Properties

Label 450.2.h.f.91.2
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $0$
Dimension $12$
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] = [450,2,Mod(91,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} - 3250 x^{3} + 3750 x^{2} - 3125 x + 15625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.2
Root \(0.220100 - 2.22521i\) of defining polynomial
Character \(\chi\) \(=\) 450.91
Dual form 450.2.h.f.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.220100 - 2.22521i) q^{5} +1.64173 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.220100 - 2.22521i) q^{5} +1.64173 q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.48601 + 1.67086i) q^{10} +(-0.232788 - 0.169130i) q^{11} +(1.02912 - 0.747697i) q^{13} +(-1.32819 - 0.964983i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(1.52297 - 4.68721i) q^{17} +(-0.745417 + 2.29416i) q^{19} +(2.18431 - 0.478300i) q^{20} +(0.0889172 + 0.273659i) q^{22} +(0.588076 + 0.427262i) q^{23} +(-4.90311 - 0.979536i) q^{25} -1.27206 q^{26} +(0.507322 + 1.56138i) q^{28} +(-1.43158 - 4.40594i) q^{29} +(2.27323 - 6.99629i) q^{31} +1.00000 q^{32} +(-3.98718 + 2.89686i) q^{34} +(0.361344 - 3.65319i) q^{35} +(6.70462 - 4.87119i) q^{37} +(1.95153 - 1.41787i) q^{38} +(-2.04829 - 0.896955i) q^{40} +(-2.21533 + 1.60953i) q^{41} +5.96937 q^{43} +(0.0889172 - 0.273659i) q^{44} +(-0.224625 - 0.691324i) q^{46} +(-1.71263 - 5.27092i) q^{47} -4.30473 q^{49} +(3.39094 + 3.67444i) q^{50} +(1.02912 + 0.747697i) q^{52} +(1.99918 + 6.15285i) q^{53} +(-0.427587 + 0.480777i) q^{55} +(0.507322 - 1.56138i) q^{56} +(-1.43158 + 4.40594i) q^{58} +(-7.03842 + 5.11371i) q^{59} +(-8.45598 - 6.14363i) q^{61} +(-5.95140 + 4.32394i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-1.43727 - 2.45457i) q^{65} +(3.78815 - 11.6587i) q^{67} +4.92843 q^{68} +(-2.43962 + 2.74310i) q^{70} +(4.76911 + 14.6778i) q^{71} +(5.40292 + 3.92545i) q^{73} -8.28736 q^{74} -2.41222 q^{76} +(-0.382175 - 0.277666i) q^{77} +(2.98419 + 9.18438i) q^{79} +(1.12988 + 1.92960i) q^{80} +2.73830 q^{82} +(-0.898338 + 2.76480i) q^{83} +(-10.0948 - 4.42058i) q^{85} +(-4.82932 - 3.50871i) q^{86} +(-0.232788 + 0.169130i) q^{88} +(12.4011 + 9.00992i) q^{89} +(1.68953 - 1.22751i) q^{91} +(-0.224625 + 0.691324i) q^{92} +(-1.71263 + 5.27092i) q^{94} +(4.94091 + 2.16365i) q^{95} +(0.560804 + 1.72598i) q^{97} +(3.48260 + 2.53026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + q^{11} + 4 q^{13} + 8 q^{14} - 3 q^{16} - 8 q^{17} - 8 q^{19} + q^{20} - 4 q^{22} - 11 q^{25} - 16 q^{26} - 7 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} + 2 q^{34} - 18 q^{35} - 8 q^{37} + 2 q^{38} + q^{40} + 20 q^{41} + 32 q^{43} - 4 q^{44} - 10 q^{46} + 34 q^{49} + 9 q^{50} + 4 q^{52} + 2 q^{53} + 44 q^{55} - 7 q^{56} - 6 q^{58} - 19 q^{59} - 26 q^{61} + 2 q^{62} - 3 q^{64} + 16 q^{65} - 16 q^{67} + 12 q^{68} - 23 q^{70} + 48 q^{71} - 30 q^{73} - 8 q^{74} + 12 q^{76} - 39 q^{77} - 18 q^{79} - 4 q^{80} - 40 q^{82} - 29 q^{83} - 4 q^{85} + 12 q^{86} + q^{88} + 62 q^{89} - 26 q^{91} - 10 q^{92} + 6 q^{95} + 23 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 0.587785i −0.572061 0.415627i
\(3\) 0 0
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 0.220100 2.22521i 0.0984316 0.995144i
\(6\) 0 0
\(7\) 1.64173 0.620515 0.310257 0.950653i \(-0.399585\pi\)
0.310257 + 0.950653i \(0.399585\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 0 0
\(10\) −1.48601 + 1.67086i −0.469918 + 0.528373i
\(11\) −0.232788 0.169130i −0.0701883 0.0509948i 0.552138 0.833753i \(-0.313812\pi\)
−0.622326 + 0.782758i \(0.713812\pi\)
\(12\) 0 0
\(13\) 1.02912 0.747697i 0.285426 0.207374i −0.435855 0.900017i \(-0.643554\pi\)
0.721280 + 0.692643i \(0.243554\pi\)
\(14\) −1.32819 0.964983i −0.354972 0.257903i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 1.52297 4.68721i 0.369374 1.13682i −0.577822 0.816163i \(-0.696097\pi\)
0.947196 0.320654i \(-0.103903\pi\)
\(18\) 0 0
\(19\) −0.745417 + 2.29416i −0.171010 + 0.526316i −0.999429 0.0337940i \(-0.989241\pi\)
0.828419 + 0.560110i \(0.189241\pi\)
\(20\) 2.18431 0.478300i 0.488428 0.106951i
\(21\) 0 0
\(22\) 0.0889172 + 0.273659i 0.0189572 + 0.0583443i
\(23\) 0.588076 + 0.427262i 0.122622 + 0.0890903i 0.647406 0.762145i \(-0.275854\pi\)
−0.524784 + 0.851236i \(0.675854\pi\)
\(24\) 0 0
\(25\) −4.90311 0.979536i −0.980622 0.195907i
\(26\) −1.27206 −0.249471
\(27\) 0 0
\(28\) 0.507322 + 1.56138i 0.0958748 + 0.295072i
\(29\) −1.43158 4.40594i −0.265837 0.818162i −0.991499 0.130111i \(-0.958467\pi\)
0.725662 0.688051i \(-0.241533\pi\)
\(30\) 0 0
\(31\) 2.27323 6.99629i 0.408284 1.25657i −0.509837 0.860271i \(-0.670294\pi\)
0.918121 0.396299i \(-0.129706\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.98718 + 2.89686i −0.683796 + 0.496807i
\(35\) 0.361344 3.65319i 0.0610783 0.617501i
\(36\) 0 0
\(37\) 6.70462 4.87119i 1.10223 0.800819i 0.120810 0.992676i \(-0.461451\pi\)
0.981423 + 0.191857i \(0.0614509\pi\)
\(38\) 1.95153 1.41787i 0.316579 0.230008i
\(39\) 0 0
\(40\) −2.04829 0.896955i −0.323862 0.141821i
\(41\) −2.21533 + 1.60953i −0.345976 + 0.251367i −0.747179 0.664623i \(-0.768592\pi\)
0.401203 + 0.915989i \(0.368592\pi\)
\(42\) 0 0
\(43\) 5.96937 0.910320 0.455160 0.890410i \(-0.349582\pi\)
0.455160 + 0.890410i \(0.349582\pi\)
\(44\) 0.0889172 0.273659i 0.0134048 0.0412556i
\(45\) 0 0
\(46\) −0.224625 0.691324i −0.0331191 0.101930i
\(47\) −1.71263 5.27092i −0.249812 0.768843i −0.994808 0.101773i \(-0.967548\pi\)
0.744995 0.667070i \(-0.232452\pi\)
\(48\) 0 0
\(49\) −4.30473 −0.614962
\(50\) 3.39094 + 3.67444i 0.479552 + 0.519644i
\(51\) 0 0
\(52\) 1.02912 + 0.747697i 0.142713 + 0.103687i
\(53\) 1.99918 + 6.15285i 0.274609 + 0.845159i 0.989323 + 0.145742i \(0.0465569\pi\)
−0.714714 + 0.699417i \(0.753443\pi\)
\(54\) 0 0
\(55\) −0.427587 + 0.480777i −0.0576559 + 0.0648279i
\(56\) 0.507322 1.56138i 0.0677937 0.208648i
\(57\) 0 0
\(58\) −1.43158 + 4.40594i −0.187975 + 0.578528i
\(59\) −7.03842 + 5.11371i −0.916324 + 0.665748i −0.942606 0.333906i \(-0.891633\pi\)
0.0262825 + 0.999655i \(0.491633\pi\)
\(60\) 0 0
\(61\) −8.45598 6.14363i −1.08268 0.786611i −0.104529 0.994522i \(-0.533334\pi\)
