Properties

Label 588.3.m.e.313.1
Level $588$
Weight $3$
Character 588.313
Analytic conductor $16.022$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,3,Mod(313,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.313");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.m (of order \(6\), degree \(2\), not 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: \(16.0218395444\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 313.1
Root \(-0.662827 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 588.313
Dual form 588.3.m.e.325.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{3} +(-4.65891 - 2.68982i) q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{3} +(-4.65891 - 2.68982i) q^{5} +(1.50000 - 2.59808i) q^{9} +(4.29579 + 7.44053i) q^{11} -21.0158i q^{13} +9.31781 q^{15} +(-4.75120 + 2.74311i) q^{17} +(6.27088 + 3.62049i) q^{19} +(-14.0278 + 24.2969i) q^{23} +(1.97027 + 3.41261i) q^{25} +5.19615i q^{27} +40.3447 q^{29} +(-35.0828 + 20.2550i) q^{31} +(-12.8874 - 7.44053i) q^{33} +(-33.3185 + 57.7093i) q^{37} +(18.2002 + 31.5237i) q^{39} +33.6357i q^{41} +0.932907 q^{43} +(-13.9767 + 8.06946i) q^{45} +(74.1789 + 42.8272i) q^{47} +(4.75120 - 8.22933i) q^{51} +(22.2977 + 38.6207i) q^{53} -46.2197i q^{55} -12.5418 q^{57} +(-55.1615 + 31.8475i) q^{59} +(-27.7201 - 16.0042i) q^{61} +(-56.5288 + 97.9108i) q^{65} +(23.8671 + 41.3390i) q^{67} -48.5938i q^{69} +14.9676 q^{71} +(-121.501 + 70.1488i) q^{73} +(-5.91081 - 3.41261i) q^{75} +(61.1537 - 105.921i) q^{79} +(-4.50000 - 7.79423i) q^{81} +33.1852i q^{83} +29.5139 q^{85} +(-60.5171 + 34.9396i) q^{87} +(-31.2848 - 18.0623i) q^{89} +(35.0828 - 60.7651i) q^{93} +(-19.4769 - 33.7351i) q^{95} +16.2175i q^{97} +25.7748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} + 12 q^{9} - 48 q^{17} + 96 q^{19} + 8 q^{23} - 36 q^{25} + 80 q^{29} - 48 q^{31} - 64 q^{37} - 112 q^{43} + 264 q^{47} + 48 q^{51} + 72 q^{53} - 192 q^{57} - 168 q^{59} + 144 q^{61} - 120 q^{65} + 32 q^{67} + 224 q^{71} - 336 q^{73} + 108 q^{75} + 216 q^{79} - 36 q^{81} - 96 q^{85} - 120 q^{87} - 96 q^{89} + 48 q^{93} + 136 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) 0 0
\(5\) −4.65891 2.68982i −0.931781 0.537964i −0.0444067 0.999014i \(-0.514140\pi\)
−0.887374 + 0.461049i \(0.847473\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 0 0
\(11\) 4.29579 + 7.44053i 0.390527 + 0.676412i 0.992519 0.122090i \(-0.0389596\pi\)
−0.601992 + 0.798502i \(0.705626\pi\)
\(12\) 0 0
\(13\) 21.0158i 1.61660i −0.588769 0.808301i \(-0.700387\pi\)
0.588769 0.808301i \(-0.299613\pi\)
\(14\) 0 0
\(15\) 9.31781 0.621187
\(16\) 0 0
\(17\) −4.75120 + 2.74311i −0.279483 + 0.161359i −0.633189 0.773997i \(-0.718254\pi\)
0.353707 + 0.935356i \(0.384921\pi\)
\(18\) 0 0
\(19\) 6.27088 + 3.62049i 0.330046 + 0.190552i 0.655862 0.754881i \(-0.272305\pi\)
−0.325815 + 0.945433i \(0.605639\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −14.0278 + 24.2969i −0.609905 + 1.05639i 0.381350 + 0.924431i \(0.375459\pi\)
−0.991256 + 0.131956i \(0.957874\pi\)
\(24\) 0 0
\(25\) 1.97027 + 3.41261i 0.0788107 + 0.136504i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) 40.3447 1.39120 0.695599 0.718431i \(-0.255139\pi\)
0.695599 + 0.718431i \(0.255139\pi\)
\(30\) 0 0
\(31\) −35.0828 + 20.2550i −1.13170 + 0.653388i −0.944362 0.328907i \(-0.893320\pi\)
−0.187340 + 0.982295i \(0.559986\pi\)
\(32\) 0 0
\(33\) −12.8874 7.44053i −0.390527 0.225471i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −33.3185 + 57.7093i −0.900500 + 1.55971i −0.0736541 + 0.997284i \(0.523466\pi\)
−0.826846 + 0.562428i \(0.809867\pi\)
\(38\) 0 0
\(39\) 18.2002 + 31.5237i 0.466673 + 0.808301i
\(40\) 0 0
\(41\) 33.6357i 0.820383i 0.911999 + 0.410191i \(0.134538\pi\)
−0.911999 + 0.410191i \(0.865462\pi\)
\(42\) 0 0
\(43\) 0.932907 0.0216955 0.0108478 0.999941i \(-0.496547\pi\)
0.0108478 + 0.999941i \(0.496547\pi\)
\(44\) 0 0
\(45\) −13.9767 + 8.06946i −0.310594 + 0.179321i
\(46\) 0 0
\(47\) 74.1789 + 42.8272i 1.57827 + 0.911217i 0.995100 + 0.0988687i \(0.0315224\pi\)
0.583173 + 0.812348i \(0.301811\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.75120 8.22933i 0.0931609 0.161359i
\(52\) 0 0
\(53\) 22.2977 + 38.6207i 0.420711 + 0.728693i 0.996009 0.0892508i \(-0.0284473\pi\)
−0.575298 + 0.817944i \(0.695114\pi\)
\(54\) 0 0
\(55\) 46.2197i 0.840358i
\(56\) 0 0
\(57\) −12.5418 −0.220031
\(58\) 0 0
\(59\) −55.1615 + 31.8475i −0.934940 + 0.539788i −0.888371 0.459127i \(-0.848162\pi\)
−0.0465695 + 0.998915i \(0.514829\pi\)
\(60\) 0 0
\(61\) −27.7201 16.0042i −0.454427 0.262364i 0.255271 0.966870i \(-0.417835\pi\)
−0.709698 + 0.704506i \(0.751169\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −56.5288 + 97.9108i −0.869674 + 1.50632i
\(66\) 0 0
\(67\) 23.8671 + 41.3390i 0.356225 + 0.617000i 0.987327 0.158700i \(-0.0507304\pi\)
−0.631102 + 0.775700i \(0.717397\pi\)
\(68\) 0 0
\(69\) 48.5938i 0.704258i
\(70\) 0 0
\(71\) 14.9676 0.210811 0.105405 0.994429i \(-0.466386\pi\)
