Properties

Label 605.2.g.i.251.1
Level $605$
Weight $2$
Character 605.251
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, 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("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 251.1
Root \(1.40126 - 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.i.511.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-1.40126 - 1.01807i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\) \(q+(-0.535233 + 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.535233 + 1.64728i) q^{6} +(-1.40126 - 1.01807i) q^{7} +(-1.40126 + 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} +1.73205 q^{10} -1.00000 q^{12} +(-1.07047 + 3.29456i) q^{13} +(2.42705 - 1.76336i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(2.14093 + 6.58911i) q^{17} +(-2.80252 - 2.03615i) q^{18} +(-2.80252 + 2.03615i) q^{19} +(-0.309017 + 0.951057i) q^{20} -1.73205 q^{21} +(-0.535233 + 1.64728i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.85410 - 3.52671i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.535233 + 1.64728i) q^{28} +(1.40126 - 1.01807i) q^{30} +(-2.47214 + 7.60845i) q^{31} +5.19615 q^{32} -12.0000 q^{34} +(-0.535233 + 1.64728i) q^{35} +(1.61803 - 1.17557i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-1.85410 - 5.70634i) q^{38} +(1.07047 + 3.29456i) q^{39} +(1.40126 + 1.01807i) q^{40} +(9.80881 - 7.12652i) q^{41} +(0.927051 - 2.85317i) q^{42} -8.66025 q^{43} +2.00000 q^{45} +(-7.28115 + 5.29007i) q^{47} +(-4.04508 - 2.93893i) q^{48} +(-1.23607 - 3.80423i) q^{49} +(-0.535233 - 1.64728i) q^{50} +(5.60503 + 4.07230i) q^{51} +(2.80252 - 2.03615i) q^{52} +(1.85410 - 5.70634i) q^{53} -8.66025 q^{54} +3.00000 q^{56} +(-1.07047 + 3.29456i) q^{57} +(9.70820 + 7.05342i) q^{59} +(0.309017 + 0.951057i) q^{60} +(-2.67617 - 8.23639i) q^{61} +(-11.2101 - 8.14459i) q^{62} +(2.80252 - 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} +3.46410 q^{65} -5.00000 q^{67} +(2.14093 - 6.58911i) q^{68} +(-2.42705 - 1.76336i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(-1.07047 - 3.29456i) q^{72} +(-11.2101 + 8.14459i) q^{74} +(-0.309017 + 0.951057i) q^{75} +3.46410 q^{76} -6.00000 q^{78} +(3.21140 - 9.88367i) q^{79} +(-4.04508 + 2.93893i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(6.48936 + 19.9722i) q^{82} +(-1.07047 - 3.29456i) q^{83} +(1.40126 + 1.01807i) q^{84} +(5.60503 - 4.07230i) q^{85} +(4.63525 - 14.2658i) q^{86} +3.00000 q^{89} +(-1.07047 + 3.29456i) q^{90} +(4.85410 - 3.52671i) q^{91} +(2.47214 + 7.60845i) q^{93} +(-4.81710 - 14.8255i) q^{94} +(2.80252 + 2.03615i) q^{95} +(4.20378 - 3.05422i) q^{96} +(-3.09017 + 9.51057i) q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9} - 8 q^{12} + 6 q^{14} - 2 q^{15} + 10 q^{16} + 2 q^{20} - 2 q^{25} - 12 q^{26} - 10 q^{27} + 16 q^{31} - 96 q^{34} + 4 q^{36} + 16 q^{37} + 12 q^{38} - 6 q^{42} + 16 q^{45} - 18 q^{47} - 10 q^{48} + 8 q^{49} - 12 q^{53} + 24 q^{56} + 24 q^{59} - 2 q^{60} - 2 q^{64} - 40 q^{67} - 6 q^{70} + 24 q^{71} + 2 q^{75} - 48 q^{78} - 10 q^{80} - 2 q^{81} - 42 q^{82} - 30 q^{86} + 24 q^{89} + 12 q^{91} - 16 q^{93} + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.535233 + 1.64728i −0.378467 + 1.16480i 0.562643 + 0.826700i \(0.309785\pi\)
−0.941110 + 0.338101i \(0.890215\pi\)
\(3\) 0.809017 0.587785i 0.467086 0.339358i −0.329218 0.944254i \(-0.606785\pi\)
0.796305 + 0.604896i \(0.206785\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) −0.309017 0.951057i −0.138197 0.425325i
\(6\) 0.535233 + 1.64728i 0.218508 + 0.672499i
\(7\) −1.40126 1.01807i −0.529626 0.384796i 0.290592 0.956847i \(-0.406148\pi\)
−0.820218 + 0.572051i \(0.806148\pi\)
\(8\) −1.40126 + 1.01807i −0.495420 + 0.359943i
\(9\) −0.618034 + 1.90211i −0.206011 + 0.634038i
\(10\) 1.73205 0.547723
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) −1.07047 + 3.29456i −0.296894 + 0.913746i 0.685685 + 0.727899i \(0.259503\pi\)
−0.982579 + 0.185847i \(0.940497\pi\)
\(14\) 2.42705 1.76336i 0.648657 0.471277i
\(15\) −0.809017 0.587785i −0.208887 0.151765i
\(16\) −1.54508 4.75528i −0.386271 1.18882i
\(17\) 2.14093 + 6.58911i 0.519252 + 1.59809i 0.775409 + 0.631459i \(0.217544\pi\)
−0.256157 + 0.966635i \(0.582456\pi\)
\(18\) −2.80252 2.03615i −0.660560 0.479925i
\(19\) −2.80252 + 2.03615i −0.642942 + 0.467124i −0.860859 0.508843i \(-0.830073\pi\)
0.217918 + 0.975967i \(0.430073\pi\)
\(20\) −0.309017 + 0.951057i −0.0690983 + 0.212663i
\(21\) −1.73205 −0.377964
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −0.535233 + 1.64728i −0.109254 + 0.336249i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −4.85410 3.52671i −0.951968 0.691645i
\(27\) 1.54508 + 4.75528i 0.297352 + 0.915155i
\(28\) 0.535233 + 1.64728i 0.101150 + 0.311306i
\(29\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(30\) 1.40126 1.01807i 0.255834 0.185874i
\(31\) −2.47214 + 7.60845i −0.444009 + 1.36652i 0.439558 + 0.898214i \(0.355135\pi\)
−0.883567 + 0.468304i \(0.844865\pi\)
\(32\) 5.19615 0.918559
\(33\) 0 0
\(34\) −12.0000 −2.05798
\(35\) −0.535233 + 1.64728i −0.0904709 + 0.278441i
\(36\) 1.61803 1.17557i 0.269672 0.195928i
\(37\) 6.47214 + 4.70228i 1.06401 + 0.773050i 0.974827 0.222965i \(-0.0715734\pi\)
0.0891861 + 0.996015i \(0.471573\pi\)
\(38\) −1.85410 5.70634i −0.300775 0.925690i
\(39\) 1.07047 + 3.29456i 0.171412 + 0.527551i
\(40\) 1.40126 + 1.01807i 0.221558 + 0.160972i
\(41\) 9.80881 7.12652i 1.53188 1.11298i 0.576696 0.816959i \(-0.304342\pi\)
0.955183 0.296016i \(-0.0956582\pi\)
\(42\) 0.927051 2.85317i 0.143047 0.440254i
\(43\) −8.66025 −1.32068 −0.660338 0.750968i \(-0.729587\pi\)
−0.660338 + 0.750968i \(0.729587\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) −7.28115 + 5.29007i −1.06207 + 0.771636i −0.974469 0.224520i \(-0.927918\pi\)
−0.0875959 + 0.996156i \(0.527918\pi\)
\(48\) −4.04508 2.93893i −0.583858 0.424197i
\(49\) −1.23607 3.80423i −0.176581 0.543461i
\(50\) −0.535233 1.64728i −0.0756934 0.232960i
\(51\) 5.60503 + 4.07230i 0.784862 + 0.570235i
\(52\) 2.80252 2.03615i 0.388639 0.282363i
\(53\) 1.85410 5.70634i 0.254680 0.783826i −0.739212 0.673473i \(-0.764802\pi\)
0.993892 0.110353i \(-0.0351982\pi\)
\(54\) −8.66025 −1.17851
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) −1.07047 + 3.29456i −0.141787 + 0.436375i
\(58\) 0 0
\(59\) 9.70820 + 7.05342i 1.26390 + 0.918277i 0.998942 0.0459824i \(-0.0146418\pi\)
0.264958 + 0.964260i \(0.414642\pi\)
\(60\) 0.309017 + 0.951057i 0.0398939 + 0.122781i
\(61\) −2.67617 8.23639i −0.342648 1.05456i −0.962831 0.270105i \(-0.912942\pi\)
0.620183 0.784457i \(-0.287058\pi\)
\(62\) −11.2101 8.14459i −1.42368 1.03436i
\(63\) 2.80252 2.03615i 0.353084 0.256531i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 3.46410 0.429669
