Properties

Label 495.2.n.b.361.2
Level $495$
Weight $2$
Character 495.361
Analytic conductor $3.953$
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] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.819390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.2
Root \(-0.755243 - 0.548716i\) of defining polynomial
Character \(\chi\) \(=\) 495.361
Dual form 495.2.n.b.181.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.288477 - 0.887841i) q^{2} +(0.912991 + 0.663327i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.65127 + 1.19972i) q^{7} +(2.36279 - 1.71667i) q^{8} +O(q^{10})\) \(q+(0.288477 - 0.887841i) q^{2} +(0.912991 + 0.663327i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.65127 + 1.19972i) q^{7} +(2.36279 - 1.71667i) q^{8} +0.933531 q^{10} +(-1.85274 + 2.75088i) q^{11} +(-0.447591 + 1.37754i) q^{13} +(1.54151 - 1.11997i) q^{14} +(-0.145054 - 0.446431i) q^{16} +(-0.267937 - 0.824626i) q^{17} +(-2.53103 + 1.83890i) q^{19} +(-0.348732 + 1.07329i) q^{20} +(1.90788 + 2.43850i) q^{22} +4.70547 q^{23} +(-0.809017 + 0.587785i) q^{25} +(1.09392 + 0.794779i) q^{26} +(0.711789 + 2.19066i) q^{28} +(1.64906 + 1.19811i) q^{29} +(3.27979 - 10.0941i) q^{31} +5.40294 q^{32} -0.809430 q^{34} +(-0.630728 + 1.94118i) q^{35} +(-3.36279 - 2.44321i) q^{37} +(0.902506 + 2.77763i) q^{38} +(2.36279 + 1.71667i) q^{40} +(-0.651268 + 0.473174i) q^{41} -2.34089 q^{43} +(-3.51627 + 1.28256i) q^{44} +(1.35742 - 4.17771i) q^{46} +(8.39782 - 6.10137i) q^{47} +(-0.875752 - 2.69529i) q^{49} +(0.288477 + 0.887841i) q^{50} +(-1.32241 + 0.960786i) q^{52} +(-2.22985 + 6.86278i) q^{53} +(-3.18877 - 0.911987i) q^{55} +5.96112 q^{56} +(1.53945 - 1.11847i) q^{58} +(-6.73386 - 4.89243i) q^{59} +(-2.70931 - 8.33841i) q^{61} +(-8.01586 - 5.82386i) q^{62} +(1.84873 - 5.68981i) q^{64} -1.44843 q^{65} -3.15664 q^{67} +(0.302372 - 0.930606i) q^{68} +(1.54151 + 1.11997i) q^{70} +(-3.97725 - 12.2407i) q^{71} +(11.9075 + 8.65128i) q^{73} +(-3.13927 + 2.28081i) q^{74} -3.53059 q^{76} +(-6.35965 + 2.31969i) q^{77} +(-5.25303 + 16.1672i) q^{79} +(0.379757 - 0.275910i) q^{80} +(0.232227 + 0.714723i) q^{82} +(-1.89782 - 5.84089i) q^{83} +(0.701468 - 0.509647i) q^{85} +(-0.675292 + 2.07833i) q^{86} +(0.344727 + 9.68030i) q^{88} -3.77194 q^{89} +(-2.39175 + 1.73771i) q^{91} +(4.29606 + 3.12127i) q^{92} +(-2.99447 - 9.21604i) q^{94} +(-2.53103 - 1.83890i) q^{95} +(-0.598859 + 1.84310i) q^{97} -2.64562 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.288477 0.887841i 0.203984 0.627798i −0.795770 0.605600i \(-0.792933\pi\)
0.999754 0.0221988i \(-0.00706668\pi\)
\(3\) 0 0
\(4\) 0.912991 + 0.663327i 0.456496 + 0.331664i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0 0
\(7\) 1.65127 + 1.19972i 0.624121 + 0.453450i 0.854358 0.519684i \(-0.173950\pi\)
−0.230238 + 0.973134i \(0.573950\pi\)
\(8\) 2.36279 1.71667i 0.835373 0.606934i
\(9\) 0 0
\(10\) 0.933531 0.295209
\(11\) −1.85274 + 2.75088i −0.558621 + 0.829423i
\(12\) 0 0
\(13\) −0.447591 + 1.37754i −0.124139 + 0.382062i −0.993743 0.111688i \(-0.964374\pi\)
0.869604 + 0.493750i \(0.164374\pi\)
\(14\) 1.54151 1.11997i 0.411986 0.299325i
\(15\) 0 0
\(16\) −0.145054 0.446431i −0.0362636 0.111608i
\(17\) −0.267937 0.824626i −0.0649843 0.200001i 0.913292 0.407305i \(-0.133531\pi\)
−0.978277 + 0.207303i \(0.933531\pi\)
\(18\) 0 0
\(19\) −2.53103 + 1.83890i −0.580657 + 0.421872i −0.838961 0.544192i \(-0.816836\pi\)
0.258304 + 0.966064i \(0.416836\pi\)
\(20\) −0.348732 + 1.07329i −0.0779788 + 0.239994i
\(21\) 0 0
\(22\) 1.90788 + 2.43850i 0.406761 + 0.519891i
\(23\) 4.70547 0.981159 0.490580 0.871396i \(-0.336785\pi\)
0.490580 + 0.871396i \(0.336785\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) 1.09392 + 0.794779i 0.214535 + 0.155869i
\(27\) 0 0
\(28\) 0.711789 + 2.19066i 0.134516 + 0.413996i
\(29\) 1.64906 + 1.19811i 0.306223 + 0.222484i 0.730274 0.683154i \(-0.239392\pi\)
−0.424051 + 0.905638i \(0.639392\pi\)
\(30\) 0 0
\(31\) 3.27979 10.0941i 0.589067 1.81296i 0.00678348 0.999977i \(-0.497841\pi\)
0.582284 0.812986i \(-0.302159\pi\)
\(32\) 5.40294 0.955113
\(33\) 0 0
\(34\) −0.809430 −0.138816
\(35\) −0.630728 + 1.94118i −0.106613 + 0.328120i
\(36\) 0 0
\(37\) −3.36279 2.44321i −0.552839 0.401661i 0.275992 0.961160i \(-0.410994\pi\)
−0.828831 + 0.559499i \(0.810994\pi\)
\(38\) 0.902506 + 2.77763i 0.146406 + 0.450591i
\(39\) 0 0
\(40\) 2.36279 + 1.71667i 0.373590 + 0.271429i
\(41\) −0.651268 + 0.473174i −0.101711 + 0.0738974i −0.637478 0.770468i \(-0.720022\pi\)
0.535767 + 0.844366i \(0.320022\pi\)
\(42\) 0 0
\(43\) −2.34089 −0.356982 −0.178491 0.983942i \(-0.557122\pi\)
−0.178491 + 0.983942i \(0.557122\pi\)
\(44\) −3.51627 + 1.28256i −0.530097 + 0.193354i
\(45\) 0 0
\(46\) 1.35742 4.17771i 0.200141 0.615970i
\(47\) 8.39782 6.10137i 1.22495 0.889977i 0.228447 0.973556i \(-0.426635\pi\)
0.996501 + 0.0835794i \(0.0266352\pi\)
\(48\) 0 0
\(49\) −0.875752 2.69529i −0.125107 0.385041i
\(50\) 0.288477 + 0.887841i 0.0407968 + 0.125560i
\(51\) 0 0
\(52\) −1.32241 + 0.960786i −0.183385 + 0.133237i
\(53\) −2.22985 + 6.86278i −0.306294 + 0.942676i 0.672897 + 0.739736i \(0.265050\pi\)
−0.979191 + 0.202940i \(0.934950\pi\)
\(54\) 0 0
\(55\) −3.18877 0.911987i −0.429974 0.122972i
\(56\) 5.96112 0.796588
\(57\) 0 0
\(58\) 1.53945 1.11847i 0.202139 0.146863i
\(59\) −6.73386 4.89243i −0.876674 0.636941i 0.0556956 0.998448i \(-0.482262\pi\)
−0.932369 + 0.361507i \(0.882262\pi\)
\(60\) 0 0
\(61\) −2.70931 8.33841i −0.346892 1.06762i −0.960563 0.278062i \(-0.910308\pi\)
0.613671 0.789562i \(-0.289692\pi\)
\(62\) −8.01586 5.82386i −1.01801 0.739631i
\(63\) 0 0
\(64\) 1.84873 5.68981i 0.231091 0.711226i
\(65\) −1.44843 −0.179656
\(66\) 0 0
\(67\) −3.15664 −0.385645 −0.192822 0.981234i \(-0.561764\pi\)
−0.192822 + 0.981234i \(0.561764\pi\)
\(68\) 0.302372 0.930606i 0.0366680 0.112853i
\(69\) 0 0
\(70\) 1.54151 + 1.11997i 0.184246 + 0.133862i
\(71\) −3.97725 12.2407i −0.472013 1.45271i −0.849944 0.526873i \(-0.823364\pi\)
0.377931 0.925834i \(-0.376636\pi\)
\(72\) 0 0
\(73\) 11.9075 + 8.65128i 1.39366 + 1.01256i 0.995452 + 0.0952617i \(0.0303688\pi\)
0.398211 + 0.917294i \(0.369631\pi\)
