Properties

Label 1152.2.p.d.959.3
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,2,Mod(191,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.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: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 16x^{14} + 178x^{12} - 1024x^{10} + 4267x^{8} - 7936x^{6} + 10594x^{4} - 2800x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.3
Root \(-0.451553 + 0.260704i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.d.191.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.524648 + 1.65068i) q^{3} +(-1.86407 + 3.22866i) q^{5} +(2.39555 - 1.38307i) q^{7} +(-2.44949 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.524648 + 1.65068i) q^{3} +(-1.86407 + 3.22866i) q^{5} +(2.39555 - 1.38307i) q^{7} +(-2.44949 - 1.73205i) q^{9} +(-2.21650 + 1.27970i) q^{11} +(-1.02619 - 0.592470i) q^{13} +(-4.35150 - 4.77089i) q^{15} -2.04989i q^{17} -4.66883 q^{19} +(1.02619 + 4.67991i) q^{21} +(-4.35150 + 7.53703i) q^{23} +(-4.44949 - 7.70674i) q^{25} +(4.14418 - 3.13461i) q^{27} +(-2.70195 - 4.67991i) q^{29} +(8.26342 + 4.77089i) q^{31} +(-0.949490 - 4.33013i) q^{33} +10.3125i q^{35} -5.27238i q^{37} +(1.51637 - 1.38307i) q^{39} +(-7.62372 - 4.40156i) q^{41} +(-2.97697 - 5.15627i) q^{43} +(10.1582 - 4.67991i) q^{45} +(2.39555 + 4.14921i) q^{47} +(0.325765 - 0.564242i) q^{49} +(3.38371 + 1.07547i) q^{51} +9.13202 q^{53} -9.54177i q^{55} +(2.44949 - 7.70674i) q^{57} +(-3.79045 - 2.18841i) q^{59} +(1.02619 - 0.592470i) q^{61} +(-8.26342 - 0.761394i) q^{63} +(3.82577 - 2.20881i) q^{65} +(5.60021 - 9.69985i) q^{67} +(-10.1582 - 11.1372i) q^{69} -3.91191 q^{71} -4.44949 q^{73} +(15.0558 - 3.30136i) q^{75} +(-3.53982 + 6.13116i) q^{77} +(-8.26342 + 4.77089i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-1.92768 + 1.11295i) q^{83} +(6.61839 + 3.82113i) q^{85} +(9.14260 - 2.00475i) q^{87} -13.9993i q^{89} -3.27771 q^{91} +(-12.2106 + 11.1372i) q^{93} +(8.70301 - 15.0741i) q^{95} +(-1.72474 - 2.98735i) q^{97} +(7.64580 + 0.704487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{25} + 24 q^{33} - 24 q^{41} + 64 q^{49} + 120 q^{65} - 32 q^{73} + 48 q^{81} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −0.524648 + 1.65068i −0.302905 + 0.953021i
\(4\) 0 0
\(5\) −1.86407 + 3.22866i −0.833636 + 1.44390i 0.0615002 + 0.998107i \(0.480412\pi\)
−0.895136 + 0.445793i \(0.852922\pi\)
\(6\) 0 0
\(7\) 2.39555 1.38307i 0.905432 0.522751i 0.0264733 0.999650i \(-0.491572\pi\)
0.878959 + 0.476898i \(0.158239\pi\)
\(8\) 0 0
\(9\) −2.44949 1.73205i −0.816497 0.577350i
\(10\) 0 0
\(11\) −2.21650 + 1.27970i −0.668301 + 0.385844i −0.795432 0.606042i \(-0.792756\pi\)
0.127132 + 0.991886i \(0.459423\pi\)
\(12\) 0 0
\(13\) −1.02619 0.592470i −0.284613 0.164322i 0.350897 0.936414i \(-0.385877\pi\)
−0.635510 + 0.772093i \(0.719210\pi\)
\(14\) 0 0
\(15\) −4.35150 4.77089i −1.12355 1.23184i
\(16\) 0 0
\(17\) 2.04989i 0.497171i −0.968610 0.248585i \(-0.920034\pi\)
0.968610 0.248585i \(-0.0799657\pi\)
\(18\) 0 0
\(19\) −4.66883 −1.07110 −0.535551 0.844503i \(-0.679896\pi\)
−0.535551 + 0.844503i \(0.679896\pi\)
\(20\) 0 0
\(21\) 1.02619 + 4.67991i 0.223933 + 1.02124i
\(22\) 0 0
\(23\) −4.35150 + 7.53703i −0.907351 + 1.57158i −0.0896218 + 0.995976i \(0.528566\pi\)
−0.817730 + 0.575603i \(0.804768\pi\)
\(24\) 0 0
\(25\) −4.44949 7.70674i −0.889898 1.54135i
\(26\) 0 0
\(27\) 4.14418 3.13461i 0.797548 0.603256i
\(28\) 0 0
\(29\) −2.70195 4.67991i −0.501739 0.869037i −0.999998 0.00200885i \(-0.999361\pi\)
0.498259 0.867028i \(-0.333973\pi\)
\(30\) 0 0
\(31\) 8.26342 + 4.77089i 1.48415 + 0.856876i 0.999838 0.0180169i \(-0.00573526\pi\)
0.484316 + 0.874893i \(0.339069\pi\)
\(32\) 0 0
\(33\) −0.949490 4.33013i −0.165285 0.753778i
\(34\) 0 0
\(35\) 10.3125i 1.74314i
\(36\) 0 0
\(37\) 5.27238i 0.866773i −0.901208 0.433387i \(-0.857318\pi\)
0.901208 0.433387i \(-0.142682\pi\)
\(38\) 0 0
\(39\) 1.51637 1.38307i 0.242813 0.221468i
\(40\) 0 0
\(41\) −7.62372 4.40156i −1.19063 0.687408i −0.232177 0.972674i \(-0.574585\pi\)
−0.958449 + 0.285265i \(0.907918\pi\)
\(42\) 0 0
\(43\) −2.97697 5.15627i −0.453984 0.786324i 0.544645 0.838667i \(-0.316664\pi\)
−0.998629 + 0.0523430i \(0.983331\pi\)
\(44\) 0 0
\(45\) 10.1582 4.67991i 1.51430 0.697639i
\(46\) 0 0
\(47\) 2.39555 + 4.14921i 0.349427 + 0.605224i 0.986148 0.165870i \(-0.0530431\pi\)
−0.636721 + 0.771094i \(0.719710\pi\)
\(48\) 0 0
\(49\) 0.325765 0.564242i 0.0465379 0.0806060i
\(50\) 0 0
\(51\) 3.38371 + 1.07547i 0.473814 + 0.150596i
\(52\) 0 0
\(53\) 9.13202 1.25438 0.627190 0.778866i \(-0.284205\pi\)
0.627190 + 0.778866i \(0.284205\pi\)
\(54\) 0 0
\(55\) 9.54177i 1.28661i
\(56\) 0 0
\(57\) 2.44949 7.70674i 0.324443 1.02078i
\(58\) 0 0
\(59\) −3.79045 2.18841i −0.493474 0.284907i 0.232541 0.972587i \(-0.425296\pi\)
−0.726015 + 0.687679i \(0.758629\pi\)
\(60\) 0 0
\(61\) 1.02619 0.592470i 0.131390 0.0758580i −0.432864 0.901459i \(-0.642497\pi\)
0.564254 + 0.825601i \(0.309164\pi\)
\(62\) 0 0
\(63\) −8.26342 0.761394i −1.04109 0.0959267i
\(64\) 0 0
\(65\) 3.82577 2.20881i 0.474528 0.273969i
\(66\) 0 0
\(67\) 5.60021 9.69985i 0.684175 1.18503i −0.289521 0.957172i \(-0.593496\pi\)
0.973695 0.227854i \(-0.0731708\pi\)
\(68\) 0 0
\(69\) −10.1582 11.1372i −1.22291 1.34076i
\(70\) 0 0
\(71\) −3.91191 −0.464259 −0.232129 0.972685i \(-0.574569\pi\)
−0.232129 + 0.972685i \(0.574569\pi\)
\(72\) 0 0
