Properties

Label 950.2.u.f.549.4
Level $950$
Weight $2$
Character 950.549
Analytic conductor $7.586$
Analytic rank $0$
Dimension $24$
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] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 549.4
Character \(\chi\) \(=\) 950.549
Dual form 950.2.u.f.199.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.984808 + 0.173648i) q^{2} +(1.68231 - 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(0.840422 - 0.485218i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +O(q^{10})\) \(q+(0.984808 + 0.173648i) q^{2} +(1.68231 - 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(0.840422 - 0.485218i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +(0.280827 - 0.486406i) q^{11} +(2.26658 - 1.30861i) q^{12} +(0.293901 + 0.350258i) q^{13} +(0.911911 - 0.331909i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.387080 + 0.0682527i) q^{17} -3.84982i q^{18} +(1.58943 - 4.05878i) q^{19} +(0.441039 - 2.50125i) q^{21} +(0.361024 - 0.430251i) q^{22} +(-1.79231 + 4.92432i) q^{23} +(2.45938 - 0.895141i) q^{24} +(0.228615 + 0.395972i) q^{26} +(-1.92618 - 1.11208i) q^{27} +(0.955692 - 0.168514i) q^{28} +(0.411474 + 2.33359i) q^{29} +(-5.44104 - 9.42416i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-0.502759 - 1.38132i) q^{33} +(0.369347 + 0.134431i) q^{34} +(0.668514 - 3.79133i) q^{36} -5.14885i q^{37} +(2.27009 - 3.72112i) q^{38} +1.19667 q^{39} +(6.14611 + 5.15720i) q^{41} +(0.868676 - 2.38667i) q^{42} +(3.49906 + 9.61359i) q^{43} +(0.430251 - 0.361024i) q^{44} +(-2.62018 + 4.53828i) q^{46} +(-12.0877 + 2.13139i) q^{47} +(2.57745 - 0.454475i) q^{48} +(-3.02913 + 5.24660i) q^{49} +(0.788030 - 0.661236i) q^{51} +(0.156382 + 0.429655i) q^{52} +(1.55164 - 4.26309i) q^{53} +(-1.70381 - 1.42967i) q^{54} +0.970436 q^{56} +(-5.46354 - 10.0148i) q^{57} +2.36959i q^{58} +(-0.759597 + 4.30789i) q^{59} +(4.02481 + 1.46491i) q^{61} +(-3.72189 - 10.2258i) q^{62} +(-2.40146 - 2.86194i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.255257 - 1.44764i) q^{66} +(-12.0001 + 2.11595i) q^{67} +(0.340392 + 0.196526i) q^{68} +(6.85757 + 11.8777i) q^{69} +(6.85757 - 2.49595i) q^{71} +(1.31672 - 3.61765i) q^{72} +(-8.96047 + 10.6787i) q^{73} +(0.894088 - 5.07062i) q^{74} +(2.88176 - 3.27039i) q^{76} -0.545048i q^{77} +(1.17849 + 0.207799i) q^{78} +(0.730080 + 0.612610i) q^{79} +(5.38288 - 1.95921i) q^{81} +(5.15720 + 6.14611i) q^{82} +(9.76080 - 5.63540i) q^{83} +(1.26992 - 2.19957i) q^{84} +(1.77652 + 10.0751i) q^{86} +(5.37084 + 3.10086i) q^{87} +(0.486406 - 0.280827i) q^{88} +(-2.69822 + 2.26408i) q^{89} +(0.416952 + 0.151758i) q^{91} +(-3.36844 + 4.01435i) q^{92} +(-28.0481 - 4.94563i) q^{93} -12.2742 q^{94} +2.61722 q^{96} +(7.10973 + 1.25364i) q^{97} +(-3.89417 + 4.64089i) q^{98} +(-2.03186 - 0.739538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 + 0.173648i 0.696364 + 0.122788i
\(3\) 1.68231 2.00490i 0.971285 1.15753i −0.0162084 0.999869i \(-0.505160\pi\)
0.987493 0.157663i \(-0.0503960\pi\)
\(4\) 0.939693 + 0.342020i 0.469846 + 0.171010i
\(5\) 0 0
\(6\) 2.00490 1.68231i 0.818499 0.686802i
\(7\) 0.840422 0.485218i 0.317650 0.183395i −0.332695 0.943035i \(-0.607958\pi\)
0.650344 + 0.759639i \(0.274625\pi\)
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) −0.668514 3.79133i −0.222838 1.26378i
\(10\) 0 0
\(11\) 0.280827 0.486406i 0.0846724 0.146657i −0.820579 0.571533i \(-0.806349\pi\)
0.905252 + 0.424876i \(0.139682\pi\)
\(12\) 2.26658 1.30861i 0.654304 0.377763i
\(13\) 0.293901 + 0.350258i 0.0815135 + 0.0971440i 0.805260 0.592922i \(-0.202026\pi\)
−0.723746 + 0.690066i \(0.757581\pi\)
\(14\) 0.911911 0.331909i 0.243719 0.0887063i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 0.387080 + 0.0682527i 0.0938807 + 0.0165537i 0.220391 0.975412i \(-0.429267\pi\)
−0.126510 + 0.991965i \(0.540378\pi\)
\(18\) 3.84982i 0.907411i
\(19\) 1.58943 4.05878i 0.364641 0.931148i
\(20\) 0 0
\(21\) 0.441039 2.50125i 0.0962425 0.545818i
\(22\) 0.361024 0.430251i 0.0769705 0.0917299i
\(23\) −1.79231 + 4.92432i −0.373722 + 1.02679i 0.600188 + 0.799859i \(0.295092\pi\)
−0.973910 + 0.226934i \(0.927130\pi\)
\(24\) 2.45938 0.895141i 0.502019 0.182720i
\(25\) 0 0
\(26\) 0.228615 + 0.395972i 0.0448350 + 0.0776565i
\(27\) −1.92618 1.11208i −0.370694 0.214020i
\(28\) 0.955692 0.168514i 0.180609 0.0318462i
\(29\) 0.411474 + 2.33359i 0.0764088 + 0.433336i 0.998882 + 0.0472746i \(0.0150536\pi\)
−0.922473 + 0.386061i \(0.873835\pi\)
\(30\) 0 0
\(31\) −5.44104 9.42416i −0.977239 1.69263i −0.672338 0.740244i \(-0.734710\pi\)
−0.304901 0.952384i \(-0.598624\pi\)
\(32\) 0.642788 + 0.766044i 0.113630 + 0.135419i
\(33\) −0.502759 1.38132i −0.0875191 0.240457i
\(34\) 0.369347 + 0.134431i 0.0633426 + 0.0230548i
\(35\) 0 0
\(36\) 0.668514 3.79133i 0.111419 0.631889i
\(37\) 5.14885i 0.846465i −0.906021 0.423232i \(-0.860895\pi\)
0.906021 0.423232i \(-0.139105\pi\)
\(38\) 2.27009 3.72112i 0.368257 0.603645i
\(39\) 1.19667 0.191620
\(40\) 0 0
\(41\) 6.14611 + 5.15720i 0.959862 + 0.805420i 0.980931 0.194358i \(-0.0622625\pi\)
−0.0210689 + 0.999778i \(0.506707\pi\)
\(42\) 0.868676 2.38667i 0.134040 0.368271i
\(43\) 3.49906 + 9.61359i 0.533602 + 1.46606i 0.854755 + 0.519031i \(0.173707\pi\)
−0.321154 + 0.947027i \(0.604071\pi\)
\(44\) 0.430251 0.361024i 0.0648628 0.0544264i
\(45\) 0 0
\(46\) −2.62018 + 4.53828i −0.386324 + 0.669133i
\(47\) −12.0877 + 2.13139i −1.76318 + 0.310896i −0.958982 0.283468i \(-0.908515\pi\)
−0.804196 + 0.594364i \(0.797404\pi\)
\(48\) 2.57745 0.454475i 0.372024 0.0655978i
\(49\) −3.02913 + 5.24660i −0.432732 + 0.749515i
\(50\) 0 0
\(51\) 0.788030 0.661236i 0.110346 0.0925915i
\(52\) 0.156382 + 0.429655i 0.0216862 + 0.0595824i
\(53\) 1.55164 4.26309i 0.213134 0.585581i −0.786347 0.617785i \(-0.788030\pi\)
0.999481 + 0.0322038i \(0.0102526\pi\)
\(54\) −1.70381 1.42967i −0.231859 0.194553i
\(55\) 0 0
\(56\) 0.970436 0.129680
\(57\) −5.46354 10.0148i −0.723663 1.32649i
\(58\) 2.36959i 0.311142i
\(59\) −0.759597 + 4.30789i −0.0988911 + 0.560839i 0.894594 + 0.446879i \(0.147465\pi\)
−0.993485 + 0.113960i \(0.963646\pi\)
\(60\) 0 0
\(61\) 4.02481 + 1.46491i 0.515324 + 0.187562i 0.586573 0.809896i \(-0.300477\pi\)
−0.0712499 + 0.997458i \(0.522699\pi\)
\(62\) −3.72189 10.2258i −0.472680 1.29868i
\(63\) −2.40146 2.86194i −0.302555 0.360571i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −0.255257 1.44764i −0.0314200 0.178192i
\(67\) −12.0001 + 2.11595i −1.46605 + 0.258504i −0.848989 0.528411i \(-0.822788\pi\)
−0.617061 + 0.786915i \(0.711677\pi\)
\(68\) 0.340392 + 0.196526i 0.0412787 + 0.0238322i
\(69\) 6.85757 + 11.8777i 0.825555 + 1.42990i
\(70\) 0 0
\(71\) 6.85757 2.49595i 0.813844 0.296215i 0.0986333 0.995124i \(-0.468553\pi\)
0.715211 + 0.698909i \(0.246331\pi\)
\(72\) 1.31672 3.61765i 0.155177 0.426344i
\(73\) −8.96047 + 10.6787i −1.04874 + 1.24984i −0.0813181 + 0.996688i \(0.525913\pi\)
