Properties

Label 441.2.bb.e.46.5
Level $441$
Weight $2$
Character 441.46
Analytic conductor $3.521$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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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: \(60\)
Relative dimension: \(5\) over \(\Q(\zeta_{21})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 46.5
Character \(\chi\) \(=\) 441.46
Dual form 441.2.bb.e.163.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.940102 - 2.39534i) q^{2} +(-3.38776 - 3.14338i) q^{4} +(3.23329 + 2.20442i) q^{5} +(2.49214 - 0.888404i) q^{7} +(-6.07754 + 2.92679i) q^{8} +O(q^{10})\) \(q+(0.940102 - 2.39534i) q^{2} +(-3.38776 - 3.14338i) q^{4} +(3.23329 + 2.20442i) q^{5} +(2.49214 - 0.888404i) q^{7} +(-6.07754 + 2.92679i) q^{8} +(8.31997 - 5.67246i) q^{10} +(-0.137579 + 0.0207367i) q^{11} +(-2.93769 - 3.68375i) q^{13} +(0.214830 - 6.80470i) q^{14} +(0.606427 + 8.09221i) q^{16} +(2.86291 + 0.883090i) q^{17} +(-0.957742 - 1.65886i) q^{19} +(-4.02428 - 17.6315i) q^{20} +(-0.0796670 + 0.349044i) q^{22} +(-2.05876 + 0.635043i) q^{23} +(3.76801 + 9.60072i) q^{25} +(-11.5856 + 3.57367i) q^{26} +(-11.2354 - 4.82404i) q^{28} +(0.872532 + 3.82281i) q^{29} +(-0.0198379 + 0.0343603i) q^{31} +(7.06195 + 2.17832i) q^{32} +(4.80673 - 6.02745i) q^{34} +(10.0162 + 2.62125i) q^{35} +(-6.45641 + 5.99067i) q^{37} +(-4.87390 + 0.734623i) q^{38} +(-26.1024 - 3.93430i) q^{40} +(-9.33613 + 4.49604i) q^{41} +(1.57333 + 0.757677i) q^{43} +(0.531270 + 0.362214i) q^{44} +(-0.414299 + 5.52843i) q^{46} +(0.367220 - 0.935662i) q^{47} +(5.42148 - 4.42805i) q^{49} +26.5393 q^{50} +(-1.62724 + 21.7140i) q^{52} +(-1.76568 - 1.63831i) q^{53} +(-0.490547 - 0.236235i) q^{55} +(-12.5459 + 12.6933i) q^{56} +(9.97720 + 1.50382i) q^{58} +(5.40007 - 3.68170i) q^{59} +(4.97882 - 4.61967i) q^{61} +(0.0636549 + 0.0798207i) q^{62} +(1.73766 - 2.17896i) q^{64} +(-1.37788 - 18.3866i) q^{65} +(4.83417 - 8.37303i) q^{67} +(-6.92296 - 11.9909i) q^{68} +(15.6951 - 21.5280i) q^{70} +(-3.02675 + 13.2611i) q^{71} +(4.98525 + 12.7022i) q^{73} +(8.28002 + 21.0971i) q^{74} +(-1.96982 + 8.63036i) q^{76} +(-0.324444 + 0.173905i) q^{77} +(-0.238309 - 0.412763i) q^{79} +(-15.8779 + 27.5013i) q^{80} +(1.99264 + 26.5900i) q^{82} +(2.89616 - 3.63168i) q^{83} +(7.30992 + 9.16635i) q^{85} +(3.29399 - 3.05638i) q^{86} +(0.775452 - 0.528694i) q^{88} +(-8.74729 - 1.31844i) q^{89} +(-10.5938 - 6.57054i) q^{91} +(8.97077 + 4.32009i) q^{92} +(-1.89601 - 1.75924i) q^{94} +(0.560162 - 7.47484i) q^{95} -4.96224 q^{97} +(-5.50994 - 17.1491i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{11}{21}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.940102 2.39534i 0.664753 1.69376i −0.0540415 0.998539i \(-0.517210\pi\)
0.718794 0.695223i \(-0.244694\pi\)
\(3\) 0 0
\(4\) −3.38776 3.14338i −1.69388 1.57169i
\(5\) 3.23329 + 2.20442i 1.44597 + 0.985848i 0.995669 + 0.0929724i \(0.0296368\pi\)
0.450304 + 0.892875i \(0.351316\pi\)
\(6\) 0 0
\(7\) 2.49214 0.888404i 0.941939 0.335785i
\(8\) −6.07754 + 2.92679i −2.14873 + 1.03478i
\(9\) 0 0
\(10\) 8.31997 5.67246i 2.63101 1.79379i
\(11\) −0.137579 + 0.0207367i −0.0414817 + 0.00625237i −0.169750 0.985487i \(-0.554296\pi\)
0.128269 + 0.991739i \(0.459058\pi\)
\(12\) 0 0
\(13\) −2.93769 3.68375i −0.814769 1.02169i −0.999245 0.0388514i \(-0.987630\pi\)
0.184476 0.982837i \(-0.440941\pi\)
\(14\) 0.214830 6.80470i 0.0574158 1.81863i
\(15\) 0 0
\(16\) 0.606427 + 8.09221i 0.151607 + 2.02305i
\(17\) 2.86291 + 0.883090i 0.694357 + 0.214181i 0.621791 0.783183i \(-0.286405\pi\)
0.0725657 + 0.997364i \(0.476881\pi\)
\(18\) 0 0
\(19\) −0.957742 1.65886i −0.219721 0.380568i 0.735002 0.678065i \(-0.237181\pi\)
−0.954723 + 0.297497i \(0.903848\pi\)
\(20\) −4.02428 17.6315i −0.899857 3.94253i
\(21\) 0 0
\(22\) −0.0796670 + 0.349044i −0.0169851 + 0.0744164i
\(23\) −2.05876 + 0.635043i −0.429281 + 0.132416i −0.501864 0.864947i \(-0.667352\pi\)
0.0725827 + 0.997362i \(0.476876\pi\)
\(24\) 0 0
\(25\) 3.76801 + 9.60072i 0.753601 + 1.92014i
\(26\) −11.5856 + 3.57367i −2.27212 + 0.700855i
\(27\) 0 0
\(28\) −11.2354 4.82404i −2.12328 0.911657i
\(29\) 0.872532 + 3.82281i 0.162025 + 0.709878i 0.989034 + 0.147689i \(0.0471835\pi\)
−0.827009 + 0.562189i \(0.809959\pi\)
\(30\) 0 0
\(31\) −0.0198379 + 0.0343603i −0.00356299 + 0.00617129i −0.867801 0.496911i \(-0.834467\pi\)
0.864238 + 0.503082i \(0.167801\pi\)
\(32\) 7.06195 + 2.17832i 1.24839 + 0.385077i
\(33\) 0 0
\(34\) 4.80673 6.02745i 0.824347 1.03370i
\(35\) 10.0162 + 2.62125i 1.69305 + 0.443072i
\(36\) 0 0
\(37\) −6.45641 + 5.99067i −1.06143 + 0.984860i −0.999912 0.0132457i \(-0.995784\pi\)
−0.0615149 + 0.998106i \(0.519593\pi\)
\(38\) −4.87390 + 0.734623i −0.790651 + 0.119172i
\(39\) 0 0
\(40\) −26.1024 3.93430i −4.12714 0.622067i
\(41\) −9.33613 + 4.49604i −1.45806 + 0.702164i −0.983973 0.178315i \(-0.942935\pi\)
−0.474085 + 0.880479i \(0.657221\pi\)
\(42\) 0 0
\(43\) 1.57333 + 0.757677i 0.239931 + 0.115545i 0.549986 0.835174i \(-0.314633\pi\)
−0.310055 + 0.950719i \(0.600347\pi\)
\(44\) 0.531270 + 0.362214i 0.0800919 + 0.0546057i
\(45\) 0 0
\(46\) −0.414299 + 5.52843i −0.0610850 + 0.815123i
\(47\) 0.367220 0.935662i 0.0535646 0.136480i −0.901587 0.432598i \(-0.857597\pi\)
0.955151 + 0.296118i \(0.0956921\pi\)
\(48\) 0 0
\(49\) 5.42148 4.42805i 0.774497 0.632578i
\(50\) 26.5393 3.75322
\(51\) 0 0
\(52\) −1.62724 + 21.7140i −0.225657 + 3.01119i
\(53\) −1.76568 1.63831i −0.242535 0.225040i 0.549534 0.835472i \(-0.314805\pi\)
−0.792069 + 0.610432i \(0.790996\pi\)
\(54\) 0 0
\(55\) −0.490547 0.236235i −0.0661453 0.0318539i
\(56\) −12.5459 + 12.6933i −1.67651 + 1.69621i
\(57\) 0 0
\(58\) 9.97720 + 1.50382i 1.31007 + 0.197461i
\(59\) 5.40007 3.68170i 0.703029 0.479317i −0.158283 0.987394i \(-0.550596\pi\)
0.861312 + 0.508077i \(0.169643\pi\)
\(60\) 0 0
\(61\) 4.97882 4.61967i 0.637472 0.591488i −0.293775 0.955874i \(-0.594912\pi\)
0.931248 + 0.364387i \(0.118721\pi\)
\(62\) 0.0636549 + 0.0798207i 0.00808418 + 0.0101372i
\(63\) 0 0
\(64\) 1.73766 2.17896i 0.217208 0.272370i
\(65\) −1.37788 18.3866i −0.170905 2.28057i
\(66\) 0 0
\(67\) 4.83417 8.37303i 0.590588 1.02293i −0.403565 0.914951i \(-0.632229\pi\)
0.994153 0.107978i \(-0.0344375\pi\)
\(68\) −6.92296 11.9909i −0.839532 1.45411i
\(69\) 0 0
\(70\) 15.6951 21.5280i 1.87592 2.57309i