\(73\) −4.44949 −0.520773 −0.260387 0.965504i \(-0.583850\pi\)
−0.260387 + 0.965504i \(0.583850\pi\)
\(74\) 0 0
\(75\) 15.0558 3.30136i 1.73849 0.381208i
\(76\) 0 0
\(77\) −3.53982 + 6.13116i −0.403400 + 0.698710i
\(78\) 0 0
\(79\) −8.26342 + 4.77089i −0.929707 + 0.536767i −0.886719 0.462309i \(-0.847021\pi\)
−0.0429881 + 0.999076i \(0.513688\pi\)
\(80\) 0 0
\(81\) 3.00000 + 8.48528i 0.333333 + 0.942809i
\(82\) 0 0
\(83\) −1.92768 + 1.11295i −0.211590 + 0.122162i −0.602050 0.798458i \(-0.705649\pi\)
0.390460 + 0.920620i \(0.372316\pi\)
\(84\) 0 0
\(85\) 6.61839 + 3.82113i 0.717865 + 0.414460i
\(86\) 0 0
\(87\) 9.14260 2.00475i 0.980190 0.214931i
\(88\) 0 0
\(89\) 13.9993i 1.48392i −0.670444 0.741960i \(-0.733896\pi\)
0.670444 0.741960i \(-0.266104\pi\)
\(90\) 0 0
\(91\) −3.27771 −0.343597
\(92\) 0 0
\(93\) −12.2106 + 11.1372i −1.26618 + 1.15488i
\(94\) 0 0
\(95\) 8.70301 15.0741i 0.892910 1.54657i
\(96\) 0 0
\(97\) −1.72474 2.98735i −0.175121 0.303319i 0.765082 0.643933i \(-0.222698\pi\)
−0.940203 + 0.340614i \(0.889365\pi\)
\(98\) 0 0
\(99\) 7.64580 + 0.704487i 0.768432 + 0.0708036i
\(100\) 0 0
\(101\) −5.59220 9.68597i −0.556445 0.963791i −0.997790 0.0664530i \(-0.978832\pi\)
0.441345 0.897338i \(-0.354502\pi\)
\(102\) 0 0
\(103\) −2.39555 1.38307i −0.236040 0.136278i 0.377315 0.926085i \(-0.376847\pi\)
−0.613355 + 0.789807i \(0.710181\pi\)
\(104\) 0 0
\(105\) −17.0227 5.41045i −1.66125 0.528006i
\(106\) 0 0
\(107\) 11.0545i 1.06868i 0.845270 + 0.534340i \(0.179440\pi\)
−0.845270 + 0.534340i \(0.820560\pi\)
\(108\) 0 0
\(109\) 18.1870i 1.74200i 0.491283 + 0.871000i \(0.336528\pi\)
−0.491283 + 0.871000i \(0.663472\pi\)
\(110\) 0 0
\(111\) 8.70301 + 2.76614i 0.826053 + 0.262550i
\(112\) 0 0
\(113\) 3.39898 + 1.96240i 0.319749 + 0.184607i 0.651281 0.758837i \(-0.274232\pi\)
−0.331532 + 0.943444i \(0.607565\pi\)
\(114\) 0 0
\(115\) −16.2230 28.0990i −1.51280 2.62025i
\(116\) 0 0
\(117\) 1.48745 + 3.22866i 0.137515 + 0.298490i
\(118\) 0 0
\(119\) −2.83514 4.91060i −0.259897 0.450154i
\(120\) 0 0
\(121\) −2.22474 + 3.85337i −0.202250 + 0.350306i
\(122\) 0 0
\(123\) 11.2653 10.2751i 1.01576 0.926471i
\(124\) 0 0
\(125\) 14.5359 1.30013
\(126\) 0 0
\(127\) 5.53228i 0.490910i 0.969408 + 0.245455i \(0.0789374\pi\)
−0.969408 + 0.245455i \(0.921063\pi\)
\(128\) 0 0
\(129\) 10.0732 2.20881i 0.886897 0.194475i
\(130\) 0 0
\(131\) 15.9342 + 9.19959i 1.39217 + 0.803772i 0.993556 0.113345i \(-0.0361564\pi\)
0.398619 + 0.917117i \(0.369490\pi\)
\(132\) 0 0
\(133\) −11.1844 + 6.45732i −0.969811 + 0.559920i
\(134\) 0 0
\(135\) 2.39555 + 19.2233i 0.206176 + 1.65447i
\(136\) 0 0
\(137\) −11.7247 + 6.76928i −1.00171 + 0.578339i −0.908755 0.417331i \(-0.862966\pi\)
−0.0929580 + 0.995670i \(0.529632\pi\)
\(138\) 0 0
\(139\) −5.31139 + 9.19959i −0.450506 + 0.780299i −0.998417 0.0562370i \(-0.982090\pi\)
0.547911 + 0.836536i \(0.315423\pi\)
\(140\) 0 0
\(141\) −8.10584 + 1.77741i −0.682635 + 0.149685i
\(142\) 0 0
\(143\) 3.03273 0.253610
\(144\) 0 0
\(145\) 20.1464 1.67307
\(146\) 0 0
\(147\) 0.760471 + 0.833763i 0.0627226 + 0.0687676i
\(148\) 0 0
\(149\) −2.70195 + 4.67991i −0.221352 + 0.383393i −0.955219 0.295901i \(-0.904380\pi\)
0.733867 + 0.679293i \(0.237714\pi\)
\(150\) 0 0
\(151\) −13.0545 + 7.53703i −1.06236 + 0.613354i −0.926084 0.377316i \(-0.876847\pi\)
−0.136277 + 0.990671i \(0.543514\pi\)
\(152\) 0 0
\(153\) −3.55051 + 5.02118i −0.287042 + 0.405938i
\(154\) 0 0
\(155\) −30.8071 + 17.7865i −2.47449 + 1.42865i
\(156\) 0 0
\(157\) −12.6718 7.31610i −1.01132 0.583888i −0.0997447 0.995013i \(-0.531803\pi\)
−0.911579 + 0.411125i \(0.865136\pi\)
\(158\) 0 0
\(159\) −4.79110 + 15.0741i −0.379959 + 1.19545i
\(160\) 0 0
\(161\) 24.0737i 1.89728i
\(162\) 0 0
\(163\) −11.4362 −0.895756 −0.447878 0.894095i \(-0.647820\pi\)
−0.447878 + 0.894095i \(0.647820\pi\)
\(164\) 0 0
\(165\) 15.7504 + 5.00607i 1.22617 + 0.389722i
\(166\) 0 0
\(167\) 6.30746 10.9248i 0.488086 0.845390i −0.511820 0.859093i \(-0.671029\pi\)
0.999906 + 0.0137030i \(0.00436193\pi\)
\(168\) 0 0
\(169\) −5.79796 10.0424i −0.445997 0.772489i
\(170\) 0 0
\(171\) 11.4362 + 8.08665i 0.874552 + 0.618401i
\(172\) 0 0
\(173\) −1.86407 3.22866i −0.141722 0.245470i 0.786423 0.617688i \(-0.211931\pi\)
−0.928145 + 0.372218i \(0.878597\pi\)
\(174\) 0 0
\(175\) −21.3179 12.3079i −1.61148 0.930391i
\(176\) 0 0
\(177\) 5.60102 5.10867i 0.420998 0.383991i
\(178\) 0 0
\(179\) 12.5384i 0.937166i 0.883419 + 0.468583i \(0.155235\pi\)
−0.883419 + 0.468583i \(0.844765\pi\)
\(180\) 0 0
\(181\) 10.0121i 0.744196i −0.928193 0.372098i \(-0.878638\pi\)
0.928193 0.372098i \(-0.121362\pi\)
\(182\) 0 0
\(183\) 0.439591 + 2.00475i 0.0324955 + 0.148195i
\(184\) 0 0
\(185\) 17.0227 + 9.82806i 1.25153 + 0.722574i
\(186\) 0 0
\(187\) 2.62324 + 4.54358i 0.191830 + 0.332260i
\(188\) 0 0
\(189\) 5.59220 13.2408i 0.406773 0.963126i
\(190\) 0 0
\(191\) −6.30746 10.9248i −0.456392 0.790494i 0.542375 0.840136i \(-0.317525\pi\)
−0.998767 + 0.0496426i \(0.984192\pi\)
\(192\) 0 0
\(193\) −12.6237 + 21.8649i −0.908676 + 1.57387i −0.0927696 + 0.995688i \(0.529572\pi\)
−0.815906 + 0.578185i \(0.803761\pi\)
\(194\) 0 0
\(195\) 1.63885 + 7.47396i 0.117361 + 0.535221i
\(196\) 0 0
\(197\) −3.35152 −0.238786 −0.119393 0.992847i \(-0.538095\pi\)
−0.119393 + 0.992847i \(0.538095\pi\)
\(198\) 0 0
\(199\) 12.3079i 0.872485i 0.899829 + 0.436242i \(0.143691\pi\)
−0.899829 + 0.436242i \(0.856309\pi\)
