Properties

Label 105.2.x.a.53.6
Level $105$
Weight $2$
Character 105.53
Analytic conductor $0.838$
Analytic rank $0$
Dimension $48$
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] = [105,2,Mod(2,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.x (of order \(12\), 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: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 53.6
Character \(\chi\) \(=\) 105.53
Dual form 105.2.x.a.2.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0799329 + 0.298314i) q^{2} +(1.29105 + 1.15464i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.596180 - 2.15513i) q^{5} +(-0.447643 + 0.292843i) q^{6} +(-2.46856 - 0.951942i) q^{7} +(-0.852694 + 0.852694i) q^{8} +(0.333606 + 2.98139i) q^{9} +O(q^{10})\) \(q+(-0.0799329 + 0.298314i) q^{2} +(1.29105 + 1.15464i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.596180 - 2.15513i) q^{5} +(-0.447643 + 0.292843i) q^{6} +(-2.46856 - 0.951942i) q^{7} +(-0.852694 + 0.852694i) q^{8} +(0.333606 + 2.98139i) q^{9} +(0.690558 - 0.00558322i) q^{10} +(-0.660315 - 0.381233i) q^{11} +(1.02994 + 3.13400i) q^{12} +(-2.27077 - 2.27077i) q^{13} +(0.481297 - 0.660315i) q^{14} +(1.71870 - 3.47074i) q^{15} +(1.71841 + 2.97637i) q^{16} +(4.69471 - 1.25794i) q^{17} +(-0.916057 - 0.138792i) q^{18} +(-1.41761 + 0.818455i) q^{19} +(1.06898 - 4.12252i) q^{20} +(-2.08788 - 4.07931i) q^{21} +(0.166508 - 0.166508i) q^{22} +(-7.39003 - 1.98015i) q^{23} +(-2.08542 + 0.116312i) q^{24} +(-4.28914 + 2.56969i) q^{25} +(0.858909 - 0.495891i) q^{26} +(-3.01174 + 4.23432i) q^{27} +(-3.16523 - 3.92102i) q^{28} +4.94251 q^{29} +(0.897990 + 0.790139i) q^{30} +(2.96413 - 5.13403i) q^{31} +(-3.35485 + 0.898930i) q^{32} +(-0.412310 - 1.25462i) q^{33} +1.50105i q^{34} +(-0.579845 + 5.88760i) q^{35} +(-2.28894 + 5.23535i) q^{36} +(3.41587 + 0.915280i) q^{37} +(-0.130843 - 0.488313i) q^{38} +(-0.309745 - 5.55358i) q^{39} +(2.34602 + 1.32930i) q^{40} -4.35963i q^{41} +(1.38380 - 0.296773i) q^{42} +(2.69037 + 2.69037i) q^{43} +(-0.726104 - 1.25765i) q^{44} +(6.22639 - 2.49641i) q^{45} +(1.18141 - 2.04627i) q^{46} +(-1.10971 + 4.14148i) q^{47} +(-1.21809 + 5.82678i) q^{48} +(5.18761 + 4.69986i) q^{49} +(-0.423730 - 1.48491i) q^{50} +(7.51357 + 3.79665i) q^{51} +(-1.58304 - 5.90798i) q^{52} +(1.79889 + 6.71354i) q^{53} +(-1.02242 - 1.23690i) q^{54} +(-0.427939 + 1.65035i) q^{55} +(2.91664 - 1.29321i) q^{56} +(-2.77522 - 0.580162i) q^{57} +(-0.395069 + 1.47442i) q^{58} +(-3.84501 + 6.65975i) q^{59} +(6.14013 - 4.08808i) q^{60} +(-2.19699 - 3.80529i) q^{61} +(1.29462 + 1.29462i) q^{62} +(2.01458 - 7.67733i) q^{63} +5.80098i q^{64} +(-3.54000 + 6.24757i) q^{65} +(0.407227 - 0.0227126i) q^{66} +(0.0126297 + 0.0471345i) q^{67} +(8.94164 + 2.39591i) q^{68} +(-7.25451 - 11.0893i) q^{69} +(-1.71000 - 0.643588i) q^{70} +12.4172i q^{71} +(-2.82668 - 2.25775i) q^{72} +(-1.34043 + 0.359168i) q^{73} +(-0.546081 + 0.945840i) q^{74} +(-8.50455 - 1.63483i) q^{75} -3.11769 q^{76} +(1.26712 + 1.56968i) q^{77} +(1.68147 + 0.351513i) q^{78} +(3.66808 - 2.11777i) q^{79} +(5.38997 - 5.47784i) q^{80} +(-8.77741 + 1.98922i) q^{81} +(1.30054 + 0.348478i) q^{82} +(5.05351 - 5.05351i) q^{83} +(0.440911 - 8.71692i) q^{84} +(-5.50993 - 9.36774i) q^{85} +(-1.01762 + 0.587525i) q^{86} +(6.38101 + 5.70683i) q^{87} +(0.888122 - 0.237971i) q^{88} +(0.453600 + 0.785658i) q^{89} +(0.247020 + 2.05696i) q^{90} +(3.44389 + 7.76716i) q^{91} +(-10.3038 - 10.3038i) q^{92} +(9.75480 - 3.20576i) q^{93} +(-1.14676 - 0.662081i) q^{94} +(2.60902 + 2.56717i) q^{95} +(-5.36921 - 2.71309i) q^{96} +(3.73061 - 3.73061i) q^{97} +(-1.81669 + 1.17186i) q^{98} +(0.916321 - 2.09584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7} - 8 q^{10} - 10 q^{12} - 16 q^{13} + 4 q^{15} - 8 q^{16} + 14 q^{18} - 28 q^{21} - 8 q^{22} + 4 q^{25} + 40 q^{27} - 60 q^{28} + 40 q^{30} - 24 q^{31} - 4 q^{33} + 8 q^{36} + 4 q^{37} - 16 q^{40} + 14 q^{42} + 16 q^{43} + 40 q^{45} - 32 q^{46} + 44 q^{48} + 8 q^{51} + 36 q^{52} - 40 q^{55} - 88 q^{57} + 56 q^{58} - 50 q^{60} - 8 q^{61} + 44 q^{63} + 76 q^{66} + 12 q^{67} + 140 q^{70} - 34 q^{72} + 52 q^{73} + 6 q^{75} + 64 q^{76} - 120 q^{78} + 20 q^{81} + 104 q^{82} - 24 q^{85} - 46 q^{87} - 84 q^{90} + 72 q^{91} - 44 q^{93} + 12 q^{96} - 120 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0799329 + 0.298314i −0.0565211 + 0.210940i −0.988411 0.151802i \(-0.951492\pi\)
0.931890 + 0.362741i \(0.118159\pi\)
\(3\) 1.29105 + 1.15464i 0.745386 + 0.666633i
\(4\) 1.64945 + 0.952310i 0.824725 + 0.476155i
\(5\) −0.596180 2.15513i −0.266620 0.963802i
\(6\) −0.447643 + 0.292843i −0.182749 + 0.119553i
\(7\) −2.46856 0.951942i −0.933029 0.359800i
\(8\) −0.852694 + 0.852694i −0.301473 + 0.301473i
\(9\) 0.333606 + 2.98139i 0.111202 + 0.993798i
\(10\) 0.690558 0.00558322i 0.218374 0.00176557i
\(11\) −0.660315 0.381233i −0.199092 0.114946i 0.397140 0.917758i \(-0.370003\pi\)
−0.596232 + 0.802812i \(0.703336\pi\)
\(12\) 1.02994 + 3.13400i 0.297318 + 0.904708i
\(13\) −2.27077 2.27077i −0.629797 0.629797i 0.318220 0.948017i \(-0.396915\pi\)
−0.948017 + 0.318220i \(0.896915\pi\)
\(14\) 0.481297 0.660315i 0.128632 0.176477i
\(15\) 1.71870 3.47074i 0.443767 0.896142i
\(16\) 1.71841 + 2.97637i 0.429602 + 0.744092i
\(17\) 4.69471 1.25794i 1.13864 0.305096i 0.360233 0.932862i \(-0.382697\pi\)
