Properties

Label 324.3.j.a.199.31
Level $324$
Weight $3$
Character 324.199
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.31
Character \(\chi\) \(=\) 324.199
Dual form 324.3.j.a.127.31

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.93570 - 0.503058i) q^{2} +(3.49386 - 1.94754i) q^{4} +(-3.67109 + 1.33617i) q^{5} +(2.42790 - 0.428104i) q^{7} +(5.78335 - 5.52747i) q^{8} +O(q^{10})\) \(q+(1.93570 - 0.503058i) q^{2} +(3.49386 - 1.94754i) q^{4} +(-3.67109 + 1.33617i) q^{5} +(2.42790 - 0.428104i) q^{7} +(5.78335 - 5.52747i) q^{8} +(-6.43396 + 4.43320i) q^{10} +(6.11759 - 16.8080i) q^{11} +(15.7646 + 13.2281i) q^{13} +(4.48432 - 2.05006i) q^{14} +(8.41418 - 13.6089i) q^{16} +(11.4681 - 19.8634i) q^{17} +(6.65039 - 3.83960i) q^{19} +(-10.2241 + 11.8180i) q^{20} +(3.38644 - 35.6127i) q^{22} +(-1.94638 - 0.343200i) q^{23} +(-7.45952 + 6.25928i) q^{25} +(37.1701 + 17.6751i) q^{26} +(7.64900 - 6.22417i) q^{28} +(-33.6153 + 28.2066i) q^{29} +(20.3189 + 3.58277i) q^{31} +(9.44126 - 30.5755i) q^{32} +(12.2064 - 44.2187i) q^{34} +(-8.34103 + 4.81570i) q^{35} +(-15.3854 + 26.6483i) q^{37} +(10.9416 - 10.7778i) q^{38} +(-13.8456 + 28.0194i) q^{40} +(4.57109 + 3.83560i) q^{41} +(10.9148 - 29.9881i) q^{43} +(-11.3601 - 70.6390i) q^{44} +(-3.94026 + 0.314813i) q^{46} +(-53.8769 + 9.49995i) q^{47} +(-40.3335 + 14.6802i) q^{49} +(-11.2906 + 15.8687i) q^{50} +(80.8418 + 15.5149i) q^{52} -19.4599 q^{53} +69.8777i q^{55} +(11.6751 - 15.8960i) q^{56} +(-50.8796 + 71.5100i) q^{58} +(19.2036 + 52.7614i) q^{59} +(-2.78225 - 15.7789i) q^{61} +(41.1336 - 3.28642i) q^{62} +(2.89417 - 63.9345i) q^{64} +(-75.5485 - 27.4974i) q^{65} +(1.41276 - 1.68366i) q^{67} +(1.38337 - 91.7347i) q^{68} +(-13.7232 + 13.5178i) q^{70} +(86.0838 + 49.7005i) q^{71} +(31.8044 + 55.0868i) q^{73} +(-16.3759 + 59.3229i) q^{74} +(15.7578 - 26.3669i) q^{76} +(7.65735 - 43.4270i) q^{77} +(-12.9960 - 15.4880i) q^{79} +(-12.7055 + 61.2023i) q^{80} +(10.7778 + 5.12504i) q^{82} +(-33.4876 - 39.9089i) q^{83} +(-15.5598 + 88.2438i) q^{85} +(6.04197 - 63.5388i) q^{86} +(-57.5253 - 131.021i) q^{88} +(8.30808 + 14.3900i) q^{89} +(43.9380 + 25.3676i) q^{91} +(-7.46880 + 2.59157i) q^{92} +(-99.5105 + 45.4923i) q^{94} +(-19.2838 + 22.9816i) q^{95} +(-120.060 - 43.6982i) q^{97} +(-70.6886 + 48.7066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93570 0.503058i 0.967850 0.251529i
\(3\) 0 0
\(4\) 3.49386 1.94754i 0.873466 0.486885i
\(5\) −3.67109 + 1.33617i −0.734219 + 0.267234i −0.681950 0.731399i \(-0.738868\pi\)
−0.0522694 + 0.998633i \(0.516645\pi\)
\(6\) 0 0
\(7\) 2.42790 0.428104i 0.346843 0.0611577i 0.00248686 0.999997i \(-0.499208\pi\)
0.344356 + 0.938839i \(0.388097\pi\)
\(8\) 5.78335 5.52747i 0.722918 0.690934i
\(9\) 0 0
\(10\) −6.43396 + 4.43320i −0.643396 + 0.443320i
\(11\) 6.11759 16.8080i 0.556145 1.52800i −0.269038 0.963130i \(-0.586706\pi\)
0.825183 0.564866i \(-0.191072\pi\)
\(12\) 0 0
\(13\) 15.7646 + 13.2281i 1.21266 + 1.01755i 0.999175 + 0.0406014i \(0.0129274\pi\)
0.213490 + 0.976945i \(0.431517\pi\)
\(14\) 4.48432 2.05006i 0.320309 0.146433i
\(15\) 0 0
\(16\) 8.41418 13.6089i 0.525886 0.850555i
\(17\) 11.4681 19.8634i 0.674597 1.16844i −0.301990 0.953311i \(-0.597651\pi\)
0.976587 0.215125i \(-0.0690157\pi\)
\(18\) 0 0
\(19\) 6.65039 3.83960i 0.350020 0.202084i −0.314674 0.949200i \(-0.601895\pi\)
0.664694 + 0.747116i \(0.268562\pi\)
\(20\) −10.2241 + 11.8180i −0.511203 + 0.590900i
\(21\) 0 0
\(22\) 3.38644 35.6127i 0.153929 1.61876i
\(23\) −1.94638 0.343200i −0.0846254 0.0149217i 0.131175 0.991359i \(-0.458125\pi\)
−0.215801 + 0.976437i \(0.569236\pi\)
\(24\) 0 0
\(25\) −7.45952 + 6.25928i −0.298381 + 0.250371i
\(26\) 37.1701 + 17.6751i 1.42962 + 0.679812i
\(27\) 0 0
\(28\) 7.64900 6.22417i 0.273179 0.222292i
\(29\) −33.6153 + 28.2066i −1.15915 + 0.972641i −0.999893 0.0145960i \(-0.995354\pi\)
−0.159255 + 0.987237i \(0.550909\pi\)
\(30\) 0 0
\(31\) 20.3189 + 3.58277i 0.655448 + 0.115573i 0.491475 0.870892i \(-0.336458\pi\)
0.163973 + 0.986465i \(0.447569\pi\)
\(32\) 9.44126 30.5755i 0.295039 0.955485i
\(33\) 0 0
\(34\) 12.2064 44.2187i 0.359012 1.30055i
\(35\) −8.34103 + 4.81570i −0.238315 + 0.137591i
\(36\) 0 0
\(37\) −15.3854 + 26.6483i −0.415822 + 0.720225i −0.995514 0.0946106i \(-0.969839\pi\)
0.579692 + 0.814835i \(0.303173\pi\)
\(38\) 10.9416 10.7778i 0.287937 0.283628i
\(39\) 0 0
\(40\) −13.8456 + 28.0194i −0.346139 + 0.700485i
\(41\) 4.57109 + 3.83560i 0.111490 + 0.0935512i 0.696828 0.717238i \(-0.254594\pi\)
−0.585338 + 0.810789i \(0.699038\pi\)
\(42\) 0 0
\(43\) 10.9148 29.9881i 0.253832 0.697399i −0.745684 0.666300i \(-0.767877\pi\)
0.999516 0.0310988i \(-0.00990066\pi\)
\(44\) −11.3601 70.6390i −0.258184 1.60543i
\(45\) 0 0
\(46\) −3.94026 + 0.314813i −0.0856579 + 0.00684375i
\(47\) −53.8769 + 9.49995i −1.14632 + 0.202127i −0.714367 0.699771i \(-0.753285\pi\)
−0.431950 + 0.901898i \(0.642174\pi\)
\(48\) 0 0
\(49\) −40.3335 + 14.6802i −0.823133 + 0.299596i
\(50\) −11.2906 + 15.8687i −0.225812 + 0.317373i
\(51\) 0 0
\(52\) 80.8418 + 15.5149i 1.55465 + 0.298364i
\(53\) −19.4599 −0.367168 −0.183584 0.983004i \(-0.558770\pi\)
−0.183584 + 0.983004i \(0.558770\pi\)
\(54\) 0 0
\(55\) 69.8777i 1.27050i
\(56\) 11.6751 15.8960i 0.208483 0.283857i
\(57\) 0 0
\(58\) −50.8796 + 71.5100i −0.877234 + 1.23293i
\(59\) 19.2036 + 52.7614i 0.325484 + 0.894261i 0.989239 + 0.146310i \(0.0467398\pi\)
−0.663754 + 0.747951i \(0.731038\pi\)
\(60\) 0 0
\(61\) −2.78225 15.7789i −0.0456107 0.258671i 0.953473 0.301480i \(-0.0974806\pi\)
−0.999083 + 0.0428085i \(0.986369\pi\)
\(62\) 41.1336 3.28642i 0.663445 0.0530068i
\(63\) 0 0
\(64\) 2.89417 63.9345i 0.0452214 0.998977i
\(65\) −75.5485 27.4974i −1.16228 0.423037i
\(66\) 0 0
\(67\) 1.41276 1.68366i 0.0210859 0.0251292i −0.755398 0.655266i \(-0.772557\pi\)
0.776484 + 0.630137i \(0.217001\pi\)
\(68\) 1.38337 91.7347i 0.0203436 1.34904i
\(69\) 0 0
\(70\) −13.7232 + 13.5178i −0.196045 + 0.193111i
\(71\) 86.0838 + 49.7005i 1.21245 + 0.700007i 0.963292 0.268456i \(-0.0865134\pi\)
0.249156 + 0.968463i \(0.419847\pi\)
\(72\) 0 0
\(73\) 31.8044 + 55.0868i 0.435676 + 0.754614i 0.997351 0.0727449i \(-0.0231759\pi\)
−0.561674 + 0.827358i \(0.689843\pi\)
\(74\) −16.3759 + 59.3229i −0.221296 + 0.801661i
\(75\) 0 0