\(200\) 0 0
\(201\) 13.0732 + 14.3332i 0.922113 + 1.01098i
\(202\) 0 0
\(203\) −12.9453 7.47396i −0.908580 0.524569i
\(204\) 0 0
\(205\) 28.4223 16.4096i 1.98510 1.14610i
\(206\) 0 0
\(207\) 23.7135 10.9248i 1.64820 0.759329i
\(208\) 0 0
\(209\) 10.3485 5.97469i 0.715819 0.413278i
\(210\) 0 0
\(211\) 10.5049 18.1950i 0.723185 1.25259i −0.236532 0.971624i \(-0.576011\pi\)
0.959717 0.280969i \(-0.0906558\pi\)
\(212\) 0 0
\(213\) 2.05238 6.45732i 0.140626 0.442448i
\(214\) 0 0
\(215\) 22.1971 1.51383
\(216\) 0 0
\(217\) 26.3939 1.79173
\(218\) 0 0
\(219\) 2.33441 7.34468i 0.157745 0.496308i
\(220\) 0 0
\(221\) −1.21450 + 2.10357i −0.0816959 + 0.141501i
\(222\) 0 0
\(223\) 14.1313 8.15870i 0.946301 0.546347i 0.0543710 0.998521i \(-0.482685\pi\)
0.891930 + 0.452174i \(0.149351\pi\)
\(224\) 0 0
\(225\) −2.44949 + 26.5843i −0.163299 + 1.77229i
\(226\) 0 0
\(227\) −8.64210 + 4.98952i −0.573596 + 0.331166i −0.758584 0.651575i \(-0.774109\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(228\) 0 0
\(229\) 12.6718 + 7.31610i 0.837379 + 0.483461i 0.856373 0.516358i \(-0.172713\pi\)
−0.0189932 + 0.999820i \(0.506046\pi\)
\(230\) 0 0
\(231\) −8.26342 9.05981i −0.543693 0.596092i
\(232\) 0 0
\(233\) 4.09978i 0.268585i 0.990942 + 0.134293i \(0.0428762\pi\)
−0.990942 + 0.134293i \(0.957124\pi\)
\(234\) 0 0
\(235\) −17.8618 −1.16518
\(236\) 0 0
\(237\) −3.53982 16.1433i −0.229936 1.04862i
\(238\) 0 0
\(239\) −12.1753 + 21.0883i −0.787557 + 1.36409i 0.139903 + 0.990165i \(0.455321\pi\)
−0.927460 + 0.373923i \(0.878012\pi\)
\(240\) 0 0
\(241\) 0.0505103 + 0.0874863i 0.00325365 + 0.00563549i 0.867648 0.497180i \(-0.165631\pi\)
−0.864394 + 0.502815i \(0.832298\pi\)
\(242\) 0 0
\(243\) −15.5804 + 0.500258i −0.999485 + 0.0320915i
\(244\) 0 0
\(245\) 1.21450 + 2.10357i 0.0775914 + 0.134392i
\(246\) 0 0
\(247\) 4.79110 + 2.76614i 0.304850 + 0.176005i
\(248\) 0 0
\(249\) −0.825765 3.76588i −0.0523308 0.238653i
\(250\) 0 0
\(251\) 8.75366i 0.552526i 0.961082 + 0.276263i \(0.0890961\pi\)
−0.961082 + 0.276263i \(0.910904\pi\)
\(252\) 0 0
\(253\) 22.2744i 1.40038i
\(254\) 0 0
\(255\) −9.77978 + 8.92010i −0.612434 + 0.558598i
\(256\) 0 0
\(257\) −9.94949 5.74434i −0.620632 0.358322i 0.156483 0.987681i \(-0.449984\pi\)
−0.777115 + 0.629359i \(0.783318\pi\)
\(258\) 0 0
\(259\) −7.29207 12.6302i −0.453107 0.784804i
\(260\) 0 0
\(261\) −1.48745 + 16.1433i −0.0920708 + 0.999245i
\(262\) 0 0
\(263\) −3.47232 6.01424i −0.214113 0.370854i 0.738885 0.673831i \(-0.235353\pi\)
−0.952998 + 0.302978i \(0.902019\pi\)
\(264\) 0 0
\(265\) −17.0227 + 29.4842i −1.04570 + 1.81120i
\(266\) 0 0
\(267\) 23.1083 + 7.34468i 1.41421 + 0.449487i
\(268\) 0 0
\(269\) −16.5883 −1.01141 −0.505703 0.862708i \(-0.668767\pi\)
−0.505703 + 0.862708i \(0.668767\pi\)
\(270\) 0 0
\(271\) 11.0646i 0.672124i −0.941840 0.336062i \(-0.890905\pi\)
0.941840 0.336062i \(-0.109095\pi\)
\(272\) 0 0
\(273\) 1.71964 5.41045i 0.104077 0.327455i
\(274\) 0 0
\(275\) 19.7246 + 11.3880i 1.18944 + 0.686723i
\(276\) 0 0
\(277\) −16.7766 + 9.68597i −1.00801 + 0.581974i −0.910608 0.413271i \(-0.864386\pi\)
−0.0974004 + 0.995245i \(0.531053\pi\)
\(278\) 0 0
\(279\) −11.9777 25.9989i −0.717088 1.55651i
\(280\) 0 0
\(281\) −1.92679 + 1.11243i −0.114942 + 0.0663620i −0.556369 0.830935i \(-0.687806\pi\)
0.441427 + 0.897297i \(0.354473\pi\)
\(282\) 0 0
\(283\) −3.21280 + 5.56473i −0.190981 + 0.330789i −0.945576 0.325402i \(-0.894500\pi\)
0.754595 + 0.656191i \(0.227834\pi\)
\(284\) 0 0
\(285\) 20.3164 + 22.2744i 1.20344 + 1.31942i
\(286\) 0 0
\(287\) −24.3507 −1.43737
\(288\) 0 0
\(289\) 12.7980 0.752821
\(290\) 0 0
\(291\) 5.83604 1.27970i 0.342114 0.0750172i
\(292\) 0 0
\(293\) 1.86407 3.22866i 0.108900 0.188620i −0.806425 0.591336i \(-0.798601\pi\)
0.915325 + 0.402716i \(0.131934\pi\)
\(294\) 0 0
\(295\) 14.1313 8.15870i 0.822755 0.475018i
\(296\) 0 0
\(297\) −5.17423 + 12.2512i −0.300240 + 0.710885i
\(298\) 0 0
\(299\) 8.93092 5.15627i 0.516489 0.298195i
\(300\) 0 0
\(301\) −14.2630 8.23473i −0.822104 0.474642i
\(302\) 0 0
\(303\) 18.9224 4.14921i 1.08706 0.238366i
\(304\) 0 0
\(305\) 4.41761i 0.252952i
\(306\) 0 0
\(307\) −9.33766 −0.532928 −0.266464 0.963845i \(-0.585855\pi\)
−0.266464 + 0.963845i \(0.585855\pi\)
\(308\) 0 0
\(309\) 3.53982 3.22866i 0.201374 0.183672i
\(310\) 0 0
\(311\) −5.23069 + 9.05981i −0.296605 + 0.513735i −0.975357 0.220633i \(-0.929188\pi\)
0.678752 + 0.734368i \(0.262521\pi\)
\(312\) 0 0
\(313\) 2.94949 + 5.10867i 0.166715 + 0.288759i 0.937263 0.348623i \(-0.113351\pi\)
−0.770548 + 0.637382i \(0.780017\pi\)
\(314\) 0 0
\(315\) 17.8618 25.2605i 1.00640 1.42327i
\(316\) 0 0
\(317\) 11.8340 + 20.4970i 0.664662 + 1.15123i 0.979377 + 0.202042i \(0.0647578\pi\)
−0.314715 + 0.949186i \(0.601909\pi\)
\(318\) 0 0
\(319\) 11.9777 + 6.91535i 0.670625 + 0.387185i
\(320\) 0 0
\(321\) −18.2474 5.79972i −1.01847 0.323709i
\(322\) 0 0
\(323\) 9.57058i 0.532521i
\(324\) 0 0
\(325\) 10.5448i 0.584918i
\(326\) 0 0
\(327\) −30.0209 9.54177i −1.66016 0.527661i
\(328\) 0 0
\(329\) 11.4773 + 6.62642i 0.632764 + 0.365326i
\(330\) 0 0
\(331\) 4.07927 + 7.06550i 0.224217 + 0.388355i 0.956084 0.293092i \(-0.0946843\pi\)
−0.731867 + 0.681447i \(0.761351\pi\)
\(332\) 0 0
\(333\) −9.13202 + 12.9146i −0.500432 + 0.707718i
\(334\) 0 0
\(335\) 20.8783 + 36.1623i 1.14071 + 1.97576i
\(336\) 0 0
