Properties

Label 756.2.be.c.107.6
Level $756$
Weight $2$
Character 756.107
Analytic conductor $6.037$
Analytic rank $0$
Dimension $28$
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(107,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.be (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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.6
Character \(\chi\) \(=\) 756.107
Dual form 756.2.be.c.431.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.253271 - 1.39135i) q^{2} +(-1.87171 + 0.704776i) q^{4} +(2.47695 + 1.43007i) q^{5} +(2.52686 + 0.784194i) q^{7} +(1.45464 + 2.42570i) q^{8} +O(q^{10})\) \(q+(-0.253271 - 1.39135i) q^{2} +(-1.87171 + 0.704776i) q^{4} +(2.47695 + 1.43007i) q^{5} +(2.52686 + 0.784194i) q^{7} +(1.45464 + 2.42570i) q^{8} +(1.36239 - 3.80850i) q^{10} +(0.887062 + 1.53644i) q^{11} -4.70960 q^{13} +(0.451108 - 3.71436i) q^{14} +(3.00658 - 2.63827i) q^{16} +(-6.08556 + 3.51350i) q^{17} +(6.93224 + 4.00233i) q^{19} +(-5.64401 - 0.930975i) q^{20} +(1.91305 - 1.62335i) q^{22} +(-2.46180 + 4.26396i) q^{23} +(1.59019 + 2.75429i) q^{25} +(1.19280 + 6.55270i) q^{26} +(-5.28223 + 0.313090i) q^{28} +7.21461i q^{29} +(1.31172 - 0.757322i) q^{31} +(-4.43223 - 3.51501i) q^{32} +(6.42980 + 7.57728i) q^{34} +(5.13747 + 5.55600i) q^{35} +(1.38862 - 2.40515i) q^{37} +(3.81291 - 10.6588i) q^{38} +(0.134149 + 8.08858i) q^{40} -4.94219i q^{41} -7.39300i q^{43} +(-2.74316 - 2.25058i) q^{44} +(6.55615 + 2.34528i) q^{46} +(2.78654 - 4.82642i) q^{47} +(5.77008 + 3.96310i) q^{49} +(3.42943 - 2.91009i) q^{50} +(8.81500 - 3.31921i) q^{52} +(-2.87828 + 1.66178i) q^{53} +5.07423i q^{55} +(1.77345 + 7.27014i) q^{56} +(10.0380 - 1.82725i) q^{58} +(-0.717330 - 1.24245i) q^{59} +(7.30221 - 12.6478i) q^{61} +(-1.38592 - 1.63325i) q^{62} +(-3.76805 + 7.05704i) q^{64} +(-11.6654 - 6.73505i) q^{65} +(-2.58315 + 1.49138i) q^{67} +(8.91416 - 10.8652i) q^{68} +(6.42917 - 8.55518i) q^{70} +11.4553 q^{71} +(0.0244370 + 0.0423261i) q^{73} +(-3.69810 - 1.32290i) q^{74} +(-15.7959 - 2.60552i) q^{76} +(1.03662 + 4.57799i) q^{77} +(1.15816 + 0.668665i) q^{79} +(11.2201 - 2.23525i) q^{80} +(-6.87631 + 1.25171i) q^{82} +9.02165 q^{83} -20.0982 q^{85} +(-10.2862 + 1.87243i) q^{86} +(-2.43658 + 4.38671i) q^{88} +(-5.61463 - 3.24161i) q^{89} +(-11.9005 - 3.69324i) q^{91} +(1.60263 - 9.71589i) q^{92} +(-7.42099 - 2.65465i) q^{94} +(11.4472 + 19.8271i) q^{95} -1.07208 q^{97} +(4.05267 - 9.03193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.253271 1.39135i −0.179089 0.983833i
\(3\) 0 0
\(4\) −1.87171 + 0.704776i −0.935854 + 0.352388i
\(5\) 2.47695 + 1.43007i 1.10773 + 0.639546i 0.938239 0.345987i \(-0.112456\pi\)
0.169487 + 0.985532i \(0.445789\pi\)
\(6\) 0 0
\(7\) 2.52686 + 0.784194i 0.955065 + 0.296398i
\(8\) 1.45464 + 2.42570i 0.514292 + 0.857615i
\(9\) 0 0
\(10\) 1.36239 3.80850i 0.430824 1.20435i
\(11\) 0.887062 + 1.53644i 0.267459 + 0.463253i 0.968205 0.250158i \(-0.0804826\pi\)
−0.700746 + 0.713411i \(0.747149\pi\)
\(12\) 0 0
\(13\) −4.70960 −1.30621 −0.653104 0.757268i \(-0.726534\pi\)
−0.653104 + 0.757268i \(0.726534\pi\)
\(14\) 0.451108 3.71436i 0.120564 0.992706i
\(15\) 0 0
\(16\) 3.00658 2.63827i 0.751645 0.659567i
\(17\) −6.08556 + 3.51350i −1.47597 + 0.852149i −0.999632 0.0271159i \(-0.991368\pi\)
−0.476333 + 0.879265i \(0.658034\pi\)
\(18\) 0 0
\(19\) 6.93224 + 4.00233i 1.59036 + 0.918197i 0.993244 + 0.116046i \(0.0370219\pi\)
0.597121 + 0.802152i \(0.296311\pi\)
\(20\) −5.64401 0.930975i −1.26204 0.208172i
\(21\) 0 0
\(22\) 1.91305 1.62335i 0.407864 0.346099i
\(23\) −2.46180 + 4.26396i −0.513320 + 0.889096i 0.486561 + 0.873647i \(0.338251\pi\)
−0.999881 + 0.0154494i \(0.995082\pi\)
\(24\) 0 0
\(25\) 1.59019 + 2.75429i 0.318038 + 0.550858i
\(26\) 1.19280 + 6.55270i 0.233928 + 1.28509i
\(27\) 0 0
\(28\) −5.28223 + 0.313090i −0.998248 + 0.0591684i
\(29\) 7.21461i 1.33972i 0.742487 + 0.669860i \(0.233646\pi\)
−0.742487 + 0.669860i \(0.766354\pi\)
\(30\) 0 0
\(31\) 1.31172 0.757322i 0.235592 0.136019i −0.377557 0.925986i \(-0.623236\pi\)
0.613149 + 0.789967i \(0.289903\pi\)
\(32\) −4.43223 3.51501i −0.783516 0.621372i
\(33\) 0 0
\(34\) 6.42980 + 7.57728i 1.10270 + 1.29949i
\(35\) 5.13747 + 5.55600i 0.868390 + 0.939135i
\(36\) 0 0
\(37\) 1.38862 2.40515i 0.228287 0.395405i −0.729013 0.684499i \(-0.760021\pi\)
0.957301 + 0.289095i \(0.0933542\pi\)
\(38\) 3.81291 10.6588i 0.618535 1.72909i
\(39\) 0 0
\(40\) 0.134149 + 8.08858i 0.0212109 + 1.27892i
\(41\) 4.94219i 0.771840i −0.922532 0.385920i \(-0.873884\pi\)
0.922532 0.385920i \(-0.126116\pi\)
\(42\) 0 0
\(43\) 7.39300i 1.12742i −0.825972 0.563711i \(-0.809373\pi\)
0.825972 0.563711i \(-0.190627\pi\)
\(44\) −2.74316 2.25058i −0.413547 0.339288i
\(45\) 0 0
\(46\) 6.55615 + 2.34528i 0.966652 + 0.345793i
\(47\) 2.78654 4.82642i 0.406458 0.704006i −0.588032 0.808838i \(-0.700097\pi\)
0.994490 + 0.104832i \(0.0334304\pi\)
\(48\) 0 0
\(49\) 5.77008 + 3.96310i 0.824297 + 0.566158i
\(50\) 3.42943 2.91009i 0.484995 0.411549i
\(51\) 0 0
\(52\) 8.81500 3.31921i 1.22242 0.460292i
\(53\) −2.87828 + 1.66178i −0.395362 + 0.228262i −0.684481 0.729031i \(-0.739971\pi\)
0.289119 + 0.957293i \(0.406638\pi\)
\(54\) 0 0
\(55\) 5.07423i 0.684210i
\(56\) 1.77345 + 7.27014i 0.236987 + 0.971513i
\(57\) 0 0
\(58\) 10.0380 1.82725i 1.31806 0.239930i
\(59\) −0.717330 1.24245i −0.0933884 0.161753i 0.815546 0.578692i \(-0.196436\pi\)
−0.908935 + 0.416938i \(0.863103\pi\)
\(60\) 0 0
\(61\) 7.30221 12.6478i 0.934952 1.61938i 0.160233 0.987079i \(-0.448775\pi\)
0.774719 0.632306i \(-0.217891\pi\)
\(62\) −1.38592 1.63325i −0.176012 0.207423i
\(63\) 0 0
\(64\) −3.76805 + 7.05704i −0.471007 + 0.882130i
\(65\) −11.6654 6.73505i −1.44692 0.835380i
\(66\) 0 0
\(67\) −2.58315 + 1.49138i −0.315582 + 0.182201i −0.649422 0.760428i \(-0.724989\pi\)
0.333840 + 0.942630i \(0.391656\pi\)
\(68\) 8.91416 10.8652i 1.08100 1.31760i
\(69\) 0 0
\(70\) 6.42917 8.55518i 0.768433 1.02254i
\(71\) 11.4553 1.35949 0.679747 0.733447i \(-0.262090\pi\)
0.679747 + 0.733447i \(0.262090\pi\)
\(72\) 0 0
\(73\) 0.0244370 + 0.0423261i 0.00286014 + 0.00495390i 0.867452 0.497521i \(-0.165756\pi\)