\(74\) −3.13927 + 2.28081i −0.364933 + 0.265139i
\(75\) 0 0
\(76\) −3.53059 −0.404987
\(77\) −6.35965 + 2.31969i −0.724749 + 0.264353i
\(78\) 0 0
\(79\) −5.25303 + 16.1672i −0.591012 + 1.81895i −0.0173618 + 0.999849i \(0.505527\pi\)
−0.573651 + 0.819100i \(0.694473\pi\)
\(80\) 0.379757 0.275910i 0.0424581 0.0308476i
\(81\) 0 0
\(82\) 0.232227 + 0.714723i 0.0256452 + 0.0789279i
\(83\) −1.89782 5.84089i −0.208313 0.641121i −0.999561 0.0296262i \(-0.990568\pi\)
0.791248 0.611495i \(-0.209432\pi\)
\(84\) 0 0
\(85\) 0.701468 0.509647i 0.0760849 0.0552789i
\(86\) −0.675292 + 2.07833i −0.0728186 + 0.224113i
\(87\) 0 0
\(88\) 0.344727 + 9.68030i 0.0367480 + 1.03192i
\(89\) −3.77194 −0.399825 −0.199913 0.979814i \(-0.564066\pi\)
−0.199913 + 0.979814i \(0.564066\pi\)
\(90\) 0 0
\(91\) −2.39175 + 1.73771i −0.250724 + 0.182162i
\(92\) 4.29606 + 3.12127i 0.447895 + 0.325415i
\(93\) 0 0
\(94\) −2.99447 9.21604i −0.308856 0.950562i
\(95\) −2.53103 1.83890i −0.259678 0.188667i
\(96\) 0 0
\(97\) −0.598859 + 1.84310i −0.0608049 + 0.187138i −0.976845 0.213949i \(-0.931367\pi\)
0.916040 + 0.401087i \(0.131367\pi\)
\(98\) −2.64562 −0.267248
\(99\) 0 0
\(100\) −1.12852 −0.112852
\(101\) 1.62288 4.99472i 0.161483 0.496993i −0.837277 0.546779i \(-0.815854\pi\)
0.998760 + 0.0497857i \(0.0158538\pi\)
\(102\) 0 0
\(103\) 11.0032 + 7.99426i 1.08417 + 0.787698i 0.978406 0.206693i \(-0.0662700\pi\)
0.105768 + 0.994391i \(0.466270\pi\)
\(104\) 1.30722 + 4.02321i 0.128184 + 0.394508i
\(105\) 0 0
\(106\) 5.44980 + 3.95951i 0.529331 + 0.384582i
\(107\) −8.08259 + 5.87235i −0.781374 + 0.567701i −0.905391 0.424579i \(-0.860422\pi\)
0.124017 + 0.992280i \(0.460422\pi\)
\(108\) 0 0
\(109\) −6.75183 −0.646708 −0.323354 0.946278i \(-0.604811\pi\)
−0.323354 + 0.946278i \(0.604811\pi\)
\(110\) −1.72959 + 2.56804i −0.164910 + 0.244853i
\(111\) 0 0
\(112\) 0.296067 0.911202i 0.0279757 0.0861005i
\(113\) −4.24298 + 3.08270i −0.399146 + 0.289996i −0.769193 0.639017i \(-0.779342\pi\)
0.370047 + 0.929013i \(0.379342\pi\)
\(114\) 0 0
\(115\) 1.45407 + 4.47517i 0.135593 + 0.417312i
\(116\) 0.710837 + 2.18773i 0.0659996 + 0.203126i
\(117\) 0 0
\(118\) −6.28627 + 4.56724i −0.578698 + 0.420449i
\(119\) 0.546881 1.68313i 0.0501325 0.154292i
\(120\) 0 0
\(121\) −4.13473 10.1933i −0.375885 0.926666i
\(122\) −8.18476 −0.741013
\(123\) 0 0
\(124\) 9.69014 7.04030i 0.870200 0.632237i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0 0
\(127\) −6.38897 19.6632i −0.566929 1.74483i −0.662149 0.749372i \(-0.730355\pi\)
0.0952195 0.995456i \(-0.469645\pi\)
\(128\) 4.22380 + 3.06877i 0.373335 + 0.271244i
\(129\) 0 0
\(130\) −0.417840 + 1.28598i −0.0366470 + 0.112788i
\(131\) −20.3089 −1.77439 −0.887197 0.461392i \(-0.847350\pi\)
−0.887197 + 0.461392i \(0.847350\pi\)
\(132\) 0 0
\(133\) −6.38556 −0.553698
\(134\) −0.910618 + 2.80259i −0.0786654 + 0.242107i
\(135\) 0 0
\(136\) −2.04869 1.48846i −0.175674 0.127634i
\(137\) 1.07532 + 3.30950i 0.0918710 + 0.282750i 0.986426 0.164209i \(-0.0525071\pi\)
−0.894555 + 0.446959i \(0.852507\pi\)
\(138\) 0 0
\(139\) −2.20931 1.60516i −0.187392 0.136148i 0.490134 0.871647i \(-0.336948\pi\)
−0.677526 + 0.735499i \(0.736948\pi\)
\(140\) −1.86349 + 1.35390i −0.157494 + 0.114426i
\(141\) 0 0
\(142\) −12.0152 −1.00829
\(143\) −2.96019 3.78350i −0.247544 0.316392i
\(144\) 0 0
\(145\) −0.629885 + 1.93859i −0.0523091 + 0.160991i
\(146\) 11.1160 8.07624i 0.919966 0.668394i
\(147\) 0 0
\(148\) −1.44955 4.46126i −0.119152 0.366713i
\(149\) 2.81465 + 8.66261i 0.230585 + 0.709669i 0.997676 + 0.0681306i \(0.0217035\pi\)
−0.767091 + 0.641538i \(0.778297\pi\)
\(150\) 0 0
\(151\) −17.4541 + 12.6811i −1.42039 + 1.03198i −0.428687 + 0.903453i \(0.641024\pi\)
−0.991706 + 0.128523i \(0.958976\pi\)
\(152\) −2.82351 + 8.68986i −0.229017 + 0.704841i
\(153\) 0 0
\(154\) 0.224903 + 6.31553i 0.0181232 + 0.508920i
\(155\) 10.6136 0.852506
\(156\) 0 0
\(157\) 19.2497 13.9857i 1.53629 1.11618i 0.583688 0.811978i \(-0.301609\pi\)
0.952607 0.304205i \(-0.0983909\pi\)
\(158\) 12.8385 + 9.32772i 1.02138 + 0.742073i
\(159\) 0 0
\(160\) 1.66960 + 5.13850i 0.131993 + 0.406234i
\(161\) 7.77000 + 5.64523i 0.612362 + 0.444907i
\(162\) 0 0
\(163\) −0.557258 + 1.71506i −0.0436478 + 0.134334i −0.970506 0.241078i \(-0.922499\pi\)
0.926858 + 0.375412i \(0.122499\pi\)
\(164\) −0.908472 −0.0709397
\(165\) 0 0
\(166\) −5.73326 −0.444988
\(167\) 7.59792 23.3840i 0.587945 1.80951i 0.000837897 1.00000i \(-0.499733\pi\)
0.587107 0.809509i \(-0.300267\pi\)
\(168\) 0 0
\(169\) 8.81993 + 6.40806i 0.678456 + 0.492927i
\(170\) −0.250128 0.769814i −0.0191839 0.0590420i
\(171\) 0 0
\(172\) −2.13721 1.55277i −0.162961 0.118398i
\(173\) −13.1154 + 9.52890i −0.997146 + 0.724469i −0.961474 0.274894i \(-0.911357\pi\)
−0.0356719 + 0.999364i \(0.511357\pi\)
\(174\) 0 0
\(175\) −2.04108 −0.154291
\(176\) 1.49683 + 0.428092i 0.112828 + 0.0322686i
\(177\) 0 0
\(178\) −1.08812 + 3.34888i −0.0815579 + 0.251010i
\(179\) 13.7287 9.97452i 1.02613 0.745530i 0.0586031 0.998281i \(-0.481335\pi\)
0.967531 + 0.252751i \(0.0813353\pi\)
\(180\) 0 0
\(181\) 5.67071 + 17.4526i 0.421500 + 1.29725i 0.906306 + 0.422623i \(0.138891\pi\)
−0.484805 + 0.874622i \(0.661109\pi\)
\(182\) 0.852845 + 2.62479i 0.0632171 + 0.194562i
\(183\) 0 0
\(184\) 11.1181 8.07774i 0.819634 0.595499i
\(185\) 1.28447 3.95320i 0.0944363 0.290645i
\(186\) 0 0
\(187\) 2.76487 + 0.790750i 0.202187 + 0.0578254i
\(188\) 11.7143 0.854356
\(189\) 0 0
\(190\) −2.36279 + 1.71667i −0.171415 + 0.124540i
\(191\) −12.4577 9.05102i −0.901405 0.654909i 0.0374216 0.999300i \(-0.488086\pi\)
−0.938826 + 0.344391i \(0.888086\pi\)
\(192\) 0 0
\(193\) −2.28037 7.01824i −0.164144 0.505184i 0.834828 0.550511i \(-0.185567\pi\)
−0.998972 + 0.0453268i \(0.985567\pi\)
\(194\) 1.46362 + 1.06338i 0.105082 + 0.0763465i
\(195\) 0 0
\(196\) 0.988303 3.04168i 0.0705931 0.217263i
\(197\) −3.14676 −0.224197 −0.112099 0.993697i \(-0.535757\pi\)
−0.112099 + 0.993697i \(0.535757\pi\)
\(198\) 0 0
\(199\) −3.25757 −0.230923 −0.115462 0.993312i \(-0.536835\pi\)
−0.115462 + 0.993312i \(0.536835\pi\)
\(200\) −0.902506 + 2.77763i −0.0638168 + 0.196408i
\(201\) 0 0
