Properties

Label 756.2.b.e.55.5
Level $756$
Weight $2$
Character 756.55
Analytic conductor $6.037$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(55,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("756.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.b (of order \(2\), degree \(1\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.5
Root \(-0.748450 - 1.19993i\) of defining polynomial
Character \(\chi\) \(=\) 756.55
Dual form 756.2.b.e.55.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.748450 - 1.19993i) q^{2} +(-0.879646 + 1.79617i) q^{4} +3.90968i q^{5} +(-1.12924 + 2.39266i) q^{7} +(2.81364 - 0.288831i) q^{8} +O(q^{10})\) \(q+(-0.748450 - 1.19993i) q^{2} +(-0.879646 + 1.79617i) q^{4} +3.90968i q^{5} +(-1.12924 + 2.39266i) q^{7} +(2.81364 - 0.288831i) q^{8} +(4.69133 - 2.92620i) q^{10} +5.01901i q^{11} -5.59667i q^{13} +(3.71619 - 0.435784i) q^{14} +(-2.45244 - 3.15999i) q^{16} -2.41029i q^{17} -3.11590 q^{19} +(-7.02245 - 3.43914i) q^{20} +(6.02245 - 3.75648i) q^{22} +3.45254i q^{23} -10.2856 q^{25} +(-6.71560 + 4.18883i) q^{26} +(-3.30429 - 4.13300i) q^{28} -4.76986 q^{29} -0.482412 q^{31} +(-1.95622 + 5.30784i) q^{32} +(-2.89217 + 1.80398i) q^{34} +(-9.35454 - 4.41496i) q^{35} +5.90489 q^{37} +(2.33209 + 3.73885i) q^{38} +(1.12924 + 11.0004i) q^{40} +1.51033i q^{41} -1.77561i q^{43} +(-9.01499 - 4.41496i) q^{44} +(4.14280 - 2.58406i) q^{46} -2.38630 q^{47} +(-4.44965 - 5.40376i) q^{49} +(7.69825 + 12.3420i) q^{50} +(10.0526 + 4.92309i) q^{52} +5.62728 q^{53} -19.6227 q^{55} +(-2.48619 + 7.05825i) q^{56} +(3.57000 + 5.72348i) q^{58} -6.38071 q^{59} -6.94384i q^{61} +(0.361061 + 0.578859i) q^{62} +(7.83315 - 1.62533i) q^{64} +21.8812 q^{65} +3.92062i q^{67} +(4.32929 + 2.12021i) q^{68} +(1.70378 + 14.5291i) q^{70} -8.25225i q^{71} +3.59159i q^{73} +(-4.41951 - 7.08543i) q^{74} +(2.74089 - 5.59667i) q^{76} +(-12.0088 - 5.66766i) q^{77} +9.32969i q^{79} +(12.3545 - 9.58827i) q^{80} +(1.81228 - 1.13040i) q^{82} +5.76701 q^{83} +9.42347 q^{85} +(-2.13060 + 1.32895i) q^{86} +(1.44965 + 14.1217i) q^{88} +17.6553i q^{89} +(13.3909 + 6.31997i) q^{91} +(-6.20135 - 3.03702i) q^{92} +(1.78603 + 2.86339i) q^{94} -12.1822i q^{95} +15.5685i q^{97} +(-3.15378 + 9.38369i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{14} + 4 q^{16} - 26 q^{20} + 10 q^{22} - 20 q^{25} - 6 q^{26} - 11 q^{28} - 6 q^{35} + 8 q^{37} - 20 q^{38} - 6 q^{46} - 8 q^{47} - 14 q^{49} + 21 q^{56} + 14 q^{58} - 44 q^{59} + 48 q^{62} + 24 q^{64} - 2 q^{68} - 27 q^{70} + 54 q^{80} + 4 q^{83} + 8 q^{85} - 34 q^{88} - 47 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.748450 1.19993i −0.529234 0.848476i
\(3\) 0 0
\(4\) −0.879646 + 1.79617i −0.439823 + 0.898084i
\(5\) 3.90968i 1.74846i 0.485510 + 0.874231i \(0.338634\pi\)
−0.485510 + 0.874231i \(0.661366\pi\)
\(6\) 0 0
\(7\) −1.12924 + 2.39266i −0.426812 + 0.904341i
\(8\) 2.81364 0.288831i 0.994772 0.102117i
\(9\) 0 0
\(10\) 4.69133 2.92620i 1.48353 0.925345i
\(11\) 5.01901i 1.51329i 0.653826 + 0.756645i \(0.273163\pi\)
−0.653826 + 0.756645i \(0.726837\pi\)
\(12\) 0 0
\(13\) 5.59667i 1.55224i −0.630586 0.776119i \(-0.717186\pi\)
0.630586 0.776119i \(-0.282814\pi\)
\(14\) 3.71619 0.435784i 0.993194 0.116468i
\(15\) 0 0
\(16\) −2.45244 3.15999i −0.613111 0.789997i
\(17\) 2.41029i 0.584582i −0.956329 0.292291i \(-0.905582\pi\)
0.956329 0.292291i \(-0.0944176\pi\)
\(18\) 0 0
\(19\) −3.11590 −0.714836 −0.357418 0.933945i \(-0.616343\pi\)
−0.357418 + 0.933945i \(0.616343\pi\)
\(20\) −7.02245 3.43914i −1.57027 0.769014i
\(21\) 0 0
\(22\) 6.02245 3.75648i 1.28399 0.800884i
\(23\) 3.45254i 0.719905i 0.932971 + 0.359953i \(0.117207\pi\)
−0.932971 + 0.359953i \(0.882793\pi\)
\(24\) 0 0
\(25\) −10.2856 −2.05712
\(26\) −6.71560 + 4.18883i −1.31704 + 0.821497i
\(27\) 0 0
\(28\) −3.30429 4.13300i −0.624453 0.781063i
\(29\) −4.76986 −0.885741 −0.442870 0.896586i \(-0.646040\pi\)
−0.442870 + 0.896586i \(0.646040\pi\)
\(30\) 0 0
\(31\) −0.482412 −0.0866437 −0.0433219 0.999061i \(-0.513794\pi\)
−0.0433219 + 0.999061i \(0.513794\pi\)
\(32\) −1.95622 + 5.30784i −0.345814 + 0.938303i
\(33\) 0 0
\(34\) −2.89217 + 1.80398i −0.496004 + 0.309381i
\(35\) −9.35454 4.41496i −1.58121 0.746264i
\(36\) 0 0
\(37\) 5.90489 0.970758 0.485379 0.874304i \(-0.338682\pi\)
0.485379 + 0.874304i \(0.338682\pi\)
\(38\) 2.33209 + 3.73885i 0.378315 + 0.606521i
\(39\) 0 0
\(40\) 1.12924 + 11.0004i 0.178548 + 1.73932i
\(41\) 1.51033i 0.235873i 0.993021 + 0.117937i \(0.0376280\pi\)
−0.993021 + 0.117937i \(0.962372\pi\)
\(42\) 0 0
\(43\) 1.77561i 0.270778i −0.990793 0.135389i \(-0.956772\pi\)
0.990793 0.135389i \(-0.0432284\pi\)
\(44\) −9.01499 4.41496i −1.35906 0.665580i
\(45\) 0 0
\(46\) 4.14280 2.58406i 0.610822 0.380998i
\(47\) −2.38630 −0.348078 −0.174039 0.984739i \(-0.555682\pi\)
−0.174039 + 0.984739i \(0.555682\pi\)
\(48\) 0 0
\(49\) −4.44965 5.40376i −0.635664 0.771966i
\(50\) 7.69825 + 12.3420i 1.08870 + 1.74542i
\(51\) 0 0
\(52\) 10.0526 + 4.92309i 1.39404 + 0.682710i
\(53\) 5.62728 0.772967 0.386483 0.922296i \(-0.373690\pi\)
0.386483 + 0.922296i \(0.373690\pi\)
\(54\) 0 0
\(55\) −19.6227 −2.64593
\(56\) −2.48619 + 7.05825i −0.332232 + 0.943198i
\(57\) 0 0
\(58\) 3.57000 + 5.72348i 0.468764 + 0.751530i
\(59\) −6.38071 −0.830697 −0.415349 0.909662i \(-0.636340\pi\)
−0.415349 + 0.909662i \(0.636340\pi\)
\(60\) 0 0
\(61\) 6.94384i 0.889067i −0.895762 0.444534i \(-0.853369\pi\)
0.895762 0.444534i \(-0.146631\pi\)
\(62\) 0.361061 + 0.578859i 0.0458548 + 0.0735151i
\(63\) 0 0
\(64\) 7.83315 1.62533i 0.979144 0.203167i
\(65\) 21.8812 2.71403
\(66\) 0 0
