Properties

Label 729.2.e.m.568.1
Level $729$
Weight $2$
Character 729.568
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.1
Root \(0.984808 + 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.m.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642788 - 0.233956i) q^{2} +(-1.17365 - 0.984808i) q^{4} +(0.181985 - 1.03209i) q^{5} +(-0.0923963 + 0.0775297i) q^{7} +(1.20805 + 2.09240i) q^{8} +O(q^{10})\) \(q+(-0.642788 - 0.233956i) q^{2} +(-1.17365 - 0.984808i) q^{4} +(0.181985 - 1.03209i) q^{5} +(-0.0923963 + 0.0775297i) q^{7} +(1.20805 + 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-0.943555 - 5.35117i) q^{11} +(4.29813 - 1.56439i) q^{13} +(0.0775297 - 0.0282185i) q^{14} +(0.245100 + 1.39003i) q^{16} +(-2.38917 + 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(-1.23000 + 1.03209i) q^{20} +(-0.645430 + 3.66041i) q^{22} +(-5.97205 - 5.01114i) q^{23} +(3.66637 + 1.33445i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(-4.76400 - 1.73396i) q^{29} +(-6.70961 - 5.63003i) q^{31} +(1.00676 - 5.70961i) q^{32} +(2.50387 - 2.10100i) q^{34} +(0.0632028 + 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.0699065 - 0.396459i) q^{38} +(2.37939 - 0.866025i) q^{40} +(-7.10257 + 2.58512i) q^{41} +(-0.226682 - 1.28558i) q^{43} +(-4.16247 + 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(1.85083 - 1.55303i) q^{47} +(-1.21301 + 6.87933i) q^{49} +(-2.04450 - 1.71554i) q^{50} +(-6.58512 - 2.39679i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(-0.273842 - 0.0996702i) q^{56} +(2.65657 + 2.22913i) q^{58} +(-0.00762319 + 0.0432332i) q^{59} +(-7.82295 + 6.56423i) q^{61} +(2.99568 + 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-0.832396 - 4.72075i) q^{65} +(1.74763 - 0.636084i) q^{67} +(6.87933 - 2.50387i) q^{68} +(-0.0150147 - 0.0851529i) q^{70} +(3.25519 - 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(-1.14484 + 0.960637i) q^{74} +(0.156574 - 0.887975i) q^{76} +(0.502055 + 0.421274i) q^{77} +(-0.659978 - 0.240212i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(-6.36792 - 2.31773i) q^{83} +(3.83615 + 3.21891i) q^{85} +(-0.155059 + 0.879385i) q^{86} +(10.0569 - 8.43874i) q^{88} +(-3.42782 - 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(2.07407 + 11.7626i) q^{92} +(-1.55303 + 0.565258i) q^{94} +(0.579585 - 0.210952i) q^{95} +(-1.56758 - 8.89020i) q^{97} +(2.38917 - 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 0.233956i −0.454519 0.165432i 0.104608 0.994514i \(-0.466641\pi\)
−0.559127 + 0.829082i \(0.688864\pi\)
\(3\) 0 0
\(4\) −1.17365 0.984808i −0.586824 0.492404i
\(5\) 0.181985 1.03209i 0.0813862 0.461564i −0.916692 0.399595i \(-0.869151\pi\)
0.998078 0.0619693i \(-0.0197381\pi\)
\(6\) 0 0
\(7\) −0.0923963 + 0.0775297i −0.0349225 + 0.0293035i −0.660082 0.751194i \(-0.729478\pi\)
0.625159 + 0.780497i \(0.285034\pi\)
\(8\) 1.20805 + 2.09240i 0.427109 + 0.739774i
\(9\) 0 0
\(10\) −0.358441 + 0.620838i −0.113349 + 0.196326i
\(11\) −0.943555 5.35117i −0.284493 1.61344i −0.707092 0.707121i \(-0.749994\pi\)
0.422600 0.906316i \(-0.361118\pi\)
\(12\) 0 0
\(13\) 4.29813 1.56439i 1.19209 0.433884i 0.331632 0.943409i \(-0.392401\pi\)
0.860456 + 0.509525i \(0.170179\pi\)
\(14\) 0.0775297 0.0282185i 0.0207207 0.00754171i
\(15\) 0 0
\(16\) 0.245100 + 1.39003i 0.0612750 + 0.347508i
\(17\) −2.38917 + 4.13816i −0.579458 + 1.00365i 0.416084 + 0.909326i \(0.363402\pi\)
−0.995542 + 0.0943239i \(0.969931\pi\)
\(18\) 0 0
\(19\) 0.294263 + 0.509678i 0.0675085 + 0.116928i 0.897804 0.440395i \(-0.145162\pi\)
−0.830295 + 0.557323i \(0.811828\pi\)
\(20\) −1.23000 + 1.03209i −0.275035 + 0.230782i
\(21\) 0 0
\(22\) −0.645430 + 3.66041i −0.137606 + 0.780403i
\(23\) −5.97205 5.01114i −1.24526 1.04490i −0.997094 0.0761778i \(-0.975728\pi\)
−0.248164 0.968718i \(-0.579827\pi\)
\(24\) 0 0
\(25\) 3.66637 + 1.33445i 0.733275 + 0.266890i
\(26\) −3.12879 −0.613605
\(27\) 0 0
\(28\) 0.184793 0.0349225
\(29\) −4.76400 1.73396i −0.884653 0.321987i −0.140567 0.990071i \(-0.544893\pi\)
−0.744086 + 0.668084i \(0.767115\pi\)
\(30\) 0 0
\(31\) −6.70961 5.63003i −1.20508 1.01118i −0.999470 0.0325493i \(-0.989637\pi\)
−0.205611 0.978634i \(-0.565918\pi\)
\(32\) 1.00676 5.70961i 0.177971 1.00933i
\(33\) 0 0
\(34\) 2.50387 2.10100i 0.429410 0.360318i
\(35\) 0.0632028 + 0.109470i 0.0106832 + 0.0185039i
\(36\) 0 0
\(37\) 1.09240 1.89209i 0.179589 0.311057i −0.762151 0.647399i \(-0.775857\pi\)
0.941740 + 0.336342i \(0.109190\pi\)
\(38\) −0.0699065 0.396459i −0.0113403 0.0643142i
\(39\) 0 0
\(40\) 2.37939 0.866025i 0.376214 0.136931i
\(41\) −7.10257 + 2.58512i −1.10923 + 0.403728i −0.830713 0.556702i \(-0.812067\pi\)
−0.278522 + 0.960430i \(0.589844\pi\)
\(42\) 0 0
\(43\) −0.226682 1.28558i −0.0345686 0.196048i 0.962633 0.270810i \(-0.0872915\pi\)
−0.997201 + 0.0747616i \(0.976180\pi\)
\(44\) −4.16247 + 7.20961i −0.627516 + 1.08689i
\(45\) 0 0
\(46\) 2.66637 + 4.61830i 0.393135 + 0.680931i
\(47\) 1.85083 1.55303i 0.269972 0.226533i −0.497744 0.867324i \(-0.665838\pi\)
0.767715 + 0.640791i \(0.221393\pi\)
\(48\) 0 0
\(49\) −1.21301 + 6.87933i −0.173287 + 0.982761i
\(50\) −2.04450 1.71554i −0.289136 0.242614i
\(51\) 0 0
\(52\) −6.58512 2.39679i −0.913192 0.332375i
\(53\) −3.04628 −0.418439 −0.209219 0.977869i \(-0.567092\pi\)
−0.209219 + 0.977869i \(0.567092\pi\)
\(54\) 0 0
\(55\) −5.69459 −0.767859
\(56\) −0.273842 0.0996702i −0.0365936 0.0133190i
\(57\) 0 0
\(58\) 2.65657 + 2.22913i 0.348825 + 0.292699i
\(59\) −0.00762319 + 0.0432332i −0.000992454 + 0.00562849i −0.985300 0.170833i \(-0.945354\pi\)
0.984308 + 0.176462i \(0.0564652\pi\)
\(60\) 0 0
\(61\) −7.82295 + 6.56423i −1.00163 + 0.840464i −0.987209 0.159432i \(-0.949034\pi\)
−0.0144170 + 0.999896i \(0.504589\pi\)
\(62\) 2.99568 + 5.18866i 0.380451 + 0.658961i
\(63\) 0 0
\(64\) −0.571452 + 0.989783i −0.0714315 + 0.123723i
\(65\) −0.832396 4.72075i −0.103246 0.585537i
\(66\) 0 0
\(67\) 1.74763 0.636084i 0.213507 0.0777100i −0.233053 0.972464i \(-0.574871\pi\)
0.446559 + 0.894754i \(0.352649\pi\)
\(68\) 6.87933 2.50387i 0.834241 0.303639i
\(69\) 0 0
\(70\) −0.0150147 0.0851529i −0.00179461 0.0101777i
\(71\) 3.25519 5.63816i 0.386320 0.669126i −0.605631 0.795745i \(-0.707079\pi\)
0.991951 + 0.126619i \(0.0404127\pi\)
\(72\) 0 0
\(73\) −6.11721 10.5953i −0.715965 1.24009i −0.962586 0.270976i \(-0.912653\pi\)
