Properties

Label 504.2.cj.d.37.2
Level $504$
Weight $2$
Character 504.37
Analytic conductor $4.024$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(37,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cj (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 37.2
Root \(-1.01214 - 0.987711i\) of defining polynomial
Character \(\chi\) \(=\) 504.37
Dual form 504.2.cj.d.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.01214 + 0.987711i) q^{2} +(0.0488544 - 1.99940i) q^{4} +(2.26303 + 1.30656i) q^{5} +(2.62132 + 0.358719i) q^{7} +(1.92538 + 2.07193i) q^{8} +O(q^{10})\) \(q+(-1.01214 + 0.987711i) q^{2} +(0.0488544 - 1.99940i) q^{4} +(2.26303 + 1.30656i) q^{5} +(2.62132 + 0.358719i) q^{7} +(1.92538 + 2.07193i) q^{8} +(-3.58101 + 0.912798i) q^{10} +(1.87476 - 1.08239i) q^{11} -6.50490i q^{13} +(-3.00745 + 2.22603i) q^{14} +(-3.99523 - 0.195359i) q^{16} +(0.797521 + 1.38135i) q^{17} +(-1.27620 - 0.736813i) q^{19} +(2.72291 - 4.46088i) q^{20} +(-0.828427 + 2.94725i) q^{22} +(-1.92538 + 3.33486i) q^{23} +(0.914214 + 1.58346i) q^{25} +(6.42496 + 6.58387i) q^{26} +(0.845288 - 5.22355i) q^{28} -7.39104i q^{29} +(1.79289 + 3.10538i) q^{31} +(4.23669 - 3.74840i) q^{32} +(-2.17157 - 0.610396i) q^{34} +(5.46345 + 4.23671i) q^{35} +(6.69064 + 3.86285i) q^{37} +(2.01945 - 0.514756i) q^{38} +(1.65010 + 7.20448i) q^{40} +7.70154 q^{41} +2.69442i q^{43} +(-2.07255 - 3.80128i) q^{44} +(-1.34512 - 5.27707i) q^{46} +(-5.77615 + 10.0046i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-2.48932 - 0.699709i) q^{50} +(-13.0059 - 0.317793i) q^{52} +(-8.66386 + 5.00208i) q^{53} +5.65685 q^{55} +(4.30381 + 6.12186i) q^{56} +(7.30021 + 7.48076i) q^{58} +(-8.11475 + 4.68506i) q^{59} +(-3.60963 - 2.08402i) q^{61} +(-4.88188 - 1.37222i) q^{62} +(-0.585786 + 7.97852i) q^{64} +(8.49906 - 14.7208i) q^{65} +(9.99062 - 5.76809i) q^{67} +(2.80083 - 1.52708i) q^{68} +(-9.71442 + 1.10816i) q^{70} -14.7424 q^{71} +(1.50000 + 2.59808i) q^{73} +(-10.5872 + 2.69868i) q^{74} +(-1.53553 + 2.51564i) q^{76} +(5.30262 - 2.16478i) q^{77} +(-3.62132 + 6.27231i) q^{79} +(-8.78608 - 5.66212i) q^{80} +(-7.79504 + 7.60689i) q^{82} -7.20533i q^{83} +4.16804i q^{85} +(-2.66131 - 2.72713i) q^{86} +(5.85227 + 1.80035i) q^{88} +(3.85077 - 6.66973i) q^{89} +(2.33343 - 17.0514i) q^{91} +(6.57368 + 4.01254i) q^{92} +(-4.03537 - 15.8312i) q^{94} +(-1.92538 - 3.33486i) q^{95} +0.828427 q^{97} +(-8.68202 + 4.75631i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{4} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 32 q^{22} - 8 q^{25} - 16 q^{28} + 40 q^{31} - 80 q^{34} - 32 q^{40} - 8 q^{46} + 40 q^{49} + 8 q^{52} - 32 q^{64} - 16 q^{70} + 24 q^{73} + 32 q^{76} - 24 q^{79} - 16 q^{82} - 32 q^{88} - 24 q^{94} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.01214 + 0.987711i −0.715691 + 0.698417i
\(3\) 0 0
\(4\) 0.0488544 1.99940i 0.0244272 0.999702i
\(5\) 2.26303 + 1.30656i 1.01206 + 0.584313i 0.911794 0.410648i \(-0.134697\pi\)
0.100265 + 0.994961i \(0.468031\pi\)
\(6\) 0 0
\(7\) 2.62132 + 0.358719i 0.990766 + 0.135583i
\(8\) 1.92538 + 2.07193i 0.680726 + 0.732538i
\(9\) 0 0
\(10\) −3.58101 + 0.912798i −1.13242 + 0.288652i
\(11\) 1.87476 1.08239i 0.565261 0.326354i −0.189993 0.981785i \(-0.560847\pi\)
0.755254 + 0.655432i \(0.227513\pi\)
\(12\) 0 0
\(13\) 6.50490i 1.80413i −0.431596 0.902067i \(-0.642049\pi\)
0.431596 0.902067i \(-0.357951\pi\)
\(14\) −3.00745 + 2.22603i −0.803776 + 0.594932i
\(15\) 0 0
\(16\) −3.99523 0.195359i −0.998807 0.0488398i
\(17\) 0.797521 + 1.38135i 0.193427 + 0.335026i 0.946384 0.323045i \(-0.104706\pi\)
−0.752957 + 0.658070i \(0.771373\pi\)
\(18\) 0 0
\(19\) −1.27620 0.736813i −0.292780 0.169036i 0.346415 0.938081i \(-0.387399\pi\)
−0.639195 + 0.769045i \(0.720732\pi\)
\(20\) 2.72291 4.46088i 0.608860 0.997484i
\(21\) 0 0
\(22\) −0.828427 + 2.94725i −0.176621 + 0.628356i
\(23\) −1.92538 + 3.33486i −0.401470 + 0.695367i −0.993904 0.110252i \(-0.964834\pi\)
0.592433 + 0.805620i \(0.298167\pi\)
\(24\) 0 0
\(25\) 0.914214 + 1.58346i 0.182843 + 0.316693i
\(26\) 6.42496 + 6.58387i 1.26004 + 1.29120i
\(27\) 0 0
\(28\) 0.845288 5.22355i 0.159744 0.987158i
\(29\) 7.39104i 1.37248i −0.727375 0.686240i \(-0.759260\pi\)
0.727375 0.686240i \(-0.240740\pi\)
\(30\) 0 0
\(31\) 1.79289 + 3.10538i 0.322013 + 0.557743i 0.980903 0.194496i \(-0.0623071\pi\)
−0.658890 + 0.752239i \(0.728974\pi\)
\(32\) 4.23669 3.74840i 0.748947 0.662629i
\(33\) 0 0
\(34\) −2.17157 0.610396i −0.372422 0.104682i
\(35\) 5.46345 + 4.23671i 0.923491 + 0.716135i
\(36\) 0 0
\(37\) 6.69064 + 3.86285i 1.09994 + 0.635048i 0.936204 0.351457i \(-0.114314\pi\)
0.163731 + 0.986505i \(0.447647\pi\)
\(38\) 2.01945 0.514756i 0.327598 0.0835045i
\(39\) 0 0
\(40\) 1.65010 + 7.20448i 0.260904 + 1.13913i
\(41\) 7.70154 1.20278 0.601389 0.798956i \(-0.294614\pi\)
0.601389 + 0.798956i \(0.294614\pi\)
\(42\) 0 0
\(43\) 2.69442i 0.410895i 0.978668 + 0.205447i \(0.0658649\pi\)
−0.978668 + 0.205447i \(0.934135\pi\)
\(44\) −2.07255 3.80128i −0.312448 0.573064i
\(45\) 0 0
\(46\) −1.34512 5.27707i −0.198328 0.778062i
\(47\) −5.77615 + 10.0046i −0.842539 + 1.45932i 0.0452029 + 0.998978i \(0.485607\pi\)
−0.887742 + 0.460342i \(0.847727\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) −2.48932 0.699709i −0.352043 0.0989538i
\(51\) 0 0
\(52\) −13.0059 0.317793i −1.80360 0.0440700i
\(53\) −8.66386 + 5.00208i −1.19007 + 0.687089i −0.958323 0.285687i \(-0.907778\pi\)
−0.231749 + 0.972776i \(0.574445\pi\)
\(54\) 0 0
\(55\) 5.65685 0.762770
\(56\) 4.30381 + 6.12186i 0.575121 + 0.818069i
\(57\) 0 0
\(58\) 7.30021 + 7.48076i 0.958564 + 0.982272i
\(59\) −8.11475 + 4.68506i −1.05645 + 0.609942i −0.924448 0.381307i \(-0.875474\pi\)
−0.132003 + 0.991249i \(0.542141\pi\)
\(60\) 0 0
\(61\) −3.60963 2.08402i −0.462166 0.266832i 0.250789 0.968042i \(-0.419310\pi\)
−0.712955 + 0.701210i \(0.752643\pi\)
\(62\) −4.88188 1.37222i −0.619999 0.174272i
\(63\) 0 0
\(64\) −0.585786 + 7.97852i −0.0732233 + 0.997316i
\(65\) 8.49906 14.7208i 1.05418 1.82589i
\(66\) 0 0
\(67\) 9.99062 5.76809i 1.22055 0.704684i 0.255513 0.966806i \(-0.417756\pi\)
0.965035 + 0.262122i \(0.0844222\pi\)
\(68\) 2.80083 1.52708i 0.339651 0.185186i
\(69\) 0 0
\(70\) −9.71442 + 1.10816i −1.16110 + 0.132450i
