Properties

Label 572.2.p.a.485.6
Level $572$
Weight $2$
Character 572.485
Analytic conductor $4.567$
Analytic rank $0$
Dimension $24$
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] = [572,2,Mod(309,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.309");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.p (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: \(4.56744299562\)
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 485.6
Character \(\chi\) \(=\) 572.485
Dual form 572.2.p.a.309.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.308986 + 0.535180i) q^{3} +3.59217i q^{5} +(-1.27174 + 0.734239i) q^{7} +(1.30905 + 2.26735i) q^{9} +O(q^{10})\) \(q+(-0.308986 + 0.535180i) q^{3} +3.59217i q^{5} +(-1.27174 + 0.734239i) q^{7} +(1.30905 + 2.26735i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(3.34121 - 1.35512i) q^{13} +(-1.92246 - 1.10993i) q^{15} +(-3.71480 - 6.43423i) q^{17} +(-5.72329 + 3.30435i) q^{19} -0.907479i q^{21} +(-3.07847 + 5.33207i) q^{23} -7.90366 q^{25} -3.47184 q^{27} +(1.37531 - 2.38211i) q^{29} +4.07233i q^{31} +(0.535180 - 0.308986i) q^{33} +(-2.63751 - 4.56830i) q^{35} +(9.03139 + 5.21428i) q^{37} +(-0.307155 + 2.20686i) q^{39} +(5.15608 + 2.97686i) q^{41} +(1.23482 + 2.13877i) q^{43} +(-8.14470 + 4.70234i) q^{45} -10.6258i q^{47} +(-2.42179 + 4.19466i) q^{49} +4.59129 q^{51} -4.18535 q^{53} +(1.79608 - 3.11091i) q^{55} -4.08399i q^{57} +(1.01791 - 0.587690i) q^{59} +(-0.509296 - 0.882126i) q^{61} +(-3.32955 - 1.92232i) q^{63} +(4.86781 + 12.0022i) q^{65} +(6.14619 + 3.54850i) q^{67} +(-1.90241 - 3.29508i) q^{69} +(1.15016 - 0.664048i) q^{71} +10.6727i q^{73} +(2.44212 - 4.22988i) q^{75} +1.46848 q^{77} -11.3896 q^{79} +(-2.85441 + 4.94399i) q^{81} -1.48873i q^{83} +(23.1128 - 13.3442i) q^{85} +(0.849907 + 1.47208i) q^{87} +(7.53139 + 4.34825i) q^{89} +(-3.25416 + 4.17660i) q^{91} +(-2.17943 - 1.25829i) q^{93} +(-11.8698 - 20.5590i) q^{95} +(-2.07905 + 1.20034i) q^{97} -2.61811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) −0.308986 + 0.535180i −0.178393 + 0.308986i −0.941330 0.337486i \(-0.890423\pi\)
0.762937 + 0.646473i \(0.223757\pi\)
\(4\) 0 0
\(5\) 3.59217i 1.60647i 0.595665 + 0.803233i \(0.296889\pi\)
−0.595665 + 0.803233i \(0.703111\pi\)
\(6\) 0 0
\(7\) −1.27174 + 0.734239i −0.480672 + 0.277516i −0.720697 0.693251i \(-0.756178\pi\)
0.240024 + 0.970767i \(0.422845\pi\)
\(8\) 0 0
\(9\) 1.30905 + 2.26735i 0.436352 + 0.755783i
\(10\) 0 0
\(11\) −0.866025 0.500000i −0.261116 0.150756i
\(12\) 0 0
\(13\) 3.34121 1.35512i 0.926684 0.375842i
\(14\) 0 0
\(15\) −1.92246 1.10993i −0.496376 0.286583i
\(16\) 0 0
\(17\) −3.71480 6.43423i −0.900972 1.56053i −0.826235 0.563326i \(-0.809522\pi\)
−0.0747372 0.997203i \(-0.523812\pi\)
\(18\) 0 0
\(19\) −5.72329 + 3.30435i −1.31301 + 0.758069i −0.982594 0.185765i \(-0.940524\pi\)
−0.330420 + 0.943834i \(0.607190\pi\)
\(20\) 0 0
\(21\) 0.907479i 0.198028i
\(22\) 0 0
\(23\) −3.07847 + 5.33207i −0.641906 + 1.11181i 0.343101 + 0.939299i \(0.388523\pi\)
−0.985007 + 0.172515i \(0.944811\pi\)
\(24\) 0 0
\(25\) −7.90366 −1.58073
\(26\) 0 0
\(27\) −3.47184 −0.668156
\(28\) 0 0
\(29\) 1.37531 2.38211i 0.255389 0.442347i −0.709612 0.704593i \(-0.751130\pi\)
0.965001 + 0.262245i \(0.0844630\pi\)
\(30\) 0 0
\(31\) 4.07233i 0.731412i 0.930730 + 0.365706i \(0.119172\pi\)
−0.930730 + 0.365706i \(0.880828\pi\)
\(32\) 0 0
\(33\) 0.535180 0.308986i 0.0931629 0.0537876i
\(34\) 0 0
\(35\) −2.63751 4.56830i −0.445820 0.772183i
\(36\) 0 0
\(37\) 9.03139 + 5.21428i 1.48475 + 0.857222i 0.999850 0.0173470i \(-0.00552200\pi\)
0.484902 + 0.874569i \(0.338855\pi\)
\(38\) 0 0
\(39\) −0.307155 + 2.20686i −0.0491842 + 0.353380i
\(40\) 0 0
\(41\) 5.15608 + 2.97686i 0.805244 + 0.464908i 0.845302 0.534289i \(-0.179421\pi\)
−0.0400573 + 0.999197i \(0.512754\pi\)
\(42\) 0 0
\(43\) 1.23482 + 2.13877i 0.188308 + 0.326160i 0.944686 0.327975i \(-0.106366\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(44\) 0 0
\(45\) −8.14470 + 4.70234i −1.21414 + 0.700984i
\(46\) 0 0
\(47\) 10.6258i 1.54994i −0.631999 0.774969i \(-0.717765\pi\)
0.631999 0.774969i \(-0.282235\pi\)
\(48\) 0 0
\(49\) −2.42179 + 4.19466i −0.345969 + 0.599237i
\(50\) 0 0
\(51\) 4.59129 0.642910
\(52\) 0 0
\(53\) −4.18535 −0.574902 −0.287451 0.957795i \(-0.592808\pi\)
−0.287451 + 0.957795i \(0.592808\pi\)
\(54\) 0 0
\(55\) 1.79608 3.11091i 0.242184 0.419475i
\(56\) 0 0
\(57\) 4.08399i 0.540938i
\(58\) 0 0
\(59\) 1.01791 0.587690i 0.132520 0.0765107i −0.432274 0.901742i \(-0.642289\pi\)
0.564795 + 0.825232i \(0.308955\pi\)
\(60\) 0 0
\(61\) −0.509296 0.882126i −0.0652087 0.112945i 0.831578 0.555408i \(-0.187438\pi\)
−0.896787 + 0.442463i \(0.854105\pi\)
\(62\) 0 0
\(63\) −3.32955 1.92232i −0.419484 0.242189i
\(64\) 0 0
\(65\) 4.86781 + 12.0022i 0.603777 + 1.48869i
\(66\) 0 0
\(67\) 6.14619 + 3.54850i 0.750876 + 0.433518i 0.826010 0.563655i \(-0.190605\pi\)
−0.0751343 + 0.997173i \(0.523939\pi\)
\(68\) 0 0
\(69\) −1.90241 3.29508i −0.229024 0.396680i
\(70\) 0 0
\(71\) 1.15016 0.664048i 0.136499 0.0788080i −0.430195 0.902736i \(-0.641555\pi\)
0.566695 + 0.823928i \(0.308222\pi\)
\(72\) 0 0
