 + 17.3684i 1.40110 + 0.808925i 0.994506 0.104684i \(-0.0333832\pi\)
0.406594 + 0.913609i \(0.366716\pi\)
\(462\) 0 0
\(463\) 8.95687i 0.416261i 0.978101 + 0.208130i \(0.0667378\pi\)
−0.978101 + 0.208130i \(0.933262\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.282420 −0.0130689 −0.00653443 0.999979i \(-0.502080\pi\)
−0.00653443 + 0.999979i \(0.502080\pi\)
\(468\) 0 0
\(469\) −14.6397 25.3566i −0.675996 1.17086i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.98605 + 2.87870i 0.229259 + 0.132363i
\(474\) 0 0
\(475\) −2.59276 + 7.93327i −0.118964 + 0.364004i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.93957 10.2876i −0.271386 0.470054i 0.697831 0.716263i \(-0.254149\pi\)
−0.969217 + 0.246208i \(0.920815\pi\)
\(480\) 0 0
\(481\) −3.27918 5.67971i −0.149518 0.258972i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.7969 7.38828i 0.581076 0.335484i
\(486\) 0 0
\(487\) 6.04436i 0.273896i −0.990578 0.136948i \(-0.956271\pi\)
0.990578 0.136948i \(-0.0437294\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.76957 + 11.7252i −0.305506 + 0.529153i −0.977374 0.211519i \(-0.932159\pi\)
0.671868 + 0.740671i \(0.265492\pi\)
\(492\) 0 0
\(493\) −34.6056 −1.55856
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 26.1759 + 15.1127i 1.17415 + 0.677896i
\(498\) 0 0
\(499\) 22.1361 + 12.7803i 0.990950 + 0.572125i 0.905558 0.424222i \(-0.139453\pi\)
0.0853915 + 0.996347i \(0.472786\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.234869 0.406806i −0.0104723 0.0181386i 0.860742 0.509042i \(-0.170000\pi\)
−0.871214 + 0.490903i \(0.836667\pi\)
\(504\) 0 0
\(505\) 51.2889 2.28233
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.39853 3.11684i 0.239285 0.138152i −0.375563 0.926797i \(-0.622551\pi\)
0.614848 + 0.788645i \(0.289217\pi\)
\(510\) 0 0
\(511\) −29.9334 17.2821i −1.32418 0.764514i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25.8296 + 44.7382i −1.13819 + 1.97140i
\(516\) 0 0
\(517\) 0.937937 + 1.62455i 0.0412504 + 0.0714478i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 24.7521i 1.08441i 0.840247 + 0.542204i \(0.182410\pi\)
−0.840247 + 0.542204i \(0.817590\pi\)
\(522\) 0 0
\(523\) 16.9312 9.77523i 0.740350 0.427441i −0.0818469 0.996645i \(-0.526082\pi\)
0.822196 + 0.569204i \(0.192749\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.7035 + 34.1274i −0.858297 + 1.48661i
\(528\) 0 0
\(529\) 1.52669 2.64430i 0.0663778 0.114970i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18.0419i 0.781481i
\(534\) 0 0
\(535\) 33.2743 + 19.2109i 1.43858 + 0.830562i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.53688 0.0661979
\(540\) 0 0
\(541\) 6.43658 + 11.1485i 0.276730 + 0.479311i 0.970570 0.240819i \(-0.0774159\pi\)
−0.693840 + 0.720129i \(0.744083\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.7711 + 7.37341i −0.547055 + 0.315842i
\(546\) 0 0
\(547\) −5.74630 + 3.31763i −0.245694 + 0.141852i −0.617791 0.786342i \(-0.711972\pi\)
0.372097 + 0.928194i \(0.378639\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 23.2082 + 7.58493i 0.988703 + 0.323129i
\(552\) 0 0