\(71\) −14.7424 −1.74960 −0.874800 0.484484i \(-0.839007\pi\)
−0.874800 + 0.484484i \(0.839007\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) −10.5872 + 2.69868i −1.23074 + 0.313715i
\(75\) 0 0
\(76\) −1.53553 + 2.51564i −0.176138 + 0.288563i
\(77\) 5.30262 2.16478i 0.604289 0.246700i
\(78\) 0 0
\(79\) −3.62132 + 6.27231i −0.407430 + 0.705690i −0.994601 0.103773i \(-0.966908\pi\)
0.587171 + 0.809463i \(0.300242\pi\)
\(80\) −8.78608 5.66212i −0.982314 0.633044i
\(81\) 0 0
\(82\) −7.79504 + 7.60689i −0.860818 + 0.840041i
\(83\) 7.20533i 0.790887i −0.918490 0.395444i \(-0.870591\pi\)
0.918490 0.395444i \(-0.129409\pi\)
\(84\) 0 0
\(85\) 4.16804i 0.452088i
\(86\) −2.66131 2.72713i −0.286976 0.294074i
\(87\) 0 0
\(88\) 5.85227 + 1.80035i 0.623854 + 0.191918i
\(89\) 3.85077 6.66973i 0.408181 0.706990i −0.586505 0.809945i \(-0.699497\pi\)
0.994686 + 0.102956i \(0.0328300\pi\)
\(90\) 0 0
\(91\) 2.33343 17.0514i 0.244610 1.78747i
\(92\) 6.57368 + 4.01254i 0.685353 + 0.418337i
\(93\) 0 0
\(94\) −4.03537 15.8312i −0.416217 1.63287i
\(95\) −1.92538 3.33486i −0.197540 0.342150i
\(96\) 0 0
\(97\) 0.828427 0.0841140 0.0420570 0.999115i \(-0.486609\pi\)
0.0420570 + 0.999115i \(0.486609\pi\)
\(98\) −8.68202 + 4.75631i −0.877017 + 0.480460i
\(99\) 0 0
\(100\) 3.21065 1.75052i 0.321065 0.175052i
\(101\) −3.74952 + 2.16478i −0.373091 + 0.215404i −0.674808 0.737993i \(-0.735774\pi\)
0.301717 + 0.953398i \(0.402440\pi\)
\(102\) 0 0
\(103\) 5.20711 9.01897i 0.513071 0.888666i −0.486814 0.873506i \(-0.661841\pi\)
0.999885 0.0151600i \(-0.00482576\pi\)
\(104\) 13.4777 12.5244i 1.32160 1.22812i
\(105\) 0 0
\(106\) 3.82843 13.6202i 0.371850 1.32291i
\(107\) 2.81214 + 1.62359i 0.271860 + 0.156958i 0.629732 0.776812i \(-0.283165\pi\)
−0.357873 + 0.933770i \(0.616498\pi\)
\(108\) 0 0
\(109\) −9.24304 + 5.33647i −0.885323 + 0.511141i −0.872410 0.488775i \(-0.837444\pi\)
−0.0129129 + 0.999917i \(0.504110\pi\)
\(110\) −5.72553 + 5.58734i −0.545908 + 0.532732i
\(111\) 0 0
\(112\) −10.4027 1.94526i −0.982962 0.183810i
\(113\) 9.29658 0.874549 0.437274 0.899328i \(-0.355944\pi\)
0.437274 + 0.899328i \(0.355944\pi\)
\(114\) 0 0
\(115\) −8.71442 + 5.03127i −0.812624 + 0.469169i
\(116\) −14.7777 0.361085i −1.37207 0.0335259i
\(117\) 0 0
\(118\) 3.58579 12.7570i 0.330098 1.17437i
\(119\) 1.59504 + 3.90704i 0.146217 + 0.358157i
\(120\) 0 0
\(121\) −3.15685 + 5.46783i −0.286987 + 0.497076i
\(122\) 5.71186 1.45595i 0.517128 0.131816i
\(123\) 0 0
\(124\) 6.29650 3.43300i 0.565443 0.308293i
\(125\) 8.28772i 0.741276i
\(126\) 0 0
\(127\) −10.0711 −0.893663 −0.446831 0.894618i \(-0.647448\pi\)
−0.446831 + 0.894618i \(0.647448\pi\)
\(128\) −7.28758 8.65397i −0.644137 0.764910i
\(129\) 0 0
\(130\) 5.93766 + 23.2941i 0.520767 + 2.04303i
\(131\) 4.52607 + 2.61313i 0.395444 + 0.228310i 0.684516 0.728997i \(-0.260013\pi\)
−0.289072 + 0.957307i \(0.593347\pi\)
\(132\) 0 0
\(133\) −3.08101 2.38922i −0.267158 0.207172i
\(134\) −4.41470 + 15.7060i −0.381372 + 1.35679i
\(135\) 0 0
\(136\) −1.32652 + 4.31203i −0.113748 + 0.369753i
\(137\) −7.70154 13.3395i −0.657987 1.13967i −0.981136 0.193319i \(-0.938075\pi\)
0.323149 0.946348i \(-0.395258\pi\)
\(138\) 0 0
\(139\) 15.7042i 1.33201i 0.745945 + 0.666007i \(0.231998\pi\)
−0.745945 + 0.666007i \(0.768002\pi\)
\(140\) 8.73781 10.7166i 0.738480 0.905722i
\(141\) 0 0
\(142\) 14.9214 14.5612i 1.25217 1.22195i
\(143\) −7.04085 12.1951i −0.588786 1.01981i
\(144\) 0 0
\(145\) 9.65685 16.7262i 0.801958 1.38903i
\(146\) −4.08436 1.14805i −0.338024 0.0950133i
\(147\) 0 0
\(148\) 8.05025 13.1886i 0.661727 1.08409i
\(149\) −9.05213 5.22625i −0.741580 0.428151i 0.0810637 0.996709i \(-0.474168\pi\)
−0.822643 + 0.568558i \(0.807502\pi\)
\(150\) 0 0
\(151\) −4.41421 7.64564i −0.359224 0.622194i 0.628608 0.777723i \(-0.283625\pi\)
−0.987831 + 0.155529i \(0.950292\pi\)
\(152\) −0.930546 4.06284i −0.0754773 0.329540i
\(153\) 0 0
\(154\) −3.22881 + 7.42852i −0.260185 + 0.598607i
\(155\) 9.37011i 0.752625i
\(156\) 0 0
\(157\) 7.21926 4.16804i 0.576160 0.332646i −0.183446 0.983030i \(-0.558725\pi\)
0.759606 + 0.650384i \(0.225392\pi\)
\(158\) −2.52995 9.92527i −0.201272 0.789612i
\(159\) 0 0
\(160\) 14.4853 2.94725i 1.14516 0.233001i
\(161\) −6.24333 + 8.05107i −0.492043 + 0.634514i
\(162\) 0 0
\(163\) −8.71442 5.03127i −0.682566 0.394080i 0.118255 0.992983i \(-0.462270\pi\)
−0.800821 + 0.598904i \(0.795603\pi\)
\(164\) 0.376254 15.3985i 0.0293805 1.20242i
\(165\) 0 0
\(166\) 7.11678 + 7.29280i 0.552369 + 0.566031i
\(167\) 14.7424 1.14080 0.570400 0.821367i \(-0.306788\pi\)
0.570400 + 0.821367i \(0.306788\pi\)
\(168\) 0 0
\(169\) −29.3137 −2.25490
\(170\) −4.11682 4.21864i −0.315746 0.323555i
\(171\) 0 0
\(172\) 5.38723 + 0.131634i 0.410772 + 0.0100370i
\(173\) −5.23600 3.02301i −0.398086 0.229835i 0.287572 0.957759i \(-0.407152\pi\)
−0.685658 + 0.727924i \(0.740485\pi\)
\(174\) 0 0
\(175\) 1.82843 + 4.47871i 0.138216 + 0.338559i
\(176\) −7.70154 + 3.95815i −0.580525 + 0.298357i
\(177\) 0 0
\(178\) 2.69025 + 10.5541i 0.201642 + 0.791067i
\(179\) −19.0416 + 10.9937i −1.42324 + 0.821708i −0.996574 0.0827020i \(-0.973645\pi\)
−0.426665 + 0.904410i \(0.640312\pi\)
\(180\) 0 0
\(181\) 4.77844i 0.355179i −0.984105 0.177589i \(-0.943170\pi\)
0.984105 0.177589i \(-0.0568299\pi\)
\(182\) 14.4801 + 19.5632i 1.07334 + 1.45012i
\(183\) 0 0
\(184\) −10.6167 + 2.43164i −0.782674 + 0.179263i
\(185\) 10.0941 + 17.4835i 0.742133 + 1.28541i
\(186\) 0 0
\(187\) 2.99032 + 1.72646i 0.218674 + 0.126251i
\(188\) 19.7210 + 12.0376i 1.43830 + 0.877934i
\(189\) 0 0
\(190\) 5.24264 + 1.47363i 0.380341 + 0.106908i
\(191\) −8.96624 + 15.5300i −0.648774 + 1.12371i 0.334642 + 0.942345i \(0.391385\pi\)
−0.983416 + 0.181364i \(0.941949\pi\)
\(192\) 0 0
\(193\) −5.15685 8.93193i −0.371198 0.642935i 0.618552 0.785744i \(-0.287720\pi\)
−0.989750 + 0.142809i \(0.954386\pi\)
\(194\) −0.838484 + 0.818246i −0.0601997 + 0.0587467i
\(195\) 0 0
\(196\) 4.08956 13.3894i 0.292111 0.956384i
\(197\) 19.5600i 1.39359i 0.717270 + 0.696796i \(0.245392\pi\)
−0.717270 + 0.696796i \(0.754608\pi\)
\(198\) 0 0
\(199\) 0.414214 + 0.717439i 0.0293628 + 0.0508579i 0.880333 0.474355i \(-0.157319\pi\)