−0.978148 + 0.207911i \(0.933334\pi\)
\(62\) −5.95140 + 4.32394i −0.755828 + 0.549141i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −1.43727 2.45457i −0.178272 0.304452i
\(66\) 0 0
\(67\) 3.78815 11.6587i 0.462797 1.42434i −0.398936 0.916979i \(-0.630620\pi\)
0.861733 0.507363i \(-0.169380\pi\)
\(68\) 4.92843 0.597660
\(69\) 0 0
\(70\) −2.43962 + 2.74310i −0.291591 + 0.327863i
\(71\) 4.76911 + 14.6778i 0.565989 + 1.74194i 0.664994 + 0.746849i \(0.268434\pi\)
−0.0990047 + 0.995087i \(0.531566\pi\)
\(72\) 0 0
\(73\) 5.40292 + 3.92545i 0.632364 + 0.459440i 0.857219 0.514953i \(-0.172191\pi\)
−0.224854 + 0.974392i \(0.572191\pi\)
\(74\) −8.28736 −0.963387
\(75\) 0 0
\(76\) −2.41222 −0.276700
\(77\) −0.382175 0.277666i −0.0435528 0.0316430i
\(78\) 0 0
\(79\) 2.98419 + 9.18438i 0.335747 + 1.03332i 0.966353 + 0.257220i \(0.0828066\pi\)
−0.630605 + 0.776104i \(0.717193\pi\)
\(80\) 1.12988 + 1.92960i 0.126324 + 0.215736i
\(81\) 0 0
\(82\) 2.73830 0.302394
\(83\) −0.898338 + 2.76480i −0.0986054 + 0.303476i −0.988177 0.153321i \(-0.951003\pi\)
0.889571 + 0.456797i \(0.151003\pi\)
\(84\) 0 0
\(85\) −10.0948 4.42058i −1.09494 0.479479i
\(86\) −4.82932 3.50871i −0.520759 0.378354i
\(87\) 0 0
\(88\) −0.232788 + 0.169130i −0.0248153 + 0.0180294i
\(89\) 12.4011 + 9.00992i 1.31451 + 0.955049i 0.999983 + 0.00580136i \(0.00184664\pi\)
0.314529 + 0.949248i \(0.398153\pi\)
\(90\) 0 0
\(91\) 1.68953 1.22751i 0.177111 0.128679i
\(92\) −0.224625 + 0.691324i −0.0234188 + 0.0720755i
\(93\) 0 0
\(94\) −1.71263 + 5.27092i −0.176644 + 0.543654i
\(95\) 4.94091 + 2.16365i 0.506927 + 0.221986i
\(96\) 0 0
\(97\) 0.560804 + 1.72598i 0.0569410 + 0.175246i 0.975482 0.220079i \(-0.0706317\pi\)
−0.918541 + 0.395326i \(0.870632\pi\)
\(98\) 3.48260 + 2.53026i 0.351796 + 0.255595i
\(99\) 0 0
\(100\) −0.583551 4.96583i −0.0583551 0.496583i
\(101\) −1.35931 −0.135257 −0.0676283 0.997711i \(-0.521543\pi\)
−0.0676283 + 0.997711i \(0.521543\pi\)
\(102\) 0 0
\(103\) 5.53474 + 17.0342i 0.545354 + 1.67843i 0.720146 + 0.693823i \(0.244075\pi\)
−0.174791 + 0.984606i \(0.555925\pi\)
\(104\) −0.393088 1.20980i −0.0385454 0.118631i
\(105\) 0 0
\(106\) 1.99918 6.15285i 0.194178 0.597617i
\(107\) 6.32873 0.611821 0.305911 0.952060i \(-0.401039\pi\)
0.305911 + 0.952060i \(0.401039\pi\)
\(108\) 0 0
\(109\) −6.65751 + 4.83696i −0.637673 + 0.463297i −0.859050 0.511891i \(-0.828945\pi\)
0.221377 + 0.975188i \(0.428945\pi\)
\(110\) 0.628519 0.137627i 0.0599269 0.0131222i
\(111\) 0 0
\(112\) −1.32819 + 0.964983i −0.125502 + 0.0911823i
\(113\) −10.1263 + 7.35719i −0.952602 + 0.692106i −0.951421 0.307893i \(-0.900376\pi\)
−0.00118151 + 0.999999i \(0.500376\pi\)
\(114\) 0 0
\(115\) 1.08018 1.21455i 0.100728 0.113257i
\(116\) 3.74791 2.72302i 0.347985 0.252826i
\(117\) 0 0
\(118\) 8.69996 0.800896
\(119\) 2.50030 7.69513i 0.229202 0.705411i
\(120\) 0 0
\(121\) −3.37360 10.3829i −0.306691 0.943898i
\(122\) 3.22990 + 9.94060i 0.292421 + 0.899980i
\(123\) 0 0
\(124\) 7.35633 0.660618
\(125\) −3.25885 + 10.6949i −0.291480 + 0.956577i
\(126\) 0 0
\(127\) 16.4816 + 11.9746i 1.46250 + 1.06257i 0.982702 + 0.185192i \(0.0592905\pi\)
0.479799 + 0.877378i \(0.340709\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) −0.279980 + 2.83060i −0.0245559 + 0.248260i
\(131\) −3.51255 + 10.8105i −0.306893 + 0.944519i 0.672071 + 0.740486i \(0.265405\pi\)
−0.978964 + 0.204033i \(0.934595\pi\)
\(132\) 0 0
\(133\) −1.22377 + 3.76638i −0.106114 + 0.326587i
\(134\) −9.91751 + 7.20550i −0.856743 + 0.622460i
\(135\) 0 0
\(136\) −3.98718 2.89686i −0.341898 0.248404i
\(137\) −3.96485 + 2.88063i −0.338740 + 0.246109i −0.744130 0.668035i \(-0.767136\pi\)
0.405390 + 0.914144i \(0.367136\pi\)
\(138\) 0 0
\(139\) 7.61833 + 5.53504i 0.646178 + 0.469476i 0.861967 0.506964i \(-0.169232\pi\)
−0.215789 + 0.976440i \(0.569232\pi\)
\(140\) 3.58605 0.785238i 0.303076 0.0663647i
\(141\) 0 0
\(142\) 4.76911 14.6778i 0.400215 1.23173i
\(143\) −0.366025 −0.0306085
\(144\) 0 0
\(145\) −10.1192 + 2.21581i −0.840356 + 0.184013i
\(146\) −2.06373 6.35152i −0.170796 0.525655i
\(147\) 0 0
\(148\) 6.70462 + 4.87119i 0.551116 + 0.400409i
\(149\) 15.0495 1.23290 0.616452 0.787392i \(-0.288569\pi\)
0.616452 + 0.787392i \(0.288569\pi\)
\(150\) 0 0
\(151\) 3.06961 0.249801 0.124901 0.992169i \(-0.460139\pi\)
0.124901 + 0.992169i \(0.460139\pi\)
\(152\) 1.95153 + 1.41787i 0.158290 + 0.115004i
\(153\) 0 0
\(154\) 0.145978 + 0.449273i 0.0117632 + 0.0362035i
\(155\) −15.0679 6.59830i −1.21028 0.529988i
\(156\) 0 0
\(157\) −15.6140 −1.24613 −0.623066 0.782170i \(-0.714113\pi\)
−0.623066 + 0.782170i \(0.714113\pi\)
\(158\) 2.98419 9.18438i 0.237409 0.730670i
\(159\) 0 0
\(160\) 0.220100 2.22521i 0.0174004 0.175918i
\(161\) 0.965460 + 0.701447i 0.0760889 + 0.0552818i
\(162\) 0 0
\(163\) 7.16908 5.20864i 0.561526 0.407972i −0.270491 0.962722i \(-0.587186\pi\)
0.832017 + 0.554750i \(0.187186\pi\)
\(164\) −2.21533 1.60953i −0.172988 0.125683i
\(165\) 0 0
\(166\) 2.35188 1.70874i 0.182541 0.132624i
\(167\) 5.42191 16.6869i 0.419560 1.29127i −0.488548 0.872537i \(-0.662473\pi\)
0.908108 0.418736i \(-0.137527\pi\)
\(168\) 0 0
\(169\) −3.51719 + 10.8248i −0.270553 + 0.832677i
\(170\) 5.56854 + 9.50991i 0.427087 + 0.729377i
\(171\) 0 0
\(172\) 1.84464 + 5.67721i 0.140652 + 0.432883i
\(173\) −13.9942 10.1674i −1.06396 0.773012i −0.0891431 0.996019i \(-0.528413\pi\)
−0.974817 + 0.223007i \(0.928413\pi\)
\(174\) 0 0
\(175\) −8.04957 1.60813i −0.608491 0.121563i
\(176\) 0.287742 0.0216894
\(177\) 0 0
\(178\) −4.73679 14.5783i −0.355038 1.09269i
\(179\) −1.22409 3.76738i −0.0914931 0.281587i 0.894831 0.446406i \(-0.147296\pi\)
−0.986324 + 0.164819i \(0.947296\pi\)
\(180\) 0 0
\(181\) 1.61586 4.97310i 0.120106 0.369647i −0.872872 0.487949i \(-0.837745\pi\)
0.992978 + 0.118302i \(0.0377451\pi\)
\(182\) −2.08837 −0.154801
\(183\) 0 0
\(184\) 0.588076 0.427262i 0.0433535 0.0314982i
\(185\) −9.36373 15.9913i −0.688435 1.17571i
\(186\) 0 0
\(187\) −1.14728 + 0.833548i −0.0838974 + 0.0609550i
\(188\) 4.48371 3.25761i 0.327008 0.237586i
\(189\) 0 0
\(190\) −2.72552 4.65463i −0.197730 0.337682i
\(191\) 9.68041 7.03323i 0.700450 0.508906i −0.179629 0.983734i \(-0.557490\pi\)