\(337\) −4.94949 + 8.57277i −0.269616 + 0.466988i −0.968763 0.247990i \(-0.920230\pi\)
0.699147 + 0.714978i \(0.253563\pi\)
\(338\) 0 0
\(339\) −5.02256 + 4.58106i −0.272788 + 0.248809i
\(340\) 0 0
\(341\) −24.4212 −1.32248
\(342\) 0 0
\(343\) 17.5608i 0.948192i
\(344\) 0 0
\(345\) 54.8939 12.0369i 2.95539 0.648043i
\(346\) 0 0
\(347\) −18.7932 10.8503i −1.00887 0.582473i −0.0980117 0.995185i \(-0.531248\pi\)
−0.910862 + 0.412712i \(0.864582\pi\)
\(348\) 0 0
\(349\) −21.8039 + 12.5885i −1.16713 + 0.673845i −0.953003 0.302959i \(-0.902025\pi\)
−0.214131 + 0.976805i \(0.568692\pi\)
\(350\) 0 0
\(351\) −6.10987 + 0.761394i −0.326121 + 0.0406402i
\(352\) 0 0
\(353\) 7.62372 4.40156i 0.405770 0.234271i −0.283201 0.959061i \(-0.591396\pi\)
0.688971 + 0.724789i \(0.258063\pi\)
\(354\) 0 0
\(355\) 7.29207 12.6302i 0.387023 0.670343i
\(356\) 0 0
\(357\) 9.59329 2.10357i 0.507731 0.111333i
\(358\) 0 0
\(359\) −1.75836 −0.0928029 −0.0464015 0.998923i \(-0.514775\pi\)
−0.0464015 + 0.998923i \(0.514775\pi\)
\(360\) 0 0
\(361\) 2.79796 0.147261
\(362\) 0 0
\(363\) −5.19348 5.69400i −0.272587 0.298858i
\(364\) 0 0
\(365\) 8.29415 14.3659i 0.434135 0.751945i
\(366\) 0 0
\(367\) 17.8456 10.3032i 0.931533 0.537821i 0.0442370 0.999021i \(-0.485914\pi\)
0.887296 + 0.461200i \(0.152581\pi\)
\(368\) 0 0
\(369\) 11.0505 + 23.9863i 0.575267 + 1.24867i
\(370\) 0 0
\(371\) 21.8762 12.6302i 1.13576 0.655729i
\(372\) 0 0
\(373\) −8.10584 4.67991i −0.419704 0.242316i 0.275246 0.961374i \(-0.411241\pi\)
−0.694951 + 0.719057i \(0.744574\pi\)
\(374\) 0 0
\(375\) −7.62623 + 23.9941i −0.393817 + 1.23905i
\(376\) 0 0
\(377\) 6.40329i 0.329786i
\(378\) 0 0
\(379\) 33.2594 1.70842 0.854212 0.519926i \(-0.174040\pi\)
0.854212 + 0.519926i \(0.174040\pi\)
\(380\) 0 0
\(381\) −9.13202 2.90250i −0.467848 0.148699i
\(382\) 0 0
\(383\) −7.18664 + 12.4476i −0.367220 + 0.636044i −0.989130 0.147045i \(-0.953024\pi\)
0.621910 + 0.783089i \(0.286357\pi\)
\(384\) 0 0
\(385\) −13.1969 22.8578i −0.672578 1.16494i
\(386\) 0 0
\(387\) −1.63885 + 17.7865i −0.0833077 + 0.904139i
\(388\) 0 0
\(389\) 12.6718 + 21.9483i 0.642488 + 1.11282i 0.984876 + 0.173263i \(0.0554312\pi\)
−0.342387 + 0.939559i \(0.611235\pi\)
\(390\) 0 0
\(391\) 15.4501 + 8.92010i 0.781343 + 0.451109i
\(392\) 0 0
\(393\) −23.5454 + 21.4757i −1.18771 + 1.08330i
\(394\) 0 0
\(395\) 35.5730i 1.78987i
\(396\) 0 0
\(397\) 33.4715i 1.67989i 0.542673 + 0.839944i \(0.317412\pi\)
−0.542673 + 0.839944i \(0.682588\pi\)
\(398\) 0 0
\(399\) −4.79110 21.8497i −0.239855 1.09385i
\(400\) 0 0
\(401\) −4.37628 2.52664i −0.218541 0.126175i 0.386734 0.922191i \(-0.373603\pi\)
−0.605274 + 0.796017i \(0.706937\pi\)
\(402\) 0 0
\(403\) −5.65321 9.79165i −0.281607 0.487757i
\(404\) 0 0
\(405\) −32.9883 6.13116i −1.63920 0.304660i
\(406\) 0 0
\(407\) 6.74705 + 11.6862i 0.334439 + 0.579265i
\(408\) 0 0
\(409\) 7.60102 13.1654i 0.375846 0.650985i −0.614607 0.788833i \(-0.710685\pi\)
0.990453 + 0.137849i \(0.0440187\pi\)
\(410\) 0 0
\(411\) −5.02256 22.9053i −0.247745 1.12983i
\(412\) 0 0
\(413\) −12.1069 −0.595743
\(414\) 0 0
\(415\) 8.29842i 0.407353i
\(416\) 0 0
\(417\) −12.3990 13.5939i −0.607181 0.665698i
\(418\) 0 0
\(419\) 5.94204 + 3.43064i 0.290287 + 0.167598i 0.638071 0.769977i \(-0.279732\pi\)
−0.347784 + 0.937575i \(0.613066\pi\)
\(420\) 0 0
\(421\) 32.5270 18.7795i 1.58527 0.915256i 0.591198 0.806526i \(-0.298655\pi\)
0.994071 0.108730i \(-0.0346783\pi\)
\(422\) 0 0
\(423\) 1.31877 14.3127i 0.0641210 0.695905i
\(424\) 0 0
\(425\) −15.7980 + 9.12096i −0.766314 + 0.442431i
\(426\) 0 0
\(427\) 1.63885 2.83858i 0.0793097 0.137368i
\(428\) 0 0
\(429\) −1.59111 + 5.00607i −0.0768197 + 0.241695i
\(430\) 0 0
\(431\) −17.4060 −0.838418 −0.419209 0.907890i \(-0.637693\pi\)
−0.419209 + 0.907890i \(0.637693\pi\)
\(432\) 0 0
\(433\) −1.75255 −0.0842222 −0.0421111 0.999113i \(-0.513408\pi\)
−0.0421111 + 0.999113i \(0.513408\pi\)
\(434\) 0 0
\(435\) −10.5698 + 33.2553i −0.506782 + 1.59447i
\(436\) 0 0
\(437\) 20.3164 35.1891i 0.971866 1.68332i
\(438\) 0 0
\(439\) 17.8456 10.3032i 0.851724 0.491743i −0.00950794 0.999955i \(-0.503027\pi\)
0.861232 + 0.508212i \(0.169693\pi\)
\(440\) 0 0
\(441\) −1.77526 + 0.817863i −0.0845360 + 0.0389459i
\(442\) 0 0
\(443\) −8.80110 + 5.08132i −0.418153 + 0.241421i −0.694287 0.719699i \(-0.744280\pi\)
0.276134 + 0.961119i \(0.410947\pi\)
\(444\) 0 0
\(445\) 45.1989 + 26.0956i 2.14263 + 1.23705i
\(446\) 0 0
\(447\) −6.30746 6.91535i −0.298333 0.327085i
\(448\) 0 0
\(449\) 10.1852i 0.480670i −0.970690 0.240335i \(-0.922743\pi\)
0.970690 0.240335i \(-0.0772574\pi\)
\(450\) 0 0
\(451\) 22.5307 1.06093
\(452\) 0 0
\(453\) −5.59220 25.5031i −0.262744 1.19824i
\(454\) 0 0
\(455\) 6.10987 10.5826i 0.286435 0.496120i
\(456\) 0 0
\(457\) −5.07321 8.78706i −0.237315 0.411042i 0.722628 0.691237i \(-0.242934\pi\)
−0.959943 + 0.280196i \(0.909601\pi\)
\(458\) 0 0
\(459\) −6.42559 8.49511i −0.299921 0.396518i
\(460\) 0 0
\(461\) −1.02619 1.77741i −0.0477943 0.0827822i 0.841139 0.540820i \(-0.181886\pi\)
−0.888933 + 0.458037i \(0.848553\pi\)
\(462\) 0 0
\(463\) −8.26342 4.77089i −0.384034 0.221722i 0.295538 0.955331i \(-0.404501\pi\)
−0.679572 + 0.733609i \(0.737834\pi\)
\(464\) 0 0
\(465\) −13.1969 60.1843i −0.611993 2.79098i
\(466\) 0 0
\(467\) 0.667010i 0.0308656i −0.999881 0.0154328i \(-0.995087\pi\)
0.999881 0.0154328i \(-0.00491260\pi\)
\(468\) 0 0
\(469\) 30.9819i 1.43061i
