Properties

Label 1264.2.n.i.735.9
Level $1264$
Weight $2$
Character 1264.735
Analytic conductor $10.093$
Analytic rank $0$
Dimension $28$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1264,2,Mod(735,1264)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1264, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1264.735");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1264 = 2^{4} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1264.n (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: \(10.0930908155\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 735.9
Character \(\chi\) \(=\) 1264.735
Dual form 1264.2.n.i.767.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.214059 - 0.370761i) q^{3} +(0.323998 + 0.561181i) q^{5} +(-2.03778 - 3.52953i) q^{7} +(1.40836 + 2.43935i) q^{9} +O(q^{10})\) \(q+(0.214059 - 0.370761i) q^{3} +(0.323998 + 0.561181i) q^{5} +(-2.03778 - 3.52953i) q^{7} +(1.40836 + 2.43935i) q^{9} +(-0.217813 + 0.125754i) q^{11} +(-1.64580 + 2.85061i) q^{13} +0.277419 q^{15} -1.82066i q^{17} +(5.79726 - 3.34705i) q^{19} -1.74482 q^{21} +(3.50593 - 2.02415i) q^{23} +(2.29005 - 3.96648i) q^{25} +2.49024 q^{27} +(3.46896 - 2.00281i) q^{29} +(-1.92075 + 1.10895i) q^{31} +0.107676i q^{33} +(1.32047 - 2.28712i) q^{35} +(-1.78297 - 1.02940i) q^{37} +(0.704596 + 1.22040i) q^{39} -11.9481i q^{41} +(1.51660 - 2.62683i) q^{43} +(-0.912609 + 1.58069i) q^{45} +(-1.32047 - 2.28712i) q^{47} +(-4.80508 + 8.32264i) q^{49} +(-0.675030 - 0.389729i) q^{51} +(-4.27622 + 2.46887i) q^{53} +(-0.141142 - 0.0814883i) q^{55} -2.86587i q^{57} +(4.25897 - 7.37676i) q^{59} -0.126162i q^{61} +(5.73984 - 9.94169i) q^{63} -2.13294 q^{65} -1.30540i q^{67} -1.73315i q^{69} -8.95357 q^{71} +(3.80224 + 6.58568i) q^{73} +(-0.980413 - 1.69812i) q^{75} +(0.887709 + 0.512519i) q^{77} +(5.88156 - 6.66387i) q^{79} +(-3.69201 + 6.39475i) q^{81} +(-1.06076 + 0.612431i) q^{83} +(1.02172 - 0.589890i) q^{85} -1.71488i q^{87} +10.9283 q^{89} +13.4151 q^{91} +0.949521i q^{93} +(3.75660 + 2.16887i) q^{95} +1.93543 q^{97} +(-0.613517 - 0.354214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times\).

\(n\) \(159\) \(161\) \(949\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) 0.214059 0.370761i 0.123587 0.214059i −0.797593 0.603196i \(-0.793893\pi\)
0.921180 + 0.389137i \(0.127227\pi\)
\(4\) 0 0
\(5\) 0.323998 + 0.561181i 0.144896 + 0.250968i 0.929334 0.369240i \(-0.120382\pi\)
−0.784438 + 0.620207i \(0.787049\pi\)
\(6\) 0 0
\(7\) −2.03778 3.52953i −0.770208 1.33404i −0.937449 0.348123i \(-0.886819\pi\)
0.167241 0.985916i \(-0.446514\pi\)
\(8\) 0 0
\(9\) 1.40836 + 2.43935i 0.469452 + 0.813115i
\(10\) 0 0
\(11\) −0.217813 + 0.125754i −0.0656731 + 0.0379164i −0.532477 0.846444i \(-0.678739\pi\)
0.466804 + 0.884361i \(0.345405\pi\)
\(12\) 0 0
\(13\) −1.64580 + 2.85061i −0.456462 + 0.790616i −0.998771 0.0495635i \(-0.984217\pi\)
0.542309 + 0.840179i \(0.317550\pi\)
\(14\) 0 0
\(15\) 0.277419 0.0716292
\(16\) 0 0
\(17\) 1.82066i 0.441575i −0.975322 0.220787i \(-0.929137\pi\)
0.975322 0.220787i \(-0.0708627\pi\)
\(18\) 0 0
\(19\) 5.79726 3.34705i 1.32998 0.767866i 0.344686 0.938718i \(-0.387986\pi\)
0.985297 + 0.170853i \(0.0546522\pi\)
\(20\) 0 0
\(21\) −1.74482 −0.380751
\(22\) 0 0
\(23\) 3.50593 2.02415i 0.731037 0.422065i −0.0877642 0.996141i \(-0.527972\pi\)
0.818802 + 0.574077i \(0.194639\pi\)
\(24\) 0 0
\(25\) 2.29005 3.96648i 0.458010 0.793297i
\(26\) 0 0
\(27\) 2.49024 0.479247
\(28\) 0 0
\(29\) 3.46896 2.00281i 0.644170 0.371912i −0.142049 0.989860i \(-0.545369\pi\)
0.786219 + 0.617948i \(0.212036\pi\)
\(30\) 0 0
\(31\) −1.92075 + 1.10895i −0.344977 + 0.199173i −0.662471 0.749088i \(-0.730492\pi\)
0.317494 + 0.948260i \(0.397159\pi\)
\(32\) 0 0
\(33\) 0.107676i 0.0187439i
\(34\) 0 0
\(35\) 1.32047 2.28712i 0.223200 0.386594i
\(36\) 0 0
\(37\) −1.78297 1.02940i −0.293118 0.169232i 0.346229 0.938150i \(-0.387462\pi\)
−0.639347 + 0.768918i \(0.720795\pi\)
\(38\) 0 0
\(39\) 0.704596 + 1.22040i 0.112826 + 0.195420i
\(40\) 0 0
\(41\) 11.9481i 1.86598i −0.359904 0.932989i \(-0.617191\pi\)
0.359904 0.932989i \(-0.382809\pi\)
\(42\) 0 0
\(43\) 1.51660 2.62683i 0.231279 0.400588i −0.726906 0.686737i \(-0.759042\pi\)
0.958185 + 0.286150i \(0.0923755\pi\)
\(44\) 0 0
\(45\) −0.912609 + 1.58069i −0.136044 + 0.235635i
\(46\) 0 0
\(47\) −1.32047 2.28712i −0.192610 0.333611i 0.753504 0.657443i \(-0.228362\pi\)
−0.946115 + 0.323832i \(0.895029\pi\)
\(48\) 0 0
\(49\) −4.80508 + 8.32264i −0.686440 + 1.18895i
\(50\) 0 0
\(51\) −0.675030 0.389729i −0.0945231 0.0545730i
\(52\) 0 0
\(53\) −4.27622 + 2.46887i −0.587383 + 0.339126i −0.764062 0.645143i \(-0.776798\pi\)
0.176679 + 0.984269i \(0.443465\pi\)
\(54\) 0 0
\(55\) −0.141142 0.0814883i −0.0190316 0.0109879i
\(56\) 0 0
\(57\) 2.86587i 0.379593i
\(58\) 0 0
\(59\) 4.25897 7.37676i 0.554471 0.960372i −0.443473 0.896288i \(-0.646254\pi\)
0.997944 0.0640847i \(-0.0204128\pi\)
\(60\) 0 0
\(61\) 0.126162i 0.0161534i −0.999967 0.00807671i \(-0.997429\pi\)
0.999967 0.00807671i \(-0.00257092\pi\)
\(62\) 0 0
\(63\) 5.73984 9.94169i 0.723152 1.25254i
\(64\) 0 0
\(65\) −2.13294 −0.264559
\(66\) 0 0
\(67\) 1.30540i 0.159480i −0.996816 0.0797401i \(-0.974591\pi\)
