Properties

Label 441.2.bb.f.37.6
Level $441$
Weight $2$
Character 441.37
Analytic conductor $3.521$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(37,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bb (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 37.6
Character \(\chi\) \(=\) 441.37
Dual form 441.2.bb.f.298.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.14208 - 1.46044i) q^{2} +(1.72492 - 4.39502i) q^{4} +(-0.478860 - 0.147709i) q^{5} +(-1.61928 - 2.09235i) q^{7} +(-1.56997 - 6.87850i) q^{8} +O(q^{10})\) \(q+(2.14208 - 1.46044i) q^{2} +(1.72492 - 4.39502i) q^{4} +(-0.478860 - 0.147709i) q^{5} +(-1.61928 - 2.09235i) q^{7} +(-1.56997 - 6.87850i) q^{8} +(-1.24148 + 0.382945i) q^{10} +(0.0946027 + 1.26239i) q^{11} +(0.903002 + 0.434863i) q^{13} +(-6.52438 - 2.11713i) q^{14} +(-6.48661 - 6.01869i) q^{16} +(5.00923 + 0.755020i) q^{17} +(-2.61750 + 4.53365i) q^{19} +(-1.47518 + 1.84982i) q^{20} +(2.04629 + 2.56597i) q^{22} +(6.24943 - 0.941950i) q^{23} +(-3.92370 - 2.67514i) q^{25} +(2.56939 - 0.387274i) q^{26} +(-11.9891 + 3.50761i) q^{28} +(2.11330 - 2.64999i) q^{29} +(3.27011 + 5.66400i) q^{31} +(-8.73161 - 1.31608i) q^{32} +(11.8328 - 5.69839i) q^{34} +(0.466347 + 1.24113i) q^{35} +(-3.23703 - 8.24781i) q^{37} +(1.01424 + 13.5341i) q^{38} +(-0.264218 + 3.52574i) q^{40} +(2.41122 + 10.5643i) q^{41} +(-0.774658 + 3.39400i) q^{43} +(5.71139 + 1.76173i) q^{44} +(12.0111 - 11.1447i) q^{46} +(1.03733 - 0.707237i) q^{47} +(-1.75590 + 6.77620i) q^{49} -12.3118 q^{50} +(3.46884 - 3.21861i) q^{52} +(-0.189183 + 0.482029i) q^{53} +(0.141164 - 0.618480i) q^{55} +(-11.8500 + 14.4231i) q^{56} +(0.656685 - 8.76285i) q^{58} +(-14.3965 + 4.44074i) q^{59} +(-3.09099 - 7.87572i) q^{61} +(15.2768 + 7.35691i) q^{62} +(-4.68092 + 2.25421i) q^{64} +(-0.368179 - 0.341620i) q^{65} +(1.83517 + 3.17860i) q^{67} +(11.9588 - 20.7133i) q^{68} +(2.81155 + 1.97752i) q^{70} +(6.96988 + 8.73996i) q^{71} +(-6.17593 - 4.21068i) q^{73} +(-18.9794 - 12.9400i) q^{74} +(15.4105 + 19.3242i) q^{76} +(2.48817 - 2.24209i) q^{77} +(-5.29950 + 9.17900i) q^{79} +(2.21717 + 3.84024i) q^{80} +(20.5935 + 19.1080i) q^{82} +(13.6995 - 6.59732i) q^{83} +(-2.28720 - 1.10146i) q^{85} +(3.29737 + 8.40155i) q^{86} +(8.53479 - 2.63263i) q^{88} +(0.531312 - 7.08986i) q^{89} +(-0.552321 - 2.59356i) q^{91} +(6.63987 - 29.0912i) q^{92} +(1.18915 - 3.02991i) q^{94} +(1.92308 - 1.78436i) q^{95} -7.82435 q^{97} +(6.13499 + 17.0795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{16}{21}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.14208 1.46044i 1.51468 1.03269i 0.532134 0.846660i \(-0.321390\pi\)
0.982544 0.186029i \(-0.0595620\pi\)
\(3\) 0 0
\(4\) 1.72492 4.39502i 0.862459 2.19751i
\(5\) −0.478860 0.147709i −0.214153 0.0660574i 0.185822 0.982583i \(-0.440505\pi\)
−0.399975 + 0.916526i \(0.630981\pi\)
\(6\) 0 0
\(7\) −1.61928 2.09235i −0.612028 0.790836i
\(8\) −1.56997 6.87850i −0.555069 2.43192i
\(9\) 0 0
\(10\) −1.24148 + 0.382945i −0.392589 + 0.121098i
\(11\) 0.0946027 + 1.26239i 0.0285238 + 0.380623i 0.993137 + 0.116955i \(0.0373134\pi\)
−0.964613 + 0.263668i \(0.915068\pi\)
\(12\) 0 0
\(13\) 0.903002 + 0.434863i 0.250448 + 0.120609i 0.554896 0.831919i \(-0.312758\pi\)
−0.304449 + 0.952529i \(0.598472\pi\)
\(14\) −6.52438 2.11713i −1.74371 0.565826i
\(15\) 0 0
\(16\) −6.48661 6.01869i −1.62165 1.50467i
\(17\) 5.00923 + 0.755020i 1.21492 + 0.183119i 0.725061 0.688685i \(-0.241812\pi\)
0.489855 + 0.871804i \(0.337050\pi\)
\(18\) 0 0
\(19\) −2.61750 + 4.53365i −0.600496 + 1.04009i 0.392250 + 0.919859i \(0.371697\pi\)
−0.992746 + 0.120231i \(0.961636\pi\)
\(20\) −1.47518 + 1.84982i −0.329860 + 0.413631i
\(21\) 0 0
\(22\) 2.04629 + 2.56597i 0.436270 + 0.547066i
\(23\) 6.24943 0.941950i 1.30310 0.196410i 0.539435 0.842028i \(-0.318638\pi\)
0.763661 + 0.645617i \(0.223400\pi\)
\(24\) 0 0
\(25\) −3.92370 2.67514i −0.784741 0.535027i
\(26\) 2.56939 0.387274i 0.503900 0.0759506i
\(27\) 0 0
\(28\) −11.9891 + 3.50761i −2.26572 + 0.662875i
\(29\) 2.11330 2.64999i 0.392430 0.492092i −0.545891 0.837856i \(-0.683809\pi\)
0.938321 + 0.345764i \(0.112380\pi\)
\(30\) 0 0
\(31\) 3.27011 + 5.66400i 0.587329 + 1.01728i 0.994581 + 0.103968i \(0.0331540\pi\)
−0.407251 + 0.913316i \(0.633513\pi\)
\(32\) −8.73161 1.31608i −1.54355 0.232652i
\(33\) 0 0
\(34\) 11.8328 5.69839i 2.02931 0.977265i
\(35\) 0.466347 + 1.24113i 0.0788271 + 0.209789i
\(36\) 0 0
\(37\) −3.23703 8.24781i −0.532164 1.35593i −0.903960 0.427617i \(-0.859353\pi\)
0.371796 0.928315i \(-0.378742\pi\)
\(38\) 1.01424 + 13.5341i 0.164532 + 2.19553i
\(39\) 0 0
\(40\) −0.264218 + 3.52574i −0.0417765 + 0.557468i
\(41\) 2.41122 + 10.5643i 0.376570 + 1.64986i 0.707875 + 0.706337i \(0.249654\pi\)
−0.331305 + 0.943524i \(0.607489\pi\)
\(42\) 0 0
\(43\) −0.774658 + 3.39400i −0.118134 + 0.517580i 0.880886 + 0.473328i \(0.156948\pi\)
−0.999020 + 0.0442518i \(0.985910\pi\)
\(44\) 5.71139 + 1.76173i 0.861025 + 0.265591i
\(45\) 0 0
\(46\) 12.0111 11.1447i 1.77094 1.64319i
\(47\) 1.03733 0.707237i 0.151310 0.103161i −0.485299 0.874348i \(-0.661289\pi\)
0.636608 + 0.771187i \(0.280337\pi\)
\(48\) 0 0
\(49\) −1.75590 + 6.77620i −0.250842 + 0.968028i
\(50\) −12.3118 −1.74115
\(51\) 0 0
\(52\) 3.46884 3.21861i 0.481041 0.446341i
\(53\) −0.189183 + 0.482029i −0.0259862 + 0.0662118i −0.943278 0.332004i \(-0.892275\pi\)
0.917292 + 0.398216i \(0.130370\pi\)
\(54\) 0 0
\(55\) 0.141164 0.618480i 0.0190346 0.0833958i
\(56\) −11.8500 + 14.4231i −1.58353 + 1.92737i
\(57\) 0 0
\(58\) 0.656685 8.76285i 0.0862269 1.15062i
\(59\) −14.3965 + 4.44074i −1.87427 + 0.578135i −0.879508 + 0.475883i \(0.842128\pi\)
−0.994759 + 0.102252i \(0.967395\pi\)
\(60\) 0 0
\(61\) −3.09099 7.87572i −0.395761 1.00838i −0.980387 0.197080i \(-0.936854\pi\)
0.584626 0.811303i \(-0.301241\pi\)
\(62\) 15.2768 + 7.35691i 1.94015 + 0.934329i
\(63\) 0 0
\(64\) −4.68092 + 2.25421i −0.585114 + 0.281776i
\(65\) −0.368179 0.341620i −0.0456670 0.0423727i
\(66\) 0 0
\(67\) 1.83517 + 3.17860i 0.224201 + 0.388328i 0.956080 0.293107i \(-0.0946893\pi\)
−0.731878 + 0.681436i \(0.761356\pi\)
\(68\) 11.9588 20.7133i 1.45022 2.51186i
\(69\) 0 0
\(70\) 2.81155 + 1.97752i 0.336044 + 0.236358i
\(71\) 6.96988 + 8.73996i 0.827173 + 1.03724i 0.998644 + 0.0520530i \(0.0165765\pi\)