\(67\) 3.92062i 0.478980i 0.970899 + 0.239490i \(0.0769802\pi\)
−0.970899 + 0.239490i \(0.923020\pi\)
\(68\) 4.32929 + 2.12021i 0.525004 + 0.257113i
\(69\) 0 0
\(70\) 1.70378 + 14.5291i 0.203640 + 1.73656i
\(71\) 8.25225i 0.979362i −0.871902 0.489681i \(-0.837113\pi\)
0.871902 0.489681i \(-0.162887\pi\)
\(72\) 0 0
\(73\) 3.59159i 0.420364i 0.977662 + 0.210182i \(0.0674057\pi\)
−0.977662 + 0.210182i \(0.932594\pi\)
\(74\) −4.41951 7.08543i −0.513758 0.823665i
\(75\) 0 0
\(76\) 2.74089 5.59667i 0.314401 0.641983i
\(77\) −12.0088 5.66766i −1.36853 0.645889i
\(78\) 0 0
\(79\) 9.32969i 1.04967i 0.851203 + 0.524836i \(0.175873\pi\)
−0.851203 + 0.524836i \(0.824127\pi\)
\(80\) 12.3545 9.58827i 1.38128 1.07200i
\(81\) 0 0
\(82\) 1.81228 1.13040i 0.200133 0.124832i
\(83\) 5.76701 0.633012 0.316506 0.948591i \(-0.397490\pi\)
0.316506 + 0.948591i \(0.397490\pi\)
\(84\) 0 0
\(85\) 9.42347 1.02212
\(86\) −2.13060 + 1.32895i −0.229748 + 0.143305i
\(87\) 0 0
\(88\) 1.44965 + 14.1217i 0.154533 + 1.50538i
\(89\) 17.6553i 1.87146i 0.352722 + 0.935728i \(0.385256\pi\)
−0.352722 + 0.935728i \(0.614744\pi\)
\(90\) 0 0
\(91\) 13.3909 + 6.31997i 1.40375 + 0.662513i
\(92\) −6.20135 3.03702i −0.646536 0.316631i
\(93\) 0 0
\(94\) 1.78603 + 2.86339i 0.184215 + 0.295336i
\(95\) 12.1822i 1.24986i
\(96\) 0 0
\(97\) 15.5685i 1.58074i 0.612630 + 0.790370i \(0.290112\pi\)
−0.612630 + 0.790370i \(0.709888\pi\)
\(98\) −3.15378 + 9.38369i −0.318580 + 0.947896i
\(99\) 0 0
\(100\) 9.04769 18.4747i 0.904769 1.84747i
\(101\) 5.42001i 0.539311i −0.962957 0.269655i \(-0.913090\pi\)
0.962957 0.269655i \(-0.0869098\pi\)
\(102\) 0 0
\(103\) −4.89196 −0.482019 −0.241009 0.970523i \(-0.577478\pi\)
−0.241009 + 0.970523i \(0.577478\pi\)
\(104\) −1.61649 15.7470i −0.158510 1.54412i
\(105\) 0 0
\(106\) −4.21174 6.75232i −0.409080 0.655844i
\(107\) 12.4743i 1.20594i 0.797766 + 0.602968i \(0.206015\pi\)
−0.797766 + 0.602968i \(0.793985\pi\)
\(108\) 0 0
\(109\) 5.90489 0.565586 0.282793 0.959181i \(-0.408739\pi\)
0.282793 + 0.959181i \(0.408739\pi\)
\(110\) 14.6866 + 23.5458i 1.40031 + 2.24501i
\(111\) 0 0
\(112\) 10.3302 2.29949i 0.976109 0.217282i
\(113\) −15.3353 −1.44262 −0.721311 0.692611i \(-0.756460\pi\)
−0.721311 + 0.692611i \(0.756460\pi\)
\(114\) 0 0
\(115\) −13.4983 −1.25873
\(116\) 4.19579 8.56748i 0.389569 0.795470i
\(117\) 0 0
\(118\) 4.77564 + 7.65638i 0.439633 + 0.704827i
\(119\) 5.76701 + 2.72179i 0.528661 + 0.249506i
\(120\) 0 0
\(121\) −14.1905 −1.29004
\(122\) −8.33209 + 5.19711i −0.754352 + 0.470524i
\(123\) 0 0
\(124\) 0.424352 0.866493i 0.0381079 0.0778134i
\(125\) 20.6650i 1.84833i
\(126\) 0 0
\(127\) 0.910906i 0.0808298i 0.999183 + 0.0404149i \(0.0128680\pi\)
−0.999183 + 0.0404149i \(0.987132\pi\)
\(128\) −7.81300 8.18273i −0.690578 0.723258i
\(129\) 0 0
\(130\) −16.3770 26.2558i −1.43636 2.30279i
\(131\) 15.9421 1.39286 0.696432 0.717623i \(-0.254770\pi\)
0.696432 + 0.717623i \(0.254770\pi\)
\(132\) 0 0
\(133\) 3.51859 7.45528i 0.305100 0.646455i
\(134\) 4.70445 2.93439i 0.406403 0.253492i
\(135\) 0 0
\(136\) −0.696168 6.78170i −0.0596959 0.581526i
\(137\) −0.627922 −0.0536470 −0.0268235 0.999640i \(-0.508539\pi\)
−0.0268235 + 0.999640i \(0.508539\pi\)
\(138\) 0 0
\(139\) −17.3643 −1.47282 −0.736409 0.676537i \(-0.763480\pi\)
−0.736409 + 0.676537i \(0.763480\pi\)
\(140\) 16.1587 12.9187i 1.36566 1.09183i
\(141\) 0 0
\(142\) −9.90209 + 6.17639i −0.830965 + 0.518311i
\(143\) 28.0898 2.34899
\(144\) 0 0
\(145\) 18.6486i 1.54868i
\(146\) 4.30965 2.68813i 0.356669 0.222471i
\(147\) 0 0
\(148\) −5.19421 + 10.6062i −0.426962 + 0.871822i
\(149\) −0.726607 −0.0595259 −0.0297630 0.999557i \(-0.509475\pi\)
−0.0297630 + 0.999557i \(0.509475\pi\)
\(150\) 0 0
\(151\) 6.27377i 0.510552i 0.966868 + 0.255276i \(0.0821663\pi\)
−0.966868 + 0.255276i \(0.917834\pi\)
\(152\) −8.76701 + 0.899968i −0.711099 + 0.0729970i
\(153\) 0 0
\(154\) 2.18721 + 18.6516i 0.176250 + 1.50299i
\(155\) 1.88608i 0.151493i
\(156\) 0 0
\(157\) 19.9958i 1.59584i 0.602765 + 0.797919i \(0.294066\pi\)
−0.602765 + 0.797919i \(0.705934\pi\)
\(158\) 11.1949 6.98280i 0.890621 0.555522i
\(159\) 0 0
\(160\) −20.7520 7.64819i −1.64059 0.604643i
\(161\) −8.26077 3.89874i −0.651040 0.307264i
\(162\) 0 0
\(163\) 18.0490i 1.41371i −0.707360 0.706854i \(-0.750114\pi\)
0.707360 0.706854i \(-0.249886\pi\)
\(164\) −2.71280 1.32855i −0.211834 0.103743i
\(165\) 0 0
\(166\) −4.31632 6.91999i −0.335011 0.537095i
\(167\) −19.7035 −1.52470 −0.762350 0.647164i \(-0.775955\pi\)
−0.762350 + 0.647164i \(0.775955\pi\)
\(168\) 0 0
\(169\) −18.3228 −1.40944
\(170\) −7.05300 11.3075i −0.540940 0.867244i
\(171\) 0 0
\(172\) 3.18929 + 1.56191i 0.243181 + 0.119094i
\(173\) 0.621296i 0.0472363i −0.999721 0.0236181i \(-0.992481\pi\)
0.999721 0.0236181i \(-0.00751859\pi\)
\(174\) 0 0
\(175\) 11.6149 24.6099i 0.878002 1.86034i
\(176\) 15.8600 12.3089i 1.19549 0.927815i
\(177\) 0 0
\(178\) 21.1850 13.2141i 1.58789 0.990438i
\(179\) 12.1294i 0.906591i 0.891360 + 0.453296i \(0.149752\pi\)
−0.891360 + 0.453296i \(0.850248\pi\)
\(180\) 0 0
\(181\) 21.5510i 1.60187i −0.598750 0.800936i \(-0.704336\pi\)
0.598750 0.800936i \(-0.295664\pi\)
\(182\) −2.43894 20.7983i −0.180787 1.54167i
\(183\) 0 0
\(184\) 0.997202 + 9.71422i 0.0735147 + 0.716142i
\(185\) 23.0862i 1.69733i
\(186\) 0 0
\(187\) 12.0973 0.884642
\(188\) 2.09910 4.28620i 0.153093 0.312604i
\(189\) 0 0
\(190\) −14.6177 + 9.11773i −1.06048 + 0.661470i
\(191\) 12.3487i 0.893519i 0.894654 + 0.446759i \(0.147422\pi\)
−0.894654 + 0.446759i \(0.852578\pi\)
\(192\) 0 0
\(193\) 18.0526 1.29946 0.649728 0.760167i \(-0.274883\pi\)
0.649728 + 0.760167i \(0.274883\pi\)
