Properties

Label 891.2.f.e.730.8
Level $891$
Weight $2$
Character 891.730
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
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([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), 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: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 730.8
Character \(\chi\) \(=\) 891.730
Dual form 891.2.f.e.487.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.25085 + 0.908796i) q^{2} +(0.120683 + 0.371424i) q^{4} +(0.478964 - 0.347988i) q^{5} +(0.223095 + 0.686616i) q^{7} +(0.768973 - 2.36665i) q^{8} +0.915362 q^{10} +(0.539627 + 3.27243i) q^{11} +(1.27417 + 0.925741i) q^{13} +(-0.344935 + 1.06160i) q^{14} +(3.74458 - 2.72060i) q^{16} +(3.71501 - 2.69911i) q^{17} +(0.775200 - 2.38582i) q^{19} +(0.187054 + 0.135902i) q^{20} +(-2.29898 + 4.58373i) q^{22} +4.45200 q^{23} +(-1.43677 + 4.42194i) q^{25} +(0.752490 + 2.31593i) q^{26} +(-0.228102 + 0.165726i) q^{28} +(-2.15651 - 6.63706i) q^{29} +(7.38490 + 5.36545i) q^{31} +2.17948 q^{32} +7.09986 q^{34} +(0.345788 + 0.251230i) q^{35} +(0.893583 + 2.75017i) q^{37} +(3.13788 - 2.27981i) q^{38} +(-0.455256 - 1.40114i) q^{40} +(0.356643 - 1.09763i) q^{41} -4.21448 q^{43} +(-1.15033 + 0.595357i) q^{44} +(5.56879 + 4.04596i) q^{46} +(0.0703185 - 0.216418i) q^{47} +(5.24145 - 3.80814i) q^{49} +(-5.81583 + 4.22545i) q^{50} +(-0.190071 + 0.584979i) q^{52} +(-4.61430 - 3.35249i) q^{53} +(1.39723 + 1.37959i) q^{55} +1.79654 q^{56} +(3.33426 - 10.2618i) q^{58} +(-2.20439 - 6.78441i) q^{59} +(-3.68827 + 2.67969i) q^{61} +(4.36131 + 13.4227i) q^{62} +(-4.76295 - 3.46049i) q^{64} +0.932429 q^{65} -8.09142 q^{67} +(1.45085 + 1.05411i) q^{68} +(0.204213 + 0.628502i) q^{70} +(-9.95852 + 7.23528i) q^{71} +(4.78461 + 14.7255i) q^{73} +(-1.38160 + 4.25213i) q^{74} +0.979704 q^{76} +(-2.12651 + 1.10058i) q^{77} +(11.8275 + 8.59316i) q^{79} +(0.846785 - 2.60614i) q^{80} +(1.44363 - 1.04886i) q^{82} +(-5.62510 + 4.08687i) q^{83} +(0.840097 - 2.58555i) q^{85} +(-5.27169 - 3.83010i) q^{86} +(8.15967 + 1.23930i) q^{88} -12.4803 q^{89} +(-0.351367 + 1.08140i) q^{91} +(0.537280 + 1.65358i) q^{92} +(0.284638 - 0.206802i) q^{94} +(-0.458943 - 1.41248i) q^{95} +(-11.4722 - 8.33507i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.25085 + 0.908796i 0.884485 + 0.642616i 0.934434 0.356136i \(-0.115906\pi\)
−0.0499492 + 0.998752i \(0.515906\pi\)
\(3\) 0 0
\(4\) 0.120683 + 0.371424i 0.0603415 + 0.185712i
\(5\) 0.478964 0.347988i 0.214199 0.155625i −0.475512 0.879709i \(-0.657737\pi\)
0.689712 + 0.724084i \(0.257737\pi\)
\(6\) 0 0
\(7\) 0.223095 + 0.686616i 0.0843220 + 0.259516i 0.984324 0.176369i \(-0.0564353\pi\)
−0.900002 + 0.435886i \(0.856435\pi\)
\(8\) 0.768973 2.36665i 0.271873 0.836739i
\(9\) 0 0
\(10\) 0.915362 0.289463
\(11\) 0.539627 + 3.27243i 0.162704 + 0.986675i
\(12\) 0 0
\(13\) 1.27417 + 0.925741i 0.353392 + 0.256754i 0.750291 0.661108i \(-0.229914\pi\)
−0.396899 + 0.917862i \(0.629914\pi\)
\(14\) −0.344935 + 1.06160i −0.0921878 + 0.283725i
\(15\) 0 0
\(16\) 3.74458 2.72060i 0.936145 0.680149i
\(17\) 3.71501 2.69911i 0.901022 0.654631i −0.0377065 0.999289i \(-0.512005\pi\)
0.938728 + 0.344658i \(0.112005\pi\)
\(18\) 0 0
\(19\) 0.775200 2.38582i 0.177843 0.547345i −0.821909 0.569619i \(-0.807091\pi\)
0.999752 + 0.0222743i \(0.00709072\pi\)
\(20\) 0.187054 + 0.135902i 0.0418265 + 0.0303887i
\(21\) 0 0
\(22\) −2.29898 + 4.58373i −0.490144 + 0.977255i
\(23\) 4.45200 0.928306 0.464153 0.885755i \(-0.346359\pi\)
0.464153 + 0.885755i \(0.346359\pi\)
\(24\) 0 0
\(25\) −1.43677 + 4.42194i −0.287355 + 0.884387i
\(26\) 0.752490 + 2.31593i 0.147576 + 0.454191i
\(27\) 0 0
\(28\) −0.228102 + 0.165726i −0.0431072 + 0.0313192i
\(29\) −2.15651 6.63706i −0.400454 1.23247i −0.924632 0.380863i \(-0.875627\pi\)
0.524177 0.851609i \(-0.324373\pi\)
\(30\) 0 0
\(31\) 7.38490 + 5.36545i 1.32637 + 0.963662i 0.999829 + 0.0184785i \(0.00588222\pi\)
0.326538 + 0.945184i \(0.394118\pi\)
\(32\) 2.17948 0.385282
\(33\) 0 0
\(34\) 7.09986 1.21762
\(35\) 0.345788 + 0.251230i 0.0584489 + 0.0424656i
\(36\) 0 0
\(37\) 0.893583 + 2.75017i 0.146904 + 0.452125i 0.997251 0.0740981i \(-0.0236078\pi\)
−0.850347 + 0.526223i \(0.823608\pi\)
\(38\) 3.13788 2.27981i 0.509032 0.369833i
\(39\) 0 0
\(40\) −0.455256 1.40114i −0.0719824 0.221539i
\(41\) 0.356643 1.09763i 0.0556982 0.171421i −0.919337 0.393470i \(-0.871274\pi\)
0.975036 + 0.222049i \(0.0712744\pi\)
\(42\) 0 0
\(43\) −4.21448 −0.642702 −0.321351 0.946960i \(-0.604137\pi\)
−0.321351 + 0.946960i \(0.604137\pi\)
\(44\) −1.15033 + 0.595357i −0.173419 + 0.0897534i
\(45\) 0 0
\(46\) 5.56879 + 4.04596i 0.821073 + 0.596544i
\(47\) 0.0703185 0.216418i 0.0102570 0.0315678i −0.945797 0.324758i \(-0.894717\pi\)
0.956054 + 0.293191i \(0.0947170\pi\)
\(48\) 0 0
\(49\) 5.24145 3.80814i 0.748778 0.544019i
\(50\) −5.81583 + 4.22545i −0.822482 + 0.597568i
\(51\) 0 0
\(52\) −0.190071 + 0.584979i −0.0263581 + 0.0811220i
\(53\) −4.61430 3.35249i −0.633823 0.460500i 0.223899 0.974612i \(-0.428121\pi\)
−0.857723 + 0.514113i \(0.828121\pi\)
\(54\) 0 0
\(55\) 1.39723 + 1.37959i 0.188402 + 0.186024i
\(56\) 1.79654 0.240072
\(57\) 0 0
\(58\) 3.33426 10.2618i 0.437810 1.34744i
\(59\) −2.20439 6.78441i −0.286987 0.883255i −0.985796 0.167947i \(-0.946286\pi\)
0.698809 0.715308i \(-0.253714\pi\)
\(60\) 0 0
\(61\) −3.68827 + 2.67969i −0.472235 + 0.343099i −0.798312 0.602244i \(-0.794273\pi\)
0.326077 + 0.945343i \(0.394273\pi\)
\(62\) 4.36131 + 13.4227i 0.553887 + 1.70469i
\(63\) 0 0
\(64\) −4.76295 3.46049i −0.595369 0.432561i
\(65\) 0.932429 0.115654
\(66\) 0 0
\(67\) −8.09142 −0.988524 −0.494262 0.869313i \(-0.664562\pi\)
−0.494262 + 0.869313i \(0.664562\pi\)
\(68\) 1.45085 + 1.05411i 0.175942 + 0.127829i
\(69\) 0 0
\(70\) 0.204213 + 0.628502i 0.0244081 + 0.0751204i
\(71\) −9.95852 + 7.23528i −1.18186 + 0.858670i −0.992380 0.123215i \(-0.960680\pi\)
−0.189478 + 0.981885i \(0.560680\pi\)
\(72\) 0 0
\(73\) 4.78461 + 14.7255i 0.559996 + 1.72349i 0.682370 + 0.731007i \(0.260950\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(74\) −1.38160 + 4.25213i −0.160608 + 0.494300i
\(75\) 0 0