\(202\) −3.96635 2.88172i −0.279072 0.202757i
\(203\) 1.28564 + 3.95681i 0.0902346 + 0.277713i
\(204\) 0 0
\(205\) −0.651268 0.473174i −0.0454866 0.0330479i
\(206\) 10.2718 7.46290i 0.715670 0.519965i
\(207\) 0 0
\(208\) 0.679903 0.0471428
\(209\) −0.369272 10.3696i −0.0255431 0.717277i
\(210\) 0 0
\(211\) 6.15690 18.9490i 0.423859 1.30450i −0.480224 0.877146i \(-0.659445\pi\)
0.904083 0.427357i \(-0.140555\pi\)
\(212\) −6.58811 + 4.78654i −0.452473 + 0.328741i
\(213\) 0 0
\(214\) 2.88207 + 8.87009i 0.197014 + 0.606347i
\(215\) −0.723374 2.22631i −0.0493337 0.151833i
\(216\) 0 0
\(217\) 17.5259 12.7333i 1.18974 0.864395i
\(218\) −1.94775 + 5.99455i −0.131918 + 0.406002i
\(219\) 0 0
\(220\) −2.30638 2.94784i −0.155496 0.198743i
\(221\) 1.25588 0.0844799
\(222\) 0 0
\(223\) −8.47862 + 6.16008i −0.567770 + 0.412509i −0.834295 0.551319i \(-0.814125\pi\)
0.266524 + 0.963828i \(0.414125\pi\)
\(224\) 8.92170 + 6.48199i 0.596106 + 0.433096i
\(225\) 0 0
\(226\) 1.51295 + 4.65638i 0.100640 + 0.309738i
\(227\) 14.2979 + 10.3880i 0.948982 + 0.689476i 0.950566 0.310523i \(-0.100504\pi\)
−0.00158404 + 0.999999i \(0.500504\pi\)
\(228\) 0 0
\(229\) 1.27614 3.92755i 0.0843297 0.259540i −0.899997 0.435897i \(-0.856431\pi\)
0.984326 + 0.176357i \(0.0564312\pi\)
\(230\) 4.39271 0.289646
\(231\) 0 0
\(232\) 5.95314 0.390843
\(233\) −4.20231 + 12.9334i −0.275303 + 0.847294i 0.713837 + 0.700312i \(0.246956\pi\)
−0.989139 + 0.146982i \(0.953044\pi\)
\(234\) 0 0
\(235\) 8.39782 + 6.10137i 0.547813 + 0.398010i
\(236\) −2.90267 8.93350i −0.188948 0.581521i
\(237\) 0 0
\(238\) −1.33659 0.971087i −0.0866380 0.0629462i
\(239\) 6.47725 4.70600i 0.418979 0.304406i −0.358248 0.933626i \(-0.616626\pi\)
0.777227 + 0.629221i \(0.216626\pi\)
\(240\) 0 0
\(241\) −0.501943 −0.0323330 −0.0161665 0.999869i \(-0.505146\pi\)
−0.0161665 + 0.999869i \(0.505146\pi\)
\(242\) −10.2428 + 0.730444i −0.658434 + 0.0469547i
\(243\) 0 0
\(244\) 3.05751 9.41006i 0.195737 0.602417i
\(245\) 2.29275 1.66578i 0.146478 0.106423i
\(246\) 0 0
\(247\) −1.40030 4.30967i −0.0890988 0.274218i
\(248\) −9.57885 29.4807i −0.608258 1.87202i
\(249\) 0 0
\(250\) −0.755243 + 0.548716i −0.0477657 + 0.0347038i
\(251\) 5.72933 17.6331i 0.361632 1.11299i −0.590431 0.807088i \(-0.701042\pi\)
0.952063 0.305901i \(-0.0989578\pi\)
\(252\) 0 0
\(253\) −8.71800 + 12.9442i −0.548096 + 0.813796i
\(254\) −19.3009 −1.21105
\(255\) 0 0
\(256\) 13.6231 9.89779i 0.851446 0.618612i
\(257\) 5.97062 + 4.33791i 0.372437 + 0.270592i 0.758221 0.651998i \(-0.226069\pi\)
−0.385784 + 0.922589i \(0.626069\pi\)
\(258\) 0 0
\(259\) −2.62171 8.06879i −0.162905 0.501370i
\(260\) −1.32241 0.960786i −0.0820123 0.0595854i
\(261\) 0 0
\(262\) −5.85864 + 18.0310i −0.361948 + 1.11396i
\(263\) 3.05950 0.188657 0.0943285 0.995541i \(-0.469930\pi\)
0.0943285 + 0.995541i \(0.469930\pi\)
\(264\) 0 0
\(265\) −7.21596 −0.443273
\(266\) −1.84209 + 5.66936i −0.112946 + 0.347611i
\(267\) 0 0
\(268\) −2.88198 2.09388i −0.176045 0.127904i
\(269\) 5.46345 + 16.8148i 0.333112 + 1.02521i 0.967644 + 0.252318i \(0.0811928\pi\)
−0.634532 + 0.772896i \(0.718807\pi\)
\(270\) 0 0
\(271\) 12.3773 + 8.99262i 0.751866 + 0.546263i 0.896405 0.443236i \(-0.146170\pi\)
−0.144538 + 0.989499i \(0.546170\pi\)
\(272\) −0.329273 + 0.239231i −0.0199651 + 0.0145055i
\(273\) 0 0
\(274\) 3.24852 0.196250
\(275\) −0.118034 3.31452i −0.00711772 0.199873i
\(276\) 0 0
\(277\) −5.50785 + 16.9514i −0.330934 + 1.01851i 0.637756 + 0.770239i \(0.279863\pi\)
−0.968690 + 0.248273i \(0.920137\pi\)
\(278\) −2.06246 + 1.49847i −0.123698 + 0.0898721i
\(279\) 0 0
\(280\) 1.84209 + 5.66936i 0.110086 + 0.338809i
\(281\) 5.34568 + 16.4523i 0.318896 + 0.981462i 0.974121 + 0.226028i \(0.0725741\pi\)
−0.655224 + 0.755434i \(0.727426\pi\)
\(282\) 0 0
\(283\) 20.8535 15.1510i 1.23961 0.900633i 0.242042 0.970266i \(-0.422183\pi\)
0.997573 + 0.0696333i \(0.0221829\pi\)
\(284\) 4.48840 13.8139i 0.266338 0.819704i
\(285\) 0 0
\(286\) −4.21309 + 1.53673i −0.249125 + 0.0908688i
\(287\) −1.64309 −0.0969888
\(288\) 0 0
\(289\) 13.1451 9.55045i 0.773240 0.561791i
\(290\) 1.53945 + 1.11847i 0.0903995 + 0.0656791i
\(291\) 0 0
\(292\) 5.13278 + 15.7971i 0.300373 + 0.924454i
\(293\) 10.9465 + 7.95310i 0.639502 + 0.464625i 0.859679 0.510835i \(-0.170664\pi\)
−0.220177 + 0.975460i \(0.570664\pi\)
\(294\) 0 0
\(295\) 2.57211 7.91613i 0.149754 0.460895i
\(296\) −12.1398 −0.705609
\(297\) 0 0
\(298\) 8.50299 0.492565
\(299\) −2.10613 + 6.48199i −0.121800 + 0.374863i
\(300\) 0 0
\(301\) −3.86543 2.80840i −0.222800 0.161873i
\(302\) 6.22373 + 19.1547i 0.358135 + 1.10223i
\(303\) 0 0
\(304\) 1.18808 + 0.863188i 0.0681409 + 0.0495073i
\(305\) 7.09308 5.15342i 0.406148 0.295084i
\(306\) 0 0
\(307\) −13.0268 −0.743478 −0.371739 0.928337i \(-0.621238\pi\)
−0.371739 + 0.928337i \(0.621238\pi\)
\(308\) −7.34502 2.10067i −0.418521 0.119697i
\(309\) 0 0
\(310\) 3.06178 9.42320i 0.173898 0.535202i
\(311\) 1.53971 1.11867i 0.0873092 0.0634339i −0.543274 0.839555i \(-0.682816\pi\)
0.630584 + 0.776121i \(0.282816\pi\)
\(312\) 0 0
\(313\) 3.37829 + 10.3973i 0.190952 + 0.587691i 1.00000 5.23383e-5i \(-1.66598e-5\pi\)
−0.809048 + 0.587743i \(0.800017\pi\)
\(314\) −6.86401 21.1252i −0.387358 1.19217i
\(315\) 0 0
\(316\) −15.5201 + 11.2760i −0.873074 + 0.634325i
\(317\) 4.96660 15.2856i 0.278952 0.858526i −0.709194 0.705013i \(-0.750941\pi\)
0.988147 0.153513i \(-0.0490588\pi\)
\(318\) 0 0
\(319\) −6.35114 + 2.31659i −0.355596 + 0.129704i
\(320\) 5.98262 0.334439
\(321\) 0 0
\(322\) 7.25354 5.27000i 0.404224 0.293686i
\(323\) 2.19456 + 1.59444i 0.122108 + 0.0887170i
\(324\) 0 0
\(325\) −0.447591 1.37754i −0.0248279 0.0764124i
\(326\) 1.36195 + 0.989513i 0.0754313 + 0.0548040i
\(327\) 0 0
\(328\) −0.726528 + 2.23602i −0.0401158 + 0.123464i
\(329\) 21.1870 1.16808
\(330\) 0 0
\(331\) 1.39579 0.0767195 0.0383597 0.999264i \(-0.487787\pi\)
0.0383597 + 0.999264i \(0.487787\pi\)
\(332\) 2.14173 6.59156i 0.117543 0.361759i
\(333\) 0 0
\(334\) −18.5695 13.4915i −1.01608 0.738222i
\(335\) −0.975455 3.00214i −0.0532948 0.164025i
\(336\) 0 0
\(337\) 2.23564 + 1.62429i 0.121783 + 0.0884805i 0.647009 0.762482i \(-0.276019\pi\)