0.996816 0.0797401i \(-0.0254090\pi\)
\(68\) 0 0
\(69\) 1.73315i 0.208647i
\(70\) 0 0
\(71\) −8.95357 −1.06259 −0.531297 0.847186i \(-0.678295\pi\)
−0.531297 + 0.847186i \(0.678295\pi\)
\(72\) 0 0
\(73\) 3.80224 + 6.58568i 0.445019 + 0.770795i 0.998054 0.0623629i \(-0.0198636\pi\)
−0.553035 + 0.833158i \(0.686530\pi\)
\(74\) 0 0
\(75\) −0.980413 1.69812i −0.113208 0.196083i
\(76\) 0 0
\(77\) 0.887709 + 0.512519i 0.101164 + 0.0584070i
\(78\) 0 0
\(79\) 5.88156 6.66387i 0.661728 0.749744i
\(80\) 0 0
\(81\) −3.69201 + 6.39475i −0.410224 + 0.710528i
\(82\) 0 0
\(83\) −1.06076 + 0.612431i −0.116434 + 0.0672231i −0.557086 0.830455i \(-0.688081\pi\)
0.440652 + 0.897678i \(0.354747\pi\)
\(84\) 0 0
\(85\) 1.02172 0.589890i 0.110821 0.0639825i
\(86\) 0 0
\(87\) 1.71488i 0.183854i
\(88\) 0 0
\(89\) 10.9283 1.15840 0.579201 0.815185i \(-0.303365\pi\)
0.579201 + 0.815185i \(0.303365\pi\)
\(90\) 0 0
\(91\) 13.4151 1.40628
\(92\) 0 0
\(93\) 0.949521i 0.0984608i
\(94\) 0 0
\(95\) 3.75660 + 2.16887i 0.385419 + 0.222522i
\(96\) 0 0
\(97\) 1.93543 0.196513 0.0982565 0.995161i \(-0.468673\pi\)
0.0982565 + 0.995161i \(0.468673\pi\)
\(98\) 0 0
\(99\) −0.613517 0.354214i −0.0616608 0.0355999i
\(100\) 0 0
\(101\) 5.53221 0.550475 0.275238 0.961376i \(-0.411243\pi\)
0.275238 + 0.961376i \(0.411243\pi\)
\(102\) 0 0
\(103\) −4.29337 + 7.43633i −0.423038 + 0.732724i −0.996235 0.0866941i \(-0.972370\pi\)
0.573197 + 0.819418i \(0.305703\pi\)
\(104\) 0 0
\(105\) −0.565318 0.979159i −0.0551694 0.0955562i
\(106\) 0 0
\(107\) 3.65735 6.33472i 0.353570 0.612400i −0.633303 0.773904i \(-0.718301\pi\)
0.986872 + 0.161504i \(0.0516344\pi\)
\(108\) 0 0
\(109\) 10.2976 + 5.94534i 0.986334 + 0.569460i 0.904176 0.427159i \(-0.140486\pi\)
0.0821574 + 0.996619i \(0.473819\pi\)
\(110\) 0 0
\(111\) −0.763320 + 0.440703i −0.0724511 + 0.0418297i
\(112\) 0 0
\(113\) −5.61258 3.24043i −0.527987 0.304834i 0.212209 0.977224i \(-0.431934\pi\)
−0.740197 + 0.672391i \(0.765268\pi\)
\(114\) 0 0
\(115\) 2.27183 + 1.31164i 0.211849 + 0.122311i
\(116\) 0 0
\(117\) −9.27149 −0.857149
\(118\) 0 0
\(119\) −6.42608 + 3.71010i −0.589078 + 0.340104i
\(120\) 0 0
\(121\) −5.46837 + 9.47150i −0.497125 + 0.861045i
\(122\) 0 0
\(123\) −4.42989 2.55760i −0.399430 0.230611i
\(124\) 0 0
\(125\) 6.20786 0.555248
\(126\) 0 0
\(127\) −8.72691 15.1155i −0.774388 1.34128i −0.935138 0.354285i \(-0.884724\pi\)
0.160749 0.986995i \(-0.448609\pi\)
\(128\) 0 0
\(129\) −0.649284 1.12459i −0.0571663 0.0990149i
\(130\) 0 0
\(131\) 3.25418i 0.284319i 0.989844 + 0.142159i \(0.0454046\pi\)
−0.989844 + 0.142159i \(0.954595\pi\)
\(132\) 0 0
\(133\) −23.6270 13.6411i −2.04872 1.18283i
\(134\) 0 0
\(135\) 0.806833 + 1.39748i 0.0694411 + 0.120276i
\(136\) 0 0
\(137\) 12.7326i 1.08782i 0.839145 + 0.543908i \(0.183056\pi\)
−0.839145 + 0.543908i \(0.816944\pi\)
\(138\) 0 0
\(139\) 9.01282 + 15.6107i 0.764458 + 1.32408i 0.940533 + 0.339703i \(0.110327\pi\)
−0.176075 + 0.984377i \(0.556340\pi\)
\(140\) 0 0
\(141\) −1.13064 −0.0952167
\(142\) 0 0
\(143\) 0.827865i 0.0692296i
\(144\) 0 0
\(145\) 2.24787 + 1.29781i 0.186676 + 0.107777i
\(146\) 0 0
\(147\) 2.05714 + 3.56307i 0.169670 + 0.293877i
\(148\) 0 0
\(149\) 14.3862 8.30586i 1.17856 0.680442i 0.222879 0.974846i \(-0.428454\pi\)
0.955681 + 0.294404i \(0.0951211\pi\)
\(150\) 0 0
\(151\) 8.37145 4.83326i 0.681259 0.393325i −0.119070 0.992886i \(-0.537991\pi\)
0.800329 + 0.599561i \(0.204658\pi\)
\(152\) 0 0
\(153\) 4.44122 2.56414i 0.359051 0.207298i
\(154\) 0 0
\(155\) −1.24464 0.718593i −0.0999718 0.0577188i
\(156\) 0 0
\(157\) 16.4350i 1.31166i −0.754910 0.655829i \(-0.772319\pi\)
0.754910 0.655829i \(-0.227681\pi\)
\(158\) 0 0
\(159\) 2.11394i 0.167646i
\(160\) 0 0
\(161\) −14.2886 8.24954i −1.12610 0.650155i
\(162\) 0 0
\(163\) −6.84978 + 3.95472i −0.536516 + 0.309758i −0.743666 0.668551i \(-0.766915\pi\)
0.207149 + 0.978309i \(0.433581\pi\)
\(164\) 0 0
\(165\) −0.0604254 + 0.0348866i −0.00470411 + 0.00271592i
\(166\) 0 0
\(167\) −18.3902 + 10.6176i −1.42307 + 0.821612i −0.996560 0.0828698i \(-0.973591\pi\)
−0.426513 + 0.904481i \(0.640258\pi\)
\(168\) 0 0
\(169\) 1.08270 + 1.87529i 0.0832845 + 0.144253i
\(170\) 0 0
\(171\) 16.3292 + 9.42768i 1.24873 + 0.720953i
\(172\) 0 0
\(173\) 7.27842i 0.553368i 0.960961 + 0.276684i \(0.0892355\pi\)
−0.960961 + 0.276684i \(0.910765\pi\)
\(174\) 0 0
\(175\) −18.6665 −1.41105
\(176\) 0 0
\(177\) −1.82335 3.15813i −0.137051 0.237379i
\(178\) 0 0
\(179\) 8.50441i 0.635650i −0.948149 0.317825i \(-0.897048\pi\)
0.948149 0.317825i \(-0.102952\pi\)
\(180\) 0 0
\(181\) 1.34138 + 2.32334i 0.0997039 + 0.172692i 0.911562 0.411163i \(-0.134877\pi\)
−0.811858 + 0.583855i \(0.801544\pi\)
\(182\) 0 0
\(183\) −0.0467761 0.0270062i −0.00345779 0.00199636i
\(184\) 0 0
\(185\) 1.33409i 0.0980841i
\(186\) 0 0
\(187\) 0.228956 + 0.396563i 0.0167429 + 0.0289996i
\(188\) 0 0
\(189\) −5.07456 8.78940i −0.369120 0.639335i
\(190\) 0 0
\(191\) −22.8345 −1.65225 −0.826124 0.563489i \(-0.809459\pi\)
−0.826124 + 0.563489i \(0.809459\pi\)
\(192\) 0 0
\(193\) −0.121216 0.0699839i −0.00872529 0.00503755i 0.495631 0.868533i \(-0.334937\pi\)
−0.504356 + 0.863496i \(0.668270\pi\)
\(194\) 0 0