\(76\) 0.979704 0.112380
\(77\) −2.12651 + 1.10058i −0.242339 + 0.125423i
\(78\) 0 0
\(79\) 11.8275 + 8.59316i 1.33069 + 0.966806i 0.999732 + 0.0231619i \(0.00737332\pi\)
0.330962 + 0.943644i \(0.392627\pi\)
\(80\) 0.846785 2.60614i 0.0946734 0.291375i
\(81\) 0 0
\(82\) 1.44363 1.04886i 0.159422 0.115827i
\(83\) −5.62510 + 4.08687i −0.617435 + 0.448593i −0.852024 0.523502i \(-0.824625\pi\)
0.234590 + 0.972094i \(0.424625\pi\)
\(84\) 0 0
\(85\) 0.840097 2.58555i 0.0911214 0.280443i
\(86\) −5.27169 3.83010i −0.568461 0.413011i
\(87\) 0 0
\(88\) 8.15967 + 1.23930i 0.869824 + 0.132110i
\(89\) −12.4803 −1.32291 −0.661453 0.749986i \(-0.730060\pi\)
−0.661453 + 0.749986i \(0.730060\pi\)
\(90\) 0 0
\(91\) −0.351367 + 1.08140i −0.0368332 + 0.113361i
\(92\) 0.537280 + 1.65358i 0.0560153 + 0.172397i
\(93\) 0 0
\(94\) 0.284638 0.206802i 0.0293582 0.0213300i
\(95\) −0.458943 1.41248i −0.0470866 0.144918i
\(96\) 0 0
\(97\) −11.4722 8.33507i −1.16483 0.846298i −0.174449 0.984666i \(-0.555814\pi\)
−0.990381 + 0.138368i \(0.955814\pi\)
\(98\) 10.0171 1.01188
\(99\) 0 0
\(100\) −1.81581 −0.181581
\(101\) −11.6244 8.44561i −1.15667 0.840370i −0.167317 0.985903i \(-0.553510\pi\)
−0.989353 + 0.145533i \(0.953510\pi\)
\(102\) 0 0
\(103\) −1.36859 4.21209i −0.134851 0.415029i 0.860716 0.509086i \(-0.170017\pi\)
−0.995567 + 0.0940566i \(0.970017\pi\)
\(104\) 3.17071 2.30366i 0.310914 0.225892i
\(105\) 0 0
\(106\) −2.72508 8.38693i −0.264683 0.814610i
\(107\) 4.86529 14.9738i 0.470345 1.44757i −0.381788 0.924250i \(-0.624692\pi\)
0.852134 0.523324i \(-0.175308\pi\)
\(108\) 0 0
\(109\) −13.6970 −1.31194 −0.655969 0.754788i \(-0.727740\pi\)
−0.655969 + 0.754788i \(0.727740\pi\)
\(110\) 0.493954 + 2.99546i 0.0470967 + 0.285606i
\(111\) 0 0
\(112\) 2.70340 + 1.96414i 0.255447 + 0.185593i
\(113\) −2.48145 + 7.63711i −0.233435 + 0.718439i 0.763890 + 0.645346i \(0.223287\pi\)
−0.997325 + 0.0730926i \(0.976713\pi\)
\(114\) 0 0
\(115\) 2.13235 1.54924i 0.198842 0.144467i
\(116\) 2.20491 1.60196i 0.204721 0.148738i
\(117\) 0 0
\(118\) 3.40829 10.4896i 0.313758 0.965648i
\(119\) 2.68205 + 1.94862i 0.245863 + 0.178630i
\(120\) 0 0
\(121\) −10.4176 + 3.53178i −0.947055 + 0.321071i
\(122\) −7.04877 −0.638166
\(123\) 0 0
\(124\) −1.10162 + 3.39045i −0.0989286 + 0.304471i
\(125\) 1.76536 + 5.43321i 0.157898 + 0.485961i
\(126\) 0 0
\(127\) 9.70522 7.05126i 0.861199 0.625698i −0.0670118 0.997752i \(-0.521347\pi\)
0.928211 + 0.372054i \(0.121347\pi\)
\(128\) −4.15986 12.8027i −0.367683 1.13161i
\(129\) 0 0
\(130\) 1.16633 + 0.847388i 0.102294 + 0.0743209i
\(131\) 6.89109 0.602077 0.301039 0.953612i \(-0.402667\pi\)
0.301039 + 0.953612i \(0.402667\pi\)
\(132\) 0 0
\(133\) 1.81109 0.157041
\(134\) −10.1212 7.35345i −0.874335 0.635242i
\(135\) 0 0
\(136\) −3.53112 10.8677i −0.302791 0.931896i
\(137\) 7.48062 5.43499i 0.639112 0.464342i −0.220433 0.975402i \(-0.570747\pi\)
0.859545 + 0.511060i \(0.170747\pi\)
\(138\) 0 0
\(139\) 6.67826 + 20.5536i 0.566442 + 1.74333i 0.663627 + 0.748064i \(0.269016\pi\)
−0.0971841 + 0.995266i \(0.530984\pi\)
\(140\) −0.0515820 + 0.158753i −0.00435948 + 0.0134171i
\(141\) 0 0
\(142\) −19.0320 −1.59713
\(143\) −2.34184 + 4.66920i −0.195835 + 0.390458i
\(144\) 0 0
\(145\) −3.34251 2.42847i −0.277580 0.201674i
\(146\) −7.39766 + 22.7677i −0.612235 + 1.88426i
\(147\) 0 0
\(148\) −0.913637 + 0.663796i −0.0751005 + 0.0545637i
\(149\) −0.927483 + 0.673856i −0.0759824 + 0.0552044i −0.625128 0.780522i \(-0.714953\pi\)
0.549146 + 0.835727i \(0.314953\pi\)
\(150\) 0 0
\(151\) 0.272133 0.837539i 0.0221459 0.0681579i −0.939373 0.342898i \(-0.888592\pi\)
0.961519 + 0.274740i \(0.0885916\pi\)
\(152\) −5.05031 3.66926i −0.409634 0.297616i
\(153\) 0 0
\(154\) −3.66015 0.555908i −0.294944 0.0447963i
\(155\) 5.40421 0.434077
\(156\) 0 0
\(157\) −3.02411 + 9.30724i −0.241350 + 0.742799i 0.754865 + 0.655880i \(0.227702\pi\)
−0.996215 + 0.0869191i \(0.972298\pi\)
\(158\) 6.98497 + 21.4975i 0.555694 + 1.71025i
\(159\) 0 0
\(160\) 1.04389 0.758434i 0.0825271 0.0599594i
\(161\) 0.993219 + 3.05681i 0.0782766 + 0.240911i
\(162\) 0 0
\(163\) −3.74555 2.72130i −0.293374 0.213149i 0.431355 0.902182i \(-0.358035\pi\)
−0.724730 + 0.689033i \(0.758035\pi\)
\(164\) 0.450728 0.0351959
\(165\) 0 0
\(166\) −10.7503 −0.834384
\(167\) −13.7431 9.98493i −1.06347 0.772657i −0.0887440 0.996054i \(-0.528285\pi\)
−0.974727 + 0.223397i \(0.928285\pi\)
\(168\) 0 0
\(169\) −3.25070 10.0046i −0.250054 0.769587i
\(170\) 3.40058 2.47066i 0.260812 0.189491i
\(171\) 0 0
\(172\) −0.508616 1.56536i −0.0387816 0.119357i
\(173\) 0.182646 0.562127i 0.0138863 0.0427378i −0.943873 0.330308i \(-0.892847\pi\)
0.957760 + 0.287570i \(0.0928474\pi\)
\(174\) 0 0
\(175\) −3.35671 −0.253743
\(176\) 10.9236 + 10.7858i 0.823401 + 0.813008i
\(177\) 0 0
\(178\) −15.6110 11.3420i −1.17009 0.850121i
\(179\) 2.97921 9.16907i 0.222677 0.685328i −0.775842 0.630927i \(-0.782675\pi\)
0.998519 0.0544017i \(-0.0173251\pi\)
\(180\) 0 0
\(181\) 3.85243 2.79896i 0.286349 0.208045i −0.435333 0.900270i \(-0.643369\pi\)
0.721682 + 0.692225i \(0.243369\pi\)
\(182\) −1.42228 + 1.03334i −0.105426 + 0.0765965i
\(183\) 0 0
\(184\) 3.42347 10.5363i 0.252381 0.776750i
\(185\) 1.38502 + 1.00627i 0.101829 + 0.0739828i
\(186\) 0 0
\(187\) 10.8374 + 10.7006i 0.792507 + 0.782505i
\(188\) 0.0888691 0.00648144
\(189\) 0 0
\(190\) 0.709589 2.18389i 0.0514790 0.158436i
\(191\) 1.60628 + 4.94362i 0.116226 + 0.357707i 0.992201 0.124650i \(-0.0397807\pi\)
−0.875975 + 0.482357i \(0.839781\pi\)
\(192\) 0 0
\(193\) −2.64390 + 1.92091i −0.190312 + 0.138270i −0.678861 0.734266i \(-0.737526\pi\)
0.488549 + 0.872536i \(0.337526\pi\)
\(194\) −6.77518 20.8519i −0.486430 1.49708i
\(195\) 0 0
\(196\) 2.04699 + 1.48722i 0.146213 + 0.106230i
\(197\) 22.4626 1.60039 0.800197 0.599737i \(-0.204728\pi\)
0.800197 + 0.599737i \(0.204728\pi\)
\(198\) 0 0
\(199\) −20.8291 −1.47654 −0.738269 0.674507i \(-0.764356\pi\)
−0.738269 + 0.674507i \(0.764356\pi\)
\(200\) 9.36035 + 6.80070i 0.661877 + 0.480882i
\(201\) 0 0
\(202\) −6.86504 21.1284i −0.483022 1.48659i
\(203\) 4.07600 2.96139i 0.286079 0.207849i
\(204\) 0 0
\(205\) −0.211144 0.649834i −0.0147469 0.0453864i
