Properties

Label 891.2.n.d.136.1
Level $891$
Weight $2$
Character 891.136
Analytic conductor $7.115$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.n (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 136.1
Root \(-0.104528 + 0.994522i\) of defining polynomial
Character \(\chi\) \(=\) 891.136
Dual form 891.2.n.d.190.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.47815 - 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(-0.348943 - 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(-0.690983 + 2.12663i) q^{8} +O(q^{10})\) \(q+(1.47815 - 0.658114i) q^{2} +(0.413545 - 0.459289i) q^{4} +(-0.348943 - 0.155360i) q^{5} +(-2.93444 - 0.623735i) q^{7} +(-0.690983 + 2.12663i) q^{8} -0.618034 q^{10} +(-2.93162 + 1.55100i) q^{11} +(-0.651847 + 6.20191i) q^{13} +(-4.74803 + 1.00922i) q^{14} +(0.507392 + 4.82751i) q^{16} +(0.500000 - 0.363271i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(-0.215659 + 0.0960175i) q^{20} +(-3.31263 + 4.22195i) q^{22} +(2.73607 + 4.73901i) q^{23} +(-3.24803 - 3.60730i) q^{25} +(3.11803 + 9.59632i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(4.37441 + 0.929809i) q^{29} +(0.402863 - 3.83299i) q^{31} +(1.69098 + 2.92887i) q^{32} +(0.500000 - 0.866025i) q^{34} +(0.927051 + 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(0.144455 + 1.37440i) q^{38} +(0.571506 - 0.634721i) q^{40} +(-5.81438 + 1.23588i) q^{41} +(-0.881966 + 1.52761i) q^{43} +(-0.500000 + 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(-0.413545 - 0.459289i) q^{47} +(1.82709 + 0.813473i) q^{49} +(-7.17508 - 3.19455i) q^{50} +(2.57890 + 2.86416i) q^{52} +(5.97214 + 4.33901i) q^{53} +(1.26393 - 0.0857567i) q^{55} +(3.35410 - 5.80948i) q^{56} +(7.07794 - 1.50446i) q^{58} +(-3.56395 + 3.95817i) q^{59} +(-0.119779 - 1.13962i) q^{61} +(-1.92705 - 5.93085i) q^{62} +(-3.42705 - 2.48990i) q^{64} +(1.19098 - 2.06284i) q^{65} +(-5.28115 - 9.14723i) q^{67} +(0.0399263 - 0.379874i) q^{68} +(1.81359 + 0.385489i) q^{70} +(-11.7812 + 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(-4.58629 - 5.09359i) q^{74} +(0.263932 + 0.457144i) q^{76} +(9.57008 - 2.72277i) q^{77} +(0.482228 - 0.214702i) q^{79} +(0.572949 - 1.76336i) q^{80} +(-7.78115 + 5.65334i) q^{82} +(1.32837 + 12.6386i) q^{83} +(-0.230909 + 0.0490813i) q^{85} +(-0.298335 + 2.83847i) q^{86} +(-1.27270 - 7.30618i) q^{88} +9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(3.30806 + 0.703150i) q^{92} +(-0.913545 - 0.406737i) q^{94} +(0.218296 - 0.242442i) q^{95} +(13.7346 - 6.11506i) q^{97} +3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 6 q^{14} - 9 q^{16} + 4 q^{17} - 20 q^{19} - 3 q^{20} + 8 q^{22} + 4 q^{23} + 6 q^{25} + 16 q^{26} - 12 q^{28} + 10 q^{29} - 8 q^{31} + 18 q^{32} + 4 q^{34} - 6 q^{35} - 6 q^{37} - 10 q^{40} - 23 q^{41} - 16 q^{43} - 4 q^{44} + 26 q^{46} + 3 q^{47} + 2 q^{49} - 12 q^{50} - 7 q^{52} + 12 q^{53} + 28 q^{55} + 20 q^{59} - 3 q^{61} - 2 q^{62} - 14 q^{64} + 14 q^{65} - 2 q^{67} + q^{68} + 9 q^{70} - 54 q^{71} + 12 q^{73} + 4 q^{74} + 20 q^{76} + 3 q^{77} - 5 q^{79} + 18 q^{80} - 22 q^{82} - 21 q^{83} - 7 q^{85} + 7 q^{86} + 25 q^{88} + 40 q^{89} + 6 q^{91} - 7 q^{92} - q^{94} - 25 q^{95} + 33 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.47815 0.658114i 1.04521 0.465357i 0.188994 0.981978i \(-0.439477\pi\)
0.856214 + 0.516622i \(0.172811\pi\)
\(3\) 0 0
\(4\) 0.413545 0.459289i 0.206773 0.229644i
\(5\) −0.348943 0.155360i −0.156052 0.0694789i 0.327224 0.944947i \(-0.393887\pi\)
−0.483276 + 0.875468i \(0.660553\pi\)
\(6\) 0 0
\(7\) −2.93444 0.623735i −1.10912 0.235750i −0.383289 0.923628i \(-0.625209\pi\)
−0.725826 + 0.687879i \(0.758542\pi\)
\(8\) −0.690983 + 2.12663i −0.244299 + 0.751876i
\(9\) 0 0
\(10\) −0.618034 −0.195440
\(11\) −2.93162 + 1.55100i −0.883917 + 0.467645i
\(12\) 0 0
\(13\) −0.651847 + 6.20191i −0.180790 + 1.72010i 0.408993 + 0.912537i \(0.365880\pi\)
−0.589783 + 0.807562i \(0.700787\pi\)
\(14\) −4.74803 + 1.00922i −1.26896 + 0.269727i
\(15\) 0 0
\(16\) 0.507392 + 4.82751i 0.126848 + 1.20688i
\(17\) 0.500000 0.363271i 0.121268 0.0881062i −0.525498 0.850795i \(-0.676121\pi\)
0.646766 + 0.762688i \(0.276121\pi\)
\(18\) 0 0
\(19\) −0.263932 + 0.812299i −0.0605502 + 0.186354i −0.976756 0.214353i \(-0.931236\pi\)
0.916206 + 0.400707i \(0.131236\pi\)
\(20\) −0.215659 + 0.0960175i −0.0482228 + 0.0214702i
\(21\) 0 0
\(22\) −3.31263 + 4.22195i −0.706255 + 0.900123i
\(23\) 2.73607 + 4.73901i 0.570510 + 0.988152i 0.996514 + 0.0834304i \(0.0265876\pi\)
−0.426004 + 0.904721i \(0.640079\pi\)
\(24\) 0 0
\(25\) −3.24803 3.60730i −0.649606 0.721460i
\(26\) 3.11803 + 9.59632i 0.611497 + 1.88199i
\(27\) 0 0
\(28\) −1.50000 + 1.08981i −0.283473 + 0.205955i
\(29\) 4.37441 + 0.929809i 0.812307 + 0.172661i 0.595295 0.803508i \(-0.297035\pi\)
0.217013 + 0.976169i \(0.430369\pi\)
\(30\) 0 0
\(31\) 0.402863 3.83299i 0.0723564 0.688425i −0.896877 0.442281i \(-0.854170\pi\)
0.969233 0.246145i \(-0.0791638\pi\)
\(32\) 1.69098 + 2.92887i 0.298926 + 0.517756i
\(33\) 0 0
\(34\) 0.500000 0.866025i 0.0857493 0.148522i
\(35\) 0.927051 + 0.673542i 0.156700 + 0.113849i
\(36\) 0 0
\(37\) −1.30902 4.02874i −0.215201 0.662321i −0.999139 0.0414819i \(-0.986792\pi\)
0.783938 0.620839i \(-0.213208\pi\)
\(38\) 0.144455 + 1.37440i 0.0234337 + 0.222956i
\(39\) 0 0
\(40\) 0.571506 0.634721i 0.0903630 0.100358i
\(41\) −5.81438 + 1.23588i −0.908053 + 0.193013i −0.638183 0.769884i \(-0.720314\pi\)
−0.269869 + 0.962897i \(0.586981\pi\)
\(42\) 0 0
\(43\) −0.881966 + 1.52761i −0.134499 + 0.232958i −0.925406 0.378978i \(-0.876276\pi\)
0.790907 + 0.611936i \(0.209609\pi\)
\(44\) −0.500000 + 1.98787i −0.0753778 + 0.299683i
\(45\) 0 0
\(46\) 7.16312 + 5.20431i 1.05614 + 0.767334i
\(47\) −0.413545 0.459289i −0.0603218 0.0669942i 0.712229 0.701948i \(-0.247686\pi\)
−0.772550 + 0.634953i \(0.781019\pi\)
\(48\) 0 0
\(49\) 1.82709 + 0.813473i 0.261013 + 0.116210i
\(50\) −7.17508 3.19455i −1.01471 0.451778i
\(51\) 0 0
\(52\) 2.57890 + 2.86416i 0.357629 + 0.397187i
\(53\) 5.97214 + 4.33901i 0.820336 + 0.596009i 0.916809 0.399327i \(-0.130756\pi\)
−0.0964728 + 0.995336i \(0.530756\pi\)
\(54\) 0 0
\(55\) 1.26393 0.0857567i 0.170429 0.0115634i
\(56\) 3.35410 5.80948i 0.448211 0.776324i
\(57\) 0 0
\(58\) 7.07794 1.50446i 0.929379 0.197546i
\(59\) −3.56395 + 3.95817i −0.463987 + 0.515309i −0.929043 0.369972i \(-0.879367\pi\)
0.465056 + 0.885281i \(0.346034\pi\)
\(60\) 0 0
\(61\) −0.119779 1.13962i −0.0153361 0.145913i 0.984174 0.177204i \(-0.0567051\pi\)
−0.999510 + 0.0312901i \(0.990038\pi\)
\(62\) −1.92705 5.93085i −0.244736 0.753219i
\(63\) 0 0
