Properties

Label 891.2.f.e.487.8
Level $891$
Weight $2$
Character 891.487
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 487.8
Character \(\chi\) \(=\) 891.487
Dual form 891.2.f.e.730.8

$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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 −0.0499492 0.998752i \(-0.515906\pi\)
0.934434 + 0.356136i \(0.115906\pi\)
\(3\) 0 0
\(4\) 0.120683 0.371424i 0.0603415 0.185712i
\(5\) 0.478964 + 0.347988i 0.214199 + 0.155625i 0.689712 0.724084i \(-0.257737\pi\)
−0.475512 + 0.879709i \(0.657737\pi\)
\(6\) 0 0
\(7\) 0.223095 0.686616i 0.0843220 0.259516i −0.900002 0.435886i \(-0.856435\pi\)
0.984324 + 0.176369i \(0.0564353\pi\)
\(8\) 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 −0.396899 0.917862i \(-0.629914\pi\)
0.750291 + 0.661108i \(0.229914\pi\)
\(14\) −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 0.938728 0.344658i \(-0.112005\pi\)
−0.0377065 + 0.999289i \(0.512005\pi\)
\(18\) 0 0
\(19\) 0.775200 + 2.38582i 0.177843 + 0.547345i 0.999752 0.0222743i \(-0.00709072\pi\)
−0.821909 + 0.569619i \(0.807091\pi\)
\(20\) 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 0.524177 + 0.851609i \(0.324373\pi\)
−0.924632 + 0.380863i \(0.875627\pi\)
\(30\) 0 0
\(31\) 7.38490 5.36545i 1.32637 0.963662i 0.326538 0.945184i \(-0.394118\pi\)
0.999829 0.0184785i \(-0.00588222\pi\)
\(32\) 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 −0.850347 0.526223i \(-0.823608\pi\)
0.997251 + 0.0740981i \(0.0236078\pi\)
\(38\) 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 0.975036 0.222049i \(-0.0712744\pi\)
−0.919337 + 0.393470i \(0.871274\pi\)
\(42\) 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 0.956054 0.293191i \(-0.0947170\pi\)
−0.945797 + 0.324758i \(0.894717\pi\)
\(48\) 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 −0.857723 0.514113i \(-0.828121\pi\)
0.223899 + 0.974612i \(0.428121\pi\)
\(54\) 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 0.698809 + 0.715308i \(0.253714\pi\)
−0.985796 + 0.167947i \(0.946286\pi\)
\(60\) 0 0
\(61\) −3.68827 2.67969i −0.472235 0.343099i 0.326077 0.945343i \(-0.394273\pi\)
−0.798312 + 0.602244i \(0.794273\pi\)
\(62\) 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 −0.189478 0.981885i \(-0.560680\pi\)
−0.992380 + 0.123215i \(0.960680\pi\)
\(72\) 0 0
\(73\) 4.78461 14.7255i 0.559996 1.72349i −0.122373 0.992484i \(-0.539050\pi\)
0.682370 0.731007i \(-0.260950\pi\)
\(74\) −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 0.330962 0.943644i \(-0.392627\pi\)
0.999732 0.0231619i \(-0.00737332\pi\)
\(80\) 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 0.234590 0.972094i \(-0.424625\pi\)
−0.852024 + 0.523502i \(0.824625\pi\)
\(84\) 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 −0.990381 0.138368i \(-0.955814\pi\)
−0.174449 + 0.984666i \(0.555814\pi\)
\(98\) 10.0171 1.01188
\(99\) 0 0
\(100\) −1.81581 −0.181581
\(101\) −11.6244 + 8.44561i −1.15667 + 0.840370i −0.989353 0.145533i \(-0.953510\pi\)
−0.167317 + 0.985903i \(0.553510\pi\)
\(102\) 0 0
\(103\) −1.36859 + 4.21209i −0.134851 + 0.415029i −0.995567 0.0940566i \(-0.970017\pi\)
0.860716 + 0.509086i \(0.170017\pi\)
\(104\) 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 0.852134 + 0.523324i \(0.175308\pi\)
−0.381788 + 0.924250i \(0.624692\pi\)