0.105405 + 0.994429i \(0.466386\pi\)
\(72\) 0 0
\(73\) −121.501 + 70.1488i −1.66440 + 0.960942i −0.693825 + 0.720144i \(0.744076\pi\)
−0.970575 + 0.240798i \(0.922591\pi\)
\(74\) 0 0
\(75\) −5.91081 3.41261i −0.0788107 0.0455014i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 61.1537 105.921i 0.774098 1.34078i −0.161202 0.986921i \(-0.551537\pi\)
0.935300 0.353856i \(-0.115130\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 33.1852i 0.399822i 0.979814 + 0.199911i \(0.0640652\pi\)
−0.979814 + 0.199911i \(0.935935\pi\)
\(84\) 0 0
\(85\) 29.5139 0.347222
\(86\) 0 0
\(87\) −60.5171 + 34.9396i −0.695599 + 0.401604i
\(88\) 0 0
\(89\) −31.2848 18.0623i −0.351515 0.202947i 0.313838 0.949477i \(-0.398385\pi\)
−0.665352 + 0.746530i \(0.731719\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 35.0828 60.7651i 0.377234 0.653388i
\(94\) 0 0
\(95\) −19.4769 33.7351i −0.205021 0.355106i
\(96\) 0 0
\(97\) 16.2175i 0.167191i 0.996500 + 0.0835956i \(0.0266404\pi\)
−0.996500 + 0.0835956i \(0.973360\pi\)
\(98\) 0 0
\(99\) 25.7748 0.260351
\(100\) 0 0
\(101\) 103.459 59.7322i 1.02435 0.591407i 0.108987 0.994043i \(-0.465239\pi\)
0.915360 + 0.402636i \(0.131906\pi\)
\(102\) 0 0
\(103\) 7.73523 + 4.46594i 0.0750994 + 0.0433586i 0.537079 0.843532i \(-0.319528\pi\)
−0.461980 + 0.886890i \(0.652861\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −86.9279 + 150.564i −0.812410 + 1.40714i 0.0987623 + 0.995111i \(0.468512\pi\)
−0.911173 + 0.412025i \(0.864822\pi\)
\(108\) 0 0
\(109\) 80.1573 + 138.837i 0.735388 + 1.27373i 0.954553 + 0.298042i \(0.0963334\pi\)
−0.219165 + 0.975688i \(0.570333\pi\)
\(110\) 0 0
\(111\) 115.419i 1.03981i
\(112\) 0 0
\(113\) −81.4420 −0.720725 −0.360363 0.932812i \(-0.617347\pi\)
−0.360363 + 0.932812i \(0.617347\pi\)
\(114\) 0 0
\(115\) 130.709 75.4646i 1.13660 0.656214i
\(116\) 0 0
\(117\) −54.6007 31.5237i −0.466673 0.269434i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 23.5923 40.8631i 0.194978 0.337711i
\(122\) 0 0
\(123\) −29.1294 50.4536i −0.236824 0.410191i
\(124\) 0 0
\(125\) 113.292i 0.906339i
\(126\) 0 0
\(127\) 117.172 0.922613 0.461307 0.887241i \(-0.347381\pi\)
0.461307 + 0.887241i \(0.347381\pi\)
\(128\) 0 0
\(129\) −1.39936 + 0.807922i −0.0108478 + 0.00626296i
\(130\) 0 0
\(131\) 211.440 + 122.075i 1.61404 + 0.931869i 0.988420 + 0.151745i \(0.0484893\pi\)
0.625625 + 0.780124i \(0.284844\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 13.9767 24.2084i 0.103531 0.179321i
\(136\) 0 0
\(137\) −122.706 212.533i −0.895663 1.55133i −0.832981 0.553301i \(-0.813368\pi\)
−0.0626820 0.998034i \(-0.519965\pi\)
\(138\) 0 0
\(139\) 17.1371i 0.123288i −0.998098 0.0616441i \(-0.980366\pi\)
0.998098 0.0616441i \(-0.0196344\pi\)
\(140\) 0 0
\(141\) −148.358 −1.05218
\(142\) 0 0
\(143\) 156.369 90.2797i 1.09349 0.631326i
\(144\) 0 0
\(145\) −187.962 108.520i −1.29629 0.748414i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −67.1209 + 116.257i −0.450476 + 0.780247i −0.998416 0.0562707i \(-0.982079\pi\)
0.547940 + 0.836518i \(0.315412\pi\)
\(150\) 0 0
\(151\) −99.5047 172.347i −0.658971 1.14137i −0.980882 0.194602i \(-0.937659\pi\)
0.321911 0.946770i \(-0.395675\pi\)
\(152\) 0 0
\(153\) 16.4587i 0.107573i
\(154\) 0 0
\(155\) 217.930 1.40600
\(156\) 0 0
\(157\) 66.7004 38.5095i 0.424843 0.245283i −0.272304 0.962211i \(-0.587786\pi\)
0.697147 + 0.716928i \(0.254452\pi\)
\(158\) 0 0
\(159\) −66.8931 38.6207i −0.420711 0.242898i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 115.190 199.514i 0.706684 1.22401i −0.259396 0.965771i \(-0.583523\pi\)
0.966080 0.258242i \(-0.0831432\pi\)
\(164\) 0 0
\(165\) 40.0274 + 69.3295i 0.242590 + 0.420179i
\(166\) 0 0
\(167\) 229.231i 1.37264i 0.727298 + 0.686321i \(0.240776\pi\)
−0.727298 + 0.686321i \(0.759224\pi\)
\(168\) 0 0
\(169\) −272.665 −1.61340
\(170\) 0 0
\(171\) 18.8126 10.8615i 0.110015 0.0635174i
\(172\) 0 0
\(173\) 97.4044 + 56.2365i 0.563031 + 0.325066i 0.754361 0.656459i \(-0.227947\pi\)
−0.191330 + 0.981526i \(0.561280\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 55.1615 95.5425i 0.311647 0.539788i
\(178\) 0 0
\(179\) −52.7470 91.3605i −0.294676 0.510394i 0.680234 0.732995i \(-0.261878\pi\)
−0.974909 + 0.222602i \(0.928545\pi\)
\(180\) 0 0
\(181\) 15.2683i 0.0843553i 0.999110 + 0.0421776i \(0.0134295\pi\)
−0.999110 + 0.0421776i \(0.986570\pi\)
\(182\) 0 0
\(183\) 55.4401 0.302951
\(184\) 0 0
\(185\) 310.456 179.242i 1.67814 0.968874i
\(186\) 0 0
\(187\) −40.8204 23.5677i −0.218291 0.126030i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 153.093 265.165i 0.801534 1.38830i −0.117073 0.993123i \(-0.537351\pi\)
0.918606 0.395174i \(-0.129316\pi\)
\(192\) 0 0
\(193\) 0.920499 + 1.59435i 0.00476943 + 0.00826089i 0.868400 0.495864i \(-0.165149\pi\)
−0.863631 + 0.504125i \(0.831815\pi\)
\(194\) 0 0
\(195\) 195.822i 1.00421i
\(196\) 0 0
\(197\) −255.334 −1.29611 −0.648056 0.761593i \(-0.724418\pi\)
−0.648056 + 0.761593i \(0.724418\pi\)
\(198\) 0 0