0.778402 + 0.627766i \(0.216030\pi\)
\(18\) −0.916057 0.138792i −0.215917 0.0327136i
\(19\) −1.41761 + 0.818455i −0.325221 + 0.187767i −0.653717 0.756739i \(-0.726791\pi\)
0.328496 + 0.944505i \(0.393458\pi\)
\(20\) 1.06898 4.12252i 0.239031 0.921823i
\(21\) −2.08788 4.07931i −0.455613 0.890178i
\(22\) 0.166508 0.166508i 0.0354996 0.0354996i
\(23\) −7.39003 1.98015i −1.54093 0.412890i −0.614363 0.789024i \(-0.710587\pi\)
−0.926566 + 0.376133i \(0.877253\pi\)
\(24\) −2.08542 + 0.116312i −0.425685 + 0.0237422i
\(25\) −4.28914 + 2.56969i −0.857828 + 0.513937i
\(26\) 0.858909 0.495891i 0.168446 0.0972523i
\(27\) −3.01174 + 4.23432i −0.579610 + 0.814894i
\(28\) −3.16523 3.92102i −0.598172 0.741003i
\(29\) 4.94251 0.917801 0.458900 0.888488i \(-0.348243\pi\)
0.458900 + 0.888488i \(0.348243\pi\)
\(30\) 0.897990 + 0.790139i 0.163950 + 0.144259i
\(31\) 2.96413 5.13403i 0.532374 0.922099i −0.466911 0.884304i \(-0.654633\pi\)
0.999286 0.0377949i \(-0.0120334\pi\)
\(32\) −3.35485 + 0.898930i −0.593060 + 0.158910i
\(33\) −0.412310 1.25462i −0.0717740 0.218401i
\(34\) 1.50105i 0.257428i
\(35\) −0.579845 + 5.88760i −0.0980117 + 0.995185i
\(36\) −2.28894 + 5.23535i −0.381491 + 0.872559i
\(37\) 3.41587 + 0.915280i 0.561566 + 0.150471i 0.528426 0.848980i \(-0.322783\pi\)
0.0331401 + 0.999451i \(0.489449\pi\)
\(38\) −0.130843 0.488313i −0.0212255 0.0792148i
\(39\) −0.309745 5.55358i −0.0495990 0.889285i
\(40\) 2.34602 + 1.32930i 0.370939 + 0.210181i
\(41\) 4.35963i 0.680860i −0.940270 0.340430i \(-0.889427\pi\)
0.940270 0.340430i \(-0.110573\pi\)
\(42\) 1.38380 0.296773i 0.213526 0.0457930i
\(43\) 2.69037 + 2.69037i 0.410277 + 0.410277i 0.881835 0.471558i \(-0.156308\pi\)
−0.471558 + 0.881835i \(0.656308\pi\)
\(44\) −0.726104 1.25765i −0.109464 0.189598i
\(45\) 6.22639 2.49641i 0.928175 0.372143i
\(46\) 1.18141 2.04627i 0.174190 0.301706i
\(47\) −1.10971 + 4.14148i −0.161867 + 0.604097i 0.836552 + 0.547888i \(0.184568\pi\)
−0.998419 + 0.0562089i \(0.982099\pi\)
\(48\) −1.21809 + 5.82678i −0.175817 + 0.841023i
\(49\) 5.18761 + 4.69986i 0.741088 + 0.671408i
\(50\) −0.423730 1.48491i −0.0599244 0.209998i
\(51\) 7.51357 + 3.79665i 1.05211 + 0.531637i
\(52\) −1.58304 5.90798i −0.219528 0.819290i
\(53\) 1.79889 + 6.71354i 0.247096 + 0.922176i 0.972318 + 0.233661i \(0.0750705\pi\)
−0.725222 + 0.688515i \(0.758263\pi\)
\(54\) −1.02242 1.23690i −0.139133 0.168321i
\(55\) −0.427939 + 1.65035i −0.0577032 + 0.222533i
\(56\) 2.91664 1.29321i 0.389753 0.172813i
\(57\) −2.77522 0.580162i −0.367587 0.0768444i
\(58\) −0.395069 + 1.47442i −0.0518751 + 0.193601i
\(59\) −3.84501 + 6.65975i −0.500577 + 0.867026i 0.499422 + 0.866359i \(0.333546\pi\)
−1.00000 0.000666931i \(0.999788\pi\)
\(60\) 6.14013 4.08808i 0.792688 0.527769i
\(61\) −2.19699 3.80529i −0.281295 0.487218i 0.690409 0.723420i \(-0.257431\pi\)
−0.971704 + 0.236202i \(0.924097\pi\)
\(62\) 1.29462 + 1.29462i 0.164417 + 0.164417i
\(63\) 2.01458 7.67733i 0.253814 0.967253i
\(64\) 5.80098i 0.725122i
\(65\) −3.54000 + 6.24757i −0.439083 + 0.774916i
\(66\) 0.407227 0.0227126i 0.0501261 0.00279573i
\(67\) 0.0126297 + 0.0471345i 0.00154296 + 0.00575840i 0.966693 0.255939i \(-0.0823845\pi\)
−0.965150 + 0.261697i \(0.915718\pi\)
\(68\) 8.94164 + 2.39591i 1.08433 + 0.290546i
\(69\) −7.25451 11.0893i −0.873341 1.33500i
\(70\) −1.71000 0.643588i −0.204384 0.0769235i
\(71\) 12.4172i 1.47365i 0.676082 + 0.736826i \(0.263676\pi\)
−0.676082 + 0.736826i \(0.736324\pi\)
\(72\) −2.82668 2.25775i −0.333127 0.266079i
\(73\) −1.34043 + 0.359168i −0.156886 + 0.0420374i −0.336407 0.941717i \(-0.609212\pi\)
0.179521 + 0.983754i \(0.442545\pi\)
\(74\) −0.546081 + 0.945840i −0.0634806 + 0.109952i
\(75\) −8.50455 1.63483i −0.982021 0.188774i
\(76\) −3.11769 −0.357624
\(77\) 1.26712 + 1.56968i 0.144401 + 0.178882i
\(78\) 1.68147 + 0.351513i 0.190389 + 0.0398010i
\(79\) 3.66808 2.11777i 0.412692 0.238268i −0.279254 0.960217i \(-0.590087\pi\)
0.691946 + 0.721950i \(0.256754\pi\)
\(80\) 5.38997 5.47784i 0.602617 0.612441i
\(81\) −8.77741 + 1.98922i −0.975268 + 0.221025i
\(82\) 1.30054 + 0.348478i 0.143620 + 0.0384830i
\(83\) 5.05351 5.05351i 0.554695 0.554695i −0.373097 0.927792i \(-0.621704\pi\)
0.927792 + 0.373097i \(0.121704\pi\)
\(84\) 0.440911 8.71692i 0.0481074 0.951094i
\(85\) −5.50993 9.36774i −0.597635 1.01607i
\(86\) −1.01762 + 0.587525i −0.109733 + 0.0633544i
\(87\) 6.38101 + 5.70683i 0.684116 + 0.611836i
\(88\) 0.888122 0.237971i 0.0946741 0.0253678i
\(89\) 0.453600 + 0.785658i 0.0480815 + 0.0832796i 0.889065 0.457782i \(-0.151356\pi\)
−0.840983 + 0.541061i \(0.818023\pi\)
\(90\) 0.247020 + 2.05696i 0.0260382 + 0.216823i
\(91\) 3.44389 + 7.76716i 0.361018 + 0.814220i
\(92\) −10.3038 10.3038i −1.07424 1.07424i
\(93\) 9.75480 3.20576i 1.01153 0.332422i
\(94\) −1.14676 0.662081i −0.118279 0.0682884i
\(95\) 2.60902 + 2.56717i 0.267680 + 0.263386i
\(96\) −5.36921 2.71309i −0.547993 0.276904i
\(97\) 3.73061 3.73061i 0.378786 0.378786i −0.491878 0.870664i \(-0.663689\pi\)
0.870664 + 0.491878i \(0.163689\pi\)
\(98\) −1.81669 + 1.17186i −0.183514 + 0.118376i
\(99\) 0.916321 2.09584i 0.0920937 0.210640i
\(100\) −9.52185 + 0.153980i −0.952185 + 0.0153980i
\(101\) −16.4444 9.49420i −1.63628 0.944708i −0.982098 0.188373i \(-0.939679\pi\)
−0.654185 0.756335i \(-0.726988\pi\)
\(102\) −1.73317 + 1.93792i −0.171610 + 0.191883i