0.246621 0.969112i \(-0.420680\pi\)
\(74\) −1.14484 + 0.960637i −0.133085 + 0.111672i
\(75\) 0 0
\(76\) 0.156574 0.887975i 0.0179603 0.101858i
\(77\) 0.502055 + 0.421274i 0.0572145 + 0.0480087i
\(78\) 0 0
\(79\) −0.659978 0.240212i −0.0742533 0.0270260i 0.304626 0.952472i \(-0.401468\pi\)
−0.378880 + 0.925446i \(0.623691\pi\)
\(80\) 1.47924 0.165384
\(81\) 0 0
\(82\) 5.17024 0.570958
\(83\) −6.36792 2.31773i −0.698970 0.254404i −0.0319990 0.999488i \(-0.510187\pi\)
−0.666971 + 0.745084i \(0.732410\pi\)
\(84\) 0 0
\(85\) 3.83615 + 3.21891i 0.416089 + 0.349140i
\(86\) −0.155059 + 0.879385i −0.0167205 + 0.0948265i
\(87\) 0 0
\(88\) 10.0569 8.43874i 1.07207 0.899573i
\(89\) −3.42782 5.93717i −0.363349 0.629338i 0.625161 0.780496i \(-0.285033\pi\)
−0.988510 + 0.151157i \(0.951700\pi\)
\(90\) 0 0
\(91\) −0.275845 + 0.477777i −0.0289164 + 0.0500846i
\(92\) 2.07407 + 11.7626i 0.216237 + 1.22634i
\(93\) 0 0
\(94\) −1.55303 + 0.565258i −0.160183 + 0.0583019i
\(95\) 0.579585 0.210952i 0.0594642 0.0216432i
\(96\) 0 0
\(97\) −1.56758 8.89020i −0.159164 0.902663i −0.954880 0.296993i \(-0.904016\pi\)
0.795716 0.605670i \(-0.207095\pi\)
\(98\) 2.38917 4.13816i 0.241342 0.418017i
\(99\) 0 0
\(100\) −2.98886 5.17685i −0.298886 0.517685i
\(101\) 9.95253 8.35117i 0.990314 0.830972i 0.00470087 0.999989i \(-0.498504\pi\)
0.985613 + 0.169017i \(0.0540592\pi\)
\(102\) 0 0
\(103\) 1.57532 8.93410i 0.155221 0.880303i −0.803362 0.595491i \(-0.796958\pi\)
0.958583 0.284812i \(-0.0919312\pi\)
\(104\) 8.46567 + 7.10354i 0.830127 + 0.696559i
\(105\) 0 0
\(106\) 1.95811 + 0.712694i 0.190189 + 0.0692230i
\(107\) 11.3865 1.10077 0.550386 0.834911i \(-0.314481\pi\)
0.550386 + 0.834911i \(0.314481\pi\)
\(108\) 0 0
\(109\) 2.89899 0.277672 0.138836 0.990315i \(-0.455664\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(110\) 3.66041 + 1.33228i 0.349007 + 0.127028i
\(111\) 0 0
\(112\) −0.130415 0.109431i −0.0123231 0.0103403i
\(113\) −2.01087 + 11.4042i −0.189167 + 1.07282i 0.731318 + 0.682037i \(0.238906\pi\)
−0.920484 + 0.390780i \(0.872205\pi\)
\(114\) 0 0
\(115\) −6.25877 + 5.25173i −0.583633 + 0.489727i
\(116\) 3.88365 + 6.72668i 0.360588 + 0.624557i
\(117\) 0 0
\(118\) 0.0150147 0.0260063i 0.00138222 0.00239407i
\(119\) −0.100080 0.567581i −0.00917431 0.0520301i
\(120\) 0 0
\(121\) −17.4081 + 6.33602i −1.58255 + 0.576002i
\(122\) 6.56423 2.38919i 0.594298 0.216307i
\(123\) 0 0
\(124\) 2.33022 + 13.2153i 0.209260 + 1.18677i
\(125\) 4.66452 8.07919i 0.417208 0.722625i
\(126\) 0 0
\(127\) 7.70961 + 13.3534i 0.684117 + 1.18493i 0.973713 + 0.227777i \(0.0731456\pi\)
−0.289596 + 0.957149i \(0.593521\pi\)
\(128\) −8.28368 + 6.95084i −0.732181 + 0.614373i
\(129\) 0 0
\(130\) −0.569392 + 3.22918i −0.0499390 + 0.283218i
\(131\) 10.2314 + 8.58512i 0.893917 + 0.750086i 0.968992 0.247092i \(-0.0794751\pi\)
−0.0750747 + 0.997178i \(0.523920\pi\)
\(132\) 0 0
\(133\) −0.0667040 0.0242783i −0.00578397 0.00210519i
\(134\) −1.27217 −0.109899
\(135\) 0 0
\(136\) −11.5449 −0.989965
\(137\) 18.4402 + 6.71167i 1.57545 + 0.573416i 0.974208 0.225652i \(-0.0724511\pi\)
0.601241 + 0.799068i \(0.294673\pi\)
\(138\) 0 0
\(139\) 12.4914 + 10.4815i 1.05951 + 0.889030i 0.994061 0.108826i \(-0.0347091\pi\)
0.0654443 + 0.997856i \(0.479154\pi\)
\(140\) 0.0336295 0.190722i 0.00284221 0.0161190i
\(141\) 0 0
\(142\) −3.41147 + 2.86257i −0.286285 + 0.240221i
\(143\) −12.4269 21.5239i −1.03919 1.79992i
\(144\) 0 0
\(145\) −2.65657 + 4.60132i −0.220616 + 0.382119i
\(146\) 1.45323 + 8.24170i 0.120270 + 0.682088i
\(147\) 0 0
\(148\) −3.14543 + 1.14484i −0.258553 + 0.0941055i
\(149\) −10.3814 + 3.77853i −0.850480 + 0.309549i −0.730236 0.683195i \(-0.760590\pi\)
−0.120244 + 0.992744i \(0.538368\pi\)
\(150\) 0 0
\(151\) −1.18092 6.69734i −0.0961021 0.545022i −0.994404 0.105643i \(-0.966310\pi\)
0.898302 0.439379i \(-0.144801\pi\)
\(152\) −0.710966 + 1.23143i −0.0576670 + 0.0998821i
\(153\) 0 0
\(154\) −0.224155 0.388249i −0.0180630 0.0312860i
\(155\) −7.03174 + 5.90033i −0.564803 + 0.473926i
\(156\) 0 0
\(157\) 2.93242 16.6306i 0.234032 1.32726i −0.610609 0.791932i \(-0.709075\pi\)
0.844642 0.535332i \(-0.179814\pi\)
\(158\) 0.368026 + 0.308811i 0.0292786 + 0.0245677i
\(159\) 0 0
\(160\) −5.70961 2.07813i −0.451384 0.164290i
\(161\) 0.940307 0.0741066
\(162\) 0 0
\(163\) 8.41147 0.658838 0.329419 0.944184i \(-0.393147\pi\)
0.329419 + 0.944184i \(0.393147\pi\)
\(164\) 10.8818 + 3.96064i 0.849723 + 0.309274i
\(165\) 0 0
\(166\) 3.55097 + 2.97962i 0.275609 + 0.231263i
\(167\) −0.455827 + 2.58512i −0.0352729 + 0.200043i −0.997352 0.0727289i \(-0.976829\pi\)
0.962079 + 0.272772i \(0.0879403\pi\)
\(168\) 0 0
\(169\) 6.06805 5.09170i 0.466773 0.391669i
\(170\) −1.71275 2.96657i −0.131362 0.227525i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 2.27536 + 12.9042i 0.172992 + 0.981088i 0.940436 + 0.339971i \(0.110417\pi\)
−0.767443 + 0.641117i \(0.778471\pi\)
\(174\) 0 0
\(175\) −0.442219 + 0.160954i −0.0334286 + 0.0121670i
\(176\) 7.20702 2.62314i 0.543250 0.197727i
\(177\) 0 0
\(178\) 0.814330 + 4.61830i 0.0610366 + 0.346156i
\(179\) 11.0494 19.1382i 0.825872 1.43045i −0.0753784 0.997155i \(-0.524016\pi\)
0.901251 0.433298i \(-0.142650\pi\)
\(180\) 0 0
\(181\) 1.02956 + 1.78325i 0.0765268 + 0.132548i 0.901749 0.432260i \(-0.142284\pi\)
−0.825222 + 0.564808i \(0.808950\pi\)
\(182\) 0.289088 0.242574i 0.0214286 0.0179808i
\(183\) 0 0
\(184\) 3.27079 18.5496i 0.241126 1.36749i
\(185\) −1.75400 1.47178i −0.128957 0.108208i
\(186\) 0 0
\(187\) 24.3983 + 8.88024i 1.78418 + 0.649388i
\(188\) −3.70167 −0.269972
\(189\) 0 0
\(190\) −0.421903 −0.0306081
\(191\) 3.71102 + 1.35070i 0.268520 + 0.0977332i 0.472771 0.881185i \(-0.343254\pi\)
−0.204251 + 0.978918i \(0.565476\pi\)
\(192\) 0 0
\(193\) −6.47044 5.42934i −0.465752 0.390813i 0.379490 0.925196i \(-0.376099\pi\)
−0.845242 + 0.534383i \(0.820544\pi\)
\(194\) −1.07229 + 6.08125i −0.0769858 + 0.436608i
\(195\) 0 0
\(196\) 8.19846 6.87933i 0.585605 0.491381i
\(197\) 1.14749 + 1.98751i 0.0817553 + 0.141604i 0.904004 0.427524i \(-0.140614\pi\)
−0.822249 + 0.569128i \(0.807281\pi\)
\(198\) 0 0
\(199\) 11.7515 20.3542i 0.833042 1.44287i −0.0625736 0.998040i \(-0.519931\pi\)
0.895615 0.444830i \(-0.146736\pi\)
\(200\) 1.63695 + 9.28359i 0.115750 + 0.656449i
\(201\) 0 0
\(202\) −8.35117 + 3.03958i −0.587586 + 0.213864i