\(553\) −3.10666 + 5.38089i −0.132109 + 0.228819i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.8855 + 14.3676i −1.05443 + 0.608776i −0.923887 0.382666i \(-0.875006\pi\)
−0.130545 + 0.991442i \(0.541673\pi\)
\(558\) 0 0
\(559\) 34.7018i 1.46773i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −35.7237 −1.50558 −0.752788 0.658263i \(-0.771291\pi\)
−0.752788 + 0.658263i \(0.771291\pi\)
\(564\) 0 0
\(565\) −7.30248 + 12.6483i −0.307218 + 0.532116i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.2818i 0.976023i 0.872837 + 0.488011i \(0.162278\pi\)
−0.872837 + 0.488011i \(0.837722\pi\)
\(570\) 0 0
\(571\) 23.1334i 0.968102i 0.875040 + 0.484051i \(0.160835\pi\)
−0.875040 + 0.484051i \(0.839165\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.27580 + 7.40590i −0.178313 + 0.308847i
\(576\) 0 0
\(577\) −14.6533 −0.610023 −0.305012 0.952349i \(-0.598660\pi\)
−0.305012 + 0.952349i \(0.598660\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22.1490i 0.918897i
\(582\) 0 0
\(583\) 6.73701 3.88962i 0.279019 0.161091i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.1867 + 22.8401i −0.544275 + 0.942712i 0.454377 + 0.890810i \(0.349862\pi\)
−0.998652 + 0.0519029i \(0.983471\pi\)
\(588\) 0 0
\(589\) 20.6942 18.5688i 0.852690 0.765116i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 32.8529 18.9676i 1.34911 0.778908i 0.360985 0.932572i \(-0.382441\pi\)
0.988123 + 0.153664i \(0.0491072\pi\)
\(594\) 0 0
\(595\) −42.4488 + 24.5078i −1.74023 + 1.00472i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.55133 + 2.68698i 0.0633856 + 0.109787i 0.895977 0.444101i \(-0.146477\pi\)
−0.832591 + 0.553888i \(0.813144\pi\)
\(600\) 0 0
\(601\) −43.4637 −1.77292 −0.886460 0.462805i \(-0.846843\pi\)
−0.886460 + 0.462805i \(0.846843\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 23.8344 + 13.7608i 0.969008 + 0.559457i
\(606\) 0 0
\(607\) 2.19694i 0.0891708i −0.999006 0.0445854i \(-0.985803\pi\)
0.999006 0.0445854i \(-0.0141967\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.65326 9.79173i 0.228706 0.396131i
\(612\) 0 0
\(613\) 2.82963 4.90107i 0.114288 0.197952i −0.803207 0.595700i \(-0.796875\pi\)
0.917495 + 0.397748i \(0.130208\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.6435 + 10.1865i −0.710302 + 0.410093i −0.811173 0.584807i \(-0.801170\pi\)
0.100871 + 0.994900i \(0.467837\pi\)
\(618\) 0 0
\(619\) 40.3661i 1.62245i −0.584735 0.811224i \(-0.698801\pi\)
0.584735 0.811224i \(-0.301199\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.86866 6.70072i −0.154995 0.268459i
\(624\) 0 0
\(625\) 15.4537 26.7667i 0.618150 1.07067i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.96762 + 4.60011i 0.317690 + 0.183418i
\(630\) 0 0
\(631\) 32.0420 18.4995i 1.27557 0.736452i 0.299541 0.954083i \(-0.403166\pi\)
0.976031 + 0.217631i \(0.0698330\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.06315 −0.240609
\(636\) 0 0
\(637\) −4.63163 8.02222i −0.183512 0.317852i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.37740 4.83669i −0.330887 0.191038i 0.325348 0.945594i \(-0.394519\pi\)
−0.656235 + 0.754557i \(0.727852\pi\)
\(642\) 0 0
\(643\) 31.6351 + 18.2645i 1.24757 + 0.720282i 0.970623 0.240604i \(-0.0773457\pi\)