\(76\) 15.7578 26.3669i 0.207339 0.346933i
\(77\) 7.65735 43.4270i 0.0994461 0.563987i
\(78\) 0 0
\(79\) −12.9960 15.4880i −0.164506 0.196051i 0.677494 0.735529i \(-0.263066\pi\)
−0.842000 + 0.539478i \(0.818622\pi\)
\(80\) −12.7055 + 61.2023i −0.158819 + 0.765028i
\(81\) 0 0
\(82\) 10.7778 + 5.12504i 0.131436 + 0.0625005i
\(83\) −33.4876 39.9089i −0.403465 0.480830i 0.525608 0.850727i \(-0.323838\pi\)
−0.929073 + 0.369896i \(0.879393\pi\)
\(84\) 0 0
\(85\) −15.5598 + 88.2438i −0.183056 + 1.03816i
\(86\) 6.04197 63.5388i 0.0702554 0.738823i
\(87\) 0 0
\(88\) −57.5253 131.021i −0.653696 1.48888i
\(89\) 8.30808 + 14.3900i 0.0933492 + 0.161686i 0.908918 0.416974i \(-0.136909\pi\)
−0.815569 + 0.578659i \(0.803576\pi\)
\(90\) 0 0
\(91\) 43.9380 + 25.3676i 0.482835 + 0.278765i
\(92\) −7.46880 + 2.59157i −0.0811826 + 0.0281692i
\(93\) 0 0
\(94\) −99.5105 + 45.4923i −1.05862 + 0.483960i
\(95\) −19.2838 + 22.9816i −0.202988 + 0.241911i
\(96\) 0 0
\(97\) −120.060 43.6982i −1.23773 0.450497i −0.361492 0.932375i \(-0.617733\pi\)
−0.876238 + 0.481878i \(0.839955\pi\)
\(98\) −70.6886 + 48.7066i −0.721312 + 0.497006i
\(99\) 0 0
\(100\) −13.8724 + 36.3968i −0.138724 + 0.363968i
\(101\) 19.5922 + 111.113i 0.193982 + 1.10013i 0.913861 + 0.406027i \(0.133086\pi\)
−0.719879 + 0.694100i \(0.755803\pi\)
\(102\) 0 0
\(103\) −47.3891 130.200i −0.460088 1.26408i −0.925419 0.378945i \(-0.876287\pi\)
0.465331 0.885137i \(-0.345935\pi\)
\(104\) 164.290 10.6359i 1.57971 0.102268i
\(105\) 0 0
\(106\) −37.6685 + 9.78947i −0.355364 + 0.0923535i
\(107\) 151.616i 1.41697i 0.705724 + 0.708487i \(0.250622\pi\)
−0.705724 + 0.708487i \(0.749378\pi\)
\(108\) 0 0
\(109\) 128.248 1.17659 0.588295 0.808646i \(-0.299799\pi\)
0.588295 + 0.808646i \(0.299799\pi\)
\(110\) 35.1526 + 135.262i 0.319569 + 1.22966i
\(111\) 0 0
\(112\) 14.6028 36.6431i 0.130382 0.327171i
\(113\) −135.610 + 49.3580i −1.20009 + 0.436797i −0.863255 0.504768i \(-0.831578\pi\)
−0.336833 + 0.941564i \(0.609356\pi\)
\(114\) 0 0
\(115\) 7.60393 1.34078i 0.0661212 0.0116589i
\(116\) −62.5139 + 164.017i −0.538913 + 1.41394i
\(117\) 0 0
\(118\) 63.7144 + 92.4697i 0.539953 + 0.783641i
\(119\) 19.3399 53.1359i 0.162520 0.446520i
\(120\) 0 0
\(121\) −152.391 127.871i −1.25943 1.05679i
\(122\) −13.3233 29.1437i −0.109208 0.238882i
\(123\) 0 0
\(124\) 77.9690 27.0541i 0.628782 0.218178i
\(125\) 67.8549 117.528i 0.542839 0.940225i
\(126\) 0 0
\(127\) −186.595 + 107.731i −1.46925 + 0.848273i −0.999406 0.0344751i \(-0.989024\pi\)
−0.469847 + 0.882748i \(0.655691\pi\)
\(128\) −26.5606 125.214i −0.207504 0.978234i
\(129\) 0 0
\(130\) −160.072 15.2214i −1.23132 0.117088i
\(131\) −37.7245 6.65185i −0.287974 0.0507775i 0.0277954 0.999614i \(-0.491151\pi\)
−0.315769 + 0.948836i \(0.602262\pi\)
\(132\) 0 0
\(133\) 14.5027 12.1692i 0.109043 0.0914980i
\(134\) 1.88769 3.96975i 0.0140873 0.0296250i
\(135\) 0 0
\(136\) −43.4701 178.267i −0.319633 1.31078i
\(137\) −43.0492 + 36.1225i −0.314227 + 0.263668i −0.786237 0.617925i \(-0.787973\pi\)
0.472009 + 0.881594i \(0.343529\pi\)
\(138\) 0 0
\(139\) 233.131 + 41.1073i 1.67720 + 0.295736i 0.929643 0.368461i \(-0.120115\pi\)
0.747558 + 0.664196i \(0.231226\pi\)
\(140\) −19.7637 + 33.0699i −0.141169 + 0.236213i
\(141\) 0 0
\(142\) 191.635 + 52.9001i 1.34954 + 0.372536i
\(143\) 318.779 184.047i 2.22922 1.28704i
\(144\) 0 0
\(145\) 85.7162 148.465i 0.591146 1.02390i
\(146\) 89.2756 + 90.6320i 0.611477 + 0.620767i
\(147\) 0 0
\(148\) −1.85590 + 123.069i −0.0125398 + 0.831550i
\(149\) 25.6459 + 21.5194i 0.172120 + 0.144426i 0.724778 0.688982i \(-0.241942\pi\)
−0.552659 + 0.833408i \(0.686387\pi\)
\(150\) 0 0
\(151\) −12.5948 + 34.6040i −0.0834093 + 0.229165i −0.974385 0.224885i \(-0.927799\pi\)
0.890976 + 0.454051i \(0.150021\pi\)
\(152\) 17.2382 58.9656i 0.113409 0.387931i
\(153\) 0 0
\(154\) −7.02398 87.9137i −0.0456103 0.570868i
\(155\) −79.3797 + 13.9968i −0.512127 + 0.0903018i
\(156\) 0 0
\(157\) 81.9630 29.8321i 0.522057 0.190013i −0.0675312 0.997717i \(-0.521512\pi\)
0.589588 + 0.807704i \(0.299290\pi\)
\(158\) −32.9477 23.4424i −0.208530 0.148370i
\(159\) 0 0
\(160\) 6.19431 + 124.861i 0.0387145 + 0.780380i
\(161\) −4.87255 −0.0302643
\(162\) 0 0
\(163\) 265.936i 1.63151i 0.578398 + 0.815755i \(0.303678\pi\)
−0.578398 + 0.815755i \(0.696322\pi\)
\(164\) 23.4408 + 4.49869i 0.142931 + 0.0274310i
\(165\) 0 0
\(166\) −84.8984 60.4055i −0.511436 0.363888i
\(167\) 5.34309 + 14.6800i 0.0319945 + 0.0879042i 0.954661 0.297694i \(-0.0962174\pi\)
−0.922667 + 0.385598i \(0.873995\pi\)
\(168\) 0 0
\(169\) 44.1947 + 250.640i 0.261507 + 1.48308i
\(170\) 14.2728 + 178.641i 0.0839574 + 1.05083i
\(171\) 0 0
\(172\) −20.2683 126.031i −0.117839 0.732741i
\(173\) 179.041 + 65.1656i 1.03492 + 0.376680i 0.802952 0.596044i \(-0.203262\pi\)
0.231967 + 0.972724i \(0.425484\pi\)
\(174\) 0 0
\(175\) −15.4313 + 18.3904i −0.0881791 + 0.105088i
\(176\) −177.263 224.679i −1.00718 1.27658i
\(177\) 0 0
\(178\) 23.3210 + 23.6753i 0.131017 + 0.133007i
\(179\) −235.124 135.749i −1.31354 0.758374i −0.330862 0.943679i \(-0.607339\pi\)
−0.982681 + 0.185305i \(0.940673\pi\)
\(180\) 0 0
\(181\) 6.50826 + 11.2726i 0.0359573 + 0.0622798i 0.883444 0.468537i \(-0.155219\pi\)
−0.847487 + 0.530817i \(0.821885\pi\)
\(182\) 97.8121 + 27.0007i 0.537429 + 0.148355i
\(183\) 0 0
\(184\) −13.1536 + 8.77373i −0.0714872 + 0.0476833i
\(185\) 20.8747 118.386i 0.112836 0.639924i
\(186\) 0 0
\(187\) −263.706 314.272i −1.41019 1.68060i
\(188\) −169.737 + 138.119i −0.902857 + 0.734675i
\(189\) 0 0
\(190\) −25.7666 + 54.1863i −0.135614 + 0.285191i
\(191\) −189.368 225.680i −0.991457 1.18157i −0.983372 0.181605i \(-0.941871\pi\)
−0.00808536 0.999967i \(-0.502574\pi\)
\(192\) 0 0
\(193\) 44.6187 253.045i 0.231185 1.31112i −0.619316 0.785142i \(-0.712590\pi\)
0.850501 0.525974i \(-0.176299\pi\)
\(194\) −254.382 24.1895i −1.31125 0.124688i
\(195\) 0 0
\(196\) −112.330 + 129.842i −0.573110 + 0.662458i
\(197\) 42.7613 + 74.0647i 0.217062 + 0.375963i 0.953909 0.300097i \(-0.0970191\pi\)
−0.736846 + 0.676060i \(0.763686\pi\)
\(198\) 0 0
\(199\) 15.8969 + 9.17807i 0.0798839 + 0.0461210i 0.539410 0.842043i \(-0.318647\pi\)
−0.459526 + 0.888164i \(0.651981\pi\)
\(200\) −8.54300 + 77.4319i −0.0427150 + 0.387159i
\(201\) 0 0
\(202\) 93.8208 + 205.225i 0.464460 + 1.01597i