−0.171471 + 0.985189i \(0.554852\pi\)
\(72\) 0 0
\(73\) −6.17593 4.21068i −0.722838 0.492823i 0.145149 0.989410i \(-0.453634\pi\)
−0.867987 + 0.496587i \(0.834586\pi\)
\(74\) −18.9794 12.9400i −2.20631 1.50424i
\(75\) 0 0
\(76\) 15.4105 + 19.3242i 1.76771 + 2.21663i
\(77\) 2.48817 2.24209i 0.283553 0.255510i
\(78\) 0 0
\(79\) −5.29950 + 9.17900i −0.596240 + 1.03272i 0.397130 + 0.917762i \(0.370006\pi\)
−0.993371 + 0.114956i \(0.963327\pi\)
\(80\) 2.21717 + 3.84024i 0.247887 + 0.429352i
\(81\) 0 0
\(82\) 20.5935 + 19.1080i 2.27418 + 2.11013i
\(83\) 13.6995 6.59732i 1.50371 0.724150i 0.512782 0.858519i \(-0.328615\pi\)
0.990931 + 0.134369i \(0.0429007\pi\)
\(84\) 0 0
\(85\) −2.28720 1.10146i −0.248081 0.119470i
\(86\) 3.29737 + 8.40155i 0.355564 + 0.905963i
\(87\) 0 0
\(88\) 8.53479 2.63263i 0.909812 0.280640i
\(89\) 0.531312 7.08986i 0.0563189 0.751524i −0.895539 0.444983i \(-0.853210\pi\)
0.951858 0.306540i \(-0.0991714\pi\)
\(90\) 0 0
\(91\) −0.552321 2.59356i −0.0578990 0.271879i
\(92\) 6.63987 29.0912i 0.692254 3.03296i
\(93\) 0 0
\(94\) 1.18915 3.02991i 0.122652 0.312512i
\(95\) 1.92308 1.78436i 0.197304 0.183071i
\(96\) 0 0
\(97\) −7.82435 −0.794442 −0.397221 0.917723i \(-0.630025\pi\)
−0.397221 + 0.917723i \(0.630025\pi\)
\(98\) 6.13499 + 17.0795i 0.619727 + 1.72529i
\(99\) 0 0
\(100\) −18.5254 + 12.6304i −1.85254 + 1.26304i
\(101\) −3.59164 + 3.33256i −0.357382 + 0.331602i −0.838346 0.545138i \(-0.816477\pi\)
0.480964 + 0.876740i \(0.340287\pi\)
\(102\) 0 0
\(103\) −8.69583 2.68231i −0.856826 0.264296i −0.164941 0.986303i \(-0.552743\pi\)
−0.691885 + 0.722008i \(0.743219\pi\)
\(104\) 1.57352 6.89402i 0.154296 0.676014i
\(105\) 0 0
\(106\) 0.298733 + 1.30883i 0.0290155 + 0.127125i
\(107\) 0.305692 4.07918i 0.0295524 0.394349i −0.962740 0.270429i \(-0.912834\pi\)
0.992292 0.123920i \(-0.0395466\pi\)
\(108\) 0 0
\(109\) 0.243937 + 3.25512i 0.0233649 + 0.311784i 0.996626 + 0.0820805i \(0.0261565\pi\)
−0.973261 + 0.229703i \(0.926225\pi\)
\(110\) −0.600871 1.53099i −0.0572908 0.145975i
\(111\) 0 0
\(112\) −2.08964 + 23.3182i −0.197452 + 2.20336i
\(113\) −17.7940 + 8.56912i −1.67391 + 0.806115i −0.676334 + 0.736595i \(0.736432\pi\)
−0.997581 + 0.0695198i \(0.977853\pi\)
\(114\) 0 0
\(115\) −3.13174 0.472033i −0.292036 0.0440173i
\(116\) −8.00151 13.8590i −0.742922 1.28678i
\(117\) 0 0
\(118\) −24.3530 + 30.5377i −2.24188 + 2.81122i
\(119\) −6.53155 11.7037i −0.598746 1.07287i
\(120\) 0 0
\(121\) 9.29247 1.40061i 0.844770 0.127329i
\(122\) −18.1232 12.3562i −1.64080 1.11868i
\(123\) 0 0
\(124\) 30.5341 4.60227i 2.74204 0.413296i
\(125\) 3.04599 + 3.81956i 0.272442 + 0.341631i
\(126\) 0 0
\(127\) −1.77882 + 2.23058i −0.157845 + 0.197932i −0.854465 0.519509i \(-0.826115\pi\)
0.696620 + 0.717440i \(0.254686\pi\)
\(128\) 2.09550 3.62952i 0.185218 0.320807i
\(129\) 0 0
\(130\) −1.28758 0.194072i −0.112929 0.0170213i
\(131\) −10.1006 9.37199i −0.882494 0.818835i 0.101903 0.994794i \(-0.467507\pi\)
−0.984397 + 0.175959i \(0.943697\pi\)
\(132\) 0 0
\(133\) 13.7245 1.86448i 1.19006 0.161671i
\(134\) 8.57325 + 4.12866i 0.740616 + 0.356662i
\(135\) 0 0
\(136\) −2.67095 35.6413i −0.229032 3.05622i
\(137\) 13.2725 4.09401i 1.13394 0.349775i 0.329706 0.944084i \(-0.393051\pi\)
0.804237 + 0.594309i \(0.202574\pi\)
\(138\) 0 0
\(139\) −3.50077 15.3379i −0.296932 1.30094i −0.874670 0.484720i \(-0.838922\pi\)
0.577738 0.816222i \(-0.303936\pi\)
\(140\) 6.25919 + 0.0912368i 0.528998 + 0.00771092i
\(141\) 0 0
\(142\) 27.6943 + 8.54255i 2.32405 + 0.716874i
\(143\) −0.463538 + 1.18108i −0.0387630 + 0.0987665i
\(144\) 0 0
\(145\) −1.40340 + 0.956824i −0.116546 + 0.0794599i
\(146\) −19.3788 −1.60380
\(147\) 0 0
\(148\) −41.8329 −3.43865
\(149\) 10.9222 7.44663i 0.894782 0.610052i −0.0262003 0.999657i \(-0.508341\pi\)
0.920982 + 0.389605i \(0.127388\pi\)
\(150\) 0 0
\(151\) −3.68158 + 9.38050i −0.299602 + 0.763375i 0.699222 + 0.714904i \(0.253530\pi\)
−0.998825 + 0.0484702i \(0.984565\pi\)
\(152\) 35.2941 + 10.8868i 2.86273 + 0.883035i
\(153\) 0 0
\(154\) 2.05540 8.43657i 0.165629 0.679838i
\(155\) −0.729304 3.19529i −0.0585791 0.256652i
\(156\) 0 0
\(157\) 11.6442 3.59175i 0.929307 0.286653i 0.207092 0.978322i \(-0.433600\pi\)
0.722215 + 0.691668i \(0.243124\pi\)
\(158\) 2.05348 + 27.4018i 0.163366 + 2.17997i
\(159\) 0 0
\(160\) 3.98683 + 1.91995i 0.315186 + 0.151786i
\(161\) −12.0904 11.5507i −0.952860 0.910326i
\(162\) 0 0
\(163\) −0.0142615 0.0132327i −0.00111704 0.00103646i 0.679614 0.733570i \(-0.262147\pi\)
−0.680731 + 0.732533i \(0.738338\pi\)
\(164\) 50.5893 + 7.62512i 3.95036 + 0.595422i
\(165\) 0 0
\(166\) 19.7103 34.1393i 1.52982 2.64972i
\(167\) −12.3035 + 15.4281i −0.952073 + 1.19386i 0.0288729 + 0.999583i \(0.490808\pi\)
−0.980946 + 0.194279i \(0.937763\pi\)
\(168\) 0 0
\(169\) −7.47906 9.37845i −0.575312 0.721419i
\(170\) −6.50797 + 0.980919i −0.499139 + 0.0752330i
\(171\) 0 0
\(172\) 13.5805 + 9.25901i 1.03550 + 0.705993i
\(173\) −21.1355 + 3.18567i −1.60690 + 0.242202i −0.890332 0.455312i \(-0.849528\pi\)
−0.716572 + 0.697513i \(0.754290\pi\)
\(174\) 0 0
\(175\) 0.756223 + 12.5416i 0.0571651 + 0.948053i
\(176\) 6.98426 8.75799i 0.526458 0.660158i
\(177\) 0 0
\(178\) −9.21623 15.9630i −0.690786 1.19648i
\(179\) 6.42268 + 0.968064i 0.480054 + 0.0723565i 0.384612 0.923079i \(-0.374335\pi\)
0.0954422 + 0.995435i \(0.469573\pi\)
\(180\) 0 0
\(181\) 11.2657 5.42528i 0.837374 0.403258i 0.0344985 0.999405i \(-0.489017\pi\)
0.802876 + 0.596147i \(0.203302\pi\)
\(182\) −4.97087 4.74898i −0.368465 0.352018i
\(183\) 0 0
\(184\) −16.2906 41.5078i −1.20096 3.06000i
\(185\) 0.331809 + 4.42769i 0.0243951 + 0.325530i
\(186\) 0 0
\(187\) −0.479239 + 6.39500i −0.0350454 + 0.467649i
\(188\) −1.31902 5.77900i −0.0961994 0.421477i
\(189\) 0 0
\(190\) 1.51343 6.63078i 0.109796 0.481047i
\(191\) −2.90720 0.896752i −0.210357 0.0648867i 0.187786 0.982210i \(-0.439869\pi\)
−0.398143 + 0.917323i \(0.630345\pi\)
\(192\) 0 0
\(193\) −12.7409 + 11.8219i −0.917112 + 0.850955i −0.989219 0.146441i \(-0.953218\pi\)
0.0721075 + 0.997397i \(0.477028\pi\)
\(194\) −16.7604 + 11.4270i −1.20332 + 0.820412i
\(195\) 0 0
\(196\) 26.7527 + 19.4056i 1.91091 + 1.38611i
\(197\) −5.32151 −0.379142 −0.189571 0.981867i \(-0.560710\pi\)
−0.189571 + 0.981867i \(0.560710\pi\)