0.276942 + 0.960887i \(0.410679\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.0388 −1.18095 −0.590474 0.807057i \(-0.701059\pi\)
−0.590474 + 0.807057i \(0.701059\pi\)
\(648\) 0 0
\(649\) 0.789791 1.36796i 0.0310020 0.0536970i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 35.2628i 1.37994i 0.723838 + 0.689970i \(0.242376\pi\)
−0.723838 + 0.689970i \(0.757624\pi\)
\(654\) 0 0
\(655\) −19.3326 + 11.1617i −0.755389 + 0.436124i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 15.8773 + 27.5002i 0.618490 + 1.07126i 0.989761 + 0.142732i \(0.0455886\pi\)
−0.371272 + 0.928524i \(0.621078\pi\)
\(660\) 0 0
\(661\) 10.1533 + 17.5861i 0.394919 + 0.684020i 0.993091 0.117348i \(-0.0374394\pi\)
−0.598172 + 0.801368i \(0.704106\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 33.8399 7.13213i 1.31226 0.276572i
\(666\) 0 0
\(667\) 21.6654 + 12.5085i 0.838889 + 0.484333i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.11842 + 5.40127i 0.120385 + 0.208514i
\(672\) 0 0
\(673\) −36.6513 −1.41280 −0.706402 0.707811i \(-0.749683\pi\)
−0.706402 + 0.707811i \(0.749683\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23.6921i 0.910562i 0.890348 + 0.455281i \(0.150461\pi\)
−0.890348 + 0.455281i \(0.849539\pi\)
\(678\) 0 0
\(679\) −14.6831 8.47728i −0.563485 0.325328i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.59785 −0.175932 −0.0879659 0.996123i \(-0.528037\pi\)
−0.0879659 + 0.996123i \(0.528037\pi\)
\(684\) 0 0
\(685\) 20.3094 0.775981
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −40.6062 23.4440i −1.54697 0.893146i
\(690\) 0 0
\(691\) 33.3184i 1.26749i 0.773542 + 0.633745i \(0.218483\pi\)
−0.773542 + 0.633745i \(0.781517\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 26.3056 0.997828
\(696\) 0 0
\(697\) 12.6548 + 21.9187i 0.479334 + 0.830231i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15.9031 + 9.18164i 0.600651 + 0.346786i 0.769297 0.638891i \(-0.220606\pi\)
−0.168647 + 0.985677i \(0.553940\pi\)
\(702\) 0 0
\(703\) −4.33521 4.83141i −0.163506 0.182220i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −29.4244 50.9645i −1.10662 1.91672i
\(708\) 0 0
\(709\) −19.5671 33.8913i −0.734860 1.27281i −0.954785 0.297298i \(-0.903915\pi\)
0.219925 0.975517i \(-0.429419\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.6714 14.2440i 0.923949 0.533442i
\(714\) 0 0
\(715\) 8.46151i 0.316443i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.0577 22.6166i 0.486969 0.843455i −0.512919 0.858437i \(-0.671436\pi\)
0.999888 + 0.0149819i \(0.00476905\pi\)
\(720\) 0 0
\(721\) 59.2736 2.20746
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.28849 + 5.36271i 0.344966 + 0.199166i
\(726\) 0 0
\(727\) 35.3018 + 20.3815i 1.30927 + 0.755907i 0.981974 0.189015i \(-0.0605295\pi\)
0.327295 + 0.944922i \(0.393863\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 24.3402 + 42.1584i 0.900254 + 1.55929i
\(732\) 0 0
\(733\) 23.0259 0.850482 0.425241 0.905080i \(-0.360189\pi\)
0.425241 + 0.905080i \(0.360189\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.14055 3.54525i 0.226190 0.130591i
\(738\) 0 0