−0.525227 + 0.850962i \(0.676019\pi\)
\(338\) 8.23368 5.98212i 0.447853 0.325384i
\(339\) 0 0
\(340\) 0.978497 0.0530664
\(341\) 21.6913 + 27.7241i 1.17465 + 1.50135i
\(342\) 0 0
\(343\) 6.20258 19.0896i 0.334908 1.03074i
\(344\) −5.53103 + 4.01853i −0.298213 + 0.216664i
\(345\) 0 0
\(346\) 4.67666 + 14.3933i 0.251419 + 0.773787i
\(347\) 0.966244 + 2.97379i 0.0518707 + 0.159642i 0.973636 0.228106i \(-0.0732532\pi\)
−0.921766 + 0.387748i \(0.873253\pi\)
\(348\) 0 0
\(349\) −10.6205 + 7.71626i −0.568504 + 0.413042i −0.834561 0.550915i \(-0.814279\pi\)
0.266058 + 0.963957i \(0.414279\pi\)
\(350\) −0.588805 + 1.81215i −0.0314729 + 0.0968637i
\(351\) 0 0
\(352\) −10.0102 + 14.8629i −0.533546 + 0.792193i
\(353\) −10.7984 −0.574739 −0.287370 0.957820i \(-0.592781\pi\)
−0.287370 + 0.957820i \(0.592781\pi\)
\(354\) 0 0
\(355\) 10.4126 7.56518i 0.552642 0.401518i
\(356\) −3.44375 2.50203i −0.182518 0.132607i
\(357\) 0 0
\(358\) −4.89536 15.0664i −0.258728 0.796282i
\(359\) 19.3934 + 14.0901i 1.02354 + 0.743649i 0.967007 0.254752i \(-0.0819937\pi\)
0.0565382 + 0.998400i \(0.481994\pi\)
\(360\) 0 0
\(361\) −2.84678 + 8.76148i −0.149830 + 0.461131i
\(362\) 17.1310 0.900388
\(363\) 0 0
\(364\) −3.33632 −0.174871
\(365\) −4.54825 + 13.9981i −0.238066 + 0.732692i
\(366\) 0 0
\(367\) −7.17831 5.21534i −0.374705 0.272239i 0.384455 0.923144i \(-0.374390\pi\)
−0.759159 + 0.650905i \(0.774390\pi\)
\(368\) −0.682549 2.10067i −0.0355803 0.109505i
\(369\) 0 0
\(370\) −3.13927 2.28081i −0.163203 0.118574i
\(371\) −11.9155 + 8.65711i −0.618621 + 0.449455i
\(372\) 0 0
\(373\) −26.3389 −1.36378 −0.681888 0.731456i \(-0.738841\pi\)
−0.681888 + 0.731456i \(0.738841\pi\)
\(374\) 1.49966 2.22665i 0.0775456 0.115137i
\(375\) 0 0
\(376\) 9.36826 28.8325i 0.483131 1.48693i
\(377\) −2.38855 + 1.73539i −0.123017 + 0.0893770i
\(378\) 0 0
\(379\) 1.45118 + 4.46626i 0.0745419 + 0.229416i 0.981385 0.192053i \(-0.0615145\pi\)
−0.906843 + 0.421469i \(0.861515\pi\)
\(380\) −1.09101 3.35779i −0.0559678 0.172251i
\(381\) 0 0
\(382\) −11.6296 + 8.44941i −0.595023 + 0.432310i
\(383\) 2.13200 6.56163i 0.108940 0.335284i −0.881695 0.471820i \(-0.843597\pi\)
0.990635 + 0.136537i \(0.0435971\pi\)
\(384\) 0 0
\(385\) −4.17140 5.33156i −0.212594 0.271722i
\(386\) −6.88892 −0.350637
\(387\) 0 0
\(388\) −1.76933 + 1.28549i −0.0898242 + 0.0652611i
\(389\) 1.94538 + 1.41340i 0.0986348 + 0.0716624i 0.636009 0.771681i \(-0.280584\pi\)
−0.537375 + 0.843344i \(0.680584\pi\)
\(390\) 0 0
\(391\) −1.26077 3.88025i −0.0637599 0.196233i
\(392\) −6.69613 4.86503i −0.338206 0.245721i
\(393\) 0 0
\(394\) −0.907768 + 2.79382i −0.0457327 + 0.140751i
\(395\) −16.9992 −0.855321
\(396\) 0 0
\(397\) 37.6715 1.89068 0.945338 0.326091i \(-0.105732\pi\)
0.945338 + 0.326091i \(0.105732\pi\)
\(398\) −0.939734 + 2.89221i −0.0471046 + 0.144973i
\(399\) 0 0
\(400\) 0.379757 + 0.275910i 0.0189878 + 0.0137955i
\(401\) 3.86791 + 11.9042i 0.193154 + 0.594467i 0.999993 + 0.00369578i \(0.00117641\pi\)
−0.806839 + 0.590771i \(0.798824\pi\)
\(402\) 0 0
\(403\) 12.4371 + 9.03610i 0.619537 + 0.450120i
\(404\) 4.79481 3.48363i 0.238551 0.173317i
\(405\) 0 0
\(406\) 3.88390 0.192754
\(407\) 12.9514 4.72402i 0.641975 0.234161i
\(408\) 0 0
\(409\) −8.17728 + 25.1671i −0.404340 + 1.24443i 0.517104 + 0.855922i \(0.327010\pi\)
−0.921445 + 0.388510i \(0.872990\pi\)
\(410\) −0.607979 + 0.441723i −0.0300260 + 0.0218151i
\(411\) 0 0
\(412\) 4.74298 + 14.5974i 0.233670 + 0.719162i
\(413\) −5.24987 16.1574i −0.258329 0.795056i
\(414\) 0 0
\(415\) 4.96856 3.60987i 0.243897 0.177202i
\(416\) −2.41831 + 7.44278i −0.118567 + 0.364912i
\(417\) 0 0
\(418\) −9.31304 2.66352i −0.455516 0.130277i
\(419\) −30.9711 −1.51304 −0.756518 0.653973i \(-0.773101\pi\)
−0.756518 + 0.653973i \(0.773101\pi\)
\(420\) 0 0
\(421\) −14.7593 + 10.7232i −0.719323 + 0.522618i −0.886168 0.463365i \(-0.846642\pi\)
0.166845 + 0.985983i \(0.446642\pi\)
\(422\) −15.0476 10.9327i −0.732505 0.532196i
\(423\) 0 0
\(424\) 6.51245 + 20.0432i 0.316272 + 0.973386i
\(425\) 0.701468 + 0.509647i 0.0340262 + 0.0247215i
\(426\) 0 0
\(427\) 5.52993 17.0194i 0.267612 0.823625i
\(428\) −11.2746 −0.544979
\(429\) 0 0
\(430\) −2.18529 −0.105384
\(431\) −9.37829 + 28.8634i −0.451736 + 1.39030i 0.423188 + 0.906042i \(0.360911\pi\)
−0.874924 + 0.484260i \(0.839089\pi\)
\(432\) 0 0
\(433\) −10.2755 7.46560i −0.493810 0.358774i 0.312838 0.949807i \(-0.398720\pi\)
−0.806648 + 0.591033i \(0.798720\pi\)
\(434\) −6.24935 19.2335i −0.299978 0.923238i
\(435\) 0 0
\(436\) −6.16436 4.47867i −0.295220 0.214490i
\(437\) −11.9097 + 8.65288i −0.569717 + 0.413924i
\(438\) 0 0
\(439\) −25.6564 −1.22451 −0.612257 0.790659i \(-0.709738\pi\)
−0.612257 + 0.790659i \(0.709738\pi\)
\(440\) −9.09999 + 3.31923i −0.433825 + 0.158238i
\(441\) 0 0
\(442\) 0.362294 1.11502i 0.0172325 0.0530363i
\(443\) −21.2082 + 15.4087i −1.00763 + 0.732088i −0.963711 0.266947i \(-0.913985\pi\)
−0.0439211 + 0.999035i \(0.513985\pi\)
\(444\) 0 0
\(445\) −1.16559 3.58733i −0.0552545 0.170056i
\(446\) 3.02328 + 9.30470i 0.143157 + 0.440590i
\(447\) 0 0
\(448\) 9.87891 7.17745i 0.466735 0.339103i
\(449\) 3.71010 11.4185i 0.175091 0.538873i −0.824547 0.565793i \(-0.808570\pi\)
0.999638 + 0.0269202i \(0.00856999\pi\)
\(450\) 0 0
\(451\) −0.0950188 2.66823i −0.00447426 0.125642i
\(452\) −5.91864 −0.278390
\(453\) 0 0
\(454\) 13.3475 9.69752i 0.626429 0.455127i
\(455\) −2.39175 1.73771i −0.112127 0.0814652i
\(456\) 0 0
\(457\) 4.26104 + 13.1141i 0.199323 + 0.613453i 0.999899 + 0.0142215i \(0.00452701\pi\)
−0.800576 + 0.599231i \(0.795473\pi\)
\(458\) −3.11891 2.26602i −0.145737 0.105884i
\(459\) 0 0
\(460\) −1.64095 + 5.05032i −0.0765096 + 0.235472i
\(461\) −11.3262 −0.527515 −0.263758 0.964589i \(-0.584962\pi\)
−0.263758 + 0.964589i \(0.584962\pi\)
\(462\) 0 0
\(463\) 6.18784 0.287573 0.143787 0.989609i \(-0.454072\pi\)
0.143787 + 0.989609i \(0.454072\pi\)
\(464\) 0.295671 0.909983i 0.0137262 0.0422449i
\(465\) 0 0
\(466\) 10.2705 + 7.46197i 0.475773 + 0.345669i
\(467\) −2.62135 8.06770i −0.121302 0.373328i 0.871907 0.489671i \(-0.162883\pi\)
−0.993209 + 0.116342i \(0.962883\pi\)