\(203\) −69.5393 + 82.8737i −0.342558 + 0.408245i
\(204\) 0 0
\(205\) −21.9059 7.97310i −0.106858 0.0388932i
\(206\) −157.229 228.189i −0.763250 1.10772i
\(207\) 0 0
\(208\) 312.666 103.235i 1.50320 0.496324i
\(209\) −23.8515 135.269i −0.114122 0.647218i
\(210\) 0 0
\(211\) −61.6793 169.463i −0.292319 0.803140i −0.995726 0.0923529i \(-0.970561\pi\)
0.703407 0.710787i \(-0.251661\pi\)
\(212\) −67.9903 + 37.8990i −0.320709 + 0.178769i
\(213\) 0 0
\(214\) 76.2718 + 293.483i 0.356410 + 1.37142i
\(215\) 124.673i 0.579876i
\(216\) 0 0
\(217\) 50.8660 0.234406
\(218\) 248.250 64.5164i 1.13876 0.295947i
\(219\) 0 0
\(220\) 136.090 + 244.143i 0.618589 + 1.10974i
\(221\) 443.546 161.438i 2.00700 0.730487i
\(222\) 0 0
\(223\) −51.7471 + 9.12442i −0.232050 + 0.0409167i −0.288464 0.957491i \(-0.593144\pi\)
0.0564138 + 0.998407i \(0.482033\pi\)
\(224\) 9.83292 78.2762i 0.0438970 0.349447i
\(225\) 0 0
\(226\) −237.670 + 163.762i −1.05164 + 0.724611i
\(227\) 27.9881 76.8966i 0.123295 0.338752i −0.862654 0.505794i \(-0.831200\pi\)
0.985950 + 0.167043i \(0.0534218\pi\)
\(228\) 0 0
\(229\) 18.8776 + 15.8402i 0.0824351 + 0.0691713i 0.683074 0.730349i \(-0.260643\pi\)
−0.600639 + 0.799520i \(0.705087\pi\)
\(230\) 14.0444 6.42057i 0.0610628 0.0279155i
\(231\) 0 0
\(232\) −38.4979 + 348.936i −0.165939 + 1.50404i
\(233\) 39.6338 68.6477i 0.170102 0.294625i −0.768353 0.640026i \(-0.778924\pi\)
0.938455 + 0.345401i \(0.112257\pi\)
\(234\) 0 0
\(235\) 185.094 106.864i 0.787633 0.454740i
\(236\) 169.850 + 146.941i 0.719702 + 0.622633i
\(237\) 0 0
\(238\) 10.7058 112.584i 0.0449821 0.473043i
\(239\) −144.601 25.4971i −0.605027 0.106683i −0.137261 0.990535i \(-0.543830\pi\)
−0.467766 + 0.883852i \(0.654941\pi\)
\(240\) 0 0
\(241\) 272.438 228.603i 1.13045 0.948559i 0.131364 0.991334i \(-0.458064\pi\)
0.999085 + 0.0427750i \(0.0136199\pi\)
\(242\) −359.310 170.859i −1.48475 0.706027i
\(243\) 0 0
\(244\) −40.4509 49.7109i −0.165783 0.203733i
\(245\) 128.453 107.785i 0.524298 0.439938i
\(246\) 0 0
\(247\) 155.632 + 27.4421i 0.630088 + 0.111101i
\(248\) 137.315 91.5916i 0.553688 0.369321i
\(249\) 0 0
\(250\) 72.2231 261.634i 0.288893 1.04654i
\(251\) 206.394 119.161i 0.822285 0.474747i −0.0289186 0.999582i \(-0.509206\pi\)
0.851204 + 0.524835i \(0.175873\pi\)
\(252\) 0 0
\(253\) −17.6757 + 30.6152i −0.0698643 + 0.121009i
\(254\) −306.997 + 302.402i −1.20865 + 1.19056i
\(255\) 0 0
\(256\) −114.403 229.015i −0.446887 0.894590i
\(257\) 278.987 + 234.098i 1.08555 + 0.910887i 0.996370 0.0851281i \(-0.0271300\pi\)
0.0891830 + 0.996015i \(0.471574\pi\)
\(258\) 0 0
\(259\) −25.9460 + 71.2860i −0.100178 + 0.275236i
\(260\) −317.508 + 51.0615i −1.22119 + 0.196390i
\(261\) 0 0
\(262\) −76.3696 + 6.10166i −0.291487 + 0.0232888i
\(263\) 320.879 56.5796i 1.22007 0.215131i 0.473715 0.880678i \(-0.342913\pi\)
0.746356 + 0.665547i \(0.231802\pi\)
\(264\) 0 0
\(265\) 71.4392 26.0017i 0.269582 0.0981198i
\(266\) 21.9511 30.8517i 0.0825228 0.115984i
\(267\) 0 0
\(268\) 1.65699 8.63387i 0.00618280 0.0322159i
\(269\) −95.8215 −0.356214 −0.178107 0.984011i \(-0.556997\pi\)
−0.178107 + 0.984011i \(0.556997\pi\)
\(270\) 0 0
\(271\) 494.220i 1.82369i −0.410537 0.911844i \(-0.634659\pi\)
0.410537 0.911844i \(-0.365341\pi\)
\(272\) −173.824 323.203i −0.639058 1.18825i
\(273\) 0 0
\(274\) −65.1585 + 91.5786i −0.237805 + 0.334229i
\(275\) 59.5714 + 163.671i 0.216623 + 0.595167i
\(276\) 0 0
\(277\) 48.7599 + 276.531i 0.176028 + 0.998307i 0.936950 + 0.349463i \(0.113636\pi\)
−0.760922 + 0.648844i \(0.775253\pi\)
\(278\) 471.951 37.7072i 1.69767 0.135637i
\(279\) 0 0
\(280\) −21.6204 + 73.9556i −0.0772159 + 0.264127i
\(281\) −106.961 38.9307i −0.380645 0.138543i 0.144609 0.989489i \(-0.453808\pi\)
−0.525254 + 0.850945i \(0.676030\pi\)
\(282\) 0 0
\(283\) 198.767 236.881i 0.702356 0.837036i −0.290435 0.956895i \(-0.593800\pi\)
0.992791 + 0.119859i \(0.0382443\pi\)
\(284\) 397.559 + 5.99522i 1.39986 + 0.0211099i
\(285\) 0 0
\(286\) 524.474 516.625i 1.83383 1.80638i
\(287\) 12.7402 + 7.35555i 0.0443909 + 0.0256291i
\(288\) 0 0
\(289\) −118.537 205.311i −0.410161 0.710420i
\(290\) 91.2344 330.504i 0.314601 1.13967i
\(291\) 0 0
\(292\) 218.404 + 130.526i 0.747959 + 0.447005i
\(293\) −84.2825 + 477.990i −0.287654 + 1.63136i 0.407996 + 0.912984i \(0.366228\pi\)
−0.695650 + 0.718381i \(0.744884\pi\)
\(294\) 0 0
\(295\) −140.996 168.033i −0.477953 0.569603i
\(296\) 58.3186 + 239.159i 0.197022 + 0.807969i
\(297\) 0 0
\(298\) 60.4682 + 28.7538i 0.202913 + 0.0964892i
\(299\) −26.1442 31.1574i −0.0874387 0.104205i
\(300\) 0 0
\(301\) 13.6620 77.4809i 0.0453886 0.257412i
\(302\) −6.97196 + 73.3188i −0.0230859 + 0.242777i
\(303\) 0 0
\(304\) 3.70485 122.811i 0.0121870 0.403985i
\(305\) 31.2973 + 54.2084i 0.102614 + 0.177733i
\(306\) 0 0
\(307\) −70.4883 40.6964i −0.229604 0.132562i 0.380786 0.924663i \(-0.375654\pi\)
−0.610389 + 0.792102i \(0.708987\pi\)
\(308\) −57.8220 166.641i −0.187734 0.541042i
\(309\) 0 0
\(310\) −146.614 + 67.0262i −0.472949 + 0.216214i
\(311\) −249.268 + 297.066i −0.801505 + 0.955196i −0.999688 0.0249688i \(-0.992051\pi\)
0.198183 + 0.980165i \(0.436496\pi\)
\(312\) 0 0
\(313\) −479.995 174.704i −1.53353 0.558160i −0.569048 0.822304i \(-0.692688\pi\)
−0.964483 + 0.264145i \(0.914910\pi\)
\(314\) 143.648 98.9781i 0.457479 0.315217i
\(315\) 0 0
\(316\) −75.5697 28.8028i −0.239145 0.0911481i
\(317\) −31.1223 176.503i −0.0981775 0.556792i −0.993727 0.111831i \(-0.964329\pi\)
0.895550 0.444961i \(-0.146783\pi\)
\(318\) 0 0
\(319\) 268.450 + 737.561i 0.841537 + 2.31210i
\(320\) 74.8026 + 238.577i 0.233758 + 0.745553i
\(321\) 0 0
\(322\) −9.43179 + 2.45118i −0.0292913 + 0.00761235i
\(323\) 176.132i 0.545302i
\(324\) 0 0
\(325\) −200.395 −0.616601
\(326\) 133.781 + 514.772i 0.410372 + 1.57906i
\(327\) 0 0
\(328\) 47.6374 3.08396i 0.145236 0.00940232i
\(329\) −126.741 + 46.1299i −0.385230 + 0.140212i
\(330\) 0 0
\(331\) −130.882 + 23.0781i −0.395415 + 0.0697223i −0.367820 0.929897i \(-0.619896\pi\)
−0.0275947 + 0.999619i \(0.508785\pi\)
\(332\) −194.725 74.2180i −0.586522 0.223548i
\(333\) 0 0
\(334\) 17.7275 + 25.7282i 0.0530764 + 0.0770305i
\(335\) −2.93671 + 8.06855i −0.00876630 + 0.0240852i
\(336\) 0 0
\(337\) 236.956 + 198.829i 0.703132 + 0.589998i 0.922663 0.385608i \(-0.126008\pi\)