\(108\) 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 −0.997325 0.0730926i \(-0.976713\pi\)
0.763890 0.645346i \(-0.223287\pi\)
\(114\) 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 0.928211 0.372054i \(-0.121347\pi\)
−0.0670118 + 0.997752i \(0.521347\pi\)
\(128\) −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 0.859545 0.511060i \(-0.170747\pi\)
−0.220433 + 0.975402i \(0.570747\pi\)
\(138\) 0 0
\(139\) 6.67826 20.5536i 0.566442 1.74333i −0.0971841 0.995266i \(-0.530984\pi\)
0.663627 0.748064i \(-0.269016\pi\)
\(140\) −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 0.549146 0.835727i \(-0.314953\pi\)
−0.625128 + 0.780522i \(0.714953\pi\)
\(150\) 0 0
\(151\) 0.272133 + 0.837539i 0.0221459 + 0.0681579i 0.961519 0.274740i \(-0.0885916\pi\)
−0.939373 + 0.342898i \(0.888592\pi\)
\(152\) −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 −0.996215 0.0869191i \(-0.972298\pi\)
0.754865 0.655880i \(-0.227702\pi\)
\(158\) 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 −0.724730 0.689033i \(-0.758035\pi\)
0.431355 + 0.902182i \(0.358035\pi\)
\(164\) 0.450728 0.0351959
\(165\) 0 0
\(166\) −10.7503 −0.834384
\(167\) −13.7431 + 9.98493i −1.06347 + 0.772657i −0.974727 0.223397i \(-0.928285\pi\)
−0.0887440 + 0.996054i \(0.528285\pi\)
\(168\) 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 0.957760 0.287570i \(-0.0928474\pi\)
−0.943873 + 0.330308i \(0.892847\pi\)
\(174\) 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 0.998519 + 0.0544017i \(0.0173251\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(180\) 0 0
\(181\) 3.85243 + 2.79896i 0.286349 + 0.208045i 0.721682 0.692225i \(-0.243369\pi\)
−0.435333 + 0.900270i \(0.643369\pi\)
\(182\) −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 −0.875975 0.482357i \(-0.839781\pi\)
0.992201 + 0.124650i \(0.0397807\pi\)
\(192\) 0 0
\(193\) −2.64390 1.92091i −0.190312 0.138270i 0.488549 0.872536i \(-0.337526\pi\)
−0.678861 + 0.734266i \(0.737526\pi\)
\(194\) −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 −0.678224 0.734855i \(-0.737250\pi\)
0.489306 + 0.872112i \(0.337250\pi\)
\(212\) 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 −0.997954 0.0639353i \(-0.979635\pi\)
0.769782 0.638307i \(-0.220365\pi\)
\(224\) 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 −0.871033 0.491224i \(-0.836549\pi\)
0.993415 + 0.114571i \(0.0365495\pi\)
\(228\) 0 0
\(229\) −20.0237 + 14.5481i −1.32320 + 0.961364i −0.323318 + 0.946290i \(0.604798\pi\)
−0.999886 + 0.0150739i \(0.995202\pi\)
\(230\) 4.07519 0.268710
\(231\) 0 0
\(232\) −17.3659 −1.14013
\(233\) 3.38850 2.46189i 0.221988 0.161284i −0.471233 0.882009i \(-0.656191\pi\)
0.693221 + 0.720725i \(0.256191\pi\)
\(234\) 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 0.997309 0.0733190i \(-0.0233591\pi\)
−0.849935 + 0.526887i \(0.823359\pi\)
\(240\) 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 0.0782385 0.996935i \(-0.475070\pi\)
0.972318 + 0.233661i \(0.0750704\pi\)
\(252\) 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 −0.913150 0.407623i \(-0.866358\pi\)
0.978349 + 0.206962i \(0.0663577\pi\)
\(258\) 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 0.741065 0.671433i \(-0.234321\pi\)
−0.409570 + 0.912279i \(0.634321\pi\)
\(270\) 0 0
\(271\) −1.23000 + 3.78554i −0.0747170 + 0.229955i −0.981439 0.191773i \(-0.938576\pi\)
0.906722 + 0.421728i \(0.138576\pi\)