\(203\) 0.574609 0.209141i 0.0403297 0.0146788i
\(204\) 0 0
\(205\) 1.37551 + 7.80093i 0.0960701 + 0.544841i
\(206\) −3.10278 + 5.37417i −0.216181 + 0.374436i
\(207\) 0 0
\(208\) 3.22803 + 5.59110i 0.223823 + 0.387673i
\(209\) 2.44972 2.05556i 0.169451 0.142186i
\(210\) 0 0
\(211\) −0.289515 + 1.64192i −0.0199310 + 0.113035i −0.993150 0.116845i \(-0.962722\pi\)
0.973219 + 0.229879i \(0.0738331\pi\)
\(212\) 3.57526 + 3.00000i 0.245550 + 0.206041i
\(213\) 0 0
\(214\) −7.31908 2.66393i −0.500322 0.182102i
\(215\) −1.36808 −0.0933023
\(216\) 0 0
\(217\) 1.05644 0.0717156
\(218\) −1.86343 0.678234i −0.126208 0.0459358i
\(219\) 0 0
\(220\) 6.68345 + 5.60808i 0.450598 + 0.378097i
\(221\) −3.79525 + 21.5239i −0.255296 + 1.44786i
\(222\) 0 0
\(223\) −7.50774 + 6.29974i −0.502756 + 0.421862i −0.858571 0.512694i \(-0.828647\pi\)
0.355816 + 0.934556i \(0.384203\pi\)
\(224\) 0.349643 + 0.605600i 0.0233615 + 0.0404634i
\(225\) 0 0
\(226\) 3.96064 6.86002i 0.263458 0.456322i
\(227\) −2.68820 15.2456i −0.178422 1.01188i −0.934119 0.356962i \(-0.883813\pi\)
0.755697 0.654922i \(-0.227299\pi\)
\(228\) 0 0
\(229\) 10.5753 3.84910i 0.698837 0.254356i 0.0319227 0.999490i \(-0.489837\pi\)
0.666914 + 0.745134i \(0.267615\pi\)
\(230\) 5.25173 1.91147i 0.346289 0.126039i
\(231\) 0 0
\(232\) −2.12701 12.0629i −0.139645 0.791967i
\(233\) 2.61738 4.53343i 0.171470 0.296995i −0.767464 0.641092i \(-0.778482\pi\)
0.938934 + 0.344097i \(0.111815\pi\)
\(234\) 0 0
\(235\) −1.26604 2.19285i −0.0825876 0.143046i
\(236\) 0.0515234 0.0432332i 0.00335389 0.00281424i
\(237\) 0 0
\(238\) −0.0684587 + 0.388249i −0.00443752 + 0.0251664i
\(239\) 7.89776 + 6.62701i 0.510864 + 0.428666i 0.861433 0.507871i \(-0.169567\pi\)
−0.350569 + 0.936537i \(0.614012\pi\)
\(240\) 0 0
\(241\) −10.0963 3.67474i −0.650358 0.236711i −0.00428982 0.999991i \(-0.501365\pi\)
−0.646068 + 0.763280i \(0.723588\pi\)
\(242\) 12.6720 0.814590
\(243\) 0 0
\(244\) 15.6459 1.00163
\(245\) 6.87933 + 2.50387i 0.439504 + 0.159966i
\(246\) 0 0
\(247\) 2.06212 + 1.73032i 0.131209 + 0.110098i
\(248\) 3.67474 20.8405i 0.233346 1.32337i
\(249\) 0 0
\(250\) −4.88847 + 4.10191i −0.309174 + 0.259428i
\(251\) 7.53644 + 13.0535i 0.475696 + 0.823930i 0.999612 0.0278401i \(-0.00886291\pi\)
−0.523916 + 0.851770i \(0.675530\pi\)
\(252\) 0 0
\(253\) −21.1805 + 36.6857i −1.33161 + 2.30641i
\(254\) −1.83153 10.3871i −0.114920 0.651746i
\(255\) 0 0
\(256\) 9.09879 3.31169i 0.568675 0.206981i
\(257\) −3.12208 + 1.13634i −0.194750 + 0.0708832i −0.437554 0.899192i \(-0.644155\pi\)
0.242804 + 0.970075i \(0.421933\pi\)
\(258\) 0 0
\(259\) 0.0457595 + 0.259515i 0.00284335 + 0.0161255i
\(260\) −3.67209 + 6.36025i −0.227734 + 0.394446i
\(261\) 0 0
\(262\) −4.56805 7.91209i −0.282215 0.488811i
\(263\) −6.77082 + 5.68139i −0.417506 + 0.350329i −0.827214 0.561888i \(-0.810075\pi\)
0.409707 + 0.912217i \(0.365631\pi\)
\(264\) 0 0
\(265\) −0.554378 + 3.14403i −0.0340551 + 0.193136i
\(266\) 0.0371965 + 0.0312115i 0.00228066 + 0.00191370i
\(267\) 0 0
\(268\) −2.67752 0.974537i −0.163555 0.0595293i
\(269\) −8.09267 −0.493419 −0.246709 0.969090i \(-0.579349\pi\)
−0.246709 + 0.969090i \(0.579349\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) −6.33775 2.30675i −0.384282 0.139867i
\(273\) 0 0
\(274\) −10.2829 8.62835i −0.621211 0.521258i
\(275\) 3.68144 20.8785i 0.221999 1.25902i
\(276\) 0 0
\(277\) −3.23989 + 2.71859i −0.194666 + 0.163344i −0.734911 0.678164i \(-0.762776\pi\)
0.540245 + 0.841508i \(0.318332\pi\)
\(278\) −5.57710 9.65982i −0.334492 0.579357i
\(279\) 0 0
\(280\) −0.152704 + 0.264490i −0.00912579 + 0.0158063i
\(281\) −1.26800 7.19119i −0.0756426 0.428990i −0.998986 0.0450159i \(-0.985666\pi\)
0.923344 0.383975i \(-0.125445\pi\)
\(282\) 0 0
\(283\) −15.0544 + 5.47935i −0.894890 + 0.325713i −0.748203 0.663470i \(-0.769083\pi\)
−0.146687 + 0.989183i \(0.546861\pi\)
\(284\) −9.37295 + 3.41147i −0.556182 + 0.202434i
\(285\) 0 0
\(286\) 2.95218 + 16.7427i 0.174566 + 0.990014i
\(287\) 0.455827 0.789515i 0.0269066 0.0466036i
\(288\) 0 0
\(289\) −2.91622 5.05104i −0.171542 0.297120i
\(290\) 2.78412 2.33615i 0.163489 0.137184i
\(291\) 0 0
\(292\) −3.25490 + 18.4595i −0.190479 + 1.08026i
\(293\) −13.7923 11.5731i −0.805754 0.676108i 0.143836 0.989601i \(-0.454056\pi\)
−0.949590 + 0.313494i \(0.898501\pi\)
\(294\) 0 0
\(295\) 0.0432332 + 0.0157356i 0.00251714 + 0.000916163i
\(296\) 5.27866 0.306816
\(297\) 0 0
\(298\) 7.55707 0.437769
\(299\) −33.5081 12.1959i −1.93782 0.705309i
\(300\) 0 0
\(301\) 0.120615 + 0.101208i 0.00695212 + 0.00583352i
\(302\) −0.807798 + 4.58125i −0.0464836 + 0.263621i
\(303\) 0 0
\(304\) −0.636345 + 0.533957i −0.0364969 + 0.0306245i
\(305\) 5.35121 + 9.26857i 0.306409 + 0.530717i
\(306\) 0 0
\(307\) 6.75537 11.7006i 0.385549 0.667791i −0.606296 0.795239i \(-0.707345\pi\)
0.991845 + 0.127448i \(0.0406787\pi\)
\(308\) −0.174362 0.988856i −0.00993519 0.0563453i
\(309\) 0 0
\(310\) 5.90033 2.14754i 0.335116 0.121972i
\(311\) 15.4319 5.61674i 0.875062 0.318496i 0.134846 0.990867i \(-0.456946\pi\)
0.740215 + 0.672370i \(0.234724\pi\)
\(312\) 0 0
\(313\) −3.39739 19.2676i −0.192032 1.08907i −0.916582 0.399846i \(-0.869064\pi\)
0.724550 0.689222i \(-0.242047\pi\)
\(314\) −5.77574 + 10.0039i −0.325944 + 0.564551i
\(315\) 0 0
\(316\) 0.538019 + 0.931876i 0.0302659 + 0.0524221i
\(317\) 18.6751 15.6702i 1.04890 0.880129i 0.0559193 0.998435i \(-0.482191\pi\)
0.992977 + 0.118307i \(0.0377466\pi\)
\(318\) 0 0
\(319\) −4.78359 + 27.1291i −0.267829 + 1.51894i
\(320\) 0.917549 + 0.769915i 0.0512925 + 0.0430395i
\(321\) 0 0
\(322\) −0.604418 0.219990i −0.0336829 0.0122596i
\(323\) −2.81217 −0.156473
\(324\) 0 0
\(325\) 17.8462 0.989927
\(326\) −5.40679 1.96791i −0.299454 0.108993i
\(327\) 0 0
\(328\) −13.9893 11.7384i −0.772431 0.648147i
\(329\) −0.0506039 + 0.286989i −0.00278988 + 0.0158222i
\(330\) 0 0
\(331\) 21.8314 18.3187i 1.19996 1.00689i 0.200331 0.979728i \(-0.435798\pi\)
0.999631 0.0271599i \(-0.00864633\pi\)
\(332\) 5.19118 + 8.99138i 0.284903 + 0.493466i
\(333\) 0 0
\(334\) 0.897804 1.55504i 0.0491256 0.0850881i
\(335\) −0.338453 1.91946i −0.0184917 0.104871i
\(336\) 0 0
\(337\) 16.3944 5.96707i 0.893060 0.325047i 0.145592 0.989345i \(-0.453491\pi\)
0.747468 + 0.664298i \(0.231269\pi\)
\(338\) −5.09170 + 1.85323i −0.276952 + 0.100802i
