Properties

Label 450.2.h.d.91.2
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.1064390625.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.2
Root \(2.36886 - 0.0809628i\) of defining polynomial
Character \(\chi\) \(=\) 450.91
Dual form 450.2.h.d.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.05984 - 0.870094i) q^{5} +2.92807 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(2.05984 - 0.870094i) q^{5} +2.92807 q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.17787 - 0.506822i) q^{10} +(0.154000 + 0.111888i) q^{11} +(-0.250822 + 0.182233i) q^{13} +(-2.36886 - 1.72107i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.86886 + 5.75175i) q^{17} +(1.00000 - 3.07768i) q^{19} +(1.46403 + 1.69015i) q^{20} +(-0.0588229 - 0.181038i) q^{22} +(3.61803 + 2.62866i) q^{23} +(3.48587 - 3.58451i) q^{25} +0.310033 q^{26} +(0.904822 + 2.78476i) q^{28} +(-2.10492 - 6.47829i) q^{29} +(-0.522856 + 1.60919i) q^{31} +1.00000 q^{32} +(4.89273 - 3.55478i) q^{34} +(6.03135 - 2.54769i) q^{35} +(7.89273 - 5.73440i) q^{37} +(-2.61803 + 1.90211i) q^{38} +(-0.190983 - 2.22790i) q^{40} +(4.10492 - 2.98240i) q^{41} -10.2394 q^{43} +(-0.0588229 + 0.181038i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(3.31003 + 10.1872i) q^{47} +1.57358 q^{49} +(-4.92705 + 0.850981i) q^{50} +(-0.250822 - 0.182233i) q^{52} +(-3.08144 - 9.48370i) q^{53} +(0.414569 + 0.0964762i) q^{55} +(0.904822 - 2.78476i) q^{56} +(-2.10492 + 6.47829i) q^{58} +(6.00810 - 4.36514i) q^{59} +(4.48689 + 3.25992i) q^{61} +(1.36886 - 0.994532i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-0.358093 + 0.593609i) q^{65} +(-4.66375 + 14.3535i) q^{67} -6.04775 q^{68} +(-6.37696 - 1.48401i) q^{70} +(-2.11842 - 6.51983i) q^{71} +(-9.41496 - 6.84037i) q^{73} -9.75595 q^{74} +3.23607 q^{76} +(0.450924 + 0.327615i) q^{77} +(0.485246 + 1.49343i) q^{79} +(-1.15502 + 1.91466i) q^{80} -5.07397 q^{82} +(-4.02324 + 12.3823i) q^{83} +(1.15502 + 13.4738i) q^{85} +(8.28381 + 6.01854i) q^{86} +(0.154000 - 0.111888i) q^{88} +(-7.51076 - 5.45689i) q^{89} +(-0.734424 + 0.533590i) q^{91} +(-1.38197 + 4.25325i) q^{92} +(3.31003 - 10.1872i) q^{94} +(-0.618034 - 7.20963i) q^{95} +(0.537611 + 1.65460i) q^{97} +(-1.27305 - 0.924925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) \) 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
\(5\) 2.05984 0.870094i 0.921188 0.389118i
\(6\) 0 0
\(7\) 2.92807 1.10671 0.553353 0.832947i \(-0.313348\pi\)
0.553353 + 0.832947i \(0.313348\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 0 0
\(10\) −2.17787 0.506822i −0.688704 0.160271i
\(11\) 0.154000 + 0.111888i 0.0464329 + 0.0337355i 0.610760 0.791816i \(-0.290864\pi\)
−0.564327 + 0.825552i \(0.690864\pi\)
\(12\) 0 0
\(13\) −0.250822 + 0.182233i −0.0695655 + 0.0505423i −0.622025 0.782998i \(-0.713690\pi\)
0.552459 + 0.833540i \(0.313690\pi\)
\(14\) −2.36886 1.72107i −0.633103 0.459977i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −1.86886 + 5.75175i −0.453264 + 1.39500i 0.419897 + 0.907572i \(0.362066\pi\)
−0.873161 + 0.487432i \(0.837934\pi\)
\(18\) 0 0
\(19\) 1.00000 3.07768i 0.229416 0.706069i −0.768398 0.639973i \(-0.778946\pi\)
0.997813 0.0660962i \(-0.0210544\pi\)
\(20\) 1.46403 + 1.69015i 0.327368 + 0.377929i
\(21\) 0 0
\(22\) −0.0588229 0.181038i −0.0125411 0.0385975i
\(23\) 3.61803 + 2.62866i 0.754412 + 0.548113i 0.897191 0.441642i \(-0.145604\pi\)
−0.142779 + 0.989755i \(0.545604\pi\)
\(24\) 0 0
\(25\) 3.48587 3.58451i 0.697175 0.716901i
\(26\) 0.310033 0.0608025
\(27\) 0 0
\(28\) 0.904822 + 2.78476i 0.170995 + 0.526270i
\(29\) −2.10492 6.47829i −0.390875 1.20299i −0.932128 0.362129i \(-0.882050\pi\)
0.541253 0.840859i \(-0.317950\pi\)
\(30\) 0 0
\(31\) −0.522856 + 1.60919i −0.0939078 + 0.289018i −0.986968 0.160920i \(-0.948554\pi\)
0.893060 + 0.449938i \(0.148554\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 4.89273 3.55478i 0.839096 0.609639i
\(35\) 6.03135 2.54769i 1.01948 0.430639i
\(36\) 0 0
\(37\) 7.89273 5.73440i 1.29756 0.942730i 0.297628 0.954682i \(-0.403804\pi\)
0.999929 + 0.0119519i \(0.00380449\pi\)
\(38\) −2.61803 + 1.90211i −0.424701 + 0.308563i
\(39\) 0 0
\(40\) −0.190983 2.22790i −0.0301971 0.352261i
\(41\) 4.10492 2.98240i 0.641081 0.465773i −0.219140 0.975693i \(-0.570325\pi\)
0.860222 + 0.509920i \(0.170325\pi\)
\(42\) 0 0
\(43\) −10.2394 −1.56149 −0.780744 0.624852i \(-0.785159\pi\)
−0.780744 + 0.624852i \(0.785159\pi\)
\(44\) −0.0588229 + 0.181038i −0.00886789 + 0.0272926i
\(45\) 0 0
\(46\) −1.38197 4.25325i −0.203760 0.627108i
\(47\) 3.31003 + 10.1872i 0.482818 + 1.48596i 0.835116 + 0.550073i \(0.185400\pi\)
−0.352299 + 0.935888i \(0.614600\pi\)
\(48\) 0 0
\(49\) 1.57358 0.224797
\(50\) −4.92705 + 0.850981i −0.696790 + 0.120347i
\(51\) 0 0
\(52\) −0.250822 0.182233i −0.0347828 0.0252712i
\(53\) −3.08144 9.48370i −0.423268 1.30269i −0.904643 0.426171i \(-0.859862\pi\)
0.481374 0.876515i \(-0.340138\pi\)
\(54\) 0 0
\(55\) 0.414569 + 0.0964762i 0.0559005 + 0.0130088i
\(56\) 0.904822 2.78476i 0.120912 0.372129i
\(57\) 0 0
\(58\) −2.10492 + 6.47829i −0.276390 + 0.850641i
\(59\) 6.00810 4.36514i 0.782188 0.568293i −0.123447 0.992351i \(-0.539395\pi\)
0.905635 + 0.424058i \(0.139395\pi\)
\(60\) 0 0
\(61\) 4.48689 + 3.25992i 0.574487 + 0.417390i 0.836733 0.547612i \(-0.184463\pi\)
−0.262245 + 0.965001i \(0.584463\pi\)
\(62\) 1.36886 0.994532i 0.173845 0.126306i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −0.358093 + 0.593609i −0.0444160 + 0.0736282i
\(66\) 0 0
\(67\) −4.66375 + 14.3535i −0.569767 + 1.75356i 0.0835754 + 0.996501i \(0.473366\pi\)
−0.653343 + 0.757062i \(0.726634\pi\)
\(68\) −6.04775 −0.733397
\(69\) 0 0
\(70\) −6.37696 1.48401i −0.762192 0.177373i
\(71\) −2.11842 6.51983i −0.251410 0.773762i −0.994516 0.104587i \(-0.966648\pi\)
0.743105 0.669175i \(-0.233352\pi\)
\(72\) 0 0
\(73\) −9.41496 6.84037i −1.10194 0.800604i −0.120562 0.992706i \(-0.538470\pi\)
−0.981375 + 0.192101i \(0.938470\pi\)
\(74\) −9.75595 −1.13411
\(75\) 0 0
\(76\) 3.23607 0.371202
\(77\) 0.450924 + 0.327615i 0.0513875 + 0.0373352i
\(78\) 0 0
\(79\) 0.485246 + 1.49343i 0.0545944 + 0.168024i 0.974636 0.223797i \(-0.0718452\pi\)