−0.850971 + 0.525213i \(0.823986\pi\)
\(200\) −1.52061 + 4.94296i −0.107524 + 0.349520i
\(201\) 0 0
\(202\) 1.65685 5.89450i 0.116576 0.414736i
\(203\) 2.65131 19.3743i 0.186085 1.35981i
\(204\) 0 0
\(205\) 17.4288 + 10.0625i 1.21728 + 0.702799i
\(206\) 3.63782 + 14.2716i 0.253459 + 0.994348i
\(207\) 0 0
\(208\) −1.27079 + 25.9885i −0.0881136 + 1.80198i
\(209\) −3.19008 −0.220663
\(210\) 0 0
\(211\) 20.1251i 1.38547i 0.721193 + 0.692734i \(0.243594\pi\)
−0.721193 + 0.692734i \(0.756406\pi\)
\(212\) 9.57791 + 17.5669i 0.657814 + 1.20650i
\(213\) 0 0
\(214\) −4.44991 + 1.13428i −0.304190 + 0.0775378i
\(215\) −3.52043 + 6.09756i −0.240091 + 0.415850i
\(216\) 0 0
\(217\) 3.58579 + 8.78335i 0.243419 + 0.596252i
\(218\) 4.08436 14.5307i 0.276628 0.984144i
\(219\) 0 0
\(220\) 0.276362 11.3103i 0.0186323 0.762542i
\(221\) 8.98552 5.18779i 0.604431 0.348969i
\(222\) 0 0
\(223\) −16.1421 −1.08096 −0.540479 0.841358i \(-0.681757\pi\)
−0.540479 + 0.841358i \(0.681757\pi\)
\(224\) 12.4503 8.30597i 0.831873 0.554966i
\(225\) 0 0
\(226\) −9.40944 + 9.18233i −0.625907 + 0.610800i
\(227\) 13.8999 8.02509i 0.922566 0.532644i 0.0381132 0.999273i \(-0.487865\pi\)
0.884453 + 0.466630i \(0.154532\pi\)
\(228\) 0 0
\(229\) −13.9099 8.03089i −0.919192 0.530696i −0.0358151 0.999358i \(-0.511403\pi\)
−0.883377 + 0.468662i \(0.844736\pi\)
\(230\) 3.85077 13.6997i 0.253912 0.903330i
\(231\) 0 0
\(232\) 15.3137 14.2306i 1.00539 0.934284i
\(233\) 6.24333 10.8138i 0.409014 0.708433i −0.585765 0.810481i \(-0.699206\pi\)
0.994780 + 0.102047i \(0.0325393\pi\)
\(234\) 0 0
\(235\) −26.1433 + 15.0938i −1.70540 + 0.984612i
\(236\) 8.97087 + 16.4536i 0.583954 + 1.07104i
\(237\) 0 0
\(238\) −5.47343 2.37903i −0.354790 0.154210i
\(239\) −4.51146 −0.291822 −0.145911 0.989298i \(-0.546611\pi\)
−0.145911 + 0.989298i \(0.546611\pi\)
\(240\) 0 0
\(241\) 1.58579 + 2.74666i 0.102149 + 0.176928i 0.912570 0.408920i \(-0.134095\pi\)
−0.810421 + 0.585849i \(0.800761\pi\)
\(242\) −2.20546 8.65227i −0.141772 0.556189i
\(243\) 0 0
\(244\) −4.34315 + 7.11529i −0.278041 + 0.455510i
\(245\) 12.8017 + 13.0656i 0.817867 + 0.834732i
\(246\) 0 0
\(247\) −4.79289 + 8.30153i −0.304964 + 0.528214i
\(248\) −2.98212 + 9.69380i −0.189365 + 0.615557i
\(249\) 0 0
\(250\) 8.18587 + 8.38833i 0.517720 + 0.530525i
\(251\) 5.04054i 0.318156i −0.987266 0.159078i \(-0.949148\pi\)
0.987266 0.159078i \(-0.0508522\pi\)
\(252\) 0 0
\(253\) 8.33609i 0.524085i
\(254\) 10.1933 9.94730i 0.639586 0.624149i
\(255\) 0 0
\(256\) 15.9237 + 1.56101i 0.995229 + 0.0975631i
\(257\) −6.90402 + 11.9581i −0.430661 + 0.745926i −0.996930 0.0782937i \(-0.975053\pi\)
0.566269 + 0.824220i \(0.308386\pi\)
\(258\) 0 0
\(259\) 16.1526 + 12.5258i 1.00368 + 0.778317i
\(260\) −29.0176 17.7122i −1.79960 1.09847i
\(261\) 0 0
\(262\) −7.16203 + 1.82560i −0.442471 + 0.112786i
\(263\) 5.44581 + 9.43242i 0.335803 + 0.581628i 0.983639 0.180152i \(-0.0576590\pi\)
−0.647836 + 0.761780i \(0.724326\pi\)
\(264\) 0 0
\(265\) −26.1421 −1.60590
\(266\) 5.47827 0.624926i 0.335895 0.0383167i
\(267\) 0 0
\(268\) −11.0446 20.2571i −0.674659 1.23740i
\(269\) 18.1043 10.4525i 1.10384 0.637300i 0.166611 0.986023i \(-0.446718\pi\)
0.937226 + 0.348722i \(0.113384\pi\)
\(270\) 0 0
\(271\) 12.0711 20.9077i 0.733265 1.27005i −0.222215 0.974998i \(-0.571329\pi\)
0.955480 0.295055i \(-0.0953379\pi\)
\(272\) −2.91642 5.67459i −0.176834 0.344073i
\(273\) 0 0
\(274\) 20.9706 + 5.89450i 1.26688 + 0.356100i
\(275\) 3.42786 + 1.97908i 0.206708 + 0.119343i
\(276\) 0 0
\(277\) −7.74788 + 4.47324i −0.465525 + 0.268771i −0.714365 0.699774i \(-0.753284\pi\)
0.248840 + 0.968545i \(0.419951\pi\)
\(278\) −15.5112 15.8949i −0.930301 0.953311i
\(279\) 0 0
\(280\) 1.74106 + 19.4772i 0.104048 + 1.16398i
\(281\) 4.78512 0.285457 0.142728 0.989762i \(-0.454413\pi\)
0.142728 + 0.989762i \(0.454413\pi\)
\(282\) 0 0
\(283\) 20.8195 12.0202i 1.23759 0.714524i 0.268990 0.963143i \(-0.413310\pi\)
0.968601 + 0.248619i \(0.0799768\pi\)
\(284\) −0.720231 + 29.4760i −0.0427378 + 1.74908i
\(285\) 0 0
\(286\) 19.1716 + 5.38883i 1.13364 + 0.318648i
\(287\) 20.1882 + 2.76269i 1.19167 + 0.163077i
\(288\) 0 0
\(289\) 7.22792 12.5191i 0.425172 0.736419i
\(290\) 6.74652 + 26.4674i 0.396170 + 1.55422i
\(291\) 0 0
\(292\) 5.26788 2.87218i 0.308280 0.168081i
\(293\) 10.8239i 0.632340i −0.948703 0.316170i \(-0.897603\pi\)
0.948703 0.316170i \(-0.102397\pi\)
\(294\) 0 0
\(295\) −24.4853 −1.42559
\(296\) 4.87852 + 21.3000i 0.283558 + 1.23804i
\(297\) 0 0
\(298\) 14.3241 3.65119i 0.829770 0.211508i
\(299\) 21.6930 + 12.5244i 1.25454 + 0.724307i
\(300\) 0 0
\(301\) −0.966540 + 7.06293i −0.0557104 + 0.407101i
\(302\) 12.0195 + 3.37849i 0.691644 + 0.194410i
\(303\) 0 0
\(304\) 4.95475 + 3.19305i 0.284175 + 0.183134i
\(305\) −5.44581 9.43242i −0.311826 0.540099i
\(306\) 0 0
\(307\) 10.3154i 0.588730i −0.955693 0.294365i \(-0.904892\pi\)
0.955693 0.294365i \(-0.0951081\pi\)
\(308\) −4.06922 10.7078i −0.231865 0.610135i
\(309\) 0 0
\(310\) −9.25496 9.48386i −0.525646 0.538647i
\(311\) −16.9981 29.4416i −0.963875 1.66948i −0.712608 0.701563i \(-0.752486\pi\)
−0.251267 0.967918i \(-0.580847\pi\)
\(312\) 0 0
\(313\) −2.98528 + 5.17066i −0.168738 + 0.292263i −0.937976 0.346699i \(-0.887303\pi\)
0.769238 + 0.638962i \(0.220636\pi\)
\(314\) −3.19008 + 11.3492i −0.180027 + 0.640472i
\(315\) 0 0
\(316\) 12.3640 + 7.54691i 0.695527 + 0.424547i
\(317\) −8.73048 5.04054i −0.490352 0.283105i 0.234368 0.972148i \(-0.424698\pi\)
−0.724721 + 0.689043i \(0.758031\pi\)
\(318\) 0 0
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) −11.7501 + 17.2903i −0.656851 + 0.966557i
\(321\) 0 0
\(322\) −1.63301 14.3154i −0.0910041 0.797767i
\(323\) 2.35049i 0.130785i
\(324\) 0 0
\(325\) 10.3003 5.94687i 0.571356 0.329873i
\(326\) 13.7897 3.51498i 0.763738 0.194677i
\(327\) 0 0
\(328\) 14.8284 + 15.9570i 0.818763 + 0.881081i
\(329\) −18.7300 + 24.1532i −1.03262 + 1.33161i
\(330\) 0 0
\(331\) 4.88583 + 2.82083i 0.268549 + 0.155047i 0.628228 0.778029i \(-0.283780\pi\)
−0.359679 + 0.933076i \(0.617114\pi\)
\(332\) −14.4064 0.352012i −0.790651 0.0193192i
\(333\) 0 0
\(334\) −14.9214 + 14.5612i −0.816461 + 0.796755i
\(335\) 30.1455 1.64702
\(336\) 0 0
\(337\) 12.6569 0.689463 0.344731 0.938701i \(-0.387970\pi\)