\(66\) 0 0
\(67\) −5.00000 −0.610847 −0.305424 0.952217i \(-0.598798\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) 2.14093 6.58911i 0.259626 0.799047i
\(69\) 0 0
\(70\) −2.42705 1.76336i −0.290088 0.210761i
\(71\) −3.70820 11.4127i −0.440083 1.35444i −0.887787 0.460254i \(-0.847758\pi\)
0.447704 0.894182i \(-0.352242\pi\)
\(72\) −1.07047 3.29456i −0.126156 0.388267i
\(73\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(74\) −11.2101 + 8.14459i −1.30314 + 0.946790i
\(75\) −0.309017 + 0.951057i −0.0356822 + 0.109819i
\(76\) 3.46410 0.397360
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) 3.21140 9.88367i 0.361311 1.11200i −0.590949 0.806709i \(-0.701246\pi\)
0.952259 0.305291i \(-0.0987536\pi\)
\(80\) −4.04508 + 2.93893i −0.452254 + 0.328582i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 6.48936 + 19.9722i 0.716630 + 2.20556i
\(83\) −1.07047 3.29456i −0.117499 0.361625i 0.874961 0.484193i \(-0.160887\pi\)
−0.992460 + 0.122569i \(0.960887\pi\)
\(84\) 1.40126 + 1.01807i 0.152890 + 0.111081i
\(85\) 5.60503 4.07230i 0.607951 0.441702i
\(86\) 4.63525 14.2658i 0.499832 1.53833i
\(87\) 0 0
\(88\) 0 0
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) −1.07047 + 3.29456i −0.112837 + 0.347277i
\(91\) 4.85410 3.52671i 0.508848 0.369700i
\(92\) 0 0
\(93\) 2.47214 + 7.60845i 0.256349 + 0.788960i
\(94\) −4.81710 14.8255i −0.496846 1.52913i
\(95\) 2.80252 + 2.03615i 0.287532 + 0.208904i
\(96\) 4.20378 3.05422i 0.429046 0.311720i
\(97\) −3.09017 + 9.51057i −0.313759 + 0.965652i 0.662503 + 0.749059i \(0.269494\pi\)
−0.976262 + 0.216592i \(0.930506\pi\)
\(98\) 6.92820 0.699854
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 0.535233 1.64728i 0.0532577 0.163910i −0.920890 0.389823i \(-0.872536\pi\)
0.974148 + 0.225912i \(0.0725363\pi\)
\(102\) −9.70820 + 7.05342i −0.961255 + 0.698393i
\(103\) 3.23607 + 2.35114i 0.318859 + 0.231665i 0.735689 0.677320i \(-0.236859\pi\)
−0.416829 + 0.908985i \(0.636859\pi\)
\(104\) −1.85410 5.70634i −0.181810 0.559553i
\(105\) 0.535233 + 1.64728i 0.0522334 + 0.160758i
\(106\) 8.40755 + 6.10844i 0.816614 + 0.593304i
\(107\) 1.40126 1.01807i 0.135465 0.0984209i −0.517989 0.855387i \(-0.673319\pi\)
0.653454 + 0.756966i \(0.273319\pi\)
\(108\) 1.54508 4.75528i 0.148676 0.457577i
\(109\) −1.73205 −0.165900 −0.0829502 0.996554i \(-0.526434\pi\)
−0.0829502 + 0.996554i \(0.526434\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −2.67617 + 8.23639i −0.252874 + 0.778266i
\(113\) 4.85410 3.52671i 0.456636 0.331765i −0.335575 0.942014i \(-0.608930\pi\)
0.792210 + 0.610249i \(0.208930\pi\)
\(114\) −4.85410 3.52671i −0.454628 0.330307i
\(115\) 0 0
\(116\) 0 0
\(117\) −5.60503 4.07230i −0.518186 0.376484i
\(118\) −16.8151 + 12.2169i −1.54796 + 1.12466i
\(119\) 3.70820 11.4127i 0.339930 1.04620i
\(120\) 1.73205 0.158114
\(121\) 0 0
\(122\) 15.0000 1.35804
\(123\) 3.74663 11.5309i 0.337822 1.03971i
\(124\) 6.47214 4.70228i 0.581215 0.422277i
\(125\) 0.809017 + 0.587785i 0.0723607 + 0.0525731i
\(126\) 1.85410 + 5.70634i 0.165177 + 0.508361i
\(127\) −0.535233 1.64728i −0.0474943 0.146172i 0.924497 0.381189i \(-0.124485\pi\)
−0.971991 + 0.235017i \(0.924485\pi\)
\(128\) 9.80881 + 7.12652i 0.866984 + 0.629901i
\(129\) −7.00629 + 5.09037i −0.616870 + 0.448182i
\(130\) −1.85410 + 5.70634i −0.162615 + 0.500479i
\(131\) 3.46410 0.302660 0.151330 0.988483i \(-0.451644\pi\)
0.151330 + 0.988483i \(0.451644\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) 2.67617 8.23639i 0.231186 0.711516i
\(135\) 4.04508 2.93893i 0.348145 0.252942i
\(136\) −9.70820 7.05342i −0.832472 0.604826i
\(137\) 5.56231 + 17.1190i 0.475220 + 1.46258i 0.845661 + 0.533720i \(0.179207\pi\)
−0.370441 + 0.928856i \(0.620793\pi\)
\(138\) 0 0
\(139\) 11.2101 + 8.14459i 0.950826 + 0.690815i 0.951002 0.309185i \(-0.100056\pi\)
−0.000176405 1.00000i \(0.500056\pi\)
\(140\) 1.40126 1.01807i 0.118428 0.0860430i
\(141\) −2.78115 + 8.55951i −0.234215 + 0.720841i
\(142\) 20.7846 1.74421
\(143\) 0 0
\(144\) 10.0000 0.833333
\(145\) 0 0
\(146\) 0 0
\(147\) −3.23607 2.35114i −0.266906 0.193919i
\(148\) −2.47214 7.60845i −0.203208 0.625411i
\(149\) 5.88756 + 18.1201i 0.482328 + 1.48445i 0.835814 + 0.549013i \(0.184996\pi\)
−0.353486 + 0.935440i \(0.615004\pi\)
\(150\) −1.40126 1.01807i −0.114412 0.0831254i
\(151\) −16.8151 + 12.2169i −1.36839 + 0.994196i −0.370533 + 0.928819i \(0.620825\pi\)
−0.997861 + 0.0653769i \(0.979175\pi\)
\(152\) 1.85410 5.70634i 0.150388 0.462845i
\(153\) −13.8564 −1.12022
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 1.07047 3.29456i 0.0857059 0.263776i
\(157\) −3.23607 + 2.35114i −0.258266 + 0.187641i −0.709382 0.704824i \(-0.751026\pi\)
0.451116 + 0.892465i \(0.351026\pi\)
\(158\) 14.5623 + 10.5801i 1.15851 + 0.841710i
\(159\) −1.85410 5.70634i −0.147040 0.452542i
\(160\) −1.60570 4.94183i −0.126942 0.390686i
\(161\) 0 0
\(162\) 1.40126 1.01807i 0.110093 0.0799874i
\(163\) −5.87132 + 18.0701i −0.459878 + 1.41536i 0.405435 + 0.914124i \(0.367120\pi\)
−0.865312 + 0.501233i \(0.832880\pi\)
\(164\) −12.1244 −0.946753
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) 1.60570 4.94183i 0.124253 0.382411i −0.869511 0.493913i \(-0.835566\pi\)
0.993764 + 0.111502i \(0.0355662\pi\)
\(168\) 2.42705 1.76336i 0.187251 0.136046i
\(169\) 0.809017 + 0.587785i 0.0622321 + 0.0452143i
\(170\) 3.70820 + 11.4127i 0.284406 + 0.875312i
\(171\) −2.14093 6.58911i −0.163721 0.503882i
\(172\) 7.00629 + 5.09037i 0.534225 + 0.388137i
\(173\) 8.40755 6.10844i 0.639214 0.464416i −0.220366 0.975417i \(-0.570725\pi\)
0.859580 + 0.511001i \(0.170725\pi\)
\(174\) 0 0
\(175\) 1.73205 0.130931
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) −1.60570 + 4.94183i −0.120352 + 0.370406i
\(179\) 14.5623 10.5801i 1.08844 0.790796i 0.109303 0.994008i \(-0.465138\pi\)
0.979135 + 0.203212i \(0.0651381\pi\)
\(180\) −1.61803 1.17557i −0.120601 0.0876219i
\(181\) 3.39919 + 10.4616i 0.252660 + 0.777606i 0.994282 + 0.106788i \(0.0340567\pi\)
−0.741622 + 0.670818i \(0.765943\pi\)
\(182\) 3.21140 + 9.88367i 0.238045 + 0.732626i
\(183\) −7.00629 5.09037i −0.517920 0.376291i
\(184\) 0 0
\(185\) 2.47214 7.60845i 0.181755 0.559385i
\(186\) −13.8564 −1.01600
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) 2.67617 8.23639i 0.194662 0.599109i
\(190\) −4.85410 + 3.52671i −0.352154 + 0.255855i
\(191\) 4.85410 + 3.52671i 0.351230 + 0.255184i 0.749385 0.662134i \(-0.230349\pi\)
−0.398155 + 0.917318i \(0.630349\pi\)
\(192\) −0.309017 0.951057i −0.0223014 0.0686366i
\(193\) 1.07047 + 3.29456i 0.0770538 + 0.237147i 0.982163 0.188032i \(-0.0602109\pi\)
−0.905109 + 0.425180i \(0.860211\pi\)
