Properties

Label 891.2.k.a.161.7
Level $891$
Weight $2$
Character 891.161
Analytic conductor $7.115$
Analytic rank $0$
Dimension $80$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(161,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.k (of order \(10\), degree \(4\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 161.7
Character \(\chi\) \(=\) 891.161
Dual form 891.2.k.a.404.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.931921 - 0.677080i) q^{2} +(-0.207995 - 0.640143i) q^{4} +(-0.551104 - 0.758530i) q^{5} +(-0.824408 + 0.267866i) q^{7} +(-0.951517 + 2.92847i) q^{8} +1.08003i q^{10} +(1.59130 + 2.90994i) q^{11} +(0.693143 - 0.954029i) q^{13} +(0.949650 + 0.308560i) q^{14} +(1.78047 - 1.29359i) q^{16} +(-2.52191 + 1.83228i) q^{17} +(6.59786 + 2.14377i) q^{19} +(-0.370941 + 0.510556i) q^{20} +(0.487302 - 3.78927i) q^{22} +2.36655i q^{23} +(1.27343 - 3.91922i) q^{25} +(-1.29191 + 0.419767i) q^{26} +(0.342946 + 0.472024i) q^{28} +(1.11875 + 3.44315i) q^{29} +(5.13662 + 3.73198i) q^{31} +3.62323 q^{32} +3.59082 q^{34} +(0.657520 + 0.477716i) q^{35} +(-2.46847 - 7.59716i) q^{37} +(-4.69717 - 6.46511i) q^{38} +(2.74572 - 0.892138i) q^{40} +(1.11348 - 3.42695i) q^{41} -3.83119i q^{43} +(1.53180 - 1.62391i) q^{44} +(1.60234 - 2.20543i) q^{46} +(0.152329 + 0.0494946i) q^{47} +(-5.05522 + 3.67283i) q^{49} +(-3.84037 + 2.79019i) q^{50} +(-0.754886 - 0.245277i) q^{52} +(5.71174 - 7.86153i) q^{53} +(1.33031 - 2.81073i) q^{55} -2.66913i q^{56} +(1.28870 - 3.96622i) q^{58} +(-8.27039 + 2.68721i) q^{59} +(7.97576 + 10.9777i) q^{61} +(-2.26008 - 6.95581i) q^{62} +(-6.93750 - 5.04039i) q^{64} -1.10565 q^{65} +6.64298 q^{67} +(1.69746 + 1.23328i) q^{68} +(-0.289304 - 0.890387i) q^{70} +(6.53958 + 9.00097i) q^{71} +(3.29787 - 1.07154i) q^{73} +(-2.84347 + 8.75130i) q^{74} -4.66947i q^{76} +(-2.09135 - 1.97273i) q^{77} +(4.43649 - 6.10630i) q^{79} +(-1.96245 - 0.637639i) q^{80} +(-3.35800 + 2.43973i) q^{82} +(11.6734 - 8.48120i) q^{83} +(2.77967 + 0.903171i) q^{85} +(-2.59402 + 3.57037i) q^{86} +(-10.0358 + 1.89120i) q^{88} -9.28531i q^{89} +(-0.315880 + 0.972179i) q^{91} +(1.51493 - 0.492230i) q^{92} +(-0.108446 - 0.149264i) q^{94} +(-2.00999 - 6.18612i) q^{95} +(9.85618 + 7.16093i) q^{97} +7.19787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.931921 0.677080i −0.658967 0.478768i 0.207347 0.978268i \(-0.433517\pi\)
−0.866314 + 0.499500i \(0.833517\pi\)
\(3\) 0 0
\(4\) −0.207995 0.640143i −0.103998 0.320072i
\(5\) −0.551104 0.758530i −0.246461 0.339225i 0.667807 0.744335i \(-0.267233\pi\)
−0.914268 + 0.405110i \(0.867233\pi\)
\(6\) 0 0
\(7\) −0.824408 + 0.267866i −0.311597 + 0.101244i −0.460641 0.887587i \(-0.652380\pi\)
0.149044 + 0.988831i \(0.452380\pi\)
\(8\) −0.951517 + 2.92847i −0.336412 + 1.03537i
\(9\) 0 0
\(10\) 1.08003i 0.341536i
\(11\) 1.59130 + 2.90994i 0.479794 + 0.877381i
\(12\) 0 0
\(13\) 0.693143 0.954029i 0.192243 0.264600i −0.702004 0.712173i \(-0.747711\pi\)
0.894248 + 0.447572i \(0.147711\pi\)
\(14\) 0.949650 + 0.308560i 0.253805 + 0.0824661i
\(15\) 0 0
\(16\) 1.78047 1.29359i 0.445117 0.323397i
\(17\) −2.52191 + 1.83228i −0.611653 + 0.444392i −0.849996 0.526789i \(-0.823396\pi\)
0.238343 + 0.971181i \(0.423396\pi\)
\(18\) 0 0
\(19\) 6.59786 + 2.14377i 1.51365 + 0.491816i 0.943965 0.330046i \(-0.107064\pi\)
0.569688 + 0.821861i \(0.307064\pi\)
\(20\) −0.370941 + 0.510556i −0.0829449 + 0.114164i
\(21\) 0 0
\(22\) 0.487302 3.78927i 0.103893 0.807876i
\(23\) 2.36655i 0.493459i 0.969084 + 0.246730i \(0.0793559\pi\)
−0.969084 + 0.246730i \(0.920644\pi\)
\(24\) 0 0
\(25\) 1.27343 3.91922i 0.254687 0.783845i
\(26\) −1.29191 + 0.419767i −0.253364 + 0.0823230i
\(27\) 0 0
\(28\) 0.342946 + 0.472024i 0.0648106 + 0.0892042i
\(29\) 1.11875 + 3.44315i 0.207746 + 0.639376i 0.999589 + 0.0286522i \(0.00912152\pi\)
−0.791844 + 0.610724i \(0.790878\pi\)
\(30\) 0 0
\(31\) 5.13662 + 3.73198i 0.922565 + 0.670283i 0.944161 0.329484i \(-0.106875\pi\)
−0.0215963 + 0.999767i \(0.506875\pi\)
\(32\) 3.62323 0.640503
\(33\) 0 0
\(34\) 3.59082 0.615820
\(35\) 0.657520 + 0.477716i 0.111141 + 0.0807487i
\(36\) 0 0
\(37\) −2.46847 7.59716i −0.405813 1.24897i −0.920214 0.391415i \(-0.871986\pi\)
0.514401 0.857550i \(-0.328014\pi\)
\(38\) −4.69717 6.46511i −0.761982 1.04878i
\(39\) 0 0
\(40\) 2.74572 0.892138i 0.434136 0.141059i
\(41\) 1.11348 3.42695i 0.173897 0.535199i −0.825685 0.564132i \(-0.809211\pi\)
0.999581 + 0.0289327i \(0.00921085\pi\)
\(42\) 0 0
\(43\) 3.83119i 0.584251i −0.956380 0.292126i \(-0.905637\pi\)
0.956380 0.292126i \(-0.0943625\pi\)
\(44\) 1.53180 1.62391i 0.230927 0.244814i
\(45\) 0 0
\(46\) 1.60234 2.20543i 0.236252 0.325174i
\(47\) 0.152329 + 0.0494946i 0.0222194 + 0.00721952i 0.320106 0.947382i \(-0.396282\pi\)
−0.297886 + 0.954601i \(0.596282\pi\)
\(48\) 0 0
\(49\) −5.05522 + 3.67283i −0.722175 + 0.524691i
\(50\) −3.84037 + 2.79019i −0.543110 + 0.394592i
\(51\) 0 0
\(52\) −0.754886 0.245277i −0.104684 0.0340138i
\(53\) 5.71174 7.86153i 0.784567 1.07986i −0.210196 0.977659i \(-0.567410\pi\)
0.994763 0.102205i \(-0.0325898\pi\)
\(54\) 0 0
\(55\) 1.33031 2.81073i 0.179379 0.378999i
\(56\) 2.66913i 0.356678i
\(57\) 0 0
\(58\) 1.28870 3.96622i 0.169215 0.520790i
\(59\) −8.27039 + 2.68721i −1.07671 + 0.349845i −0.793099 0.609093i \(-0.791534\pi\)
−0.283614 + 0.958938i \(0.591534\pi\)
\(60\) 0 0
\(61\) 7.97576 + 10.9777i 1.02119 + 1.40555i 0.911365 + 0.411598i \(0.135029\pi\)
0.109826 + 0.993951i \(0.464971\pi\)
\(62\) −2.26008 6.95581i −0.287030 0.883389i
\(63\) 0 0
\(64\) −6.93750 5.04039i −0.867188 0.630049i
\(65\) −1.10565 −0.137140
\(66\) 0 0
\(67\) 6.64298 0.811569 0.405785 0.913969i \(-0.366998\pi\)
0.405785 + 0.913969i \(0.366998\pi\)
\(68\) 1.69746 + 1.23328i 0.205848 + 0.149557i
\(69\) 0 0
\(70\) −0.289304 0.890387i −0.0345785 0.106422i
\(71\) 6.53958 + 9.00097i 0.776106 + 1.06822i 0.995701 + 0.0926270i \(0.0295264\pi\)
−0.219595 + 0.975591i \(0.570474\pi\)
\(72\) 0 0
\(73\) 3.29787 1.07154i 0.385987 0.125415i −0.109594 0.993976i \(-0.534955\pi\)
0.495581 + 0.868562i \(0.334955\pi\)
\(74\) −2.84347 + 8.75130i −0.330547 + 1.01732i