−0.219531 + 0.975606i \(0.570453\pi\)
\(338\) 211.634 + 462.932i 0.626137 + 1.36962i
\(339\) 0 0
\(340\) 117.495 + 338.615i 0.345572 + 0.995927i
\(341\) 184.522 319.601i 0.541119 0.937246i
\(342\) 0 0
\(343\) −196.259 + 113.310i −0.572184 + 0.330350i
\(344\) −102.635 233.763i −0.298356 0.679543i
\(345\) 0 0
\(346\) 379.352 + 36.0729i 1.09639 + 0.104257i
\(347\) 182.964 + 32.2614i 0.527273 + 0.0929724i 0.430947 0.902377i \(-0.358180\pi\)
0.0963261 + 0.995350i \(0.469291\pi\)
\(348\) 0 0
\(349\) −53.3290 + 44.7483i −0.152805 + 0.128219i −0.715985 0.698115i \(-0.754022\pi\)
0.563180 + 0.826334i \(0.309578\pi\)
\(350\) −20.6190 + 43.3611i −0.0589115 + 0.123889i
\(351\) 0 0
\(352\) −456.154 345.737i −1.29589 0.982207i
\(353\) −245.397 + 205.912i −0.695175 + 0.583321i −0.920396 0.390987i \(-0.872134\pi\)
0.225221 + 0.974308i \(0.427689\pi\)
\(354\) 0 0
\(355\) −382.430 67.4328i −1.07727 0.189951i
\(356\) 57.0524 + 34.0964i 0.160260 + 0.0957765i
\(357\) 0 0
\(358\) −523.419 144.488i −1.46207 0.403598i
\(359\) −117.892 + 68.0648i −0.328389 + 0.189596i −0.655126 0.755520i \(-0.727384\pi\)
0.326736 + 0.945115i \(0.394051\pi\)
\(360\) 0 0
\(361\) −151.015 + 261.565i −0.418324 + 0.724558i
\(362\) 18.2688 + 18.5464i 0.0504664 + 0.0512332i
\(363\) 0 0
\(364\) 202.918 + 3.06002i 0.557466 + 0.00840664i
\(365\) −190.362 159.733i −0.521540 0.437624i
\(366\) 0 0
\(367\) −109.598 + 301.117i −0.298631 + 0.820482i 0.696098 + 0.717947i \(0.254918\pi\)
−0.994729 + 0.102536i \(0.967304\pi\)
\(368\) −21.0478 + 23.6004i −0.0571951 + 0.0641314i
\(369\) 0 0
\(370\) −19.1480 239.661i −0.0517514 0.647732i
\(371\) −47.2467 + 8.33087i −0.127350 + 0.0224552i
\(372\) 0 0
\(373\) 122.229 44.4878i 0.327692 0.119270i −0.172935 0.984933i \(-0.555325\pi\)
0.500627 + 0.865663i \(0.333103\pi\)
\(374\) −668.552 475.677i −1.78757 1.27186i
\(375\) 0 0
\(376\) −259.078 + 352.744i −0.689037 + 0.938150i
\(377\) −903.053 −2.39537
\(378\) 0 0
\(379\) 555.420i 1.46549i 0.680504 + 0.732745i \(0.261761\pi\)
−0.680504 + 0.732745i \(0.738239\pi\)
\(380\) −22.6176 + 117.851i −0.0595199 + 0.310133i
\(381\) 0 0
\(382\) −480.090 341.586i −1.25678 0.894204i
\(383\) −13.6389 37.4725i −0.0356106 0.0978393i 0.920613 0.390476i \(-0.127690\pi\)
−0.956224 + 0.292637i \(0.905467\pi\)
\(384\) 0 0
\(385\) 29.9150 + 169.656i 0.0777012 + 0.440665i
\(386\) −40.9282 512.266i −0.106032 1.32711i
\(387\) 0 0
\(388\) −504.577 + 81.1457i −1.30046 + 0.209138i
\(389\) −400.841 145.894i −1.03044 0.375049i −0.229191 0.973381i \(-0.573608\pi\)
−0.801248 + 0.598332i \(0.795830\pi\)
\(390\) 0 0
\(391\) −29.1385 + 34.7259i −0.0745231 + 0.0888132i
\(392\) −152.118 + 307.843i −0.388057 + 0.785314i
\(393\) 0 0
\(394\) 120.032 + 121.856i 0.304650 + 0.309278i
\(395\) 68.4041 + 39.4931i 0.173175 + 0.0999825i
\(396\) 0 0
\(397\) 189.792 + 328.730i 0.478066 + 0.828035i 0.999684 0.0251445i \(-0.00800458\pi\)
−0.521618 + 0.853179i \(0.674671\pi\)
\(398\) 35.3887 + 9.76893i 0.0889163 + 0.0245450i
\(399\) 0 0
\(400\) 22.4161 + 154.182i 0.0560402 + 0.385456i
\(401\) −20.0090 + 113.477i −0.0498977 + 0.282984i −0.999539 0.0303545i \(-0.990336\pi\)
0.949641 + 0.313339i \(0.101447\pi\)
\(402\) 0 0
\(403\) 272.927 + 325.261i 0.677237 + 0.807100i
\(404\) 284.849 + 350.057i 0.705072 + 0.866477i
\(405\) 0 0
\(406\) −92.9168 + 195.401i −0.228859 + 0.481283i
\(407\) 353.782 + 421.621i 0.869243 + 1.03592i
\(408\) 0 0
\(409\) 37.7554 214.121i 0.0923114 0.523524i −0.903227 0.429164i \(-0.858808\pi\)
0.995538 0.0943603i \(-0.0300806\pi\)
\(410\) −46.4142 4.41357i −0.113205 0.0107648i
\(411\) 0 0
\(412\) −419.142 362.611i −1.01733 0.880123i
\(413\) 69.2117 + 119.878i 0.167583 + 0.290262i
\(414\) 0 0
\(415\) 176.261 + 101.764i 0.424726 + 0.245215i
\(416\) 553.294 357.122i 1.33003 0.858467i
\(417\) 0 0
\(418\) −114.217 249.840i −0.273247 0.597705i
\(419\) 83.3828 99.3717i 0.199004 0.237164i −0.657309 0.753622i \(-0.728305\pi\)
0.856313 + 0.516458i \(0.172750\pi\)
\(420\) 0 0
\(421\) 94.8522 + 34.5234i 0.225302 + 0.0820033i 0.452205 0.891914i \(-0.350638\pi\)
−0.226903 + 0.973917i \(0.572860\pi\)
\(422\) −204.642 297.000i −0.484934 0.703792i
\(423\) 0 0
\(424\) −112.543 + 107.564i −0.265433 + 0.253689i
\(425\) 38.7838 + 219.954i 0.0912560 + 0.517539i
\(426\) 0 0
\(427\) −13.5101 37.1186i −0.0316395 0.0869288i
\(428\) 295.279 + 529.726i 0.689903 + 1.23768i
\(429\) 0 0
\(430\) 62.7180 + 241.330i 0.145856 + 0.561233i
\(431\) 17.3757i 0.0403148i 0.999797 + 0.0201574i \(0.00641674\pi\)
−0.999797 + 0.0201574i \(0.993583\pi\)
\(432\) 0 0
\(433\) −737.761 −1.70384 −0.851918 0.523676i \(-0.824560\pi\)
−0.851918 + 0.523676i \(0.824560\pi\)
\(434\) 98.4613 25.5886i 0.226869 0.0589598i
\(435\) 0 0
\(436\) 448.082 249.769i 1.02771 0.572864i
\(437\) −14.2620 + 5.19093i −0.0326361 + 0.0118786i
\(438\) 0 0
\(439\) 380.391 67.0733i 0.866495 0.152786i 0.277306 0.960782i \(-0.410558\pi\)
0.589189 + 0.807995i \(0.299447\pi\)
\(440\) 386.247 + 404.127i 0.877834 + 0.918471i
\(441\) 0 0
\(442\) 777.360 535.625i 1.75873 1.21182i
\(443\) −71.4245 + 196.237i −0.161229 + 0.442973i −0.993832 0.110897i \(-0.964628\pi\)
0.832603 + 0.553871i \(0.186850\pi\)
\(444\) 0 0
\(445\) −49.7272 41.7261i −0.111747 0.0937665i
\(446\) −95.5768 + 43.6940i −0.214298 + 0.0979685i
\(447\) 0 0
\(448\) −20.3439 156.466i −0.0454105 0.349254i
\(449\) −181.887 + 315.038i −0.405094 + 0.701644i −0.994332 0.106316i \(-0.966095\pi\)
0.589238 + 0.807959i \(0.299428\pi\)
\(450\) 0 0
\(451\) 92.4327 53.3660i 0.204950 0.118328i
\(452\) −377.676 + 436.556i −0.835567 + 0.965832i
\(453\) 0 0
\(454\) 15.4930 162.928i 0.0341256 0.358873i
\(455\) −195.196 34.4183i −0.429002 0.0756446i
\(456\) 0 0
\(457\) 424.330 356.056i 0.928513 0.779115i −0.0470369 0.998893i \(-0.514978\pi\)
0.975550 + 0.219778i \(0.0705334\pi\)
\(458\) 44.5100 + 21.1654i 0.0971834 + 0.0462126i
\(459\) 0 0
\(460\) 23.9559 19.4935i 0.0520780 0.0423771i
\(461\) 362.858 304.474i 0.787110 0.660463i −0.157919 0.987452i \(-0.550478\pi\)
0.945028 + 0.326989i \(0.106034\pi\)
\(462\) 0 0
\(463\) 37.9817 + 6.69720i 0.0820339 + 0.0144648i 0.214514 0.976721i \(-0.431183\pi\)
−0.132481 + 0.991186i \(0.542294\pi\)
\(464\) 101.015 + 694.802i 0.217705 + 1.49742i
\(465\) 0 0
\(466\) 42.1853 152.819i 0.0905263 0.327939i