\(194\) 18.6810 11.6522i 1.34122 0.836581i
\(195\) 0 0
\(196\) 13.6202 3.23892i 0.972870 0.231351i
\(197\) 6.84502 0.487687 0.243844 0.969815i \(-0.421592\pi\)
0.243844 + 0.969815i \(0.421592\pi\)
\(198\) 0 0
\(199\) 12.4174 0.880246 0.440123 0.897937i \(-0.354935\pi\)
0.440123 + 0.897937i \(0.354935\pi\)
\(200\) −28.9400 + 2.97080i −2.04637 + 0.210067i
\(201\) 0 0
\(202\) −6.50361 + 4.05660i −0.457592 + 0.285421i
\(203\) 5.38630 11.4127i 0.378044 0.801011i
\(204\) 0 0
\(205\) −5.90489 −0.412415
\(206\) 3.66138 + 5.86999i 0.255101 + 0.408982i
\(207\) 0 0
\(208\) −17.6854 + 13.7255i −1.22626 + 0.951695i
\(209\) 15.6387i 1.08175i
\(210\) 0 0
\(211\) 20.0194i 1.37819i 0.724671 + 0.689095i \(0.241992\pi\)
−0.724671 + 0.689095i \(0.758008\pi\)
\(212\) −4.95002 + 10.1075i −0.339969 + 0.694189i
\(213\) 0 0
\(214\) 14.9682 9.33638i 1.02321 0.638222i
\(215\) 6.94206 0.473445
\(216\) 0 0
\(217\) 0.544757 1.15425i 0.0369805 0.0783555i
\(218\) −4.41951 7.08543i −0.299327 0.479886i
\(219\) 0 0
\(220\) 17.2611 35.2457i 1.16374 2.37627i
\(221\) −13.4896 −0.907410
\(222\) 0 0
\(223\) 26.3982 1.76775 0.883876 0.467722i \(-0.154925\pi\)
0.883876 + 0.467722i \(0.154925\pi\)
\(224\) −10.4908 10.6744i −0.700948 0.713212i
\(225\) 0 0
\(226\) 11.4777 + 18.4012i 0.763484 + 1.22403i
\(227\) −2.00560 −0.133116 −0.0665580 0.997783i \(-0.521202\pi\)
−0.0665580 + 0.997783i \(0.521202\pi\)
\(228\) 0 0
\(229\) 14.3991i 0.951520i −0.879575 0.475760i \(-0.842173\pi\)
0.879575 0.475760i \(-0.157827\pi\)
\(230\) 10.1028 + 16.1970i 0.666161 + 1.06800i
\(231\) 0 0
\(232\) −13.4207 + 1.37768i −0.881111 + 0.0904494i
\(233\) −12.6031 −0.825658 −0.412829 0.910809i \(-0.635459\pi\)
−0.412829 + 0.910809i \(0.635459\pi\)
\(234\) 0 0
\(235\) 9.32969i 0.608602i
\(236\) 5.61277 11.4608i 0.365360 0.746036i
\(237\) 0 0
\(238\) −1.05037 8.95711i −0.0680852 0.580604i
\(239\) 2.58274i 0.167064i −0.996505 0.0835319i \(-0.973380\pi\)
0.996505 0.0835319i \(-0.0266201\pi\)
\(240\) 0 0
\(241\) 9.63816i 0.620848i 0.950598 + 0.310424i \(0.100471\pi\)
−0.950598 + 0.310424i \(0.899529\pi\)
\(242\) 10.6209 + 17.0275i 0.682735 + 1.09457i
\(243\) 0 0
\(244\) 12.4723 + 6.10812i 0.798457 + 0.391032i
\(245\) 21.1270 17.3967i 1.34975 1.11143i
\(246\) 0 0
\(247\) 17.4387i 1.10960i
\(248\) −1.35733 + 0.139336i −0.0861908 + 0.00884782i
\(249\) 0 0
\(250\) −24.7965 + 15.4667i −1.56827 + 0.978201i
\(251\) −12.9421 −0.816896 −0.408448 0.912782i \(-0.633930\pi\)
−0.408448 + 0.912782i \(0.633930\pi\)
\(252\) 0 0
\(253\) −17.3284 −1.08942
\(254\) 1.09302 0.681767i 0.0685822 0.0427779i
\(255\) 0 0
\(256\) −3.97103 + 15.4994i −0.248189 + 0.968712i
\(257\) 19.7541i 1.23223i 0.787658 + 0.616113i \(0.211294\pi\)
−0.787658 + 0.616113i \(0.788706\pi\)
\(258\) 0 0
\(259\) −6.66802 + 14.1284i −0.414331 + 0.877896i
\(260\) −19.2477 + 39.3023i −1.19369 + 2.43743i
\(261\) 0 0
\(262\) −11.9318 19.1293i −0.737151 1.18181i
\(263\) 4.77439i 0.294401i −0.989107 0.147201i \(-0.952974\pi\)
0.989107 0.147201i \(-0.0470263\pi\)
\(264\) 0 0
\(265\) 22.0009i 1.35150i
\(266\) −11.5793 + 1.35786i −0.709971 + 0.0832557i
\(267\) 0 0
\(268\) −7.04209 3.44876i −0.430164 0.210666i
\(269\) 2.19366i 0.133750i 0.997761 + 0.0668750i \(0.0213029\pi\)
−0.997761 + 0.0668750i \(0.978697\pi\)
\(270\) 0 0
\(271\) 12.5797 0.764163 0.382081 0.924129i \(-0.375207\pi\)
0.382081 + 0.924129i \(0.375207\pi\)
\(272\) −7.61649 + 5.91111i −0.461818 + 0.358414i
\(273\) 0 0
\(274\) 0.469968 + 0.753460i 0.0283918 + 0.0455182i
\(275\) 51.6235i 3.11302i
\(276\) 0 0
\(277\) 21.7035 1.30404 0.652018 0.758204i \(-0.273923\pi\)
0.652018 + 0.758204i \(0.273923\pi\)
\(278\) 12.9963 + 20.8358i 0.779465 + 1.24965i
\(279\) 0 0
\(280\) −27.5955 9.72022i −1.64915 0.580894i
\(281\) 18.2595 1.08927 0.544635 0.838673i \(-0.316668\pi\)
0.544635 + 0.838673i \(0.316668\pi\)
\(282\) 0 0
\(283\) 4.88324 0.290279 0.145139 0.989411i \(-0.453637\pi\)
0.145139 + 0.989411i \(0.453637\pi\)
\(284\) 14.8224 + 7.25906i 0.879550 + 0.430746i
\(285\) 0 0
\(286\) −21.0238 33.7057i −1.24316 1.99306i
\(287\) −3.61370 1.70552i −0.213310 0.100673i
\(288\) 0 0
\(289\) 11.1905 0.658264
\(290\) −22.3770 + 13.9576i −1.31402 + 0.819616i
\(291\) 0 0
\(292\) −6.45111 3.15933i −0.377522 0.184886i
\(293\) 15.2450i 0.890622i −0.895376 0.445311i \(-0.853093\pi\)
0.895376 0.445311i \(-0.146907\pi\)
\(294\) 0 0
\(295\) 24.9465i 1.45244i
\(296\) 16.6142 1.70552i 0.965683 0.0991311i
\(297\) 0 0
\(298\) 0.543828 + 0.871874i 0.0315031 + 0.0505063i
\(299\) 19.3228 1.11746
\(300\) 0 0
\(301\) 4.24843 + 2.00508i 0.244875 + 0.115571i
\(302\) 7.52806 4.69560i 0.433191 0.270201i
\(303\) 0 0
\(304\) 7.64156 + 9.84619i 0.438274 + 0.564718i
\(305\) 27.1482 1.55450
\(306\) 0 0
\(307\) −6.30173 −0.359659 −0.179829 0.983698i \(-0.557555\pi\)
−0.179829 + 0.983698i \(0.557555\pi\)
\(308\) 20.7436 16.5843i 1.18197 0.944977i
\(309\) 0 0
\(310\) −2.26315 + 1.41163i −0.128538 + 0.0801754i
\(311\) −18.4761 −1.04768 −0.523841 0.851816i \(-0.675502\pi\)
−0.523841 + 0.851816i \(0.675502\pi\)
\(312\) 0 0
\(313\) 18.7951i 1.06236i 0.847258 + 0.531181i \(0.178252\pi\)
−0.847258 + 0.531181i \(0.821748\pi\)
\(314\) 23.9935 14.9658i 1.35403 0.844571i
\(315\) 0 0
\(316\) −16.7577 8.20682i −0.942694 0.461670i
\(317\) −2.06678 −0.116082 −0.0580410 0.998314i \(-0.518485\pi\)
−0.0580410 + 0.998314i \(0.518485\pi\)
\(318\) 0 0
\(319\) 23.9400i 1.34038i
\(320\) 6.35454 + 30.6251i 0.355229 + 1.71200i
\(321\) 0 0
\(322\) 1.50456 + 12.8303i 0.0838461 + 0.715006i
\(323\) 7.51022i 0.417880i
\(324\) 0 0
\(325\) 57.5651i 3.19314i
\(326\) −21.6575 + 13.5088i −1.19950 + 0.748182i