\(75\) 0 0
\(76\) 4.66947i 0.535625i
\(77\) −2.09135 1.97273i −0.238332 0.224813i
\(78\) 0 0
\(79\) 4.43649 6.10630i 0.499144 0.687012i −0.482898 0.875677i \(-0.660416\pi\)
0.982042 + 0.188664i \(0.0604158\pi\)
\(80\) −1.96245 0.637639i −0.219409 0.0712902i
\(81\) 0 0
\(82\) −3.35800 + 2.43973i −0.370829 + 0.269423i
\(83\) 11.6734 8.48120i 1.28132 0.930933i 0.281727 0.959495i \(-0.409093\pi\)
0.999592 + 0.0285622i \(0.00909286\pi\)
\(84\) 0 0
\(85\) 2.77967 + 0.903171i 0.301498 + 0.0979626i
\(86\) −2.59402 + 3.57037i −0.279721 + 0.385003i
\(87\) 0 0
\(88\) −10.0358 + 1.89120i −1.06982 + 0.201603i
\(89\) 9.28531i 0.984241i −0.870527 0.492120i \(-0.836222\pi\)
0.870527 0.492120i \(-0.163778\pi\)
\(90\) 0 0
\(91\) −0.315880 + 0.972179i −0.0331132 + 0.101912i
\(92\) 1.51493 0.492230i 0.157942 0.0513186i
\(93\) 0 0
\(94\) −0.108446 0.149264i −0.0111854 0.0153954i
\(95\) −2.00999 6.18612i −0.206221 0.634682i
\(96\) 0 0
\(97\) 9.85618 + 7.16093i 1.00074 + 0.727082i 0.962247 0.272176i \(-0.0877434\pi\)
0.0384957 + 0.999259i \(0.487743\pi\)
\(98\) 7.19787 0.727095
\(99\) 0 0
\(100\) −2.77373 −0.277373
\(101\) 4.90121 + 3.56094i 0.487689 + 0.354327i 0.804295 0.594230i \(-0.202543\pi\)
−0.316606 + 0.948557i \(0.602543\pi\)
\(102\) 0 0
\(103\) −1.23254 3.79337i −0.121446 0.373772i 0.871791 0.489878i \(-0.162959\pi\)
−0.993237 + 0.116106i \(0.962959\pi\)
\(104\) 2.13431 + 2.93762i 0.209286 + 0.288058i
\(105\) 0 0
\(106\) −10.6458 + 3.45902i −1.03401 + 0.335970i
\(107\) −1.90097 + 5.85057i −0.183773 + 0.565596i −0.999925 0.0122414i \(-0.996103\pi\)
0.816152 + 0.577838i \(0.196103\pi\)
\(108\) 0 0
\(109\) 16.9364i 1.62221i 0.584897 + 0.811107i \(0.301135\pi\)
−0.584897 + 0.811107i \(0.698865\pi\)
\(110\) −3.14283 + 1.71865i −0.299657 + 0.163867i
\(111\) 0 0
\(112\) −1.12132 + 1.54337i −0.105955 + 0.145835i
\(113\) 7.61414 + 2.47398i 0.716278 + 0.232733i 0.644409 0.764681i \(-0.277104\pi\)
0.0718692 + 0.997414i \(0.477104\pi\)
\(114\) 0 0
\(115\) 1.79510 1.30421i 0.167394 0.121619i
\(116\) 1.97141 1.43232i 0.183041 0.132987i
\(117\) 0 0
\(118\) 9.52681 + 3.09545i 0.877014 + 0.284959i
\(119\) 1.58828 2.18608i 0.145597 0.200397i
\(120\) 0 0
\(121\) −5.93555 + 9.26117i −0.539595 + 0.841925i
\(122\) 15.6306i 1.41512i
\(123\) 0 0
\(124\) 1.32061 4.06441i 0.118594 0.364995i
\(125\) −8.13317 + 2.64263i −0.727453 + 0.236364i
\(126\) 0 0
\(127\) −3.73492 5.14068i −0.331421 0.456161i 0.610490 0.792024i \(-0.290972\pi\)
−0.941911 + 0.335862i \(0.890972\pi\)
\(128\) 0.813175 + 2.50270i 0.0718752 + 0.221209i
\(129\) 0 0
\(130\) 1.03038 + 0.748616i 0.0903705 + 0.0656580i
\(131\) 17.3740 1.51797 0.758985 0.651109i \(-0.225696\pi\)
0.758985 + 0.651109i \(0.225696\pi\)
\(132\) 0 0
\(133\) −6.01357 −0.521443
\(134\) −6.19073 4.49783i −0.534798 0.388553i
\(135\) 0 0
\(136\) −2.96612 9.12878i −0.254343 0.782787i
\(137\) −10.4042 14.3201i −0.888890 1.22345i −0.973878 0.227070i \(-0.927085\pi\)
0.0849882 0.996382i \(-0.472915\pi\)
\(138\) 0 0
\(139\) −5.87651 + 1.90939i −0.498439 + 0.161953i −0.547438 0.836846i \(-0.684397\pi\)
0.0489992 + 0.998799i \(0.484397\pi\)
\(140\) 0.169046 0.520269i 0.0142870 0.0439708i
\(141\) 0 0
\(142\) 12.8160i 1.07550i
\(143\) 3.87917 + 0.498862i 0.324392 + 0.0417170i
\(144\) 0 0
\(145\) 1.99518 2.74614i 0.165691 0.228054i
\(146\) −3.79887 1.23433i −0.314397 0.102154i
\(147\) 0 0
\(148\) −4.34984 + 3.16034i −0.357555 + 0.259779i
\(149\) 5.97193 4.33886i 0.489239 0.355453i −0.315652 0.948875i \(-0.602223\pi\)
0.804892 + 0.593422i \(0.202223\pi\)
\(150\) 0 0
\(151\) −12.8241 4.16680i −1.04361 0.339090i −0.263453 0.964672i \(-0.584861\pi\)
−0.780158 + 0.625583i \(0.784861\pi\)
\(152\) −12.5560 + 17.2818i −1.01842 + 1.40174i
\(153\) 0 0
\(154\) 0.613283 + 3.25444i 0.0494198 + 0.262250i
\(155\) 5.95299i 0.478156i
\(156\) 0 0
\(157\) −0.906116 + 2.78874i −0.0723160 + 0.222566i −0.980681 0.195611i \(-0.937331\pi\)
0.908366 + 0.418177i \(0.137331\pi\)
\(158\) −8.26891 + 2.68673i −0.657839 + 0.213745i
\(159\) 0 0
\(160\) −1.99678 2.74833i −0.157859 0.217275i
\(161\) −0.633918 1.95100i −0.0499598 0.153760i
\(162\) 0 0
\(163\) 17.8134 + 12.9422i 1.39525 + 1.01371i 0.995266 + 0.0971873i \(0.0309846\pi\)
0.399985 + 0.916522i \(0.369015\pi\)
\(164\) −2.42534 −0.189387
\(165\) 0 0
\(166\) −16.6211 −1.29005
\(167\) −0.521597 0.378963i −0.0403624 0.0293250i 0.567421 0.823428i \(-0.307941\pi\)
−0.607784 + 0.794103i \(0.707941\pi\)
\(168\) 0 0
\(169\) 3.58750 + 11.0412i 0.275961 + 0.849321i
\(170\) −1.97892 2.72374i −0.151776 0.208902i
\(171\) 0 0
\(172\) −2.45251 + 0.796869i −0.187002 + 0.0607607i
\(173\) −4.16978 + 12.8333i −0.317023 + 0.975695i 0.657891 + 0.753113i \(0.271449\pi\)
−0.974914 + 0.222582i \(0.928551\pi\)
\(174\) 0 0
\(175\) 3.57215i 0.270029i
\(176\) 6.59752 + 3.12259i 0.497307 + 0.235374i
\(177\) 0 0
\(178\) −6.28690 + 8.65317i −0.471223 + 0.648583i
\(179\) −1.06341 0.345524i −0.0794832 0.0258256i 0.269005 0.963139i \(-0.413305\pi\)
−0.348489 + 0.937313i \(0.613305\pi\)
\(180\) 0 0
\(181\) −18.7897 + 13.6515i −1.39663 + 1.01471i −0.401530 + 0.915846i \(0.631521\pi\)
−0.995101 + 0.0988656i \(0.968479\pi\)
\(182\) 0.952618 0.692118i 0.0706128 0.0513032i
\(183\) 0 0
\(184\) −6.93036 2.25181i −0.510913 0.166006i
\(185\) −4.40229 + 6.05923i −0.323663 + 0.445484i
\(186\) 0 0
\(187\) −9.34493 4.42293i −0.683369 0.323436i
\(188\) 0.107807i 0.00786262i
\(189\) 0 0
\(190\) −2.31534 + 7.12590i −0.167973 + 0.516967i
\(191\) −2.84491 + 0.924368i −0.205851 + 0.0668849i −0.410127 0.912028i \(-0.634516\pi\)
0.204277 + 0.978913i \(0.434516\pi\)
\(192\) 0 0
\(193\) 5.81321 + 8.00120i 0.418444 + 0.575939i 0.965253 0.261319i \(-0.0841573\pi\)
−0.546808 + 0.837258i \(0.684157\pi\)
\(194\) −4.33665 13.3468i −0.311353 0.958247i
\(195\) 0 0
\(196\) 3.40260 + 2.47214i 0.243043 + 0.176581i
\(197\) 4.94568 0.352365 0.176183 0.984357i \(-0.443625\pi\)
0.176183 + 0.984357i \(0.443625\pi\)
\(198\) 0 0
\(199\) −7.64868 −0.542200 −0.271100 0.962551i \(-0.587387\pi\)
−0.271100 + 0.962551i \(0.587387\pi\)
\(200\) 10.2656 + 7.45842i 0.725890 + 0.527390i
\(201\) 0 0