−0.864592 + 0.502475i \(0.832423\pi\)
\(74\) −3.69810 1.32290i −0.429896 0.153784i
\(75\) 0 0
\(76\) −15.7959 2.60552i −1.81191 0.298873i
\(77\) 1.03662 + 4.57799i 0.118134 + 0.521711i
\(78\) 0 0
\(79\) 1.15816 + 0.668665i 0.130303 + 0.0752307i 0.563735 0.825956i \(-0.309364\pi\)
−0.433431 + 0.901187i \(0.642697\pi\)
\(80\) 11.2201 2.23525i 1.25444 0.249908i
\(81\) 0 0
\(82\) −6.87631 + 1.25171i −0.759362 + 0.138228i
\(83\) 9.02165 0.990255 0.495128 0.868820i \(-0.335121\pi\)
0.495128 + 0.868820i \(0.335121\pi\)
\(84\) 0 0
\(85\) −20.0982 −2.17995
\(86\) −10.2862 + 1.87243i −1.10919 + 0.201909i
\(87\) 0 0
\(88\) −2.43658 + 4.38671i −0.259740 + 0.467624i
\(89\) −5.61463 3.24161i −0.595149 0.343610i 0.171982 0.985100i \(-0.444983\pi\)
−0.767131 + 0.641491i \(0.778316\pi\)
\(90\) 0 0
\(91\) −11.9005 3.69324i −1.24751 0.387157i
\(92\) 1.60263 9.71589i 0.167086 1.01295i
\(93\) 0 0
\(94\) −7.42099 2.65465i −0.765416 0.273807i
\(95\) 11.4472 + 19.8271i 1.17446 + 2.03422i
\(96\) 0 0
\(97\) −1.07208 −0.108853 −0.0544267 0.998518i \(-0.517333\pi\)
−0.0544267 + 0.998518i \(0.517333\pi\)
\(98\) 4.05267 9.03193i 0.409382 0.912363i
\(99\) 0 0
\(100\) −4.91753 4.03450i −0.491753 0.403450i
\(101\) 5.30278 3.06156i 0.527646 0.304637i −0.212411 0.977180i \(-0.568132\pi\)
0.740058 + 0.672544i \(0.234798\pi\)
\(102\) 0 0
\(103\) 6.18578 + 3.57136i 0.609503 + 0.351897i 0.772771 0.634685i \(-0.218870\pi\)
−0.163268 + 0.986582i \(0.552204\pi\)
\(104\) −6.85077 11.4241i −0.671773 1.12022i
\(105\) 0 0
\(106\) 3.04109 + 3.58382i 0.295377 + 0.348091i
\(107\) −1.29481 + 2.24267i −0.125174 + 0.216807i −0.921801 0.387664i \(-0.873282\pi\)
0.796627 + 0.604471i \(0.206615\pi\)
\(108\) 0 0
\(109\) −1.37701 2.38505i −0.131894 0.228447i 0.792513 0.609855i \(-0.208772\pi\)
−0.924407 + 0.381409i \(0.875439\pi\)
\(110\) 7.06004 1.28515i 0.673148 0.122535i
\(111\) 0 0
\(112\) 9.66614 4.30880i 0.913364 0.407144i
\(113\) 18.3520i 1.72641i 0.504854 + 0.863205i \(0.331546\pi\)
−0.504854 + 0.863205i \(0.668454\pi\)
\(114\) 0 0
\(115\) −12.1955 + 7.04107i −1.13724 + 0.656583i
\(116\) −5.08469 13.5036i −0.472101 1.25378i
\(117\) 0 0
\(118\) −1.54701 + 1.31273i −0.142413 + 0.120847i
\(119\) −18.1326 + 4.10587i −1.66222 + 0.376385i
\(120\) 0 0
\(121\) 3.92624 6.80045i 0.356931 0.618223i
\(122\) −19.4469 6.95661i −1.76064 0.629822i
\(123\) 0 0
\(124\) −1.92141 + 2.34195i −0.172548 + 0.210314i
\(125\) 5.20436i 0.465492i
\(126\) 0 0
\(127\) 8.18873i 0.726632i −0.931666 0.363316i \(-0.881645\pi\)
0.931666 0.363316i \(-0.118355\pi\)
\(128\) 10.7731 + 3.45534i 0.952220 + 0.305412i
\(129\) 0 0
\(130\) −6.41629 + 17.9365i −0.562746 + 1.57314i
\(131\) −0.153906 + 0.266573i −0.0134469 + 0.0232906i −0.872671 0.488309i \(-0.837614\pi\)
0.859224 + 0.511600i \(0.170947\pi\)
\(132\) 0 0
\(133\) 14.3782 + 15.5496i 1.24675 + 1.34832i
\(134\) 2.72927 + 3.21634i 0.235773 + 0.277850i
\(135\) 0 0
\(136\) −17.3750 9.65088i −1.48989 0.827556i
\(137\) 3.64686 2.10552i 0.311573 0.179887i −0.336057 0.941842i \(-0.609094\pi\)
0.647630 + 0.761955i \(0.275760\pi\)
\(138\) 0 0
\(139\) 10.5488i 0.894736i −0.894350 0.447368i \(-0.852361\pi\)
0.894350 0.447368i \(-0.147639\pi\)
\(140\) −13.5316 6.77844i −1.14363 0.572883i
\(141\) 0 0
\(142\) −2.90129 15.9383i −0.243471 1.33751i
\(143\) −4.17771 7.23600i −0.349357 0.605105i
\(144\) 0 0
\(145\) −10.3174 + 17.8702i −0.856813 + 1.48404i
\(146\) 0.0527013 0.0447204i 0.00436159 0.00370109i
\(147\) 0 0
\(148\) −0.903989 + 5.48041i −0.0743075 + 0.450487i
\(149\) 14.8380 + 8.56672i 1.21558 + 0.701813i 0.963969 0.266016i \(-0.0857075\pi\)
0.251607 + 0.967829i \(0.419041\pi\)
\(150\) 0 0
\(151\) 6.08270 3.51185i 0.495003 0.285790i −0.231645 0.972800i \(-0.574411\pi\)
0.726648 + 0.687010i \(0.241077\pi\)
\(152\) 0.375444 + 22.6375i 0.0304525 + 1.83614i
\(153\) 0 0
\(154\) 6.10704 2.60177i 0.492120 0.209657i
\(155\) 4.33209 0.347962
\(156\) 0 0
\(157\) −1.01600 1.75976i −0.0810853 0.140444i 0.822631 0.568576i \(-0.192505\pi\)
−0.903716 + 0.428132i \(0.859172\pi\)
\(158\) 0.637019 1.78076i 0.0506785 0.141670i
\(159\) 0 0
\(160\) −5.95172 15.0449i −0.470525 1.18940i
\(161\) −9.56439 + 8.84391i −0.753780 + 0.696997i
\(162\) 0 0
\(163\) −4.79027 2.76566i −0.375203 0.216623i 0.300526 0.953774i \(-0.402838\pi\)
−0.675729 + 0.737150i \(0.736171\pi\)
\(164\) 3.48314 + 9.25033i 0.271987 + 0.722330i
\(165\) 0 0
\(166\) −2.28492 12.5523i −0.177344 0.974246i
\(167\) −6.37142 −0.493035 −0.246518 0.969138i \(-0.579286\pi\)
−0.246518 + 0.969138i \(0.579286\pi\)
\(168\) 0 0
\(169\) 9.18033 0.706180
\(170\) 5.09028 + 27.9636i 0.390407 + 2.14471i
\(171\) 0 0
\(172\) 5.21041 + 13.8375i 0.397290 + 1.05510i
\(173\) −18.3863 10.6153i −1.39788 0.807069i −0.403714 0.914885i \(-0.632281\pi\)
−0.994171 + 0.107816i \(0.965614\pi\)
\(174\) 0 0
\(175\) 1.85829 + 8.20673i 0.140474 + 0.620371i
\(176\) 6.72056 + 2.27911i 0.506581 + 0.171795i
\(177\) 0 0
\(178\) −3.08819 + 8.63291i −0.231469 + 0.647064i
\(179\) −10.2453 17.7453i −0.765768 1.32635i −0.939840 0.341616i \(-0.889026\pi\)
0.174072 0.984733i \(-0.444307\pi\)
\(180\) 0 0
\(181\) −16.5989 −1.23379 −0.616894 0.787046i \(-0.711609\pi\)
−0.616894 + 0.787046i \(0.711609\pi\)
\(182\) −2.12454 + 17.4932i −0.157481 + 1.29668i
\(183\) 0 0
\(184\) −13.9241 + 0.230932i −1.02650 + 0.0170245i
\(185\) 6.87907 3.97163i 0.505759 0.292000i
\(186\) 0 0
\(187\) −10.7965 6.23338i −0.789521 0.455830i
\(188\) −1.81404 + 10.9975i −0.132302 + 0.802078i
\(189\) 0 0
\(190\) 24.6873 20.9487i 1.79100 1.51978i
\(191\) 3.51133 6.08181i 0.254071 0.440064i −0.710572 0.703625i \(-0.751564\pi\)
0.964643 + 0.263561i \(0.0848969\pi\)
\(192\) 0 0
\(193\) 8.66227 + 15.0035i 0.623524 + 1.07997i 0.988824 + 0.149085i \(0.0476329\pi\)
−0.365301 + 0.930890i \(0.619034\pi\)
\(194\) 0.271527 + 1.49164i 0.0194945 + 0.107094i
\(195\) 0 0
\(196\) −13.5930 3.35116i −0.970929 0.239369i
\(197\) 4.41987i 0.314902i −0.987527 0.157451i \(-0.949672\pi\)
0.987527 0.157451i \(-0.0503277\pi\)
\(198\) 0 0
\(199\) −0.539285 + 0.311356i −0.0382289 + 0.0220715i −0.518993 0.854779i \(-0.673693\pi\)
0.480764 + 0.876850i \(0.340359\pi\)