\(199\) −31.7384 + 18.3242i −0.159489 + 0.0920812i −0.577620 0.816305i \(-0.696019\pi\)
0.418131 + 0.908387i \(0.362685\pi\)
\(200\) 0 0
\(201\) −71.6012 41.3390i −0.356225 0.205667i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 90.4740 156.706i 0.441337 0.764417i
\(206\) 0 0
\(207\) 42.0835 + 72.8907i 0.203302 + 0.352129i
\(208\) 0 0
\(209\) 62.2116i 0.297663i
\(210\) 0 0
\(211\) −126.571 −0.599862 −0.299931 0.953961i \(-0.596964\pi\)
−0.299931 + 0.953961i \(0.596964\pi\)
\(212\) 0 0
\(213\) −22.4513 + 12.9623i −0.105405 + 0.0608558i
\(214\) 0 0
\(215\) −4.34633 2.50935i −0.0202155 0.0116714i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 121.501 210.446i 0.554800 0.960942i
\(220\) 0 0
\(221\) 57.6487 + 99.8505i 0.260854 + 0.451812i
\(222\) 0 0
\(223\) 212.193i 0.951536i −0.879571 0.475768i \(-0.842170\pi\)
0.879571 0.475768i \(-0.157830\pi\)
\(224\) 0 0
\(225\) 11.8216 0.0525405
\(226\) 0 0
\(227\) −91.3560 + 52.7444i −0.402449 + 0.232354i −0.687540 0.726146i \(-0.741310\pi\)
0.285091 + 0.958500i \(0.407976\pi\)
\(228\) 0 0
\(229\) −6.05426 3.49543i −0.0264378 0.0152639i 0.486723 0.873556i \(-0.338192\pi\)
−0.513161 + 0.858293i \(0.671526\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −168.023 + 291.024i −0.721128 + 1.24903i 0.239419 + 0.970916i \(0.423043\pi\)
−0.960548 + 0.278115i \(0.910290\pi\)
\(234\) 0 0
\(235\) −230.395 399.056i −0.980404 1.69811i
\(236\) 0 0
\(237\) 211.843i 0.893851i
\(238\) 0 0
\(239\) −232.382 −0.972309 −0.486155 0.873873i \(-0.661601\pi\)
−0.486155 + 0.873873i \(0.661601\pi\)
\(240\) 0 0
\(241\) −55.1958 + 31.8673i −0.229028 + 0.132229i −0.610124 0.792306i \(-0.708880\pi\)
0.381095 + 0.924536i \(0.375547\pi\)
\(242\) 0 0
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 76.0876 131.788i 0.308047 0.533553i
\(248\) 0 0
\(249\) −28.7392 49.7778i −0.115419 0.199911i
\(250\) 0 0
\(251\) 415.450i 1.65518i 0.561334 + 0.827589i \(0.310288\pi\)
−0.561334 + 0.827589i \(0.689712\pi\)
\(252\) 0 0
\(253\) −241.043 −0.952737
\(254\) 0 0
\(255\) −44.2708 + 25.5598i −0.173611 + 0.100234i
\(256\) 0 0
\(257\) −230.014 132.799i −0.894998 0.516727i −0.0194240 0.999811i \(-0.506183\pi\)
−0.875574 + 0.483084i \(0.839517\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 60.5171 104.819i 0.231866 0.401604i
\(262\) 0 0
\(263\) −78.1866 135.423i −0.297288 0.514917i 0.678227 0.734853i \(-0.262749\pi\)
−0.975514 + 0.219935i \(0.929415\pi\)
\(264\) 0 0
\(265\) 239.907i 0.905310i
\(266\) 0 0
\(267\) 62.5696 0.234343
\(268\) 0 0
\(269\) 288.266 166.431i 1.07162 0.618701i 0.142998 0.989723i \(-0.454326\pi\)
0.928624 + 0.371022i \(0.120992\pi\)
\(270\) 0 0
\(271\) 181.076 + 104.544i 0.668178 + 0.385773i 0.795386 0.606103i \(-0.207268\pi\)
−0.127208 + 0.991876i \(0.540602\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.9277 + 29.3197i −0.0615554 + 0.106617i
\(276\) 0 0
\(277\) 131.616 + 227.965i 0.475146 + 0.822978i 0.999595 0.0284646i \(-0.00906180\pi\)
−0.524448 + 0.851442i \(0.675728\pi\)
\(278\) 0 0
\(279\) 121.530i 0.435592i
\(280\) 0 0
\(281\) 391.519 1.39331 0.696653 0.717408i \(-0.254672\pi\)
0.696653 + 0.717408i \(0.254672\pi\)
\(282\) 0 0
\(283\) 94.7376 54.6968i 0.334762 0.193275i −0.323191 0.946334i \(-0.604756\pi\)
0.657953 + 0.753059i \(0.271422\pi\)
\(284\) 0 0
\(285\) 58.4308 + 33.7351i 0.205021 + 0.118369i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −129.451 + 224.215i −0.447926 + 0.775831i
\(290\) 0 0
\(291\) −14.0448 24.3263i −0.0482639 0.0835956i
\(292\) 0 0
\(293\) 35.3685i 0.120712i 0.998177 + 0.0603558i \(0.0192235\pi\)
−0.998177 + 0.0603558i \(0.980776\pi\)
\(294\) 0 0
\(295\) 342.656 1.16155
\(296\) 0 0
\(297\) −38.6622 + 22.3216i −0.130176 + 0.0751569i
\(298\) 0 0
\(299\) 510.619 + 294.806i 1.70776 + 0.985974i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −103.459 + 179.196i −0.341449 + 0.591407i
\(304\) 0 0
\(305\) 86.0968 + 149.124i 0.282284 + 0.488931i
\(306\) 0 0
\(307\) 125.621i 0.409189i 0.978847 + 0.204594i \(0.0655875\pi\)
−0.978847 + 0.204594i \(0.934412\pi\)
\(308\) 0 0
\(309\) −15.4705 −0.0500662
\(310\) 0 0
\(311\) −273.435 + 157.868i −0.879211 + 0.507613i −0.870398 0.492348i \(-0.836139\pi\)
−0.00881288 + 0.999961i \(0.502805\pi\)
\(312\) 0 0
\(313\) 44.6909 + 25.8023i 0.142782 + 0.0824355i 0.569689 0.821860i \(-0.307064\pi\)
−0.426907 + 0.904296i \(0.640397\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.49696 4.32486i 0.00787683 0.0136431i −0.862060 0.506806i \(-0.830826\pi\)
0.869937 + 0.493163i \(0.164159\pi\)
\(318\) 0 0
\(319\) 173.313 + 300.186i 0.543300 + 0.941023i
\(320\) 0 0
\(321\) 301.127i 0.938091i
\(322\) 0 0
\(323\) −39.7256 −0.122990
\(324\) 0 0
\(325\) 71.7187 41.4068i 0.220673 0.127406i
\(326\) 0 0
\(327\) −240.472 138.837i −0.735388 0.424577i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −227.390 + 393.851i −0.686980 + 1.18988i 0.285831 + 0.958280i \(0.407731\pi\)
−0.972810 + 0.231603i \(0.925603\pi\)
\(332\) 0 0
\(333\) 99.9555 + 173.128i 0.300167 + 0.519904i
\(334\) 0 0
\(335\) 256.792i 0.766545i