\(206\) 2.11603 6.51246i 0.147431 0.453745i
\(207\) 0 0
\(208\) 7.28981 0.505457
\(209\) 8.22575 + 1.24934i 0.568987 + 0.0864183i
\(210\) 0 0
\(211\) −2.74420 1.99378i −0.188919 0.137258i 0.489306 0.872112i \(-0.337250\pi\)
−0.678224 + 0.734855i \(0.737250\pi\)
\(212\) 0.688326 2.11845i 0.0472744 0.145496i
\(213\) 0 0
\(214\) 19.6939 14.3085i 1.34625 0.978106i
\(215\) −2.01858 + 1.46659i −0.137666 + 0.100020i
\(216\) 0 0
\(217\) −2.03646 + 6.26759i −0.138244 + 0.425472i
\(218\) −17.1329 12.4478i −1.16039 0.843072i
\(219\) 0 0
\(220\) −0.343792 + 0.685457i −0.0231785 + 0.0462135i
\(221\) 7.23224 0.486493
\(222\) 0 0
\(223\) −3.40734 + 10.4867i −0.228172 + 0.702243i 0.769782 + 0.638307i \(0.220365\pi\)
−0.997954 + 0.0639353i \(0.979635\pi\)
\(224\) 0.486232 + 1.49647i 0.0324877 + 0.0999870i
\(225\) 0 0
\(226\) −10.0445 + 7.29775i −0.668150 + 0.485439i
\(227\) 1.84387 + 5.67485i 0.122382 + 0.376653i 0.993415 0.114571i \(-0.0365495\pi\)
−0.871033 + 0.491224i \(0.836549\pi\)
\(228\) 0 0
\(229\) −20.0237 14.5481i −1.32320 0.961364i −0.999886 0.0150739i \(-0.995202\pi\)
−0.323318 0.946290i \(-0.604798\pi\)
\(230\) 4.07519 0.268710
\(231\) 0 0
\(232\) −17.3659 −1.14013
\(233\) 3.38850 + 2.46189i 0.221988 + 0.161284i 0.693221 0.720725i \(-0.256191\pi\)
−0.471233 + 0.882009i \(0.656191\pi\)
\(234\) 0 0
\(235\) −0.0416308 0.128126i −0.00271569 0.00835805i
\(236\) 2.25386 1.63753i 0.146714 0.106594i
\(237\) 0 0
\(238\) 1.58394 + 4.87488i 0.102672 + 0.315991i
\(239\) 2.27833 7.01199i 0.147373 0.453568i −0.849935 0.526887i \(-0.823359\pi\)
0.997309 + 0.0733190i \(0.0233591\pi\)
\(240\) 0 0
\(241\) −8.82924 −0.568741 −0.284371 0.958714i \(-0.591785\pi\)
−0.284371 + 0.958714i \(0.591785\pi\)
\(242\) −16.2405 5.04975i −1.04398 0.324610i
\(243\) 0 0
\(244\) −1.44041 1.04652i −0.0922129 0.0669966i
\(245\) 1.18528 3.64792i 0.0757248 0.233057i
\(246\) 0 0
\(247\) 3.19639 2.32231i 0.203381 0.147765i
\(248\) 18.3769 13.3516i 1.16694 0.847829i
\(249\) 0 0
\(250\) −2.72948 + 8.40048i −0.172628 + 0.531293i
\(251\) 16.6439 + 12.0925i 1.05056 + 0.763274i 0.972318 0.233661i \(-0.0750704\pi\)
0.0782385 + 0.996935i \(0.475070\pi\)
\(252\) 0 0
\(253\) 2.40242 + 14.5689i 0.151039 + 0.915936i
\(254\) 18.5479 1.16380
\(255\) 0 0
\(256\) 2.79314 8.59640i 0.174571 0.537275i
\(257\) 1.04521 + 3.21684i 0.0651987 + 0.200661i 0.978349 0.206962i \(-0.0663577\pi\)
−0.913150 + 0.407623i \(0.866358\pi\)
\(258\) 0 0
\(259\) −1.68895 + 1.22710i −0.104946 + 0.0762481i
\(260\) 0.112528 + 0.346326i 0.00697871 + 0.0214783i
\(261\) 0 0
\(262\) 8.61973 + 6.26260i 0.532528 + 0.386905i
\(263\) 14.2822 0.880681 0.440341 0.897831i \(-0.354858\pi\)
0.440341 + 0.897831i \(0.354858\pi\)
\(264\) 0 0
\(265\) −3.37671 −0.207430
\(266\) 2.26540 + 1.64591i 0.138900 + 0.100917i
\(267\) 0 0
\(268\) −0.976496 3.00535i −0.0596490 0.183581i
\(269\) 5.43693 3.95016i 0.331495 0.240845i −0.409570 0.912279i \(-0.634321\pi\)
0.741065 + 0.671433i \(0.234321\pi\)
\(270\) 0 0
\(271\) −1.23000 3.78554i −0.0747170 0.229955i 0.906722 0.421728i \(-0.138576\pi\)
−0.981439 + 0.191773i \(0.938576\pi\)
\(272\) 6.56795 20.2141i 0.398241 1.22566i
\(273\) 0 0
\(274\) 14.2964 0.863679
\(275\) −15.2458 2.31555i −0.919356 0.139633i
\(276\) 0 0
\(277\) 10.6240 + 7.71880i 0.638335 + 0.463778i 0.859278 0.511509i \(-0.170913\pi\)
−0.220943 + 0.975287i \(0.570913\pi\)
\(278\) −10.3255 + 31.7786i −0.619282 + 1.90595i
\(279\) 0 0
\(280\) 0.860476 0.625172i 0.0514233 0.0373612i
\(281\) −2.40106 + 1.74447i −0.143235 + 0.104066i −0.657095 0.753808i \(-0.728215\pi\)
0.513860 + 0.857874i \(0.328215\pi\)
\(282\) 0 0
\(283\) 2.50081 7.69669i 0.148657 0.457521i −0.848806 0.528705i \(-0.822678\pi\)
0.997463 + 0.0711843i \(0.0226778\pi\)
\(284\) −3.88918 2.82565i −0.230780 0.167672i
\(285\) 0 0
\(286\) −7.17265 + 3.71221i −0.424128 + 0.219508i
\(287\) 0.833217 0.0491833
\(288\) 0 0
\(289\) 1.26279 3.88648i 0.0742820 0.228616i
\(290\) −1.97399 6.07532i −0.115917 0.356755i
\(291\) 0 0
\(292\) −4.89199 + 3.55424i −0.286282 + 0.207996i
\(293\) 4.85638 + 14.9464i 0.283713 + 0.873178i 0.986782 + 0.162056i \(0.0518126\pi\)
−0.703069 + 0.711122i \(0.748187\pi\)
\(294\) 0 0
\(295\) −3.41671 2.48239i −0.198929 0.144530i
\(296\) 7.19584 0.418249
\(297\) 0 0
\(298\) −1.77254 −0.102681
\(299\) 5.67262 + 4.12140i 0.328056 + 0.238347i
\(300\) 0 0
\(301\) −0.940229 2.89373i −0.0541939 0.166792i
\(302\) 1.10155 0.800323i 0.0633871 0.0460534i
\(303\) 0 0
\(304\) −3.58806 11.0429i −0.205789 0.633354i
\(305\) −0.834052 + 2.56695i −0.0477577 + 0.146983i
\(306\) 0 0
\(307\) −3.51315 −0.200506 −0.100253 0.994962i \(-0.531965\pi\)
−0.100253 + 0.994962i \(0.531965\pi\)
\(308\) −0.665415 0.657017i −0.0379156 0.0374370i
\(309\) 0 0
\(310\) 6.75986 + 4.91133i 0.383934 + 0.278945i
\(311\) −8.13778 + 25.0455i −0.461451 + 1.42020i 0.401940 + 0.915666i \(0.368336\pi\)
−0.863391 + 0.504535i \(0.831664\pi\)
\(312\) 0 0
\(313\) 1.99111 1.44662i 0.112544 0.0817679i −0.530090 0.847942i \(-0.677842\pi\)
0.642634 + 0.766174i \(0.277842\pi\)
\(314\) −12.2411 + 8.89367i −0.690805 + 0.501899i
\(315\) 0 0
\(316\) −1.76433 + 5.43005i −0.0992513 + 0.305464i
\(317\) −21.4447 15.5805i −1.20446 0.875089i −0.209740 0.977757i \(-0.567262\pi\)
−0.994716 + 0.102669i \(0.967262\pi\)
\(318\) 0 0
\(319\) 20.5556 10.6386i 1.15089 0.595646i
\(320\) −3.48549 −0.194845
\(321\) 0 0
\(322\) −1.53565 + 4.72625i −0.0855785 + 0.263384i
\(323\) −3.55972 10.9557i −0.198068 0.609591i
\(324\) 0 0
\(325\) −5.92427 + 4.30423i −0.328619 + 0.238756i
\(326\) −2.21202 6.80789i −0.122512 0.377054i
\(327\) 0 0
\(328\) −2.32347 1.68810i −0.128292 0.0932097i
\(329\) 0.164284 0.00905726
\(330\) 0 0
\(331\) 8.10397 0.445434 0.222717 0.974883i \(-0.428507\pi\)
0.222717 + 0.974883i \(0.428507\pi\)
\(332\) −2.19681 1.59608i −0.120566 0.0875962i
\(333\) 0 0
\(334\) −8.11627 24.9793i −0.444103 1.36681i
\(335\) −3.87550 + 2.81571i −0.211741 + 0.153839i
\(336\) 0 0
\(337\) 7.63910 + 23.5107i 0.416128 + 1.28071i 0.911238 + 0.411880i \(0.135128\pi\)
−0.495110 + 0.868830i \(0.664872\pi\)
\(338\) 5.02603 15.4685i 0.273380 0.841376i
\(339\) 0 0
\(340\) 1.06172 0.0575799