0.344731 + 0.938701i \(0.387970\pi\)
\(338\) 29.6696 28.9535i 1.61381 1.57486i
\(339\) 0 0
\(340\) 8.33360 + 0.203627i 0.451953 + 0.0110432i
\(341\) 6.72248 + 3.88123i 0.364043 + 0.210180i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) −5.58264 + 5.18779i −0.300996 + 0.279707i
\(345\) 0 0
\(346\) 8.28542 2.11195i 0.445427 0.113539i
\(347\) 11.5426 6.66413i 0.619640 0.357749i −0.157089 0.987584i \(-0.550211\pi\)
0.776729 + 0.629835i \(0.216878\pi\)
\(348\) 0 0
\(349\) 24.2931i 1.30038i 0.759771 + 0.650191i \(0.225311\pi\)
−0.759771 + 0.650191i \(0.774689\pi\)
\(350\) −6.27430 2.72713i −0.335375 0.145771i
\(351\) 0 0
\(352\) 3.88553 11.6131i 0.207099 0.618980i
\(353\) 6.24333 + 10.8138i 0.332299 + 0.575559i 0.982962 0.183808i \(-0.0588424\pi\)
−0.650663 + 0.759366i \(0.725509\pi\)
\(354\) 0 0
\(355\) −33.3625 19.2619i −1.77070 1.02231i
\(356\) −13.1474 8.02509i −0.696808 0.425329i
\(357\) 0 0
\(358\) 8.41421 29.9348i 0.444705 1.58210i
\(359\) −1.59504 + 2.76269i −0.0841830 + 0.145809i −0.905043 0.425320i \(-0.860161\pi\)
0.820860 + 0.571130i \(0.193495\pi\)
\(360\) 0 0
\(361\) −8.41421 14.5738i −0.442853 0.767044i
\(362\) 4.71972 + 4.83645i 0.248063 + 0.254198i
\(363\) 0 0
\(364\) −33.9787 5.49851i −1.78097 0.288200i
\(365\) 7.83938i 0.410332i
\(366\) 0 0
\(367\) 15.6924 + 27.1800i 0.819136 + 1.41879i 0.906320 + 0.422593i \(0.138880\pi\)
−0.0871836 + 0.996192i \(0.527787\pi\)
\(368\) 8.34385 12.9474i 0.434953 0.674930i
\(369\) 0 0
\(370\) −27.4853 7.72569i −1.42889 0.401640i
\(371\) −24.5051 + 10.0042i −1.27224 + 0.519390i
\(372\) 0 0
\(373\) −20.5099 11.8414i −1.06196 0.613123i −0.135986 0.990711i \(-0.543420\pi\)
−0.925974 + 0.377588i \(0.876754\pi\)
\(374\) −4.73186 + 1.20615i −0.244679 + 0.0623685i
\(375\) 0 0
\(376\) −31.8501 + 7.29491i −1.64255 + 0.376206i
\(377\) −48.0779 −2.47614
\(378\) 0 0
\(379\) 16.2099i 0.832646i −0.909217 0.416323i \(-0.863319\pi\)
0.909217 0.416323i \(-0.136681\pi\)
\(380\) −6.76180 + 3.68670i −0.346873 + 0.189124i
\(381\) 0 0
\(382\) −6.26404 24.5746i −0.320496 1.25734i
\(383\) 15.0727 26.1067i 0.770181 1.33399i −0.167283 0.985909i \(-0.553499\pi\)
0.937464 0.348083i \(-0.113167\pi\)
\(384\) 0 0
\(385\) 14.8284 + 2.02922i 0.755727 + 0.103419i
\(386\) 14.0416 + 3.94689i 0.714700 + 0.200891i
\(387\) 0 0
\(388\) 0.0404723 1.65636i 0.00205467 0.0840889i
\(389\) −7.88731 + 4.55374i −0.399902 + 0.230884i −0.686442 0.727185i \(-0.740828\pi\)
0.286539 + 0.958068i \(0.407495\pi\)
\(390\) 0 0
\(391\) −6.14214 −0.310621
\(392\) 9.08563 + 17.5912i 0.458894 + 0.888491i
\(393\) 0 0
\(394\) −19.3196 19.7974i −0.973308 0.997381i
\(395\) −16.3903 + 9.46297i −0.824687 + 0.476133i
\(396\) 0 0
\(397\) −15.4051 8.89412i −0.773158 0.446383i 0.0608420 0.998147i \(-0.480621\pi\)
−0.834000 + 0.551764i \(0.813955\pi\)
\(398\) −1.12786 0.317025i −0.0565347 0.0158910i
\(399\) 0 0
\(400\) −3.34315 6.50490i −0.167157 0.325245i
\(401\) −5.30898 + 9.19542i −0.265118 + 0.459197i −0.967594 0.252509i \(-0.918744\pi\)
0.702477 + 0.711707i \(0.252077\pi\)
\(402\) 0 0
\(403\) 20.2002 11.6626i 1.00624 0.580955i
\(404\) 4.14510 + 7.60255i 0.206226 + 0.378241i
\(405\) 0 0
\(406\) 16.4527 + 22.2282i 0.816533 + 1.10317i
\(407\) 16.7245 0.829000
\(408\) 0 0
\(409\) 14.4706 + 25.0637i 0.715523 + 1.23932i 0.962757 + 0.270367i \(0.0871450\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −27.5793 + 7.02995i −1.36205 + 0.347185i
\(411\) 0 0
\(412\) −17.7782 10.8517i −0.875868 0.534626i
\(413\) −22.9520 + 9.37011i −1.12939 + 0.461073i
\(414\) 0 0
\(415\) 9.41421 16.3059i 0.462126 0.800425i
\(416\) −24.3829 27.5592i −1.19547 1.35120i
\(417\) 0 0
\(418\) 3.22881 3.15088i 0.157926 0.154115i
\(419\) 18.7402i 0.915520i −0.889076 0.457760i \(-0.848652\pi\)
0.889076 0.457760i \(-0.151348\pi\)
\(420\) 0 0
\(421\) 0.610396i 0.0297489i 0.999889 + 0.0148744i \(0.00473485\pi\)
−0.999889 + 0.0148744i \(0.995265\pi\)
\(422\) −19.8778 20.3694i −0.967635 0.991567i
\(423\) 0 0
\(424\) −27.0452 8.31998i −1.31343 0.404054i
\(425\) −1.45821 + 2.52569i −0.0707335 + 0.122514i
\(426\) 0 0
\(427\) −8.71442 6.75773i −0.421720 0.327030i
\(428\) 3.38359 5.54328i 0.163552 0.267944i
\(429\) 0 0
\(430\) −2.45946 9.64874i −0.118606 0.465304i
\(431\) 3.52043 + 6.09756i 0.169573 + 0.293709i 0.938270 0.345904i \(-0.112428\pi\)
−0.768697 + 0.639613i \(0.779094\pi\)
\(432\) 0 0
\(433\) 32.7990 1.57622 0.788109 0.615535i \(-0.211060\pi\)
0.788109 + 0.615535i \(0.211060\pi\)
\(434\) −12.3047 5.34826i −0.590646 0.256724i
\(435\) 0 0
\(436\) 10.2182 + 18.7413i 0.489363 + 0.897544i
\(437\) 4.91434 2.83730i 0.235085 0.135726i
\(438\) 0 0
\(439\) −0.757359 + 1.31178i −0.0361468 + 0.0626081i −0.883533 0.468369i \(-0.844842\pi\)
0.847386 + 0.530977i \(0.178175\pi\)
\(440\) 10.8916 + 11.7206i 0.519238 + 0.558758i
\(441\) 0 0
\(442\) −3.97056 + 14.1259i −0.188860 + 0.671899i
\(443\) −32.1650 18.5704i −1.52820 0.882308i −0.999437 0.0335407i \(-0.989322\pi\)
−0.528766 0.848768i \(-0.677345\pi\)
\(444\) 0 0
\(445\) 17.4288 10.0625i 0.826206 0.477010i
\(446\) 16.3381 15.9438i 0.773631 0.754959i
\(447\) 0 0
\(448\) −4.39759 + 20.7041i −0.207766 + 0.978178i
\(449\) 1.59504 0.0752746 0.0376373 0.999291i \(-0.488017\pi\)
0.0376373 + 0.999291i \(0.488017\pi\)
\(450\) 0 0
\(451\) 14.4385 8.33609i 0.679884 0.392531i
\(452\) 0.454179 18.5876i 0.0213628 0.874288i
\(453\) 0 0
\(454\) −6.14214 + 21.8516i −0.288265 + 1.02554i
\(455\) 27.5594 35.5392i 1.29200 1.66610i
\(456\) 0 0
\(457\) −21.2279 + 36.7678i −0.993000 + 1.71993i −0.394212 + 0.919019i \(0.628983\pi\)
−0.598788 + 0.800908i \(0.704351\pi\)
\(458\) 22.0110 5.61058i 1.02850 0.262165i
\(459\) 0 0
\(460\) 9.63381 + 17.6694i 0.449179 + 0.823842i
\(461\) 39.1200i 1.82200i 0.412408 + 0.910999i \(0.364688\pi\)
−0.412408 + 0.910999i \(0.635312\pi\)
\(462\) 0 0
\(463\) 18.2132 0.846439 0.423220 0.906027i \(-0.360900\pi\)
0.423220 + 0.906027i \(0.360900\pi\)
\(464\) −1.44391 + 29.5289i −0.0670317 + 1.37084i
\(465\) 0 0
\(466\) 4.36175 + 17.1117i 0.202054 + 0.792682i
\(467\) −29.1920 16.8540i −1.35084 0.779910i −0.362476 0.931993i \(-0.618069\pi\)
−0.988368 + 0.152083i \(0.951402\pi\)
\(468\) 0 0
\(469\) 28.2577 11.5362i 1.30482 0.532691i