\(103\) −3.26921 + 12.2009i −0.322125 + 1.20219i 0.595046 + 0.803692i \(0.297134\pi\)
−0.917171 + 0.398494i \(0.869533\pi\)
\(104\) 3.87254 0.379733
\(105\) −7.54667 + 6.93165i −0.736480 + 0.676460i
\(106\) −2.14653 −0.208490
\(107\) 0.564395 2.10635i 0.0545621 0.203629i −0.933264 0.359192i \(-0.883052\pi\)
0.987826 + 0.155563i \(0.0497191\pi\)
\(108\) −9.00009 + 4.11618i −0.866034 + 0.396079i
\(109\) −2.04357 1.17986i −0.195739 0.113010i 0.398928 0.916982i \(-0.369382\pi\)
−0.594666 + 0.803973i \(0.702716\pi\)
\(110\) −0.458114 0.259577i −0.0436795 0.0247497i
\(111\) 3.35323 + 5.12578i 0.318275 + 0.486517i
\(112\) −1.40867 8.98318i −0.133107 0.848831i
\(113\) 11.9386 11.9386i 1.12309 1.12309i 0.131814 0.991274i \(-0.457920\pi\)
0.991274 0.131814i \(-0.0420801\pi\)
\(114\) 0.394902 0.781512i 0.0369859 0.0731953i
\(115\) 0.138311 + 17.1070i 0.0128976 + 1.59523i
\(116\) 8.15242 + 4.70680i 0.756933 + 0.437015i
\(117\) 6.01250 7.52759i 0.555856 0.695925i
\(118\) −1.67935 1.67935i −0.154597 0.154597i
\(119\) −12.7867 1.36378i −1.17215 0.125017i
\(120\) 1.49396 + 4.42501i 0.136379 + 0.403946i
\(121\) −5.20932 9.02281i −0.473575 0.820256i
\(122\) 1.31078 0.351223i 0.118673 0.0317983i
\(123\) 5.03381 5.62849i 0.453884 0.507504i
\(124\) 9.77837 5.64555i 0.878124 0.506985i
\(125\) 8.09510 + 7.71164i 0.724048 + 0.689750i
\(126\) 2.12922 + 1.21465i 0.189686 + 0.108210i
\(127\) 4.46126 4.46126i 0.395873 0.395873i −0.480901 0.876775i \(-0.659691\pi\)
0.876775 + 0.480901i \(0.159691\pi\)
\(128\) −8.44022 2.26155i −0.746017 0.199895i
\(129\) 0.366982 + 6.57980i 0.0323109 + 0.579319i
\(130\) −1.58077 1.55542i −0.138643 0.136419i
\(131\) −1.86149 + 1.07473i −0.162639 + 0.0938999i −0.579111 0.815249i \(-0.696600\pi\)
0.416471 + 0.909149i \(0.363267\pi\)
\(132\) 0.514699 2.46207i 0.0447988 0.214296i
\(133\) 4.27857 0.670931i 0.370999 0.0581771i
\(134\) −0.0150704 −0.00130188
\(135\) 10.9210 + 3.96626i 0.939932 + 0.341362i
\(136\) −2.93051 + 5.07580i −0.251289 + 0.435246i
\(137\) 8.51678 2.28207i 0.727638 0.194970i 0.124061 0.992275i \(-0.460408\pi\)
0.603577 + 0.797305i \(0.293742\pi\)
\(138\) 3.88797 1.27772i 0.330966 0.108767i
\(139\) 10.3626i 0.878941i 0.898257 + 0.439471i \(0.144834\pi\)
−0.898257 + 0.439471i \(0.855166\pi\)
\(140\) −6.56324 + 9.15910i −0.554695 + 0.774085i
\(141\) −6.21461 + 4.06553i −0.523364 + 0.342380i
\(142\) −3.70423 0.992544i −0.310852 0.0832925i
\(143\) 0.633730 + 2.36511i 0.0529951 + 0.197780i
\(144\) −8.30046 + 6.11618i −0.691705 + 0.509682i
\(145\) −2.94663 10.6517i −0.244704 0.884578i
\(146\) 0.428578i 0.0354694i
\(147\) 1.27081 + 12.0576i 0.104814 + 0.994492i
\(148\) 4.76267 + 4.76267i 0.391489 + 0.391489i
\(149\) −8.72716 15.1159i −0.714957 1.23834i −0.962976 0.269586i \(-0.913113\pi\)
0.248019 0.968755i \(-0.420220\pi\)
\(150\) 1.16749 2.40635i 0.0953248 0.196477i
\(151\) 7.60786 13.1772i 0.619119 1.07235i −0.370528 0.928821i \(-0.620823\pi\)
0.989647 0.143524i \(-0.0458434\pi\)
\(152\) 0.510892 1.90668i 0.0414388 0.154652i
\(153\) 5.31661 + 13.5771i 0.429823 + 1.09765i
\(154\) −0.569541 + 0.252530i −0.0458949 + 0.0203494i
\(155\) −12.8316 3.32727i −1.03066 0.267253i
\(156\) 4.77782 9.45533i 0.382532 0.757032i
\(157\) 2.36469 + 8.82516i 0.188723 + 0.704324i 0.993803 + 0.111158i \(0.0354558\pi\)
−0.805080 + 0.593167i \(0.797878\pi\)
\(158\) 0.338559 + 1.26352i 0.0269343 + 0.100520i
\(159\) −5.42929 + 10.7446i −0.430570 + 0.852100i
\(160\) 3.93740 + 6.69421i 0.311279 + 0.529223i
\(161\) 16.3578 + 11.9230i 1.28917 + 0.939665i
\(162\) 0.108192 2.77743i 0.00850040 0.218215i
\(163\) 0.700710 2.61508i 0.0548838 0.204829i −0.933039 0.359775i \(-0.882854\pi\)
0.987923 + 0.154946i \(0.0495202\pi\)
\(164\) 4.15172 7.19099i 0.324195 0.561522i
\(165\) −2.45805 + 1.63656i −0.191359 + 0.127406i
\(166\) 1.10359 + 1.91147i 0.0856551 + 0.148359i
\(167\) −3.85551 3.85551i −0.298348 0.298348i 0.542018 0.840367i \(-0.317660\pi\)
−0.840367 + 0.542018i \(0.817660\pi\)
\(168\) 5.25872 + 1.69808i 0.405719 + 0.131010i
\(169\) 2.68725i 0.206712i
\(170\) 3.23495 0.894896i 0.248109 0.0686354i
\(171\) −2.91306 3.95340i −0.222767 0.302324i
\(172\) 1.87556 + 6.99969i 0.143010 + 0.533721i
\(173\) −1.27815 0.342481i −0.0971763 0.0260383i 0.209903 0.977722i \(-0.432685\pi\)
−0.307080 + 0.951684i \(0.599352\pi\)
\(174\) −2.21248 + 1.44738i −0.167727 + 0.109726i
\(175\) 13.0342 2.26043i 0.985293 0.170872i
\(176\) 2.62045i 0.197524i
\(177\) −12.6537 + 4.15845i −0.951111 + 0.312568i
\(178\) −0.270630 + 0.0725151i −0.0202846 + 0.00543524i
\(179\) −0.120836 + 0.209294i −0.00903168 + 0.0156433i −0.870506 0.492158i \(-0.836208\pi\)
0.861474 + 0.507801i \(0.169542\pi\)
\(180\) 12.6475 + 1.81175i 0.942687 + 0.135040i
\(181\) 18.6864 1.38895 0.694475 0.719517i \(-0.255637\pi\)
0.694475 + 0.719517i \(0.255637\pi\)
\(182\) −2.59233 + 0.406508i −0.192156 + 0.0301324i
\(183\) 1.55734 7.44955i 0.115122 0.550686i
\(184\) 7.98990 4.61297i 0.589023 0.340073i
\(185\) −0.0639312 7.90730i −0.00470032 0.581357i
\(186\) 0.176594 + 3.16624i 0.0129485 + 0.232160i
\(187\) −3.57956 0.959140i −0.261763 0.0701393i
\(188\) −5.77437 + 5.77437i −0.421140 + 0.421140i
\(189\) 11.4655 7.58568i 0.833992 0.551777i
\(190\) −0.974370 + 0.573106i −0.0706882 + 0.0415775i
\(191\) 12.3330 7.12049i 0.892388 0.515220i 0.0176651 0.999844i \(-0.494377\pi\)