\(71\) −3.02675 + 13.2611i −0.359209 + 1.57380i 0.395959 + 0.918268i \(0.370412\pi\)
−0.755169 + 0.655531i \(0.772445\pi\)
\(72\) 0 0
\(73\) 4.98525 + 12.7022i 0.583480 + 1.48668i 0.852070 + 0.523428i \(0.175347\pi\)
−0.268590 + 0.963255i \(0.586558\pi\)
\(74\) 8.28002 + 21.0971i 0.962533 + 2.45249i
\(75\) 0 0
\(76\) −1.96982 + 8.63036i −0.225954 + 0.989971i
\(77\) −0.324444 + 0.173905i −0.0369738 + 0.0198183i
\(78\) 0 0
\(79\) −0.238309 0.412763i −0.0268119 0.0464395i 0.852308 0.523040i \(-0.175202\pi\)
−0.879120 + 0.476600i \(0.841869\pi\)
\(80\) −15.8779 + 27.5013i −1.77520 + 3.07474i
\(81\) 0 0
\(82\) 1.99264 + 26.5900i 0.220050 + 2.93637i
\(83\) 2.89616 3.63168i 0.317895 0.398628i −0.597051 0.802203i \(-0.703661\pi\)
0.914947 + 0.403575i \(0.132233\pi\)
\(84\) 0 0
\(85\) 7.30992 + 9.16635i 0.792872 + 0.994230i
\(86\) 3.29399 3.05638i 0.355200 0.329577i
\(87\) 0 0
\(88\) 0.775452 0.528694i 0.0826635 0.0563590i
\(89\) −8.74729 1.31844i −0.927210 0.139754i −0.331959 0.943294i \(-0.607710\pi\)
−0.595252 + 0.803539i \(0.702948\pi\)
\(90\) 0 0
\(91\) −10.5938 6.57054i −1.11053 0.688780i
\(92\) 8.97077 + 4.32009i 0.935267 + 0.450401i
\(93\) 0 0
\(94\) −1.89601 1.75924i −0.195558 0.181451i
\(95\) 0.560162 7.47484i 0.0574714 0.766902i
\(96\) 0 0
\(97\) −4.96224 −0.503839 −0.251920 0.967748i \(-0.581062\pi\)
−0.251920 + 0.967748i \(0.581062\pi\)
\(98\) −5.50994 17.1491i −0.556588 1.73232i
\(99\) 0 0
\(100\) 17.4136 44.3692i 1.74136 4.43692i
\(101\) −0.384443 + 5.13003i −0.0382535 + 0.510457i 0.944862 + 0.327470i \(0.106196\pi\)
−0.983115 + 0.182988i \(0.941423\pi\)
\(102\) 0 0
\(103\) −4.49958 3.06776i −0.443357 0.302276i 0.320988 0.947083i \(-0.395985\pi\)
−0.764345 + 0.644808i \(0.776938\pi\)
\(104\) 28.6355 + 13.7901i 2.80794 + 1.35223i
\(105\) 0 0
\(106\) −5.58424 + 2.68923i −0.542389 + 0.261201i
\(107\) −2.63328 0.396903i −0.254569 0.0383701i 0.0205179 0.999789i \(-0.493468\pi\)
−0.275087 + 0.961419i \(0.588707\pi\)
\(108\) 0 0
\(109\) 11.1209 1.67621i 1.06519 0.160551i 0.407018 0.913420i \(-0.366569\pi\)
0.658171 + 0.752869i \(0.271331\pi\)
\(110\) −1.02703 + 0.952942i −0.0979232 + 0.0908595i
\(111\) 0 0
\(112\) 8.70045 + 19.6281i 0.822115 + 1.85468i
\(113\) 4.22018 5.29194i 0.397001 0.497824i −0.542649 0.839959i \(-0.682579\pi\)
0.939651 + 0.342135i \(0.111150\pi\)
\(114\) 0 0
\(115\) −8.05647 2.48509i −0.751270 0.231736i
\(116\) 9.06063 15.6935i 0.841259 1.45710i
\(117\) 0 0
\(118\) −3.74232 16.3962i −0.344509 1.50939i
\(119\) 7.91929 0.342640i 0.725961 0.0314097i
\(120\) 0 0
\(121\) −10.4928 + 3.23660i −0.953891 + 0.294236i
\(122\) −6.38508 16.2689i −0.578078 1.47292i
\(123\) 0 0
\(124\) 0.175214 0.0540462i 0.0157346 0.00485350i
\(125\) −4.62706 + 20.2725i −0.413856 + 1.81322i
\(126\) 0 0
\(127\) −4.61933 20.2386i −0.409899 1.79588i −0.584665 0.811275i \(-0.698774\pi\)
0.174766 0.984610i \(-0.444083\pi\)
\(128\) 3.80450 + 6.58959i 0.336274 + 0.582443i
\(129\) 0 0
\(130\) −45.3374 13.9847i −3.97636 1.22654i
\(131\) 0.493760 + 6.58877i 0.0431400 + 0.575663i 0.976331 + 0.216282i \(0.0693931\pi\)
−0.933191 + 0.359381i \(0.882988\pi\)
\(132\) 0 0
\(133\) −3.86056 3.28323i −0.334753 0.284693i
\(134\) −15.5116 19.4510i −1.34000 1.68031i
\(135\) 0 0
\(136\) −19.9841 + 3.01211i −1.71362 + 0.258286i
\(137\) −12.6515 + 8.62566i −1.08089 + 0.736940i −0.966544 0.256501i \(-0.917430\pi\)
−0.114348 + 0.993441i \(0.536478\pi\)
\(138\) 0 0
\(139\) 5.13767 2.47417i 0.435771 0.209856i −0.203119 0.979154i \(-0.565108\pi\)
0.638891 + 0.769298i \(0.279394\pi\)
\(140\) −25.6930 40.3650i −2.17145 3.41146i
\(141\) 0 0
\(142\) 28.9193 + 19.7169i 2.42685 + 1.65460i
\(143\) 0.480555 + 0.445890i 0.0401860 + 0.0372872i
\(144\) 0 0
\(145\) −5.60594 + 14.2837i −0.465548 + 1.18620i
\(146\) 35.1128 2.90596
\(147\) 0 0
\(148\) 40.7038 3.34583
\(149\) −7.66287 + 19.5247i −0.627767 + 1.59952i 0.162465 + 0.986714i \(0.448056\pi\)
−0.790231 + 0.612809i \(0.790040\pi\)
\(150\) 0 0
\(151\) 7.50439 + 6.96306i 0.610699 + 0.566645i 0.923705 0.383106i \(-0.125146\pi\)
−0.313006 + 0.949751i \(0.601336\pi\)
\(152\) 10.6758 + 7.27866i 0.865925 + 0.590378i
\(153\) 0 0
\(154\) 0.111551 + 0.940642i 0.00898905 + 0.0757991i
\(155\) −0.139886 + 0.0673657i −0.0112359 + 0.00541094i
\(156\) 0 0
\(157\) 10.0848 6.87573i 0.804858 0.548743i −0.0895567 0.995982i \(-0.528545\pi\)
0.894415 + 0.447239i \(0.147593\pi\)
\(158\) −1.21274 + 0.182792i −0.0964807 + 0.0145421i
\(159\) 0 0
\(160\) 18.0314 + 22.6107i 1.42551 + 1.78753i
\(161\) −4.56653 + 3.41162i −0.359893 + 0.268874i
\(162\) 0 0
\(163\) 0.763165 + 10.1837i 0.0597757 + 0.797651i 0.943865 + 0.330332i \(0.107161\pi\)
−0.884089 + 0.467318i \(0.845220\pi\)
\(164\) 45.7614 + 14.1155i 3.57336 + 1.10224i
\(165\) 0 0
\(166\) −5.97641 10.3514i −0.463859 0.803428i
\(167\) −2.46611 10.8047i −0.190833 0.836095i −0.976167 0.217022i \(-0.930366\pi\)
0.785334 0.619073i \(-0.212491\pi\)
\(168\) 0 0
\(169\) −2.04720 + 8.96939i −0.157477 + 0.689953i
\(170\) 28.8286 8.89244i 2.21105 0.682019i
\(171\) 0 0
\(172\) −2.94841 7.51242i −0.224814 0.572817i
\(173\) 2.28093 0.703575i 0.173416 0.0534918i −0.206831 0.978377i \(-0.566315\pi\)
0.380247 + 0.924885i \(0.375839\pi\)
\(174\) 0 0
\(175\) 17.9197 + 20.5788i 1.35460 + 1.55561i
\(176\) −0.251238 1.10075i −0.0189378 0.0829718i
\(177\) 0 0
\(178\) −11.3815 + 19.7133i −0.853076 + 1.47757i
\(179\) 2.31602 + 0.714398i 0.173108 + 0.0533966i 0.380097 0.924946i \(-0.375890\pi\)
−0.206990 + 0.978343i \(0.566367\pi\)
\(180\) 0 0
\(181\) −5.00021 + 6.27006i −0.371663 + 0.466050i −0.932129 0.362127i \(-0.882051\pi\)
0.560466 + 0.828177i \(0.310622\pi\)
\(182\) −25.6979 + 19.1987i −1.90486 + 1.42311i
\(183\) 0 0
\(184\) 10.6536 9.88505i 0.785390 0.728736i
\(185\) −34.0814 + 5.13695i −2.50572 + 0.377676i
\(186\) 0 0
\(187\) −0.412189 0.0621276i −0.0301423 0.00454322i
\(188\) −4.18520 + 2.01549i −0.305237 + 0.146994i
\(189\) 0 0
\(190\) −17.3782 8.36889i −1.26075 0.607143i
\(191\) 6.26583 + 4.27197i 0.453379 + 0.309109i 0.768393 0.639978i \(-0.221057\pi\)
−0.315014 + 0.949087i \(0.602009\pi\)
\(192\) 0 0
\(193\) −0.956849 + 12.7683i −0.0688755 + 0.919079i 0.850570 + 0.525862i \(0.176257\pi\)
−0.919445 + 0.393218i \(0.871362\pi\)
\(194\) −4.66501 + 11.8863i −0.334928 + 0.853384i
\(195\) 0 0
\(196\) −32.2857 2.04061i −2.30612 0.145758i
