Properties

Label 891.2.k.a.161.14
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 161.14
Character \(\chi\) \(=\) 891.161
Dual form 891.2.k.a.404.14

$q$-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 0.866314 0.499500i \(-0.166483\pi\)
−0.207347 + 0.978268i \(0.566483\pi\)
\(3\) 0 0
\(4\) −0.207995 0.640143i −0.103998 0.320072i
\(5\) 0.551104 + 0.758530i 0.246461 + 0.339225i 0.914268 0.405110i \(-0.132767\pi\)
−0.667807 + 0.744335i \(0.732767\pi\)
\(6\) 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 −0.238343 0.971181i \(-0.576604\pi\)
0.849996 + 0.526789i \(0.176604\pi\)
\(18\) 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 \(-0.920644\pi\)
0.969084 0.246730i \(-0.0793559\pi\)
\(24\) 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 \(-0.990878\pi\)
0.791844 0.610724i \(-0.209122\pi\)
\(30\) 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 −0.999581 0.0289327i \(-0.990789\pi\)
0.825685 + 0.564132i \(0.190789\pi\)
\(42\) 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 0.297886 0.954601i \(-0.403718\pi\)
−0.320106 + 0.947382i \(0.603718\pi\)
\(48\) 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 \(0.432590\pi\)
−0.994763 + 0.102205i \(0.967410\pi\)
\(54\) 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 0.283614 0.958938i \(-0.408466\pi\)
0.793099 + 0.609093i \(0.208466\pi\)
\(60\) 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 \(-0.970474\pi\)
0.219595 0.975591i \(-0.429526\pi\)
\(72\) 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 −0.999592 0.0285622i \(-0.990907\pi\)
−0.281727 + 0.959495i \(0.590907\pi\)
\(84\) 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 \(0.163778\pi\)
−0.870527 + 0.492120i \(0.836222\pi\)
\(90\) 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 0.316606 0.948557i \(-0.397457\pi\)
−0.804295 + 0.594230i \(0.797457\pi\)
\(102\) 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 −0.816152 0.577838i \(-0.803897\pi\)
0.999925 + 0.0122414i \(0.00389667\pi\)
\(108\) 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 −0.0718692 0.997414i \(-0.522896\pi\)
−0.644409 + 0.764681i \(0.722896\pi\)
\(114\) 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 \(-0.774304\pi\)
−0.758985 + 0.651109i \(0.774304\pi\)
\(132\) 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 \(0.0729147\pi\)
−0.0849882 + 0.996382i \(0.527085\pi\)
\(138\) 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 −0.804892 0.593422i \(-0.797777\pi\)
0.315652 + 0.948875i \(0.397777\pi\)
\(150\) 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 0.607784 0.794103i \(-0.292059\pi\)
−0.567421 + 0.823428i \(0.692059\pi\)
\(168\) 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 \(-0.728551\pi\)
0.974914 0.222582i \(-0.0714487\pi\)
\(174\) 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 0.348489 0.937313i \(-0.386695\pi\)
−0.269005 + 0.963139i \(0.586695\pi\)
\(180\) 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 −0.204277 0.978913i \(-0.565484\pi\)
0.410127 + 0.912028i \(0.365484\pi\)
\(192\) 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 \(-0.556375\pi\)
−0.176183 + 0.984357i \(0.556375\pi\)
\(198\) 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 \(0.0289671\pi\)
−0.752253 + 0.658874i \(0.771033\pi\)
\(228\) 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 0.0917755 0.995780i \(-0.470746\pi\)
−0.918683 + 0.394997i \(0.870746\pi\)
\(234\) 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 \(-0.478904\pi\)
0.532918 0.846167i \(-0.321096\pi\)
\(240\) 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 −0.755696 0.654922i \(-0.772701\pi\)
0.856391 + 0.516328i \(0.172701\pi\)
\(252\) 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 −0.0451186 0.998982i \(-0.514367\pi\)
0.550685 + 0.834713i \(0.314367\pi\)
\(258\) 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 \(-0.236991\pi\)
0.735407 + 0.677626i \(0.236991\pi\)
\(264\) 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 \(0.0620898\pi\)
−0.118817 + 0.992916i \(0.537910\pi\)