\(339\) 0 0
\(340\) −1.33228 7.55574i −0.0722531 0.409768i
\(341\) −23.7963 + 41.2165i −1.28864 + 2.23200i
\(342\) 0 0
\(343\) −0.843426 1.46086i −0.0455407 0.0788788i
\(344\) 2.41609 2.02734i 0.130267 0.109307i
\(345\) 0 0
\(346\) 1.55644 8.82699i 0.0836746 0.474542i
\(347\) −19.2959 16.1912i −1.03586 0.869189i −0.0443222 0.999017i \(-0.514113\pi\)
−0.991536 + 0.129829i \(0.958557\pi\)
\(348\) 0 0
\(349\) 11.1373 + 4.05364i 0.596165 + 0.216986i 0.622439 0.782669i \(-0.286142\pi\)
−0.0262739 + 0.999655i \(0.508364\pi\)
\(350\) 0.321909 0.0172068
\(351\) 0 0
\(352\) −31.5030 −1.67912
\(353\) −7.89106 2.87211i −0.419999 0.152867i 0.123371 0.992361i \(-0.460630\pi\)
−0.543370 + 0.839494i \(0.682852\pi\)
\(354\) 0 0
\(355\) −5.22668 4.38571i −0.277403 0.232769i
\(356\) −1.82391 + 10.3439i −0.0966669 + 0.548225i
\(357\) 0 0
\(358\) −11.5799 + 9.71670i −0.612017 + 0.513543i
\(359\) 1.32012 + 2.28652i 0.0696735 + 0.120678i 0.898758 0.438446i \(-0.144471\pi\)
−0.829084 + 0.559124i \(0.811138\pi\)
\(360\) 0 0
\(361\) 9.32682 16.1545i 0.490885 0.850238i
\(362\) −0.244588 1.38713i −0.0128552 0.0729057i
\(363\) 0 0
\(364\) 0.794263 0.289088i 0.0416307 0.0151523i
\(365\) −12.0486 + 4.38532i −0.630650 + 0.229538i
\(366\) 0 0
\(367\) 1.59714 + 9.05785i 0.0833702 + 0.472816i 0.997696 + 0.0678375i \(0.0216099\pi\)
−0.914326 + 0.404979i \(0.867279\pi\)
\(368\) 5.50190 9.52956i 0.286806 0.496763i
\(369\) 0 0
\(370\) 0.783119 + 1.35640i 0.0407124 + 0.0705159i
\(371\) 0.281465 0.236177i 0.0146129 0.0122617i
\(372\) 0 0
\(373\) −4.65224 + 26.3841i −0.240884 + 1.36612i 0.588978 + 0.808149i \(0.299531\pi\)
−0.829861 + 0.557970i \(0.811580\pi\)
\(374\) −13.6053 11.4162i −0.703515 0.590319i
\(375\) 0 0
\(376\) 5.48545 + 1.99654i 0.282891 + 0.102964i
\(377\) −23.1889 −1.19429
\(378\) 0 0
\(379\) −27.1242 −1.39328 −0.696639 0.717422i \(-0.745322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(380\) −0.887975 0.323197i −0.0455522 0.0165796i
\(381\) 0 0
\(382\) −2.06939 1.73643i −0.105879 0.0888433i
\(383\) 5.97815 33.9038i 0.305469 1.73240i −0.315818 0.948820i \(-0.602279\pi\)
0.621287 0.783583i \(-0.286610\pi\)
\(384\) 0 0
\(385\) 0.526159 0.441500i 0.0268156 0.0225009i
\(386\) 2.88889 + 5.00371i 0.147041 + 0.254682i
\(387\) 0 0
\(388\) −6.91534 + 11.9777i −0.351073 + 0.608077i
\(389\) 0.131381 + 0.745100i 0.00666129 + 0.0377781i 0.987957 0.154727i \(-0.0494499\pi\)
−0.981296 + 0.192505i \(0.938339\pi\)
\(390\) 0 0
\(391\) 35.0051 12.7408i 1.77028 0.644331i
\(392\) −15.8597 + 5.77244i −0.801033 + 0.291552i
\(393\) 0 0
\(394\) −0.272603 1.54601i −0.0137335 0.0778868i
\(395\) −0.368026 + 0.637441i −0.0185174 + 0.0320731i
\(396\) 0 0
\(397\) −3.50387 6.06888i −0.175854 0.304588i 0.764602 0.644502i \(-0.222935\pi\)
−0.940457 + 0.339914i \(0.889602\pi\)
\(398\) −12.3157 + 10.3341i −0.617330 + 0.518001i
\(399\) 0 0
\(400\) −0.956300 + 5.42345i −0.0478150 + 0.271172i
\(401\) −7.23973 6.07486i −0.361535 0.303364i 0.443867 0.896093i \(-0.353606\pi\)
−0.805402 + 0.592729i \(0.798051\pi\)
\(402\) 0 0
\(403\) −37.6464 13.7022i −1.87530 0.682553i
\(404\) −19.9051 −0.990314
\(405\) 0 0
\(406\) −0.418281 −0.0207590
\(407\) −11.1556 4.06031i −0.552963 0.201262i
\(408\) 0 0
\(409\) 4.22668 + 3.54661i 0.208996 + 0.175368i 0.741277 0.671199i \(-0.234221\pi\)
−0.532281 + 0.846568i \(0.678665\pi\)
\(410\) 0.940908 5.33615i 0.0464681 0.263534i
\(411\) 0 0
\(412\) −10.6472 + 8.93410i −0.524552 + 0.440151i
\(413\) −0.00264750 0.00458561i −0.000130275 0.000225643i
\(414\) 0 0
\(415\) −3.55097 + 6.15047i −0.174310 + 0.301915i
\(416\) −4.60489 26.1156i −0.225773 1.28042i
\(417\) 0 0
\(418\) −2.05556 + 0.748163i −0.100541 + 0.0365938i
\(419\) 0.438252 0.159511i 0.0214100 0.00779261i −0.331293 0.943528i \(-0.607485\pi\)
0.352703 + 0.935735i \(0.385263\pi\)
\(420\) 0 0
\(421\) −0.419215 2.37749i −0.0204313 0.115872i 0.972886 0.231283i \(-0.0742924\pi\)
−0.993318 + 0.115412i \(0.963181\pi\)
\(422\) 0.570234 0.987674i 0.0277585 0.0480792i
\(423\) 0 0
\(424\) −3.68004 6.37402i −0.178719 0.309550i
\(425\) −14.2817 + 11.9838i −0.692766 + 0.581300i
\(426\) 0 0
\(427\) 0.213888 1.21302i 0.0103508 0.0587022i
\(428\) −13.3637 11.2135i −0.645959 0.542024i
\(429\) 0 0
\(430\) 0.879385 + 0.320070i 0.0424077 + 0.0154351i
\(431\) 12.0992 0.582796 0.291398 0.956602i \(-0.405880\pi\)
0.291398 + 0.956602i \(0.405880\pi\)
\(432\) 0 0
\(433\) 33.3509 1.60274 0.801371 0.598167i \(-0.204104\pi\)
0.801371 + 0.598167i \(0.204104\pi\)
\(434\) −0.679065 0.247159i −0.0325961 0.0118640i
\(435\) 0 0
\(436\) −3.40239 2.85494i −0.162945 0.136727i
\(437\) 0.796719 4.51842i 0.0381122 0.216145i
\(438\) 0 0
\(439\) −6.92855 + 5.81374i −0.330682 + 0.277475i −0.792977 0.609251i \(-0.791470\pi\)
0.462296 + 0.886726i \(0.347026\pi\)
\(440\) −6.87933 11.9153i −0.327959 0.568042i
\(441\) 0 0
\(442\) 7.47519 12.9474i 0.355558 0.615845i
\(443\) 0.812174 + 4.60607i 0.0385875 + 0.218841i 0.998004 0.0631526i \(-0.0201155\pi\)
−0.959416 + 0.281993i \(0.909004\pi\)
\(444\) 0 0
\(445\) −6.75150 + 2.45734i −0.320052 + 0.116489i
\(446\) 6.29974 2.29292i 0.298301 0.108573i
\(447\) 0 0
\(448\) −0.0239376 0.135757i −0.00113094 0.00641390i
\(449\) −13.3534 + 23.1288i −0.630187 + 1.09152i 0.357326 + 0.933980i \(0.383689\pi\)
−0.987513 + 0.157537i \(0.949645\pi\)
\(450\) 0 0
\(451\) 20.5351 + 35.5678i 0.966959 + 1.67482i
\(452\) 13.5910 11.4042i 0.639267 0.536408i
\(453\) 0 0
\(454\) −1.83884 + 10.4286i −0.0863011 + 0.489438i
\(455\) 0.442909 + 0.371644i 0.0207639 + 0.0174230i
\(456\) 0 0
\(457\) 0.618089 + 0.224966i 0.0289130 + 0.0105235i 0.356436 0.934320i \(-0.383992\pi\)
−0.327523 + 0.944843i \(0.606214\pi\)
\(458\) −7.69820 −0.359713
\(459\) 0 0
\(460\) 12.5175 0.583633
\(461\) 19.4551 + 7.08109i 0.906116 + 0.329799i 0.752701 0.658363i \(-0.228751\pi\)
0.153415 + 0.988162i \(0.450973\pi\)
\(462\) 0 0
\(463\) −19.0162 15.9565i −0.883758 0.741561i 0.0831906 0.996534i \(-0.473489\pi\)
−0.966948 + 0.254973i \(0.917933\pi\)
\(464\) 1.24259 7.04710i 0.0576860 0.327154i
\(465\) 0 0
\(466\) −2.74304 + 2.30168i −0.127069 + 0.106623i
\(467\) 13.3365 + 23.0994i 0.617138 + 1.06891i 0.990005 + 0.141029i \(0.0450412\pi\)
−0.372868 + 0.927884i \(0.621625\pi\)
\(468\) 0 0
\(469\) −0.112159 + 0.194265i −0.00517901 + 0.00897031i
\(470\) 0.300767 + 1.70574i 0.0138734 + 0.0786798i