\(470\) 11.5523 41.0990i 0.532868 1.89576i
\(471\) 0 0
\(472\) −25.3311 7.79267i −1.16596 0.358687i
\(473\) 2.91642 + 5.05138i 0.134097 + 0.232263i
\(474\) 0 0
\(475\) 2.69442i 0.123628i
\(476\) 7.88967 2.99825i 0.361622 0.137425i
\(477\) 0 0
\(478\) 4.56623 4.45602i 0.208854 0.203813i
\(479\) −14.4120 24.9624i −0.658503 1.14056i −0.981003 0.193992i \(-0.937857\pi\)
0.322500 0.946569i \(-0.395477\pi\)
\(480\) 0 0
\(481\) 25.1274 43.5220i 1.14571 1.98443i
\(482\) −4.31795 1.21371i −0.196677 0.0552829i
\(483\) 0 0
\(484\) 10.7782 + 6.57895i 0.489917 + 0.299043i
\(485\) 1.87476 + 1.08239i 0.0851284 + 0.0491489i
\(486\) 0 0
\(487\) 5.13604 + 8.89588i 0.232736 + 0.403111i 0.958612 0.284715i \(-0.0918988\pi\)
−0.725876 + 0.687825i \(0.758565\pi\)
\(488\) −2.63198 11.4914i −0.119144 0.520193i
\(489\) 0 0
\(490\) −25.8621 0.579916i −1.16833 0.0261979i
\(491\) 7.39104i 0.333553i 0.985995 + 0.166776i \(0.0533358\pi\)
−0.985995 + 0.166776i \(0.946664\pi\)
\(492\) 0 0
\(493\) 10.2096 5.89450i 0.459816 0.265475i
\(494\) −3.34844 13.1363i −0.150653 0.591030i
\(495\) 0 0
\(496\) −6.55635 12.7570i −0.294389 0.572805i
\(497\) −38.6445 5.28838i −1.73344 0.237216i
\(498\) 0 0
\(499\) 8.49546 + 4.90486i 0.380309 + 0.219572i 0.677953 0.735106i \(-0.262867\pi\)
−0.297644 + 0.954677i \(0.596201\pi\)
\(500\) −16.5705 0.404892i −0.741055 0.0181073i
\(501\) 0 0
\(502\) 4.97860 + 5.10173i 0.222206 + 0.227702i
\(503\) 24.9733 1.11351 0.556753 0.830678i \(-0.312047\pi\)
0.556753 + 0.830678i \(0.312047\pi\)
\(504\) 0 0
\(505\) −11.3137 −0.503453
\(506\) −8.23364 8.43729i −0.366030 0.375083i
\(507\) 0 0
\(508\) −0.492016 + 20.1361i −0.0218297 + 0.893396i
\(509\) 14.2881 + 8.24926i 0.633310 + 0.365642i 0.782033 0.623237i \(-0.214183\pi\)
−0.148723 + 0.988879i \(0.547516\pi\)
\(510\) 0 0
\(511\) 3.00000 + 7.34847i 0.132712 + 0.325077i
\(512\) −17.6588 + 14.1480i −0.780416 + 0.625260i
\(513\) 0 0
\(514\) −4.82332 18.9225i −0.212748 0.834634i
\(515\) 23.5677 13.6068i 1.03852 0.599588i
\(516\) 0 0
\(517\) 25.0083i 1.09986i
\(518\) −28.7206 + 3.27626i −1.26191 + 0.143951i
\(519\) 0 0
\(520\) 46.8644 10.7338i 2.05514 0.470706i
\(521\) 14.7424 + 25.5346i 0.645876 + 1.11869i 0.984098 + 0.177624i \(0.0568410\pi\)
−0.338223 + 0.941066i \(0.609826\pi\)
\(522\) 0 0
\(523\) 19.7623 + 11.4098i 0.864144 + 0.498914i 0.865398 0.501085i \(-0.167066\pi\)
−0.00125385 + 0.999999i \(0.500399\pi\)
\(524\) 5.44581 8.92177i 0.237901 0.389749i
\(525\) 0 0
\(526\) −14.8284 4.16804i −0.646550 0.181735i
\(527\) −2.85974 + 4.95321i −0.124572 + 0.215765i
\(528\) 0 0
\(529\) 4.08579 + 7.07679i 0.177643 + 0.307687i
\(530\) 26.4595 25.8209i 1.14933 1.12159i
\(531\) 0 0
\(532\) −4.92753 + 6.04346i −0.213636 + 0.262017i
\(533\) 50.0977i 2.16997i
\(534\) 0 0
\(535\) 4.24264 + 7.34847i 0.183425 + 0.317702i
\(536\) 31.1869 + 9.59407i 1.34707 + 0.414401i
\(537\) 0 0
\(538\) −8.00000 + 28.4612i −0.344904 + 1.22705i
\(539\) 14.6764 3.77244i 0.632158 0.162491i
\(540\) 0 0
\(541\) −36.8815 21.2935i −1.58566 0.915480i −0.994011 0.109283i \(-0.965145\pi\)
−0.591647 0.806197i \(-0.701522\pi\)
\(542\) 8.43316 + 33.0842i 0.362235 + 1.42109i
\(543\) 0 0
\(544\) 8.55668 + 2.86291i 0.366865 + 0.122746i
\(545\) −27.8897 −1.19467
\(546\) 0 0
\(547\) 16.6722i 0.712851i 0.934324 + 0.356425i \(0.116005\pi\)
−0.934324 + 0.356425i \(0.883995\pi\)
\(548\) −27.0472 + 14.7468i −1.15540 + 0.629952i
\(549\) 0 0
\(550\) −5.42423 + 1.38263i −0.231290 + 0.0589556i
\(551\) −5.44581 + 9.43242i −0.231999 + 0.401835i
\(552\) 0 0
\(553\) −11.7426 + 15.1427i −0.499348 + 0.643933i
\(554\) 3.42367 12.1802i 0.145458 0.517488i
\(555\) 0 0
\(556\) 31.3991 + 0.767220i 1.33162 + 0.0325374i
\(557\) −11.7034 + 6.75699i −0.495891 + 0.286303i −0.727015 0.686622i \(-0.759093\pi\)
0.231124 + 0.972924i \(0.425760\pi\)
\(558\) 0 0
\(559\) 17.5269 0.741309
\(560\) −21.0000 17.9940i −0.887413 0.760384i
\(561\) 0 0
\(562\) −4.84321 + 4.72632i −0.204299 + 0.199368i
\(563\) −23.8894 + 13.7925i −1.00682 + 0.581286i −0.910258 0.414041i \(-0.864117\pi\)
−0.0965588 + 0.995327i \(0.530784\pi\)
\(564\) 0 0
\(565\) 21.0385 + 12.1466i 0.885095 + 0.511010i
\(566\) −9.19982 + 32.7297i −0.386697 + 1.37573i
\(567\) 0 0
\(568\) −28.3848 30.5452i −1.19100 1.28165i
\(569\) 14.7424 25.5346i 0.618033 1.07046i −0.371811 0.928308i \(-0.621263\pi\)
0.989844 0.142156i \(-0.0454036\pi\)
\(570\) 0 0
\(571\) −28.4767 + 16.4410i −1.19171 + 0.688036i −0.958695 0.284437i \(-0.908193\pi\)
−0.233018 + 0.972472i \(0.574860\pi\)
\(572\) −24.7269 + 13.4817i −1.03388 + 0.563699i
\(573\) 0 0
\(574\) −23.1620 + 17.1439i −0.966764 + 0.715572i
\(575\) −7.04085 −0.293624
\(576\) 0 0
\(577\) 8.67157 + 15.0196i 0.361002 + 0.625274i 0.988126 0.153645i \(-0.0491013\pi\)
−0.627124 + 0.778920i \(0.715768\pi\)
\(578\) 5.04961 + 19.8102i 0.210036 + 0.823996i
\(579\) 0 0
\(580\) −32.9706 20.1251i −1.36903 0.835649i
\(581\) 2.58469 18.8875i 0.107231 0.783584i
\(582\) 0 0
\(583\) −10.8284 + 18.7554i −0.448468 + 0.776769i
\(584\) −2.49495 + 8.11019i −0.103242 + 0.335602i
\(585\) 0 0
\(586\) 10.6909 + 10.9553i 0.441637 + 0.452560i
\(587\) 20.5336i 0.847512i 0.905776 + 0.423756i \(0.139289\pi\)
−0.905776 + 0.423756i \(0.860711\pi\)
\(588\) 0 0
\(589\) 5.28411i 0.217728i
\(590\) 24.7825 24.1844i 1.02028 0.995655i
\(591\) 0 0
\(592\) −25.9760 16.7400i −1.06761 0.688011i
\(593\) 11.5523 20.0092i 0.474396 0.821679i −0.525174 0.850995i \(-0.676000\pi\)
0.999570 + 0.0293163i \(0.00933299\pi\)
\(594\) 0 0
\(595\) −1.49516 + 10.9258i −0.0612955 + 0.447913i
\(596\) −10.8916 + 17.8435i −0.446138 + 0.730900i
\(597\) 0 0
\(598\) −34.3268 + 8.74989i −1.40373 + 0.357810i
\(599\) −0.660688 1.14434i −0.0269950 0.0467567i 0.852212 0.523196i \(-0.175260\pi\)
−0.879207 + 0.476439i \(0.841927\pi\)
\(600\) 0 0
\(601\) −12.7990 −0.522082 −0.261041 0.965328i \(-0.584066\pi\)
−0.261041 + 0.965328i \(0.584066\pi\)
\(602\) −5.99786 8.10334i −0.244455 0.330267i
\(603\) 0 0
\(604\) −15.5024 + 8.45227i −0.630783 + 0.343918i
\(605\) −14.2881 + 8.24926i −0.580895 + 0.335380i
\(606\) 0 0
\(607\) 5.96447 10.3308i 0.242090 0.419313i −0.719219 0.694783i \(-0.755500\pi\)
0.961309 + 0.275471i \(0.0888337\pi\)
\(608\) −8.16872 + 1.66205i −0.331285 + 0.0674050i
\(609\) 0 0