\(468\) 0 0
\(469\) −5.21246 3.78707i −0.240689 0.174871i
\(470\) 7.83963 5.69582i 0.361615 0.262729i
\(471\) 0 0
\(472\) −24.3094 −1.11893
\(473\) 4.33705 6.43951i 0.199418 0.296089i
\(474\) 0 0
\(475\) 0.966766 2.97540i 0.0443582 0.136521i
\(476\) 1.61576 1.17392i 0.0740583 0.0538065i
\(477\) 0 0
\(478\) −2.30964 7.10834i −0.105640 0.325128i
\(479\) −2.85394 8.78352i −0.130400 0.401329i 0.864446 0.502725i \(-0.167669\pi\)
−0.994846 + 0.101396i \(0.967669\pi\)
\(480\) 0 0
\(481\) 4.87078 3.53883i 0.222089 0.161357i
\(482\) −0.144799 + 0.445645i −0.00659541 + 0.0202986i
\(483\) 0 0
\(484\) 2.98654 12.0491i 0.135752 0.547686i
\(485\) −1.93795 −0.0879977
\(486\) 0 0
\(487\) −16.3185 + 11.8561i −0.739461 + 0.537250i −0.892542 0.450964i \(-0.851080\pi\)
0.153081 + 0.988214i \(0.451080\pi\)
\(488\) −20.7158 15.0509i −0.937762 0.681324i
\(489\) 0 0
\(490\) −0.817542 2.51613i −0.0369328 0.113667i
\(491\) −4.31686 3.13638i −0.194817 0.141543i 0.486100 0.873903i \(-0.338419\pi\)
−0.680918 + 0.732360i \(0.738419\pi\)
\(492\) 0 0
\(493\) 0.546149 1.68087i 0.0245973 0.0757028i
\(494\) −4.23026 −0.190328
\(495\) 0 0
\(496\) −4.98209 −0.223702
\(497\) 8.11789 24.9843i 0.364137 1.12070i
\(498\) 0 0
\(499\) 31.7795 + 23.0891i 1.42265 + 1.03361i 0.991328 + 0.131412i \(0.0419510\pi\)
0.431317 + 0.902200i \(0.358049\pi\)
\(500\) −0.348732 1.07329i −0.0155958 0.0479988i
\(501\) 0 0
\(502\) −14.0026 10.1735i −0.624966 0.454064i
\(503\) 26.2268 19.0549i 1.16940 0.849616i 0.178460 0.983947i \(-0.442889\pi\)
0.990936 + 0.134331i \(0.0428886\pi\)
\(504\) 0 0
\(505\) 5.25176 0.233700
\(506\) 8.97746 + 11.4743i 0.399097 + 0.510095i
\(507\) 0 0
\(508\) 7.21007 22.1903i 0.319895 0.984536i
\(509\) −13.8064 + 10.0309i −0.611958 + 0.444613i −0.850103 0.526616i \(-0.823461\pi\)
0.238145 + 0.971229i \(0.423461\pi\)
\(510\) 0 0
\(511\) 9.28333 + 28.5712i 0.410671 + 1.26391i
\(512\) −1.63100 5.01971i −0.0720808 0.221842i
\(513\) 0 0
\(514\) 5.57376 4.04958i 0.245848 0.178619i
\(515\) −4.20283 + 12.9350i −0.185199 + 0.569984i
\(516\) 0 0
\(517\) 1.22523 + 34.4057i 0.0538854 + 1.51316i
\(518\) −7.92011 −0.347990
\(519\) 0 0
\(520\) −3.42235 + 2.48648i −0.150080 + 0.109039i
\(521\) −12.1733 8.84445i −0.533324 0.387482i 0.288276 0.957547i \(-0.406918\pi\)
−0.821600 + 0.570065i \(0.806918\pi\)
\(522\) 0 0
\(523\) −11.4465 35.2287i −0.500520 1.54044i −0.808173 0.588945i \(-0.799544\pi\)
0.307653 0.951499i \(-0.400456\pi\)
\(524\) −18.5418 13.4714i −0.810003 0.588502i
\(525\) 0 0
\(526\) 0.882596 2.71635i 0.0384830 0.118439i
\(527\) −9.20267 −0.400875
\(528\) 0 0
\(529\) −0.858520 −0.0373270
\(530\) −2.08164 + 6.40662i −0.0904206 + 0.278286i
\(531\) 0 0
\(532\) −5.82996 4.23571i −0.252761 0.183641i
\(533\) −0.360316 1.10894i −0.0156070 0.0480335i
\(534\) 0 0
\(535\) −8.08259 5.87235i −0.349441 0.253884i
\(536\) −7.45848 + 5.41890i −0.322157 + 0.234061i
\(537\) 0 0
\(538\) 16.5049 0.711577
\(539\) 9.03696 + 2.58457i 0.389250 + 0.111325i
\(540\) 0 0
\(541\) 0.0547265 0.168431i 0.00235288 0.00724141i −0.949873 0.312635i \(-0.898788\pi\)
0.952226 + 0.305394i \(0.0987882\pi\)
\(542\) 11.5546 8.39489i 0.496312 0.360592i
\(543\) 0 0
\(544\) −1.44765 4.45540i −0.0620674 0.191024i
\(545\) −2.08643 6.42137i −0.0893729 0.275061i
\(546\) 0 0
\(547\) −0.981092 + 0.712805i −0.0419484 + 0.0304773i −0.608562 0.793506i \(-0.708253\pi\)
0.566613 + 0.823984i \(0.308253\pi\)
\(548\) −1.21352 + 3.73484i −0.0518391 + 0.159544i
\(549\) 0 0
\(550\) −2.97682 0.851369i −0.126932 0.0363025i
\(551\) −6.37702 −0.271670
\(552\) 0 0
\(553\) −28.0702 + 20.3942i −1.19367 + 0.867249i
\(554\) 13.4613 + 9.78018i 0.571914 + 0.415520i
\(555\) 0 0
\(556\) −0.952338 2.93100i −0.0403881 0.124302i
\(557\) 1.56825 + 1.13940i 0.0664488 + 0.0482778i 0.620514 0.784196i \(-0.286924\pi\)
−0.554065 + 0.832473i \(0.686924\pi\)
\(558\) 0 0
\(559\) 1.04776 3.22467i 0.0443155 0.136389i
\(560\) 0.958094 0.0404869
\(561\) 0 0
\(562\) 16.1491 0.681210
\(563\) 6.48805 19.9682i 0.273439 0.841558i −0.716190 0.697906i \(-0.754115\pi\)
0.989628 0.143652i \(-0.0458845\pi\)
\(564\) 0 0
\(565\) −4.24298 3.08270i −0.178503 0.129690i
\(566\) −7.43590 22.8853i −0.312554 0.961943i
\(567\) 0 0
\(568\) −30.4107 22.0946i −1.27600 0.927071i
\(569\) −31.8556 + 23.1444i −1.33546 + 0.970265i −0.335857 + 0.941913i \(0.609026\pi\)
−0.999598 + 0.0283521i \(0.990974\pi\)
\(570\) 0 0
\(571\) 30.6796 1.28390 0.641950 0.766746i \(-0.278126\pi\)
0.641950 + 0.766746i \(0.278126\pi\)
\(572\) −0.192937 5.41788i −0.00806709 0.226533i
\(573\) 0 0
\(574\) −0.473995 + 1.45881i −0.0197842 + 0.0608894i
\(575\) −3.80681 + 2.76581i −0.158755 + 0.115342i
\(576\) 0 0
\(577\) −10.7241 33.0053i −0.446448 1.37403i −0.880887 0.473326i \(-0.843053\pi\)
0.434439 0.900701i \(-0.356947\pi\)
\(578\) −4.68723 14.4258i −0.194963 0.600035i
\(579\) 0 0
\(580\) −1.86100 + 1.35209i −0.0772736 + 0.0561426i
\(581\) 3.87361 11.9217i 0.160704 0.494597i
\(582\) 0 0
\(583\) −14.7474 18.8490i −0.610775 0.780646i
\(584\) 42.9862 1.77878
\(585\) 0 0
\(586\) 10.2189 7.42447i 0.422139 0.306702i
\(587\) 6.51833 + 4.73584i 0.269040 + 0.195469i 0.714123 0.700020i \(-0.246826\pi\)
−0.445083 + 0.895489i \(0.646826\pi\)
\(588\) 0 0
\(589\) 10.2609 + 31.5797i 0.422792 + 1.30122i
\(590\) −6.28627 4.56724i −0.258802 0.188030i
\(591\) 0 0
\(592\) −0.602938 + 1.85565i −0.0247806 + 0.0762669i
\(593\) 28.1409 1.15561 0.577805 0.816175i \(-0.303909\pi\)
0.577805 + 0.816175i \(0.303909\pi\)
\(594\) 0 0
\(595\) 1.76974 0.0725524
\(596\) −3.17639 + 9.77593i −0.130110 + 0.400438i
\(597\) 0 0
\(598\) 5.14741 + 3.73981i 0.210493 + 0.152932i
\(599\) 8.83751 + 27.1991i 0.361091 + 1.11132i 0.952393 + 0.304873i \(0.0986141\pi\)
−0.591302 + 0.806450i \(0.701386\pi\)
\(600\) 0 0
\(601\) 5.88649 + 4.27679i 0.240115 + 0.174454i 0.701335 0.712832i \(-0.252588\pi\)
−0.461219 + 0.887286i \(0.652588\pi\)
\(602\) −3.60850 + 2.62173i −0.147072 + 0.106854i
\(603\) 0 0
\(604\) −24.3472 −0.990672
\(605\) 8.41673 7.08228i 0.342189 0.287936i
\(606\) 0 0
\(607\) −1.65258 + 5.08611i −0.0670761 + 0.206439i −0.978977 0.203972i \(-0.934615\pi\)
0.911901 + 0.410411i \(0.134615\pi\)