\(341\) −13.5730 + 27.0619i −0.735017 + 1.46549i
\(342\) 0 0
\(343\) 7.87256 + 5.71975i 0.425078 + 0.308837i
\(344\) −3.24082 + 9.97422i −0.174733 + 0.537774i
\(345\) 0 0
\(346\) 0.739322 0.537149i 0.0397462 0.0288773i
\(347\) −1.67438 + 1.21651i −0.0898853 + 0.0653055i −0.631820 0.775115i \(-0.717692\pi\)
0.541935 + 0.840420i \(0.317692\pi\)
\(348\) 0 0
\(349\) −1.61130 + 4.95906i −0.0862507 + 0.265452i −0.984875 0.173267i \(-0.944568\pi\)
0.898624 + 0.438719i \(0.144568\pi\)
\(350\) −4.19874 3.05056i −0.224432 0.163059i
\(351\) 0 0
\(352\) 1.17611 + 7.13221i 0.0626868 + 0.380148i
\(353\) −21.6725 −1.15351 −0.576756 0.816917i \(-0.695681\pi\)
−0.576756 + 0.816917i \(0.695681\pi\)
\(354\) 0 0
\(355\) −2.25198 + 6.93088i −0.119523 + 0.367853i
\(356\) −1.50616 4.63547i −0.0798261 0.245680i
\(357\) 0 0
\(358\) 12.0594 8.76164i 0.637357 0.463067i
\(359\) −2.70478 8.32446i −0.142753 0.439348i 0.853962 0.520335i \(-0.174193\pi\)
−0.996715 + 0.0809868i \(0.974193\pi\)
\(360\) 0 0
\(361\) 10.2801 + 7.46894i 0.541059 + 0.393102i
\(362\) 7.36250 0.386964
\(363\) 0 0
\(364\) −0.444060 −0.0232751
\(365\) 7.41595 + 5.38801i 0.388169 + 0.282021i
\(366\) 0 0
\(367\) −2.09088 6.43506i −0.109143 0.335908i 0.881537 0.472114i \(-0.156509\pi\)
−0.990680 + 0.136206i \(0.956509\pi\)
\(368\) 16.6709 12.1121i 0.869029 0.631387i
\(369\) 0 0
\(370\) 0.817952 + 2.51740i 0.0425233 + 0.130873i
\(371\) 1.27244 3.91618i 0.0660620 0.203318i
\(372\) 0 0
\(373\) −21.8933 −1.13359 −0.566797 0.823857i \(-0.691818\pi\)
−0.566797 + 0.823857i \(0.691818\pi\)
\(374\) 3.83128 + 23.2338i 0.198111 + 1.20139i
\(375\) 0 0
\(376\) −0.458114 0.332839i −0.0236254 0.0171649i
\(377\) 3.39643 10.4531i 0.174925 0.538364i
\(378\) 0 0
\(379\) 27.3639 19.8810i 1.40559 1.02122i 0.411642 0.911346i \(-0.364955\pi\)
0.993946 0.109873i \(-0.0350445\pi\)
\(380\) 0.469243 0.340925i 0.0240716 0.0174891i
\(381\) 0 0
\(382\) −2.48353 + 7.64350i −0.127068 + 0.391076i
\(383\) −14.8648 10.7999i −0.759555 0.551849i 0.139219 0.990262i \(-0.455541\pi\)
−0.898774 + 0.438413i \(0.855541\pi\)
\(384\) 0 0
\(385\) −0.635536 + 1.26714i −0.0323899 + 0.0645794i
\(386\) −5.05284 −0.257183
\(387\) 0 0
\(388\) 1.71134 5.26696i 0.0868801 0.267390i
\(389\) 9.51975 + 29.2988i 0.482670 + 1.48551i 0.835327 + 0.549754i \(0.185278\pi\)
−0.352657 + 0.935753i \(0.614722\pi\)
\(390\) 0 0
\(391\) 16.5392 12.0164i 0.836424 0.607698i
\(392\) −4.98201 15.3331i −0.251630 0.774436i
\(393\) 0 0
\(394\) 28.0974 + 20.4139i 1.41552 + 1.02844i
\(395\) 8.65524 0.435493
\(396\) 0 0
\(397\) −8.29578 −0.416353 −0.208177 0.978091i \(-0.566753\pi\)
−0.208177 + 0.978091i \(0.566753\pi\)
\(398\) −26.0541 18.9294i −1.30598 0.948847i
\(399\) 0 0
\(400\) 6.65019 + 20.4672i 0.332509 + 1.02336i
\(401\) −3.18237 + 2.31212i −0.158920 + 0.115462i −0.664403 0.747374i \(-0.731314\pi\)
0.505483 + 0.862836i \(0.331314\pi\)
\(402\) 0 0
\(403\) 4.44263 + 13.6730i 0.221303 + 0.681101i
\(404\) 1.73404 5.33682i 0.0862716 0.265517i
\(405\) 0 0
\(406\) 7.78977 0.386600
\(407\) −8.51753 + 4.40825i −0.422198 + 0.218509i
\(408\) 0 0
\(409\) 2.02598 + 1.47196i 0.100178 + 0.0727839i 0.636747 0.771073i \(-0.280280\pi\)
−0.536568 + 0.843857i \(0.680280\pi\)
\(410\) 0.326457 1.00473i 0.0161226 0.0496202i
\(411\) 0 0
\(412\) 1.39930 1.01665i 0.0689388 0.0500870i
\(413\) 4.16650 3.02714i 0.205020 0.148956i
\(414\) 0 0
\(415\) −1.27204 + 3.91493i −0.0624419 + 0.192176i
\(416\) 2.77704 + 2.01764i 0.136156 + 0.0989228i
\(417\) 0 0
\(418\) 9.15380 + 9.03826i 0.447727 + 0.442076i
\(419\) −10.7394 −0.524654 −0.262327 0.964979i \(-0.584490\pi\)
−0.262327 + 0.964979i \(0.584490\pi\)
\(420\) 0 0
\(421\) 6.85630 21.1015i 0.334156 1.02843i −0.632981 0.774167i \(-0.718169\pi\)
0.967136 0.254258i \(-0.0818311\pi\)
\(422\) −1.62065 4.98785i −0.0788920 0.242805i
\(423\) 0 0
\(424\) −11.4825 + 8.34249i −0.557637 + 0.405147i
\(425\) 6.59767 + 20.3055i 0.320034 + 0.984963i
\(426\) 0 0
\(427\) −2.66275 1.93460i −0.128860 0.0936219i
\(428\) 6.14879 0.297213
\(429\) 0 0
\(430\) −3.85778 −0.186038
\(431\) −14.9330 10.8495i −0.719297 0.522600i 0.166862 0.985980i \(-0.446636\pi\)
−0.886160 + 0.463380i \(0.846636\pi\)
\(432\) 0 0
\(433\) 4.67130 + 14.3768i 0.224488 + 0.690904i 0.998343 + 0.0575408i \(0.0183259\pi\)
−0.773855 + 0.633363i \(0.781674\pi\)
\(434\) −8.24328 + 5.98909i −0.395690 + 0.287486i
\(435\) 0 0
\(436\) −1.65300 5.08740i −0.0791642 0.243642i
\(437\) 3.45119 10.6217i 0.165093 0.508103i
\(438\) 0 0
\(439\) 23.9553 1.14333 0.571663 0.820488i \(-0.306298\pi\)
0.571663 + 0.820488i \(0.306298\pi\)
\(440\) 4.33945 2.24589i 0.206875 0.107068i
\(441\) 0 0
\(442\) 9.04645 + 6.57263i 0.430296 + 0.312628i
\(443\) −7.87922 + 24.2498i −0.374353 + 1.15214i 0.569561 + 0.821949i \(0.307113\pi\)
−0.943914 + 0.330192i \(0.892887\pi\)
\(444\) 0 0
\(445\) −5.97760 + 4.34298i −0.283366 + 0.205877i
\(446\) −13.7924 + 10.0207i −0.653088 + 0.474496i
\(447\) 0 0
\(448\) 1.31343 4.04234i 0.0620539 0.190982i
\(449\) −18.1886 13.2148i −0.858375 0.623646i 0.0690672 0.997612i \(-0.477998\pi\)
−0.927442 + 0.373966i \(0.877998\pi\)
\(450\) 0 0
\(451\) 3.78438 + 0.574776i 0.178200 + 0.0270651i
\(452\) −3.13607 −0.147508
\(453\) 0 0
\(454\) −2.85087 + 8.77409i −0.133798 + 0.411788i
\(455\) 0.208020 + 0.640221i 0.00975214 + 0.0300140i
\(456\) 0 0
\(457\) −17.5472 + 12.7488i −0.820825 + 0.596364i −0.916949 0.399005i \(-0.869356\pi\)
0.0961237 + 0.995369i \(0.469356\pi\)
\(458\) −11.8254 36.3950i −0.552566 1.70062i
\(459\) 0 0
\(460\) 0.832763 + 0.605037i 0.0388278 + 0.0282100i
\(461\) 12.1036 0.563722 0.281861 0.959455i \(-0.409048\pi\)
0.281861 + 0.959455i \(0.409048\pi\)
\(462\) 0 0
\(463\) 20.0308 0.930910 0.465455 0.885071i \(-0.345891\pi\)
0.465455 + 0.885071i \(0.345891\pi\)
\(464\) −26.1320 18.9860i −1.21315 0.881404i
\(465\) 0 0
\(466\) 2.00115 + 6.15891i 0.0927015 + 0.285306i
\(467\) 4.90871 3.56639i 0.227148 0.165033i −0.468390 0.883522i \(-0.655166\pi\)
0.695538 + 0.718489i \(0.255166\pi\)
\(468\) 0 0
\(469\) −1.80516 5.55570i −0.0833543 0.256538i
\(470\) 0.0643669 0.198101i 0.00296902 0.00913772i
\(471\) 0 0
\(472\) −17.7515 −0.817078
\(473\) −2.27425 13.7916i −0.104570 0.634138i
\(474\) 0 0