\(200\) −4.36793 + 7.86382i −0.308860 + 0.556056i
\(201\) 0 0
\(202\) −5.60274 6.60262i −0.394208 0.464559i
\(203\) −5.65766 + 18.2303i −0.397090 + 1.27952i
\(204\) 0 0
\(205\) 7.06767 12.2416i 0.493627 0.854988i
\(206\) 3.40234 9.51110i 0.237052 0.662670i
\(207\) 0 0
\(208\) −14.1598 + 12.4252i −0.981805 + 0.861532i
\(209\) 14.2013i 0.982321i
\(210\) 0 0
\(211\) 19.0072i 1.30851i 0.756275 + 0.654253i \(0.227017\pi\)
−0.756275 + 0.654253i \(0.772983\pi\)
\(212\) 4.21612 5.13890i 0.289564 0.352941i
\(213\) 0 0
\(214\) 3.44828 + 1.23353i 0.235719 + 0.0843222i
\(215\) 10.5725 18.3121i 0.721038 1.24887i
\(216\) 0 0
\(217\) 3.90842 0.885005i 0.265321 0.0600781i
\(218\) −2.96969 + 2.51997i −0.201133 + 0.170674i
\(219\) 0 0
\(220\) −3.57620 9.49749i −0.241107 0.640320i
\(221\) 28.6606 16.5472i 1.92792 1.11308i
\(222\) 0 0
\(223\) 13.3599i 0.894643i 0.894373 + 0.447321i \(0.147622\pi\)
−0.894373 + 0.447321i \(0.852378\pi\)
\(224\) −8.44320 12.3577i −0.564135 0.825683i
\(225\) 0 0
\(226\) 25.5340 4.64802i 1.69850 0.309182i
\(227\) −1.96956 3.41138i −0.130724 0.226421i 0.793232 0.608920i \(-0.208397\pi\)
−0.923956 + 0.382499i \(0.875064\pi\)
\(228\) 0 0
\(229\) −1.44488 + 2.50261i −0.0954804 + 0.165377i −0.909809 0.415027i \(-0.863772\pi\)
0.814329 + 0.580404i \(0.197105\pi\)
\(230\) 12.8854 + 15.1849i 0.849635 + 1.00126i
\(231\) 0 0
\(232\) −17.5005 + 10.4947i −1.14896 + 0.689008i
\(233\) −12.9746 7.49088i −0.849993 0.490744i 0.0106555 0.999943i \(-0.496608\pi\)
−0.860648 + 0.509200i \(0.829942\pi\)
\(234\) 0 0
\(235\) 13.8042 7.96987i 0.900488 0.519897i
\(236\) 2.21828 + 1.81995i 0.144398 + 0.118469i
\(237\) 0 0
\(238\) 10.3052 + 24.1890i 0.667985 + 1.56794i
\(239\) −9.74049 −0.630060 −0.315030 0.949082i \(-0.602015\pi\)
−0.315030 + 0.949082i \(0.602015\pi\)
\(240\) 0 0
\(241\) −3.01158 5.21621i −0.193993 0.336006i 0.752577 0.658504i \(-0.228811\pi\)
−0.946570 + 0.322499i \(0.895477\pi\)
\(242\) −10.4562 3.74042i −0.672151 0.240443i
\(243\) 0 0
\(244\) −4.75374 + 28.8194i −0.304327 + 1.84497i
\(245\) 8.62469 + 18.0680i 0.551011 + 1.15432i
\(246\) 0 0
\(247\) −32.6481 18.8494i −2.07735 1.19936i
\(248\) 3.74511 + 2.08021i 0.237815 + 0.132094i
\(249\) 0 0
\(250\) −7.24108 + 1.31811i −0.457966 + 0.0833647i
\(251\) −2.95805 −0.186710 −0.0933551 0.995633i \(-0.529759\pi\)
−0.0933551 + 0.995633i \(0.529759\pi\)
\(252\) 0 0
\(253\) −8.73506 −0.549168
\(254\) −11.3934 + 2.07396i −0.714884 + 0.130132i
\(255\) 0 0
\(256\) 2.07907 15.8643i 0.129942 0.991522i
\(257\) −1.04960 0.605984i −0.0654719 0.0378002i 0.466907 0.884307i \(-0.345368\pi\)
−0.532379 + 0.846506i \(0.678702\pi\)
\(258\) 0 0
\(259\) 5.39495 4.98855i 0.335226 0.309973i
\(260\) 26.5810 + 4.38452i 1.64848 + 0.271916i
\(261\) 0 0
\(262\) 0.409877 + 0.146622i 0.0253223 + 0.00905835i
\(263\) 5.43216 + 9.40878i 0.334962 + 0.580171i 0.983477 0.181031i \(-0.0579433\pi\)
−0.648516 + 0.761201i \(0.724610\pi\)
\(264\) 0 0
\(265\) −9.50581 −0.583937
\(266\) 17.9933 23.9434i 1.10324 1.46806i
\(267\) 0 0
\(268\) 3.78381 4.61198i 0.231133 0.281721i
\(269\) −6.63128 + 3.82857i −0.404316 + 0.233432i −0.688345 0.725384i \(-0.741662\pi\)
0.284028 + 0.958816i \(0.408329\pi\)
\(270\) 0 0
\(271\) −17.2222 9.94322i −1.04617 0.604008i −0.124597 0.992207i \(-0.539764\pi\)
−0.921575 + 0.388200i \(0.873097\pi\)
\(272\) −9.02718 + 26.6190i −0.547353 + 1.61401i
\(273\) 0 0
\(274\) −3.85316 4.54080i −0.232778 0.274320i
\(275\) −2.82119 + 4.88645i −0.170124 + 0.294664i
\(276\) 0 0
\(277\) −3.33158 5.77046i −0.200175 0.346713i 0.748410 0.663237i \(-0.230818\pi\)
−0.948585 + 0.316523i \(0.897484\pi\)
\(278\) −14.6770 + 2.67170i −0.880271 + 0.160238i
\(279\) 0 0
\(280\) −6.00404 + 20.5439i −0.358810 + 1.22773i
\(281\) 9.71892i 0.579782i −0.957060 0.289891i \(-0.906381\pi\)
0.957060 0.289891i \(-0.0936190\pi\)
\(282\) 0 0
\(283\) 6.55255 3.78312i 0.389509 0.224883i −0.292439 0.956284i \(-0.594467\pi\)
0.681947 + 0.731401i \(0.261133\pi\)
\(284\) −21.4410 + 8.07342i −1.27229 + 0.479069i
\(285\) 0 0
\(286\) −9.00971 + 7.64532i −0.532756 + 0.452077i
\(287\) 3.87564 12.4882i 0.228772 0.737157i
\(288\) 0 0
\(289\) 16.1894 28.0408i 0.952316 1.64946i
\(290\) 27.4768 + 9.82909i 1.61350 + 0.577184i
\(291\) 0 0
\(292\) −0.0755694 0.0619996i −0.00442236 0.00362825i
\(293\) 5.44847i 0.318303i −0.987254 0.159151i \(-0.949124\pi\)
0.987254 0.159151i \(-0.0508758\pi\)
\(294\) 0 0
\(295\) 4.10332i 0.238905i
\(296\) 7.85412 0.130261i 0.456511 0.00757126i
\(297\) 0 0
\(298\) 8.16128 22.8145i 0.472770 1.32161i
\(299\) 11.5941 20.0815i 0.670503 1.16134i
\(300\) 0 0
\(301\) 5.79755 18.6811i 0.334165 1.07676i
\(302\) −6.42678 7.57371i −0.369819 0.435818i
\(303\) 0 0
\(304\) 31.4016 6.25578i 1.80100 0.358794i
\(305\) 36.1744 20.8853i 2.07134 1.19589i
\(306\) 0 0
\(307\) 1.58786i 0.0906240i 0.998973 + 0.0453120i \(0.0144282\pi\)
−0.998973 + 0.0453120i \(0.985572\pi\)
\(308\) −5.16671 7.83808i −0.294400 0.446616i
\(309\) 0 0
\(310\) −1.09719 6.02745i −0.0623162 0.342336i
\(311\) −9.92410 17.1891i −0.562744 0.974702i −0.997256 0.0740353i \(-0.976412\pi\)
0.434511 0.900666i \(-0.356921\pi\)
\(312\) 0 0
\(313\) −5.26944 + 9.12693i −0.297846 + 0.515885i −0.975643 0.219365i \(-0.929602\pi\)
0.677797 + 0.735249i \(0.262935\pi\)
\(314\) −2.19112 + 1.85930i −0.123652 + 0.104926i
\(315\) 0 0
\(316\) −2.63900 0.435301i −0.148455 0.0244876i
\(317\) −11.5912 6.69221i −0.651029 0.375872i 0.137821 0.990457i \(-0.455990\pi\)
−0.788850 + 0.614585i \(0.789323\pi\)
\(318\) 0 0
\(319\) −11.0848 + 6.39981i −0.620629 + 0.358320i
\(320\) −19.4253 + 12.0914i −1.08591 + 0.675927i
\(321\) 0 0
\(322\) 14.7273 + 11.0675i 0.820723 + 0.616768i
\(323\) −56.2487 −3.12976
\(324\) 0 0
\(325\) −7.48916 12.9716i −0.415424 0.719535i
\(326\) −2.63477 + 7.36540i −0.145926 + 0.407932i
\(327\) 0 0
\(328\) 11.9883 7.18910i 0.661942 0.396952i
\(329\) 10.8260 10.0105i 0.596859 0.551898i
\(330\) 0 0
\(331\) 24.0106 + 13.8625i 1.31974 + 0.761952i 0.983687 0.179891i \(-0.0575744\pi\)
0.336053 + 0.941843i \(0.390908\pi\)
\(332\) −16.8859 + 6.35824i −0.926734 + 0.348954i
\(333\) 0 0