\(73\) 10.6727i 1.24915i 0.780965 + 0.624575i \(0.214728\pi\)
−0.780965 + 0.624575i \(0.785272\pi\)
\(74\) 0 0
\(75\) 2.44212 4.22988i 0.281992 0.488425i
\(76\) 0 0
\(77\) 1.46848 0.167349
\(78\) 0 0
\(79\) −11.3896 −1.28143 −0.640717 0.767777i \(-0.721363\pi\)
−0.640717 + 0.767777i \(0.721363\pi\)
\(80\) 0 0
\(81\) −2.85441 + 4.94399i −0.317157 + 0.549332i
\(82\) 0 0
\(83\) 1.48873i 0.163410i −0.996657 0.0817048i \(-0.973964\pi\)
0.996657 0.0817048i \(-0.0260365\pi\)
\(84\) 0 0
\(85\) 23.1128 13.3442i 2.50694 1.44738i
\(86\) 0 0
\(87\) 0.849907 + 1.47208i 0.0911196 + 0.157824i
\(88\) 0 0
\(89\) 7.53139 + 4.34825i 0.798326 + 0.460914i 0.842885 0.538093i \(-0.180855\pi\)
−0.0445596 + 0.999007i \(0.514188\pi\)
\(90\) 0 0
\(91\) −3.25416 + 4.17660i −0.341129 + 0.437827i
\(92\) 0 0
\(93\) −2.17943 1.25829i −0.225996 0.130479i
\(94\) 0 0
\(95\) −11.8698 20.5590i −1.21781 2.10931i
\(96\) 0 0
\(97\) −2.07905 + 1.20034i −0.211096 + 0.121876i −0.601820 0.798631i \(-0.705558\pi\)
0.390725 + 0.920508i \(0.372224\pi\)
\(98\) 0 0
\(99\) 2.61811i 0.263130i
\(100\) 0 0
\(101\) 4.07520 7.05845i 0.405498 0.702342i −0.588882 0.808219i \(-0.700432\pi\)
0.994379 + 0.105877i \(0.0337649\pi\)
\(102\) 0 0
\(103\) 18.6538 1.83801 0.919004 0.394247i \(-0.128995\pi\)
0.919004 + 0.394247i \(0.128995\pi\)
\(104\) 0 0
\(105\) 3.25982 0.318126
\(106\) 0 0
\(107\) 4.37610 7.57962i 0.423053 0.732750i −0.573183 0.819427i \(-0.694292\pi\)
0.996236 + 0.0866777i \(0.0276250\pi\)
\(108\) 0 0
\(109\) 9.88343i 0.946661i −0.880885 0.473331i \(-0.843052\pi\)
0.880885 0.473331i \(-0.156948\pi\)
\(110\) 0 0
\(111\) −5.58115 + 3.22228i −0.529740 + 0.305845i
\(112\) 0 0
\(113\) 1.42305 + 2.46480i 0.133869 + 0.231869i 0.925165 0.379565i \(-0.123926\pi\)
−0.791296 + 0.611434i \(0.790593\pi\)
\(114\) 0 0
\(115\) −19.1537 11.0584i −1.78609 1.03120i
\(116\) 0 0
\(117\) 7.44635 + 5.80176i 0.688415 + 0.536373i
\(118\) 0 0
\(119\) 9.44852 + 5.45511i 0.866144 + 0.500069i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) −3.18632 + 1.83962i −0.287301 + 0.165873i
\(124\) 0 0
\(125\) 10.4304i 0.932926i
\(126\) 0 0
\(127\) −1.74628 + 3.02465i −0.154957 + 0.268394i −0.933044 0.359763i \(-0.882857\pi\)
0.778086 + 0.628158i \(0.216191\pi\)
\(128\) 0 0
\(129\) −1.52617 −0.134372
\(130\) 0 0
\(131\) 19.7087 1.72195 0.860977 0.508644i \(-0.169853\pi\)
0.860977 + 0.508644i \(0.169853\pi\)
\(132\) 0 0
\(133\) 4.85236 8.40453i 0.420753 0.728765i
\(134\) 0 0
\(135\) 12.4714i 1.07337i
\(136\) 0 0
\(137\) −10.0911 + 5.82613i −0.862145 + 0.497760i −0.864730 0.502237i \(-0.832510\pi\)
0.00258506 + 0.999997i \(0.499177\pi\)
\(138\) 0 0
\(139\) 2.33648 + 4.04691i 0.198178 + 0.343254i 0.947938 0.318456i \(-0.103164\pi\)
−0.749760 + 0.661710i \(0.769831\pi\)
\(140\) 0 0
\(141\) 5.68674 + 3.28324i 0.478910 + 0.276499i
\(142\) 0 0
\(143\) −3.57113 0.497036i −0.298633 0.0415643i
\(144\) 0 0
\(145\) 8.55695 + 4.94036i 0.710616 + 0.410274i
\(146\) 0 0
\(147\) −1.49660 2.59218i −0.123437 0.213800i
\(148\) 0 0
\(149\) −17.7149 + 10.2277i −1.45126 + 0.837885i −0.998553 0.0537753i \(-0.982875\pi\)
−0.452706 + 0.891660i \(0.649541\pi\)
\(150\) 0 0
\(151\) 19.5794i 1.59335i 0.604408 + 0.796675i \(0.293410\pi\)
−0.604408 + 0.796675i \(0.706590\pi\)
\(152\) 0 0
\(153\) 9.72576 16.8455i 0.786281 1.36188i
\(154\) 0 0
\(155\) −14.6285 −1.17499
\(156\) 0 0
\(157\) 16.9554 1.35319 0.676594 0.736357i \(-0.263455\pi\)
0.676594 + 0.736357i \(0.263455\pi\)
\(158\) 0 0
\(159\) 1.29322 2.23992i 0.102559 0.177637i
\(160\) 0 0
\(161\) 9.04134i 0.712558i
\(162\) 0 0
\(163\) 20.5196 11.8470i 1.60722 0.927929i 0.617232 0.786782i \(-0.288254\pi\)
0.989989 0.141147i \(-0.0450792\pi\)
\(164\) 0 0
\(165\) 1.10993 + 1.92246i 0.0864080 + 0.149663i
\(166\) 0 0
\(167\) 9.45956 + 5.46148i 0.732003 + 0.422622i 0.819154 0.573573i \(-0.194443\pi\)
−0.0871516 + 0.996195i \(0.527776\pi\)
\(168\) 0 0
\(169\) 9.32731 9.05545i 0.717485 0.696573i
\(170\) 0 0
\(171\) −14.9842 8.65114i −1.14587 0.661569i
\(172\) 0 0
\(173\) −2.69744 4.67210i −0.205083 0.355214i 0.745076 0.666979i \(-0.232413\pi\)
−0.950159 + 0.311766i \(0.899080\pi\)
\(174\) 0 0
\(175\) 10.0514 5.80317i 0.759814 0.438679i
\(176\) 0 0
\(177\) 0.726353i 0.0545960i
\(178\) 0 0
\(179\) −11.2109 + 19.4179i −0.837944 + 1.45136i 0.0536663 + 0.998559i \(0.482909\pi\)
−0.891611 + 0.452803i \(0.850424\pi\)
\(180\) 0 0
\(181\) 5.61937 0.417684 0.208842 0.977949i \(-0.433030\pi\)
0.208842 + 0.977949i \(0.433030\pi\)
\(182\) 0 0
\(183\) 0.629462 0.0465312
\(184\) 0 0
\(185\) −18.7305 + 32.4423i −1.37710 + 2.38520i
\(186\) 0 0
\(187\) 7.42960i 0.543307i
\(188\) 0 0
\(189\) 4.41527 2.54916i 0.321164 0.185424i
\(190\) 0 0
\(191\) −6.07987 10.5306i −0.439924 0.761971i 0.557759 0.830003i \(-0.311661\pi\)
−0.997683 + 0.0680320i \(0.978328\pi\)
\(192\) 0 0
\(193\) 14.3554 + 8.28808i 1.03332 + 0.596589i 0.917935 0.396731i \(-0.129856\pi\)
0.115388 + 0.993320i \(0.463189\pi\)
\(194\) 0 0
\(195\) −7.92741 1.10335i −0.567693 0.0790127i
\(196\) 0 0
\(197\) 9.83822 + 5.68010i 0.700944 + 0.404690i 0.807699 0.589595i \(-0.200713\pi\)
−0.106755 + 0.994285i \(0.534046\pi\)
\(198\) 0 0