\(467\) −136.396 + 78.7483i −0.292069 + 0.168626i −0.638874 0.769311i \(-0.720600\pi\)
0.346806 + 0.937937i \(0.387266\pi\)
\(468\) 0 0
\(469\) 2.70925 4.69256i 0.00577665 0.0100055i
\(470\) 304.527 299.969i 0.647930 0.638233i
\(471\) 0 0
\(472\) 402.698 + 198.990i 0.853173 + 0.421589i
\(473\) −437.267 366.911i −0.924455 0.775709i
\(474\) 0 0
\(475\) −25.5755 + 70.2682i −0.0538433 + 0.147933i
\(476\) −35.9133 223.315i −0.0754482 0.469149i
\(477\) 0 0
\(478\) −292.732 + 23.3882i −0.612409 + 0.0489292i
\(479\) −457.399 + 80.6517i −0.954903 + 0.168375i −0.629327 0.777141i \(-0.716669\pi\)
−0.325576 + 0.945516i \(0.605558\pi\)
\(480\) 0 0
\(481\) −595.052 + 216.581i −1.23712 + 0.450273i
\(482\) 412.358 579.559i 0.855514 1.20240i
\(483\) 0 0
\(484\) −781.468 149.977i −1.61460 0.309870i
\(485\) 499.139 1.02915
\(486\) 0 0
\(487\) 883.498i 1.81416i −0.420954 0.907082i \(-0.638305\pi\)
0.420954 0.907082i \(-0.361695\pi\)
\(488\) −103.308 75.8763i −0.211697 0.155484i
\(489\) 0 0
\(490\) 194.424 273.258i 0.396784 0.557670i
\(491\) −166.771 458.199i −0.339656 0.933196i −0.985492 0.169720i \(-0.945714\pi\)
0.645837 0.763476i \(-0.276509\pi\)
\(492\) 0 0
\(493\) 174.774 + 991.192i 0.354511 + 2.01053i
\(494\) 315.061 25.1722i 0.637775 0.0509559i
\(495\) 0 0
\(496\) 219.724 246.371i 0.442992 0.496716i
\(497\) 230.280 + 83.8150i 0.463340 + 0.168642i
\(498\) 0 0
\(499\) −166.489 + 198.413i −0.333644 + 0.397622i −0.906618 0.421952i \(-0.861345\pi\)
0.572974 + 0.819574i \(0.305790\pi\)
\(500\) 8.18512 542.777i 0.0163702 1.08555i
\(501\) 0 0
\(502\) 339.571 334.489i 0.676436 0.666312i
\(503\) −227.274 131.217i −0.451837 0.260868i 0.256769 0.966473i \(-0.417342\pi\)
−0.708606 + 0.705605i \(0.750675\pi\)
\(504\) 0 0
\(505\) −220.390 381.727i −0.436416 0.755896i
\(506\) −18.8136 + 68.1537i −0.0371810 + 0.134691i
\(507\) 0 0
\(508\) −442.128 + 739.798i −0.870331 + 1.45629i
\(509\) 11.4399 64.8787i 0.0224752 0.127463i −0.971506 0.237016i \(-0.923831\pi\)
0.993981 + 0.109553i \(0.0349418\pi\)
\(510\) 0 0
\(511\) 100.801 + 120.130i 0.197262 + 0.235087i
\(512\) −336.658 385.753i −0.657535 0.753424i
\(513\) 0 0
\(514\) 657.800 + 312.797i 1.27977 + 0.608554i
\(515\) 347.940 + 414.658i 0.675611 + 0.805162i
\(516\) 0 0
\(517\) −169.922 + 963.677i −0.328670 + 1.86398i
\(518\) −14.3626 + 151.041i −0.0277270 + 0.291584i
\(519\) 0 0
\(520\) −588.914 + 258.565i −1.13253 + 0.497240i
\(521\) −112.991 195.706i −0.216874 0.375636i 0.736977 0.675918i \(-0.236253\pi\)
−0.953851 + 0.300282i \(0.902919\pi\)
\(522\) 0 0
\(523\) −197.182 113.843i −0.377021 0.217673i 0.299501 0.954096i \(-0.403180\pi\)
−0.676521 + 0.736423i \(0.736513\pi\)
\(524\) −144.759 + 50.2294i −0.276258 + 0.0958575i
\(525\) 0 0
\(526\) 592.662 270.942i 1.12673 0.515098i
\(527\) 304.186 362.514i 0.577203 0.687883i
\(528\) 0 0
\(529\) −493.427 179.593i −0.932754 0.339495i
\(530\) 125.204 86.2696i 0.236235 0.162773i
\(531\) 0 0
\(532\) 26.9705 70.7623i 0.0506964 0.133012i
\(533\) 21.3239 + 120.934i 0.0400073 + 0.226893i
\(534\) 0 0
\(535\) −202.585 556.597i −0.378663 1.04037i
\(536\) −1.13591 17.5461i −0.00211923 0.0327353i
\(537\) 0 0
\(538\) −185.482 + 48.2038i −0.344761 + 0.0895981i
\(539\) 767.731i 1.42436i
\(540\) 0 0
\(541\) 786.104 1.45306 0.726529 0.687136i \(-0.241132\pi\)
0.726529 + 0.687136i \(0.241132\pi\)
\(542\) −248.621 956.660i −0.458711 1.76506i
\(543\) 0 0
\(544\) −499.060 538.180i −0.917390 0.989302i
\(545\) −470.812 + 171.361i −0.863875 + 0.314425i
\(546\) 0 0
\(547\) 1054.07 185.862i 1.92701 0.339783i 0.927580 0.373624i \(-0.121885\pi\)
0.999427 + 0.0338407i \(0.0107739\pi\)
\(548\) −80.0579 + 210.047i −0.146091 + 0.383298i
\(549\) 0 0
\(550\) 197.648 + 286.850i 0.359361 + 0.521546i
\(551\) −115.253 + 316.654i −0.209170 + 0.574690i
\(552\) 0 0
\(553\) −38.1834 32.0397i −0.0690478 0.0579380i
\(554\) 233.496 + 510.752i 0.421472 + 0.921935i
\(555\) 0 0
\(556\) 894.586 310.409i 1.60897 0.558289i
\(557\) −200.833 + 347.853i −0.360562 + 0.624512i −0.988053 0.154112i \(-0.950748\pi\)
0.627492 + 0.778623i \(0.284082\pi\)
\(558\) 0 0
\(559\) 568.754 328.370i 1.01745 0.587425i
\(560\) −4.64669 + 154.032i −0.00829766 + 0.275058i
\(561\) 0 0
\(562\) −226.629 21.5504i −0.403255 0.0383459i
\(563\) 768.923 + 135.582i 1.36576 + 0.240820i 0.808000 0.589182i \(-0.200550\pi\)
0.557760 + 0.830003i \(0.311661\pi\)
\(564\) 0 0
\(565\) 431.887 362.396i 0.764401 0.641409i
\(566\) 265.588 558.522i 0.469236 0.986788i
\(567\) 0 0
\(568\) 772.571 188.390i 1.36016 0.331673i
\(569\) −108.765 + 91.2651i −0.191152 + 0.160396i −0.733341 0.679861i \(-0.762040\pi\)
0.542189 + 0.840257i \(0.317596\pi\)
\(570\) 0 0
\(571\) −905.067 159.588i −1.58506 0.279488i −0.689449 0.724334i \(-0.742147\pi\)
−0.895607 + 0.444846i \(0.853258\pi\)
\(572\) 755.332 1263.87i 1.32051 2.20956i
\(573\) 0 0
\(574\) 28.3614 + 7.82908i 0.0494102 + 0.0136395i
\(575\) 16.6673 9.62286i 0.0289866 0.0167354i
\(576\) 0 0
\(577\) 33.2353 57.5652i 0.0576001 0.0997663i −0.835788 0.549053i \(-0.814988\pi\)
0.893388 + 0.449287i \(0.148322\pi\)
\(578\) −332.735 337.790i −0.575666 0.584412i
\(579\) 0 0
\(580\) 10.3397 685.652i 0.0178270 1.18216i
\(581\) −98.3896 82.5587i −0.169345 0.142098i
\(582\) 0 0
\(583\) −119.048 + 327.081i −0.204199 + 0.561032i
\(584\) 488.426 + 142.788i 0.836346 + 0.244500i
\(585\) 0 0
\(586\) 77.3112 + 967.644i 0.131930 + 1.65127i
\(587\) 522.614 92.1509i 0.890313 0.156986i 0.290262 0.956947i \(-0.406258\pi\)
0.600052 + 0.799961i \(0.295147\pi\)
\(588\) 0 0
\(589\) 148.885 54.1896i 0.252776 0.0920028i
\(590\) −357.457 254.332i −0.605859 0.431071i
\(591\) 0 0
\(592\) 233.198 + 433.602i 0.393916 + 0.732436i
\(593\) 307.107 0.517887 0.258944 0.965892i \(-0.416626\pi\)
0.258944 + 0.965892i \(0.416626\pi\)
\(594\) 0 0
\(595\) 220.908i 0.371275i
\(596\) 131.513 + 25.2396i 0.220660 + 0.0423484i
\(597\) 0 0
\(598\) −66.2812 47.1593i −0.110838 0.0788617i
\(599\) −89.0609 244.693i −0.148683 0.408502i 0.842885 0.538094i \(-0.180856\pi\)
−0.991567 + 0.129592i \(0.958633\pi\)
\(600\) 0 0
\(601\) −76.4196 433.397i −0.127154 0.721126i −0.980005 0.198972i \(-0.936240\pi\)
0.852851 0.522154i \(-0.174871\pi\)
\(602\) −12.5319 156.852i −0.0208172 0.260552i
\(603\) 0 0
\(604\) 23.3880 + 145.430i 0.0387219 + 0.240779i