\(327\) 0 0
\(328\) 0.436229 + 4.24951i 0.0240867 + 0.234640i
\(329\) 2.69470 5.70962i 0.148564 0.314781i
\(330\) 0 0
\(331\) 31.2531i 1.71783i −0.512121 0.858913i \(-0.671140\pi\)
0.512121 0.858913i \(-0.328860\pi\)
\(332\) −5.07293 + 10.3585i −0.278413 + 0.568498i
\(333\) 0 0
\(334\) 14.7471 + 23.6427i 0.806923 + 1.29367i
\(335\) −15.3284 −0.837478
\(336\) 0 0
\(337\) 14.4550 0.787417 0.393708 0.919235i \(-0.371192\pi\)
0.393708 + 0.919235i \(0.371192\pi\)
\(338\) 13.7137 + 21.9860i 0.745925 + 1.19588i
\(339\) 0 0
\(340\) −8.28932 + 16.9262i −0.449552 + 0.917949i
\(341\) 2.42123i 0.131117i
\(342\) 0 0
\(343\) 17.9541 4.54436i 0.969429 0.245373i
\(344\) −0.512851 4.99592i −0.0276511 0.269362i
\(345\) 0 0
\(346\) −0.745510 + 0.465009i −0.0400789 + 0.0249990i
\(347\) 16.6510i 0.893871i 0.894566 + 0.446936i \(0.147485\pi\)
−0.894566 + 0.446936i \(0.852515\pi\)
\(348\) 0 0
\(349\) 17.0294i 0.911561i 0.890092 + 0.455781i \(0.150640\pi\)
−0.890092 + 0.455781i \(0.849360\pi\)
\(350\) −38.2233 + 4.48230i −2.04312 + 0.239589i
\(351\) 0 0
\(352\) −26.6401 9.81829i −1.41992 0.523317i
\(353\) 26.9850i 1.43627i 0.695906 + 0.718133i \(0.255003\pi\)
−0.695906 + 0.718133i \(0.744997\pi\)
\(354\) 0 0
\(355\) 32.2637 1.71238
\(356\) −31.7119 15.5304i −1.68073 0.823110i
\(357\) 0 0
\(358\) 14.5543 9.07822i 0.769221 0.479799i
\(359\) 12.9242i 0.682112i 0.940043 + 0.341056i \(0.110785\pi\)
−0.940043 + 0.341056i \(0.889215\pi\)
\(360\) 0 0
\(361\) −9.29119 −0.489010
\(362\) −25.8596 + 16.1298i −1.35915 + 0.847765i
\(363\) 0 0
\(364\) −23.1310 + 18.4931i −1.21240 + 0.969299i
\(365\) −14.0420 −0.734991
\(366\) 0 0
\(367\) −33.8798 −1.76851 −0.884256 0.467003i \(-0.845334\pi\)
−0.884256 + 0.467003i \(0.845334\pi\)
\(368\) 10.9100 8.46717i 0.568723 0.441382i
\(369\) 0 0
\(370\) 27.7018 17.2789i 1.44015 0.898286i
\(371\) −6.35454 + 13.4642i −0.329911 + 0.699025i
\(372\) 0 0
\(373\) 14.1849 0.734466 0.367233 0.930129i \(-0.380305\pi\)
0.367233 + 0.930129i \(0.380305\pi\)
\(374\) −9.05421 14.5159i −0.468182 0.750597i
\(375\) 0 0
\(376\) −6.71420 + 0.689239i −0.346259 + 0.0355448i
\(377\) 26.6954i 1.37488i
\(378\) 0 0
\(379\) 10.5772i 0.543313i 0.962394 + 0.271657i \(0.0875715\pi\)
−0.962394 + 0.271657i \(0.912429\pi\)
\(380\) 21.8812 + 10.7160i 1.12248 + 0.549719i
\(381\) 0 0
\(382\) 14.8175 9.24236i 0.758129 0.472880i
\(383\) −15.1477 −0.774012 −0.387006 0.922077i \(-0.626491\pi\)
−0.387006 + 0.922077i \(0.626491\pi\)
\(384\) 0 0
\(385\) 22.1587 46.9505i 1.12931 2.39282i
\(386\) −13.5115 21.6618i −0.687716 1.10256i
\(387\) 0 0
\(388\) −27.9636 13.6948i −1.41964 0.695246i
\(389\) −28.1976 −1.42968 −0.714838 0.699290i \(-0.753500\pi\)
−0.714838 + 0.699290i \(0.753500\pi\)
\(390\) 0 0
\(391\) 8.32164 0.420844
\(392\) −14.0805 13.9191i −0.711172 0.703018i
\(393\) 0 0
\(394\) −5.12315 8.21352i −0.258101 0.413791i
\(395\) −36.4761 −1.83531
\(396\) 0 0
\(397\) 7.98758i 0.400885i 0.979705 + 0.200443i \(0.0642380\pi\)
−0.979705 + 0.200443i \(0.935762\pi\)
\(398\) −9.29380 14.9000i −0.465856 0.746868i
\(399\) 0 0
\(400\) 25.2249 + 32.5024i 1.26124 + 1.62512i
\(401\) −11.8129 −0.589908 −0.294954 0.955512i \(-0.595304\pi\)
−0.294954 + 0.955512i \(0.595304\pi\)
\(402\) 0 0
\(403\) 2.69990i 0.134492i
\(404\) 9.73524 + 4.76769i 0.484347 + 0.237201i
\(405\) 0 0
\(406\) −17.7257 + 2.07863i −0.879713 + 0.103161i
\(407\) 29.6367i 1.46904i
\(408\) 0 0
\(409\) 6.79736i 0.336108i 0.985778 + 0.168054i \(0.0537483\pi\)
−0.985778 + 0.168054i \(0.946252\pi\)
\(410\) 4.41951 + 7.08543i 0.218264 + 0.349925i
\(411\) 0 0
\(412\) 4.30319 8.78678i 0.212003 0.432894i
\(413\) 7.20533 15.2669i 0.354551 0.751233i
\(414\) 0 0
\(415\) 22.5472i 1.10680i
\(416\) 29.7063 + 10.9483i 1.45647 + 0.536786i
\(417\) 0 0
\(418\) −18.7653 + 11.7048i −0.917841 + 0.572500i
\(419\) 15.7091 0.767438 0.383719 0.923450i \(-0.374643\pi\)
0.383719 + 0.923450i \(0.374643\pi\)
\(420\) 0 0
\(421\) 12.0154 0.585597 0.292798 0.956174i \(-0.405414\pi\)
0.292798 + 0.956174i \(0.405414\pi\)
\(422\) 24.0218 14.9835i 1.16936 0.729385i
\(423\) 0 0
\(424\) 15.8332 1.62533i 0.768926 0.0789332i
\(425\) 24.7913i 1.20255i
\(426\) 0 0
\(427\) 16.6142 + 7.84124i 0.804019 + 0.379464i
\(428\) −22.4059 10.9730i −1.08303 0.530398i
\(429\) 0 0
\(430\) −5.19578 8.32996i −0.250563 0.401706i
\(431\) 10.0380i 0.483515i −0.970337 0.241757i \(-0.922276\pi\)
0.970337 0.241757i \(-0.0777238\pi\)
\(432\) 0 0
\(433\) 25.7389i 1.23693i 0.785811 + 0.618467i \(0.212246\pi\)
−0.785811 + 0.618467i \(0.787754\pi\)
\(434\) −1.79274 + 0.210228i −0.0860541 + 0.0100912i
\(435\) 0 0
\(436\) −5.19421 + 10.6062i −0.248758 + 0.507944i
\(437\) 10.7578i 0.514614i
\(438\) 0 0
\(439\) 28.6653 1.36812 0.684061 0.729425i \(-0.260212\pi\)
0.684061 + 0.729425i \(0.260212\pi\)
\(440\) −55.2113 + 5.66766i −2.63210 + 0.270195i
\(441\) 0 0
\(442\) 10.0963 + 16.1866i 0.480232 + 0.769916i
\(443\) 3.16702i 0.150470i −0.997166 0.0752348i \(-0.976029\pi\)
0.997166 0.0752348i \(-0.0239706\pi\)
\(444\) 0 0
\(445\) −69.0265 −3.27217
\(446\) −19.7577 31.6758i −0.935554 1.49989i
\(447\) 0 0
\(448\) −4.95662 + 20.5775i −0.234178 + 0.972194i
\(449\) 32.1416 1.51685 0.758427 0.651758i \(-0.225968\pi\)
0.758427 + 0.651758i \(0.225968\pi\)
\(450\) 0 0
\(451\) −7.58034 −0.356944
\(452\) 13.4896 27.5448i 0.634499 1.29560i
\(453\) 0 0
\(454\) 1.50109 + 2.40657i 0.0704495 + 0.112946i
\(455\) −24.7091 + 52.3543i −1.15838 + 2.45441i
\(456\) 0 0
\(457\) 20.4389 0.956092 0.478046 0.878335i \(-0.341345\pi\)
0.478046 + 0.878335i \(0.341345\pi\)
\(458\) −17.2779 + 10.7770i −0.807342 + 0.503577i
\(459\) 0 0
\(460\) 11.8738 24.2453i 0.553617 1.13044i