\(272\) 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 −0.220943 0.975287i \(-0.570913\pi\)
0.859278 + 0.511509i \(0.170913\pi\)
\(278\) −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 0.513860 0.857874i \(-0.328215\pi\)
−0.657095 + 0.753808i \(0.728215\pi\)
\(282\) 0 0
\(283\) 2.50081 + 7.69669i 0.148657 + 0.457521i 0.997463 0.0711843i \(-0.0226778\pi\)
−0.848806 + 0.528705i \(0.822678\pi\)
\(284\) −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 −0.703069 0.711122i \(-0.748187\pi\)
0.986782 0.162056i \(-0.0518126\pi\)
\(294\) 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 −0.863391 0.504535i \(-0.831664\pi\)
0.401940 0.915666i \(-0.368336\pi\)
\(312\) 0 0
\(313\) 1.99111 + 1.44662i 0.112544 + 0.0817679i 0.642634 0.766174i \(-0.277842\pi\)
−0.530090 + 0.847942i \(0.677842\pi\)
\(314\) −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 −0.994716 0.102669i \(-0.967262\pi\)
−0.209740 + 0.977757i \(0.567262\pi\)
\(318\) 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 −0.495110 0.868830i \(-0.664872\pi\)
0.911238 0.411880i \(-0.135128\pi\)
\(338\) 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 0.541935 0.840420i \(-0.317692\pi\)
−0.631820 + 0.775115i \(0.717692\pi\)
\(348\) 0 0
\(349\) −1.61130 4.95906i −0.0862507 0.265452i 0.898624 0.438719i \(-0.144568\pi\)
−0.984875 + 0.173267i \(0.944568\pi\)
\(350\) −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 −0.996715 0.0809868i \(-0.974193\pi\)
0.853962 + 0.520335i \(0.174193\pi\)
\(360\) 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 −0.990680 0.136206i \(-0.956509\pi\)
0.881537 + 0.472114i \(0.156509\pi\)
\(368\) 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 0.993946 + 0.109873i \(0.0350445\pi\)
0.411642 + 0.911346i \(0.364955\pi\)
\(380\) 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 −0.898774 0.438413i \(-0.855541\pi\)
0.139219 + 0.990262i \(0.455541\pi\)
\(384\) 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 −0.352657 0.935753i \(-0.614722\pi\)
0.835327 0.549754i \(-0.185278\pi\)
\(390\) 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 0.505483 0.862836i \(-0.331314\pi\)
−0.664403 + 0.747374i \(0.731314\pi\)
\(402\) 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 −0.536568 0.843857i \(-0.680280\pi\)
0.636747 + 0.771073i \(0.280280\pi\)
\(410\) 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 0.967136 + 0.254258i \(0.0818311\pi\)
−0.632981 + 0.774167i \(0.718169\pi\)
\(422\) −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 −0.886160 0.463380i \(-0.846636\pi\)
0.166862 + 0.985980i \(0.446636\pi\)
\(432\) 0 0
\(433\) 4.67130 14.3768i 0.224488 0.690904i −0.773855 0.633363i \(-0.781674\pi\)
0.998343 0.0575408i \(-0.0183259\pi\)
\(434\) −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 −0.943914 0.330192i \(-0.892887\pi\)
0.569561 0.821949i \(-0.307113\pi\)
\(444\) 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 −0.927442 0.373966i \(-0.877998\pi\)
0.0690672 + 0.997612i \(0.477998\pi\)
\(450\) 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 0.0961237 0.995369i \(-0.469356\pi\)
−0.916949 + 0.399005i \(0.869356\pi\)
\(458\) −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 0.695538 0.718489i \(-0.255166\pi\)
−0.468390 + 0.883522i \(0.655166\pi\)
\(468\) 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 0.999413 + 0.0342489i \(0.0109039\pi\)