\(64\) −3.42705 2.48990i −0.428381 0.311237i
\(65\) 1.19098 2.06284i 0.147723 0.255864i
\(66\) 0 0
\(67\) −5.28115 9.14723i −0.645196 1.11751i −0.984256 0.176747i \(-0.943443\pi\)
0.339061 0.940764i \(-0.389891\pi\)
\(68\) 0.0399263 0.379874i 0.00484178 0.0460664i
\(69\) 0 0
\(70\) 1.81359 + 0.385489i 0.216765 + 0.0460748i
\(71\) −11.7812 + 8.55951i −1.39817 + 1.01583i −0.403253 + 0.915089i \(0.632120\pi\)
−0.994913 + 0.100738i \(0.967880\pi\)
\(72\) 0 0
\(73\) 0.381966 + 1.17557i 0.0447057 + 0.137590i 0.970918 0.239412i \(-0.0769548\pi\)
−0.926212 + 0.377003i \(0.876955\pi\)
\(74\) −4.58629 5.09359i −0.533145 0.592118i
\(75\) 0 0
\(76\) 0.263932 + 0.457144i 0.0302751 + 0.0524380i
\(77\) 9.57008 2.72277i 1.09061 0.310289i
\(78\) 0 0
\(79\) 0.482228 0.214702i 0.0542549 0.0241558i −0.379430 0.925221i \(-0.623880\pi\)
0.433685 + 0.901065i \(0.357213\pi\)
\(80\) 0.572949 1.76336i 0.0640576 0.197149i
\(81\) 0 0
\(82\) −7.78115 + 5.65334i −0.859285 + 0.624307i
\(83\) 1.32837 + 12.6386i 0.145807 + 1.38727i 0.785608 + 0.618724i \(0.212350\pi\)
−0.639801 + 0.768541i \(0.720983\pi\)
\(84\) 0 0
\(85\) −0.230909 + 0.0490813i −0.0250456 + 0.00532361i
\(86\) −0.298335 + 2.83847i −0.0321703 + 0.306080i
\(87\) 0 0
\(88\) −1.27270 7.30618i −0.135671 0.778841i
\(89\) 9.47214 1.00404 0.502022 0.864855i \(-0.332590\pi\)
0.502022 + 0.864855i \(0.332590\pi\)
\(90\) 0 0
\(91\) 5.78115 17.7926i 0.606029 1.86517i
\(92\) 3.30806 + 0.703150i 0.344889 + 0.0733085i
\(93\) 0 0
\(94\) −0.913545 0.406737i −0.0942250 0.0419517i
\(95\) 0.218296 0.242442i 0.0223967 0.0248740i
\(96\) 0 0
\(97\) 13.7346 6.11506i 1.39454 0.620890i 0.434481 0.900681i \(-0.356932\pi\)
0.960061 + 0.279791i \(0.0902651\pi\)
\(98\) 3.23607 0.326892
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −2.74064 + 1.22021i −0.272704 + 0.121415i −0.538532 0.842605i \(-0.681021\pi\)
0.265829 + 0.964020i \(0.414354\pi\)
\(102\) 0 0
\(103\) −4.01478 + 4.45887i −0.395588 + 0.439345i −0.907729 0.419556i \(-0.862186\pi\)
0.512141 + 0.858901i \(0.328852\pi\)
\(104\) −12.7387 5.67165i −1.24913 0.556151i
\(105\) 0 0
\(106\) 11.6833 + 2.48335i 1.13478 + 0.241205i
\(107\) 0.0729490 0.224514i 0.00705225 0.0217046i −0.947468 0.319849i \(-0.896368\pi\)
0.954521 + 0.298145i \(0.0963678\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 1.81184 0.958572i 0.172752 0.0913963i
\(111\) 0 0
\(112\) 1.52218 14.4825i 0.143832 1.36847i
\(113\) 12.4305 2.64218i 1.16936 0.248556i 0.418001 0.908446i \(-0.362731\pi\)
0.751362 + 0.659891i \(0.229397\pi\)
\(114\) 0 0
\(115\) −0.218482 2.07872i −0.0203736 0.193842i
\(116\) 2.23607 1.62460i 0.207614 0.150840i
\(117\) 0 0
\(118\) −2.66312 + 8.19624i −0.245160 + 0.754525i
\(119\) −1.69381 + 0.754131i −0.155271 + 0.0691311i
\(120\) 0 0
\(121\) 6.18878 9.09390i 0.562617 0.826718i
\(122\) −0.927051 1.60570i −0.0839313 0.145373i
\(123\) 0 0
\(124\) −1.59385 1.77015i −0.143132 0.158964i
\(125\) 1.16312 + 3.57971i 0.104033 + 0.320179i
\(126\) 0 0
\(127\) −7.85410 + 5.70634i −0.696939 + 0.506356i −0.878934 0.476944i \(-0.841745\pi\)
0.181995 + 0.983299i \(0.441745\pi\)
\(128\) −13.3204 2.83135i −1.17737 0.250258i
\(129\) 0 0
\(130\) 0.402863 3.83299i 0.0353335 0.336175i
\(131\) 6.92705 + 11.9980i 0.605219 + 1.04827i 0.992017 + 0.126106i \(0.0402479\pi\)
−0.386798 + 0.922165i \(0.626419\pi\)
\(132\) 0 0
\(133\) 1.28115 2.21902i 0.111090 0.192414i
\(134\) −13.8262 10.0453i −1.19441 0.867786i
\(135\) 0 0
\(136\) 0.427051 + 1.31433i 0.0366193 + 0.112703i
\(137\) 0.153880 + 1.46407i 0.0131469 + 0.125084i 0.999127 0.0417795i \(-0.0133027\pi\)
−0.985980 + 0.166864i \(0.946636\pi\)
\(138\) 0 0
\(139\) 3.91716 4.35045i 0.332249 0.369000i −0.553753 0.832681i \(-0.686805\pi\)
0.886002 + 0.463681i \(0.153472\pi\)
\(140\) 0.692728 0.147244i 0.0585462 0.0124444i
\(141\) 0 0
\(142\) −11.7812 + 20.4056i −0.988652 + 1.71240i
\(143\) −7.70820 19.1926i −0.644592 1.60497i
\(144\) 0 0
\(145\) −1.38197 1.00406i −0.114766 0.0833824i
\(146\) 1.33826 + 1.48629i 0.110755 + 0.123006i
\(147\) 0 0
\(148\) −2.39169 1.06485i −0.196596 0.0875302i
\(149\) 13.7032 + 6.10105i 1.12261 + 0.499817i 0.882210 0.470857i \(-0.156055\pi\)
0.240399 + 0.970674i \(0.422722\pi\)
\(150\) 0 0
\(151\) 1.33826 + 1.48629i 0.108906 + 0.120953i 0.795133 0.606435i \(-0.207401\pi\)
−0.686227 + 0.727388i \(0.740734\pi\)
\(152\) −1.54508 1.12257i −0.125323 0.0910524i
\(153\) 0 0
\(154\) 12.3541 10.3229i 0.995522 0.831840i
\(155\) −0.736068 + 1.27491i −0.0591224 + 0.102403i
\(156\) 0 0
\(157\) −9.49606 + 2.01845i −0.757868 + 0.161090i −0.570610 0.821221i \(-0.693293\pi\)
−0.187258 + 0.982311i \(0.559960\pi\)
\(158\) 0.571506 0.634721i 0.0454666 0.0504957i
\(159\) 0 0
\(160\) −0.135029 1.28472i −0.0106750 0.101566i
\(161\) −5.07295 15.6129i −0.399804 1.23047i
\(162\) 0 0
\(163\) 12.3541 + 8.97578i 0.967648 + 0.703037i 0.954914 0.296882i \(-0.0959467\pi\)
0.0127336 + 0.999919i \(0.495947\pi\)
\(164\) −1.83688 + 3.18157i −0.143436 + 0.248439i
\(165\) 0 0
\(166\) 10.2812 + 17.8075i 0.797972 + 1.38213i
\(167\) 1.98964 18.9302i 0.153963 1.46486i −0.595789 0.803141i \(-0.703160\pi\)
0.749752 0.661719i \(-0.230173\pi\)
\(168\) 0 0
\(169\) −25.3228 5.38253i −1.94791 0.414041i
\(170\) −0.309017 + 0.224514i −0.0237005 + 0.0172194i
\(171\) 0 0
\(172\) 0.336881 + 1.03681i 0.0256869 + 0.0790563i
\(173\) 11.7888 + 13.0928i 0.896283 + 0.995423i 1.00000 0.000816499i \(0.000259900\pi\)
−0.103716 + 0.994607i \(0.533073\pi\)
\(174\) 0 0
\(175\) 7.28115 + 12.6113i 0.550403 + 0.953327i
\(176\) −8.97496 13.3655i −0.676513 1.00746i
\(177\) 0 0
\(178\) 14.0012 6.23374i 1.04944 0.467239i
\(179\) 0.690983 2.12663i 0.0516465 0.158952i −0.921907 0.387412i \(-0.873369\pi\)
0.973553 + 0.228460i \(0.0733691\pi\)
\(180\) 0 0
\(181\) 6.89919 5.01255i 0.512813 0.372580i −0.301077 0.953600i \(-0.597346\pi\)
0.813889 + 0.581020i \(0.197346\pi\)
\(182\) −3.16413 30.1047i −0.234541 2.23151i
\(183\) 0 0
\(184\) −11.9687 + 2.54402i −0.882343 + 0.187548i
\(185\) −0.169131 + 1.60917i −0.0124347 + 0.118309i
\(186\) 0 0
\(187\) −0.902375 + 1.84047i −0.0659882 + 0.134589i
\(188\) −0.381966 −0.0278577
\(189\) 0 0
\(190\) 0.163119 0.502029i 0.0118339 0.0364210i
\(191\) −1.43997 0.306074i −0.104192 0.0221468i 0.155520 0.987833i \(-0.450295\pi\)
−0.259713 + 0.965686i \(0.583628\pi\)
\(192\) 0 0
\(193\) 1.42724 + 0.635447i 0.102735 + 0.0457405i 0.457461 0.889230i \(-0.348759\pi\)
−0.354726 + 0.934970i \(0.615426\pi\)
\(194\) 16.2774 18.0779i 1.16865 1.29792i
\(195\) 0 0
\(196\) 1.12920 0.502754i 0.0806574 0.0359110i
\(197\) 26.6180 1.89646 0.948228 0.317590i \(-0.102873\pi\)