\(270\) 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 −0.602497 0.798121i \(-0.705827\pi\)
0.572877 + 0.819642i \(0.305827\pi\)
\(282\) 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 0.968242 0.250017i \(-0.0804361\pi\)
−0.930280 + 0.366850i \(0.880436\pi\)
\(294\) 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 0.590330 0.807162i \(-0.298997\pi\)
0.00314963 + 0.999995i \(0.498997\pi\)
\(312\) 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 \(-0.592514\pi\)
0.999723 0.0235153i \(-0.00748586\pi\)
\(318\) 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 −0.815479 0.578787i \(-0.803526\pi\)
0.298462 + 0.954421i \(0.403526\pi\)
\(348\) 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 \(0.316290\pi\)
−0.545632 + 0.838025i \(0.683710\pi\)
\(354\) 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 \(0.161581\pi\)
−0.421279 + 0.906931i \(0.638419\pi\)
\(360\) 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 −0.933523 0.358517i \(-0.883282\pi\)
0.629445 + 0.777045i \(0.283282\pi\)
\(384\) 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 −0.0752534 0.997164i \(-0.523977\pi\)
0.525237 + 0.850956i \(0.323977\pi\)
\(390\) 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 0.969180 0.246355i \(-0.0792328\pi\)
−0.533790 + 0.845617i \(0.679233\pi\)
\(402\) 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 \(0.329000\pi\)
−0.511743 + 0.859139i \(0.671000\pi\)
\(420\) 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 −0.161160 0.986928i \(-0.551523\pi\)
−0.988426 + 0.151706i \(0.951523\pi\)
\(432\) 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 0.658085 0.752943i \(-0.271367\pi\)
0.0898330 + 0.995957i \(0.471367\pi\)
\(444\) 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 −0.812606 0.582813i \(-0.801952\pi\)
0.805397 + 0.592736i \(0.201952\pi\)
\(450\) 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 \(-0.739669\pi\)
−0.683789 + 0.729679i \(0.739669\pi\)
\(462\) 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 0.815759 0.578392i \(-0.196320\pi\)
−0.802167 + 0.597100i \(0.796320\pi\)
\(468\) 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 −0.768424 0.639942i \(-0.778959\pi\)
0.371165 + 0.928567i \(0.378959\pi\)
\(480\) 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 \(-0.908590\pi\)
0.609402 0.792862i \(-0.291410\pi\)
\(492\) 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 \(-0.596273\pi\)
0.802079 0.597218i \(-0.203727\pi\)
\(504\) 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 0.587940 0.808905i \(-0.299939\pi\)
0.000190870 1.00000i \(0.499939\pi\)
\(510\) 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 −0.452963 0.891529i \(-0.649633\pi\)
0.157573 + 0.987507i \(0.449633\pi\)
\(522\) 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 \(0.0608514\pi\)
−0.682595 + 0.730797i \(0.739149\pi\)
\(558\) 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 0.387363 0.921927i \(-0.373386\pi\)
−0.757103 + 0.653296i \(0.773386\pi\)
\(564\) 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 \(0.214697\pi\)
−0.998934 + 0.0461553i \(0.985303\pi\)
\(570\) 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 0.0166304 0.999862i \(-0.494706\pi\)
0.601158 + 0.799130i \(0.294706\pi\)
\(588\) 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 \(-0.348699\pi\)
0.457629 + 0.889143i \(0.348699\pi\)
\(594\) 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 0.999991 0.00417130i \(-0.00132777\pi\)
−0.312981 + 0.949759i \(0.601328\pi\)
\(600\) 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 \(-0.783885\pi\)
0.778236 0.627972i \(-0.216115\pi\)
\(618\) 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 0.160690 0.987005i \(-0.448628\pi\)
−0.450146 + 0.892955i \(0.648628\pi\)
\(642\) 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 \(0.644366\pi\)
−0.719511 + 0.694482i \(0.755634\pi\)
\(648\) 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 0.0377511 0.999287i \(-0.487981\pi\)
0.617908 + 0.786251i \(0.287981\pi\)
\(654\) 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 \(-0.635033\pi\)