0.341408 + 0.939915i \(0.389096\pi\)
\(480\) 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 0.871655 0.490120i \(-0.163047\pi\)
−0.993269 + 0.115830i \(0.963047\pi\)
\(488\) 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 −0.398567 0.917139i \(-0.630492\pi\)
0.861529 0.507709i \(-0.169508\pi\)
\(492\) 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 −0.696433 0.717622i \(-0.745231\pi\)
0.985234 0.171215i \(-0.0547692\pi\)
\(500\) −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 −0.973085 0.230448i \(-0.925981\pi\)
0.651788 0.758401i \(-0.274019\pi\)
\(504\) 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 0.896808 0.442420i \(-0.145880\pi\)
−0.985581 + 0.169205i \(0.945880\pi\)
\(510\) 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 −0.427738 0.903903i \(-0.640689\pi\)
0.877348 0.479855i \(-0.159311\pi\)
\(522\) 0 0
\(523\) 32.4728 + 23.5929i 1.41994 + 1.03164i 0.991782 + 0.127938i \(0.0408359\pi\)
0.428154 + 0.903706i \(0.359164\pi\)
\(524\) 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 −0.927158 0.374671i \(-0.877756\pi\)
0.0698260 + 0.997559i \(0.477756\pi\)
\(542\) 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 0.964292 + 0.264841i \(0.0853195\pi\)
−0.624459 + 0.781058i \(0.714681\pi\)
\(548\) 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 −0.997948 0.0640357i \(-0.979603\pi\)
0.844996 + 0.534773i \(0.179603\pi\)
\(558\) 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 −0.440647 0.897681i \(-0.645251\pi\)
0.717578 + 0.696478i \(0.245251\pi\)
\(564\) 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 0.997346 + 0.0728046i \(0.0231950\pi\)
−0.764077 + 0.645126i \(0.776805\pi\)
\(570\) 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 −0.192409 0.981315i \(-0.561630\pi\)
−0.992744 + 0.120251i \(0.961630\pi\)
\(578\) 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 0.680955 + 0.732325i \(0.261565\pi\)
−0.981354 + 0.192208i \(0.938435\pi\)
\(588\) 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 0.985846 0.167653i \(-0.0536188\pi\)
0.145196 + 0.989403i \(0.453619\pi\)
\(600\) 0 0
\(601\) 8.97030 27.6077i 0.365906 1.12614i −0.583505 0.812109i \(-0.698319\pi\)
0.949412 0.314034i \(-0.101681\pi\)
\(602\) 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 −0.534756 0.845007i \(-0.679596\pi\)
0.638401 + 0.769704i \(0.279596\pi\)
\(608\) 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 0.904309 + 0.426878i \(0.140387\pi\)
−0.480689 + 0.876891i \(0.659613\pi\)
\(614\) −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 0.993874 + 0.110521i \(0.0352519\pi\)
−0.739098 + 0.673598i \(0.764748\pi\)
\(620\) 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 −0.581087 0.813841i \(-0.697372\pi\)
0.948473 0.316857i \(-0.102628\pi\)
\(632\) 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 0.858640 + 0.512579i \(0.171310\pi\)
−0.393368 + 0.919381i \(0.628690\pi\)
\(642\) 0 0
\(643\) 13.6118 + 9.88957i 0.536798 + 0.390006i 0.822894 0.568194i \(-0.192358\pi\)
−0.286097 + 0.958201i \(0.592358\pi\)
\(644\) −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 −0.869056 0.494713i \(-0.835273\pi\)
0.201947 + 0.979396i \(0.435273\pi\)
\(648\) 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 0.757530 + 0.652801i \(0.226406\pi\)
−0.996561 + 0.0828623i \(0.973594\pi\)