−0.967426 + 0.253156i \(0.918531\pi\)
\(74\) 0.894088 5.07062i 0.103936 0.589448i
\(75\) 0 0
\(76\) 2.88176 3.27039i 0.330561 0.375139i
\(77\) 0.545048i 0.0621140i
\(78\) 1.17849 + 0.207799i 0.133437 + 0.0235286i
\(79\) 0.730080 + 0.612610i 0.0821404 + 0.0689240i 0.682933 0.730481i \(-0.260704\pi\)
−0.600793 + 0.799405i \(0.705148\pi\)
\(80\) 0 0
\(81\) 5.38288 1.95921i 0.598098 0.217690i
\(82\) 5.15720 + 6.14611i 0.569518 + 0.678725i
\(83\) 9.76080 5.63540i 1.07139 0.618566i 0.142827 0.989748i \(-0.454381\pi\)
0.928560 + 0.371182i \(0.121047\pi\)
\(84\) 1.26992 2.19957i 0.138560 0.239992i
\(85\) 0 0
\(86\) 1.77652 + 10.0751i 0.191567 + 1.08643i
\(87\) 5.37084 + 3.10086i 0.575815 + 0.332447i
\(88\) 0.486406 0.280827i 0.0518511 0.0299362i
\(89\) −2.69822 + 2.26408i −0.286011 + 0.239992i −0.774493 0.632582i \(-0.781995\pi\)
0.488482 + 0.872574i \(0.337551\pi\)
\(90\) 0 0
\(91\) 0.416952 + 0.151758i 0.0437085 + 0.0159086i
\(92\) −3.36844 + 4.01435i −0.351184 + 0.418524i
\(93\) −28.0481 4.94563i −2.90845 0.512838i
\(94\) −12.2742 −1.26599
\(95\) 0 0
\(96\) 2.61722 0.267119
\(97\) 7.10973 + 1.25364i 0.721883 + 0.127288i 0.522506 0.852635i \(-0.324997\pi\)
0.199377 + 0.979923i \(0.436108\pi\)
\(98\) −3.89417 + 4.64089i −0.393371 + 0.468801i
\(99\) −2.03186 0.739538i −0.204210 0.0743264i
\(100\) 0 0
\(101\) 9.72875 8.16339i 0.968046 0.812287i −0.0141968 0.999899i \(-0.504519\pi\)
0.982243 + 0.187612i \(0.0600747\pi\)
\(102\) 0.890881 0.514350i 0.0882103 0.0509283i
\(103\) −9.93425 5.73554i −0.978851 0.565140i −0.0769276 0.997037i \(-0.524511\pi\)
−0.901923 + 0.431897i \(0.857844\pi\)
\(104\) 0.0793970 + 0.450283i 0.00778552 + 0.0441539i
\(105\) 0 0
\(106\) 2.26834 3.92889i 0.220321 0.381607i
\(107\) −10.8549 + 6.26711i −1.04939 + 0.605864i −0.922478 0.386050i \(-0.873839\pi\)
−0.126909 + 0.991914i \(0.540506\pi\)
\(108\) −1.42967 1.70381i −0.137570 0.163949i
\(109\) −5.34478 + 1.94534i −0.511937 + 0.186330i −0.585055 0.810993i \(-0.698927\pi\)
0.0731182 + 0.997323i \(0.476705\pi\)
\(110\) 0 0
\(111\) −10.3229 8.66198i −0.979810 0.822158i
\(112\) 0.955692 + 0.168514i 0.0903045 + 0.0159231i
\(113\) 4.13698i 0.389174i 0.980885 + 0.194587i \(0.0623367\pi\)
−0.980885 + 0.194587i \(0.937663\pi\)
\(114\) −3.64148 10.8114i −0.341056 1.01258i
\(115\) 0 0
\(116\) −0.411474 + 2.33359i −0.0382044 + 0.216668i
\(117\) 1.13147 1.34843i 0.104604 0.124662i
\(118\) −1.49611 + 4.11054i −0.137728 + 0.378406i
\(119\) 0.358428 0.130457i 0.0328570 0.0119590i
\(120\) 0 0
\(121\) 5.34227 + 9.25309i 0.485661 + 0.841190i
\(122\) 3.70928 + 2.14155i 0.335823 + 0.193887i
\(123\) 20.6794 3.64633i 1.86460 0.328779i
\(124\) −1.88965 10.7168i −0.169696 0.962393i
\(125\) 0 0
\(126\) −1.86800 3.23547i −0.166415 0.288239i
\(127\) 1.30258 + 1.55236i 0.115585 + 0.137749i 0.820735 0.571310i \(-0.193564\pi\)
−0.705149 + 0.709059i \(0.749120\pi\)
\(128\) 0.342020 + 0.939693i 0.0302306 + 0.0830579i
\(129\) 25.1608 + 9.15780i 2.21529 + 0.806299i
\(130\) 0 0
\(131\) −1.26179 + 7.15598i −0.110243 + 0.625221i 0.878753 + 0.477278i \(0.158376\pi\)
−0.988996 + 0.147943i \(0.952735\pi\)
\(132\) 1.46997i 0.127944i
\(133\) −0.633597 4.18231i −0.0549398 0.362652i
\(134\) −12.1853 −1.05265
\(135\) 0 0
\(136\) 0.301095 + 0.252649i 0.0258187 + 0.0216644i
\(137\) −2.59205 + 7.12159i −0.221454 + 0.608439i −0.999812 0.0193814i \(-0.993830\pi\)
0.778359 + 0.627820i \(0.216053\pi\)
\(138\) 4.69086 + 12.8880i 0.399312 + 1.09710i
\(139\) 8.72724 7.32303i 0.740235 0.621131i −0.192666 0.981264i \(-0.561713\pi\)
0.932901 + 0.360133i \(0.117269\pi\)
\(140\) 0 0
\(141\) −16.0621 + 27.8204i −1.35268 + 2.34290i
\(142\) 7.18681 1.26723i 0.603103 0.106343i
\(143\) 0.252903 0.0445936i 0.0211488 0.00372910i
\(144\) 1.92491 3.33404i 0.160409 0.277837i
\(145\) 0 0
\(146\) −10.6787 + 8.96047i −0.883773 + 0.741574i
\(147\) 5.42299 + 14.8995i 0.447281 + 1.22889i
\(148\) 1.76101 4.83833i 0.144754 0.397708i
\(149\) 0.00665635 + 0.00558534i 0.000545309 + 0.000457569i 0.643060 0.765816i \(-0.277664\pi\)
−0.642515 + 0.766273i \(0.722109\pi\)
\(150\) 0 0
\(151\) −15.3824 −1.25180 −0.625901 0.779902i \(-0.715269\pi\)
−0.625901 + 0.779902i \(0.715269\pi\)
\(152\) 3.40588 2.72029i 0.276253 0.220645i
\(153\) 1.51318i 0.122333i
\(154\) 0.0946467 0.536768i 0.00762684 0.0432540i
\(155\) 0 0
\(156\) 1.12450 + 0.409284i 0.0900320 + 0.0327690i
\(157\) 6.17365 + 16.9620i 0.492711 + 1.35371i 0.898190 + 0.439607i \(0.144882\pi\)
−0.405479 + 0.914104i \(0.632895\pi\)
\(158\) 0.612610 + 0.730080i 0.0487366 + 0.0580821i
\(159\) −5.93675 10.2827i −0.470815 0.815475i
\(160\) 0 0
\(161\) 0.883075 + 5.00817i 0.0695961 + 0.394699i
\(162\) 5.64132 0.994716i 0.443224 0.0781523i
\(163\) 4.25257 + 2.45522i 0.333087 + 0.192308i 0.657211 0.753707i \(-0.271736\pi\)
−0.324124 + 0.946015i \(0.605069\pi\)
\(164\) 4.01159 + 6.94828i 0.313253 + 0.542569i
\(165\) 0 0
\(166\) 10.5911 3.85484i 0.822028 0.299194i
\(167\) 5.69511 15.6472i 0.440701 1.21082i −0.498331 0.866987i \(-0.666054\pi\)
0.939032 0.343829i \(-0.111724\pi\)
\(168\) 1.63258 1.94563i 0.125956 0.150109i
\(169\) 2.22112 12.5966i 0.170856 0.968971i
\(170\) 0 0
\(171\) −16.4507 3.31272i −1.25802 0.253330i
\(172\) 10.2306i 0.780073i
\(173\) 11.6116 + 2.04745i 0.882817 + 0.155664i 0.596637 0.802512i \(-0.296503\pi\)
0.286180 + 0.958176i \(0.407615\pi\)
\(174\) 4.75079 + 3.98639i 0.360156 + 0.302207i
\(175\) 0 0
\(176\) 0.527781 0.192097i 0.0397830 0.0144798i
\(177\) 7.35902 + 8.77014i 0.553138 + 0.659204i
\(178\) −3.05038 + 1.76114i −0.228636 + 0.132003i
\(179\) −7.87873 + 13.6464i −0.588884 + 1.01998i 0.405495 + 0.914097i \(0.367099\pi\)
−0.994379 + 0.105879i \(0.966234\pi\)
\(180\) 0 0
\(181\) −2.58243 14.6457i −0.191951 1.08861i −0.916695 0.399588i \(-0.869153\pi\)
0.724744 0.689018i \(-0.241958\pi\)
\(182\) 0.384265 + 0.221856i 0.0284836 + 0.0164450i
\(183\) 9.70799 5.60491i 0.717635 0.414327i
\(184\) −4.01435 + 3.36844i −0.295941 + 0.248324i
\(185\) 0 0
\(186\) −26.7631 9.74099i −1.96237 0.714244i
\(187\) 0.141901 0.169111i 0.0103768 0.0123666i
\(188\) −12.0877 2.13139i −0.881589 0.155448i
\(189\) −2.15841 −0.157001
\(190\) 0 0
\(191\) 26.1567 1.89263 0.946315 0.323247i \(-0.104774\pi\)
0.946315 + 0.323247i \(0.104774\pi\)
\(192\) 2.57745 + 0.454475i 0.186012 + 0.0327989i
\(193\) −7.86704 + 9.37557i −0.566282 + 0.674868i −0.970863 0.239634i \(-0.922973\pi\)
0.404582 + 0.914502i \(0.367417\pi\)
\(194\) 6.78402 + 2.46918i 0.487064 + 0.177277i
\(195\) 0 0
\(196\) −4.64089 + 3.89417i −0.331492 + 0.278155i
\(197\) 0.271540 0.156773i 0.0193464 0.0111696i −0.490296 0.871556i \(-0.663111\pi\)
0.509642 + 0.860387i \(0.329778\pi\)
\(198\) −1.87258 1.08113i −0.133078 0.0768327i
\(199\) −3.72685 21.1360i −0.264189 1.49829i −0.771334 0.636430i \(-0.780410\pi\)
0.507145 0.861861i \(-0.330701\pi\)
\(200\) 0 0