\(605\) 730.299 + 265.807i 1.20711 + 0.439351i
\(606\) 0 0
\(607\) 485.664 578.791i 0.800105 0.953528i −0.199548 0.979888i \(-0.563947\pi\)
0.999653 + 0.0263602i \(0.00839169\pi\)
\(608\) −54.6098 239.590i −0.0898188 0.394062i
\(609\) 0 0
\(610\) 87.8521 + 89.1869i 0.144020 + 0.146208i
\(611\) −975.017 562.926i −1.59577 0.921319i
\(612\) 0 0
\(613\) 204.218 + 353.715i 0.333145 + 0.577024i 0.983127 0.182926i \(-0.0585569\pi\)
−0.649982 + 0.759950i \(0.725224\pi\)
\(614\) −156.917 43.3163i −0.255565 0.0705478i
\(615\) 0 0
\(616\) −195.756 293.479i −0.317786 0.476427i
\(617\) 158.965 901.535i 0.257642 1.46116i −0.531558 0.847022i \(-0.678393\pi\)
0.789200 0.614136i \(-0.210496\pi\)
\(618\) 0 0
\(619\) −364.506 434.402i −0.588863 0.701780i 0.386524 0.922279i \(-0.373676\pi\)
−0.975387 + 0.220499i \(0.929231\pi\)
\(620\) −250.083 + 203.498i −0.403359 + 0.328223i
\(621\) 0 0
\(622\) −333.066 + 700.427i −0.535476 + 1.12609i
\(623\) 26.3316 + 31.3808i 0.0422658 + 0.0503704i
\(624\) 0 0
\(625\) −49.7908 + 282.378i −0.0796653 + 0.451805i
\(626\) −1017.01 96.7087i −1.62462 0.154487i
\(627\) 0 0
\(628\) 228.268 263.855i 0.363485 0.420152i
\(629\) 352.884 + 611.213i 0.561024 + 0.971723i
\(630\) 0 0
\(631\) −276.842 159.835i −0.438736 0.253304i 0.264326 0.964434i \(-0.414851\pi\)
−0.703061 + 0.711129i \(0.748184\pi\)
\(632\) −160.770 17.7376i −0.254382 0.0280658i
\(633\) 0 0
\(634\) −149.035 326.001i −0.235071 0.514197i
\(635\) 541.062 644.812i 0.852065 1.01545i
\(636\) 0 0
\(637\) −830.035 302.108i −1.30304 0.474267i
\(638\) 890.676 + 1292.65i 1.39604 + 2.02610i
\(639\) 0 0
\(640\) 264.813 + 424.183i 0.413771 + 0.662786i
\(641\) −69.5108 394.215i −0.108441 0.615000i −0.989790 0.142534i \(-0.954475\pi\)
0.881349 0.472466i \(-0.156636\pi\)
\(642\) 0 0
\(643\) 266.185 + 731.338i 0.413974 + 1.13738i 0.955059 + 0.296416i \(0.0957915\pi\)
−0.541085 + 0.840968i \(0.681986\pi\)
\(644\) −17.0240 + 9.48949i −0.0264348 + 0.0147352i
\(645\) 0 0
\(646\) −88.6049 340.939i −0.137159 0.527770i
\(647\) 429.893i 0.664440i −0.943202 0.332220i \(-0.892202\pi\)
0.943202 0.332220i \(-0.107798\pi\)
\(648\) 0 0
\(649\) 1004.29 1.54744
\(650\) −387.905 + 100.810i −0.596777 + 0.155093i
\(651\) 0 0
\(652\) 517.921 + 929.144i 0.794357 + 1.42507i
\(653\) 173.069 62.9920i 0.265037 0.0964655i −0.206084 0.978534i \(-0.566072\pi\)
0.471120 + 0.882069i \(0.343850\pi\)
\(654\) 0 0
\(655\) 147.378 25.9868i 0.225005 0.0396745i
\(656\) 90.6602 29.9340i 0.138202 0.0456311i
\(657\) 0 0
\(658\) −222.126 + 153.052i −0.337578 + 0.232601i
\(659\) 275.221 756.165i 0.417635 1.14744i −0.535404 0.844596i \(-0.679841\pi\)
0.953039 0.302847i \(-0.0979370\pi\)
\(660\) 0 0
\(661\) −97.5532 81.8569i −0.147584 0.123838i 0.566006 0.824401i \(-0.308488\pi\)
−0.713591 + 0.700563i \(0.752932\pi\)
\(662\) −241.739 + 110.514i −0.365165 + 0.166939i
\(663\) 0 0
\(664\) −414.266 45.7056i −0.623894 0.0688338i
\(665\) −36.9807 + 64.0525i −0.0556101 + 0.0963195i
\(666\) 0 0
\(667\) 75.1088 43.3641i 0.112607 0.0650136i
\(668\) 47.2579 + 40.8841i 0.0707454 + 0.0612037i
\(669\) 0 0
\(670\) −1.62564 + 17.0956i −0.00242633 + 0.0255159i
\(671\) −282.232 49.7652i −0.420615 0.0741657i
\(672\) 0 0
\(673\) 385.770 323.700i 0.573210 0.480980i −0.309500 0.950900i \(-0.600162\pi\)
0.882709 + 0.469919i \(0.155717\pi\)
\(674\) 558.698 + 265.671i 0.828928 + 0.394171i
\(675\) 0 0
\(676\) 642.542 + 789.633i 0.950506 + 1.16810i
\(677\) 277.563 232.903i 0.409990 0.344023i −0.414350 0.910118i \(-0.635991\pi\)
0.824340 + 0.566095i \(0.191547\pi\)
\(678\) 0 0
\(679\) −310.201 54.6967i −0.456849 0.0805548i
\(680\) 397.778 + 596.351i 0.584967 + 0.876986i
\(681\) 0 0
\(682\) 196.401 711.476i 0.287977 1.04322i
\(683\) −882.660 + 509.604i −1.29233 + 0.746126i −0.979067 0.203541i \(-0.934755\pi\)
−0.313262 + 0.949667i \(0.601422\pi\)
\(684\) 0 0
\(685\) 109.772 190.130i 0.160251 0.277562i
\(686\) −322.897 + 318.064i −0.470695 + 0.463650i
\(687\) 0 0
\(688\) −316.266 400.864i −0.459689 0.582651i
\(689\) −306.779 257.418i −0.445252 0.373611i
\(690\) 0 0
\(691\) 22.0977 60.7129i 0.0319793 0.0878624i −0.922676 0.385577i \(-0.874002\pi\)
0.954655 + 0.297715i \(0.0962245\pi\)
\(692\) 752.458 121.010i 1.08737 0.174870i
\(693\) 0 0
\(694\) 370.392 29.5930i 0.533706 0.0426412i
\(695\) −910.772 + 160.594i −1.31046 + 0.231070i
\(696\) 0 0
\(697\) 128.610 46.8102i 0.184519 0.0671596i
\(698\) −80.7179 + 113.447i −0.115642 + 0.162531i
\(699\) 0 0
\(700\) −18.0991 + 94.3066i −0.0258558 + 0.134724i
\(701\) 847.120 1.20845 0.604223 0.796815i \(-0.293484\pi\)
0.604223 + 0.796815i \(0.293484\pi\)
\(702\) 0 0
\(703\) 236.295i 0.336124i
\(704\) −1056.90 439.771i −1.50128 0.624674i
\(705\) 0 0
\(706\) −371.428 + 522.033i −0.526103 + 0.739424i
\(707\) 95.1357 + 261.383i 0.134563 + 0.369708i
\(708\) 0 0
\(709\) 34.9456 + 198.186i 0.0492885 + 0.279529i 0.999484 0.0321259i \(-0.0102278\pi\)
−0.950195 + 0.311655i \(0.899117\pi\)
\(710\) −774.192 + 61.8552i −1.09041 + 0.0871199i
\(711\) 0 0
\(712\) 127.589 + 37.2998i 0.179198 + 0.0523873i
\(713\) −38.3187 13.9469i −0.0537430 0.0195608i
\(714\) 0 0
\(715\) −924.350 + 1101.60i −1.29280 + 1.54070i
\(716\) −1085.87 16.3750i −1.51658 0.0228701i
\(717\) 0 0
\(718\) −193.962 + 191.059i −0.270143 + 0.266100i
\(719\) 513.183 + 296.286i 0.713745 + 0.412081i 0.812446 0.583036i \(-0.198135\pi\)
−0.0987011 + 0.995117i \(0.531469\pi\)
\(720\) 0 0
\(721\) −170.795 295.826i −0.236887 0.410300i
\(722\) −160.737 + 582.281i −0.222627 + 0.806484i
\(723\) 0 0
\(724\) 44.6929 + 26.7100i 0.0617305 + 0.0368922i
\(725\) 74.2011 420.816i 0.102346 0.580435i
\(726\) 0 0
\(727\) 362.352 + 431.835i 0.498421 + 0.593995i 0.955338 0.295514i \(-0.0954909\pi\)
−0.456917 + 0.889509i \(0.651046\pi\)
\(728\) 394.327 96.1562i 0.541658 0.132083i
\(729\) 0 0
\(730\) −448.839 213.431i −0.614848 0.292372i
\(731\) −470.494 560.713i −0.643631 0.767049i
\(732\) 0 0
\(733\) 86.4998 490.565i 0.118008 0.669256i −0.867209 0.497944i \(-0.834088\pi\)
0.985217 0.171312i \(-0.0548006\pi\)
\(734\) −60.6686 + 638.006i −0.0826548 + 0.869218i
\(735\) 0 0
\(736\) −28.8698 + 56.2715i −0.0392253 + 0.0764558i
\(737\) −19.6562 34.0455i −0.0266705 0.0461947i
\(738\) 0 0
\(739\) 64.8835 + 37.4605i 0.0877990 + 0.0506908i 0.543257 0.839567i \(-0.317191\pi\)