\(336\) 0 0
\(337\) −183.824 −0.545471 −0.272736 0.962089i \(-0.587928\pi\)
−0.272736 + 0.962089i \(0.587928\pi\)
\(338\) 0 0
\(339\) 122.163 70.5308i 0.360363 0.208055i
\(340\) 0 0
\(341\) −301.417 174.023i −0.883920 0.510331i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −130.709 + 226.394i −0.378865 + 0.656214i
\(346\) 0 0
\(347\) −72.3882 125.380i −0.208611 0.361326i 0.742666 0.669662i \(-0.233561\pi\)
−0.951277 + 0.308337i \(0.900228\pi\)
\(348\) 0 0
\(349\) 187.069i 0.536015i 0.963417 + 0.268007i \(0.0863651\pi\)
−0.963417 + 0.268007i \(0.913635\pi\)
\(350\) 0 0
\(351\) 109.201 0.311115
\(352\) 0 0
\(353\) −192.778 + 111.300i −0.546113 + 0.315299i −0.747553 0.664202i \(-0.768771\pi\)
0.201440 + 0.979501i \(0.435438\pi\)
\(354\) 0 0
\(355\) −69.7324 40.2600i −0.196429 0.113409i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.4928 + 54.5472i −0.0877237 + 0.151942i −0.906549 0.422101i \(-0.861293\pi\)
0.818825 + 0.574043i \(0.194626\pi\)
\(360\) 0 0
\(361\) −154.284 267.228i −0.427380 0.740243i
\(362\) 0 0
\(363\) 81.7261i 0.225141i
\(364\) 0 0
\(365\) 754.750 2.06781
\(366\) 0 0
\(367\) −473.803 + 273.550i −1.29102 + 0.745368i −0.978834 0.204654i \(-0.934393\pi\)
−0.312181 + 0.950023i \(0.601060\pi\)
\(368\) 0 0
\(369\) 87.3881 + 50.4536i 0.236824 + 0.136730i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.2208 28.0953i 0.0434875 0.0753226i −0.843462 0.537188i \(-0.819486\pi\)
0.886950 + 0.461866i \(0.152820\pi\)
\(374\) 0 0
\(375\) −98.1141 169.939i −0.261637 0.453169i
\(376\) 0 0
\(377\) 847.878i 2.24901i
\(378\) 0 0
\(379\) 508.859 1.34263 0.671317 0.741170i \(-0.265729\pi\)
0.671317 + 0.741170i \(0.265729\pi\)
\(380\) 0 0
\(381\) −175.758 + 101.474i −0.461307 + 0.266336i
\(382\) 0 0
\(383\) −22.7625 13.1419i −0.0594321 0.0343131i 0.469990 0.882672i \(-0.344258\pi\)
−0.529422 + 0.848359i \(0.677591\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.39936 2.42376i 0.00361592 0.00626296i
\(388\) 0 0
\(389\) 180.064 + 311.880i 0.462890 + 0.801749i 0.999104 0.0423337i \(-0.0134793\pi\)
−0.536214 + 0.844082i \(0.680146\pi\)
\(390\) 0 0
\(391\) 153.919i 0.393656i
\(392\) 0 0
\(393\) −422.880 −1.07603
\(394\) 0 0
\(395\) −569.819 + 328.985i −1.44258 + 0.832874i
\(396\) 0 0
\(397\) −494.494 285.496i −1.24558 0.719134i −0.275352 0.961343i \(-0.588794\pi\)
−0.970224 + 0.242210i \(0.922128\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −34.2007 + 59.2373i −0.0852885 + 0.147724i −0.905514 0.424316i \(-0.860515\pi\)
0.820226 + 0.572040i \(0.193848\pi\)
\(402\) 0 0
\(403\) 425.677 + 737.293i 1.05627 + 1.82951i
\(404\) 0 0
\(405\) 48.4168i 0.119548i
\(406\) 0 0
\(407\) −572.518 −1.40668
\(408\) 0 0
\(409\) −13.3064 + 7.68246i −0.0325340 + 0.0187835i −0.516179 0.856481i \(-0.672646\pi\)
0.483645 + 0.875264i \(0.339313\pi\)
\(410\) 0 0
\(411\) 368.118 + 212.533i 0.895663 + 0.517112i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 89.2622 154.607i 0.215090 0.372546i
\(416\) 0 0
\(417\) 14.8411 + 25.7056i 0.0355902 + 0.0616441i
\(418\) 0 0
\(419\) 366.079i 0.873696i −0.899535 0.436848i \(-0.856095\pi\)
0.899535 0.436848i \(-0.143905\pi\)
\(420\) 0 0
\(421\) 607.135 1.44213 0.721063 0.692870i \(-0.243654\pi\)
0.721063 + 0.692870i \(0.243654\pi\)
\(422\) 0 0
\(423\) 222.537 128.482i 0.526091 0.303739i
\(424\) 0 0
\(425\) −18.7223 10.8093i −0.0440525 0.0254337i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −156.369 + 270.839i −0.364497 + 0.631326i
\(430\) 0 0
\(431\) 293.177 + 507.797i 0.680224 + 1.17818i 0.974912 + 0.222590i \(0.0714510\pi\)
−0.294688 + 0.955594i \(0.595216\pi\)
\(432\) 0 0
\(433\) 518.769i 1.19808i 0.800719 + 0.599040i \(0.204451\pi\)
−0.800719 + 0.599040i \(0.795549\pi\)
\(434\) 0 0
\(435\) 375.924 0.864194
\(436\) 0 0
\(437\) −175.933 + 101.575i −0.402594 + 0.232438i
\(438\) 0 0
\(439\) 191.845 + 110.762i 0.437005 + 0.252305i 0.702326 0.711855i \(-0.252145\pi\)
−0.265321 + 0.964160i \(0.585478\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 113.208 196.081i 0.255548 0.442622i −0.709496 0.704709i \(-0.751078\pi\)
0.965044 + 0.262087i \(0.0844109\pi\)
\(444\) 0 0
\(445\) 97.1686 + 168.301i 0.218356 + 0.378205i
\(446\) 0 0
\(447\) 232.514i 0.520165i
\(448\) 0 0
\(449\) −378.422 −0.842810 −0.421405 0.906873i \(-0.638463\pi\)
−0.421405 + 0.906873i \(0.638463\pi\)
\(450\) 0 0
\(451\) −250.268 + 144.492i −0.554917 + 0.320382i
\(452\) 0 0
\(453\) 298.514 + 172.347i 0.658971 + 0.380457i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −219.077 + 379.452i −0.479380 + 0.830311i −0.999720 0.0236483i \(-0.992472\pi\)
0.520340 + 0.853959i \(0.325805\pi\)
\(458\) 0 0
\(459\) −14.2536 24.6880i −0.0310536 0.0537865i
\(460\) 0 0
\(461\) 46.3981i 0.100647i 0.998733 + 0.0503234i \(0.0160252\pi\)
−0.998733 + 0.0503234i \(0.983975\pi\)
\(462\) 0 0
\(463\) 367.455 0.793639 0.396820 0.917897i \(-0.370114\pi\)
0.396820 + 0.917897i \(0.370114\pi\)
\(464\) 0 0
\(465\) −326.895 + 188.733i −0.702999 + 0.405877i
\(466\) 0 0