\(461\) 6.14287i 0.286102i −0.989715 0.143051i \(-0.954309\pi\)
0.989715 0.143051i \(-0.0456913\pi\)
\(462\) 0 0
\(463\) 2.13162i 0.0990649i −0.998773 0.0495324i \(-0.984227\pi\)
0.998773 0.0495324i \(-0.0157731\pi\)
\(464\) 11.6978 + 15.0727i 0.543058 + 0.699732i
\(465\) 0 0
\(466\) 9.43280 + 15.1228i 0.436966 + 0.700551i
\(467\) −11.4817 −0.531309 −0.265654 0.964068i \(-0.585588\pi\)
−0.265654 + 0.964068i \(0.585588\pi\)
\(468\) 0 0
\(469\) −9.38071 4.42731i −0.433161 0.204434i
\(470\) −11.1949 + 6.98280i −0.516384 + 0.322093i
\(471\) 0 0
\(472\) −17.9530 + 1.84295i −0.826355 + 0.0848285i
\(473\) 8.91180 0.409765
\(474\) 0 0
\(475\) 32.0489 1.47050
\(476\) −9.96173 + 7.96431i −0.456595 + 0.365044i
\(477\) 0 0
\(478\) −3.09910 + 1.93305i −0.141750 + 0.0884159i
\(479\) 14.3863 0.657327 0.328664 0.944447i \(-0.393402\pi\)
0.328664 + 0.944447i \(0.393402\pi\)
\(480\) 0 0
\(481\) 33.0477i 1.50685i
\(482\) 11.5651 7.21368i 0.526775 0.328574i
\(483\) 0 0
\(484\) 12.4826 25.4885i 0.567391 1.15857i
\(485\) −60.8678 −2.76386
\(486\) 0 0
\(487\) 20.3888i 0.923904i 0.886905 + 0.461952i \(0.152851\pi\)
−0.886905 + 0.461952i \(0.847149\pi\)
\(488\) −2.00560 19.5375i −0.0907890 0.884419i
\(489\) 0 0
\(490\) −36.6872 12.3303i −1.65736 0.557025i
\(491\) 19.9296i 0.899409i 0.893177 + 0.449705i \(0.148471\pi\)
−0.893177 + 0.449705i \(0.851529\pi\)
\(492\) 0 0
\(493\) 11.4968i 0.517788i
\(494\) 20.9251 13.0520i 0.941465 0.587235i
\(495\) 0 0
\(496\) 1.18309 + 1.52442i 0.0531222 + 0.0684483i
\(497\) 19.7448 + 9.31875i 0.885677 + 0.418003i
\(498\) 0 0
\(499\) 7.62706i 0.341434i −0.985320 0.170717i \(-0.945392\pi\)
0.985320 0.170717i \(-0.0546084\pi\)
\(500\) 37.1178 + 18.1779i 1.65996 + 0.812940i
\(501\) 0 0
\(502\) 9.68648 + 15.5295i 0.432329 + 0.693116i
\(503\) 30.4761 1.35886 0.679431 0.733740i \(-0.262227\pi\)
0.679431 + 0.733740i \(0.262227\pi\)
\(504\) 0 0
\(505\) 21.1905 0.942964
\(506\) 12.9694 + 20.7928i 0.576560 + 0.924351i
\(507\) 0 0
\(508\) −1.63614 0.801275i −0.0725920 0.0355508i
\(509\) 6.22512i 0.275923i −0.990438 0.137962i \(-0.955945\pi\)
0.990438 0.137962i \(-0.0440551\pi\)
\(510\) 0 0
\(511\) −8.59346 4.05576i −0.380152 0.179416i
\(512\) 21.5702 6.83557i 0.953279 0.302092i
\(513\) 0 0
\(514\) 23.7035 14.7849i 1.04551 0.652136i
\(515\) 19.1260i 0.842792i
\(516\) 0 0
\(517\) 11.9769i 0.526743i
\(518\) 21.9437 2.57326i 0.964151 0.113062i
\(519\) 0 0
\(520\) 61.5659 6.31997i 2.69984 0.277149i
\(521\) 4.99769i 0.218953i −0.993989 0.109476i \(-0.965083\pi\)
0.993989 0.109476i \(-0.0349174\pi\)
\(522\) 0 0
\(523\) −4.95318 −0.216587 −0.108294 0.994119i \(-0.534539\pi\)
−0.108294 + 0.994119i \(0.534539\pi\)
\(524\) −14.0234 + 28.6346i −0.612614 + 1.25091i
\(525\) 0 0
\(526\) −5.72891 + 3.57339i −0.249792 + 0.155807i
\(527\) 1.16275i 0.0506504i
\(528\) 0 0
\(529\) 11.0799 0.481736
\(530\) 26.3994 16.4665i 1.14672 0.715261i
\(531\) 0 0
\(532\) 10.2958 + 12.8780i 0.446381 + 0.558331i
\(533\) 8.45280 0.366131
\(534\) 0 0
\(535\) −48.7705 −2.10853
\(536\) 1.13240 + 11.0312i 0.0489121 + 0.476476i
\(537\) 0 0
\(538\) 2.63224 1.64185i 0.113484 0.0707851i
\(539\) 27.1215 22.3328i 1.16821 0.961943i
\(540\) 0 0
\(541\) −31.8044 −1.36738 −0.683690 0.729773i \(-0.739626\pi\)
−0.683690 + 0.729773i \(0.739626\pi\)
\(542\) −9.41527 15.0947i −0.404421 0.648374i
\(543\) 0 0
\(544\) 12.7935 + 4.71506i 0.548515 + 0.202157i
\(545\) 23.0862i 0.988905i
\(546\) 0 0
\(547\) 40.9363i 1.75031i −0.483844 0.875154i \(-0.660760\pi\)
0.483844 0.875154i \(-0.339240\pi\)
\(548\) 0.552349 1.12785i 0.0235952 0.0481795i
\(549\) 0 0
\(550\) −61.9445 + 38.6376i −2.64132 + 1.64751i
\(551\) 14.8624 0.633159
\(552\) 0 0
\(553\) −22.3228 10.5354i −0.949261 0.448012i
\(554\) −16.2440 26.0426i −0.690140 1.10644i
\(555\) 0 0
\(556\) 15.2744 31.1891i 0.647779 1.32271i
\(557\) −13.9112 −0.589435 −0.294717 0.955584i \(-0.595226\pi\)
−0.294717 + 0.955584i \(0.595226\pi\)
\(558\) 0 0
\(559\) −9.93750 −0.420312
\(560\) 8.99028 + 40.3876i 0.379909 + 1.70669i
\(561\) 0 0
\(562\) −13.6663 21.9100i −0.576478 0.924219i
\(563\) 37.5659 1.58321 0.791606 0.611032i \(-0.209245\pi\)
0.791606 + 0.611032i \(0.209245\pi\)
\(564\) 0 0
\(565\) 59.9561i 2.52237i
\(566\) −3.65486 5.85953i −0.153625 0.246294i
\(567\) 0 0
\(568\) −2.38351 23.2189i −0.100010 0.974242i
\(569\) 4.83108 0.202529 0.101265 0.994860i \(-0.467711\pi\)
0.101265 + 0.994860i \(0.467711\pi\)
\(570\) 0 0
\(571\) 35.4877i 1.48511i −0.669784 0.742556i \(-0.733613\pi\)
0.669784 0.742556i \(-0.266387\pi\)
\(572\) −24.7091 + 50.4540i −1.03314 + 2.10959i
\(573\) 0 0
\(574\) 0.658176 + 5.61266i 0.0274717 + 0.234268i
\(575\) 35.5115i 1.48093i
\(576\) 0 0
\(577\) 10.9331i 0.455153i 0.973760 + 0.227576i \(0.0730801\pi\)
−0.973760 + 0.227576i \(0.926920\pi\)
\(578\) −8.37552 13.4278i −0.348376 0.558521i
\(579\) 0 0
\(580\) 33.4961 + 16.4042i 1.39085 + 0.681147i
\(581\) −6.51232 + 13.7985i −0.270177 + 0.572458i
\(582\) 0 0
\(583\) 28.2434i 1.16972i
\(584\) 1.03736 + 10.1055i 0.0429264 + 0.418167i
\(585\) 0 0
\(586\) −18.2929 + 11.4101i −0.755671 + 0.471347i
\(587\) −12.1477 −0.501390 −0.250695 0.968066i \(-0.580659\pi\)
−0.250695 + 0.968066i \(0.580659\pi\)
\(588\) 0 0
\(589\) 1.50315 0.0619360
\(590\) −29.9340 + 18.6712i −1.23236 + 0.768682i
\(591\) 0 0
\(592\) −14.4814 18.6594i −0.595182 0.766895i
\(593\) 2.60504i 0.106976i −0.998568 0.0534882i \(-0.982966\pi\)
0.998568 0.0534882i \(-0.0170339\pi\)
\(594\) 0 0
\(595\) −10.6413 + 22.5472i −0.436252 + 0.924344i
\(596\) 0.639157 1.30511i 0.0261809 0.0534593i
\(597\) 0 0
\(598\) −14.4621 23.1859i −0.591400 0.948142i