0.874723 + 0.484624i \(0.161043\pi\)
\(192\) −6.69805 + 7.48934i −0.483390 + 0.540496i
\(193\) −6.58385 + 1.76414i −0.473916 + 0.126985i −0.487868 0.872917i \(-0.662225\pi\)
0.0139523 + 0.999903i \(0.495559\pi\)
\(194\) 0.814694 + 1.41109i 0.0584916 + 0.101310i
\(195\) −11.7840 + 3.97848i −0.843871 + 0.284905i
\(196\) 4.08099 + 12.6924i 0.291499 + 0.906599i
\(197\) 7.65626 + 7.65626i 0.545486 + 0.545486i 0.925132 0.379646i \(-0.123954\pi\)
−0.379646 + 0.925132i \(0.623954\pi\)
\(198\) 0.551974 + 0.440878i 0.0392271 + 0.0313318i
\(199\) −14.1855 8.19000i −1.00558 0.580573i −0.0956874 0.995411i \(-0.530505\pi\)
−0.909895 + 0.414838i \(0.863838\pi\)
\(200\) 1.46617 5.84848i 0.103674 0.413550i
\(201\) −0.0381180 + 0.0754356i −0.00268864 + 0.00532082i
\(202\) 4.14670 4.14670i 0.291761 0.291761i
\(203\) −12.2009 4.70498i −0.856335 0.330225i
\(204\) 8.77767 + 13.4176i 0.614560 + 0.939421i
\(205\) −9.39556 + 2.59913i −0.656214 + 0.181531i
\(206\) −3.37836 1.95050i −0.235382 0.135898i
\(207\) 3.43826 22.6932i 0.238975 1.57729i
\(208\) 2.85654 10.6607i 0.198065 0.739189i
\(209\) 1.24809 0.0863321
\(210\) −1.46458 2.80534i −0.101066 0.193587i
\(211\) −25.5028 −1.75568 −0.877842 0.478950i \(-0.841018\pi\)
−0.877842 + 0.478950i \(0.841018\pi\)
\(212\) −3.42620 + 12.7867i −0.235312 + 0.878197i
\(213\) −14.3374 + 16.0312i −0.982385 + 1.09844i
\(214\) 0.583239 + 0.336733i 0.0398694 + 0.0230186i
\(215\) 4.19414 7.40203i 0.286038 0.504814i
\(216\) −1.04248 6.17867i −0.0709320 0.420405i
\(217\) −12.2044 + 9.85200i −0.828492 + 0.668797i
\(218\) 0.515316 0.515316i 0.0349016 0.0349016i
\(219\) −2.14527 1.08402i −0.144964 0.0732510i
\(220\) −2.27750 + 2.31463i −0.153549 + 0.156052i
\(221\) −13.5171 7.80410i −0.909258 0.524960i
\(222\) −1.79712 + 0.590596i −0.120615 + 0.0396382i
\(223\) −15.4546 15.4546i −1.03491 1.03491i −0.999368 0.0355465i \(-0.988683\pi\)
−0.0355465 0.999368i \(-0.511317\pi\)
\(224\) 9.13740 + 0.974557i 0.610518 + 0.0651154i
\(225\) −9.09213 11.9303i −0.606142 0.795356i
\(226\) 2.60716 + 4.51573i 0.173426 + 0.300382i
\(227\) −12.4101 + 3.32527i −0.823686 + 0.220706i −0.645957 0.763374i \(-0.723542\pi\)
−0.177728 + 0.984080i \(0.556875\pi\)
\(228\) −4.02509 3.59982i −0.266568 0.238404i
\(229\) −13.2508 + 7.65038i −0.875641 + 0.505551i −0.869219 0.494428i \(-0.835378\pi\)
−0.00642204 + 0.999979i \(0.502044\pi\)
\(230\) −5.11430 1.32615i −0.337227 0.0874438i
\(231\) −0.176508 + 3.48960i −0.0116134 + 0.229599i
\(232\) −4.21445 + 4.21445i −0.276692 + 0.276692i
\(233\) 6.62761 + 1.77586i 0.434189 + 0.116341i 0.469292 0.883043i \(-0.344509\pi\)
−0.0351029 + 0.999384i \(0.511176\pi\)
\(234\) 1.76498 + 2.39531i 0.115381 + 0.156587i
\(235\) 9.58699 0.0775117i 0.625387 0.00505630i
\(236\) −12.6843 + 7.32328i −0.825677 + 0.476705i
\(237\) 7.18093 + 1.50118i 0.466452 + 0.0975122i
\(238\) 1.42891 3.70543i 0.0926225 0.240188i
\(239\) 18.7082 1.21013 0.605067 0.796174i \(-0.293146\pi\)
0.605067 + 0.796174i \(0.293146\pi\)
\(240\) 13.2836 0.848664i 0.857456 0.0547810i
\(241\) 0.986063 1.70791i 0.0635179 0.110016i −0.832518 0.553998i \(-0.813101\pi\)
0.896036 + 0.443982i \(0.146435\pi\)
\(242\) 3.10802 0.832793i 0.199791 0.0535339i
\(243\) −13.6289 7.56659i −0.874294 0.485397i
\(244\) 8.36885i 0.535761i
\(245\) 7.03603 13.9819i 0.449516 0.893272i
\(246\) 1.27669 + 1.95156i 0.0813987 + 0.124427i
\(247\) 5.07757 + 1.36053i 0.323078 + 0.0865685i
\(248\) 1.85026 + 6.90525i 0.117491 + 0.438484i
\(249\) 12.3593 0.689328i 0.783240 0.0436844i
\(250\) −2.94755 + 1.79847i −0.186420 + 0.113745i
\(251\) 17.9016i 1.12994i −0.825112 0.564970i \(-0.808888\pi\)
0.825112 0.564970i \(-0.191112\pi\)
\(252\) 10.6342 10.7449i 0.669889 0.676863i
\(253\) 4.12485 + 4.12485i 0.259327 + 0.259327i
\(254\) 0.974254 + 1.68746i 0.0611301 + 0.105881i
\(255\) 3.70281 18.4562i 0.231879 1.15577i
\(256\) −4.45168 + 7.71053i −0.278230 + 0.481908i
\(257\) 5.10358 19.0468i 0.318353 1.18811i −0.602475 0.798138i \(-0.705819\pi\)
0.920827 0.389971i \(-0.127515\pi\)
\(258\) −1.99218 0.416467i −0.124028 0.0259281i
\(259\) −7.56100 5.51114i −0.469818 0.342445i
\(260\) −11.7887 + 6.93387i −0.731102 + 0.430021i
\(261\) 1.64885 + 14.7356i 0.102061 + 0.912109i
\(262\) −0.171813 0.641215i −0.0106147 0.0396144i
\(263\) 1.43607 + 5.35948i 0.0885517 + 0.330480i 0.995963 0.0897640i \(-0.0286113\pi\)
−0.907411 + 0.420244i \(0.861945\pi\)
\(264\) 1.42138 + 0.718230i 0.0874798 + 0.0442040i
\(265\) 13.3961 7.87931i 0.822914 0.484022i
\(266\) −0.141851 + 1.32999i −0.00869744 + 0.0815467i
\(267\) −0.321534 + 1.53807i −0.0196776 + 0.0941281i
\(268\) −0.0240547 + 0.0897733i −0.00146937 + 0.00548378i
\(269\) −5.02321 + 8.70045i −0.306270 + 0.530476i −0.977543 0.210734i \(-0.932414\pi\)
0.671273 + 0.741210i \(0.265748\pi\)
\(270\) −2.05614 + 2.94086i −0.125133 + 0.178975i
\(271\) 2.82028 + 4.88486i 0.171320 + 0.296734i 0.938881 0.344241i \(-0.111864\pi\)
−0.767562 + 0.640975i \(0.778530\pi\)
\(272\) 11.8115 + 11.8115i 0.716180 + 0.716180i
\(273\) −4.52206 + 14.0042i −0.273688 + 0.847575i
\(274\) 2.72309i 0.164508i
\(275\) 3.81183 0.0616420i 0.229862 0.00371715i
\(276\) −1.40549 25.1998i −0.0846007 1.51685i
\(277\) 2.91038 + 10.8617i 0.174868 + 0.652615i 0.996574 + 0.0827040i \(0.0263556\pi\)
−0.821707 + 0.569911i \(0.806978\pi\)
\(278\) −3.09130 0.828310i −0.185404 0.0496787i