\(199\) −0.559399 0.968908i −0.0396548 0.0686841i 0.845517 0.533949i \(-0.179292\pi\)
−0.885172 + 0.465265i \(0.845959\pi\)
\(200\) 0 0
\(201\) −3.79817 + 2.19288i −0.267903 + 0.154674i
\(202\) 0 0
\(203\) 4.03924i 0.283499i
\(204\) 0 0
\(205\) −10.6934 + 18.5215i −0.746859 + 1.29360i
\(206\) 0 0
\(207\) −16.1196 −1.12039
\(208\) 0 0
\(209\) 6.60869 0.457133
\(210\) 0 0
\(211\) −6.25639 + 10.8364i −0.430708 + 0.746008i −0.996934 0.0782419i \(-0.975069\pi\)
0.566227 + 0.824250i \(0.308403\pi\)
\(212\) 0 0
\(213\) 0.820727i 0.0562353i
\(214\) 0 0
\(215\) −7.68282 + 4.43568i −0.523964 + 0.302511i
\(216\) 0 0
\(217\) −2.99006 5.17894i −0.202979 0.351569i
\(218\) 0 0
\(219\) −5.71184 3.29773i −0.385970 0.222840i
\(220\) 0 0
\(221\) −21.1311 16.4641i −1.42143 1.10749i
\(222\) 0 0
\(223\) 6.49158 + 3.74792i 0.434708 + 0.250979i 0.701350 0.712817i \(-0.252581\pi\)
−0.266642 + 0.963796i \(0.585914\pi\)
\(224\) 0 0
\(225\) −10.3463 17.9204i −0.689755 1.19469i
\(226\) 0 0
\(227\) 16.7364 9.66276i 1.11083 0.641340i 0.171788 0.985134i \(-0.445046\pi\)
0.939045 + 0.343794i \(0.111712\pi\)
\(228\) 0 0
\(229\) 18.8527i 1.24582i −0.782293 0.622910i \(-0.785950\pi\)
0.782293 0.622910i \(-0.214050\pi\)
\(230\) 0 0
\(231\) −0.453740 + 0.785900i −0.0298539 + 0.0517084i
\(232\) 0 0
\(233\) −15.8404 −1.03774 −0.518868 0.854854i \(-0.673646\pi\)
−0.518868 + 0.854854i \(0.673646\pi\)
\(234\) 0 0
\(235\) 38.1698 2.48992
\(236\) 0 0
\(237\) 3.51924 6.09550i 0.228599 0.395945i
\(238\) 0 0
\(239\) 13.3455i 0.863246i 0.902054 + 0.431623i \(0.142059\pi\)
−0.902054 + 0.431623i \(0.857941\pi\)
\(240\) 0 0
\(241\) 14.7823 8.53454i 0.952209 0.549758i 0.0584428 0.998291i \(-0.481386\pi\)
0.893767 + 0.448532i \(0.148053\pi\)
\(242\) 0 0
\(243\) −6.97171 12.0754i −0.447235 0.774634i
\(244\) 0 0
\(245\) −15.0679 8.69946i −0.962653 0.555788i
\(246\) 0 0
\(247\) −14.6449 + 18.7962i −0.931834 + 1.19598i
\(248\) 0 0
\(249\) 0.796740 + 0.459998i 0.0504913 + 0.0291512i
\(250\) 0 0
\(251\) −6.13738 10.6303i −0.387388 0.670976i 0.604709 0.796446i \(-0.293289\pi\)
−0.992097 + 0.125470i \(0.959956\pi\)
\(252\) 0 0
\(253\) 5.33207 3.07847i 0.335225 0.193542i
\(254\) 0 0
\(255\) 16.4927i 1.03281i
\(256\) 0 0
\(257\) −13.1767 + 22.8226i −0.821937 + 1.42364i 0.0823006 + 0.996608i \(0.473773\pi\)
−0.904238 + 0.427029i \(0.859560\pi\)
\(258\) 0 0
\(259\) −15.3141 −0.951572
\(260\) 0 0
\(261\) 7.20145 0.445758
\(262\) 0 0
\(263\) 5.24704 9.08814i 0.323546 0.560399i −0.657671 0.753306i \(-0.728458\pi\)
0.981217 + 0.192907i \(0.0617915\pi\)
\(264\) 0 0
\(265\) 15.0345i 0.923560i
\(266\) 0 0
\(267\) −4.65419 + 2.68710i −0.284832 + 0.164448i
\(268\) 0 0
\(269\) −9.24887 16.0195i −0.563914 0.976727i −0.997150 0.0754468i \(-0.975962\pi\)
0.433236 0.901280i \(-0.357372\pi\)
\(270\) 0 0
\(271\) −16.1061 9.29886i −0.978376 0.564865i −0.0765963 0.997062i \(-0.524405\pi\)
−0.901779 + 0.432197i \(0.857739\pi\)
\(272\) 0 0
\(273\) −1.22974 3.03207i −0.0744273 0.183510i
\(274\) 0 0
\(275\) 6.84477 + 3.95183i 0.412755 + 0.238304i
\(276\) 0 0
\(277\) 6.47146 + 11.2089i 0.388832 + 0.673477i 0.992293 0.123916i \(-0.0395452\pi\)
−0.603461 + 0.797393i \(0.706212\pi\)
\(278\) 0 0
\(279\) −9.23339 + 5.33090i −0.552789 + 0.319153i
\(280\) 0 0
\(281\) 8.19174i 0.488678i 0.969690 + 0.244339i \(0.0785710\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(282\) 0 0
\(283\) 2.13215 3.69299i 0.126743 0.219525i −0.795670 0.605731i \(-0.792881\pi\)
0.922413 + 0.386205i \(0.126214\pi\)
\(284\) 0 0
\(285\) 14.6704 0.868998
\(286\) 0 0
\(287\) −8.74292 −0.516078
\(288\) 0 0
\(289\) −19.0995 + 33.0813i −1.12350 + 1.94596i
\(290\) 0 0
\(291\) 1.48356i 0.0869676i
\(292\) 0 0
\(293\) 4.23456 2.44482i 0.247386 0.142828i −0.371181 0.928561i \(-0.621047\pi\)
0.618567 + 0.785732i \(0.287714\pi\)
\(294\) 0 0
\(295\) 2.11108 + 3.65650i 0.122912 + 0.212890i
\(296\) 0 0
\(297\) 3.00670 + 1.73592i 0.174466 + 0.100728i
\(298\) 0 0
\(299\) −3.06023 + 21.9872i −0.176978 + 1.27156i
\(300\) 0 0
\(301\) −3.14074 1.81331i −0.181029 0.104517i
\(302\) 0 0
\(303\) 2.51836 + 4.36193i 0.144676 + 0.250586i
\(304\) 0 0
\(305\) 3.16874 1.82948i 0.181442 0.104755i
\(306\) 0 0
\(307\) 18.7105i 1.06787i 0.845526 + 0.533933i \(0.179287\pi\)
−0.845526 + 0.533933i \(0.820713\pi\)
\(308\) 0 0
\(309\) −5.76375 + 9.98312i −0.327889 + 0.567920i
\(310\) 0 0
\(311\) −8.84936 −0.501801 −0.250901 0.968013i \(-0.580727\pi\)
−0.250901 + 0.968013i \(0.580727\pi\)
\(312\) 0 0
\(313\) 3.52830 0.199431 0.0997157 0.995016i \(-0.468207\pi\)
0.0997157 + 0.995016i \(0.468207\pi\)
\(314\) 0 0
\(315\) 6.90529 11.9603i 0.389069 0.673887i
\(316\) 0 0
\(317\) 23.1339i 1.29933i −0.760222 0.649664i \(-0.774910\pi\)
0.760222 0.649664i \(-0.225090\pi\)
\(318\) 0 0
\(319\) −2.38211 + 1.37531i −0.133373 + 0.0770028i
\(320\) 0 0
\(321\) 2.70431 + 4.68400i 0.150940 + 0.261435i
\(322\) 0 0
\(323\) 42.5218 + 24.5500i 2.36598 + 1.36600i
\(324\) 0 0
\(325\) −26.4078 + 10.7104i −1.46484 + 0.594106i
\(326\) 0 0
\(327\) 5.28942 + 3.05385i 0.292505 + 0.168878i
\(328\) 0 0
\(329\) 7.80191 + 13.5133i 0.430133 + 0.745013i
\(330\) 0 0
\(331\) −13.2579 + 7.65443i −0.728718 + 0.420725i −0.817953 0.575285i \(-0.804891\pi\)