\(195\) −0.456575 + 0.790812i −0.0326960 + 0.0566312i
\(196\) 0 0
\(197\) 6.36138 3.67275i 0.453230 0.261672i −0.255963 0.966686i \(-0.582393\pi\)
0.709193 + 0.705014i \(0.249059\pi\)
\(198\) 0 0
\(199\) 4.34860 0.308264 0.154132 0.988050i \(-0.450742\pi\)
0.154132 + 0.988050i \(0.450742\pi\)
\(200\) 0 0
\(201\) −0.483993 0.279433i −0.0341382 0.0197097i
\(202\) 0 0
\(203\) −14.1379 8.16255i −0.992289 0.572899i
\(204\) 0 0
\(205\) 6.70504 3.87116i 0.468300 0.270373i
\(206\) 0 0
\(207\) 9.87521 + 5.70146i 0.686375 + 0.396279i
\(208\) 0 0
\(209\) −0.841812 + 1.45806i −0.0582294 + 0.100856i
\(210\) 0 0
\(211\) 10.5023 + 18.1905i 0.723007 + 1.25228i 0.959789 + 0.280722i \(0.0905738\pi\)
−0.236782 + 0.971563i \(0.576093\pi\)
\(212\) 0 0
\(213\) −1.91659 + 3.31964i −0.131323 + 0.227458i
\(214\) 0 0
\(215\) 1.96550 0.134046
\(216\) 0 0
\(217\) 7.82813 + 4.51958i 0.531408 + 0.306809i
\(218\) 0 0
\(219\) 3.25562 0.219994
\(220\) 0 0
\(221\) 5.18998 + 2.99644i 0.349116 + 0.201562i
\(222\) 0 0
\(223\) 7.68996i 0.514958i 0.966284 + 0.257479i \(0.0828918\pi\)
−0.966284 + 0.257479i \(0.917108\pi\)
\(224\) 0 0
\(225\) 12.9008 0.860056
\(226\) 0 0
\(227\) 19.8021 1.31431 0.657156 0.753755i \(-0.271759\pi\)
0.657156 + 0.753755i \(0.271759\pi\)
\(228\) 0 0
\(229\) 4.50599i 0.297764i 0.988855 + 0.148882i \(0.0475675\pi\)
−0.988855 + 0.148882i \(0.952433\pi\)
\(230\) 0 0
\(231\) 0.380045 0.219419i 0.0250051 0.0144367i
\(232\) 0 0
\(233\) −12.2258 + 7.05859i −0.800941 + 0.462423i −0.843800 0.536658i \(-0.819687\pi\)
0.0428593 + 0.999081i \(0.486353\pi\)
\(234\) 0 0
\(235\) 0.855659 1.48205i 0.0558171 0.0966780i
\(236\) 0 0
\(237\) −1.21170 3.60712i −0.0787086 0.234308i
\(238\) 0 0
\(239\) −8.23117 4.75227i −0.532430 0.307399i 0.209575 0.977792i \(-0.432792\pi\)
−0.742005 + 0.670394i \(0.766125\pi\)
\(240\) 0 0
\(241\) −2.03509 3.52488i −0.131092 0.227058i 0.793006 0.609214i \(-0.208515\pi\)
−0.924098 + 0.382156i \(0.875182\pi\)
\(242\) 0 0
\(243\) 5.31598 + 9.20755i 0.341020 + 0.590665i
\(244\) 0 0
\(245\) −6.22734 −0.397850
\(246\) 0 0
\(247\) 22.0343i 1.40201i
\(248\) 0 0
\(249\) 0.524386i 0.0332316i
\(250\) 0 0
\(251\) −20.5951 −1.29995 −0.649976 0.759955i \(-0.725221\pi\)
−0.649976 + 0.759955i \(0.725221\pi\)
\(252\) 0 0
\(253\) −0.509092 + 0.881773i −0.0320063 + 0.0554366i
\(254\) 0 0
\(255\) 0.505085i 0.0316297i
\(256\) 0 0
\(257\) −7.02256 + 12.1634i −0.438055 + 0.758734i −0.997539 0.0701069i \(-0.977666\pi\)
0.559484 + 0.828841i \(0.310999\pi\)
\(258\) 0 0
\(259\) 8.39072i 0.521374i
\(260\) 0 0
\(261\) 9.77108 + 5.64133i 0.604814 + 0.349190i
\(262\) 0 0
\(263\) −13.1299 + 7.58055i −0.809624 + 0.467437i −0.846825 0.531871i \(-0.821489\pi\)
0.0372013 + 0.999308i \(0.488156\pi\)
\(264\) 0 0
\(265\) −2.77097 1.59982i −0.170219 0.0982761i
\(266\) 0 0
\(267\) 2.33931 4.05181i 0.143164 0.247967i
\(268\) 0 0
\(269\) 13.8062 + 23.9130i 0.841779 + 1.45800i 0.888389 + 0.459091i \(0.151825\pi\)
−0.0466102 + 0.998913i \(0.514842\pi\)
\(270\) 0 0
\(271\) −10.8644 + 18.8177i −0.659964 + 1.14309i 0.320660 + 0.947194i \(0.396095\pi\)
−0.980624 + 0.195898i \(0.937238\pi\)
\(272\) 0 0
\(273\) 2.87162 4.97379i 0.173798 0.301028i
\(274\) 0 0
\(275\) 1.15194i 0.0694644i
\(276\) 0 0
\(277\) 7.88524 + 13.6576i 0.473778 + 0.820608i 0.999549 0.0300183i \(-0.00955655\pi\)
−0.525771 + 0.850626i \(0.676223\pi\)
\(278\) 0 0
\(279\) −5.41021 3.12359i −0.323901 0.187004i
\(280\) 0 0
\(281\) 4.99206 8.64651i 0.297802 0.515807i −0.677831 0.735218i \(-0.737080\pi\)
0.975633 + 0.219410i \(0.0704133\pi\)
\(282\) 0 0
\(283\) 18.5877i 1.10492i −0.833539 0.552461i \(-0.813689\pi\)
0.833539 0.552461i \(-0.186311\pi\)
\(284\) 0 0
\(285\) 1.60827 0.928534i 0.0952656 0.0550016i
\(286\) 0 0
\(287\) −42.1712 + 24.3476i −2.48929 + 1.43719i
\(288\) 0 0
\(289\) 13.6852 0.805012
\(290\) 0 0
\(291\) 0.414296 0.717582i 0.0242865 0.0420654i
\(292\) 0 0
\(293\) −10.1425 + 5.85576i −0.592529 + 0.342097i −0.766097 0.642725i \(-0.777804\pi\)
0.173568 + 0.984822i \(0.444470\pi\)
\(294\) 0 0
\(295\) 5.51959 0.321363
\(296\) 0 0
\(297\) −0.542407 + 0.313159i −0.0314737 + 0.0181713i
\(298\) 0 0
\(299\) 13.3254i 0.770626i
\(300\) 0 0
\(301\) −12.3620 −0.712532
\(302\) 0 0
\(303\) 1.18422 2.05113i 0.0680317 0.117834i
\(304\) 0 0
\(305\) 0.0707998 0.0408763i 0.00405399 0.00234057i
\(306\) 0 0
\(307\) 10.3842 + 17.9859i 0.592656 + 1.02651i 0.993873 + 0.110527i \(0.0352538\pi\)
−0.401218 + 0.915983i \(0.631413\pi\)
\(308\) 0 0
\(309\) 1.83807 + 3.18363i 0.104564 + 0.181110i
\(310\) 0 0
\(311\) 8.31463 + 14.4014i 0.471480 + 0.816627i 0.999468 0.0326251i \(-0.0103867\pi\)
−0.527988 + 0.849252i \(0.677053\pi\)
\(312\) 0 0
\(313\) 12.3010 21.3060i 0.695295 1.20429i −0.274786 0.961505i \(-0.588607\pi\)
0.970081 0.242781i \(-0.0780595\pi\)
\(314\) 0 0
\(315\) 7.43878 0.419128
\(316\) 0 0
\(317\) −6.37605 −0.358115 −0.179057 0.983839i \(-0.557305\pi\)
−0.179057 + 0.983839i \(0.557305\pi\)
\(318\) 0 0
\(319\) −0.503723 + 0.872475i −0.0282031 + 0.0488492i
\(320\) 0 0
\(321\) −1.56578 2.71201i −0.0873933 0.151370i
\(322\) 0 0
\(323\) −6.09384 10.5548i −0.339070 0.587287i
\(324\) 0 0
\(325\) 7.53792 + 13.0561i 0.418129 + 0.724220i
\(326\) 0 0