\(279\) 16.2954 + 7.12451i 0.975581 + 0.426533i
\(280\) −4.52589 5.51475i −0.270473 0.329569i
\(281\) 1.92831i 0.115033i 0.998345 + 0.0575167i \(0.0183183\pi\)
−0.998345 + 0.0575167i \(0.981682\pi\)
\(282\) −0.716052 2.17887i −0.0426403 0.129750i
\(283\) 25.4667 6.82379i 1.51384 0.405632i 0.596132 0.802887i \(-0.296704\pi\)
0.917709 + 0.397254i \(0.130037\pi\)
\(284\) −11.8250 + 20.4816i −0.701687 + 1.21536i
\(285\) 0.404207 + 6.32683i 0.0239432 + 0.374769i
\(286\) −0.756201 −0.0447151
\(287\) −4.15012 + 10.7620i −0.244974 + 0.635263i
\(288\) −3.79926 9.70225i −0.223874 0.571710i
\(289\) 5.73548 3.31138i 0.337381 0.194787i
\(290\) 3.41309 0.0275951i 0.200424 0.00162044i
\(291\) 9.12392 0.508877i 0.534853 0.0298309i
\(292\) −2.55301 0.684078i −0.149404 0.0400326i
\(293\) −7.83332 + 7.83332i −0.457627 + 0.457627i −0.897876 0.440249i \(-0.854890\pi\)
0.440249 + 0.897876i \(0.354890\pi\)
\(294\) −3.69852 0.584698i −0.215702 0.0341003i
\(295\) 16.6449 + 4.31607i 0.969105 + 0.251291i
\(296\) −3.69315 + 2.13224i −0.214660 + 0.123934i
\(297\) 3.60296 1.64781i 0.209065 0.0956155i
\(298\) 5.20686 1.39517i 0.301625 0.0808203i
\(299\) 12.2846 + 21.2775i 0.710435 + 1.23051i
\(300\) −12.4710 10.7955i −0.720011 0.623280i
\(301\) −4.08027 9.20242i −0.235183 0.530418i
\(302\) 3.32282 + 3.32282i 0.191207 + 0.191207i
\(303\) −10.2681 31.2449i −0.589890 1.79497i
\(304\) −4.87205 2.81288i −0.279431 0.161330i
\(305\) −6.89109 + 7.00343i −0.394583 + 0.401015i
\(306\) −4.47522 + 0.500759i −0.255831 + 0.0286265i
\(307\) −17.0769 + 17.0769i −0.974628 + 0.974628i −0.999686 0.0250576i \(-0.992023\pi\)
0.0250576 + 0.999686i \(0.492023\pi\)
\(308\) 0.595226 + 3.79579i 0.0339161 + 0.216285i
\(309\) −18.3083 + 11.9771i −1.04152 + 0.681354i
\(310\) 2.01824 3.56190i 0.114628 0.202302i
\(311\) 20.4797 + 11.8240i 1.16130 + 0.670475i 0.951615 0.307294i \(-0.0994235\pi\)
0.209683 + 0.977769i \(0.432757\pi\)
\(312\) 4.99963 + 4.47139i 0.283048 + 0.253143i
\(313\) −3.20409 + 11.9578i −0.181106 + 0.675895i 0.814325 + 0.580409i \(0.197107\pi\)
−0.995431 + 0.0954864i \(0.969559\pi\)
\(314\) −2.82168 −0.159237
\(315\) −17.7467 + 0.235390i −0.999912 + 0.0132627i
\(316\) 8.06709 0.453809
\(317\) −1.13684 + 4.24276i −0.0638515 + 0.238297i −0.990475 0.137694i \(-0.956031\pi\)
0.926623 + 0.375991i \(0.122698\pi\)
\(318\) −2.77127 2.47848i −0.155405 0.138986i
\(319\) −3.26361 1.88425i −0.182727 0.105498i
\(320\) 12.5018 3.45843i 0.698874 0.193332i
\(321\) 3.16074 2.06772i 0.176415 0.115409i
\(322\) −4.86432 + 3.92671i −0.271078 + 0.218827i
\(323\) −5.62568 + 5.62568i −0.313021 + 0.313021i
\(324\) −16.3723 5.07770i −0.909570 0.282094i
\(325\) 15.5748 + 3.90447i 0.863933 + 0.216581i
\(326\) 0.724106 + 0.418063i 0.0401045 + 0.0231543i
\(327\) −1.27604 3.88284i −0.0705650 0.214722i
\(328\) 3.71743 + 3.71743i 0.205261 + 0.205261i
\(329\) 6.68183 9.16713i 0.368381 0.505400i
\(330\) −0.291729 0.864084i −0.0160592 0.0475662i
\(331\) 3.10933 + 5.38552i 0.170904 + 0.296015i 0.938736 0.344636i \(-0.111998\pi\)
−0.767832 + 0.640651i \(0.778664\pi\)
\(332\) 13.1480 3.52300i 0.721591 0.193350i
\(333\) −1.58925 + 10.4894i −0.0870906 + 0.574815i
\(334\) 1.45833 0.841970i 0.0797965 0.0460705i
\(335\) 0.0940513 0.0553192i 0.00513857 0.00302241i
\(336\) 8.55370 13.2242i 0.466642 0.721440i
\(337\) 15.0501 15.0501i 0.819833 0.819833i −0.166250 0.986084i \(-0.553166\pi\)
0.986084 + 0.166250i \(0.0531659\pi\)
\(338\) 0.801644 + 0.214800i 0.0436037 + 0.0116836i
\(339\) 29.1981 1.62849i 1.58582 0.0884476i
\(340\) −0.167351 20.6988i −0.00907590 1.12255i
\(341\) −3.91452 + 2.26005i −0.211983 + 0.122389i
\(342\) 1.41220 0.552999i 0.0763632 0.0299027i
\(343\) −8.33197 16.5402i −0.449884 0.893087i
\(344\) −4.58812 −0.247375
\(345\) −19.5739 + 22.2456i −1.05382 + 1.19766i
\(346\) 0.204333 0.353916i 0.0109850 0.0190266i
\(347\) −18.6057 + 4.98539i −0.998808 + 0.267630i −0.720946 0.692991i \(-0.756292\pi\)
−0.277862 + 0.960621i \(0.589626\pi\)
\(348\) 5.09049 + 15.4898i 0.272879 + 0.830342i
\(349\) 9.24369i 0.494803i 0.968913 + 0.247402i \(0.0795767\pi\)
−0.968913 + 0.247402i \(0.920423\pi\)
\(350\) −0.367545 + 4.06896i −0.0196461 + 0.217495i
\(351\) 16.4541 2.77618i 0.878254 0.148182i
\(352\) 2.55796 + 0.685404i 0.136340 + 0.0365321i
\(353\) 3.05649 + 11.4070i 0.162681 + 0.607132i 0.998325 + 0.0578609i \(0.0184280\pi\)
−0.835644 + 0.549271i \(0.814905\pi\)
\(354\) −0.229073 4.10717i −0.0121751 0.218294i
\(355\) 26.7607 7.40290i 1.42031 0.392905i
\(356\) 1.72787i 0.0915769i
\(357\) −14.9335 16.5247i −0.790367 0.874582i
\(358\) −0.0527764 0.0527764i −0.00278932 0.00278932i
\(359\) 6.98129 + 12.0920i 0.368459 + 0.638189i 0.989325 0.145728i \(-0.0465523\pi\)
−0.620866 + 0.783917i \(0.713219\pi\)
\(360\) −3.18053 + 7.43788i −0.167629 + 0.392011i
\(361\) −8.16026 + 14.1340i −0.429487 + 0.743894i
\(362\) −1.49366 + 5.57441i −0.0785050 + 0.292985i
\(363\) 3.69263 17.6638i 0.193813 0.927108i
\(364\) −1.71622 + 16.0912i −0.0899544 + 0.843408i
\(365\) 1.57319 + 2.67467i 0.0823446 + 0.139999i
\(366\) 2.09782 + 1.06004i 0.109655 + 0.0554091i
\(367\) −3.90370 14.5688i −0.203771 0.760485i −0.989821 0.142321i \(-0.954543\pi\)
0.786049 0.618164i \(-0.212123\pi\)
\(368\) −6.80542 25.3982i −0.354757 1.32397i
\(369\) 12.9978 1.45440i 0.676638 0.0757130i
\(370\) 2.36397 + 0.612982i 0.122897 + 0.0318674i