\(475\) 9.43616 + 6.85577i 0.432961 + 0.314564i
\(476\) −0.400088 + 1.23134i −0.0183380 + 0.0564385i
\(477\) 0 0
\(478\) 9.22233 6.70041i 0.421819 0.306470i
\(479\) 29.3453 21.3206i 1.34082 0.974164i 0.341408 0.939915i \(-0.389096\pi\)
0.999413 0.0342489i \(-0.0109039\pi\)
\(480\) 0 0
\(481\) −1.40736 + 4.33141i −0.0641702 + 0.197496i
\(482\) −11.0441 8.02398i −0.503043 0.365482i
\(483\) 0 0
\(484\) −2.56902 3.44312i −0.116773 0.156505i
\(485\) −8.39529 −0.381211
\(486\) 0 0
\(487\) −2.68379 + 8.25986i −0.121614 + 0.374290i −0.993269 0.115830i \(-0.963047\pi\)
0.871655 + 0.490120i \(0.163047\pi\)
\(488\) 3.50571 + 10.7895i 0.158696 + 0.488417i
\(489\) 0 0
\(490\) 4.79782 3.48582i 0.216744 0.157473i
\(491\) 10.2585 + 31.5725i 0.462961 + 1.42485i 0.861529 + 0.507709i \(0.169508\pi\)
−0.398567 + 0.917139i \(0.630492\pi\)
\(492\) 0 0
\(493\) −25.9256 18.8361i −1.16763 0.848334i
\(494\) 6.10872 0.274844
\(495\) 0 0
\(496\) 42.2506 1.89711
\(497\) −7.18956 5.22352i −0.322496 0.234307i
\(498\) 0 0
\(499\) 6.45131 + 19.8551i 0.288800 + 0.888837i 0.985234 + 0.171215i \(0.0547692\pi\)
−0.696433 + 0.717622i \(0.745231\pi\)
\(500\) −1.80497 + 1.31139i −0.0807209 + 0.0586472i
\(501\) 0 0
\(502\) 9.82944 + 30.2519i 0.438710 + 1.35021i
\(503\) −7.20593 + 22.1776i −0.321297 + 0.988850i 0.651788 + 0.758401i \(0.274019\pi\)
−0.973085 + 0.230448i \(0.925981\pi\)
\(504\) 0 0
\(505\) −8.50663 −0.378540
\(506\) −10.2351 + 20.4068i −0.455004 + 0.907192i
\(507\) 0 0
\(508\) 3.79026 + 2.75378i 0.168166 + 0.122179i
\(509\) −2.00280 + 6.16400i −0.0887728 + 0.273214i −0.985581 0.169205i \(-0.945880\pi\)
0.896808 + 0.442420i \(0.145880\pi\)
\(510\) 0 0
\(511\) −9.04335 + 6.57038i −0.400054 + 0.290656i
\(512\) −10.4751 + 7.61063i −0.462940 + 0.336346i
\(513\) 0 0
\(514\) −1.61605 + 4.97368i −0.0712807 + 0.219379i
\(515\) −2.12126 1.54119i −0.0934739 0.0679128i
\(516\) 0 0
\(517\) 0.746159 + 0.113327i 0.0328160 + 0.00498413i
\(518\) −3.22781 −0.141822
\(519\) 0 0
\(520\) 0.717013 2.20674i 0.0314431 0.0967719i
\(521\) 10.2625 + 31.5848i 0.449610 + 1.38376i 0.877348 + 0.479855i \(0.159311\pi\)
−0.427738 + 0.903903i \(0.640689\pi\)
\(522\) 0 0
\(523\) 32.4728 23.5929i 1.41994 1.03164i 0.428154 0.903706i \(-0.359164\pi\)
0.991782 0.127938i \(-0.0408359\pi\)
\(524\) 0.831637 + 2.55952i 0.0363302 + 0.111813i
\(525\) 0 0
\(526\) 17.8650 + 12.9797i 0.778949 + 0.565940i
\(527\) 41.9169 1.82593
\(528\) 0 0
\(529\) −3.17970 −0.138248
\(530\) −4.22376 3.06874i −0.183468 0.133298i
\(531\) 0 0
\(532\) 0.218567 + 0.672680i 0.00947608 + 0.0291644i
\(533\) 1.47055 1.06842i 0.0636965 0.0462782i
\(534\) 0 0
\(535\) −2.88041 8.86498i −0.124531 0.383267i
\(536\) −6.22208 + 19.1496i −0.268753 + 0.827137i
\(537\) 0 0
\(538\) 10.3907 0.447974
\(539\) 15.2903 + 15.0973i 0.658599 + 0.650287i
\(540\) 0 0
\(541\) −19.9410 14.4880i −0.857332 0.622888i 0.0698260 0.997559i \(-0.477756\pi\)
−0.927158 + 0.374671i \(0.877756\pi\)
\(542\) 1.90174 5.85296i 0.0816868 0.251406i
\(543\) 0 0
\(544\) 8.09680 5.88267i 0.347147 0.252217i
\(545\) −6.56038 + 4.76640i −0.281016 + 0.204170i
\(546\) 0 0
\(547\) 7.94803 24.4615i 0.339833 1.04590i −0.624459 0.781058i \(-0.714681\pi\)
0.964292 0.264841i \(-0.0853195\pi\)
\(548\) 2.92147 + 2.12257i 0.124799 + 0.0906716i
\(549\) 0 0
\(550\) −16.9659 16.7517i −0.723427 0.714296i
\(551\) −17.5066 −0.745805
\(552\) 0 0
\(553\) −3.26155 + 10.0380i −0.138695 + 0.426860i
\(554\) 6.27424 + 19.3101i 0.266567 + 0.820409i
\(555\) 0 0
\(556\) −6.82813 + 4.96093i −0.289577 + 0.210390i
\(557\) −3.60979 11.1098i −0.152952 0.470737i 0.844996 0.534773i \(-0.179603\pi\)
−0.997948 + 0.0640357i \(0.979603\pi\)
\(558\) 0 0
\(559\) −5.36998 3.90152i −0.227126 0.165017i
\(560\) 1.97833 0.0835996
\(561\) 0 0
\(562\) −4.58873 −0.193564
\(563\) 6.57092 + 4.77405i 0.276931 + 0.201202i 0.717578 0.696478i \(-0.245251\pi\)
−0.440647 + 0.897681i \(0.645251\pi\)
\(564\) 0 0
\(565\) 1.46910 + 4.52141i 0.0618053 + 0.190217i
\(566\) 10.1229 7.35468i 0.425495 0.309140i
\(567\) 0 0
\(568\) 9.46559 + 29.1321i 0.397167 + 1.22236i
\(569\) 5.56435 17.1253i 0.233270 0.717930i −0.764077 0.645126i \(-0.776805\pi\)
0.997346 0.0728046i \(-0.0231950\pi\)
\(570\) 0 0
\(571\) −2.60645 −0.109076 −0.0545382 0.998512i \(-0.517369\pi\)
−0.0545382 + 0.998512i \(0.517369\pi\)
\(572\) −2.01687 0.306324i −0.0843296 0.0128081i
\(573\) 0 0
\(574\) 1.04223 + 0.757225i 0.0435019 + 0.0316059i
\(575\) −6.39652 + 19.6865i −0.266753 + 0.820982i
\(576\) 0 0
\(577\) −28.4684 + 20.6835i −1.18515 + 0.861064i −0.992744 0.120251i \(-0.961630\pi\)
−0.192409 + 0.981315i \(0.561630\pi\)
\(578\) 5.11158 3.71378i 0.212614 0.154473i
\(579\) 0 0
\(580\) 0.498609 1.53456i 0.0207036 0.0637192i
\(581\) −4.06104 2.95052i −0.168480 0.122408i
\(582\) 0 0
\(583\) 8.48078 16.9091i 0.351238 0.700303i
\(584\) 38.5294 1.59436
\(585\) 0 0
\(586\) −7.50863 + 23.1092i −0.310179 + 0.954631i
\(587\) −7.27809 22.3997i −0.300399 0.924533i −0.981354 0.192208i \(-0.938435\pi\)
0.680955 0.732325i \(-0.261565\pi\)
\(588\) 0 0
\(589\) 18.5258 13.4598i 0.763341 0.554600i
\(590\) −2.01781 6.21019i −0.0830721 0.255670i
\(591\) 0 0
\(592\) 10.8282 + 7.86714i 0.445036 + 0.323337i
\(593\) −13.1828 −0.541354 −0.270677 0.962670i \(-0.587248\pi\)
−0.270677 + 0.962670i \(0.587248\pi\)
\(594\) 0 0
\(595\) 1.96270 0.0804630
\(596\) −0.362218 0.263166i −0.0148370 0.0107797i
\(597\) 0 0
\(598\) 3.35009 + 10.3105i 0.136995 + 0.421628i
\(599\) 27.6817 20.1119i 1.13104 0.821750i 0.145196 0.989403i \(-0.453619\pi\)
0.985846 + 0.167653i \(0.0536188\pi\)
\(600\) 0 0
\(601\) 8.97030 + 27.6077i 0.365906 + 1.12614i 0.949412 + 0.314034i \(0.101681\pi\)
−0.583505 + 0.812109i \(0.698319\pi\)
\(602\) 1.45372 4.47410i 0.0592493 0.182351i
\(603\) 0 0
\(604\) 0.343924 0.0139941
\(605\) −3.76064 + 5.31680i −0.152892 + 0.216158i
\(606\) 0 0
\(607\) 2.55354 + 1.85526i 0.103645 + 0.0753026i 0.638401 0.769704i \(-0.279596\pi\)
−0.534756 + 0.845007i \(0.679596\pi\)
\(608\) 1.68954 5.19986i 0.0685197 0.210882i
\(609\) 0 0
\(610\) −3.37611 + 2.45288i −0.136695 + 0.0993144i
\(611\) 0.289945 0.210657i 0.0117299 0.00852229i
\(612\) 0 0