\(198\) 0 0
\(199\) 5.38131 4.99313i 0.381471 0.353953i −0.466010 0.884780i \(-0.654309\pi\)
0.847481 + 0.530826i \(0.178118\pi\)
\(200\) −12.2408 + 31.1891i −0.865556 + 2.20540i
\(201\) 0 0
\(202\) −2.82657 + 12.3840i −0.198877 + 0.871335i
\(203\) −8.96674 0.130703i −0.629342 0.00917357i
\(204\) 0 0
\(205\) 0.405796 5.41497i 0.0283420 0.378198i
\(206\) −22.5445 + 6.95406i −1.57075 + 0.484512i
\(207\) 0 0
\(208\) −3.24012 8.25568i −0.224662 0.572428i
\(209\) −5.97083 2.87540i −0.413011 0.198896i
\(210\) 0 0
\(211\) −15.1249 + 7.28375i −1.04124 + 0.501434i −0.874732 0.484607i \(-0.838963\pi\)
−0.166506 + 0.986040i \(0.553248\pi\)
\(212\) 1.79220 + 1.66292i 0.123089 + 0.114210i
\(213\) 0 0
\(214\) −5.30260 9.18437i −0.362478 0.627830i
\(215\) 0.872277 1.51083i 0.0594888 0.103038i
\(216\) 0 0
\(217\) 6.55589 16.0138i 0.445043 1.08709i
\(218\) 5.27645 + 6.61645i 0.357366 + 0.448123i
\(219\) 0 0
\(220\) −2.47474 1.68725i −0.166847 0.113754i
\(221\) 4.19501 + 2.86011i 0.282187 + 0.192392i
\(222\) 0 0
\(223\) 10.2978 + 12.9130i 0.689589 + 0.864718i 0.996198 0.0871180i \(-0.0277657\pi\)
−0.306609 + 0.951836i \(0.599194\pi\)
\(224\) 11.3852 + 20.4007i 0.760704 + 1.36308i
\(225\) 0 0
\(226\) −25.6013 + 44.3428i −1.70297 + 2.94964i
\(227\) 0.874935 + 1.51543i 0.0580715 + 0.100583i 0.893600 0.448865i \(-0.148172\pi\)
−0.835528 + 0.549448i \(0.814838\pi\)
\(228\) 0 0
\(229\) −3.66713 3.40260i −0.242331 0.224850i 0.549652 0.835394i \(-0.314760\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(230\) −7.39780 + 3.56259i −0.487797 + 0.234911i
\(231\) 0 0
\(232\) −21.5458 10.3759i −1.41455 0.681212i
\(233\) −4.43676 11.3047i −0.290662 0.740594i −0.999384 0.0351063i \(-0.988823\pi\)
0.708722 0.705488i \(-0.249272\pi\)
\(234\) 0 0
\(235\) −0.601200 + 0.185446i −0.0392180 + 0.0120971i
\(236\) −5.31569 + 70.9329i −0.346022 + 4.61734i
\(237\) 0 0
\(238\) −31.0836 15.5312i −2.01485 1.00674i
\(239\) −2.08550 + 9.13718i −0.134900 + 0.591035i 0.861611 + 0.507570i \(0.169456\pi\)
−0.996511 + 0.0834655i \(0.973401\pi\)
\(240\) 0 0
\(241\) 1.93785 4.93757i 0.124828 0.318057i −0.854775 0.518999i \(-0.826305\pi\)
0.979603 + 0.200942i \(0.0644002\pi\)
\(242\) 17.8597 16.5714i 1.14806 1.06525i
\(243\) 0 0
\(244\) −39.9457 −2.55726
\(245\) 1.84173 2.98549i 0.117664 0.190736i
\(246\) 0 0
\(247\) −4.33513 + 2.95564i −0.275837 + 0.188063i
\(248\) 33.8258 31.3858i 2.14794 1.99300i
\(249\) 0 0
\(250\) 12.1030 + 3.73328i 0.765461 + 0.236113i
\(251\) −1.01753 + 4.45807i −0.0642257 + 0.281391i −0.996835 0.0794961i \(-0.974669\pi\)
0.932610 + 0.360887i \(0.117526\pi\)
\(252\) 0 0
\(253\) 1.78032 + 7.80007i 0.111927 + 0.490386i
\(254\) −0.552750 + 7.37594i −0.0346826 + 0.462808i
\(255\) 0 0
\(256\) −1.58849 21.1969i −0.0992803 1.32480i
\(257\) −1.78701 4.55324i −0.111471 0.284023i 0.864242 0.503076i \(-0.167798\pi\)
−0.975713 + 0.219053i \(0.929703\pi\)
\(258\) 0 0
\(259\) −12.0157 + 20.1285i −0.746620 + 1.25072i
\(260\) −2.13651 + 1.02889i −0.132500 + 0.0638089i
\(261\) 0 0
\(262\) −35.3236 5.32417i −2.18230 0.328928i
\(263\) 5.20794 + 9.02042i 0.321136 + 0.556223i 0.980723 0.195405i \(-0.0626022\pi\)
−0.659587 + 0.751628i \(0.729269\pi\)
\(264\) 0 0
\(265\) 0.161792 0.202881i 0.00993881 0.0124629i
\(266\) 26.6759 24.0377i 1.63560 1.47384i
\(267\) 0 0
\(268\) 17.1356 2.58277i 1.04672 0.157768i
\(269\) −20.1994 13.7717i −1.23158 0.839677i −0.240203 0.970723i \(-0.577214\pi\)
−0.991376 + 0.131046i \(0.958166\pi\)
\(270\) 0 0
\(271\) 8.54692 1.28824i 0.519189 0.0782551i 0.115780 0.993275i \(-0.463063\pi\)
0.403409 + 0.915020i \(0.367825\pi\)
\(272\) −27.9487 35.0465i −1.69464 2.12501i
\(273\) 0 0
\(274\) 22.4516 28.1534i 1.35635 1.70081i
\(275\) 3.00586 5.20630i 0.181260 0.313952i
\(276\) 0 0
\(277\) 21.9168 + 3.30343i 1.31685 + 0.198484i 0.769624 0.638498i \(-0.220444\pi\)
0.547231 + 0.836982i \(0.315682\pi\)
\(278\) −29.8990 27.7423i −1.79323 1.66387i
\(279\) 0 0
\(280\) 7.80494 5.15630i 0.466434 0.308148i
\(281\) 13.1753 + 6.34490i 0.785974 + 0.378505i 0.783421 0.621492i \(-0.213473\pi\)
0.00255305 + 0.999997i \(0.499187\pi\)
\(282\) 0 0
\(283\) 0.979933 + 13.0763i 0.0582509 + 0.777305i 0.947474 + 0.319832i \(0.103626\pi\)
−0.889223 + 0.457473i \(0.848755\pi\)
\(284\) 50.4348 15.5571i 2.99275 0.923142i
\(285\) 0 0
\(286\) 0.731960 + 3.20693i 0.0432817 + 0.189630i
\(287\) 18.1998 22.1516i 1.07430 1.30757i
\(288\) 0 0
\(289\) 8.27757 + 2.55329i 0.486916 + 0.150194i
\(290\) −1.60881 + 4.09918i −0.0944726 + 0.240712i
\(291\) 0 0
\(292\) −29.1590 + 19.8803i −1.70640 + 1.16341i
\(293\) 21.2625 1.24217 0.621083 0.783745i \(-0.286693\pi\)
0.621083 + 0.783745i \(0.286693\pi\)
\(294\) 0 0
\(295\) 7.54986 0.439570
\(296\) −51.6505 + 35.2147i −3.00213 + 2.04681i
\(297\) 0 0
\(298\) 12.5208 31.9025i 0.725312 1.84806i
\(299\) 6.05286 + 1.86706i 0.350046 + 0.107975i
\(300\) 0 0
\(301\) 8.35583 3.87496i 0.481622 0.223349i
\(302\) 5.81348 + 25.4705i 0.334528 + 1.46566i
\(303\) 0 0
\(304\) 44.2654 13.6541i 2.53879 0.783114i
\(305\) 0.316840 + 4.22794i 0.0181422 + 0.242091i
\(306\) 0 0
\(307\) −13.1563 6.33573i −0.750868 0.361599i 0.0189851 0.999820i \(-0.493956\pi\)
−0.769854 + 0.638221i \(0.779671\pi\)
\(308\) −5.56215 14.8030i −0.316933 0.843478i
\(309\) 0 0
\(310\) −6.22877 5.77945i −0.353770 0.328251i
\(311\) −21.4855 3.23841i −1.21833 0.183634i −0.491762 0.870729i \(-0.663647\pi\)
−0.726567 + 0.687096i \(0.758885\pi\)
\(312\) 0 0
\(313\) 6.78282 11.7482i 0.383387 0.664046i −0.608157 0.793817i \(-0.708091\pi\)
0.991544 + 0.129771i \(0.0414241\pi\)
\(314\) 19.6972 24.6995i 1.11158 1.39387i
\(315\) 0 0
\(316\) 31.2007 + 39.1244i 1.75518 + 2.20092i
\(317\) 8.19586 1.23533i 0.460326 0.0693829i 0.0852142 0.996363i \(-0.472843\pi\)
0.375111 + 0.926980i \(0.377604\pi\)
\(318\) 0 0
\(319\) 3.54524 + 2.41710i 0.198495 + 0.135332i
\(320\) 2.57447 0.388039i 0.143917 0.0216921i
\(321\) 0 0
\(322\) −42.7679 7.08519i −2.38336 0.394842i
\(323\) −16.5347 + 20.7338i −0.920013 + 1.15366i
\(324\) 0 0
\(325\) −2.37980 4.12193i −0.132007 0.228643i
\(326\) −0.0498747 0.00751741i −0.00276231 0.000416351i
\(327\) 0 0
\(328\) 68.8807 33.1712i 3.80330 1.83157i
\(329\) −3.15951 1.02524i −0.174189 0.0565235i
\(330\) 0 0
\(331\) −11.7052 29.8243i −0.643374 1.63929i −0.762944 0.646464i \(-0.776247\pi\)