\(654\) 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 −0.851001 0.525163i \(-0.824004\pi\)
0.236486 + 0.971635i \(0.424004\pi\)
\(674\) −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 0.377822 0.925878i \(-0.376673\pi\)
−0.763809 + 0.645443i \(0.776673\pi\)
\(678\) 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 −0.623254 0.782020i \(-0.714190\pi\)
0.551149 + 0.834407i \(0.314190\pi\)
\(692\) 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 0.973591 0.228301i \(-0.0733170\pi\)
−0.921843 + 0.387563i \(0.873317\pi\)
\(702\) 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 0.0325612 0.999470i \(-0.489634\pi\)
−0.940490 + 0.339821i \(0.889634\pi\)
\(710\) −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 −0.745603 0.666390i \(-0.767838\pi\)
0.994900 0.100867i \(-0.0321616\pi\)
\(720\) 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 −0.0558724 + 0.998438i \(0.517794\pi\)
−0.541665 + 0.840594i \(0.682206\pi\)
\(734\) 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 0.393122 0.919486i \(-0.371395\pi\)
0.995965 0.0897445i \(-0.0286051\pi\)
\(740\) −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 0.213827 0.976871i \(-0.431407\pi\)
−0.862984 + 0.505232i \(0.831407\pi\)
\(744\) 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 0.880888 + 0.473326i \(0.156947\pi\)
−0.434439 + 0.900701i \(0.643053\pi\)
\(752\) −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 −0.873551 0.486733i \(-0.838189\pi\)
0.192968 + 0.981205i \(0.438189\pi\)
\(758\) 52.2959 1.89947
\(759\) 0 0
\(760\) −3.69577 −0.134060
\(761\) −12.0486 + 8.75381i −0.436761 + 0.317325i −0.784346 0.620323i \(-0.787002\pi\)
0.347586 + 0.937648i \(0.387002\pi\)
\(762\) 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 0.979117 0.203300i \(-0.0651666\pi\)
−0.911619 + 0.411037i \(0.865167\pi\)
\(774\) 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 −0.979053 0.203604i \(-0.934735\pi\)
−0.496183 0.868218i \(-0.665265\pi\)
\(788\) 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 0.163723 0.986506i \(-0.447650\pi\)
−0.887630 + 0.460557i \(0.847650\pi\)
\(798\) 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 0.983380 + 0.181561i \(0.0581150\pi\)
0.476556 + 0.879144i \(0.341885\pi\)
\(810\) 0 0
\(811\) 1.40476 + 4.32339i 0.0493276 + 0.151815i 0.972686 0.232124i \(-0.0745674\pi\)
−0.923359 + 0.383939i \(0.874567\pi\)
\(812\) 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 −0.992414 0.122941i \(-0.960767\pi\)
0.875143 + 0.483865i \(0.160767\pi\)
\(822\) 0 0
\(823\) 19.1059 13.8812i 0.665988 0.483869i −0.202692 0.979243i \(-0.564969\pi\)
0.868680 + 0.495374i \(0.164969\pi\)
\(824\) −11.0210 −0.383934
\(825\) 0 0
\(826\) 7.96271 0.277058
\(827\) −22.3321 + 16.2252i −0.776564 + 0.564207i −0.903946 0.427647i \(-0.859343\pi\)
0.127382 + 0.991854i \(0.459343\pi\)
\(828\) 0 0
\(829\) −4.97546 + 15.3129i −0.172805 + 0.531839i −0.999526 0.0307727i \(-0.990203\pi\)
0.826722 + 0.562611i \(0.190203\pi\)
\(830\) −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 0.999611 + 0.0279012i \(0.00888236\pi\)
−0.792302 + 0.610129i \(0.791118\pi\)
\(840\) 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 0.827071 0.562098i \(-0.190006\pi\)
−0.279008 + 0.960289i \(0.590006\pi\)
\(854\) −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 0.550073 0.835117i \(-0.314600\pi\)