−0.920041 + 0.391821i \(0.871845\pi\)
\(80\) −1.15502 + 1.91466i −0.129135 + 0.214066i
\(81\) 0 0
\(82\) −5.07397 −0.560326
\(83\) −4.02324 + 12.3823i −0.441608 + 1.35913i 0.444552 + 0.895753i \(0.353363\pi\)
−0.886161 + 0.463378i \(0.846637\pi\)
\(84\) 0 0
\(85\) 1.15502 + 13.4738i 0.125279 + 1.46143i
\(86\) 8.28381 + 6.01854i 0.893267 + 0.648996i
\(87\) 0 0
\(88\) 0.154000 0.111888i 0.0164165 0.0119273i
\(89\) −7.51076 5.45689i −0.796139 0.578429i 0.113640 0.993522i \(-0.463749\pi\)
−0.909779 + 0.415093i \(0.863749\pi\)
\(90\) 0 0
\(91\) −0.734424 + 0.533590i −0.0769885 + 0.0559354i
\(92\) −1.38197 + 4.25325i −0.144080 + 0.443432i
\(93\) 0 0
\(94\) 3.31003 10.1872i 0.341404 1.05073i
\(95\) −0.618034 7.20963i −0.0634089 0.739692i
\(96\) 0 0
\(97\) 0.537611 + 1.65460i 0.0545861 + 0.167999i 0.974633 0.223810i \(-0.0718495\pi\)
−0.920047 + 0.391809i \(0.871850\pi\)
\(98\) −1.27305 0.924925i −0.128598 0.0934316i
\(99\) 0 0
\(100\) 4.48626 + 2.20759i 0.448626 + 0.220759i
\(101\) 0.765188 0.0761391 0.0380695 0.999275i \(-0.487879\pi\)
0.0380695 + 0.999275i \(0.487879\pi\)
\(102\) 0 0
\(103\) 1.74069 + 5.35728i 0.171515 + 0.527869i 0.999457 0.0329445i \(-0.0104885\pi\)
−0.827942 + 0.560814i \(0.810488\pi\)
\(104\) 0.0958055 + 0.294859i 0.00939450 + 0.0289133i
\(105\) 0 0
\(106\) −3.08144 + 9.48370i −0.299296 + 0.921138i
\(107\) 8.81042 0.851736 0.425868 0.904785i \(-0.359969\pi\)
0.425868 + 0.904785i \(0.359969\pi\)
\(108\) 0 0
\(109\) −12.8447 + 9.33220i −1.23030 + 0.893862i −0.996912 0.0785223i \(-0.974980\pi\)
−0.233384 + 0.972385i \(0.574980\pi\)
\(110\) −0.278686 0.321728i −0.0265717 0.0306756i
\(111\) 0 0
\(112\) −2.36886 + 1.72107i −0.223836 + 0.162626i
\(113\) −15.4845 + 11.2502i −1.45666 + 1.05833i −0.472447 + 0.881359i \(0.656629\pi\)
−0.984217 + 0.176969i \(0.943371\pi\)
\(114\) 0 0
\(115\) 9.73974 + 2.26658i 0.908236 + 0.211360i
\(116\) 5.51076 4.00380i 0.511661 0.371744i
\(117\) 0 0
\(118\) −7.42642 −0.683658
\(119\) −5.47214 + 16.8415i −0.501630 + 1.54386i
\(120\) 0 0
\(121\) −3.38799 10.4272i −0.307999 0.947924i
\(122\) −1.71384 5.27466i −0.155164 0.477545i
\(123\) 0 0
\(124\) −1.69200 −0.151946
\(125\) 4.06148 10.4165i 0.363270 0.931684i
\(126\) 0 0
\(127\) 6.58371 + 4.78335i 0.584210 + 0.424453i 0.840239 0.542216i \(-0.182414\pi\)
−0.256029 + 0.966669i \(0.582414\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) 0.638618 0.269758i 0.0560105 0.0236593i
\(131\) −5.13588 + 15.8066i −0.448724 + 1.38103i 0.429623 + 0.903008i \(0.358646\pi\)
−0.878347 + 0.478023i \(0.841354\pi\)
\(132\) 0 0
\(133\) 2.92807 9.01166i 0.253896 0.781410i
\(134\) 12.2098 8.87097i 1.05477 0.766335i
\(135\) 0 0
\(136\) 4.89273 + 3.55478i 0.419548 + 0.304819i
\(137\) −8.60657 + 6.25304i −0.735309 + 0.534233i −0.891238 0.453535i \(-0.850163\pi\)
0.155930 + 0.987768i \(0.450163\pi\)
\(138\) 0 0
\(139\) −18.5199 13.4555i −1.57084 1.14128i −0.926351 0.376662i \(-0.877072\pi\)
−0.644485 0.764617i \(-0.722928\pi\)
\(140\) 4.28679 + 4.94887i 0.362300 + 0.418256i
\(141\) 0 0
\(142\) −2.11842 + 6.51983i −0.177774 + 0.547132i
\(143\) −0.0590164 −0.00493520
\(144\) 0 0
\(145\) −9.97252 11.5128i −0.828173 0.956082i
\(146\) 3.59619 + 11.0679i 0.297623 + 0.915990i
\(147\) 0 0
\(148\) 7.89273 + 5.73440i 0.648778 + 0.471365i
\(149\) −1.40819 −0.115363 −0.0576815 0.998335i \(-0.518371\pi\)
−0.0576815 + 0.998335i \(0.518371\pi\)
\(150\) 0 0
\(151\) −7.87234 −0.640642 −0.320321 0.947309i \(-0.603791\pi\)
−0.320321 + 0.947309i \(0.603791\pi\)
\(152\) −2.61803 1.90211i −0.212351 0.154282i
\(153\) 0 0
\(154\) −0.172237 0.530092i −0.0138793 0.0427161i
\(155\) 0.323143 + 3.76960i 0.0259555 + 0.302782i
\(156\) 0 0
\(157\) −6.95554 −0.555113 −0.277556 0.960709i \(-0.589525\pi\)
−0.277556 + 0.960709i \(0.589525\pi\)
\(158\) 0.485246 1.49343i 0.0386041 0.118811i
\(159\) 0 0
\(160\) 2.05984 0.870094i 0.162845 0.0687869i
\(161\) 10.5938 + 7.69688i 0.834912 + 0.606599i
\(162\) 0 0
\(163\) 11.3262 8.22899i 0.887139 0.644545i −0.0479912 0.998848i \(-0.515282\pi\)
0.935131 + 0.354303i \(0.115282\pi\)
\(164\) 4.10492 + 2.98240i 0.320541 + 0.232886i
\(165\) 0 0
\(166\) 10.5330 7.65267i 0.817519 0.593962i
\(167\) −0.425647 + 1.31001i −0.0329375 + 0.101371i −0.966174 0.257892i \(-0.916972\pi\)
0.933236 + 0.359263i \(0.116972\pi\)
\(168\) 0 0
\(169\) −3.98752 + 12.2723i −0.306732 + 0.944025i
\(170\) 6.98525 11.5794i 0.535744 0.888099i
\(171\) 0 0
\(172\) −3.16414 9.73821i −0.241263 0.742531i
\(173\) −3.33555 2.42342i −0.253597 0.184249i 0.453722 0.891143i \(-0.350096\pi\)
−0.707320 + 0.706894i \(0.750096\pi\)
\(174\) 0 0
\(175\) 10.2069 10.4957i 0.771567 0.793398i
\(176\) −0.190355 −0.0143485
\(177\) 0 0
\(178\) 2.86886 + 8.82943i 0.215030 + 0.661794i
\(179\) −1.33125 4.09715i −0.0995020 0.306236i 0.888899 0.458104i \(-0.151471\pi\)
−0.988401 + 0.151868i \(0.951471\pi\)
\(180\) 0 0
\(181\) 4.01475 12.3561i 0.298414 0.918425i −0.683639 0.729820i \(-0.739604\pi\)
0.982053 0.188604i \(-0.0603964\pi\)
\(182\) 0.907798 0.0672904
\(183\) 0 0
\(184\) 3.61803 2.62866i 0.266725 0.193787i
\(185\) 11.2683 18.6794i 0.828461 1.37333i
\(186\) 0 0
\(187\) −0.931355 + 0.676669i −0.0681075 + 0.0494830i
\(188\) −8.66578 + 6.29606i −0.632017 + 0.459187i
\(189\) 0 0
\(190\) −3.73771 + 6.19598i −0.271162 + 0.449504i
\(191\) −1.00000 + 0.726543i −0.0723575 + 0.0525708i −0.623376 0.781922i \(-0.714239\pi\)
0.551018 + 0.834493i \(0.314239\pi\)
\(192\) 0 0
\(193\) 17.4250 1.25428 0.627140 0.778906i \(-0.284225\pi\)
0.627140 + 0.778906i \(0.284225\pi\)
\(194\) 0.537611 1.65460i 0.0385982 0.118793i
\(195\) 0 0
\(196\) 0.486262 + 1.49656i 0.0347330 + 0.106897i
\(197\) −4.61741 14.2109i −0.328977 1.01249i −0.969614 0.244642i \(-0.921330\pi\)
0.640637 0.767844i \(-0.278670\pi\)
\(198\) 0 0
\(199\) −4.90436 −0.347661 −0.173830 0.984776i \(-0.555614\pi\)
−0.173830 + 0.984776i \(0.555614\pi\)
\(200\) −2.33187 4.42294i −0.164888 0.312749i
\(201\) 0 0
\(202\) −0.619050 0.449766i −0.0435562 0.0316454i
\(203\) −6.16336 18.9689i −0.432583 1.33135i
\(204\) 0 0
\(205\) 5.86051 9.71494i 0.409316 0.678521i
\(206\) 1.74069 5.35728i 0.121279 0.373260i
\(207\) 0 0