\(470\) 0 0
\(471\) 18.7248 17.0788i 0.862793 0.786949i
\(472\) 0 0
\(473\) 13.1969 + 7.61926i 0.606796 + 0.350334i
\(474\) 0 0
\(475\) 20.7739 + 35.9815i 0.953172 + 1.65094i
\(476\) 0 0
\(477\) −22.3688 15.8171i −1.02420 0.724217i
\(478\) 0 0
\(479\) −16.9664 29.3867i −0.775216 1.34271i −0.934673 0.355508i \(-0.884308\pi\)
0.159457 0.987205i \(-0.449026\pi\)
\(480\) 0 0
\(481\) −3.12372 + 5.41045i −0.142430 + 0.246695i
\(482\) 0 0
\(483\) −39.7380 12.6302i −1.80814 0.574695i
\(484\) 0 0
\(485\) 12.8602 0.583950
\(486\) 0 0
\(487\) 11.0646i 0.501383i 0.968067 + 0.250692i \(0.0806580\pi\)
−0.968067 + 0.250692i \(0.919342\pi\)
\(488\) 0 0
\(489\) 6.00000 18.8776i 0.271329 0.853674i
\(490\) 0 0
\(491\) −3.21280 1.85491i −0.144992 0.0837109i 0.425749 0.904841i \(-0.360011\pi\)
−0.570741 + 0.821130i \(0.693344\pi\)
\(492\) 0 0
\(493\) −9.59329 + 5.53869i −0.432060 + 0.249450i
\(494\) 0 0
\(495\) −16.5268 + 23.3725i −0.742826 + 1.05051i
\(496\) 0 0
\(497\) −9.37117 + 5.41045i −0.420355 + 0.242692i
\(498\) 0 0
\(499\) −18.6104 + 32.2342i −0.833116 + 1.44300i 0.0624392 + 0.998049i \(0.480112\pi\)
−0.895555 + 0.444950i \(0.853221\pi\)
\(500\) 0 0
\(501\) 14.7242 + 16.1433i 0.657830 + 0.721229i
\(502\) 0 0
\(503\) −19.5596 −0.872118 −0.436059 0.899918i \(-0.643626\pi\)
−0.436059 + 0.899918i \(0.643626\pi\)
\(504\) 0 0
\(505\) 41.6969 1.85549
\(506\) 0 0
\(507\) 19.6186 4.30188i 0.871293 0.191053i
\(508\) 0 0
\(509\) 12.2106 21.1494i 0.541225 0.937429i −0.457609 0.889153i \(-0.651294\pi\)
0.998834 0.0482755i \(-0.0153725\pi\)
\(510\) 0 0
\(511\) −10.6590 + 6.15396i −0.471525 + 0.272235i
\(512\) 0 0
\(513\) −19.3485 + 14.6349i −0.854256 + 0.646149i
\(514\) 0 0
\(515\) 8.93092 5.15627i 0.393543 0.227212i
\(516\) 0 0
\(517\) −10.6195 6.13116i −0.467044 0.269648i
\(518\) 0 0
\(519\) 6.30746 1.38307i 0.276867 0.0607100i
\(520\) 0 0
\(521\) 21.4203i 0.938440i −0.883081 0.469220i \(-0.844535\pi\)
0.883081 0.469220i \(-0.155465\pi\)
\(522\) 0 0
\(523\) −32.3162 −1.41309 −0.706543 0.707670i \(-0.749746\pi\)
−0.706543 + 0.707670i \(0.749746\pi\)
\(524\) 0 0
\(525\) 31.5008 28.7318i 1.37481 1.25396i
\(526\) 0 0
\(527\) 9.77978 16.9391i 0.426014 0.737878i
\(528\) 0 0
\(529\) −26.3712 45.6762i −1.14657 1.98592i
\(530\) 0 0
\(531\) 5.49421 + 11.9257i 0.238428 + 0.517533i
\(532\) 0 0
\(533\) 5.21558 + 9.03365i 0.225912 + 0.391291i
\(534\) 0 0
\(535\) −35.6912 20.6063i −1.54307 0.890889i
\(536\) 0 0
\(537\) −20.6969 6.57826i −0.893139 0.283873i
\(538\) 0 0
\(539\) 1.66753i 0.0718254i
\(540\) 0 0
\(541\) 3.43512i 0.147687i 0.997270 + 0.0738436i \(0.0235266\pi\)
−0.997270 + 0.0738436i \(0.976473\pi\)
\(542\) 0 0
\(543\) 16.5268 + 5.25284i 0.709234 + 0.225421i
\(544\) 0 0
\(545\) −58.7196 33.9018i −2.51527 1.45219i
\(546\) 0 0
\(547\) 3.26580 + 5.65653i 0.139635 + 0.241856i 0.927359 0.374174i \(-0.122074\pi\)
−0.787723 + 0.616029i \(0.788740\pi\)
\(548\) 0 0
\(549\) −3.53982 0.326161i −0.151076 0.0139202i
\(550\) 0 0
\(551\) 12.6149 + 21.8497i 0.537414 + 0.930828i
\(552\) 0 0
\(553\) −13.1969 + 22.8578i −0.561191 + 0.972011i
\(554\) 0 0
\(555\) −25.1539 + 22.9428i −1.06772 + 0.973866i
\(556\) 0 0
\(557\) 5.78051 0.244928 0.122464 0.992473i \(-0.460920\pi\)
0.122464 + 0.992473i \(0.460920\pi\)
\(558\) 0 0
\(559\) 7.05507i 0.298398i
\(560\) 0 0
\(561\) −8.87628 + 1.94635i −0.374757 + 0.0821749i
\(562\) 0 0
\(563\) −6.07186 3.50559i −0.255898 0.147743i 0.366564 0.930393i \(-0.380534\pi\)
−0.622462 + 0.782650i \(0.713868\pi\)
\(564\) 0 0
\(565\) −12.6718 + 7.31610i −0.533109 + 0.307790i
\(566\) 0 0
\(567\) 18.9224 + 16.1777i 0.794665 + 0.679399i
\(568\) 0 0
\(569\) 35.2980 20.3793i 1.47977 0.854344i 0.480030 0.877252i \(-0.340626\pi\)
0.999738 + 0.0229080i \(0.00729249\pi\)
\(570\) 0 0
\(571\) −14.1244 + 24.4642i −0.591088 + 1.02379i 0.402999 + 0.915201i \(0.367968\pi\)
−0.994086 + 0.108593i \(0.965365\pi\)
\(572\) 0 0
\(573\) 21.3426 4.67991i 0.891600 0.195506i
\(574\) 0 0
\(575\) 77.4479 3.22980
\(576\) 0 0
\(577\) −1.55051 −0.0645486 −0.0322743 0.999479i \(-0.510275\pi\)
−0.0322743 + 0.999479i \(0.510275\pi\)
\(578\) 0 0
\(579\) −29.4690 32.3091i −1.22469 1.34272i
\(580\) 0 0
\(581\) −3.07856 + 5.33223i −0.127720 + 0.221218i
\(582\) 0 0
\(583\) −20.2412 + 11.6862i −0.838303 + 0.483994i
\(584\) 0 0
\(585\) −13.1969 1.21597i −0.545626 0.0502742i
\(586\) 0 0
\(587\) 24.8002 14.3184i 1.02361 0.590983i 0.108464 0.994100i \(-0.465407\pi\)
0.915148 + 0.403117i \(0.132073\pi\)
\(588\) 0 0
\(589\) −38.5805 22.2744i −1.58968 0.917803i
\(590\) 0 0
\(591\) 1.75836 5.53228i 0.0723295 0.227568i
\(592\) 0 0
\(593\) 4.87832i 0.200328i −0.994971 0.100164i \(-0.968063\pi\)
0.994971 0.100164i \(-0.0319368\pi\)
\(594\) 0 0
\(595\) 21.1396 0.866637
\(596\) 0 0
\(597\) −20.3164 6.45732i −0.831496 0.264280i
\(598\) 0 0
\(599\) 6.30746 10.9248i 0.257716 0.446377i −0.707914 0.706299i \(-0.750363\pi\)
0.965630 + 0.259922i \(0.0836968\pi\)
\(600\) 0 0
\(601\) −14.2753 24.7255i −0.582300 1.00857i −0.995206 0.0977994i \(-0.968820\pi\)
0.412906 0.910773i \(-0.364514\pi\)
\(602\) 0 0
\(603\) −30.5183 + 14.0598i −1.24280 + 0.572561i
\(604\) 0 0
\(605\) −8.29415 14.3659i −0.337205 0.584056i
\(606\) 0 0
\(607\) 4.54910 + 2.62642i 0.184642 + 0.106603i 0.589472 0.807789i \(-0.299336\pi\)
−0.404830 + 0.914392i \(0.632669\pi\)
\(608\) 0 0
\(609\) 19.1288 17.4473i 0.775139 0.707001i
\(610\) 0 0
\(611\) 5.67716i 0.229673i