\(197\) 10.0075 0.713008 0.356504 0.934294i \(-0.383969\pi\)
0.356504 + 0.934294i \(0.383969\pi\)
\(198\) 0 0
\(199\) 1.72364 23.0003i 0.122185 1.63045i −0.513209 0.858264i \(-0.671543\pi\)
0.635394 0.772188i \(-0.280838\pi\)
\(200\) −50.9995 47.3206i −3.60621 3.34607i
\(201\) 0 0
\(202\) 11.9268 + 5.74363i 0.839164 + 0.404120i
\(203\) 5.57067 + 8.75180i 0.390984 + 0.614256i
\(204\) 0 0
\(205\) −40.0976 6.04375i −2.80054 0.422114i
\(206\) −11.5784 + 7.89402i −0.806706 + 0.550003i
\(207\) 0 0
\(208\) 28.0282 26.0063i 1.94340 1.80322i
\(209\) 0.166165 + 0.208364i 0.0114939 + 0.0144128i
\(210\) 0 0
\(211\) −8.00976 + 10.0439i −0.551415 + 0.691452i −0.976945 0.213492i \(-0.931516\pi\)
0.425530 + 0.904944i \(0.360088\pi\)
\(212\) 0.831862 + 11.1004i 0.0571325 + 0.762381i
\(213\) 0 0
\(214\) −3.42627 + 5.93448i −0.234215 + 0.405672i
\(215\) 3.41681 + 5.91808i 0.233024 + 0.403610i
\(216\) 0 0
\(217\) −0.0189129 + 0.103255i −0.00128389 + 0.00700937i
\(218\) 6.43969 28.2141i 0.436151 1.91090i
\(219\) 0 0
\(220\) 0.919279 + 2.34229i 0.0619778 + 0.157917i
\(221\) −5.15726 13.1405i −0.346915 0.883925i
\(222\) 0 0
\(223\) 2.26898 9.94104i 0.151942 0.665701i −0.840378 0.542001i \(-0.817667\pi\)
0.992320 0.123700i \(-0.0394760\pi\)
\(224\) 19.5346 0.845191i 1.30521 0.0564717i
\(225\) 0 0
\(226\) −8.70860 15.0837i −0.579288 1.00336i
\(227\) 6.46298 11.1942i 0.428963 0.742985i −0.567818 0.823154i \(-0.692212\pi\)
0.996781 + 0.0801683i \(0.0255458\pi\)
\(228\) 0 0
\(229\) −0.469288 6.26222i −0.0310115 0.413819i −0.991008 0.133806i \(-0.957280\pi\)
0.959996 0.280013i \(-0.0903389\pi\)
\(230\) −13.5266 + 16.9618i −0.891914 + 1.11843i
\(231\) 0 0
\(232\) −16.4914 20.6796i −1.08271 1.35768i
\(233\) 11.2800 10.4663i 0.738977 0.685671i −0.217963 0.975957i \(-0.569941\pi\)
0.956940 + 0.290286i \(0.0937506\pi\)
\(234\) 0 0
\(235\) 3.24993 2.21576i 0.212002 0.144540i
\(236\) −29.8672 4.50175i −1.94419 0.293039i
\(237\) 0 0
\(238\) 6.62421 19.2915i 0.429383 1.25048i
\(239\) −8.34810 4.02023i −0.539993 0.260047i 0.143946 0.989585i \(-0.454021\pi\)
−0.683940 + 0.729538i \(0.739735\pi\)
\(240\) 0 0
\(241\) −8.98638 8.33814i −0.578864 0.537107i 0.335479 0.942048i \(-0.391102\pi\)
−0.914343 + 0.404941i \(0.867292\pi\)
\(242\) −2.11154 + 28.1766i −0.135735 + 1.81126i
\(243\) 0 0
\(244\) −31.3884 −2.00944
\(245\) 27.2905 2.36595i 1.74353 0.151155i
\(246\) 0 0
\(247\) −3.29726 + 8.40129i −0.209800 + 0.534561i
\(248\) 0.0200004 0.266887i 0.00127003 0.0169474i
\(249\) 0 0
\(250\) 44.2095 + 30.1415i 2.79606 + 1.90632i
\(251\) −6.08284 2.92934i −0.383945 0.184898i 0.231947 0.972728i \(-0.425490\pi\)
−0.615893 + 0.787830i \(0.711205\pi\)
\(252\) 0 0
\(253\) 0.270074 0.130061i 0.0169794 0.00817685i
\(254\) −52.8210 7.96148i −3.31428 0.499548i
\(255\) 0 0
\(256\) 24.8727 3.74895i 1.55454 0.234310i
\(257\) 10.7485 9.97318i 0.670475 0.622110i −0.269643 0.962960i \(-0.586906\pi\)
0.940117 + 0.340851i \(0.110715\pi\)
\(258\) 0 0
\(259\) −10.7681 + 20.6655i −0.669098 + 1.28409i
\(260\) −53.1281 + 66.6205i −3.29486 + 4.13163i
\(261\) 0 0
\(262\) 16.2465 + 5.01139i 1.00371 + 0.309605i
\(263\) 13.1948 22.8541i 0.813626 1.40924i −0.0966842 0.995315i \(-0.530824\pi\)
0.910310 0.413927i \(-0.135843\pi\)
\(264\) 0 0
\(265\) −2.09743 9.18945i −0.128844 0.564504i
\(266\) −11.4938 + 6.16078i −0.704729 + 0.377741i
\(267\) 0 0
\(268\) −42.6967 + 13.1702i −2.60811 + 0.804497i
\(269\) −7.58128 19.3168i −0.462239 1.17777i −0.952051 0.305938i \(-0.901030\pi\)
0.489813 0.871828i \(-0.337065\pi\)
\(270\) 0 0
\(271\) 3.41986 1.05489i 0.207742 0.0640799i −0.189138 0.981951i \(-0.560569\pi\)
0.396880 + 0.917871i \(0.370093\pi\)
\(272\) −5.41000 + 23.7028i −0.328030 + 1.43719i
\(273\) 0 0
\(274\) 8.76768 + 38.4137i 0.529675 + 2.32066i
\(275\) −0.717487 1.24272i −0.0432661 0.0749391i
\(276\) 0 0
\(277\) 13.2980 + 4.10190i 0.799001 + 0.246459i 0.667260 0.744825i \(-0.267467\pi\)
0.131741 + 0.991284i \(0.457943\pi\)
\(278\) −1.09655 14.6324i −0.0657667 0.877595i
\(279\) 0 0
\(280\) −68.5458 + 13.3846i −4.09640 + 0.799885i
\(281\) −10.0866 12.6482i −0.601715 0.754527i 0.383929 0.923363i \(-0.374571\pi\)
−0.985644 + 0.168836i \(0.945999\pi\)
\(282\) 0 0
\(283\) −29.6636 + 4.47107i −1.76332 + 0.265777i −0.949143 0.314844i \(-0.898048\pi\)
−0.814173 + 0.580622i \(0.802810\pi\)
\(284\) 51.9385 35.4111i 3.08198 2.10126i
\(285\) 0 0
\(286\) 1.51983 0.731911i 0.0898693 0.0432788i
\(287\) −19.2726 + 19.4990i −1.13763 + 1.15099i
\(288\) 0 0
\(289\) −6.62967 4.52003i −0.389980 0.265884i
\(290\) 28.9442 + 26.8563i 1.69966 + 1.57705i
\(291\) 0 0
\(292\) 23.0391 58.7027i 1.34826 3.43531i
\(293\) −16.1579 −0.943957 −0.471978 0.881610i \(-0.656460\pi\)
−0.471978 + 0.881610i \(0.656460\pi\)
\(294\) 0 0
\(295\) 25.5760 1.48909
\(296\) 21.7057 55.3051i 1.26162 3.21454i
\(297\) 0 0
\(298\) 39.5644 + 36.7104i 2.29190 + 2.12657i
\(299\) 8.38734 + 5.71839i 0.485052 + 0.330703i
\(300\) 0 0
\(301\) 4.59408 + 0.490478i 0.264799 + 0.0282707i
\(302\) 23.7338 11.4296i 1.36573 0.657699i
\(303\) 0 0
\(304\) 12.8430 8.75622i 0.736597 0.502204i
\(305\) 26.2817 3.96133i 1.50488 0.226825i
\(306\) 0 0
\(307\) 17.4101 + 21.8316i 0.993648 + 1.24600i 0.969195 + 0.246294i \(0.0792130\pi\)
0.0244531 + 0.999701i \(0.492216\pi\)
\(308\) 1.64579 + 0.430703i 0.0937775 + 0.0245416i
\(309\) 0 0
\(310\) 0.0298564 + 0.398406i 0.00169573 + 0.0226279i
\(311\) −7.27265 2.24332i −0.412394 0.127207i 0.0816140 0.996664i \(-0.473993\pi\)
−0.494008 + 0.869457i \(0.664469\pi\)
\(312\) 0 0
\(313\) −7.60290 13.1686i −0.429741 0.744334i 0.567109 0.823643i \(-0.308062\pi\)
−0.996850 + 0.0793092i \(0.974729\pi\)
\(314\) −6.98893 30.6205i −0.394408 1.72802i
\(315\) 0 0
\(316\) −0.490140 + 2.14744i −0.0275725 + 0.120803i
\(317\) −20.6410 + 6.36691i −1.15931 + 0.357601i −0.813988 0.580882i \(-0.802708\pi\)
−0.345326 + 0.938483i \(0.612232\pi\)
\(318\) 0 0
\(319\) −0.199315 0.507846i −0.0111595 0.0284339i
\(320\) 10.4217 3.21468i 0.582592 0.179706i
\(321\) 0 0
\(322\) 3.87900 + 14.1457i 0.216168 + 0.788307i
\(323\) −1.27701 5.59493i −0.0710545 0.311310i
\(324\) 0 0
\(325\) 24.2974 42.0844i 1.34778 2.33442i
\(326\) 25.1109 + 7.74570i 1.39077 + 0.428995i
\(327\) 0 0
\(328\) 43.5817 54.6498i 2.40640 3.01753i
\(329\) 0.0839165 2.65804i 0.00462646 0.146542i
\(330\) 0 0