0.948228 + 0.317590i \(0.102873\pi\)
\(198\) 0 0
\(199\) −3.29180 −0.233349 −0.116675 0.993170i \(-0.537223\pi\)
−0.116675 + 0.993170i \(0.537223\pi\)
\(200\) 9.91572 4.41476i 0.701147 0.312171i
\(201\) 0 0
\(202\) −3.24803 + 3.60730i −0.228530 + 0.253809i
\(203\) −12.2565 5.45694i −0.860238 0.383002i
\(204\) 0 0
\(205\) 2.22089 + 0.472066i 0.155114 + 0.0329705i
\(206\) −3.00000 + 9.23305i −0.209020 + 0.643297i
\(207\) 0 0
\(208\) −30.2705 −2.09888
\(209\) −0.486130 2.79071i −0.0336263 0.193038i
\(210\) 0 0
\(211\) −1.17809 + 11.2088i −0.0811030 + 0.771643i 0.876081 + 0.482164i \(0.160149\pi\)
−0.957184 + 0.289480i \(0.906518\pi\)
\(212\) 4.46261 0.948557i 0.306493 0.0651471i
\(213\) 0 0
\(214\) −0.0399263 0.379874i −0.00272931 0.0259676i
\(215\) 0.545085 0.396027i 0.0371745 0.0270088i
\(216\) 0 0
\(217\) −3.57295 + 10.9964i −0.242548 + 0.746485i
\(218\) 0 0
\(219\) 0 0
\(220\) 0.483306 0.615974i 0.0325845 0.0415290i
\(221\) 1.92705 + 3.33775i 0.129627 + 0.224521i
\(222\) 0 0
\(223\) −8.50345 9.44404i −0.569433 0.632419i 0.387798 0.921744i \(-0.373236\pi\)
−0.957231 + 0.289325i \(0.906569\pi\)
\(224\) −3.13525 9.64932i −0.209483 0.644722i
\(225\) 0 0
\(226\) 16.6353 12.0862i 1.10656 0.803963i
\(227\) −10.6506 2.26386i −0.706905 0.150257i −0.159589 0.987183i \(-0.551017\pi\)
−0.547316 + 0.836926i \(0.684350\pi\)
\(228\) 0 0
\(229\) −1.04528 + 9.94522i −0.0690744 + 0.657199i 0.904130 + 0.427257i \(0.140520\pi\)
−0.973204 + 0.229941i \(0.926147\pi\)
\(230\) −1.69098 2.92887i −0.111500 0.193124i
\(231\) 0 0
\(232\) −5.00000 + 8.66025i −0.328266 + 0.568574i
\(233\) −7.01722 5.09831i −0.459713 0.334001i 0.333705 0.942677i \(-0.391701\pi\)
−0.793419 + 0.608676i \(0.791701\pi\)
\(234\) 0 0
\(235\) 0.0729490 + 0.224514i 0.00475867 + 0.0146457i
\(236\) 0.344086 + 3.27376i 0.0223981 + 0.213104i
\(237\) 0 0
\(238\) −2.00739 + 2.22943i −0.130120 + 0.144513i
\(239\) 17.1785 3.65141i 1.11119 0.236190i 0.384477 0.923135i \(-0.374382\pi\)
0.726710 + 0.686945i \(0.241049\pi\)
\(240\) 0 0
\(241\) −8.56231 + 14.8303i −0.551547 + 0.955307i 0.446617 + 0.894725i \(0.352629\pi\)
−0.998163 + 0.0605813i \(0.980705\pi\)
\(242\) 3.16312 17.5150i 0.203333 1.12591i
\(243\) 0 0
\(244\) −0.572949 0.416272i −0.0366793 0.0266491i
\(245\) −0.511170 0.567712i −0.0326575 0.0362698i
\(246\) 0 0
\(247\) −4.86576 2.16638i −0.309601 0.137843i
\(248\) 7.87297 + 3.50527i 0.499934 + 0.222585i
\(249\) 0 0
\(250\) 4.07512 + 4.52588i 0.257733 + 0.286242i
\(251\) −13.5902 9.87384i −0.857804 0.623231i 0.0694827 0.997583i \(-0.477865\pi\)
−0.927287 + 0.374352i \(0.877865\pi\)
\(252\) 0 0
\(253\) −15.3713 9.64932i −0.966387 0.606648i
\(254\) −7.85410 + 13.6037i −0.492810 + 0.853572i
\(255\) 0 0
\(256\) −13.2659 + 2.81976i −0.829121 + 0.176235i
\(257\) −18.2848 + 20.3074i −1.14058 + 1.26674i −0.181562 + 0.983380i \(0.558115\pi\)
−0.959014 + 0.283358i \(0.908551\pi\)
\(258\) 0 0
\(259\) 1.32837 + 12.6386i 0.0825408 + 0.785324i
\(260\) −0.454915 1.40008i −0.0282126 0.0868296i
\(261\) 0 0
\(262\) 18.1353 + 13.1760i 1.12040 + 0.814018i
\(263\) 0.336881 0.583495i 0.0207730 0.0359798i −0.855452 0.517882i \(-0.826721\pi\)
0.876225 + 0.481902i \(0.160054\pi\)
\(264\) 0 0
\(265\) −1.40983 2.44190i −0.0866052 0.150005i
\(266\) 0.433364 4.12319i 0.0265713 0.252809i
\(267\) 0 0
\(268\) −6.38521 1.35722i −0.390039 0.0829054i
\(269\) −19.7984 + 14.3844i −1.20713 + 0.877030i −0.994967 0.100205i \(-0.968050\pi\)
−0.212161 + 0.977235i \(0.568050\pi\)
\(270\) 0 0
\(271\) 1.93769 + 5.96361i 0.117707 + 0.362263i 0.992502 0.122229i \(-0.0390043\pi\)
−0.874795 + 0.484493i \(0.839004\pi\)
\(272\) 2.00739 + 2.22943i 0.121716 + 0.135179i
\(273\) 0 0
\(274\) 1.19098 + 2.06284i 0.0719499 + 0.124621i
\(275\) 15.1169 + 5.53753i 0.911584 + 0.333926i
\(276\) 0 0
\(277\) 9.53531 4.24539i 0.572921 0.255081i −0.0997623 0.995011i \(-0.531808\pi\)
0.672683 + 0.739930i \(0.265142\pi\)
\(278\) 2.92705 9.00854i 0.175553 0.540296i
\(279\) 0 0
\(280\) −2.07295 + 1.50609i −0.123882 + 0.0900058i
\(281\) 0.547318 + 5.20738i 0.0326503 + 0.310647i 0.998643 + 0.0520775i \(0.0165843\pi\)
−0.965993 + 0.258569i \(0.916749\pi\)
\(282\) 0 0
\(283\) 21.6956 4.61155i 1.28967 0.274128i 0.488501 0.872563i \(-0.337544\pi\)
0.801171 + 0.598435i \(0.204211\pi\)
\(284\) −0.940756 + 8.95070i −0.0558236 + 0.531126i
\(285\) 0 0
\(286\) −24.0248 23.2967i −1.42062 1.37756i
\(287\) 17.8328 1.05264
\(288\) 0 0
\(289\) −5.13525 + 15.8047i −0.302074 + 0.929688i
\(290\) −2.70353 0.574654i −0.158757 0.0337448i
\(291\) 0 0
\(292\) 0.697887 + 0.310719i 0.0408407 + 0.0181835i
\(293\) 12.0071 13.3352i 0.701460 0.779050i −0.282148 0.959371i \(-0.591047\pi\)
0.983608 + 0.180321i \(0.0577135\pi\)
\(294\) 0 0
\(295\) 1.85856 0.827482i 0.108209 0.0481779i
\(296\) 9.47214 0.550557
\(297\) 0 0
\(298\) 24.2705 1.40595
\(299\) −31.1744 + 13.8797i −1.80286 + 0.802686i
\(300\) 0 0
\(301\) 3.54090 3.93257i 0.204094 0.226670i
\(302\) 2.95630 + 1.31623i 0.170116 + 0.0757404i
\(303\) 0 0
\(304\) −4.05530 0.861981i −0.232587 0.0494380i
\(305\) −0.135255 + 0.416272i −0.00774467 + 0.0238357i
\(306\) 0 0
\(307\) −19.5623 −1.11648 −0.558240 0.829680i \(-0.688523\pi\)
−0.558240 + 0.829680i \(0.688523\pi\)
\(308\) 2.70713 5.52142i 0.154253 0.314612i
\(309\) 0 0
\(310\) −0.248983 + 2.36892i −0.0141413 + 0.134545i
\(311\) −11.2214 + 2.38519i −0.636310 + 0.135252i −0.514761 0.857334i \(-0.672119\pi\)
−0.121549 + 0.992585i \(0.538786\pi\)
\(312\) 0 0
\(313\) 2.90932 + 27.6803i 0.164445 + 1.56459i 0.696300 + 0.717751i \(0.254828\pi\)
−0.531856 + 0.846835i \(0.678505\pi\)
\(314\) −12.7082 + 9.23305i −0.717165 + 0.521051i
\(315\) 0 0
\(316\) 0.100813 0.310271i 0.00567118 0.0174541i
\(317\) 23.1681 10.3151i 1.30125 0.579355i 0.365106 0.930966i \(-0.381033\pi\)
0.936146 + 0.351611i \(0.114366\pi\)
\(318\) 0 0
\(319\) −14.2662 + 4.05887i −0.798756 + 0.227253i
\(320\) 0.809017 + 1.40126i 0.0452254 + 0.0783327i
\(321\) 0 0
\(322\) −17.7737 19.7396i −0.990487 1.10005i
\(323\) 0.163119 + 0.502029i 0.00907618 + 0.0279336i
\(324\) 0 0
\(325\) 24.4894 17.7926i 1.35843 0.986954i
\(326\) 24.1683 + 5.13712i 1.33856 + 0.284519i
\(327\) 0 0
\(328\) 1.38937 13.2190i 0.0767152 0.729896i
\(329\) 0.927051 + 1.60570i 0.0511100 + 0.0885251i
\(330\) 0 0
\(331\) 11.2984 19.5694i 0.621015 1.07563i −0.368282 0.929714i \(-0.620054\pi\)
0.989297 0.145915i \(-0.0466127\pi\)
\(332\) 6.35410 + 4.61653i 0.348727 + 0.253365i
\(333\) 0 0
\(334\) −9.51722 29.2910i −0.520759 1.60273i
\(335\) 0.421714 + 4.01234i 0.0230407 + 0.219218i
\(336\) 0 0
\(337\) −9.17258 + 10.1872i −0.499662 + 0.554931i −0.939235 0.343276i \(-0.888463\pi\)