\(334\) 1.61369 + 8.86487i 0.0882974 + 0.485064i
\(335\) −8.53112 −0.466105
\(336\) 0 0
\(337\) 19.2739 1.04992 0.524959 0.851128i \(-0.324081\pi\)
0.524959 + 0.851128i \(0.324081\pi\)
\(338\) −2.32511 12.7731i −0.126469 0.694763i
\(339\) 0 0
\(340\) 37.6179 14.1647i 2.04012 0.768190i
\(341\) 2.32715 + 1.34358i 0.126022 + 0.0727590i
\(342\) 0 0
\(343\) 11.4724 + 14.5391i 0.619449 + 0.785037i
\(344\) 17.9332 10.7541i 0.966894 0.579824i
\(345\) 0 0
\(346\) −10.1129 + 28.2703i −0.543675 + 1.51982i
\(347\) 0.676069 + 1.17099i 0.0362933 + 0.0628618i 0.883602 0.468240i \(-0.155112\pi\)
−0.847308 + 0.531102i \(0.821778\pi\)
\(348\) 0 0
\(349\) −34.3047 −1.83629 −0.918145 0.396245i \(-0.870313\pi\)
−0.918145 + 0.396245i \(0.870313\pi\)
\(350\) 10.9478 4.66406i 0.585184 0.249305i
\(351\) 0 0
\(352\) 1.46892 9.92787i 0.0782939 0.529158i
\(353\) 10.7257 6.19247i 0.570870 0.329592i −0.186627 0.982431i \(-0.559756\pi\)
0.757497 + 0.652839i \(0.226422\pi\)
\(354\) 0 0
\(355\) 28.3742 + 16.3819i 1.50595 + 0.869458i
\(356\) 12.7935 + 2.11029i 0.678057 + 0.111845i
\(357\) 0 0
\(358\) −22.0951 + 18.7491i −1.16776 + 0.990922i
\(359\) 6.36683 11.0277i 0.336028 0.582018i −0.647653 0.761935i \(-0.724250\pi\)
0.983682 + 0.179917i \(0.0575829\pi\)
\(360\) 0 0
\(361\) 22.5373 + 39.0357i 1.18617 + 2.05451i
\(362\) 4.20402 + 23.0949i 0.220958 + 1.21384i
\(363\) 0 0
\(364\) 24.8772 1.47453i 1.30392 0.0772862i
\(365\) 0.139786i 0.00731675i
\(366\) 0 0
\(367\) 11.2735 6.50873i 0.588469 0.339753i −0.176023 0.984386i \(-0.556323\pi\)
0.764492 + 0.644633i \(0.222990\pi\)
\(368\) 3.84787 + 19.3148i 0.200584 + 1.00685i
\(369\) 0 0
\(370\) −7.26819 8.56529i −0.377855 0.445288i
\(371\) −8.57618 + 1.94195i −0.445253 + 0.100821i
\(372\) 0 0
\(373\) 2.92708 5.06985i 0.151558 0.262507i −0.780242 0.625477i \(-0.784904\pi\)
0.931801 + 0.362971i \(0.118238\pi\)
\(374\) −5.93837 + 16.6005i −0.307066 + 0.858391i
\(375\) 0 0
\(376\) 15.7609 0.261394i 0.812804 0.0134804i
\(377\) 33.9779i 1.74995i
\(378\) 0 0
\(379\) 23.7003i 1.21740i 0.793399 + 0.608701i \(0.208309\pi\)
−0.793399 + 0.608701i \(0.791691\pi\)
\(380\) −35.3995 29.0429i −1.81596 1.48987i
\(381\) 0 0
\(382\) −9.35124 3.34515i −0.478451 0.171153i
\(383\) −8.19122 + 14.1876i −0.418552 + 0.724953i −0.995794 0.0916198i \(-0.970796\pi\)
0.577242 + 0.816573i \(0.304129\pi\)
\(384\) 0 0
\(385\) −3.97919 + 12.8219i −0.202798 + 0.653464i
\(386\) 18.6812 15.8522i 0.950848 0.806855i
\(387\) 0 0
\(388\) 2.00663 0.755578i 0.101871 0.0383587i
\(389\) 6.59701 3.80878i 0.334482 0.193113i −0.323348 0.946280i \(-0.604808\pi\)
0.657829 + 0.753167i \(0.271475\pi\)
\(390\) 0 0
\(391\) 34.5981i 1.74970i
\(392\) −1.21993 + 19.7614i −0.0616158 + 0.998100i
\(393\) 0 0
\(394\) −6.14958 + 1.11942i −0.309811 + 0.0563957i
\(395\) 1.91247 + 3.31250i 0.0962270 + 0.166670i
\(396\) 0 0
\(397\) 4.18986 7.25706i 0.210283 0.364221i −0.741520 0.670931i \(-0.765895\pi\)
0.951803 + 0.306710i \(0.0992281\pi\)
\(398\) 0.569791 + 0.671477i 0.0285610 + 0.0336581i
\(399\) 0 0
\(400\) 12.0476 + 4.08565i 0.602380 + 0.204282i
\(401\) 19.2770 + 11.1296i 0.962648 + 0.555785i 0.896987 0.442057i \(-0.145751\pi\)
0.0656611 + 0.997842i \(0.479084\pi\)
\(402\) 0 0
\(403\) −6.17767 + 3.56668i −0.307732 + 0.177669i
\(404\) −7.76754 + 9.46762i −0.386450 + 0.471032i
\(405\) 0 0
\(406\) 26.7977 + 3.25457i 1.32995 + 0.161522i
\(407\) 4.92715 0.244230
\(408\) 0 0
\(409\) 9.60372 + 16.6341i 0.474873 + 0.822505i 0.999586 0.0287748i \(-0.00916058\pi\)
−0.524713 + 0.851279i \(0.675827\pi\)
\(410\) −18.8223 6.73317i −0.929568 0.332528i
\(411\) 0 0
\(412\) −14.0950 2.32496i −0.694410 0.114542i
\(413\) −0.838271 3.70203i −0.0412486 0.182165i
\(414\) 0 0
\(415\) 22.3462 + 12.9016i 1.09693 + 0.633314i
\(416\) 20.8741 + 16.5543i 1.02343 + 0.811641i
\(417\) 0 0
\(418\) 19.7589 3.59676i 0.966440 0.175923i
\(419\) 37.1132 1.81310 0.906550 0.422098i \(-0.138706\pi\)
0.906550 + 0.422098i \(0.138706\pi\)
\(420\) 0 0
\(421\) −1.14540 −0.0558236 −0.0279118 0.999610i \(-0.508886\pi\)
−0.0279118 + 0.999610i \(0.508886\pi\)
\(422\) 26.4456 4.81395i 1.28735 0.234340i
\(423\) 0 0
\(424\) −8.21783 4.56456i −0.399093 0.221675i
\(425\) −19.3544 11.1743i −0.938826 0.542032i
\(426\) 0 0
\(427\) 28.3700 26.2329i 1.37292 1.26950i
\(428\) 0.842920 5.11018i 0.0407441 0.247010i
\(429\) 0 0
\(430\) −28.1562 10.0721i −1.35781 0.485721i
\(431\) 16.4788 + 28.5421i 0.793756 + 1.37483i 0.923626 + 0.383295i \(0.125211\pi\)
−0.129870 + 0.991531i \(0.541456\pi\)
\(432\) 0 0
\(433\) 28.0131 1.34623 0.673113 0.739540i \(-0.264957\pi\)
0.673113 + 0.739540i \(0.264957\pi\)
\(434\) −2.22124 5.21384i −0.106623 0.250272i
\(435\) 0 0
\(436\) 4.25829 + 3.49364i 0.203935 + 0.167315i
\(437\) −34.1315 + 19.7058i −1.63273 + 0.942658i
\(438\) 0 0
\(439\) −13.1619 7.59904i −0.628184 0.362682i 0.151864 0.988401i \(-0.451472\pi\)
−0.780048 + 0.625719i \(0.784806\pi\)
\(440\) −12.3086 + 7.38118i −0.586788 + 0.351884i
\(441\) 0 0
\(442\) −30.2818 35.6859i −1.44036 1.69741i
\(443\) 15.4210 26.7099i 0.732673 1.26903i −0.223064 0.974804i \(-0.571606\pi\)
0.955737 0.294223i \(-0.0950608\pi\)
\(444\) 0 0
\(445\) −9.27144 16.0586i −0.439508 0.761251i
\(446\) 18.5882 3.38366i 0.880179 0.160221i
\(447\) 0 0
\(448\) −15.0554 + 14.8773i −0.711303 + 0.702885i
\(449\) 24.0119i 1.13319i 0.823995 + 0.566596i \(0.191740\pi\)
−0.823995 + 0.566596i \(0.808260\pi\)
\(450\) 0 0
\(451\) 7.59336 4.38403i 0.357557 0.206436i
\(452\) −12.9340 34.3495i −0.608366 1.61567i
\(453\) 0 0
\(454\) −4.24759 + 3.60435i −0.199349 + 0.169160i
\(455\) −24.1954 26.1665i −1.13430 1.22671i
\(456\) 0 0
\(457\) −17.3211 + 30.0010i −0.810246 + 1.40339i 0.102446 + 0.994739i \(0.467333\pi\)
−0.912692 + 0.408649i \(0.866000\pi\)
\(458\) 3.84794 + 1.37650i 0.179803 + 0.0643195i
\(459\) 0 0
\(460\) 17.8640 21.7739i 0.832915 1.01521i
\(461\) 25.4518i 1.18541i −0.805421 0.592704i \(-0.798061\pi\)
0.805421 0.592704i \(-0.201939\pi\)
\(462\) 0 0
\(463\) 27.9163i 1.29738i 0.761053 + 0.648690i \(0.224683\pi\)
−0.761053 + 0.648690i \(0.775317\pi\)
\(464\) 19.0341 + 21.6913i 0.883636 + 1.00699i
\(465\) 0 0
\(466\) −7.13635 + 19.9494i −0.330585 + 0.924138i