0.880079 + 0.474828i \(0.157490\pi\)
\(192\) 0 0
\(193\) −13.9654 −1.00525 −0.502624 0.864505i \(-0.667632\pi\)
−0.502624 + 0.864505i \(0.667632\pi\)
\(194\) 0.560804 1.72598i 0.0402634 0.123918i
\(195\) 0 0
\(196\) −1.33024 4.09404i −0.0950168 0.292432i
\(197\) 4.24836 + 13.0751i 0.302683 + 0.931563i 0.980532 + 0.196362i \(0.0629126\pi\)
−0.677848 + 0.735202i \(0.737087\pi\)
\(198\) 0 0
\(199\) −13.0562 −0.925531 −0.462765 0.886481i \(-0.653143\pi\)
−0.462765 + 0.886481i \(0.653143\pi\)
\(200\) −2.44674 + 4.36044i −0.173011 + 0.308330i
\(201\) 0 0
\(202\) 1.09971 + 0.798984i 0.0773751 + 0.0562163i
\(203\) −2.35026 7.23335i −0.164956 0.507682i
\(204\) 0 0
\(205\) 3.09395 + 5.28383i 0.216091 + 0.369039i
\(206\) 5.53474 17.0342i 0.385624 1.18683i
\(207\) 0 0
\(208\) −0.393088 + 1.20980i −0.0272557 + 0.0838845i
\(209\) 0.561536 0.407980i 0.0388423 0.0282205i
\(210\) 0 0
\(211\) −6.54646 4.75628i −0.450677 0.327436i 0.339186 0.940719i \(-0.389848\pi\)
−0.789863 + 0.613283i \(0.789848\pi\)
\(212\) −5.23392 + 3.80267i −0.359467 + 0.261168i
\(213\) 0 0
\(214\) −5.12005 3.71993i −0.349999 0.254289i
\(215\) 1.31386 13.2831i 0.0896043 0.905900i
\(216\) 0 0
\(217\) 3.73203 11.4860i 0.253346 0.779720i
\(218\) 8.22913 0.557347
\(219\) 0 0
\(220\) −0.589378 0.258092i −0.0397358 0.0174005i
\(221\) −1.93730 5.96241i −0.130317 0.401075i
\(222\) 0 0
\(223\) 4.11685 + 2.99107i 0.275685 + 0.200297i 0.717033 0.697039i \(-0.245500\pi\)
−0.441348 + 0.897336i \(0.645500\pi\)
\(224\) 1.64173 0.109693
\(225\) 0 0
\(226\) 12.5168 0.832605
\(227\) −20.0528 14.5692i −1.33095 0.966993i −0.999725 0.0234412i \(-0.992538\pi\)
−0.331226 0.943551i \(-0.607462\pi\)
\(228\) 0 0
\(229\) −0.457059 1.40668i −0.0302033 0.0929562i 0.934819 0.355126i \(-0.115562\pi\)
−0.965022 + 0.262170i \(0.915562\pi\)
\(230\) −1.58778 + 0.347677i −0.104695 + 0.0229251i
\(231\) 0 0
\(232\) −4.63268 −0.304150
\(233\) 0.215440 0.663055i 0.0141139 0.0434382i −0.943752 0.330656i \(-0.892730\pi\)
0.957865 + 0.287217i \(0.0927302\pi\)
\(234\) 0 0
\(235\) −12.1059 + 2.65082i −0.789699 + 0.172921i
\(236\) −7.03842 5.11371i −0.458162 0.332874i
\(237\) 0 0
\(238\) −6.54587 + 4.75585i −0.424306 + 0.308276i
\(239\) 23.6136 + 17.1563i 1.52744 + 1.10975i 0.957642 + 0.287961i \(0.0929773\pi\)
0.569795 + 0.821787i \(0.307023\pi\)
\(240\) 0 0
\(241\) −14.0170 + 10.1840i −0.902915 + 0.656006i −0.939213 0.343335i \(-0.888443\pi\)
0.0362980 + 0.999341i \(0.488443\pi\)
\(242\) −3.37360 + 10.3829i −0.216863 + 0.667437i
\(243\) 0 0
\(244\) 3.22990 9.94060i 0.206773 0.636382i
\(245\) −0.947471 + 9.57893i −0.0605317 + 0.611975i
\(246\) 0 0
\(247\) 0.948214 + 2.91830i 0.0603334 + 0.185687i
\(248\) −5.95140 4.32394i −0.377914 0.274571i
\(249\) 0 0
\(250\) 8.92274 6.73682i 0.564324 0.426074i
\(251\) 1.10083 0.0694837 0.0347419 0.999396i \(-0.488939\pi\)
0.0347419 + 0.999396i \(0.488939\pi\)
\(252\) 0 0
\(253\) −0.0646340 0.198923i −0.00406350 0.0125062i
\(254\) −6.29540 19.3752i −0.395008 1.21571i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 29.4887 1.83945 0.919726 0.392560i \(-0.128410\pi\)
0.919726 + 0.392560i \(0.128410\pi\)
\(258\) 0 0
\(259\) 11.0072 7.99717i 0.683951 0.496920i
\(260\) 1.89029 2.12543i 0.117231 0.131814i
\(261\) 0 0
\(262\) 9.19597 6.68126i 0.568129 0.412770i
\(263\) −0.647992 + 0.470794i −0.0399569 + 0.0290304i −0.607584 0.794255i \(-0.707861\pi\)
0.567628 + 0.823285i \(0.307861\pi\)
\(264\) 0 0
\(265\) 14.1314 3.09436i 0.868084 0.190085i
\(266\) 3.20387 2.32775i 0.196442 0.142724i
\(267\) 0 0
\(268\) 12.2587 0.748821
\(269\) 8.75585 26.9477i 0.533853 1.64303i −0.212260 0.977213i \(-0.568082\pi\)
0.746114 0.665819i \(-0.231918\pi\)
\(270\) 0 0
\(271\) 8.05031 + 24.7763i 0.489021 + 1.50505i 0.826071 + 0.563566i \(0.190571\pi\)
−0.337049 + 0.941487i \(0.609429\pi\)
\(272\) 1.52297 + 4.68721i 0.0923435 + 0.284204i
\(273\) 0 0
\(274\) 4.90083 0.296070
\(275\) 0.975717 + 1.05729i 0.0588379 + 0.0637570i
\(276\) 0 0
\(277\) −1.13826 0.826993i −0.0683913 0.0496892i 0.553064 0.833139i \(-0.313458\pi\)
−0.621456 + 0.783449i \(0.713458\pi\)
\(278\) −2.90994 8.95588i −0.174527 0.537138i
\(279\) 0 0
\(280\) −3.36273 1.47256i −0.200961 0.0880020i
\(281\) 5.01989 15.4496i 0.299461 0.921647i −0.682225 0.731142i \(-0.738988\pi\)
0.981686 0.190505i \(-0.0610125\pi\)
\(282\) 0 0
\(283\) 4.18580 12.8826i 0.248820 0.765790i −0.746164 0.665762i \(-0.768107\pi\)
0.994985 0.100028i \(-0.0318932\pi\)
\(284\) −12.4857 + 9.07139i −0.740890 + 0.538288i
\(285\) 0 0
\(286\) 0.296120 + 0.215144i 0.0175099 + 0.0127217i
\(287\) −3.63697 + 2.64241i −0.214683 + 0.155977i
\(288\) 0 0
\(289\) −5.89726 4.28461i −0.346898 0.252036i
\(290\) 9.48904 + 4.15530i 0.557216 + 0.244008i
\(291\) 0 0
\(292\) −2.06373 + 6.35152i −0.120771 + 0.371694i
\(293\) −23.3958 −1.36679 −0.683397 0.730047i \(-0.739498\pi\)
−0.683397 + 0.730047i \(0.739498\pi\)
\(294\) 0 0
\(295\) 9.82992 + 16.7875i 0.572320 + 0.977405i
\(296\) −2.56094 7.88175i −0.148851 0.458118i
\(297\) 0 0
\(298\) −12.1753 8.84588i −0.705297 0.512428i
\(299\) 0.924661 0.0534745
\(300\) 0 0
\(301\) 9.80008 0.564867
\(302\) −2.48337 1.80427i −0.142902 0.103824i
\(303\) 0 0
\(304\) −0.745417 2.29416i −0.0427526 0.131579i
\(305\) −15.5320 + 17.4641i −0.889361 + 0.999992i
\(306\) 0 0
\(307\) −1.94345 −0.110919 −0.0554593 0.998461i \(-0.517662\pi\)
−0.0554593 + 0.998461i \(0.517662\pi\)
\(308\) 0.145978 0.449273i 0.00831785 0.0255997i
\(309\) 0 0
\(310\) 8.31178 + 14.1948i 0.472077 + 0.806211i
\(311\) 7.84831 + 5.70213i 0.445037 + 0.323338i 0.787633 0.616144i \(-0.211306\pi\)
−0.342596 + 0.939483i \(0.611306\pi\)
\(312\) 0 0
\(313\) −4.04903 + 2.94179i −0.228865 + 0.166280i −0.696308 0.717743i \(-0.745175\pi\)
0.467443 + 0.884023i \(0.345175\pi\)
\(314\) 12.6320 + 9.17767i 0.712864 + 0.517926i
\(315\) 0 0
\(316\) −7.81270 + 5.67626i −0.439499 + 0.319315i
\(317\) 2.72402 8.38366i 0.152996 0.470873i −0.844956 0.534835i \(-0.820374\pi\)
0.997952 + 0.0639620i \(0.0203737\pi\)
\(318\) 0 0
\(319\) −0.411924 + 1.26777i −0.0230633 + 0.0709817i
\(320\) −1.48601 + 1.67086i −0.0830705 + 0.0934039i
\(321\) 0 0
\(322\) −0.368773 1.13497i −0.0205509 0.0632492i