\(331\) 20.1800 18.7243i 1.10919 1.02918i 0.109812 0.993952i \(-0.464975\pi\)
0.999379 0.0352268i \(-0.0112153\pi\)
\(332\) −21.2273 + 3.19950i −1.16500 + 0.175595i
\(333\) 0 0
\(334\) −28.1994 4.25037i −1.54300 0.232570i
\(335\) 34.0880 16.4159i 1.86243 0.896897i
\(336\) 0 0
\(337\) −8.68910 4.18445i −0.473326 0.227942i 0.181985 0.983301i \(-0.441748\pi\)
−0.655310 + 0.755360i \(0.727462\pi\)
\(338\) 19.5602 + 13.3359i 1.06393 + 0.725377i
\(339\) 0 0
\(340\) 4.04909 54.0313i 0.219592 2.93026i
\(341\) 0.00201677 0.00513864i 0.000109214 0.000278273i
\(342\) 0 0
\(343\) 9.57715 15.8518i 0.517118 0.855914i
\(344\) −11.7796 −0.635111
\(345\) 0 0
\(346\) 0.459009 6.12504i 0.0246765 0.329284i
\(347\) 22.3873 + 20.7723i 1.20181 + 1.11512i 0.990473 + 0.137705i \(0.0439725\pi\)
0.211338 + 0.977413i \(0.432218\pi\)
\(348\) 0 0
\(349\) −11.3398 5.46098i −0.607007 0.292319i 0.105021 0.994470i \(-0.466509\pi\)
−0.712028 + 0.702151i \(0.752223\pi\)
\(350\) 66.1395 23.5776i 3.53531 1.26028i
\(351\) 0 0
\(352\) −1.01675 0.153250i −0.0541929 0.00816827i
\(353\) 15.4520 10.5350i 0.822427 0.560721i −0.0773841 0.997001i \(-0.524657\pi\)
0.899811 + 0.436280i \(0.143704\pi\)
\(354\) 0 0
\(355\) −39.0194 + 36.2047i −2.07093 + 1.92154i
\(356\) 25.4894 + 31.9626i 1.35093 + 1.69402i
\(357\) 0 0
\(358\) 3.88853 4.87606i 0.205515 0.257708i
\(359\) −0.695229 9.27718i −0.0366928 0.489631i −0.985032 0.172372i \(-0.944857\pi\)
0.948339 0.317259i \(-0.102762\pi\)
\(360\) 0 0
\(361\) 7.66546 13.2770i 0.403445 0.698788i
\(362\) 10.3182 + 17.8717i 0.542314 + 0.939316i
\(363\) 0 0
\(364\) 15.2355 + 55.5598i 0.798556 + 2.91212i
\(365\) −11.8823 + 52.0596i −0.621946 + 2.72492i
\(366\) 0 0
\(367\) −6.03188 15.3690i −0.314862 0.802254i −0.997444 0.0714459i \(-0.977239\pi\)
0.682583 0.730808i \(-0.260857\pi\)
\(368\) −6.38738 16.2748i −0.332965 0.848382i
\(369\) 0 0
\(370\) −19.7353 + 86.4659i −1.02599 + 4.49515i
\(371\) −5.85580 2.51426i −0.304018 0.130534i
\(372\) 0 0
\(373\) 9.79667 + 16.9683i 0.507253 + 0.878587i 0.999965 + 0.00839486i \(0.00267220\pi\)
−0.492712 + 0.870192i \(0.663994\pi\)
\(374\) −0.536317 + 0.928928i −0.0277323 + 0.0480337i
\(375\) 0 0
\(376\) 0.506689 + 6.76130i 0.0261305 + 0.348687i
\(377\) 11.5190 14.4444i 0.593261 0.743926i
\(378\) 0 0
\(379\) −4.35557 5.46171i −0.223730 0.280549i 0.657279 0.753647i \(-0.271707\pi\)
−0.881010 + 0.473098i \(0.843136\pi\)
\(380\) −25.3940 + 23.5622i −1.30268 + 1.20871i
\(381\) 0 0
\(382\) 16.1233 10.9927i 0.824942 0.562436i
\(383\) −17.3675 2.61773i −0.887439 0.133760i −0.310525 0.950565i \(-0.600505\pi\)
−0.576914 + 0.816805i \(0.695743\pi\)
\(384\) 0 0
\(385\) −1.43238 0.152925i −0.0730009 0.00779380i
\(386\) 29.6848 + 14.2954i 1.51092 + 0.727619i
\(387\) 0 0
\(388\) 16.8109 + 15.5982i 0.853444 + 0.791880i
\(389\) −0.530297 + 7.07632i −0.0268871 + 0.358784i 0.967492 + 0.252903i \(0.0813853\pi\)
−0.994379 + 0.105881i \(0.966234\pi\)
\(390\) 0 0
\(391\) −6.45484 −0.326435
\(392\) −19.9893 + 42.7792i −1.00961 + 2.16067i
\(393\) 0 0
\(394\) 9.40812 23.9715i 0.473974 1.20767i
\(395\) 0.139382 1.85992i 0.00701305 0.0935827i
\(396\) 0 0
\(397\) −3.43094 2.33917i −0.172194 0.117400i 0.474156 0.880441i \(-0.342753\pi\)
−0.646350 + 0.763041i \(0.723705\pi\)
\(398\) −53.4733 25.7514i −2.68037 1.29080i
\(399\) 0 0
\(400\) −75.4060 + 36.3136i −3.77030 + 1.81568i
\(401\) −33.2580 5.01284i −1.66083 0.250329i −0.749497 0.662008i \(-0.769704\pi\)
−0.911329 + 0.411679i \(0.864943\pi\)
\(402\) 0 0
\(403\) 0.184852 0.0278620i 0.00920815 0.00138791i
\(404\) 17.4281 16.1709i 0.867079 0.804532i
\(405\) 0 0
\(406\) 26.2005 5.11606i 1.30031 0.253906i
\(407\) 0.764042 0.958078i 0.0378721 0.0474902i
\(408\) 0 0
\(409\) −4.04761 1.24852i −0.200142 0.0617355i 0.193064 0.981186i \(-0.438158\pi\)
−0.393205 + 0.919451i \(0.628634\pi\)
\(410\) −52.1727 + 90.3658i −2.57663 + 4.46285i
\(411\) 0 0
\(412\) 5.60036 + 24.5368i 0.275910 + 1.20884i
\(413\) 10.1869 13.9727i 0.501263 0.687554i
\(414\) 0 0
\(415\) 17.3699 5.35790i 0.852655 0.263009i
\(416\) −12.7214 32.4137i −0.623720 1.58921i
\(417\) 0 0
\(418\) 0.655315 0.202138i 0.0320525 0.00988688i
\(419\) 7.98259 34.9740i 0.389975 1.70859i −0.274760 0.961513i \(-0.588598\pi\)
0.664735 0.747079i \(-0.268544\pi\)
\(420\) 0 0
\(421\) 8.26851 + 36.2267i 0.402982 + 1.76558i 0.615212 + 0.788362i \(0.289070\pi\)
−0.212230 + 0.977220i \(0.568073\pi\)
\(422\) 16.5286 + 28.6284i 0.804601 + 1.39361i
\(423\) 0 0
\(424\) 15.5260 + 4.78914i 0.754009 + 0.232581i
\(425\) 2.30915 + 30.8135i 0.112010 + 1.49467i
\(426\) 0 0
\(427\) 8.30375 15.9360i 0.401847 0.771199i
\(428\) 7.67331 + 9.62203i 0.370904 + 0.465098i
\(429\) 0 0
\(430\) 17.3880 2.62082i 0.838523 0.126387i
\(431\) 13.1900 8.99282i 0.635342 0.433169i −0.202349 0.979314i \(-0.564857\pi\)
0.837691 + 0.546145i \(0.183905\pi\)
\(432\) 0 0
\(433\) 17.3540 8.35727i 0.833982 0.401625i 0.0323749 0.999476i \(-0.489693\pi\)
0.801607 + 0.597851i \(0.203979\pi\)
\(434\) 0.229550 + 0.142373i 0.0110187 + 0.00683411i
\(435\) 0 0
\(436\) −42.9439 29.2787i −2.05664 1.40219i
\(437\) 3.02520 + 2.80698i 0.144715 + 0.134276i
\(438\) 0 0
\(439\) −0.118250 + 0.301295i −0.00564375 + 0.0143800i −0.933668 0.358140i \(-0.883411\pi\)
0.928024 + 0.372520i \(0.121506\pi\)
\(440\) 3.67273 0.175090
\(441\) 0 0
\(442\) −36.3243 −1.72777
\(443\) −8.30603 + 21.1634i −0.394631 + 1.00550i 0.586117 + 0.810227i \(0.300656\pi\)
−0.980748 + 0.195278i \(0.937439\pi\)
\(444\) 0 0
\(445\) −25.3761 23.5456i −1.20294 1.11617i
\(446\) −21.6791 14.7806i −1.02654 0.699880i
\(447\) 0 0
\(448\) 2.39469 6.97401i 0.113139 0.329491i
\(449\) −21.6475 + 10.4249i −1.02161 + 0.491981i −0.868217 0.496184i \(-0.834734\pi\)
−0.153393 + 0.988165i \(0.549020\pi\)
\(450\) 0 0
\(451\) 1.19123 0.812164i 0.0560926 0.0382433i
\(452\) −30.9316 + 4.66219i −1.45490 + 0.219291i
\(453\) 0 0
\(454\) −20.7381 26.0047i −0.973286 1.22046i
\(455\) −19.7686 44.5977i −0.926765 2.09077i
\(456\) 0 0
\(457\) −0.588905 7.85838i −0.0275478 0.367600i −0.993893 0.110350i \(-0.964803\pi\)
0.966345 0.257250i \(-0.0828163\pi\)
\(458\) −15.4413 4.76302i −0.721526 0.222561i
\(459\) 0 0
\(460\) 19.4818 + 33.7435i 0.908344 + 1.57330i
\(461\) 1.64847 + 7.22240i 0.0767767 + 0.336381i 0.998699 0.0509943i \(-0.0162390\pi\)
−0.921922 + 0.387375i \(0.873382\pi\)
\(462\) 0 0