\(202\) −2.15650 6.63703i −0.151731 0.466980i
\(203\) −1.84461 2.53888i −0.129466 0.178195i
\(204\) 0 0
\(205\) −3.21309 + 1.04400i −0.224412 + 0.0729158i
\(206\) −1.41978 + 4.36965i −0.0989211 + 0.304448i
\(207\) 0 0
\(208\) 2.59526i 0.179949i
\(209\) 4.26089 + 22.6108i 0.294732 + 1.56402i
\(210\) 0 0
\(211\) 13.8159 19.0160i 0.951128 1.30912i 0.000104069 1.00000i \(-0.499967\pi\)
0.951024 0.309116i \(-0.100033\pi\)
\(212\) −6.22052 2.02117i −0.427227 0.138814i
\(213\) 0 0
\(214\) 5.73286 4.16516i 0.391890 0.284725i
\(215\) −2.90607 + 2.11139i −0.198193 + 0.143995i
\(216\) 0 0
\(217\) −5.23434 1.70074i −0.355330 0.115454i
\(218\) 11.4673 15.7834i 0.776664 1.06899i
\(219\) 0 0
\(220\) −2.07597 0.266970i −0.139962 0.0179991i
\(221\) 3.67601i 0.247275i
\(222\) 0 0
\(223\) −6.45815 + 19.8761i −0.432470 + 1.33100i 0.463188 + 0.886260i \(0.346705\pi\)
−0.895658 + 0.444744i \(0.853295\pi\)
\(224\) −2.98702 + 0.970542i −0.199579 + 0.0648470i
\(225\) 0 0
\(226\) −5.42069 7.46094i −0.360579 0.496294i
\(227\) −3.67034 11.2961i −0.243609 0.749752i −0.995862 0.0908773i \(-0.971033\pi\)
0.752253 0.658874i \(-0.228967\pi\)
\(228\) 0 0
\(229\) −7.92914 5.76086i −0.523972 0.380688i 0.294126 0.955767i \(-0.404972\pi\)
−0.818098 + 0.575078i \(0.804972\pi\)
\(230\) −2.55595 −0.168534
\(231\) 0 0
\(232\) −11.1477 −0.731879
\(233\) 12.6222 + 9.17056i 0.826907 + 0.600783i 0.918683 0.394997i \(-0.129254\pi\)
−0.0917755 + 0.995780i \(0.529254\pi\)
\(234\) 0 0
\(235\) −0.0464058 0.142823i −0.00302718 0.00931671i
\(236\) 3.44040 + 4.73531i 0.223951 + 0.308242i
\(237\) 0 0
\(238\) −2.96030 + 0.961860i −0.191888 + 0.0623481i
\(239\) −9.26252 + 28.5071i −0.599143 + 1.84397i −0.0662251 + 0.997805i \(0.521096\pi\)
−0.532918 + 0.846167i \(0.678904\pi\)
\(240\) 0 0
\(241\) 1.89778i 0.122247i 0.998130 + 0.0611235i \(0.0194684\pi\)
−0.998130 + 0.0611235i \(0.980532\pi\)
\(242\) 11.8020 4.61184i 0.758662 0.296460i
\(243\) 0 0
\(244\) 5.36837 7.38893i 0.343675 0.473028i
\(245\) 5.57191 + 1.81042i 0.355976 + 0.115664i
\(246\) 0 0
\(247\) 6.61848 4.80861i 0.421124 0.305964i
\(248\) −15.8166 + 11.4914i −1.00435 + 0.729705i
\(249\) 0 0
\(250\) 9.36874 + 3.04409i 0.592531 + 0.192525i
\(251\) −1.59530 + 2.19574i −0.100694 + 0.138594i −0.856391 0.516328i \(-0.827299\pi\)
0.755696 + 0.654922i \(0.227299\pi\)
\(252\) 0 0
\(253\) −6.88652 + 3.76588i −0.432952 + 0.236759i
\(254\) 7.31955i 0.459269i
\(255\) 0 0
\(256\) −4.36307 + 13.4281i −0.272692 + 0.839259i
\(257\) −8.10484 + 2.63342i −0.505566 + 0.164268i −0.550685 0.834713i \(-0.685633\pi\)
0.0451186 + 0.998982i \(0.485633\pi\)
\(258\) 0 0
\(259\) 4.07005 + 5.60194i 0.252900 + 0.348088i
\(260\) 0.229971 + 0.707777i 0.0142622 + 0.0438945i
\(261\) 0 0
\(262\) −16.1911 11.7636i −1.00029 0.726755i
\(263\) −23.8526 −1.47081 −0.735407 0.677626i \(-0.763009\pi\)
−0.735407 + 0.677626i \(0.763009\pi\)
\(264\) 0 0
\(265\) −9.11097 −0.559682
\(266\) 5.60417 + 4.07167i 0.343614 + 0.249650i
\(267\) 0 0
\(268\) −1.38171 4.25246i −0.0844012 0.259760i
\(269\) −14.1414 19.4640i −0.862219 1.18674i −0.981036 0.193826i \(-0.937910\pi\)
0.118817 0.992916i \(-0.462090\pi\)
\(270\) 0 0
\(271\) 12.2868 3.99222i 0.746370 0.242510i 0.0889514 0.996036i \(-0.471648\pi\)
0.657418 + 0.753526i \(0.271648\pi\)
\(272\) −2.11998 + 6.52463i −0.128543 + 0.395614i
\(273\) 0 0
\(274\) 20.3897i 1.23179i
\(275\) 13.4311 2.53103i 0.809928 0.152627i
\(276\) 0 0
\(277\) 3.92290 5.39940i 0.235704 0.324419i −0.674737 0.738059i \(-0.735743\pi\)
0.910441 + 0.413640i \(0.135743\pi\)
\(278\) 6.76925 + 2.19946i 0.405993 + 0.131915i
\(279\) 0 0
\(280\) −2.02462 + 1.47097i −0.120994 + 0.0879073i
\(281\) 0.496529 0.360749i 0.0296204 0.0215205i −0.572877 0.819642i \(-0.694173\pi\)
0.602497 + 0.798121i \(0.294173\pi\)
\(282\) 0 0
\(283\) 17.9806 + 5.84225i 1.06883 + 0.347286i 0.790034 0.613063i \(-0.210063\pi\)
0.278801 + 0.960349i \(0.410063\pi\)
\(284\) 4.40171 6.05843i 0.261193 0.359502i
\(285\) 0 0
\(286\) −3.27731 3.09141i −0.193791 0.182799i
\(287\) 3.12347i 0.184372i
\(288\) 0 0
\(289\) −2.25049 + 6.92628i −0.132381 + 0.407428i
\(290\) −3.71871 + 1.20828i −0.218370 + 0.0709527i
\(291\) 0 0
\(292\) −1.37188 1.88823i −0.0802833 0.110501i
\(293\) −0.649796 1.99987i −0.0379615 0.116833i 0.930280 0.366850i \(-0.119564\pi\)
−0.968242 + 0.250017i \(0.919564\pi\)
\(294\) 0 0
\(295\) 6.59618 + 4.79241i 0.384044 + 0.279025i
\(296\) 24.5968 1.42966
\(297\) 0 0
\(298\) −8.50312 −0.492572
\(299\) 2.25776 + 1.64036i 0.130569 + 0.0948642i
\(300\) 0 0
\(301\) 1.02625 + 3.15846i 0.0591519 + 0.182051i
\(302\) 9.12979 + 12.5661i 0.525360 + 0.723096i
\(303\) 0 0
\(304\) 14.5204 4.71798i 0.832805 0.270595i
\(305\) 3.93143 12.0997i 0.225113 0.692827i
\(306\) 0 0
\(307\) 17.6110i 1.00511i −0.864545 0.502556i \(-0.832393\pi\)
0.864545 0.502556i \(-0.167607\pi\)
\(308\) −0.827835 + 1.74908i −0.0471703 + 0.0996633i
\(309\) 0 0
\(310\) −4.03065 + 5.54772i −0.228926 + 0.315089i
\(311\) −10.4661 3.40065i −0.593480 0.192833i −0.00314963 0.999995i \(-0.501003\pi\)
−0.590330 + 0.807162i \(0.701003\pi\)
\(312\) 0 0
\(313\) 3.15636 2.29323i 0.178408 0.129621i −0.494997 0.868895i \(-0.664831\pi\)
0.673405 + 0.739274i \(0.264831\pi\)
\(314\) 2.73263 1.98537i 0.154211 0.112041i
\(315\) 0 0
\(316\) −4.83167 1.56991i −0.271803 0.0883141i
\(317\) −12.6974 + 17.4765i −0.713156 + 0.981576i 0.286567 + 0.958060i \(0.407486\pi\)
−0.999723 + 0.0235153i \(0.992514\pi\)
\(318\) 0 0
\(319\) −8.23910 + 8.73456i −0.461301 + 0.489041i
\(320\) 8.04009i 0.449455i
\(321\) 0 0
\(322\) −0.730222 + 2.24739i −0.0406937 + 0.125242i
\(323\) −20.5672 + 6.68269i −1.14439 + 0.371835i
\(324\) 0 0
\(325\) −2.85638 3.93148i −0.158444 0.218079i
\(326\) −7.83776 24.1222i −0.434094 1.33600i
\(327\) 0 0
\(328\) 8.97621 + 6.52160i 0.495629 + 0.360095i
\(329\) −0.138839 −0.00765443
\(330\) 0 0
\(331\) −6.85205 −0.376623 −0.188311 0.982109i \(-0.560301\pi\)
−0.188311 + 0.982109i \(0.560301\pi\)
\(332\) −7.85719 5.70858i −0.431219 0.313299i
\(333\) 0 0
\(334\) 0.229499 + 0.706326i 0.0125576 + 0.0386485i
\(335\) −3.66098 5.03890i −0.200020 0.275305i
\(336\) 0 0