−0.411609 + 0.911360i \(0.635033\pi\)
\(660\) 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 −0.203976 0.978976i \(-0.565386\pi\)
0.868029 + 0.496513i \(0.165386\pi\)
\(678\) 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 \(0.107103\pi\)
−0.943925 + 0.330161i \(0.892897\pi\)
\(684\) 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 \(-0.524128\pi\)
0.647364 0.762181i \(-0.275872\pi\)
\(702\) 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 −0.771984 0.635642i \(-0.780736\pi\)
−0.250927 + 0.968006i \(0.580736\pi\)
\(720\) 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 −0.216860 0.976203i \(-0.569581\pi\)
0.861411 + 0.507909i \(0.169581\pi\)
\(744\) 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 0.248934 0.968521i \(-0.419920\pi\)
−0.844193 + 0.536039i \(0.819920\pi\)
\(762\) 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 0.531056 0.847337i \(-0.321795\pi\)
−0.0684183 + 0.997657i \(0.521795\pi\)
\(774\) 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 \(0.131580\pi\)
0.0990490 + 0.995083i \(0.468420\pi\)
\(798\) 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 −0.513143 0.858303i \(-0.671519\pi\)
0.657725 + 0.753258i \(0.271519\pi\)
\(810\) 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 \(0.104792\pi\)
−0.575540 + 0.817774i \(0.695208\pi\)
\(822\) 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 0.904969 0.425479i \(-0.139894\pi\)
−0.125004 + 0.992156i \(0.539894\pi\)
\(828\) 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 −0.0702762 0.997528i \(-0.522388\pi\)
−0.643187 + 0.765709i \(0.722388\pi\)
\(840\) 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 \(-0.540850\pi\)
−0.127981 + 0.991777i \(0.540850\pi\)
\(858\) 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 0.956657 0.291217i \(-0.0940603\pi\)
−0.572587 + 0.819844i \(0.694060\pi\)
\(864\) 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 \(-0.911501\pi\)
0.961598 0.274461i \(-0.0884994\pi\)
\(882\) 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 0.956745 0.290929i \(-0.0939642\pi\)
−0.945026 + 0.326994i \(0.893964\pi\)
\(888\) 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 −0.845465 0.534031i \(-0.820677\pi\)
0.769157 + 0.639060i \(0.220677\pi\)
\(912\) 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 0.761073 0.648667i \(-0.224673\pi\)
−0.852103 + 0.523374i \(0.824673\pi\)
\(930\) 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 \(0.678984\pi\)
−0.969372 + 0.245597i \(0.921016\pi\)
\(942\) 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 \(0.00485516\pi\)
−0.999884 + 0.0152524i \(0.995145\pi\)
\(948\) 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 0.878087 0.478500i \(-0.158819\pi\)
−0.991643 + 0.129012i \(0.958819\pi\)
\(954\) 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 −0.0968441 0.995300i \(-0.530875\pi\)
−0.663371 + 0.748291i \(0.730875\pi\)
\(972\) 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 −0.732773 0.680473i \(-0.761774\pi\)
0.873608 + 0.486631i \(0.161774\pi\)
\(978\) 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 −0.388743 0.921346i \(-0.627091\pi\)
0.227054 + 0.973882i \(0.427091\pi\)
\(984\) 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.161.14 80
3.2 odd 2 inner 891.2.k.a.161.7 80
9.2 odd 6 297.2.t.a.260.3 80
9.4 even 3 297.2.t.a.62.3 80
9.5 odd 6 99.2.p.a.29.8 80
9.7 even 3 99.2.p.a.95.8 yes 80
11.8 odd 10 inner 891.2.k.a.404.7 80
33.8 even 10 inner 891.2.k.a.404.14 80
99.41 even 30 99.2.p.a.74.8 yes 80
99.52 odd 30 99.2.p.a.41.8 yes 80
99.74 even 30 297.2.t.a.206.3 80
99.85 odd 30 297.2.t.a.8.3 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.8 80 9.5 odd 6
99.2.p.a.41.8 yes 80 99.52 odd 30
99.2.p.a.74.8 yes 80 99.41 even 30
99.2.p.a.95.8 yes 80 9.7 even 3
297.2.t.a.8.3 80 99.85 odd 30
297.2.t.a.62.3 80 9.4 even 3
297.2.t.a.206.3 80 99.74 even 30
297.2.t.a.260.3 80 9.2 odd 6
891.2.k.a.161.7 80 3.2 odd 2 inner
891.2.k.a.161.14 80 1.1 even 1 trivial
891.2.k.a.404.7 80 11.8 odd 10 inner
891.2.k.a.404.14 80 33.8 even 10 inner