\(463\) −4.92874 + 21.5942i −0.229058 + 1.00357i 0.721352 + 0.692568i \(0.243521\pi\)
−0.950410 + 0.310999i \(0.899336\pi\)
\(464\) −30.4058 + 9.37896i −1.41156 + 0.435407i
\(465\) 0 0
\(466\) −14.4660 36.8588i −0.670126 1.70745i
\(467\) 37.6718 11.6202i 1.74324 0.537719i 0.750810 0.660519i \(-0.229664\pi\)
0.992431 + 0.122800i \(0.0391873\pi\)
\(468\) 0 0
\(469\) 4.60877 25.1614i 0.212813 1.16185i
\(470\) −2.25224 9.86772i −0.103888 0.455164i
\(471\) 0 0
\(472\) −22.0436 + 38.1806i −1.01464 + 1.75740i
\(473\) −0.232170 0.0716149i −0.0106752 0.00329286i
\(474\) 0 0
\(475\) 12.3174 15.4456i 0.565163 0.708692i
\(476\) −27.9057 23.7326i −1.27906 1.08778i
\(477\) 0 0
\(478\) −17.4779 + 16.2171i −0.799420 + 0.741753i
\(479\) 21.6401 3.26172i 0.988761 0.149032i 0.365303 0.930889i \(-0.380965\pi\)
0.623458 + 0.781857i \(0.285727\pi\)
\(480\) 0 0
\(481\) 41.0351 + 6.18504i 1.87104 + 0.282014i
\(482\) −28.4208 + 13.6867i −1.29453 + 0.623414i
\(483\) 0 0
\(484\) 45.7210 + 22.0181i 2.07823 + 1.00082i
\(485\) −16.0444 10.9389i −0.728538 0.496709i
\(486\) 0 0
\(487\) 0.715270 9.54461i 0.0324120 0.432508i −0.957267 0.289206i \(-0.906609\pi\)
0.989679 0.143302i \(-0.0457721\pi\)
\(488\) −16.7382 + 42.6482i −0.757701 + 1.93059i
\(489\) 0 0
\(490\) 19.9886 67.5943i 0.902993 3.05360i
\(491\) −38.5914 −1.74161 −0.870804 0.491631i \(-0.836401\pi\)
−0.870804 + 0.491631i \(0.836401\pi\)
\(492\) 0 0
\(493\) −0.877909 + 11.7149i −0.0395390 + 0.527612i
\(494\) 17.0242 + 15.7961i 0.765955 + 0.710702i
\(495\) 0 0
\(496\) −0.290081 0.139695i −0.0130250 0.00627251i
\(497\) 4.23811 + 35.7373i 0.190105 + 1.60304i
\(498\) 0 0
\(499\) −4.47023 0.673779i −0.200115 0.0301625i 0.0482197 0.998837i \(-0.484645\pi\)
−0.248335 + 0.968674i \(0.579883\pi\)
\(500\) 79.3995 54.1336i 3.55085 2.42093i
\(501\) 0 0
\(502\) −12.7353 + 11.8166i −0.568402 + 0.527400i
\(503\) 12.2438 + 15.3532i 0.545924 + 0.684568i 0.975886 0.218279i \(-0.0700444\pi\)
−0.429962 + 0.902847i \(0.641473\pi\)
\(504\) 0 0
\(505\) −12.5518 + 15.7394i −0.558547 + 0.700396i
\(506\) −0.0576428 0.769189i −0.00256253 0.0341946i
\(507\) 0 0
\(508\) −47.9685 + 83.0838i −2.12826 + 3.68625i
\(509\) 2.51327 + 4.35312i 0.111399 + 0.192948i 0.916334 0.400414i \(-0.131134\pi\)
−0.804936 + 0.593362i \(0.797800\pi\)
\(510\) 0 0
\(511\) 23.7086 + 27.2267i 1.04881 + 1.20444i
\(512\) 11.0165 48.2665i 0.486865 2.13310i
\(513\) 0 0
\(514\) −13.7844 35.1222i −0.608006 1.54917i
\(515\) −7.78583 19.8380i −0.343085 0.874165i
\(516\) 0 0
\(517\) −0.0311193 + 0.136343i −0.00136863 + 0.00599635i
\(518\) 39.3777 + 45.2209i 1.73016 + 1.98689i
\(519\) 0 0
\(520\) 62.1877 + 107.712i 2.72711 + 4.72350i
\(521\) 20.2977 35.1566i 0.889257 1.54024i 0.0485023 0.998823i \(-0.484555\pi\)
0.840755 0.541416i \(-0.182111\pi\)
\(522\) 0 0
\(523\) 2.02070 + 26.9644i 0.0883590 + 1.17907i 0.848458 + 0.529262i \(0.177531\pi\)
−0.760099 + 0.649807i \(0.774850\pi\)
\(524\) 19.0383 23.8733i 0.831691 1.04291i
\(525\) 0 0
\(526\) −42.3388 53.0912i −1.84606 2.31489i
\(527\) −0.0871373 + 0.0808516i −0.00379576 + 0.00352195i
\(528\) 0 0
\(529\) −15.1683 + 10.3416i −0.659491 + 0.449633i
\(530\) −23.9837 3.61496i −1.04178 0.157024i
\(531\) 0 0
\(532\) 2.75818 + 23.2580i 0.119582 + 1.00836i
\(533\) 43.9890 + 21.1840i 1.90537 + 0.917580i
\(534\) 0 0
\(535\) −7.63923 7.08817i −0.330273 0.306448i
\(536\) −4.87378 + 65.0360i −0.210515 + 2.80913i
\(537\) 0 0
\(538\) −53.3975 −2.30213
\(539\) −0.654060 + 0.721632i −0.0281723 + 0.0310829i
\(540\) 0 0
\(541\) 3.64749 9.29366i 0.156818 0.399566i −0.830774 0.556611i \(-0.812102\pi\)
0.987591 + 0.157045i \(0.0501968\pi\)
\(542\) 0.688204 9.18344i 0.0295609 0.394462i
\(543\) 0 0
\(544\) 18.2941 + 12.4727i 0.784351 + 0.534761i
\(545\) 39.6522 + 19.0955i 1.69851 + 0.817961i
\(546\) 0 0
\(547\) 27.6917 13.3356i 1.18401 0.570190i 0.264934 0.964267i \(-0.414650\pi\)
0.919078 + 0.394077i \(0.128936\pi\)
\(548\) 69.9741 + 10.5469i 2.98915 + 0.450541i
\(549\) 0 0
\(550\) −3.65126 + 0.550339i −0.155690 + 0.0234665i
\(551\) 5.50584 5.10867i 0.234557 0.217637i
\(552\) 0 0
\(553\) −0.960599 0.816948i −0.0408488 0.0347401i
\(554\) 22.3269 27.9971i 0.948581 1.18948i
\(555\) 0 0
\(556\) −25.1825 7.76776i −1.06797 0.329427i
\(557\) 8.61938 14.9292i 0.365215 0.632571i −0.623596 0.781747i \(-0.714329\pi\)
0.988811 + 0.149176i \(0.0476622\pi\)
\(558\) 0 0
\(559\) −1.83088 8.02159i −0.0774378 0.339277i
\(560\) −15.1376 + 82.6429i −0.639679 + 3.49230i
\(561\) 0 0
\(562\) −39.7791 + 12.2702i −1.67798 + 0.517588i
\(563\) 11.7324 + 29.8938i 0.494463 + 1.25987i 0.932583 + 0.360955i \(0.117549\pi\)
−0.438120 + 0.898916i \(0.644356\pi\)
\(564\) 0 0
\(565\) 25.3108 7.80734i 1.06483 0.328457i
\(566\) −17.1771 + 75.2576i −0.722006 + 3.16331i
\(567\) 0 0
\(568\) −20.4171 89.4533i −0.856684 3.75338i
\(569\) 2.41715 + 4.18663i 0.101332 + 0.175513i 0.912234 0.409670i \(-0.134356\pi\)
−0.810901 + 0.585183i \(0.801023\pi\)
\(570\) 0 0
\(571\) 28.8673 + 8.90440i 1.20806 + 0.372637i 0.832429 0.554132i \(-0.186950\pi\)
0.375632 + 0.926769i \(0.377426\pi\)
\(572\) −0.226403 3.02114i −0.00946638 0.126320i
\(573\) 0 0
\(574\) 28.5886 + 64.4955i 1.19326 + 2.69199i
\(575\) −13.8543 17.3727i −0.577763 0.724493i
\(576\) 0 0
\(577\) 29.0522 4.37891i 1.20946 0.182296i 0.486807 0.873510i \(-0.338162\pi\)
0.722651 + 0.691213i \(0.242924\pi\)
\(578\) −17.0596 + 11.6310i −0.709585 + 0.483787i
\(579\) 0 0
\(580\) 63.8907 30.7682i 2.65292 1.27758i
\(581\) 3.99124 11.6236i 0.165584 0.482228i
\(582\) 0 0
\(583\) 0.276895 + 0.188784i 0.0114678 + 0.00781861i
\(584\) −67.4748 62.6075i −2.79213 2.59072i
\(585\) 0 0
\(586\) −15.1901 + 38.7038i −0.627498 + 1.59884i
\(587\) −37.6226 −1.55285 −0.776426 0.630209i \(-0.782969\pi\)
−0.776426 + 0.630209i \(0.782969\pi\)
\(588\) 0 0
\(589\) 0.0759984 0.00313146
\(590\) 24.0441 61.2633i 0.989879 2.52217i
\(591\) 0 0
\(592\) −52.3931 48.6137i −2.15334 1.99801i
\(593\) 4.36557 + 2.97639i 0.179272 + 0.122226i 0.649631 0.760249i \(-0.274923\pi\)
−0.470359 + 0.882475i \(0.655876\pi\)
\(594\) 0 0
\(595\) 26.3607 + 16.3496i 1.08068 + 0.670269i
\(596\) 87.3335 42.0576i 3.57732 1.72275i
\(597\) 0 0
\(598\) 21.5824 14.7147i 0.882572 0.601727i
\(599\) −12.3024 + 1.85428i −0.502661 + 0.0757639i −0.395478 0.918475i \(-0.629421\pi\)
−0.107183 + 0.994239i \(0.534183\pi\)
\(600\) 0 0