\(208\) 0.0958055 0.294859i 0.00664292 0.0204448i
\(209\) 0.498356 0.362077i 0.0344720 0.0250454i
\(210\) 0 0
\(211\) 0.996712 + 0.724153i 0.0686165 + 0.0498528i 0.621565 0.783363i \(-0.286497\pi\)
−0.552948 + 0.833216i \(0.686497\pi\)
\(212\) 8.06731 5.86125i 0.554065 0.402552i
\(213\) 0 0
\(214\) −7.12778 5.17864i −0.487245 0.354004i
\(215\) −21.0914 + 8.90920i −1.43842 + 0.607602i
\(216\) 0 0
\(217\) −1.53096 + 4.71181i −0.103928 + 0.319858i
\(218\) 15.8769 1.07532
\(219\) 0 0
\(220\) 0.0363546 + 0.424091i 0.00245102 + 0.0285922i
\(221\) −0.579407 1.78323i −0.0389752 0.119953i
\(222\) 0 0
\(223\) −3.77203 2.74054i −0.252594 0.183520i 0.454282 0.890858i \(-0.349896\pi\)
−0.706876 + 0.707338i \(0.749896\pi\)
\(224\) 2.92807 0.195640
\(225\) 0 0
\(226\) 19.1399 1.27317
\(227\) 0.464034 + 0.337140i 0.0307990 + 0.0223768i 0.603078 0.797682i \(-0.293941\pi\)
−0.572279 + 0.820059i \(0.693941\pi\)
\(228\) 0 0
\(229\) 9.18801 + 28.2778i 0.607161 + 1.86865i 0.481195 + 0.876614i \(0.340203\pi\)
0.125966 + 0.992035i \(0.459797\pi\)
\(230\) −6.54736 7.55858i −0.431720 0.498398i
\(231\) 0 0
\(232\) −6.81168 −0.447209
\(233\) 4.28819 13.1977i 0.280929 0.864610i −0.706661 0.707553i \(-0.749799\pi\)
0.987589 0.157057i \(-0.0502008\pi\)
\(234\) 0 0
\(235\) 15.6820 + 18.1040i 1.02298 + 1.18098i
\(236\) 6.00810 + 4.36514i 0.391094 + 0.284147i
\(237\) 0 0
\(238\) 14.3262 10.4086i 0.928632 0.674691i
\(239\) −1.73442 1.26013i −0.112191 0.0815112i 0.530275 0.847825i \(-0.322089\pi\)
−0.642466 + 0.766314i \(0.722089\pi\)
\(240\) 0 0
\(241\) −1.40748 + 1.02260i −0.0906639 + 0.0658712i −0.632194 0.774810i \(-0.717845\pi\)
0.541530 + 0.840682i \(0.317845\pi\)
\(242\) −3.38799 + 10.4272i −0.217788 + 0.670283i
\(243\) 0 0
\(244\) −1.71384 + 5.27466i −0.109717 + 0.337675i
\(245\) 3.24132 1.36916i 0.207080 0.0874724i
\(246\) 0 0
\(247\) 0.310033 + 0.954184i 0.0197269 + 0.0607133i
\(248\) 1.36886 + 0.994532i 0.0869224 + 0.0631529i
\(249\) 0 0
\(250\) −9.40850 + 6.03988i −0.595046 + 0.381996i
\(251\) 6.39691 0.403770 0.201885 0.979409i \(-0.435293\pi\)
0.201885 + 0.979409i \(0.435293\pi\)
\(252\) 0 0
\(253\) 0.263064 + 0.809628i 0.0165387 + 0.0509009i
\(254\) −2.51475 7.73962i −0.157790 0.485627i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 6.31003 0.393609 0.196805 0.980443i \(-0.436944\pi\)
0.196805 + 0.980443i \(0.436944\pi\)
\(258\) 0 0
\(259\) 23.1104 16.7907i 1.43601 1.04332i
\(260\) −0.675213 0.157132i −0.0418749 0.00974490i
\(261\) 0 0
\(262\) 13.4459 9.76903i 0.830691 0.603533i
\(263\) 2.31332 1.68073i 0.142646 0.103638i −0.514174 0.857686i \(-0.671901\pi\)
0.656819 + 0.754048i \(0.271901\pi\)
\(264\) 0 0
\(265\) −14.5990 16.8537i −0.896808 1.03532i
\(266\) −7.66578 + 5.56951i −0.470019 + 0.341489i
\(267\) 0 0
\(268\) −15.0922 −0.921903
\(269\) 2.99937 9.23112i 0.182875 0.562831i −0.817030 0.576595i \(-0.804381\pi\)
0.999905 + 0.0137635i \(0.00438119\pi\)
\(270\) 0 0
\(271\) 5.30503 + 16.3272i 0.322257 + 0.991806i 0.972663 + 0.232219i \(0.0745988\pi\)
−0.650406 + 0.759587i \(0.725401\pi\)
\(272\) −1.86886 5.75175i −0.113316 0.348751i
\(273\) 0 0
\(274\) 10.6383 0.642683
\(275\) 0.937889 0.161988i 0.0565568 0.00976827i
\(276\) 0 0
\(277\) 1.65337 + 1.20125i 0.0993415 + 0.0721758i 0.636347 0.771403i \(-0.280445\pi\)
−0.537006 + 0.843579i \(0.680445\pi\)
\(278\) 7.07397 + 21.7714i 0.424268 + 1.30576i
\(279\) 0 0
\(280\) −0.559211 6.52343i −0.0334193 0.389850i
\(281\) −1.59416 + 4.90632i −0.0950997 + 0.292687i −0.987280 0.158993i \(-0.949175\pi\)
0.892180 + 0.451680i \(0.149175\pi\)
\(282\) 0 0
\(283\) −2.90059 + 8.92710i −0.172422 + 0.530661i −0.999506 0.0314171i \(-0.989998\pi\)
0.827084 + 0.562078i \(0.189998\pi\)
\(284\) 5.54610 4.02948i 0.329101 0.239106i
\(285\) 0 0
\(286\) 0.0477452 + 0.0346889i 0.00282323 + 0.00205120i
\(287\) 12.0195 8.73267i 0.709488 0.515473i
\(288\) 0 0
\(289\) −15.8367 11.5060i −0.931570 0.676825i
\(290\) 1.30091 + 15.1757i 0.0763923 + 0.891149i
\(291\) 0 0
\(292\) 3.59619 11.0679i 0.210451 0.647703i
\(293\) 8.18160 0.477974 0.238987 0.971023i \(-0.423185\pi\)
0.238987 + 0.971023i \(0.423185\pi\)
\(294\) 0 0
\(295\) 8.57764 14.2191i 0.499410 0.827868i
\(296\) −3.01475 9.27846i −0.175229 0.539299i
\(297\) 0 0
\(298\) 1.13925 + 0.827711i 0.0659948 + 0.0479480i
\(299\) −1.38651 −0.0801840
\(300\) 0 0
\(301\) −29.9815 −1.72811
\(302\) 6.36886 + 4.62724i 0.366486 + 0.266268i
\(303\) 0 0
\(304\) 1.00000 + 3.07768i 0.0573539 + 0.176517i
\(305\) 12.0787 + 2.81089i 0.691625 + 0.160951i
\(306\) 0 0
\(307\) 5.85865 0.334371 0.167185 0.985925i \(-0.446532\pi\)
0.167185 + 0.985925i \(0.446532\pi\)
\(308\) −0.172237 + 0.530092i −0.00981414 + 0.0302048i
\(309\) 0 0
\(310\) 1.95429 3.23961i 0.110996 0.183997i
\(311\) −15.4035 11.1913i −0.873452 0.634600i 0.0580591 0.998313i \(-0.481509\pi\)
−0.931511 + 0.363713i \(0.881509\pi\)
\(312\) 0 0
\(313\) 9.70542 7.05140i 0.548583 0.398569i −0.278680 0.960384i \(-0.589897\pi\)
0.827263 + 0.561815i \(0.189897\pi\)
\(314\) 5.62715 + 4.08837i 0.317559 + 0.230720i
\(315\) 0 0
\(316\) −1.27039 + 0.922993i −0.0714650 + 0.0519224i
\(317\) −10.0778 + 31.0164i −0.566028 + 1.74205i 0.0988506 + 0.995102i \(0.468483\pi\)
−0.664878 + 0.746952i \(0.731517\pi\)
\(318\) 0 0
\(319\) 0.400683 1.23317i 0.0224339 0.0690445i
\(320\) −2.17787 0.506822i −0.121747 0.0283322i
\(321\) 0 0
\(322\) −4.04649 12.4538i −0.225502 0.694024i
\(323\) 15.8332 + 11.5035i 0.880983 + 0.640072i
\(324\) 0 0
\(325\) −0.221119 + 1.53431i −0.0122655 + 0.0851084i
\(326\) −14.0000 −0.775388
\(327\) 0 0
\(328\) −1.56794 4.82563i −0.0865751 0.266451i
\(329\) 9.69200 + 29.8289i 0.534337 + 1.64452i
\(330\) 0 0
\(331\) 0.998744 3.07382i 0.0548959 0.168952i −0.919849 0.392272i \(-0.871689\pi\)
0.974745 + 0.223319i \(0.0716893\pi\)
\(332\) −13.0195 −0.714538
\(333\) 0 0
\(334\) 1.11436 0.809628i 0.0609749 0.0443009i
\(335\) 2.88235 + 33.6239i 0.157480 + 1.83707i
\(336\) 0 0
\(337\) −17.2445 + 12.5289i −0.939367 + 0.682490i −0.948268 0.317470i \(-0.897167\pi\)
0.00890132 + 0.999960i \(0.497167\pi\)
\(338\) 10.4395 7.58471i 0.567832 0.412554i
\(339\) 0 0
\(340\) −12.4574 + 5.26211i −0.675596 + 0.285378i