−0.624261 + 0.781216i \(0.714600\pi\)
\(864\) 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 −0.998966 0.0454669i \(-0.985522\pi\)
0.781456 0.623961i \(-0.214478\pi\)
\(878\) 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 0.998644 0.0520667i \(-0.0165808\pi\)
−0.838524 + 0.544865i \(0.816581\pi\)
\(884\) 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 −0.915703 0.401855i \(-0.868366\pi\)
0.977024 + 0.213130i \(0.0683657\pi\)
\(888\) 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 0.682644 0.730751i \(-0.260830\pi\)
−0.484037 + 0.875047i \(0.660830\pi\)
\(908\) −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 −0.761586 0.648064i \(-0.775579\pi\)
0.381002 + 0.924574i \(0.375579\pi\)
\(912\) 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 0.982870 0.184299i \(-0.0590013\pi\)
0.128445 + 0.991717i \(0.459001\pi\)
\(920\) −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 0.0340108 0.999421i \(-0.489172\pi\)
−0.939996 + 0.341184i \(0.889172\pi\)
\(930\) 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 −0.367889 + 0.929870i \(0.619919\pi\)
−0.998043 + 0.0625376i \(0.980081\pi\)
\(938\) 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 0.799340 0.600878i \(-0.205182\pi\)
−0.324460 + 0.945900i \(0.605182\pi\)
\(942\) 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 −0.999182 0.0404331i \(-0.987126\pi\)
0.832121 + 0.554594i \(0.187126\pi\)
\(954\) 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 0.906603 0.421985i \(-0.138667\pi\)
−0.981494 + 0.191495i \(0.938667\pi\)
\(972\) 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 −0.561174 0.827698i \(-0.689650\pi\)
0.613775 + 0.789481i \(0.289650\pi\)
\(978\) 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 0.639744 + 0.768588i \(0.279040\pi\)
−0.969329 + 0.245769i \(0.920960\pi\)
\(984\) 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 −0.840580 0.541688i \(-0.817785\pi\)
0.998439 + 0.0558453i \(0.0177854\pi\)
\(998\) −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.487.8 36
3.2 odd 2 891.2.f.f.487.2 36
9.2 odd 6 99.2.m.b.58.8 yes 72
9.4 even 3 297.2.n.b.289.8 72
9.5 odd 6 99.2.m.b.25.2 yes 72
9.7 even 3 297.2.n.b.91.2 72
11.2 odd 10 9801.2.a.cn.1.15 18
11.4 even 5 inner 891.2.f.e.730.8 36
11.9 even 5 9801.2.a.cp.1.4 18
33.2 even 10 9801.2.a.co.1.4 18
33.20 odd 10 9801.2.a.cm.1.15 18
33.26 odd 10 891.2.f.f.730.2 36
99.2 even 30 1089.2.e.o.364.15 36
99.4 even 15 297.2.n.b.235.2 72
99.20 odd 30 1089.2.e.p.364.4 36
99.59 odd 30 99.2.m.b.70.8 yes 72
99.68 even 30 1089.2.e.o.727.15 36
99.70 even 15 297.2.n.b.37.8 72
99.86 odd 30 1089.2.e.p.727.4 36
99.92 odd 30 99.2.m.b.4.2 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 99.92 odd 30
99.2.m.b.25.2 yes 72 9.5 odd 6
99.2.m.b.58.8 yes 72 9.2 odd 6
99.2.m.b.70.8 yes 72 99.59 odd 30
297.2.n.b.37.8 72 99.70 even 15
297.2.n.b.91.2 72 9.7 even 3
297.2.n.b.235.2 72 99.4 even 15
297.2.n.b.289.8 72 9.4 even 3
891.2.f.e.487.8 36 1.1 even 1 trivial
891.2.f.e.730.8 36 11.4 even 5 inner
891.2.f.f.487.2 36 3.2 odd 2
891.2.f.f.730.2 36 33.26 odd 10
1089.2.e.o.364.15 36 99.2 even 30
1089.2.e.o.727.15 36 99.68 even 30
1089.2.e.p.364.4 36 99.20 odd 30
1089.2.e.p.727.4 36 99.86 odd 30
9801.2.a.cm.1.15 18 33.20 odd 10
9801.2.a.cn.1.15 18 11.2 odd 10
9801.2.a.co.1.4 18 33.2 even 10
9801.2.a.cp.1.4 18 11.9 even 5