\(323\) 9.61796 + 6.98786i 0.535158 + 0.388815i
\(324\) 0 0
\(325\) −5.77827 + 2.65799i −0.320521 + 0.147439i
\(326\) −8.86147 −0.490791
\(327\) 0 0
\(328\) 0.846180 + 2.60428i 0.0467225 + 0.143797i
\(329\) −2.81167 8.65342i −0.155012 0.477078i
\(330\) 0 0
\(331\) −0.197287 + 0.607187i −0.0108439 + 0.0333740i −0.956332 0.292282i \(-0.905585\pi\)
0.945488 + 0.325656i \(0.105585\pi\)
\(332\) −2.90708 −0.159547
\(333\) 0 0
\(334\) −14.1947 + 10.3131i −0.776702 + 0.564307i
\(335\) −25.1094 10.9955i −1.37187 0.600749i
\(336\) 0 0
\(337\) −4.75679 + 3.45601i −0.259119 + 0.188261i −0.709759 0.704445i \(-0.751196\pi\)
0.450640 + 0.892706i \(0.351196\pi\)
\(338\) 9.20812 6.69009i 0.500856 0.363893i
\(339\) 0 0
\(340\) 1.08475 10.9668i 0.0588286 0.594757i
\(341\) −1.71247 + 1.24418i −0.0927353 + 0.0673761i
\(342\) 0 0
\(343\) −18.5593 −1.00211
\(344\) 1.84464 5.67721i 0.0994561 0.306095i
\(345\) 0 0
\(346\) 5.34531 + 16.4512i 0.287366 + 0.884421i
\(347\) 6.69935 + 20.6185i 0.359640 + 1.10686i 0.953270 + 0.302120i \(0.0976943\pi\)
−0.593630 + 0.804738i \(0.702306\pi\)
\(348\) 0 0
\(349\) −1.18292 −0.0633205 −0.0316602 0.999499i \(-0.510079\pi\)
−0.0316602 + 0.999499i \(0.510079\pi\)
\(350\) 5.56701 + 6.03243i 0.297569 + 0.322447i
\(351\) 0 0
\(352\) −0.232788 0.169130i −0.0124076 0.00901468i
\(353\) −0.639222 1.96732i −0.0340223 0.104710i 0.932603 0.360903i \(-0.117532\pi\)
−0.966626 + 0.256193i \(0.917532\pi\)
\(354\) 0 0
\(355\) 33.7109 7.38168i 1.78919 0.391779i
\(356\) −4.73679 + 14.5783i −0.251050 + 0.772651i
\(357\) 0 0
\(358\) −1.22409 + 3.76738i −0.0646954 + 0.199112i
\(359\) −29.6026 + 21.5076i −1.56237 + 1.13513i −0.628331 + 0.777946i \(0.716262\pi\)
−0.934036 + 0.357179i \(0.883738\pi\)
\(360\) 0 0
\(361\) 10.6638 + 7.74771i 0.561253 + 0.407774i
\(362\) −4.23037 + 3.07354i −0.222343 + 0.161542i
\(363\) 0 0
\(364\) 1.68953 + 1.22751i 0.0885554 + 0.0643393i
\(365\) 9.92414 11.1586i 0.519453 0.584070i
\(366\) 0 0
\(367\) −2.35254 + 7.24037i −0.122801 + 0.377944i −0.993494 0.113883i \(-0.963671\pi\)
0.870693 + 0.491828i \(0.163671\pi\)
\(368\) −0.726901 −0.0378924
\(369\) 0 0
\(370\) −1.82405 + 18.4411i −0.0948277 + 0.958708i
\(371\) 3.28211 + 10.1013i 0.170399 + 0.524433i
\(372\) 0 0
\(373\) −8.22653 5.97692i −0.425953 0.309473i 0.354075 0.935217i \(-0.384796\pi\)
−0.780029 + 0.625744i \(0.784796\pi\)
\(374\) 1.41812 0.0733290
\(375\) 0 0
\(376\) −5.54218 −0.285816
\(377\) −4.76757 3.46384i −0.245542 0.178397i
\(378\) 0 0
\(379\) −10.9182 33.6026i −0.560828 1.72605i −0.680034 0.733181i \(-0.738035\pi\)
0.119206 0.992870i \(-0.461965\pi\)
\(380\) −0.530929 + 5.36769i −0.0272361 + 0.275357i
\(381\) 0 0
\(382\) −11.9656 −0.612215
\(383\) −3.41810 + 10.5198i −0.174657 + 0.537538i −0.999618 0.0276519i \(-0.991197\pi\)
0.824961 + 0.565190i \(0.191197\pi\)
\(384\) 0 0
\(385\) −0.701982 + 0.789304i −0.0357763 + 0.0402267i
\(386\) 11.2982 + 8.20863i 0.575064 + 0.417808i
\(387\) 0 0
\(388\) −1.46820 + 1.06671i −0.0745367 + 0.0541541i
\(389\) 27.6451 + 20.0853i 1.40166 + 1.01837i 0.994470 + 0.105024i \(0.0334918\pi\)
0.407191 + 0.913343i \(0.366508\pi\)
\(390\) 0 0
\(391\) 2.89829 2.10573i 0.146573 0.106491i
\(392\) −1.33024 + 4.09404i −0.0671870 + 0.206780i
\(393\) 0 0
\(394\) 4.24836 13.0751i 0.214029 0.658715i
\(395\) 21.0940 4.61896i 1.06135 0.232405i
\(396\) 0 0
\(397\) 5.60979 + 17.2652i 0.281547 + 0.866514i 0.987412 + 0.158167i \(0.0505585\pi\)
−0.705865 + 0.708346i \(0.749441\pi\)
\(398\) 10.5627 + 7.67425i 0.529460 + 0.384676i
\(399\) 0 0
\(400\) 4.54246 2.08952i 0.227123 0.104476i
\(401\) −2.68524 −0.134094 −0.0670472 0.997750i \(-0.521358\pi\)
−0.0670472 + 0.997750i \(0.521358\pi\)
\(402\) 0 0
\(403\) −2.89168 8.89969i −0.144045 0.443325i
\(404\) −0.420051 1.29278i −0.0208983 0.0643184i
\(405\) 0 0
\(406\) −2.35026 + 7.23335i −0.116641 + 0.358985i
\(407\) −2.38462 −0.118201
\(408\) 0 0
\(409\) 26.9131 19.5535i 1.33077 0.966858i 0.331036 0.943618i \(-0.392602\pi\)
0.999730 0.0232401i \(-0.00739821\pi\)
\(410\) 0.602699 6.09329i 0.0297652 0.300926i
\(411\) 0 0
\(412\) −14.4901 + 10.5277i −0.713878 + 0.518663i
\(413\) −11.5552 + 8.39532i −0.568592 + 0.413106i
\(414\) 0 0
\(415\) 5.95453 + 2.60752i 0.292297 + 0.127998i
\(416\) 1.02912 0.747697i 0.0504566 0.0366589i
\(417\) 0 0
\(418\) −0.694097 −0.0339494
\(419\) −3.70892 + 11.4149i −0.181192 + 0.557653i −0.999862 0.0166119i \(-0.994712\pi\)
0.818670 + 0.574265i \(0.194712\pi\)
\(420\) 0 0
\(421\) 7.31823 + 22.5232i 0.356669 + 1.09771i 0.955035 + 0.296492i \(0.0958167\pi\)
−0.598367 + 0.801223i \(0.704183\pi\)
\(422\) 2.50053 + 7.69583i 0.121724 + 0.374627i
\(423\) 0 0
\(424\) 6.46949 0.314186
\(425\) −12.0586 + 21.4901i −0.584927 + 1.04242i
\(426\) 0 0
\(427\) −13.8824 10.0862i −0.671817 0.488104i
\(428\) 1.95568 + 6.01898i 0.0945316 + 0.290938i
\(429\) 0 0
\(430\) −8.87054 + 9.97398i −0.427775 + 0.480988i
\(431\) −8.82145 + 27.1496i −0.424914 + 1.30775i 0.478162 + 0.878271i \(0.341303\pi\)
−0.903076 + 0.429480i \(0.858697\pi\)
\(432\) 0 0
\(433\) 10.2515 31.5507i 0.492653 1.51623i −0.327928 0.944703i \(-0.606350\pi\)
0.820582 0.571529i \(-0.193650\pi\)
\(434\) −9.77057 + 7.09874i −0.469002 + 0.340750i
\(435\) 0 0
\(436\) −6.65751 4.83696i −0.318837 0.231648i
\(437\) −1.41857 + 1.03065i −0.0678593 + 0.0493026i
\(438\) 0 0
\(439\) 14.9511 + 10.8626i 0.713575 + 0.518442i 0.884325 0.466872i \(-0.154619\pi\)
−0.170750 + 0.985314i \(0.554619\pi\)
\(440\) 0.325114 + 0.555228i 0.0154992 + 0.0264695i
\(441\) 0 0
\(442\) −1.93730 + 5.96241i −0.0921482 + 0.283603i
\(443\) 18.7642 0.891515 0.445757 0.895154i \(-0.352934\pi\)
0.445757 + 0.895154i \(0.352934\pi\)
\(444\) 0 0
\(445\) 22.7784 25.6119i 1.07980 1.21412i
\(446\) −1.57250 4.83965i −0.0744599 0.229164i
\(447\) 0 0
\(448\) −1.32819 0.964983i −0.0627509 0.0455912i
\(449\) 4.33462 0.204563 0.102282 0.994755i \(-0.467386\pi\)
0.102282 + 0.994755i \(0.467386\pi\)
\(450\) 0 0
\(451\) 0.787923 0.0371018
\(452\) −10.1263 7.35719i −0.476301 0.346053i
\(453\) 0 0
\(454\) 7.65949 + 23.5735i 0.359478 + 1.10636i
\(455\) −2.35961 4.02973i −0.110620 0.188917i
\(456\) 0 0
\(457\) −27.6962 −1.29557 −0.647786 0.761822i \(-0.724305\pi\)