\(201\) −15.9457 + 27.6188i −1.12473 + 1.94808i
\(202\) 10.9985 6.34999i 0.773852 0.446784i
\(203\) 1.47811 + 1.76154i 0.103743 + 0.123636i
\(204\) 0.966662 0.351836i 0.0676799 0.0246335i
\(205\) 0 0
\(206\) −8.78736 7.37347i −0.612244 0.513734i
\(207\) 19.8679 + 3.50325i 1.38092 + 0.243493i
\(208\) 0.457229i 0.0317031i
\(209\) −1.52786 1.91292i −0.105684 0.132320i
\(210\) 0 0
\(211\) 2.27645 12.9104i 0.156717 0.888788i −0.800482 0.599357i \(-0.795423\pi\)
0.957199 0.289431i \(-0.0934660\pi\)
\(212\) 2.91613 3.47530i 0.200280 0.238685i
\(213\) 6.53245 17.9477i 0.447596 1.22976i
\(214\) −11.7783 + 4.28695i −0.805148 + 0.293050i
\(215\) 0 0
\(216\) −1.11208 1.92618i −0.0756676 0.131060i
\(217\) −9.14554 5.28018i −0.620839 0.358442i
\(218\) −5.60139 + 0.987675i −0.379374 + 0.0668938i
\(219\) 6.33539 + 35.9298i 0.428106 + 2.42791i
\(220\) 0 0
\(221\) 0.0898573 + 0.155637i 0.00604445 + 0.0104693i
\(222\) −8.66198 10.3229i −0.581354 0.692830i
\(223\) 7.50031 + 20.6069i 0.502258 + 1.37994i 0.889065 + 0.457782i \(0.151356\pi\)
−0.386806 + 0.922161i \(0.626422\pi\)
\(224\) 0.911911 + 0.331909i 0.0609296 + 0.0221766i
\(225\) 0 0
\(226\) −0.718379 + 4.07413i −0.0477859 + 0.271007i
\(227\) 3.93628i 0.261260i −0.991431 0.130630i \(-0.958300\pi\)
0.991431 0.130630i \(-0.0417000\pi\)
\(228\) −1.70878 11.2795i −0.113167 0.747002i
\(229\) −12.4712 −0.824122 −0.412061 0.911156i \(-0.635191\pi\)
−0.412061 + 0.911156i \(0.635191\pi\)
\(230\) 0 0
\(231\) −1.09277 0.916943i −0.0718990 0.0603304i
\(232\) −0.810446 + 2.22668i −0.0532084 + 0.146189i
\(233\) 4.58978 + 12.6103i 0.300687 + 0.826130i 0.994381 + 0.105860i \(0.0337597\pi\)
−0.693694 + 0.720270i \(0.744018\pi\)
\(234\) 1.34843 1.13147i 0.0881496 0.0739663i
\(235\) 0 0
\(236\) −2.18717 + 3.78829i −0.142373 + 0.246597i
\(237\) 2.45645 0.433138i 0.159563 0.0281353i
\(238\) 0.375636 0.0662348i 0.0243489 0.00429336i
\(239\) 0.766043 1.32682i 0.0495512 0.0858252i −0.840186 0.542298i \(-0.817554\pi\)
0.889737 + 0.456473i \(0.150888\pi\)
\(240\) 0 0
\(241\) −10.7084 + 8.98543i −0.689790 + 0.578802i −0.918849 0.394610i \(-0.870880\pi\)
0.229059 + 0.973413i \(0.426435\pi\)
\(242\) 3.65433 + 10.0402i 0.234909 + 0.645408i
\(243\) 7.40980 20.3583i 0.475339 1.30598i
\(244\) 3.28105 + 2.75313i 0.210048 + 0.176251i
\(245\) 0 0
\(246\) 20.9984 1.33881
\(247\) 1.88876 0.636169i 0.120179 0.0404784i
\(248\) 10.8821i 0.691013i
\(249\) 5.12230 29.0500i 0.324612 1.84097i
\(250\) 0 0
\(251\) −15.7226 5.72255i −0.992400 0.361204i −0.205751 0.978604i \(-0.565964\pi\)
−0.786649 + 0.617400i \(0.788186\pi\)
\(252\) −1.27779 3.51069i −0.0804931 0.221153i
\(253\) 1.89189 + 2.25467i 0.118942 + 0.141750i
\(254\) 1.01323 + 1.75496i 0.0635756 + 0.110116i
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) −5.91343 + 1.04270i −0.368870 + 0.0650417i −0.355011 0.934862i \(-0.615523\pi\)
−0.0138590 + 0.999904i \(0.504412\pi\)
\(258\) 23.1884 + 13.3878i 1.44364 + 0.833488i
\(259\) −2.49831 4.32720i −0.155238 0.268879i
\(260\) 0 0
\(261\) 8.57233 3.12007i 0.530614 0.193128i
\(262\) −2.48525 + 6.82816i −0.153539 + 0.421845i
\(263\) −4.05502 + 4.83259i −0.250043 + 0.297990i −0.876437 0.481517i \(-0.840086\pi\)
0.626393 + 0.779507i \(0.284530\pi\)
\(264\) 0.255257 1.44764i 0.0157100 0.0890958i
\(265\) 0 0
\(266\) 0.102280 4.22879i 0.00627116 0.259284i
\(267\) 9.21857i 0.564167i
\(268\) −12.0001 2.11595i −0.733025 0.129252i
\(269\) 16.7593 + 14.0627i 1.02183 + 0.857418i 0.989856 0.142071i \(-0.0453762\pi\)
0.0319740 + 0.999489i \(0.489821\pi\)
\(270\) 0 0
\(271\) −9.43077 + 3.43252i −0.572879 + 0.208511i −0.612182 0.790717i \(-0.709708\pi\)
0.0393039 + 0.999227i \(0.487486\pi\)
\(272\) 0.252649 + 0.301095i 0.0153191 + 0.0182566i
\(273\) 1.00571 0.580644i 0.0608681 0.0351422i
\(274\) −3.78932 + 6.56329i −0.228921 + 0.396503i
\(275\) 0 0
\(276\) 2.38161 + 13.5068i 0.143356 + 0.813013i
\(277\) −14.7281 8.50328i −0.884927 0.510913i −0.0126472 0.999920i \(-0.504026\pi\)
−0.872280 + 0.489007i \(0.837359\pi\)
\(278\) 9.86629 5.69630i 0.591741 0.341642i
\(279\) −32.0927 + 26.9290i −1.92134 + 1.61220i
\(280\) 0 0
\(281\) 0.993565 + 0.361628i 0.0592711 + 0.0215729i 0.371486 0.928439i \(-0.378849\pi\)
−0.312214 + 0.950012i \(0.601071\pi\)
\(282\) −20.6491 + 24.6086i −1.22963 + 1.46542i
\(283\) −23.2379 4.09746i −1.38135 0.243569i −0.566891 0.823793i \(-0.691854\pi\)
−0.814457 + 0.580224i \(0.802965\pi\)
\(284\) 7.29768 0.433037
\(285\) 0 0
\(286\) 0.256804 0.0151852
\(287\) 7.66769 + 1.35202i 0.452610 + 0.0798073i
\(288\) 2.47462 2.94913i 0.145818 0.173779i
\(289\) −15.8296 5.76150i −0.931153 0.338912i
\(290\) 0 0
\(291\) 14.4742 12.1453i 0.848494 0.711971i
\(292\) −12.0724 + 6.97001i −0.706484 + 0.407889i
\(293\) −19.2967 11.1409i −1.12732 0.650860i −0.184063 0.982915i \(-0.558925\pi\)
−0.943260 + 0.332054i \(0.892258\pi\)
\(294\) 2.75332 + 15.6149i 0.160577 + 0.910678i
\(295\) 0 0
\(296\) 2.57442 4.45903i 0.149635 0.259176i
\(297\) −1.08185 + 0.624605i −0.0627751 + 0.0362432i
\(298\) 0.00558534 + 0.00665635i 0.000323550 + 0.000385592i
\(299\) −2.25154 + 0.819495i −0.130210 + 0.0473926i
\(300\) 0 0
\(301\) 7.60537 + 6.38166i 0.438366 + 0.367833i
\(302\) −15.1487 2.67113i −0.871710 0.153706i
\(303\) 33.2386i 1.90951i
\(304\) 3.82651 2.08754i 0.219465 0.119728i
\(305\) 0 0
\(306\) 0.262760 1.49019i 0.0150210 0.0851884i
\(307\) 17.5713 20.9406i 1.00284 1.19514i 0.0221182 0.999755i \(-0.492959\pi\)
0.980726 0.195388i \(-0.0625966\pi\)
\(308\) 0.186418 0.512178i 0.0106221 0.0291840i
\(309\) −28.2117 + 10.2682i −1.60491 + 0.584139i
\(310\) 0 0
\(311\) −15.6908 27.1772i −0.889743 1.54108i −0.840179 0.542309i \(-0.817550\pi\)
−0.0495638 0.998771i \(-0.515783\pi\)
\(312\) 1.03634 + 0.598334i 0.0586715 + 0.0338740i
\(313\) −1.13336 + 0.199842i −0.0640613 + 0.0112957i −0.205587 0.978639i \(-0.565910\pi\)
0.141526 + 0.989935i \(0.454799\pi\)
\(314\) 3.13444 + 17.7763i 0.176887 + 1.00318i
\(315\) 0 0
\(316\) 0.476526 + 0.825367i 0.0268067 + 0.0464305i
\(317\) −13.2783 15.8245i −0.745784 0.888791i 0.251077 0.967967i \(-0.419215\pi\)
−0.996861 + 0.0791766i \(0.974771\pi\)
\(318\) −4.06097 11.1574i −0.227728 0.625678i
\(319\) 1.25062 + 0.455190i 0.0700214 + 0.0254857i
\(320\) 0 0
\(321\) −5.69648 + 32.3064i −0.317947 + 1.80317i
\(322\) 5.08543i 0.283400i
\(323\) 0.892261 1.46259i 0.0496467 0.0813807i
\(324\) 5.72834 0.318241
\(325\) 0 0
\(326\) 3.76162 + 3.15637i 0.208337 + 0.174815i
\(327\) −5.09138 + 13.9884i −0.281554 + 0.773563i
\(328\) 2.74409 + 7.53932i 0.151517 + 0.416290i
\(329\) −9.12461 + 7.65645i −0.503056 + 0.422114i
\(330\) 0 0
\(331\) 5.97822 10.3546i 0.328593 0.569139i −0.653640 0.756806i \(-0.726759\pi\)
0.982233 + 0.187666i \(0.0600923\pi\)
\(332\) 11.0996 1.95715i 0.609168 0.107413i
\(333\) −19.5210 + 3.44208i −1.06974 + 0.188625i
\(334\) 8.32569 14.4205i 0.455562 0.789056i
\(335\) 0 0
\(336\) 1.94563 1.63258i 0.106143 0.0890644i