\(467\) −458.530 264.733i −0.981863 0.566879i −0.0790311 0.996872i \(-0.525183\pi\)
−0.902832 + 0.429993i \(0.858516\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −66.7004 + 115.528i −0.141614 + 0.245283i
\(472\) 0 0
\(473\) 4.00758 + 6.94133i 0.00847268 + 0.0146751i
\(474\) 0 0
\(475\) 28.5334i 0.0600702i
\(476\) 0 0
\(477\) 133.786 0.280474
\(478\) 0 0
\(479\) −250.940 + 144.880i −0.523883 + 0.302464i −0.738522 0.674229i \(-0.764476\pi\)
0.214639 + 0.976694i \(0.431143\pi\)
\(480\) 0 0
\(481\) 1212.81 + 700.216i 2.52143 + 1.45575i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 43.6223 75.5560i 0.0899428 0.155786i
\(486\) 0 0
\(487\) −219.818 380.736i −0.451372 0.781799i 0.547100 0.837067i \(-0.315732\pi\)
−0.998472 + 0.0552685i \(0.982399\pi\)
\(488\) 0 0
\(489\) 399.028i 0.816009i
\(490\) 0 0
\(491\) −320.561 −0.652874 −0.326437 0.945219i \(-0.605848\pi\)
−0.326437 + 0.945219i \(0.605848\pi\)
\(492\) 0 0
\(493\) −191.686 + 110.670i −0.388815 + 0.224483i
\(494\) 0 0
\(495\) −120.082 69.3295i −0.242590 0.140060i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −385.986 + 668.548i −0.773520 + 1.33978i 0.162103 + 0.986774i \(0.448172\pi\)
−0.935623 + 0.353002i \(0.885161\pi\)
\(500\) 0 0
\(501\) −198.520 343.847i −0.396248 0.686321i
\(502\) 0 0
\(503\) 101.632i 0.202052i 0.994884 + 0.101026i \(0.0322126\pi\)
−0.994884 + 0.101026i \(0.967787\pi\)
\(504\) 0 0
\(505\) −642.675 −1.27262
\(506\) 0 0
\(507\) 408.998 236.135i 0.806701 0.465749i
\(508\) 0 0
\(509\) −524.298 302.704i −1.03006 0.594703i −0.113055 0.993589i \(-0.536063\pi\)
−0.917000 + 0.398886i \(0.869397\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −18.8126 + 32.5844i −0.0366718 + 0.0635174i
\(514\) 0 0
\(515\) −24.0252 41.6128i −0.0466508 0.0808015i
\(516\) 0 0
\(517\) 735.907i 1.42342i
\(518\) 0 0
\(519\) −194.809 −0.375354
\(520\) 0 0
\(521\) −331.942 + 191.647i −0.637124 + 0.367844i −0.783506 0.621384i \(-0.786571\pi\)
0.146382 + 0.989228i \(0.453237\pi\)
\(522\) 0 0
\(523\) −388.061 224.047i −0.741991 0.428389i 0.0808018 0.996730i \(-0.474252\pi\)
−0.822793 + 0.568341i \(0.807585\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 111.124 192.472i 0.210861 0.365221i
\(528\) 0 0
\(529\) −129.059 223.538i −0.243969 0.422566i
\(530\) 0 0
\(531\) 191.085i 0.359859i
\(532\) 0 0
\(533\) 706.882 1.32623
\(534\) 0 0
\(535\) 809.978 467.641i 1.51398 0.874095i
\(536\) 0 0
\(537\) 158.241 + 91.3605i 0.294676 + 0.170131i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 135.629 234.916i 0.250700 0.434226i −0.713019 0.701145i \(-0.752672\pi\)
0.963719 + 0.266920i \(0.0860058\pi\)
\(542\) 0 0
\(543\) −13.2227 22.9025i −0.0243513 0.0421776i
\(544\) 0 0
\(545\) 862.435i 1.58245i
\(546\) 0 0
\(547\) −590.544 −1.07961 −0.539803 0.841791i \(-0.681501\pi\)
−0.539803 + 0.841791i \(0.681501\pi\)
\(548\) 0 0
\(549\) −83.1602 + 48.0126i −0.151476 + 0.0874546i
\(550\) 0 0
\(551\) 252.997 + 146.068i 0.459159 + 0.265096i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −310.456 + 537.725i −0.559379 + 0.968874i
\(556\) 0 0
\(557\) −94.1473 163.068i −0.169026 0.292761i 0.769052 0.639186i \(-0.220729\pi\)
−0.938078 + 0.346425i \(0.887395\pi\)
\(558\) 0 0
\(559\) 19.6058i 0.0350730i
\(560\) 0 0
\(561\) 81.6408 0.145527
\(562\) 0 0
\(563\) 176.805 102.078i 0.314041 0.181312i −0.334692 0.942327i \(-0.608632\pi\)
0.648733 + 0.761016i \(0.275299\pi\)
\(564\) 0 0
\(565\) 379.430 + 219.064i 0.671558 + 0.387724i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 330.456 572.367i 0.580767 1.00592i −0.414622 0.909994i \(-0.636086\pi\)
0.995389 0.0959241i \(-0.0305806\pi\)
\(570\) 0 0
\(571\) 266.989 + 462.438i 0.467581 + 0.809874i 0.999314 0.0370381i \(-0.0117923\pi\)
−0.531733 + 0.846912i \(0.678459\pi\)
\(572\) 0 0
\(573\) 530.329i 0.925531i
\(574\) 0 0
\(575\) −110.554 −0.192268
\(576\) 0 0
\(577\) −46.2750 + 26.7169i −0.0801993 + 0.0463031i −0.539563 0.841945i \(-0.681411\pi\)
0.459364 + 0.888248i \(0.348077\pi\)
\(578\) 0 0
\(579\) −2.76150 1.59435i −0.00476943 0.00275363i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −191.573 + 331.813i −0.328598 + 0.569148i
\(584\) 0 0
\(585\) 169.586 + 293.732i 0.289891 + 0.502107i
\(586\) 0 0
\(587\) 413.063i 0.703684i 0.936059 + 0.351842i \(0.114445\pi\)
−0.936059 + 0.351842i \(0.885555\pi\)
\(588\) 0 0
\(589\) −293.333 −0.498018
\(590\) 0 0
\(591\) 383.001 221.126i 0.648056 0.374155i
\(592\) 0 0
\(593\) 106.047 + 61.2261i 0.178831 + 0.103248i 0.586743 0.809773i \(-0.300410\pi\)
−0.407912 + 0.913021i \(0.633743\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 31.7384 54.9725i 0.0531631 0.0920812i
\(598\) 0 0
\(599\) 322.568 + 558.704i 0.538511 + 0.932728i 0.998985 + 0.0450546i \(0.0143462\pi\)
−0.460474 + 0.887673i \(0.652320\pi\)
\(600\) 0 0
\(601\) 683.488i 1.13725i −0.822596 0.568626i \(-0.807475\pi\)
0.822596 0.568626i \(-0.192525\pi\)
\(602\) 0 0
\(603\) 143.202 0.237483
\(604\) 0 0
\(605\) −219.829 + 126.918i −0.363353 + 0.209782i
\(606\) 0 0