\(337\) 0.702984 0.228413i 0.0382940 0.0124425i −0.289807 0.957085i \(-0.593591\pi\)
0.328101 + 0.944643i \(0.393591\pi\)
\(338\) 4.13250 12.7185i 0.224778 0.691796i
\(339\) 0 0
\(340\) 1.96724i 0.106689i
\(341\) −2.68594 + 20.8860i −0.145452 + 1.13104i
\(342\) 0 0
\(343\) 6.75032 9.29102i 0.364483 0.501668i
\(344\) 11.2195 + 3.64544i 0.604916 + 0.196549i
\(345\) 0 0
\(346\) 12.5751 9.13631i 0.676039 0.491171i
\(347\) 9.63095 6.99730i 0.517017 0.375635i −0.298462 0.954421i \(-0.596474\pi\)
0.815479 + 0.578787i \(0.196474\pi\)
\(348\) 0 0
\(349\) 9.68842 + 3.14796i 0.518609 + 0.168506i 0.556614 0.830771i \(-0.312100\pi\)
−0.0380047 + 0.999278i \(0.512100\pi\)
\(350\) 2.41863 3.32896i 0.129281 0.177940i
\(351\) 0 0
\(352\) 5.76564 + 10.5434i 0.307310 + 0.561965i
\(353\) 31.4901i 1.67605i −0.545632 0.838025i \(-0.683710\pi\)
0.545632 0.838025i \(-0.316290\pi\)
\(354\) 0 0
\(355\) 3.22351 9.92094i 0.171086 0.526549i
\(356\) −5.94393 + 1.93130i −0.315028 + 0.102359i
\(357\) 0 0
\(358\) 0.757069 + 1.04202i 0.0400123 + 0.0550722i
\(359\) −8.57599 26.3942i −0.452624 1.39303i −0.873903 0.486101i \(-0.838419\pi\)
0.421279 0.906931i \(-0.361581\pi\)
\(360\) 0 0
\(361\) 23.5646 + 17.1207i 1.24024 + 0.901090i
\(362\) 26.7537 1.40615
\(363\) 0 0
\(364\) 0.688035 0.0360629
\(365\) −2.63027 1.91100i −0.137675 0.100026i
\(366\) 0 0
\(367\) −5.21807 16.0596i −0.272381 0.838302i −0.989901 0.141764i \(-0.954723\pi\)
0.717520 0.696538i \(-0.245277\pi\)
\(368\) 3.06133 + 4.21357i 0.159583 + 0.219647i
\(369\) 0 0
\(370\) 8.20517 2.66602i 0.426567 0.138600i
\(371\) −2.60296 + 8.01109i −0.135139 + 0.415915i
\(372\) 0 0
\(373\) 6.00920i 0.311145i −0.987824 0.155572i \(-0.950278\pi\)
0.987824 0.155572i \(-0.0497222\pi\)
\(374\) 5.71406 + 10.4491i 0.295467 + 0.540309i
\(375\) 0 0
\(376\) −0.289887 + 0.398995i −0.0149498 + 0.0205766i
\(377\) 4.06031 + 1.31928i 0.209117 + 0.0679462i
\(378\) 0 0
\(379\) −6.88315 + 5.00090i −0.353563 + 0.256879i −0.750362 0.661027i \(-0.770121\pi\)
0.396799 + 0.917906i \(0.370121\pi\)
\(380\) −3.54193 + 2.57336i −0.181697 + 0.132011i
\(381\) 0 0
\(382\) 3.27710 + 1.06480i 0.167671 + 0.0544797i
\(383\) 5.95093 8.19075i 0.304078 0.418528i −0.629445 0.777045i \(-0.716718\pi\)
0.933523 + 0.358517i \(0.116718\pi\)
\(384\) 0 0
\(385\) −0.343817 + 2.67353i −0.0175226 + 0.136256i
\(386\) 11.3925i 0.579863i
\(387\) 0 0
\(388\) 2.53398 7.79880i 0.128644 0.395924i
\(389\) −8.87507 + 2.88369i −0.449984 + 0.146209i −0.525237 0.850956i \(-0.676023\pi\)
0.0752534 + 0.997164i \(0.476023\pi\)
\(390\) 0 0
\(391\) −4.33617 5.96822i −0.219289 0.301826i
\(392\) −5.94565 18.2988i −0.300301 0.924230i
\(393\) 0 0
\(394\) −4.60898 3.34862i −0.232197 0.168701i
\(395\) −7.07678 −0.356071
\(396\) 0 0
\(397\) 10.3328 0.518587 0.259294 0.965799i \(-0.416510\pi\)
0.259294 + 0.965799i \(0.416510\pi\)
\(398\) 7.12796 + 5.17877i 0.357292 + 0.259588i
\(399\) 0 0
\(400\) −2.80255 8.62536i −0.140127 0.431268i
\(401\) −8.71867 12.0002i −0.435390 0.599262i 0.533790 0.845617i \(-0.320767\pi\)
−0.969180 + 0.246355i \(0.920767\pi\)
\(402\) 0 0
\(403\) 7.12083 2.31370i 0.354714 0.115253i
\(404\) 1.26008 3.87814i 0.0626915 0.192944i
\(405\) 0 0
\(406\) 3.61498i 0.179409i
\(407\) 18.1792 19.2724i 0.901111 0.955299i
\(408\) 0 0
\(409\) 5.13485 7.06751i 0.253902 0.349466i −0.662971 0.748645i \(-0.730705\pi\)
0.916873 + 0.399179i \(0.130705\pi\)
\(410\) 3.70121 + 1.20260i 0.182790 + 0.0593920i
\(411\) 0 0
\(412\) −2.17194 + 1.57800i −0.107004 + 0.0777427i
\(413\) 6.09836 4.43072i 0.300081 0.218021i
\(414\) 0 0
\(415\) −12.8665 4.18058i −0.631591 0.205216i
\(416\) 2.51142 3.45667i 0.123132 0.169477i
\(417\) 0 0
\(418\) 11.3385 23.9564i 0.554584 1.17175i
\(419\) 35.1723i 1.71828i −0.511743 0.859139i \(-0.671000\pi\)
0.511743 0.859139i \(-0.329000\pi\)
\(420\) 0 0
\(421\) −0.493004 + 1.51731i −0.0240276 + 0.0739492i −0.962351 0.271809i \(-0.912378\pi\)
0.938324 + 0.345758i \(0.112378\pi\)
\(422\) −25.7507 + 8.36692i −1.25353 + 0.407295i
\(423\) 0 0
\(424\) 17.5874 + 24.2070i 0.854121 + 1.17560i
\(425\) 3.96962 + 12.2172i 0.192555 + 0.592622i
\(426\) 0 0
\(427\) −9.51583 6.91366i −0.460503 0.334575i
\(428\) 4.14060 0.200143
\(429\) 0 0
\(430\) 4.13781 0.199543
\(431\) 23.8660 + 17.3397i 1.14959 + 0.835223i 0.988426 0.151706i \(-0.0484766\pi\)
0.161160 + 0.986928i \(0.448477\pi\)
\(432\) 0 0
\(433\) 3.54190 + 10.9008i 0.170213 + 0.523861i 0.999383 0.0351356i \(-0.0111863\pi\)
−0.829170 + 0.558997i \(0.811186\pi\)
\(434\) 3.72645 + 5.12903i 0.178876 + 0.246201i
\(435\) 0 0
\(436\) 10.8417 3.52269i 0.519225 0.168706i
\(437\) −5.07334 + 15.6141i −0.242691 + 0.746926i
\(438\) 0 0
\(439\) 3.03783i 0.144988i 0.997369 + 0.0724938i \(0.0230957\pi\)
−0.997369 + 0.0724938i \(0.976904\pi\)
\(440\) 6.96532 + 6.57023i 0.332059 + 0.313223i
\(441\) 0 0
\(442\) 2.48895 3.42575i 0.118387 0.162946i
\(443\) −15.7419 5.11484i −0.747918 0.243013i −0.0898330 0.995957i \(-0.528633\pi\)
−0.658085 + 0.752943i \(0.728633\pi\)
\(444\) 0 0
\(445\) −7.04319 + 5.11717i −0.333879 + 0.242577i
\(446\) 19.4762 14.1503i 0.922225 0.670036i
\(447\) 0 0
\(448\) 7.06948 + 2.29701i 0.334002 + 0.108524i
\(449\) 0.152765 0.210263i 0.00720943 0.00992293i −0.805397 0.592736i \(-0.798048\pi\)
0.812606 + 0.582813i \(0.198048\pi\)
\(450\) 0 0
\(451\) 11.7441 2.21312i 0.553009 0.104212i
\(452\) 5.38872i 0.253464i
\(453\) 0 0
\(454\) −4.22793 + 13.0122i −0.198427 + 0.610694i
\(455\) 0.911510 0.296168i 0.0427323 0.0138845i
\(456\) 0 0
\(457\) −3.19749 4.40097i −0.149572 0.205869i 0.727656 0.685943i \(-0.240610\pi\)
−0.877228 + 0.480074i \(0.840610\pi\)
\(458\) 3.48877 + 10.7373i 0.163019 + 0.501722i
\(459\) 0 0
\(460\) −1.20826 0.877849i −0.0563352 0.0409299i
\(461\) 29.3632 1.36758 0.683789 0.729679i \(-0.260331\pi\)
0.683789 + 0.729679i \(0.260331\pi\)
\(462\) 0 0
\(463\) 20.3827 0.947264 0.473632 0.880723i \(-0.342943\pi\)
0.473632 + 0.880723i \(0.342943\pi\)
\(464\) 6.44590 + 4.68322i 0.299244 + 0.217413i
\(465\) 0 0
\(466\) −5.55368 17.0925i −0.257269 0.791793i
\(467\) −0.293731 0.404285i −0.0135922 0.0187081i 0.802167 0.597100i \(-0.203680\pi\)