\(739\) −6.72833 3.88460i −0.247505 0.142897i 0.371116 0.928587i \(-0.378975\pi\)
−0.618621 + 0.785689i \(0.712309\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.661917 1.14647i 0.0242834 0.0420600i −0.853628 0.520883i \(-0.825603\pi\)
0.877912 + 0.478823i \(0.158936\pi\)
\(744\) 0 0
\(745\) −1.36286 2.36055i −0.0499314 0.0864838i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 44.0851i 1.61084i
\(750\) 0 0
\(751\) −10.5737 + 6.10474i −0.385841 + 0.222765i −0.680356 0.732881i \(-0.738175\pi\)
0.294516 + 0.955647i \(0.404842\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −28.3654 + 49.1303i −1.03232 + 1.78804i
\(756\) 0 0
\(757\) 10.3695 17.9606i 0.376888 0.652788i −0.613720 0.789524i \(-0.710328\pi\)
0.990608 + 0.136735i \(0.0436610\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 41.6236i 1.50886i −0.656383 0.754428i \(-0.727914\pi\)
0.656383 0.754428i \(-0.272086\pi\)
\(762\) 0 0
\(763\) 14.6535 + 8.46022i 0.530494 + 0.306281i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.52066 −0.343771
\(768\) 0 0
\(769\) −1.74896 3.02929i −0.0630692 0.109239i 0.832767 0.553624i \(-0.186756\pi\)
−0.895836 + 0.444385i \(0.853422\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.20851 + 0.697735i −0.0434672 + 0.0250958i −0.521576 0.853205i \(-0.674656\pi\)
0.478109 + 0.878301i \(0.341322\pi\)
\(774\) 0 0
\(775\) 10.5772 6.10675i 0.379944 0.219361i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.68272 17.4734i −0.131947 0.626051i
\(780\) 0 0
\(781\) −3.65979 + 6.33895i −0.130958 + 0.226825i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 35.5005 20.4962i 1.26707 0.731541i
\(786\) 0 0
\(787\) 12.6125i 0.449586i 0.974407 + 0.224793i \(0.0721706\pi\)
−0.974407 + 0.224793i \(0.927829\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 16.7577 0.595834
\(792\) 0 0
\(793\) 18.7958 32.5552i 0.667458 1.15607i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13.6012i 0.481780i 0.970552 + 0.240890i \(0.0774393\pi\)
−0.970552 + 0.240890i \(0.922561\pi\)
\(798\) 0 0
\(799\) 15.8610i 0.561123i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.18515 7.24889i 0.147691 0.255808i
\(804\) 0 0
\(805\) 35.4344 1.24890
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.53063i 0.299921i 0.988692 + 0.149960i \(0.0479146\pi\)
−0.988692 + 0.149960i \(0.952085\pi\)
\(810\) 0 0
\(811\) 45.3271 26.1696i 1.59165 0.918939i 0.598624 0.801030i \(-0.295714\pi\)
0.993024 0.117908i \(-0.0376189\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 23.9998 41.5688i 0.840675 1.45609i
\(816\) 0 0
\(817\) −7.08334 33.6084i −0.247815 1.17581i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26.3083 15.1891i 0.918165 0.530103i 0.0351160 0.999383i \(-0.488820\pi\)
0.883049 + 0.469280i \(0.155487\pi\)
\(822\) 0 0
\(823\) −31.4836 + 18.1770i −1.09745 + 0.633612i −0.935550 0.353195i \(-0.885095\pi\)
−0.161899 + 0.986807i \(0.551762\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 18.2908 + 31.6806i 0.636033 + 1.10164i 0.986295 + 0.164989i \(0.0527590\pi\)
−0.350263 + 0.936652i \(0.613908\pi\)
\(828\) 0 0
\(829\) 13.1047 0.455147 0.227573 0.973761i \(-0.426921\pi\)