\(467\) 19.5636 33.8852i 0.905297 1.56802i 0.0847796 0.996400i \(-0.472981\pi\)
0.820518 0.571621i \(-0.193685\pi\)
\(468\) 0 0
\(469\) −7.69680 + 1.74283i −0.355405 + 0.0804763i
\(470\) −14.5851 17.1880i −0.672760 0.792822i
\(471\) 0 0
\(472\) 1.97036 3.54735i 0.0906932 0.163280i
\(473\) 11.3589 6.55805i 0.522281 0.301539i
\(474\) 0 0
\(475\) 25.4579i 1.16809i
\(476\) 31.0453 20.4645i 1.42296 0.937987i
\(477\) 0 0
\(478\) 2.46698 + 13.5524i 0.112837 + 0.619873i
\(479\) −14.2074 24.6080i −0.649155 1.12437i −0.983325 0.181857i \(-0.941789\pi\)
0.334170 0.942513i \(-0.391544\pi\)
\(480\) 0 0
\(481\) −6.53983 + 11.3273i −0.298190 + 0.516481i
\(482\) −6.49483 + 5.51127i −0.295831 + 0.251032i
\(483\) 0 0
\(484\) −2.55599 + 15.4956i −0.116181 + 0.704345i
\(485\) −2.65550 1.53315i −0.120580 0.0696168i
\(486\) 0 0
\(487\) 28.0663 16.2041i 1.27180 0.734276i 0.296476 0.955040i \(-0.404188\pi\)
0.975327 + 0.220764i \(0.0708551\pi\)
\(488\) 41.3019 0.684993i 1.86965 0.0310082i
\(489\) 0 0
\(490\) 22.9546 16.5761i 1.03698 0.748830i
\(491\) −19.3004 −0.871017 −0.435508 0.900185i \(-0.643431\pi\)
−0.435508 + 0.900185i \(0.643431\pi\)
\(492\) 0 0
\(493\) −25.3485 43.9050i −1.14164 1.97738i
\(494\) −17.9573 + 50.1989i −0.807936 + 2.25855i
\(495\) 0 0
\(496\) 1.94577 5.73762i 0.0873678 0.257627i
\(497\) 28.9460 + 8.98318i 1.29840 + 0.402951i
\(498\) 0 0
\(499\) 22.5026 + 12.9919i 1.00735 + 0.581596i 0.910416 0.413694i \(-0.135762\pi\)
0.0969381 + 0.995290i \(0.469095\pi\)
\(500\) 3.66791 + 9.74104i 0.164034 + 0.435633i
\(501\) 0 0
\(502\) 0.749186 + 4.11568i 0.0334378 + 0.183692i
\(503\) 17.7613 0.791939 0.395969 0.918264i \(-0.370409\pi\)
0.395969 + 0.918264i \(0.370409\pi\)
\(504\) 0 0
\(505\) 17.5130 0.779317
\(506\) 2.21233 + 12.1535i 0.0983502 + 0.540290i
\(507\) 0 0
\(508\) 5.77122 + 15.3269i 0.256056 + 0.680022i
\(509\) −22.5593 13.0246i −0.999923 0.577306i −0.0916978 0.995787i \(-0.529229\pi\)
−0.908226 + 0.418481i \(0.862563\pi\)
\(510\) 0 0
\(511\) 0.0285571 + 0.126116i 0.00126329 + 0.00557903i
\(512\) −22.5994 + 1.12526i −0.998763 + 0.0497300i
\(513\) 0 0
\(514\) −0.577304 + 1.61383i −0.0254638 + 0.0711831i
\(515\) 10.2146 + 17.6922i 0.450108 + 0.779610i
\(516\) 0 0
\(517\) 9.88731 0.434844
\(518\) −8.30720 6.24281i −0.364997 0.274293i
\(519\) 0 0
\(520\) −0.631790 38.0940i −0.0277058 1.67053i
\(521\) −29.2252 + 16.8732i −1.28038 + 0.739228i −0.976918 0.213615i \(-0.931476\pi\)
−0.303463 + 0.952843i \(0.598143\pi\)
\(522\) 0 0
\(523\) −17.2979 9.98697i −0.756386 0.436700i 0.0716106 0.997433i \(-0.477186\pi\)
−0.827997 + 0.560733i \(0.810519\pi\)
\(524\) 0.100193 0.607417i 0.00437695 0.0265351i
\(525\) 0 0
\(526\) 11.7151 9.94101i 0.510803 0.433449i
\(527\) −5.32170 + 9.21745i −0.231817 + 0.401519i
\(528\) 0 0
\(529\) −0.620877 1.07539i −0.0269946 0.0467561i
\(530\) 2.40754 + 13.2259i 0.104577 + 0.574497i
\(531\) 0 0
\(532\) −37.8708 18.9708i −1.64191 0.822489i
\(533\) 23.2757i 1.00818i
\(534\) 0 0
\(535\) −6.41435 + 3.70333i −0.277316 + 0.160109i
\(536\) −7.37520 4.09653i −0.318560 0.176943i
\(537\) 0 0
\(538\) 7.00639 + 8.25676i 0.302067 + 0.355974i
\(539\) −0.970640 + 12.3809i −0.0418084 + 0.533282i
\(540\) 0 0
\(541\) 3.91821 6.78654i 0.168457 0.291776i −0.769421 0.638743i \(-0.779455\pi\)
0.937878 + 0.346966i \(0.112788\pi\)
\(542\) −9.47263 + 26.4804i −0.406884 + 1.13743i
\(543\) 0 0
\(544\) 39.3226 + 5.81815i 1.68594 + 0.249451i
\(545\) 7.87688i 0.337409i
\(546\) 0 0
\(547\) 42.3065i 1.80890i −0.426584 0.904448i \(-0.640283\pi\)
0.426584 0.904448i \(-0.359717\pi\)
\(548\) −5.34195 + 6.51114i −0.228197 + 0.278142i
\(549\) 0 0
\(550\) 7.51329 + 2.68767i 0.320368 + 0.114603i
\(551\) −28.8753 + 50.0134i −1.23013 + 2.13064i
\(552\) 0 0
\(553\) 2.40215 + 2.59785i 0.102150 + 0.110472i
\(554\) −7.18493 + 6.09687i −0.305259 + 0.259031i
\(555\) 0 0
\(556\) 7.43453 + 19.7442i 0.315294 + 0.837342i
\(557\) −9.26900 + 5.35146i −0.392740 + 0.226749i −0.683347 0.730094i \(-0.739476\pi\)
0.290607 + 0.956843i \(0.406143\pi\)
\(558\) 0 0
\(559\) 34.8181i 1.47265i
\(560\) 30.1044 + 3.15054i 1.27214 + 0.133135i
\(561\) 0 0
\(562\) −13.5224 + 2.46152i −0.570408 + 0.103833i
\(563\) 4.57187 + 7.91870i 0.192681 + 0.333734i 0.946138 0.323764i \(-0.104948\pi\)
−0.753457 + 0.657497i \(0.771615\pi\)
\(564\) 0 0
\(565\) −26.2446 + 45.4570i −1.10412 + 1.91239i
\(566\) −6.92320 8.15873i −0.291004 0.342937i
\(567\) 0 0
\(568\) 16.6633 + 27.7871i 0.699177 + 1.16592i
\(569\) 25.5092 + 14.7277i 1.06940 + 0.617419i 0.928018 0.372536i \(-0.121512\pi\)
0.141384 + 0.989955i \(0.454845\pi\)
\(570\) 0 0
\(571\) −28.0410 + 16.1895i −1.17348 + 0.677508i −0.954497 0.298221i \(-0.903607\pi\)
−0.218982 + 0.975729i \(0.570274\pi\)
\(572\) 12.9192 + 10.5993i 0.540179 + 0.443180i
\(573\) 0 0
\(574\) −18.3571 2.22946i −0.766210 0.0930560i
\(575\) −15.6589 −0.653021
\(576\) 0 0
\(577\) −2.89208 5.00923i −0.120399 0.208537i 0.799526 0.600631i \(-0.205084\pi\)
−0.919925 + 0.392094i \(0.871751\pi\)
\(578\) −43.1149 15.4232i −1.79334 0.641519i
\(579\) 0 0
\(580\) 6.71662 40.7193i 0.278893 1.69078i
\(581\) 22.7965 + 7.07473i 0.945758 + 0.293509i
\(582\) 0 0
\(583\) −5.10642 2.94820i −0.211486 0.122102i
\(584\) −0.0671236 + 0.120846i −0.00277759 + 0.00500065i
\(585\) 0 0
\(586\) −7.58073 + 1.37994i −0.313157 + 0.0570047i
\(587\) −30.3210 −1.25148 −0.625740 0.780032i \(-0.715203\pi\)
−0.625740 + 0.780032i \(0.715203\pi\)
\(588\) 0 0
\(589\) 12.1242 0.499569
\(590\) −5.70916 + 1.03925i −0.235042 + 0.0427853i
\(591\) 0 0
\(592\) −2.17046 10.8948i −0.0892052 0.447775i
\(593\) 15.6450 + 9.03263i 0.642462 + 0.370926i 0.785562 0.618782i \(-0.212374\pi\)
−0.143100 + 0.989708i \(0.545707\pi\)
\(594\) 0 0
\(595\) −50.7854 15.7609i −2.08200 0.646133i
\(596\) −33.8100 5.57694i −1.38491 0.228440i
\(597\) 0 0
\(598\) −30.8769 11.0454i −1.26265 0.451678i
\(599\) −1.36569 2.36544i −0.0558006 0.0966494i 0.836776 0.547546i \(-0.184438\pi\)
−0.892576 + 0.450896i \(0.851104\pi\)
\(600\) 0 0
\(601\) 12.7951 0.521925 0.260962 0.965349i \(-0.415960\pi\)
0.260962 + 0.965349i \(0.415960\pi\)
\(602\) −27.4603 3.33504i −1.11920 0.135926i