\(471\) 0 0
\(472\) −0.0996702 + 0.0362770i −0.00458769 + 0.00166978i
\(473\) −6.66544 + 2.42602i −0.306477 + 0.111549i
\(474\) 0 0
\(475\) 0.398737 + 2.26135i 0.0182953 + 0.103758i
\(476\) −0.441500 + 0.764700i −0.0202361 + 0.0350500i
\(477\) 0 0
\(478\) −3.52616 6.10749i −0.161283 0.279350i
\(479\) 2.47167 2.07398i 0.112934 0.0947625i −0.584572 0.811342i \(-0.698738\pi\)
0.697506 + 0.716579i \(0.254293\pi\)
\(480\) 0 0
\(481\) 1.73530 9.84137i 0.0791229 0.448728i
\(482\) 5.63003 + 4.72416i 0.256441 + 0.215179i
\(483\) 0 0
\(484\) 26.6707 + 9.70735i 1.21231 + 0.441243i
\(485\) −9.46075 −0.429590
\(486\) 0 0
\(487\) −7.77930 −0.352514 −0.176257 0.984344i \(-0.556399\pi\)
−0.176257 + 0.984344i \(0.556399\pi\)
\(488\) −23.1855 8.43882i −1.04956 0.382007i
\(489\) 0 0
\(490\) −3.83615 3.21891i −0.173300 0.145416i
\(491\) −2.96000 + 16.7870i −0.133583 + 0.757586i 0.842253 + 0.539082i \(0.181229\pi\)
−0.975836 + 0.218504i \(0.929882\pi\)
\(492\) 0 0
\(493\) 18.5574 15.5715i 0.835782 0.701304i
\(494\) −0.920686 1.59467i −0.0414236 0.0717478i
\(495\) 0 0
\(496\) 6.18139 10.7065i 0.277553 0.480735i
\(497\) 0.136357 + 0.773318i 0.00611644 + 0.0346881i
\(498\) 0 0
\(499\) −7.45249 + 2.71248i −0.333619 + 0.121427i −0.503398 0.864055i \(-0.667917\pi\)
0.169779 + 0.985482i \(0.445695\pi\)
\(500\) −13.4310 + 4.88847i −0.600651 + 0.218619i
\(501\) 0 0
\(502\) −1.79039 10.1538i −0.0799091 0.453187i
\(503\) 12.4748 21.6070i 0.556224 0.963409i −0.441583 0.897220i \(-0.645583\pi\)
0.997807 0.0661881i \(-0.0210837\pi\)
\(504\) 0 0
\(505\) −6.80793 11.7917i −0.302949 0.524723i
\(506\) 22.1974 18.6258i 0.986795 0.828019i
\(507\) 0 0
\(508\) 4.10220 23.2647i 0.182006 1.03220i
\(509\) 31.0010 + 26.0130i 1.37410 + 1.15300i 0.971339 + 0.237697i \(0.0763926\pi\)
0.402757 + 0.915307i \(0.368052\pi\)
\(510\) 0 0
\(511\) 1.38666 + 0.504703i 0.0613422 + 0.0223267i
\(512\) 15.0038 0.663080
\(513\) 0 0
\(514\) 2.27269 0.100244
\(515\) −8.93410 3.25174i −0.393683 0.143289i
\(516\) 0 0
\(517\) −10.0569 8.43874i −0.442302 0.371136i
\(518\) 0.0313013 0.177519i 0.00137530 0.00779972i
\(519\) 0 0
\(520\) 8.87211 7.44459i 0.389068 0.326467i
\(521\) 12.6837 + 21.9688i 0.555684 + 0.962473i 0.997850 + 0.0655394i \(0.0208768\pi\)
−0.442166 + 0.896933i \(0.645790\pi\)
\(522\) 0 0
\(523\) −6.36097 + 11.0175i −0.278146 + 0.481762i −0.970924 0.239388i \(-0.923053\pi\)
0.692778 + 0.721151i \(0.256386\pi\)
\(524\) −3.55331 20.1518i −0.155227 0.880337i
\(525\) 0 0
\(526\) 5.68139 2.06786i 0.247720 0.0901628i
\(527\) 39.3283 14.3143i 1.71317 0.623542i
\(528\) 0 0
\(529\) 6.55990 + 37.2030i 0.285213 + 1.61752i
\(530\) 1.09191 1.89124i 0.0474296 0.0821504i
\(531\) 0 0
\(532\) 0.0543776 + 0.0941848i 0.00235757 + 0.00408343i
\(533\) −26.4836 + 22.2224i −1.14713 + 0.962559i
\(534\) 0 0
\(535\) 2.07217 11.7518i 0.0895876 0.508076i
\(536\) 3.44215 + 2.88831i 0.148678 + 0.124756i
\(537\) 0 0
\(538\) 5.20187 + 1.89332i 0.224268 + 0.0816270i
\(539\) 37.9570 1.63492
\(540\) 0 0
\(541\) 2.09327 0.0899969 0.0449984 0.998987i \(-0.485672\pi\)
0.0449984 + 0.998987i \(0.485672\pi\)
\(542\) 12.2130 + 4.44516i 0.524592 + 0.190936i
\(543\) 0 0
\(544\) 21.2219 + 17.8073i 0.909883 + 0.763482i
\(545\) 0.527572 2.99201i 0.0225987 0.128164i
\(546\) 0 0
\(547\) 2.64362 2.21826i 0.113033 0.0948459i −0.584519 0.811380i \(-0.698717\pi\)
0.697552 + 0.716534i \(0.254272\pi\)
\(548\) −15.0326 26.0371i −0.642159 1.11225i
\(549\) 0 0
\(550\) −7.25103 + 12.5592i −0.309185 + 0.535524i
\(551\) −0.518110 2.93835i −0.0220722 0.125178i
\(552\) 0 0
\(553\) 0.0796030 0.0289731i 0.00338507 0.00123206i
\(554\) 2.71859 0.989485i 0.115502 0.0420392i
\(555\) 0 0
\(556\) −4.33821 24.6032i −0.183981 1.04341i
\(557\) −5.55017 + 9.61318i −0.235168 + 0.407323i −0.959322 0.282316i \(-0.908897\pi\)
0.724153 + 0.689639i \(0.242231\pi\)
\(558\) 0 0
\(559\) −2.98545 5.17095i −0.126271 0.218708i
\(560\) −0.136676 + 0.114685i −0.00577562 + 0.00484632i
\(561\) 0 0
\(562\) −0.867364 + 4.91906i −0.0365875 + 0.207498i
\(563\) −18.6231 15.6266i −0.784868 0.658583i 0.159601 0.987182i \(-0.448979\pi\)
−0.944470 + 0.328599i \(0.893424\pi\)
\(564\) 0 0
\(565\) 11.4042 + 4.15079i 0.479778 + 0.174625i
\(566\) 10.9587 0.460628
\(567\) 0 0
\(568\) 15.7297 0.660002
\(569\) 40.1850 + 14.6261i 1.68464 + 0.613159i 0.993934 0.109975i \(-0.0350771\pi\)
0.690707 + 0.723134i \(0.257299\pi\)
\(570\) 0 0
\(571\) 13.8105 + 11.5884i 0.577950 + 0.484957i 0.884273 0.466970i \(-0.154654\pi\)
−0.306323 + 0.951928i \(0.599099\pi\)
\(572\) −6.61219 + 37.4996i −0.276470 + 1.56794i
\(573\) 0 0
\(574\) −0.477711 + 0.400847i −0.0199393 + 0.0167310i
\(575\) −15.2086 26.3421i −0.634244 1.09854i
\(576\) 0 0
\(577\) −12.6382 + 21.8899i −0.526133 + 0.911290i 0.473403 + 0.880846i \(0.343025\pi\)
−0.999536 + 0.0304438i \(0.990308\pi\)
\(578\) 0.692791 + 3.92902i 0.0288163 + 0.163425i
\(579\) 0 0
\(580\) 7.64930 2.78412i 0.317620 0.115604i
\(581\) 0.768065 0.279553i 0.0318647 0.0115978i
\(582\) 0 0
\(583\) 2.87433 + 16.3012i 0.119043 + 0.675125i
\(584\) 14.7797 25.5993i 0.611590 1.05930i
\(585\) 0 0
\(586\) 6.15792 + 10.6658i 0.254381 + 0.440601i
\(587\) −21.8823 + 18.3614i −0.903179 + 0.757857i −0.970809 0.239853i \(-0.922901\pi\)
0.0676298 + 0.997710i \(0.478456\pi\)
\(588\) 0 0
\(589\) 0.895115 5.07645i 0.0368826 0.209172i
\(590\) −0.0241084 0.0202293i −0.000992525 0.000832828i
\(591\) 0 0
\(592\) 2.89780 + 1.05471i 0.119099 + 0.0433485i
\(593\) −20.6009 −0.845977 −0.422989 0.906135i \(-0.639019\pi\)
−0.422989 + 0.906135i \(0.639019\pi\)
\(594\) 0 0
\(595\) −0.604007 −0.0247619
\(596\) 15.9053 + 5.78905i 0.651506 + 0.237129i
\(597\) 0 0
\(598\) 18.6853 + 15.6788i 0.764097 + 0.641154i
\(599\) 2.51352 14.2549i 0.102700 0.582439i −0.889414 0.457102i \(-0.848887\pi\)
0.992114 0.125338i \(-0.0400014\pi\)
\(600\) 0 0
\(601\) −10.2306 + 8.58445i −0.417313 + 0.350167i −0.827140 0.561996i \(-0.810034\pi\)
0.409827 + 0.912163i \(0.365589\pi\)
\(602\) −0.0538515 0.0932736i −0.00219483 0.00380155i
\(603\) 0 0
\(604\) −5.20961 + 9.02330i −0.211976 + 0.367153i
\(605\) 3.37133 + 19.1197i 0.137064 + 0.777328i
\(606\) 0 0
\(607\) −29.3307 + 10.6755i −1.19050 + 0.433305i −0.859898 0.510466i \(-0.829473\pi\)
−0.330598 + 0.943772i \(0.607251\pi\)
\(608\) 3.20631 1.16700i 0.130033 0.0473282i
\(609\) 0 0