\(341\) −0.260569 + 0.189314i −0.0141106 + 0.0102519i
\(342\) 0 0
\(343\) −15.8889 −0.857922
\(344\) −3.16414 + 9.73821i −0.170599 + 0.525049i
\(345\) 0 0
\(346\) 1.27407 + 3.92117i 0.0684942 + 0.210804i
\(347\) −5.91496 18.2044i −0.317532 0.977262i −0.974700 0.223518i \(-0.928246\pi\)
0.657168 0.753744i \(-0.271754\pi\)
\(348\) 0 0
\(349\) 14.3745 0.769447 0.384724 0.923032i \(-0.374297\pi\)
0.384724 + 0.923032i \(0.374297\pi\)
\(350\) −14.4267 + 2.49173i −0.771141 + 0.133189i
\(351\) 0 0
\(352\) 0.154000 + 0.111888i 0.00820825 + 0.00596364i
\(353\) −7.53609 23.1937i −0.401105 1.23448i −0.924104 0.382142i \(-0.875187\pi\)
0.522998 0.852334i \(-0.324813\pi\)
\(354\) 0 0
\(355\) −10.0365 11.5866i −0.532681 0.614952i
\(356\) 2.86886 8.82943i 0.152049 0.467959i
\(357\) 0 0
\(358\) −1.33125 + 4.09715i −0.0703585 + 0.216541i
\(359\) −17.2576 + 12.5384i −0.910821 + 0.661750i −0.941222 0.337788i \(-0.890321\pi\)
0.0304014 + 0.999538i \(0.490321\pi\)
\(360\) 0 0
\(361\) 6.89919 + 5.01255i 0.363115 + 0.263819i
\(362\) −10.5108 + 7.63652i −0.552433 + 0.401366i
\(363\) 0 0
\(364\) −0.734424 0.533590i −0.0384943 0.0279677i
\(365\) −25.3451 5.89816i −1.32662 0.308724i
\(366\) 0 0
\(367\) −3.28553 + 10.1118i −0.171503 + 0.527833i −0.999457 0.0329641i \(-0.989505\pi\)
0.827953 + 0.560797i \(0.189505\pi\)
\(368\) −4.47214 −0.233126
\(369\) 0 0
\(370\) −20.0957 + 8.48859i −1.04472 + 0.441301i
\(371\) −9.02266 27.7689i −0.468433 1.44169i
\(372\) 0 0
\(373\) −0.997968 0.725066i −0.0516728 0.0375425i 0.561649 0.827376i \(-0.310167\pi\)
−0.613322 + 0.789833i \(0.710167\pi\)
\(374\) 1.15122 0.0595281
\(375\) 0 0
\(376\) 10.7115 0.552403
\(377\) 1.70852 + 1.24131i 0.0879932 + 0.0639308i
\(378\) 0 0
\(379\) 7.82585 + 24.0855i 0.401987 + 1.23719i 0.923385 + 0.383875i \(0.125411\pi\)
−0.521398 + 0.853314i \(0.674589\pi\)
\(380\) 6.66578 2.81568i 0.341947 0.144441i
\(381\) 0 0
\(382\) 1.23607 0.0632427
\(383\) −5.92681 + 18.2408i −0.302846 + 0.932064i 0.677626 + 0.735406i \(0.263009\pi\)
−0.980472 + 0.196657i \(0.936991\pi\)
\(384\) 0 0
\(385\) 1.21389 + 0.282489i 0.0618654 + 0.0143970i
\(386\) −14.0971 10.2422i −0.717525 0.521313i
\(387\) 0 0
\(388\) −1.40748 + 1.02260i −0.0714541 + 0.0519145i
\(389\) −6.71282 4.87715i −0.340354 0.247281i 0.404457 0.914557i \(-0.367460\pi\)
−0.744811 + 0.667275i \(0.767460\pi\)
\(390\) 0 0
\(391\) −21.8809 + 15.8974i −1.10657 + 0.803968i
\(392\) 0.486262 1.49656i 0.0245599 0.0755877i
\(393\) 0 0
\(394\) −4.61741 + 14.2109i −0.232622 + 0.715936i
\(395\) 2.29896 + 2.65402i 0.115673 + 0.133538i
\(396\) 0 0
\(397\) −9.73897 29.9735i −0.488785 1.50432i −0.826423 0.563049i \(-0.809628\pi\)
0.337639 0.941276i \(-0.390372\pi\)
\(398\) 3.96771 + 2.88271i 0.198883 + 0.144497i
\(399\) 0 0
\(400\) −0.713211 + 4.94887i −0.0356606 + 0.247444i
\(401\) 13.6940 0.683847 0.341924 0.939728i \(-0.388922\pi\)
0.341924 + 0.939728i \(0.388922\pi\)
\(402\) 0 0
\(403\) −0.162103 0.498901i −0.00807492 0.0248520i
\(404\) 0.236456 + 0.727737i 0.0117641 + 0.0362063i
\(405\) 0 0
\(406\) −6.16336 + 18.9689i −0.305882 + 0.941409i
\(407\) 1.85709 0.0920527
\(408\) 0 0
\(409\) 24.3488 17.6904i 1.20397 0.874735i 0.209300 0.977851i \(-0.432881\pi\)
0.994669 + 0.103116i \(0.0328814\pi\)
\(410\) −10.4516 + 4.41483i −0.516165 + 0.218033i
\(411\) 0 0
\(412\) −4.55718 + 3.31098i −0.224516 + 0.163120i
\(413\) 17.5921 12.7814i 0.865652 0.628933i
\(414\) 0 0
\(415\) 2.48650 + 29.0061i 0.122058 + 1.42385i
\(416\) −0.250822 + 0.182233i −0.0122976 + 0.00893470i
\(417\) 0 0
\(418\) −0.616002 −0.0301296
\(419\) −3.28756 + 10.1181i −0.160608 + 0.494301i −0.998686 0.0512500i \(-0.983679\pi\)
0.838078 + 0.545551i \(0.183679\pi\)
\(420\) 0 0
\(421\) 3.73916 + 11.5080i 0.182236 + 0.560864i 0.999890 0.0148461i \(-0.00472583\pi\)
−0.817654 + 0.575710i \(0.804726\pi\)
\(422\) −0.380710 1.17170i −0.0185327 0.0570377i
\(423\) 0 0
\(424\) −9.97175 −0.484271
\(425\) 14.1026 + 26.7488i 0.684075 + 1.29751i
\(426\) 0 0
\(427\) 13.1379 + 9.54525i 0.635788 + 0.461927i
\(428\) 2.72257 + 8.37921i 0.131600 + 0.405024i
\(429\) 0 0
\(430\) 22.3000 + 5.18954i 1.07540 + 0.250262i
\(431\) 0.337509 1.03875i 0.0162572 0.0500346i −0.942599 0.333927i \(-0.891626\pi\)
0.958856 + 0.283893i \(0.0916260\pi\)
\(432\) 0 0
\(433\) 3.74722 11.5328i 0.180080 0.554229i −0.819749 0.572723i \(-0.805887\pi\)
0.999829 + 0.0184940i \(0.00588716\pi\)
\(434\) 4.00810 2.91206i 0.192395 0.139783i
\(435\) 0 0
\(436\) −12.8447 9.33220i −0.615148 0.446931i
\(437\) 11.7082 8.50651i 0.560079 0.406921i
\(438\) 0 0
\(439\) −11.2409 8.16698i −0.536498 0.389789i 0.286285 0.958145i \(-0.407580\pi\)
−0.822783 + 0.568356i \(0.807580\pi\)
\(440\) 0.219863 0.364466i 0.0104816 0.0173752i
\(441\) 0 0
\(442\) −0.579407 + 1.78323i −0.0275596 + 0.0848197i
\(443\) 38.2047 1.81516 0.907579 0.419880i \(-0.137928\pi\)
0.907579 + 0.419880i \(0.137928\pi\)
\(444\) 0 0
\(445\) −20.2190 4.70524i −0.958471 0.223050i
\(446\) 1.44079 + 4.43429i 0.0682233 + 0.209970i
\(447\) 0 0
\(448\) −2.36886 1.72107i −0.111918 0.0813131i
\(449\) −14.8092 −0.698888 −0.349444 0.936957i \(-0.613629\pi\)
−0.349444 + 0.936957i \(0.613629\pi\)
\(450\) 0 0
\(451\) 0.965855 0.0454803
\(452\) −15.4845 11.2502i −0.728332 0.529164i
\(453\) 0 0
\(454\) −0.177245 0.545504i −0.00831852 0.0256018i
\(455\) −1.04852 + 1.73813i −0.0491554 + 0.0814847i
\(456\) 0 0
\(457\) 4.86286 0.227475 0.113738 0.993511i \(-0.463718\pi\)
0.113738 + 0.993511i \(0.463718\pi\)
\(458\) 9.18801 28.2778i 0.429327 1.32133i
\(459\) 0 0
\(460\) 0.854102 + 9.96346i 0.0398227 + 0.464549i
\(461\) −16.4278 11.9355i −0.765117 0.555890i 0.135359 0.990797i \(-0.456781\pi\)
−0.900475 + 0.434907i \(0.856781\pi\)
\(462\) 0 0
\(463\) −32.3465 + 23.5011i −1.50327 + 1.09219i −0.534213 + 0.845350i \(0.679392\pi\)
−0.969056 + 0.246840i \(0.920608\pi\)
\(464\) 5.51076 + 4.00380i 0.255831 + 0.185872i
\(465\) 0 0
\(466\) −11.2266 + 8.15663i −0.520064 + 0.377848i
\(467\) 4.92623 15.1614i 0.227959 0.701585i −0.770019 0.638021i \(-0.779753\pi\)
0.997978 0.0635638i \(-0.0202466\pi\)
\(468\) 0 0
\(469\) −13.6558 + 42.0281i −0.630565 + 1.94068i
\(470\) −2.04571 23.8641i −0.0943617 1.10077i