\(194\) −14.0126 10.1807i −1.00605 0.730934i
\(195\) 2.80252 2.03615i 0.200692 0.145812i
\(196\) −1.23607 + 3.80423i −0.0882906 + 0.271730i
\(197\) 10.3923 0.740421 0.370211 0.928948i \(-0.379286\pi\)
0.370211 + 0.928948i \(0.379286\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0.535233 1.64728i 0.0378467 0.116480i
\(201\) −4.04508 + 2.93893i −0.285318 + 0.207296i
\(202\) 2.42705 + 1.76336i 0.170767 + 0.124069i
\(203\) 0 0
\(204\) −2.14093 6.58911i −0.149895 0.461330i
\(205\) −9.80881 7.12652i −0.685077 0.497738i
\(206\) −5.60503 + 4.07230i −0.390521 + 0.283730i
\(207\) 0 0
\(208\) 17.3205 1.20096
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(212\) −4.85410 + 3.52671i −0.333381 + 0.242216i
\(213\) −9.70820 7.05342i −0.665195 0.483293i
\(214\) 0.927051 + 2.85317i 0.0633719 + 0.195039i
\(215\) 2.67617 + 8.23639i 0.182513 + 0.561717i
\(216\) −7.00629 5.09037i −0.476718 0.346356i
\(217\) 11.2101 8.14459i 0.760989 0.552891i
\(218\) 0.927051 2.85317i 0.0627878 0.193241i
\(219\) 0 0
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) −4.28187 + 13.1782i −0.287380 + 0.884465i
\(223\) 15.3713 11.1679i 1.02934 0.747859i 0.0611635 0.998128i \(-0.480519\pi\)
0.968176 + 0.250269i \(0.0805189\pi\)
\(224\) −7.28115 5.29007i −0.486492 0.353457i
\(225\) −0.618034 1.90211i −0.0412023 0.126808i
\(226\) 3.21140 + 9.88367i 0.213619 + 0.657452i
\(227\) 15.4138 + 11.1988i 1.02305 + 0.743291i 0.966906 0.255131i \(-0.0821187\pi\)
0.0561463 + 0.998423i \(0.482119\pi\)
\(228\) 2.80252 2.03615i 0.185601 0.134847i
\(229\) 2.16312 6.65740i 0.142943 0.439933i −0.853798 0.520605i \(-0.825707\pi\)
0.996741 + 0.0806717i \(0.0257065\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.07047 3.29456i 0.0701286 0.215834i −0.909850 0.414938i \(-0.863803\pi\)
0.979978 + 0.199104i \(0.0638033\pi\)
\(234\) 9.70820 7.05342i 0.634645 0.461097i
\(235\) 7.28115 + 5.29007i 0.474970 + 0.345086i
\(236\) −3.70820 11.4127i −0.241384 0.742902i
\(237\) −3.21140 9.88367i −0.208603 0.642013i
\(238\) 16.8151 + 12.2169i 1.08996 + 0.791903i
\(239\) 2.80252 2.03615i 0.181280 0.131707i −0.493445 0.869777i \(-0.664262\pi\)
0.674724 + 0.738070i \(0.264262\pi\)
\(240\) −1.54508 + 4.75528i −0.0997348 + 0.306952i
\(241\) 19.0526 1.22728 0.613642 0.789585i \(-0.289704\pi\)
0.613642 + 0.789585i \(0.289704\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) −2.67617 + 8.23639i −0.171324 + 0.527281i
\(245\) −3.23607 + 2.35114i −0.206745 + 0.150209i
\(246\) 16.9894 + 12.3435i 1.08320 + 0.786992i
\(247\) −3.70820 11.4127i −0.235947 0.726171i
\(248\) −4.28187 13.1782i −0.271899 0.836818i
\(249\) −2.80252 2.03615i −0.177602 0.129036i
\(250\) −1.40126 + 1.01807i −0.0886234 + 0.0643886i
\(251\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(252\) −3.46410 −0.218218
\(253\) 0 0
\(254\) 3.00000 0.188237
\(255\) 2.14093 6.58911i 0.134070 0.412626i
\(256\) −15.3713 + 11.1679i −0.960708 + 0.697995i
\(257\) −9.70820 7.05342i −0.605581 0.439980i 0.242274 0.970208i \(-0.422107\pi\)
−0.847856 + 0.530227i \(0.822107\pi\)
\(258\) −4.63525 14.2658i −0.288578 0.888153i
\(259\) −4.28187 13.1782i −0.266062 0.818855i
\(260\) −2.80252 2.03615i −0.173805 0.126277i
\(261\) 0 0
\(262\) −1.85410 + 5.70634i −0.114547 + 0.352539i
\(263\) −24.2487 −1.49524 −0.747620 0.664127i \(-0.768803\pi\)
−0.747620 + 0.664127i \(0.768803\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −3.21140 + 9.88367i −0.196903 + 0.606007i
\(267\) 2.42705 1.76336i 0.148533 0.107916i
\(268\) 4.04508 + 2.93893i 0.247093 + 0.179523i
\(269\) −4.63525 14.2658i −0.282616 0.869804i −0.987103 0.160087i \(-0.948823\pi\)
0.704486 0.709717i \(-0.251177\pi\)
\(270\) 2.67617 + 8.23639i 0.162866 + 0.501251i
\(271\) −11.2101 8.14459i −0.680963 0.494749i 0.192714 0.981255i \(-0.438271\pi\)
−0.873677 + 0.486506i \(0.838271\pi\)
\(272\) 28.0252 20.3615i 1.69928 1.23460i
\(273\) 1.85410 5.70634i 0.112215 0.345363i
\(274\) −31.1769 −1.88347
\(275\) 0 0
\(276\) 0 0
\(277\) −3.21140 + 9.88367i −0.192954 + 0.593852i 0.807040 + 0.590497i \(0.201068\pi\)
−0.999994 + 0.00335552i \(0.998932\pi\)
\(278\) −19.4164 + 14.1068i −1.16452 + 0.846072i
\(279\) −12.9443 9.40456i −0.774953 0.563037i
\(280\) −0.927051 2.85317i −0.0554019 0.170509i
\(281\) 2.14093 + 6.58911i 0.127717 + 0.393074i 0.994386 0.105810i \(-0.0337435\pi\)
−0.866669 + 0.498884i \(0.833744\pi\)
\(282\) −12.6113 9.16267i −0.750994 0.545629i
\(283\) −4.20378 + 3.05422i −0.249889 + 0.181555i −0.705677 0.708533i \(-0.749357\pi\)
0.455789 + 0.890088i \(0.349357\pi\)
\(284\) −3.70820 + 11.4127i −0.220041 + 0.677218i
\(285\) 3.46410 0.205196
\(286\) 0 0
\(287\) −21.0000 −1.23959
\(288\) −3.21140 + 9.88367i −0.189233 + 0.582401i
\(289\) −25.0795 + 18.2213i −1.47527 + 1.07184i
\(290\) 0 0
\(291\) 3.09017 + 9.51057i 0.181149 + 0.557519i
\(292\) 0 0
\(293\) −5.60503 4.07230i −0.327450 0.237906i 0.411898 0.911230i \(-0.364866\pi\)
−0.739348 + 0.673324i \(0.764866\pi\)
\(294\) 5.60503 4.07230i 0.326892 0.237501i
\(295\) 3.70820 11.4127i 0.215900 0.664472i
\(296\) −13.8564 −0.805387
\(297\) 0 0
\(298\) −33.0000 −1.91164
\(299\) 0 0
\(300\) 0.809017 0.587785i 0.0467086 0.0339358i
\(301\) 12.1353 + 8.81678i 0.699464 + 0.508191i
\(302\) −11.1246 34.2380i −0.640149 1.97018i
\(303\) −0.535233 1.64728i −0.0307483 0.0946337i
\(304\) 14.0126 + 10.1807i 0.803677 + 0.583905i
\(305\) −7.00629 + 5.09037i −0.401179 + 0.291474i
\(306\) 7.41641 22.8254i 0.423968 1.30484i
\(307\) 10.3923 0.593120 0.296560 0.955014i \(-0.404160\pi\)
0.296560 + 0.955014i \(0.404160\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) −4.28187 + 13.1782i −0.243194 + 0.748473i
\(311\) 4.85410 3.52671i 0.275251 0.199981i −0.441592 0.897216i \(-0.645586\pi\)
0.716843 + 0.697234i \(0.245586\pi\)
\(312\) −4.85410 3.52671i −0.274809 0.199661i
\(313\) 3.09017 + 9.51057i 0.174667 + 0.537569i 0.999618 0.0276348i \(-0.00879755\pi\)
−0.824951 + 0.565204i \(0.808798\pi\)
\(314\) −2.14093 6.58911i −0.120820 0.371845i
\(315\) −2.80252 2.03615i −0.157904 0.114724i
\(316\) −8.40755 + 6.10844i −0.472962 + 0.343627i
\(317\) −1.85410 + 5.70634i −0.104137 + 0.320500i −0.989527 0.144349i \(-0.953891\pi\)
0.885390 + 0.464849i \(0.153891\pi\)
\(318\) 10.3923 0.582772
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 0.535233 1.64728i 0.0298738 0.0919421i
\(322\) 0 0
\(323\) −19.4164 14.1068i −1.08036 0.784926i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) −1.07047 3.29456i −0.0593788 0.182749i
\(326\) −26.6239 19.3434i −1.47456 1.07133i
\(327\) −1.40126 + 1.01807i −0.0774898 + 0.0562996i
\(328\) −6.48936 + 19.9722i −0.358315 + 1.10278i
\(329\) 15.5885 0.859419
\(330\) 0 0
\(331\) −34.0000 −1.86881 −0.934405 0.356214i \(-0.884068\pi\)