0.119571 0.992826i \(-0.461848\pi\)
\(332\) −5.36488 71.5893i −0.294436 3.92898i
\(333\) 0 0
\(334\) −3.82318 + 51.0168i −0.209195 + 2.79151i
\(335\) −0.409281 1.79318i −0.0223614 0.0979718i
\(336\) 0 0
\(337\) 1.73597 7.60577i 0.0945641 0.414313i −0.905383 0.424596i \(-0.860416\pi\)
0.999947 + 0.0102833i \(0.00327333\pi\)
\(338\) −29.7174 9.16661i −1.61641 0.498598i
\(339\) 0 0
\(340\) −8.78616 + 8.15236i −0.476496 + 0.442124i
\(341\) −6.84079 + 4.66397i −0.370449 + 0.252568i
\(342\) 0 0
\(343\) 17.0215 7.29857i 0.919074 0.394086i
\(344\) 24.5618 1.32428
\(345\) 0 0
\(346\) −40.6214 + 37.6912i −2.18382 + 2.02629i
\(347\) −1.68856 + 4.30238i −0.0906467 + 0.230964i −0.969006 0.247037i \(-0.920543\pi\)
0.878359 + 0.478001i \(0.158638\pi\)
\(348\) 0 0
\(349\) 2.51083 11.0006i 0.134401 0.588851i −0.862207 0.506557i \(-0.830918\pi\)
0.996608 0.0822944i \(-0.0262248\pi\)
\(350\) 19.9361 + 25.7606i 1.06563 + 1.37696i
\(351\) 0 0
\(352\) 0.835364 11.1472i 0.0445251 0.594146i
\(353\) 8.26087 2.54814i 0.439682 0.135624i −0.0670078 0.997752i \(-0.521345\pi\)
0.506690 + 0.862129i \(0.330869\pi\)
\(354\) 0 0
\(355\) −2.04663 5.21473i −0.108624 0.276769i
\(356\) −30.2436 14.5646i −1.60291 0.771920i
\(357\) 0 0
\(358\) 15.1717 7.30630i 0.801849 0.386150i
\(359\) −15.3835 14.2738i −0.811909 0.753341i 0.160397 0.987053i \(-0.448722\pi\)
−0.972306 + 0.233711i \(0.924913\pi\)
\(360\) 0 0
\(361\) −4.20264 7.27919i −0.221192 0.383115i
\(362\) 16.2087 28.0743i 0.851911 1.47555i
\(363\) 0 0
\(364\) −12.3515 2.04622i −0.647393 0.107251i
\(365\) 2.33545 + 2.92857i 0.122243 + 0.153288i
\(366\) 0 0
\(367\) 30.2272 + 20.6086i 1.57785 + 1.07576i 0.956302 + 0.292380i \(0.0944472\pi\)
0.621545 + 0.783378i \(0.286505\pi\)
\(368\) −46.2069 31.5033i −2.40870 1.64222i
\(369\) 0 0
\(370\) 7.17715 + 8.99986i 0.373122 + 0.467881i
\(371\) 1.31491 0.384701i 0.0682670 0.0199727i
\(372\) 0 0
\(373\) 7.88220 13.6524i 0.408125 0.706893i −0.586555 0.809909i \(-0.699516\pi\)
0.994680 + 0.103017i \(0.0328495\pi\)
\(374\) 8.31297 + 14.3985i 0.429854 + 0.744528i
\(375\) 0 0
\(376\) −6.49330 6.02491i −0.334867 0.310711i
\(377\) 3.06070 1.47395i 0.157634 0.0759125i
\(378\) 0 0
\(379\) 11.4063 + 5.49298i 0.585901 + 0.282155i 0.703258 0.710935i \(-0.251728\pi\)
−0.117357 + 0.993090i \(0.537442\pi\)
\(380\) −4.52513 11.5298i −0.232134 0.591468i
\(381\) 0 0
\(382\) −7.53710 + 2.32489i −0.385632 + 0.118952i
\(383\) −0.723077 + 9.64879i −0.0369475 + 0.493030i 0.947780 + 0.318926i \(0.103322\pi\)
−0.984727 + 0.174104i \(0.944297\pi\)
\(384\) 0 0
\(385\) −1.52266 + 0.706124i −0.0776021 + 0.0359874i
\(386\) −10.0269 + 43.9307i −0.510356 + 2.23602i
\(387\) 0 0
\(388\) −13.4964 + 34.3882i −0.685174 + 1.74580i
\(389\) 18.9064 17.5425i 0.958591 0.889442i −0.0353484 0.999375i \(-0.511254\pi\)
0.993939 + 0.109933i \(0.0350636\pi\)
\(390\) 0 0
\(391\) 32.0160 1.61912
\(392\) 49.3668 + 1.43949i 2.49340 + 0.0727052i
\(393\) 0 0
\(394\) −11.3991 + 7.77176i −0.574277 + 0.391536i
\(395\) 3.89354 3.61268i 0.195905 0.181773i
\(396\) 0 0
\(397\) −18.0552 5.56929i −0.906164 0.279515i −0.193566 0.981087i \(-0.562005\pi\)
−0.712598 + 0.701573i \(0.752482\pi\)
\(398\) 4.23501 18.5548i 0.212282 0.930067i
\(399\) 0 0
\(400\) 9.35071 + 40.9681i 0.467536 + 2.04841i
\(401\) −1.57452 + 21.0105i −0.0786276 + 1.04921i 0.808745 + 0.588159i \(0.200147\pi\)
−0.887373 + 0.461053i \(0.847472\pi\)
\(402\) 0 0
\(403\) 0.489854 + 6.53665i 0.0244014 + 0.325614i
\(404\) 8.45137 + 21.5338i 0.420472 + 1.07134i
\(405\) 0 0
\(406\) −19.3983 + 12.8154i −0.962724 + 0.636020i
\(407\) 10.1057 4.86664i 0.500920 0.241230i
\(408\) 0 0
\(409\) 25.7879 + 3.88690i 1.27513 + 0.192195i 0.751490 0.659744i \(-0.229335\pi\)
0.523641 + 0.851939i \(0.324574\pi\)
\(410\) −7.03901 12.1919i −0.347632 0.602116i
\(411\) 0 0
\(412\) −26.7884 + 33.5916i −1.31977 + 1.65494i
\(413\) 32.6035 + 22.9318i 1.60431 + 1.12840i
\(414\) 0 0
\(415\) −7.53462 + 1.13566i −0.369860 + 0.0557474i
\(416\) −7.31235 4.98548i −0.358517 0.244433i
\(417\) 0 0
\(418\) −16.9894 + 2.56073i −0.830976 + 0.125250i
\(419\) 16.2545 + 20.3825i 0.794085 + 0.995751i 0.999853 + 0.0171499i \(0.00545926\pi\)
−0.205768 + 0.978601i \(0.565969\pi\)
\(420\) 0 0
\(421\) −15.3925 + 19.3016i −0.750186 + 0.940704i −0.999617 0.0276890i \(-0.991185\pi\)
0.249430 + 0.968393i \(0.419757\pi\)
\(422\) −21.7611 + 37.6914i −1.05931 + 1.83479i
\(423\) 0 0
\(424\) 3.61265 + 0.544519i 0.175446 + 0.0264442i
\(425\) −17.6349 16.3628i −0.855421 0.793714i
\(426\) 0 0
\(427\) −11.4736 + 19.2204i −0.555248 + 0.930141i
\(428\) −17.4008 8.37978i −0.841099 0.405052i
\(429\) 0 0
\(430\) −0.337994 4.51022i −0.0162995 0.217502i
\(431\) 28.2452 8.71248i 1.36052 0.419665i 0.473256 0.880925i \(-0.343078\pi\)
0.887265 + 0.461259i \(0.152602\pi\)
\(432\) 0 0
\(433\) −4.72367 20.6957i −0.227005 0.994574i −0.952067 0.305890i \(-0.901046\pi\)
0.725062 0.688684i \(-0.241811\pi\)
\(434\) −9.34405 43.8773i −0.448529 2.10618i
\(435\) 0 0
\(436\) 14.7271 + 4.54270i 0.705299 + 0.217556i
\(437\) −12.0874 + 30.7983i −0.578220 + 1.47328i
\(438\) 0 0
\(439\) −25.5837 + 17.4427i −1.22104 + 0.832493i −0.990085 0.140471i \(-0.955138\pi\)
−0.230958 + 0.972964i \(0.574186\pi\)
\(440\) −4.47584 −0.213377
\(441\) 0 0
\(442\) 13.1631 0.626104
\(443\) 28.4375 19.3884i 1.35111 0.921169i 0.351221 0.936293i \(-0.385767\pi\)
0.999886 + 0.0151235i \(0.00481413\pi\)
\(444\) 0 0
\(445\) −1.30166 + 3.31657i −0.0617046 + 0.157221i
\(446\) 40.9173 + 12.6213i 1.93749 + 0.597637i
\(447\) 0 0
\(448\) 12.2963 + 6.14395i 0.580945 + 0.290274i
\(449\) 7.03787 + 30.8349i 0.332138 + 1.45519i 0.814983 + 0.579485i \(0.196746\pi\)
−0.482845 + 0.875706i \(0.660397\pi\)
\(450\) 0 0
\(451\) −13.1081 + 4.04330i −0.617235 + 0.190392i
\(452\) 6.96833 + 92.9859i 0.327763 + 4.37369i
\(453\) 0 0
\(454\) 4.08738 + 1.96838i 0.191830 + 0.0923807i
\(455\) −0.118607 + 1.32354i −0.00556040 + 0.0620484i
\(456\) 0 0
\(457\) −10.5953 9.83104i −0.495629 0.459877i 0.392313 0.919832i \(-0.371675\pi\)
−0.887942 + 0.459955i \(0.847866\pi\)
\(458\) −12.8246 1.93299i −0.599253 0.0903229i
\(459\) 0 0
\(460\) −7.47659 + 12.9498i −0.348598 + 0.603789i
\(461\) −10.8455 + 13.5998i −0.505125 + 0.633406i −0.967377 0.253342i \(-0.918470\pi\)
0.462252 + 0.886749i \(0.347042\pi\)
\(462\) 0 0