0.439572 + 0.898207i \(0.355130\pi\)
\(338\) −40.9732 + 8.70912i −2.22865 + 0.473714i
\(339\) 0 0
\(340\) −0.0729490 + 0.126351i −0.00395622 + 0.00685237i
\(341\) 4.76393 + 11.8617i 0.257981 + 0.642347i
\(342\) 0 0
\(343\) 12.1353 + 8.81678i 0.655242 + 0.476061i
\(344\) −2.63923 2.93117i −0.142298 0.158038i
\(345\) 0 0
\(346\) 26.0421 + 11.5947i 1.40003 + 0.623333i
\(347\) −2.79155 1.24288i −0.149858 0.0667211i 0.330437 0.943828i \(-0.392804\pi\)
−0.480295 + 0.877107i \(0.659470\pi\)
\(348\) 0 0
\(349\) 20.1573 + 22.3869i 1.07900 + 1.19835i 0.979107 + 0.203347i \(0.0651821\pi\)
0.0998889 + 0.994999i \(0.468151\pi\)
\(350\) 19.0623 + 13.8496i 1.01892 + 0.740291i
\(351\) 0 0
\(352\) −9.50000 5.96361i −0.506352 0.317861i
\(353\) 0.763932 1.32317i 0.0406600 0.0704252i −0.844979 0.534799i \(-0.820387\pi\)
0.885639 + 0.464374i \(0.153721\pi\)
\(354\) 0 0
\(355\) 5.44076 1.15647i 0.288765 0.0613790i
\(356\) 3.91716 4.35045i 0.207609 0.230573i
\(357\) 0 0
\(358\) −0.378188 3.59821i −0.0199878 0.190172i
\(359\) −5.32624 16.3925i −0.281108 0.865162i −0.987538 0.157379i \(-0.949696\pi\)
0.706430 0.707783i \(-0.250304\pi\)
\(360\) 0 0
\(361\) 14.7812 + 10.7391i 0.777955 + 0.565218i
\(362\) 6.89919 11.9497i 0.362613 0.628065i
\(363\) 0 0
\(364\) −5.78115 10.0133i −0.303015 0.524837i
\(365\) 0.0493516 0.469550i 0.00258318 0.0245773i
\(366\) 0 0
\(367\) 14.2441 + 3.02767i 0.743535 + 0.158043i 0.564077 0.825722i \(-0.309232\pi\)
0.179458 + 0.983766i \(0.442565\pi\)
\(368\) −21.4894 + 15.6129i −1.12021 + 0.813880i
\(369\) 0 0
\(370\) 0.809017 + 2.48990i 0.0420588 + 0.129444i
\(371\) −14.8185 16.4576i −0.769338 0.854437i
\(372\) 0 0
\(373\) −11.2082 19.4132i −0.580339 1.00518i −0.995439 0.0954006i \(-0.969587\pi\)
0.415100 0.909776i \(-0.363747\pi\)
\(374\) −0.122602 + 3.31436i −0.00633962 + 0.171381i
\(375\) 0 0
\(376\) 1.26249 0.562096i 0.0651079 0.0289879i
\(377\) −8.61803 + 26.5236i −0.443851 + 1.36603i
\(378\) 0 0
\(379\) −22.9894 + 16.7027i −1.18088 + 0.857962i −0.992271 0.124089i \(-0.960399\pi\)
−0.188613 + 0.982052i \(0.560399\pi\)
\(380\) −0.0210757 0.200522i −0.00108116 0.0102865i
\(381\) 0 0
\(382\) −2.32991 + 0.495239i −0.119209 + 0.0253386i
\(383\) 0.929106 8.83985i 0.0474751 0.451695i −0.944801 0.327645i \(-0.893745\pi\)
0.992276 0.124050i \(-0.0395884\pi\)
\(384\) 0 0
\(385\) −3.76243 0.536711i −0.191751 0.0273533i
\(386\) 2.52786 0.128665
\(387\) 0 0
\(388\) 2.87132 8.83702i 0.145769 0.448632i
\(389\) 9.06793 + 1.92745i 0.459762 + 0.0977255i 0.431969 0.901888i \(-0.357819\pi\)
0.0277927 + 0.999614i \(0.491152\pi\)
\(390\) 0 0
\(391\) 3.08958 + 1.37557i 0.156247 + 0.0695655i
\(392\) −2.99244 + 3.32344i −0.151141 + 0.167859i
\(393\) 0 0
\(394\) 39.3454 17.5177i 1.98219 0.882529i
\(395\) −0.201626 −0.0101449
\(396\) 0 0
\(397\) −25.2918 −1.26936 −0.634679 0.772776i \(-0.718868\pi\)
−0.634679 + 0.772776i \(0.718868\pi\)
\(398\) −4.86576 + 2.16638i −0.243899 + 0.108591i
\(399\) 0 0
\(400\) 15.7663 17.5102i 0.788313 0.875510i
\(401\) −13.6208 6.06437i −0.680191 0.302840i 0.0374052 0.999300i \(-0.488091\pi\)
−0.717596 + 0.696460i \(0.754757\pi\)
\(402\) 0 0
\(403\) 23.5092 + 4.99704i 1.17108 + 0.248920i
\(404\) −0.572949 + 1.76336i −0.0285053 + 0.0877302i
\(405\) 0 0
\(406\) −21.7082 −1.07736
\(407\) 10.0861 + 9.78044i 0.499951 + 0.484799i
\(408\) 0 0
\(409\) 3.02550 28.7857i 0.149601 1.42336i −0.619882 0.784695i \(-0.712820\pi\)
0.769483 0.638667i \(-0.220514\pi\)
\(410\) 3.59348 0.763818i 0.177469 0.0377223i
\(411\) 0 0
\(412\) 0.387613 + 3.68789i 0.0190963 + 0.181689i
\(413\) 12.9271 9.39205i 0.636099 0.462153i
\(414\) 0 0
\(415\) 1.50000 4.61653i 0.0736321 0.226616i
\(416\) −19.2668 + 8.57814i −0.944634 + 0.420578i
\(417\) 0 0
\(418\) −2.55518 3.80515i −0.124978 0.186116i
\(419\) 10.7533 + 18.6252i 0.525333 + 0.909903i 0.999565 + 0.0295028i \(0.00939240\pi\)
−0.474232 + 0.880400i \(0.657274\pi\)
\(420\) 0 0
\(421\) −2.49552 2.77155i −0.121624 0.135077i 0.679257 0.733900i \(-0.262302\pi\)
−0.800881 + 0.598823i \(0.795635\pi\)
\(422\) 5.63525 + 17.3435i 0.274320 + 0.844270i
\(423\) 0 0
\(424\) −13.3541 + 9.70232i −0.648533 + 0.471186i
\(425\) −2.93444 0.623735i −0.142341 0.0302556i
\(426\) 0 0
\(427\) −0.359337 + 3.41886i −0.0173895 + 0.165450i
\(428\) −0.0729490 0.126351i −0.00352612 0.00610743i
\(429\) 0 0
\(430\) 0.545085 0.944115i 0.0262863 0.0455293i
\(431\) 1.20820 + 0.877812i 0.0581971 + 0.0422827i 0.616503 0.787352i \(-0.288549\pi\)
−0.558306 + 0.829635i \(0.688549\pi\)
\(432\) 0 0
\(433\) −1.85410 5.70634i −0.0891025 0.274229i 0.896569 0.442903i \(-0.146051\pi\)
−0.985672 + 0.168674i \(0.946051\pi\)
\(434\) 1.95554 + 18.6057i 0.0938689 + 0.893103i
\(435\) 0 0
\(436\) 0 0
\(437\) −4.57163 + 0.971730i −0.218691 + 0.0464841i
\(438\) 0 0
\(439\) −8.35410 + 14.4697i −0.398720 + 0.690602i −0.993568 0.113235i \(-0.963879\pi\)
0.594849 + 0.803838i \(0.297212\pi\)
\(440\) −0.690983 + 2.74717i −0.0329413 + 0.130966i
\(441\) 0 0
\(442\) 5.04508 + 3.66547i 0.239970 + 0.174349i
\(443\) −0.585749 0.650540i −0.0278298 0.0309081i 0.729069 0.684440i \(-0.239953\pi\)
−0.756899 + 0.653532i \(0.773287\pi\)
\(444\) 0 0
\(445\) −3.30524 1.47159i −0.156683 0.0697599i
\(446\) −18.7846 8.36344i −0.889477 0.396021i
\(447\) 0 0
\(448\) 8.50345 + 9.44404i 0.401750 + 0.446189i
\(449\) 12.5623 + 9.12705i 0.592852 + 0.430732i 0.843334 0.537389i \(-0.180589\pi\)
−0.250483 + 0.968121i \(0.580589\pi\)
\(450\) 0 0
\(451\) 15.1287 12.6412i 0.712382 0.595253i
\(452\) 3.92705 6.80185i 0.184713 0.319932i
\(453\) 0 0
\(454\) −17.2330 + 3.66300i −0.808787 + 0.171913i
\(455\) −4.78154 + 5.31044i −0.224162 + 0.248957i
\(456\) 0 0
\(457\) −3.42836 32.6187i −0.160372 1.52584i −0.718174 0.695864i \(-0.755022\pi\)
0.557801 0.829974i \(-0.311645\pi\)
\(458\) 5.00000 + 15.3884i 0.233635 + 0.719054i
\(459\) 0 0
\(460\) −1.04508 0.759299i −0.0487273 0.0354025i
\(461\) 4.95492 8.58216i 0.230773 0.399711i −0.727263 0.686359i \(-0.759208\pi\)
0.958036 + 0.286648i \(0.0925411\pi\)
\(462\) 0 0
\(463\) −4.39919 7.61962i −0.204448 0.354114i 0.745509 0.666496i \(-0.232206\pi\)
−0.949957 + 0.312382i \(0.898873\pi\)
\(464\) −2.26913 + 21.5893i −0.105341 + 1.00226i
\(465\) 0 0
\(466\) −13.7278 2.91792i −0.635926 0.135170i
\(467\) 11.5172 8.36775i 0.532953 0.387213i −0.288508 0.957478i \(-0.593159\pi\)
0.821461 + 0.570264i \(0.193159\pi\)
\(468\) 0 0
\(469\) 9.79180 + 30.1360i 0.452143 + 1.39155i
\(470\) 0.255585 + 0.283856i 0.0117893 + 0.0130933i
\(471\) 0 0
\(472\) −5.95492 10.3142i −0.274097 0.474750i
\(473\) 0.216262 5.84630i 0.00994375 0.268813i