\(599\) 34.5554i 1.41190i −0.708263 0.705948i \(-0.750521\pi\)
0.708263 0.705948i \(-0.249479\pi\)
\(600\) 0 0
\(601\) 12.3627i 0.504286i −0.967690 0.252143i \(-0.918865\pi\)
0.967690 0.252143i \(-0.0811353\pi\)
\(602\) −0.773782 6.59850i −0.0315370 0.268935i
\(603\) 0 0
\(604\) −11.2687 5.51870i −0.458519 0.224553i
\(605\) 55.4803i 2.25559i
\(606\) 0 0
\(607\) 3.43840 0.139560 0.0697802 0.997562i \(-0.477770\pi\)
0.0697802 + 0.997562i \(0.477770\pi\)
\(608\) 6.09538 16.5387i 0.247200 0.670732i
\(609\) 0 0
\(610\) −20.3190 32.5758i −0.822694 1.31896i
\(611\) 13.3554i 0.540300i
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 4.71653 + 7.56161i 0.190344 + 0.305162i
\(615\) 0 0
\(616\) −35.4254 12.4782i −1.42733 0.502762i
\(617\) 38.7921 1.56171 0.780856 0.624710i \(-0.214783\pi\)
0.780856 + 0.624710i \(0.214783\pi\)
\(618\) 0 0
\(619\) −38.0592 −1.52973 −0.764865 0.644191i \(-0.777194\pi\)
−0.764865 + 0.644191i \(0.777194\pi\)
\(620\) 3.38771 + 1.65908i 0.136054 + 0.0666303i
\(621\) 0 0
\(622\) 13.8284 + 22.1699i 0.554469 + 0.888934i
\(623\) −42.2431 19.9370i −1.69243 0.798759i
\(624\) 0 0
\(625\) 29.3655 1.17462
\(626\) 22.5527 14.0672i 0.901389 0.562238i
\(627\) 0 0
\(628\) −35.9158 17.5892i −1.43320 0.701886i
\(629\) 14.2325i 0.567487i
\(630\) 0 0
\(631\) 41.8076i 1.66434i −0.554524 0.832168i \(-0.687100\pi\)
0.554524 0.832168i \(-0.312900\pi\)
\(632\) 2.69470 + 26.2504i 0.107190 + 1.04418i
\(633\) 0 0
\(634\) 1.54688 + 2.47999i 0.0614345 + 0.0984928i
\(635\) −3.56135 −0.141328
\(636\) 0 0
\(637\) −30.2431 + 24.9032i −1.19828 + 0.986702i
\(638\) −28.7262 + 17.9179i −1.13728 + 0.709376i
\(639\) 0 0
\(640\) 31.9918 30.5463i 1.26459 1.20745i
\(641\) −29.5836 −1.16848 −0.584242 0.811580i \(-0.698608\pi\)
−0.584242 + 0.811580i \(0.698608\pi\)
\(642\) 0 0
\(643\) 34.8510 1.37439 0.687194 0.726474i \(-0.258842\pi\)
0.687194 + 0.726474i \(0.258842\pi\)
\(644\) 14.2694 11.4082i 0.562291 0.449547i
\(645\) 0 0
\(646\) 9.01171 5.62102i 0.354561 0.221156i
\(647\) −22.8512 −0.898373 −0.449187 0.893438i \(-0.648286\pi\)
−0.449187 + 0.893438i \(0.648286\pi\)
\(648\) 0 0
\(649\) 32.0249i 1.25709i
\(650\) 69.0739 43.0846i 2.70930 1.68992i
\(651\) 0 0
\(652\) 32.4191 + 15.8767i 1.26963 + 0.621781i
\(653\) 6.41751 0.251136 0.125568 0.992085i \(-0.459925\pi\)
0.125568 + 0.992085i \(0.459925\pi\)
\(654\) 0 0
\(655\) 62.3284i 2.43537i
\(656\) 4.77261 3.70399i 0.186339 0.144617i
\(657\) 0 0
\(658\) −8.86797 + 1.03991i −0.345709 + 0.0405401i
\(659\) 3.31350i 0.129076i −0.997915 0.0645378i \(-0.979443\pi\)
0.997915 0.0645378i \(-0.0205573\pi\)
\(660\) 0 0
\(661\) 26.3760i 1.02591i 0.858416 + 0.512954i \(0.171449\pi\)
−0.858416 + 0.512954i \(0.828551\pi\)
\(662\) −37.5014 + 23.3914i −1.45753 + 0.909132i
\(663\) 0 0
\(664\) 16.2263 1.66569i 0.629703 0.0646414i
\(665\) 29.1478 + 13.7565i 1.13030 + 0.533456i
\(666\) 0 0
\(667\) 16.4682i 0.637650i
\(668\) 17.3321 35.3908i 0.670599 1.36931i
\(669\) 0 0
\(670\) 11.4725 + 18.3929i 0.443222 + 0.710580i
\(671\) 34.8512 1.34542
\(672\) 0 0
\(673\) 20.4389 0.787862 0.393931 0.919140i \(-0.371115\pi\)
0.393931 + 0.919140i \(0.371115\pi\)
\(674\) −10.8189 17.3450i −0.416728 0.668104i
\(675\) 0 0
\(676\) 16.1176 32.9108i 0.619906 1.26580i
\(677\) 6.72464i 0.258449i 0.991615 + 0.129224i \(0.0412488\pi\)
−0.991615 + 0.129224i \(0.958751\pi\)
\(678\) 0 0
\(679\) −37.2501 17.5805i −1.42953 0.674678i
\(680\) 26.5143 2.72179i 1.01678 0.104376i
\(681\) 0 0
\(682\) −2.90530 + 1.81217i −0.111250 + 0.0693916i
\(683\) 10.7935i 0.413001i 0.978446 + 0.206501i \(0.0662075\pi\)
−0.978446 + 0.206501i \(0.933792\pi\)
\(684\) 0 0
\(685\) 2.45497i 0.0937997i
\(686\) −18.8906 18.1423i −0.721247 0.692678i
\(687\) 0 0
\(688\) −5.61090 + 4.35458i −0.213913 + 0.166017i
\(689\) 31.4941i 1.19983i
\(690\) 0 0
\(691\) −21.9337 −0.834398 −0.417199 0.908815i \(-0.636988\pi\)
−0.417199 + 0.908815i \(0.636988\pi\)
\(692\) 1.11595 + 0.546521i 0.0424222 + 0.0207756i
\(693\) 0 0
\(694\) 19.9799 12.4624i 0.758428 0.473067i
\(695\) 67.8887i 2.57517i
\(696\) 0 0
\(697\) 3.64033 0.137887
\(698\) 20.4340 12.7456i 0.773438 0.482429i
\(699\) 0 0
\(700\) 33.9866 + 42.5103i 1.28457 + 1.60674i
\(701\) 18.3612 0.693493 0.346747 0.937959i \(-0.387286\pi\)
0.346747 + 0.937959i \(0.387286\pi\)
\(702\) 0 0
\(703\) −18.3990 −0.693932
\(704\) 8.15757 + 39.3147i 0.307450 + 1.48173i
\(705\) 0 0
\(706\) 32.3800 20.1969i 1.21864 0.760120i
\(707\) 12.9682 + 6.12047i 0.487721 + 0.230184i
\(708\) 0 0
\(709\) −28.9463 −1.08710 −0.543551 0.839376i \(-0.682920\pi\)
−0.543551 + 0.839376i \(0.682920\pi\)
\(710\) −24.1477 38.7140i −0.906248 1.45291i
\(711\) 0 0
\(712\) 5.09940 + 49.6756i 0.191108 + 1.86167i
\(713\) 1.66555i 0.0623753i
\(714\) 0 0
\(715\) 109.822i 4.10711i
\(716\) −21.7864 10.6696i −0.814196 0.398740i
\(717\) 0 0
\(718\) 15.5081 9.67310i 0.578756 0.360997i
\(719\) 9.14772 0.341152 0.170576 0.985344i \(-0.445437\pi\)
0.170576 + 0.985344i \(0.445437\pi\)
\(720\) 0 0
\(721\) 5.52418 11.7048i 0.205731 0.435909i
\(722\) 6.95399 + 11.1487i 0.258801 + 0.414913i
\(723\) 0 0
\(724\) 38.7092 + 18.9572i 1.43862 + 0.704540i
\(725\) 49.0609 1.82208
\(726\) 0 0
\(727\) −14.7308 −0.546334 −0.273167 0.961967i \(-0.588071\pi\)
−0.273167 + 0.961967i \(0.588071\pi\)
\(728\) 39.5027 + 13.9144i 1.46407 + 0.515703i
\(729\) 0 0
\(730\) 10.5097 + 16.8493i 0.388982 + 0.623622i
\(731\) −4.27974 −0.158292
\(732\) 0 0
\(733\) 24.2453i 0.895521i 0.894154 + 0.447760i \(0.147778\pi\)
−0.894154 + 0.447760i \(0.852222\pi\)
\(734\) 25.3573 + 40.6533i 0.935956 + 1.50054i
\(735\) 0 0
\(736\) −18.3256 6.75394i −0.675489 0.248953i