\(601\) 7.01054 + 8.79094i 0.285966 + 0.358590i 0.903978 0.427578i \(-0.140633\pi\)
−0.618012 + 0.786168i \(0.712062\pi\)
\(602\) 5.49377 10.5433i 0.223909 0.429713i
\(603\) 0 0
\(604\) −3.53553 47.1784i −0.143859 1.91966i
\(605\) −41.0611 12.6657i −1.66937 0.514933i
\(606\) 0 0
\(607\) −3.25907 5.64487i −0.132282 0.229118i 0.792274 0.610165i \(-0.208897\pi\)
−0.924556 + 0.381047i \(0.875564\pi\)
\(608\) −3.15000 13.8010i −0.127749 0.559706i
\(609\) 0 0
\(610\) 15.2187 66.6776i 0.616189 2.69970i
\(611\) −4.52553 + 1.39594i −0.183083 + 0.0564737i
\(612\) 0 0
\(613\) −6.17952 15.7452i −0.249588 0.635941i 0.750089 0.661337i \(-0.230011\pi\)
−0.999677 + 0.0253960i \(0.991915\pi\)
\(614\) 68.6614 21.1792i 2.77095 0.854725i
\(615\) 0 0
\(616\) 1.46284 2.00649i 0.0589394 0.0808439i
\(617\) 1.97237 + 8.64151i 0.0794045 + 0.347894i 0.998987 0.0450035i \(-0.0143299\pi\)
−0.919582 + 0.392897i \(0.871473\pi\)
\(618\) 0 0
\(619\) 22.9137 39.6878i 0.920981 1.59519i 0.123081 0.992397i \(-0.460723\pi\)
0.797900 0.602789i \(-0.205944\pi\)
\(620\) 0.685658 + 0.211497i 0.0275367 + 0.00849394i
\(621\) 0 0
\(622\) −12.2105 + 15.3115i −0.489598 + 0.613936i
\(623\) −22.9707 + 4.48539i −0.920303 + 0.179703i
\(624\) 0 0
\(625\) −21.8474 + 20.2714i −0.873897 + 0.810858i
\(626\) −38.6908 + 5.83170i −1.54640 + 0.233082i
\(627\) 0 0
\(628\) −55.7781 8.40719i −2.22579 0.335484i
\(629\) −23.7744 + 11.4492i −0.947948 + 0.456508i
\(630\) 0 0
\(631\) −28.8831 13.9093i −1.14982 0.553722i −0.240838 0.970565i \(-0.577422\pi\)
−0.908979 + 0.416843i \(0.863136\pi\)
\(632\) 2.65640 + 1.81111i 0.105666 + 0.0720419i
\(633\) 0 0
\(634\) −4.15374 + 55.4278i −0.164966 + 2.20132i
\(635\) 29.6788 75.6202i 1.17777 3.00090i
\(636\) 0 0
\(637\) −32.2384 6.96312i −1.27733 0.275889i
\(638\) −1.40384 −0.0555786
\(639\) 0 0
\(640\) −2.22517 + 29.6928i −0.0879575 + 1.17371i
\(641\) −13.4779 12.5057i −0.532345 0.493944i 0.367578 0.929993i \(-0.380187\pi\)
−0.899923 + 0.436049i \(0.856378\pi\)
\(642\) 0 0
\(643\) 25.4981 + 12.2793i 1.00555 + 0.484247i 0.862818 0.505515i \(-0.168697\pi\)
0.142731 + 0.989762i \(0.454412\pi\)
\(644\) 26.1944 + 2.79659i 1.03220 + 0.110201i
\(645\) 0 0
\(646\) −14.6023 2.20094i −0.574519 0.0865948i
\(647\) −37.5509 + 25.6018i −1.47628 + 1.00651i −0.485031 + 0.874497i \(0.661192\pi\)
−0.991248 + 0.132013i \(0.957856\pi\)
\(648\) 0 0
\(649\) −0.666591 + 0.618506i −0.0261660 + 0.0242785i
\(650\) −77.9643 97.7642i −3.05801 3.83463i
\(651\) 0 0
\(652\) 29.4259 36.8990i 1.15241 1.44507i
\(653\) 0.601189 + 8.02232i 0.0235264 + 0.313937i 0.996535 + 0.0831703i \(0.0265045\pi\)
−0.973009 + 0.230767i \(0.925876\pi\)
\(654\) 0 0
\(655\) −12.9280 + 22.3919i −0.505137 + 0.874923i
\(656\) −42.0446 72.8234i −1.64157 2.84328i
\(657\) 0 0
\(658\) −6.28801 2.69983i −0.245132 0.105250i
\(659\) 4.26560 18.6888i 0.166164 0.728013i −0.821342 0.570436i \(-0.806774\pi\)
0.987507 0.157578i \(-0.0503684\pi\)
\(660\) 0 0
\(661\) 10.3734 + 26.4311i 0.403480 + 1.02805i 0.977823 + 0.209434i \(0.0671623\pi\)
−0.574343 + 0.818615i \(0.694742\pi\)
\(662\) −25.8798 65.9406i −1.00585 2.56286i
\(663\) 0 0
\(664\) −6.97241 + 30.5481i −0.270582 + 1.18550i
\(665\) −5.24468 19.1260i −0.203380 0.741673i
\(666\) 0 0
\(667\) −4.22398 7.31615i −0.163553 0.283282i
\(668\) −25.6088 + 44.3558i −0.990835 + 1.71618i
\(669\) 0 0
\(670\) −7.27551 97.0850i −0.281078 3.75072i
\(671\) −0.589186 + 0.738815i −0.0227453 + 0.0285217i
\(672\) 0 0
\(673\) 26.3707 + 33.0678i 1.01652 + 1.27467i 0.961098 + 0.276208i \(0.0890777\pi\)
0.0554181 + 0.998463i \(0.482351\pi\)
\(674\) −18.1918 + 16.8796i −0.700723 + 0.650176i
\(675\) 0 0
\(676\) 35.1297 23.9510i 1.35114 0.921193i
\(677\) 12.9418 + 1.95066i 0.497392 + 0.0749698i 0.392948 0.919561i \(-0.371455\pi\)
0.104445 + 0.994531i \(0.466693\pi\)
\(678\) 0 0
\(679\) −12.3666 + 4.40848i −0.474586 + 0.169182i
\(680\) −71.2543 34.3143i −2.73248 1.31589i
\(681\) 0 0
\(682\) −0.0104128 0.00966169i −0.000398728 0.000369965i
\(683\) −2.44303 + 32.5999i −0.0934798 + 1.24740i 0.731343 + 0.682010i \(0.238894\pi\)
−0.824823 + 0.565391i \(0.808725\pi\)
\(684\) 0 0
\(685\) −59.9207 −2.28945
\(686\) −28.9669 37.8428i −1.10596 1.44485i
\(687\) 0 0
\(688\) −5.17717 + 13.1912i −0.197378 + 0.502910i
\(689\) −0.848106 + 11.3172i −0.0323103 + 0.431151i
\(690\) 0 0
\(691\) 2.82721 + 1.92756i 0.107552 + 0.0733277i 0.615902 0.787823i \(-0.288792\pi\)
−0.508350 + 0.861151i \(0.669744\pi\)
\(692\) −9.93886 4.78631i −0.377819 0.181948i
\(693\) 0 0
\(694\) 70.8031 34.0970i 2.68765 1.29430i
\(695\) 22.0657 + 3.32587i 0.837000 + 0.126157i
\(696\) 0 0
\(697\) −30.6989 + 4.62711i −1.16280 + 0.175264i
\(698\) −23.7415 + 22.0289i −0.898629 + 0.833806i
\(699\) 0 0
\(700\) 3.97933 126.045i 0.150405 4.76404i
\(701\) −8.63359 + 10.8262i −0.326086 + 0.408899i −0.917669 0.397345i \(-0.869932\pi\)
0.591583 + 0.806244i \(0.298503\pi\)
\(702\) 0 0
\(703\) 16.1212 + 4.97274i 0.608024 + 0.187551i
\(704\) −0.193882 + 0.335814i −0.00730721 + 0.0126565i
\(705\) 0 0
\(706\) −10.7084 46.9168i −0.403018 1.76574i
\(707\) 3.59946 + 13.1263i 0.135372 + 0.493665i
\(708\) 0 0
\(709\) 25.3579 7.82187i 0.952335 0.293756i 0.220614 0.975361i \(-0.429194\pi\)
0.731721 + 0.681605i \(0.238718\pi\)
\(710\) 50.0404 + 127.501i 1.87798 + 4.78502i
\(711\) 0 0
\(712\) 57.0208 17.5886i 2.13694 0.659160i
\(713\) 0.0190212 0.0833374i 0.000712350 0.00312101i
\(714\) 0 0
\(715\) 0.570846 + 2.50104i 0.0213484 + 0.0935335i
\(716\) −5.60051 9.70036i −0.209301 0.362520i
\(717\) 0 0
\(718\) −22.8756 7.05619i −0.853710 0.263335i
\(719\) −1.28620 17.1632i −0.0479672 0.640078i −0.968436 0.249262i \(-0.919812\pi\)
0.920469 0.390816i \(-0.127807\pi\)
\(720\) 0 0
\(721\) −13.9390 3.64783i −0.519115 0.135852i
\(722\) −24.5966 30.8431i −0.915389 1.14786i
\(723\) 0 0
\(724\) 36.6487 5.52391i 1.36204 0.205294i
\(725\) −33.4140 + 22.7813i −1.24097 + 0.846076i
\(726\) 0 0
\(727\) −34.9632 + 16.8374i −1.29671 + 0.624464i −0.949631 0.313370i \(-0.898542\pi\)
−0.347083 + 0.937835i \(0.612828\pi\)
\(728\) 83.6148 + 8.92697i 3.09897 + 0.330855i
\(729\) 0 0
\(730\) 113.530 + 77.4034i 4.20193 + 2.86483i
\(731\) 3.83521 + 3.55856i 0.141850 + 0.131618i
\(732\) 0 0
\(733\) 1.73050 4.40925i 0.0639175 0.162859i −0.895347 0.445370i \(-0.853072\pi\)
0.959264 + 0.282511i \(0.0911673\pi\)
\(734\) −42.4845 −1.56813