\(474\) 0 0
\(475\) 3.78747 1.68629i 0.173781 0.0773722i
\(476\) −0.354102 + 1.08981i −0.0162302 + 0.0499515i
\(477\) 0 0
\(478\) 22.9894 16.7027i 1.05151 0.763966i
\(479\) 1.76756 + 16.8172i 0.0807618 + 0.768397i 0.957695 + 0.287785i \(0.0929189\pi\)
−0.876933 + 0.480612i \(0.840414\pi\)
\(480\) 0 0
\(481\) 25.8391 5.49228i 1.17816 0.250426i
\(482\) −2.89630 + 27.5564i −0.131923 + 1.25516i
\(483\) 0 0
\(484\) −1.61738 6.60318i −0.0735173 0.300144i
\(485\) −5.74265 −0.260760
\(486\) 0 0
\(487\) 12.1074 37.2627i 0.548638 1.68853i −0.163540 0.986537i \(-0.552291\pi\)
0.712179 0.701998i \(-0.247709\pi\)
\(488\) 2.50631 + 0.532733i 0.113455 + 0.0241157i
\(489\) 0 0
\(490\) −1.12920 0.502754i −0.0510122 0.0227121i
\(491\) −17.5411 + 19.4814i −0.791619 + 0.879182i −0.994996 0.0999183i \(-0.968142\pi\)
0.203376 + 0.979101i \(0.434809\pi\)
\(492\) 0 0
\(493\) 2.52498 1.12419i 0.113719 0.0506311i
\(494\) −8.61803 −0.387744
\(495\) 0 0
\(496\) 18.7082 0.840023
\(497\) 39.9100 17.7691i 1.79021 0.797052i
\(498\) 0 0
\(499\) 1.71452 1.90416i 0.0767523 0.0852421i −0.703545 0.710650i \(-0.748401\pi\)
0.780298 + 0.625408i \(0.215068\pi\)
\(500\) 2.12512 + 0.946166i 0.0950384 + 0.0423138i
\(501\) 0 0
\(502\) −26.5864 5.65111i −1.18661 0.252221i
\(503\) −9.29180 + 28.5972i −0.414301 + 1.27509i 0.498574 + 0.866847i \(0.333857\pi\)
−0.912875 + 0.408239i \(0.866143\pi\)
\(504\) 0 0
\(505\) 1.14590 0.0509918
\(506\) −29.0714 4.14704i −1.29238 0.184359i
\(507\) 0 0
\(508\) −0.627171 + 5.96713i −0.0278262 + 0.264749i
\(509\) −20.9147 + 4.44556i −0.927029 + 0.197046i −0.646600 0.762829i \(-0.723810\pi\)
−0.280428 + 0.959875i \(0.590476\pi\)
\(510\) 0 0
\(511\) −0.387613 3.68789i −0.0171470 0.163143i
\(512\) 4.28115 3.11044i 0.189202 0.137463i
\(513\) 0 0
\(514\) −13.6631 + 42.0508i −0.602654 + 1.85478i
\(515\) 2.09366 0.932157i 0.0922577 0.0410758i
\(516\) 0 0
\(517\) 1.92472 + 0.705050i 0.0846489 + 0.0310081i
\(518\) 10.2812 + 17.8075i 0.451728 + 0.782416i
\(519\) 0 0
\(520\) 3.56395 + 3.95817i 0.156289 + 0.173577i
\(521\) 12.0000 + 36.9322i 0.525730 + 1.61803i 0.762869 + 0.646553i \(0.223790\pi\)
−0.237139 + 0.971476i \(0.576210\pi\)
\(522\) 0 0
\(523\) −28.2984 + 20.5600i −1.23740 + 0.899025i −0.997422 0.0717533i \(-0.977141\pi\)
−0.239979 + 0.970778i \(0.577141\pi\)
\(524\) 8.37520 + 1.78020i 0.365872 + 0.0777686i
\(525\) 0 0
\(526\) 0.113954 1.08420i 0.00496862 0.0472733i
\(527\) −1.19098 2.06284i −0.0518800 0.0898589i
\(528\) 0 0
\(529\) −3.47214 + 6.01392i −0.150962 + 0.261475i
\(530\) −3.69098 2.68166i −0.160326 0.116484i
\(531\) 0 0
\(532\) −0.489357 1.50609i −0.0212163 0.0652971i
\(533\) −3.87475 36.8658i −0.167834 1.59684i
\(534\) 0 0
\(535\) −0.0603355 + 0.0670093i −0.00260853 + 0.00289707i
\(536\) 23.1019 4.91047i 0.997851 0.212100i
\(537\) 0 0
\(538\) −19.7984 + 34.2918i −0.853569 + 1.47842i
\(539\) −6.61803 + 0.449028i −0.285059 + 0.0193410i
\(540\) 0 0
\(541\) 0.454915 + 0.330515i 0.0195583 + 0.0142100i 0.597521 0.801853i \(-0.296152\pi\)
−0.577963 + 0.816063i \(0.696152\pi\)
\(542\) 6.78893 + 7.53987i 0.291610 + 0.323865i
\(543\) 0 0
\(544\) 1.90947 + 0.850149i 0.0818676 + 0.0364498i
\(545\) 0 0
\(546\) 0 0
\(547\) 12.9691 + 14.4036i 0.554517 + 0.615854i 0.953606 0.301059i \(-0.0973400\pi\)
−0.399088 + 0.916912i \(0.630673\pi\)
\(548\) 0.736068 + 0.534785i 0.0314433 + 0.0228449i
\(549\) 0 0
\(550\) 25.9894 1.76336i 1.10819 0.0751897i
\(551\) −1.90983 + 3.30792i −0.0813615 + 0.140922i
\(552\) 0 0
\(553\) −1.54899 + 0.329247i −0.0658696 + 0.0140010i
\(554\) 11.3006 12.5506i 0.480118 0.533225i
\(555\) 0 0
\(556\) −0.378188 3.59821i −0.0160387 0.152598i
\(557\) 8.06231 + 24.8132i 0.341611 + 1.05137i 0.963373 + 0.268164i \(0.0864170\pi\)
−0.621762 + 0.783206i \(0.713583\pi\)
\(558\) 0 0
\(559\) −8.89919 6.46564i −0.376396 0.273467i
\(560\) −2.78115 + 4.81710i −0.117525 + 0.203560i
\(561\) 0 0
\(562\) 4.23607 + 7.33708i 0.178688 + 0.309496i
\(563\) −2.81062 + 26.7412i −0.118453 + 1.12701i 0.760247 + 0.649635i \(0.225078\pi\)
−0.878700 + 0.477374i \(0.841589\pi\)
\(564\) 0 0
\(565\) −4.74803 1.00922i −0.199751 0.0424584i
\(566\) 29.0344 21.0948i 1.22041 0.886679i
\(567\) 0 0
\(568\) −10.0623 30.9686i −0.422205 1.29941i
\(569\) 22.7965 + 25.3181i 0.955680 + 1.06139i 0.998058 + 0.0622889i \(0.0198400\pi\)
−0.0423778 + 0.999102i \(0.513493\pi\)
\(570\) 0 0
\(571\) 12.8435 + 22.2455i 0.537482 + 0.930946i 0.999039 + 0.0438355i \(0.0139577\pi\)
−0.461557 + 0.887111i \(0.652709\pi\)
\(572\) −12.0027 4.39674i −0.501856 0.183837i
\(573\) 0 0
\(574\) 26.3595 11.7360i 1.10023 0.489852i
\(575\) 8.20820 25.2623i 0.342306 1.05351i
\(576\) 0 0
\(577\) −12.3262 + 8.95554i −0.513148 + 0.372824i −0.814016 0.580842i \(-0.802723\pi\)
0.300868 + 0.953666i \(0.402723\pi\)
\(578\) 2.81062 + 26.7412i 0.116906 + 1.11229i
\(579\) 0 0
\(580\) −1.03266 + 0.219498i −0.0428788 + 0.00911417i
\(581\) 3.98511 37.9158i 0.165330 1.57301i
\(582\) 0 0
\(583\) −24.2378 3.45753i −1.00383 0.143196i
\(584\) −2.76393 −0.114372
\(585\) 0 0
\(586\) 8.97214 27.6134i 0.370636 1.14070i
\(587\) −23.7738 5.05328i −0.981251 0.208571i −0.310760 0.950489i \(-0.600583\pi\)
−0.670491 + 0.741917i \(0.733917\pi\)
\(588\) 0 0
\(589\) 3.00721 + 1.33889i 0.123910 + 0.0551682i
\(590\) 2.20264 2.44628i 0.0906813 0.100712i
\(591\) 0 0
\(592\) 18.7846 8.36344i 0.772042 0.343735i
\(593\) −29.2148 −1.19971 −0.599854 0.800110i \(-0.704775\pi\)
−0.599854 + 0.800110i \(0.704775\pi\)
\(594\) 0 0
\(595\) 0.708204 0.0290335
\(596\) 8.46903 3.77066i 0.346905 0.154452i
\(597\) 0 0
\(598\) −36.9459 + 41.0326i −1.51083 + 1.67795i
\(599\) −19.8314 8.82952i −0.810290 0.360764i −0.0405948 0.999176i \(-0.512925\pi\)
−0.769695 + 0.638411i \(0.779592\pi\)
\(600\) 0 0
\(601\) 19.3994 + 4.12347i 0.791319 + 0.168200i 0.585803 0.810454i \(-0.300779\pi\)
0.205516 + 0.978654i \(0.434113\pi\)
\(602\) 2.64590 8.14324i 0.107839 0.331894i
\(603\) 0 0
\(604\) 1.23607 0.0502949
\(605\) −3.57236 + 2.21177i −0.145237 + 0.0899211i
\(606\) 0 0
\(607\) 0.243158 2.31349i 0.00986948 0.0939018i −0.988478 0.151363i \(-0.951634\pi\)
0.998348 + 0.0574610i \(0.0183005\pi\)
\(608\) −2.82542 + 0.600562i −0.114586 + 0.0243560i
\(609\) 0 0
\(610\) 0.0740275 + 0.704324i 0.00299728 + 0.0285173i
\(611\) 3.11803 2.26538i 0.126142 0.0916476i
\(612\) 0 0
\(613\) 1.03444 3.18368i 0.0417807 0.128588i −0.927990 0.372604i \(-0.878465\pi\)
0.969771 + 0.244016i \(0.0784650\pi\)
\(614\) −28.9160 + 12.8742i −1.16695 + 0.519561i
\(615\) 0 0
\(616\) −0.822442 + 22.2334i −0.0331371 + 0.895809i
\(617\) −23.2082 40.1978i −0.934327 1.61830i −0.775829 0.630943i \(-0.782668\pi\)