0.0892351 + 0.996011i \(0.471558\pi\)
\(332\) 0 0
\(333\) 27.3031i 1.49620i
\(334\) 0 0
\(335\) −12.7468 + 22.0781i −0.696433 + 1.20626i
\(336\) 0 0
\(337\) −18.8616 −1.02746 −0.513729 0.857952i \(-0.671736\pi\)
−0.513729 + 0.857952i \(0.671736\pi\)
\(338\) 0 0
\(339\) −1.75881 −0.0955256
\(340\) 0 0
\(341\) 2.03616 3.52674i 0.110265 0.190984i
\(342\) 0 0
\(343\) 17.3920i 0.939081i
\(344\) 0 0
\(345\) 11.8365 6.83378i 0.637254 0.367919i
\(346\) 0 0
\(347\) −6.57133 11.3819i −0.352768 0.611012i 0.633966 0.773361i \(-0.281426\pi\)
−0.986733 + 0.162350i \(0.948093\pi\)
\(348\) 0 0
\(349\) 1.67289 + 0.965846i 0.0895480 + 0.0517005i 0.544105 0.839017i \(-0.316869\pi\)
−0.454557 + 0.890717i \(0.650203\pi\)
\(350\) 0 0
\(351\) −11.6001 + 4.70475i −0.619169 + 0.251121i
\(352\) 0 0
\(353\) 8.08923 + 4.67032i 0.430546 + 0.248576i 0.699579 0.714555i \(-0.253371\pi\)
−0.269033 + 0.963131i \(0.586704\pi\)
\(354\) 0 0
\(355\) 2.38537 + 4.13158i 0.126602 + 0.219282i
\(356\) 0 0
\(357\) −5.83893 + 3.37111i −0.309029 + 0.178418i
\(358\) 0 0
\(359\) 6.11468i 0.322720i 0.986896 + 0.161360i \(0.0515881\pi\)
−0.986896 + 0.161360i \(0.948412\pi\)
\(360\) 0 0
\(361\) 12.3374 21.3690i 0.649337 1.12468i
\(362\) 0 0
\(363\) −0.617973 −0.0324352
\(364\) 0 0
\(365\) −38.3383 −2.00672
\(366\) 0 0
\(367\) 8.50143 14.7249i 0.443771 0.768634i −0.554195 0.832387i \(-0.686974\pi\)
0.997966 + 0.0637533i \(0.0203071\pi\)
\(368\) 0 0
\(369\) 15.5875i 0.811454i
\(370\) 0 0
\(371\) 5.32267 3.07305i 0.276339 0.159545i
\(372\) 0 0
\(373\) −1.23700 2.14254i −0.0640493 0.110937i 0.832223 0.554442i \(-0.187068\pi\)
−0.896272 + 0.443505i \(0.853735\pi\)
\(374\) 0 0
\(375\) 5.58216 + 3.22286i 0.288261 + 0.166428i
\(376\) 0 0
\(377\) 1.36716 9.82285i 0.0704124 0.505902i
\(378\) 0 0
\(379\) −21.6424 12.4952i −1.11169 0.641837i −0.172427 0.985022i \(-0.555161\pi\)
−0.939268 + 0.343185i \(0.888494\pi\)
\(380\) 0 0
\(381\) −1.07915 1.86915i −0.0552868 0.0957595i
\(382\) 0 0
\(383\) 25.6675 14.8192i 1.31155 0.757224i 0.329197 0.944261i \(-0.393222\pi\)
0.982353 + 0.187038i \(0.0598886\pi\)
\(384\) 0 0
\(385\) 5.27502i 0.268840i
\(386\) 0 0
\(387\) −3.23289 + 5.59954i −0.164337 + 0.284641i
\(388\) 0 0
\(389\) −20.9078 −1.06007 −0.530034 0.847977i \(-0.677821\pi\)
−0.530034 + 0.847977i \(0.677821\pi\)
\(390\) 0 0
\(391\) 45.7437 2.31336
\(392\) 0 0
\(393\) −6.08971 + 10.5477i −0.307185 + 0.532060i
\(394\) 0 0
\(395\) 40.9134i 2.05858i
\(396\) 0 0
\(397\) 1.70414 0.983887i 0.0855284 0.0493799i −0.456626 0.889659i \(-0.650942\pi\)
0.542154 + 0.840279i \(0.317609\pi\)
\(398\) 0 0
\(399\) 2.99862 + 5.19377i 0.150119 + 0.260014i
\(400\) 0 0
\(401\) 4.65134 + 2.68545i 0.232277 + 0.134105i 0.611622 0.791150i \(-0.290517\pi\)
−0.379345 + 0.925255i \(0.623851\pi\)
\(402\) 0 0
\(403\) 5.51849 + 13.6065i 0.274895 + 0.677788i
\(404\) 0 0
\(405\) −17.7596 10.2535i −0.882483 0.509502i
\(406\) 0 0
\(407\) −5.21428 9.03139i −0.258462 0.447669i
\(408\) 0 0
\(409\) 10.4464 6.03123i 0.516541 0.298225i −0.218977 0.975730i \(-0.570272\pi\)
0.735518 + 0.677505i \(0.236939\pi\)
\(410\) 0 0
\(411\) 7.20077i 0.355188i
\(412\) 0 0
\(413\) −0.863010 + 1.49478i −0.0424659 + 0.0735532i
\(414\) 0 0
\(415\) 5.34777 0.262512
\(416\) 0 0
\(417\) −2.88777 −0.141415
\(418\) 0 0
\(419\) 3.60502 6.24408i 0.176117 0.305043i −0.764430 0.644706i \(-0.776980\pi\)
0.940547 + 0.339663i \(0.110313\pi\)
\(420\) 0 0
\(421\) 14.3016i 0.697018i −0.937305 0.348509i \(-0.886688\pi\)
0.937305 0.348509i \(-0.113312\pi\)
\(422\) 0 0
\(423\) 24.0925 13.9098i 1.17142 0.676318i
\(424\) 0 0
\(425\) 29.3605 + 50.8539i 1.42420 + 2.46678i
\(426\) 0 0
\(427\) 1.29538 + 0.747890i 0.0626880 + 0.0361929i
\(428\) 0 0
\(429\) 1.36943 1.75762i 0.0661169 0.0848586i
\(430\) 0 0
\(431\) 12.8506 + 7.41932i 0.618993 + 0.357376i 0.776477 0.630146i \(-0.217005\pi\)
−0.157484 + 0.987522i \(0.550338\pi\)
\(432\) 0 0
\(433\) −9.25188 16.0247i −0.444617 0.770099i 0.553408 0.832910i \(-0.313327\pi\)
−0.998025 + 0.0628107i \(0.979994\pi\)
\(434\) 0 0
\(435\) −5.28796 + 3.05301i −0.253538 + 0.146380i
\(436\) 0 0
\(437\) 40.6894i 1.94644i
\(438\) 0 0
\(439\) −5.66147 + 9.80596i −0.270207 + 0.468013i −0.968915 0.247395i \(-0.920426\pi\)
0.698707 + 0.715408i \(0.253759\pi\)
\(440\) 0 0
\(441\) −12.6810 −0.603857
\(442\) 0 0
\(443\) −26.1660 −1.24318 −0.621592 0.783341i \(-0.713514\pi\)
−0.621592 + 0.783341i \(0.713514\pi\)
\(444\) 0 0
\(445\) −15.6196 + 27.0540i −0.740442 + 1.28248i
\(446\) 0 0
\(447\) 12.6409i 0.597892i
\(448\) 0 0
\(449\) −4.83139 + 2.78940i −0.228007 + 0.131640i −0.609652 0.792669i \(-0.708691\pi\)
0.381645 + 0.924309i \(0.375358\pi\)
\(450\) 0 0
\(451\) −2.97686 5.15608i −0.140175 0.242790i
\(452\) 0 0
\(453\) −10.4785 6.04977i −0.492324 0.284243i
\(454\) 0 0
\(455\) −15.0030 11.6895i −0.703353 0.548012i
\(456\) 0 0
\(457\) −31.6844 18.2930i −1.48213 0.855711i −0.482340 0.875984i \(-0.660213\pi\)
−0.999794 + 0.0202735i \(0.993546\pi\)
\(458\) 0 0
\(459\) 12.8972 + 22.3386i 0.601989 + 1.04268i
\(460\) 0 0
\(461\) 3.49797 2.01955i 0.162917 0.0940599i −0.416325 0.909216i \(-0.636682\pi\)