\(463\) 11.0945 + 13.9121i 0.515606 + 0.646549i 0.969669 0.244420i \(-0.0785976\pi\)
−0.454064 + 0.890969i \(0.650026\pi\)
\(464\) −29.6577 + 4.47017i −1.37682 + 0.207523i
\(465\) 0 0
\(466\) −26.0137 17.7359i −1.20506 0.821598i
\(467\) −21.4967 + 3.24010i −0.994747 + 0.149934i −0.626189 0.779671i \(-0.715386\pi\)
−0.368558 + 0.929605i \(0.620148\pi\)
\(468\) 0 0
\(469\) 3.67913 8.98686i 0.169886 0.414975i
\(470\) −1.01698 + 1.27526i −0.0469100 + 0.0588233i
\(471\) 0 0
\(472\) 53.1477 + 92.0546i 2.44632 + 4.23716i
\(473\) −4.35782 0.656835i −0.200373 0.0302013i
\(474\) 0 0
\(475\) 22.3984 10.7865i 1.02771 0.494919i
\(476\) −62.7043 + 8.51842i −2.87404 + 0.390441i
\(477\) 0 0
\(478\) 8.87703 + 22.6183i 0.406026 + 1.03454i
\(479\) −1.16990 15.6112i −0.0534539 0.713292i −0.957973 0.286859i \(-0.907389\pi\)
0.904519 0.426433i \(-0.140230\pi\)
\(480\) 0 0
\(481\) 0.663625 8.85545i 0.0302587 0.403774i
\(482\) −3.06001 13.4068i −0.139380 0.610663i
\(483\) 0 0
\(484\) 9.87303 43.2566i 0.448774 1.96621i
\(485\) 3.74677 + 1.15573i 0.170132 + 0.0524788i
\(486\) 0 0
\(487\) 3.63227 3.37025i 0.164594 0.152721i −0.593576 0.804778i \(-0.702284\pi\)
0.758170 + 0.652057i \(0.226094\pi\)
\(488\) −49.3204 + 33.6261i −2.23263 + 1.52218i
\(489\) 0 0
\(490\) −0.415005 9.08490i −0.0187480 0.410414i
\(491\) 19.1196 0.862855 0.431427 0.902148i \(-0.358010\pi\)
0.431427 + 0.902148i \(0.358010\pi\)
\(492\) 0 0
\(493\) 12.5868 11.6788i 0.566881 0.525989i
\(494\) −4.96963 + 12.6624i −0.223594 + 0.569709i
\(495\) 0 0
\(496\) 12.8779 56.4220i 0.578237 2.53342i
\(497\) 7.00093 28.7359i 0.314035 1.28898i
\(498\) 0 0
\(499\) 0.685361 9.14551i 0.0306810 0.409409i −0.960626 0.277843i \(-0.910380\pi\)
0.991307 0.131566i \(-0.0420005\pi\)
\(500\) 22.0411 6.79879i 0.985709 0.304051i
\(501\) 0 0
\(502\) 4.33115 + 11.0356i 0.193308 + 0.492542i
\(503\) 8.22428 + 3.96061i 0.366703 + 0.176595i 0.608156 0.793818i \(-0.291910\pi\)
−0.241453 + 0.970413i \(0.577624\pi\)
\(504\) 0 0
\(505\) 2.21215 1.06531i 0.0984392 0.0474058i
\(506\) 15.2051 + 14.1083i 0.675951 + 0.627191i
\(507\) 0 0
\(508\) 6.73510 + 11.6655i 0.298822 + 0.517575i
\(509\) 1.25896 2.18057i 0.0558022 0.0966523i −0.836775 0.547547i \(-0.815562\pi\)
0.892577 + 0.450895i \(0.148895\pi\)
\(510\) 0 0
\(511\) 1.19030 + 19.7405i 0.0526557 + 0.873268i
\(512\) −29.1334 36.5321i −1.28753 1.61451i
\(513\) 0 0
\(514\) −10.4777 7.14356i −0.462150 0.315089i
\(515\) 3.76789 + 2.56890i 0.166033 + 0.113199i
\(516\) 0 0
\(517\) 0.990940 + 1.24260i 0.0435815 + 0.0546495i
\(518\) 3.65794 + 60.6651i 0.160721 + 2.66547i
\(519\) 0 0
\(520\) −1.77180 + 3.06885i −0.0776987 + 0.134578i
\(521\) 2.87635 + 4.98199i 0.126015 + 0.218265i 0.922129 0.386882i \(-0.126448\pi\)
−0.796114 + 0.605147i \(0.793115\pi\)
\(522\) 0 0
\(523\) 9.66356 + 8.96647i 0.422558 + 0.392076i 0.862588 0.505906i \(-0.168842\pi\)
−0.440031 + 0.897983i \(0.645032\pi\)
\(524\) −58.6128 + 28.2265i −2.56051 + 1.23308i
\(525\) 0 0
\(526\) 24.3296 + 11.7165i 1.06082 + 0.510865i
\(527\) 12.1043 + 30.8413i 0.527272 + 1.34347i
\(528\) 0 0
\(529\) 16.1899 4.99392i 0.703908 0.217127i
\(530\) 0.0502751 0.670875i 0.00218381 0.0291409i
\(531\) 0 0
\(532\) 15.4791 63.5354i 0.671106 2.75461i
\(533\) −2.41667 + 10.5881i −0.104677 + 0.458622i
\(534\) 0 0
\(535\) −0.748915 + 1.90820i −0.0323784 + 0.0824989i
\(536\) 18.9829 17.6135i 0.819935 0.760788i
\(537\) 0 0
\(538\) −63.3815 −2.73257
\(539\) −8.72028 1.57557i −0.375609 0.0678647i
\(540\) 0 0
\(541\) −10.0372 + 6.84325i −0.431533 + 0.294214i −0.759539 0.650461i \(-0.774576\pi\)
0.328006 + 0.944675i \(0.393623\pi\)
\(542\) 16.4268 15.2418i 0.705590 0.654692i
\(543\) 0 0
\(544\) −42.7450 13.1851i −1.83268 0.565306i
\(545\) 0.363998 1.59478i 0.0155919 0.0683128i
\(546\) 0 0
\(547\) −2.19420 9.61344i −0.0938174 0.411041i 0.906111 0.423041i \(-0.139037\pi\)
−0.999928 + 0.0120000i \(0.996180\pi\)
\(548\) 4.90065 65.3946i 0.209345 2.79352i
\(549\) 0 0
\(550\) −1.16473 15.5422i −0.0496641 0.662721i
\(551\) 6.48257 + 16.5173i 0.276167 + 0.703662i
\(552\) 0 0
\(553\) 27.7871 3.77490i 1.18163 0.160525i
\(554\) 51.7720 24.9321i 2.19958 1.05926i
\(555\) 0 0
\(556\) −73.4489 11.0706i −3.11493 0.469500i
\(557\) 4.75526 + 8.23634i 0.201487 + 0.348985i 0.949008 0.315253i \(-0.102089\pi\)
−0.747521 + 0.664238i \(0.768756\pi\)
\(558\) 0 0
\(559\) −2.17544 + 2.72792i −0.0920114 + 0.115379i
\(560\) 4.44495 10.8575i 0.187833 0.458814i
\(561\) 0 0
\(562\) 37.4889 5.65055i 1.58138 0.238354i
\(563\) 29.1031 + 19.8422i 1.22655 + 0.836247i 0.990769 0.135559i \(-0.0432832\pi\)
0.235780 + 0.971806i \(0.424236\pi\)
\(564\) 0 0
\(565\) 9.78656 1.47509i 0.411724 0.0620573i
\(566\) 21.1963 + 26.5793i 0.890946 + 1.11721i
\(567\) 0 0
\(568\) 49.1753 61.6638i 2.06335 2.58736i
\(569\) 18.1634 31.4599i 0.761449 1.31887i −0.180655 0.983547i \(-0.557822\pi\)
0.942104 0.335322i \(-0.108845\pi\)
\(570\) 0 0
\(571\) −32.2813 4.86562i −1.35093 0.203620i −0.566615 0.823983i \(-0.691747\pi\)
−0.784315 + 0.620363i \(0.786985\pi\)
\(572\) 4.39129 + 4.07452i 0.183609 + 0.170364i
\(573\) 0 0
\(574\) 6.63414 74.0302i 0.276904 3.08996i
\(575\) −27.0407 13.0221i −1.12768 0.543061i
\(576\) 0 0
\(577\) −2.18140 29.1088i −0.0908131 1.21182i −0.837423 0.546555i \(-0.815939\pi\)
0.746610 0.665262i \(-0.231680\pi\)
\(578\) 21.4601 6.61957i 0.892624 0.275338i
\(579\) 0 0
\(580\) 1.78451 + 7.81843i 0.0740976 + 0.324643i
\(581\) −35.9872 17.9813i −1.49300 0.745990i
\(582\) 0 0
\(583\) −0.626404 0.193220i −0.0259430 0.00800235i
\(584\) −19.2671 + 49.0918i −0.797278 + 2.03143i
\(585\) 0 0
\(586\) 45.5459 31.0526i 1.88148 1.28277i
\(587\) −14.0362 −0.579337 −0.289668 0.957127i \(-0.593545\pi\)
−0.289668 + 0.957127i \(0.593545\pi\)
\(588\) 0 0
\(589\) −34.2381 −1.41076
\(590\) 16.1724 11.0261i 0.665807 0.453939i
\(591\) 0 0
\(592\) −28.6437 + 72.9830i −1.17725 + 2.99958i
\(593\) 31.2977 + 9.65407i 1.28524 + 0.396445i 0.860770 0.508995i \(-0.169983\pi\)
0.424474 + 0.905440i \(0.360459\pi\)
\(594\) 0 0
\(595\) 1.39896 + 6.56919i 0.0573520 + 0.269311i
\(596\) −13.8882 60.8482i −0.568883 2.49244i
\(597\) 0 0
\(598\) 15.6924 4.84048i 0.641712 0.197942i
\(599\) −0.0183362 0.244680i −0.000749197 0.00999734i 0.996817 0.0797278i \(-0.0254051\pi\)
−0.997566 + 0.0697305i \(0.977786\pi\)
\(600\) 0 0