−0.934405 + 0.356214i \(0.884068\pi\)
\(332\) −1.07047 + 3.29456i −0.0587495 + 0.180812i
\(333\) −12.9443 + 9.40456i −0.709342 + 0.515367i
\(334\) 7.28115 + 5.29007i 0.398407 + 0.289460i
\(335\) 1.54508 + 4.75528i 0.0844170 + 0.259809i
\(336\) 2.67617 + 8.23639i 0.145997 + 0.449332i
\(337\) 8.40755 + 6.10844i 0.457988 + 0.332748i 0.792742 0.609558i \(-0.208653\pi\)
−0.334753 + 0.942306i \(0.608653\pi\)
\(338\) −1.40126 + 1.01807i −0.0762184 + 0.0553759i
\(339\) 1.85410 5.70634i 0.100701 0.309926i
\(340\) −6.92820 −0.375735
\(341\) 0 0
\(342\) 12.0000 0.648886
\(343\) −5.88756 + 18.1201i −0.317899 + 0.978391i
\(344\) 12.1353 8.81678i 0.654289 0.475369i
\(345\) 0 0
\(346\) 5.56231 + 17.1190i 0.299031 + 0.920324i
\(347\) 3.74663 + 11.5309i 0.201130 + 0.619014i 0.999850 + 0.0173113i \(0.00551065\pi\)
−0.798720 + 0.601702i \(0.794489\pi\)
\(348\) 0 0
\(349\) 28.0252 20.3615i 1.50015 1.08992i 0.529833 0.848102i \(-0.322255\pi\)
0.970320 0.241823i \(-0.0777452\pi\)
\(350\) −0.927051 + 2.85317i −0.0495530 + 0.152508i
\(351\) −17.3205 −0.924500
\(352\) 0 0
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) −6.42280 + 19.7673i −0.341368 + 1.05062i
\(355\) −9.70820 + 7.05342i −0.515258 + 0.374357i
\(356\) −2.42705 1.76336i −0.128633 0.0934577i
\(357\) −3.70820 11.4127i −0.196259 0.604023i
\(358\) 9.63420 + 29.6510i 0.509183 + 1.56710i
\(359\) −2.80252 2.03615i −0.147911 0.107464i 0.511369 0.859361i \(-0.329139\pi\)
−0.659280 + 0.751898i \(0.729139\pi\)
\(360\) −2.80252 + 2.03615i −0.147706 + 0.107314i
\(361\) −2.16312 + 6.65740i −0.113848 + 0.350389i
\(362\) −19.0526 −1.00138
\(363\) 0 0
\(364\) −6.00000 −0.314485
\(365\) 0 0
\(366\) 12.1353 8.81678i 0.634320 0.460860i
\(367\) −13.7533 9.99235i −0.717916 0.521596i 0.167802 0.985821i \(-0.446333\pi\)
−0.885718 + 0.464224i \(0.846333\pi\)
\(368\) 0 0
\(369\) 7.49326 + 23.0619i 0.390084 + 1.20055i
\(370\) 11.2101 + 8.14459i 0.582784 + 0.423417i
\(371\) −8.40755 + 6.10844i −0.436498 + 0.317135i
\(372\) 2.47214 7.60845i 0.128174 0.394480i
\(373\) 13.8564 0.717458 0.358729 0.933442i \(-0.383210\pi\)
0.358729 + 0.933442i \(0.383210\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 4.81710 14.8255i 0.248423 0.764567i
\(377\) 0 0
\(378\) 12.1353 + 8.81678i 0.624170 + 0.453486i
\(379\) −10.5066 32.3359i −0.539687 1.66098i −0.733299 0.679907i \(-0.762020\pi\)
0.193612 0.981078i \(-0.437980\pi\)
\(380\) −1.07047 3.29456i −0.0549138 0.169007i
\(381\) −1.40126 1.01807i −0.0717886 0.0521575i
\(382\) −8.40755 + 6.10844i −0.430168 + 0.312535i
\(383\) 7.41641 22.8254i 0.378961 1.16632i −0.561807 0.827269i \(-0.689894\pi\)
0.940767 0.339053i \(-0.110106\pi\)
\(384\) 12.1244 0.618718
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 5.35233 16.4728i 0.272074 0.837359i
\(388\) 8.09017 5.87785i 0.410716 0.298403i
\(389\) −2.42705 1.76336i −0.123056 0.0894057i 0.524555 0.851377i \(-0.324232\pi\)
−0.647611 + 0.761971i \(0.724232\pi\)
\(390\) 1.85410 + 5.70634i 0.0938861 + 0.288952i
\(391\) 0 0
\(392\) 5.60503 + 4.07230i 0.283097 + 0.205682i
\(393\) 2.80252 2.03615i 0.141368 0.102710i
\(394\) −5.56231 + 17.1190i −0.280225 + 0.862444i
\(395\) −10.3923 −0.522894
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 7.49326 23.0619i 0.375603 1.15599i
\(399\) 4.85410 3.52671i 0.243009 0.176556i
\(400\) 4.04508 + 2.93893i 0.202254 + 0.146946i
\(401\) 8.34346 + 25.6785i 0.416652 + 1.28232i 0.910765 + 0.412926i \(0.135493\pi\)
−0.494112 + 0.869398i \(0.664507\pi\)
\(402\) −2.67617 8.23639i −0.133475 0.410794i
\(403\) −22.4201 16.2892i −1.11683 0.811422i
\(404\) −1.40126 + 1.01807i −0.0697152 + 0.0506511i
\(405\) −0.309017 + 0.951057i −0.0153552 + 0.0472584i
\(406\) 0 0
\(407\) 0 0
\(408\) −12.0000 −0.594089
\(409\) −1.60570 + 4.94183i −0.0793967 + 0.244358i −0.982874 0.184277i \(-0.941006\pi\)
0.903478 + 0.428635i \(0.141006\pi\)
\(410\) 16.9894 12.3435i 0.839045 0.609602i
\(411\) 14.5623 + 10.5801i 0.718306 + 0.521880i
\(412\) −1.23607 3.80423i −0.0608967 0.187421i
\(413\) −6.42280 19.7673i −0.316045 0.972687i
\(414\) 0 0
\(415\) −2.80252 + 2.03615i −0.137570 + 0.0999506i
\(416\) −5.56231 + 17.1190i −0.272714 + 0.839329i
\(417\) 13.8564 0.678551
\(418\) 0 0
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0.535233 1.64728i 0.0261167 0.0803789i
\(421\) 13.7533 9.99235i 0.670294 0.486997i −0.199829 0.979831i \(-0.564039\pi\)
0.870124 + 0.492833i \(0.164039\pi\)
\(422\) 0 0
\(423\) −5.56231 17.1190i −0.270449 0.832355i
\(424\) 3.21140 + 9.88367i 0.155959 + 0.479993i
\(425\) −5.60503 4.07230i −0.271884 0.197535i
\(426\) 16.8151 12.2169i 0.814694 0.591910i
\(427\) −4.63525 + 14.2658i −0.224316 + 0.690373i
\(428\) −1.73205 −0.0837218
\(429\) 0 0
\(430\) −15.0000 −0.723364
\(431\) −11.7751 + 36.2401i −0.567188 + 1.74563i 0.0941714 + 0.995556i \(0.469980\pi\)
−0.661359 + 0.750069i \(0.730020\pi\)
\(432\) 20.2254 14.6946i 0.973096 0.706996i
\(433\) −25.8885 18.8091i −1.24412 0.903909i −0.246258 0.969204i \(-0.579201\pi\)
−0.997866 + 0.0652953i \(0.979201\pi\)
\(434\) 7.41641 + 22.8254i 0.355999 + 1.09565i
\(435\) 0 0
\(436\) 1.40126 + 1.01807i 0.0671081 + 0.0487569i
\(437\) 0 0
\(438\) 0 0
\(439\) 27.7128 1.32266 0.661330 0.750095i \(-0.269992\pi\)
0.661330 + 0.750095i \(0.269992\pi\)
\(440\) 0 0
\(441\) 8.00000 0.380952
\(442\) 12.8456 39.5347i 0.611003 1.88047i
\(443\) 12.1353 8.81678i 0.576563 0.418898i −0.260920 0.965360i \(-0.584026\pi\)
0.837484 + 0.546463i \(0.184026\pi\)
\(444\) −6.47214 4.70228i −0.307154 0.223160i
\(445\) −0.927051 2.85317i −0.0439464 0.135253i
\(446\) 10.1694 + 31.2983i 0.481536 + 1.48202i
\(447\) 15.4138 + 11.1988i 0.729050 + 0.529686i
\(448\) −1.40126 + 1.01807i −0.0662032 + 0.0480995i
\(449\) −4.63525 + 14.2658i −0.218751 + 0.673247i 0.780115 + 0.625636i \(0.215161\pi\)
−0.998866 + 0.0476105i \(0.984839\pi\)
\(450\) 3.46410 0.163299
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) −6.42280 + 19.7673i −0.301769 + 0.928751i
\(454\) −26.6976 + 19.3969i −1.25298 + 0.910342i
\(455\) −4.85410 3.52671i −0.227564 0.165335i
\(456\) −1.85410 5.70634i −0.0868263 0.267224i
\(457\) −6.42280 19.7673i −0.300446 0.924677i −0.981338 0.192293i \(-0.938408\pi\)
0.680892 0.732384i \(-0.261592\pi\)
\(458\) 9.80881 + 7.12652i 0.458336 + 0.333000i
\(459\) −28.0252 + 20.3615i −1.30810 + 0.950392i
\(460\) 0 0
\(461\) 12.1244 0.564688 0.282344 0.959313i \(-0.408888\pi\)
0.282344 + 0.959313i \(0.408888\pi\)
\(462\) 0 0
\(463\) 41.0000 1.90543 0.952716 0.303863i \(-0.0982765\pi\)
0.952716 + 0.303863i \(0.0982765\pi\)
\(464\) 0 0
\(465\) 6.47214 4.70228i 0.300138 0.218063i
\(466\) 4.85410 + 3.52671i 0.224862 + 0.163372i
\(467\) 0.927051 + 2.85317i 0.0428988 + 0.132029i 0.970212 0.242257i \(-0.0778878\pi\)