\(610\) 14.8284 + 4.16804i 0.600385 + 0.168759i
\(611\) 65.0789 + 37.5733i 2.63281 + 1.52005i
\(612\) 0 0
\(613\) 10.8289 6.25206i 0.437375 0.252519i −0.265109 0.964219i \(-0.585408\pi\)
0.702483 + 0.711700i \(0.252074\pi\)
\(614\) 10.1886 + 10.4406i 0.411179 + 0.421349i
\(615\) 0 0
\(616\) 14.6949 + 6.81861i 0.592073 + 0.274730i
\(617\) −3.19008 −0.128428 −0.0642139 0.997936i \(-0.520454\pi\)
−0.0642139 + 0.997936i \(0.520454\pi\)
\(618\) 0 0
\(619\) 5.32375 3.07367i 0.213980 0.123541i −0.389180 0.921162i \(-0.627242\pi\)
0.603160 + 0.797621i \(0.293908\pi\)
\(620\) 18.7346 + 0.457771i 0.752401 + 0.0183845i
\(621\) 0 0
\(622\) 46.2843 + 13.0098i 1.85583 + 0.521645i
\(623\) 12.4867 16.1021i 0.500268 0.645119i
\(624\) 0 0
\(625\) 15.3995 26.6727i 0.615980 1.06691i
\(626\) −2.08559 8.18203i −0.0833571 0.327020i
\(627\) 0 0
\(628\) −7.98091 14.6378i −0.318473 0.584114i
\(629\) 12.3228i 0.491342i
\(630\) 0 0
\(631\) −4.82843 −0.192217 −0.0961083 0.995371i \(-0.530640\pi\)
−0.0961083 + 0.995371i \(0.530640\pi\)
\(632\) −19.9682 + 4.57349i −0.794293 + 0.181924i
\(633\) 0 0
\(634\) 13.8151 3.52145i 0.548666 0.139855i
\(635\) −22.7912 13.1585i −0.904440 0.522179i
\(636\) 0 0
\(637\) 12.2334 43.8602i 0.484703 1.73780i
\(638\) 21.7832 + 6.12293i 0.862407 + 0.242409i
\(639\) 0 0
\(640\) −5.18507 29.1059i −0.204958 1.15051i
\(641\) −0.797521 1.38135i −0.0315002 0.0545599i 0.849846 0.527032i \(-0.176695\pi\)
−0.881346 + 0.472472i \(0.843362\pi\)
\(642\) 0 0
\(643\) 8.58892i 0.338714i −0.985555 0.169357i \(-0.945831\pi\)
0.985555 0.169357i \(-0.0541691\pi\)
\(644\) 15.7923 + 12.8763i 0.622305 + 0.507396i
\(645\) 0 0
\(646\) 2.32161 + 2.37903i 0.0913424 + 0.0936016i
\(647\) 0.660688 + 1.14434i 0.0259743 + 0.0449888i 0.878720 0.477337i \(-0.158398\pi\)
−0.852746 + 0.522326i \(0.825065\pi\)
\(648\) 0 0
\(649\) −10.1421 + 17.5667i −0.398114 + 0.689553i
\(650\) −4.55153 + 16.1928i −0.178526 + 0.635132i
\(651\) 0 0
\(652\) −10.4853 + 17.1778i −0.410635 + 0.672736i
\(653\) 20.3007 + 11.7206i 0.794427 + 0.458663i 0.841519 0.540228i \(-0.181662\pi\)
−0.0470917 + 0.998891i \(0.514995\pi\)
\(654\) 0 0
\(655\) 6.82843 + 11.8272i 0.266809 + 0.462126i
\(656\) −30.7694 1.50457i −1.20134 0.0587435i
\(657\) 0 0
\(658\) −4.89903 42.9463i −0.190984 1.67422i
\(659\) 8.10201i 0.315610i −0.987470 0.157805i \(-0.949558\pi\)
0.987470 0.157805i \(-0.0504417\pi\)
\(660\) 0 0
\(661\) −9.68096 + 5.58931i −0.376546 + 0.217399i −0.676314 0.736613i \(-0.736424\pi\)
0.299769 + 0.954012i \(0.403091\pi\)
\(662\) −7.73131 + 1.97071i −0.300486 + 0.0765937i
\(663\) 0 0
\(664\) 14.9289 13.8730i 0.579355 0.538378i
\(665\) −3.85077 9.43242i −0.149326 0.365774i
\(666\) 0 0
\(667\) 24.6481 + 14.2306i 0.954378 + 0.551011i
\(668\) 0.720231 29.4760i 0.0278666 1.14046i
\(669\) 0 0
\(670\) −30.5114 + 29.7750i −1.17876 + 1.15031i
\(671\) −9.02291 −0.348326
\(672\) 0 0
\(673\) 7.62742 0.294015 0.147008 0.989135i \(-0.453036\pi\)
0.147008 + 0.989135i \(0.453036\pi\)
\(674\) −12.8105 + 12.5013i −0.493442 + 0.481533i
\(675\) 0 0
\(676\) −1.43210 + 58.6099i −0.0550809 + 2.25423i
\(677\) −0.776550 0.448342i −0.0298453 0.0172312i 0.485003 0.874512i \(-0.338818\pi\)
−0.514848 + 0.857281i \(0.672152\pi\)
\(678\) 0 0
\(679\) 2.17157 + 0.297173i 0.0833373 + 0.0114045i
\(680\) −8.63589 + 8.02509i −0.331171 + 0.307748i
\(681\) 0 0
\(682\) −10.6376 + 2.71152i −0.407336 + 0.103830i
\(683\) 25.4425 14.6892i 0.973529 0.562067i 0.0732188 0.997316i \(-0.476673\pi\)
0.900310 + 0.435249i \(0.143340\pi\)
\(684\) 0 0
\(685\) 40.2502i 1.53788i
\(686\) −24.4645 + 9.35341i −0.934061 + 0.357115i
\(687\) 0 0
\(688\) 0.526379 10.7648i 0.0200680 0.410404i
\(689\) 32.5380 + 56.3575i 1.23960 + 2.14705i
\(690\) 0 0
\(691\) −32.0863 18.5250i −1.22062 0.704726i −0.255571 0.966790i \(-0.582263\pi\)
−0.965050 + 0.262064i \(0.915597\pi\)
\(692\) −6.30001 + 10.3212i −0.239490 + 0.392353i
\(693\) 0 0
\(694\) −5.10051 + 18.1458i −0.193613 + 0.688805i
\(695\) −20.5185 + 35.5392i −0.778313 + 1.34808i
\(696\) 0 0
\(697\) 6.14214 + 10.6385i 0.232650 + 0.402962i
\(698\) −23.9946 24.5881i −0.908209 0.930671i
\(699\) 0 0
\(700\) 9.04408 3.43696i 0.341834 0.129905i
\(701\) 7.83938i 0.296089i −0.988981 0.148045i \(-0.952702\pi\)
0.988981 0.148045i \(-0.0472979\pi\)
\(702\) 0 0
\(703\) −5.69239 9.85951i −0.214692 0.371858i
\(704\) 7.53768 + 15.5919i 0.284087 + 0.587640i
\(705\) 0 0
\(706\) −17.0000 4.77844i −0.639803 0.179839i
\(707\) −10.6052 + 4.32957i −0.398851 + 0.162830i
\(708\) 0 0
\(709\) 13.8192 + 7.97852i 0.518991 + 0.299640i 0.736522 0.676414i \(-0.236467\pi\)
−0.217531 + 0.976054i \(0.569800\pi\)
\(710\) 52.7927 13.4568i 1.98127 0.505026i
\(711\) 0 0
\(712\) 21.2334 4.86327i 0.795756 0.182259i
\(713\) −13.8080 −0.517115
\(714\) 0 0
\(715\) 36.7973i 1.37614i
\(716\) 21.0506 + 38.6090i 0.786697 + 1.44289i
\(717\) 0 0
\(718\) −1.11434 4.37167i −0.0415867 0.163149i
\(719\) −7.04085 + 12.1951i −0.262579 + 0.454801i −0.966927 0.255055i \(-0.917907\pi\)
0.704347 + 0.709856i \(0.251240\pi\)
\(720\) 0 0
\(721\) 16.8848 21.7737i 0.628822 0.810896i
\(722\) 22.9111 + 6.43996i 0.852663 + 0.239671i
\(723\) 0 0
\(724\) −9.55403 0.233448i −0.355073 0.00867602i
\(725\) 11.7034 6.75699i 0.434655 0.250948i
\(726\) 0 0
\(727\) 10.8995 0.404240 0.202120 0.979361i \(-0.435217\pi\)
0.202120 + 0.979361i \(0.435217\pi\)
\(728\) 39.8221 27.9958i 1.47591 1.03759i
\(729\) 0 0
\(730\) −7.74304 7.93455i −0.286583 0.293671i
\(731\) −3.72192 + 2.14885i −0.137660 + 0.0794782i
\(732\) 0 0
\(733\) 19.4526 + 11.2310i 0.718499 + 0.414825i 0.814200 0.580585i \(-0.197176\pi\)
−0.0957011 + 0.995410i \(0.530509\pi\)
\(734\) −42.7289 12.0104i −1.57715 0.443313i
\(735\) 0 0
\(736\) 4.34315 + 21.3459i 0.160090 + 0.786820i
\(737\) 12.4867 21.6275i 0.459952 0.796660i
\(738\) 0 0
\(739\) −15.7147 + 9.07290i −0.578075 + 0.333752i −0.760368 0.649492i \(-0.774981\pi\)
0.182293 + 0.983244i \(0.441648\pi\)
\(740\) 35.4497 19.3280i 1.30316 0.710513i
\(741\) 0 0
\(742\) 14.9214 34.3296i 0.547780 1.26028i
\(743\) −26.2947 −0.964659 −0.482329 0.875990i \(-0.660209\pi\)
−0.482329 + 0.875990i \(0.660209\pi\)
\(744\) 0 0
\(745\) −13.6569 23.6544i −0.500348 0.866629i
\(746\) 32.4547 8.27268i 1.18825 0.302884i
\(747\) 0 0