−0.158498 0.987359i \(-0.550665\pi\)
\(618\) 0 0
\(619\) −20.8637 23.1715i −0.838584 0.931342i 0.159858 0.987140i \(-0.448896\pi\)
−0.998442 + 0.0557984i \(0.982230\pi\)
\(620\) 0.281153 + 0.865300i 0.0112914 + 0.0347513i
\(621\) 0 0
\(622\) −15.0172 + 10.9106i −0.602136 + 0.437477i
\(623\) −27.7954 5.90810i −1.11360 0.236703i
\(624\) 0 0
\(625\) −2.38668 + 22.7077i −0.0954672 + 0.908309i
\(626\) 22.5172 + 39.0010i 0.899969 + 1.55879i
\(627\) 0 0
\(628\) −3.00000 + 5.19615i −0.119713 + 0.207349i
\(629\) −2.11803 1.53884i −0.0844515 0.0613576i
\(630\) 0 0
\(631\) 3.93363 + 12.1065i 0.156595 + 0.481951i 0.998319 0.0579577i \(-0.0184589\pi\)
−0.841724 + 0.539908i \(0.818459\pi\)
\(632\) 0.123379 + 1.17387i 0.00490776 + 0.0466942i
\(633\) 0 0
\(634\) 27.4574 30.4945i 1.09047 1.21109i
\(635\) 3.62717 0.770979i 0.143940 0.0305954i
\(636\) 0 0
\(637\) −6.23607 + 10.8012i −0.247082 + 0.427959i
\(638\) −18.4164 + 15.3884i −0.729113 + 0.609233i
\(639\) 0 0
\(640\) 4.20820 + 3.05744i 0.166344 + 0.120856i
\(641\) −4.51171 5.01076i −0.178202 0.197913i 0.647426 0.762128i \(-0.275846\pi\)
−0.825628 + 0.564215i \(0.809179\pi\)
\(642\) 0 0
\(643\) −16.8437 7.49929i −0.664250 0.295743i 0.0467798 0.998905i \(-0.485104\pi\)
−0.711029 + 0.703162i \(0.751771\pi\)
\(644\) −9.26874 4.12671i −0.365239 0.162615i
\(645\) 0 0
\(646\) 0.571506 + 0.634721i 0.0224856 + 0.0249728i
\(647\) −2.59017 1.88187i −0.101830 0.0739839i 0.535705 0.844405i \(-0.320046\pi\)
−0.637535 + 0.770421i \(0.720046\pi\)
\(648\) 0 0
\(649\) 4.30902 17.1315i 0.169144 0.672471i
\(650\) 24.4894 42.4168i 0.960552 1.66372i
\(651\) 0 0
\(652\) 9.23146 1.96221i 0.361532 0.0768460i
\(653\) 14.6978 16.3236i 0.575170 0.638791i −0.383422 0.923573i \(-0.625254\pi\)
0.958592 + 0.284782i \(0.0919212\pi\)
\(654\) 0 0
\(655\) −0.553143 5.26281i −0.0216131 0.205635i
\(656\) −8.91641 27.4419i −0.348127 1.07143i
\(657\) 0 0
\(658\) 2.42705 + 1.76336i 0.0946163 + 0.0687428i
\(659\) −10.3262 + 17.8856i −0.402253 + 0.696723i −0.993997 0.109403i \(-0.965106\pi\)
0.591744 + 0.806126i \(0.298439\pi\)
\(660\) 0 0
\(661\) 10.5451 + 18.2646i 0.410156 + 0.710411i 0.994907 0.100802i \(-0.0321408\pi\)
−0.584750 + 0.811213i \(0.698807\pi\)
\(662\) 3.82180 36.3620i 0.148539 1.41325i
\(663\) 0 0
\(664\) −27.7954 5.90810i −1.07867 0.229279i
\(665\) −0.791796 + 0.575274i −0.0307045 + 0.0223082i
\(666\) 0 0
\(667\) 7.56231 + 23.2744i 0.292814 + 0.901188i
\(668\) −7.87161 8.74231i −0.304562 0.338250i
\(669\) 0 0
\(670\) 3.26393 + 5.65330i 0.126097 + 0.218406i
\(671\) 2.11870 + 3.15516i 0.0817915 + 0.121803i
\(672\) 0 0
\(673\) −13.1700 + 5.86368i −0.507668 + 0.226028i −0.644554 0.764558i \(-0.722957\pi\)
0.136887 + 0.990587i \(0.456290\pi\)
\(674\) −6.85410 + 21.0948i −0.264010 + 0.812540i
\(675\) 0 0
\(676\) −12.9443 + 9.40456i −0.497857 + 0.361714i
\(677\) −2.34898 22.3490i −0.0902786 0.858943i −0.942150 0.335192i \(-0.891199\pi\)
0.851871 0.523751i \(-0.175468\pi\)
\(678\) 0 0
\(679\) −44.1177 + 9.37751i −1.69308 + 0.359876i
\(680\) 0.0551768 0.524972i 0.00211593 0.0201318i
\(681\) 0 0
\(682\) 14.8481 + 14.3981i 0.568565 + 0.551333i
\(683\) −38.8885 −1.48803 −0.744014 0.668164i \(-0.767081\pi\)
−0.744014 + 0.668164i \(0.767081\pi\)
\(684\) 0 0
\(685\) 0.173762 0.534785i 0.00663911 0.0204331i
\(686\) 23.7401 + 5.04612i 0.906403 + 0.192662i
\(687\) 0 0
\(688\) −7.82206 3.48260i −0.298213 0.132773i
\(689\) −30.8031 + 34.2103i −1.17350 + 1.30331i
\(690\) 0 0
\(691\) −36.2752 + 16.1508i −1.37998 + 0.614405i −0.956561 0.291531i \(-0.905835\pi\)
−0.423414 + 0.905936i \(0.639169\pi\)
\(692\) 10.8885 0.413920
\(693\) 0 0
\(694\) −4.94427 −0.187682
\(695\) −2.04275 + 0.909491i −0.0774859 + 0.0344990i
\(696\) 0 0
\(697\) −2.45823 + 2.73014i −0.0931120 + 0.103411i
\(698\) 44.5286 + 19.8254i 1.68543 + 0.750403i
\(699\) 0 0
\(700\) 8.80333 + 1.87121i 0.332735 + 0.0707249i
\(701\) 15.3541 47.2551i 0.579916 1.78480i −0.0388752 0.999244i \(-0.512377\pi\)
0.618792 0.785555i \(-0.287623\pi\)
\(702\) 0 0
\(703\) 3.61803 0.136457
\(704\) 13.9086 + 1.98407i 0.524202 + 0.0747775i
\(705\) 0 0
\(706\) 0.258409 2.45859i 0.00972533 0.0925304i
\(707\) 8.80333 1.87121i 0.331083 0.0703739i
\(708\) 0 0
\(709\) −0.654072 6.22308i −0.0245642 0.233713i −0.999915 0.0130519i \(-0.995845\pi\)
0.975351 0.220661i \(-0.0708213\pi\)
\(710\) 7.28115 5.29007i 0.273257 0.198533i
\(711\) 0 0
\(712\) −6.54508 + 20.1437i −0.245287 + 0.754917i
\(713\) 19.2668 8.57814i 0.721548 0.321254i
\(714\) 0 0
\(715\) −0.292035 + 7.89469i −0.0109215 + 0.295245i
\(716\) −0.690983 1.19682i −0.0258232 0.0447272i
\(717\) 0 0
\(718\) −18.6611 20.7252i −0.696425 0.773459i
\(719\) −8.78115 27.0256i −0.327482 1.00789i −0.970308 0.241873i \(-0.922238\pi\)
0.642826 0.766012i \(-0.277762\pi\)
\(720\) 0 0
\(721\) 14.5623 10.5801i 0.542329 0.394025i
\(722\) 28.9163 + 6.14635i 1.07615 + 0.228743i
\(723\) 0 0
\(724\) 0.550918 5.24164i 0.0204747 0.194804i
\(725\) −10.8541 18.7999i −0.403111 0.698209i
\(726\) 0 0
\(727\) −16.0729 + 27.8392i −0.596113 + 1.03250i 0.397276 + 0.917699i \(0.369956\pi\)
−0.993389 + 0.114798i \(0.963378\pi\)
\(728\) 33.8435 + 24.5887i 1.25432 + 0.911318i
\(729\) 0 0
\(730\) −0.236068 0.726543i −0.00873727 0.0268905i
\(731\) 0.113954 + 1.08420i 0.00421473 + 0.0401005i
\(732\) 0 0
\(733\) −16.2544 + 18.0523i −0.600369 + 0.666778i −0.964350 0.264629i \(-0.914751\pi\)
0.363981 + 0.931406i \(0.381417\pi\)
\(734\) 23.0474 4.89888i 0.850696 0.180821i
\(735\) 0 0
\(736\) −9.25329 + 16.0272i −0.341081 + 0.590769i
\(737\) 29.6697 + 18.6251i 1.09290 + 0.686064i
\(738\) 0 0
\(739\) 20.2254 + 14.6946i 0.744004 + 0.540551i 0.893963 0.448142i \(-0.147914\pi\)
−0.149958 + 0.988692i \(0.547914\pi\)
\(740\) 0.669131 + 0.743145i 0.0245977 + 0.0273185i
\(741\) 0 0
\(742\) −32.7349 14.5745i −1.20174 0.535047i
\(743\) 11.7113 + 5.21423i 0.429647 + 0.191291i 0.610155 0.792282i \(-0.291107\pi\)
−0.180507 + 0.983574i \(0.557774\pi\)
\(744\) 0 0
\(745\) −3.83378 4.25784i −0.140459 0.155995i
\(746\) −29.3435 21.3193i −1.07434 0.780554i
\(747\) 0 0
\(748\) 0.472136 + 1.17557i 0.0172630 + 0.0429831i
\(749\) −0.354102 + 0.613323i −0.0129386 + 0.0224103i
\(750\) 0 0
\(751\) 51.7665 11.0033i 1.88899 0.401516i 0.890424 0.455131i \(-0.150408\pi\)
0.998562 + 0.0536148i \(0.0170743\pi\)
\(752\) 2.00739 2.22943i 0.0732020 0.0812991i
\(753\) 0 0
\(754\) 4.71681 + 44.8774i 0.171776 + 1.63434i
\(755\) −0.236068 0.726543i −0.00859139 0.0264416i
\(756\) 0 0
\(757\) 12.8992 + 9.37181i 0.468829 + 0.340624i 0.796985 0.603999i \(-0.206427\pi\)
−0.328156 + 0.944624i \(0.606427\pi\)