\(613\) 10.4884 32.2798i 0.423620 1.30377i −0.480689 0.876891i \(-0.659613\pi\)
0.904309 0.426878i \(-0.140387\pi\)
\(614\) −4.39443 3.19274i −0.177345 0.128848i
\(615\) 0 0
\(616\) 0.969460 + 5.87904i 0.0390606 + 0.236873i
\(617\) 21.6077 0.869895 0.434948 0.900456i \(-0.356767\pi\)
0.434948 + 0.900456i \(0.356767\pi\)
\(618\) 0 0
\(619\) 6.33874 19.5086i 0.254775 0.784118i −0.739098 0.673598i \(-0.764748\pi\)
0.993874 0.110521i \(-0.0352519\pi\)
\(620\) 0.652196 + 2.00725i 0.0261928 + 0.0806132i
\(621\) 0 0
\(622\) −32.9404 + 23.9326i −1.32079 + 0.959611i
\(623\) −2.78429 8.56915i −0.111550 0.343316i
\(624\) 0 0
\(625\) −16.0714 11.6765i −0.642855 0.467062i
\(626\) 3.80526 0.152089
\(627\) 0 0
\(628\) −3.82189 −0.152510
\(629\) 10.7427 + 7.80501i 0.428339 + 0.311206i
\(630\) 0 0
\(631\) 9.22863 + 28.4028i 0.367386 + 1.13070i 0.948473 + 0.316857i \(0.102628\pi\)
−0.581087 + 0.813841i \(0.697372\pi\)
\(632\) 29.4320 21.3836i 1.17074 0.850595i
\(633\) 0 0
\(634\) −12.6646 38.9778i −0.502977 1.54801i
\(635\) 2.19470 6.75459i 0.0870940 0.268048i
\(636\) 0 0
\(637\) 10.2039 0.404292
\(638\) 35.3803 + 5.37360i 1.40072 + 0.212743i
\(639\) 0 0
\(640\) −6.44762 4.68447i −0.254864 0.185170i
\(641\) 11.7797 36.2543i 0.465272 1.43196i −0.393368 0.919381i \(-0.628690\pi\)
0.858640 0.512579i \(-0.171310\pi\)
\(642\) 0 0
\(643\) 13.6118 9.88957i 0.536798 0.390006i −0.286097 0.958201i \(-0.592358\pi\)
0.822894 + 0.568194i \(0.192358\pi\)
\(644\) −1.01551 + 0.737810i −0.0400166 + 0.0290738i
\(645\) 0 0
\(646\) 5.50381 16.9390i 0.216545 0.666456i
\(647\) −16.9687 12.3285i −0.667109 0.484683i 0.201947 0.979396i \(-0.435273\pi\)
−0.869056 + 0.494713i \(0.835273\pi\)
\(648\) 0 0
\(649\) 21.0120 10.8748i 0.824792 0.426872i
\(650\) −11.3220 −0.444087
\(651\) 0 0
\(652\) 0.558733 1.71960i 0.0218817 0.0673449i
\(653\) −6.10818 18.7990i −0.239031 0.735663i −0.996561 0.0828623i \(-0.973594\pi\)
0.757530 0.652801i \(-0.226406\pi\)
\(654\) 0 0
\(655\) 3.30058 2.39801i 0.128964 0.0936982i
\(656\) −1.65074 5.08046i −0.0644506 0.198358i
\(657\) 0 0
\(658\) 0.205494 + 0.149300i 0.00801101 + 0.00582034i
\(659\) 11.8055 0.459879 0.229939 0.973205i \(-0.426147\pi\)
0.229939 + 0.973205i \(0.426147\pi\)
\(660\) 0 0
\(661\) 17.8076 0.692637 0.346318 0.938117i \(-0.387432\pi\)
0.346318 + 0.938117i \(0.387432\pi\)
\(662\) 10.1369 + 7.36485i 0.393980 + 0.286243i
\(663\) 0 0
\(664\) 5.34667 + 16.4554i 0.207491 + 0.638592i
\(665\) 0.867445 0.630235i 0.0336381 0.0244395i
\(666\) 0 0
\(667\) −9.60079 29.5482i −0.371744 1.14411i
\(668\) 2.05009 6.30952i 0.0793202 0.244123i
\(669\) 0 0
\(670\) −7.40658 −0.286141
\(671\) −10.7594 10.6236i −0.415361 0.410119i
\(672\) 0 0
\(673\) −15.9419 11.5825i −0.614515 0.446472i 0.236486 0.971635i \(-0.424004\pi\)
−0.851001 + 0.525163i \(0.824004\pi\)
\(674\) −11.8111 + 36.3508i −0.454946 + 1.40018i
\(675\) 0 0
\(676\) 3.32365 2.41477i 0.127833 0.0928760i
\(677\) −10.0431 + 7.29671i −0.385986 + 0.280436i −0.763809 0.645443i \(-0.776673\pi\)
0.377822 + 0.925878i \(0.376673\pi\)
\(678\) 0 0
\(679\) 3.16359 9.73653i 0.121408 0.373654i
\(680\) −5.47310 3.97644i −0.209884 0.152490i
\(681\) 0 0
\(682\) −41.5715 + 21.5154i −1.59186 + 0.823866i
\(683\) −2.02837 −0.0776135 −0.0388068 0.999247i \(-0.512356\pi\)
−0.0388068 + 0.999247i \(0.512356\pi\)
\(684\) 0 0
\(685\) 1.69164 5.20632i 0.0646341 0.198923i
\(686\) 4.64931 + 14.3091i 0.177511 + 0.546324i
\(687\) 0 0
\(688\) −15.7815 + 11.4659i −0.601663 + 0.437133i
\(689\) −2.77589 8.54330i −0.105753 0.325474i
\(690\) 0 0
\(691\) −1.89542 1.37710i −0.0721052 0.0523875i 0.551149 0.834407i \(-0.314190\pi\)
−0.623254 + 0.782020i \(0.714190\pi\)
\(692\) 0.230830 0.00877483
\(693\) 0 0
\(694\) −3.19995 −0.121469
\(695\) 10.3510 + 7.52046i 0.392637 + 0.285267i
\(696\) 0 0
\(697\) −1.63770 5.04033i −0.0620324 0.190916i
\(698\) −6.52227 + 4.73871i −0.246871 + 0.179363i
\(699\) 0 0
\(700\) −0.405097 1.24676i −0.0153112 0.0471231i
\(701\) 1.37008 4.21668i 0.0517473 0.159262i −0.921843 0.387563i \(-0.873317\pi\)
0.973591 + 0.228301i \(0.0733170\pi\)
\(702\) 0 0
\(703\) 7.25411 0.273594
\(704\) 8.75399 17.4538i 0.329928 0.657815i
\(705\) 0 0
\(706\) −27.1091 19.6959i −1.02026 0.741265i
\(707\) 3.20555 9.86566i 0.120557 0.371037i
\(708\) 0 0
\(709\) −24.1755 + 17.5645i −0.907929 + 0.659649i −0.940490 0.339821i \(-0.889634\pi\)
0.0325612 + 0.999470i \(0.489634\pi\)
\(710\) −9.11565 + 6.62291i −0.342104 + 0.248553i
\(711\) 0 0
\(712\) −9.59699 + 29.5365i −0.359662 + 1.10693i
\(713\) 32.8776 + 23.8870i 1.23127 + 0.894574i
\(714\) 0 0
\(715\) 0.503164 + 3.05131i 0.0188173 + 0.114113i
\(716\) 3.76515 0.140710
\(717\) 0 0
\(718\) 4.18196 12.8707i 0.156069 0.480332i
\(719\) 6.68469 + 20.5734i 0.249297 + 0.767257i 0.994900 + 0.100867i \(0.0321616\pi\)
−0.745603 + 0.666390i \(0.767838\pi\)
\(720\) 0 0
\(721\) 2.58676 1.87939i 0.0963360 0.0699922i
\(722\) 6.07115 + 18.6851i 0.225945 + 0.695386i
\(723\) 0 0
\(724\) 1.50452 + 1.09310i 0.0559151 + 0.0406247i
\(725\) 32.4471 1.20505
\(726\) 0 0
\(727\) −12.4422 −0.461455 −0.230727 0.973018i \(-0.574111\pi\)
−0.230727 + 0.973018i \(0.574111\pi\)
\(728\) 2.28910 + 1.66313i 0.0848396 + 0.0616396i
\(729\) 0 0
\(730\) 4.37965 + 13.4792i 0.162098 + 0.498887i
\(731\) −15.6568 + 11.3754i −0.579089 + 0.420733i
\(732\) 0 0
\(733\) −16.1777 49.7899i −0.597538 1.83903i −0.541665 0.840594i \(-0.682206\pi\)
−0.0558724 0.998438i \(-0.517794\pi\)
\(734\) 3.23278 9.94949i 0.119324 0.367242i
\(735\) 0 0
\(736\) 9.70306 0.357660
\(737\) −4.36635 26.4786i −0.160837 0.975352i
\(738\) 0 0
\(739\) 37.7617 + 27.4355i 1.38909 + 1.00923i 0.995965 + 0.0897445i \(0.0286051\pi\)
0.393122 + 0.919486i \(0.371395\pi\)
\(740\) −0.206606 + 0.635869i −0.00759500 + 0.0233750i
\(741\) 0 0
\(742\) 5.15064 3.74216i 0.189086 0.137379i
\(743\) −17.6947 + 12.8560i −0.649156 + 0.471640i −0.862984 0.505232i \(-0.831407\pi\)
0.213827 + 0.976871i \(0.431407\pi\)
\(744\) 0 0
\(745\) −0.209737 + 0.645506i −0.00768419 + 0.0236495i
\(746\) −27.3853 19.8966i −1.00265 0.728466i
\(747\) 0 0
\(748\) −2.66657 + 5.31664i −0.0974994 + 0.194395i
\(749\) 11.3667 0.415330
\(750\) 0 0
\(751\) 12.2346 37.6543i 0.446448 1.37403i −0.434439 0.900701i \(-0.643053\pi\)