0.227573 + 0.973761i \(0.426921\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 11.2537 + 6.49735i 0.389919 + 0.225120i
\(834\) 0 0
\(835\) 9.18175i 0.317748i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 8.94545 15.4940i 0.308831 0.534911i −0.669276 0.743014i \(-0.733396\pi\)
0.978107 + 0.208103i \(0.0667289\pi\)
\(840\) 0 0
\(841\) 1.18823 2.05807i 0.0409733 0.0709679i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 14.5628 8.40784i 0.500976 0.289238i
\(846\) 0 0
\(847\) 31.5782i 1.08504i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.32550 5.75994i −0.113997 0.197448i
\(852\) 0 0
\(853\) −5.15772 + 8.93344i −0.176597 + 0.305875i −0.940713 0.339204i \(-0.889842\pi\)
0.764116 + 0.645079i \(0.223176\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8.34720 4.81926i −0.285135 0.164623i 0.350611 0.936521i \(-0.385974\pi\)
−0.635746 + 0.771898i \(0.719307\pi\)
\(858\) 0 0
\(859\) −38.1615 + 22.0326i −1.30205 + 0.751741i −0.980756 0.195237i \(-0.937452\pi\)
−0.321298 + 0.946978i \(0.604119\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 51.0749 1.73861 0.869306 0.494275i \(-0.164566\pi\)
0.869306 + 0.494275i \(0.164566\pi\)
\(864\) 0 0
\(865\) 16.6425 + 28.8257i 0.565862 + 0.980102i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.30308 0.752331i −0.0442038 0.0255211i
\(870\) 0 0
\(871\) −37.0111 21.3684i −1.25407 0.724040i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −24.4782 −0.827515
\(876\) 0 0
\(877\) 5.91775 10.2498i 0.199828 0.346112i −0.748644 0.662972i \(-0.769295\pi\)
0.948473 + 0.316859i \(0.102628\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 17.4075i 0.586475i 0.956040 + 0.293237i \(0.0947326\pi\)
−0.956040 + 0.293237i \(0.905267\pi\)
\(882\) 0 0
\(883\) −33.2311 + 19.1860i −1.11831 + 0.645659i −0.940970 0.338490i \(-0.890084\pi\)
−0.177344 + 0.984149i \(0.556751\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11.0878 + 19.2046i 0.372292 + 0.644828i 0.989918 0.141644i \(-0.0452387\pi\)
−0.617626 + 0.786472i \(0.711905\pi\)
\(888\) 0 0
\(889\) 3.47842 + 6.02480i 0.116662 + 0.202065i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.47645 10.6372i 0.116335 0.355959i
\(894\) 0 0
\(895\) −4.45338 2.57116i −0.148860 0.0859443i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −17.8649 30.9428i −0.595826 1.03200i
\(900\) 0 0
\(901\) 65.7756 2.19130
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 20.5589i 0.683400i
\(906\) 0 0
\(907\) −3.09253 1.78547i −0.102686 0.0592856i 0.447778 0.894145i \(-0.352216\pi\)
−0.550463 + 0.834859i \(0.685549\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 33.2094 1.10028 0.550138 0.835074i \(-0.314575\pi\)
0.550138 + 0.835074i \(0.314575\pi\)
\(912\) 0 0
\(913\) −5.36377 −0.177515
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 22.1822 + 12.8069i 0.732521 + 0.422921i
\(918\) 0 0
\(919\) 12.5957i 0.415493i 0.978183 + 0.207746i \(0.0666128\pi\)
−0.978183 + 0.207746i \(0.933387\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 44.1176 1.45215
\(924\) 0 0
\(925\) −1.42572 2.46943i −0.0468775 0.0811942i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −33.2298 19.1853i −1.09024 0.629448i −0.156596 0.987663i \(-0.550052\pi\)