\(608\) −13.6750 + 9.93545i −0.554593 + 0.402936i
\(609\) 0 0
\(610\) −2.52923 7.78417i −0.102406 0.315172i
\(611\) 4.64612 + 14.2993i 0.187962 + 0.578487i
\(612\) 0 0
\(613\) 3.75464 2.72790i 0.151648 0.110179i −0.509374 0.860545i \(-0.670123\pi\)
0.661022 + 0.750366i \(0.270123\pi\)
\(614\) −3.75793 + 11.5657i −0.151658 + 0.466754i
\(615\) 0 0
\(616\) −11.0444 + 16.3983i −0.444991 + 0.660708i
\(617\) −24.5843 −0.989727 −0.494864 0.868971i \(-0.664782\pi\)
−0.494864 + 0.868971i \(0.664782\pi\)
\(618\) 0 0
\(619\) 4.96566 3.60776i 0.199587 0.145008i −0.483503 0.875343i \(-0.660636\pi\)
0.683090 + 0.730335i \(0.260636\pi\)
\(620\) 9.69014 + 7.04030i 0.389165 + 0.282745i
\(621\) 0 0
\(622\) −0.549027 1.68973i −0.0220140 0.0677521i
\(623\) −6.22849 4.52526i −0.249539 0.181301i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 10.2057 0.407902
\(627\) 0 0
\(628\) 26.8519 1.07151
\(629\) −1.11372 + 3.42767i −0.0444068 + 0.136670i
\(630\) 0 0
\(631\) 14.3265 + 10.4088i 0.570329 + 0.414368i 0.835225 0.549909i \(-0.185338\pi\)
−0.264896 + 0.964277i \(0.585338\pi\)
\(632\) 15.3419 + 47.2174i 0.610266 + 1.87821i
\(633\) 0 0
\(634\) −12.1385 8.81910i −0.482080 0.350251i
\(635\) 16.7265 12.1525i 0.663772 0.482259i
\(636\) 0 0
\(637\) 4.10485 0.162640
\(638\) 0.224603 + 6.30708i 0.00889210 + 0.249700i
\(639\) 0 0
\(640\) −1.61335 + 4.96538i −0.0637732 + 0.196274i
\(641\) 32.2492 23.4304i 1.27377 0.925444i 0.274419 0.961610i \(-0.411514\pi\)
0.999346 + 0.0361657i \(0.0115144\pi\)
\(642\) 0 0
\(643\) −5.52097 16.9918i −0.217726 0.670091i −0.998949 0.0458392i \(-0.985404\pi\)
0.781223 0.624252i \(-0.214596\pi\)
\(644\) 3.34931 + 10.3081i 0.131981 + 0.406196i
\(645\) 0 0
\(646\) 2.04869 1.48846i 0.0806045 0.0585626i
\(647\) −1.55768 + 4.79404i −0.0612386 + 0.188473i −0.976996 0.213260i \(-0.931592\pi\)
0.915757 + 0.401733i \(0.131592\pi\)
\(648\) 0 0
\(649\) 25.9346 9.45968i 1.01802 0.371325i
\(650\) −1.35216 −0.0530360
\(651\) 0 0
\(652\) −1.64642 + 1.19619i −0.0644788 + 0.0468466i
\(653\) 32.9441 + 23.9353i 1.28920 + 0.936661i 0.999789 0.0205434i \(-0.00653963\pi\)
0.289414 + 0.957204i \(0.406540\pi\)
\(654\) 0 0
\(655\) −6.27578 19.3149i −0.245215 0.754695i
\(656\) 0.305709 + 0.222111i 0.0119359 + 0.00867196i
\(657\) 0 0
\(658\) 6.11196 18.8107i 0.238269 0.733316i
\(659\) −48.7556 −1.89925 −0.949624 0.313390i \(-0.898535\pi\)
−0.949624 + 0.313390i \(0.898535\pi\)
\(660\) 0 0
\(661\) −41.0061 −1.59495 −0.797477 0.603350i \(-0.793832\pi\)
−0.797477 + 0.603350i \(0.793832\pi\)
\(662\) 0.402653 1.23924i 0.0156495 0.0481643i
\(663\) 0 0
\(664\) −14.5110 10.5429i −0.563137 0.409143i
\(665\) −1.97325 6.07303i −0.0765192 0.235502i
\(666\) 0 0
\(667\) 7.75960 + 5.63768i 0.300453 + 0.218292i
\(668\) 22.4481 16.3095i 0.868542 0.631033i
\(669\) 0 0
\(670\) −2.94682 −0.113846
\(671\) 27.9577 + 7.99587i 1.07929 + 0.308677i
\(672\) 0 0
\(673\) −9.42305 + 29.0012i −0.363232 + 1.11791i 0.587849 + 0.808971i \(0.299975\pi\)
−0.951081 + 0.308942i \(0.900025\pi\)
\(674\) 2.08704 1.51632i 0.0803897 0.0584065i
\(675\) 0 0
\(676\) 3.80189 + 11.7010i 0.146226 + 0.450038i
\(677\) 13.4244 + 41.3161i 0.515943 + 1.58791i 0.781560 + 0.623830i \(0.214424\pi\)
−0.265617 + 0.964079i \(0.585576\pi\)
\(678\) 0 0
\(679\) −3.20007 + 2.32499i −0.122808 + 0.0892249i
\(680\) 0.782529 2.40838i 0.0300086 0.0923570i
\(681\) 0 0
\(682\) 30.8720 11.2606i 1.18215 0.431191i
\(683\) 43.5970 1.66819 0.834096 0.551619i \(-0.185990\pi\)
0.834096 + 0.551619i \(0.185990\pi\)
\(684\) 0 0
\(685\) −2.81523 + 2.04539i −0.107564 + 0.0781501i
\(686\) −15.1592 11.0138i −0.578781 0.420509i
\(687\) 0 0
\(688\) 0.339555 + 1.04504i 0.0129454 + 0.0398419i
\(689\) −8.45572 6.14344i −0.322137 0.234046i
\(690\) 0 0
\(691\) −2.56761 + 7.90230i −0.0976766 + 0.300618i −0.987942 0.154824i \(-0.950519\pi\)
0.890265 + 0.455442i \(0.150519\pi\)
\(692\) −18.2950 −0.695473
\(693\) 0 0
\(694\) 2.91900 0.110804
\(695\) 0.843883 2.59720i 0.0320103 0.0985176i
\(696\) 0 0
\(697\) 0.564690 + 0.410272i 0.0213892 + 0.0155401i
\(698\) 3.78704 + 11.6553i 0.143342 + 0.441160i
\(699\) 0 0
\(700\) −1.86349 1.35390i −0.0704332 0.0511727i
\(701\) 7.35189 5.34146i 0.277677 0.201744i −0.440226 0.897887i \(-0.645102\pi\)
0.717904 + 0.696143i \(0.245102\pi\)
\(702\) 0 0
\(703\) 13.0041 0.490460
\(704\) 12.2268 + 15.6274i 0.460815 + 0.588979i
\(705\) 0 0
\(706\) −3.11508 + 9.58724i −0.117238 + 0.360821i
\(707\) 8.67206 6.30062i 0.326147 0.236959i
\(708\) 0 0
\(709\) −1.50049 4.61802i −0.0563520 0.173434i 0.918919 0.394447i \(-0.129064\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(710\) −3.71289 11.4271i −0.139342 0.428851i
\(711\) 0 0
\(712\) −8.91231 + 6.47517i −0.334003 + 0.242667i
\(713\) 15.4330 47.4977i 0.577969 1.77880i
\(714\) 0 0
\(715\) 2.68357 3.98448i 0.100360 0.149011i
\(716\) 19.1506 0.715691
\(717\) 0 0
\(718\) 18.1043 13.1536i 0.675648 0.490887i
\(719\) 19.3383 + 14.0501i 0.721196 + 0.523980i 0.886766 0.462218i \(-0.152946\pi\)
−0.165570 + 0.986198i \(0.552946\pi\)
\(720\) 0 0
\(721\) 8.57832 + 26.4014i 0.319473 + 0.983238i
\(722\) 6.95757 + 5.05497i 0.258934 + 0.188127i
\(723\) 0 0
\(724\) −6.39951 + 19.6957i −0.237836 + 0.731983i
\(725\) −2.03835 −0.0757024
\(726\) 0 0
\(727\) −11.3674 −0.421592 −0.210796 0.977530i \(-0.567606\pi\)
−0.210796 + 0.977530i \(0.567606\pi\)
\(728\) −2.66814 + 8.21170i −0.0988879 + 0.304346i
\(729\) 0 0
\(730\) 11.1160 + 8.07624i 0.411421 + 0.298915i
\(731\) 0.627210 + 1.93035i 0.0231982 + 0.0713967i
\(732\) 0 0
\(733\) 27.6019 + 20.0539i 1.01950 + 0.740709i 0.966180 0.257869i \(-0.0830202\pi\)
0.0533185 + 0.998578i \(0.483020\pi\)
\(734\) −6.70117 + 4.86869i −0.247345 + 0.179707i
\(735\) 0 0
\(736\) 25.4234 0.937118
\(737\) 5.84842 8.68355i 0.215429 0.319863i
\(738\) 0 0
\(739\) 0.722631 2.22403i 0.0265824 0.0818123i −0.936885 0.349637i \(-0.886305\pi\)
0.963468 + 0.267825i \(0.0863049\pi\)
\(740\) 3.79498 2.75721i 0.139506 0.101357i
\(741\) 0 0
\(742\) 4.24879 + 13.0764i 0.155978 + 0.480051i
\(743\) −4.47721 13.7794i −0.164253 0.505518i 0.834728 0.550663i \(-0.185625\pi\)
−0.998980 + 0.0451450i \(0.985625\pi\)
\(744\) 0 0