−0.647786 + 0.761822i \(0.724305\pi\)
\(458\) −0.457059 + 1.40668i −0.0213570 + 0.0657299i
\(459\) 0 0
\(460\) 1.48890 + 0.651998i 0.0694204 + 0.0303995i
\(461\) 9.30766 + 6.76241i 0.433501 + 0.314957i 0.783047 0.621962i \(-0.213664\pi\)
−0.349546 + 0.936919i \(0.613664\pi\)
\(462\) 0 0
\(463\) −0.940376 + 0.683223i −0.0437030 + 0.0317521i −0.609422 0.792846i \(-0.708599\pi\)
0.565719 + 0.824598i \(0.308599\pi\)
\(464\) 3.74791 + 2.72302i 0.173993 + 0.126413i
\(465\) 0 0
\(466\) −0.564028 + 0.409791i −0.0261281 + 0.0189832i
\(467\) 6.68977 20.5890i 0.309566 0.952745i −0.668368 0.743831i \(-0.733007\pi\)
0.977934 0.208915i \(-0.0669931\pi\)
\(468\) 0 0
\(469\) 6.21911 19.1405i 0.287172 0.883825i
\(470\) 11.3520 + 4.97108i 0.523627 + 0.229299i
\(471\) 0 0
\(472\) 2.68844 + 8.27415i 0.123745 + 0.380849i
\(473\) −1.38960 1.00960i −0.0638938 0.0464216i
\(474\) 0 0
\(475\) 5.90207 10.5183i 0.270806 0.482615i
\(476\) 8.09114 0.370857
\(477\) 0 0
\(478\) −9.01959 27.7595i −0.412547 1.26969i
\(479\) −7.53007 23.1752i −0.344058 1.05890i −0.962086 0.272745i \(-0.912068\pi\)
0.618029 0.786156i \(-0.287932\pi\)
\(480\) 0 0
\(481\) 3.25766 10.0260i 0.148537 0.457148i
\(482\) 17.3260 0.789177
\(483\) 0 0
\(484\) 8.83220 6.41697i 0.401464 0.291681i
\(485\) 3.96409 0.868018i 0.180000 0.0394147i
\(486\) 0 0
\(487\) −19.3197 + 14.0366i −0.875458 + 0.636058i −0.932046 0.362340i \(-0.881978\pi\)
0.0565877 + 0.998398i \(0.481978\pi\)
\(488\) −8.45598 + 6.14363i −0.382784 + 0.278109i
\(489\) 0 0
\(490\) 6.39687 7.19261i 0.288981 0.324929i
\(491\) −22.2993 + 16.2014i −1.00635 + 0.731158i −0.963441 0.267921i \(-0.913663\pi\)
−0.0429114 + 0.999079i \(0.513663\pi\)
\(492\) 0 0
\(493\) −22.8318 −1.02829
\(494\) 0.948214 2.91830i 0.0426621 0.131301i
\(495\) 0 0
\(496\) 2.27323 + 6.99629i 0.102071 + 0.314143i
\(497\) 7.82958 + 24.0970i 0.351205 + 1.08090i
\(498\) 0 0
\(499\) 12.7308 0.569911 0.284955 0.958541i \(-0.408021\pi\)
0.284955 + 0.958541i \(0.408021\pi\)
\(500\) −11.1785 + 0.205544i −0.499915 + 0.00919219i
\(501\) 0 0
\(502\) −0.890590 0.647051i −0.0397490 0.0288793i
\(503\) 8.58376 + 26.4181i 0.382731 + 1.17792i 0.938113 + 0.346329i \(0.112572\pi\)
−0.555382 + 0.831595i \(0.687428\pi\)
\(504\) 0 0
\(505\) −0.299185 + 3.02476i −0.0133135 + 0.134600i
\(506\) −0.0646340 + 0.198923i −0.00287333 + 0.00884321i
\(507\) 0 0
\(508\) −6.29540 + 19.3752i −0.279313 + 0.859637i
\(509\) −18.2595 + 13.2663i −0.809338 + 0.588019i −0.913639 0.406527i \(-0.866740\pi\)
0.104300 + 0.994546i \(0.466740\pi\)
\(510\) 0 0
\(511\) 8.87013 + 6.44452i 0.392391 + 0.285089i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −23.8568 17.3330i −1.05228 0.764526i
\(515\) 39.1228 8.56674i 1.72396 0.377496i
\(516\) 0 0
\(517\) −0.492794 + 1.51667i −0.0216731 + 0.0667029i
\(518\) −13.6056 −0.597795
\(519\) 0 0
\(520\) −2.77858 + 0.608426i −0.121849 + 0.0266812i
\(521\) −7.98129 24.5639i −0.349667 1.07616i −0.959038 0.283278i \(-0.908578\pi\)
0.609371 0.792885i \(-0.291422\pi\)
\(522\) 0 0
\(523\) −23.0192 16.7244i −1.00656 0.731308i −0.0430742 0.999072i \(-0.513715\pi\)
−0.963484 + 0.267764i \(0.913715\pi\)
\(524\) −11.3668 −0.496563
\(525\) 0 0
\(526\) 0.800963 0.0349236
\(527\) −29.3310 21.3102i −1.27768 0.928289i
\(528\) 0 0
\(529\) −6.94411 21.3718i −0.301918 0.929208i
\(530\) −13.2514 5.80284i −0.575602 0.252059i
\(531\) 0 0
\(532\) −3.96021 −0.171697
\(533\) −1.07639 + 3.31279i −0.0466237 + 0.143493i
\(534\) 0 0
\(535\) 1.39295 14.0827i 0.0602226 0.608850i
\(536\) −9.91751 7.20550i −0.428371 0.311230i
\(537\) 0 0
\(538\) −22.9231 + 16.6546i −0.988285 + 0.718031i
\(539\) 1.00209 + 0.728061i 0.0431631 + 0.0313598i
\(540\) 0 0
\(541\) −20.3737 + 14.8024i −0.875933 + 0.636403i −0.932172 0.362014i \(-0.882089\pi\)
0.0562391 + 0.998417i \(0.482089\pi\)
\(542\) 8.05031 24.7763i 0.345790 1.06423i
\(543\) 0 0
\(544\) 1.52297 4.68721i 0.0652967 0.200963i
\(545\) 9.29794 + 15.8790i 0.398280 + 0.680180i
\(546\) 0 0
\(547\) −2.56321 7.88874i −0.109595 0.337298i 0.881187 0.472769i \(-0.156745\pi\)
−0.990781 + 0.135471i \(0.956745\pi\)
\(548\) −3.96485 2.88063i −0.169370 0.123055i
\(549\) 0 0
\(550\) −0.167912 1.42888i −0.00715979 0.0609275i
\(551\) 11.1750 0.476072
\(552\) 0 0
\(553\) 4.89922 + 15.0783i 0.208336 + 0.641193i
\(554\) 0.434776 + 1.33810i 0.0184719 + 0.0568506i
\(555\) 0 0
\(556\) −2.90994 + 8.95588i −0.123409 + 0.379814i
\(557\) 14.4884 0.613894 0.306947 0.951727i \(-0.400693\pi\)
0.306947 + 0.951727i \(0.400693\pi\)
\(558\) 0 0
\(559\) 6.14318 4.46328i 0.259829 0.188777i
\(560\) 1.85496 + 3.16788i 0.0783862 + 0.133867i
\(561\) 0 0
\(562\) −13.1422 + 9.54839i −0.554372 + 0.402775i
\(563\) 31.7433 23.0629i 1.33782 0.971984i 0.338300 0.941038i \(-0.390148\pi\)
0.999521 0.0309456i \(-0.00985185\pi\)
\(564\) 0 0
\(565\) 14.1425 + 24.1525i 0.594979 + 1.01610i
\(566\) −10.9586 + 7.96187i −0.460623 + 0.334662i
\(567\) 0 0
\(568\) 15.4332 0.647561
\(569\) 7.49004 23.0520i 0.313999 0.966389i −0.662166 0.749357i \(-0.730363\pi\)
0.976165 0.217031i \(-0.0696374\pi\)
\(570\) 0 0
\(571\) −7.52079 23.1466i −0.314735 0.968656i −0.975863 0.218383i \(-0.929922\pi\)
0.661128 0.750273i \(-0.270078\pi\)
\(572\) −0.113108 0.348110i −0.00472928 0.0145552i
\(573\) 0 0
\(574\) 4.49554 0.187640
\(575\) −2.46488 2.67095i −0.102793 0.111386i
\(576\) 0 0
\(577\) 13.6665 + 9.92928i 0.568943 + 0.413361i 0.834721 0.550673i \(-0.185629\pi\)
−0.265778 + 0.964034i \(0.585629\pi\)
\(578\) 2.25255 + 6.93264i 0.0936938 + 0.288360i
\(579\) 0 0
\(580\) −5.23437 8.93923i −0.217345 0.371181i
\(581\) −1.47483 + 4.53905i −0.0611861 + 0.188311i
\(582\) 0 0
\(583\) 0.575248 1.77043i 0.0238244 0.0733238i
\(584\) 5.40292 3.92545i 0.223575 0.162436i
\(585\) 0 0
\(586\) 18.9276 + 13.7517i 0.781890 + 0.568077i
\(587\) −27.9308 + 20.2929i −1.15283 + 0.837577i −0.988854 0.148888i \(-0.952431\pi\)
−0.163972 + 0.986465i \(0.552431\pi\)
\(588\) 0 0
\(589\) 14.3561 + 10.4303i 0.591532 + 0.429773i
\(590\) 1.91486 19.3592i 0.0788335 0.797007i
\(591\) 0 0
\(592\) −2.56094 + 7.88175i −0.105254 + 0.323938i
\(593\) −2.75615 −0.113181 −0.0565907 0.998397i \(-0.518023\pi\)
−0.0565907 + 0.998397i \(0.518023\pi\)