\(337\) 5.65212 + 15.5291i 0.307891 + 0.845923i 0.993067 + 0.117546i \(0.0375028\pi\)
−0.685177 + 0.728377i \(0.740275\pi\)
\(338\) 4.37476 12.0196i 0.237956 0.653778i
\(339\) 8.29425 + 6.95970i 0.450482 + 0.377999i
\(340\) 0 0
\(341\) −6.11195 −0.330981
\(342\) −15.6256 6.11904i −0.844934 0.330880i
\(343\) 12.6722i 0.684234i
\(344\) −1.77652 + 10.0751i −0.0957835 + 0.543215i
\(345\) 0 0
\(346\) 11.0797 + 4.03268i 0.595648 + 0.216798i
\(347\) 1.24681 + 3.42558i 0.0669321 + 0.183895i 0.968649 0.248432i \(-0.0799151\pi\)
−0.901717 + 0.432326i \(0.857693\pi\)
\(348\) 3.98639 + 4.75079i 0.213693 + 0.254669i
\(349\) −9.09715 15.7567i −0.486959 0.843438i 0.512928 0.858431i \(-0.328561\pi\)
−0.999888 + 0.0149933i \(0.995227\pi\)
\(350\) 0 0
\(351\) −0.176592 1.00150i −0.00942579 0.0534563i
\(352\) 0.553121 0.0975301i 0.0294814 0.00519837i
\(353\) 5.60251 + 3.23461i 0.298191 + 0.172161i 0.641630 0.767014i \(-0.278258\pi\)
−0.343439 + 0.939175i \(0.611592\pi\)
\(354\) 5.72430 + 9.91478i 0.304243 + 0.526965i
\(355\) 0 0
\(356\) −3.30986 + 1.20469i −0.175422 + 0.0638485i
\(357\) 0.341434 0.938083i 0.0180706 0.0496486i
\(358\) −10.1287 + 12.0709i −0.535318 + 0.637968i
\(359\) 3.90895 22.1687i 0.206306 1.17002i −0.689065 0.724700i \(-0.741978\pi\)
0.895371 0.445321i \(-0.146910\pi\)
\(360\) 0 0
\(361\) −13.9474 12.9023i −0.734073 0.679070i
\(362\) 14.8716i 0.781636i
\(363\) 27.5389 + 4.85586i 1.44542 + 0.254866i
\(364\) 0.339903 + 0.285212i 0.0178157 + 0.0149492i
\(365\) 0 0
\(366\) 10.5338 3.83398i 0.550610 0.200406i
\(367\) −1.73931 2.07282i −0.0907910 0.108200i 0.718736 0.695283i \(-0.244721\pi\)
−0.809527 + 0.587082i \(0.800276\pi\)
\(368\) −4.53828 + 2.62018i −0.236574 + 0.136586i
\(369\) 15.4439 26.7496i 0.803978 1.39253i
\(370\) 0 0
\(371\) −0.764497 4.33568i −0.0396907 0.225097i
\(372\) −24.6651 14.2404i −1.27882 0.738329i
\(373\) −17.0106 + 9.82107i −0.880775 + 0.508516i −0.870914 0.491436i \(-0.836472\pi\)
−0.00986133 + 0.999951i \(0.503139\pi\)
\(374\) 0.169111 0.141901i 0.00874452 0.00733752i
\(375\) 0 0
\(376\) −11.5340 4.19803i −0.594820 0.216497i
\(377\) −0.696424 + 0.829966i −0.0358677 + 0.0427454i
\(378\) −2.12562 0.374804i −0.109330 0.0192778i
\(379\) 29.6893 1.52504 0.762519 0.646966i \(-0.223962\pi\)
0.762519 + 0.646966i \(0.223962\pi\)
\(380\) 0 0
\(381\) 5.30368 0.271716
\(382\) 25.7593 + 4.54206i 1.31796 + 0.232392i
\(383\) −11.0417 + 13.1589i −0.564203 + 0.672391i −0.970430 0.241381i \(-0.922400\pi\)
0.406228 + 0.913772i \(0.366844\pi\)
\(384\) 2.45938 + 0.895141i 0.125505 + 0.0456800i
\(385\) 0 0
\(386\) −9.37557 + 7.86704i −0.477204 + 0.400422i
\(387\) 34.1091 19.6929i 1.73387 1.00105i
\(388\) 6.25219 + 3.60970i 0.317407 + 0.183255i
\(389\) 1.09317 + 6.19966i 0.0554258 + 0.314335i 0.999898 0.0142548i \(-0.00453759\pi\)
−0.944473 + 0.328590i \(0.893426\pi\)
\(390\) 0 0
\(391\) −1.02986 + 1.78378i −0.0520825 + 0.0902095i
\(392\) −5.24660 + 3.02913i −0.264993 + 0.152994i
\(393\) 12.2243 + 14.5684i 0.616635 + 0.734878i
\(394\) 0.294638 0.107239i 0.0148436 0.00540264i
\(395\) 0 0
\(396\) −1.65639 1.38988i −0.0832368 0.0698439i
\(397\) −9.73449 1.71645i −0.488560 0.0861463i −0.0760588 0.997103i \(-0.524234\pi\)
−0.412501 + 0.910957i \(0.635345\pi\)
\(398\) 21.4620i 1.07580i
\(399\) −9.45104 5.76566i −0.473144 0.288644i
\(400\) 0 0
\(401\) 5.40131 30.6323i 0.269728 1.52971i −0.485496 0.874239i \(-0.661361\pi\)
0.755224 0.655467i \(-0.227528\pi\)
\(402\) −20.4994 + 24.4303i −1.02242 + 1.21847i
\(403\) 1.70176 4.67554i 0.0847705 0.232905i
\(404\) 11.9341 4.34365i 0.593742 0.216105i
\(405\) 0 0
\(406\) 1.14976 + 1.99145i 0.0570619 + 0.0988341i
\(407\) −2.50443 1.44593i −0.124140 0.0716722i
\(408\) 1.01307 0.178632i 0.0501545 0.00884360i
\(409\) −5.49089 31.1404i −0.271507 1.53979i −0.749843 0.661616i \(-0.769871\pi\)
0.478336 0.878177i \(-0.341240\pi\)
\(410\) 0 0
\(411\) 9.91747 + 17.1776i 0.489193 + 0.847306i
\(412\) −7.37347 8.78736i −0.363265 0.432922i
\(413\) 1.45188 + 3.98901i 0.0714424 + 0.196287i
\(414\) 18.9578 + 6.90006i 0.931723 + 0.339120i
\(415\) 0 0
\(416\) −0.0793970 + 0.450283i −0.00389276 + 0.0220769i
\(417\) 29.8169i 1.46014i
\(418\) −1.17247 2.14917i −0.0573475 0.105119i
\(419\) −4.66623 −0.227960 −0.113980 0.993483i \(-0.536360\pi\)
−0.113980 + 0.993483i \(0.536360\pi\)
\(420\) 0 0
\(421\) 7.29791 + 6.12367i 0.355678 + 0.298449i 0.803065 0.595891i \(-0.203201\pi\)
−0.447387 + 0.894340i \(0.647645\pi\)
\(422\) 4.48373 12.3190i 0.218265 0.599677i
\(423\) 16.1617 + 44.4038i 0.785806 + 2.15899i
\(424\) 3.47530 2.91613i 0.168776 0.141620i
\(425\) 0 0
\(426\) 9.54980 16.5407i 0.462689 0.801401i
\(427\) 4.09333 0.721765i 0.198090 0.0349287i
\(428\) −12.3438 + 2.17654i −0.596659 + 0.105207i
\(429\) 0.336056 0.582066i 0.0162249 0.0281024i
\(430\) 0 0
\(431\) 12.6794 10.6393i 0.610746 0.512477i −0.284133 0.958785i \(-0.591706\pi\)
0.894880 + 0.446308i \(0.147261\pi\)
\(432\) −0.760709 2.09003i −0.0365996 0.100557i
\(433\) 13.2275 36.3423i 0.635674 1.74650i −0.0292319 0.999573i \(-0.509306\pi\)
0.664906 0.746927i \(-0.268472\pi\)
\(434\) −8.08970 6.78807i −0.388318 0.325838i
\(435\) 0 0
\(436\) −5.68780 −0.272396
\(437\) 17.1380 + 15.1015i 0.819821 + 0.722401i
\(438\) 36.4840i 1.74327i
\(439\) 4.93804 28.0050i 0.235680 1.33661i −0.605497 0.795848i \(-0.707026\pi\)
0.841177 0.540760i \(-0.181863\pi\)
\(440\) 0 0
\(441\) 21.9166 + 7.97700i 1.04365 + 0.379857i
\(442\) 0.0614660 + 0.168876i 0.00292364 + 0.00803263i
\(443\) −11.8053 14.0691i −0.560889 0.668442i 0.408845 0.912604i \(-0.365932\pi\)
−0.969734 + 0.244162i \(0.921487\pi\)
\(444\) −6.73782 11.6702i −0.319763 0.553845i
\(445\) 0 0
\(446\) 3.80801 + 21.5963i 0.180314 + 1.02261i
\(447\) 0.0223961 0.00394904i 0.00105930 0.000186783i
\(448\) 0.840422 + 0.485218i 0.0397062 + 0.0229244i
\(449\) 1.25413 + 2.17222i 0.0591861 + 0.102513i 0.894100 0.447867i \(-0.147816\pi\)
−0.834914 + 0.550380i \(0.814483\pi\)
\(450\) 0 0
\(451\) 4.23449 1.54123i 0.199394 0.0725735i
\(452\) −1.41493 + 3.88749i −0.0665527 + 0.182852i
\(453\) −25.8780 + 30.8402i −1.21586 + 1.44900i
\(454\) 0.683528 3.87648i 0.0320796 0.181932i
\(455\) 0 0
\(456\) 0.275843 11.4048i 0.0129175 0.534081i
\(457\) 32.8737i 1.53777i −0.639389 0.768884i \(-0.720813\pi\)
0.639389 0.768884i \(-0.279187\pi\)
\(458\) −12.2818 2.16561i −0.573889 0.101192i
\(459\) −0.669685 0.561932i −0.0312582 0.0262287i
\(460\) 0 0
\(461\) −1.13291 + 0.412346i −0.0527649 + 0.0192049i −0.368268 0.929720i \(-0.620049\pi\)
0.315503 + 0.948925i \(0.397827\pi\)
\(462\) −0.916943 1.09277i −0.0426600 0.0508402i
\(463\) −11.0746 + 6.39390i −0.514678 + 0.297150i −0.734755 0.678333i \(-0.762703\pi\)
0.220076 + 0.975483i \(0.429369\pi\)
\(464\) −1.18479 + 2.05212i −0.0550026 + 0.0952673i
\(465\) 0 0
\(466\) 2.33029 + 13.2158i 0.107949 + 0.612208i