\(607\) −222.788 128.627i −0.367031 0.211905i 0.305130 0.952311i \(-0.401300\pi\)
−0.672161 + 0.740405i \(0.734634\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 900.049 1558.93i 1.47307 2.55144i
\(612\) 0 0
\(613\) −442.856 767.050i −0.722441 1.25130i −0.960019 0.279936i \(-0.909687\pi\)
0.237578 0.971369i \(-0.423647\pi\)
\(614\) 0 0
\(615\) 313.411i 0.509612i
\(616\) 0 0
\(617\) 46.0724 0.0746717 0.0373358 0.999303i \(-0.488113\pi\)
0.0373358 + 0.999303i \(0.488113\pi\)
\(618\) 0 0
\(619\) 949.446 548.163i 1.53384 0.885562i 0.534658 0.845069i \(-0.320440\pi\)
0.999180 0.0404930i \(-0.0128928\pi\)
\(620\) 0 0
\(621\) −126.250 72.8907i −0.203302 0.117376i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 353.993 613.134i 0.566388 0.981014i
\(626\) 0 0
\(627\) −53.8768 93.3173i −0.0859279 0.148831i
\(628\) 0 0
\(629\) 365.585i 0.581217i
\(630\) 0 0
\(631\) 606.319 0.960886 0.480443 0.877026i \(-0.340476\pi\)
0.480443 + 0.877026i \(0.340476\pi\)
\(632\) 0 0
\(633\) 189.856 109.614i 0.299931 0.173165i
\(634\) 0 0
\(635\) −545.893 315.171i −0.859674 0.496333i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 22.4513 38.8869i 0.0351351 0.0608558i
\(640\) 0 0
\(641\) −469.592 813.357i −0.732593 1.26889i −0.955771 0.294111i \(-0.904977\pi\)
0.223178 0.974778i \(-0.428357\pi\)
\(642\) 0 0
\(643\) 992.960i 1.54426i −0.635464 0.772131i \(-0.719191\pi\)
0.635464 0.772131i \(-0.280809\pi\)
\(644\) 0 0
\(645\) 8.69266 0.0134770
\(646\) 0 0
\(647\) 229.656 132.592i 0.354955 0.204933i −0.311910 0.950112i \(-0.600969\pi\)
0.666865 + 0.745178i \(0.267636\pi\)
\(648\) 0 0
\(649\) −473.925 273.620i −0.730238 0.421603i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 567.071 982.196i 0.868409 1.50413i 0.00478648 0.999989i \(-0.498476\pi\)
0.863622 0.504139i \(-0.168190\pi\)
\(654\) 0 0
\(655\) −656.719 1137.47i −1.00262 1.73660i
\(656\) 0 0
\(657\) 420.893i 0.640628i
\(658\) 0 0
\(659\) −924.147 −1.40235 −0.701174 0.712990i \(-0.747340\pi\)
−0.701174 + 0.712990i \(0.747340\pi\)
\(660\) 0 0
\(661\) 202.968 117.184i 0.307062 0.177282i −0.338549 0.940949i \(-0.609936\pi\)
0.645611 + 0.763666i \(0.276603\pi\)
\(662\) 0 0
\(663\) −172.946 99.8505i −0.260854 0.150604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −565.948 + 980.251i −0.848498 + 1.46964i
\(668\) 0 0
\(669\) 183.764 + 318.289i 0.274685 + 0.475768i
\(670\) 0 0
\(671\) 275.003i 0.409840i
\(672\) 0 0
\(673\) −465.127 −0.691125 −0.345563 0.938396i \(-0.612312\pi\)
−0.345563 + 0.938396i \(0.612312\pi\)
\(674\) 0 0
\(675\) −17.7324 + 10.2378i −0.0262702 + 0.0151671i
\(676\) 0 0
\(677\) −1122.31 647.964i −1.65776 0.957110i −0.973744 0.227647i \(-0.926897\pi\)
−0.684020 0.729463i \(-0.739770\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 91.3560 158.233i 0.134150 0.232354i
\(682\) 0 0
\(683\) −8.13060 14.0826i −0.0119042 0.0206188i 0.860012 0.510274i \(-0.170456\pi\)
−0.871916 + 0.489655i \(0.837123\pi\)
\(684\) 0 0
\(685\) 1320.23i 1.92734i
\(686\) 0 0
\(687\) 12.1085 0.0176252
\(688\) 0 0
\(689\) 811.647 468.604i 1.17801 0.680123i
\(690\) 0 0
\(691\) 59.3542 + 34.2682i 0.0858962 + 0.0495922i 0.542333 0.840164i \(-0.317541\pi\)
−0.456437 + 0.889756i \(0.650875\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −46.0956 + 79.8400i −0.0663246 + 0.114878i
\(696\) 0 0
\(697\) −92.2664 159.810i −0.132376 0.229283i
\(698\) 0 0
\(699\) 582.048i 0.832687i
\(700\) 0 0
\(701\) 923.360 1.31720 0.658602 0.752491i \(-0.271148\pi\)
0.658602 + 0.752491i \(0.271148\pi\)
\(702\) 0 0
\(703\) −417.872 + 241.259i −0.594413 + 0.343185i
\(704\) 0 0
\(705\) 691.185 + 399.056i 0.980404 + 0.566036i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 456.431 790.562i 0.643768 1.11504i −0.340817 0.940130i \(-0.610704\pi\)
0.984585 0.174909i \(-0.0559631\pi\)
\(710\) 0 0
\(711\) −183.461 317.764i −0.258033 0.446926i
\(712\) 0 0
\(713\) 1136.54i 1.59402i
\(714\) 0 0
\(715\) −971.345 −1.35852
\(716\) 0 0
\(717\) 348.573 201.249i 0.486155 0.280681i
\(718\) 0 0
\(719\) −472.001 272.510i −0.656469 0.379013i 0.134461 0.990919i \(-0.457070\pi\)
−0.790930 + 0.611906i \(0.790403\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 55.1958 95.6019i 0.0763427 0.132229i
\(724\) 0 0
\(725\) 79.4899 + 137.681i 0.109641 + 0.189904i
\(726\) 0 0
\(727\) 750.292i 1.03204i 0.856577 + 0.516019i \(0.172587\pi\)
−0.856577 + 0.516019i \(0.827413\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −4.43243 + 2.55907i −0.00606352 + 0.00350078i
\(732\) 0 0
\(733\) 802.458 + 463.299i 1.09476 + 0.632059i 0.934839 0.355071i \(-0.115543\pi\)
0.159919 + 0.987130i \(0.448877\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −205.056 + 355.167i −0.278231 + 0.481910i
\(738\) 0 0
\(739\) −244.073 422.748i −0.330275 0.572054i 0.652290 0.757969i \(-0.273808\pi\)
−0.982566 + 0.185915i \(0.940475\pi\)
\(740\) 0 0
\(741\) 263.575i 0.355702i
\(742\) 0 0
\(743\) −1091.72 −1.46935 −0.734674 0.678421i \(-0.762665\pi\)
−0.734674 + 0.678421i \(0.762665\pi\)
\(744\) 0 0
\(745\) 625.420 361.086i 0.839490 0.484680i