\(601\) 13.6526 + 6.57475i 0.556902 + 0.268190i 0.691093 0.722766i \(-0.257129\pi\)
−0.134191 + 0.990955i \(0.542844\pi\)
\(602\) 12.2397 20.5037i 0.498852 0.835668i
\(603\) 0 0
\(604\) 34.8771 + 32.3612i 1.41913 + 1.31676i
\(605\) −4.65668 0.701882i −0.189321 0.0285355i
\(606\) 0 0
\(607\) −16.9706 + 29.3939i −0.688815 + 1.19306i 0.283407 + 0.959000i \(0.408535\pi\)
−0.972222 + 0.234063i \(0.924798\pi\)
\(608\) 28.8217 36.1412i 1.16887 1.46572i
\(609\) 0 0
\(610\) 6.85337 + 8.59385i 0.277485 + 0.347955i
\(611\) 1.24426 0.187542i 0.0503373 0.00758713i
\(612\) 0 0
\(613\) 13.6223 + 9.28750i 0.550198 + 0.375119i 0.806278 0.591537i \(-0.201479\pi\)
−0.256080 + 0.966656i \(0.582431\pi\)
\(614\) −37.4347 + 5.64238i −1.51074 + 0.227708i
\(615\) 0 0
\(616\) −19.3286 13.5948i −0.778771 0.547752i
\(617\) 5.49056 6.88494i 0.221042 0.277177i −0.658929 0.752205i \(-0.728990\pi\)
0.879971 + 0.475027i \(0.157562\pi\)
\(618\) 0 0
\(619\) −5.12486 8.87651i −0.205985 0.356777i 0.744461 0.667666i \(-0.232707\pi\)
−0.950446 + 0.310889i \(0.899373\pi\)
\(620\) −15.3014 2.30631i −0.614517 0.0926236i
\(621\) 0 0
\(622\) −50.7531 + 24.4414i −2.03501 + 0.980010i
\(623\) −15.6948 + 10.3687i −0.628801 + 0.415415i
\(624\) 0 0
\(625\) 7.78037 + 19.8241i 0.311215 + 0.792962i
\(626\) −2.62824 35.0714i −0.105046 1.40174i
\(627\) 0 0
\(628\) 4.29943 57.3719i 0.171566 2.28939i
\(629\) −9.98775 43.7592i −0.398238 1.74479i
\(630\) 0 0
\(631\) −2.73961 + 12.0030i −0.109062 + 0.477832i 0.890669 + 0.454652i \(0.150236\pi\)
−0.999731 + 0.0231802i \(0.992621\pi\)
\(632\) 71.4578 + 22.0418i 2.84244 + 0.876776i
\(633\) 0 0
\(634\) 15.7521 14.6158i 0.625594 0.580466i
\(635\) 1.18128 0.805386i 0.0468779 0.0319608i
\(636\) 0 0
\(637\) −4.53229 + 5.35534i −0.179576 + 0.212186i
\(638\) 11.1242 0.440412
\(639\) 0 0
\(640\) −1.53956 + 1.42851i −0.0608566 + 0.0564667i
\(641\) −9.98068 + 25.4304i −0.394213 + 1.00444i 0.586667 + 0.809828i \(0.300440\pi\)
−0.980881 + 0.194611i \(0.937656\pi\)
\(642\) 0 0
\(643\) −1.28431 + 5.62692i −0.0506481 + 0.221904i −0.993918 0.110123i \(-0.964875\pi\)
0.943270 + 0.332027i \(0.107733\pi\)
\(644\) −71.6208 + 33.2136i −2.82225 + 1.30880i
\(645\) 0 0
\(646\) −5.13796 + 68.5614i −0.202151 + 2.69751i
\(647\) −10.0696 + 3.10606i −0.395877 + 0.122112i −0.486301 0.873791i \(-0.661654\pi\)
0.0904236 + 0.995903i \(0.471178\pi\)
\(648\) 0 0
\(649\) −6.96787 17.7538i −0.273513 0.696899i
\(650\) −11.1176 5.35393i −0.436066 0.209998i
\(651\) 0 0
\(652\) −0.0827578 + 0.0398541i −0.00324105 + 0.00156081i
\(653\) −10.3211 9.57660i −0.403897 0.374761i 0.451904 0.892066i \(-0.350745\pi\)
−0.855801 + 0.517305i \(0.826935\pi\)
\(654\) 0 0
\(655\) 3.45245 + 5.97983i 0.134899 + 0.233651i
\(656\) 47.9424 83.0387i 1.87184 3.24212i
\(657\) 0 0
\(658\) −8.26522 + 2.41813i −0.322212 + 0.0942687i
\(659\) −24.7173 30.9945i −0.962850 1.20738i −0.978236 0.207494i \(-0.933469\pi\)
0.0153867 0.999882i \(-0.495102\pi\)
\(660\) 0 0
\(661\) −32.0344 21.8407i −1.24599 0.849503i −0.252975 0.967473i \(-0.581409\pi\)
−0.993017 + 0.117970i \(0.962361\pi\)
\(662\) −68.6300 46.7912i −2.66738 1.81859i
\(663\) 0 0
\(664\) −66.8875 83.8742i −2.59574 3.25495i
\(665\) −6.84750 1.13440i −0.265535 0.0439901i
\(666\) 0 0
\(667\) 10.7108 18.5516i 0.414722 0.718320i
\(668\) 46.5843 + 80.6864i 1.80240 + 3.12185i
\(669\) 0 0
\(670\) −3.49555 3.24340i −0.135045 0.125303i
\(671\) 9.64978 4.64709i 0.372526 0.179399i
\(672\) 0 0
\(673\) −24.3509 11.7268i −0.938660 0.452035i −0.0989637 0.995091i \(-0.531553\pi\)
−0.839696 + 0.543056i \(0.817267\pi\)
\(674\) −7.38922 18.8274i −0.284622 0.725206i
\(675\) 0 0
\(676\) −54.1192 + 16.6936i −2.08151 + 0.642061i
\(677\) 1.79261 23.9208i 0.0688958 0.919350i −0.850489 0.525992i \(-0.823694\pi\)
0.919385 0.393358i \(-0.128687\pi\)
\(678\) 0 0
\(679\) 12.6698 + 16.3713i 0.486221 + 0.628273i
\(680\) −3.98553 + 17.4617i −0.152838 + 0.669627i
\(681\) 0 0
\(682\) −7.84203 + 19.9812i −0.300287 + 0.765119i
\(683\) −0.597376 + 0.554284i −0.0228580 + 0.0212091i −0.691519 0.722358i \(-0.743058\pi\)
0.668661 + 0.743567i \(0.266868\pi\)
\(684\) 0 0
\(685\) −6.96038 −0.265942
\(686\) 25.8022 40.4930i 0.985132 1.54603i
\(687\) 0 0
\(688\) 25.4523 17.3531i 0.970362 0.661581i
\(689\) −0.380449 + 0.353005i −0.0144939 + 0.0134484i
\(690\) 0 0
\(691\) −26.3353 8.12336i −1.00184 0.309027i −0.249910 0.968269i \(-0.580401\pi\)
−0.751931 + 0.659242i \(0.770877\pi\)
\(692\) −22.4560 + 98.3861i −0.853648 + 3.74008i
\(693\) 0 0
\(694\) 2.66636 + 11.6821i 0.101214 + 0.443446i
\(695\) −0.589160 + 7.86180i −0.0223481 + 0.298215i
\(696\) 0 0
\(697\) 4.10215 + 54.7393i 0.155380 + 2.07340i
\(698\) −10.6874 27.2312i −0.404526 1.03071i
\(699\) 0 0
\(700\) 56.4249 + 18.3096i 2.13266 + 0.692036i
\(701\) 12.9825 6.25205i 0.490343 0.236137i −0.172339 0.985038i \(-0.555132\pi\)
0.662682 + 0.748901i \(0.269418\pi\)
\(702\) 0 0
\(703\) 45.8656 + 6.91313i 1.72985 + 0.260734i
\(704\) −3.28851 5.69586i −0.123940 0.214671i
\(705\) 0 0
\(706\) 13.9740 17.5229i 0.525919 0.659481i
\(707\) 12.7888 + 2.11866i 0.480971 + 0.0796806i
\(708\) 0 0
\(709\) 10.1265 1.52633i 0.380310 0.0573225i 0.0438945 0.999036i \(-0.486023\pi\)
0.336415 + 0.941714i \(0.390785\pi\)
\(710\) −11.9999 8.18137i −0.450347 0.307041i
\(711\) 0 0
\(712\) −49.6017 + 7.47626i −1.85890 + 0.280185i
\(713\) 25.7715 + 32.3165i 0.965151 + 1.21026i
\(714\) 0 0
\(715\) 0.396425 0.497102i 0.0148255 0.0185905i
\(716\) 15.3333 26.5580i 0.573031 0.992519i
\(717\) 0 0
\(718\) −53.7987 8.10884i −2.00775 0.302619i
\(719\) −18.6476 17.3024i −0.695437 0.645271i 0.251065 0.967970i \(-0.419219\pi\)
−0.946502 + 0.322699i \(0.895410\pi\)
\(720\) 0 0
\(721\) 8.46860 + 22.5382i 0.315387 + 0.839365i
\(722\) −19.6332 9.45487i −0.730673 0.351874i
\(723\) 0 0
\(724\) −4.41179 58.8712i −0.163963 2.18793i
\(725\) −15.3811 + 4.74443i −0.571238 + 0.176204i
\(726\) 0 0
\(727\) 1.50454 + 6.59180i 0.0558001 + 0.244476i 0.995134 0.0985268i \(-0.0314130\pi\)
−0.939334 + 0.343003i \(0.888556\pi\)
\(728\) −16.9727 + 7.87096i −0.629050 + 0.291717i
\(729\) 0 0
\(730\) 9.27973 + 2.86242i 0.343458 + 0.105943i
\(731\) −6.44297 + 16.4164i −0.238302 + 0.607184i
\(732\) 0 0
\(733\) 33.0844 22.5566i 1.22200 0.833146i 0.231796 0.972764i \(-0.425540\pi\)
0.990205 + 0.139618i \(0.0445875\pi\)