−0.815759 + 0.578392i \(0.803680\pi\)
\(468\) 0 0
\(469\) −5.47653 + 1.77943i −0.252882 + 0.0821665i
\(470\) −0.0534557 + 0.164520i −0.00246573 + 0.00758873i
\(471\) 0 0
\(472\) 26.7765i 1.23249i
\(473\) 11.1486 6.09657i 0.512611 0.280320i
\(474\) 0 0
\(475\) 16.8039 23.1285i 0.771014 1.06121i
\(476\) −1.72976 0.562032i −0.0792833 0.0257607i
\(477\) 0 0
\(478\) 27.9335 20.2949i 1.27765 0.928267i
\(479\) 8.69444 6.31688i 0.397259 0.288625i −0.371165 0.928567i \(-0.621041\pi\)
0.768424 + 0.639942i \(0.221041\pi\)
\(480\) 0 0
\(481\) −8.95891 2.91093i −0.408491 0.132727i
\(482\) 1.28495 1.76858i 0.0585279 0.0805568i
\(483\) 0 0
\(484\) 7.16304 + 1.87332i 0.325593 + 0.0851509i
\(485\) 11.4226i 0.518675i
\(486\) 0 0
\(487\) 9.43244 29.0301i 0.427425 1.31548i −0.473228 0.880940i \(-0.656911\pi\)
0.900653 0.434539i \(-0.143089\pi\)
\(488\) −39.7369 + 12.9113i −1.79880 + 0.584467i
\(489\) 0 0
\(490\) −3.96678 5.45980i −0.179201 0.246649i
\(491\) 7.74766 + 23.8448i 0.349647 + 1.07610i 0.959049 + 0.283241i \(0.0914097\pi\)
−0.609402 + 0.792862i \(0.708590\pi\)
\(492\) 0 0
\(493\) −9.13017 6.63346i −0.411202 0.298756i
\(494\) −9.42371 −0.423993
\(495\) 0 0
\(496\) 13.9732 0.627417
\(497\) −7.80234 5.66873i −0.349983 0.254277i
\(498\) 0 0
\(499\) 1.53591 + 4.72705i 0.0687568 + 0.211612i 0.979531 0.201293i \(-0.0645143\pi\)
−0.910774 + 0.412905i \(0.864514\pi\)
\(500\) 3.38332 + 4.65674i 0.151307 + 0.208256i
\(501\) 0 0
\(502\) 2.97339 0.966111i 0.132709 0.0431197i
\(503\) −11.3085 + 34.8039i −0.504219 + 1.55183i 0.297860 + 0.954610i \(0.403727\pi\)
−0.802079 + 0.597218i \(0.796273\pi\)
\(504\) 0 0
\(505\) 5.68017i 0.252764i
\(506\) 8.96749 + 1.15322i 0.398654 + 0.0512670i
\(507\) 0 0
\(508\) −2.51392 + 3.46012i −0.111537 + 0.153518i
\(509\) −13.2688 4.31130i −0.588131 0.191095i −0.000190870 1.00000i \(-0.500061\pi\)
−0.587940 + 0.808905i \(0.700061\pi\)
\(510\) 0 0
\(511\) −2.43176 + 1.76678i −0.107575 + 0.0781576i
\(512\) 17.4158 12.6533i 0.769677 0.559203i
\(513\) 0 0
\(514\) 9.33611 + 3.03349i 0.411798 + 0.133801i
\(515\) −2.19813 + 3.02546i −0.0968610 + 0.133318i
\(516\) 0 0
\(517\) 0.0983737 + 0.522028i 0.00432647 + 0.0229588i
\(518\) 7.97631i 0.350459i
\(519\) 0 0
\(520\) 1.05205 3.23787i 0.0461354 0.141990i
\(521\) 6.74242 2.19075i 0.295391 0.0959783i −0.157573 0.987507i \(-0.550367\pi\)
0.452963 + 0.891529i \(0.350367\pi\)
\(522\) 0 0
\(523\) 7.47929 + 10.2944i 0.327047 + 0.450141i 0.940602 0.339510i \(-0.110261\pi\)
−0.613556 + 0.789651i \(0.710261\pi\)
\(524\) −3.61370 11.1218i −0.157865 0.485859i
\(525\) 0 0
\(526\) 22.2287 + 16.1501i 0.969218 + 0.704178i
\(527\) −19.7921 −0.862158
\(528\) 0 0
\(529\) 17.3995 0.756498
\(530\) 8.49070 + 6.16886i 0.368813 + 0.267958i
\(531\) 0 0
\(532\) 1.25079 + 3.84955i 0.0542288 + 0.166899i
\(533\) −2.49761 3.43766i −0.108183 0.148902i
\(534\) 0 0
\(535\) 5.48547 1.78234i 0.237157 0.0770571i
\(536\) −6.32091 + 19.4538i −0.273022 + 0.840275i
\(537\) 0 0
\(538\) 27.7138i 1.19483i
\(539\) −18.7321 8.86584i −0.806849 0.381879i
\(540\) 0 0
\(541\) 2.30481 3.17230i 0.0990915 0.136388i −0.756592 0.653887i \(-0.773137\pi\)
0.855684 + 0.517499i \(0.173137\pi\)
\(542\) −14.1534 4.59871i −0.607940 0.197532i
\(543\) 0 0
\(544\) −9.13747 + 6.63876i −0.391766 + 0.284634i
\(545\) 12.8468 9.33374i 0.550296 0.399813i
\(546\) 0 0
\(547\) −10.2734 3.33803i −0.439259 0.142724i 0.0810349 0.996711i \(-0.474177\pi\)
−0.520294 + 0.853987i \(0.674177\pi\)
\(548\) −7.00292 + 9.63869i −0.299150 + 0.411745i
\(549\) 0 0
\(550\) −14.2305 6.73523i −0.606789 0.287191i
\(551\) 25.1157i 1.06997i
\(552\) 0 0
\(553\) −2.02180 + 6.22247i −0.0859758 + 0.264606i
\(554\) −7.31166 + 2.37570i −0.310643 + 0.100934i
\(555\) 0 0
\(556\) 2.44457 + 3.36466i 0.103673 + 0.142693i
\(557\) −7.06108 21.7318i −0.299188 0.920805i −0.981783 0.190008i \(-0.939149\pi\)
0.682595 0.730797i \(-0.260851\pi\)
\(558\) 0 0
\(559\) −3.65507 2.65556i −0.154593 0.112318i
\(560\) 1.78866 0.0755847
\(561\) 0 0
\(562\) −0.706982 −0.0298222
\(563\) 8.77304 + 6.37399i 0.369740 + 0.268632i 0.757103 0.653296i \(-0.226614\pi\)
−0.387363 + 0.921927i \(0.626614\pi\)
\(564\) 0 0
\(565\) −2.31959 7.13898i −0.0975861 0.300339i
\(566\) −12.8008 17.6188i −0.538058 0.740574i
\(567\) 0 0
\(568\) −32.5816 + 10.5864i −1.36709 + 0.444195i
\(569\) 5.19794 15.9976i 0.217909 0.670655i −0.781025 0.624499i \(-0.785303\pi\)
0.998934 0.0461553i \(-0.0146969\pi\)
\(570\) 0 0
\(571\) 16.3097i 0.682541i −0.939965 0.341271i \(-0.889143\pi\)
0.939965 0.341271i \(-0.110857\pi\)
\(572\) −0.487505 2.58698i −0.0203836 0.108167i
\(573\) 0 0
\(574\) 2.11484 2.91082i 0.0882716 0.121495i
\(575\) 9.27503 + 3.01364i 0.386795 + 0.125677i
\(576\) 0 0
\(577\) 6.51886 4.73623i 0.271384 0.197172i −0.443767 0.896142i \(-0.646358\pi\)
0.715150 + 0.698971i \(0.246358\pi\)
\(578\) 6.78692 4.93099i 0.282299 0.205102i
\(579\) 0 0
\(580\) −2.17291 0.706021i −0.0902251 0.0293159i
\(581\) −7.35179 + 10.1189i −0.305004 + 0.419801i
\(582\) 0 0
\(583\) 31.9657 + 4.11080i 1.32388 + 0.170252i
\(584\) 10.6773i 0.441830i
\(585\) 0 0
\(586\) −0.748511 + 2.30368i −0.0309207 + 0.0951642i
\(587\) −14.9678 + 4.86334i −0.617789 + 0.200732i −0.601158 0.799130i \(-0.705294\pi\)
−0.0166304 + 0.999862i \(0.505294\pi\)
\(588\) 0 0
\(589\) 25.8902 + 35.6348i 1.06679 + 1.46831i
\(590\) −2.90228 8.93228i −0.119485 0.367736i
\(591\) 0 0
\(592\) −14.2226 10.3333i −0.584546 0.424697i
\(593\) −22.2880 −0.915258 −0.457629 0.889143i \(-0.651301\pi\)
−0.457629 + 0.889143i \(0.651301\pi\)
\(594\) 0 0
\(595\) −2.53351 −0.103864
\(596\) −4.01962 2.92043i −0.164650 0.119625i
\(597\) 0 0
\(598\) −0.993397 3.05736i −0.0406230 0.125025i
\(599\) −16.8142 23.1428i −0.687010 0.945588i 0.312981 0.949759i \(-0.398672\pi\)
−0.999991 + 0.00417130i \(0.998672\pi\)
\(600\) 0 0
\(601\) −6.78070 + 2.20318i −0.276591 + 0.0898697i −0.444028 0.896013i \(-0.646451\pi\)
0.167437 + 0.985883i \(0.446451\pi\)
\(602\) 1.18215 3.63829i 0.0481809 0.148286i
\(603\) 0 0
\(604\) 9.07594i 0.369295i
\(605\) 10.2960 0.601583i 0.418591 0.0244578i
\(606\) 0 0
\(607\) −2.68531 + 3.69601i −0.108993 + 0.150017i −0.860029 0.510245i \(-0.829555\pi\)