\(748\) 3.59798 5.89450i 0.131555 0.215524i
\(749\) 6.78910 + 5.26471i 0.248068 + 0.192368i
\(750\) 0 0
\(751\) 16.8640 29.2092i 0.615375 1.06586i −0.374944 0.927047i \(-0.622338\pi\)
0.990319 0.138813i \(-0.0443286\pi\)
\(752\) 25.0315 38.8422i 0.912806 1.41643i
\(753\) 0 0
\(754\) 48.6616 47.4871i 1.77215 1.72938i
\(755\) 23.0698i 0.839596i
\(756\) 0 0
\(757\) 24.2931i 0.882949i 0.897274 + 0.441475i \(0.145544\pi\)
−0.897274 + 0.441475i \(0.854456\pi\)
\(758\) 16.0107 + 16.4067i 0.581534 + 0.595917i
\(759\) 0 0
\(760\) 3.20250 10.4102i 0.116167 0.377616i
\(761\) −3.98760 + 6.90673i −0.144550 + 0.250369i −0.929205 0.369564i \(-0.879507\pi\)
0.784655 + 0.619933i \(0.212840\pi\)
\(762\) 0 0
\(763\) −26.1433 + 10.6729i −0.946450 + 0.386386i
\(764\) 30.6126 + 18.6858i 1.10753 + 0.676030i
\(765\) 0 0
\(766\) 10.5302 + 41.3112i 0.380471 + 1.49263i
\(767\) 30.4758 + 52.7857i 1.10042 + 1.90598i
\(768\) 0 0
\(769\) 16.1716 0.583162 0.291581 0.956546i \(-0.405819\pi\)
0.291581 + 0.956546i \(0.405819\pi\)
\(770\) −17.0127 + 12.5923i −0.613096 + 0.453796i
\(771\) 0 0
\(772\) −18.1105 + 9.87427i −0.651810 + 0.355383i
\(773\) 39.6364 22.8841i 1.42562 0.823083i 0.428851 0.903375i \(-0.358919\pi\)
0.996771 + 0.0802922i \(0.0255853\pi\)
\(774\) 0 0
\(775\) −3.27817 + 5.67796i −0.117756 + 0.203959i
\(776\) 1.59504 + 1.71644i 0.0572586 + 0.0616167i
\(777\) 0 0
\(778\) 3.48528 12.3994i 0.124953 0.444540i
\(779\) −9.82868 5.67459i −0.352149 0.203313i
\(780\) 0 0
\(781\) −27.6384 + 15.9570i −0.988980 + 0.570988i
\(782\) 6.21670 6.06665i 0.222309 0.216943i
\(783\) 0 0
\(784\) −26.5710 8.83081i −0.948963 0.315386i
\(785\) 21.7832 0.777477
\(786\) 0 0
\(787\) 8.71442 5.03127i 0.310636 0.179346i −0.336575 0.941657i \(-0.609269\pi\)
0.647211 + 0.762311i \(0.275935\pi\)
\(788\) 39.1083 + 0.955591i 1.39318 + 0.0340415i
\(789\) 0 0
\(790\) 7.24264 25.7668i 0.257682 0.916740i
\(791\) 24.3693 + 3.33486i 0.866473 + 0.118574i
\(792\) 0 0
\(793\) −13.5563 + 23.4803i −0.481400 + 0.833809i
\(794\) 24.3769 6.21366i 0.865104 0.220514i
\(795\) 0 0
\(796\) 1.45469 0.793130i 0.0515600 0.0281117i
\(797\) 41.3617i 1.46511i 0.680710 + 0.732553i \(0.261671\pi\)
−0.680710 + 0.732553i \(0.738329\pi\)
\(798\) 0 0
\(799\) −18.4264 −0.651879
\(800\) 9.80869 + 3.28181i 0.346790 + 0.116029i
\(801\) 0 0
\(802\) −3.70899 14.5508i −0.130969 0.513806i
\(803\) 5.62427 + 3.24718i 0.198476 + 0.114590i
\(804\) 0 0
\(805\) −24.6481 + 10.0625i −0.868731 + 0.354658i
\(806\) −8.92616 + 31.7561i −0.314411 + 1.11856i
\(807\) 0 0
\(808\) −11.7045 3.60069i −0.411764 0.126672i
\(809\) 9.43341 + 16.3392i 0.331661 + 0.574454i 0.982838 0.184472i \(-0.0590576\pi\)
−0.651177 + 0.758926i \(0.725724\pi\)
\(810\) 0 0
\(811\) 16.6722i 0.585439i −0.956198 0.292720i \(-0.905440\pi\)
0.956198 0.292720i \(-0.0945602\pi\)
\(812\) −38.6075 6.24755i −1.35486 0.219246i
\(813\) 0 0
\(814\) −16.9275 + 16.5189i −0.593308 + 0.578988i
\(815\) −13.1474 22.7719i −0.460532 0.797664i
\(816\) 0 0
\(817\) 1.98528 3.43861i 0.0694562 0.120302i
\(818\) −39.4020 11.0753i −1.37766 0.387238i
\(819\) 0 0
\(820\) 20.9706 34.3557i 0.732324 1.19975i
\(821\) −0.709933 0.409880i −0.0247768 0.0143049i 0.487560 0.873089i \(-0.337887\pi\)
−0.512337 + 0.858784i \(0.671220\pi\)
\(822\) 0 0
\(823\) 6.89949 + 11.9503i 0.240501 + 0.416560i 0.960857 0.277044i \(-0.0893548\pi\)
−0.720356 + 0.693605i \(0.756022\pi\)
\(824\) 28.7124 6.57623i 1.00024 0.229094i
\(825\) 0 0
\(826\) 13.9757 32.1538i 0.486276 1.11877i
\(827\) 16.2359i 0.564577i −0.959330 0.282288i \(-0.908906\pi\)
0.959330 0.282288i \(-0.0910935\pi\)
\(828\) 0 0
\(829\) −47.7104 + 27.5456i −1.65705 + 0.956698i −0.682983 + 0.730434i \(0.739318\pi\)
−0.974066 + 0.226263i \(0.927349\pi\)
\(830\) 6.57701 + 25.8024i 0.228291 + 0.895613i
\(831\) 0 0
\(832\) 51.8995 + 3.81048i 1.79929 + 0.132105i
\(833\) 2.77958 + 10.8138i 0.0963069 + 0.374675i
\(834\) 0 0
\(835\) 33.3625 + 19.2619i 1.15456 + 0.666584i
\(836\) −0.155850 + 6.37826i −0.00539017 + 0.220597i
\(837\) 0 0
\(838\) 18.5099 + 18.9677i 0.639415 + 0.655229i
\(839\) −23.1046 −0.797660 −0.398830 0.917025i \(-0.630584\pi\)
−0.398830 + 0.917025i \(0.630584\pi\)
\(840\) 0 0
\(841\) −25.6274 −0.883704
\(842\) −0.602895 0.617806i −0.0207771 0.0212910i
\(843\) 0 0
\(844\) 40.2382 + 0.983199i 1.38506 + 0.0338431i
\(845\) −66.3379 38.3002i −2.28209 1.31757i
\(846\) 0 0
\(847\) −10.2365 + 13.2005i −0.351732 + 0.453575i
\(848\) 35.5913 18.2919i 1.22221 0.628146i
\(849\) 0 0
\(850\) −1.01874 3.99664i −0.0349425 0.137084i
\(851\) −25.7641 + 14.8749i −0.883183 + 0.509906i
\(852\) 0 0
\(853\) 7.01057i 0.240037i 0.992772 + 0.120019i \(0.0382954\pi\)
−0.992772 + 0.120019i \(0.961705\pi\)
\(854\) 15.4949 1.76756i 0.530225 0.0604845i
\(855\) 0 0
\(856\) 2.05049 + 8.95258i 0.0700842 + 0.305993i
\(857\) −2.91642 5.05138i −0.0996229 0.172552i 0.811906 0.583789i \(-0.198430\pi\)
−0.911529 + 0.411237i \(0.865097\pi\)
\(858\) 0 0
\(859\) 7.21926 + 4.16804i 0.246318 + 0.142212i 0.618077 0.786117i \(-0.287912\pi\)
−0.371759 + 0.928329i \(0.621245\pi\)
\(860\) 12.0195 + 7.33664i 0.409861 + 0.250177i
\(861\) 0 0
\(862\) −9.58579 2.69442i −0.326493 0.0917722i
\(863\) −17.6588 + 30.5860i −0.601113 + 1.04116i 0.391540 + 0.920161i \(0.371942\pi\)
−0.992653 + 0.120997i \(0.961391\pi\)
\(864\) 0 0
\(865\) −7.89949 13.6823i −0.268591 0.465213i
\(866\) −33.1972 + 32.3959i −1.12809 + 1.10086i
\(867\) 0 0
\(868\) 17.7366 6.74033i 0.602021 0.228782i
\(869\) 15.6788i 0.531865i
\(870\) 0 0
\(871\) −37.5208 64.9880i −1.27134 2.20203i
\(872\) −28.8532 8.87617i −0.977093 0.300585i
\(873\) 0 0
\(874\) −2.17157 + 7.72569i −0.0734545 + 0.261325i
\(875\) 2.97297 21.7248i 0.100505 0.734431i
\(876\) 0 0
\(877\) 24.0288 + 13.8730i 0.811395 + 0.468459i 0.847440 0.530891i \(-0.178143\pi\)
−0.0360454 + 0.999350i \(0.511476\pi\)
\(878\) −0.529111 2.07576i −0.0178566 0.0700536i
\(879\) 0 0
\(880\) −22.6004 1.10512i −0.761860 0.0372536i
\(881\) −23.3783 −0.787634 −0.393817 0.919189i \(-0.628846\pi\)
−0.393817 + 0.919189i \(0.628846\pi\)
\(882\) 0 0
\(883\) 12.0418i 0.405240i 0.979257 + 0.202620i \(0.0649457\pi\)
−0.979257 + 0.202620i \(0.935054\pi\)
\(884\) −9.93350 18.2191i −0.334100 0.612775i
\(885\) 0 0
\(886\) 50.8977 12.9738i 1.70994 0.435863i