−0.933639 + 0.358215i \(0.883386\pi\)
\(930\) 0 0
\(931\) −6.12320 6.82406i −0.200680 0.223649i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.93500 10.2797i −0.194095 0.336183i
\(936\) 0 0
\(937\) −28.0371 48.5617i −0.915932 1.58644i −0.805530 0.592555i \(-0.798119\pi\)
−0.110402 0.993887i \(-0.535214\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −11.3546 + 6.55556i −0.370148 + 0.213705i −0.673523 0.739166i \(-0.735220\pi\)
0.303375 + 0.952871i \(0.401887\pi\)
\(942\) 0 0
\(943\) 18.2968i 0.595824i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 24.3590 42.1910i 0.791560 1.37102i −0.133441 0.991057i \(-0.542603\pi\)
0.925001 0.379965i \(-0.124064\pi\)
\(948\) 0 0
\(949\) −50.4506 −1.63770
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −13.6474 7.87933i −0.442083 0.255237i 0.262398 0.964960i \(-0.415487\pi\)
−0.704481 + 0.709723i \(0.748820\pi\)
\(954\) 0 0
\(955\) −3.13746 1.81141i −0.101526 0.0586159i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.6515 20.1809i −0.376245 0.651675i
\(960\) 0 0
\(961\) −9.68697 −0.312483
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −12.1800 + 7.03210i −0.392086 + 0.226371i
\(966\) 0 0
\(967\) 42.7997 + 24.7104i 1.37635 + 0.794633i 0.991718 0.128438i \(-0.0409964\pi\)
0.384628 + 0.923072i \(0.374330\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −8.95664 + 15.5134i −0.287432 + 0.497848i −0.973196 0.229977i \(-0.926135\pi\)
0.685764 + 0.727824i \(0.259468\pi\)
\(972\) 0 0
\(973\) −15.0915 26.1392i −0.483810 0.837984i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46.2005i 1.47808i 0.673660 + 0.739042i \(0.264721\pi\)
−0.673660 + 0.739042i \(0.735279\pi\)
\(978\) 0 0
\(979\) 1.62269 0.936863i 0.0518615 0.0299423i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −24.8820 + 43.0970i −0.793614 + 1.37458i 0.130102 + 0.991501i \(0.458470\pi\)
−0.923716 + 0.383079i \(0.874864\pi\)
\(984\) 0 0
\(985\) −27.8115 + 48.1709i −0.886147 + 1.53485i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 35.1920i 1.11904i
\(990\) 0 0
\(991\) 12.8014 + 7.39089i 0.406650 + 0.234779i 0.689349 0.724429i \(-0.257897\pi\)
−0.282699 + 0.959209i \(0.591230\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −24.9757 −0.791784
\(996\) 0 0
\(997\) −1.77321 3.07130i −0.0561582 0.0972689i 0.836580 0.547845i \(-0.184552\pi\)
−0.892738 + 0.450576i \(0.851218\pi\)
\(998\) 0 0
\(999\) 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 2736.2.cg.a.1151.2 24
3.2 odd 2 inner 2736.2.cg.a.1151.11 yes 24
4.3 odd 2 2736.2.cg.b.1151.2 yes 24
12.11 even 2 2736.2.cg.b.1151.11 yes 24
19.7 even 3 2736.2.cg.b.2591.11 yes 24
57.26 odd 6 2736.2.cg.b.2591.2 yes 24
76.7 odd 6 inner 2736.2.cg.a.2591.11 yes 24
228.83 even 6 inner 2736.2.cg.a.2591.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.cg.a.1151.2 24 1.1 even 1 trivial
2736.2.cg.a.1151.11 yes 24 3.2 odd 2 inner
2736.2.cg.a.2591.2 yes 24 228.83 even 6 inner
2736.2.cg.a.2591.11 yes 24 76.7 odd 6 inner
2736.2.cg.b.1151.2 yes 24 4.3 odd 2
2736.2.cg.b.1151.11 yes 24 12.11 even 2
2736.2.cg.b.2591.2 yes 24 57.26 odd 6
2736.2.cg.b.2591.11 yes 24 19.7 even 3