\(471\) 0 0
\(472\) −2.29489 7.06295i −0.105631 0.325099i
\(473\) −1.57687 1.14566i −0.0725043 0.0526775i
\(474\) 0 0
\(475\) −7.54610 14.3129i −0.346239 0.656722i
\(476\) −17.7082 −0.811654
\(477\) 0 0
\(478\) 0.662491 + 2.03894i 0.0303016 + 0.0932588i
\(479\) 2.42768 + 7.47163i 0.110923 + 0.341387i 0.991075 0.133305i \(-0.0425591\pi\)
−0.880152 + 0.474693i \(0.842559\pi\)
\(480\) 0 0
\(481\) −0.934674 + 2.87663i −0.0426174 + 0.131163i
\(482\) 1.73974 0.0792432
\(483\) 0 0
\(484\) 8.86987 6.44434i 0.403176 0.292925i
\(485\) 2.54704 + 2.94043i 0.115655 + 0.133518i
\(486\) 0 0
\(487\) 33.1264 24.0677i 1.50110 1.09061i 0.531158 0.847273i \(-0.321757\pi\)
0.969941 0.243340i \(-0.0782430\pi\)
\(488\) 4.48689 3.25992i 0.203112 0.147569i
\(489\) 0 0
\(490\) −3.42705 0.797524i −0.154818 0.0360285i
\(491\) −6.08238 + 4.41911i −0.274494 + 0.199432i −0.716512 0.697574i \(-0.754263\pi\)
0.442018 + 0.897006i \(0.354263\pi\)
\(492\) 0 0
\(493\) 41.1953 1.85534
\(494\) 0.310033 0.954184i 0.0139490 0.0429308i
\(495\) 0 0
\(496\) −0.522856 1.60919i −0.0234769 0.0722546i
\(497\) −6.20288 19.0905i −0.278237 0.856326i
\(498\) 0 0
\(499\) 15.7513 0.705123 0.352561 0.935789i \(-0.385311\pi\)
0.352561 + 0.935789i \(0.385311\pi\)
\(500\) 11.1618 + 0.643811i 0.499170 + 0.0287921i
\(501\) 0 0
\(502\) −5.17521 3.76001i −0.230981 0.167818i
\(503\) −0.253049 0.778805i −0.0112829 0.0347252i 0.945257 0.326328i \(-0.105811\pi\)
−0.956539 + 0.291603i \(0.905811\pi\)
\(504\) 0 0
\(505\) 1.57616 0.665785i 0.0701384 0.0296271i
\(506\) 0.263064 0.809628i 0.0116946 0.0359924i
\(507\) 0 0
\(508\) −2.51475 + 7.73962i −0.111574 + 0.343390i
\(509\) 21.8047 15.8420i 0.966477 0.702186i 0.0118309 0.999930i \(-0.496234\pi\)
0.954646 + 0.297744i \(0.0962340\pi\)
\(510\) 0 0
\(511\) −27.5676 20.0291i −1.21952 0.886033i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −5.10492 3.70894i −0.225169 0.163595i
\(515\) 8.24688 + 9.52058i 0.363401 + 0.419527i
\(516\) 0 0
\(517\) −0.630081 + 1.93919i −0.0277109 + 0.0852855i
\(518\) −28.5661 −1.25512
\(519\) 0 0
\(520\) 0.453899 + 0.524002i 0.0199048 + 0.0229790i
\(521\) 4.77653 + 14.7007i 0.209264 + 0.644048i 0.999511 + 0.0312598i \(0.00995193\pi\)
−0.790248 + 0.612788i \(0.790048\pi\)
\(522\) 0 0
\(523\) −8.35778 6.07228i −0.365460 0.265522i 0.389866 0.920872i \(-0.372521\pi\)
−0.755326 + 0.655349i \(0.772521\pi\)
\(524\) −16.6201 −0.726051
\(525\) 0 0
\(526\) −2.85942 −0.124677
\(527\) −8.27849 6.01468i −0.360617 0.262003i
\(528\) 0 0
\(529\) −0.927051 2.85317i −0.0403066 0.124051i
\(530\) 1.90443 + 22.2160i 0.0827233 + 0.965003i
\(531\) 0 0
\(532\) 9.47542 0.410812
\(533\) −0.486114 + 1.49610i −0.0210559 + 0.0648035i
\(534\) 0 0
\(535\) 18.1480 7.66589i 0.784609 0.331425i
\(536\) 12.2098 + 8.87097i 0.527385 + 0.383168i
\(537\) 0 0
\(538\) −7.85246 + 5.70514i −0.338543 + 0.245966i
\(539\) 0.242332 + 0.176064i 0.0104380 + 0.00758362i
\(540\) 0 0
\(541\) 29.9620 21.7687i 1.28817 0.935908i 0.288400 0.957510i \(-0.406877\pi\)
0.999767 + 0.0216018i \(0.00687662\pi\)
\(542\) 5.30503 16.3272i 0.227870 0.701313i
\(543\) 0 0
\(544\) −1.86886 + 5.75175i −0.0801265 + 0.246604i
\(545\) −18.3381 + 30.3989i −0.785516 + 1.30215i
\(546\) 0 0
\(547\) −7.48341 23.0316i −0.319967 0.984758i −0.973661 0.227999i \(-0.926782\pi\)
0.653694 0.756759i \(-0.273218\pi\)
\(548\) −8.60657 6.25304i −0.367654 0.267117i
\(549\) 0 0
\(550\) −0.853982 0.420226i −0.0364139 0.0179185i
\(551\) −22.0431 −0.939066
\(552\) 0 0
\(553\) 1.42083 + 4.37287i 0.0604199 + 0.185953i
\(554\) −0.631532 1.94366i −0.0268312 0.0825780i
\(555\) 0 0
\(556\) 7.07397 21.7714i 0.300003 0.923314i
\(557\) −26.3623 −1.11701 −0.558504 0.829502i \(-0.688624\pi\)
−0.558504 + 0.829502i \(0.688624\pi\)
\(558\) 0 0
\(559\) 2.56826 1.86595i 0.108626 0.0789212i
\(560\) −3.38197 + 5.60626i −0.142914 + 0.236908i
\(561\) 0 0
\(562\) 4.17357 3.03228i 0.176051 0.127909i
\(563\) 12.2197 8.87811i 0.514998 0.374168i −0.299718 0.954028i \(-0.596893\pi\)
0.814716 + 0.579860i \(0.196893\pi\)
\(564\) 0 0
\(565\) −22.1070 + 36.6466i −0.930047 + 1.54173i
\(566\) 7.59385 5.51725i 0.319193 0.231907i
\(567\) 0 0
\(568\) −6.85536 −0.287644
\(569\) 3.55757 10.9491i 0.149141 0.459009i −0.848379 0.529389i \(-0.822421\pi\)
0.997520 + 0.0703802i \(0.0224213\pi\)
\(570\) 0 0
\(571\) −9.73974 29.9759i −0.407596 1.25445i −0.918708 0.394937i \(-0.870767\pi\)
0.511113 0.859514i \(-0.329233\pi\)
\(572\) −0.0182371 0.0561279i −0.000762530 0.00234682i
\(573\) 0 0
\(574\) −14.8569 −0.620115
\(575\) 22.0344 3.80570i 0.918900 0.158709i
\(576\) 0 0
\(577\) 10.6769 + 7.75719i 0.444483 + 0.322936i 0.787414 0.616425i \(-0.211420\pi\)
−0.342930 + 0.939361i \(0.611420\pi\)
\(578\) 6.04908 + 18.6171i 0.251608 + 0.774371i
\(579\) 0 0
\(580\) 7.86760 13.0421i 0.326684 0.541543i
\(581\) −11.7803 + 36.2561i −0.488730 + 1.50416i
\(582\) 0 0
\(583\) 0.586567 1.80527i 0.0242931 0.0747666i
\(584\) −9.41496 + 6.84037i −0.389594 + 0.283056i
\(585\) 0 0
\(586\) −6.61905 4.80902i −0.273430 0.198659i
\(587\) 24.9839 18.1519i 1.03120 0.749208i 0.0626487 0.998036i \(-0.480045\pi\)
0.968548 + 0.248828i \(0.0800452\pi\)
\(588\) 0 0
\(589\) 4.42971 + 3.21837i 0.182523 + 0.132611i
\(590\) −15.2972 + 6.46168i −0.629777 + 0.266023i
\(591\) 0 0
\(592\) −3.01475 + 9.27846i −0.123906 + 0.381342i
\(593\) −5.13588 −0.210905 −0.105453 0.994424i \(-0.533629\pi\)
−0.105453 + 0.994424i \(0.533629\pi\)
\(594\) 0 0
\(595\) 3.38197 + 39.4521i 0.138647 + 1.61738i
\(596\) −0.435153 1.33926i −0.0178246 0.0548584i
\(597\) 0 0
\(598\) 1.12171 + 0.814970i 0.0458701 + 0.0333266i
\(599\) 42.2558 1.72653 0.863263 0.504755i \(-0.168417\pi\)
0.863263 + 0.504755i \(0.168417\pi\)
\(600\) 0 0
\(601\) 4.38893 0.179028 0.0895141 0.995986i \(-0.471469\pi\)
0.0895141 + 0.995986i \(0.471469\pi\)
\(602\) 24.2556 + 17.6227i 0.988583 + 0.718247i
\(603\) 0 0
\(604\) −2.43269 7.48704i −0.0989846 0.304643i
\(605\) −16.0513 18.5304i −0.652579 0.753368i
\(606\) 0 0
\(607\) −30.0265 −1.21874 −0.609368 0.792887i \(-0.708577\pi\)
−0.609368 + 0.792887i \(0.708577\pi\)
\(608\) 1.00000 3.07768i 0.0405554 0.124817i
\(609\) 0 0
\(610\) −8.11968 9.37374i −0.328756 0.379532i