\(746\) 0 0
\(747\) 86.2177 + 49.7778i 0.115419 + 0.0666369i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 240.222 416.076i 0.319869 0.554029i −0.660591 0.750746i \(-0.729694\pi\)
0.980460 + 0.196716i \(0.0630278\pi\)
\(752\) 0 0
\(753\) −359.790 623.175i −0.477809 0.827589i
\(754\) 0 0
\(755\) 1070.60i 1.41801i
\(756\) 0 0
\(757\) 941.400 1.24359 0.621796 0.783179i \(-0.286403\pi\)
0.621796 + 0.783179i \(0.286403\pi\)
\(758\) 0 0
\(759\) 361.564 208.749i 0.476369 0.275032i
\(760\) 0 0
\(761\) 1032.60 + 596.172i 1.35690 + 0.783407i 0.989205 0.146540i \(-0.0468136\pi\)
0.367695 + 0.929946i \(0.380147\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 44.2708 76.6793i 0.0578704 0.100234i
\(766\) 0 0
\(767\) 669.301 + 1159.26i 0.872622 + 1.51143i
\(768\) 0 0
\(769\) 908.294i 1.18114i −0.806988 0.590568i \(-0.798904\pi\)
0.806988 0.590568i \(-0.201096\pi\)
\(770\) 0 0
\(771\) 460.029 0.596665
\(772\) 0 0
\(773\) 1030.03 594.690i 1.33251 0.769328i 0.346830 0.937928i \(-0.387258\pi\)
0.985685 + 0.168600i \(0.0539246\pi\)
\(774\) 0 0
\(775\) −138.245 79.8158i −0.178381 0.102988i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −121.778 + 210.925i −0.156326 + 0.270764i
\(780\) 0 0
\(781\) 64.2976 + 111.367i 0.0823272 + 0.142595i
\(782\) 0 0
\(783\) 209.637i 0.267736i
\(784\) 0 0
\(785\) −414.334 −0.527814
\(786\) 0 0
\(787\) 915.492 528.559i 1.16327 0.671613i 0.211183 0.977447i \(-0.432269\pi\)
0.952085 + 0.305834i \(0.0989352\pi\)
\(788\) 0 0
\(789\) 234.560 + 135.423i 0.297288 + 0.171639i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −336.341 + 582.560i −0.424138 + 0.734628i
\(794\) 0 0
\(795\) 207.766 + 359.861i 0.261340 + 0.452655i
\(796\) 0 0
\(797\) 1037.94i 1.30231i 0.758945 + 0.651154i \(0.225715\pi\)
−0.758945 + 0.651154i \(0.774285\pi\)
\(798\) 0 0
\(799\) −469.919 −0.588133
\(800\) 0 0
\(801\) −93.8544 + 54.1869i −0.117172 + 0.0676490i
\(802\) 0 0
\(803\) −1043.89 602.689i −1.29999 0.750547i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −288.266 + 499.292i −0.357207 + 0.618701i
\(808\) 0 0
\(809\) −543.681 941.684i −0.672041 1.16401i −0.977324 0.211748i \(-0.932084\pi\)
0.305283 0.952262i \(-0.401249\pi\)
\(810\) 0 0
\(811\) 926.995i 1.14303i 0.820593 + 0.571514i \(0.193644\pi\)
−0.820593 + 0.571514i \(0.806356\pi\)
\(812\) 0 0
\(813\) −362.153 −0.445452
\(814\) 0 0
\(815\) −1073.31 + 619.678i −1.31695 + 0.760342i
\(816\) 0 0
\(817\) 5.85015 + 3.37758i 0.00716052 + 0.00413413i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 215.150 372.651i 0.262058 0.453898i −0.704730 0.709475i \(-0.748932\pi\)
0.966789 + 0.255577i \(0.0822654\pi\)
\(822\) 0 0
\(823\) 522.368 + 904.767i 0.634712 + 1.09935i 0.986576 + 0.163302i \(0.0522144\pi\)
−0.351865 + 0.936051i \(0.614452\pi\)
\(824\) 0 0
\(825\) 58.6394i 0.0710781i
\(826\) 0 0
\(827\) −610.313 −0.737984 −0.368992 0.929433i \(-0.620297\pi\)
−0.368992 + 0.929433i \(0.620297\pi\)
\(828\) 0 0
\(829\) −1224.47 + 706.950i −1.47705 + 0.852775i −0.999664 0.0259193i \(-0.991749\pi\)
−0.477385 + 0.878694i \(0.658415\pi\)
\(830\) 0 0
\(831\) −394.847 227.965i −0.475146 0.274326i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 616.591 1067.97i 0.738433 1.27900i
\(836\) 0 0
\(837\) −105.248 182.295i −0.125745 0.217796i
\(838\) 0 0
\(839\) 46.3303i 0.0552209i 0.999619 + 0.0276105i \(0.00878980\pi\)
−0.999619 + 0.0276105i \(0.991210\pi\)
\(840\) 0 0
\(841\) 786.696 0.935430
\(842\) 0 0
\(843\) −587.278 + 339.065i −0.696653 + 0.402213i
\(844\) 0 0
\(845\) 1270.32 + 733.420i 1.50334 + 0.867953i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −94.7376 + 164.090i −0.111587 + 0.193275i
\(850\) 0 0
\(851\) −934.772 1619.07i −1.09844 1.90255i
\(852\) 0 0
\(853\) 773.111i 0.906343i 0.891423 + 0.453172i \(0.149708\pi\)
−0.891423 + 0.453172i \(0.850292\pi\)
\(854\) 0 0
\(855\) −116.862 −0.136680
\(856\) 0 0
\(857\) 379.457 219.080i 0.442774 0.255636i −0.262000 0.965068i \(-0.584382\pi\)
0.704774 + 0.709432i \(0.251049\pi\)
\(858\) 0 0
\(859\) −62.6499 36.1710i −0.0729336 0.0421082i 0.463090 0.886311i \(-0.346741\pi\)
−0.536023 + 0.844203i \(0.680074\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −213.247 + 369.355i −0.247100 + 0.427990i −0.962720 0.270500i \(-0.912811\pi\)
0.715620 + 0.698490i \(0.246144\pi\)
\(864\) 0 0
\(865\) −302.532 524.001i −0.349748 0.605781i
\(866\) 0 0
\(867\) 448.430i 0.517221i
\(868\) 0 0
\(869\) 1050.82 1.20922
\(870\) 0 0
\(871\) 868.773 501.586i 0.997443 0.575874i
\(872\) 0 0
\(873\) 42.1344 + 24.3263i 0.0482639 + 0.0278652i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −208.243 + 360.687i −0.237449 + 0.411273i −0.959982 0.280063i \(-0.909645\pi\)
0.722533 + 0.691337i \(0.242978\pi\)
\(878\) 0 0
\(879\) −30.6300 53.0527i −0.0348464 0.0603558i
\(880\) 0 0
\(881\) 1249.01i 1.41771i −0.705353 0.708857i \(-0.749211\pi\)
0.705353 0.708857i \(-0.250789\pi\)
\(882\) 0 0
\(883\) 81.5906 0.0924016 0.0462008 0.998932i \(-0.485289\pi\)
0.0462008 + 0.998932i \(0.485289\pi\)