0.579242 + 0.815156i \(0.303349\pi\)
\(462\) 0 0
\(463\) 10.7499i 0.499590i −0.968299 0.249795i \(-0.919637\pi\)
0.968299 0.249795i \(-0.0803632\pi\)
\(464\) 0 0
\(465\) 4.52000 7.82887i 0.209610 0.363055i
\(466\) 0 0
\(467\) −27.8116 −1.28697 −0.643483 0.765460i \(-0.722511\pi\)
−0.643483 + 0.765460i \(0.722511\pi\)
\(468\) 0 0
\(469\) −10.4218 −0.481234
\(470\) 0 0
\(471\) −5.23898 + 9.07419i −0.241400 + 0.418116i
\(472\) 0 0
\(473\) 2.46964i 0.113554i
\(474\) 0 0
\(475\) 45.2350 26.1164i 2.07552 1.19830i
\(476\) 0 0
\(477\) −5.47885 9.48965i −0.250859 0.434501i
\(478\) 0 0
\(479\) −7.28513 4.20607i −0.332866 0.192180i 0.324247 0.945972i \(-0.394889\pi\)
−0.657113 + 0.753792i \(0.728222\pi\)
\(480\) 0 0
\(481\) 37.2417 + 5.18337i 1.69807 + 0.236341i
\(482\) 0 0
\(483\) 4.83875 + 2.79365i 0.220171 + 0.127116i
\(484\) 0 0
\(485\) −4.31182 7.46830i −0.195790 0.339118i
\(486\) 0 0
\(487\) 0.608545 0.351343i 0.0275758 0.0159209i −0.486149 0.873876i \(-0.661599\pi\)
0.513725 + 0.857955i \(0.328265\pi\)
\(488\) 0 0
\(489\) 14.6423i 0.662145i
\(490\) 0 0
\(491\) 21.2907 36.8767i 0.960838 1.66422i 0.240434 0.970666i \(-0.422710\pi\)
0.720404 0.693554i \(-0.243956\pi\)
\(492\) 0 0
\(493\) −20.4361 −0.920395
\(494\) 0 0
\(495\) 9.40469 0.422709
\(496\) 0 0
\(497\) −0.975139 + 1.68899i −0.0437410 + 0.0757616i
\(498\) 0 0
\(499\) 17.6730i 0.791154i 0.918433 + 0.395577i \(0.129455\pi\)
−0.918433 + 0.395577i \(0.870545\pi\)
\(500\) 0 0
\(501\) −5.84575 + 3.37505i −0.261169 + 0.150786i
\(502\) 0 0
\(503\) −6.15000 10.6521i −0.274215 0.474954i 0.695722 0.718311i \(-0.255085\pi\)
−0.969937 + 0.243357i \(0.921751\pi\)
\(504\) 0 0
\(505\) 25.3551 + 14.6388i 1.12829 + 0.651418i
\(506\) 0 0
\(507\) 1.96429 + 7.78980i 0.0872370 + 0.345957i
\(508\) 0 0
\(509\) −15.3876 8.88404i −0.682044 0.393778i 0.118581 0.992944i \(-0.462166\pi\)
−0.800625 + 0.599166i \(0.795499\pi\)
\(510\) 0 0
\(511\) −7.83635 13.5730i −0.346660 0.600432i
\(512\) 0 0
\(513\) 19.8704 11.4722i 0.877297 0.506508i
\(514\) 0 0
\(515\) 67.0074i 2.95270i
\(516\) 0 0
\(517\) −5.31292 + 9.20225i −0.233662 + 0.404715i
\(518\) 0 0
\(519\) 3.33389 0.146341
\(520\) 0 0
\(521\) 35.3705 1.54961 0.774806 0.632200i \(-0.217848\pi\)
0.774806 + 0.632200i \(0.217848\pi\)
\(522\) 0 0
\(523\) 9.82895 17.0242i 0.429790 0.744418i −0.567065 0.823673i \(-0.691921\pi\)
0.996854 + 0.0792556i \(0.0252543\pi\)
\(524\) 0 0
\(525\) 7.17241i 0.313030i
\(526\) 0 0
\(527\) 26.2023 15.1279i 1.14139 0.658982i
\(528\) 0 0
\(529\) −7.45400 12.9107i −0.324087 0.561335i
\(530\) 0 0
\(531\) 2.66500 + 1.53864i 0.115651 + 0.0667712i
\(532\) 0 0
\(533\) 21.2615 + 2.95922i 0.920939 + 0.128178i
\(534\) 0 0
\(535\) 27.2273 + 15.7197i 1.17714 + 0.679620i
\(536\) 0 0
\(537\) −6.92805 11.9997i −0.298967 0.517827i
\(538\) 0 0
\(539\) 4.19466 2.42179i 0.180677 0.104314i
\(540\) 0 0
\(541\) 16.5141i 0.709995i −0.934867 0.354998i \(-0.884482\pi\)
0.934867 0.354998i \(-0.115518\pi\)
\(542\) 0 0
\(543\) −1.73631 + 3.00737i −0.0745121 + 0.129059i
\(544\) 0 0
\(545\) 35.5029 1.52078
\(546\) 0 0
\(547\) 13.4780 0.576278 0.288139 0.957589i \(-0.406964\pi\)
0.288139 + 0.957589i \(0.406964\pi\)
\(548\) 0 0
\(549\) 1.33339 2.30950i 0.0569078 0.0985672i
\(550\) 0 0
\(551\) 18.1781i 0.774411i
\(552\) 0 0
\(553\) 14.4846 8.36271i 0.615949 0.355619i
\(554\) 0 0
\(555\) −11.5750 20.0484i −0.491330 0.851008i
\(556\) 0 0
\(557\) 16.6588 + 9.61798i 0.705857 + 0.407527i 0.809525 0.587085i \(-0.199725\pi\)
−0.103668 + 0.994612i \(0.533058\pi\)
\(558\) 0 0
\(559\) 7.02408 + 5.47275i 0.297087 + 0.231473i
\(560\) 0 0
\(561\) −3.97618 2.29565i −0.167874 0.0969223i
\(562\) 0 0
\(563\) −20.0896 34.7962i −0.846676 1.46649i −0.884158 0.467188i \(-0.845267\pi\)
0.0374825 0.999297i \(-0.488066\pi\)
\(564\) 0 0
\(565\) −8.85396 + 5.11184i −0.372489 + 0.215057i
\(566\) 0 0
\(567\) 8.38329i 0.352065i
\(568\) 0 0
\(569\) −4.36255 + 7.55615i −0.182887 + 0.316770i −0.942863 0.333182i \(-0.891878\pi\)
0.759975 + 0.649952i \(0.225211\pi\)
\(570\) 0 0
\(571\) 34.2638 1.43389 0.716947 0.697128i \(-0.245539\pi\)
0.716947 + 0.697128i \(0.245539\pi\)
\(572\) 0 0
\(573\) 7.51439 0.313918
\(574\) 0 0
\(575\) 24.3312 42.1429i 1.01468 1.75748i
\(576\) 0 0
\(577\) 33.1689i 1.38084i 0.723409 + 0.690420i \(0.242574\pi\)
−0.723409 + 0.690420i \(0.757426\pi\)
\(578\) 0 0
\(579\) −8.87123 + 5.12181i −0.368676 + 0.212855i
\(580\) 0 0
\(581\) 1.09309 + 1.89328i 0.0453488 + 0.0785464i
\(582\) 0 0
\(583\) 3.62462 + 2.09267i 0.150116 + 0.0866697i
\(584\) 0 0
\(585\) −20.8409 + 26.7485i −0.861664 + 1.10592i
\(586\) 0 0
\(587\) 21.5975 + 12.4693i 0.891424 + 0.514664i 0.874408 0.485191i \(-0.161250\pi\)
0.0170158 + 0.999855i \(0.494583\pi\)
\(588\) 0 0
\(589\) −13.4564 23.3071i −0.554461 0.960354i
\(590\) 0 0
\(591\) −6.07975 + 3.51015i −0.250088 + 0.144388i
\(592\) 0 0
\(593\) 6.29002i 0.258300i 0.991625 + 0.129150i \(0.0412249\pi\)
−0.991625 + 0.129150i \(0.958775\pi\)
\(594\) 0 0
\(595\) −19.5956 + 33.9407i −0.803343 + 1.39143i
\(596\) 0 0
\(597\) 0.691387 0.0282966
\(598\) 0 0
\(599\) 40.7583 1.66534 0.832670 0.553770i \(-0.186811\pi\)
0.832670 + 0.553770i \(0.186811\pi\)