\(887\) 9.29658 16.1021i 0.312149 0.540657i −0.666679 0.745345i \(-0.732285\pi\)
0.978827 + 0.204688i \(0.0656180\pi\)
\(888\) 0 0
\(889\) −26.3995 3.61269i −0.885411 0.121166i
\(890\) −7.70154 + 27.3994i −0.258156 + 0.918429i
\(891\) 0 0
\(892\) −0.788614 + 32.2746i −0.0264048 + 1.08063i
\(893\) 14.7430 8.51189i 0.493357 0.284840i
\(894\) 0 0
\(895\) −57.4558 −1.92054
\(896\) −15.9987 25.2990i −0.534480 0.845181i
\(897\) 0 0
\(898\) −1.61440 + 1.57544i −0.0538734 + 0.0525731i
\(899\) 22.9520 13.2513i 0.765492 0.441957i
\(900\) 0 0
\(901\) −13.8192 7.97852i −0.460385 0.265803i
\(902\) −6.38016 + 22.6984i −0.212436 + 0.755773i
\(903\) 0 0
\(904\) 17.8995 + 19.2619i 0.595328 + 0.640640i
\(905\) 6.24333 10.8138i 0.207535 0.359462i
\(906\) 0 0
\(907\) 36.7532 21.2195i 1.22037 0.704581i 0.255373 0.966843i \(-0.417802\pi\)
0.964997 + 0.262262i \(0.0844684\pi\)
\(908\) −15.3663 28.1835i −0.509949 0.935302i
\(909\) 0 0
\(910\) 7.20845 + 63.1913i 0.238958 + 2.09477i
\(911\) −28.8241 −0.954985 −0.477492 0.878636i \(-0.658454\pi\)
−0.477492 + 0.878636i \(0.658454\pi\)
\(912\) 0 0
\(913\) −7.79899 13.5082i −0.258109 0.447058i
\(914\) −14.8304 58.1812i −0.490545 1.92446i
\(915\) 0 0
\(916\) −16.7365 + 27.4192i −0.552991 + 0.905955i
\(917\) 10.9269 + 8.47343i 0.360838 + 0.279817i
\(918\) 0 0
\(919\) −10.6213 + 18.3967i −0.350365 + 0.606850i −0.986313 0.164882i \(-0.947276\pi\)
0.635948 + 0.771732i \(0.280609\pi\)
\(920\) −27.2031 8.36853i −0.896858 0.275902i
\(921\) 0 0
\(922\) −38.6392 39.5949i −1.27251 1.30399i
\(923\) 95.8978i 3.15651i
\(924\) 0 0
\(925\) 14.1259i 0.464455i
\(926\) −18.4343 + 17.9894i −0.605789 + 0.591168i
\(927\) 0 0
\(928\) −27.7045 31.3135i −0.909446 1.02792i
\(929\) 21.6464 37.4927i 0.710196 1.23009i −0.254588 0.967050i \(-0.581940\pi\)
0.964783 0.263045i \(-0.0847269\pi\)
\(930\) 0 0
\(931\) −7.21926 7.36813i −0.236602 0.241481i
\(932\) −21.3161 13.0112i −0.698231 0.426197i
\(933\) 0 0
\(934\) 46.1933 11.7746i 1.51149 0.385278i
\(935\) 4.51146 + 7.81407i 0.147540 + 0.255548i
\(936\) 0 0
\(937\) −28.1716 −0.920325 −0.460163 0.887835i \(-0.652209\pi\)
−0.460163 + 0.887835i \(0.652209\pi\)
\(938\) −17.2064 + 39.5867i −0.561808 + 1.29255i
\(939\) 0 0
\(940\) 28.9014 + 53.0083i 0.942660 + 1.72894i
\(941\) −8.66386 + 5.00208i −0.282434 + 0.163063i −0.634525 0.772903i \(-0.718804\pi\)
0.352091 + 0.935966i \(0.385471\pi\)
\(942\) 0 0
\(943\) −14.8284 + 25.6836i −0.482880 + 0.836373i
\(944\) 33.3356 17.1326i 1.08498 0.557618i
\(945\) 0 0
\(946\) −7.94113 2.23213i −0.258188 0.0725728i
\(947\) 41.0563 + 23.7038i 1.33415 + 0.770271i 0.985933 0.167143i \(-0.0534541\pi\)
0.348216 + 0.937414i \(0.386787\pi\)
\(948\) 0 0
\(949\) 16.9002 9.75735i 0.548604 0.316737i
\(950\) 2.66131 + 2.72713i 0.0863441 + 0.0884797i
\(951\) 0 0
\(952\) −5.02404 + 10.8274i −0.162830 + 0.350917i
\(953\) 49.6730 1.60907 0.804533 0.593908i \(-0.202416\pi\)
0.804533 + 0.593908i \(0.202416\pi\)
\(954\) 0 0
\(955\) −40.5818 + 23.4299i −1.31320 + 0.758174i
\(956\) −0.220405 + 9.02022i −0.00712839 + 0.291735i
\(957\) 0 0
\(958\) 39.2426 + 11.0305i 1.26787 + 0.356379i
\(959\) −15.4031 37.7297i −0.497391 1.21836i
\(960\) 0 0
\(961\) 9.07107 15.7116i 0.292615 0.506824i
\(962\) 17.5547 + 68.8689i 0.565985 + 2.22042i
\(963\) 0 0
\(964\) 5.56916 3.03644i 0.179371 0.0977971i
\(965\) 26.9510i 0.867584i
\(966\) 0 0
\(967\) −7.58579 −0.243942 −0.121971 0.992534i \(-0.538922\pi\)
−0.121971 + 0.992534i \(0.538922\pi\)
\(968\) −17.4071 + 3.98690i −0.559486 + 0.128144i
\(969\) 0 0
\(970\) −2.96661 + 0.756187i −0.0952521 + 0.0242797i
\(971\) 7.65986 + 4.42242i 0.245817 + 0.141922i 0.617847 0.786298i \(-0.288005\pi\)
−0.372031 + 0.928220i \(0.621338\pi\)
\(972\) 0 0
\(973\) −5.63341 + 41.1658i −0.180599 + 1.31971i
\(974\) −13.9849 3.93095i −0.448107 0.125956i
\(975\) 0 0
\(976\) 14.0142 + 9.03131i 0.448582 + 0.289085i
\(977\) −10.8916 18.8648i −0.348454 0.603540i 0.637521 0.770433i \(-0.279960\pi\)
−0.985975 + 0.166893i \(0.946627\pi\)
\(978\) 0 0
\(979\) 16.6722i 0.532845i
\(980\) 26.7489 24.9573i 0.854462 0.797233i
\(981\) 0 0
\(982\) −7.30021 7.48076i −0.232959 0.238721i
\(983\) −6.71051 11.6229i −0.214032 0.370714i 0.738941 0.673770i \(-0.235326\pi\)
−0.952973 + 0.303056i \(0.901993\pi\)
\(984\) 0 0
\(985\) −25.5563 + 44.2649i −0.814293 + 1.41040i
\(986\) −4.51146 + 16.0502i −0.143674 + 0.511142i
\(987\) 0 0
\(988\) 16.3640 + 9.98849i 0.520607 + 0.317776i
\(989\) −8.98552 5.18779i −0.285723 0.164962i
\(990\) 0 0
\(991\) −25.7635 44.6236i −0.818403 1.41752i −0.906858 0.421436i \(-0.861526\pi\)
0.0884551 0.996080i \(-0.471807\pi\)
\(992\) 19.2361 + 6.43605i 0.610748 + 0.204345i
\(993\) 0 0
\(994\) 44.3371 32.8170i 1.40629 1.04089i
\(995\) 2.16478i 0.0686283i
\(996\) 0 0
\(997\) −7.30996 + 4.22041i −0.231509 + 0.133662i −0.611268 0.791424i \(-0.709340\pi\)
0.379759 + 0.925085i \(0.376007\pi\)
\(998\) −13.4432 + 3.42666i −0.425536 + 0.108469i
\(999\) 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 504.2.cj.d.37.2 16
3.2 odd 2 inner 504.2.cj.d.37.7 yes 16
4.3 odd 2 2016.2.cr.d.1297.7 16
7.4 even 3 inner 504.2.cj.d.109.3 yes 16
8.3 odd 2 2016.2.cr.d.1297.2 16
8.5 even 2 inner 504.2.cj.d.37.3 yes 16
12.11 even 2 2016.2.cr.d.1297.1 16
21.11 odd 6 inner 504.2.cj.d.109.6 yes 16
24.5 odd 2 inner 504.2.cj.d.37.6 yes 16
24.11 even 2 2016.2.cr.d.1297.8 16
28.11 odd 6 2016.2.cr.d.1873.1 16
56.11 odd 6 2016.2.cr.d.1873.8 16
56.53 even 6 inner 504.2.cj.d.109.2 yes 16
84.11 even 6 2016.2.cr.d.1873.7 16
168.11 even 6 2016.2.cr.d.1873.2 16
168.53 odd 6 inner 504.2.cj.d.109.7 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.cj.d.37.2 16 1.1 even 1 trivial
504.2.cj.d.37.3 yes 16 8.5 even 2 inner
504.2.cj.d.37.6 yes 16 24.5 odd 2 inner
504.2.cj.d.37.7 yes 16 3.2 odd 2 inner
504.2.cj.d.109.2 yes 16 56.53 even 6 inner
504.2.cj.d.109.3 yes 16 7.4 even 3 inner
504.2.cj.d.109.6 yes 16 21.11 odd 6 inner
504.2.cj.d.109.7 yes 16 168.53 odd 6 inner
2016.2.cr.d.1297.1 16 12.11 even 2
2016.2.cr.d.1297.2 16 8.3 odd 2
2016.2.cr.d.1297.7 16 4.3 odd 2
2016.2.cr.d.1297.8 16 24.11 even 2
2016.2.cr.d.1873.1 16 28.11 odd 6
2016.2.cr.d.1873.2 16 168.11 even 6
2016.2.cr.d.1873.7 16 84.11 even 6
2016.2.cr.d.1873.8 16 56.11 odd 6