\(612\) 0 0
\(613\) 28.7318i 1.16047i 0.814451 + 0.580233i \(0.197038\pi\)
−0.814451 + 0.580233i \(0.802962\pi\)
\(614\) 0 0
\(615\) 12.1753 + 55.5253i 0.490957 + 2.23900i
\(616\) 0 0
\(617\) 22.6237 + 13.0618i 0.910797 + 0.525849i 0.880687 0.473698i \(-0.157081\pi\)
0.0301094 + 0.999547i \(0.490414\pi\)
\(618\) 0 0
\(619\) 6.30768 + 10.9252i 0.253527 + 0.439122i 0.964494 0.264103i \(-0.0850759\pi\)
−0.710967 + 0.703225i \(0.751743\pi\)
\(620\) 0 0
\(621\) 5.59220 + 44.8751i 0.224407 + 1.80077i
\(622\) 0 0
\(623\) −19.3620 33.5359i −0.775721 1.34359i
\(624\) 0 0
\(625\) −4.84847 + 8.39780i −0.193939 + 0.335912i
\(626\) 0 0
\(627\) 4.43300 + 20.2166i 0.177037 + 0.807374i
\(628\) 0 0
\(629\) −10.8078 −0.430935
\(630\) 0 0
\(631\) 27.1025i 1.07893i −0.842007 0.539467i \(-0.818626\pi\)
0.842007 0.539467i \(-0.181374\pi\)
\(632\) 0 0
\(633\) 24.5227 + 26.8861i 0.974690 + 1.06863i
\(634\) 0 0
\(635\) −17.8618 10.3125i −0.708826 0.409241i
\(636\) 0 0
\(637\) −0.668593 + 0.386012i −0.0264906 + 0.0152944i
\(638\) 0 0
\(639\) 9.58219 + 6.77563i 0.379066 + 0.268040i
\(640\) 0 0
\(641\) 9.70204 5.60148i 0.383208 0.221245i −0.296005 0.955186i \(-0.595655\pi\)
0.679213 + 0.733941i \(0.262321\pi\)
\(642\) 0 0
\(643\) 1.40303 2.43012i 0.0553301 0.0958346i −0.837034 0.547151i \(-0.815712\pi\)
0.892364 + 0.451317i \(0.149046\pi\)
\(644\) 0 0
\(645\) −11.6457 + 36.6403i −0.458547 + 1.44271i
\(646\) 0 0
\(647\) −28.7466 −1.13014 −0.565072 0.825041i \(-0.691152\pi\)
−0.565072 + 0.825041i \(0.691152\pi\)
\(648\) 0 0
\(649\) 11.2020 0.439719
\(650\) 0 0
\(651\) −13.8475 + 43.5678i −0.542726 + 1.70756i
\(652\) 0 0
\(653\) −7.64458 + 13.2408i −0.299155 + 0.518152i −0.975943 0.218026i \(-0.930038\pi\)
0.676788 + 0.736178i \(0.263372\pi\)
\(654\) 0 0
\(655\) −59.4047 + 34.2973i −2.32113 + 1.34011i
\(656\) 0 0
\(657\) 10.8990 + 7.70674i 0.425210 + 0.300669i
\(658\) 0 0
\(659\) 41.6657 24.0557i 1.62307 0.937078i 0.636972 0.770887i \(-0.280186\pi\)
0.986094 0.166191i \(-0.0531468\pi\)
\(660\) 0 0
\(661\) 28.8835 + 16.6759i 1.12344 + 0.648618i 0.942277 0.334836i \(-0.108681\pi\)
0.181162 + 0.983453i \(0.442014\pi\)
\(662\) 0 0
\(663\) −2.83514 3.10838i −0.110108 0.120719i
\(664\) 0 0
\(665\) 48.1475i 1.86708i
\(666\) 0 0
\(667\) 47.0301 1.82101
\(668\) 0 0
\(669\) 6.05346 + 27.6067i 0.234040 + 1.06734i
\(670\) 0 0
\(671\) −1.51637 + 2.62642i −0.0585386 + 0.101392i
\(672\) 0 0
\(673\) −15.0732 26.1076i −0.581030 1.00637i −0.995358 0.0962453i \(-0.969317\pi\)
0.414328 0.910128i \(-0.364017\pi\)
\(674\) 0 0
\(675\) −42.5971 17.9907i −1.63956 0.692463i
\(676\) 0 0
\(677\) 7.64458 + 13.2408i 0.293805 + 0.508885i 0.974706 0.223490i \(-0.0717451\pi\)
−0.680901 + 0.732375i \(0.738412\pi\)
\(678\) 0 0
\(679\) −8.26342 4.77089i −0.317121 0.183090i
\(680\) 0 0
\(681\) −3.70204 16.8831i −0.141863 0.646961i
\(682\) 0 0
\(683\) 37.4654i 1.43357i −0.697293 0.716787i \(-0.745612\pi\)
0.697293 0.716787i \(-0.254388\pi\)
\(684\) 0 0
\(685\) 50.4736i 1.92850i
\(686\) 0 0
\(687\) −18.7248 + 17.0788i −0.714395 + 0.651597i
\(688\) 0 0
\(689\) −9.37117 5.41045i −0.357013 0.206122i
\(690\) 0 0
\(691\) 14.6490 + 25.3729i 0.557276 + 0.965230i 0.997723 + 0.0674514i \(0.0214868\pi\)
−0.440447 + 0.897779i \(0.645180\pi\)
\(692\) 0 0
\(693\) 19.2902 8.88705i 0.732776 0.337591i
\(694\) 0 0
\(695\) −19.8016 34.2973i −0.751116 1.30097i
\(696\) 0 0
\(697\) −9.02270 + 15.6278i −0.341759 + 0.591944i
\(698\) 0 0
\(699\) −6.76742 2.15094i −0.255967 0.0813559i
\(700\) 0 0
\(701\) −43.0618 −1.62642 −0.813212 0.581968i \(-0.802283\pi\)
−0.813212 + 0.581968i \(0.802283\pi\)
\(702\) 0 0
\(703\) 24.6158i 0.928403i
\(704\) 0 0
\(705\) 9.37117 29.4842i 0.352939 1.11044i
\(706\) 0 0
\(707\) −26.7928 15.4688i −1.00765 0.581764i
\(708\) 0 0
\(709\) 3.53982 2.04372i 0.132941 0.0767535i −0.432055 0.901847i \(-0.642211\pi\)
0.564996 + 0.825094i \(0.308878\pi\)
\(710\) 0 0
\(711\) 28.5046 + 2.62642i 1.06900 + 0.0984985i
\(712\) 0 0
\(713\) −71.9166 + 41.5211i −2.69330 + 1.55498i
\(714\) 0 0
\(715\) −5.65321 + 9.79165i −0.211418 + 0.366187i
\(716\) 0 0
\(717\) −28.4223 31.1615i −1.06145 1.16375i
\(718\) 0 0
\(719\) 19.1644 0.714711 0.357355 0.933968i \(-0.383678\pi\)
0.357355 + 0.933968i \(0.383678\pi\)
\(720\) 0 0
\(721\) −7.65153 −0.284958
\(722\) 0 0
\(723\) −0.170912 + 0.0374768i −0.00635629 + 0.00139378i
\(724\) 0 0
\(725\) −24.0446 + 41.6464i −0.892992 + 1.54671i
\(726\) 0 0
\(727\) −19.9992 + 11.5465i −0.741728 + 0.428237i −0.822697 0.568480i \(-0.807532\pi\)
0.0809695 + 0.996717i \(0.474198\pi\)
\(728\) 0 0
\(729\) 7.34847 25.9808i 0.272166 0.962250i
\(730\) 0 0
\(731\) −10.5698 + 6.10246i −0.390937 + 0.225708i
\(732\) 0 0
\(733\) 19.2902 + 11.1372i 0.712501 + 0.411363i 0.811986 0.583676i \(-0.198386\pi\)
−0.0994853 + 0.995039i \(0.531720\pi\)
\(734\) 0 0
\(735\) −4.10950 + 0.901113i −0.151581 + 0.0332380i
\(736\) 0 0
\(737\) 28.6663i 1.05594i
\(738\) 0 0
\(739\) 6.18977 0.227694 0.113847 0.993498i \(-0.463683\pi\)
0.113847 + 0.993498i \(0.463683\pi\)
\(740\) 0 0
\(741\) −7.07965 + 6.45732i −0.260077 + 0.237215i
\(742\) 0 0
\(743\) 2.39555 4.14921i 0.0878841 0.152220i −0.818732 0.574175i \(-0.805323\pi\)
0.906617 + 0.421955i \(0.138656\pi\)
\(744\) 0 0
\(745\) −10.0732 17.4473i −0.369054 0.639220i
\(746\) 0 0
\(747\) 6.64951 + 0.612688i 0.243293 + 0.0224171i
\(748\) 0 0
\(749\) 15.2892 + 26.4816i 0.558653 + 0.967616i
\(750\) 0 0