\(734\) 94.8467 3.50086
\(735\) 0 0
\(736\) −55.8073 −2.05708
\(737\) −3.83901 + 2.61739i −0.141412 + 0.0964129i
\(738\) 0 0
\(739\) −5.03054 + 12.8176i −0.185051 + 0.471503i −0.993052 0.117679i \(-0.962455\pi\)
0.808000 + 0.589182i \(0.200550\pi\)
\(740\) 20.0321 + 6.17909i 0.736396 + 0.227148i
\(741\) 0 0
\(742\) 2.25482 2.74442i 0.0827769 0.100751i
\(743\) −2.63763 11.5562i −0.0967653 0.423957i 0.903221 0.429176i \(-0.141196\pi\)
−0.999986 + 0.00521900i \(0.998339\pi\)
\(744\) 0 0
\(745\) −6.33014 + 1.95259i −0.231919 + 0.0715374i
\(746\) −3.05424 40.7559i −0.111824 1.49218i
\(747\) 0 0
\(748\) 27.2795 + 13.1371i 0.997438 + 0.480341i
\(749\) −9.03009 + 5.96570i −0.329952 + 0.217982i
\(750\) 0 0
\(751\) −13.0231 12.0836i −0.475218 0.440938i 0.405841 0.913944i \(-0.366979\pi\)
−0.881060 + 0.473005i \(0.843169\pi\)
\(752\) −10.9854 1.65578i −0.400596 0.0603801i
\(753\) 0 0
\(754\) 4.40363 7.62730i 0.160371 0.277770i
\(755\) 3.14855 3.94815i 0.114587 0.143688i
\(756\) 0 0
\(757\) −23.9187 29.9931i −0.869341 1.09012i −0.995180 0.0980679i \(-0.968734\pi\)
0.125839 0.992051i \(-0.459838\pi\)
\(758\) 32.4553 4.89185i 1.17883 0.177680i
\(759\) 0 0
\(760\) −15.2929 10.4265i −0.554731 0.378209i
\(761\) 20.1809 3.04178i 0.731556 0.110264i 0.227308 0.973823i \(-0.427008\pi\)
0.504248 + 0.863559i \(0.331770\pi\)
\(762\) 0 0
\(763\) 6.41585 5.78133i 0.232270 0.209298i
\(764\) −8.95592 + 11.2304i −0.324014 + 0.406301i
\(765\) 0 0
\(766\) 12.5426 + 21.7245i 0.453184 + 0.784937i
\(767\) −14.9312 2.25052i −0.539134 0.0812614i
\(768\) 0 0
\(769\) −35.6497 + 17.1680i −1.28556 + 0.619094i −0.946813 0.321784i \(-0.895718\pi\)
−0.338748 + 0.940877i \(0.610003\pi\)
\(770\) −2.23041 + 3.73634i −0.0803783 + 0.134648i
\(771\) 0 0
\(772\) 29.9802 + 76.3884i 1.07901 + 2.74928i
\(773\) −1.32310 17.6555i −0.0475886 0.635026i −0.969099 0.246672i \(-0.920663\pi\)
0.921510 0.388354i \(-0.126956\pi\)
\(774\) 0 0
\(775\) 2.32102 30.9719i 0.0833735 1.11254i
\(776\) 12.2840 + 53.8198i 0.440970 + 1.93202i
\(777\) 0 0
\(778\) 14.8790 65.1892i 0.533438 2.33714i
\(779\) −54.2060 16.7204i −1.94213 0.599069i
\(780\) 0 0
\(781\) −10.3738 + 9.62550i −0.371205 + 0.344428i
\(782\) 68.5807 46.7576i 2.45244 1.67205i
\(783\) 0 0
\(784\) 52.1737 33.3863i 1.86335 1.19237i
\(785\) −6.10647 −0.217949
\(786\) 0 0
\(787\) 9.68271 8.98424i 0.345151 0.320254i −0.488480 0.872575i \(-0.662448\pi\)
0.833631 + 0.552322i \(0.186258\pi\)
\(788\) −9.17917 + 23.3881i −0.326994 + 0.833168i
\(789\) 0 0
\(790\) 3.06415 13.4249i 0.109018 0.477638i
\(791\) 46.7429 + 23.3555i 1.66199 + 0.830426i
\(792\) 0 0
\(793\) 0.633686 8.45595i 0.0225029 0.300280i
\(794\) −46.8093 + 14.4387i −1.66120 + 0.512412i
\(795\) 0 0
\(796\) −12.6626 32.2637i −0.448813 1.14356i
\(797\) −31.3045 15.0754i −1.10886 0.533999i −0.212427 0.977177i \(-0.568137\pi\)
−0.896434 + 0.443178i \(0.853851\pi\)
\(798\) 0 0
\(799\) 5.73018 2.75951i 0.202719 0.0976245i
\(800\) 30.7396 + 28.5222i 1.08681 + 1.00841i
\(801\) 0 0
\(802\) 27.3119 + 47.3055i 0.964415 + 1.67042i
\(803\) 4.73124 8.19475i 0.166962 0.289186i
\(804\) 0 0
\(805\) 4.08348 + 7.31706i 0.143924 + 0.257892i
\(806\) 10.5957 + 13.2866i 0.373218 + 0.468001i
\(807\) 0 0
\(808\) 28.5618 + 19.4731i 1.00480 + 0.685061i
\(809\) −37.9991 25.9074i −1.33598 0.910855i −0.336454 0.941700i \(-0.609228\pi\)
−0.999524 + 0.0308452i \(0.990180\pi\)
\(810\) 0 0
\(811\) −29.4008 36.8675i −1.03240 1.29459i −0.954686 0.297616i \(-0.903808\pi\)
−0.0777170 0.996975i \(-0.524763\pi\)
\(812\) −16.0413 + 39.1836i −0.562941 + 1.37507i
\(813\) 0 0
\(814\) 14.5397 25.1835i 0.509616 0.882682i
\(815\) 0.00487466 + 0.00844316i 0.000170752 + 0.000295751i
\(816\) 0 0
\(817\) −13.3595 12.3958i −0.467391 0.433675i
\(818\) 60.9163 29.3358i 2.12989 1.02570i
\(819\) 0 0
\(820\) −23.0989 11.1239i −0.806650 0.388462i
\(821\) 14.6704 + 37.3797i 0.512002 + 1.30456i 0.920122 + 0.391631i \(0.128089\pi\)
−0.408120 + 0.912928i \(0.633816\pi\)
\(822\) 0 0
\(823\) 6.29182 1.94077i 0.219319 0.0676510i −0.183148 0.983085i \(-0.558629\pi\)
0.402467 + 0.915434i \(0.368153\pi\)
\(824\) −4.79804 + 64.0254i −0.167148 + 2.23043i
\(825\) 0 0
\(826\) 103.330 + 1.50618i 3.59531 + 0.0524068i
\(827\) −0.364452 + 1.59677i −0.0126732 + 0.0555251i −0.980869 0.194668i \(-0.937637\pi\)
0.968196 + 0.250193i \(0.0804941\pi\)
\(828\) 0 0
\(829\) −4.67915 + 11.9223i −0.162514 + 0.414078i −0.988814 0.149151i \(-0.952346\pi\)
0.826301 + 0.563229i \(0.190441\pi\)
\(830\) −14.4812 + 13.4366i −0.502649 + 0.466390i
\(831\) 0 0
\(832\) −5.20715 −0.180525
\(833\) −13.9118 + 32.6178i −0.482017 + 1.13014i
\(834\) 0 0
\(835\) 8.17053 5.57057i 0.282753 0.192778i
\(836\) −22.9367 + 21.2821i −0.793281 + 0.736057i
\(837\) 0 0
\(838\) 64.5859 + 19.9221i 2.23108 + 0.688198i
\(839\) 4.44861 19.4907i 0.153583 0.672892i −0.838243 0.545297i \(-0.816417\pi\)
0.991826 0.127595i \(-0.0407259\pi\)
\(840\) 0 0
\(841\) 3.89667 + 17.0724i 0.134368 + 0.588705i
\(842\) −4.78306 + 63.8255i −0.164835 + 2.19957i
\(843\) 0 0
\(844\) 5.92308 + 79.0379i 0.203881 + 2.72060i
\(845\) 2.19615 + 5.59569i 0.0755497 + 0.192498i
\(846\) 0 0
\(847\) −17.9777 17.1752i −0.617719 0.590146i
\(848\) 4.12834 1.98810i 0.141768 0.0682718i
\(849\) 0 0
\(850\) −61.6724 9.29562i −2.11535 0.318837i
\(851\) −27.9986 48.4950i −0.959779 1.66239i
\(852\) 0 0
\(853\) 5.39466 6.76469i 0.184710 0.231619i −0.680852 0.732421i \(-0.738390\pi\)
0.865562 + 0.500802i \(0.166962\pi\)
\(854\) 3.49292 + 57.9282i 0.119525 + 1.98226i
\(855\) 0 0
\(856\) −28.5386 + 4.30150i −0.975428 + 0.147022i
\(857\) −20.4243 13.9251i −0.697682 0.475671i 0.161809 0.986822i \(-0.448267\pi\)
−0.859491 + 0.511151i \(0.829219\pi\)
\(858\) 0 0
\(859\) −22.5949 + 3.40564i −0.770929 + 0.116199i −0.522716 0.852507i \(-0.675081\pi\)
−0.248213 + 0.968706i \(0.579843\pi\)
\(860\) −5.13551 6.43973i −0.175120 0.219593i
\(861\) 0 0
\(862\) 47.7792 59.9133i 1.62737 2.04065i
\(863\) −20.5066 + 35.5184i −0.698052 + 1.20906i 0.271089 + 0.962554i \(0.412616\pi\)
−0.969141 + 0.246508i \(0.920717\pi\)
\(864\) 0 0
\(865\) 10.5915 + 1.59641i 0.360122 + 0.0542797i
\(866\) −40.3434 37.4332i −1.37093 1.27203i
\(867\) 0 0
\(868\) −59.0727 56.4358i −2.00506 1.91556i
\(869\) −12.0888 5.82165i −0.410084 0.197486i
\(870\) 0 0