−0.455458 + 0.890257i \(0.650524\pi\)
\(740\) −157.628 454.279i −0.213011 0.613890i
\(741\) 0 0
\(742\) −87.2645 + 39.8939i −0.117607 + 0.0537654i
\(743\) 393.521 468.979i 0.529637 0.631197i −0.433194 0.901301i \(-0.642613\pi\)
0.962831 + 0.270104i \(0.0870579\pi\)
\(744\) 0 0
\(745\) −122.902 44.7327i −0.164969 0.0600438i
\(746\) 214.219 147.604i 0.287157 0.197860i
\(747\) 0 0
\(748\) −1533.41 584.447i −2.05001 0.781347i
\(749\) 64.9075 + 368.109i 0.0866589 + 0.491467i
\(750\) 0 0
\(751\) −9.88829 27.1679i −0.0131668 0.0361756i 0.932935 0.360045i \(-0.117239\pi\)
−0.946102 + 0.323869i \(0.895016\pi\)
\(752\) −324.046 + 813.139i −0.430913 + 1.08130i
\(753\) 0 0
\(754\) −1748.04 + 454.289i −2.31836 + 0.602505i
\(755\) 143.863i 0.190547i
\(756\) 0 0
\(757\) −1216.32 −1.60676 −0.803380 0.595467i \(-0.796967\pi\)
−0.803380 + 0.595467i \(0.796967\pi\)
\(758\) 279.409 + 1075.13i 0.368613 + 1.41837i
\(759\) 0 0
\(760\) 15.5049 + 239.501i 0.0204012 + 0.315133i
\(761\) −132.675 + 48.2896i −0.174342 + 0.0634554i −0.427717 0.903913i \(-0.640682\pi\)
0.253374 + 0.967368i \(0.418460\pi\)
\(762\) 0 0
\(763\) 311.374 54.9036i 0.408092 0.0719576i
\(764\) −1101.15 419.694i −1.44129 0.549338i
\(765\) 0 0
\(766\) −45.2516 65.6743i −0.0590752 0.0857367i
\(767\) −395.196 + 1085.79i −0.515249 + 1.41563i
\(768\) 0 0
\(769\) 377.149 + 316.466i 0.490441 + 0.411529i 0.854184 0.519970i \(-0.174057\pi\)
−0.363743 + 0.931499i \(0.618501\pi\)
\(770\) 143.253 + 313.354i 0.186043 + 0.406954i
\(771\) 0 0
\(772\) −336.924 971.003i −0.436430 1.25778i
\(773\) −139.762 + 242.074i −0.180804 + 0.313162i −0.942155 0.335179i \(-0.891203\pi\)
0.761350 + 0.648341i \(0.224537\pi\)
\(774\) 0 0
\(775\) −173.995 + 100.456i −0.224509 + 0.129620i
\(776\) −935.888 + 410.905i −1.20604 + 0.529517i
\(777\) 0 0
\(778\) −849.301 80.7609i −1.09165 0.103806i
\(779\) 45.1267 + 7.95705i 0.0579290 + 0.0102144i
\(780\) 0 0
\(781\) 1361.99 1142.85i 1.74391 1.46331i
\(782\) −38.9343 + 81.8774i −0.0497881 + 0.104703i
\(783\) 0 0
\(784\) −139.592 + 672.416i −0.178051 + 0.857673i
\(785\) −261.033 + 219.033i −0.332526 + 0.279023i
\(786\) 0 0
\(787\) −930.818 164.128i −1.18274 0.208549i −0.452517 0.891756i \(-0.649474\pi\)
−0.730225 + 0.683207i \(0.760585\pi\)
\(788\) 293.646 + 175.493i 0.372647 + 0.222707i
\(789\) 0 0
\(790\) 152.277 + 42.0355i 0.192756 + 0.0532095i
\(791\) −308.117 + 177.892i −0.389529 + 0.224894i
\(792\) 0 0
\(793\) 164.864 285.553i 0.207900 0.360093i
\(794\) 532.751 + 540.846i 0.670971 + 0.681166i
\(795\) 0 0
\(796\) 73.4162 + 1.10712i 0.0922314 + 0.00139086i
\(797\) 674.688 + 566.131i 0.846535 + 0.710327i 0.959024 0.283326i \(-0.0914378\pi\)
−0.112489 + 0.993653i \(0.535882\pi\)
\(798\) 0 0
\(799\) −429.167 + 1179.13i −0.537130 + 1.47575i
\(800\) 120.954 + 287.174i 0.151192 + 0.358968i
\(801\) 0 0
\(802\) 18.3540 + 229.722i 0.0228853 + 0.286437i
\(803\) 1120.46 197.568i 1.39535 0.246037i
\(804\) 0 0
\(805\) 17.8876 6.51055i 0.0222206 0.00808764i
\(806\) 691.929 + 492.310i 0.858473 + 0.610807i
\(807\) 0 0
\(808\) 727.481 + 534.309i 0.900348 + 0.661273i
\(809\) 752.685 0.930389 0.465195 0.885208i \(-0.345984\pi\)
0.465195 + 0.885208i \(0.345984\pi\)
\(810\) 0 0
\(811\) 765.315i 0.943669i −0.881687 0.471834i \(-0.843592\pi\)
0.881687 0.471834i \(-0.156408\pi\)
\(812\) −81.5610 + 424.980i −0.100445 + 0.523374i
\(813\) 0 0
\(814\) 896.916 + 638.158i 1.10186 + 0.783978i
\(815\) −355.335 976.276i −0.435994 1.19788i
\(816\) 0 0
\(817\) −42.5550 241.341i −0.0520869 0.295399i
\(818\) −34.6325 433.468i −0.0423380 0.529912i
\(819\) 0 0
\(820\) −92.0642 + 14.8057i −0.112273 + 0.0180557i
\(821\) −315.409 114.799i −0.384176 0.139829i 0.142710 0.989765i \(-0.454418\pi\)
−0.526886 + 0.849936i \(0.676641\pi\)
\(822\) 0 0
\(823\) −334.820 + 399.023i −0.406828 + 0.484839i −0.930089 0.367333i \(-0.880271\pi\)
0.523261 + 0.852173i \(0.324715\pi\)
\(824\) −993.746 491.052i −1.20600 0.595937i
\(825\) 0 0
\(826\) 194.279 + 197.231i 0.235204 + 0.238778i
\(827\) 546.337 + 315.428i 0.660625 + 0.381412i 0.792515 0.609852i \(-0.208771\pi\)
−0.131890 + 0.991264i \(0.542105\pi\)
\(828\) 0 0
\(829\) −225.729 390.973i −0.272290 0.471620i 0.697158 0.716918i \(-0.254448\pi\)
−0.969448 + 0.245297i \(0.921114\pi\)
\(830\) 392.382 + 108.316i 0.472749 + 0.130501i
\(831\) 0 0
\(832\) 891.358 969.621i 1.07134 1.16541i
\(833\) −170.952 + 969.516i −0.205224 + 1.16388i
\(834\) 0 0
\(835\) −39.2300 46.7524i −0.0469820 0.0559909i
\(836\) −346.775 426.158i −0.414802 0.509759i
\(837\) 0 0
\(838\) 111.414 234.300i 0.132953 0.279595i
\(839\) 637.673 + 759.949i 0.760040 + 0.905780i 0.997851 0.0655314i \(-0.0208743\pi\)
−0.237811 + 0.971312i \(0.576430\pi\)
\(840\) 0 0
\(841\) 188.339 1068.12i 0.223947 1.27006i
\(842\) 200.973 + 19.1107i 0.238685 + 0.0226968i
\(843\) 0 0
\(844\) −545.534 471.956i −0.646367 0.559190i
\(845\) −497.141 861.073i −0.588332 1.01902i
\(846\) 0 0
\(847\) −424.732 245.219i −0.501455 0.289515i
\(848\) −163.739 + 264.828i −0.193089 + 0.312297i
\(849\) 0 0
\(850\) 185.723 + 406.254i 0.218498 + 0.477946i
\(851\) 39.0916 46.5876i 0.0459361 0.0547445i
\(852\) 0 0
\(853\) −117.818 42.8824i −0.138122 0.0502725i 0.272034 0.962288i \(-0.412304\pi\)
−0.410156 + 0.912015i \(0.634526\pi\)
\(854\) −44.8242 65.0541i −0.0524874 0.0761758i
\(855\) 0 0
\(856\) 838.054 + 876.849i 0.979035 + 1.02436i
\(857\) 5.06668 + 28.7346i 0.00591211 + 0.0335292i 0.987621 0.156858i \(-0.0501366\pi\)
−0.981709 + 0.190388i \(0.939026\pi\)
\(858\) 0 0
\(859\) −477.457 1311.80i −0.555829 1.52713i −0.825630 0.564211i \(-0.809180\pi\)
0.269802 0.962916i \(-0.413042\pi\)
\(860\) 242.806 + 435.592i 0.282333 + 0.506502i
\(861\) 0 0
\(862\) 8.74099 + 33.6341i 0.0101404 + 0.0390187i
\(863\) 791.555i 0.917213i −0.888639 0.458606i \(-0.848349\pi\)
0.888639 0.458606i \(-0.151651\pi\)
\(864\) 0 0
\(865\) −744.349 −0.860519
\(866\) −1428.08 + 371.137i −1.64906 + 0.428564i
\(867\) 0 0
\(868\) 177.719 99.0635i 0.204745 0.114129i
\(869\) −339.826 + 123.686i −0.391054 + 0.142332i
\(870\) 0 0
\(871\) 44.5432 7.85417i 0.0511403 0.00901742i
\(872\) 741.704 708.888i 0.850578 0.812945i
\(873\) 0 0
\(874\) −24.9955 + 17.2227i −0.0285990 + 0.0197056i
\(875\) 114.431 314.395i 0.130778 0.359309i
\(876\) 0 0
\(877\) 740.892 + 621.682i 0.844803 + 0.708874i 0.958639 0.284626i \(-0.0918693\pi\)