0.751036 + 0.660262i \(0.229555\pi\)
\(608\) 23.9056 + 7.76739i 0.969499 + 0.315009i
\(609\) 0 0
\(610\) −11.8563 + 8.61407i −0.480046 + 0.348774i
\(611\) 0.152805 0.111019i 0.00618182 0.00449135i
\(612\) 0 0
\(613\) −37.1400 12.0675i −1.50007 0.487402i −0.560032 0.828471i \(-0.689211\pi\)
−0.940038 + 0.341069i \(0.889211\pi\)
\(614\) −11.9240 + 16.4120i −0.481215 + 0.662336i
\(615\) 0 0
\(616\) 7.76703 4.24738i 0.312942 0.171132i
\(617\) 31.1970i 1.25594i 0.778236 + 0.627972i \(0.216115\pi\)
−0.778236 + 0.627972i \(0.783885\pi\)
\(618\) 0 0
\(619\) 9.95813 30.6480i 0.400251 1.23185i −0.524545 0.851383i \(-0.675765\pi\)
0.924796 0.380463i \(-0.124235\pi\)
\(620\) −3.81077 + 1.23819i −0.153044 + 0.0497270i
\(621\) 0 0
\(622\) 7.45109 + 10.2556i 0.298762 + 0.411210i
\(623\) 2.48722 + 7.65488i 0.0996484 + 0.306686i
\(624\) 0 0
\(625\) −10.1827 7.39818i −0.407309 0.295927i
\(626\) −4.49418 −0.179623
\(627\) 0 0
\(628\) 1.97366 0.0787576
\(629\) 20.1453 + 14.6365i 0.803248 + 0.583594i
\(630\) 0 0
\(631\) −0.555911 1.71092i −0.0221305 0.0681105i 0.939381 0.342874i \(-0.111400\pi\)
−0.961512 + 0.274764i \(0.911400\pi\)
\(632\) 13.6607 + 18.8024i 0.543394 + 0.747918i
\(633\) 0 0
\(634\) 23.6659 7.68952i 0.939894 0.305390i
\(635\) −1.84103 + 5.66610i −0.0730590 + 0.224852i
\(636\) 0 0
\(637\) 7.36863i 0.291956i
\(638\) 13.5922 2.56138i 0.538120 0.101406i
\(639\) 0 0
\(640\) 1.45023 1.99606i 0.0573252 0.0789014i
\(641\) 7.32843 + 2.38115i 0.289456 + 0.0940499i 0.450146 0.892955i \(-0.351372\pi\)
−0.160690 + 0.987005i \(0.551372\pi\)
\(642\) 0 0
\(643\) −17.1627 + 12.4695i −0.676832 + 0.491747i −0.872305 0.488962i \(-0.837376\pi\)
0.195473 + 0.980709i \(0.437376\pi\)
\(644\) −1.11707 + 0.811597i −0.0440186 + 0.0319814i
\(645\) 0 0
\(646\) 23.6917 + 7.69791i 0.932138 + 0.302870i
\(647\) 29.4465 40.5296i 1.15766 1.59338i 0.438150 0.898902i \(-0.355634\pi\)
0.719511 0.694482i \(-0.244366\pi\)
\(648\) 0 0
\(649\) −20.9803 19.7902i −0.823548 0.776834i
\(650\) 5.59782i 0.219565i
\(651\) 0 0
\(652\) 4.57975 14.0950i 0.179357 0.552004i
\(653\) −16.7546 + 5.44390i −0.655659 + 0.213036i −0.617908 0.786251i \(-0.712019\pi\)
−0.0377511 + 0.999287i \(0.512019\pi\)
\(654\) 0 0
\(655\) −9.57486 13.1787i −0.374121 0.514933i
\(656\) −2.45053 7.54197i −0.0956772 0.294464i
\(657\) 0 0
\(658\) 0.129387 + 0.0940050i 0.00504402 + 0.00366470i
\(659\) 21.1328 0.823218 0.411609 0.911360i \(-0.364967\pi\)
0.411609 + 0.911360i \(0.364967\pi\)
\(660\) 0 0
\(661\) −11.0329 −0.429131 −0.214566 0.976710i \(-0.568834\pi\)
−0.214566 + 0.976710i \(0.568834\pi\)
\(662\) 6.38557 + 4.63939i 0.248182 + 0.180315i
\(663\) 0 0
\(664\) 13.7295 + 42.2551i 0.532809 + 1.63982i
\(665\) 3.31411 + 4.56147i 0.128515 + 0.176886i
\(666\) 0 0
\(667\) −8.14837 + 2.64757i −0.315506 + 0.102514i
\(668\) −0.134101 + 0.412719i −0.00518851 + 0.0159686i
\(669\) 0 0
\(670\) 7.17463i 0.277180i
\(671\) −19.2527 + 40.6778i −0.743240 + 1.57035i
\(672\) 0 0
\(673\) −18.2818 + 25.1627i −0.704712 + 0.969952i 0.295183 + 0.955441i \(0.404619\pi\)
−0.999895 + 0.0145116i \(0.995381\pi\)
\(674\) −0.809780 0.263113i −0.0311915 0.0101347i
\(675\) 0 0
\(676\) 6.32175 4.59302i 0.243144 0.176655i
\(677\) −17.2782 + 12.5533i −0.664053 + 0.482463i −0.868029 0.496513i \(-0.834614\pi\)
0.203976 + 0.978976i \(0.434614\pi\)
\(678\) 0 0
\(679\) −10.0437 3.26339i −0.385441 0.125237i
\(680\) −5.28981 + 7.28081i −0.202855 + 0.279206i
\(681\) 0 0
\(682\) 16.6446 17.6455i 0.637353 0.675680i
\(683\) 17.2570i 0.660321i −0.943925 0.330161i \(-0.892897\pi\)
0.943925 0.330161i \(-0.107103\pi\)
\(684\) 0 0
\(685\) −5.12846 + 15.7838i −0.195949 + 0.603068i
\(686\) −12.5815 + 4.08799i −0.480365 + 0.156080i
\(687\) 0 0
\(688\) −4.95598 6.82132i −0.188945 0.260060i
\(689\) −3.54108 10.8983i −0.134904 0.415193i
\(690\) 0 0
\(691\) −16.9524 12.3166i −0.644898 0.468546i 0.216631 0.976253i \(-0.430493\pi\)
−0.861529 + 0.507708i \(0.830493\pi\)
\(692\) 9.08243 0.345262
\(693\) 0 0
\(694\) −13.7130 −0.520539
\(695\) 4.68690 + 3.40523i 0.177784 + 0.129168i
\(696\) 0 0
\(697\) 3.47101 + 10.6827i 0.131474 + 0.404635i
\(698\) −6.89742 9.49349i −0.261071 0.359334i
\(699\) 0 0
\(700\) 2.28669 0.742990i 0.0864286 0.0280824i
\(701\) −15.1348 + 46.5802i −0.571634 + 1.75931i 0.0757293 + 0.997128i \(0.475872\pi\)
−0.647364 + 0.762181i \(0.724128\pi\)
\(702\) 0 0
\(703\) 55.4168i 2.09008i
\(704\) 3.62762 28.2085i 0.136721 1.06315i
\(705\) 0 0
\(706\) −21.3213 + 29.3463i −0.802439 + 1.10446i
\(707\) −4.99445 1.62280i −0.187836 0.0610315i
\(708\) 0 0
\(709\) −33.6162 + 24.4236i −1.26248 + 0.917248i −0.998877 0.0473823i \(-0.984912\pi\)
−0.263607 + 0.964630i \(0.584912\pi\)
\(710\) −9.72133 + 7.06296i −0.364835 + 0.265068i
\(711\) 0 0
\(712\) 27.1917 + 8.83513i 1.01905 + 0.331111i
\(713\) −8.83189 + 12.1561i −0.330757 + 0.455248i
\(714\) 0 0
\(715\) −1.75942 3.21739i −0.0657988 0.120324i
\(716\) 0.752603i 0.0281261i
\(717\) 0 0
\(718\) −9.87884 + 30.4039i −0.368675 + 1.13466i
\(719\) 27.4285 8.91207i 1.02291 0.332364i 0.250927 0.968006i \(-0.419264\pi\)
0.771984 + 0.635642i \(0.219264\pi\)
\(720\) 0 0
\(721\) 2.03223 + 2.79713i 0.0756843 + 0.104170i
\(722\) −10.3683 31.9103i −0.385868 1.18758i
\(723\) 0 0
\(724\) 12.6471 + 9.18867i 0.470027 + 0.341494i
\(725\) 14.9191 0.554082
\(726\) 0 0
\(727\) 18.3843 0.681838 0.340919 0.940093i \(-0.389262\pi\)
0.340919 + 0.940093i \(0.389262\pi\)
\(728\) −2.54643 1.85009i −0.0943770 0.0685689i
\(729\) 0 0
\(730\) 1.15730 + 3.56181i 0.0428336 + 0.131828i
\(731\) 7.01980 + 9.66193i 0.259637 + 0.357359i
\(732\) 0 0
\(733\) −30.0104 + 9.75096i −1.10846 + 0.360160i −0.805352 0.592797i \(-0.798024\pi\)
−0.303106 + 0.952957i \(0.598024\pi\)
\(734\) −6.01078 + 18.4993i −0.221862 + 0.682821i
\(735\) 0 0
\(736\) 8.57455i 0.316062i
\(737\) 10.5710 + 19.3307i 0.389386 + 0.712055i
\(738\) 0 0
\(739\) −26.9990 + 37.1609i −0.993173 + 1.36698i −0.0637507 + 0.997966i \(0.520306\pi\)
−0.929422 + 0.369019i \(0.879694\pi\)
\(740\) 4.79443 + 1.55781i 0.176247 + 0.0572661i
\(741\) 0 0
\(742\) 7.84990 5.70329i 0.288179 0.209374i