\(467\) 28.1216 + 16.2360i 1.30131 + 0.751313i 0.980629 0.195873i \(-0.0627542\pi\)
0.320683 + 0.947187i \(0.396088\pi\)
\(468\) 1.52442 0.880125i 0.0704664 0.0406838i
\(469\) −9.05848 + 7.60097i −0.418282 + 0.350980i
\(470\) 0 0
\(471\) 44.3931 + 16.1578i 2.04553 + 0.744511i
\(472\) −2.81177 + 3.35094i −0.129422 + 0.154240i
\(473\) 5.65874 + 0.997788i 0.260189 + 0.0458783i
\(474\) 2.49434 0.114569
\(475\) 0 0
\(476\) 0.381431 0.0174829
\(477\) −17.2001 3.03284i −0.787538 0.138864i
\(478\) 0.984806 1.17365i 0.0450440 0.0536813i
\(479\) 16.3221 + 5.94076i 0.745775 + 0.271440i 0.686827 0.726821i \(-0.259003\pi\)
0.0589485 + 0.998261i \(0.481225\pi\)
\(480\) 0 0
\(481\) 1.80342 1.51325i 0.0822290 0.0689984i
\(482\) −12.1060 + 6.98942i −0.551415 + 0.318359i
\(483\) 11.5265 + 6.65483i 0.524474 + 0.302805i
\(484\) 1.85535 + 10.5222i 0.0843342 + 0.478283i
\(485\) 0 0
\(486\) 10.8324 18.7623i 0.491368 0.851074i
\(487\) 6.64068 3.83400i 0.300918 0.173735i −0.341937 0.939723i \(-0.611083\pi\)
0.642855 + 0.765988i \(0.277750\pi\)
\(488\) 2.75313 + 3.28105i 0.124628 + 0.148526i
\(489\) 12.0766 4.39554i 0.546124 0.198773i
\(490\) 0 0
\(491\) 25.9882 + 21.8067i 1.17283 + 0.984124i 1.00000 0.000827334i \(-0.000263349\pi\)
0.172833 + 0.984951i \(0.444708\pi\)
\(492\) 20.6794 + 3.64633i 0.932299 + 0.164389i
\(493\) 0.931369i 0.0419467i
\(494\) 1.97053 0.298525i 0.0886584 0.0134313i
\(495\) 0 0
\(496\) 1.88965 10.7168i 0.0848479 0.481196i
\(497\) 4.55217 5.42507i 0.204193 0.243348i
\(498\) 10.0890 27.7192i 0.452097 1.24213i
\(499\) −5.54507 + 2.01824i −0.248231 + 0.0903488i −0.463139 0.886285i \(-0.653277\pi\)
0.214908 + 0.976634i \(0.431055\pi\)
\(500\) 0 0
\(501\) −21.7901 37.7416i −0.973512 1.68617i
\(502\) −14.4900 8.36580i −0.646720 0.373384i
\(503\) 39.4651 6.95876i 1.75966 0.310276i 0.801819 0.597567i \(-0.203866\pi\)
0.957843 + 0.287292i \(0.0927549\pi\)
\(504\) −0.648750 3.67924i −0.0288976 0.163887i
\(505\) 0 0
\(506\) 1.47163 + 2.54894i 0.0654220 + 0.113314i
\(507\) −21.5184 25.6446i −0.955665 1.13892i
\(508\) 0.693090 + 1.90425i 0.0307509 + 0.0844873i
\(509\) 15.8140 + 5.75583i 0.700944 + 0.255123i 0.667814 0.744328i \(-0.267230\pi\)
0.0331303 + 0.999451i \(0.489452\pi\)
\(510\) 0 0
\(511\) −2.34909 + 13.3224i −0.103918 + 0.589347i
\(512\) 1.00000i 0.0441942i
\(513\) −7.57524 + 6.05037i −0.334455 + 0.267130i
\(514\) −6.00465 −0.264854
\(515\) 0 0
\(516\) 20.5113 + 17.2110i 0.902960 + 0.757673i
\(517\) −2.35784 + 6.47810i −0.103697 + 0.284907i
\(518\) −1.70895 4.69529i −0.0750868 0.206299i
\(519\) 23.6394 19.8358i 1.03765 0.870694i
\(520\) 0 0
\(521\) −1.40131 + 2.42714i −0.0613926 + 0.106335i −0.895088 0.445889i \(-0.852887\pi\)
0.833696 + 0.552224i \(0.186221\pi\)
\(522\) 8.98389 1.58410i 0.393214 0.0693342i
\(523\) 9.59389 1.69166i 0.419512 0.0739712i 0.0400921 0.999196i \(-0.487235\pi\)
0.379419 + 0.925225i \(0.376124\pi\)
\(524\) −3.63319 + 6.29286i −0.158716 + 0.274905i
\(525\) 0 0
\(526\) −4.83259 + 4.05502i −0.210711 + 0.176807i
\(527\) −1.46289 4.01927i −0.0637247 0.175082i
\(528\) 0.502759 1.38132i 0.0218798 0.0601142i
\(529\) −3.41757 2.86768i −0.148590 0.124682i
\(530\) 0 0
\(531\) 16.8404 0.730813
\(532\) 0.835048 4.14679i 0.0362039 0.179786i
\(533\) 3.66843i 0.158897i
\(534\) −1.60079 + 9.07852i −0.0692729 + 0.392866i
\(535\) 0 0
\(536\) −11.4504 4.16760i −0.494582 0.180013i
\(537\) 14.1051 + 38.7536i 0.608682 + 1.67234i
\(538\) 14.0627 + 16.7593i 0.606286 + 0.722543i
\(539\) 1.70132 + 2.94677i 0.0732810 + 0.126926i
\(540\) 0 0
\(541\) 4.09756 + 23.2384i 0.176168 + 0.999097i 0.936787 + 0.349899i \(0.113784\pi\)
−0.760620 + 0.649198i \(0.775105\pi\)
\(542\) −9.88355 + 1.74274i −0.424535 + 0.0748569i
\(543\) −33.7077 19.4611i −1.44654 0.835158i
\(544\) 0.196526 + 0.340392i 0.00842597 + 0.0145942i
\(545\) 0 0
\(546\) 1.09125 0.397184i 0.0467014 0.0169979i
\(547\) −1.43898 + 3.95356i −0.0615263 + 0.169042i −0.966647 0.256113i \(-0.917558\pi\)
0.905121 + 0.425155i \(0.139780\pi\)
\(548\) −4.87145 + 5.80557i −0.208098 + 0.248002i
\(549\) 2.86332 16.2387i 0.122204 0.693050i
\(550\) 0 0
\(551\) 10.1255 + 2.03900i 0.431362 + 0.0868643i
\(552\) 13.7151i 0.583755i
\(553\) 0.910825 + 0.160603i 0.0387322 + 0.00682953i
\(554\) −13.0278 10.9316i −0.553498 0.464440i
\(555\) 0 0
\(556\) 10.7055 3.89650i 0.454016 0.165248i
\(557\) 1.14222 + 1.36125i 0.0483975 + 0.0576779i 0.789700 0.613493i \(-0.210236\pi\)
−0.741303 + 0.671171i \(0.765792\pi\)
\(558\) −36.2813 + 20.9470i −1.53591 + 0.886758i
\(559\) −2.33886 + 4.05102i −0.0989231 + 0.171340i
\(560\) 0 0
\(561\) −0.100329 0.568995i −0.00423590 0.0240230i
\(562\) 0.915675 + 0.528665i 0.0386254 + 0.0223004i
\(563\) 31.5639 18.2234i 1.33026 0.768025i 0.344919 0.938632i \(-0.387906\pi\)
0.985339 + 0.170607i \(0.0545729\pi\)
\(564\) −24.6086 + 20.6491i −1.03621 + 0.869483i
\(565\) 0 0
\(566\) −22.1733 8.07043i −0.932014 0.339225i
\(567\) 3.57325 4.25843i 0.150062 0.178837i
\(568\) 7.18681 + 1.26723i 0.301552 + 0.0531717i
\(569\) 22.6982 0.951556 0.475778 0.879565i \(-0.342167\pi\)
0.475778 + 0.879565i \(0.342167\pi\)
\(570\) 0 0
\(571\) 9.60500 0.401957 0.200978 0.979596i \(-0.435588\pi\)
0.200978 + 0.979596i \(0.435588\pi\)
\(572\) 0.252903 + 0.0445936i 0.0105744 + 0.00186455i
\(573\) 44.0037 52.4416i 1.83828 2.19078i
\(574\) 7.31643 + 2.66296i 0.305382 + 0.111150i
\(575\) 0 0
\(576\) 2.94913 2.47462i 0.122881 0.103109i
\(577\) −1.38657 + 0.800539i −0.0577238 + 0.0333269i −0.528584 0.848881i \(-0.677277\pi\)
0.470860 + 0.882208i \(0.343944\pi\)
\(578\) −14.5886 8.42276i −0.606807 0.350340i
\(579\) 5.56229 + 31.5453i 0.231161 + 1.31098i
\(580\) 0 0
\(581\) 5.46879 9.47223i 0.226884 0.392974i
\(582\) 16.3633 9.44737i 0.678282 0.391606i
\(583\) −1.63785 1.95192i −0.0678329 0.0808401i
\(584\) −13.0993 + 4.76777i −0.542054 + 0.197292i
\(585\) 0 0
\(586\) −17.0689 14.3225i −0.705110 0.591657i
\(587\) 13.0152 + 2.29493i 0.537196 + 0.0947221i 0.435663 0.900110i \(-0.356514\pi\)
0.101533 + 0.994832i \(0.467625\pi\)
\(588\) 15.8558i 0.653881i
\(589\) −46.8988 + 7.10490i −1.93243 + 0.292752i
\(590\) 0 0
\(591\) 0.142499 0.808153i 0.00586163 0.0332430i
\(592\) 3.30961 3.94424i 0.136024 0.162107i
\(593\) −3.08987 + 8.48936i −0.126886 + 0.348616i −0.986827 0.161776i \(-0.948278\pi\)
0.859942 + 0.510393i \(0.170500\pi\)
\(594\) −1.17387 + 0.427255i −0.0481646 + 0.0175305i
\(595\) 0 0
\(596\) 0.00434462 + 0.00752511i 0.000177963 + 0.000308240i
\(597\) −48.6454 28.0854i −1.99092 1.14946i
\(598\) −2.35964 + 0.416069i −0.0964929 + 0.0170143i
\(599\) −4.00135 22.6928i −0.163491 0.927203i −0.950607 0.310398i \(-0.899538\pi\)
0.787116 0.616805i \(-0.211573\pi\)
\(600\) 0 0
\(601\) −16.0194 27.7465i −0.653447 1.13180i −0.982281 0.187415i \(-0.939989\pi\)
0.328834 0.944388i \(-0.393344\pi\)
\(602\) 6.38166 + 7.60537i 0.260097 + 0.309972i
\(603\) 16.0445 + 44.0820i 0.653384 + 1.79516i