\(371\) 1.95023 18.2852i 0.101251 0.949323i
\(372\) 19.1429 + 4.00185i 0.992515 + 0.207486i
\(373\) −9.01635 + 33.6495i −0.466849 + 1.74230i 0.183837 + 0.982957i \(0.441148\pi\)
−0.650686 + 0.759347i \(0.725519\pi\)
\(374\) 0.572249 0.991165i 0.0295903 0.0512519i
\(375\) 1.54698 + 19.3030i 0.0798857 + 0.996804i
\(376\) −2.58517 4.47765i −0.133320 0.230917i
\(377\) −11.2233 11.2233i −0.578028 0.578028i
\(378\) 1.34644 + 4.02666i 0.0692535 + 0.207109i
\(379\) 19.0602i 0.979056i −0.871988 0.489528i \(-0.837169\pi\)
0.871988 0.489528i \(-0.162831\pi\)
\(380\) 1.85871 + 6.71902i 0.0953496 + 0.344678i
\(381\) 10.9109 0.608542i 0.558980 0.0311765i
\(382\) 1.13832 + 4.24828i 0.0582417 + 0.217361i
\(383\) −9.81007 2.62860i −0.501271 0.134315i −0.000681261 1.00000i \(-0.500217\pi\)
−0.500590 + 0.865685i \(0.666884\pi\)
\(384\) −8.28544 12.6652i −0.422815 0.646318i
\(385\) 2.62743 3.66661i 0.133906 0.186868i
\(386\) 2.10507i 0.107145i
\(387\) −7.12352 + 8.91857i −0.362109 + 0.453356i
\(388\) 9.70615 2.60076i 0.492755 0.132033i
\(389\) 18.6290 32.2664i 0.944528 1.63597i 0.187835 0.982201i \(-0.439853\pi\)
0.756693 0.653770i \(-0.226814\pi\)
\(390\) −0.244904 3.83334i −0.0124012 0.194109i
\(391\) −37.1850 −1.88053
\(392\) −8.43099 + 0.415908i −0.425829 + 0.0210065i
\(393\) −3.64421 0.761825i −0.183826 0.0384290i
\(394\) −2.89595 + 1.67198i −0.145896 + 0.0842331i
\(395\) −6.75090 6.64261i −0.339675 0.334226i
\(396\) 3.50731 2.58436i 0.176249 0.129869i
\(397\) 8.58658 + 2.30077i 0.430948 + 0.115472i 0.467771 0.883850i \(-0.345057\pi\)
−0.0368231 + 0.999322i \(0.511724\pi\)
\(398\) 3.57708 3.57708i 0.179303 0.179303i
\(399\) 6.29852 + 4.07401i 0.315321 + 0.203956i
\(400\) −15.0188 8.35029i −0.750941 0.417514i
\(401\) 4.02832 2.32575i 0.201165 0.116142i −0.396034 0.918236i \(-0.629614\pi\)
0.597199 + 0.802093i \(0.296280\pi\)
\(402\) −0.0194566 0.0174009i −0.000970407 0.000867878i
\(403\) −18.3890 + 4.92733i −0.916023 + 0.245448i
\(404\) −18.0828 31.3204i −0.899655 1.55825i
\(405\) 9.51994 + 17.7305i 0.473050 + 0.881036i
\(406\) 2.37881 3.26361i 0.118059 0.161970i
\(407\) −1.90662 1.90662i −0.0945074 0.0945074i
\(408\) −9.64415 + 3.16940i −0.477457 + 0.156909i
\(409\) −23.0006 13.2794i −1.13731 0.656626i −0.191546 0.981484i \(-0.561350\pi\)
−0.945763 + 0.324858i \(0.894683\pi\)
\(410\) −0.0243408 3.01058i −0.00120211 0.148682i
\(411\) 13.6305 + 6.88758i 0.672345 + 0.339739i
\(412\) −17.0114 + 17.0114i −0.838091 + 0.838091i
\(413\) 15.8313 12.7798i 0.779009 0.628853i
\(414\) 6.49486 + 2.83961i 0.319205 + 0.139559i
\(415\) −13.9038 7.87815i −0.682508 0.386723i
\(416\) 9.65934 + 5.57682i 0.473588 + 0.273426i
\(417\) −11.9650 + 13.3786i −0.585931 + 0.655151i
\(418\) −0.0997634 + 0.372322i −0.00487959 + 0.0182109i
\(419\) −25.8278 −1.26177 −0.630885 0.775876i \(-0.717308\pi\)
−0.630885 + 0.775876i \(0.717308\pi\)
\(420\) −19.0489 + 4.24664i −0.929492 + 0.207215i
\(421\) 0.432430 0.0210753 0.0105377 0.999944i \(-0.496646\pi\)
0.0105377 + 0.999944i \(0.496646\pi\)
\(422\) 2.03851 7.60783i 0.0992332 0.370343i
\(423\) −12.7176 1.92685i −0.618350 0.0936866i
\(424\) −7.25850 4.19070i −0.352504 0.203518i
\(425\) −16.9038 + 17.4594i −0.819952 + 0.846908i
\(426\) −3.63630 5.55847i −0.176179 0.269309i
\(427\) 1.80099 + 11.4850i 0.0871558 + 0.555799i
\(428\) 2.93684 2.93684i 0.141957 0.141957i
\(429\) −1.91268 + 3.78520i −0.0923451 + 0.182751i
\(430\) 1.87288 + 1.84283i 0.0903181 + 0.0888694i
\(431\) −14.1264 8.15586i −0.680443 0.392854i 0.119579 0.992825i \(-0.461846\pi\)
−0.800022 + 0.599971i \(0.795179\pi\)
\(432\) −17.7783 1.68777i −0.855358 0.0812029i
\(433\) −0.514238 0.514238i −0.0247127 0.0247127i 0.694642 0.719355i \(-0.255563\pi\)
−0.719355 + 0.694642i \(0.755563\pi\)
\(434\) −1.96345 4.42825i −0.0942486 0.212563i
\(435\) 8.49470 17.1542i 0.407290 0.822480i
\(436\) −2.24718 3.89223i −0.107620 0.186404i
\(437\) 12.0968 3.24133i 0.578669 0.155054i
\(438\) 0.494855 0.553315i 0.0236451 0.0264384i
\(439\) 13.2487 7.64917i 0.632328 0.365075i −0.149325 0.988788i \(-0.547710\pi\)
0.781653 + 0.623713i \(0.214377\pi\)
\(440\) −1.04234 1.77214i −0.0496916 0.0844835i
\(441\) −12.2815 + 17.0342i −0.584834 + 0.811153i
\(442\) 3.40853 3.40853i 0.162127 0.162127i
\(443\) 8.81439 + 2.36181i 0.418784 + 0.112213i 0.462057 0.886850i \(-0.347112\pi\)
−0.0432723 + 0.999063i \(0.513778\pi\)
\(444\) 0.649656 + 11.6480i 0.0308313 + 0.552791i
\(445\) 1.42276 1.44596i 0.0674455 0.0685450i
\(446\) 5.84564 3.37498i 0.276799 0.159810i
\(447\) 6.18625 29.5921i 0.292600 1.39966i
\(448\) 5.52219 14.3201i 0.260899 0.676560i
\(449\) −9.40891 −0.444034 −0.222017 0.975043i \(-0.571264\pi\)
−0.222017 + 0.975043i \(0.571264\pi\)
\(450\) 4.28575 1.75868i 0.202032 0.0829050i
\(451\) −1.66204 + 2.87873i −0.0782622 + 0.135554i
\(452\) 31.0613 8.32286i 1.46100 0.391474i
\(453\) 25.0370 8.22804i 1.17634 0.386587i
\(454\) 3.96789i 0.186222i
\(455\) 14.6860 12.0527i 0.688492 0.565037i
\(456\) 2.86111 1.87171i 0.133984 0.0876509i
\(457\) 33.3520 + 8.93665i 1.56014 + 0.418039i 0.932708 0.360631i \(-0.117439\pi\)
0.627434 + 0.778670i \(0.284105\pi\)
\(458\) −1.22303 4.56443i −0.0571486 0.213282i
\(459\) −8.81272 + 23.6675i −0.411343 + 1.10470i
\(460\) −16.0630 + 28.3488i −0.748942 + 1.32177i
\(461\) 36.9326i 1.72012i 0.510192 + 0.860061i \(0.329574\pi\)
−0.510192 + 0.860061i \(0.670426\pi\)