\(745\) −7.36886 + 5.35379i −0.269974 + 0.196148i
\(746\) −7.59817 + 23.3848i −0.278189 + 0.856177i
\(747\) 0 0
\(748\) 1.99977 + 2.55596i 0.0731190 + 0.0934551i
\(749\) −20.3917 −0.745096
\(750\) 0 0
\(751\) −26.9567 + 19.5852i −0.983663 + 0.714673i −0.958524 0.285011i \(-0.908003\pi\)
−0.0251387 + 0.999684i \(0.508003\pi\)
\(752\) −3.94198 2.86402i −0.143749 0.104440i
\(753\) 0 0
\(754\) 0.851704 + 2.62128i 0.0310172 + 0.0954612i
\(755\) −17.4541 12.6811i −0.635219 0.461514i
\(756\) 0 0
\(757\) 12.4774 38.4015i 0.453499 1.39573i −0.419389 0.907807i \(-0.637756\pi\)
0.872888 0.487921i \(-0.162244\pi\)
\(758\) 4.38396 0.159233
\(759\) 0 0
\(760\) −9.13706 −0.331436
\(761\) 15.4190 47.4549i 0.558940 1.72024i −0.126364 0.991984i \(-0.540331\pi\)
0.685304 0.728257i \(-0.259669\pi\)
\(762\) 0 0
\(763\) −11.1491 8.10029i −0.403624 0.293250i
\(764\) −5.36995 16.5270i −0.194278 0.597926i
\(765\) 0 0
\(766\) −5.21065 3.78576i −0.188268 0.136785i
\(767\) 9.75356 7.08637i 0.352180 0.255874i
\(768\) 0 0
\(769\) 4.93932 0.178116 0.0890582 0.996026i \(-0.471614\pi\)
0.0890582 + 0.996026i \(0.471614\pi\)
\(770\) −5.93693 + 2.16550i −0.213952 + 0.0780393i
\(771\) 0 0
\(772\) 2.57344 7.92022i 0.0926200 0.285055i
\(773\) −27.0786 + 19.6738i −0.973950 + 0.707616i −0.956348 0.292229i \(-0.905603\pi\)
−0.0176019 + 0.999845i \(0.505603\pi\)
\(774\) 0 0
\(775\) 3.27979 + 10.0941i 0.117813 + 0.362593i
\(776\) 1.74901 + 5.38290i 0.0627858 + 0.193235i
\(777\) 0 0
\(778\) 1.81607 1.31946i 0.0651094 0.0473048i
\(779\) 0.778258 2.39523i 0.0278840 0.0858181i
\(780\) 0 0
\(781\) 41.0416 + 11.7379i 1.46858 + 0.420014i
\(782\) −3.80875 −0.136201
\(783\) 0 0
\(784\) −1.07623 + 0.781926i −0.0384367 + 0.0279259i
\(785\) 19.2497 + 13.9857i 0.687052 + 0.499172i
\(786\) 0 0
\(787\) 8.01590 + 24.6704i 0.285736 + 0.879405i 0.986177 + 0.165695i \(0.0529867\pi\)
−0.700441 + 0.713710i \(0.747013\pi\)
\(788\) −2.87296 2.08733i −0.102345 0.0743581i
\(789\) 0 0
\(790\) −4.90387 + 15.0926i −0.174472 + 0.536969i
\(791\) −10.7047 −0.380614
\(792\) 0 0
\(793\) 12.6992 0.450961
\(794\) 10.8674 33.4463i 0.385668 1.18696i
\(795\) 0 0
\(796\) −2.97413 2.16083i −0.105415 0.0765888i
\(797\) −3.04772 9.37993i −0.107956 0.332254i 0.882457 0.470393i \(-0.155888\pi\)
−0.990413 + 0.138139i \(0.955888\pi\)
\(798\) 0 0
\(799\) −7.28144 5.29027i −0.257599 0.187156i
\(800\) −4.37107 + 3.17577i −0.154541 + 0.112280i
\(801\) 0 0
\(802\) 11.6848 0.412606
\(803\) −45.8601 + 16.7275i −1.61837 + 0.590301i
\(804\) 0 0
\(805\) −2.96788 + 9.13418i −0.104604 + 0.321938i
\(806\) 11.6104 8.43548i 0.408960 0.297127i
\(807\) 0 0
\(808\) −4.73974 14.5874i −0.166744 0.513184i
\(809\) 10.2158 + 31.4410i 0.359168 + 1.10541i 0.953553 + 0.301225i \(0.0973956\pi\)
−0.594385 + 0.804181i \(0.702604\pi\)
\(810\) 0 0
\(811\) −4.21750 + 3.06419i −0.148096 + 0.107598i −0.659366 0.751822i \(-0.729175\pi\)
0.511270 + 0.859420i \(0.329175\pi\)
\(812\) −1.45088 + 4.46533i −0.0509157 + 0.156703i
\(813\) 0 0
\(814\) −0.458013 12.8615i −0.0160534 0.450796i
\(815\) −1.80332 −0.0631677
\(816\) 0 0
\(817\) 5.92484 4.30465i 0.207284 0.150601i
\(818\) 19.9854 + 14.5202i 0.698773 + 0.507689i
\(819\) 0 0
\(820\) −0.280733 0.864008i −0.00980363 0.0301725i
\(821\) −1.32625 0.963576i −0.0462864 0.0336290i 0.564401 0.825500i \(-0.309107\pi\)
−0.610688 + 0.791871i \(0.709107\pi\)
\(822\) 0 0
\(823\) −5.52814 + 17.0139i −0.192699 + 0.593066i 0.807297 + 0.590145i \(0.200930\pi\)
−0.999996 + 0.00292037i \(0.999070\pi\)
\(824\) 39.7217 1.38377
\(825\) 0 0
\(826\) −15.8597 −0.551830
\(827\) −10.9840 + 33.8052i −0.381951 + 1.17552i 0.556718 + 0.830702i \(0.312061\pi\)
−0.938668 + 0.344821i \(0.887939\pi\)
\(828\) 0 0
\(829\) 21.8039 + 15.8415i 0.757282 + 0.550198i 0.898076 0.439841i \(-0.144965\pi\)
−0.140793 + 0.990039i \(0.544965\pi\)
\(830\) −1.77168 5.45266i −0.0614958 0.189265i
\(831\) 0 0
\(832\) 7.01049 + 5.09342i 0.243045 + 0.176582i
\(833\) −1.98796 + 1.44433i −0.0688786 + 0.0500432i
\(834\) 0 0
\(835\) 24.5874 0.850882
\(836\) 6.54126 9.71226i 0.226234 0.335905i
\(837\) 0 0
\(838\) −8.93444 + 27.4974i −0.308635 + 0.949881i
\(839\) −9.57654 + 6.95776i −0.330619 + 0.240209i −0.740693 0.671843i \(-0.765503\pi\)
0.410074 + 0.912052i \(0.365503\pi\)
\(840\) 0 0
\(841\) −7.67757 23.6291i −0.264744 0.814797i
\(842\) 5.26282 + 16.1973i 0.181369 + 0.558195i
\(843\) 0 0
\(844\) 18.1906 13.2162i 0.626146 0.454922i
\(845\) −3.36891 + 10.3685i −0.115894 + 0.356686i
\(846\) 0 0
\(847\) 5.40155 21.7924i 0.185600 0.748797i
\(848\) 3.38721 0.116317
\(849\) 0 0
\(850\) 0.654843 0.475771i 0.0224609 0.0163188i
\(851\) −15.8235 11.4965i −0.542423 0.394094i
\(852\) 0 0
\(853\) −9.36453 28.8211i −0.320635 0.986814i −0.973372 0.229230i \(-0.926379\pi\)
0.652737 0.757585i \(-0.273621\pi\)
\(854\) −13.5152 9.81939i −0.462482 0.336013i
\(855\) 0 0
\(856\) −9.01660 + 27.7503i −0.308181 + 0.948484i
\(857\) 29.2318 0.998540 0.499270 0.866446i \(-0.333602\pi\)
0.499270 + 0.866446i \(0.333602\pi\)
\(858\) 0 0
\(859\) −36.7151 −1.25270 −0.626351 0.779541i \(-0.715452\pi\)
−0.626351 + 0.779541i \(0.715452\pi\)
\(860\) 0.816341 2.51244i 0.0278370 0.0856735i
\(861\) 0 0
\(862\) 22.9207 + 16.6529i 0.780682 + 0.567199i
\(863\) −13.4657 41.4431i −0.458377 1.41074i −0.867125 0.498091i \(-0.834034\pi\)
0.408748 0.912647i \(-0.365966\pi\)
\(864\) 0 0
\(865\) −13.1154 9.52890i −0.445937 0.323992i
\(866\) −9.59252 + 6.96937i −0.325967 + 0.236829i
\(867\) 0 0
\(868\) 24.4474 0.829798
\(869\) −34.7415 44.4040i −1.17853 1.50630i
\(870\) 0 0
\(871\) 1.41288 4.34841i 0.0478737 0.147340i
\(872\) −15.9532 + 11.5907i −0.540243 + 0.392509i
\(873\) 0 0
\(874\) 4.24672 + 13.0701i 0.143647 + 0.442101i
\(875\) −0.630728 1.94118i −0.0213225 0.0656239i
\(876\) 0 0
\(877\) 8.99407 6.53457i 0.303708 0.220657i −0.425484 0.904966i \(-0.639896\pi\)
0.729192 + 0.684309i \(0.239896\pi\)
\(878\) −7.40129 + 22.7788i −0.249781 + 0.768748i
\(879\) 0 0
\(880\) 0.0554058 + 1.55586i 0.00186773 + 0.0524479i
\(881\) 39.1155 1.31783 0.658917 0.752216i \(-0.271015\pi\)
0.658917 + 0.752216i \(0.271015\pi\)
\(882\) 0 0
\(883\) −15.7910 + 11.4728i −0.531408 + 0.386091i −0.820884 0.571094i \(-0.806519\pi\)