−0.927313 + 0.374286i \(0.877888\pi\)
\(468\) 2.14093 + 6.58911i 0.0989646 + 0.304582i
\(469\) 7.00629 + 5.09037i 0.323521 + 0.235051i
\(470\) −12.6113 + 9.16267i −0.581717 + 0.422642i
\(471\) −1.23607 + 3.80423i −0.0569550 + 0.175289i
\(472\) −20.7846 −0.956689
\(473\) 0 0
\(474\) 18.0000 0.826767
\(475\) 1.07047 3.29456i 0.0491164 0.151165i
\(476\) −9.70820 + 7.05342i −0.444975 + 0.323293i
\(477\) 9.70820 + 7.05342i 0.444508 + 0.322954i
\(478\) 1.85410 + 5.70634i 0.0848047 + 0.261002i
\(479\) −3.21140 9.88367i −0.146733 0.451596i 0.850497 0.525980i \(-0.176301\pi\)
−0.997230 + 0.0743832i \(0.976301\pi\)
\(480\) −4.20378 3.05422i −0.191875 0.139406i
\(481\) −22.4201 + 16.2892i −1.02227 + 0.742723i
\(482\) −10.1976 + 31.3849i −0.464486 + 1.42954i
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 8.56373 26.3565i 0.388459 1.19555i
\(487\) 16.1803 11.7557i 0.733201 0.532702i −0.157373 0.987539i \(-0.550303\pi\)
0.890575 + 0.454837i \(0.150303\pi\)
\(488\) 12.1353 + 8.81678i 0.549337 + 0.399117i
\(489\) 5.87132 + 18.0701i 0.265510 + 0.817157i
\(490\) −2.14093 6.58911i −0.0967175 0.297666i
\(491\) 19.6176 + 14.2530i 0.885331 + 0.643230i 0.934656 0.355552i \(-0.115707\pi\)
−0.0493256 + 0.998783i \(0.515707\pi\)
\(492\) −9.80881 + 7.12652i −0.442215 + 0.321288i
\(493\) 0 0
\(494\) 20.7846 0.935144
\(495\) 0 0
\(496\) 40.0000 1.79605
\(497\) −6.42280 + 19.7673i −0.288102 + 0.886686i
\(498\) 4.85410 3.52671i 0.217518 0.158036i
\(499\) 30.7426 + 22.3358i 1.37623 + 0.999890i 0.997221 + 0.0744963i \(0.0237349\pi\)
0.379009 + 0.925393i \(0.376265\pi\)
\(500\) −0.309017 0.951057i −0.0138197 0.0425325i
\(501\) −1.60570 4.94183i −0.0717374 0.220785i
\(502\) 0 0
\(503\) 7.00629 5.09037i 0.312395 0.226968i −0.420528 0.907279i \(-0.638155\pi\)
0.732924 + 0.680311i \(0.238155\pi\)
\(504\) −1.85410 + 5.70634i −0.0825883 + 0.254181i
\(505\) −1.73205 −0.0770752
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) −0.535233 + 1.64728i −0.0237471 + 0.0730862i
\(509\) −12.1353 + 8.81678i −0.537886 + 0.390797i −0.823299 0.567608i \(-0.807869\pi\)
0.285413 + 0.958404i \(0.407869\pi\)
\(510\) 9.70820 + 7.05342i 0.429886 + 0.312331i
\(511\) 0 0
\(512\) −2.67617 8.23639i −0.118271 0.364000i
\(513\) −14.0126 10.1807i −0.618671 0.449491i
\(514\) 16.8151 12.2169i 0.741682 0.538864i
\(515\) 1.23607 3.80423i 0.0544677 0.167634i
\(516\) 8.66025 0.381246
\(517\) 0 0
\(518\) 24.0000 1.05450
\(519\) 3.21140 9.88367i 0.140965 0.433845i
\(520\) −4.85410 + 3.52671i −0.212866 + 0.154657i
\(521\) −12.1353 8.81678i −0.531655 0.386270i 0.289321 0.957232i \(-0.406570\pi\)
−0.820977 + 0.570962i \(0.806570\pi\)
\(522\) 0 0
\(523\) 5.35233 + 16.4728i 0.234041 + 0.720304i 0.997247 + 0.0741493i \(0.0236241\pi\)
−0.763206 + 0.646155i \(0.776376\pi\)
\(524\) −2.80252 2.03615i −0.122429 0.0889495i
\(525\) 1.40126 1.01807i 0.0611559 0.0444324i
\(526\) 12.9787 39.9444i 0.565899 1.74166i
\(527\) −55.4256 −2.41438
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 3.21140 9.88367i 0.139494 0.429319i
\(531\) −19.4164 + 14.1068i −0.842600 + 0.612185i
\(532\) −4.85410 3.52671i −0.210452 0.152902i
\(533\) 12.9787 + 39.9444i 0.562170 + 1.73018i
\(534\) 1.60570 + 4.94183i 0.0694854 + 0.213854i
\(535\) −1.40126 1.01807i −0.0605817 0.0440152i
\(536\) 7.00629 5.09037i 0.302626 0.219870i
\(537\) 5.56231 17.1190i 0.240031 0.738740i
\(538\) 25.9808 1.12011
\(539\) 0 0
\(540\) −5.00000 −0.215166
\(541\) 1.60570 4.94183i 0.0690344 0.212466i −0.910588 0.413316i \(-0.864370\pi\)
0.979622 + 0.200850i \(0.0643704\pi\)
\(542\) 19.4164 14.1068i 0.834006 0.605941i
\(543\) 8.89919 + 6.46564i 0.381901 + 0.277467i
\(544\) 11.1246 + 34.2380i 0.476964 + 1.46794i
\(545\) 0.535233 + 1.64728i 0.0229269 + 0.0705616i
\(546\) 8.40755 + 6.10844i 0.359810 + 0.261417i
\(547\) −36.4327 + 26.4699i −1.55775 + 1.13177i −0.619927 + 0.784659i \(0.712838\pi\)
−0.937823 + 0.347113i \(0.887162\pi\)
\(548\) 5.56231 17.1190i 0.237610 0.731288i
\(549\) 17.3205 0.739221
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −14.5623 + 10.5801i −0.619252 + 0.449913i
\(554\) −14.5623 10.5801i −0.618693 0.449507i
\(555\) −2.47214 7.60845i −0.104936 0.322961i
\(556\) −4.28187 13.1782i −0.181592 0.558881i
\(557\) −5.60503 4.07230i −0.237493 0.172549i 0.462673 0.886529i \(-0.346891\pi\)
−0.700166 + 0.713980i \(0.746891\pi\)
\(558\) 22.4201 16.2892i 0.949120 0.689576i
\(559\) 9.27051 28.5317i 0.392101 1.20676i
\(560\) 8.66025 0.365963
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) 4.81710 14.8255i 0.203016 0.624820i −0.796773 0.604279i \(-0.793461\pi\)
0.999789 0.0205411i \(-0.00653891\pi\)
\(564\) 7.28115 5.29007i 0.306592 0.222752i
\(565\) −4.85410 3.52671i −0.204214 0.148370i
\(566\) −2.78115 8.55951i −0.116901 0.359783i
\(567\) 0.535233 + 1.64728i 0.0224777 + 0.0691792i
\(568\) 16.8151 + 12.2169i 0.705546 + 0.512609i
\(569\) −1.40126 + 1.01807i −0.0587438 + 0.0426799i −0.616770 0.787144i \(-0.711559\pi\)
0.558026 + 0.829824i \(0.311559\pi\)
\(570\) −1.85410 + 5.70634i −0.0776598 + 0.239012i
\(571\) 3.46410 0.144968 0.0724841 0.997370i \(-0.476907\pi\)
0.0724841 + 0.997370i \(0.476907\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 11.2399 34.5928i 0.469144 1.44388i
\(575\) 0 0
\(576\) 1.61803 + 1.17557i 0.0674181 + 0.0489821i
\(577\) −6.18034 19.0211i −0.257291 0.791860i −0.993370 0.114964i \(-0.963325\pi\)
0.736079 0.676896i \(-0.236675\pi\)
\(578\) −16.5922 51.0656i −0.690146 2.12405i
\(579\) 2.80252 + 2.03615i 0.116469 + 0.0846194i
\(580\) 0 0
\(581\) −1.85410 + 5.70634i −0.0769211 + 0.236739i
\(582\) −17.3205 −0.717958
\(583\) 0 0
\(584\) 0 0
\(585\) −2.14093 + 6.58911i −0.0885167 + 0.272426i
\(586\) 9.70820 7.05342i 0.401042 0.291374i
\(587\) −16.9894 12.3435i −0.701226 0.509470i 0.179105 0.983830i \(-0.442680\pi\)
−0.880331 + 0.474360i \(0.842680\pi\)
\(588\) 1.23607 + 3.80423i 0.0509746 + 0.156884i
\(589\) −8.56373 26.3565i −0.352862 1.08600i
\(590\) 16.8151 + 12.2169i 0.692267 + 0.502961i
\(591\) 8.40755 6.10844i 0.345840 0.251268i
\(592\) 12.3607 38.0423i 0.508021 1.56353i
\(593\) −24.2487 −0.995775 −0.497888 0.867242i \(-0.665891\pi\)
−0.497888 + 0.867242i \(0.665891\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 5.88756 18.1201i 0.241164 0.742227i
\(597\) −11.3262 + 8.22899i −0.463552 + 0.336790i
\(598\) 0 0
\(599\) 9.27051 + 28.5317i 0.378783 + 1.16577i 0.940891 + 0.338710i \(0.109990\pi\)
−0.562108 + 0.827064i \(0.690010\pi\)
\(600\) −0.535233 1.64728i −0.0218508 0.0672499i
\(601\) 16.8151 + 12.2169i 0.685902 + 0.498337i 0.875311 0.483561i \(-0.160657\pi\)
−0.189408 + 0.981898i \(0.560657\pi\)
\(602\) −21.0189 + 15.2711i −0.856666 + 0.622404i
\(603\) 3.09017 9.51057i 0.125841 0.387300i