\(735\) 0 0
\(736\) −15.9222 −0.586899
\(737\) −0.491453 + 1.25220i −0.0181029 + 0.0461254i
\(738\) 0 0
\(739\) −29.8437 27.6909i −1.09782 1.01863i −0.999725 0.0234493i \(-0.992535\pi\)
−0.0980933 0.995177i \(-0.531274\pi\)
\(740\) 131.607 + 89.7283i 4.83798 + 3.29848i
\(741\) 0 0
\(742\) −11.5276 + 11.6630i −0.423190 + 0.428161i
\(743\) −18.2058 + 8.76747i −0.667908 + 0.321647i −0.736931 0.675968i \(-0.763726\pi\)
0.0690235 + 0.997615i \(0.478012\pi\)
\(744\) 0 0
\(745\) −67.8169 + 46.2368i −2.48462 + 1.69398i
\(746\) 49.8548 7.51441i 1.82531 0.275122i
\(747\) 0 0
\(748\) 1.20111 + 1.50614i 0.0439169 + 0.0550700i
\(749\) −6.91510 + 1.35028i −0.252672 + 0.0493382i
\(750\) 0 0
\(751\) −1.80730 24.1167i −0.0659492 0.880031i −0.927850 0.372954i \(-0.878345\pi\)
0.861901 0.507077i \(-0.169274\pi\)
\(752\) 7.79426 + 2.40421i 0.284228 + 0.0876726i
\(753\) 0 0
\(754\) −23.7703 41.1713i −0.865662 1.49937i
\(755\) 8.91438 + 39.0564i 0.324427 + 1.42141i
\(756\) 0 0
\(757\) −2.93906 + 12.8769i −0.106822 + 0.468017i 0.893016 + 0.450025i \(0.148585\pi\)
−0.999838 + 0.0179929i \(0.994272\pi\)
\(758\) −17.1773 + 5.29850i −0.623909 + 0.192450i
\(759\) 0 0
\(760\) 18.4729 + 47.0681i 0.670081 + 1.70734i
\(761\) −36.5574 + 11.2765i −1.32520 + 0.408771i −0.874986 0.484148i \(-0.839130\pi\)
−0.450217 + 0.892919i \(0.648653\pi\)
\(762\) 0 0
\(763\) 26.2256 14.0572i 0.949431 0.508904i
\(764\) −7.79869 34.1683i −0.282147 1.23617i
\(765\) 0 0
\(766\) −22.5976 + 39.1402i −0.816485 + 1.41419i
\(767\) −29.4262 9.07679i −1.06252 0.327744i
\(768\) 0 0
\(769\) 1.76607 2.21458i 0.0636861 0.0798599i −0.748968 0.662606i \(-0.769450\pi\)
0.812654 + 0.582746i \(0.198022\pi\)
\(770\) −1.71289 + 3.28728i −0.0617284 + 0.118465i
\(771\) 0 0
\(772\) 43.3771 40.2481i 1.56118 1.44856i
\(773\) 45.0280 6.78688i 1.61954 0.244107i 0.724235 0.689553i \(-0.242193\pi\)
0.895309 + 0.445446i \(0.146955\pi\)
\(774\) 0 0
\(775\) −0.404633 0.0609886i −0.0145348 0.00219077i
\(776\) 30.1582 14.5234i 1.08262 0.521361i
\(777\) 0 0
\(778\) 16.4517 + 7.92271i 0.589821 + 0.284043i
\(779\) 16.3999 + 11.1813i 0.587587 + 0.400610i
\(780\) 0 0
\(781\) 0.141427 1.88721i 0.00506066 0.0675298i
\(782\) −6.06820 + 15.4615i −0.216999 + 0.552903i
\(783\) 0 0
\(784\) 39.1204 + 41.1864i 1.39716 + 1.47094i
\(785\) 47.7643 1.70478
\(786\) 0 0
\(787\) −0.508738 + 6.78864i −0.0181346 + 0.241989i 0.980769 + 0.195172i \(0.0625267\pi\)
−0.998904 + 0.0468165i \(0.985092\pi\)
\(788\) −33.9032 31.4576i −1.20775 1.12063i
\(789\) 0 0
\(790\) −4.32411 2.08238i −0.153845 0.0740878i
\(791\) 5.81588 16.9375i 0.206789 0.602227i
\(792\) 0 0
\(793\) −31.6439 4.76956i −1.12371 0.169372i
\(794\) −8.82855 + 6.01920i −0.313313 + 0.213614i
\(795\) 0 0
\(796\) −78.1382 + 72.5017i −2.76954 + 2.56975i
\(797\) −6.78998 8.51437i −0.240513 0.301594i 0.646894 0.762580i \(-0.276067\pi\)
−0.887408 + 0.460985i \(0.847496\pi\)
\(798\) 0 0
\(799\) 1.87759 2.35443i 0.0664244 0.0832936i
\(800\) 5.69599 + 76.0077i 0.201384 + 2.68728i
\(801\) 0 0
\(802\) −43.2734 + 74.9517i −1.52804 + 2.64664i
\(803\) −0.949271 1.64419i −0.0334990 0.0580220i
\(804\) 0 0
\(805\) −22.2856 + 0.964218i −0.785464 + 0.0339842i
\(806\) 0.107041 0.468977i 0.00377036 0.0165190i
\(807\) 0 0
\(808\) −12.6781 32.3032i −0.446013 1.13642i
\(809\) 4.61438 + 11.7572i 0.162233 + 0.413362i 0.988756 0.149541i \(-0.0477796\pi\)
−0.826523 + 0.562903i \(0.809684\pi\)
\(810\) 0 0
\(811\) 4.64550 20.3532i 0.163125 0.714699i −0.825513 0.564384i \(-0.809114\pi\)
0.988638 0.150316i \(-0.0480290\pi\)
\(812\) 8.63817 47.1598i 0.303140 1.65498i
\(813\) 0 0
\(814\) −1.57665 2.73083i −0.0552614 0.0957156i
\(815\) −19.9817 + 34.6093i −0.699928 + 1.21231i
\(816\) 0 0
\(817\) −0.249968 3.33559i −0.00874528 0.116698i
\(818\) −6.79581 + 8.52168i −0.237610 + 0.297953i
\(819\) 0 0
\(820\) 116.843 + 146.517i 4.08035 + 5.11660i
\(821\) 27.7928 25.7880i 0.969977 0.900007i −0.0250428 0.999686i \(-0.507972\pi\)
0.995020 + 0.0996794i \(0.0317817\pi\)
\(822\) 0 0
\(823\) 5.92098 4.03686i 0.206393 0.140716i −0.455713 0.890127i \(-0.650616\pi\)
0.662105 + 0.749411i \(0.269663\pi\)
\(824\) 36.3251 + 5.47513i 1.26544 + 0.190735i
\(825\) 0 0
\(826\) −23.8928 37.5368i −0.831337 1.30607i
\(827\) −12.8544 6.19037i −0.446992 0.215260i 0.196826 0.980438i \(-0.436937\pi\)
−0.643819 + 0.765178i \(0.722651\pi\)
\(828\) 0 0
\(829\) 0.196249 + 0.182092i 0.00681599 + 0.00632432i 0.683573 0.729882i \(-0.260425\pi\)
−0.676757 + 0.736206i \(0.736615\pi\)
\(830\) 3.49547 46.6438i 0.121330 1.61903i
\(831\) 0 0
\(832\) −13.1315 −0.455252
\(833\) 19.4316 7.88944i 0.673263 0.273353i
\(834\) 0 0
\(835\) 15.8445 40.3712i 0.548322 1.39710i
\(836\) 0.0920414 1.22821i 0.00318332 0.0424784i
\(837\) 0 0
\(838\) −76.2702 52.0002i −2.63471 1.79632i
\(839\) 19.5223 + 9.40144i 0.673984 + 0.324574i 0.739383 0.673285i \(-0.235117\pi\)
−0.0653982 + 0.997859i \(0.520832\pi\)
\(840\) 0 0
\(841\) 12.2755 5.91158i 0.423294 0.203848i
\(842\) 94.5485 + 14.2509i 3.25836 + 0.491118i
\(843\) 0 0
\(844\) 58.7071 8.84866i 2.02078 0.304584i
\(845\) −26.3915 + 24.4878i −0.907896 + 0.842405i
\(846\) 0 0
\(847\) −23.2741 + 17.3879i −0.799707 + 0.597455i
\(848\) 12.1868 15.2818i 0.418497 0.524778i
\(849\) 0 0
\(850\) 75.9796 + 23.4366i 2.60608 + 0.803869i
\(851\) 9.48785 16.4334i 0.325239 0.563331i
\(852\) 0 0
\(853\) 7.93423 + 34.7621i 0.271663 + 1.19023i 0.908050 + 0.418863i \(0.137571\pi\)
−0.636387 + 0.771370i \(0.719572\pi\)
\(854\) −30.3659 34.8718i −1.03910 1.19329i
\(855\) 0 0
\(856\) 17.1655 5.29486i 0.586706 0.180975i
\(857\) −6.40780 16.3268i −0.218886 0.557714i 0.778681 0.627420i \(-0.215889\pi\)
−0.997568 + 0.0697064i \(0.977794\pi\)
\(858\) 0 0
\(859\) 11.6099 3.58118i 0.396125 0.122188i −0.0902918 0.995915i \(-0.528780\pi\)
0.486416 + 0.873727i \(0.338304\pi\)
\(860\) 7.02748 30.7894i 0.239635 1.04991i
\(861\) 0 0
\(862\) −9.14088 40.0488i −0.311340 1.36407i
\(863\) −12.8507 22.2581i −0.437444 0.757676i 0.560047 0.828461i \(-0.310783\pi\)
−0.997492 + 0.0707849i \(0.977450\pi\)
\(864\) 0 0
\(865\) 8.92590 + 2.75328i 0.303490 + 0.0936142i
\(866\) −3.70393 49.4255i −0.125865 1.67955i
\(867\) 0 0
\(868\) 0.388641 0.290351i 0.0131913 0.00985516i
\(869\) 0.0413458 + 0.0518460i 0.00140256 + 0.00175875i
\(870\) 0 0
\(871\) −45.0455 + 6.78951i −1.52631 + 0.230054i