\(737\) −19.6776 −0.724835
\(738\) 0 0
\(739\) 31.2993i 1.15136i 0.817674 + 0.575682i \(0.195263\pi\)
−0.817674 + 0.575682i \(0.804737\pi\)
\(740\) −41.4668 20.3077i −1.52435 0.746526i
\(741\) 0 0
\(742\) 20.9121 2.45228i 0.767706 0.0900261i
\(743\) 35.0388i 1.28545i 0.766098 + 0.642724i \(0.222196\pi\)
−0.766098 + 0.642724i \(0.777804\pi\)
\(744\) 0 0
\(745\) 2.84080i 0.104079i
\(746\) −10.6167 17.0208i −0.388704 0.623177i
\(747\) 0 0
\(748\) −10.6413 + 21.7288i −0.389086 + 0.794483i
\(749\) −29.8467 14.0864i −1.09058 0.514707i
\(750\) 0 0
\(751\) 12.7356i 0.464728i 0.972629 + 0.232364i \(0.0746460\pi\)
−0.972629 + 0.232364i \(0.925354\pi\)
\(752\) 5.85228 + 7.54069i 0.213411 + 0.274981i
\(753\) 0 0
\(754\) 32.0325 19.9801i 1.16655 0.727633i
\(755\) −24.5284 −0.892681
\(756\) 0 0
\(757\) −12.8565 −0.467278 −0.233639 0.972323i \(-0.575063\pi\)
−0.233639 + 0.972323i \(0.575063\pi\)
\(758\) 12.6918 7.91649i 0.460988 0.287540i
\(759\) 0 0
\(760\) −3.51859 34.2762i −0.127633 1.24333i
\(761\) 1.27182i 0.0461034i −0.999734 0.0230517i \(-0.992662\pi\)
0.999734 0.0230517i \(-0.00733824\pi\)
\(762\) 0 0
\(763\) −6.66802 + 14.1284i −0.241399 + 0.511482i
\(764\) −22.1803 10.8625i −0.802455 0.392990i
\(765\) 0 0
\(766\) 11.3373 + 18.1761i 0.409634 + 0.656731i
\(767\) 35.7108i 1.28944i
\(768\) 0 0
\(769\) 10.2961i 0.371286i −0.982617 0.185643i \(-0.940563\pi\)
0.982617 0.185643i \(-0.0594368\pi\)
\(770\) −72.9219 + 8.55128i −2.62792 + 0.308167i
\(771\) 0 0
\(772\) −15.8799 + 32.4255i −0.571531 + 1.16702i
\(773\) 32.7274i 1.17712i 0.808453 + 0.588561i \(0.200305\pi\)
−0.808453 + 0.588561i \(0.799695\pi\)
\(774\) 0 0
\(775\) 4.96190 0.178237
\(776\) 4.49666 + 43.8041i 0.161421 + 1.57248i
\(777\) 0 0
\(778\) 21.1045 + 33.8351i 0.756633 + 1.21305i
\(779\) 4.70602i 0.168611i
\(780\) 0 0
\(781\) 41.4181 1.48206
\(782\) −6.22833 9.98536i −0.222725 0.357076i
\(783\) 0 0
\(784\) −6.16330 + 27.3133i −0.220118 + 0.975473i
\(785\) −78.1771 −2.79026
\(786\) 0 0
\(787\) −7.89413 −0.281395 −0.140698 0.990053i \(-0.544935\pi\)
−0.140698 + 0.990053i \(0.544935\pi\)
\(788\) −6.02120 + 12.2948i −0.214496 + 0.437984i
\(789\) 0 0
\(790\) 27.3005 + 43.7686i 0.971309 + 1.55722i
\(791\) 17.3172 36.6921i 0.615728 1.30462i
\(792\) 0 0
\(793\) −38.8624 −1.38004
\(794\) 9.58451 5.97830i 0.340142 0.212162i
\(795\) 0 0
\(796\) −10.9229 + 22.3037i −0.387153 + 0.790535i
\(797\) 37.8578i 1.34099i −0.741913 0.670496i \(-0.766081\pi\)
0.741913 0.670496i \(-0.233919\pi\)
\(798\) 0 0
\(799\) 5.75169i 0.203480i
\(800\) 20.1209 54.5943i 0.711381 1.93020i
\(801\) 0 0
\(802\) 8.84135 + 14.1746i 0.312199 + 0.500522i
\(803\) −18.0262 −0.636132
\(804\) 0 0
\(805\) 15.2428 32.2970i 0.537239 1.13832i
\(806\) 3.23968 2.02074i 0.114113 0.0711776i
\(807\) 0 0
\(808\) −1.56547 15.2500i −0.0550729 0.536491i
\(809\) −20.6718 −0.726783 −0.363392 0.931636i \(-0.618381\pi\)
−0.363392 + 0.931636i \(0.618381\pi\)
\(810\) 0 0
\(811\) 3.86591 0.135751 0.0678753 0.997694i \(-0.478378\pi\)
0.0678753 + 0.997694i \(0.478378\pi\)
\(812\) 15.7610 + 19.7138i 0.553103 + 0.691819i
\(813\) 0 0
\(814\) 35.5619 22.1816i 1.24644 0.777464i
\(815\) 70.5659 2.47181
\(816\) 0 0
\(817\) 5.53261i 0.193562i
\(818\) 8.15633 5.08748i 0.285179 0.177880i
\(819\) 0 0
\(820\) 5.19421 10.6062i 0.181390 0.370384i
\(821\) 29.6449 1.03461 0.517306 0.855800i \(-0.326935\pi\)
0.517306 + 0.855800i \(0.326935\pi\)
\(822\) 0 0
\(823\) 27.7188i 0.966216i −0.875561 0.483108i \(-0.839508\pi\)
0.875561 0.483108i \(-0.160492\pi\)
\(824\) −13.7642 + 1.41295i −0.479499 + 0.0492224i
\(825\) 0 0
\(826\) −23.7119 + 2.78061i −0.825044 + 0.0967499i
\(827\) 42.1357i 1.46520i −0.680658 0.732601i \(-0.738306\pi\)
0.680658 0.732601i \(-0.261694\pi\)
\(828\) 0 0
\(829\) 41.5795i 1.44412i −0.691832 0.722058i \(-0.743196\pi\)
0.691832 0.722058i \(-0.256804\pi\)
\(830\) 27.0549 16.8754i 0.939091 0.585755i
\(831\) 0 0
\(832\) −9.09647 43.8396i −0.315363 1.51987i
\(833\) −13.0246 + 10.7250i −0.451277 + 0.371598i
\(834\) 0 0
\(835\) 77.0343i 2.66588i
\(836\) 28.0898 + 13.7565i 0.971505 + 0.475780i
\(837\) 0 0
\(838\) −11.7574 18.8497i −0.406154 0.651153i
\(839\) 40.2704 1.39029 0.695145 0.718870i \(-0.255340\pi\)
0.695145 + 0.718870i \(0.255340\pi\)
\(840\) 0 0
\(841\) −6.24843 −0.215463
\(842\) −8.99295 14.4176i −0.309918 0.496865i
\(843\) 0 0
\(844\) −35.9582 17.6100i −1.23773 0.606160i
\(845\) 71.6362i 2.46436i
\(846\) 0 0
\(847\) 16.0244 33.9530i 0.550606 1.16664i
\(848\) −13.8006 17.7821i −0.473915 0.610641i
\(849\) 0 0
\(850\) 29.7477 18.5550i 1.02034 0.636433i
\(851\) 20.3869i 0.698854i
\(852\) 0 0
\(853\) 28.2555i 0.967449i 0.875220 + 0.483724i \(0.160716\pi\)
−0.875220 + 0.483724i \(0.839284\pi\)
\(854\) −3.02601 25.8046i −0.103548 0.883016i
\(855\) 0 0
\(856\) 3.60296 + 35.0982i 0.123147 + 1.19963i
\(857\) 51.6638i 1.76480i 0.470499 + 0.882400i \(0.344074\pi\)
−0.470499 + 0.882400i \(0.655926\pi\)
\(858\) 0 0
\(859\) −40.9603 −1.39755 −0.698774 0.715343i \(-0.746271\pi\)
−0.698774 + 0.715343i \(0.746271\pi\)
\(860\) −6.10656 + 12.4691i −0.208232 + 0.425193i
\(861\) 0 0
\(862\) −12.0449 + 7.51296i −0.410251 + 0.255892i
\(863\) 51.1388i 1.74078i 0.492360 + 0.870392i \(0.336134\pi\)
−0.492360 + 0.870392i \(0.663866\pi\)
\(864\) 0 0
\(865\) 2.42907 0.0825909
\(866\) 30.8848 19.2643i 1.04951 0.654628i
\(867\) 0 0
\(868\) 1.59403 + 1.99381i 0.0541049 + 0.0676742i
\(869\) −46.8258 −1.58846
\(870\) 0 0
\(871\) 21.9424 0.743491
\(872\) 16.6142 1.70552i 0.562629 0.0577560i
\(873\) 0 0
\(874\) −12.9085 + 8.05165i −0.436638 + 0.272351i
\(875\) 49.4443 + 23.3357i 1.67152 + 0.788890i
\(876\) 0 0