\(600\) 0 0
\(601\) −9.92944 + 17.1983i −0.405030 + 0.701533i −0.994325 0.106385i \(-0.966072\pi\)
0.589295 + 0.807918i \(0.299406\pi\)
\(602\) 0 0
\(603\) 18.5807i 0.756666i
\(604\) 0 0
\(605\) −3.11091 + 1.79608i −0.126476 + 0.0730212i
\(606\) 0 0
\(607\) 8.08744 + 14.0079i 0.328259 + 0.568561i 0.982166 0.188013i \(-0.0602048\pi\)
−0.653908 + 0.756574i \(0.726871\pi\)
\(608\) 0 0
\(609\) −2.16172 1.24807i −0.0875973 0.0505743i
\(610\) 0 0
\(611\) −14.3993 35.5031i −0.582532 1.43630i
\(612\) 0 0
\(613\) 1.64700 + 0.950895i 0.0665216 + 0.0384063i 0.532892 0.846183i \(-0.321105\pi\)
−0.466370 + 0.884590i \(0.654439\pi\)
\(614\) 0 0
\(615\) −6.60822 11.4458i −0.266469 0.461538i
\(616\) 0 0
\(617\) 12.4208 7.17115i 0.500043 0.288700i −0.228689 0.973500i \(-0.573444\pi\)
0.728731 + 0.684800i \(0.240110\pi\)
\(618\) 0 0
\(619\) 5.40168i 0.217112i −0.994090 0.108556i \(-0.965377\pi\)
0.994090 0.108556i \(-0.0346226\pi\)
\(620\) 0 0
\(621\) 10.6880 18.5121i 0.428893 0.742865i
\(622\) 0 0
\(623\) −12.7706 −0.511644
\(624\) 0 0
\(625\) −2.05046 −0.0820184
\(626\) 0 0
\(627\) −2.04200 + 3.53684i −0.0815494 + 0.141248i
\(628\) 0 0
\(629\) 77.4800i 3.08933i
\(630\) 0 0
\(631\) −21.6314 + 12.4889i −0.861131 + 0.497174i −0.864391 0.502821i \(-0.832296\pi\)
0.00325992 + 0.999995i \(0.498962\pi\)
\(632\) 0 0
\(633\) −3.86628 6.69659i −0.153671 0.266166i
\(634\) 0 0
\(635\) −10.8650 6.27293i −0.431166 0.248934i
\(636\) 0 0
\(637\) −2.40743 + 17.2970i −0.0953859 + 0.685333i
\(638\) 0 0
\(639\) 3.01126 + 1.73855i 0.119123 + 0.0687760i
\(640\) 0 0
\(641\) −11.5883 20.0716i −0.457711 0.792779i 0.541128 0.840940i \(-0.317997\pi\)
−0.998840 + 0.0481607i \(0.984664\pi\)
\(642\) 0 0
\(643\) −33.3510 + 19.2552i −1.31524 + 0.759352i −0.982958 0.183830i \(-0.941150\pi\)
−0.332278 + 0.943182i \(0.607817\pi\)
\(644\) 0 0
\(645\) 5.48226i 0.215864i
\(646\) 0 0
\(647\) 7.24614 12.5507i 0.284875 0.493418i −0.687704 0.725991i \(-0.741381\pi\)
0.972579 + 0.232573i \(0.0747145\pi\)
\(648\) 0 0
\(649\) −1.17538 −0.0461377
\(650\) 0 0
\(651\) 3.69555 0.144840
\(652\) 0 0
\(653\) 22.9699 39.7851i 0.898882 1.55691i 0.0699567 0.997550i \(-0.477714\pi\)
0.828925 0.559359i \(-0.188953\pi\)
\(654\) 0 0
\(655\) 70.7968i 2.76626i
\(656\) 0 0
\(657\) −24.1988 + 13.9712i −0.944087 + 0.545069i
\(658\) 0 0
\(659\) 17.6798 + 30.6223i 0.688707 + 1.19288i 0.972256 + 0.233918i \(0.0751549\pi\)
−0.283549 + 0.958958i \(0.591512\pi\)
\(660\) 0 0
\(661\) 10.0952 + 5.82848i 0.392659 + 0.226702i 0.683311 0.730127i \(-0.260539\pi\)
−0.290653 + 0.956829i \(0.593872\pi\)
\(662\) 0 0
\(663\) 15.3405 6.22174i 0.595774 0.241632i
\(664\) 0 0
\(665\) 30.1905 + 17.4305i 1.17074 + 0.675925i
\(666\) 0 0
\(667\) 8.46774 + 14.6666i 0.327872 + 0.567891i
\(668\) 0 0
\(669\) −4.01162 + 2.31611i −0.155098 + 0.0895460i
\(670\) 0 0
\(671\) 1.01859i 0.0393223i
\(672\) 0 0
\(673\) 17.2170 29.8207i 0.663666 1.14950i −0.315979 0.948766i \(-0.602333\pi\)
0.979645 0.200738i \(-0.0643339\pi\)
\(674\) 0 0
\(675\) 27.4402 1.05617
\(676\) 0 0
\(677\) −3.03487 −0.116640 −0.0583198 0.998298i \(-0.518574\pi\)
−0.0583198 + 0.998298i \(0.518574\pi\)
\(678\) 0 0
\(679\) 1.76267 3.05304i 0.0676452 0.117165i
\(680\) 0 0
\(681\) 11.9426i 0.457643i
\(682\) 0 0
\(683\) −13.9798 + 8.07126i −0.534923 + 0.308838i −0.743019 0.669270i \(-0.766607\pi\)
0.208096 + 0.978108i \(0.433273\pi\)
\(684\) 0 0
\(685\) −20.9284 36.2491i −0.799634 1.38501i
\(686\) 0 0
\(687\) 10.0896 + 5.82522i 0.384942 + 0.222246i
\(688\) 0 0
\(689\) −13.9841 + 5.67164i −0.532752 + 0.216072i
\(690\) 0 0
\(691\) 39.0825 + 22.5643i 1.48677 + 0.858387i 0.999886 0.0150798i \(-0.00480022\pi\)
0.486884 + 0.873467i \(0.338134\pi\)
\(692\) 0 0
\(693\) 1.92232 + 3.32955i 0.0730228 + 0.126479i
\(694\) 0 0
\(695\) −14.5372 + 8.39304i −0.551426 + 0.318366i
\(696\) 0 0
\(697\) 44.2339i 1.67548i
\(698\) 0 0
\(699\) 4.89445 8.47744i 0.185125 0.320646i
\(700\) 0 0
\(701\) −25.5529 −0.965121 −0.482561 0.875863i \(-0.660293\pi\)
−0.482561 + 0.875863i \(0.660293\pi\)
\(702\) 0 0
\(703\) −68.9191 −2.59933
\(704\) 0 0
\(705\) −11.7939 + 20.4277i −0.444186 + 0.769352i
\(706\) 0 0
\(707\) 11.9687i 0.450129i
\(708\) 0 0
\(709\) −10.0192 + 5.78456i −0.376277 + 0.217244i −0.676197 0.736721i \(-0.736373\pi\)
0.299920 + 0.953964i \(0.403040\pi\)
\(710\) 0 0
\(711\) −14.9096 25.8243i −0.559156 0.968486i
\(712\) 0 0
\(713\) −21.7140 12.5366i −0.813194 0.469498i
\(714\) 0 0
\(715\) 1.78544 12.8281i 0.0667716 0.479743i
\(716\) 0 0
\(717\) −7.14222 4.12357i −0.266731 0.153997i
\(718\) 0 0
\(719\) −2.53709 4.39438i −0.0946176 0.163883i 0.814831 0.579698i \(-0.196830\pi\)
−0.909449 + 0.415816i \(0.863496\pi\)
\(720\) 0 0
\(721\) −23.7227 + 13.6963i −0.883480 + 0.510077i
\(722\) 0 0
\(723\) 10.5482i 0.392293i
\(724\) 0 0
\(725\) −10.8700 + 18.8274i −0.403702 + 0.699233i
\(726\) 0 0
\(727\) 44.7840 1.66095 0.830474 0.557058i \(-0.188070\pi\)
0.830474 + 0.557058i \(0.188070\pi\)
\(728\) 0 0
\(729\) −8.50983 −0.315179
\(730\) 0 0
\(731\) 9.17423 15.8902i 0.339321 0.587721i
\(732\) 0 0
\(733\) 36.9408i 1.36444i −0.731147 0.682220i \(-0.761015\pi\)
0.731147 0.682220i \(-0.238985\pi\)