\(603\) 0 0
\(604\) −8.90997 + 10.8601i −0.362541 + 0.441891i
\(605\) 19.4502 11.2296i 0.790764 0.456548i
\(606\) 0 0
\(607\) −21.6019 12.4718i −0.876792 0.506216i −0.00719299 0.999974i \(-0.502290\pi\)
−0.869599 + 0.493758i \(0.835623\pi\)
\(608\) −16.6571 42.1062i −0.675534 1.70763i
\(609\) 0 0
\(610\) −38.2207 45.0416i −1.54751 1.82368i
\(611\) −13.1235 + 22.7305i −0.530919 + 0.919578i
\(612\) 0 0
\(613\) −14.8231 25.6744i −0.598699 1.03698i −0.993013 0.118002i \(-0.962351\pi\)
0.394314 0.918976i \(-0.370982\pi\)
\(614\) 2.20927 0.402158i 0.0891589 0.0162298i
\(615\) 0 0
\(616\) −9.59694 + 9.17385i −0.386672 + 0.369625i
\(617\) 26.3663i 1.06147i 0.847539 + 0.530734i \(0.178083\pi\)
−0.847539 + 0.530734i \(0.821917\pi\)
\(618\) 0 0
\(619\) −17.3094 + 9.99359i −0.695724 + 0.401676i −0.805753 0.592252i \(-0.798239\pi\)
0.110029 + 0.993928i \(0.464906\pi\)
\(620\) −8.10840 + 3.05315i −0.325641 + 0.122617i
\(621\) 0 0
\(622\) −21.4025 + 18.1614i −0.858162 + 0.728205i
\(623\) −11.6453 12.5941i −0.466561 0.504570i
\(624\) 0 0
\(625\) 15.3935 26.6624i 0.615742 1.06650i
\(626\) 14.0333 + 5.02004i 0.560885 + 0.200641i
\(627\) 0 0
\(628\) 3.14188 + 2.57770i 0.125375 + 0.102861i
\(629\) 19.5156i 0.778138i
\(630\) 0 0
\(631\) 7.91131i 0.314944i −0.987523 0.157472i \(-0.949666\pi\)
0.987523 0.157472i \(-0.0503344\pi\)
\(632\) 0.0627250 + 3.78202i 0.00249507 + 0.150441i
\(633\) 0 0
\(634\) −6.37548 + 17.8224i −0.253203 + 0.707819i
\(635\) 11.7104 20.2831i 0.464715 0.804909i
\(636\) 0 0
\(637\) −27.1748 18.6646i −1.07670 0.739520i
\(638\) 11.7118 + 13.8019i 0.463675 + 0.546424i
\(639\) 0 0
\(640\) 21.7432 + 23.9650i 0.859474 + 0.947301i
\(641\) −30.8675 + 17.8214i −1.21919 + 0.703902i −0.964746 0.263185i \(-0.915227\pi\)
−0.254448 + 0.967086i \(0.581894\pi\)
\(642\) 0 0
\(643\) 7.96178i 0.313982i −0.987600 0.156991i \(-0.949821\pi\)
0.987600 0.156991i \(-0.0501794\pi\)
\(644\) 11.6688 23.2940i 0.459814 0.917911i
\(645\) 0 0
\(646\) 14.2462 + 78.2617i 0.560507 + 3.07916i
\(647\) 24.0551 + 41.6647i 0.945704 + 1.63801i 0.754336 + 0.656489i \(0.227959\pi\)
0.191368 + 0.981518i \(0.438708\pi\)
\(648\) 0 0
\(649\) 1.27263 2.20426i 0.0499552 0.0865249i
\(650\) −16.1513 + 13.7054i −0.633504 + 0.537569i
\(651\) 0 0
\(652\) 10.9152 + 1.80045i 0.427470 + 0.0705109i
\(653\) −29.0569 16.7760i −1.13708 0.656495i −0.191376 0.981517i \(-0.561295\pi\)
−0.945706 + 0.325022i \(0.894628\pi\)
\(654\) 0 0
\(655\) −0.762436 + 0.440193i −0.0297909 + 0.0171998i
\(656\) −13.0388 14.8591i −0.509081 0.580150i
\(657\) 0 0
\(658\) −16.6701 12.5274i −0.649866 0.488371i
\(659\) −9.10230 −0.354575 −0.177288 0.984159i \(-0.556732\pi\)
−0.177288 + 0.984159i \(0.556732\pi\)
\(660\) 0 0
\(661\) −7.12959 12.3488i −0.277309 0.480313i 0.693406 0.720547i \(-0.256109\pi\)
−0.970715 + 0.240234i \(0.922776\pi\)
\(662\) 13.2064 36.9181i 0.513282 1.43486i
\(663\) 0 0
\(664\) 13.1232 + 21.8838i 0.509281 + 0.849258i
\(665\) 13.3772 + 59.0773i 0.518745 + 2.29092i
\(666\) 0 0
\(667\) −30.7628 17.7609i −1.19114 0.687705i
\(668\) 11.9254 4.49042i 0.461409 0.173740i
\(669\) 0 0
\(670\) 2.16068 + 11.8698i 0.0834744 + 0.458569i
\(671\) 25.9100 1.00025
\(672\) 0 0
\(673\) 1.00872 0.0388833 0.0194417 0.999811i \(-0.493811\pi\)
0.0194417 + 0.999811i \(0.493811\pi\)
\(674\) −4.88152 26.8168i −0.188029 1.03294i
\(675\) 0 0
\(676\) −17.1829 + 6.47008i −0.660881 + 0.248849i
\(677\) −30.2292 17.4528i −1.16180 0.670766i −0.210066 0.977687i \(-0.567368\pi\)
−0.951735 + 0.306921i \(0.900701\pi\)
\(678\) 0 0
\(679\) −2.70901 0.840721i −0.103962 0.0322639i
\(680\) −29.2356 48.7522i −1.12113 1.86956i
\(681\) 0 0
\(682\) 1.27999 3.57817i 0.0490135 0.137015i
\(683\) 22.7839 + 39.4629i 0.871803 + 1.51001i 0.860130 + 0.510075i \(0.170382\pi\)
0.0116726 + 0.999932i \(0.496284\pi\)
\(684\) 0 0
\(685\) 12.0441 0.460183
\(686\) 17.3233 19.6444i 0.661408 0.750026i
\(687\) 0 0
\(688\) −19.5047 22.2277i −0.743611 0.847422i
\(689\) 13.5555 7.82630i 0.516425 0.298158i
\(690\) 0 0
\(691\) 6.57653 + 3.79696i 0.250183 + 0.144443i 0.619848 0.784722i \(-0.287194\pi\)
−0.369665 + 0.929165i \(0.620528\pi\)
\(692\) 41.8952 + 6.91059i 1.59262 + 0.262701i
\(693\) 0 0
\(694\) 1.45802 1.23723i 0.0553458 0.0469644i
\(695\) 15.0855 26.1288i 0.572225 0.991122i
\(696\) 0 0
\(697\) 17.3644 + 30.0760i 0.657723 + 1.13921i
\(698\) 8.68838 + 47.7299i 0.328860 + 1.80660i
\(699\) 0 0
\(700\) −9.26209 14.0509i −0.350074 0.531075i
\(701\) 44.3539i 1.67522i −0.546267 0.837611i \(-0.683951\pi\)
0.546267 0.837611i \(-0.316049\pi\)
\(702\) 0 0
\(703\) 19.2524 11.1154i 0.726119 0.419225i
\(704\) −14.1852 + 0.470653i −0.534624 + 0.0177384i
\(705\) 0 0
\(706\) −11.3324 13.3548i −0.426500 0.502614i
\(707\) 15.8003 3.57774i 0.594230 0.134555i
\(708\) 0 0
\(709\) 12.1387 21.0249i 0.455879 0.789605i −0.542860 0.839823i \(-0.682658\pi\)
0.998738 + 0.0502185i \(0.0159918\pi\)
\(710\) 15.6065 43.6275i 0.585703 1.63731i
\(711\) 0 0
\(712\) −0.304083 18.3348i −0.0113960 0.687125i
\(713\) 7.45748i 0.279285i
\(714\) 0 0
\(715\) 23.8976i 0.893720i
\(716\) 31.6826 + 25.9935i 1.18404 + 0.971421i
\(717\) 0 0
\(718\) −16.9559 6.06550i −0.632788 0.226362i
\(719\) 13.9425 24.1491i 0.519967 0.900610i −0.479763 0.877398i \(-0.659277\pi\)
0.999731 0.0232120i \(-0.00738927\pi\)
\(720\) 0 0
\(721\) 12.8300 + 13.8752i 0.477813 + 0.516739i
\(722\) 48.6043 41.2438i 1.80886 1.53494i
\(723\) 0 0
\(724\) 31.0683 11.6985i 1.15465 0.434772i
\(725\) −19.8711 + 11.4726i −0.737996 + 0.426082i
\(726\) 0 0
\(727\) 0.853452i 0.0316528i −0.999875 0.0158264i \(-0.994962\pi\)
0.999875 0.0158264i \(-0.00503791\pi\)
\(728\) −8.35225 34.2394i −0.309555 1.26900i
\(729\) 0 0
\(730\) 0.194492 0.0354038i 0.00719846 0.00131035i
\(731\) 25.9753 + 44.9906i 0.960731 + 1.66404i
\(732\) 0 0
\(733\) 12.7372 22.0614i 0.470458 0.814857i −0.528971 0.848640i \(-0.677422\pi\)
0.999429 + 0.0337825i \(0.0107553\pi\)
\(734\) −11.9112 14.0368i −0.439649 0.518109i
\(735\) 0 0
\(736\) 25.8991 10.2456i 0.954654 0.377658i
\(737\) −4.58283 2.64590i −0.168811 0.0974629i
\(738\) 0 0
\(739\) −30.3461 + 17.5203i −1.11630 + 0.644496i −0.940454 0.339921i \(-0.889599\pi\)