\(594\) 0 0
\(595\) −16.5730 7.25738i −0.679425 0.297524i
\(596\) 4.65056 + 14.3129i 0.190494 + 0.586281i
\(597\) 0 0
\(598\) −0.748066 0.543502i −0.0305907 0.0222255i
\(599\) −21.3977 −0.874286 −0.437143 0.899392i \(-0.644010\pi\)
−0.437143 + 0.899392i \(0.644010\pi\)
\(600\) 0 0
\(601\) 17.1818 0.700860 0.350430 0.936589i \(-0.386036\pi\)
0.350430 + 0.936589i \(0.386036\pi\)
\(602\) −7.92843 5.76034i −0.323139 0.234774i
\(603\) 0 0
\(604\) 0.948562 + 2.91937i 0.0385964 + 0.118788i
\(605\) −23.8466 + 5.22170i −0.969502 + 0.212292i
\(606\) 0 0
\(607\) −22.8963 −0.929332 −0.464666 0.885486i \(-0.653826\pi\)
−0.464666 + 0.885486i \(0.653826\pi\)
\(608\) −0.745417 + 2.29416i −0.0302306 + 0.0930403i
\(609\) 0 0
\(610\) 22.8308 4.99927i 0.924393 0.202415i
\(611\) −5.70355 4.14387i −0.230741 0.167643i
\(612\) 0 0
\(613\) 36.4310 26.4687i 1.47143 1.06906i 0.491239 0.871025i \(-0.336544\pi\)
0.980195 0.198035i \(-0.0634560\pi\)
\(614\) 1.57228 + 1.14233i 0.0634522 + 0.0461007i
\(615\) 0 0
\(616\) −0.382175 + 0.277666i −0.0153983 + 0.0111875i
\(617\) 3.64878 11.2298i 0.146894 0.452094i −0.850355 0.526209i \(-0.823613\pi\)
0.997250 + 0.0741144i \(0.0236130\pi\)
\(618\) 0 0
\(619\) 2.47764 7.62539i 0.0995848 0.306490i −0.888837 0.458224i \(-0.848486\pi\)
0.988421 + 0.151734i \(0.0484857\pi\)
\(620\) 1.61913 16.3694i 0.0650257 0.657410i
\(621\) 0 0
\(622\) −2.99779 9.22625i −0.120200 0.369939i
\(623\) 20.3592 + 14.7918i 0.815674 + 0.592622i
\(624\) 0 0
\(625\) 23.0810 + 9.60555i 0.923241 + 0.384222i
\(626\) 5.00488 0.200035
\(627\) 0 0
\(628\) −4.82499 14.8498i −0.192538 0.592571i
\(629\) −12.6214 38.8447i −0.503248 1.54884i
\(630\) 0 0
\(631\) −14.7444 + 45.3785i −0.586964 + 1.80649i 0.00427117 + 0.999991i \(0.498640\pi\)
−0.591235 + 0.806499i \(0.701360\pi\)
\(632\) 9.65703 0.384136
\(633\) 0 0
\(634\) −7.13157 + 5.18139i −0.283231 + 0.205779i
\(635\) 30.2735 34.0393i 1.20137 1.35081i
\(636\) 0 0
\(637\) −4.43007 + 3.21864i −0.175526 + 0.127527i
\(638\) 1.07843 0.783527i 0.0426955 0.0310201i
\(639\) 0 0
\(640\) 2.18431 0.478300i 0.0863426 0.0189065i
\(641\) 6.95681 5.05442i 0.274778 0.199638i −0.441859 0.897085i \(-0.645681\pi\)
0.716636 + 0.697447i \(0.245681\pi\)
\(642\) 0 0
\(643\) −30.8943 −1.21835 −0.609176 0.793035i \(-0.708500\pi\)
−0.609176 + 0.793035i \(0.708500\pi\)
\(644\) −0.368773 + 1.13497i −0.0145317 + 0.0447239i
\(645\) 0 0
\(646\) −3.67373 11.3066i −0.144541 0.444852i
\(647\) −14.5077 44.6503i −0.570358 1.75538i −0.651466 0.758677i \(-0.725846\pi\)
0.0811081 0.996705i \(-0.474154\pi\)
\(648\) 0 0
\(649\) 2.50334 0.0982648
\(650\) 6.23704 + 1.24603i 0.244637 + 0.0488732i
\(651\) 0 0
\(652\) 7.16908 + 5.20864i 0.280763 + 0.203986i
\(653\) −11.9897 36.9004i −0.469192 1.44402i −0.853633 0.520875i \(-0.825606\pi\)
0.384441 0.923150i \(-0.374394\pi\)
\(654\) 0 0
\(655\) 23.2825 + 10.1955i 0.909724 + 0.398373i
\(656\) 0.846180 2.60428i 0.0330378 0.101680i
\(657\) 0 0
\(658\) −2.81167 + 8.65342i −0.109610 + 0.337345i
\(659\) −39.8805 + 28.9749i −1.55352 + 1.12870i −0.612445 + 0.790513i \(0.709814\pi\)
−0.941079 + 0.338188i \(0.890186\pi\)
\(660\) 0 0
\(661\) 2.16132 + 1.57029i 0.0840658 + 0.0610773i 0.629024 0.777386i \(-0.283455\pi\)
−0.544959 + 0.838463i \(0.683455\pi\)
\(662\) 0.516504 0.375262i 0.0200745 0.0145850i
\(663\) 0 0
\(664\) 2.35188 + 1.70874i 0.0912706 + 0.0663120i
\(665\) 8.11163 + 3.55213i 0.314556 + 0.137746i
\(666\) 0 0
\(667\) 1.04061 3.20268i 0.0402928 0.124008i
\(668\) 17.5457 0.678863
\(669\) 0 0
\(670\) 13.8509 + 23.6545i 0.535107 + 0.913852i
\(671\) 0.929377 + 2.86033i 0.0358782 + 0.110422i
\(672\) 0 0
\(673\) 7.04983 + 5.12200i 0.271751 + 0.197439i 0.715311 0.698806i \(-0.246285\pi\)
−0.443560 + 0.896244i \(0.646285\pi\)
\(674\) 5.87972 0.226478
\(675\) 0 0
\(676\) −11.3819 −0.437764
\(677\) 10.4655 + 7.60363i 0.402222 + 0.292231i 0.770445 0.637506i \(-0.220034\pi\)
−0.368224 + 0.929737i \(0.620034\pi\)
\(678\) 0 0
\(679\) 0.920687 + 2.83358i 0.0353327 + 0.108743i
\(680\) −7.32369 + 8.23472i −0.280851 + 0.315787i
\(681\) 0 0
\(682\) 2.11673 0.0810536
\(683\) 7.56254 23.2751i 0.289373 0.890597i −0.695681 0.718351i \(-0.744897\pi\)
0.985054 0.172247i \(-0.0551026\pi\)
\(684\) 0 0
\(685\) 5.53735 + 9.45665i 0.211571 + 0.361320i
\(686\) 15.0148 + 10.9089i 0.573267 + 0.416503i
\(687\) 0 0
\(688\) −4.82932 + 3.50871i −0.184116 + 0.133768i
\(689\) 6.65786 + 4.83722i 0.253644 + 0.184283i
\(690\) 0 0
\(691\) 20.9259 15.2036i 0.796060 0.578371i −0.113696 0.993516i \(-0.536269\pi\)
0.909756 + 0.415144i \(0.136269\pi\)
\(692\) 5.34531 16.4512i 0.203198 0.625380i
\(693\) 0 0
\(694\) 6.69935 20.6185i 0.254304 0.782667i
\(695\) 13.9934 15.7341i 0.530800 0.596829i
\(696\) 0 0
\(697\) 4.17034 + 12.8350i 0.157963 + 0.486160i
\(698\) 0.957006 + 0.695305i 0.0362232 + 0.0263177i
\(699\) 0 0
\(700\) −0.958031 8.15254i −0.0362102 0.308137i
\(701\) −2.50610 −0.0946542 −0.0473271 0.998879i \(-0.515070\pi\)
−0.0473271 + 0.998879i \(0.515070\pi\)
\(702\) 0 0
\(703\) 6.17754 + 19.0125i 0.232990 + 0.717070i
\(704\) 0.0889172 + 0.273659i 0.00335119 + 0.0103139i
\(705\) 0 0
\(706\) −0.639222 + 1.96732i −0.0240574 + 0.0740411i
\(707\) −2.23162 −0.0839288
\(708\) 0 0
\(709\) 1.52309 1.10659i 0.0572009 0.0415589i −0.558817 0.829291i \(-0.688745\pi\)
0.616018 + 0.787732i \(0.288745\pi\)
\(710\) −31.6115 13.8429i −1.18636 0.519513i
\(711\) 0 0
\(712\) 12.4011 9.00992i 0.464750 0.337661i
\(713\) 4.32608 3.14308i 0.162013 0.117709i
\(714\) 0 0
\(715\) −0.0805619 + 0.814481i −0.00301285 + 0.0304599i
\(716\) 3.20472 2.32837i 0.119766 0.0870151i
\(717\) 0 0
\(718\) 36.5909 1.36556
\(719\) 8.94181 27.5201i 0.333473 1.02632i −0.633996 0.773336i \(-0.718586\pi\)
0.967469 0.252989i \(-0.0814135\pi\)
\(720\) 0 0
\(721\) 9.08654 + 27.9655i 0.338400 + 1.04149i
\(722\) −4.07321 12.5361i −0.151589 0.466544i
\(723\) 0 0
\(724\) 5.22902 0.194335
\(725\) 2.70340 + 23.0051i 0.100402 + 0.854388i
\(726\) 0 0
\(727\) −7.04183 5.11619i −0.261167 0.189749i 0.449494 0.893283i \(-0.351604\pi\)
−0.710661 + 0.703534i \(0.751604\pi\)
\(728\) −0.645343 1.98616i −0.0239180 0.0736120i
\(729\) 0 0
\(730\) −14.5877 + 3.19427i −0.539914 + 0.118225i