\(734\) 0 0
\(735\) 9.31155 5.37603i 0.343462 0.198298i
\(736\) 0 0
\(737\) −3.54850 6.14619i −0.130711 0.226398i
\(738\) 0 0
\(739\) −5.39244 3.11333i −0.198364 0.114526i 0.397528 0.917590i \(-0.369868\pi\)
−0.595892 + 0.803064i \(0.703201\pi\)
\(740\) 0 0
\(741\) −5.53429 13.6455i −0.203307 0.501278i
\(742\) 0 0
\(743\) −15.0738 8.70285i −0.553003 0.319277i 0.197329 0.980337i \(-0.436773\pi\)
−0.750332 + 0.661061i \(0.770107\pi\)
\(744\) 0 0
\(745\) −36.7395 63.6348i −1.34603 2.33140i
\(746\) 0 0
\(747\) 3.37548 1.94883i 0.123502 0.0713040i
\(748\) 0 0
\(749\) 12.8524i 0.469616i
\(750\) 0 0
\(751\) −12.3057 + 21.3140i −0.449040 + 0.777759i −0.998324 0.0578762i \(-0.981567\pi\)
0.549284 + 0.835636i \(0.314900\pi\)
\(752\) 0 0
\(753\) 7.58547 0.276430
\(754\) 0 0
\(755\) −70.3325 −2.55966
\(756\) 0 0
\(757\) 13.5596 23.4859i 0.492832 0.853610i −0.507134 0.861867i \(-0.669295\pi\)
0.999966 + 0.00825749i \(0.00262847\pi\)
\(758\) 0 0
\(759\) 3.80483i 0.138106i
\(760\) 0 0
\(761\) −46.6440 + 26.9299i −1.69084 + 0.976209i −0.737006 + 0.675886i \(0.763761\pi\)
−0.953838 + 0.300323i \(0.902906\pi\)
\(762\) 0 0
\(763\) 7.25680 + 12.5692i 0.262714 + 0.455034i
\(764\) 0 0
\(765\) 60.5119 + 34.9366i 2.18781 + 1.26313i
\(766\) 0 0
\(767\) 2.60465 3.34298i 0.0940486 0.120708i
\(768\) 0 0
\(769\) −35.9602 20.7616i −1.29676 0.748683i −0.316914 0.948454i \(-0.602647\pi\)
−0.979842 + 0.199772i \(0.935980\pi\)
\(770\) 0 0
\(771\) −8.14281 14.1038i −0.293256 0.507935i
\(772\) 0 0
\(773\) 18.7613 10.8318i 0.674796 0.389594i −0.123095 0.992395i \(-0.539282\pi\)
0.797891 + 0.602801i \(0.205949\pi\)
\(774\) 0 0
\(775\) 32.1863i 1.15617i
\(776\) 0 0
\(777\) 4.73185 8.19580i 0.169754 0.294023i
\(778\) 0 0
\(779\) −39.3464 −1.40973
\(780\) 0 0
\(781\) −1.32810 −0.0475230
\(782\) 0 0
\(783\) −4.77487 + 8.27031i −0.170640 + 0.295557i
\(784\) 0 0
\(785\) 60.9066i 2.17385i
\(786\) 0 0
\(787\) −0.109582 + 0.0632672i −0.00390618 + 0.00225523i −0.501952 0.864896i \(-0.667385\pi\)
0.498046 + 0.867151i \(0.334051\pi\)
\(788\) 0 0
\(789\) 3.24253 + 5.61622i 0.115437 + 0.199943i
\(790\) 0 0
\(791\) −3.61950 2.08972i −0.128695 0.0743019i
\(792\) 0 0
\(793\) −2.89705 2.25721i −0.102877 0.0801559i
\(794\) 0 0
\(795\) 8.04615 + 4.64545i 0.285367 + 0.164757i
\(796\) 0 0
\(797\) 13.5318 + 23.4378i 0.479322 + 0.830211i 0.999719 0.0237140i \(-0.00754911\pi\)
−0.520396 + 0.853925i \(0.674216\pi\)
\(798\) 0 0
\(799\) −68.3691 + 39.4729i −2.41872 + 1.39645i
\(800\) 0 0
\(801\) 22.7684i 0.804482i
\(802\) 0 0
\(803\) 5.33637 9.24287i 0.188317 0.326174i
\(804\) 0 0
\(805\) 32.4780 1.14470
\(806\) 0 0
\(807\) 11.4311 0.402394
\(808\) 0 0
\(809\) −4.18619 + 7.25069i −0.147179 + 0.254921i −0.930184 0.367095i \(-0.880353\pi\)
0.783005 + 0.622015i \(0.213686\pi\)
\(810\) 0 0
\(811\) 3.13534i 0.110097i 0.998484 + 0.0550483i \(0.0175313\pi\)
−0.998484 + 0.0550483i \(0.982469\pi\)
\(812\) 0 0
\(813\) 9.95313 5.74644i 0.349071 0.201536i
\(814\) 0 0
\(815\) 42.5564 + 73.7099i 1.49069 + 2.58194i
\(816\) 0 0
\(817\) −14.1345 8.16054i −0.494503 0.285501i
\(818\) 0 0
\(819\) −13.7297 1.91092i −0.479754 0.0667731i
\(820\) 0 0
\(821\) 45.7774 + 26.4296i 1.59764 + 0.922399i 0.991940 + 0.126707i \(0.0404409\pi\)
0.605702 + 0.795692i \(0.292892\pi\)
\(822\) 0 0
\(823\) 8.73749 + 15.1338i 0.304570 + 0.527530i 0.977165 0.212480i \(-0.0681540\pi\)
−0.672596 + 0.740010i \(0.734821\pi\)
\(824\) 0 0
\(825\) −4.22988 + 2.44212i −0.147266 + 0.0850238i
\(826\) 0 0
\(827\) 3.40361i 0.118355i 0.998247 + 0.0591776i \(0.0188478\pi\)
−0.998247 + 0.0591776i \(0.981152\pi\)
\(828\) 0 0
\(829\) −12.3166 + 21.3330i −0.427774 + 0.740926i −0.996675 0.0814801i \(-0.974035\pi\)
0.568901 + 0.822406i \(0.307369\pi\)
\(830\) 0 0
\(831\) −7.99837 −0.277460
\(832\) 0 0
\(833\) 35.9858 1.24684
\(834\) 0 0
\(835\) −19.6185 + 33.9803i −0.678928 + 1.17594i
\(836\) 0 0
\(837\) 14.1385i 0.488697i
\(838\) 0 0
\(839\) 11.1012 6.40930i 0.383257 0.221274i −0.295977 0.955195i \(-0.595645\pi\)
0.679235 + 0.733921i \(0.262312\pi\)
\(840\) 0 0
\(841\) 10.7170 + 18.5624i 0.369552 + 0.640084i
\(842\) 0 0
\(843\) −4.38406 2.53114i −0.150995 0.0871770i
\(844\) 0 0
\(845\) 32.5287 + 33.5053i 1.11902 + 1.15262i
\(846\) 0 0
\(847\) −1.27174 0.734239i −0.0436975 0.0252287i
\(848\) 0 0
\(849\) 1.31761 + 2.28217i 0.0452202 + 0.0783238i
\(850\) 0 0
\(851\) −55.6058 + 32.1040i −1.90614 + 1.10051i
\(852\) 0 0
\(853\) 10.7738i 0.368887i −0.982843 0.184443i \(-0.940952\pi\)
0.982843 0.184443i \(-0.0590482\pi\)
\(854\) 0 0
\(855\) 31.0763 53.8258i 1.06279 1.84080i
\(856\) 0 0
\(857\) −19.3011 −0.659313 −0.329656 0.944101i \(-0.606933\pi\)
−0.329656 + 0.944101i \(0.606933\pi\)
\(858\) 0 0
\(859\) 7.64223 0.260749 0.130375 0.991465i \(-0.458382\pi\)
0.130375 + 0.991465i \(0.458382\pi\)
\(860\) 0 0
\(861\) 2.70144 4.67904i 0.0920649 0.159461i
\(862\) 0 0
\(863\) 11.0181i 0.375061i −0.982259 0.187531i \(-0.939952\pi\)
0.982259 0.187531i \(-0.0600484\pi\)
\(864\) 0 0
\(865\) 16.7830 9.68966i 0.570638 0.329458i
\(866\) 0 0
\(867\) −11.8030 20.4434i −0.400850 0.694293i
\(868\) 0 0
\(869\) 9.86371 + 5.69481i 0.334603 + 0.193183i
\(870\) 0 0