\(611\) −2.68668 1.95199i −0.108691 0.0789689i
\(612\) 0 0
\(613\) −3.62512 + 2.63380i −0.146417 + 0.106378i −0.658582 0.752509i \(-0.728844\pi\)
0.512165 + 0.858887i \(0.328844\pi\)
\(614\) −4.73974 3.44363i −0.191281 0.138973i
\(615\) 0 0
\(616\) 0.450924 0.327615i 0.0181682 0.0132000i
\(617\) 4.31692 13.2861i 0.173793 0.534879i −0.825783 0.563987i \(-0.809267\pi\)
0.999576 + 0.0291080i \(0.00926666\pi\)
\(618\) 0 0
\(619\) 7.54813 23.2308i 0.303385 0.933723i −0.676890 0.736084i \(-0.736673\pi\)
0.980275 0.197639i \(-0.0633274\pi\)
\(620\) −3.48525 + 1.47220i −0.139971 + 0.0591249i
\(621\) 0 0
\(622\) 5.88361 + 18.1079i 0.235911 + 0.726060i
\(623\) −21.9920 15.9781i −0.881092 0.640150i
\(624\) 0 0
\(625\) −0.697366 24.9903i −0.0278946 0.999611i
\(626\) −11.9966 −0.479479
\(627\) 0 0
\(628\) −2.14938 6.61511i −0.0857696 0.263972i
\(629\) 18.2325 + 56.1138i 0.726976 + 2.23740i
\(630\) 0 0
\(631\) 3.06269 9.42600i 0.121924 0.375243i −0.871404 0.490566i \(-0.836790\pi\)
0.993328 + 0.115322i \(0.0367901\pi\)
\(632\) 1.57029 0.0624627
\(633\) 0 0
\(634\) 26.3841 19.1692i 1.04785 0.761306i
\(635\) 17.7233 + 4.12448i 0.703330 + 0.163675i
\(636\) 0 0
\(637\) −0.394688 + 0.286758i −0.0156381 + 0.0113617i
\(638\) −1.04900 + 0.762144i −0.0415304 + 0.0301736i
\(639\) 0 0
\(640\) 1.46403 + 1.69015i 0.0578710 + 0.0668090i
\(641\) 31.9691 23.2269i 1.26270 0.917407i 0.263816 0.964573i \(-0.415019\pi\)
0.998887 + 0.0471657i \(0.0150189\pi\)
\(642\) 0 0
\(643\) 22.9508 0.905093 0.452547 0.891741i \(-0.350516\pi\)
0.452547 + 0.891741i \(0.350516\pi\)
\(644\) −4.04649 + 12.4538i −0.159454 + 0.490749i
\(645\) 0 0
\(646\) −6.04775 18.6130i −0.237945 0.732320i
\(647\) 0.761900 + 2.34489i 0.0299534 + 0.0921870i 0.964916 0.262560i \(-0.0845669\pi\)
−0.934962 + 0.354747i \(0.884567\pi\)
\(648\) 0 0
\(649\) 1.41366 0.0554909
\(650\) 1.08074 1.11132i 0.0423900 0.0435894i
\(651\) 0 0
\(652\) 11.3262 + 8.22899i 0.443570 + 0.322272i
\(653\) 8.27484 + 25.4673i 0.323820 + 0.996614i 0.971971 + 0.235102i \(0.0755426\pi\)
−0.648151 + 0.761512i \(0.724457\pi\)
\(654\) 0 0
\(655\) 3.17415 + 37.0278i 0.124024 + 1.44680i
\(656\) −1.56794 + 4.82563i −0.0612178 + 0.188409i
\(657\) 0 0
\(658\) 9.69200 29.8289i 0.377833 1.16285i
\(659\) 23.1334 16.8074i 0.901150 0.654724i −0.0376112 0.999292i \(-0.511975\pi\)
0.938761 + 0.344569i \(0.111975\pi\)
\(660\) 0 0
\(661\) 1.89981 + 1.38030i 0.0738942 + 0.0536873i 0.624119 0.781329i \(-0.285458\pi\)
−0.550225 + 0.835017i \(0.685458\pi\)
\(662\) −2.61475 + 1.89972i −0.101625 + 0.0738349i
\(663\) 0 0
\(664\) 10.5330 + 7.65267i 0.408759 + 0.296981i
\(665\) −1.80964 21.1103i −0.0701750 0.818621i
\(666\) 0 0
\(667\) 9.41351 28.9718i 0.364492 1.12179i
\(668\) −1.37742 −0.0532940
\(669\) 0 0
\(670\) 17.4317 28.8965i 0.673447 1.11637i
\(671\) 0.326238 + 1.00406i 0.0125943 + 0.0387612i
\(672\) 0 0
\(673\) 28.3700 + 20.6120i 1.09358 + 0.794534i 0.980001 0.198994i \(-0.0637675\pi\)
0.113582 + 0.993529i \(0.463767\pi\)
\(674\) 21.3154 0.821037
\(675\) 0 0
\(676\) −12.9039 −0.496303
\(677\) 26.0549 + 18.9300i 1.00137 + 0.727539i 0.962382 0.271701i \(-0.0875861\pi\)
0.0389895 + 0.999240i \(0.487586\pi\)
\(678\) 0 0
\(679\) 1.57416 + 4.84477i 0.0604107 + 0.185925i
\(680\) 13.1712 + 3.06513i 0.505093 + 0.117542i
\(681\) 0 0
\(682\) 0.322080 0.0123331
\(683\) −4.26867 + 13.1376i −0.163336 + 0.502697i −0.998910 0.0466814i \(-0.985135\pi\)
0.835574 + 0.549378i \(0.185135\pi\)
\(684\) 0 0
\(685\) −12.2874 + 20.3688i −0.469478 + 0.778251i
\(686\) 12.8544 + 9.33928i 0.490784 + 0.356575i
\(687\) 0 0
\(688\) 8.28381 6.01854i 0.315817 0.229455i
\(689\) 2.50113 + 1.81718i 0.0952856 + 0.0692291i
\(690\) 0 0
\(691\) 20.9940 15.2531i 0.798651 0.580254i −0.111867 0.993723i \(-0.535683\pi\)
0.910518 + 0.413469i \(0.135683\pi\)
\(692\) 1.27407 3.92117i 0.0484327 0.149061i
\(693\) 0 0
\(694\) −5.91496 + 18.2044i −0.224529 + 0.691028i
\(695\) −49.8555 11.6021i −1.89113 0.440093i
\(696\) 0 0
\(697\) 9.48251 + 29.1842i 0.359176 + 1.10543i
\(698\) −11.6292 8.44910i −0.440171 0.319803i
\(699\) 0 0
\(700\) 13.1361 + 6.46397i 0.496497 + 0.244315i
\(701\) −37.4437 −1.41423 −0.707115 0.707098i \(-0.750004\pi\)
−0.707115 + 0.707098i \(0.750004\pi\)
\(702\) 0 0
\(703\) −9.75595 30.0257i −0.367953 1.13244i
\(704\) −0.0588229 0.181038i −0.00221697 0.00682314i
\(705\) 0 0
\(706\) −7.53609 + 23.1937i −0.283624 + 0.872906i
\(707\) 2.24052 0.0842635
\(708\) 0 0
\(709\) 14.0996 10.2440i 0.529522 0.384720i −0.290657 0.956827i \(-0.593874\pi\)
0.820179 + 0.572107i \(0.193874\pi\)
\(710\) 1.30926 + 15.2730i 0.0491355 + 0.573187i
\(711\) 0 0
\(712\) −7.51076 + 5.45689i −0.281478 + 0.204506i
\(713\) −6.12171 + 4.44768i −0.229260 + 0.166567i
\(714\) 0 0
\(715\) −0.121564 + 0.0513498i −0.00454624 + 0.00192037i
\(716\) 3.48525 2.53218i 0.130250 0.0946320i
\(717\) 0 0
\(718\) 21.3316 0.796087
\(719\) 10.9650 33.7469i 0.408926 1.25855i −0.508646 0.860976i \(-0.669854\pi\)
0.917572 0.397570i \(-0.130146\pi\)
\(720\) 0 0
\(721\) 5.09685 + 15.6865i 0.189817 + 0.584195i
\(722\) −2.63525 8.11048i −0.0980740 0.301841i
\(723\) 0 0
\(724\) 12.9920 0.482845
\(725\) −30.5590 15.0374i −1.13493 0.558475i
\(726\) 0 0
\(727\) 15.4459 + 11.2221i 0.572857 + 0.416205i 0.836142 0.548513i \(-0.184806\pi\)
−0.263285 + 0.964718i \(0.584806\pi\)
\(728\) 0.280525 + 0.863367i 0.0103969 + 0.0319985i
\(729\) 0 0
\(730\) 17.0377 + 19.6692i 0.630595 + 0.727988i
\(731\) 19.1359 58.8942i 0.707766 2.17828i
\(732\) 0 0
\(733\) 3.38352 10.4134i 0.124973 0.384628i −0.868923 0.494947i \(-0.835187\pi\)
0.993896 + 0.110319i \(0.0351874\pi\)
\(734\) 8.60164 6.24945i 0.317492 0.230672i
\(735\) 0 0
\(736\) 3.61803 + 2.62866i 0.133363 + 0.0968935i
\(737\) −2.32421 + 1.68863i −0.0856132 + 0.0622016i
\(738\) 0 0
\(739\) −38.7566 28.1583i −1.42568 1.03582i −0.990800 0.135333i \(-0.956790\pi\)
−0.434884 0.900487i \(-0.643210\pi\)
\(740\) 21.2472 + 4.94453i 0.781063 + 0.181765i
\(741\) 0 0
\(742\) −9.02266 + 27.7689i −0.331232 + 1.01943i
\(743\) −38.6016 −1.41615 −0.708077 0.706135i \(-0.750437\pi\)
−0.708077 + 0.706135i \(0.750437\pi\)
\(744\) 0 0
\(745\) −2.90064 + 1.22525i −0.106271 + 0.0448898i