\(731\) 9.09116 27.9797i 0.336249 1.03487i
\(732\) 0 0
\(733\) −6.34806 + 19.5373i −0.234471 + 0.721627i 0.762720 + 0.646729i \(0.223863\pi\)
−0.997191 + 0.0748988i \(0.976137\pi\)
\(734\) 6.15902 4.47479i 0.227334 0.165168i
\(735\) 0 0
\(736\) 0.588076 + 0.427262i 0.0216768 + 0.0157491i
\(737\) −2.85368 + 2.07332i −0.105117 + 0.0763718i
\(738\) 0 0
\(739\) −30.9932 22.5179i −1.14010 0.828333i −0.152969 0.988231i \(-0.548884\pi\)
−0.987134 + 0.159898i \(0.948884\pi\)
\(740\) 12.3151 13.8470i 0.452712 0.509027i
\(741\) 0 0
\(742\) 3.28211 10.1013i 0.120490 0.370830i
\(743\) 5.03337 0.184657 0.0923283 0.995729i \(-0.470569\pi\)
0.0923283 + 0.995729i \(0.470569\pi\)
\(744\) 0 0
\(745\) 3.31240 33.4883i 0.121357 1.22692i
\(746\) 3.14225 + 9.67086i 0.115046 + 0.354075i
\(747\) 0 0
\(748\) −1.14728 0.833548i −0.0419487 0.0304775i
\(749\) 10.3900 0.379644
\(750\) 0 0
\(751\) −41.7544 −1.52364 −0.761820 0.647789i \(-0.775694\pi\)
−0.761820 + 0.647789i \(0.775694\pi\)
\(752\) 4.48371 + 3.25761i 0.163504 + 0.118793i
\(753\) 0 0
\(754\) 1.82105 + 5.60461i 0.0663187 + 0.204108i
\(755\) 0.675621 6.83052i 0.0245884 0.248588i
\(756\) 0 0
\(757\) 42.0525 1.52843 0.764213 0.644964i \(-0.223128\pi\)
0.764213 + 0.644964i \(0.223128\pi\)
\(758\) −10.9182 + 33.6026i −0.396565 + 1.22050i
\(759\) 0 0
\(760\) 3.58458 4.03048i 0.130026 0.146201i
\(761\) −30.9063 22.4548i −1.12035 0.813984i −0.136090 0.990696i \(-0.543454\pi\)
−0.984263 + 0.176712i \(0.943454\pi\)
\(762\) 0 0
\(763\) −10.9298 + 7.94097i −0.395686 + 0.287482i
\(764\) 9.68041 + 7.03323i 0.350225 + 0.254453i
\(765\) 0 0
\(766\) 8.94869 6.50161i 0.323329 0.234913i
\(767\) −3.41985 + 10.5252i −0.123484 + 0.380043i
\(768\) 0 0
\(769\) −10.2945 + 31.6832i −0.371229 + 1.14253i 0.574758 + 0.818323i \(0.305096\pi\)
−0.945988 + 0.324203i \(0.894904\pi\)
\(770\) 1.03186 0.225946i 0.0371855 0.00814253i
\(771\) 0 0
\(772\) −4.31553 13.2818i −0.155319 0.478024i
\(773\) −3.70547 2.69218i −0.133277 0.0968311i 0.519150 0.854683i \(-0.326249\pi\)
−0.652426 + 0.757852i \(0.726249\pi\)
\(774\) 0 0
\(775\) −17.9990 + 32.0769i −0.646544 + 1.15224i
\(776\) 1.81480 0.0651475
\(777\) 0 0
\(778\) −10.5595 32.4987i −0.378576 1.16514i
\(779\) −2.04117 6.28208i −0.0731326 0.225079i
\(780\) 0 0
\(781\) 1.37227 4.22342i 0.0491038 0.151126i
\(782\) −3.58248 −0.128109
\(783\) 0 0
\(784\) 3.48260 2.53026i 0.124379 0.0903663i
\(785\) −3.43663 + 34.7444i −0.122659 + 1.24008i
\(786\) 0 0
\(787\) −12.1753 + 8.84587i −0.434002 + 0.315321i −0.783247 0.621710i \(-0.786438\pi\)
0.349245 + 0.937032i \(0.386438\pi\)
\(788\) −11.1224 + 8.08087i −0.396218 + 0.287869i
\(789\) 0 0
\(790\) −19.7804 8.66192i −0.703754 0.308177i
\(791\) −16.6246 + 12.0785i −0.591104 + 0.429462i
\(792\) 0 0
\(793\) −13.2958 −0.472146
\(794\) 5.60979 17.2652i 0.199084 0.612718i
\(795\) 0 0
\(796\) −4.03459 12.4172i −0.143002 0.440116i
\(797\) 8.77965 + 27.0210i 0.310991 + 0.957132i 0.977373 + 0.211522i \(0.0678419\pi\)
−0.666382 + 0.745610i \(0.732158\pi\)
\(798\) 0 0
\(799\) −27.3142 −0.966308
\(800\) −4.90311 0.979536i −0.173351 0.0346318i
\(801\) 0 0
\(802\) 2.17240 + 1.57834i 0.0767102 + 0.0557332i
\(803\) −0.593823 1.82760i −0.0209555 0.0644945i
\(804\) 0 0
\(805\) 1.77336 1.99396i 0.0625029 0.0702779i
\(806\) −2.89168 + 8.89969i −0.101855 + 0.313478i
\(807\) 0 0
\(808\) −0.420051 + 1.29278i −0.0147773 + 0.0454800i
\(809\) −25.1848 + 18.2978i −0.885449 + 0.643317i −0.934688 0.355470i \(-0.884321\pi\)
0.0492382 + 0.998787i \(0.484321\pi\)
\(810\) 0 0
\(811\) 3.32933 + 2.41890i 0.116909 + 0.0849390i 0.644703 0.764433i \(-0.276981\pi\)
−0.527795 + 0.849372i \(0.676981\pi\)
\(812\) 6.15305 4.47046i 0.215930 0.156882i
\(813\) 0 0
\(814\) 1.92920 + 1.40165i 0.0676184 + 0.0491277i
\(815\) −10.0124 17.0991i −0.350719 0.598956i
\(816\) 0 0
\(817\) −4.44967 + 13.6947i −0.155674 + 0.479116i
\(818\) −33.2664 −1.16313
\(819\) 0 0
\(820\) −4.06914 + 4.57531i −0.142100 + 0.159777i
\(821\) −6.29922 19.3870i −0.219844 0.676611i −0.998774 0.0494998i \(-0.984237\pi\)
0.778930 0.627111i \(-0.215763\pi\)
\(822\) 0 0
\(823\) −5.60716 4.07384i −0.195453 0.142005i 0.485754 0.874095i \(-0.338545\pi\)
−0.681208 + 0.732090i \(0.738545\pi\)
\(824\) 17.9108 0.623952
\(825\) 0 0
\(826\) 14.2830 0.496968
\(827\) −1.96999 1.43128i −0.0685032 0.0497705i 0.553007 0.833177i \(-0.313480\pi\)
−0.621510 + 0.783406i \(0.713480\pi\)
\(828\) 0 0
\(829\) −3.46417 10.6616i −0.120316 0.370293i 0.872703 0.488251i \(-0.162365\pi\)
−0.993019 + 0.117958i \(0.962365\pi\)
\(830\) −3.28466 5.60952i −0.114012 0.194709i
\(831\) 0 0
\(832\) −1.27206 −0.0441007
\(833\) −6.55597 + 20.1772i −0.227151 + 0.699099i
\(834\) 0 0
\(835\) −35.9385 15.7377i −1.24370 0.544625i
\(836\) 0.561536 + 0.407980i 0.0194211 + 0.0141103i
\(837\) 0 0
\(838\) 9.71007 7.05478i 0.335429 0.243703i
\(839\) 23.2407 + 16.8854i 0.802359 + 0.582948i 0.911605 0.411067i \(-0.134844\pi\)
−0.109246 + 0.994015i \(0.534844\pi\)
\(840\) 0 0
\(841\) 6.09861 4.43090i 0.210297 0.152790i
\(842\) 7.31823 22.5232i 0.252203 0.776201i
\(843\) 0 0
\(844\) 2.50053 7.69583i 0.0860717 0.264901i
\(845\) 23.3133 + 10.2090i 0.802002 + 0.351201i
\(846\) 0 0
\(847\) −5.53853 17.0459i −0.190306 0.585703i
\(848\) −5.23392 3.80267i −0.179734 0.130584i
\(849\) 0 0
\(850\) 22.3872 10.2980i 0.767874 0.353219i
\(851\) 6.02410 0.206503
\(852\) 0 0
\(853\) 6.31242 + 19.4276i 0.216133 + 0.665190i 0.999071 + 0.0430898i \(0.0137202\pi\)
−0.782938 + 0.622100i \(0.786280\pi\)
\(854\) 5.30261 + 16.3198i 0.181452 + 0.558450i
\(855\) 0 0
\(856\) 1.95568 6.01898i 0.0668439 0.205724i
\(857\) 14.6791 0.501427 0.250714 0.968061i \(-0.419335\pi\)
0.250714 + 0.968061i \(0.419335\pi\)
\(858\) 0 0
\(859\) −18.4207 + 13.3834i −0.628506 + 0.456637i −0.855882 0.517170i \(-0.826985\pi\)
0.227376 + 0.973807i \(0.426985\pi\)
\(860\) 13.0390 2.85515i 0.444626 0.0973598i
\(861\) 0 0
\(862\) 23.0948 16.7794i 0.786614 0.571508i
\(863\) −1.33585 + 0.970550i −0.0454728 + 0.0330379i −0.610289 0.792178i \(-0.708947\pi\)
0.564817 + 0.825216i \(0.308947\pi\)
\(864\) 0 0
\(865\) −25.7047 + 28.9022i −0.873986 + 0.982704i
\(866\) −26.8387 + 19.4994i −0.912015 + 0.662617i
\(867\) 0 0