\(604\) −14.4547 5.26109i −0.588155 0.214071i
\(605\) 0 0
\(606\) 5.77182 32.7336i 0.234464 1.32971i
\(607\) 7.01008i 0.284530i −0.989829 0.142265i \(-0.954561\pi\)
0.989829 0.142265i \(-0.0454386\pi\)
\(608\) 4.13088 1.39136i 0.167529 0.0564269i
\(609\) 6.01837 0.243877
\(610\) 0 0
\(611\) −4.29914 3.60741i −0.173925 0.145940i
\(612\) 0.517537 1.42192i 0.0209202 0.0574778i
\(613\) −12.6172 34.6655i −0.509604 1.40013i −0.881646 0.471911i \(-0.843564\pi\)
0.372042 0.928216i \(-0.378658\pi\)
\(614\) 20.9406 17.5713i 0.845094 0.709118i
\(615\) 0 0
\(616\) 0.272524 0.472026i 0.0109803 0.0190185i
\(617\) −26.6741 + 4.70336i −1.07386 + 0.189350i −0.682498 0.730887i \(-0.739107\pi\)
−0.391360 + 0.920237i \(0.627995\pi\)
\(618\) −29.5662 + 5.21332i −1.18933 + 0.209710i
\(619\) −11.3313 + 19.6265i −0.455445 + 0.788855i −0.998714 0.0507046i \(-0.983853\pi\)
0.543268 + 0.839559i \(0.317187\pi\)
\(620\) 0 0
\(621\) 8.92857 7.49196i 0.358291 0.300642i
\(622\) −10.7331 29.4890i −0.430359 1.18240i
\(623\) −1.16908 + 3.21201i −0.0468380 + 0.128686i
\(624\) 0.916701 + 0.769203i 0.0366974 + 0.0307928i
\(625\) 0 0
\(626\) −1.15084 −0.0459970
\(627\) −6.40557 0.154928i −0.255814 0.00618723i
\(628\) 18.0505i 0.720295i
\(629\) 0.351422 1.99302i 0.0140121 0.0794667i
\(630\) 0 0
\(631\) −12.4587 4.53461i −0.495974 0.180520i 0.0819082 0.996640i \(-0.473899\pi\)
−0.577882 + 0.816120i \(0.696121\pi\)
\(632\) 0.325963 + 0.895576i 0.0129661 + 0.0356241i
\(633\) −22.0544 26.2834i −0.876583 1.04467i
\(634\) −10.3287 17.8898i −0.410205 0.710495i
\(635\) 0 0
\(636\) −2.06181 11.6931i −0.0817561 0.463662i
\(637\) −2.72793 + 0.481007i −0.108084 + 0.0190582i
\(638\) 1.15258 + 0.665443i 0.0456311 + 0.0263451i
\(639\) −14.0474 24.3308i −0.555705 0.962510i
\(640\) 0 0
\(641\) −2.21754 + 0.807120i −0.0875877 + 0.0318793i −0.385442 0.922732i \(-0.625951\pi\)
0.297855 + 0.954611i \(0.403729\pi\)
\(642\) −11.2199 + 30.8264i −0.442813 + 1.21662i
\(643\) 17.9758 21.4227i 0.708895 0.844828i −0.284607 0.958644i \(-0.591863\pi\)
0.993502 + 0.113816i \(0.0363075\pi\)
\(644\) −0.883075 + 5.00817i −0.0347980 + 0.197349i
\(645\) 0 0
\(646\) 1.13268 1.28543i 0.0445648 0.0505746i
\(647\) 26.0773i 1.02520i −0.858626 0.512602i \(-0.828682\pi\)
0.858626 0.512602i \(-0.171318\pi\)
\(648\) 5.64132 + 0.994716i 0.221612 + 0.0390761i
\(649\) 1.88207 + 1.57924i 0.0738776 + 0.0619907i
\(650\) 0 0
\(651\) −25.9719 + 9.45300i −1.01792 + 0.370492i
\(652\) 3.15637 + 3.76162i 0.123613 + 0.147316i
\(653\) −32.5381 + 18.7859i −1.27332 + 0.735149i −0.975611 0.219509i \(-0.929555\pi\)
−0.297705 + 0.954658i \(0.596221\pi\)
\(654\) −7.44310 + 12.8918i −0.291048 + 0.504110i
\(655\) 0 0
\(656\) 1.39321 + 7.90129i 0.0543957 + 0.308494i
\(657\) 46.4766 + 26.8333i 1.81323 + 1.04687i
\(658\) −10.3155 + 5.95566i −0.402141 + 0.232176i
\(659\) −34.5955 + 29.0291i −1.34765 + 1.13081i −0.368060 + 0.929802i \(0.619978\pi\)
−0.979589 + 0.201010i \(0.935578\pi\)
\(660\) 0 0
\(661\) 19.6153 + 7.13939i 0.762947 + 0.277690i 0.694043 0.719933i \(-0.255828\pi\)
0.0689038 + 0.997623i \(0.478050\pi\)
\(662\) 7.68545 9.15917i 0.298704 0.355981i
\(663\) 0.463206 + 0.0816757i 0.0179894 + 0.00317202i
\(664\) 11.2708 0.437392
\(665\) 0 0
\(666\) −19.8221 −0.768092
\(667\) −12.2288 2.15627i −0.473502 0.0834911i
\(668\) 10.7033 12.7557i 0.414123 0.493533i
\(669\) 53.9328 + 19.6299i 2.08516 + 0.758937i
\(670\) 0 0
\(671\) 1.84281 1.54630i 0.0711410 0.0596944i
\(672\) 2.19957 1.26992i 0.0848501 0.0489882i
\(673\) −6.59380 3.80693i −0.254172 0.146747i 0.367501 0.930023i \(-0.380214\pi\)
−0.621673 + 0.783277i \(0.713547\pi\)
\(674\) 2.86966 + 16.2746i 0.110535 + 0.626876i
\(675\) 0 0
\(676\) 6.39547 11.0773i 0.245980 0.426049i
\(677\) −22.0697 + 12.7420i −0.848209 + 0.489714i −0.860046 0.510216i \(-0.829565\pi\)
0.0118369 + 0.999930i \(0.496232\pi\)
\(678\) 6.95970 + 8.29425i 0.267286 + 0.318539i
\(679\) 6.58346 2.39618i 0.252650 0.0919570i
\(680\) 0 0
\(681\) −7.89187 6.62206i −0.302417 0.253758i
\(682\) −6.01910 1.06133i −0.230483 0.0406404i
\(683\) 46.2882i 1.77117i −0.464478 0.885585i \(-0.653758\pi\)
0.464478 0.885585i \(-0.346242\pi\)
\(684\) −14.3256 8.73943i −0.547754 0.334160i
\(685\) 0 0
\(686\) −2.20050 + 12.4797i −0.0840156 + 0.476476i
\(687\) −20.9805 + 25.0036i −0.800457 + 0.953948i
\(688\) −3.49906 + 9.61359i −0.133400 + 0.366515i
\(689\) 1.94921 0.709454i 0.0742590 0.0270281i
\(690\) 0 0
\(691\) −10.4011 18.0153i −0.395677 0.685333i 0.597510 0.801861i \(-0.296157\pi\)
−0.993187 + 0.116528i \(0.962823\pi\)
\(692\) 10.2111 + 5.89538i 0.388168 + 0.224109i
\(693\) −2.06646 + 0.364373i −0.0784983 + 0.0138414i
\(694\) 0.633021 + 3.59004i 0.0240291 + 0.136276i
\(695\) 0 0
\(696\) 3.10086 + 5.37084i 0.117538 + 0.203581i
\(697\) 2.02705 + 2.41574i 0.0767798 + 0.0915026i
\(698\) −6.22282 17.0970i −0.235537 0.647133i
\(699\) 33.0040 + 12.0125i 1.24832 + 0.454353i
\(700\) 0 0
\(701\) −4.88207 + 27.6876i −0.184393 + 1.04575i 0.742339 + 0.670025i \(0.233716\pi\)
−0.926732 + 0.375722i \(0.877395\pi\)
\(702\) 1.01695i 0.0383824i
\(703\) −20.8980 8.18375i −0.788184 0.308656i
\(704\) 0.561653 0.0211681
\(705\) 0 0
\(706\) 4.95571 + 4.15833i 0.186511 + 0.156501i
\(707\) 4.21523 11.5813i 0.158530 0.435558i
\(708\) 3.91565 + 10.7582i 0.147159 + 0.404317i
\(709\) −3.40036 + 2.85324i −0.127703 + 0.107156i −0.704402 0.709801i \(-0.748785\pi\)
0.576699 + 0.816957i \(0.304340\pi\)
\(710\) 0 0
\(711\) 1.83454 3.17752i 0.0688006 0.119166i
\(712\) −3.46877 + 0.611638i −0.129998 + 0.0229221i
\(713\) 56.1596 9.90245i 2.10319 0.370850i
\(714\) 0.499144 0.864542i 0.0186800 0.0323547i
\(715\) 0 0
\(716\) −12.0709 + 10.1287i −0.451111 + 0.378527i
\(717\) −1.37143 3.76798i −0.0512171 0.140718i
\(718\) 7.69912 21.1532i 0.287329 0.789429i
\(719\) 14.7672 + 12.3912i 0.550725 + 0.462113i 0.875186 0.483786i \(-0.160739\pi\)
−0.324461 + 0.945899i \(0.605183\pi\)
\(720\) 0 0
\(721\) −11.1319 −0.414575
\(722\) −11.4950 15.1283i −0.427801 0.563015i
\(723\) 36.5857i 1.36064i
\(724\) 2.58243 14.6457i 0.0959754 0.544303i
\(725\) 0 0
\(726\) 26.2773 + 9.56417i 0.975244 + 0.354960i
\(727\) −14.6024 40.1199i −0.541575 1.48796i −0.844819 0.535052i \(-0.820292\pi\)
0.303244 0.952913i \(-0.401930\pi\)
\(728\) 0.285212 + 0.339903i 0.0105707 + 0.0125976i
\(729\) −19.7582 34.2223i −0.731786 1.26749i
\(730\) 0 0
\(731\) 0.698263 + 3.96005i 0.0258262 + 0.146468i
\(732\) 11.0395 1.94657i 0.408032 0.0719471i
\(733\) −5.59661 3.23120i −0.206715 0.119347i 0.393069 0.919509i \(-0.371414\pi\)
−0.599784 + 0.800162i \(0.704747\pi\)
\(734\) −1.35294 2.34336i −0.0499379 0.0864950i
\(735\) 0 0
\(736\) −4.92432 + 1.79231i −0.181513 + 0.0660653i
\(737\) −2.34075 + 6.43115i −0.0862226 + 0.236895i
\(738\) 19.8543 23.6614i 0.730847 0.870990i
\(739\) −3.08387 + 17.4895i −0.113442 + 0.643361i 0.874068 + 0.485804i \(0.161473\pi\)
−0.987510 + 0.157557i \(0.949638\pi\)