\(746\) 0.381190 + 1.17318i 0.0139563 + 0.0429532i
\(747\) 0 0
\(748\) −0.931355 0.676669i −0.0340537 0.0247415i
\(749\) 25.7975 0.942620
\(750\) 0 0
\(751\) −29.2670 −1.06797 −0.533984 0.845495i \(-0.679306\pi\)
−0.533984 + 0.845495i \(0.679306\pi\)
\(752\) −8.66578 6.29606i −0.316008 0.229594i
\(753\) 0 0
\(754\) −0.652596 2.00848i −0.0237662 0.0731447i
\(755\) −16.2158 + 6.84967i −0.590152 + 0.249285i
\(756\) 0 0
\(757\) −12.0788 −0.439012 −0.219506 0.975611i \(-0.570444\pi\)
−0.219506 + 0.975611i \(0.570444\pi\)
\(758\) 7.82585 24.0855i 0.284248 0.874824i
\(759\) 0 0
\(760\) −7.04775 1.64011i −0.255649 0.0594931i
\(761\) −1.72093 1.25033i −0.0623835 0.0453243i 0.556156 0.831078i \(-0.312276\pi\)
−0.618540 + 0.785753i \(0.712276\pi\)
\(762\) 0 0
\(763\) −37.6101 + 27.3253i −1.36158 + 0.989242i
\(764\) −1.00000 0.726543i −0.0361787 0.0262854i
\(765\) 0 0
\(766\) 15.5166 11.2735i 0.560637 0.407327i
\(767\) −0.711492 + 2.18975i −0.0256905 + 0.0790672i
\(768\) 0 0
\(769\) −2.77310 + 8.53471i −0.100000 + 0.307770i −0.988525 0.151060i \(-0.951731\pi\)
0.888524 + 0.458830i \(0.151731\pi\)
\(770\) −0.816012 0.942042i −0.0294070 0.0339489i
\(771\) 0 0
\(772\) 5.38463 + 16.5722i 0.193797 + 0.596446i
\(773\) 23.2575 + 16.8976i 0.836515 + 0.607764i 0.921395 0.388628i \(-0.127051\pi\)
−0.0848801 + 0.996391i \(0.527051\pi\)
\(774\) 0 0
\(775\) 3.94553 + 7.48360i 0.141728 + 0.268819i
\(776\) 1.73974 0.0624532
\(777\) 0 0
\(778\) 2.56407 + 7.89140i 0.0919264 + 0.282920i
\(779\) −5.07397 15.6161i −0.181794 0.559503i
\(780\) 0 0
\(781\) 0.403252 1.24108i 0.0144295 0.0444094i
\(782\) 27.0463 0.967175
\(783\) 0 0
\(784\) −1.27305 + 0.924925i −0.0454661 + 0.0330330i
\(785\) −14.3273 + 6.05197i −0.511363 + 0.216004i
\(786\) 0 0
\(787\) 39.9330 29.0130i 1.42346 1.03420i 0.432269 0.901745i \(-0.357713\pi\)
0.991189 0.132458i \(-0.0422869\pi\)
\(788\) 12.0885 8.78283i 0.430636 0.312875i
\(789\) 0 0
\(790\) −0.299898 3.49844i −0.0106699 0.124469i
\(791\) −45.3398 + 32.9413i −1.61210 + 1.17126i
\(792\) 0 0
\(793\) −1.71948 −0.0610603
\(794\) −9.73897 + 29.9735i −0.345623 + 1.06372i
\(795\) 0 0
\(796\) −1.51553 4.66432i −0.0537165 0.165323i
\(797\) −0.907289 2.79235i −0.0321378 0.0989101i 0.933701 0.358054i \(-0.116560\pi\)
−0.965839 + 0.259144i \(0.916560\pi\)
\(798\) 0 0
\(799\) −64.7804 −2.29176
\(800\) 3.48587 3.58451i 0.123244 0.126731i
\(801\) 0 0
\(802\) −11.0787 8.04915i −0.391203 0.284225i
\(803\) −0.684553 2.10684i −0.0241574 0.0743487i
\(804\) 0 0
\(805\) 28.5186 + 6.63669i 1.00515 + 0.233913i
\(806\) −0.162103 + 0.498901i −0.00570983 + 0.0175730i
\(807\) 0 0
\(808\) 0.236456 0.727737i 0.00831850 0.0256017i
\(809\) −29.2720 + 21.2674i −1.02915 + 0.747721i −0.968138 0.250416i \(-0.919433\pi\)
−0.0610115 + 0.998137i \(0.519433\pi\)
\(810\) 0 0
\(811\) 36.5650 + 26.5660i 1.28397 + 0.932858i 0.999665 0.0258756i \(-0.00823738\pi\)
0.284304 + 0.958734i \(0.408237\pi\)
\(812\) 16.1359 11.7234i 0.566258 0.411411i
\(813\) 0 0
\(814\) −1.50242 1.09157i −0.0526598 0.0382596i
\(815\) 16.1702 26.8053i 0.566419 0.938948i
\(816\) 0 0
\(817\) −10.2394 + 31.5135i −0.358230 + 1.10252i
\(818\) −30.0967 −1.05231
\(819\) 0 0
\(820\) 11.0505 + 2.57160i 0.385899 + 0.0898041i
\(821\) 6.03945 + 18.5875i 0.210778 + 0.648709i 0.999426 + 0.0338640i \(0.0107813\pi\)
−0.788648 + 0.614845i \(0.789219\pi\)
\(822\) 0 0
\(823\) 14.1755 + 10.2991i 0.494128 + 0.359005i 0.806770 0.590866i \(-0.201214\pi\)
−0.312642 + 0.949871i \(0.601214\pi\)
\(824\) 5.63298 0.196234
\(825\) 0 0
\(826\) −21.7451 −0.756608
\(827\) −20.1268 14.6230i −0.699879 0.508492i 0.180014 0.983664i \(-0.442386\pi\)
−0.879893 + 0.475172i \(0.842386\pi\)
\(828\) 0 0
\(829\) −4.93738 15.1957i −0.171482 0.527768i 0.827973 0.560768i \(-0.189494\pi\)
−0.999455 + 0.0329996i \(0.989494\pi\)
\(830\) 15.0377 24.9279i 0.521967 0.865262i
\(831\) 0 0
\(832\) 0.310033 0.0107485
\(833\) −2.94079 + 9.05082i −0.101892 + 0.313592i
\(834\) 0 0
\(835\) 0.263064 + 3.06875i 0.00910371 + 0.106199i
\(836\) 0.498356 + 0.362077i 0.0172360 + 0.0125227i
\(837\) 0 0
\(838\) 8.60696 6.25332i 0.297322 0.216017i
\(839\) −32.7244 23.7757i −1.12977 0.820827i −0.144110 0.989562i \(-0.546032\pi\)
−0.985662 + 0.168734i \(0.946032\pi\)
\(840\) 0 0
\(841\) −14.0760 + 10.2268i −0.485381 + 0.352650i
\(842\) 3.73916 11.5080i 0.128860 0.396590i
\(843\) 0 0
\(844\) −0.380710 + 1.17170i −0.0131046 + 0.0403317i
\(845\) 2.46442 + 28.7485i 0.0847787 + 0.988979i
\(846\) 0 0
\(847\) −9.92026 30.5314i −0.340864 1.04907i
\(848\) 8.06731 + 5.86125i 0.277033 + 0.201276i
\(849\) 0 0
\(850\) 4.31332 29.9295i 0.147946 1.02657i
\(851\) 43.6299 1.49561
\(852\) 0 0
\(853\) −13.3509 41.0898i −0.457126 1.40689i −0.868621 0.495476i \(-0.834993\pi\)
0.411496 0.911412i \(-0.365007\pi\)
\(854\) −5.01824 15.4445i −0.171721 0.528501i
\(855\) 0 0
\(856\) 2.72257 8.37921i 0.0930555 0.286395i
\(857\) −21.6193 −0.738501 −0.369250 0.929330i \(-0.620386\pi\)
−0.369250 + 0.929330i \(0.620386\pi\)
\(858\) 0 0
\(859\) 31.5871 22.9494i 1.07774 0.783023i 0.100451 0.994942i \(-0.467971\pi\)
0.977287 + 0.211919i \(0.0679713\pi\)
\(860\) −14.9908 17.3060i −0.511181 0.590131i
\(861\) 0 0
\(862\) −0.883610 + 0.641980i −0.0300959 + 0.0218659i
\(863\) −17.3283 + 12.5897i −0.589861 + 0.428559i −0.842266 0.539063i \(-0.818779\pi\)
0.252405 + 0.967622i \(0.418779\pi\)
\(864\) 0 0
\(865\) −8.97930 2.08961i −0.305305 0.0710489i
\(866\) −9.81035 + 7.12763i −0.333369 + 0.242207i
\(867\) 0 0
\(868\) −4.95429 −0.168159
\(869\) −0.0923690 + 0.284283i −0.00313340 + 0.00964362i
\(870\) 0 0
\(871\) −1.44592 4.45007i −0.0489930 0.150785i
\(872\) 4.90623 + 15.0998i 0.166146 + 0.511344i
\(873\) 0 0
\(874\) −14.4721 −0.489527
\(875\) 11.8923 30.5003i 0.402033 1.03110i
\(876\) 0 0
\(877\) −37.9859 27.5984i −1.28269 0.931930i −0.283061 0.959102i \(-0.591350\pi\)
−0.999631 + 0.0271718i \(0.991350\pi\)
\(878\) 4.29363 + 13.2144i 0.144903 + 0.445966i
\(879\) 0 0
\(880\) −0.392101 + 0.165627i −0.0132177 + 0.00558327i
\(881\) −0.100961 + 0.310727i −0.00340147 + 0.0104687i −0.952743 0.303778i \(-0.901752\pi\)
0.949341 + 0.314247i \(0.101752\pi\)
\(882\) 0 0