\(462\) −1.02689 0.331588i −0.0477751 0.0154269i
\(463\) 26.3687 + 26.3687i 1.22546 + 1.22546i 0.965664 + 0.259794i \(0.0836548\pi\)
0.259794 + 0.965664i \(0.416345\pi\)
\(464\) 8.49325 + 14.7107i 0.394289 + 0.682929i
\(465\) −12.7244 19.1116i −0.590082 0.886280i
\(466\) −1.05953 + 1.83516i −0.0490817 + 0.0850120i
\(467\) −2.63979 + 9.85183i −0.122155 + 0.455888i −0.999722 0.0235650i \(-0.992498\pi\)
0.877567 + 0.479453i \(0.159165\pi\)
\(468\) 17.0859 6.69060i 0.789797 0.309273i
\(469\) 0.0136922 0.128377i 0.000632247 0.00592791i
\(470\) −0.743194 + 2.86613i −0.0342810 + 0.132205i
\(471\) −7.13696 + 14.1241i −0.328854 + 0.650803i
\(472\) −2.40011 8.95734i −0.110474 0.412295i
\(473\) −0.750833 2.80215i −0.0345233 0.128843i
\(474\) −1.02182 + 2.02218i −0.0469336 + 0.0928817i
\(475\) 3.97713 7.15327i 0.182483 0.328215i
\(476\) −19.7923 14.4264i −0.907177 0.661232i
\(477\) −19.4156 + 7.60287i −0.888979 + 0.348112i
\(478\) −1.49540 + 5.58092i −0.0683981 + 0.255265i
\(479\) −6.85350 + 11.8706i −0.313144 + 0.542382i −0.979041 0.203662i \(-0.934716\pi\)
0.665897 + 0.746044i \(0.268049\pi\)
\(480\) −2.64603 + 13.1888i −0.120774 + 0.601985i
\(481\) −5.67825 9.83503i −0.258906 0.448439i
\(482\) 0.430674 + 0.430674i 0.0196167 + 0.0196167i
\(483\) 7.35185 + 34.2805i 0.334521 + 1.55982i
\(484\) 19.8436i 0.901980i
\(485\) −10.2641 5.81582i −0.466067 0.264083i
\(486\) 3.34661 3.46087i 0.151805 0.156988i
\(487\) −5.91662 22.0811i −0.268108 1.00059i −0.960321 0.278898i \(-0.910031\pi\)
0.692213 0.721693i \(-0.256636\pi\)
\(488\) 5.11811 + 1.37139i 0.231686 + 0.0620800i
\(489\) 3.92413 2.56713i 0.177455 0.116090i
\(490\) 3.60859 + 3.21656i 0.163019 + 0.145309i
\(491\) 23.7476i 1.07172i 0.844308 + 0.535858i \(0.180012\pi\)
−0.844308 + 0.535858i \(0.819988\pi\)
\(492\) 13.6631 4.49016i 0.615980 0.202432i
\(493\) 23.2037 6.21740i 1.04504 0.280018i
\(494\) −0.811730 + 1.40596i −0.0365215 + 0.0632570i
\(495\) −5.06309 0.725288i −0.227569 0.0325993i
\(496\) 20.3744 0.914836
\(497\) 11.8205 30.6527i 0.530220 1.37496i
\(498\) −0.782280 + 3.74205i −0.0350548 + 0.167685i
\(499\) −2.80187 + 1.61766i −0.125429 + 0.0724165i −0.561402 0.827543i \(-0.689738\pi\)
0.435973 + 0.899960i \(0.356404\pi\)
\(500\) 6.00859 + 20.4290i 0.268712 + 0.913612i
\(501\) −0.525914 9.42938i −0.0234961 0.421274i
\(502\) 5.34029 + 1.43093i 0.238349 + 0.0638654i
\(503\) 2.62851 2.62851i 0.117199 0.117199i −0.646075 0.763274i \(-0.723591\pi\)
0.763274 + 0.646075i \(0.223591\pi\)
\(504\) 4.82859 + 8.26424i 0.215083 + 0.368118i
\(505\) −10.6573 + 41.1001i −0.474246 + 1.82893i
\(506\) −1.56021 + 0.900788i −0.0693598 + 0.0400449i
\(507\) 3.10281 3.46937i 0.137801 0.154080i
\(508\) 11.6071 3.11012i 0.514983 0.137989i
\(509\) −6.91189 11.9717i −0.306364 0.530638i 0.671200 0.741276i \(-0.265779\pi\)
−0.977564 + 0.210638i \(0.932446\pi\)
\(510\) 5.20976 + 2.57985i 0.230692 + 0.114238i
\(511\) 3.65085 + 0.389385i 0.161504 + 0.0172254i
\(512\) −14.3017 14.3017i −0.632050 0.632050i
\(513\) 0.803863 8.46757i 0.0354914 0.373852i
\(514\) 5.27399 + 3.04494i 0.232626 + 0.134306i
\(515\) 28.2434 0.228350i 1.24455 0.0100623i
\(516\) −5.66069 + 11.2025i −0.249198 + 0.493164i
\(517\) 2.31162 2.31162i 0.101665 0.101665i
\(518\) 2.24842 1.81503i 0.0987899 0.0797478i
\(519\) −1.25472 1.91797i −0.0550759 0.0841895i
\(520\) −2.30873 8.34580i −0.101244 0.365988i
\(521\) −9.49156 5.47996i −0.415833 0.240081i 0.277460 0.960737i \(-0.410507\pi\)
−0.693293 + 0.720656i \(0.743841\pi\)
\(522\) −4.52762 0.685982i −0.198168 0.0300246i
\(523\) 3.54814 13.2418i 0.155149 0.579026i −0.843943 0.536433i \(-0.819771\pi\)
0.999093 0.0425929i \(-0.0135618\pi\)
\(524\) −4.09392 −0.178844
\(525\) 19.4378 + 12.1315i 0.848333 + 0.529463i
\(526\) −1.71360 −0.0747163
\(527\) 7.45743 27.8315i 0.324851 1.21236i
\(528\) 3.02569 3.38313i 0.131676 0.147232i
\(529\) 30.7730 + 17.7668i 1.33796 + 0.772469i
\(530\) 1.27972 + 4.62605i 0.0555875 + 0.200943i
\(531\) −21.1381 9.24175i −0.917313 0.401058i
\(532\) 7.69622 + 2.96786i 0.333674 + 0.128673i
\(533\) −9.89970 + 9.89970i −0.428804 + 0.428804i
\(534\) −0.433125 0.218860i −0.0187432 0.00947101i
\(535\) −4.87593 + 0.0394223i −0.210805 + 0.00170438i
\(536\) −0.0509605 0.0294221i −0.00220116 0.00127084i
\(537\) −0.397664 + 0.130686i −0.0171605 + 0.00563952i
\(538\) −2.19394 2.19394i −0.0945876 0.0945876i
\(539\) −1.63372 5.08108i −0.0703692 0.218857i
\(540\) 14.2366 + 16.9423i 0.612644 + 0.729083i
\(541\) −3.53276 6.11892i −0.151885 0.263073i 0.780035 0.625735i \(-0.215201\pi\)
−0.931920 + 0.362663i \(0.881868\pi\)
\(542\) −1.68265 + 0.450866i −0.0722762 + 0.0193663i
\(543\) 24.1250 + 21.5761i 1.03530 + 0.925919i
\(544\) −14.6193 + 8.44044i −0.626796 + 0.361881i
\(545\) −1.32440 + 5.10756i −0.0567312 + 0.218784i
\(546\) −3.81619 2.46839i −0.163318 0.105637i
\(547\) −19.7665 + 19.7665i −0.845154 + 0.845154i −0.989524 0.144370i \(-0.953885\pi\)
0.144370 + 0.989524i \(0.453885\pi\)
\(548\) 16.2212 + 4.34647i 0.692937 + 0.185672i
\(549\) 10.6121 7.81955i 0.452915 0.333730i
\(550\) −0.286302 + 1.14205i −0.0122080 + 0.0486971i
\(551\) −7.00653 + 4.04522i −0.298488 + 0.172332i
\(552\) 15.6417 + 3.26991i 0.665753 + 0.139176i
\(553\) −11.0709 + 1.73605i −0.470782 + 0.0738242i
\(554\) −3.47282 −0.147546
\(555\) 9.04756 10.2825i 0.384048 0.436469i
\(556\) −9.86837 + 17.0925i −0.418512 + 0.724884i