\(604\) 20.7846 0.845714
\(605\) 0 0
\(606\) 3.00000 0.121867
\(607\) 1.07047 3.29456i 0.0434489 0.133722i −0.926979 0.375113i \(-0.877604\pi\)
0.970428 + 0.241391i \(0.0776038\pi\)
\(608\) −14.5623 + 10.5801i −0.590579 + 0.429081i
\(609\) 0 0
\(610\) −4.63525 14.2658i −0.187676 0.577607i
\(611\) −9.63420 29.6510i −0.389758 1.19955i
\(612\) 11.2101 + 8.14459i 0.453140 + 0.329226i
\(613\) −8.40755 + 6.10844i −0.339578 + 0.246718i −0.744484 0.667641i \(-0.767304\pi\)
0.404906 + 0.914358i \(0.367304\pi\)
\(614\) −5.56231 + 17.1190i −0.224476 + 0.690867i
\(615\) −12.1244 −0.488901
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) −2.14093 + 6.58911i −0.0861209 + 0.265053i
\(619\) −16.1803 + 11.7557i −0.650343 + 0.472502i −0.863388 0.504541i \(-0.831662\pi\)
0.213045 + 0.977042i \(0.431662\pi\)
\(620\) −6.47214 4.70228i −0.259927 0.188848i
\(621\) 0 0
\(622\) 3.21140 + 9.88367i 0.128765 + 0.396299i
\(623\) −4.20378 3.05422i −0.168421 0.122365i
\(624\) 14.0126 10.1807i 0.560952 0.407556i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) −17.3205 −0.692267
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) −17.1275 + 52.7129i −0.682917 + 2.10180i
\(630\) 4.85410 3.52671i 0.193392 0.140508i
\(631\) −22.6525 16.4580i −0.901781 0.655182i 0.0371420 0.999310i \(-0.488175\pi\)
−0.938923 + 0.344128i \(0.888175\pi\)
\(632\) 5.56231 + 17.1190i 0.221257 + 0.680958i
\(633\) 0 0
\(634\) −8.40755 6.10844i −0.333907 0.242597i
\(635\) −1.40126 + 1.01807i −0.0556072 + 0.0404010i
\(636\) −1.85410 + 5.70634i −0.0735199 + 0.226271i
\(637\) 13.8564 0.549011
\(638\) 0 0
\(639\) 24.0000 0.949425
\(640\) 3.74663 11.5309i 0.148099 0.455801i
\(641\) −24.2705 + 17.6336i −0.958628 + 0.696484i −0.952832 0.303500i \(-0.901845\pi\)
−0.00579592 + 0.999983i \(0.501845\pi\)
\(642\) 2.42705 + 1.76336i 0.0957881 + 0.0695941i
\(643\) −9.57953 29.4828i −0.377780 1.16269i −0.941584 0.336778i \(-0.890663\pi\)
0.563804 0.825908i \(-0.309337\pi\)
\(644\) 0 0
\(645\) 7.00629 + 5.09037i 0.275873 + 0.200433i
\(646\) 33.6302 24.4338i 1.32316 0.961334i
\(647\) 10.1976 31.3849i 0.400907 1.23387i −0.523357 0.852114i \(-0.675321\pi\)
0.924264 0.381753i \(-0.124679\pi\)
\(648\) 1.73205 0.0680414
\(649\) 0 0
\(650\) 6.00000 0.235339
\(651\) 4.28187 13.1782i 0.167820 0.516495i
\(652\) 15.3713 11.1679i 0.601987 0.437369i
\(653\) 24.2705 + 17.6336i 0.949778 + 0.690054i 0.950754 0.309945i \(-0.100311\pi\)
−0.000976014 1.00000i \(0.500311\pi\)
\(654\) −0.927051 2.85317i −0.0362506 0.111568i
\(655\) −1.07047 3.29456i −0.0418266 0.128729i
\(656\) −49.0440 35.6326i −1.91485 1.39122i
\(657\) 0 0
\(658\) −8.34346 + 25.6785i −0.325262 + 1.00105i
\(659\) −3.46410 −0.134942 −0.0674711 0.997721i \(-0.521493\pi\)
−0.0674711 + 0.997721i \(0.521493\pi\)
\(660\) 0 0
\(661\) 37.0000 1.43913 0.719567 0.694423i \(-0.244340\pi\)
0.719567 + 0.694423i \(0.244340\pi\)
\(662\) 18.1979 56.0075i 0.707283 2.17679i
\(663\) −19.4164 + 14.1068i −0.754071 + 0.547865i
\(664\) 4.85410 + 3.52671i 0.188376 + 0.136863i
\(665\) −1.85410 5.70634i −0.0718990 0.221282i
\(666\) −8.56373 26.3565i −0.331838 1.02129i
\(667\) 0 0
\(668\) −4.20378 + 3.05422i −0.162649 + 0.118171i
\(669\) 5.87132 18.0701i 0.226998 0.698629i
\(670\) −8.66025 −0.334575
\(671\) 0 0
\(672\) −9.00000 −0.347183
\(673\) 6.42280 19.7673i 0.247581 0.761975i −0.747621 0.664126i \(-0.768804\pi\)
0.995201 0.0978489i \(-0.0311962\pi\)
\(674\) −14.5623 + 10.5801i −0.560919 + 0.407532i
\(675\) −4.04508 2.93893i −0.155695 0.113119i
\(676\) −0.309017 0.951057i −0.0118853 0.0365791i
\(677\) −8.56373 26.3565i −0.329131 1.01296i −0.969541 0.244928i \(-0.921236\pi\)
0.640410 0.768033i \(-0.278764\pi\)
\(678\) 8.40755 + 6.10844i 0.322890 + 0.234593i
\(679\) 14.0126 10.1807i 0.537754 0.390701i
\(680\) −3.70820 + 11.4127i −0.142203 + 0.437656i
\(681\) 19.0526 0.730096
\(682\) 0 0
\(683\) −21.0000 −0.803543 −0.401771 0.915740i \(-0.631605\pi\)
−0.401771 + 0.915740i \(0.631605\pi\)
\(684\) −2.14093 + 6.58911i −0.0818606 + 0.251941i
\(685\) 14.5623 10.5801i 0.556397 0.404246i
\(686\) −26.6976 19.3969i −1.01932 0.740578i
\(687\) −2.16312 6.65740i −0.0825281 0.253995i
\(688\) 13.3808 + 41.1820i 0.510139 + 1.57005i
\(689\) 16.8151 + 12.2169i 0.640604 + 0.465426i
\(690\) 0 0
\(691\) −3.09017 + 9.51057i −0.117556 + 0.361799i −0.992471 0.122476i \(-0.960917\pi\)
0.874916 + 0.484275i \(0.160917\pi\)
\(692\) −10.3923 −0.395056
\(693\) 0 0
\(694\) −21.0000 −0.797149
\(695\) 4.28187 13.1782i 0.162420 0.499879i
\(696\) 0 0
\(697\) 67.9574 + 49.3740i 2.57407 + 1.87017i
\(698\) 18.5410 + 57.0634i 0.701788 + 2.15988i
\(699\) −1.07047 3.29456i −0.0404888 0.124612i
\(700\) −1.40126 1.01807i −0.0529626 0.0384796i
\(701\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(702\) 9.27051 28.5317i 0.349893 1.07686i
\(703\) −27.7128 −1.04521
\(704\) 0 0
\(705\) 9.00000 0.338960
\(706\) −12.8456 + 39.5347i −0.483450 + 1.48791i
\(707\) −2.42705 + 1.76336i −0.0912786 + 0.0663178i
\(708\) −9.70820 7.05342i −0.364857 0.265084i
\(709\) 7.72542 + 23.7764i 0.290134 + 0.892942i 0.984813 + 0.173621i \(0.0555468\pi\)
−0.694678 + 0.719321i \(0.744453\pi\)
\(710\) −6.42280 19.7673i −0.241043 0.741855i
\(711\) 16.8151 + 12.2169i 0.630616 + 0.458169i
\(712\) −4.20378 + 3.05422i −0.157543 + 0.114462i
\(713\) 0 0
\(714\) 20.7846 0.777844
\(715\) 0 0
\(716\) −18.0000 −0.672692
\(717\) 1.07047 3.29456i 0.0399773 0.123037i
\(718\) 4.85410 3.52671i 0.181153 0.131616i
\(719\) −4.85410 3.52671i −0.181027 0.131524i 0.493581 0.869700i \(-0.335688\pi\)
−0.674609 + 0.738176i \(0.735688\pi\)
\(720\) −3.09017 9.51057i −0.115164 0.354438i
\(721\) −2.14093 6.58911i −0.0797325 0.245391i
\(722\) −9.80881 7.12652i −0.365046 0.265222i
\(723\) 15.4138 11.1988i 0.573247 0.416488i
\(724\) 3.39919 10.4616i 0.126330 0.388803i
\(725\) 0 0
\(726\) 0 0
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) −3.21140 + 9.88367i −0.119022 + 0.366313i
\(729\) −10.5172 + 7.64121i −0.389527 + 0.283008i
\(730\) 0 0
\(731\) −18.5410 57.0634i −0.685764 2.11057i
\(732\) 2.67617 + 8.23639i 0.0989139 + 0.304426i
\(733\) −16.8151 12.2169i −0.621080 0.451241i 0.232219 0.972664i \(-0.425402\pi\)
−0.853299 + 0.521423i \(0.825402\pi\)
\(734\) 23.8214 17.3073i 0.879264 0.638823i
\(735\) −1.23607 + 3.80423i −0.0455931 + 0.140321i
\(736\) 0 0
\(737\) 0 0
\(738\) −42.0000 −1.54604
\(739\) −1.07047 + 3.29456i −0.0393777 + 0.121192i −0.968813 0.247793i \(-0.920295\pi\)
0.929435 + 0.368985i \(0.120295\pi\)
\(740\) −6.47214 + 4.70228i −0.237920 + 0.172859i
\(741\) −9.70820 7.05342i −0.356640 0.259114i
\(742\) −5.56231 17.1190i −0.204199 0.628459i
\(743\) −1.60570 4.94183i −0.0589074 0.181298i 0.917273 0.398259i \(-0.130386\pi\)