\(884\) 0 0
\(885\) −513.984 + 296.749i −0.580773 + 0.335309i
\(886\) 0 0
\(887\) 794.777 + 458.865i 0.896028 + 0.517322i 0.875910 0.482475i \(-0.160262\pi\)
0.0201189 + 0.999798i \(0.493596\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 38.6622 66.9648i 0.0433919 0.0751569i
\(892\) 0 0
\(893\) 310.111 + 537.128i 0.347269 + 0.601487i
\(894\) 0 0
\(895\) 567.520i 0.634100i
\(896\) 0 0
\(897\) −1021.24 −1.13850
\(898\) 0 0
\(899\) −1415.40 + 817.184i −1.57442 + 0.908992i
\(900\) 0 0
\(901\) −211.882 122.330i −0.235163 0.135771i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 41.0690 71.1336i 0.0453801 0.0786007i
\(906\) 0 0
\(907\) 725.700 + 1256.95i 0.800110 + 1.38583i 0.919543 + 0.392989i \(0.128559\pi\)
−0.119433 + 0.992842i \(0.538108\pi\)
\(908\) 0 0
\(909\) 358.393i 0.394272i
\(910\) 0 0
\(911\) −562.064 −0.616975 −0.308487 0.951228i \(-0.599823\pi\)
−0.308487 + 0.951228i \(0.599823\pi\)
\(912\) 0 0
\(913\) −246.916 + 142.557i −0.270444 + 0.156141i
\(914\) 0 0
\(915\) −258.290 149.124i −0.282284 0.162977i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −269.079 + 466.059i −0.292795 + 0.507137i −0.974470 0.224519i \(-0.927919\pi\)
0.681674 + 0.731656i \(0.261252\pi\)
\(920\) 0 0
\(921\) −108.791 188.431i −0.118123 0.204594i
\(922\) 0 0
\(923\) 314.556i 0.340797i
\(924\) 0 0
\(925\) −262.586 −0.283876
\(926\) 0 0
\(927\) 23.2057 13.3978i 0.0250331 0.0144529i
\(928\) 0 0
\(929\) −716.272 413.540i −0.771014 0.445145i 0.0622221 0.998062i \(-0.480181\pi\)
−0.833236 + 0.552917i \(0.813515\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 273.435 473.603i 0.293070 0.507613i
\(934\) 0 0
\(935\) 126.786 + 219.599i 0.135600 + 0.234865i
\(936\) 0 0
\(937\) 1501.10i 1.60203i −0.598644 0.801016i \(-0.704293\pi\)
0.598644 0.801016i \(-0.295707\pi\)
\(938\) 0 0
\(939\) −89.3818 −0.0951883
\(940\) 0 0
\(941\) −663.958 + 383.336i −0.705587 + 0.407371i −0.809425 0.587223i \(-0.800221\pi\)
0.103838 + 0.994594i \(0.466888\pi\)
\(942\) 0 0
\(943\) −817.243 471.836i −0.866642 0.500356i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −681.117 + 1179.73i −0.719237 + 1.24576i 0.242065 + 0.970260i \(0.422175\pi\)
−0.961302 + 0.275495i \(0.911158\pi\)
\(948\) 0 0
\(949\) 1474.23 + 2553.45i 1.55346 + 2.69067i
\(950\) 0 0
\(951\) 8.64971i 0.00909538i
\(952\) 0 0
\(953\) 1431.37 1.50196 0.750980 0.660325i \(-0.229581\pi\)
0.750980 + 0.660325i \(0.229581\pi\)
\(954\) 0 0
\(955\) −1426.49 + 823.585i −1.49371 + 0.862393i
\(956\) 0 0
\(957\) −519.938 300.186i −0.543300 0.313674i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 340.034 588.955i 0.353833 0.612857i
\(962\) 0 0
\(963\) 260.784 + 451.691i 0.270803 + 0.469045i
\(964\) 0 0
\(965\) 9.90391i 0.0102631i
\(966\) 0 0
\(967\) −426.276 −0.440823 −0.220411 0.975407i \(-0.570740\pi\)
−0.220411 + 0.975407i \(0.570740\pi\)
\(968\) 0 0
\(969\) 59.5884 34.4034i 0.0614948 0.0355040i
\(970\) 0 0
\(971\) 1496.84 + 864.203i 1.54155 + 0.890013i 0.998741 + 0.0501561i \(0.0159719\pi\)
0.542807 + 0.839857i \(0.317361\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −71.7187 + 124.220i −0.0735577 + 0.127406i
\(976\) 0 0
\(977\) 356.160 + 616.887i 0.364545 + 0.631410i 0.988703 0.149888i \(-0.0478914\pi\)
−0.624158 + 0.781298i \(0.714558\pi\)
\(978\) 0 0
\(979\) 310.368i 0.317025i
\(980\) 0 0
\(981\) 480.944 0.490259
\(982\) 0 0
\(983\) 902.887 521.282i 0.918502 0.530297i 0.0353451 0.999375i \(-0.488747\pi\)
0.883157 + 0.469078i \(0.155414\pi\)
\(984\) 0 0
\(985\) 1189.58 + 686.803i 1.20769 + 0.697262i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.0867 + 22.6668i −0.0132322 + 0.0229189i
\(990\) 0 0
\(991\) −698.706 1210.19i −0.705052 1.22119i −0.966673 0.256015i \(-0.917590\pi\)
0.261621 0.965171i \(-0.415743\pi\)
\(992\) 0 0
\(993\) 787.703i 0.793256i
\(994\) 0 0
\(995\) 197.155 0.198146
\(996\) 0 0
\(997\) −621.773 + 358.981i −0.623644 + 0.360061i −0.778286 0.627909i \(-0.783911\pi\)
0.154642 + 0.987971i \(0.450578\pi\)
\(998\) 0 0
\(999\) −299.867 173.128i −0.300167 0.173301i
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 588.3.m.e.313.1 8
3.2 odd 2 1764.3.z.m.901.4 8
7.2 even 3 588.3.d.c.97.4 8
7.3 odd 6 inner 588.3.m.e.325.1 8
7.4 even 3 588.3.m.f.325.4 8
7.5 odd 6 588.3.d.c.97.5 yes 8
7.6 odd 2 588.3.m.f.313.4 8
21.2 odd 6 1764.3.d.h.685.2 8
21.5 even 6 1764.3.d.h.685.7 8
21.11 odd 6 1764.3.z.l.325.1 8
21.17 even 6 1764.3.z.m.325.4 8
21.20 even 2 1764.3.z.l.901.1 8
28.19 even 6 2352.3.f.j.97.1 8
28.23 odd 6 2352.3.f.j.97.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.3.d.c.97.4 8 7.2 even 3
588.3.d.c.97.5 yes 8 7.5 odd 6
588.3.m.e.313.1 8 1.1 even 1 trivial
588.3.m.e.325.1 8 7.3 odd 6 inner
588.3.m.f.313.4 8 7.6 odd 2
588.3.m.f.325.4 8 7.4 even 3
1764.3.d.h.685.2 8 21.2 odd 6
1764.3.d.h.685.7 8 21.5 even 6
1764.3.z.l.325.1 8 21.11 odd 6
1764.3.z.l.901.1 8 21.20 even 2
1764.3.z.m.325.4 8 21.17 even 6
1764.3.z.m.901.4 8 3.2 odd 2
2352.3.f.j.97.1 8 28.19 even 6
2352.3.f.j.97.8 8 28.23 odd 6