−0.175846 + 0.984418i \(0.556266\pi\)
\(740\) −10.0765 + 12.2819i −0.370419 + 0.451493i
\(741\) 0 0
\(742\) 4.87402 + 11.4406i 0.178931 + 0.419998i
\(743\) 28.8253 1.05750 0.528750 0.848778i \(-0.322661\pi\)
0.528750 + 0.848778i \(0.322661\pi\)
\(744\) 0 0
\(745\) 24.5020 + 42.4387i 0.897684 + 1.55483i
\(746\) −7.79527 2.78854i −0.285405 0.102096i
\(747\) 0 0
\(748\) 24.6011 + 4.05793i 0.899505 + 0.148373i
\(749\) −5.03049 + 4.65154i −0.183810 + 0.169964i
\(750\) 0 0
\(751\) −24.7734 14.3029i −0.903994 0.521921i −0.0255004 0.999675i \(-0.508118\pi\)
−0.878494 + 0.477753i \(0.841451\pi\)
\(752\) −4.35545 21.8627i −0.158827 0.797249i
\(753\) 0 0
\(754\) −47.2752 + 8.60561i −1.72166 + 0.313398i
\(755\) 20.0887 0.731103
\(756\) 0 0
\(757\) −27.4539 −0.997830 −0.498915 0.866651i \(-0.666268\pi\)
−0.498915 + 0.866651i \(0.666268\pi\)
\(758\) 32.9754 6.00259i 1.19772 0.218024i
\(759\) 0 0
\(760\) −31.4432 + 56.6088i −1.14056 + 2.05342i
\(761\) −24.7788 14.3060i −0.898231 0.518594i −0.0216049 0.999767i \(-0.506878\pi\)
−0.876626 + 0.481173i \(0.840211\pi\)
\(762\) 0 0
\(763\) −1.60917 7.10655i −0.0582560 0.257274i
\(764\) −2.28588 + 13.8581i −0.0827002 + 0.501368i
\(765\) 0 0
\(766\) 21.8145 + 7.80355i 0.788191 + 0.281954i
\(767\) 3.37834 + 5.85145i 0.121985 + 0.211284i
\(768\) 0 0
\(769\) 4.97212 0.179299 0.0896496 0.995973i \(-0.471425\pi\)
0.0896496 + 0.995973i \(0.471425\pi\)
\(770\) 18.8476 + 2.28903i 0.679219 + 0.0824909i
\(771\) 0 0
\(772\) −26.7873 21.9772i −0.964097 0.790977i
\(773\) −36.9413 + 21.3281i −1.32869 + 0.767117i −0.985096 0.172003i \(-0.944976\pi\)
−0.343589 + 0.939120i \(0.611643\pi\)
\(774\) 0 0
\(775\) 4.17177 + 2.40857i 0.149854 + 0.0865184i
\(776\) −1.55949 2.60055i −0.0559825 0.0933544i
\(777\) 0 0
\(778\) −6.97018 8.21409i −0.249893 0.294489i
\(779\) 19.7803 34.2604i 0.708702 1.22751i
\(780\) 0 0
\(781\) 10.1616 + 17.6003i 0.363609 + 0.629789i
\(782\) −48.1380 + 8.76268i −1.72141 + 0.313353i
\(783\) 0 0
\(784\) 27.8039 3.30763i 0.992998 0.118129i
\(785\) 5.81177i 0.207431i
\(786\) 0 0
\(787\) −3.83610 + 2.21477i −0.136742 + 0.0789481i −0.566810 0.823848i \(-0.691823\pi\)
0.430068 + 0.902796i \(0.358489\pi\)
\(788\) 3.11502 + 8.27270i 0.110968 + 0.294703i
\(789\) 0 0
\(790\) 4.12448 3.49988i 0.146742 0.124520i
\(791\) −14.3915 + 46.3730i −0.511704 + 1.64883i
\(792\) 0 0
\(793\) −34.3905 + 59.5661i −1.22124 + 2.11525i
\(794\) −11.1583 3.99157i −0.395992 0.141655i
\(795\) 0 0
\(796\) 0.789948 0.962844i 0.0279990 0.0341271i
\(797\) 1.10654i 0.0391957i −0.999808 0.0195979i \(-0.993761\pi\)
0.999808 0.0195979i \(-0.00623859\pi\)
\(798\) 0 0
\(799\) 39.1620i 1.38545i
\(800\) 2.63326 17.7972i 0.0930999 0.629226i
\(801\) 0 0
\(802\) 10.6028 29.6399i 0.374400 1.04662i
\(803\) −0.0433543 + 0.0750918i −0.00152994 + 0.00264993i
\(804\) 0 0
\(805\) −36.3379 + 8.22819i −1.28074 + 0.290006i
\(806\) 6.52713 + 7.69197i 0.229908 + 0.270938i
\(807\) 0 0
\(808\) 15.1401 + 8.40950i 0.532626 + 0.295845i
\(809\) 40.2345 23.2294i 1.41457 0.816702i 0.418755 0.908099i \(-0.362467\pi\)
0.995815 + 0.0913970i \(0.0291332\pi\)
\(810\) 0 0
\(811\) 12.2358i 0.429657i 0.976652 + 0.214829i \(0.0689193\pi\)
−0.976652 + 0.214829i \(0.931081\pi\)
\(812\) −2.25882 38.1093i −0.0792691 1.33737i
\(813\) 0 0
\(814\) −1.24790 6.85539i −0.0437390 0.240281i
\(815\) −7.91017 13.7008i −0.277081 0.479919i
\(816\) 0 0
\(817\) 29.5892 51.2500i 1.03520 1.79301i
\(818\) 20.7115 17.5751i 0.724162 0.614498i
\(819\) 0 0
\(820\) −4.60105 + 27.8937i −0.160676 + 0.974092i
\(821\) −10.1503 5.86030i −0.354249 0.204526i 0.312306 0.949982i \(-0.398899\pi\)
−0.666555 + 0.745456i \(0.732232\pi\)
\(822\) 0 0
\(823\) −29.5545 + 17.0633i −1.03021 + 0.594790i −0.917044 0.398787i \(-0.869431\pi\)
−0.113162 + 0.993577i \(0.536098\pi\)
\(824\) 0.335016 + 20.1999i 0.0116708 + 0.703697i
\(825\) 0 0
\(826\) −4.93851 + 2.10394i −0.171833 + 0.0732056i
\(827\) −29.7930 −1.03600 −0.518001 0.855380i \(-0.673324\pi\)
−0.518001 + 0.855380i \(0.673324\pi\)
\(828\) 0 0
\(829\) 21.6981 + 37.5822i 0.753605 + 1.30528i 0.946065 + 0.323978i \(0.105020\pi\)
−0.192459 + 0.981305i \(0.561646\pi\)
\(830\) 12.2910 34.3590i 0.426626 1.19262i
\(831\) 0 0
\(832\) 17.7460 33.2358i 0.615233 1.15224i
\(833\) −49.0385 3.84454i −1.69908 0.133205i
\(834\) 0 0
\(835\) −15.7817 9.11156i −0.546148 0.315319i
\(836\) −10.0087 26.5806i −0.346158 0.919309i
\(837\) 0 0
\(838\) −9.39969 51.6375i −0.324707 1.78379i
\(839\) 52.4272 1.80999 0.904995 0.425423i \(-0.139875\pi\)
0.904995 + 0.425423i \(0.139875\pi\)
\(840\) 0 0
\(841\) −23.0506 −0.794850
\(842\) 0.290097 + 1.59366i 0.00999741 + 0.0549211i
\(843\) 0 0
\(844\) −13.3958 35.5759i −0.461102 1.22457i
\(845\) 22.7392 + 13.1285i 0.782253 + 0.451634i
\(846\) 0 0
\(847\) 15.2540 14.1049i 0.524132 0.484649i
\(848\) −4.26957 + 12.5899i −0.146618 + 0.432340i
\(849\) 0 0
\(850\) −10.6454 + 29.7589i −0.365135 + 1.02072i
\(851\) 6.83698 + 11.8420i 0.234369 + 0.405938i
\(852\) 0 0
\(853\) 12.6354 0.432628 0.216314 0.976324i \(-0.430597\pi\)
0.216314 + 0.976324i \(0.430597\pi\)
\(854\) −43.6844 32.8286i −1.49485 1.12337i
\(855\) 0 0
\(856\) −7.32353 + 0.121461i −0.250313 + 0.00415145i
\(857\) −10.6106 + 6.12603i −0.362451 + 0.209261i −0.670155 0.742221i \(-0.733773\pi\)
0.307704 + 0.951482i \(0.400439\pi\)
\(858\) 0 0
\(859\) 45.0377 + 26.0026i 1.53667 + 0.887196i 0.999031 + 0.0440193i \(0.0140163\pi\)
0.537637 + 0.843176i \(0.319317\pi\)
\(860\) −6.88270 + 41.7261i −0.234698 + 1.42285i
\(861\) 0 0
\(862\) 35.5385 30.1567i 1.21045 1.02714i
\(863\) −6.94583 + 12.0305i −0.236439 + 0.409524i −0.959690 0.281061i \(-0.909314\pi\)
0.723251 + 0.690585i \(0.242647\pi\)
\(864\) 0 0
\(865\) −30.3613 52.5873i −1.03232 1.78802i
\(866\) −7.09491 38.9761i −0.241095 1.32446i
\(867\) 0 0
\(868\) −6.69170 + 4.41103i −0.227131 + 0.149720i
\(869\) 2.37259i 0.0804846i
\(870\) 0 0
\(871\) 12.1656 7.02382i 0.412216 0.237993i
\(872\) 3.78238 6.80961i 0.128087 0.230603i
\(873\) 0 0
\(874\) 36.0622 + 42.4980i 1.21982 + 1.43751i
\(875\) 4.08123 13.1507i 0.137971 0.444575i
\(876\) 0 0