−0.976180 + 0.216961i \(0.930386\pi\)
\(744\) −11.2101 8.14459i −0.410981 0.298595i
\(745\) 15.4138 11.1988i 0.564720 0.410293i
\(746\) −7.41641 + 22.8254i −0.271534 + 0.835696i
\(747\) 6.92820 0.253490
\(748\) 0 0
\(749\) −3.00000 −0.109618
\(750\) −0.535233 + 1.64728i −0.0195440 + 0.0601501i
\(751\) 11.3262 8.22899i 0.413300 0.300280i −0.361636 0.932319i \(-0.617782\pi\)
0.774937 + 0.632039i \(0.217782\pi\)
\(752\) 36.4058 + 26.4503i 1.32758 + 0.964545i
\(753\) 0 0
\(754\) 0 0
\(755\) 16.8151 + 12.2169i 0.611964 + 0.444618i
\(756\) −7.00629 + 5.09037i −0.254816 + 0.185135i
\(757\) −0.618034 + 1.90211i −0.0224628 + 0.0691335i −0.961660 0.274246i \(-0.911572\pi\)
0.939197 + 0.343380i \(0.111572\pi\)
\(758\) 58.8897 2.13897
\(759\) 0 0
\(760\) −6.00000 −0.217643
\(761\) −10.7047 + 32.9456i −0.388044 + 1.19428i 0.546204 + 0.837652i \(0.316072\pi\)
−0.934248 + 0.356624i \(0.883928\pi\)
\(762\) 2.42705 1.76336i 0.0879228 0.0638796i
\(763\) 2.42705 + 1.76336i 0.0878651 + 0.0638378i
\(764\) −1.85410 5.70634i −0.0670791 0.206448i
\(765\) 4.28187 + 13.1782i 0.154811 + 0.476460i
\(766\) 33.6302 + 24.4338i 1.21511 + 0.882828i
\(767\) −33.6302 + 24.4338i −1.21432 + 0.882252i
\(768\) −5.87132 + 18.0701i −0.211863 + 0.652048i
\(769\) −27.7128 −0.999350 −0.499675 0.866213i \(-0.666547\pi\)
−0.499675 + 0.866213i \(0.666547\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 1.07047 3.29456i 0.0385269 0.118574i
\(773\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(774\) 24.2705 + 17.6336i 0.872385 + 0.633825i
\(775\) −2.47214 7.60845i −0.0888017 0.273304i
\(776\) −5.35233 16.4728i −0.192137 0.591338i
\(777\) −11.2101 8.14459i −0.402159 0.292186i
\(778\) 4.20378 3.05422i 0.150713 0.109499i
\(779\) −12.9787 + 39.9444i −0.465011 + 1.43116i
\(780\) −3.46410 −0.124035
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −16.1803 + 11.7557i −0.577869 + 0.419847i
\(785\) 3.23607 + 2.35114i 0.115500 + 0.0839158i
\(786\) 1.85410 + 5.70634i 0.0661336 + 0.203538i
\(787\) 8.02850 + 24.7092i 0.286185 + 0.880787i 0.986041 + 0.166503i \(0.0532475\pi\)
−0.699856 + 0.714284i \(0.746752\pi\)
\(788\) −8.40755 6.10844i −0.299507 0.217604i
\(789\) −19.6176 + 14.2530i −0.698406 + 0.507421i
\(790\) 5.56231 17.1190i 0.197898 0.609067i
\(791\) −10.3923 −0.369508
\(792\) 0 0
\(793\) 30.0000 1.06533
\(794\) −10.7047 + 32.9456i −0.379894 + 1.16919i
\(795\) −4.85410 + 3.52671i −0.172157 + 0.125080i
\(796\) 11.3262 + 8.22899i 0.401448 + 0.291669i
\(797\) −3.70820 11.4127i −0.131351 0.404258i 0.863653 0.504086i \(-0.168171\pi\)
−0.995005 + 0.0998284i \(0.968171\pi\)
\(798\) 3.21140 + 9.88367i 0.113682 + 0.349878i
\(799\) −50.4453 36.6507i −1.78463 1.29661i
\(800\) −4.20378 + 3.05422i −0.148626 + 0.107983i
\(801\) −1.85410 + 5.70634i −0.0655115 + 0.201624i
\(802\) −46.7654 −1.65134
\(803\) 0 0
\(804\) 5.00000 0.176336
\(805\) 0 0
\(806\) 38.8328 28.2137i 1.36783 0.993785i
\(807\) −12.1353 8.81678i −0.427181 0.310365i
\(808\) 0.927051 + 2.85317i 0.0326135 + 0.100374i
\(809\) 14.9865 + 46.1238i 0.526898 + 1.62163i 0.760531 + 0.649301i \(0.224939\pi\)
−0.233633 + 0.972325i \(0.575061\pi\)
\(810\) −1.40126 1.01807i −0.0492352 0.0357715i
\(811\) 5.60503 4.07230i 0.196819 0.142998i −0.485011 0.874508i \(-0.661184\pi\)
0.681830 + 0.731511i \(0.261184\pi\)
\(812\) 0 0
\(813\) −13.8564 −0.485965
\(814\) 0 0
\(815\) 19.0000 0.665541
\(816\) 10.7047 32.9456i 0.374738 1.15333i
\(817\) 24.2705 17.6336i 0.849118 0.616920i
\(818\) −7.28115 5.29007i −0.254580 0.184963i
\(819\) 3.70820 + 11.4127i 0.129575 + 0.398791i
\(820\) 3.74663 + 11.5309i 0.130838 + 0.402678i
\(821\) 23.8214 + 17.3073i 0.831372 + 0.604027i 0.919947 0.392042i \(-0.128231\pi\)
−0.0885749 + 0.996070i \(0.528231\pi\)
\(822\) −25.2227 + 18.3253i −0.879741 + 0.639169i
\(823\) 5.25329 16.1680i 0.183118 0.563580i −0.816793 0.576931i \(-0.804250\pi\)
0.999911 + 0.0133515i \(0.00425006\pi\)
\(824\) −6.92820 −0.241355
\(825\) 0 0
\(826\) 36.0000 1.25260
\(827\) −9.09896 + 28.0037i −0.316402 + 0.973785i 0.658772 + 0.752343i \(0.271076\pi\)
−0.975174 + 0.221442i \(0.928924\pi\)
\(828\) 0 0
\(829\) −23.4615 17.0458i −0.814851 0.592024i 0.100382 0.994949i \(-0.467994\pi\)
−0.915233 + 0.402925i \(0.867994\pi\)
\(830\) −1.85410 5.70634i −0.0643568 0.198070i
\(831\) 3.21140 + 9.88367i 0.111402 + 0.342861i
\(832\) 2.80252 + 2.03615i 0.0971598 + 0.0705907i
\(833\) 22.4201 16.2892i 0.776812 0.564387i
\(834\) −7.41641 + 22.8254i −0.256809 + 0.790377i
\(835\) −5.19615 −0.179820
\(836\) 0 0
\(837\) −40.0000 −1.38260
\(838\) −9.63420 + 29.6510i −0.332808 + 1.02428i
\(839\) 33.9787 24.6870i 1.17308 0.852289i 0.181702 0.983354i \(-0.441839\pi\)
0.991374 + 0.131064i \(0.0418395\pi\)
\(840\) −2.42705 1.76336i −0.0837412 0.0608416i
\(841\) −8.96149 27.5806i −0.309017 0.951057i
\(842\) 9.09896 + 28.0037i 0.313571 + 0.965072i
\(843\) 5.60503 + 4.07230i 0.193048 + 0.140257i
\(844\) 0 0
\(845\) 0.309017 0.951057i 0.0106305 0.0327173i
\(846\) 31.1769 1.07188
\(847\) 0 0
\(848\) −30.0000 −1.03020
\(849\) −1.60570 + 4.94183i −0.0551075 + 0.169603i
\(850\) 9.70820 7.05342i 0.332989 0.241930i
\(851\) 0 0
\(852\) 3.70820 + 11.4127i 0.127041 + 0.390992i
\(853\) 10.7047 + 32.9456i 0.366521 + 1.12803i 0.949023 + 0.315206i \(0.102074\pi\)
−0.582503 + 0.812829i \(0.697926\pi\)
\(854\) −21.0189 15.2711i −0.719251 0.522567i
\(855\) −5.60503 + 4.07230i −0.191688 + 0.139270i
\(856\) −0.927051 + 2.85317i −0.0316860 + 0.0975193i
\(857\) 10.3923 0.354994 0.177497 0.984121i \(-0.443200\pi\)
0.177497 + 0.984121i \(0.443200\pi\)
\(858\) 0 0
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) 2.67617 8.23639i 0.0912565 0.280859i
\(861\) −16.9894 + 12.3435i −0.578996 + 0.420665i
\(862\) −53.3951 38.7938i −1.81865 1.32132i
\(863\) 6.48936 + 19.9722i 0.220900 + 0.679861i 0.998682 + 0.0513266i \(0.0163449\pi\)
−0.777782 + 0.628535i \(0.783655\pi\)
\(864\) 8.02850 + 24.7092i 0.273135 + 0.840623i
\(865\) −8.40755 6.10844i −0.285865 0.207693i
\(866\) 44.8403 32.5784i 1.52373 1.10706i
\(867\) −9.57953 + 29.4828i −0.325338 + 1.00129i
\(868\) −13.8564 −0.470317
\(869\) 0 0
\(870\) 0 0
\(871\) 5.35233 16.4728i 0.181357 0.558159i
\(872\) 2.42705 1.76336i 0.0821903 0.0597148i
\(873\) −16.1803 11.7557i −0.547622 0.397870i
\(874\) 0 0
\(875\) −0.535233 1.64728i −0.0180942 0.0556882i
\(876\) 0 0
\(877\) −22.4201 + 16.2892i −0.757074 + 0.550047i −0.898012 0.439972i \(-0.854988\pi\)
0.140937 + 0.990019i \(0.454988\pi\)
\(878\) −14.8328 + 45.6507i −0.500583 + 1.54064i
\(879\) −6.92820 −0.233682
\(880\) 0 0
\(881\) −21.0000 −0.707508 −0.353754 0.935339i \(-0.615095\pi\)
−0.353754 + 0.935339i \(0.615095\pi\)
\(882\) −4.28187 + 13.1782i −0.144178 + 0.443734i