\(751\) 40.2403 + 23.2328i 1.46839 + 0.847775i 0.999373 0.0354139i \(-0.0112750\pi\)
0.469017 + 0.883189i \(0.344608\pi\)
\(752\) 0 0
\(753\) −14.4495 4.59259i −0.526569 0.167363i
\(754\) 0 0
\(755\) 56.1981i 2.04526i
\(756\) 0 0
\(757\) 37.4393i 1.36075i 0.732863 + 0.680376i \(0.238184\pi\)
−0.732863 + 0.680376i \(0.761816\pi\)
\(758\) 0 0
\(759\) 36.7680 + 11.6862i 1.33459 + 0.424183i
\(760\) 0 0
\(761\) −5.97219 3.44805i −0.216492 0.124992i 0.387833 0.921730i \(-0.373224\pi\)
−0.604325 + 0.796738i \(0.706557\pi\)
\(762\) 0 0
\(763\) 25.1539 + 43.5678i 0.910633 + 1.57726i
\(764\) 0 0
\(765\) −9.59329 20.8232i −0.346846 0.752864i
\(766\) 0 0
\(767\) 2.59314 + 4.49145i 0.0936328 + 0.162177i
\(768\) 0 0
\(769\) 3.60102 6.23715i 0.129856 0.224917i −0.793765 0.608225i \(-0.791882\pi\)
0.923621 + 0.383308i \(0.125215\pi\)
\(770\) 0 0
\(771\) 14.7020 13.4097i 0.529481 0.482937i
\(772\) 0 0
\(773\) −16.5883 −0.596639 −0.298320 0.954466i \(-0.596426\pi\)
−0.298320 + 0.954466i \(0.596426\pi\)
\(774\) 0 0
\(775\) 84.9120i 3.05013i
\(776\) 0 0
\(777\) 24.6742 5.41045i 0.885183 0.194099i
\(778\) 0 0
\(779\) 35.5939 + 20.5501i 1.27528 + 0.736285i
\(780\) 0 0
\(781\) 8.67076 5.00607i 0.310264 0.179131i
\(782\) 0 0
\(783\) −25.8670 10.9248i −0.924412 0.390422i
\(784\) 0 0
\(785\) 47.2423 27.2754i 1.68615 0.973500i
\(786\) 0 0
\(787\) 14.6490 25.3729i 0.522182 0.904446i −0.477485 0.878640i \(-0.658451\pi\)
0.999667 0.0258059i \(-0.00821519\pi\)
\(788\) 0 0
\(789\) 11.7493 2.57634i 0.418287 0.0917200i
\(790\) 0 0
\(791\) 10.8566 0.386015
\(792\) 0 0
\(793\) −1.40408 −0.0498604
\(794\) 0 0
\(795\) −39.7380 43.5678i −1.40936 1.54519i
\(796\) 0 0
\(797\) −4.37770 + 7.58240i −0.155066 + 0.268583i −0.933083 0.359661i \(-0.882892\pi\)
0.778017 + 0.628243i \(0.216226\pi\)
\(798\) 0 0
\(799\) 8.50542 4.91060i 0.300900 0.173725i
\(800\) 0 0
\(801\) −24.2474 + 34.2911i −0.856741 + 1.21162i
\(802\) 0 0
\(803\) 9.86230 5.69400i 0.348033 0.200937i
\(804\) 0 0
\(805\) −77.7259 44.8751i −2.73948 1.58164i
\(806\) 0 0
\(807\) 8.70301 27.3820i 0.306360 0.963891i
\(808\) 0 0
\(809\) 20.6417i 0.725725i −0.931843 0.362863i \(-0.881799\pi\)
0.931843 0.362863i \(-0.118201\pi\)
\(810\) 0 0
\(811\) −0.683648 −0.0240061 −0.0120031 0.999928i \(-0.503821\pi\)
−0.0120031 + 0.999928i \(0.503821\pi\)
\(812\) 0 0
\(813\) 18.2640 + 5.80500i 0.640548 + 0.203590i
\(814\) 0 0
\(815\) 21.3179 36.9237i 0.746734 1.29338i
\(816\) 0 0
\(817\) 13.8990 + 24.0737i 0.486264 + 0.842234i
\(818\) 0 0
\(819\) 8.02871 + 5.67716i 0.280546 + 0.198376i
\(820\) 0 0
\(821\) −11.8340 20.4970i −0.413008 0.715352i 0.582209 0.813039i \(-0.302189\pi\)
−0.995217 + 0.0976878i \(0.968855\pi\)
\(822\) 0 0
\(823\) 27.4278 + 15.8354i 0.956073 + 0.551989i 0.894962 0.446142i \(-0.147202\pi\)
0.0611107 + 0.998131i \(0.480536\pi\)
\(824\) 0 0
\(825\) −29.1464 + 26.5843i −1.01475 + 0.925548i
\(826\) 0 0
\(827\) 3.63487i 0.126397i 0.998001 + 0.0631983i \(0.0201301\pi\)
−0.998001 + 0.0631983i \(0.979870\pi\)
\(828\) 0 0
\(829\) 28.7318i 0.997895i −0.866632 0.498948i \(-0.833720\pi\)
0.866632 0.498948i \(-0.166280\pi\)
\(830\) 0 0
\(831\) −7.18664 32.7745i −0.249302 1.13694i
\(832\) 0 0
\(833\) −1.15663 0.667783i −0.0400750 0.0231373i
\(834\) 0 0
\(835\) 23.5151 + 40.7293i 0.813772 + 1.40949i
\(836\) 0 0
\(837\) 49.1999 6.13116i 1.70060 0.211924i
\(838\) 0 0
\(839\) 11.9777 + 20.7461i 0.413517 + 0.716233i 0.995272 0.0971315i \(-0.0309667\pi\)
−0.581754 + 0.813365i \(0.697633\pi\)
\(840\) 0 0
\(841\) −0.101021 + 0.174973i −0.00348347 + 0.00603354i
\(842\) 0 0
\(843\) −0.825383 3.76414i −0.0284277 0.129644i
\(844\) 0 0
\(845\) 43.2311 1.48720
\(846\) 0 0
\(847\) 12.3079i 0.422905i
\(848\) 0 0
\(849\) −7.50000 8.22282i −0.257399 0.282207i
\(850\) 0 0
\(851\) 39.7380 + 22.9428i 1.36220 + 0.786468i
\(852\) 0 0
\(853\) 46.6863 26.9544i 1.59851 0.922900i 0.606734 0.794905i \(-0.292479\pi\)
0.991775 0.127995i \(-0.0408540\pi\)
\(854\) 0 0
\(855\) −47.4270 + 21.8497i −1.62197 + 0.747243i
\(856\) 0 0
\(857\) −4.67934 + 2.70162i −0.159843 + 0.0922855i −0.577788 0.816187i \(-0.696084\pi\)
0.417945 + 0.908472i \(0.362751\pi\)
\(858\) 0 0
\(859\) 1.74485 3.02218i 0.0595337 0.103115i −0.834722 0.550671i \(-0.814372\pi\)
0.894256 + 0.447555i \(0.147705\pi\)
\(860\) 0 0
\(861\) 12.7755 40.1951i 0.435388 1.36985i
\(862\) 0 0
\(863\) −17.4060 −0.592508 −0.296254 0.955109i \(-0.595737\pi\)
−0.296254 + 0.955109i \(0.595737\pi\)
\(864\) 0 0
\(865\) 13.8990 0.472579
\(866\) 0 0
\(867\) −6.71442 + 21.1253i −0.228034 + 0.717454i
\(868\) 0 0
\(869\) 12.2106 21.1494i 0.414216 0.717443i
\(870\) 0 0
\(871\) −11.4937 + 6.63591i −0.389450 + 0.224849i
\(872\) 0 0
\(873\) −0.949490 + 10.3048i −0.0321354 + 0.348765i
\(874\) 0 0
\(875\) 34.8215 20.1042i 1.17718 0.679646i
\(876\) 0 0
\(877\) 27.4997 + 15.8770i 0.928600 + 0.536128i 0.886369 0.462980i \(-0.153220\pi\)
0.0422317 + 0.999108i \(0.486553\pi\)
\(878\) 0 0
\(879\) 4.35150 + 4.77089i 0.146773 + 0.160918i
\(880\) 0 0
\(881\) 24.0416i 0.809983i 0.914320 + 0.404992i \(0.132726\pi\)
−0.914320 + 0.404992i \(0.867274\pi\)
\(882\) 0 0
\(883\) −13.0632 −0.439611 −0.219806 0.975544i \(-0.570542\pi\)
−0.219806 + 0.975544i \(0.570542\pi\)
\(884\) 0 0
\(885\) 6.05346 + 27.6067i 0.203485 + 0.927988i
\(886\) 0 0
\(887\) −20.8783 + 36.1623i −0.701026 + 1.21421i 0.267081 + 0.963674i \(0.413941\pi\)
−0.968107 + 0.250538i \(0.919392\pi\)