0.289476 + 0.957185i \(0.406519\pi\)
\(884\) 1.14661 + 0.833061i 0.0385647 + 0.0280189i
\(885\) 0 0
\(886\) 7.56236 + 23.2746i 0.254063 + 0.781924i
\(887\) −4.19967 3.05124i −0.141011 0.102451i 0.515043 0.857164i \(-0.327776\pi\)
−0.656054 + 0.754714i \(0.727776\pi\)
\(888\) 0 0
\(889\) 13.0404 40.1342i 0.437361 1.34606i
\(890\) −3.52123 −0.118032
\(891\) 0 0
\(892\) −11.8270 −0.395999
\(893\) −10.0353 + 30.8855i −0.335818 + 1.03354i
\(894\) 0 0
\(895\) 13.7287 + 9.97452i 0.458901 + 0.333411i
\(896\) 3.29298 + 10.1347i 0.110011 + 0.338578i
\(897\) 0 0
\(898\) −9.06755 6.58796i −0.302588 0.219843i
\(899\) 17.5025 12.7163i 0.583740 0.424112i
\(900\) 0 0
\(901\) 6.25669 0.208440
\(902\) −2.39638 0.685362i −0.0797906 0.0228201i
\(903\) 0 0
\(904\) −4.73329 + 14.5676i −0.157427 + 0.484510i
\(905\) −14.8461 + 10.7863i −0.493501 + 0.358550i
\(906\) 0 0
\(907\) −13.1140 40.3608i −0.435444 1.34016i −0.892631 0.450789i \(-0.851143\pi\)
0.457187 0.889371i \(-0.348857\pi\)
\(908\) 6.16318 + 18.9683i 0.204532 + 0.629485i
\(909\) 0 0
\(910\) −2.23278 + 1.62221i −0.0740159 + 0.0537757i
\(911\) 6.10306 18.7833i 0.202203 0.622318i −0.797613 0.603169i \(-0.793904\pi\)
0.999817 0.0191487i \(-0.00609558\pi\)
\(912\) 0 0
\(913\) 19.5838 + 5.60095i 0.648129 + 0.185364i
\(914\) 12.8725 0.425783
\(915\) 0 0
\(916\) 3.77036 2.73932i 0.124576 0.0905098i
\(917\) −33.5354 24.3649i −1.10744 0.804599i
\(918\) 0 0
\(919\) −7.56638 23.2869i −0.249592 0.768165i −0.994847 0.101385i \(-0.967672\pi\)
0.745255 0.666779i \(-0.232328\pi\)
\(920\) 11.1181 + 8.07774i 0.366551 + 0.266315i
\(921\) 0 0
\(922\) −3.26736 + 10.0559i −0.107605 + 0.331173i
\(923\) 18.6423 0.613619
\(924\) 0 0
\(925\) 4.15664 0.136669
\(926\) 1.78505 5.49382i 0.0586604 0.180538i
\(927\) 0 0
\(928\) 8.90976 + 6.47332i 0.292477 + 0.212497i
\(929\) 1.87044 + 5.75664i 0.0613673 + 0.188869i 0.977040 0.213055i \(-0.0683415\pi\)
−0.915673 + 0.401924i \(0.868341\pi\)
\(930\) 0 0
\(931\) 7.17291 + 5.21142i 0.235083 + 0.170797i
\(932\) −12.4157 + 9.02056i −0.406691 + 0.295478i
\(933\) 0 0
\(934\) −7.91903 −0.259119
\(935\) 0.102343 + 2.87390i 0.00334697 + 0.0939866i
\(936\) 0 0
\(937\) 2.11326 6.50394i 0.0690372 0.212475i −0.910586 0.413320i \(-0.864369\pi\)
0.979623 + 0.200846i \(0.0643690\pi\)
\(938\) −4.86599 + 3.53535i −0.158880 + 0.115433i
\(939\) 0 0
\(940\) 3.61993 + 11.1410i 0.118069 + 0.363379i
\(941\) 1.22191 + 3.76064i 0.0398330 + 0.122593i 0.968996 0.247078i \(-0.0794703\pi\)
−0.929163 + 0.369671i \(0.879470\pi\)
\(942\) 0 0
\(943\) −3.06453 + 2.22651i −0.0997947 + 0.0725051i
\(944\) −1.20736 + 3.71587i −0.0392962 + 0.120941i
\(945\) 0 0
\(946\) −4.46612 5.70826i −0.145206 0.185591i
\(947\) 40.1742 1.30549 0.652743 0.757579i \(-0.273618\pi\)
0.652743 + 0.757579i \(0.273618\pi\)
\(948\) 0 0
\(949\) −17.2472 + 12.5308i −0.559867 + 0.406767i
\(950\) −2.36279 1.71667i −0.0766591 0.0556961i
\(951\) 0 0
\(952\) −1.59720 4.91569i −0.0517657 0.159318i
\(953\) −33.3696 24.2444i −1.08095 0.785353i −0.103098 0.994671i \(-0.532876\pi\)
−0.977848 + 0.209318i \(0.932876\pi\)
\(954\) 0 0
\(955\) 4.75840 14.6449i 0.153978 0.473897i
\(956\) 9.03529 0.292222
\(957\) 0 0
\(958\) −8.62166 −0.278553
\(959\) −2.19482 + 6.75496i −0.0708744 + 0.218129i
\(960\) 0 0
\(961\) −66.0553 47.9920i −2.13082 1.54813i
\(962\) −1.73681 5.34535i −0.0559970 0.172341i
\(963\) 0 0
\(964\) −0.458269 0.332952i −0.0147599 0.0107237i
\(965\) 5.97007 4.33751i 0.192183 0.139629i
\(966\) 0 0
\(967\) 9.16826 0.294831 0.147416 0.989075i \(-0.452904\pi\)
0.147416 + 0.989075i \(0.452904\pi\)
\(968\) −27.2681 16.9867i −0.876429 0.545975i
\(969\) 0 0
\(970\) −0.559054 + 1.72059i −0.0179501 + 0.0552448i
\(971\) −3.00359 + 2.18224i −0.0963899 + 0.0700313i −0.634936 0.772565i \(-0.718974\pi\)
0.538546 + 0.842596i \(0.318974\pi\)
\(972\) 0 0
\(973\) −1.72243 5.30110i −0.0552186 0.169946i
\(974\) 5.81880 + 17.9084i 0.186446 + 0.573823i
\(975\) 0 0
\(976\) −3.32953 + 2.41904i −0.106576 + 0.0774317i
\(977\) −3.82972 + 11.7867i −0.122524 + 0.377089i −0.993442 0.114339i \(-0.963525\pi\)
0.870918 + 0.491428i \(0.163525\pi\)
\(978\) 0 0
\(979\) 6.98842 10.3762i 0.223351 0.331624i
\(980\) 3.19822 0.102163
\(981\) 0 0
\(982\) −4.02993 + 2.92791i −0.128600 + 0.0934335i
\(983\) 18.8460 + 13.6924i 0.601093 + 0.436720i 0.846267 0.532760i \(-0.178845\pi\)
−0.245174 + 0.969479i \(0.578845\pi\)
\(984\) 0 0
\(985\) −0.972402 2.99275i −0.0309833 0.0953568i
\(986\) −1.33480 0.969788i −0.0425086 0.0308843i
\(987\) 0 0
\(988\) 1.58026 4.86355i 0.0502748 0.154730i
\(989\) −11.0150 −0.350256
\(990\) 0 0
\(991\) −37.7826 −1.20020 −0.600101 0.799924i \(-0.704873\pi\)
−0.600101 + 0.799924i \(0.704873\pi\)
\(992\) 17.7205 54.5380i 0.562626 1.73158i
\(993\) 0 0
\(994\) −19.8403 14.4148i −0.629295 0.457209i
\(995\) −1.00664 3.09813i −0.0319128 0.0982175i
\(996\) 0 0
\(997\) −6.37174 4.62934i −0.201795 0.146613i 0.482299 0.876007i \(-0.339802\pi\)
−0.684094 + 0.729394i \(0.739802\pi\)
\(998\) 29.6671 21.5544i 0.939097 0.682294i
\(999\) 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 495.2.n.b.361.2 8
3.2 odd 2 165.2.m.b.31.1 yes 8
11.4 even 5 5445.2.a.bk.1.3 4
11.5 even 5 inner 495.2.n.b.181.2 8
11.7 odd 10 5445.2.a.br.1.2 4
15.2 even 4 825.2.bx.g.724.2 16
15.8 even 4 825.2.bx.g.724.3 16
15.14 odd 2 825.2.n.i.526.2 8
33.5 odd 10 165.2.m.b.16.1 8
33.26 odd 10 1815.2.a.v.1.2 4
33.29 even 10 1815.2.a.r.1.3 4
165.29 even 10 9075.2.a.dg.1.2 4
165.38 even 20 825.2.bx.g.49.2 16
165.59 odd 10 9075.2.a.cq.1.3 4
165.104 odd 10 825.2.n.i.676.2 8
165.137 even 20 825.2.bx.g.49.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.b.16.1 8 33.5 odd 10
165.2.m.b.31.1 yes 8 3.2 odd 2
495.2.n.b.181.2 8 11.5 even 5 inner
495.2.n.b.361.2 8 1.1 even 1 trivial
825.2.n.i.526.2 8 15.14 odd 2
825.2.n.i.676.2 8 165.104 odd 10
825.2.bx.g.49.2 16 165.38 even 20
825.2.bx.g.49.3 16 165.137 even 20
825.2.bx.g.724.2 16 15.2 even 4
825.2.bx.g.724.3 16 15.8 even 4
1815.2.a.r.1.3 4 33.29 even 10
1815.2.a.v.1.2 4 33.26 odd 10
5445.2.a.bk.1.3 4 11.4 even 5
5445.2.a.br.1.2 4 11.7 odd 10
9075.2.a.cq.1.3 4 165.59 odd 10
9075.2.a.dg.1.2 4 165.29 even 10