\(743\) −17.5692 + 12.7648i −0.644551 + 0.468294i −0.861411 0.507909i \(-0.830419\pi\)
0.216860 + 0.976203i \(0.430419\pi\)
\(744\) 0 0
\(745\) −6.58231 2.13872i −0.241157 0.0783567i
\(746\) −4.06871 + 5.60010i −0.148966 + 0.205034i
\(747\) 0 0
\(748\) −0.887605 + 6.90204i −0.0324541 + 0.252364i
\(749\) 5.33246i 0.194844i
\(750\) 0 0
\(751\) 5.25583 16.1758i 0.191788 0.590262i −0.808211 0.588893i \(-0.799564\pi\)
0.999999 0.00136956i \(-0.000435943\pi\)
\(752\) 0.335242 0.108927i 0.0122250 0.00397215i
\(753\) 0 0
\(754\) −2.89064 3.97862i −0.105271 0.144893i
\(755\) 3.90677 + 12.0238i 0.142182 + 0.437591i
\(756\) 0 0
\(757\) −18.8951 13.7281i −0.686756 0.498957i 0.188836 0.982009i \(-0.439528\pi\)
−0.875592 + 0.483051i \(0.839528\pi\)
\(758\) 9.80055 0.355972
\(759\) 0 0
\(760\) 20.0284 0.726506
\(761\) 16.4210 + 11.9305i 0.595259 + 0.432481i 0.844193 0.536039i \(-0.180080\pi\)
−0.248934 + 0.968521i \(0.580080\pi\)
\(762\) 0 0
\(763\) −4.53670 13.9625i −0.164239 0.505477i
\(764\) 1.18346 + 1.62889i 0.0428159 + 0.0589310i
\(765\) 0 0
\(766\) −11.0916 + 3.60388i −0.400755 + 0.130213i
\(767\) −3.16888 + 9.75282i −0.114422 + 0.352154i
\(768\) 0 0
\(769\) 23.5119i 0.847859i 0.905695 + 0.423930i \(0.139350\pi\)
−0.905695 + 0.423930i \(0.860650\pi\)
\(770\) 2.13061 2.25873i 0.0767817 0.0813989i
\(771\) 0 0
\(772\) 3.91280 5.38550i 0.140825 0.193828i
\(773\) −12.8627 4.17933i −0.462638 0.150320i 0.0684183 0.997657i \(-0.478205\pi\)
−0.531056 + 0.847337i \(0.678205\pi\)
\(774\) 0 0
\(775\) 21.1676 15.3792i 0.760362 0.552436i
\(776\) −30.3489 + 22.0498i −1.08946 + 0.791540i
\(777\) 0 0
\(778\) 10.2233 + 3.32177i 0.366525 + 0.119091i
\(779\) 14.6932 20.2235i 0.526439 0.724581i
\(780\) 0 0
\(781\) −15.7859 + 33.3530i −0.564863 + 1.19347i
\(782\) 8.49784i 0.303882i
\(783\) 0 0
\(784\) −4.24954 + 13.0787i −0.151769 + 0.467098i
\(785\) 2.61471 0.849570i 0.0933229 0.0303225i
\(786\) 0 0
\(787\) −27.2391 37.4914i −0.970968 1.33642i −0.941557 0.336855i \(-0.890637\pi\)
−0.0294111 0.999567i \(-0.509363\pi\)
\(788\) −1.02868 3.16595i −0.0366451 0.112782i
\(789\) 0 0
\(790\) 6.59500 + 4.79155i 0.234639 + 0.170476i
\(791\) −6.93985 −0.246753
\(792\) 0 0
\(793\) 16.0014 0.568226
\(794\) −9.62933 6.99612i −0.341732 0.248283i
\(795\) 0 0
\(796\) 1.59089 + 4.89625i 0.0563875 + 0.173543i
\(797\) −28.6496 39.4328i −1.01482 1.39678i −0.915772 0.401699i \(-0.868420\pi\)
−0.0990490 0.995083i \(-0.531580\pi\)
\(798\) 0 0
\(799\) −0.474847 + 0.154287i −0.0167989 + 0.00545829i
\(800\) 4.61394 14.2003i 0.163127 0.502055i
\(801\) 0 0
\(802\) 17.0865i 0.603345i
\(803\) 8.36602 + 7.89147i 0.295231 + 0.278484i
\(804\) 0 0
\(805\) −1.13054 + 1.55605i −0.0398462 + 0.0548436i
\(806\) −8.20261 2.66519i −0.288924 0.0938773i
\(807\) 0 0
\(808\) −15.0917 + 10.9648i −0.530924 + 0.385739i
\(809\) −4.11235 + 2.98780i −0.144583 + 0.105045i −0.657725 0.753258i \(-0.728481\pi\)
0.513143 + 0.858303i \(0.328481\pi\)
\(810\) 0 0
\(811\) 5.95516 + 1.93495i 0.209114 + 0.0679453i 0.411701 0.911319i \(-0.364935\pi\)
−0.202587 + 0.979264i \(0.564935\pi\)
\(812\) −1.24158 + 1.70889i −0.0435709 + 0.0599702i
\(813\) 0 0
\(814\) −29.9906 + 5.65158i −1.05117 + 0.198088i
\(815\) 20.6445i 0.723144i
\(816\) 0 0
\(817\) 8.21321 25.2777i 0.287344 0.884353i
\(818\) −9.57054 + 3.10966i −0.334626 + 0.108727i
\(819\) 0 0
\(820\) 1.33661 + 1.83969i 0.0466766 + 0.0642448i
\(821\) −10.6233 32.6953i −0.370757 1.14107i −0.946297 0.323299i \(-0.895208\pi\)
0.575540 0.817774i \(-0.304792\pi\)
\(822\) 0 0
\(823\) −8.54662 6.20948i −0.297916 0.216449i 0.428778 0.903410i \(-0.358944\pi\)
−0.726694 + 0.686961i \(0.758944\pi\)
\(824\) 12.2815 0.427848
\(825\) 0 0
\(826\) −8.68314 −0.302125
\(827\) −22.4299 16.2963i −0.779965 0.566678i 0.125004 0.992156i \(-0.460106\pi\)
−0.904969 + 0.425479i \(0.860106\pi\)
\(828\) 0 0
\(829\) 7.49749 + 23.0749i 0.260399 + 0.801425i 0.992718 + 0.120463i \(0.0384379\pi\)
−0.732319 + 0.680962i \(0.761562\pi\)
\(830\) 9.15996 + 12.6076i 0.317947 + 0.437616i
\(831\) 0 0
\(832\) −9.61736 + 3.12487i −0.333422 + 0.108335i
\(833\) 6.01918 18.5251i 0.208552 0.641858i
\(834\) 0 0
\(835\) 0.604495i 0.0209194i
\(836\) 13.5879 7.43051i 0.469947 0.256990i
\(837\) 0 0
\(838\) −23.8144 + 32.7778i −0.822656 + 1.13229i
\(839\) 20.6658 + 6.71473i 0.713463 + 0.231818i 0.643187 0.765709i \(-0.277612\pi\)
0.0702762 + 0.997528i \(0.477612\pi\)
\(840\) 0 0
\(841\) 12.8578 9.34176i 0.443373 0.322130i
\(842\) 1.48678 1.08021i 0.0512379 0.0372265i
\(843\) 0 0
\(844\) −15.0466 4.88894i −0.517926 0.168284i
\(845\) 6.39798 8.80607i 0.220097 0.302938i
\(846\) 0 0
\(847\) 2.41255 9.22492i 0.0828963 0.316972i
\(848\) 21.3858i 0.734393i
\(849\) 0 0
\(850\) 4.57267 14.0732i 0.156841 0.482708i
\(851\) 17.9790 5.84174i 0.616313 0.200252i
\(852\) 0 0
\(853\) −24.1254 33.2058i −0.826039 1.13695i −0.988647 0.150255i \(-0.951991\pi\)
0.162608 0.986691i \(-0.448009\pi\)
\(854\) 4.18690 + 12.8860i 0.143273 + 0.440948i
\(855\) 0 0
\(856\) −15.3244 11.1338i −0.523778 0.380547i
\(857\) 7.49320 0.255963 0.127981 0.991777i \(-0.459150\pi\)
0.127981 + 0.991777i \(0.459150\pi\)
\(858\) 0 0
\(859\) 1.63002 0.0556156 0.0278078 0.999613i \(-0.491147\pi\)
0.0278078 + 0.999613i \(0.491147\pi\)
\(860\) 1.95604 + 1.42115i 0.0667004 + 0.0484607i
\(861\) 0 0
\(862\) −10.5009 32.3184i −0.357662 1.10077i
\(863\) −11.2828 15.5294i −0.384070 0.528626i 0.572587 0.819844i \(-0.305940\pi\)
−0.956657 + 0.291217i \(0.905940\pi\)
\(864\) 0 0
\(865\) 12.0324 3.90957i 0.409114 0.132929i
\(866\) 4.07998 12.5569i 0.138643 0.426700i
\(867\) 0 0
\(868\) 3.70448i 0.125738i
\(869\) 24.8288 + 3.19299i 0.842258 + 0.108315i
\(870\) 0 0
\(871\) 4.60454 6.33760i 0.156019 0.214741i
\(872\) −49.5978 16.1153i −1.67959 0.545733i
\(873\) 0 0
\(874\) 15.3000 11.1161i 0.517529 0.376007i
\(875\) 5.99718 4.35721i 0.202742 0.147300i
\(876\) 0 0
\(877\) −53.4401 17.3637i −1.80454 0.586332i −0.804573 0.593854i \(-0.797606\pi\)
−0.999972 + 0.00752149i \(0.997606\pi\)
\(878\) 2.05685 2.83101i 0.0694154 0.0955421i
\(879\) 0 0
\(880\) −1.26735 6.72529i −0.0427223 0.226709i