\(327\) 4.40860 2.54531i 0.243796 0.140756i
\(328\) 0 0
\(329\) −5.38165 + 9.32130i −0.296700 + 0.513900i
\(330\) 0 0
\(331\) 9.62347 0.528954 0.264477 0.964392i \(-0.414801\pi\)
0.264477 + 0.964392i \(0.414801\pi\)
\(332\) 0 0
\(333\) 5.79903i 0.317785i
\(334\) 0 0
\(335\) 0.732566 0.422947i 0.0400244 0.0231081i
\(336\) 0 0
\(337\) −25.2743 −1.37678 −0.688389 0.725342i \(-0.741682\pi\)
−0.688389 + 0.725342i \(0.741682\pi\)
\(338\) 0 0
\(339\) −2.40285 + 1.38729i −0.130505 + 0.0753470i
\(340\) 0 0
\(341\) 0.278910 0.483086i 0.0151038 0.0261606i
\(342\) 0 0
\(343\) 10.6378 0.574389
\(344\) 0 0
\(345\) 0.972612 0.561538i 0.0523636 0.0302322i
\(346\) 0 0
\(347\) −25.1964 + 14.5472i −1.35262 + 0.780933i −0.988615 0.150466i \(-0.951923\pi\)
−0.364000 + 0.931399i \(0.618589\pi\)
\(348\) 0 0
\(349\) 22.8231i 1.22169i −0.791749 0.610847i \(-0.790829\pi\)
0.791749 0.610847i \(-0.209171\pi\)
\(350\) 0 0
\(351\) −4.09844 + 7.09870i −0.218758 + 0.378901i
\(352\) 0 0
\(353\) −16.3547 9.44239i −0.870473 0.502568i −0.00296746 0.999996i \(-0.500945\pi\)
−0.867505 + 0.497428i \(0.834278\pi\)
\(354\) 0 0
\(355\) −2.90094 5.02457i −0.153966 0.266677i
\(356\) 0 0
\(357\) 3.17672i 0.168130i
\(358\) 0 0
\(359\) −7.21599 + 12.4985i −0.380845 + 0.659644i −0.991183 0.132498i \(-0.957700\pi\)
0.610338 + 0.792141i \(0.291034\pi\)
\(360\) 0 0
\(361\) 12.9055 22.3529i 0.679235 1.17647i
\(362\) 0 0
\(363\) 2.34111 + 4.05492i 0.122876 + 0.212828i
\(364\) 0 0
\(365\) −2.46384 + 4.26749i −0.128963 + 0.223371i
\(366\) 0 0
\(367\) −13.8709 8.00838i −0.724056 0.418034i 0.0921878 0.995742i \(-0.470614\pi\)
−0.816244 + 0.577708i \(0.803947\pi\)
\(368\) 0 0
\(369\) 29.1455 16.8272i 1.51726 0.875988i
\(370\) 0 0
\(371\) 17.4280 + 10.0620i 0.904814 + 0.522395i
\(372\) 0 0
\(373\) 11.6904i 0.605305i 0.953101 + 0.302652i \(0.0978721\pi\)
−0.953101 + 0.302652i \(0.902128\pi\)
\(374\) 0 0
\(375\) 1.32885 2.30164i 0.0686215 0.118856i
\(376\) 0 0
\(377\) 13.1849i 0.679055i
\(378\) 0 0
\(379\) 14.8390 25.7019i 0.762228 1.32022i −0.179471 0.983763i \(-0.557439\pi\)
0.941700 0.336455i \(-0.109228\pi\)
\(380\) 0 0
\(381\) −7.47230 −0.382818
\(382\) 0 0
\(383\) 29.9847i 1.53215i −0.642753 0.766074i \(-0.722208\pi\)
0.642753 0.766074i \(-0.277792\pi\)
\(384\) 0 0
\(385\) 0.664220i 0.0338518i
\(386\) 0 0
\(387\) 8.54366 0.434299
\(388\) 0 0
\(389\) −17.4045 30.1455i −0.882445 1.52844i −0.848614 0.529012i \(-0.822563\pi\)
−0.0338308 0.999428i \(-0.510771\pi\)
\(390\) 0 0
\(391\) −3.68529 6.38311i −0.186373 0.322808i
\(392\) 0 0
\(393\) 1.20652 + 0.696586i 0.0608610 + 0.0351381i
\(394\) 0 0
\(395\) 5.64525 + 1.14154i 0.284043 + 0.0574371i
\(396\) 0 0
\(397\) −12.5291 + 21.7010i −0.628815 + 1.08914i 0.358974 + 0.933347i \(0.383127\pi\)
−0.987790 + 0.155793i \(0.950207\pi\)
\(398\) 0 0
\(399\) −10.1152 + 5.84000i −0.506392 + 0.292366i
\(400\) 0 0
\(401\) −21.4052 + 12.3583i −1.06892 + 0.617143i −0.927887 0.372862i \(-0.878377\pi\)
−0.141036 + 0.990005i \(0.545043\pi\)
\(402\) 0 0
\(403\) 7.30041i 0.363659i
\(404\) 0 0
\(405\) −4.78482 −0.237759
\(406\) 0 0
\(407\) 0.517804 0.0256666
\(408\) 0 0
\(409\) 18.7975i 0.929478i −0.885448 0.464739i \(-0.846148\pi\)
0.885448 0.464739i \(-0.153852\pi\)
\(410\) 0 0
\(411\) 4.72074 + 2.72552i 0.232857 + 0.134440i
\(412\) 0 0
\(413\) −34.7154 −1.70823
\(414\) 0 0
\(415\) −0.687369 0.396853i −0.0337416 0.0194807i
\(416\) 0 0
\(417\) 7.71711 0.377909
\(418\) 0 0
\(419\) −17.1062 + 29.6289i −0.835694 + 1.44746i 0.0577703 + 0.998330i \(0.481601\pi\)
−0.893464 + 0.449134i \(0.851732\pi\)
\(420\) 0 0
\(421\) 2.13861 + 3.70419i 0.104230 + 0.180531i 0.913423 0.407011i \(-0.133429\pi\)
−0.809194 + 0.587542i \(0.800096\pi\)
\(422\) 0 0
\(423\) 3.71939 6.44217i 0.180843 0.313229i
\(424\) 0 0
\(425\) −7.22162 4.16940i −0.350300 0.202246i
\(426\) 0 0
\(427\) −0.445294 + 0.257091i −0.0215493 + 0.0124415i
\(428\) 0 0
\(429\) −0.306941 0.177212i −0.0148192 0.00855589i
\(430\) 0 0
\(431\) 20.4216 + 11.7904i 0.983674 + 0.567925i 0.903377 0.428846i \(-0.141080\pi\)
0.0802970 + 0.996771i \(0.474413\pi\)
\(432\) 0 0
\(433\) 24.3783 1.17155 0.585774 0.810475i \(-0.300791\pi\)
0.585774 + 0.810475i \(0.300791\pi\)
\(434\) 0 0
\(435\) 0.962355 0.555616i 0.0461414 0.0266398i
\(436\) 0 0
\(437\) 13.5499 23.4690i 0.648178 1.12268i
\(438\) 0 0
\(439\) −17.7602 10.2539i −0.847648 0.489390i 0.0122085 0.999925i \(-0.496114\pi\)
−0.859857 + 0.510536i \(0.829447\pi\)
\(440\) 0 0
\(441\) −27.0691 −1.28900
\(442\) 0 0
\(443\) −18.2591 31.6258i −0.867518 1.50258i −0.864525 0.502589i \(-0.832381\pi\)
−0.00299253 0.999996i \(-0.500953\pi\)
\(444\) 0 0
\(445\) 3.54076 + 6.13278i 0.167848 + 0.290722i
\(446\) 0 0
\(447\) 7.11178i 0.336376i
\(448\) 0 0
\(449\) 1.76503 + 1.01904i 0.0832969 + 0.0480915i 0.541070 0.840978i \(-0.318019\pi\)
−0.457773 + 0.889069i \(0.651353\pi\)
\(450\) 0 0
\(451\) 1.50253 + 2.60245i 0.0707512 + 0.122545i
\(452\) 0 0
\(453\) 4.13841i 0.194440i
\(454\) 0 0
\(455\) 4.34646 + 7.52828i 0.203765 + 0.352931i
\(456\) 0 0
\(457\) 2.54795 0.119188 0.0595939 0.998223i \(-0.481019\pi\)
0.0595939 + 0.998223i \(0.481019\pi\)
\(458\) 0 0
\(459\) 4.53388i 0.211624i
\(460\) 0 0