\(758\) −22.9894 + 39.8187i −0.835011 + 1.44628i
\(759\) 0 0
\(760\) 0.364745 + 0.631757i 0.0132307 + 0.0229162i
\(761\) −0.510992 + 4.86176i −0.0185234 + 0.176239i −0.999872 0.0159979i \(-0.994907\pi\)
0.981349 + 0.192237i \(0.0615741\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.736068 + 0.534785i −0.0266300 + 0.0193478i
\(765\) 0 0
\(766\) −4.44427 13.6781i −0.160578 0.494208i
\(767\) −22.2250 24.6834i −0.802499 0.891266i
\(768\) 0 0
\(769\) 23.8435 + 41.2981i 0.859817 + 1.48925i 0.872103 + 0.489322i \(0.162756\pi\)
−0.0122858 + 0.999925i \(0.503911\pi\)
\(770\) −5.91464 + 1.68277i −0.213149 + 0.0606427i
\(771\) 0 0
\(772\) 0.882081 0.392728i 0.0317468 0.0141346i
\(773\) 15.2188 46.8388i 0.547384 1.68467i −0.167870 0.985809i \(-0.553689\pi\)
0.715253 0.698865i \(-0.246311\pi\)
\(774\) 0 0
\(775\) −15.1353 + 10.9964i −0.543674 + 0.395003i
\(776\) 3.51404 + 33.4339i 0.126147 + 1.20021i
\(777\) 0 0
\(778\) 14.6722 3.11868i 0.526024 0.111810i
\(779\) 0.530693 5.04920i 0.0190140 0.180906i
\(780\) 0 0
\(781\) 21.2620 43.3658i 0.760816 1.55175i
\(782\) 5.47214 0.195683
\(783\) 0 0
\(784\) −3.00000 + 9.23305i −0.107143 + 0.329752i
\(785\) 3.62717 + 0.770979i 0.129459 + 0.0275174i
\(786\) 0 0
\(787\) −21.6585 9.64300i −0.772043 0.343736i −0.0173805 0.999849i \(-0.505533\pi\)
−0.754662 + 0.656113i \(0.772199\pi\)
\(788\) 11.0078 12.2254i 0.392135 0.435511i
\(789\) 0 0
\(790\) −0.298033 + 0.132693i −0.0106035 + 0.00472100i
\(791\) −38.1246 −1.35556
\(792\) 0 0
\(793\) 7.14590 0.253758
\(794\) −37.3850 + 16.6449i −1.32674 + 0.590705i
\(795\) 0 0
\(796\) −1.36131 + 1.51188i −0.0482503 + 0.0535873i
\(797\) 13.9188 + 6.19707i 0.493031 + 0.219511i 0.638164 0.769901i \(-0.279694\pi\)
−0.145133 + 0.989412i \(0.546361\pi\)
\(798\) 0 0
\(799\) −0.373619 0.0794152i −0.0132177 0.00280951i
\(800\) 5.07295 15.6129i 0.179356 0.552000i
\(801\) 0 0
\(802\) −24.1246 −0.851870
\(803\) −2.94309 2.85390i −0.103859 0.100712i
\(804\) 0 0
\(805\) −0.655447 + 6.23616i −0.0231015 + 0.219796i
\(806\) 38.0387 8.08538i 1.33986 0.284795i
\(807\) 0 0
\(808\) −0.701198 6.67146i −0.0246681 0.234701i
\(809\) −20.4894 + 14.8864i −0.720367 + 0.523378i −0.886502 0.462726i \(-0.846872\pi\)
0.166134 + 0.986103i \(0.446872\pi\)
\(810\) 0 0
\(811\) 14.1353 43.5038i 0.496356 1.52763i −0.318477 0.947931i \(-0.603171\pi\)
0.814833 0.579696i \(-0.196829\pi\)
\(812\) −7.57493 + 3.37258i −0.265828 + 0.118354i
\(813\) 0 0
\(814\) 21.3454 + 7.81912i 0.748157 + 0.274060i
\(815\) −2.91641 5.05137i −0.102157 0.176942i
\(816\) 0 0
\(817\) −1.00810 1.11961i −0.0352689 0.0391700i
\(818\) −14.4721 44.5407i −0.506006 1.55733i
\(819\) 0 0
\(820\) 1.13525 0.824811i 0.0396448 0.0288036i
\(821\) −13.2868 2.82419i −0.463711 0.0985648i −0.0298691 0.999554i \(-0.509509\pi\)
−0.433842 + 0.900989i \(0.642842\pi\)
\(822\) 0 0
\(823\) 2.77292 26.3825i 0.0966578 0.919638i −0.833510 0.552504i \(-0.813672\pi\)
0.930168 0.367134i \(-0.119661\pi\)
\(824\) −6.70820 11.6190i −0.233691 0.404765i
\(825\) 0 0
\(826\) 12.9271 22.3903i 0.449790 0.779058i
\(827\) −10.4164 7.56796i −0.362214 0.263164i 0.391761 0.920067i \(-0.371866\pi\)
−0.753975 + 0.656903i \(0.771866\pi\)
\(828\) 0 0
\(829\) −13.1910 40.5977i −0.458142 1.41002i −0.867407 0.497600i \(-0.834215\pi\)
0.409265 0.912416i \(-0.365785\pi\)
\(830\) −0.820977 7.81108i −0.0284965 0.271126i
\(831\) 0 0
\(832\) 17.6760 19.6312i 0.612806 0.680590i
\(833\) 1.20906 0.256993i 0.0418913 0.00890428i
\(834\) 0 0
\(835\) −3.63525 + 6.29645i −0.125803 + 0.217898i
\(836\) −1.48278 0.930812i −0.0512830 0.0321928i
\(837\) 0 0
\(838\) 28.1525 + 20.4540i 0.972511 + 0.706571i
\(839\) −15.5853 17.3092i −0.538063 0.597579i 0.411402 0.911454i \(-0.365039\pi\)
−0.949464 + 0.313875i \(0.898373\pi\)
\(840\) 0 0
\(841\) −8.22191 3.66063i −0.283514 0.126229i
\(842\) −5.51274 2.45443i −0.189981 0.0845852i
\(843\) 0 0
\(844\) 4.66087 + 5.17642i 0.160434 + 0.178180i
\(845\) 8.00000 + 5.81234i 0.275208 + 0.199951i
\(846\) 0 0
\(847\) −23.8328 + 22.8254i −0.818905 + 0.784289i
\(848\) −17.9164 + 31.0321i −0.615252 + 1.06565i
\(849\) 0 0
\(850\) −4.74803 + 1.00922i −0.162856 + 0.0346161i
\(851\) 15.5107 17.2263i 0.531699 0.590512i
\(852\) 0 0
\(853\) −0.830403 7.90075i −0.0284324 0.270517i −0.999497 0.0317011i \(-0.989908\pi\)
0.971065 0.238816i \(-0.0767591\pi\)
\(854\) 1.71885 + 5.29007i 0.0588177 + 0.181022i
\(855\) 0 0
\(856\) 0.427051 + 0.310271i 0.0145963 + 0.0106048i
\(857\) 20.8607 36.1318i 0.712587 1.23424i −0.251296 0.967910i \(-0.580857\pi\)
0.963883 0.266327i \(-0.0858101\pi\)
\(858\) 0 0
\(859\) −21.4443 37.1426i −0.731669 1.26729i −0.956169 0.292814i \(-0.905408\pi\)
0.224500 0.974474i \(-0.427925\pi\)
\(860\) 0.0435265 0.414127i 0.00148424 0.0141216i
\(861\) 0 0
\(862\) 2.36360 + 0.502399i 0.0805047 + 0.0171118i
\(863\) 19.3262 14.0413i 0.657873 0.477973i −0.208071 0.978114i \(-0.566719\pi\)
0.865944 + 0.500141i \(0.166719\pi\)
\(864\) 0 0
\(865\) −2.07953 6.40013i −0.0707060 0.217611i
\(866\) −6.49606 7.21460i −0.220745 0.245162i
\(867\) 0 0
\(868\) 3.57295 + 6.18853i 0.121274 + 0.210052i
\(869\) −1.08071 + 1.37736i −0.0366604 + 0.0467237i
\(870\) 0 0
\(871\) 60.1727 26.7906i 2.03888 0.907766i
\(872\) 0 0
\(873\) 0 0
\(874\) −6.11803 + 4.44501i −0.206946 + 0.150355i
\(875\) −1.18031 11.2299i −0.0399019 0.379641i
\(876\) 0 0
\(877\) 19.9703 4.24481i 0.674348 0.143337i 0.142005 0.989866i \(-0.454645\pi\)
0.532343 + 0.846529i \(0.321312\pi\)
\(878\) −2.82587 + 26.8863i −0.0953684 + 0.907370i
\(879\) 0 0
\(880\) 1.05530 + 6.05813i 0.0355742 + 0.204220i
\(881\) 25.0902 0.845309 0.422655 0.906291i \(-0.361098\pi\)
0.422655 + 0.906291i \(0.361098\pi\)
\(882\) 0 0
\(883\) 11.5623 35.5851i 0.389103 1.19753i −0.544358 0.838853i \(-0.683226\pi\)
0.933460 0.358681i \(-0.116774\pi\)
\(884\) 2.32991 + 0.495239i 0.0783635 + 0.0166567i
\(885\) 0 0
\(886\) −1.29395 0.576105i −0.0434712 0.0193546i
\(887\) 2.00739 2.22943i 0.0674016 0.0748571i −0.708501 0.705710i \(-0.750628\pi\)
0.775902 + 0.630853i \(0.217295\pi\)
\(888\) 0 0
\(889\) 26.6067 11.8460i 0.892359 0.397304i
\(890\) −5.85410 −0.196230
\(891\) 0 0
\(892\) −7.85410 −0.262975
\(893\) 0.482228 0.214702i 0.0161371 0.00718472i
\(894\) 0 0
\(895\) −0.571506 + 0.634721i −0.0191033 + 0.0212164i
\(896\) 37.3221 + 16.6169i 1.24684 + 0.555130i
\(897\) 0 0
\(898\) 24.5756 + 5.22370i 0.820098 + 0.174317i
\(899\) 5.32624 16.3925i 0.177640 0.546720i
\(900\) 0 0
\(901\) 4.56231 0.151992
\(902\) 14.0430 28.6420i 0.467582 0.953675i
\(903\) 0 0
\(904\) −2.97032 + 28.2607i −0.0987915 + 0.939938i
\(905\) −3.18617 + 0.677242i −0.105912 + 0.0225123i