\(872\) −62.6818 + 42.7357i −2.12267 + 1.44721i
\(873\) 0 0
\(874\) 9.56767 4.60755i 0.323631 0.155853i
\(875\) 6.47889 + 54.6324i 0.219026 + 1.84691i
\(876\) 0 0
\(877\) 36.5998 + 24.9533i 1.23589 + 0.842614i 0.991882 0.127160i \(-0.0405862\pi\)
0.244005 + 0.969774i \(0.421539\pi\)
\(878\) 0.610538 + 0.566497i 0.0206047 + 0.0191183i
\(879\) 0 0
\(880\) 1.61418 4.11287i 0.0544140 0.138645i
\(881\) 24.0701 0.810943 0.405471 0.914108i \(-0.367107\pi\)
0.405471 + 0.914108i \(0.367107\pi\)
\(882\) 0 0
\(883\) −18.3146 −0.616335 −0.308167 0.951332i \(-0.599716\pi\)
−0.308167 + 0.951332i \(0.599716\pi\)
\(884\) −23.8340 + 60.7281i −0.801625 + 2.04251i
\(885\) 0 0
\(886\) 42.8851 + 39.7915i 1.44075 + 1.33682i
\(887\) −7.22206 4.92391i −0.242493 0.165329i 0.435975 0.899959i \(-0.356404\pi\)
−0.678468 + 0.734630i \(0.737356\pi\)
\(888\) 0 0
\(889\) −29.4920 46.3335i −0.989131 1.55397i
\(890\) −80.2560 + 38.6492i −2.69019 + 1.29553i
\(891\) 0 0
\(892\) −38.9353 + 26.5456i −1.30365 + 0.888813i
\(893\) −1.90383 + 0.286956i −0.0637093 + 0.00960263i
\(894\) 0 0
\(895\) 5.91355 + 7.41535i 0.197668 + 0.247868i
\(896\) 15.3356 + 13.0422i 0.512325 + 0.435710i
\(897\) 0 0
\(898\) 4.62030 + 61.6537i 0.154182 + 2.05741i
\(899\) −0.148662 0.0458561i −0.00495815 0.00152939i
\(900\) 0 0
\(901\) −3.60820 6.24959i −0.120207 0.208204i
\(902\) −0.825536 3.61691i −0.0274873 0.120430i
\(903\) 0 0
\(904\) −10.1599 + 44.5136i −0.337914 + 1.48050i
\(905\) −29.9890 + 9.25038i −0.996868 + 0.307493i
\(906\) 0 0
\(907\) −4.37900 11.1575i −0.145402 0.370479i 0.839555 0.543274i \(-0.182816\pi\)
−0.984958 + 0.172795i \(0.944720\pi\)
\(908\) −57.0827 + 17.6077i −1.89436 + 0.584332i
\(909\) 0 0
\(910\) −125.411 + 5.42609i −4.15734 + 0.179873i
\(911\) 13.0297 + 57.0869i 0.431693 + 1.89137i 0.452832 + 0.891596i \(0.350414\pi\)
−0.0211384 + 0.999777i \(0.506729\pi\)
\(912\) 0 0
\(913\) −0.323143 + 0.559701i −0.0106945 + 0.0185234i
\(914\) −19.3771 5.97706i −0.640939 0.197703i
\(915\) 0 0
\(916\) −18.0947 + 22.6901i −0.597866 + 0.749701i
\(917\) 7.08401 + 15.9814i 0.233934 + 0.527754i
\(918\) 0 0
\(919\) −40.2197 + 37.3184i −1.32673 + 1.23102i −0.373912 + 0.927464i \(0.621984\pi\)
−0.952813 + 0.303557i \(0.901826\pi\)
\(920\) 56.2369 8.47635i 1.85408 0.279457i
\(921\) 0 0
\(922\) 18.8498 + 2.84115i 0.620786 + 0.0935685i
\(923\) 57.7421 27.8071i 1.90060 0.915283i
\(924\) 0 0
\(925\) −81.8426 39.4133i −2.69097 1.29590i
\(926\) 47.0920 + 32.1068i 1.54754 + 1.05509i
\(927\) 0 0
\(928\) −2.16554 + 28.8971i −0.0710874 + 0.948595i
\(929\) −9.53961 + 24.3065i −0.312984 + 0.797471i 0.684659 + 0.728863i \(0.259951\pi\)
−0.997644 + 0.0686080i \(0.978144\pi\)
\(930\) 0 0
\(931\) −12.5379 4.75253i −0.410912 0.155758i
\(932\) −71.1136 −2.32940
\(933\) 0 0
\(934\) 7.58096 101.161i 0.248057 3.31009i
\(935\) −1.19577 1.10952i −0.0391060 0.0362851i
\(936\) 0 0
\(937\) 52.5264 + 25.2954i 1.71596 + 0.826365i 0.990404 + 0.138206i \(0.0441335\pi\)
0.725560 + 0.688159i \(0.241581\pi\)
\(938\) −55.9375 34.6939i −1.82642 1.13280i
\(939\) 0 0
\(940\) −17.9750 2.70929i −0.586279 0.0883673i
\(941\) 18.7874 12.8090i 0.612453 0.417563i −0.216975 0.976177i \(-0.569619\pi\)
0.829428 + 0.558614i \(0.188667\pi\)
\(942\) 0 0
\(943\) 16.3657 15.1851i 0.532939 0.494495i
\(944\) 33.0679 + 41.4658i 1.07627 + 1.34960i
\(945\) 0 0
\(946\) −0.389806 + 0.488801i −0.0126737 + 0.0158923i
\(947\) 1.90274 + 25.3902i 0.0618306 + 0.825072i 0.938786 + 0.344500i \(0.111952\pi\)
−0.876956 + 0.480571i \(0.840429\pi\)
\(948\) 0 0
\(949\) 32.1467 55.6796i 1.04352 1.80744i
\(950\) −25.4178 44.0249i −0.824662 1.42836i
\(951\) 0 0
\(952\) −47.1270 + 25.2605i −1.52739 + 0.818698i
\(953\) 1.63674 7.17102i 0.0530191 0.232292i −0.941475 0.337082i \(-0.890560\pi\)
0.994494 + 0.104790i \(0.0334171\pi\)
\(954\) 0 0
\(955\) 10.8420 + 27.6251i 0.350840 + 0.893926i
\(956\) 15.6442 + 39.8609i 0.505971 + 1.28919i
\(957\) 0 0
\(958\) 12.5310 54.9017i 0.404857 1.77379i
\(959\) −23.8662 + 32.7360i −0.770681 + 1.05710i
\(960\) 0 0
\(961\) 15.4992 + 26.8454i 0.499975 + 0.865981i
\(962\) 53.3925 92.4784i 1.72144 2.98162i
\(963\) 0 0
\(964\) 4.23374 + 56.4953i 0.136359 + 1.81959i
\(965\) −31.2404 + 39.1742i −1.00566 + 1.26106i
\(966\) 0 0
\(967\) −30.5855 38.3530i −0.983564 1.23335i −0.972378 0.233412i \(-0.925011\pi\)
−0.0111857 0.999937i \(-0.503561\pi\)
\(968\) 54.2976 50.3808i 1.74519 1.61930i
\(969\) 0 0
\(970\) −41.2857 + 28.1481i −1.32560 + 0.903781i
\(971\) −13.7082 2.06618i −0.439916 0.0663067i −0.0746501 0.997210i \(-0.523784\pi\)
−0.365266 + 0.930903i \(0.619022\pi\)
\(972\) 0 0
\(973\) 10.6057 10.7303i 0.340003 0.343997i
\(974\) −22.1902 10.6862i −0.711019 0.342409i
\(975\) 0 0
\(976\) 40.4026 + 37.4881i 1.29326 + 1.19997i
\(977\) −0.782597 + 10.4430i −0.0250375 + 0.334102i 0.970593 + 0.240725i \(0.0773852\pi\)
−0.995631 + 0.0933770i \(0.970234\pi\)
\(978\) 0 0
\(979\) 1.23079 0.0393361
\(980\) −99.8909 77.7693i −3.19090 2.48425i
\(981\) 0 0
\(982\) −36.2799 + 92.4396i −1.15774 + 2.94987i
\(983\) 2.61102 34.8417i 0.0832786 1.11128i −0.786420 0.617693i \(-0.788068\pi\)
0.869698 0.493584i \(-0.164313\pi\)
\(984\) 0 0
\(985\) 32.3573 + 22.0609i 1.03099 + 0.702918i
\(986\) 27.2358 + 13.1161i 0.867365 + 0.417701i
\(987\) 0 0
\(988\) 37.5788 18.0970i 1.19554 0.575743i
\(989\) −3.72027 0.560741i −0.118298 0.0178305i
\(990\) 0 0
\(991\) −36.7994 + 5.54662i −1.16897 + 0.176194i −0.704705 0.709501i \(-0.748921\pi\)
−0.464268 + 0.885695i \(0.653683\pi\)
\(992\) −0.214942 + 0.199437i −0.00682442 + 0.00633213i
\(993\) 0 0
\(994\) 89.5874 + 23.4450i 2.84154 + 0.743631i
\(995\) 56.2755 70.5673i 1.78405 2.23713i
\(996\) 0 0
\(997\) 17.8986 + 5.52100i 0.566856 + 0.174852i 0.564919 0.825146i \(-0.308907\pi\)
0.00193654 + 0.999998i \(0.499384\pi\)
\(998\) −5.81640 + 10.0743i −0.184115 + 0.318897i
\(999\) 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.e.46.5 60
3.2 odd 2 147.2.m.b.46.1 yes 60
49.16 even 21 inner 441.2.bb.e.163.5 60
147.53 odd 42 7203.2.a.n.1.1 30
147.65 odd 42 147.2.m.b.16.1 60
147.143 even 42 7203.2.a.m.1.1 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.m.b.16.1 60 147.65 odd 42
147.2.m.b.46.1 yes 60 3.2 odd 2
441.2.bb.e.46.5 60 1.1 even 1 trivial
441.2.bb.e.163.5 60 49.16 even 21 inner
7203.2.a.m.1.1 30 147.143 even 42
7203.2.a.n.1.1 30 147.53 odd 42