\(461\) 31.5946 + 18.2411i 1.47151 + 0.849575i 0.999487 0.0320132i \(-0.0101919\pi\)
0.472019 + 0.881588i \(0.343525\pi\)
\(462\) 0 0
\(463\) −9.38770 16.2600i −0.436283 0.755665i 0.561116 0.827737i \(-0.310372\pi\)
−0.997399 + 0.0720721i \(0.977039\pi\)
\(464\) 0 0
\(465\) −0.532853 + 0.307643i −0.0247105 + 0.0142666i
\(466\) 0 0
\(467\) −11.7847 + 6.80390i −0.545331 + 0.314847i −0.747237 0.664558i \(-0.768620\pi\)
0.201906 + 0.979405i \(0.435287\pi\)
\(468\) 0 0
\(469\) −4.60746 + 2.66012i −0.212753 + 0.122833i
\(470\) 0 0
\(471\) −6.09347 3.51807i −0.280772 0.162104i
\(472\) 0 0
\(473\) 0.762877i 0.0350771i
\(474\) 0 0
\(475\) 30.6596i 1.40676i
\(476\) 0 0
\(477\) −12.0449 6.95411i −0.551497 0.318407i
\(478\) 0 0
\(479\) 2.22736 1.28597i 0.101771 0.0587572i −0.448251 0.893908i \(-0.647953\pi\)
0.550021 + 0.835151i \(0.314620\pi\)
\(480\) 0 0
\(481\) 5.86880 3.38835i 0.267594 0.154496i
\(482\) 0 0
\(483\) −6.11722 + 3.53178i −0.278343 + 0.160702i
\(484\) 0 0
\(485\) 0.627075 + 1.08613i 0.0284740 + 0.0493184i
\(486\) 0 0
\(487\) 26.0836 + 15.0594i 1.18196 + 0.682407i 0.956468 0.291838i \(-0.0942667\pi\)
0.225495 + 0.974244i \(0.427600\pi\)
\(488\) 0 0
\(489\) 3.38618i 0.153128i
\(490\) 0 0
\(491\) −37.6098 −1.69731 −0.848654 0.528948i \(-0.822587\pi\)
−0.848654 + 0.528948i \(0.822587\pi\)
\(492\) 0 0
\(493\) −3.64643 6.31580i −0.164227 0.284449i
\(494\) 0 0
\(495\) 0.459059i 0.0206331i
\(496\) 0 0
\(497\) 18.2454 + 31.6020i 0.818418 + 1.41754i
\(498\) 0 0
\(499\) 30.6866 + 17.7169i 1.37372 + 0.793119i 0.991395 0.130908i \(-0.0417893\pi\)
0.382328 + 0.924027i \(0.375123\pi\)
\(500\) 0 0
\(501\) 9.09115i 0.406163i
\(502\) 0 0
\(503\) 4.42363 + 7.66195i 0.197240 + 0.341630i 0.947633 0.319363i \(-0.103469\pi\)
−0.750393 + 0.660992i \(0.770136\pi\)
\(504\) 0 0
\(505\) 1.79242 + 3.10457i 0.0797618 + 0.138151i
\(506\) 0 0
\(507\) 0.927046 0.0411716
\(508\) 0 0
\(509\) −3.65270 2.10889i −0.161903 0.0934747i 0.416859 0.908971i \(-0.363131\pi\)
−0.578762 + 0.815496i \(0.696464\pi\)
\(510\) 0 0
\(511\) 15.4963 26.8403i 0.685514 1.18734i
\(512\) 0 0
\(513\) 14.4366 8.33496i 0.637391 0.367998i
\(514\) 0 0
\(515\) −5.56417 −0.245187
\(516\) 0 0
\(517\) 0.575232 + 0.332110i 0.0252987 + 0.0146062i
\(518\) 0 0
\(519\) 2.69856 + 1.55801i 0.118453 + 0.0683891i
\(520\) 0 0
\(521\) 22.7980 13.1624i 0.998797 0.576656i 0.0909046 0.995860i \(-0.471024\pi\)
0.907892 + 0.419204i \(0.137691\pi\)
\(522\) 0 0
\(523\) 12.4848 + 7.20808i 0.545920 + 0.315187i 0.747475 0.664290i \(-0.231266\pi\)
−0.201555 + 0.979477i \(0.564599\pi\)
\(524\) 0 0
\(525\) −3.99573 + 6.92080i −0.174388 + 0.302049i
\(526\) 0 0
\(527\) 2.01901 + 3.49704i 0.0879497 + 0.152333i
\(528\) 0 0
\(529\) −3.30563 + 5.72551i −0.143723 + 0.248935i
\(530\) 0 0
\(531\) 23.9926 1.04119
\(532\) 0 0
\(533\) 34.0593 + 19.6641i 1.47527 + 0.851749i
\(534\) 0 0
\(535\) 4.73990 0.204924
\(536\) 0 0
\(537\) −3.15311 1.82045i −0.136067 0.0785581i
\(538\) 0 0
\(539\) 2.41704i 0.104109i
\(540\) 0 0
\(541\) 11.2183 0.482313 0.241157 0.970486i \(-0.422473\pi\)
0.241157 + 0.970486i \(0.422473\pi\)
\(542\) 0 0
\(543\) 1.14854 0.0492885
\(544\) 0 0
\(545\) 7.70511i 0.330050i
\(546\) 0 0
\(547\) 13.3680 7.71801i 0.571574 0.329998i −0.186204 0.982511i \(-0.559619\pi\)
0.757778 + 0.652513i \(0.226285\pi\)
\(548\) 0 0
\(549\) 0.307753 0.177682i 0.0131346 0.00758326i
\(550\) 0 0
\(551\) 13.4070 23.2216i 0.571157 0.989272i
\(552\) 0 0
\(553\) −35.5057 7.17969i −1.50986 0.305312i
\(554\) 0 0
\(555\) −0.494628 0.285574i −0.0209958 0.0121219i
\(556\) 0 0
\(557\) 2.85349 + 4.94239i 0.120906 + 0.209416i 0.920125 0.391624i \(-0.128087\pi\)
−0.799219 + 0.601040i \(0.794753\pi\)
\(558\) 0 0
\(559\) 4.99203 + 8.64646i 0.211141 + 0.365706i
\(560\) 0 0
\(561\) 0.196041 0.00827684
\(562\) 0 0
\(563\) 15.6251i 0.658520i 0.944239 + 0.329260i \(0.106799\pi\)
−0.944239 + 0.329260i \(0.893201\pi\)
\(564\) 0 0
\(565\) 4.19956i 0.176677i
\(566\) 0 0
\(567\) 30.0940 1.26383
\(568\) 0 0
\(569\) −15.7932 + 27.3546i −0.662084 + 1.14676i 0.317983 + 0.948097i \(0.396995\pi\)
−0.980067 + 0.198667i \(0.936339\pi\)
\(570\) 0 0
\(571\) 19.3532i 0.809906i 0.914338 + 0.404953i \(0.132712\pi\)
−0.914338 + 0.404953i \(0.867288\pi\)
\(572\) 0 0
\(573\) −4.88794 + 8.46616i −0.204197 + 0.353679i
\(574\) 0 0
\(575\) 18.5416i 0.773240i
\(576\) 0 0
\(577\) 10.5503 + 6.09124i 0.439216 + 0.253581i 0.703265 0.710928i \(-0.251725\pi\)
−0.264049 + 0.964509i \(0.585058\pi\)
\(578\) 0 0
\(579\) −0.0518946 + 0.0299614i −0.00215667 + 0.00124515i
\(580\) 0 0
\(581\) 4.32319 + 2.49600i 0.179356 + 0.103551i
\(582\) 0 0
\(583\) 0.620944 1.07551i 0.0257169 0.0445429i
\(584\) 0 0
\(585\) −3.00394 5.20298i −0.124198 0.215117i
\(586\) 0 0
\(587\) 11.6762 20.2237i 0.481928 0.834723i −0.517857 0.855467i \(-0.673270\pi\)
0.999785 + 0.0207437i \(0.00660341\pi\)
\(588\) 0 0
\(589\) −7.42340 + 12.8577i −0.305876 + 0.529792i
\(590\) 0 0
\(591\) 3.14474i 0.129357i
\(592\) 0 0
\(593\) 1.23972 + 2.14726i 0.0509092 + 0.0881772i 0.890357 0.455263i \(-0.150455\pi\)
−0.839448 + 0.543440i \(0.817121\pi\)
\(594\) 0 0
\(595\) −4.16407 2.40413i −0.170710 0.0985596i
\(596\) 0 0
\(597\) 0.930858 1.61229i 0.0380975 0.0659868i
\(598\) 0 0
\(599\) 12.8535i 0.525180i −0.964907 0.262590i \(-0.915423\pi\)