\(740\) 0 0
\(741\) 1.90203 4.85701i 0.0698726 0.178427i
\(742\) 4.40256i 0.161623i
\(743\) −13.3993 2.36266i −0.491572 0.0866774i −0.0776330 0.996982i \(-0.524736\pi\)
−0.413939 + 0.910305i \(0.635847\pi\)
\(744\) −21.8175 18.3071i −0.799869 0.671170i
\(745\) 0 0
\(746\) −18.4576 + 6.71801i −0.675780 + 0.245964i
\(747\) −27.8909 33.2391i −1.02048 1.21616i
\(748\) 0.191183 0.110379i 0.00699033 0.00403587i
\(749\) −6.08182 + 10.5340i −0.222225 + 0.384905i
\(750\) 0 0
\(751\) −5.02602 28.5040i −0.183402 1.04013i −0.927991 0.372602i \(-0.878466\pi\)
0.744589 0.667523i \(-0.232646\pi\)
\(752\) −10.6298 6.13710i −0.387628 0.223797i
\(753\) −37.9235 + 21.8951i −1.38201 + 0.797902i
\(754\) −0.829966 + 0.696424i −0.0302256 + 0.0253623i
\(755\) 0 0
\(756\) −2.02824 0.738219i −0.0737664 0.0268488i
\(757\) −21.7825 + 25.9594i −0.791698 + 0.943509i −0.999398 0.0346833i \(-0.988958\pi\)
0.207700 + 0.978193i \(0.433402\pi\)
\(758\) 29.2383 + 5.15550i 1.06198 + 0.187256i
\(759\) 7.70316 0.279607
\(760\) 0 0
\(761\) −45.0675 −1.63370 −0.816848 0.576853i \(-0.804281\pi\)
−0.816848 + 0.576853i \(0.804281\pi\)
\(762\) 5.22310 + 0.920974i 0.189213 + 0.0333634i
\(763\) −3.54796 + 4.22829i −0.128445 + 0.153074i
\(764\) 24.5792 + 8.94610i 0.889245 + 0.323659i
\(765\) 0 0
\(766\) −13.1589 + 11.0417i −0.475452 + 0.398952i
\(767\) −1.73212 + 1.00004i −0.0625432 + 0.0361093i
\(768\) 2.26658 + 1.30861i 0.0817880 + 0.0472203i
\(769\) 8.12888 + 46.1012i 0.293135 + 1.66245i 0.674687 + 0.738104i \(0.264279\pi\)
−0.381552 + 0.924347i \(0.624610\pi\)
\(770\) 0 0
\(771\) −7.85774 + 13.6100i −0.282990 + 0.490152i
\(772\) −10.5992 + 6.11947i −0.381475 + 0.220244i
\(773\) 30.7840 + 36.6869i 1.10722 + 1.31954i 0.942880 + 0.333134i \(0.108106\pi\)
0.164343 + 0.986403i \(0.447450\pi\)
\(774\) 37.0106 13.4708i 1.33032 0.484196i
\(775\) 0 0
\(776\) 5.53039 + 4.64054i 0.198529 + 0.166586i
\(777\) −12.8786 2.27084i −0.462016 0.0814659i
\(778\) 6.29530i 0.225698i
\(779\) 30.7008 16.7487i 1.09997 0.600084i
\(780\) 0 0
\(781\) 0.711743 4.03649i 0.0254682 0.144437i
\(782\) −1.32397 + 1.57784i −0.0473450 + 0.0564236i
\(783\) 1.80257 4.95251i 0.0644184 0.176988i
\(784\) −5.69290 + 2.07205i −0.203318 + 0.0740016i
\(785\) 0 0
\(786\) 9.50883 + 16.4698i 0.339169 + 0.587458i
\(787\) 26.9425 + 15.5552i 0.960396 + 0.554485i 0.896295 0.443459i \(-0.146249\pi\)
0.0641009 + 0.997943i \(0.479582\pi\)
\(788\) 0.308783 0.0544469i 0.0110000 0.00193959i
\(789\) 2.86705 + 16.2599i 0.102070 + 0.578866i
\(790\) 0 0
\(791\) 2.00734 + 3.47681i 0.0713727 + 0.123621i
\(792\) −1.38988 1.65639i −0.0493871 0.0588573i
\(793\) 0.669799 + 1.84026i 0.0237853 + 0.0653495i
\(794\) −9.28854 3.38075i −0.329638 0.119978i
\(795\) 0 0
\(796\) 3.72685 21.1360i 0.132095 0.749145i
\(797\) 3.73434i 0.132277i 0.997810 + 0.0661385i \(0.0210679\pi\)
−0.997810 + 0.0661385i \(0.978932\pi\)
\(798\) −8.30626 7.31922i −0.294038 0.259098i
\(799\) −4.82439 −0.170675
\(800\) 0 0
\(801\) 10.3877 + 8.71630i 0.367031 + 0.307975i
\(802\) 10.6385 29.2290i 0.375658 1.03211i
\(803\) 2.67783 + 7.35728i 0.0944986 + 0.259633i
\(804\) −24.4303 + 20.4994i −0.861589 + 0.722959i
\(805\) 0 0
\(806\) 2.48780 4.30900i 0.0876291 0.151778i
\(807\) 56.3887 9.94285i 1.98498 0.350005i
\(808\) 12.5070 2.20533i 0.439996 0.0775832i
\(809\) −1.59342 + 2.75989i −0.0560217 + 0.0970325i −0.892676 0.450699i \(-0.851175\pi\)
0.836654 + 0.547731i \(0.184508\pi\)
\(810\) 0 0
\(811\) −18.9972 + 15.9405i −0.667081 + 0.559748i −0.912200 0.409745i \(-0.865618\pi\)
0.245119 + 0.969493i \(0.421173\pi\)
\(812\) 0.786485 + 2.16085i 0.0276002 + 0.0758310i
\(813\) −8.98365 + 24.6824i −0.315070 + 0.865648i
\(814\) −2.21530 1.85886i −0.0776462 0.0651529i
\(815\) 0 0
\(816\) 1.02870 0.0360117
\(817\) 44.5810 + 1.07826i 1.55969 + 0.0377234i
\(818\) 31.6208i 1.10559i
\(819\) 0.296627 1.68226i 0.0103650 0.0587829i
\(820\) 0 0
\(821\) −29.4494 10.7187i −1.02779 0.374085i −0.227551 0.973766i \(-0.573072\pi\)
−0.800239 + 0.599681i \(0.795294\pi\)
\(822\) 6.78395 + 18.6387i 0.236617 + 0.650101i
\(823\) −13.9157 16.5841i −0.485071 0.578085i 0.466886 0.884318i \(-0.345376\pi\)
−0.951957 + 0.306233i \(0.900931\pi\)
\(824\) −5.73554 9.93425i −0.199807 0.346076i
\(825\) 0 0
\(826\) 0.737140 + 4.18053i 0.0256484 + 0.145459i
\(827\) 7.46717 1.31666i 0.259659 0.0457849i −0.0423030 0.999105i \(-0.513469\pi\)
0.301962 + 0.953320i \(0.402358\pi\)
\(828\) 17.4716 + 10.0872i 0.607179 + 0.350555i
\(829\) 14.1716 + 24.5460i 0.492200 + 0.852516i 0.999960 0.00898284i \(-0.00285937\pi\)
−0.507759 + 0.861499i \(0.669526\pi\)
\(830\) 0 0
\(831\) −41.8256 + 15.2233i −1.45091 + 0.528089i
\(832\) −0.156382 + 0.429655i −0.00542156 + 0.0148956i
\(833\) −1.53061 + 1.82411i −0.0530325 + 0.0632016i
\(834\) 5.17765 29.3639i 0.179287 1.01679i
\(835\) 0 0
\(836\) −0.781460 2.32012i −0.0270273 0.0802430i
\(837\) 24.2035i 0.836597i
\(838\) −4.59534 0.810282i −0.158743 0.0279907i
\(839\) −12.0688 10.1269i −0.416661 0.349620i 0.410230 0.911982i \(-0.365448\pi\)
−0.826891 + 0.562362i \(0.809893\pi\)
\(840\) 0 0
\(841\) 21.9748 7.99816i 0.757751 0.275799i
\(842\) 6.12367 + 7.29791i 0.211036 + 0.251502i
\(843\) 2.39652 1.38363i 0.0825405 0.0476548i
\(844\) 6.55478 11.3532i 0.225625 0.390793i
\(845\) 0 0
\(846\) 8.20549 + 46.5356i 0.282110 + 1.59993i
\(847\) 8.97953 + 5.18433i 0.308540 + 0.178136i
\(848\) 3.92889 2.26834i 0.134919 0.0778953i
\(849\) −47.3084 + 39.6965i −1.62362 + 1.36238i
\(850\) 0 0
\(851\) 25.3546 + 9.22831i 0.869144 + 0.316342i
\(852\) 12.2770 14.6311i 0.420602 0.501255i
\(853\) 7.17004 + 1.26427i 0.245497 + 0.0432878i 0.295043 0.955484i \(-0.404666\pi\)
−0.0495453 + 0.998772i \(0.515777\pi\)
\(854\) 4.15648 0.142232
\(855\) 0 0
\(856\) −12.5342 −0.428410
\(857\) 22.3205 + 3.93570i 0.762452 + 0.134441i 0.541336 0.840806i \(-0.317919\pi\)
0.221117 + 0.975247i \(0.429030\pi\)
\(858\) 0.432025 0.514868i 0.0147491 0.0175773i
\(859\) −13.0461 4.74841i −0.445129 0.162014i 0.109724 0.993962i \(-0.465003\pi\)
−0.554853 + 0.831948i \(0.687225\pi\)
\(860\) 0 0
\(861\) 15.6101 13.0985i 0.531992 0.446395i
\(862\) 14.3343 8.27591i 0.488228 0.281879i
\(863\) −4.05238 2.33964i −0.137945 0.0796424i 0.429439 0.903096i \(-0.358711\pi\)
−0.567384 + 0.823453i \(0.692044\pi\)
\(864\) −0.386222 2.19037i −0.0131395 0.0745181i
\(865\) 0 0
\(866\) 19.3373 33.4933i 0.657109 1.13815i
\(867\) −38.1816 + 22.0442i −1.29672 + 0.748659i
\(868\) −6.78807 8.08970i −0.230402 0.274582i
\(869\) 0.503003 0.183078i 0.0170632 0.00621050i
\(870\) 0 0
\(871\) −4.26798 3.58126i −0.144615 0.121346i
\(872\) −5.60139 0.987675i −0.189687 0.0334469i
\(873\) 27.7934i 0.940665i
\(874\) 14.2553 + 17.8480i 0.482192 + 0.603719i
\(875\) 0 0
\(876\) −6.33539 + 35.9298i −0.214053 + 1.21395i
\(877\) −0.149187 + 0.177794i −0.00503770 + 0.00600369i −0.768557 0.639781i \(-0.779025\pi\)
0.763520 + 0.645785i \(0.223470\pi\)