0.880888 0.473326i \(-0.156947\pi\)
\(752\) −0.325473 1.00170i −0.0118688 0.0365284i
\(753\) 0 0
\(754\) 13.7482 9.98865i 0.500680 0.363765i
\(755\) −0.161111 0.495850i −0.00586344 0.0180458i
\(756\) 0 0
\(757\) −18.7253 13.6047i −0.680583 0.494472i 0.192968 0.981205i \(-0.438189\pi\)
−0.873551 + 0.486733i \(0.838189\pi\)
\(758\) 52.2959 1.89947
\(759\) 0 0
\(760\) −3.69577 −0.134060
\(761\) −12.0486 8.75381i −0.436761 0.317325i 0.347586 0.937648i \(-0.387002\pi\)
−0.784346 + 0.620323i \(0.787002\pi\)
\(762\) 0 0
\(763\) −3.05574 9.40460i −0.110625 0.340469i
\(764\) −1.64233 + 1.19322i −0.0594173 + 0.0431692i
\(765\) 0 0
\(766\) −8.77872 27.0181i −0.317188 0.976204i
\(767\) 3.47183 10.6852i 0.125361 0.385820i
\(768\) 0 0
\(769\) 21.6233 0.779757 0.389879 0.920866i \(-0.372517\pi\)
0.389879 + 0.920866i \(0.372517\pi\)
\(770\) −1.94653 + 1.00743i −0.0701481 + 0.0363052i
\(771\) 0 0
\(772\) −1.03255 0.750188i −0.0371621 0.0269999i
\(773\) 1.87664 5.77569i 0.0674979 0.207737i −0.911619 0.411037i \(-0.865167\pi\)
0.979117 + 0.203300i \(0.0651666\pi\)
\(774\) 0 0
\(775\) −34.3361 + 24.9466i −1.23339 + 0.896109i
\(776\) −28.5481 + 20.7414i −1.02482 + 0.744572i
\(777\) 0 0
\(778\) −14.7188 + 45.2999i −0.527695 + 1.62408i
\(779\) −2.34229 1.70177i −0.0839211 0.0609722i
\(780\) 0 0
\(781\) −29.0509 28.6842i −1.03952 1.02640i
\(782\) 31.6086 1.13032
\(783\) 0 0
\(784\) 9.26663 28.5197i 0.330951 1.01856i
\(785\) 1.79037 + 5.51018i 0.0639010 + 0.196667i
\(786\) 0 0
\(787\) −41.3856 + 30.0684i −1.47524 + 1.07182i −0.496183 + 0.868218i \(0.665265\pi\)
−0.979053 + 0.203604i \(0.934735\pi\)
\(788\) 2.71085 + 8.34314i 0.0965701 + 0.297212i
\(789\) 0 0
\(790\) 10.8264 + 7.86585i 0.385187 + 0.279854i
\(791\) −5.79736 −0.206130
\(792\) 0 0
\(793\) −7.18019 −0.254976
\(794\) −10.3768 7.53917i −0.368258 0.267555i
\(795\) 0 0
\(796\) −2.51372 7.73643i −0.0890964 0.274211i
\(797\) −20.4368 + 14.8482i −0.723907 + 0.525949i −0.887630 0.460557i \(-0.847650\pi\)
0.163723 + 0.986506i \(0.447650\pi\)
\(798\) 0 0
\(799\) −0.322903 0.993792i −0.0114235 0.0351579i
\(800\) −3.13143 + 9.63754i −0.110713 + 0.340738i
\(801\) 0 0
\(802\) −6.08192 −0.214760
\(803\) −45.6063 + 23.6036i −1.60941 + 0.832953i
\(804\) 0 0
\(805\) 1.53945 + 1.11848i 0.0542584 + 0.0394211i
\(806\) −6.86891 + 21.1403i −0.241947 + 0.744637i
\(807\) 0 0
\(808\) −28.9267 + 21.0165i −1.01764 + 0.739357i
\(809\) 41.5248 30.1696i 1.45994 1.06071i 0.476556 0.879144i \(-0.341885\pi\)
0.983380 0.181561i \(-0.0581150\pi\)
\(810\) 0 0
\(811\) 1.40476 4.32339i 0.0493276 0.151815i −0.923359 0.383939i \(-0.874567\pi\)
0.972686 + 0.232124i \(0.0745674\pi\)
\(812\) 1.59184 + 1.15654i 0.0558625 + 0.0405865i
\(813\) 0 0
\(814\) −14.6604 2.22663i −0.513845 0.0780433i
\(815\) −2.74097 −0.0960119
\(816\) 0 0
\(817\) −3.26707 + 10.0550i −0.114300 + 0.351780i
\(818\) 1.19649 + 3.68241i 0.0418342 + 0.128753i
\(819\) 0 0
\(820\) 0.215882 0.156848i 0.00753894 0.00547736i
\(821\) −3.36019 10.3416i −0.117271 0.360924i 0.875143 0.483865i \(-0.160767\pi\)
−0.992414 + 0.122941i \(0.960767\pi\)
\(822\) 0 0
\(823\) 19.1059 + 13.8812i 0.665988 + 0.483869i 0.868680 0.495374i \(-0.164969\pi\)
−0.202692 + 0.979243i \(0.564969\pi\)
\(824\) −11.0210 −0.383934
\(825\) 0 0
\(826\) 7.96271 0.277058
\(827\) −22.3321 16.2252i −0.776564 0.564207i 0.127382 0.991854i \(-0.459343\pi\)
−0.903946 + 0.427647i \(0.859343\pi\)
\(828\) 0 0
\(829\) −4.97546 15.3129i −0.172805 0.531839i 0.826722 0.562611i \(-0.190203\pi\)
−0.999526 + 0.0307727i \(0.990203\pi\)
\(830\) −5.14900 + 3.74097i −0.178724 + 0.129851i
\(831\) 0 0
\(832\) −2.86531 8.81852i −0.0993368 0.305727i
\(833\) 9.19344 28.2945i 0.318534 0.980347i
\(834\) 0 0
\(835\) −10.0571 −0.348039
\(836\) 0.528675 + 3.20601i 0.0182846 + 0.110882i
\(837\) 0 0
\(838\) −13.4334 9.75993i −0.464049 0.337151i
\(839\) 6.00479 18.4809i 0.207309 0.638030i −0.792302 0.610129i \(-0.791118\pi\)
0.999611 0.0279012i \(-0.00888236\pi\)
\(840\) 0 0
\(841\) −15.9386 + 11.5800i −0.549606 + 0.399312i
\(842\) 27.7532 20.1639i 0.956438 0.694893i
\(843\) 0 0
\(844\) 0.409359 1.25988i 0.0140907 0.0433668i
\(845\) −5.03845 3.66065i −0.173328 0.125930i
\(846\) 0 0
\(847\) −4.74909 6.36497i −0.163181 0.218703i
\(848\) −26.3994 −0.906559
\(849\) 0 0
\(850\) −10.2009 + 31.3951i −0.349888 + 1.07684i
\(851\) 3.97823 + 12.2437i 0.136372 + 0.419710i
\(852\) 0 0
\(853\) 16.0068 11.6296i 0.548063 0.398191i −0.279008 0.960289i \(-0.590006\pi\)
0.827071 + 0.562098i \(0.190006\pi\)
\(854\) −1.57255 4.83980i −0.0538114 0.165614i
\(855\) 0 0
\(856\) −31.6966 23.0289i −1.08337 0.787112i
\(857\) 4.34065 0.148274 0.0741369 0.997248i \(-0.476380\pi\)
0.0741369 + 0.997248i \(0.476380\pi\)
\(858\) 0 0
\(859\) −5.17935 −0.176717 −0.0883586 0.996089i \(-0.528162\pi\)
−0.0883586 + 0.996089i \(0.528162\pi\)
\(860\) −0.788334 0.572758i −0.0268820 0.0195309i
\(861\) 0 0
\(862\) −8.81901 27.1421i −0.300377 0.924464i
\(863\) −2.17943 + 1.58345i −0.0741886 + 0.0539011i −0.624261 0.781216i \(-0.714600\pi\)
0.550073 + 0.835117i \(0.314600\pi\)
\(864\) 0 0
\(865\) −0.108132 0.332797i −0.00367661 0.0113155i
\(866\) −7.22246 + 22.2285i −0.245429 + 0.755354i
\(867\) 0 0
\(868\) −2.57370 −0.0873571
\(869\) −21.7381 + 43.3417i −0.737414 + 1.47027i
\(870\) 0 0
\(871\) −10.3099 7.49056i −0.349337 0.253808i
\(872\) −10.5326 + 32.4161i −0.356680 + 1.09775i
\(873\) 0 0
\(874\) 13.9699 10.1497i 0.472538 0.343319i
\(875\) −3.33668 + 2.42424i −0.112800 + 0.0819543i
\(876\) 0 0
\(877\) −6.44139 + 19.8246i −0.217510 + 0.669428i 0.781456 + 0.623961i \(0.214478\pi\)
−0.998966 + 0.0454669i \(0.985522\pi\)
\(878\) 29.9646 + 21.7705i 1.01125 + 0.734720i
\(879\) 0 0
\(880\) 8.98535 + 1.36470i 0.302896 + 0.0460041i
\(881\) −11.5843 −0.390286 −0.195143 0.980775i \(-0.562517\pi\)
−0.195143 + 0.980775i \(0.562517\pi\)
\(882\) 0 0
\(883\) 4.75801 14.6437i 0.160120 0.492798i −0.838524 0.544865i \(-0.816581\pi\)
0.998644 + 0.0520667i \(0.0165808\pi\)
\(884\) 0.872808 + 2.68623i 0.0293557 + 0.0903476i
\(885\) 0 0
\(886\) −31.8938 + 23.1722i −1.07149 + 0.778486i
\(887\) 1.82628 + 5.62070i 0.0613204 + 0.188725i 0.977024 0.213130i \(-0.0683657\pi\)