\(883\) −4.29257 + 13.2112i −0.144457 + 0.444592i −0.996941 0.0781615i \(-0.975095\pi\)
0.852484 + 0.522753i \(0.175095\pi\)
\(884\) 1.51691 1.10210i 0.0510191 0.0370676i
\(885\) 0 0
\(886\) −30.9082 22.4561i −1.03838 0.754429i
\(887\) −4.39488 + 3.19307i −0.147566 + 0.107213i −0.659119 0.752039i \(-0.729070\pi\)
0.511553 + 0.859252i \(0.329070\pi\)
\(888\) 0 0
\(889\) 19.2775 + 14.0060i 0.646548 + 0.469745i
\(890\) 13.5918 + 15.6910i 0.455599 + 0.525965i
\(891\) 0 0
\(892\) 1.44079 4.43429i 0.0482412 0.148471i
\(893\) 34.6631 1.15996
\(894\) 0 0
\(895\) −6.30706 7.28117i −0.210822 0.243383i
\(896\) 0.904822 + 2.78476i 0.0302280 + 0.0930322i
\(897\) 0 0
\(898\) 11.9809 + 8.70461i 0.399807 + 0.290477i
\(899\) 11.5254 0.384392
\(900\) 0 0
\(901\) 60.3066 2.00910
\(902\) −0.781393 0.567715i −0.0260175 0.0189028i
\(903\) 0 0
\(904\) 5.91457 + 18.2032i 0.196716 + 0.605428i
\(905\) −2.48125 28.9449i −0.0824797 0.962160i
\(906\) 0 0
\(907\) −48.3381 −1.60504 −0.802521 0.596624i \(-0.796508\pi\)
−0.802521 + 0.596624i \(0.796508\pi\)
\(908\) −0.177245 + 0.545504i −0.00588208 + 0.0181032i
\(909\) 0 0
\(910\) 1.86992 0.789869i 0.0619872 0.0261839i
\(911\) 6.80839 + 4.94658i 0.225572 + 0.163888i 0.694831 0.719173i \(-0.255479\pi\)
−0.469259 + 0.883060i \(0.655479\pi\)
\(912\) 0 0
\(913\) −2.00501 + 1.45672i −0.0663561 + 0.0482105i
\(914\) −3.93414 2.85832i −0.130130 0.0945448i
\(915\) 0 0
\(916\) −24.0545 + 17.4766i −0.794784 + 0.577444i
\(917\) −15.0382 + 46.2829i −0.496605 + 1.52839i
\(918\) 0 0
\(919\) 8.87108 27.3024i 0.292630 0.900623i −0.691377 0.722494i \(-0.742996\pi\)
0.984007 0.178129i \(-0.0570043\pi\)
\(920\) 5.16539 8.56264i 0.170298 0.282302i
\(921\) 0 0
\(922\) 6.27484 + 19.3120i 0.206651 + 0.636006i
\(923\) 1.71948 + 1.24927i 0.0565972 + 0.0411203i
\(924\) 0 0
\(925\) 6.95806 48.2809i 0.228779 1.58747i
\(926\) 39.9825 1.31391
\(927\) 0 0
\(928\) −2.10492 6.47829i −0.0690975 0.212660i
\(929\) 2.14735 + 6.60886i 0.0704522 + 0.216830i 0.980083 0.198588i \(-0.0636355\pi\)
−0.909631 + 0.415417i \(0.863636\pi\)
\(930\) 0 0
\(931\) 1.57358 4.84297i 0.0515719 0.158722i
\(932\) 13.8769 0.454552
\(933\) 0 0
\(934\) −12.8970 + 9.37024i −0.422004 + 0.306604i
\(935\) −1.32968 + 2.20420i −0.0434851 + 0.0720849i
\(936\) 0 0
\(937\) −20.1124 + 14.6125i −0.657043 + 0.477370i −0.865663 0.500627i \(-0.833103\pi\)
0.208620 + 0.977997i \(0.433103\pi\)
\(938\) 35.7513 25.9748i 1.16732 0.848108i
\(939\) 0 0
\(940\) −12.3720 + 20.5089i −0.403529 + 0.668927i
\(941\) −0.380637 + 0.276549i −0.0124084 + 0.00901524i −0.593972 0.804486i \(-0.702441\pi\)
0.581564 + 0.813501i \(0.302441\pi\)
\(942\) 0 0
\(943\) 22.6915 0.738936
\(944\) −2.29489 + 7.06295i −0.0746923 + 0.229879i
\(945\) 0 0
\(946\) 0.602309 + 1.85372i 0.0195828 + 0.0602695i
\(947\) 10.1511 + 31.2420i 0.329868 + 1.01523i 0.969195 + 0.246294i \(0.0792129\pi\)
−0.639327 + 0.768935i \(0.720787\pi\)
\(948\) 0 0
\(949\) 3.60802 0.117121
\(950\) −2.30800 + 16.0149i −0.0748814 + 0.519591i
\(951\) 0 0
\(952\) 14.3262 + 10.4086i 0.464316 + 0.337345i
\(953\) 13.5051 + 41.5645i 0.437474 + 1.34641i 0.890530 + 0.454924i \(0.150334\pi\)
−0.453056 + 0.891482i \(0.649666\pi\)
\(954\) 0 0
\(955\) −1.42768 + 2.36665i −0.0461986 + 0.0765831i
\(956\) 0.662491 2.03894i 0.0214265 0.0659440i
\(957\) 0 0
\(958\) 2.42768 7.47163i 0.0784347 0.241397i
\(959\) −25.2006 + 18.3093i −0.813770 + 0.591239i
\(960\) 0 0
\(961\) 22.7634 + 16.5386i 0.734304 + 0.533503i
\(962\) 2.44701 1.77785i 0.0788947 0.0573203i
\(963\) 0 0
\(964\) −1.40748 1.02260i −0.0453320 0.0329356i
\(965\) 35.8927 15.1614i 1.15543 0.488063i
\(966\) 0 0
\(967\) −13.3952 + 41.2262i −0.430760 + 1.32574i 0.466609 + 0.884464i \(0.345476\pi\)
−0.897369 + 0.441281i \(0.854524\pi\)
\(968\) −10.9638 −0.352389
\(969\) 0 0
\(970\) −0.332262 3.87597i −0.0106683 0.124450i
\(971\) 9.30580 + 28.6403i 0.298637 + 0.919111i 0.981975 + 0.189009i \(0.0605276\pi\)
−0.683338 + 0.730102i \(0.739472\pi\)
\(972\) 0 0
\(973\) −54.2275 39.3986i −1.73845 1.26306i
\(974\) −40.9465 −1.31201
\(975\) 0 0
\(976\) −5.54610 −0.177526
\(977\) −1.14178 0.829555i −0.0365289 0.0265398i 0.569371 0.822081i \(-0.307187\pi\)
−0.605900 + 0.795541i \(0.707187\pi\)
\(978\) 0 0
\(979\) −0.546101 1.68073i −0.0174535 0.0537162i
\(980\) 2.30377 + 2.65958i 0.0735912 + 0.0849572i
\(981\) 0 0
\(982\) 7.51824 0.239917
\(983\) −3.00251 + 9.24078i −0.0957653 + 0.294735i −0.987452 0.157917i \(-0.949522\pi\)
0.891687 + 0.452652i \(0.149522\pi\)
\(984\) 0 0
\(985\) −21.8759 25.2546i −0.697025 0.804679i
\(986\) −33.3277 24.2140i −1.06137 0.771130i
\(987\) 0 0
\(988\) −0.811677 + 0.589718i −0.0258229 + 0.0187614i
\(989\) −37.0463 26.9157i −1.17801 0.855871i
\(990\) 0 0
\(991\) −15.3838 + 11.1770i −0.488683 + 0.355049i −0.804677 0.593712i \(-0.797662\pi\)
0.315995 + 0.948761i \(0.397662\pi\)
\(992\) −0.522856 + 1.60919i −0.0166007 + 0.0510917i
\(993\) 0 0
\(994\) −6.20288 + 19.0905i −0.196743 + 0.605514i
\(995\) −10.1022 + 4.26725i −0.320261 + 0.135281i
\(996\) 0 0
\(997\) −3.41070 10.4970i −0.108018 0.332445i 0.882409 0.470483i \(-0.155920\pi\)
−0.990427 + 0.138038i \(0.955920\pi\)
\(998\) −12.7430 9.25836i −0.403374 0.293068i
\(999\) 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.d.91.2 8
3.2 odd 2 150.2.g.c.91.1 yes 8
15.2 even 4 750.2.h.e.49.2 16
15.8 even 4 750.2.h.e.49.3 16
15.14 odd 2 750.2.g.d.451.1 8
25.11 even 5 inner 450.2.h.d.361.2 8
75.2 even 20 750.2.h.e.199.4 16
75.8 even 20 3750.2.c.h.1249.5 8
75.11 odd 10 150.2.g.c.61.1 8
75.14 odd 10 750.2.g.d.301.1 8
75.17 even 20 3750.2.c.h.1249.4 8
75.23 even 20 750.2.h.e.199.1 16
75.44 odd 10 3750.2.a.q.1.1 4
75.56 odd 10 3750.2.a.l.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.g.c.61.1 8 75.11 odd 10
150.2.g.c.91.1 yes 8 3.2 odd 2
450.2.h.d.91.2 8 1.1 even 1 trivial
450.2.h.d.361.2 8 25.11 even 5 inner
750.2.g.d.301.1 8 75.14 odd 10
750.2.g.d.451.1 8 15.14 odd 2
750.2.h.e.49.2 16 15.2 even 4
750.2.h.e.49.3 16 15.8 even 4
750.2.h.e.199.1 16 75.23 even 20
750.2.h.e.199.4 16 75.2 even 20
3750.2.a.l.1.4 4 75.56 odd 10
3750.2.a.q.1.1 4 75.44 odd 10
3750.2.c.h.1249.4 8 75.17 even 20
3750.2.c.h.1249.5 8 75.8 even 20