\(877\) −19.2703 + 33.3771i −0.650711 + 1.12706i 0.332240 + 0.943195i \(0.392196\pi\)
−0.982951 + 0.183870i \(0.941138\pi\)
\(878\) −7.23939 + 20.2374i −0.244318 + 0.682981i
\(879\) 0 0
\(880\) 13.3872 + 15.2561i 0.451282 + 0.514283i
\(881\) 2.21967i 0.0747826i −0.999301 0.0373913i \(-0.988095\pi\)
0.999301 0.0373913i \(-0.0119048\pi\)
\(882\) 0 0
\(883\) 43.9289i 1.47833i −0.673527 0.739163i \(-0.735221\pi\)
0.673527 0.739163i \(-0.264779\pi\)
\(884\) −41.9821 + 51.1708i −1.41201 + 1.72106i
\(885\) 0 0
\(886\) −41.0685 14.6911i −1.37972 0.493558i
\(887\) −7.80639 + 13.5211i −0.262113 + 0.453993i −0.966803 0.255522i \(-0.917753\pi\)
0.704690 + 0.709515i \(0.251086\pi\)
\(888\) 0 0
\(889\) 6.42155 20.6918i 0.215372 0.693981i
\(890\) −19.9949 + 16.9670i −0.670232 + 0.568735i
\(891\) 0 0
\(892\) −9.41571 25.0058i −0.315261 0.837255i
\(893\) 38.6338 22.3053i 1.29283 0.746417i
\(894\) 0 0
\(895\) 58.6058i 1.95897i
\(896\) 24.5126 + 17.1794i 0.818909 + 0.573924i
\(897\) 0 0
\(898\) 33.4090 6.08152i 1.11487 0.202943i
\(899\) 5.46378 + 9.46355i 0.182227 + 0.315627i
\(900\) 0 0
\(901\) 11.6773 20.2257i 0.389027 0.673815i
\(902\) −8.02289 9.45467i −0.267133 0.314806i
\(903\) 0 0
\(904\) −44.5164 + 26.6955i −1.48059 + 0.887879i
\(905\) −41.1147 23.7376i −1.36670 0.789064i
\(906\) 0 0
\(907\) 0.925872 0.534552i 0.0307431 0.0177495i −0.484550 0.874764i \(-0.661017\pi\)
0.515293 + 0.857014i \(0.327683\pi\)
\(908\) 6.09070 + 4.99701i 0.202127 + 0.165831i
\(909\) 0 0
\(910\) −30.2788 + 40.2915i −1.00373 + 1.33565i
\(911\) 35.4745 1.17532 0.587661 0.809107i \(-0.300049\pi\)
0.587661 + 0.809107i \(0.300049\pi\)
\(912\) 0 0
\(913\) 8.00276 + 13.8612i 0.264853 + 0.458739i
\(914\) 46.1288 + 16.5013i 1.52581 + 0.545815i
\(915\) 0 0
\(916\) 0.940617 5.70246i 0.0310789 0.188415i
\(917\) −0.597945 + 0.552902i −0.0197459 + 0.0182584i
\(918\) 0 0
\(919\) 37.2941 + 21.5318i 1.23022 + 0.710267i 0.967075 0.254490i \(-0.0819076\pi\)
0.263143 + 0.964757i \(0.415241\pi\)
\(920\) −34.8196 19.3404i −1.14797 0.637635i
\(921\) 0 0
\(922\) −35.4123 + 6.44619i −1.16624 + 0.212294i
\(923\) −53.9499 −1.77578
\(924\) 0 0
\(925\) 8.83265 0.290416
\(926\) 38.8413 7.07037i 1.27640 0.232347i
\(927\) 0 0
\(928\) 25.3594 31.9769i 0.832464 1.04969i
\(929\) −1.25933 0.727077i −0.0413174 0.0238546i 0.479199 0.877706i \(-0.340927\pi\)
−0.520516 + 0.853852i \(0.674261\pi\)
\(930\) 0 0
\(931\) 24.1379 + 50.5669i 0.791088 + 1.65726i
\(932\) 29.5640 + 4.87656i 0.968401 + 0.159737i
\(933\) 0 0
\(934\) −52.1011 18.6377i −1.70480 0.609845i
\(935\) −17.8283 30.8796i −0.583049 1.00987i
\(936\) 0 0
\(937\) −31.7757 −1.03807 −0.519034 0.854754i \(-0.673708\pi\)
−0.519034 + 0.854754i \(0.673708\pi\)
\(938\) 4.37426 + 10.2675i 0.142825 + 0.335247i
\(939\) 0 0
\(940\) −20.2205 + 24.6462i −0.659520 + 0.803869i
\(941\) −23.5114 + 13.5743i −0.766450 + 0.442510i −0.831607 0.555365i \(-0.812579\pi\)
0.0651568 + 0.997875i \(0.479245\pi\)
\(942\) 0 0
\(943\) 21.0733 + 12.1667i 0.686240 + 0.396201i
\(944\) −5.43463 1.84302i −0.176882 0.0599853i
\(945\) 0 0
\(946\) −12.0014 14.1432i −0.390199 0.459835i
\(947\) −25.5373 + 44.2319i −0.829852 + 1.43735i 0.0683027 + 0.997665i \(0.478242\pi\)
−0.898154 + 0.439680i \(0.855092\pi\)
\(948\) 0 0
\(949\) −0.115089 0.199339i −0.00373593 0.00647082i
\(950\) 35.4208 6.44773i 1.14920 0.209192i
\(951\) 0 0
\(952\) −36.3361 38.0118i −1.17766 1.23197i
\(953\) 18.8458i 0.610476i −0.952276 0.305238i \(-0.901264\pi\)
0.952276 0.305238i \(-0.0987361\pi\)
\(954\) 0 0
\(955\) 17.3948 10.0429i 0.562883 0.324980i
\(956\) 18.2313 6.86486i 0.589644 0.222025i
\(957\) 0 0
\(958\) −30.6400 + 26.0000i −0.989935 + 0.840022i
\(959\) 10.8663 2.46051i 0.350890 0.0794539i
\(960\) 0 0
\(961\) −14.3529 + 24.8600i −0.462998 + 0.801936i
\(962\) 17.4166 + 6.23031i 0.561534 + 0.200873i
\(963\) 0 0
\(964\) 9.31306 + 7.64073i 0.299953 + 0.246091i
\(965\) 49.5505i 1.59509i
\(966\) 0 0
\(967\) 9.75651i 0.313748i 0.987619 + 0.156874i \(0.0501417\pi\)
−0.987619 + 0.156874i \(0.949858\pi\)
\(968\) 22.2071 0.368306i 0.713764 0.0118378i
\(969\) 0 0
\(970\) −1.46059 + 4.08302i −0.0468967 + 0.131098i
\(971\) 27.7505 48.0653i 0.890557 1.54249i 0.0513476 0.998681i \(-0.483648\pi\)
0.839209 0.543809i \(-0.183018\pi\)
\(972\) 0 0
\(973\) 8.27229 26.6553i 0.265198 0.854531i
\(974\) −29.6539 34.9460i −0.950171 1.11974i
\(975\) 0 0
\(976\) −11.4136 57.2918i −0.365341 1.83387i
\(977\) −18.5299 + 10.6982i −0.592824 + 0.342267i −0.766213 0.642586i \(-0.777861\pi\)
0.173389 + 0.984853i \(0.444528\pi\)
\(978\) 0 0
\(979\) 11.5020i 0.367606i
\(980\) −28.8768 27.7396i −0.922436 0.886109i
\(981\) 0 0
\(982\) 4.88823 + 26.8537i 0.155990 + 0.856935i
\(983\) 1.01003 + 1.74942i 0.0322149 + 0.0557979i 0.881683 0.471842i \(-0.156411\pi\)
−0.849468 + 0.527639i \(0.823077\pi\)
\(984\) 0 0
\(985\) 6.32071 10.9478i 0.201395 0.348826i
\(986\) −54.6671 + 46.3885i −1.74096 + 1.47731i
\(987\) 0 0
\(988\) 74.3922 + 12.2709i 2.36673 + 0.390391i
\(989\) 31.5234 + 18.2001i 1.00239 + 0.578728i
\(990\) 0 0
\(991\) 26.8179 15.4834i 0.851900 0.491845i −0.00939132 0.999956i \(-0.502989\pi\)
0.861292 + 0.508111i \(0.169656\pi\)
\(992\) −8.47584 1.25408i −0.269108 0.0398171i
\(993\) 0 0
\(994\) 5.16758 42.5491i 0.163906 1.34958i
\(995\) −1.78104 −0.0564629
\(996\) 0 0
\(997\) 4.71534 + 8.16720i 0.149336 + 0.258658i 0.930982 0.365064i \(-0.118953\pi\)
−0.781646 + 0.623722i \(0.785620\pi\)
\(998\) 12.3770 34.5994i 0.391787 1.09523i
\(999\) 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.be.c.107.6 28
3.2 odd 2 inner 756.2.be.c.107.9 yes 28
4.3 odd 2 756.2.be.d.107.2 yes 28
7.4 even 3 756.2.be.d.431.13 yes 28
12.11 even 2 756.2.be.d.107.13 yes 28
21.11 odd 6 756.2.be.d.431.2 yes 28
28.11 odd 6 inner 756.2.be.c.431.9 yes 28
84.11 even 6 inner 756.2.be.c.431.6 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.be.c.107.6 28 1.1 even 1 trivial
756.2.be.c.107.9 yes 28 3.2 odd 2 inner
756.2.be.c.431.6 yes 28 84.11 even 6 inner
756.2.be.c.431.9 yes 28 28.11 odd 6 inner
756.2.be.d.107.2 yes 28 4.3 odd 2
756.2.be.d.107.13 yes 28 12.11 even 2
756.2.be.d.431.2 yes 28 21.11 odd 6
756.2.be.d.431.13 yes 28 7.4 even 3