0.964907 0.262590i \(-0.0845767\pi\)
\(600\) 0 0
\(601\) −20.9240 + 12.0805i −0.853507 + 0.492772i −0.861833 0.507193i \(-0.830683\pi\)
0.00832565 + 0.999965i \(0.497350\pi\)
\(602\) 0 0
\(603\) 3.18433 1.83847i 0.129676 0.0748684i
\(604\) 0 0
\(605\) −7.08696 −0.288126
\(606\) 0 0
\(607\) 14.8293 25.6851i 0.601903 1.04253i −0.390630 0.920548i \(-0.627743\pi\)
0.992533 0.121978i \(-0.0389238\pi\)
\(608\) 0 0
\(609\) −6.05272 + 3.49454i −0.245268 + 0.141606i
\(610\) 0 0
\(611\) 8.69291 0.351678
\(612\) 0 0
\(613\) 35.2853 20.3720i 1.42516 0.822816i 0.428426 0.903577i \(-0.359068\pi\)
0.996734 + 0.0807602i \(0.0257348\pi\)
\(614\) 0 0
\(615\) 3.31463i 0.133659i
\(616\) 0 0
\(617\) 11.2107 0.451326 0.225663 0.974205i \(-0.427545\pi\)
0.225663 + 0.974205i \(0.427545\pi\)
\(618\) 0 0
\(619\) −23.3506 + 40.4445i −0.938541 + 1.62560i −0.170346 + 0.985384i \(0.554489\pi\)
−0.768195 + 0.640216i \(0.778845\pi\)
\(620\) 0 0
\(621\) 8.73062 5.04063i 0.350348 0.202273i
\(622\) 0 0
\(623\) −22.2695 38.5720i −0.892210 1.54535i
\(624\) 0 0
\(625\) −9.43892 16.3487i −0.377557 0.653948i
\(626\) 0 0
\(627\) 0.360395 + 0.624223i 0.0143928 + 0.0249291i
\(628\) 0 0
\(629\) −1.87418 + 3.24617i −0.0747284 + 0.129433i
\(630\) 0 0
\(631\) 0.0645560 0.00256993 0.00128497 0.999999i \(-0.499591\pi\)
0.00128497 + 0.999999i \(0.499591\pi\)
\(632\) 0 0
\(633\) 8.99244 0.357417
\(634\) 0 0
\(635\) 5.65500 9.79475i 0.224412 0.388693i
\(636\) 0 0
\(637\) −15.8164 27.3948i −0.626667 1.08542i
\(638\) 0 0
\(639\) −12.6098 21.8409i −0.498837 0.864011i
\(640\) 0 0
\(641\) −15.6387 27.0870i −0.617690 1.06987i −0.989906 0.141725i \(-0.954735\pi\)
0.372216 0.928146i \(-0.378598\pi\)
\(642\) 0 0
\(643\) 12.5547 7.24844i 0.495108 0.285851i −0.231583 0.972815i \(-0.574391\pi\)
0.726691 + 0.686965i \(0.241057\pi\)
\(644\) 0 0
\(645\) 0.420733 0.728732i 0.0165664 0.0286938i
\(646\) 0 0
\(647\) 24.3074 0.955621 0.477811 0.878463i \(-0.341431\pi\)
0.477811 + 0.878463i \(0.341431\pi\)
\(648\) 0 0
\(649\) 2.14234i 0.0840942i
\(650\) 0 0
\(651\) 3.35137 1.93491i 0.131350 0.0758352i
\(652\) 0 0
\(653\) 32.4454 1.26969 0.634844 0.772640i \(-0.281064\pi\)
0.634844 + 0.772640i \(0.281064\pi\)
\(654\) 0 0
\(655\) −1.82618 + 1.05435i −0.0713548 + 0.0411967i
\(656\) 0 0
\(657\) −10.7098 + 18.5500i −0.417830 + 0.723704i
\(658\) 0 0
\(659\) −1.12101 −0.0436685 −0.0218343 0.999762i \(-0.506951\pi\)
−0.0218343 + 0.999762i \(0.506951\pi\)
\(660\) 0 0
\(661\) −1.96751 + 1.13594i −0.0765271 + 0.0441830i −0.537775 0.843088i \(-0.680735\pi\)
0.461248 + 0.887271i \(0.347402\pi\)
\(662\) 0 0
\(663\) 2.22193 1.28283i 0.0862925 0.0498210i
\(664\) 0 0
\(665\) 17.6787i 0.685551i
\(666\) 0 0
\(667\) 8.10796 14.0434i 0.313942 0.543763i
\(668\) 0 0
\(669\) 2.85114 + 1.64611i 0.110232 + 0.0636422i
\(670\) 0 0
\(671\) 0.0158655 + 0.0274798i 0.000612479 + 0.00106085i
\(672\) 0 0
\(673\) 41.8519i 1.61327i 0.591047 + 0.806637i \(0.298715\pi\)
−0.591047 + 0.806637i \(0.701285\pi\)
\(674\) 0 0
\(675\) 5.70278 9.87751i 0.219500 0.380185i
\(676\) 0 0
\(677\) 18.3876 31.8483i 0.706693 1.22403i −0.259384 0.965774i \(-0.583519\pi\)
0.966077 0.258254i \(-0.0831473\pi\)
\(678\) 0 0
\(679\) −3.94397 6.83116i −0.151356 0.262156i
\(680\) 0 0
\(681\) 4.23882 7.34185i 0.162432 0.281340i
\(682\) 0 0
\(683\) −39.4444 22.7732i −1.50930 0.871394i −0.999941 0.0108384i \(-0.996550\pi\)
−0.509357 0.860555i \(-0.670117\pi\)
\(684\) 0 0
\(685\) −7.14527 + 4.12532i −0.273007 + 0.157620i
\(686\) 0 0
\(687\) 1.67065 + 0.964548i 0.0637391 + 0.0367998i
\(688\) 0 0
\(689\) 16.2531i 0.619193i
\(690\) 0 0
\(691\) 20.8519 36.1166i 0.793245 1.37394i −0.130702 0.991422i \(-0.541723\pi\)
0.923947 0.382520i \(-0.124944\pi\)
\(692\) 0 0
\(693\) 2.88724i 0.109677i
\(694\) 0 0
\(695\) −5.84027 + 10.1156i −0.221534 + 0.383708i
\(696\) 0 0
\(697\) −21.7534 −0.823969
\(698\) 0 0
\(699\) 6.04382i 0.228598i
\(700\) 0 0
\(701\) 45.4596i 1.71699i −0.512824 0.858493i \(-0.671401\pi\)
0.512824 0.858493i \(-0.328599\pi\)
\(702\) 0 0
\(703\) −13.7817 −0.519788
\(704\) 0 0
\(705\) −0.366324 0.634491i −0.0137965 0.0238963i
\(706\) 0 0
\(707\) −11.2734 19.5261i −0.423980 0.734356i
\(708\) 0 0
\(709\) −20.0517 11.5769i −0.753057 0.434778i 0.0737401 0.997277i \(-0.476506\pi\)
−0.826798 + 0.562500i \(0.809840\pi\)
\(710\) 0 0
\(711\) 24.5388 + 4.96206i 0.920278 + 0.186092i
\(712\) 0 0
\(713\) −4.48935 + 7.77579i −0.168128 + 0.291205i
\(714\) 0 0
\(715\) 0.464582 0.268227i 0.0173744 0.0100311i
\(716\) 0 0
\(717\) −3.52391 + 2.03453i −0.131603 + 0.0759810i
\(718\) 0 0
\(719\) 22.2715i 0.830587i −0.909687 0.415294i \(-0.863679\pi\)
0.909687 0.415294i \(-0.136321\pi\)
\(720\) 0 0
\(721\) 34.9957 1.30331
\(722\) 0 0
\(723\) −1.74252 −0.0648051
\(724\) 0 0
\(725\) 18.3461i 0.681358i
\(726\) 0 0
\(727\) 13.6563 + 7.88445i 0.506483 + 0.292418i 0.731387 0.681963i \(-0.238873\pi\)
−0.224904 + 0.974381i \(0.572207\pi\)
\(728\) 0 0
\(729\) −17.6003 −0.651864
\(730\) 0 0
\(731\) −4.78256 2.76121i −0.176889 0.102127i
\(732\) 0 0
\(733\) −0.161586 −0.00596832 −0.00298416 0.999996i \(-0.500950\pi\)
−0.00298416 + 0.999996i \(0.500950\pi\)
\(734\) 0 0
\(735\) −1.33302 + 2.30886i −0.0491691 + 0.0851634i