\(871\) 0.274904 + 3.66833i 0.00931475 + 0.124297i
\(872\) 22.0073 6.78836i 0.745262 0.229883i
\(873\) 0 0
\(874\) 19.0869 + 83.6253i 0.645625 + 2.82867i
\(875\) 3.05956 12.5582i 0.103432 0.424545i
\(876\) 0 0
\(877\) −9.53523 2.94123i −0.321982 0.0993183i 0.129551 0.991573i \(-0.458646\pi\)
−0.451533 + 0.892255i \(0.649123\pi\)
\(878\) −29.3282 + 74.7271i −0.989779 + 2.52192i
\(879\) 0 0
\(880\) −4.63812 + 3.16222i −0.156351 + 0.106598i
\(881\) −26.0496 −0.877635 −0.438817 0.898576i \(-0.644603\pi\)
−0.438817 + 0.898576i \(0.644603\pi\)
\(882\) 0 0
\(883\) −4.62501 −0.155644 −0.0778220 0.996967i \(-0.524797\pi\)
−0.0778220 + 0.996967i \(0.524797\pi\)
\(884\) 19.8063 13.5037i 0.666158 0.454179i
\(885\) 0 0
\(886\) 32.5997 83.0628i 1.09521 2.79055i
\(887\) 3.10320 + 0.957210i 0.104195 + 0.0321400i 0.346414 0.938082i \(-0.387399\pi\)
−0.242219 + 0.970222i \(0.577875\pi\)
\(888\) 0 0
\(889\) 7.54756 + 0.110017i 0.253137 + 0.00368984i
\(890\) 2.05541 + 9.00536i 0.0688977 + 0.301860i
\(891\) 0 0
\(892\) 74.5157 22.9850i 2.49497 0.769596i
\(893\) 0.491160 + 6.55407i 0.0164360 + 0.219324i
\(894\) 0 0
\(895\) −2.93258 1.41225i −0.0980252 0.0472065i
\(896\) −10.9874 + 1.49265i −0.367064 + 0.0498660i
\(897\) 0 0
\(898\) 60.1084 + 55.7724i 2.00584 + 1.86115i
\(899\) 21.9203 + 3.30395i 0.731083 + 0.110193i
\(900\) 0 0
\(901\) −1.31160 + 2.27176i −0.0436957 + 0.0756832i
\(902\) −22.1735 + 27.8047i −0.738296 + 0.925794i
\(903\) 0 0
\(904\) 86.8787 + 108.942i 2.88954 + 3.62337i
\(905\) −6.19607 + 0.933907i −0.205964 + 0.0310441i
\(906\) 0 0
\(907\) −37.4868 25.5580i −1.24473 0.848641i −0.251848 0.967767i \(-0.581038\pi\)
−0.992879 + 0.119126i \(0.961991\pi\)
\(908\) 8.16955 1.23136i 0.271116 0.0408642i
\(909\) 0 0
\(910\) 1.67889 + 3.00834i 0.0556545 + 0.0997255i
\(911\) 5.80732 7.28215i 0.192405 0.241269i −0.676266 0.736657i \(-0.736403\pi\)
0.868671 + 0.495389i \(0.164974\pi\)
\(912\) 0 0
\(913\) 9.62437 + 16.6699i 0.318520 + 0.551693i
\(914\) −37.0537 5.58495i −1.22563 0.184734i
\(915\) 0 0
\(916\) −21.2800 + 10.2479i −0.703111 + 0.338600i
\(917\) −3.25387 + 36.3099i −0.107452 + 1.19906i
\(918\) 0 0
\(919\) 3.07307 + 7.83004i 0.101371 + 0.258289i 0.972557 0.232663i \(-0.0747440\pi\)
−0.871186 + 0.490953i \(0.836649\pi\)
\(920\) 1.66986 + 22.2827i 0.0550536 + 0.734640i
\(921\) 0 0
\(922\) −3.37012 + 44.9711i −0.110989 + 1.48104i
\(923\) 2.49314 + 10.9231i 0.0820626 + 0.359540i
\(924\) 0 0
\(925\) −9.36288 + 41.0215i −0.307850 + 1.34878i
\(926\) 44.0831 + 13.5978i 1.44866 + 0.446853i
\(927\) 0 0
\(928\) −21.9401 + 20.3575i −0.720220 + 0.668266i
\(929\) 7.45057 5.07971i 0.244445 0.166660i −0.434900 0.900479i \(-0.643216\pi\)
0.679345 + 0.733819i \(0.262264\pi\)
\(930\) 0 0
\(931\) −26.1248 25.6973i −0.856206 0.842196i
\(932\) −57.3374 −1.87815
\(933\) 0 0
\(934\) −41.3155 + 38.3352i −1.35189 + 1.25437i
\(935\) 1.17409 2.99153i 0.0383968 0.0978333i
\(936\) 0 0
\(937\) 0.155536 0.681446i 0.00508113 0.0222619i −0.972324 0.233637i \(-0.924937\pi\)
0.977405 + 0.211375i \(0.0677943\pi\)
\(938\) −5.24383 24.6237i −0.171217 0.803993i
\(939\) 0 0
\(940\) −0.221984 + 2.96217i −0.00724031 + 0.0966152i
\(941\) 14.3602 4.42954i 0.468130 0.144399i −0.0517109 0.998662i \(-0.516467\pi\)
0.519841 + 0.854263i \(0.325991\pi\)
\(942\) 0 0
\(943\) 25.0198 + 63.7494i 0.814756 + 2.07596i
\(944\) 120.112 + 57.8429i 3.90931 + 1.88263i
\(945\) 0 0
\(946\) −10.2941 + 4.95736i −0.334689 + 0.161178i
\(947\) 3.74662 + 3.47635i 0.121749 + 0.112966i 0.738698 0.674037i \(-0.235441\pi\)
−0.616949 + 0.787003i \(0.711632\pi\)
\(948\) 0 0
\(949\) −3.74581 6.48793i −0.121594 0.210607i
\(950\) 32.2261 55.8172i 1.04555 1.81095i
\(951\) 0 0
\(952\) −70.2493 + 63.3017i −2.27679 + 2.05162i
\(953\) 5.01956 + 6.29433i 0.162600 + 0.203893i 0.856456 0.516220i \(-0.172661\pi\)
−0.693857 + 0.720113i \(0.744090\pi\)
\(954\) 0 0
\(955\) 1.25968 + 0.858838i 0.0407624 + 0.0277913i
\(956\) 36.5608 + 24.9267i 1.18246 + 0.806188i
\(957\) 0 0
\(958\) −25.3052 31.7318i −0.817575 1.02521i
\(959\) −30.0579 21.1414i −0.970620 0.682690i
\(960\) 0 0
\(961\) −5.88727 + 10.1970i −0.189912 + 0.328937i
\(962\) −11.5114 19.9383i −0.371141 0.642835i
\(963\) 0 0
\(964\) −18.3581 17.0338i −0.591274 0.548623i
\(965\) 7.84732 3.77907i 0.252614 0.121653i
\(966\) 0 0
\(967\) 0.464698 + 0.223787i 0.0149437 + 0.00719650i 0.441341 0.897340i \(-0.354503\pi\)
−0.426397 + 0.904536i \(0.640217\pi\)
\(968\) −24.2231 61.7193i −0.778558 1.98373i
\(969\) 0 0
\(970\) 9.71375 2.99629i 0.311890 0.0962052i
\(971\) 0.686832 9.16513i 0.0220415 0.294123i −0.975280 0.220975i \(-0.929076\pi\)
0.997321 0.0731485i \(-0.0233047\pi\)
\(972\) 0 0
\(973\) −26.4236 + 32.1611i −0.847101 + 1.03104i
\(974\) 2.85854 12.5241i 0.0915934 0.401297i
\(975\) 0 0
\(976\) −27.3515 + 69.6905i −0.875500 + 2.23074i
\(977\) −2.87247 + 2.66526i −0.0918984 + 0.0852692i −0.724784 0.688976i \(-0.758061\pi\)
0.632886 + 0.774245i \(0.281870\pi\)
\(978\) 0 0
\(979\) 9.00040 0.287654
\(980\) −9.94445 13.2442i −0.317664 0.423070i
\(981\) 0 0
\(982\) 40.9556 27.9231i 1.30695 0.891061i
\(983\) 1.71928 1.59526i 0.0548364 0.0508808i −0.652279 0.757979i \(-0.726187\pi\)
0.707115 + 0.707099i \(0.249996\pi\)
\(984\) 0 0
\(985\) 2.54826 + 0.786034i 0.0811943 + 0.0250451i
\(986\) 9.90561 43.3993i 0.315459 1.38212i
\(987\) 0 0
\(988\) 5.51236 + 24.1512i 0.175371 + 0.768352i
\(989\) −1.64419 + 21.9402i −0.0522823 + 0.697659i
\(990\) 0 0
\(991\) −3.74324 49.9501i −0.118908 1.58672i −0.663604 0.748084i \(-0.730974\pi\)
0.544696 0.838633i \(-0.316645\pi\)
\(992\) −21.0991 53.7596i −0.669897 1.70687i
\(993\) 0 0
\(994\) −26.9706 71.7789i −0.855455 2.27669i
\(995\) −3.31443 + 1.59614i −0.105074 + 0.0506011i
\(996\) 0 0
\(997\) −22.0394 3.32191i −0.697996 0.105206i −0.209547 0.977799i \(-0.567199\pi\)
−0.488449 + 0.872593i \(0.662437\pi\)
\(998\) −11.8884 20.5913i −0.376321 0.651807i
\(999\) 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 441.2.bb.f.37.6 yes 72
3.2 odd 2 inner 441.2.bb.f.37.1 72
49.4 even 21 inner 441.2.bb.f.298.6 yes 72
147.53 odd 42 inner 441.2.bb.f.298.1 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bb.f.37.1 72 3.2 odd 2 inner
441.2.bb.f.37.6 yes 72 1.1 even 1 trivial
441.2.bb.f.298.1 yes 72 147.53 odd 42 inner
441.2.bb.f.298.6 yes 72 49.4 even 21 inner