\(868\) 12.0771 0.409923
\(869\) 0.858676 2.64273i 0.0291286 0.0896486i
\(870\) 0 0
\(871\) −4.81875 14.8306i −0.163277 0.502515i
\(872\) 2.54294 + 7.82637i 0.0861149 + 0.265034i
\(873\) 0 0
\(874\) 1.75345 0.0593112
\(875\) −5.35014 + 17.5580i −0.180868 + 0.593570i
\(876\) 0 0
\(877\) −35.4144 25.7301i −1.19586 0.868844i −0.201990 0.979388i \(-0.564741\pi\)
−0.993871 + 0.110544i \(0.964741\pi\)
\(878\) −5.71079 17.5760i −0.192730 0.593162i
\(879\) 0 0
\(880\) 0.0633320 0.640286i 0.00213492 0.0215840i
\(881\) 9.65827 29.7251i 0.325396 1.00146i −0.645866 0.763451i \(-0.723504\pi\)
0.971262 0.238014i \(-0.0764964\pi\)
\(882\) 0 0
\(883\) 14.0459 43.2290i 0.472684 1.45477i −0.376372 0.926468i \(-0.622829\pi\)
0.849056 0.528303i \(-0.177171\pi\)
\(884\) 5.07193 3.68497i 0.170587 0.123939i
\(885\) 0 0
\(886\) −15.1806 11.0293i −0.510001 0.370537i
\(887\) −19.5953 + 14.2368i −0.657945 + 0.478025i −0.865968 0.500099i \(-0.833297\pi\)
0.208024 + 0.978124i \(0.433297\pi\)
\(888\) 0 0
\(889\) 27.0582 + 19.6590i 0.907504 + 0.659340i
\(890\) −33.4824 + 7.33166i −1.12233 + 0.245758i
\(891\) 0 0
\(892\) −1.57250 + 4.83965i −0.0526511 + 0.162043i
\(893\) 13.3689 0.447375
\(894\) 0 0
\(895\) −8.65262 + 1.89467i −0.289225 + 0.0633318i
\(896\) 0.507322 + 1.56138i 0.0169484 + 0.0521619i
\(897\) 0 0
\(898\) −3.50678 2.54782i −0.117023 0.0850220i
\(899\) −34.0795 −1.13662
\(900\) 0 0
\(901\) 31.8844 1.06222
\(902\) −0.637443 0.463130i −0.0212245 0.0154205i
\(903\) 0 0
\(904\) 3.86790 + 11.9042i 0.128645 + 0.395927i
\(905\) −10.7105 4.69020i −0.356030 0.155907i
\(906\) 0 0
\(907\) 48.7013 1.61710 0.808550 0.588428i \(-0.200253\pi\)
0.808550 + 0.588428i \(0.200253\pi\)
\(908\) 7.65949 23.5735i 0.254189 0.782313i
\(909\) 0 0
\(910\) −0.459651 + 4.64707i −0.0152373 + 0.154049i
\(911\) 43.4094 + 31.5388i 1.43822 + 1.04493i 0.988411 + 0.151802i \(0.0485075\pi\)
0.449808 + 0.893125i \(0.351493\pi\)
\(912\) 0 0
\(913\) 0.676734 0.491676i 0.0223966 0.0162721i
\(914\) 22.4067 + 16.2794i 0.741147 + 0.538475i
\(915\) 0 0
\(916\) 1.19660 0.869377i 0.0395366 0.0287250i
\(917\) −5.76665 + 17.7479i −0.190431 + 0.586088i
\(918\) 0 0
\(919\) −12.3715 + 38.0755i −0.408097 + 1.25599i 0.510184 + 0.860065i \(0.329577\pi\)
−0.918281 + 0.395929i \(0.870423\pi\)
\(920\) −0.821312 1.40263i −0.0270778 0.0462434i
\(921\) 0 0
\(922\) −3.55521 10.9418i −0.117085 0.360349i
\(923\) 15.8825 + 11.5393i 0.522780 + 0.379822i
\(924\) 0 0
\(925\) −37.6450 + 17.3166i −1.23776 + 0.569366i
\(926\) 1.16237 0.0381978
\(927\) 0 0
\(928\) −1.43158 4.40594i −0.0469938 0.144632i
\(929\) 0.00519461 + 0.0159874i 0.000170430 + 0.000524528i 0.951142 0.308755i \(-0.0999122\pi\)
−0.950971 + 0.309279i \(0.899912\pi\)
\(930\) 0 0
\(931\) 3.20882 9.87573i 0.105165 0.323664i
\(932\) 0.697178 0.0228368
\(933\) 0 0
\(934\) −17.5140 + 12.7247i −0.573077 + 0.416365i
\(935\) 1.60230 + 2.73640i 0.0524009 + 0.0894899i
\(936\) 0 0
\(937\) 44.0518 32.0055i 1.43911 1.04557i 0.450881 0.892584i \(-0.351110\pi\)
0.988228 0.152990i \(-0.0488902\pi\)
\(938\) −16.2819 + 11.8295i −0.531621 + 0.386246i
\(939\) 0 0
\(940\) −6.26200 10.6942i −0.204244 0.348806i
\(941\) 15.3671 11.1649i 0.500954 0.363964i −0.308427 0.951248i \(-0.599803\pi\)
0.809381 + 0.587284i \(0.199803\pi\)
\(942\) 0 0
\(943\) −1.99047 −0.0648187
\(944\) 2.68844 8.27415i 0.0875011 0.269301i
\(945\) 0 0
\(946\) 0.530779 + 1.63357i 0.0172571 + 0.0531120i
\(947\) 15.8661 + 48.8308i 0.515578 + 1.58679i 0.782227 + 0.622994i \(0.214084\pi\)
−0.266648 + 0.963794i \(0.585916\pi\)
\(948\) 0 0
\(949\) 8.49529 0.275769
\(950\) −10.9574 + 5.04037i −0.355505 + 0.163531i
\(951\) 0 0
\(952\) −6.54587 4.75585i −0.212153 0.154138i
\(953\) −0.235824 0.725791i −0.00763908 0.0235107i 0.947164 0.320749i \(-0.103935\pi\)
−0.954803 + 0.297238i \(0.903935\pi\)
\(954\) 0 0
\(955\) −13.5197 23.0889i −0.437489 0.747141i
\(956\) −9.01959 + 27.7595i −0.291715 + 0.897805i
\(957\) 0 0
\(958\) −7.53007 + 23.1752i −0.243286 + 0.748756i
\(959\) −6.50920 + 4.72921i −0.210193 + 0.152714i
\(960\) 0 0
\(961\) −18.7009 13.5870i −0.603256 0.438291i
\(962\) −8.52867 + 6.19644i −0.274975 + 0.199781i
\(963\) 0 0
\(964\) −14.0170 10.1840i −0.451458 0.328003i
\(965\) −3.07377 + 31.0759i −0.0989483 + 1.00037i
\(966\) 0 0
\(967\) −9.05202 + 27.8593i −0.291093 + 0.895893i 0.693412 + 0.720541i \(0.256106\pi\)
−0.984506 + 0.175352i \(0.943894\pi\)
\(968\) −10.9172 −0.350892
\(969\) 0 0
\(970\) −3.71723 1.62779i −0.119353 0.0522653i
\(971\) −2.22232 6.83961i −0.0713177 0.219493i 0.909044 0.416699i \(-0.136813\pi\)
−0.980362 + 0.197206i \(0.936813\pi\)
\(972\) 0 0
\(973\) 12.5072 + 9.08703i 0.400963 + 0.291317i
\(974\) 23.8804 0.765179
\(975\) 0 0
\(976\) 10.4522 0.334566
\(977\) 30.6811 + 22.2911i 0.981576 + 0.713157i 0.958060 0.286567i \(-0.0925140\pi\)
0.0235158 + 0.999723i \(0.492514\pi\)
\(978\) 0 0
\(979\) −1.36297 4.19480i −0.0435608 0.134066i
\(980\) −9.40289 + 2.05895i −0.300364 + 0.0657709i
\(981\) 0 0
\(982\) 27.5634 0.879584
\(983\) 4.92956 15.1716i 0.157228 0.483899i −0.841151 0.540800i \(-0.818122\pi\)
0.998380 + 0.0569002i \(0.0181217\pi\)
\(984\) 0 0
\(985\) 30.0299 6.57566i 0.956833 0.209518i
\(986\) 18.4713 + 13.4202i 0.588247 + 0.427386i
\(987\) 0 0
\(988\) −2.48246 + 1.80361i −0.0789774 + 0.0573805i
\(989\) 3.51044 + 2.55048i 0.111626 + 0.0811007i
\(990\) 0 0
\(991\) 4.72420 3.43233i 0.150069 0.109032i −0.510217 0.860046i \(-0.670435\pi\)
0.660286 + 0.751014i \(0.270435\pi\)
\(992\) 2.27323 6.99629i 0.0721752 0.222132i
\(993\) 0 0
\(994\) 7.82958 24.0970i 0.248339 0.764309i
\(995\) −2.87367 + 29.0528i −0.0911015 + 0.921036i
\(996\) 0 0
\(997\) 2.89258 + 8.90245i 0.0916090 + 0.281944i 0.986355 0.164632i \(-0.0526435\pi\)
−0.894746 + 0.446575i \(0.852644\pi\)
\(998\) −10.2995 7.48300i −0.326024 0.236870i
\(999\) 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 450.2.h.f.91.2 12
3.2 odd 2 450.2.h.g.91.2 yes 12
25.11 even 5 inner 450.2.h.f.361.2 yes 12
75.11 odd 10 450.2.h.g.361.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.h.f.91.2 12 1.1 even 1 trivial
450.2.h.f.361.2 yes 12 25.11 even 5 inner
450.2.h.g.91.2 yes 12 3.2 odd 2
450.2.h.g.361.2 yes 12 75.11 odd 10