\(883\) 45.3050 32.9160i 1.52463 1.10771i 0.565503 0.824747i \(-0.308682\pi\)
0.959130 0.282964i \(-0.0913178\pi\)
\(884\) 19.4164 + 14.1068i 0.653044 + 0.474465i
\(885\) −3.70820 11.4127i −0.124650 0.383633i
\(886\) 8.02850 + 24.7092i 0.269723 + 0.830121i
\(887\) −26.6239 19.3434i −0.893943 0.649488i 0.0429597 0.999077i \(-0.486321\pi\)
−0.936903 + 0.349589i \(0.886321\pi\)
\(888\) −11.2101 + 8.14459i −0.376185 + 0.273315i
\(889\) −0.927051 + 2.85317i −0.0310923 + 0.0956922i
\(890\) 5.19615 0.174175
\(891\) 0 0
\(892\) −19.0000 −0.636167
\(893\) 9.63420 29.6510i 0.322396 0.992233i
\(894\) −26.6976 + 19.3969i −0.892900 + 0.648730i
\(895\) −14.5623 10.5801i −0.486764 0.353655i
\(896\) −6.48936 19.9722i −0.216794 0.667224i
\(897\) 0 0
\(898\) −21.0189 15.2711i −0.701409 0.509604i
\(899\) 0 0
\(900\) −0.618034 + 1.90211i −0.0206011 + 0.0634038i
\(901\) 41.5692 1.38487
\(902\) 0 0
\(903\) 15.0000 0.499169
\(904\) −3.21140 + 9.88367i −0.106810 + 0.328726i
\(905\) 8.89919 6.46564i 0.295819 0.214925i
\(906\) −29.1246 21.1603i −0.967600 0.703003i
\(907\) 5.25329 + 16.1680i 0.174433 + 0.536848i 0.999607 0.0280296i \(-0.00892326\pi\)
−0.825174 + 0.564878i \(0.808923\pi\)
\(908\) −5.88756 18.1201i −0.195386 0.601335i
\(909\) 2.80252 + 2.03615i 0.0929536 + 0.0675348i
\(910\) 8.40755 6.10844i 0.278708 0.202493i
\(911\) 1.85410 5.70634i 0.0614291 0.189059i −0.915632 0.402017i \(-0.868309\pi\)
0.977062 + 0.212957i \(0.0683094\pi\)
\(912\) 17.3205 0.573539
\(913\) 0 0
\(914\) 36.0000 1.19077
\(915\) −2.67617 + 8.23639i −0.0884713 + 0.272287i
\(916\) −5.66312 + 4.11450i −0.187115 + 0.135947i
\(917\) −4.85410 3.52671i −0.160297 0.116462i
\(918\) −18.5410 57.0634i −0.611945 1.88337i
\(919\) −11.7751 36.2401i −0.388426 1.19545i −0.933965 0.357366i \(-0.883675\pi\)
0.545539 0.838086i \(-0.316325\pi\)
\(920\) 0 0
\(921\) 8.40755 6.10844i 0.277038 0.201280i
\(922\) −6.48936 + 19.9722i −0.213716 + 0.657749i
\(923\) 41.5692 1.36827
\(924\) 0 0
\(925\) −8.00000 −0.263038
\(926\) −21.9446 + 67.5384i −0.721143 + 2.21945i
\(927\) −6.47214 + 4.70228i −0.212573 + 0.154443i
\(928\) 0 0
\(929\) 5.56231 + 17.1190i 0.182493 + 0.561657i 0.999896 0.0144098i \(-0.00458693\pi\)
−0.817403 + 0.576066i \(0.804587\pi\)
\(930\) 4.28187 + 13.1782i 0.140408 + 0.432131i
\(931\) 11.2101 + 8.14459i 0.367395 + 0.266928i
\(932\) −2.80252 + 2.03615i −0.0917995 + 0.0666962i
\(933\) 1.85410 5.70634i 0.0607006 0.186817i
\(934\) −5.19615 −0.170023
\(935\) 0 0
\(936\) 12.0000 0.392232
\(937\) 7.49326 23.0619i 0.244794 0.753399i −0.750876 0.660443i \(-0.770368\pi\)
0.995670 0.0929560i \(-0.0296316\pi\)
\(938\) −12.1353 + 8.81678i −0.396230 + 0.287878i
\(939\) 8.09017 + 5.87785i 0.264013 + 0.191816i
\(940\) −2.78115 8.55951i −0.0907112 0.279180i
\(941\) 15.5218 + 47.7711i 0.505995 + 1.55729i 0.799091 + 0.601209i \(0.205314\pi\)
−0.293097 + 0.956083i \(0.594686\pi\)
\(942\) −5.60503 4.07230i −0.182622 0.132683i
\(943\) 0 0
\(944\) 18.5410 57.0634i 0.603459 1.85726i
\(945\) −8.66025 −0.281718
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) −3.21140 + 9.88367i −0.104301 + 0.321007i
\(949\) 0 0
\(950\) 4.85410 + 3.52671i 0.157488 + 0.114422i
\(951\) 1.85410 + 5.70634i 0.0601234 + 0.185041i
\(952\) 6.42280 + 19.7673i 0.208164 + 0.640663i
\(953\) 44.8403 + 32.5784i 1.45252 + 1.05532i 0.985235 + 0.171210i \(0.0547676\pi\)
0.467284 + 0.884107i \(0.345232\pi\)
\(954\) −16.8151 + 12.2169i −0.544409 + 0.395536i
\(955\) 1.85410 5.70634i 0.0599973 0.184653i
\(956\) −3.46410 −0.112037
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) 9.63420 29.6510i 0.311104 0.957481i
\(960\) −0.809017 + 0.587785i −0.0261109 + 0.0189707i
\(961\) −26.6976 19.3969i −0.861212 0.625707i
\(962\) −14.8328 45.6507i −0.478229 1.47184i
\(963\) 1.07047 + 3.29456i 0.0344953 + 0.106166i
\(964\) −15.4138 11.1988i −0.496446 0.360689i
\(965\) 2.80252 2.03615i 0.0902162 0.0655459i
\(966\) 0 0
\(967\) −38.1051 −1.22538 −0.612689 0.790324i \(-0.709912\pi\)
−0.612689 + 0.790324i \(0.709912\pi\)
\(968\) 0 0
\(969\) −24.0000 −0.770991
\(970\) −5.35233 + 16.4728i −0.171853 + 0.528909i
\(971\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(972\) 12.9443 + 9.40456i 0.415188 + 0.301652i
\(973\) −7.41641 22.8254i −0.237759 0.731747i
\(974\) 10.7047 + 32.9456i 0.343000 + 1.05564i
\(975\) −2.80252 2.03615i −0.0897524 0.0652089i
\(976\) −35.0315 + 25.4518i −1.12133 + 0.814694i
\(977\) −7.41641 + 22.8254i −0.237272 + 0.730248i 0.759540 + 0.650461i \(0.225424\pi\)
−0.996812 + 0.0797873i \(0.974576\pi\)
\(978\) −32.9090 −1.05231
\(979\) 0 0
\(980\) 4.00000 0.127775
\(981\) 1.07047 3.29456i 0.0341774 0.105187i
\(982\) −33.9787 + 24.6870i −1.08430 + 0.787793i
\(983\) 2.42705 + 1.76336i 0.0774109 + 0.0562423i 0.625818 0.779969i \(-0.284765\pi\)
−0.548407 + 0.836212i \(0.684765\pi\)
\(984\) 6.48936 + 19.9722i 0.206873 + 0.636690i
\(985\) −3.21140 9.88367i −0.102324 0.314920i
\(986\) 0 0
\(987\) 12.6113 9.16267i 0.401423 0.291651i
\(988\) −3.70820 + 11.4127i −0.117974 + 0.363086i
\(989\) 0 0
\(990\) 0 0
\(991\) −2.00000 −0.0635321 −0.0317660 0.999495i \(-0.510113\pi\)
−0.0317660 + 0.999495i \(0.510113\pi\)
\(992\) −12.8456 + 39.5347i −0.407848 + 1.25523i
\(993\) −27.5066 + 19.9847i −0.872895 + 0.634195i
\(994\) −29.1246 21.1603i −0.923777 0.671163i
\(995\) 4.32624 + 13.3148i 0.137151 + 0.422107i
\(996\) 1.07047 + 3.29456i 0.0339190 + 0.104392i
\(997\) −36.4327 26.4699i −1.15384 0.838311i −0.164850 0.986319i \(-0.552714\pi\)
−0.988986 + 0.148008i \(0.952714\pi\)
\(998\) −53.2478 + 38.6868i −1.68553 + 1.22461i
\(999\) −12.3607 + 38.0423i −0.391075 + 1.20360i
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 605.2.g.i.251.1 8
11.2 odd 10 inner 605.2.g.i.366.1 8
11.3 even 5 inner 605.2.g.i.81.2 8
11.4 even 5 605.2.a.e.1.1 2
11.5 even 5 inner 605.2.g.i.511.1 8
11.6 odd 10 inner 605.2.g.i.511.2 8
11.7 odd 10 605.2.a.e.1.2 yes 2
11.8 odd 10 inner 605.2.g.i.81.1 8
11.9 even 5 inner 605.2.g.i.366.2 8
11.10 odd 2 inner 605.2.g.i.251.2 8
33.26 odd 10 5445.2.a.u.1.2 2
33.29 even 10 5445.2.a.u.1.1 2
44.7 even 10 9680.2.a.bu.1.2 2
44.15 odd 10 9680.2.a.bu.1.1 2
55.4 even 10 3025.2.a.l.1.2 2
55.29 odd 10 3025.2.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.e.1.1 2 11.4 even 5
605.2.a.e.1.2 yes 2 11.7 odd 10
605.2.g.i.81.1 8 11.8 odd 10 inner
605.2.g.i.81.2 8 11.3 even 5 inner
605.2.g.i.251.1 8 1.1 even 1 trivial
605.2.g.i.251.2 8 11.10 odd 2 inner
605.2.g.i.366.1 8 11.2 odd 10 inner
605.2.g.i.366.2 8 11.9 even 5 inner
605.2.g.i.511.1 8 11.5 even 5 inner
605.2.g.i.511.2 8 11.6 odd 10 inner
3025.2.a.l.1.1 2 55.29 odd 10
3025.2.a.l.1.2 2 55.4 even 10
5445.2.a.u.1.1 2 33.29 even 10
5445.2.a.u.1.2 2 33.26 odd 10
9680.2.a.bu.1.1 2 44.15 odd 10
9680.2.a.bu.1.2 2 44.7 even 10