\(877\) 15.5244 0.524223 0.262112 0.965038i \(-0.415581\pi\)
0.262112 + 0.965038i \(0.415581\pi\)
\(878\) −21.4546 34.3963i −0.724057 1.16082i
\(879\) 0 0
\(880\) 48.1237 + 62.0076i 1.62225 + 2.09027i
\(881\) 23.2196i 0.782287i 0.920330 + 0.391144i \(0.127920\pi\)
−0.920330 + 0.391144i \(0.872080\pi\)
\(882\) 0 0
\(883\) 5.98339i 0.201357i 0.994919 + 0.100678i \(0.0321013\pi\)
−0.994919 + 0.100678i \(0.967899\pi\)
\(884\) 11.8661 24.2296i 0.399100 0.814931i
\(885\) 0 0
\(886\) −3.80019 + 2.37035i −0.127670 + 0.0796336i
\(887\) −39.5090 −1.32658 −0.663291 0.748361i \(-0.730841\pi\)
−0.663291 + 0.748361i \(0.730841\pi\)
\(888\) 0 0
\(889\) −2.17949 1.02863i −0.0730977 0.0344991i
\(890\) 51.6629 + 82.8267i 1.73174 + 2.77636i
\(891\) 0 0
\(892\) −23.2210 + 47.4155i −0.777498 + 1.58759i
\(893\) 7.43547 0.248819
\(894\) 0 0
\(895\) −47.4219 −1.58514
\(896\) 28.4012 9.45362i 0.948818 0.315823i
\(897\) 0 0
\(898\) −24.0563 38.5675i −0.802770 1.28701i
\(899\) 2.30104 0.0767439
\(900\) 0 0
\(901\) 13.5634i 0.451862i
\(902\) 5.67350 + 9.09585i 0.188907 + 0.302859i
\(903\) 0 0
\(904\) −43.1480 + 4.42931i −1.43508 + 0.147317i
\(905\) 84.2574 2.80081
\(906\) 0 0
\(907\) 20.1580i 0.669335i −0.942336 0.334667i \(-0.891376\pi\)
0.942336 0.334667i \(-0.108624\pi\)
\(908\) 1.76421 3.60239i 0.0585475 0.119549i
\(909\) 0 0
\(910\) 81.3148 9.53549i 2.69556 0.316098i
\(911\) 20.5534i 0.680965i −0.940251 0.340482i \(-0.889410\pi\)
0.940251 0.340482i \(-0.110590\pi\)
\(912\) 0 0
\(913\) 28.9447i 0.957930i
\(914\) −15.2975 24.5252i −0.505996 0.811221i
\(915\) 0 0
\(916\) 25.8632 + 12.6661i 0.854546 + 0.418501i
\(917\) −18.0024 + 38.1439i −0.594491 + 1.25962i
\(918\) 0 0
\(919\) 54.4208i 1.79518i 0.440834 + 0.897588i \(0.354683\pi\)
−0.440834 + 0.897588i \(0.645317\pi\)
\(920\) −37.9795 + 3.89874i −1.25215 + 0.128538i
\(921\) 0 0
\(922\) −7.37099 + 4.59763i −0.242751 + 0.151415i
\(923\) −46.1852 −1.52020
\(924\) 0 0
\(925\) −60.7353 −1.99696
\(926\) −2.55779 + 1.59541i −0.0840542 + 0.0524285i
\(927\) 0 0
\(928\) 9.33090 25.3177i 0.306302 0.831093i
\(929\) 26.0631i 0.855103i −0.903991 0.427552i \(-0.859376\pi\)
0.903991 0.427552i \(-0.140624\pi\)
\(930\) 0 0
\(931\) 13.8646 + 16.8376i 0.454395 + 0.551829i
\(932\) 11.0863 22.6373i 0.363143 0.741510i
\(933\) 0 0
\(934\) 8.59346 + 13.7772i 0.281187 + 0.450803i
\(935\) 47.2965i 1.54676i
\(936\) 0 0
\(937\) 0.657922i 0.0214934i −0.999942 0.0107467i \(-0.996579\pi\)
0.999942 0.0107467i \(-0.00342084\pi\)
\(938\) 1.70854 + 14.5698i 0.0557859 + 0.475720i
\(939\) 0 0
\(940\) 16.7577 + 8.20682i 0.546576 + 0.267677i
\(941\) 39.3462i 1.28265i −0.767269 0.641325i \(-0.778385\pi\)
0.767269 0.641325i \(-0.221615\pi\)
\(942\) 0 0
\(943\) −5.21447 −0.169806
\(944\) 15.6483 + 20.1630i 0.509310 + 0.656248i
\(945\) 0 0
\(946\) −6.67003 10.6935i −0.216861 0.347676i
\(947\) 29.2121i 0.949267i 0.880184 + 0.474634i \(0.157419\pi\)
−0.880184 + 0.474634i \(0.842581\pi\)
\(948\) 0 0
\(949\) 20.1010 0.652505
\(950\) −23.9870 38.4563i −0.778239 1.24769i
\(951\) 0 0
\(952\) 17.0124 + 5.99245i 0.551376 + 0.194217i
\(953\) −0.0993268 −0.00321751 −0.00160876 0.999999i \(-0.500512\pi\)
−0.00160876 + 0.999999i \(0.500512\pi\)
\(954\) 0 0
\(955\) −48.2794 −1.56228
\(956\) 4.63905 + 2.27190i 0.150037 + 0.0734786i
\(957\) 0 0
\(958\) −10.7674 17.2625i −0.347880 0.557726i
\(959\) 0.709073 1.50240i 0.0228971 0.0485151i
\(960\) 0 0
\(961\) −30.7673 −0.992493
\(962\) −39.6549 + 24.7346i −1.27852 + 0.797475i
\(963\) 0 0
\(964\) −17.3118 8.47817i −0.557574 0.273063i
\(965\) 70.5799i 2.27205i
\(966\) 0 0
\(967\) 34.9194i 1.12293i −0.827500 0.561466i \(-0.810238\pi\)
0.827500 0.561466i \(-0.189762\pi\)
\(968\) −39.9269 + 4.09865i −1.28330 + 0.131736i
\(969\) 0 0
\(970\) 45.5565 + 73.0369i 1.46273 + 2.34507i
\(971\) 27.8736 0.894506 0.447253 0.894408i \(-0.352402\pi\)
0.447253 + 0.894408i \(0.352402\pi\)
\(972\) 0 0
\(973\) 19.6084 41.5468i 0.628615 1.33193i
\(974\) 24.4650 15.2600i 0.783910 0.488961i
\(975\) 0 0
\(976\) −21.9424 + 17.0294i −0.702360 + 0.545097i
\(977\) 6.42348 0.205505 0.102753 0.994707i \(-0.467235\pi\)
0.102753 + 0.994707i \(0.467235\pi\)
\(978\) 0 0
\(979\) −88.6121 −2.83205
\(980\) 12.6631 + 53.2506i 0.404509 + 1.70103i
\(981\) 0 0
\(982\) 23.9140 14.9163i 0.763127 0.475998i
\(983\) 16.8411 0.537147 0.268574 0.963259i \(-0.413448\pi\)
0.268574 + 0.963259i \(0.413448\pi\)
\(984\) 0 0
\(985\) 26.7618i 0.852703i
\(986\) 13.7953 8.60475i 0.439331 0.274031i
\(987\) 0 0
\(988\) −31.3228 15.3398i −0.996510 0.488026i
\(989\) 6.13037 0.194934
\(990\) 0 0
\(991\) 14.6792i 0.466299i −0.972441 0.233149i \(-0.925097\pi\)
0.972441 0.233149i \(-0.0749031\pi\)
\(992\) 0.943704 2.56057i 0.0299626 0.0812981i
\(993\) 0 0
\(994\) −3.59620 30.6670i −0.114065 0.972697i
\(995\) 48.5481i 1.53908i
\(996\) 0 0
\(997\) 25.0288i 0.792671i 0.918106 + 0.396336i \(0.129718\pi\)
−0.918106 + 0.396336i \(0.870282\pi\)
\(998\) −9.15191 + 5.70847i −0.289699 + 0.180698i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 756.2.b.e.55.5 16
3.2 odd 2 756.2.b.f.55.12 yes 16
4.3 odd 2 756.2.b.f.55.6 yes 16
7.6 odd 2 756.2.b.f.55.5 yes 16
12.11 even 2 inner 756.2.b.e.55.11 yes 16
21.20 even 2 inner 756.2.b.e.55.12 yes 16
28.27 even 2 inner 756.2.b.e.55.6 yes 16
84.83 odd 2 756.2.b.f.55.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.b.e.55.5 16 1.1 even 1 trivial
756.2.b.e.55.6 yes 16 28.27 even 2 inner
756.2.b.e.55.11 yes 16 12.11 even 2 inner
756.2.b.e.55.12 yes 16 21.20 even 2 inner
756.2.b.f.55.5 yes 16 7.6 odd 2
756.2.b.f.55.6 yes 16 4.3 odd 2
756.2.b.f.55.11 yes 16 84.83 odd 2
756.2.b.f.55.12 yes 16 3.2 odd 2