−0.915703 + 0.401855i \(0.868366\pi\)
\(888\) 0 0
\(889\) 7.00669 + 5.09066i 0.234997 + 0.170735i
\(890\) −11.4240 −0.382932
\(891\) 0 0
\(892\) −4.30623 −0.144183
\(893\) −0.461824 0.335535i −0.0154543 0.0112282i
\(894\) 0 0
\(895\) −1.76379 5.42838i −0.0589569 0.181451i
\(896\) 7.86251 5.71245i 0.262668 0.190840i
\(897\) 0 0
\(898\) −10.7417 33.0595i −0.358455 1.10321i
\(899\) 19.6852 60.5847i 0.656537 2.02061i
\(900\) 0 0
\(901\) −26.1909 −0.872546
\(902\) 4.21134 + 4.15819i 0.140222 + 0.138453i
\(903\) 0 0
\(904\) 16.1662 + 11.7455i 0.537681 + 0.390648i
\(905\) 0.871174 2.68120i 0.0289588 0.0891260i
\(906\) 0 0
\(907\) 5.98132 4.34568i 0.198606 0.144296i −0.484037 0.875047i \(-0.660830\pi\)
0.682644 + 0.730751i \(0.260830\pi\)
\(908\) −1.88525 + 1.36971i −0.0625642 + 0.0454556i
\(909\) 0 0
\(910\) −0.321628 + 0.989869i −0.0106619 + 0.0328138i
\(911\) −11.4871 8.34585i −0.380584 0.276510i 0.381002 0.924574i \(-0.375579\pi\)
−0.761586 + 0.648064i \(0.775579\pi\)
\(912\) 0 0
\(913\) −16.4095 16.2024i −0.543074 0.536220i
\(914\) −33.5350 −1.10924
\(915\) 0 0
\(916\) 2.98698 9.19299i 0.0986927 0.303745i
\(917\) 1.53737 + 4.73153i 0.0507684 + 0.156249i
\(918\) 0 0
\(919\) 33.6895 24.4769i 1.11132 0.807418i 0.128445 0.991717i \(-0.459001\pi\)
0.982870 + 0.184299i \(0.0590013\pi\)
\(920\) −2.02680 6.23785i −0.0668217 0.205656i
\(921\) 0 0
\(922\) 15.1398 + 10.9997i 0.498604 + 0.362257i
\(923\) −19.3869 −0.638127
\(924\) 0 0
\(925\) −13.4449 −0.442067
\(926\) 25.0555 + 18.2039i 0.823376 + 0.598218i
\(927\) 0 0
\(928\) −4.70008 14.4654i −0.154288 0.474849i
\(929\) −27.6140 + 20.0627i −0.905986 + 0.658237i −0.939996 0.341184i \(-0.889172\pi\)
0.0340108 + 0.999421i \(0.489172\pi\)
\(930\) 0 0
\(931\) −5.02236 15.4572i −0.164601 0.506590i
\(932\) −0.505470 + 1.55568i −0.0165572 + 0.0509579i
\(933\) 0 0
\(934\) 9.38118 0.306962
\(935\) 8.91439 + 1.35393i 0.291532 + 0.0442781i
\(936\) 0 0
\(937\) −41.8118 30.3780i −1.36593 0.992407i −0.998043 0.0625376i \(-0.980081\pi\)
−0.367889 0.929870i \(-0.619919\pi\)
\(938\) 2.79102 8.58987i 0.0911299 0.280469i
\(939\) 0 0
\(940\) 0.0425651 0.0309253i 0.00138832 0.00100867i
\(941\) 14.5673 10.5838i 0.474881 0.345021i −0.324460 0.945900i \(-0.605182\pi\)
0.799340 + 0.600878i \(0.205182\pi\)
\(942\) 0 0
\(943\) 1.58777 4.88666i 0.0517050 0.159132i
\(944\) −26.7122 19.4075i −0.869407 0.631661i
\(945\) 0 0
\(946\) 9.68901 19.3181i 0.315017 0.628084i
\(947\) −28.6303 −0.930360 −0.465180 0.885216i \(-0.654010\pi\)
−0.465180 + 0.885216i \(0.654010\pi\)
\(948\) 0 0
\(949\) −7.53559 + 23.1922i −0.244616 + 0.752850i
\(950\) 5.57273 + 17.1511i 0.180803 + 0.556455i
\(951\) 0 0
\(952\) 6.67415 4.84905i 0.216310 0.157159i
\(953\) −5.15728 15.8725i −0.167061 0.514160i 0.832121 0.554594i \(-0.187126\pi\)
−0.999182 + 0.0404331i \(0.987126\pi\)
\(954\) 0 0
\(955\) 2.48967 + 1.80885i 0.0805637 + 0.0585330i
\(956\) 2.87938 0.0931257
\(957\) 0 0
\(958\) 56.0827 1.81195
\(959\) 5.40063 + 3.92379i 0.174396 + 0.126706i
\(960\) 0 0
\(961\) 16.1692 + 49.7638i 0.521589 + 1.60528i
\(962\) −5.69677 + 4.13895i −0.183671 + 0.133445i
\(963\) 0 0
\(964\) −1.06554 3.27939i −0.0343187 0.105622i
\(965\) −0.597882 + 1.84009i −0.0192465 + 0.0592347i
\(966\) 0 0
\(967\) 24.3193 0.782057 0.391029 0.920379i \(-0.372119\pi\)
0.391029 + 0.920379i \(0.372119\pi\)
\(968\) 0.347660 + 27.3707i 0.0111742 + 0.879728i
\(969\) 0 0
\(970\) −10.5013 7.62961i −0.337175 0.244972i
\(971\) −2.33367 + 7.18229i −0.0748910 + 0.230491i −0.981494 0.191495i \(-0.938667\pi\)
0.906603 + 0.421985i \(0.138667\pi\)
\(972\) 0 0
\(973\) −12.6225 + 9.17079i −0.404659 + 0.294002i
\(974\) −10.8635 + 7.89283i −0.348091 + 0.252903i
\(975\) 0 0
\(976\) −6.52069 + 20.0686i −0.208722 + 0.642381i
\(977\) 1.64415 + 1.19455i 0.0526011 + 0.0382170i 0.613775 0.789481i \(-0.289650\pi\)
−0.561174 + 0.827698i \(0.689650\pi\)
\(978\) 0 0
\(979\) −6.73470 40.8408i −0.215242 1.30528i
\(980\) 1.49797 0.0478508
\(981\) 0 0
\(982\) −15.8611 + 48.8154i −0.506148 + 1.55776i
\(983\) −10.3334 31.8030i −0.329584 1.01436i −0.969329 0.245769i \(-0.920960\pi\)
0.639744 0.768588i \(-0.279040\pi\)
\(984\) 0 0
\(985\) 10.7588 7.81671i 0.342803 0.249061i
\(986\) −15.3109 47.1222i −0.487600 1.50068i
\(987\) 0 0
\(988\) 1.24831 + 0.906952i 0.0397141 + 0.0288540i
\(989\) −18.7629 −0.596624
\(990\) 0 0
\(991\) 40.1009 1.27385 0.636923 0.770927i \(-0.280207\pi\)
0.636923 + 0.770927i \(0.280207\pi\)
\(992\) 16.0953 + 11.6939i 0.511026 + 0.371282i
\(993\) 0 0
\(994\) −4.24595 13.0677i −0.134673 0.414482i
\(995\) −9.97640 + 7.24828i −0.316273 + 0.229786i
\(996\) 0 0
\(997\) 4.98448 + 15.3406i 0.157860 + 0.485843i 0.998439 0.0558453i \(-0.0177854\pi\)
−0.840580 + 0.541688i \(0.817785\pi\)
\(998\) −9.97461 + 30.6987i −0.315741 + 0.971750i
\(999\) 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.f.e.730.8 36
3.2 odd 2 891.2.f.f.730.2 36
9.2 odd 6 99.2.m.b.4.2 72
9.4 even 3 297.2.n.b.235.2 72
9.5 odd 6 99.2.m.b.70.8 yes 72
9.7 even 3 297.2.n.b.37.8 72
11.3 even 5 inner 891.2.f.e.487.8 36
11.5 even 5 9801.2.a.cp.1.4 18
11.6 odd 10 9801.2.a.cn.1.15 18
33.5 odd 10 9801.2.a.cm.1.15 18
33.14 odd 10 891.2.f.f.487.2 36
33.17 even 10 9801.2.a.co.1.4 18
99.5 odd 30 1089.2.e.p.727.4 36
99.14 odd 30 99.2.m.b.25.2 yes 72
99.25 even 15 297.2.n.b.91.2 72
99.38 odd 30 1089.2.e.p.364.4 36
99.47 odd 30 99.2.m.b.58.8 yes 72
99.50 even 30 1089.2.e.o.727.15 36
99.58 even 15 297.2.n.b.289.8 72
99.83 even 30 1089.2.e.o.364.15 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 9.2 odd 6
99.2.m.b.25.2 yes 72 99.14 odd 30
99.2.m.b.58.8 yes 72 99.47 odd 30
99.2.m.b.70.8 yes 72 9.5 odd 6
297.2.n.b.37.8 72 9.7 even 3
297.2.n.b.91.2 72 99.25 even 15
297.2.n.b.235.2 72 9.4 even 3
297.2.n.b.289.8 72 99.58 even 15
891.2.f.e.487.8 36 11.3 even 5 inner
891.2.f.e.730.8 36 1.1 even 1 trivial
891.2.f.f.487.2 36 33.14 odd 10
891.2.f.f.730.2 36 3.2 odd 2
1089.2.e.o.364.15 36 99.83 even 30
1089.2.e.o.727.15 36 99.50 even 30
1089.2.e.p.364.4 36 99.38 odd 30
1089.2.e.p.727.4 36 99.5 odd 30
9801.2.a.cm.1.15 18 33.5 odd 10
9801.2.a.cn.1.15 18 11.6 odd 10
9801.2.a.co.1.4 18 33.17 even 10
9801.2.a.cp.1.4 18 11.5 even 5