\(736\) 0 0
\(737\) 0.164160 + 0.284334i 0.00604691 + 0.0104736i
\(738\) 0 0
\(739\) 7.76076 13.4420i 0.285484 0.494473i −0.687242 0.726428i \(-0.741179\pi\)
0.972726 + 0.231955i \(0.0745123\pi\)
\(740\) 0 0
\(741\) 8.16945 + 4.71664i 0.300112 + 0.173270i
\(742\) 0 0
\(743\) −42.5993 + 24.5947i −1.56282 + 0.902293i −0.565847 + 0.824510i \(0.691451\pi\)
−0.996970 + 0.0777828i \(0.975216\pi\)
\(744\) 0 0
\(745\) 9.32217 + 5.38216i 0.341538 + 0.197187i
\(746\) 0 0
\(747\) −2.98786 1.72504i −0.109320 0.0631161i
\(748\) 0 0
\(749\) −29.8115 −1.08929
\(750\) 0 0
\(751\) 38.1288 22.0137i 1.39134 0.803291i 0.397877 0.917439i \(-0.369747\pi\)
0.993464 + 0.114147i \(0.0364136\pi\)
\(752\) 0 0
\(753\) −4.40857 + 7.63587i −0.160657 + 0.278267i
\(754\) 0 0
\(755\) 5.42466 + 3.13193i 0.197424 + 0.113983i
\(756\) 0 0
\(757\) 1.96798 0.0715274 0.0357637 0.999360i \(-0.488614\pi\)
0.0357637 + 0.999360i \(0.488614\pi\)
\(758\) 0 0
\(759\) 0.217952 + 0.377503i 0.00791114 + 0.0137025i
\(760\) 0 0
\(761\) −7.78928 13.4914i −0.282361 0.489064i 0.689605 0.724186i \(-0.257784\pi\)
−0.971966 + 0.235122i \(0.924451\pi\)
\(762\) 0 0
\(763\) 48.4611i 1.75441i
\(764\) 0 0
\(765\) 2.87789 + 1.66155i 0.104050 + 0.0600735i
\(766\) 0 0
\(767\) 14.0188 + 24.2813i 0.506190 + 0.876747i
\(768\) 0 0
\(769\) 7.38704i 0.266383i 0.991090 + 0.133192i \(0.0425226\pi\)
−0.991090 + 0.133192i \(0.957477\pi\)
\(770\) 0 0
\(771\) 3.00649 + 5.20739i 0.108276 + 0.187540i
\(772\) 0 0
\(773\) −8.84600 −0.318168 −0.159084 0.987265i \(-0.550854\pi\)
−0.159084 + 0.987265i \(0.550854\pi\)
\(774\) 0 0
\(775\) 10.1582i 0.364893i
\(776\) 0 0
\(777\) 3.11095 + 1.79611i 0.111605 + 0.0644351i
\(778\) 0 0
\(779\) −39.9908 69.2662i −1.43282 2.48172i
\(780\) 0 0
\(781\) 1.95021 1.12595i 0.0697838 0.0402897i
\(782\) 0 0
\(783\) 8.63856 4.98747i 0.308717 0.178238i
\(784\) 0 0
\(785\) 9.22301 5.32491i 0.329183 0.190054i
\(786\) 0 0
\(787\) −5.69364 3.28722i −0.202956 0.117177i 0.395077 0.918648i \(-0.370718\pi\)
−0.598034 + 0.801471i \(0.704051\pi\)
\(788\) 0 0
\(789\) 6.49074i 0.231077i
\(790\) 0 0
\(791\) 26.4131i 0.939141i
\(792\) 0 0
\(793\) 0.359639 + 0.207638i 0.0127711 + 0.00737343i
\(794\) 0 0
\(795\) −1.18630 + 0.684912i −0.0420738 + 0.0242913i
\(796\) 0 0
\(797\) −21.5375 + 12.4347i −0.762897 + 0.440459i −0.830335 0.557265i \(-0.811851\pi\)
0.0674381 + 0.997723i \(0.478517\pi\)
\(798\) 0 0
\(799\) −4.16407 + 2.40413i −0.147314 + 0.0850519i
\(800\) 0 0
\(801\) 15.3910 + 26.6580i 0.543815 + 0.941915i
\(802\) 0 0
\(803\) −1.65636 0.956298i −0.0584515 0.0337470i
\(804\) 0 0
\(805\) 10.6913i 0.376820i
\(806\) 0 0
\(807\) 11.8214 0.416132
\(808\) 0 0
\(809\) 13.1786 + 22.8260i 0.463335 + 0.802519i 0.999125 0.0418322i \(-0.0133195\pi\)
−0.535790 + 0.844351i \(0.679986\pi\)
\(810\) 0 0
\(811\) 42.6435i 1.49742i 0.662900 + 0.748708i \(0.269326\pi\)
−0.662900 + 0.748708i \(0.730674\pi\)
\(812\) 0 0
\(813\) 4.65124 + 8.05619i 0.163126 + 0.282543i
\(814\) 0 0
\(815\) −4.43863 2.56264i −0.155478 0.0897655i
\(816\) 0 0
\(817\) 20.3045i 0.710366i
\(818\) 0 0
\(819\) 18.8932 + 32.7240i 0.660183 + 1.14347i
\(820\) 0 0
\(821\) −14.2120 24.6159i −0.496002 0.859101i 0.503987 0.863711i \(-0.331866\pi\)
−0.999989 + 0.00461035i \(0.998532\pi\)
\(822\) 0 0
\(823\) 1.98464 0.0691803 0.0345901 0.999402i \(-0.488987\pi\)
0.0345901 + 0.999402i \(0.488987\pi\)
\(824\) 0 0
\(825\) 0.427093 + 0.246582i 0.0148695 + 0.00858490i
\(826\) 0 0
\(827\) −2.54889 + 4.41480i −0.0886335 + 0.153518i −0.906934 0.421273i \(-0.861583\pi\)
0.818300 + 0.574791i \(0.194917\pi\)
\(828\) 0 0
\(829\) −20.4342 + 11.7977i −0.709710 + 0.409751i −0.810954 0.585111i \(-0.801051\pi\)
0.101244 + 0.994862i \(0.467718\pi\)
\(830\) 0 0
\(831\) 6.75163 0.234211
\(832\) 0 0
\(833\) 15.1527 + 8.74841i 0.525010 + 0.303114i
\(834\) 0 0
\(835\) −11.9167 6.88013i −0.412396 0.238097i
\(836\) 0 0
\(837\) −4.78314 + 2.76155i −0.165329 + 0.0954530i
\(838\) 0 0
\(839\) 27.9043 + 16.1106i 0.963365 + 0.556199i 0.897207 0.441610i \(-0.145593\pi\)
0.0661577 + 0.997809i \(0.478926\pi\)
\(840\) 0 0
\(841\) −6.47753 + 11.2194i −0.223363 + 0.386876i
\(842\) 0 0
\(843\) −2.13719 3.70173i −0.0736089 0.127494i
\(844\) 0 0
\(845\) −0.701584 + 1.21518i −0.0241352 + 0.0418034i
\(846\) 0 0
\(847\) 44.5733 1.53156
\(848\) 0 0
\(849\) −6.89159 3.97886i −0.236519 0.136554i
\(850\) 0 0
\(851\) −8.33461 −0.285707
\(852\) 0 0
\(853\) 21.1601 + 12.2168i 0.724507 + 0.418294i 0.816409 0.577474i \(-0.195961\pi\)
−0.0919023 + 0.995768i \(0.529295\pi\)
\(854\) 0 0
\(855\) 12.2182i 0.417853i
\(856\) 0 0
\(857\) 14.8659 0.507810 0.253905 0.967229i \(-0.418285\pi\)
0.253905 + 0.967229i \(0.418285\pi\)
\(858\) 0 0
\(859\) 11.0933 0.378500 0.189250 0.981929i \(-0.439394\pi\)
0.189250 + 0.981929i \(0.439394\pi\)
\(860\) 0 0
\(861\) 20.8473i 0.710473i
\(862\) 0 0
\(863\) 18.7007 10.7968i 0.636578 0.367528i −0.146717 0.989178i \(-0.546871\pi\)
0.783295 + 0.621650i \(0.213537\pi\)
\(864\) 0 0
\(865\) −4.08451 + 2.35819i −0.138877 + 0.0801809i
\(866\) 0 0
\(867\) 2.92944 5.07394i 0.0994891 0.172320i
\(868\) 0 0
\(869\) −0.443070 + 2.19111i −0.0150301 + 0.0743283i
\(870\) 0 0
\(871\) 3.72119 + 2.14843i 0.126088 + 0.0727967i