\(888\) 0 0
\(889\) 7.65153 + 13.2528i 0.256624 + 0.444486i
\(890\) 0 0
\(891\) −17.5081 14.9686i −0.586544 0.501465i
\(892\) 0 0
\(893\) −11.1844 19.3719i −0.374272 0.648258i
\(894\) 0 0
\(895\) −40.4823 23.3725i −1.35317 0.781256i
\(896\) 0 0
\(897\) 3.82577 + 17.4473i 0.127739 + 0.582549i
\(898\) 0 0
\(899\) 51.5627i 1.71971i
\(900\) 0 0
\(901\) 18.7196i 0.623641i
\(902\) 0 0
\(903\) 21.0759 19.2233i 0.701363 0.639710i
\(904\) 0 0
\(905\) 32.3258 + 18.6633i 1.07454 + 0.620389i
\(906\) 0 0
\(907\) −23.7509 41.1377i −0.788635 1.36596i −0.926803 0.375547i \(-0.877455\pi\)
0.138168 0.990409i \(-0.455878\pi\)
\(908\) 0 0
\(909\) −3.07856 + 33.4117i −0.102110 + 1.10820i
\(910\) 0 0
\(911\) 1.31877 + 2.28418i 0.0436929 + 0.0756783i 0.887045 0.461683i \(-0.152754\pi\)
−0.843352 + 0.537362i \(0.819421\pi\)
\(912\) 0 0
\(913\) 2.84847 4.93369i 0.0942706 0.163281i
\(914\) 0 0
\(915\) −7.29207 2.31769i −0.241068 0.0766205i
\(916\) 0 0
\(917\) 50.8947 1.68069
\(918\) 0 0
\(919\) 35.6804i 1.17699i 0.808502 + 0.588494i \(0.200279\pi\)
−0.808502 + 0.588494i \(0.799721\pi\)
\(920\) 0 0
\(921\) 4.89898 15.4135i 0.161427 0.507892i
\(922\) 0 0
\(923\) 4.01436 + 2.31769i 0.132134 + 0.0762877i
\(924\) 0 0
\(925\) −40.6329 + 23.4594i −1.33600 + 0.771340i
\(926\) 0 0
\(927\) 3.47232 + 7.53703i 0.114046 + 0.247548i
\(928\) 0 0
\(929\) 21.0278 12.1404i 0.689900 0.398314i −0.113675 0.993518i \(-0.536262\pi\)
0.803575 + 0.595204i \(0.202929\pi\)
\(930\) 0 0
\(931\) −1.52094 + 2.63435i −0.0498469 + 0.0863373i
\(932\) 0 0
\(933\) −12.2106 13.3874i −0.399757 0.438284i
\(934\) 0 0
\(935\) −19.5596 −0.639666
\(936\) 0 0
\(937\) −2.85357 −0.0932221 −0.0466111 0.998913i \(-0.514842\pi\)
−0.0466111 + 0.998913i \(0.514842\pi\)
\(938\) 0 0
\(939\) −9.98022 + 2.18841i −0.325692 + 0.0714162i
\(940\) 0 0
\(941\) 7.26796 12.5885i 0.236929 0.410372i −0.722903 0.690950i \(-0.757193\pi\)
0.959831 + 0.280577i \(0.0905259\pi\)
\(942\) 0 0
\(943\) 66.3493 38.3068i 2.16063 1.24744i
\(944\) 0 0
\(945\) 32.3258 + 42.7370i 1.05156 + 1.39024i
\(946\) 0 0
\(947\) −26.3741 + 15.2271i −0.857044 + 0.494814i −0.863021 0.505168i \(-0.831431\pi\)
0.00597754 + 0.999982i \(0.498097\pi\)
\(948\) 0 0
\(949\) 4.56601 + 2.63619i 0.148219 + 0.0855743i
\(950\) 0 0
\(951\) −40.0427 + 8.78038i −1.29847 + 0.284723i
\(952\) 0 0
\(953\) 41.7121i 1.35119i 0.737274 + 0.675593i \(0.236113\pi\)
−0.737274 + 0.675593i \(0.763887\pi\)
\(954\) 0 0
\(955\) 47.0301 1.52186
\(956\) 0 0
\(957\) −17.6991 + 16.1433i −0.572131 + 0.521839i
\(958\) 0 0
\(959\) −18.7248 + 32.4323i −0.604655 + 1.04729i
\(960\) 0 0
\(961\) 30.0227 + 52.0008i 0.968474 + 1.67745i
\(962\) 0 0
\(963\) 19.1470 27.0779i 0.617002 0.872573i
\(964\) 0 0
\(965\) −47.0629 81.5154i −1.51501 2.62407i
\(966\) 0 0
\(967\) 15.2081 + 8.78038i 0.489058 + 0.282358i 0.724184 0.689607i \(-0.242217\pi\)
−0.235125 + 0.971965i \(0.575550\pi\)
\(968\) 0 0
\(969\) −15.7980 5.02118i −0.507504 0.161304i
\(970\) 0 0
\(971\) 49.5204i 1.58919i −0.607143 0.794593i \(-0.707684\pi\)
0.607143 0.794593i \(-0.292316\pi\)
\(972\) 0 0
\(973\) 29.3841i 0.942011i
\(974\) 0 0
\(975\) −17.4060 5.53228i −0.557439 0.177175i
\(976\) 0 0
\(977\) −5.05051 2.91591i −0.161580 0.0932883i 0.417029 0.908893i \(-0.363071\pi\)
−0.578610 + 0.815605i \(0.696405\pi\)
\(978\) 0 0
\(979\) 17.9148 + 31.0294i 0.572561 + 0.991704i
\(980\) 0 0
\(981\) 31.5008 44.5489i 1.00574 1.42234i
\(982\) 0 0
\(983\) 16.9664 + 29.3867i 0.541145 + 0.937290i 0.998839 + 0.0481806i \(0.0153423\pi\)
−0.457694 + 0.889110i \(0.651324\pi\)
\(984\) 0 0
\(985\) 6.24745 10.8209i 0.199060 0.344782i
\(986\) 0 0
\(987\) −16.9596 + 15.4688i −0.539831 + 0.492378i
\(988\) 0 0
\(989\) 51.8173 1.64769
\(990\) 0 0
\(991\) 2.48670i 0.0789927i −0.999220 0.0394964i \(-0.987425\pi\)
0.999220 0.0394964i \(-0.0125754\pi\)
\(992\) 0 0
\(993\) −13.8031 + 3.02667i −0.438027 + 0.0960485i
\(994\) 0 0
\(995\) −39.7380 22.9428i −1.25978 0.727335i
\(996\) 0 0
\(997\) −8.56710 + 4.94622i −0.271323 + 0.156648i −0.629489 0.777010i \(-0.716736\pi\)
0.358166 + 0.933658i \(0.383402\pi\)
\(998\) 0 0
\(999\) −16.5268 21.8497i −0.522886 0.691293i
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 1152.2.p.d.959.3 yes 16
3.2 odd 2 3456.2.p.d.2879.8 16
4.3 odd 2 inner 1152.2.p.d.959.5 yes 16
8.3 odd 2 inner 1152.2.p.d.959.4 yes 16
8.5 even 2 inner 1152.2.p.d.959.6 yes 16
9.2 odd 6 inner 1152.2.p.d.191.4 yes 16
9.7 even 3 3456.2.p.d.575.1 16
12.11 even 2 3456.2.p.d.2879.7 16
24.5 odd 2 3456.2.p.d.2879.2 16
24.11 even 2 3456.2.p.d.2879.1 16
36.7 odd 6 3456.2.p.d.575.2 16
36.11 even 6 inner 1152.2.p.d.191.6 yes 16
72.11 even 6 inner 1152.2.p.d.191.3 16
72.29 odd 6 inner 1152.2.p.d.191.5 yes 16
72.43 odd 6 3456.2.p.d.575.8 16
72.61 even 6 3456.2.p.d.575.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1152.2.p.d.191.3 16 72.11 even 6 inner
1152.2.p.d.191.4 yes 16 9.2 odd 6 inner
1152.2.p.d.191.5 yes 16 72.29 odd 6 inner
1152.2.p.d.191.6 yes 16 36.11 even 6 inner
1152.2.p.d.959.3 yes 16 1.1 even 1 trivial
1152.2.p.d.959.4 yes 16 8.3 odd 2 inner
1152.2.p.d.959.5 yes 16 4.3 odd 2 inner
1152.2.p.d.959.6 yes 16 8.5 even 2 inner
3456.2.p.d.575.1 16 9.7 even 3
3456.2.p.d.575.2 16 36.7 odd 6
3456.2.p.d.575.7 16 72.61 even 6
3456.2.p.d.575.8 16 72.43 odd 6
3456.2.p.d.2879.1 16 24.11 even 2
3456.2.p.d.2879.2 16 24.5 odd 2
3456.2.p.d.2879.7 16 12.11 even 2
3456.2.p.d.2879.8 16 3.2 odd 2