\(610\) −1.27126 7.20967i −0.0514718 0.291911i
\(611\) 5.52557 9.57057i 0.223541 0.387184i
\(612\) 0 0
\(613\) −15.0326 26.0372i −0.607159 1.05163i −0.991706 0.128525i \(-0.958976\pi\)
0.384547 0.923105i \(-0.374358\pi\)
\(614\) −7.07970 + 5.94057i −0.285713 + 0.239742i
\(615\) 0 0
\(616\) −0.274967 + 1.55942i −0.0110787 + 0.0628307i
\(617\) 32.2916 + 27.0959i 1.30001 + 1.09084i 0.990143 + 0.140058i \(0.0447290\pi\)
0.309867 + 0.950780i \(0.399715\pi\)
\(618\) 0 0
\(619\) −10.9106 3.97113i −0.438534 0.159613i 0.113312 0.993559i \(-0.463854\pi\)
−0.551846 + 0.833946i \(0.686076\pi\)
\(620\) 14.0635 0.564803
\(621\) 0 0
\(622\) −11.2335 −0.450422
\(623\) 0.777025 + 0.282814i 0.0311308 + 0.0113307i
\(624\) 0 0
\(625\) 7.45471 + 6.25524i 0.298188 + 0.250210i
\(626\) −2.32395 + 13.1798i −0.0928839 + 0.526771i
\(627\) 0 0
\(628\) −19.8195 + 16.6306i −0.790886 + 0.663632i
\(629\) 5.21983 + 9.04101i 0.208128 + 0.360489i
\(630\) 0 0
\(631\) 14.6552 25.3836i 0.583415 1.01051i −0.411655 0.911340i \(-0.635049\pi\)
0.995071 0.0991657i \(-0.0316174\pi\)
\(632\) −0.294664 1.67112i −0.0117211 0.0664737i
\(633\) 0 0
\(634\) −15.6702 + 5.70350i −0.622345 + 0.226515i
\(635\) 15.1850 5.52687i 0.602597 0.219327i
\(636\) 0 0
\(637\) 5.54829 + 31.4659i 0.219831 + 1.24672i
\(638\) 9.42182 16.3191i 0.373014 0.646078i
\(639\) 0 0
\(640\) 5.66637 + 9.81445i 0.223983 + 0.387950i
\(641\) 23.8223 19.9893i 0.940926 0.789531i −0.0368201 0.999322i \(-0.511723\pi\)
0.977746 + 0.209791i \(0.0672784\pi\)
\(642\) 0 0
\(643\) 7.30571 41.4328i 0.288109 1.63395i −0.405854 0.913938i \(-0.633026\pi\)
0.693963 0.720010i \(-0.255863\pi\)
\(644\) −1.10359 0.926022i −0.0434875 0.0364904i
\(645\) 0 0
\(646\) 1.80763 + 0.657923i 0.0711202 + 0.0258856i
\(647\) −4.66717 −0.183485 −0.0917427 0.995783i \(-0.529244\pi\)
−0.0917427 + 0.995783i \(0.529244\pi\)
\(648\) 0 0
\(649\) 0.238541 0.00936356
\(650\) −11.4713 4.17521i −0.449941 0.163765i
\(651\) 0 0
\(652\) −9.87211 8.28368i −0.386622 0.324414i
\(653\) −0.542499 + 3.07667i −0.0212296 + 0.120399i −0.993581 0.113124i \(-0.963914\pi\)
0.972351 + 0.233523i \(0.0750254\pi\)
\(654\) 0 0
\(655\) 10.7226 8.99730i 0.418965 0.351554i
\(656\) −5.33424 9.23917i −0.208267 0.360729i
\(657\) 0 0
\(658\) 0.0996702 0.172634i 0.00388555 0.00672997i
\(659\) 6.49951 + 36.8606i 0.253185 + 1.43588i 0.800689 + 0.599080i \(0.204467\pi\)
−0.547504 + 0.836803i \(0.684422\pi\)
\(660\) 0 0
\(661\) −24.9021 + 9.06364i −0.968581 + 0.352535i −0.777391 0.629018i \(-0.783457\pi\)
−0.191191 + 0.981553i \(0.561235\pi\)
\(662\) −18.3187 + 6.66747i −0.711977 + 0.259139i
\(663\) 0 0
\(664\) −2.84312 16.1241i −0.110335 0.625738i
\(665\) −0.0371965 + 0.0644262i −0.00144242 + 0.00249834i
\(666\) 0 0
\(667\) 19.7618 + 34.2284i 0.765179 + 1.32533i
\(668\) 3.08083 2.58512i 0.119201 0.100021i
\(669\) 0 0
\(670\) −0.231516 + 1.31299i −0.00894423 + 0.0507252i
\(671\) 42.5077 + 35.6682i 1.64099 + 1.37696i
\(672\) 0 0
\(673\) −1.61721 0.588617i −0.0623389 0.0226895i 0.310662 0.950520i \(-0.399449\pi\)
−0.373001 + 0.927831i \(0.621671\pi\)
\(674\) −11.9341 −0.459686
\(675\) 0 0
\(676\) −12.1361 −0.466773
\(677\) 26.5738 + 9.67206i 1.02131 + 0.371727i 0.797767 0.602966i \(-0.206015\pi\)
0.223546 + 0.974693i \(0.428237\pi\)
\(678\) 0 0
\(679\) 0.834093 + 0.699887i 0.0320095 + 0.0268592i
\(680\) −2.10100 + 11.9153i −0.0805695 + 0.456933i
\(681\) 0 0
\(682\) 24.9388 20.9262i 0.954957 0.801304i
\(683\) −12.3569 21.4029i −0.472825 0.818958i 0.526691 0.850057i \(-0.323433\pi\)
−0.999516 + 0.0310993i \(0.990099\pi\)
\(684\) 0 0
\(685\) 10.2829 17.8105i 0.392888 0.680502i
\(686\) 0.200368 + 1.13634i 0.00765009 + 0.0433858i
\(687\) 0 0
\(688\) 1.73143 0.630189i 0.0660101 0.0240257i
\(689\) −13.0933 + 4.76558i −0.498816 + 0.181554i
\(690\) 0 0
\(691\) −7.60101 43.1075i −0.289156 1.63989i −0.690050 0.723762i \(-0.742411\pi\)
0.400894 0.916125i \(-0.368700\pi\)
\(692\) 10.0377 17.3858i 0.381576 0.660908i
\(693\) 0 0
\(694\) 8.61515 + 14.9219i 0.327027 + 0.566427i
\(695\) 13.0911 10.9847i 0.496574 0.416675i
\(696\) 0 0
\(697\) 6.27156 35.5678i 0.237552 1.34723i
\(698\) −6.21053 5.21126i −0.235072 0.197249i
\(699\) 0 0
\(700\) 0.677519 + 0.246597i 0.0256078 + 0.00932048i
\(701\) 14.6504 0.553338 0.276669 0.960965i \(-0.410769\pi\)
0.276669 + 0.960965i \(0.410769\pi\)
\(702\) 0 0
\(703\) 1.28581 0.0484951
\(704\) 5.83569 + 2.12402i 0.219941 + 0.0800520i
\(705\) 0 0
\(706\) 4.40033 + 3.69232i 0.165609 + 0.138962i
\(707\) −0.272114 + 1.54323i −0.0102339 + 0.0580393i
\(708\) 0 0
\(709\) 3.88666 3.26129i 0.145967 0.122480i −0.566880 0.823800i \(-0.691850\pi\)
0.712847 + 0.701320i \(0.247405\pi\)
\(710\) 2.33359 + 4.04189i 0.0875779 + 0.151689i
\(711\) 0 0
\(712\) 8.28194 14.3447i 0.310379 0.537592i
\(713\) 11.8572 + 67.2456i 0.444056 + 2.51837i
\(714\) 0 0
\(715\) −24.4761 + 8.90858i −0.915355 + 0.333162i
\(716\) −31.8155 + 11.5799i −1.18900 + 0.432761i
\(717\) 0 0
\(718\) −0.313615 1.77860i −0.0117040 0.0663767i
\(719\) −2.66858 + 4.62212i −0.0995213 + 0.172376i −0.911487 0.411330i \(-0.865064\pi\)
0.811965 + 0.583706i \(0.198398\pi\)
\(720\) 0 0
\(721\) 0.547104 + 0.947611i 0.0203752 + 0.0352909i
\(722\) −9.77460 + 8.20187i −0.363773 + 0.305242i
\(723\) 0 0
\(724\) 0.547819 3.10684i 0.0203595 0.115465i
\(725\) −15.1527 12.7147i −0.562759 0.472211i
\(726\) 0 0
\(727\) −34.8812 12.6957i −1.29367 0.470858i −0.398741 0.917063i \(-0.630553\pi\)
−0.894931 + 0.446205i \(0.852775\pi\)
\(728\) −1.33293 −0.0494017
\(729\) 0 0
\(730\) 8.77063 0.324616
\(731\) 5.86149 + 2.13341i 0.216795 + 0.0789069i
\(732\) 0 0
\(733\) 22.9402 + 19.2491i 0.847314 + 0.710981i 0.959196 0.282740i \(-0.0912435\pi\)
−0.111882 + 0.993721i \(0.535688\pi\)
\(734\) 1.09251 6.19594i 0.0403253 0.228696i
\(735\) 0 0
\(736\) −34.6241 + 29.0530i −1.27626 + 1.07091i
\(737\) −5.05277 8.75166i −0.186121 0.322371i
\(738\) 0 0
\(739\) 14.3050 24.7770i 0.526218 0.911436i −0.473316 0.880893i \(-0.656943\pi\)
0.999533 0.0305431i \(-0.00972368\pi\)
\(740\) 0.609158 + 3.45471i 0.0223931 + 0.126998i
\(741\) 0 0
\(742\) −0.236177 + 0.0859614i −0.00867033 + 0.00315574i
\(743\) 46.6497 16.9791i 1.71141 0.622903i 0.714371 0.699767i \(-0.246713\pi\)
0.997042 + 0.0768641i \(0.0244908\pi\)
\(744\) 0 0
\(745\) 2.01052 + 11.4022i 0.0736596 + 0.417744i
\(746\) 9.16312 15.8710i 0.335486 0.581078i