−0.113836 + 0.993500i \(0.536314\pi\)
\(878\) 702.582 321.193i 0.800207 0.365823i
\(879\) 0 0
\(880\) 950.958 + 587.964i 1.08063 + 0.668141i
\(881\) 176.281 305.328i 0.200092 0.346570i −0.748466 0.663174i \(-0.769209\pi\)
0.948558 + 0.316604i \(0.102542\pi\)
\(882\) 0 0
\(883\) 49.7450 28.7203i 0.0563364 0.0325258i −0.471567 0.881830i \(-0.656312\pi\)
0.527904 + 0.849304i \(0.322978\pi\)
\(884\) 1235.28 1427.87i 1.39738 1.61523i
\(885\) 0 0
\(886\) −39.5376 + 415.787i −0.0446248 + 0.469285i
\(887\) −5.74429 1.01287i −0.00647609 0.00114191i 0.170409 0.985373i \(-0.445491\pi\)
−0.176885 + 0.984231i \(0.556602\pi\)
\(888\) 0 0
\(889\) −406.914 + 341.441i −0.457721 + 0.384074i
\(890\) −117.248 55.7535i −0.131739 0.0626444i
\(891\) 0 0
\(892\) −163.027 + 132.659i −0.182766 + 0.148721i
\(893\) −321.826 + 270.044i −0.360388 + 0.302401i
\(894\) 0 0
\(895\) 1044.55 + 184.182i 1.16709 + 0.205790i
\(896\) −118.091 292.636i −0.131798 0.326603i
\(897\) 0 0
\(898\) −193.597 + 701.319i −0.215586 + 0.780979i
\(899\) −784.083 + 452.691i −0.872173 + 0.503549i
\(900\) 0 0
\(901\) −223.169 + 386.540i −0.247690 + 0.429012i
\(902\) 152.076 149.800i 0.168598 0.166075i
\(903\) 0 0
\(904\) −511.455 + 1035.03i −0.565768 + 1.14495i
\(905\) −38.9546 32.6868i −0.0430438 0.0361180i
\(906\) 0 0
\(907\) 358.801 985.799i 0.395591 1.08688i −0.568818 0.822464i \(-0.692599\pi\)
0.964409 0.264415i \(-0.0851788\pi\)
\(908\) −51.9726 323.174i −0.0572386 0.355919i
\(909\) 0 0
\(910\) −395.155 + 31.5714i −0.434236 + 0.0346939i
\(911\) 1063.71 187.560i 1.16763 0.205884i 0.443968 0.896043i \(-0.353570\pi\)
0.723658 + 0.690159i \(0.242459\pi\)
\(912\) 0 0
\(913\) −875.651 + 318.711i −0.959092 + 0.349081i
\(914\) 642.259 902.679i 0.702691 0.987614i
\(915\) 0 0
\(916\) 96.8054 + 18.5786i 0.105683 + 0.0202824i
\(917\) −94.4391 −0.102987
\(918\) 0 0
\(919\) 64.6952i 0.0703974i −0.999380 0.0351987i \(-0.988794\pi\)
0.999380 0.0351987i \(-0.0112064\pi\)
\(920\) 36.5651 49.7847i 0.0397446 0.0541138i
\(921\) 0 0
\(922\) 549.215 771.908i 0.595678 0.837210i
\(923\) 699.637 + 1922.24i 0.758003 + 2.08260i
\(924\) 0 0
\(925\) −52.0315 295.085i −0.0562503 0.319011i
\(926\) 76.8902 6.14325i 0.0830348 0.00663418i
\(927\) 0 0
\(928\) 545.061 + 1294.11i 0.587350 + 1.39452i
\(929\) 90.3020 + 32.8673i 0.0972035 + 0.0353792i 0.390164 0.920745i \(-0.372418\pi\)
−0.292961 + 0.956125i \(0.594640\pi\)
\(930\) 0 0
\(931\) −211.867 + 252.494i −0.227570 + 0.271207i
\(932\) 4.78090 317.034i 0.00512972 0.340165i
\(933\) 0 0
\(934\) −224.407 + 221.048i −0.240264 + 0.236668i
\(935\) 1388.01 + 801.368i 1.48450 + 0.857078i
\(936\) 0 0
\(937\) 43.2795 + 74.9624i 0.0461895 + 0.0800025i 0.888196 0.459465i \(-0.151959\pi\)
−0.842006 + 0.539468i \(0.818626\pi\)
\(938\) 2.88366 10.4463i 0.00307427 0.0111368i
\(939\) 0 0
\(940\) 438.571 733.845i 0.466565 0.780686i
\(941\) 231.827 1314.76i 0.246363 1.39719i −0.570944 0.820989i \(-0.693423\pi\)
0.817306 0.576203i \(-0.195466\pi\)
\(942\) 0 0
\(943\) −7.58072 9.03435i −0.00803894 0.00958043i
\(944\) 879.606 + 182.605i 0.931786 + 0.193437i
\(945\) 0 0
\(946\) −1030.99 490.258i −1.08985 0.518243i
\(947\) −1040.19 1239.65i −1.09840 1.30903i −0.947242 0.320519i \(-0.896143\pi\)
−0.151162 0.988509i \(-0.548302\pi\)
\(948\) 0 0
\(949\) −227.309 + 1289.14i −0.239525 + 1.35841i
\(950\) −14.1575 + 148.884i −0.0149027 + 0.156720i
\(951\) 0 0
\(952\) −181.858 414.204i −0.191027 0.435088i
\(953\) −102.057 176.767i −0.107090 0.185485i 0.807500 0.589867i \(-0.200820\pi\)
−0.914590 + 0.404382i \(0.867487\pi\)
\(954\) 0 0
\(955\) 996.736 + 575.466i 1.04370 + 0.602582i
\(956\) −554.875 + 192.534i −0.580413 + 0.201395i
\(957\) 0 0
\(958\) −844.814 + 386.216i −0.881851 + 0.403148i
\(959\) −89.0548 + 106.131i −0.0928622 + 0.110669i
\(960\) 0 0
\(961\) −503.024 183.086i −0.523438 0.190516i
\(962\) −1042.89 + 718.583i −1.08408 + 0.746967i
\(963\) 0 0
\(964\) 506.649 1329.29i 0.525570 1.37893i
\(965\) 174.312 + 988.572i 0.180634 + 1.02443i
\(966\) 0 0
\(967\) −103.339 283.922i −0.106866 0.293611i 0.874721 0.484626i \(-0.161044\pi\)
−0.981587 + 0.191015i \(0.938822\pi\)
\(968\) −1588.13 + 102.813i −1.64063 + 0.106212i
\(969\) 0 0
\(970\) 966.183 251.096i 0.996065 0.258862i
\(971\) 1000.22i 1.03010i −0.857161 0.515049i \(-0.827774\pi\)
0.857161 0.515049i \(-0.172226\pi\)
\(972\) 0 0
\(973\) 583.617 0.599812
\(974\) −444.451 1710.19i −0.456315 1.75584i
\(975\) 0 0
\(976\) −238.144 94.9035i −0.244000 0.0972372i
\(977\) 95.5668 34.7835i 0.0978166 0.0356023i −0.292648 0.956220i \(-0.594537\pi\)
0.390465 + 0.920618i \(0.372314\pi\)
\(978\) 0 0
\(979\) 292.692 51.6095i 0.298970 0.0527166i
\(980\) 238.882 626.753i 0.243757 0.639544i
\(981\) 0 0
\(982\) −553.319 803.040i −0.563462 0.817760i
\(983\) −554.806 + 1524.32i −0.564400 + 1.55068i 0.248716 + 0.968576i \(0.419991\pi\)
−0.813117 + 0.582101i \(0.802231\pi\)
\(984\) 0 0
\(985\) −255.944 214.762i −0.259841 0.218033i
\(986\) 836.937 + 1830.73i 0.848821 + 1.85672i
\(987\) 0 0
\(988\) 597.200 207.220i 0.604454 0.209737i
\(989\) −31.5363 + 54.6225i −0.0318871 + 0.0552300i
\(990\) 0 0
\(991\) −1135.19 + 655.405i −1.14550 + 0.661357i −0.947788 0.318902i \(-0.896686\pi\)
−0.197717 + 0.980259i \(0.563353\pi\)
\(992\) 301.381 587.434i 0.303811 0.592172i
\(993\) 0 0
\(994\) 487.917 + 46.3965i 0.490862 + 0.0466765i
\(995\) −70.6224 12.4526i −0.0709773 0.0125152i
\(996\) 0 0
\(997\) −170.842 + 143.354i −0.171356 + 0.143785i −0.724433 0.689346i \(-0.757898\pi\)
0.553076 + 0.833131i \(0.313454\pi\)
\(998\) −222.458 + 467.822i −0.222904 + 0.468760i
\(999\) 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 324.3.j.a.199.31 204
3.2 odd 2 108.3.j.a.103.4 yes 204
4.3 odd 2 inner 324.3.j.a.199.22 204
12.11 even 2 108.3.j.a.103.13 yes 204
27.11 odd 18 108.3.j.a.43.13 yes 204
27.16 even 9 inner 324.3.j.a.127.22 204
108.11 even 18 108.3.j.a.43.4 204
108.43 odd 18 inner 324.3.j.a.127.31 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.43.4 204 108.11 even 18
108.3.j.a.43.13 yes 204 27.11 odd 18
108.3.j.a.103.4 yes 204 3.2 odd 2
108.3.j.a.103.13 yes 204 12.11 even 2
324.3.j.a.127.22 204 27.16 even 9 inner
324.3.j.a.127.31 204 108.43 odd 18 inner
324.3.j.a.199.22 204 4.3 odd 2 inner
324.3.j.a.199.31 204 1.1 even 1 trivial