\(881\) 16.2929i 0.548922i 0.961598 + 0.274461i \(0.0884994\pi\)
−0.961598 + 0.274461i \(0.911501\pi\)
\(882\) 0 0
\(883\) −9.20073 + 28.3169i −0.309629 + 0.952941i 0.668280 + 0.743910i \(0.267031\pi\)
−0.977909 + 0.209031i \(0.932969\pi\)
\(884\) 2.35317 0.764592i 0.0791457 0.0257160i
\(885\) 0 0
\(886\) 11.2070 + 15.4251i 0.376507 + 0.518217i
\(887\) −0.349006 1.07413i −0.0117185 0.0360657i 0.945026 0.326994i \(-0.106036\pi\)
−0.956745 + 0.290929i \(0.906036\pi\)
\(888\) 0 0
\(889\) 4.45611 + 3.23756i 0.149453 + 0.108584i
\(890\) 10.0284 0.336154
\(891\) 0 0
\(892\) 14.0668 0.470992
\(893\) 0.898937 + 0.653116i 0.0300818 + 0.0218557i
\(894\) 0 0
\(895\) 0.323961 + 0.997050i 0.0108288 + 0.0333277i
\(896\) −1.34078 1.84542i −0.0447922 0.0616511i
\(897\) 0 0
\(898\) −0.284730 + 0.0925143i −0.00950156 + 0.00308724i
\(899\) −7.10316 + 21.8613i −0.236904 + 0.729114i
\(900\) 0 0
\(901\) 30.2916i 1.00916i
\(902\) −12.4430 5.88925i −0.414308 0.196091i
\(903\) 0 0
\(904\) −14.4900 + 19.9437i −0.481929 + 0.663319i
\(905\) 20.7102 + 6.72916i 0.688431 + 0.223685i
\(906\) 0 0
\(907\) −21.5733 + 15.6739i −0.716330 + 0.520444i −0.885209 0.465193i \(-0.845985\pi\)
0.168880 + 0.985637i \(0.445985\pi\)
\(908\) −6.46774 + 4.69909i −0.214639 + 0.155945i
\(909\) 0 0
\(910\) −1.04998 0.341161i −0.0348066 0.0113094i
\(911\) 2.30320 3.17008i 0.0763084 0.105029i −0.769157 0.639060i \(-0.779323\pi\)
0.845465 + 0.534031i \(0.179323\pi\)
\(912\) 0 0
\(913\) 43.2556 + 20.4727i 1.43155 + 0.677549i
\(914\) 6.26632i 0.207271i
\(915\) 0 0
\(916\) −2.03855 + 6.27402i −0.0673556 + 0.207299i
\(917\) −14.3232 + 4.65390i −0.472994 + 0.153685i
\(918\) 0 0
\(919\) −7.16542 9.86236i −0.236365 0.325329i 0.674313 0.738446i \(-0.264440\pi\)
−0.910678 + 0.413117i \(0.864440\pi\)
\(920\) 2.11129 + 6.49787i 0.0696070 + 0.214228i
\(921\) 0 0
\(922\) −27.3641 19.8812i −0.901190 0.654753i
\(923\) 13.1201 0.431852
\(924\) 0 0
\(925\) −32.9184 −1.08235
\(926\) −18.9950 13.8007i −0.624216 0.453519i
\(927\) 0 0
\(928\) 4.05348 + 12.4753i 0.133062 + 0.409522i
\(929\) 2.77455 + 3.81885i 0.0910302 + 0.125292i 0.852103 0.523374i \(-0.175327\pi\)
−0.761073 + 0.648667i \(0.775327\pi\)
\(930\) 0 0
\(931\) −41.2274 + 13.3956i −1.35117 + 0.439023i
\(932\) 3.24512 9.98744i 0.106297 0.327149i
\(933\) 0 0
\(934\) 0.575641i 0.0188356i
\(935\) 1.79511 + 9.52591i 0.0587064 + 0.311530i
\(936\) 0 0
\(937\) −17.0091 + 23.4110i −0.555662 + 0.764803i −0.990767 0.135577i \(-0.956711\pi\)
0.435105 + 0.900380i \(0.356711\pi\)
\(938\) 6.30850 + 2.04976i 0.205980 + 0.0669270i
\(939\) 0 0
\(940\) −0.0817747 + 0.0594128i −0.00266720 + 0.00193783i
\(941\) 46.0903 33.4866i 1.50250 1.09163i 0.533129 0.846034i \(-0.321016\pi\)
0.969372 0.245597i \(-0.0789841\pi\)
\(942\) 0 0
\(943\) 8.11003 + 2.63511i 0.264099 + 0.0858110i
\(944\) −11.2490 + 15.4830i −0.366125 + 0.503928i
\(945\) 0 0
\(946\) −14.5174 1.86695i −0.472002 0.0606997i
\(947\) 0.938732i 0.0305047i −0.999884 0.0152524i \(-0.995145\pi\)
0.999884 0.0152524i \(-0.00485516\pi\)
\(948\) 0 0
\(949\) 1.26361 3.88900i 0.0410186 0.126242i
\(950\) −31.3197 + 10.1764i −1.01615 + 0.330166i
\(951\) 0 0
\(952\) 4.89059 + 6.73132i 0.158505 + 0.218163i
\(953\) 3.50554 + 10.7889i 0.113556 + 0.349488i 0.991643 0.129012i \(-0.0411806\pi\)
−0.878087 + 0.478500i \(0.841181\pi\)
\(954\) 0 0
\(955\) 2.26900 + 1.64853i 0.0734232 + 0.0533451i
\(956\) 20.1752 0.652512
\(957\) 0 0
\(958\) −12.3796 −0.399965
\(959\) 12.4132 + 9.01870i 0.400843 + 0.291229i
\(960\) 0 0
\(961\) 2.87773 + 8.85675i 0.0928301 + 0.285702i
\(962\) 6.37807 + 8.77866i 0.205637 + 0.283035i
\(963\) 0 0
\(964\) 1.21485 0.394730i 0.0391278 0.0127134i
\(965\) 2.86547 8.81900i 0.0922426 0.283894i
\(966\) 0 0
\(967\) 17.3054i 0.556505i 0.960508 + 0.278253i \(0.0897553\pi\)
−0.960508 + 0.278253i \(0.910245\pi\)
\(968\) −21.4733 26.1942i −0.690177 0.841914i
\(969\) 0 0
\(970\) −7.73403 + 10.6450i −0.248325 + 0.341790i
\(971\) 23.6890 + 7.69701i 0.760215 + 0.247009i 0.663371 0.748291i \(-0.269125\pi\)
0.0968441 + 0.995300i \(0.469125\pi\)
\(972\) 0 0
\(973\) 4.33318 3.14824i 0.138915 0.100928i
\(974\) −28.4460 + 20.6672i −0.911468 + 0.662220i
\(975\) 0 0
\(976\) 28.4012 + 9.22811i 0.909100 + 0.295384i
\(977\) −4.40208 + 6.05894i −0.140835 + 0.193843i −0.873608 0.486631i \(-0.838226\pi\)
0.732773 + 0.680473i \(0.238226\pi\)
\(978\) 0 0
\(979\) 27.0197 14.7757i 0.863554 0.472233i
\(980\) 3.94338i 0.125967i
\(981\) 0 0
\(982\) 8.92466 27.4673i 0.284797 0.876516i
\(983\) 5.06942 1.64715i 0.161689 0.0525361i −0.227054 0.973882i \(-0.572909\pi\)
0.388743 + 0.921346i \(0.372909\pi\)
\(984\) 0 0
\(985\) −2.72559 3.75145i −0.0868445 0.119531i
\(986\) 4.01722 + 12.3637i 0.127934 + 0.393741i
\(987\) 0 0
\(988\) −4.45481 3.23661i −0.141726 0.102970i
\(989\) 9.06669 0.288304
\(990\) 0 0
\(991\) −23.5423 −0.747846 −0.373923 0.927460i \(-0.621988\pi\)
−0.373923 + 0.927460i \(0.621988\pi\)
\(992\) 18.6112 + 13.5218i 0.590905 + 0.429318i
\(993\) 0 0
\(994\) 3.43298 + 10.5656i 0.108887 + 0.335121i
\(995\) 4.21522 + 5.80175i 0.133631 + 0.183928i
\(996\) 0 0
\(997\) −13.5097 + 4.38958i −0.427857 + 0.139019i −0.515026 0.857174i \(-0.672218\pi\)
0.0871692 + 0.996194i \(0.472218\pi\)
\(998\) 1.76924 5.44517i 0.0560044 0.172364i
\(999\) 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 891.2.k.a.161.7 80
3.2 odd 2 inner 891.2.k.a.161.14 80
9.2 odd 6 99.2.p.a.95.8 yes 80
9.4 even 3 99.2.p.a.29.8 80
9.5 odd 6 297.2.t.a.62.3 80
9.7 even 3 297.2.t.a.260.3 80
11.8 odd 10 inner 891.2.k.a.404.14 80
33.8 even 10 inner 891.2.k.a.404.7 80
99.41 even 30 297.2.t.a.8.3 80
99.52 odd 30 297.2.t.a.206.3 80
99.74 even 30 99.2.p.a.41.8 yes 80
99.85 odd 30 99.2.p.a.74.8 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.8 80 9.4 even 3
99.2.p.a.41.8 yes 80 99.74 even 30
99.2.p.a.74.8 yes 80 99.85 odd 30
99.2.p.a.95.8 yes 80 9.2 odd 6
297.2.t.a.8.3 80 99.41 even 30
297.2.t.a.62.3 80 9.5 odd 6
297.2.t.a.206.3 80 99.52 odd 30
297.2.t.a.260.3 80 9.7 even 3
891.2.k.a.161.7 80 1.1 even 1 trivial
891.2.k.a.161.14 80 3.2 odd 2 inner
891.2.k.a.404.7 80 33.8 even 10 inner
891.2.k.a.404.14 80 11.8 odd 10 inner