\(747\) 0 0
\(748\) −19.8897 34.4499i −0.727238 1.25961i
\(749\) −1.05207 + 0.882789i −0.0384417 + 0.0322564i
\(750\) 0 0
\(751\) −5.49138 + 31.1432i −0.200383 + 1.13643i 0.704158 + 0.710044i \(0.251325\pi\)
−0.904541 + 0.426387i \(0.859786\pi\)
\(752\) 2.61240 + 2.19207i 0.0952645 + 0.0799364i
\(753\) 0 0
\(754\) 14.9055 + 5.42517i 0.542828 + 0.197573i
\(755\) −7.12716 −0.259384
\(756\) 0 0
\(757\) 3.04189 0.110559 0.0552797 0.998471i \(-0.482395\pi\)
0.0552797 + 0.998471i \(0.482395\pi\)
\(758\) 17.4351 + 6.34587i 0.633272 + 0.230492i
\(759\) 0 0
\(760\) 1.14156 + 0.957882i 0.0414087 + 0.0347460i
\(761\) −6.58618 + 37.3521i −0.238749 + 1.35401i 0.595824 + 0.803115i \(0.296826\pi\)
−0.834573 + 0.550898i \(0.814286\pi\)
\(762\) 0 0
\(763\) −0.267855 + 0.224757i −0.00969702 + 0.00813676i
\(764\) −3.02525 5.23989i −0.109450 0.189572i
\(765\) 0 0
\(766\) −11.7747 + 20.3943i −0.425436 + 0.736877i
\(767\) 0.0348683 + 0.197748i 0.00125902 + 0.00714026i
\(768\) 0 0
\(769\) 19.1582 6.97302i 0.690863 0.251454i 0.0273584 0.999626i \(-0.491290\pi\)
0.663505 + 0.748172i \(0.269068\pi\)
\(770\) −0.441500 + 0.160693i −0.0159106 + 0.00579097i
\(771\) 0 0
\(772\) 2.24716 + 12.7443i 0.0808770 + 0.458676i
\(773\) 12.2332 21.1885i 0.439997 0.762097i −0.557692 0.830048i \(-0.688313\pi\)
0.997689 + 0.0679509i \(0.0216461\pi\)
\(774\) 0 0
\(775\) −17.0869 29.5954i −0.613781 1.06310i
\(776\) 16.7081 14.0198i 0.599786 0.503280i
\(777\) 0 0
\(778\) 0.0898700 0.509678i 0.00322200 0.0182729i
\(779\) −3.40760 2.85932i −0.122090 0.102446i
\(780\) 0 0
\(781\) −33.2422 12.0992i −1.18950 0.432942i
\(782\) −25.4816 −0.911221
\(783\) 0 0
\(784\) −9.85978 −0.352135
\(785\) −16.6306 6.05303i −0.593571 0.216042i
\(786\) 0 0
\(787\) 28.7841 + 24.1527i 1.02604 + 0.860950i 0.990375 0.138413i \(-0.0442003\pi\)
0.0356661 + 0.999364i \(0.488645\pi\)
\(788\) 0.610567 3.46270i 0.0217505 0.123353i
\(789\) 0 0
\(790\) 0.385696 0.323637i 0.0137224 0.0115145i
\(791\) −0.698367 1.20961i −0.0248311 0.0430087i
\(792\) 0 0
\(793\) −23.3550 + 40.4521i −0.829362 + 1.43650i
\(794\) 0.832396 + 4.72075i 0.0295406 + 0.167533i
\(795\) 0 0
\(796\) −33.8371 + 12.3157i −1.19932 + 0.436518i
\(797\) 2.16593 0.788333i 0.0767211 0.0279242i −0.303374 0.952871i \(-0.598113\pi\)
0.380096 + 0.924947i \(0.375891\pi\)
\(798\) 0 0
\(799\) 2.00475 + 11.3695i 0.0709229 + 0.402224i
\(800\) 11.3103 19.5901i 0.399881 0.692614i
\(801\) 0 0
\(802\) 3.23236 + 5.59862i 0.114139 + 0.197694i
\(803\) −50.9254 + 42.7315i −1.79712 + 1.50796i
\(804\) 0 0
\(805\) 0.171122 0.970481i 0.00603126 0.0342050i
\(806\) 20.9929 + 17.6152i 0.739444 + 0.620467i
\(807\) 0 0
\(808\) 29.4971 + 10.7361i 1.03770 + 0.377693i
\(809\) 28.8614 1.01471 0.507356 0.861736i \(-0.330623\pi\)
0.507356 + 0.861736i \(0.330623\pi\)
\(810\) 0 0
\(811\) −51.8631 −1.82116 −0.910580 0.413334i \(-0.864364\pi\)
−0.910580 + 0.413334i \(0.864364\pi\)
\(812\) −0.880352 0.320422i −0.0308943 0.0112446i
\(813\) 0 0
\(814\) 6.22075 + 5.21983i 0.218037 + 0.182955i
\(815\) 1.53076 8.68139i 0.0536203 0.304096i
\(816\) 0 0
\(817\) 0.588526 0.493832i 0.0205899 0.0172770i
\(818\) −1.88711 3.26857i −0.0659813 0.114283i
\(819\) 0 0
\(820\) 6.06805 10.5102i 0.211905 0.367031i
\(821\) −3.20226 18.1609i −0.111760 0.633820i −0.988304 0.152499i \(-0.951268\pi\)
0.876544 0.481322i \(-0.159843\pi\)
\(822\) 0 0
\(823\) 32.6698 11.8908i 1.13880 0.414489i 0.297319 0.954778i \(-0.403907\pi\)
0.841479 + 0.540289i \(0.181685\pi\)
\(824\) 20.5967 7.49660i 0.717521 0.261156i
\(825\) 0 0
\(826\) 0.000628954 0.00356697i 2.18841e−5 0.000124111i
\(827\) −16.3886 + 28.3859i −0.569889 + 0.987076i 0.426688 + 0.904399i \(0.359680\pi\)
−0.996576 + 0.0826770i \(0.973653\pi\)
\(828\) 0 0
\(829\) −2.67634 4.63555i −0.0929530 0.160999i 0.815799 0.578335i \(-0.196297\pi\)
−0.908752 + 0.417336i \(0.862964\pi\)
\(830\) 3.72146 3.12267i 0.129174 0.108390i
\(831\) 0 0
\(832\) −0.907766 + 5.14820i −0.0314711 + 0.178482i
\(833\) −25.5696 21.4555i −0.885936 0.743388i
\(834\) 0 0
\(835\) 2.58512 + 0.940908i 0.0894618 + 0.0325614i
\(836\) −4.89944 −0.169451
\(837\) 0 0
\(838\) −0.319022 −0.0110204
\(839\) 5.11040 + 1.86003i 0.176431 + 0.0642155i 0.428725 0.903435i \(-0.358963\pi\)
−0.252294 + 0.967651i \(0.581185\pi\)
\(840\) 0 0
\(841\) −2.52616 2.11970i −0.0871089 0.0730931i
\(842\) −0.286760 + 1.62630i −0.00988240 + 0.0560459i
\(843\) 0 0
\(844\) 1.95677 1.64192i 0.0673547 0.0565173i
\(845\) −4.15079 7.18938i −0.142791 0.247322i
\(846\) 0 0
\(847\) 1.11721 1.93507i 0.0383878 0.0664897i
\(848\) −0.746643 4.23442i −0.0256398 0.145411i
\(849\) 0 0
\(850\) 11.9838 4.36175i 0.411041 0.149607i
\(851\) −16.0054 + 5.82547i −0.548657 + 0.199695i
\(852\) 0 0
\(853\) −8.18180 46.4013i −0.280139 1.58875i −0.722148 0.691739i \(-0.756845\pi\)
0.442008 0.897011i \(-0.354266\pi\)
\(854\) −0.421278 + 0.729675i −0.0144158 + 0.0249690i
\(855\) 0 0
\(856\) 13.7554 + 23.8250i 0.470149 + 0.814322i
\(857\) 35.9704 30.1827i 1.22872 1.03102i 0.230404 0.973095i \(-0.425995\pi\)
0.998321 0.0579275i \(-0.0184492\pi\)
\(858\) 0 0
\(859\) 1.24392 7.05461i 0.0424419 0.240700i −0.956205 0.292697i \(-0.905447\pi\)
0.998647 + 0.0519966i \(0.0165585\pi\)
\(860\) 1.60565 + 1.34730i 0.0547520 + 0.0459424i
\(861\) 0 0
\(862\) −7.77719 2.83067i −0.264892 0.0964128i
\(863\) 35.4309 1.20608 0.603041 0.797710i \(-0.293955\pi\)
0.603041 + 0.797710i \(0.293955\pi\)
\(864\) 0 0
\(865\) 13.7324 0.466914
\(866\) −21.4376 7.80263i −0.728478 0.265144i
\(867\) 0 0
\(868\) −1.23989 1.04039i −0.0420845 0.0353130i
\(869\) −0.662690 + 3.75830i −0.0224802 + 0.127492i
\(870\) 0 0
\(871\) 6.51645 5.46795i 0.220801 0.185274i
\(872\) 3.50211 + 6.06583i 0.118596 + 0.205415i
\(873\) 0 0
\(874\) −1.56923 + 2.71799i −0.0530800 + 0.0919373i
\(875\) 0.195393 + 1.10813i 0.00660547 + 0.0374615i
\(876\) 0 0
\(877\) −7.68004 + 2.79531i −0.259337 + 0.0943908i −0.468417 0.883508i \(-0.655175\pi\)
0.209080 + 0.977899i \(0.432953\pi\)
\(878\) 5.81374 2.11603i 0.196204 0.0714125i
\(879\) 0 0
\(880\) −1.39574 7.91566i −0.0470505 0.266837i
\(881\) −16.6153 + 28.7786i −0.559785 + 0.969575i 0.437729 + 0.899107i \(0.355783\pi\)
−0.997514 + 0.0704686i \(0.977551\pi\)
\(882\) 0 0
\(883\) −16.5239 28.6203i −0.556075 0.963150i −0.997819 0.0660087i \(-0.978973\pi\)
0.441744 0.897141i \(-0.354360\pi\)