\(872\) 0 0
\(873\) 2.72577 + 4.72118i 0.0922535 + 0.159788i
\(874\) 0 0
\(875\) −12.6502 21.9109i −0.427656 0.740723i
\(876\) 0 0
\(877\) 11.4740 0.387450 0.193725 0.981056i \(-0.437943\pi\)
0.193725 + 0.981056i \(0.437943\pi\)
\(878\) 0 0
\(879\) 5.01392i 0.169115i
\(880\) 0 0
\(881\) 33.3584i 1.12387i −0.827180 0.561937i \(-0.810056\pi\)
0.827180 0.561937i \(-0.189944\pi\)
\(882\) 0 0
\(883\) −33.0578 −1.11248 −0.556242 0.831020i \(-0.687757\pi\)
−0.556242 + 0.831020i \(0.687757\pi\)
\(884\) 0 0
\(885\) 1.18152 2.04645i 0.0397163 0.0687907i
\(886\) 0 0
\(887\) 25.7081i 0.863193i 0.902067 + 0.431596i \(0.142049\pi\)
−0.902067 + 0.431596i \(0.857951\pi\)
\(888\) 0 0
\(889\) −35.5670 + 61.6039i −1.19288 + 2.06613i
\(890\) 0 0
\(891\) 1.85715i 0.0622168i
\(892\) 0 0
\(893\) −15.3102 8.83936i −0.512337 0.295798i
\(894\) 0 0
\(895\) 4.77251 2.75541i 0.159527 0.0921032i
\(896\) 0 0
\(897\) 4.94053 + 2.85242i 0.164960 + 0.0952395i
\(898\) 0 0
\(899\) −4.44201 + 7.69379i −0.148149 + 0.256602i
\(900\) 0 0
\(901\) 4.49498 + 7.78553i 0.149749 + 0.259374i
\(902\) 0 0
\(903\) −2.64619 + 4.58334i −0.0880598 + 0.152524i
\(904\) 0 0
\(905\) −0.869207 + 1.50551i −0.0288934 + 0.0500449i
\(906\) 0 0
\(907\) 44.1471i 1.46588i 0.680294 + 0.732939i \(0.261852\pi\)
−0.680294 + 0.732939i \(0.738148\pi\)
\(908\) 0 0
\(909\) 7.79133 + 13.4950i 0.258422 + 0.447600i
\(910\) 0 0
\(911\) 3.99320 + 2.30547i 0.132300 + 0.0763837i 0.564689 0.825303i \(-0.308996\pi\)
−0.432389 + 0.901687i \(0.642329\pi\)
\(912\) 0 0
\(913\) 0.154032 0.266791i 0.00509771 0.00882949i
\(914\) 0 0
\(915\) 0.0349998i 0.00115706i
\(916\) 0 0
\(917\) 11.4857 6.63129i 0.379292 0.218984i
\(918\) 0 0
\(919\) 4.90138 2.82981i 0.161682 0.0933470i −0.416976 0.908918i \(-0.636910\pi\)
0.578658 + 0.815571i \(0.303577\pi\)
\(920\) 0 0
\(921\) 8.89130 0.292978
\(922\) 0 0
\(923\) 14.7358 25.5231i 0.485034 0.840103i
\(924\) 0 0
\(925\) −8.16616 + 4.71474i −0.268502 + 0.155020i
\(926\) 0 0
\(927\) −24.1864 −0.794385
\(928\) 0 0
\(929\) 14.1205 8.15248i 0.463279 0.267474i −0.250143 0.968209i \(-0.580478\pi\)
0.713422 + 0.700735i \(0.247144\pi\)
\(930\) 0 0
\(931\) 64.3313i 2.10837i
\(932\) 0 0
\(933\) 7.11930 0.233075
\(934\) 0 0
\(935\) −0.148362 + 0.256971i −0.00485197 + 0.00840386i
\(936\) 0 0
\(937\) 33.4207 19.2954i 1.09181 0.630354i 0.157749 0.987479i \(-0.449576\pi\)
0.934056 + 0.357125i \(0.116243\pi\)
\(938\) 0 0
\(939\) −5.26629 9.12149i −0.171859 0.297669i
\(940\) 0 0
\(941\) 10.4001 + 18.0134i 0.339033 + 0.587222i 0.984251 0.176777i \(-0.0565670\pi\)
−0.645218 + 0.763998i \(0.723234\pi\)
\(942\) 0 0
\(943\) −24.1847 41.8892i −0.787564 1.36410i
\(944\) 0 0
\(945\) 3.28829 5.69549i 0.106968 0.185274i
\(946\) 0 0
\(947\) −21.7971 −0.708310 −0.354155 0.935187i \(-0.615232\pi\)
−0.354155 + 0.935187i \(0.615232\pi\)
\(948\) 0 0
\(949\) −25.0309 −0.812537
\(950\) 0 0
\(951\) −1.36485 + 2.36399i −0.0442584 + 0.0766577i
\(952\) 0 0
\(953\) 3.48839 + 6.04207i 0.113000 + 0.195722i 0.916979 0.398937i \(-0.130621\pi\)
−0.803978 + 0.594658i \(0.797287\pi\)
\(954\) 0 0
\(955\) −7.39833 12.8143i −0.239404 0.414661i
\(956\) 0 0
\(957\) 0.215653 + 0.373522i 0.00697108 + 0.0120743i
\(958\) 0 0
\(959\) 44.9400 25.9461i 1.45119 0.837845i
\(960\) 0 0
\(961\) −13.0405 + 22.5868i −0.420660 + 0.728605i
\(962\) 0 0
\(963\) 20.6034 0.663936
\(964\) 0 0
\(965\) 0.0906985i 0.00291969i
\(966\) 0 0
\(967\) 4.74544 2.73978i 0.152603 0.0881055i −0.421754 0.906710i \(-0.638585\pi\)
0.574357 + 0.818605i \(0.305252\pi\)
\(968\) 0 0
\(969\) −5.21777 −0.167619
\(970\) 0 0
\(971\) −25.6027 + 14.7817i −0.821629 + 0.474368i −0.850978 0.525202i \(-0.823990\pi\)
0.0293491 + 0.999569i \(0.490657\pi\)
\(972\) 0 0
\(973\) 36.7323 63.6221i 1.17758 2.03963i
\(974\) 0 0
\(975\) 6.45425 0.206701
\(976\) 0 0
\(977\) 32.1287 18.5495i 1.02789 0.593451i 0.111509 0.993763i \(-0.464432\pi\)
0.916379 + 0.400312i \(0.131098\pi\)
\(978\) 0 0
\(979\) −2.38034 + 1.37429i −0.0760759 + 0.0439224i
\(980\) 0 0
\(981\) 33.4926i 1.06934i
\(982\) 0 0
\(983\) −19.9452 + 34.5462i −0.636154 + 1.10185i 0.350115 + 0.936707i \(0.386142\pi\)
−0.986269 + 0.165145i \(0.947191\pi\)
\(984\) 0 0
\(985\) 4.12215 + 2.37992i 0.131343 + 0.0758307i
\(986\) 0 0
\(987\) 2.30398 + 3.99062i 0.0733366 + 0.127023i
\(988\) 0 0
\(989\) 12.2793i 0.390459i
\(990\) 0 0
\(991\) −11.2528 + 19.4904i −0.357456 + 0.619132i −0.987535 0.157399i \(-0.949689\pi\)
0.630079 + 0.776531i \(0.283022\pi\)
\(992\) 0 0
\(993\) 2.05999 3.56801i 0.0653719 0.113227i
\(994\) 0 0
\(995\) 1.40894 + 2.44035i 0.0446663 + 0.0773643i
\(996\) 0 0
\(997\) −30.9578 + 53.6205i −0.980443 + 1.69818i −0.319786 + 0.947490i \(0.603611\pi\)
−0.660658 + 0.750687i \(0.729722\pi\)
\(998\) 0 0
\(999\) −4.44002 2.56344i −0.140476 0.0811038i
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 1264.2.n.i.735.9 yes 28
4.3 odd 2 inner 1264.2.n.i.735.6 28
79.56 odd 6 inner 1264.2.n.i.767.6 yes 28
316.135 even 6 inner 1264.2.n.i.767.9 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1264.2.n.i.735.6 28 4.3 odd 2 inner
1264.2.n.i.735.9 yes 28 1.1 even 1 trivial
1264.2.n.i.767.6 yes 28 79.56 odd 6 inner
1264.2.n.i.767.9 yes 28 316.135 even 6 inner