\(878\) 9.72605 26.7221i 0.328238 0.901827i
\(879\) −54.7995 + 19.9454i −1.84834 + 0.672742i
\(880\) 0 0
\(881\) 13.0872 + 22.6677i 0.440920 + 0.763695i 0.997758 0.0669258i \(-0.0213191\pi\)
−0.556838 + 0.830621i \(0.687986\pi\)
\(882\) 20.1985 + 11.6616i 0.680118 + 0.392666i
\(883\) −20.5356 + 3.62098i −0.691079 + 0.121856i −0.508148 0.861270i \(-0.669670\pi\)
−0.182931 + 0.983126i \(0.558558\pi\)
\(884\) 0.0312071 + 0.176984i 0.00104961 + 0.00595263i
\(885\) 0 0
\(886\) −9.18293 15.9053i −0.308507 0.534349i
\(887\) 28.1503 + 33.5482i 0.945195 + 1.12644i 0.991835 + 0.127528i \(0.0407042\pi\)
−0.0466399 + 0.998912i \(0.514851\pi\)
\(888\) −4.60894 12.6630i −0.154666 0.424941i
\(889\) 1.84795 + 0.672599i 0.0619782 + 0.0225582i
\(890\) 0 0
\(891\) 0.558686 3.16846i 0.0187167 0.106148i
\(892\) 21.9294i 0.734252i
\(893\) −10.5618 + 52.4492i −0.353437 + 1.75514i
\(894\) 0.0227416 0.000760594
\(895\) 0 0
\(896\) 0.743397 + 0.623784i 0.0248351 + 0.0208392i
\(897\) −2.14480 + 5.89278i −0.0716126 + 0.196754i
\(898\) 0.857876 + 2.35700i 0.0286277 + 0.0786539i
\(899\) 19.7532 16.5749i 0.658807 0.552805i
\(900\) 0 0
\(901\) 0.891576 1.54425i 0.0297027 0.0514466i
\(902\) 4.43779 0.782501i 0.147762 0.0260544i
\(903\) 25.5892 4.51207i 0.851557 0.150152i
\(904\) −2.06849 + 3.58273i −0.0687970 + 0.119160i
\(905\) 0 0
\(906\) −30.8402 + 25.8780i −1.02460 + 0.859740i
\(907\) 3.66995 + 10.0831i 0.121859 + 0.334804i 0.985591 0.169147i \(-0.0541013\pi\)
−0.863732 + 0.503951i \(0.831879\pi\)
\(908\) 1.34629 3.69890i 0.0446781 0.122752i
\(909\) −37.4539 31.4276i −1.24227 1.04239i
\(910\) 0 0
\(911\) 9.16696 0.303715 0.151858 0.988402i \(-0.451475\pi\)
0.151858 + 0.988402i \(0.451475\pi\)
\(912\) 2.25208 11.1837i 0.0745739 0.370329i
\(913\) 6.33028i 0.209502i
\(914\) 5.70846 32.3743i 0.188819 1.07085i
\(915\) 0 0
\(916\) −11.7191 4.26541i −0.387211 0.140933i
\(917\) 2.41177 + 6.62629i 0.0796437 + 0.218819i
\(918\) −0.561932 0.669685i −0.0185465 0.0221029i
\(919\) −12.1439 21.0339i −0.400592 0.693845i 0.593206 0.805051i \(-0.297862\pi\)
−0.993797 + 0.111206i \(0.964529\pi\)
\(920\) 0 0
\(921\) −12.4235 70.4573i −0.409369 2.32165i
\(922\) −1.18730 + 0.209353i −0.0391017 + 0.00689469i
\(923\) 2.88968 + 1.66835i 0.0951148 + 0.0549146i
\(924\) −0.713255 1.23539i −0.0234644 0.0406415i
\(925\) 0 0
\(926\) −12.0166 + 4.37368i −0.394890 + 0.143728i
\(927\) −15.1042 + 41.4983i −0.496086 + 1.36298i
\(928\) −1.52314 + 1.81521i −0.0499995 + 0.0595871i
\(929\) 8.78099 49.7995i 0.288095 1.63387i −0.405921 0.913908i \(-0.633049\pi\)
0.694016 0.719960i \(-0.255840\pi\)
\(930\) 0 0
\(931\) 16.4802 + 20.6337i 0.540117 + 0.676242i
\(932\) 13.4196i 0.439575i
\(933\) −80.8846 14.2621i −2.64804 0.466921i
\(934\) 24.8750 + 20.8726i 0.813935 + 0.682973i
\(935\) 0 0
\(936\) 1.65409 0.602041i 0.0540658 0.0196783i
\(937\) 16.5715 + 19.7492i 0.541367 + 0.645177i 0.965494 0.260426i \(-0.0838632\pi\)
−0.424126 + 0.905603i \(0.639419\pi\)
\(938\) −10.2408 + 5.91251i −0.334373 + 0.193050i
\(939\) −1.50600 + 2.60847i −0.0491466 + 0.0851243i
\(940\) 0 0
\(941\) −3.67924 20.8660i −0.119940 0.680212i −0.984185 0.177142i \(-0.943315\pi\)
0.864246 0.503070i \(-0.167796\pi\)
\(942\) 40.9129 + 23.6211i 1.33301 + 0.769616i
\(943\) −36.4115 + 21.0222i −1.18572 + 0.684576i
\(944\) −3.35094 + 2.81177i −0.109064 + 0.0915155i
\(945\) 0 0
\(946\) 5.39950 + 1.96526i 0.175553 + 0.0638961i
\(947\) −16.8901 + 20.1288i −0.548855 + 0.654099i −0.967148 0.254212i \(-0.918184\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(948\) 2.45645 + 0.433138i 0.0797817 + 0.0140677i
\(949\) −6.37378 −0.206902
\(950\) 0 0
\(951\) −54.0648 −1.75317
\(952\) 0.375636 + 0.0662348i 0.0121744 + 0.00214668i
\(953\) 24.8721 29.6414i 0.805686 0.960179i −0.194097 0.980982i \(-0.562178\pi\)
0.999784 + 0.0208029i \(0.00662225\pi\)
\(954\) −16.4121 5.97353i −0.531363 0.193400i
\(955\) 0 0
\(956\) 1.17365 0.984806i 0.0379584 0.0318509i
\(957\) 3.01655 1.74161i 0.0975113 0.0562982i
\(958\) 15.0425 + 8.68480i 0.486002 + 0.280593i
\(959\) 1.27711 + 7.24285i 0.0412400 + 0.233884i
\(960\) 0 0
\(961\) −43.7098 + 75.7076i −1.40999 + 2.44218i
\(962\) 2.03880 1.17710i 0.0657335 0.0379513i
\(963\) 31.0174 + 36.9651i 0.999521 + 1.19118i
\(964\) −13.1358 + 4.78105i −0.423076 + 0.153987i
\(965\) 0 0
\(966\) 10.1958 + 8.55529i 0.328044 + 0.275262i
\(967\) 2.72211 + 0.479982i 0.0875373 + 0.0154352i 0.217245 0.976117i \(-0.430293\pi\)
−0.129708 + 0.991552i \(0.541404\pi\)
\(968\) 10.6845i 0.343414i
\(969\) −1.43129 4.24943i −0.0459796 0.136511i
\(970\) 0 0
\(971\) −8.07923 + 45.8196i −0.259275 + 1.47042i 0.525582 + 0.850743i \(0.323848\pi\)
−0.784857 + 0.619677i \(0.787263\pi\)
\(972\) 13.9259 16.5962i 0.446672 0.532323i
\(973\) 3.78130 10.3890i 0.121223 0.333058i
\(974\) 7.20556 2.62261i 0.230881 0.0840338i
\(975\) 0 0
\(976\) 2.14155 + 3.70928i 0.0685495 + 0.118731i
\(977\) 45.6660 + 26.3653i 1.46099 + 0.843500i 0.999057 0.0434169i \(-0.0138244\pi\)
0.461928 + 0.886917i \(0.347158\pi\)
\(978\) 12.6564 2.23167i 0.404708 0.0713610i
\(979\) 0.343528 + 1.94825i 0.0109792 + 0.0622662i
\(980\) 0 0
\(981\) 10.9485 + 18.9634i 0.349559 + 0.605453i
\(982\) 21.8067 + 25.9882i 0.695881 + 0.829318i
\(983\) 8.88043 + 24.3988i 0.283242 + 0.778200i 0.996971 + 0.0777783i \(0.0247826\pi\)
−0.713729 + 0.700422i \(0.752995\pi\)
\(984\) 19.7320 + 7.18188i 0.629035 + 0.228950i
\(985\) 0 0
\(986\) −0.161730 + 0.917219i −0.00515055 + 0.0292102i
\(987\) 31.1745i 0.992296i
\(988\) 1.99243 + 0.0481899i 0.0633877 + 0.00153313i
\(989\) −53.6118 −1.70476
\(990\) 0 0
\(991\) −7.40666 6.21493i −0.235280 0.197424i 0.517523 0.855669i \(-0.326854\pi\)
−0.752803 + 0.658246i \(0.771299\pi\)
\(992\) 3.72189 10.2258i 0.118170 0.324670i
\(993\) −10.7027 29.4054i −0.339640 0.933153i
\(994\) 5.42507 4.55217i 0.172073 0.144386i
\(995\) 0 0
\(996\) 14.7491 25.5461i 0.467342 0.809460i
\(997\) −32.2427 + 5.68526i −1.02114 + 0.180054i −0.659057 0.752093i \(-0.729044\pi\)
−0.362080 + 0.932147i \(0.617933\pi\)
\(998\) −5.81129 + 1.02469i −0.183953 + 0.0324359i
\(999\) −5.72594 + 9.91762i −0.181161 + 0.313780i
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 950.2.u.f.549.4 24
5.2 odd 4 950.2.l.g.701.1 12
5.3 odd 4 190.2.k.c.131.2 12
5.4 even 2 inner 950.2.u.f.549.1 24
19.9 even 9 inner 950.2.u.f.199.1 24
95.3 even 36 3610.2.a.bd.1.1 6
95.9 even 18 inner 950.2.u.f.199.4 24
95.28 odd 36 190.2.k.c.161.2 yes 12
95.47 odd 36 950.2.l.g.351.1 12
95.73 odd 36 3610.2.a.bf.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.c.131.2 12 5.3 odd 4
190.2.k.c.161.2 yes 12 95.28 odd 36
950.2.l.g.351.1 12 95.47 odd 36
950.2.l.g.701.1 12 5.2 odd 4
950.2.u.f.199.1 24 19.9 even 9 inner
950.2.u.f.199.4 24 95.9 even 18 inner
950.2.u.f.549.1 24 5.4 even 2 inner
950.2.u.f.549.4 24 1.1 even 1 trivial
3610.2.a.bd.1.1 6 95.3 even 36
3610.2.a.bf.1.6 6 95.73 odd 36