\(871\) 25.3443 + 3.52747i 0.858759 + 0.119524i
\(872\) 0 0
\(873\) −5.44318 3.14262i −0.184224 0.106362i
\(874\) 0 0
\(875\) 7.65843 + 13.2648i 0.258902 + 0.448432i
\(876\) 0 0
\(877\) −9.08586 + 5.24573i −0.306808 + 0.177136i −0.645497 0.763763i \(-0.723350\pi\)
0.338689 + 0.940898i \(0.390016\pi\)
\(878\) 0 0
\(879\) 3.02167i 0.101918i
\(880\) 0 0
\(881\) −4.00874 + 6.94334i −0.135058 + 0.233927i −0.925620 0.378455i \(-0.876455\pi\)
0.790562 + 0.612382i \(0.209789\pi\)
\(882\) 0 0
\(883\) 14.9068 0.501652 0.250826 0.968032i \(-0.419298\pi\)
0.250826 + 0.968032i \(0.419298\pi\)
\(884\) 0 0
\(885\) −2.60918 −0.0877066
\(886\) 0 0
\(887\) −10.4948 + 18.1776i −0.352381 + 0.610342i −0.986666 0.162757i \(-0.947961\pi\)
0.634285 + 0.773099i \(0.281295\pi\)
\(888\) 0 0
\(889\) 5.12875i 0.172013i
\(890\) 0 0
\(891\) 4.94399 2.85441i 0.165630 0.0956265i
\(892\) 0 0
\(893\) 35.1115 + 60.8148i 1.17496 + 2.03509i
\(894\) 0 0
\(895\) −69.7523 40.2715i −2.33156 1.34613i
\(896\) 0 0
\(897\) −10.8216 8.43153i −0.361322 0.281521i
\(898\) 0 0
\(899\) 9.70075 + 5.60073i 0.323538 + 0.186795i
\(900\) 0 0
\(901\) 15.5477 + 26.9295i 0.517970 + 0.897151i
\(902\) 0 0
\(903\) 1.94089 1.12057i 0.0645888 0.0372904i
\(904\) 0 0
\(905\) 20.1857i 0.670996i
\(906\) 0 0
\(907\) 9.13273 15.8183i 0.303247 0.525240i −0.673622 0.739076i \(-0.735263\pi\)
0.976870 + 0.213836i \(0.0685959\pi\)
\(908\) 0 0
\(909\) 21.3386 0.707758
\(910\) 0 0
\(911\) −36.4866 −1.20885 −0.604427 0.796660i \(-0.706598\pi\)
−0.604427 + 0.796660i \(0.706598\pi\)
\(912\) 0 0
\(913\) −0.744366 + 1.28928i −0.0246349 + 0.0426689i
\(914\) 0 0
\(915\) 2.26113i 0.0747507i
\(916\) 0 0
\(917\) −25.0643 + 14.4709i −0.827696 + 0.477870i
\(918\) 0 0
\(919\) −11.4739 19.8734i −0.378490 0.655564i 0.612353 0.790585i \(-0.290223\pi\)
−0.990843 + 0.135021i \(0.956890\pi\)
\(920\) 0 0
\(921\) −10.0135 5.78130i −0.329956 0.190500i
\(922\) 0 0
\(923\) 2.94307 3.77733i 0.0968724 0.124332i
\(924\) 0 0
\(925\) −71.3810 41.2119i −2.34699 1.35504i
\(926\) 0 0
\(927\) 24.4188 + 42.2946i 0.802018 + 1.38914i
\(928\) 0 0
\(929\) −6.19533 + 3.57687i −0.203262 + 0.117353i −0.598176 0.801365i \(-0.704108\pi\)
0.394914 + 0.918718i \(0.370774\pi\)
\(930\) 0 0
\(931\) 32.0097i 1.04907i
\(932\) 0 0
\(933\) 2.73433 4.73600i 0.0895180 0.155050i
\(934\) 0 0
\(935\) −26.6884 −0.872803
\(936\) 0 0
\(937\) −42.3673 −1.38408 −0.692039 0.721860i \(-0.743287\pi\)
−0.692039 + 0.721860i \(0.743287\pi\)
\(938\) 0 0
\(939\) −1.09020 + 1.88828i −0.0355772 + 0.0616216i
\(940\) 0 0
\(941\) 43.6192i 1.42194i −0.703220 0.710972i \(-0.748255\pi\)
0.703220 0.710972i \(-0.251745\pi\)
\(942\) 0 0
\(943\) −31.7457 + 18.3284i −1.03378 + 0.596855i
\(944\) 0 0
\(945\) 9.15700 + 15.8604i 0.297877 + 0.515939i
\(946\) 0 0
\(947\) 32.3522 + 18.6785i 1.05130 + 0.606971i 0.923014 0.384766i \(-0.125718\pi\)
0.128290 + 0.991737i \(0.459051\pi\)
\(948\) 0 0
\(949\) 14.4628 + 35.6598i 0.469483 + 1.15757i
\(950\) 0 0
\(951\) 12.3808 + 7.14805i 0.401474 + 0.231791i
\(952\) 0 0
\(953\) 3.63581 + 6.29741i 0.117776 + 0.203993i 0.918886 0.394523i \(-0.129090\pi\)
−0.801110 + 0.598517i \(0.795757\pi\)
\(954\) 0 0
\(955\) 37.8278 21.8399i 1.22408 0.706723i
\(956\) 0 0
\(957\) 1.69981i 0.0549472i
\(958\) 0 0
\(959\) 8.55554 14.8186i 0.276273 0.478518i
\(960\) 0 0
\(961\) 14.4161 0.465036
\(962\) 0 0
\(963\) 22.9142 0.738400
\(964\) 0 0
\(965\) −29.7722 + 51.5669i −0.958400 + 1.66000i
\(966\) 0 0
\(967\) 61.2301i 1.96903i −0.175308 0.984514i \(-0.556092\pi\)
0.175308 0.984514i \(-0.443908\pi\)
\(968\) 0 0
\(969\) −26.2773 + 15.1712i −0.844149 + 0.487370i
\(970\) 0 0
\(971\) −0.460539 0.797677i −0.0147794 0.0255987i 0.858541 0.512745i \(-0.171371\pi\)
−0.873321 + 0.487146i \(0.838038\pi\)
\(972\) 0 0
\(973\) −5.94280 3.43108i −0.190517 0.109995i
\(974\) 0 0
\(975\) 2.42765 17.4423i 0.0777470 0.558600i
\(976\) 0 0
\(977\) 13.3273 + 7.69450i 0.426377 + 0.246169i 0.697802 0.716291i \(-0.254162\pi\)
−0.271425 + 0.962460i \(0.587495\pi\)
\(978\) 0 0
\(979\) −4.34825 7.53139i −0.138971 0.240704i
\(980\) 0 0
\(981\) 22.4092 12.9380i 0.715471 0.413077i
\(982\) 0 0
\(983\) 12.6056i 0.402056i 0.979585 + 0.201028i \(0.0644283\pi\)
−0.979585 + 0.201028i \(0.935572\pi\)
\(984\) 0 0
\(985\) −20.4039 + 35.3405i −0.650121 + 1.12604i
\(986\) 0 0
\(987\) −9.64273 −0.306932
\(988\) 0 0
\(989\) −15.2054 −0.483505
\(990\) 0 0
\(991\) 28.2602 48.9482i 0.897716 1.55489i 0.0673094 0.997732i \(-0.478559\pi\)
0.830407 0.557158i \(-0.188108\pi\)
\(992\) 0 0
\(993\) 9.46045i 0.300218i
\(994\) 0 0
\(995\) 3.48048 2.00946i 0.110339 0.0637040i
\(996\) 0 0
\(997\) 0.251412 + 0.435459i 0.00796230 + 0.0137911i 0.869979 0.493089i \(-0.164132\pi\)
−0.862017 + 0.506880i \(0.830799\pi\)
\(998\) 0 0
\(999\) −31.3555 18.1031i −0.992045 0.572757i
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 572.2.p.a.485.6 yes 24
13.6 odd 12 7436.2.a.u.1.7 12
13.7 odd 12 7436.2.a.v.1.7 12
13.10 even 6 inner 572.2.p.a.309.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.p.a.309.6 24 13.10 even 6 inner
572.2.p.a.485.6 yes 24 1.1 even 1 trivial
7436.2.a.u.1.7 12 13.6 odd 12
7436.2.a.v.1.7 12 13.7 odd 12