\(884\) 25.6512 21.5239i 0.862744 0.723928i
\(885\) 0 0
\(886\) 0.555560 3.15074i 0.0186644 0.105851i
\(887\) 38.1086 + 31.9769i 1.27956 + 1.07368i 0.993304 + 0.115526i \(0.0368553\pi\)
0.286256 + 0.958153i \(0.407589\pi\)
\(888\) 0 0
\(889\) −1.74763 0.636084i −0.0586135 0.0213336i
\(890\) 4.91469 0.164741
\(891\) 0 0
\(892\) 15.0155 0.502756
\(893\) 1.33618 + 0.486329i 0.0447135 + 0.0162744i
\(894\) 0 0
\(895\) −17.7414 14.8868i −0.593031 0.497612i
\(896\) 0.226485 1.28446i 0.00756635 0.0429109i
\(897\) 0 0
\(898\) 13.9945 11.7428i 0.467004 0.391863i
\(899\) 22.2024 + 38.4556i 0.740491 + 1.28257i
\(900\) 0 0
\(901\) 7.27807 12.6060i 0.242468 0.419966i
\(902\) −4.87841 27.6668i −0.162433 0.921205i
\(903\) 0 0
\(904\) −26.2913 + 9.56926i −0.874437 + 0.318269i
\(905\) 2.02784 0.738074i 0.0674078 0.0245344i
\(906\) 0 0
\(907\) 5.99928 + 34.0236i 0.199203 + 1.12974i 0.906305 + 0.422625i \(0.138891\pi\)
−0.707102 + 0.707112i \(0.749998\pi\)
\(908\) −11.8589 + 20.5403i −0.393553 + 0.681654i
\(909\) 0 0
\(910\) −0.197748 0.342509i −0.00655528 0.0113541i
\(911\) 10.4465 8.76563i 0.346107 0.290418i −0.453117 0.891451i \(-0.649688\pi\)
0.799225 + 0.601032i \(0.205244\pi\)
\(912\) 0 0
\(913\) −6.39410 + 36.2627i −0.211614 + 1.20012i
\(914\) −0.344668 0.289210i −0.0114006 0.00956623i
\(915\) 0 0
\(916\) −16.2023 5.89717i −0.535340 0.194848i
\(917\) −1.61094 −0.0531979
\(918\) 0 0
\(919\) 32.7701 1.08099 0.540493 0.841348i \(-0.318238\pi\)
0.540493 + 0.841348i \(0.318238\pi\)
\(920\) −18.5496 6.75150i −0.611562 0.222590i
\(921\) 0 0
\(922\) −10.8489 9.10327i −0.357288 0.299800i
\(923\) 5.17095 29.3259i 0.170204 0.965275i
\(924\) 0 0
\(925\) 6.53003 5.47935i 0.214706 0.180160i
\(926\) 8.49027 + 14.7056i 0.279008 + 0.483255i
\(927\) 0 0
\(928\) −14.6964 + 25.4549i −0.482433 + 0.835599i
\(929\) −0.960529 5.44743i −0.0315140 0.178724i 0.964988 0.262294i \(-0.0844790\pi\)
−0.996502 + 0.0835696i \(0.973368\pi\)
\(930\) 0 0
\(931\) −3.86319 + 1.40609i −0.126611 + 0.0460826i
\(932\) −7.53644 + 2.74304i −0.246864 + 0.0898513i
\(933\) 0 0
\(934\) −3.16827 17.9682i −0.103669 0.587936i
\(935\) 13.6053 23.5651i 0.444942 0.770662i
\(936\) 0 0
\(937\) 0.497007 + 0.860841i 0.0162365 + 0.0281225i 0.874029 0.485873i \(-0.161498\pi\)
−0.857793 + 0.513995i \(0.828165\pi\)
\(938\) 0.117544 0.0986308i 0.00383793 0.00322041i
\(939\) 0 0
\(940\) −0.673648 + 3.82045i −0.0219720 + 0.124609i
\(941\) −8.77671 7.36453i −0.286113 0.240077i 0.488424 0.872607i \(-0.337572\pi\)
−0.774536 + 0.632530i \(0.782017\pi\)
\(942\) 0 0
\(943\) 55.3713 + 20.1535i 1.80314 + 0.656288i
\(944\) −0.0619640 −0.00201676
\(945\) 0 0
\(946\) 4.85204 0.157754
\(947\) −42.9299 15.6252i −1.39503 0.507751i −0.468333 0.883552i \(-0.655145\pi\)
−0.926700 + 0.375801i \(0.877368\pi\)
\(948\) 0 0
\(949\) −42.8678 35.9704i −1.39155 1.16765i
\(950\) 0.272752 1.54686i 0.00884925 0.0501866i
\(951\) 0 0
\(952\) 1.06670 0.895071i 0.0345721 0.0290094i
\(953\) −7.25265 12.5620i −0.234936 0.406922i 0.724318 0.689466i \(-0.242155\pi\)
−0.959254 + 0.282545i \(0.908822\pi\)
\(954\) 0 0
\(955\) 2.06939 3.58429i 0.0669640 0.115985i
\(956\) −2.74286 15.5556i −0.0887106 0.503103i
\(957\) 0 0
\(958\) −2.07398 + 0.754866i −0.0670072 + 0.0243886i
\(959\) −2.22415 + 0.809526i −0.0718217 + 0.0261410i
\(960\) 0 0
\(961\) 7.93851 + 45.0215i 0.256081 + 1.45231i
\(962\) −3.41787 + 5.91993i −0.110197 + 0.190866i
\(963\) 0 0
\(964\) 8.23055 + 14.2557i 0.265088 + 0.459146i
\(965\) −6.78109 + 5.69001i −0.218291 + 0.183168i
\(966\) 0 0
\(967\) −4.34760 + 24.6565i −0.139809 + 0.792899i 0.831580 + 0.555405i \(0.187437\pi\)
−0.971389 + 0.237493i \(0.923674\pi\)
\(968\) −34.2872 28.7704i −1.10203 0.924715i
\(969\) 0 0
\(970\) 6.08125 + 2.21339i 0.195257 + 0.0710678i
\(971\) −27.0907 −0.869383 −0.434692 0.900579i \(-0.643143\pi\)
−0.434692 + 0.900579i \(0.643143\pi\)
\(972\) 0 0
\(973\) −1.96679 −0.0630522
\(974\) 5.00044 + 1.82001i 0.160224 + 0.0583169i
\(975\) 0 0
\(976\) −11.0419 9.26525i −0.353442 0.296573i
\(977\) 0.429501 2.43582i 0.0137410 0.0779289i −0.977166 0.212477i \(-0.931847\pi\)
0.990907 + 0.134548i \(0.0429582\pi\)
\(978\) 0 0
\(979\) −28.5364 + 23.9449i −0.912028 + 0.765282i
\(980\) −5.60808 9.71348i −0.179144 0.310286i
\(981\) 0 0
\(982\) 5.83006 10.0980i 0.186045 0.322239i
\(983\) −3.31807 18.8177i −0.105830 0.600192i −0.990886 0.134707i \(-0.956991\pi\)
0.885055 0.465486i \(-0.154120\pi\)
\(984\) 0 0
\(985\) 2.26011 0.822614i 0.0720132 0.0262107i
\(986\) −15.5715 + 5.66756i −0.495897 + 0.180492i
\(987\) 0 0
\(988\) −0.716166 4.06158i −0.0227843 0.129216i
\(989\) −5.08845 + 8.81345i −0.161803 + 0.280251i
\(990\) 0 0
\(991\) 19.1582 + 33.1830i 0.608581 + 1.05409i 0.991475 + 0.130301i \(0.0415943\pi\)
−0.382894 + 0.923792i \(0.625072\pi\)
\(992\) −38.9002 + 32.6411i −1.23508 + 1.03636i
\(993\) 0 0
\(994\) 0.0932736 0.528981i 0.00295846 0.0167783i
\(995\) −18.8687 15.8327i −0.598179 0.501932i
\(996\) 0 0
\(997\) −38.8794 14.1510i −1.23132 0.448165i −0.357273 0.934000i \(-0.616294\pi\)
−0.874051 + 0.485834i \(0.838516\pi\)
\(998\) 5.42497 0.171724
\(999\) 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 729.2.e.m.568.1 12
3.2 odd 2 inner 729.2.e.m.568.2 12
9.2 odd 6 729.2.e.q.82.1 12
9.4 even 3 729.2.e.r.325.2 12
9.5 odd 6 729.2.e.r.325.1 12
9.7 even 3 729.2.e.q.82.2 12
27.2 odd 18 729.2.e.r.406.1 12
27.4 even 9 729.2.c.c.244.3 12
27.5 odd 18 729.2.c.c.487.4 12
27.7 even 9 inner 729.2.e.m.163.1 12
27.11 odd 18 729.2.e.q.649.1 12
27.13 even 9 729.2.a.c.1.4 yes 6
27.14 odd 18 729.2.a.c.1.3 6
27.16 even 9 729.2.e.q.649.2 12
27.20 odd 18 inner 729.2.e.m.163.2 12
27.22 even 9 729.2.c.c.487.3 12
27.23 odd 18 729.2.c.c.244.4 12
27.25 even 9 729.2.e.r.406.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.c.1.3 6 27.14 odd 18
729.2.a.c.1.4 yes 6 27.13 even 9
729.2.c.c.244.3 12 27.4 even 9
729.2.c.c.244.4 12 27.23 odd 18
729.2.c.c.487.3 12 27.22 even 9
729.2.c.c.487.4 12 27.5 odd 18
729.2.e.m.163.1 12 27.7 even 9 inner
729.2.e.m.163.2 12 27.20 odd 18 inner
729.2.e.m.568.1 12 1.1 even 1 trivial
729.2.e.m.568.2 12 3.2 odd 2 inner
729.2.e.q.82.1 12 9.2 odd 6
729.2.e.q.82.2 12 9.7 even 3
729.2.e.q.649.1 12 27.11 odd 18
729.2.e.q.649.2 12 27.16 even 9
729.2.e.r.325.1 12 9.5 odd 6
729.2.e.r.325.2 12 9.4 even 3
729.2.e.r.406.1 12 27.2 odd 18
729.2.e.r.406.2 12 27.25 even 9