\(906\) 0 0
\(907\) −0.415889 3.95692i −0.0138094 0.131387i 0.985445 0.169994i \(-0.0543748\pi\)
−0.999254 + 0.0386065i \(0.987708\pi\)
\(908\) −5.44427 + 3.95550i −0.180675 + 0.131268i
\(909\) 0 0
\(910\) −3.57295 + 10.9964i −0.118442 + 0.364527i
\(911\) 32.8367 14.6199i 1.08793 0.484377i 0.217194 0.976129i \(-0.430310\pi\)
0.870736 + 0.491751i \(0.163643\pi\)
\(912\) 0 0
\(913\) −23.4967 34.9912i −0.777629 1.15804i
\(914\) −26.5344 45.9590i −0.877681 1.52019i
\(915\) 0 0
\(916\) 4.13545 + 4.59289i 0.136639 + 0.151753i
\(917\) −12.8435 39.5281i −0.424128 1.30533i
\(918\) 0 0
\(919\) 37.9894 27.6009i 1.25315 0.910469i 0.254753 0.967006i \(-0.418006\pi\)
0.998400 + 0.0565371i \(0.0180059\pi\)
\(920\) 4.57163 + 0.971730i 0.150722 + 0.0320370i
\(921\) 0 0
\(922\) 1.67606 15.9466i 0.0551980 0.525173i
\(923\) −45.4058 78.6451i −1.49455 2.58863i
\(924\) 0 0
\(925\) −10.2812 + 17.8075i −0.338042 + 0.585506i
\(926\) −11.5172 8.36775i −0.378479 0.274981i
\(927\) 0 0
\(928\) 4.67376 + 14.3844i 0.153424 + 0.472190i
\(929\) −0.301935 2.87272i −0.00990617 0.0942509i 0.988452 0.151536i \(-0.0484221\pi\)
−0.998358 + 0.0572856i \(0.981755\pi\)
\(930\) 0 0
\(931\) −1.14301 + 1.26944i −0.0374607 + 0.0416043i
\(932\) −5.24354 + 1.11455i −0.171758 + 0.0365082i
\(933\) 0 0
\(934\) 11.5172 19.9484i 0.376855 0.652732i
\(935\) 0.600813 0.502029i 0.0196487 0.0164181i
\(936\) 0 0
\(937\) −26.3713 19.1599i −0.861514 0.625926i 0.0667827 0.997768i \(-0.478727\pi\)
−0.928296 + 0.371841i \(0.878727\pi\)
\(938\) 34.3067 + 38.1014i 1.12015 + 1.24406i
\(939\) 0 0
\(940\) 0.133284 + 0.0593421i 0.00434726 + 0.00193553i
\(941\) 30.7236 + 13.6790i 1.00156 + 0.445924i 0.840961 0.541096i \(-0.181990\pi\)
0.160600 + 0.987020i \(0.448657\pi\)
\(942\) 0 0
\(943\) −21.7654 24.1729i −0.708779 0.787178i
\(944\) −20.9164 15.1967i −0.680771 0.494609i
\(945\) 0 0
\(946\) −3.52786 8.78402i −0.114701 0.285593i
\(947\) −1.33688 + 2.31555i −0.0434428 + 0.0752451i −0.886929 0.461905i \(-0.847166\pi\)
0.843486 + 0.537151i \(0.180499\pi\)
\(948\) 0 0
\(949\) −7.53976 + 1.60263i −0.244751 + 0.0520234i
\(950\) 4.48866 4.98517i 0.145632 0.161740i
\(951\) 0 0
\(952\) −0.433364 4.12319i −0.0140454 0.133633i
\(953\) 18.5967 + 57.2349i 0.602408 + 1.85402i 0.513714 + 0.857961i \(0.328269\pi\)
0.0886937 + 0.996059i \(0.471731\pi\)
\(954\) 0 0
\(955\) 0.454915 + 0.330515i 0.0147207 + 0.0106952i
\(956\) 5.42705 9.39993i 0.175523 0.304015i
\(957\) 0 0
\(958\) 13.6803 + 23.6950i 0.441992 + 0.765552i
\(959\) 0.461640 4.39221i 0.0149071 0.141832i
\(960\) 0 0
\(961\) 15.7931 + 3.35692i 0.509454 + 0.108288i
\(962\) 34.5795 25.1235i 1.11489 0.810014i
\(963\) 0 0
\(964\) 3.27051 + 10.0656i 0.105336 + 0.324191i
\(965\) −0.399302 0.443470i −0.0128540 0.0142758i
\(966\) 0 0
\(967\) −12.8435 22.2455i −0.413018 0.715368i 0.582200 0.813045i \(-0.302192\pi\)
−0.995218 + 0.0976776i \(0.968859\pi\)
\(968\) 15.0630 + 19.4450i 0.484143 + 0.624985i
\(969\) 0 0
\(970\) −8.48848 + 3.77931i −0.272549 + 0.121346i
\(971\) −10.4377 + 32.1239i −0.334962 + 1.03091i 0.631779 + 0.775148i \(0.282325\pi\)
−0.966741 + 0.255757i \(0.917675\pi\)
\(972\) 0 0
\(973\) −14.2082 + 10.3229i −0.455494 + 0.330936i
\(974\) −6.62659 63.0478i −0.212330 2.02018i
\(975\) 0 0
\(976\) 5.44076 1.15647i 0.174154 0.0370177i
\(977\) 5.15960 49.0903i 0.165070 1.57054i −0.527733 0.849410i \(-0.676958\pi\)
0.692803 0.721127i \(-0.256375\pi\)
\(978\) 0 0
\(979\) −27.7687 + 14.6913i −0.887491 + 0.469536i
\(980\) −0.472136 −0.0150818
\(981\) 0 0
\(982\) −13.1074 + 40.3404i −0.418274 + 1.28731i
\(983\) −34.5335 7.34031i −1.10145 0.234120i −0.378897 0.925439i \(-0.623696\pi\)
−0.722549 + 0.691319i \(0.757030\pi\)
\(984\) 0 0
\(985\) −9.28819 4.13537i −0.295946 0.131764i
\(986\) 2.99244 3.32344i 0.0952988 0.105840i
\(987\) 0 0
\(988\) −3.00721 + 1.33889i −0.0956719 + 0.0425959i
\(989\) −9.65248 −0.306931
\(990\) 0 0
\(991\) −12.2705 −0.389786 −0.194893 0.980825i \(-0.562436\pi\)
−0.194893 + 0.980825i \(0.562436\pi\)
\(992\) 11.9076 5.30159i 0.378065 0.168325i
\(993\) 0 0
\(994\) 47.2988 52.5306i 1.50023 1.66617i
\(995\) 1.14865 + 0.511412i 0.0364147 + 0.0162129i
\(996\) 0 0
\(997\) −33.2362 7.06457i −1.05260 0.223737i −0.351050 0.936357i \(-0.614175\pi\)
−0.701551 + 0.712619i \(0.747509\pi\)
\(998\) 1.28115 3.94298i 0.0405542 0.124813i
\(999\) 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.n.d.136.1 8
3.2 odd 2 891.2.n.a.136.1 8
9.2 odd 6 99.2.f.b.37.1 4
9.4 even 3 inner 891.2.n.d.433.1 8
9.5 odd 6 891.2.n.a.433.1 8
9.7 even 3 33.2.e.a.4.1 4
11.3 even 5 inner 891.2.n.d.784.1 8
33.14 odd 10 891.2.n.a.784.1 8
36.7 odd 6 528.2.y.f.433.1 4
45.7 odd 12 825.2.bx.b.499.2 8
45.34 even 6 825.2.n.f.301.1 4
45.43 odd 12 825.2.bx.b.499.1 8
99.7 odd 30 363.2.e.c.130.1 4
99.14 odd 30 891.2.n.a.190.1 8
99.16 even 15 363.2.a.h.1.2 2
99.25 even 15 33.2.e.a.25.1 yes 4
99.38 odd 30 1089.2.a.m.1.1 2
99.43 odd 6 363.2.e.j.202.1 4
99.47 odd 30 99.2.f.b.91.1 4
99.52 odd 30 363.2.e.j.124.1 4
99.58 even 15 inner 891.2.n.d.190.1 8
99.61 odd 30 363.2.a.e.1.1 2
99.70 even 15 363.2.e.h.130.1 4
99.79 odd 30 363.2.e.c.148.1 4
99.83 even 30 1089.2.a.s.1.2 2
99.97 even 15 363.2.e.h.148.1 4
396.115 odd 30 5808.2.a.bl.1.2 2
396.223 odd 30 528.2.y.f.289.1 4
396.259 even 30 5808.2.a.bm.1.2 2
495.124 even 30 825.2.n.f.751.1 4
495.214 even 30 9075.2.a.x.1.1 2
495.223 odd 60 825.2.bx.b.124.2 8
495.259 odd 30 9075.2.a.bv.1.2 2
495.322 odd 60 825.2.bx.b.124.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.4.1 4 9.7 even 3
33.2.e.a.25.1 yes 4 99.25 even 15
99.2.f.b.37.1 4 9.2 odd 6
99.2.f.b.91.1 4 99.47 odd 30
363.2.a.e.1.1 2 99.61 odd 30
363.2.a.h.1.2 2 99.16 even 15
363.2.e.c.130.1 4 99.7 odd 30
363.2.e.c.148.1 4 99.79 odd 30
363.2.e.h.130.1 4 99.70 even 15
363.2.e.h.148.1 4 99.97 even 15
363.2.e.j.124.1 4 99.52 odd 30
363.2.e.j.202.1 4 99.43 odd 6
528.2.y.f.289.1 4 396.223 odd 30
528.2.y.f.433.1 4 36.7 odd 6
825.2.n.f.301.1 4 45.34 even 6
825.2.n.f.751.1 4 495.124 even 30
825.2.bx.b.124.1 8 495.322 odd 60
825.2.bx.b.124.2 8 495.223 odd 60
825.2.bx.b.499.1 8 45.43 odd 12
825.2.bx.b.499.2 8 45.7 odd 12
891.2.n.a.136.1 8 3.2 odd 2
891.2.n.a.190.1 8 99.14 odd 30
891.2.n.a.433.1 8 9.5 odd 6
891.2.n.a.784.1 8 33.14 odd 10
891.2.n.d.136.1 8 1.1 even 1 trivial
891.2.n.d.190.1 8 99.58 even 15 inner
891.2.n.d.433.1 8 9.4 even 3 inner
891.2.n.d.784.1 8 11.3 even 5 inner
1089.2.a.m.1.1 2 99.38 odd 30
1089.2.a.s.1.2 2 99.83 even 30
5808.2.a.bl.1.2 2 396.115 odd 30
5808.2.a.bm.1.2 2 396.259 even 30
9075.2.a.x.1.1 2 495.214 even 30
9075.2.a.bv.1.2 2 495.259 odd 30