\(557\) −42.2902 + 11.3316i −1.79189 + 0.480137i −0.992666 0.120891i \(-0.961425\pi\)
−0.799228 + 0.601028i \(0.794758\pi\)
\(558\) −3.42788 + 4.29166i −0.145114 + 0.181681i
\(559\) 12.2184i 0.516783i
\(560\) −18.5201 + 8.39146i −0.782616 + 0.354604i
\(561\) −3.51392 5.37140i −0.148358 0.226781i
\(562\) −0.575242 0.154136i −0.0242651 0.00650182i
\(563\) −2.87110 10.7151i −0.121002 0.451587i 0.878663 0.477442i \(-0.158436\pi\)
−0.999666 + 0.0258549i \(0.991769\pi\)
\(564\) −14.1223 + 0.787658i −0.594657 + 0.0331664i
\(565\) −32.8467 18.6116i −1.38187 0.782997i
\(566\) 8.14252i 0.342256i
\(567\) 23.5612 + 3.44507i 0.989479 + 0.144679i
\(568\) −10.5881 10.5881i −0.444266 0.444266i
\(569\) 6.90318 + 11.9567i 0.289396 + 0.501249i 0.973666 0.227980i \(-0.0732121\pi\)
−0.684269 + 0.729229i \(0.739879\pi\)
\(570\) −1.91969 0.385141i −0.0804069 0.0161318i
\(571\) 6.56260 11.3668i 0.274636 0.475684i −0.695407 0.718616i \(-0.744776\pi\)
0.970043 + 0.242932i \(0.0781092\pi\)
\(572\) −1.20701 + 4.50464i −0.0504678 + 0.188348i
\(573\) 24.1442 + 5.04736i 1.00864 + 0.210857i
\(574\) −2.87873 2.09828i −0.120156 0.0875804i
\(575\) 36.7852 10.4969i 1.53405 0.437752i
\(576\) −17.2950 + 1.93524i −0.720625 + 0.0806350i
\(577\) −3.94772 14.7331i −0.164346 0.613347i −0.998123 0.0612453i \(-0.980493\pi\)
0.833777 0.552101i \(-0.186174\pi\)
\(578\) 0.529377 + 1.97566i 0.0220192 + 0.0821767i
\(579\) −10.5370 5.32440i −0.437903 0.221275i
\(580\) 5.28344 20.3756i 0.219383 0.846050i
\(581\) −17.2856 + 7.66426i −0.717126 + 0.317967i
\(582\) −0.577496 + 2.76247i −0.0239380 + 0.114508i
\(583\) 1.37159 5.11885i 0.0568055 0.212001i
\(584\) 0.836718 1.44924i 0.0346236 0.0599699i
\(585\) −19.8074 8.46991i −0.818937 0.350188i
\(586\) −1.71065 2.96293i −0.0706662 0.122397i
\(587\) 5.54217 + 5.54217i 0.228750 + 0.228750i 0.812170 0.583421i \(-0.198286\pi\)
−0.583421 + 0.812170i \(0.698286\pi\)
\(588\) −9.38642 + 21.0986i −0.387089 + 0.870090i
\(589\) 9.70404i 0.399848i
\(590\) −2.61802 + 4.62041i −0.107782 + 0.190219i
\(591\) 1.04436 + 18.7248i 0.0429591 + 0.770237i
\(592\) 3.14565 + 11.7397i 0.129285 + 0.482499i
\(593\) 8.37814 + 2.24492i 0.344049 + 0.0921877i 0.426706 0.904390i \(-0.359674\pi\)
−0.0826570 + 0.996578i \(0.526341\pi\)
\(594\) 0.203568 + 1.20653i 0.00835252 + 0.0495043i
\(595\) 4.68406 + 28.3700i 0.192028 + 1.16306i
\(596\) 33.2438i 1.36172i
\(597\) −8.85763 26.9528i −0.362519 1.10311i
\(598\) −7.32931 + 1.96388i −0.299718 + 0.0803091i
\(599\) 7.93869 13.7502i 0.324366 0.561819i −0.657018 0.753875i \(-0.728182\pi\)
0.981384 + 0.192056i \(0.0615157\pi\)
\(600\) 8.64578 5.85777i 0.352963 0.239142i
\(601\) 41.5249 1.69384 0.846919 0.531722i \(-0.178455\pi\)
0.846919 + 0.531722i \(0.178455\pi\)
\(602\) 3.07135 0.481625i 0.125179 0.0196296i
\(603\) −0.136313 + 0.0533783i −0.00555110 + 0.00217373i
\(604\) 25.0976 14.4901i 1.02120 0.589593i
\(605\) −16.3396 + 16.6060i −0.664299 + 0.675129i
\(606\) 10.1415 0.565634i 0.411972 0.0229773i
\(607\) 14.7681 + 3.95710i 0.599418 + 0.160614i 0.545754 0.837945i \(-0.316243\pi\)
0.0536641 + 0.998559i \(0.482910\pi\)
\(608\) 4.02013 4.02013i 0.163038 0.163038i
\(609\) −10.3194 20.1620i −0.418162 0.817006i
\(610\) −1.53839 2.61551i −0.0622877 0.105899i
\(611\) 11.9242 6.88444i 0.482402 0.278515i
\(612\) −4.16015 + 27.4578i −0.168164 + 1.10992i
\(613\) −29.7879 + 7.98165i −1.20312 + 0.322376i −0.804060 0.594548i \(-0.797331\pi\)
−0.399063 + 0.916924i \(0.630664\pi\)
\(614\) −3.72926 6.45927i −0.150501 0.260675i
\(615\) −15.1312 7.49291i −0.610148 0.302143i
\(616\) −2.41892 0.257992i −0.0974611 0.0103948i
\(617\) 13.2098 + 13.2098i 0.531808 + 0.531808i 0.921110 0.389302i \(-0.127284\pi\)
−0.389302 + 0.921110i \(0.627284\pi\)
\(618\) −2.10950 6.41899i −0.0848566 0.258210i
\(619\) −14.7495 8.51561i −0.592831 0.342271i 0.173385 0.984854i \(-0.444529\pi\)
−0.766216 + 0.642583i \(0.777863\pi\)
\(620\) −17.9965 17.7079i −0.722758 0.711165i
\(621\) 30.6414 25.3280i 1.22960 1.01638i
\(622\) −5.16425 + 5.16425i −0.207068 + 0.207068i
\(623\) −0.371840 2.37125i −0.0148974 0.0950020i
\(624\) 15.9973 10.4652i 0.640403 0.418945i
\(625\) 11.7934 22.0435i 0.471736 0.881740i
\(626\) −3.31107 1.91165i −0.132337 0.0764047i
\(627\) 1.61134 + 1.44110i 0.0643508 + 0.0575518i
\(628\) −4.50384 + 16.8086i −0.179723 + 0.670735i
\(629\) 17.1879 0.685327
\(630\) 1.34832 5.31289i 0.0537185 0.211671i
\(631\) 6.51082 0.259191 0.129596 0.991567i \(-0.458632\pi\)
0.129596 + 0.991567i \(0.458632\pi\)
\(632\) −1.32194 + 4.93356i −0.0525841 + 0.196247i
\(633\) −32.9253 29.4466i −1.30866 1.17040i
\(634\) −1.17480 0.678272i −0.0466573 0.0269376i
\(635\) −12.2743 6.95487i −0.487091 0.275996i
\(636\) −19.1875 + 12.5523i −0.760834 + 0.497730i
\(637\) −1.10758 22.4521i −0.0438840 0.889586i
\(638\) 0.822967 0.822967i 0.0325816 0.0325816i
\(639\) −37.0206 + 4.14246i −1.46451 + 0.163873i
\(640\) 0.157967 + 19.5380i 0.00624418 + 0.772308i
\(641\) 36.6801 + 21.1773i 1.44878 + 0.836451i 0.998409 0.0563924i \(-0.0179598\pi\)
0.450367 + 0.892843i \(0.351293\pi\)
\(642\) 0.364183 + 1.10817i 0.0143732 + 0.0437360i
\(643\) 11.2098 + 11.2098i 0.442072 + 0.442072i 0.892708 0.450636i \(-0.148803\pi\)
−0.450636 + 0.892708i \(0.648803\pi\)
\(644\) 15.6269 + 35.2441i 0.615787 + 1.38881i
\(645\) 13.9615 4.71364i 0.549734 0.185599i
\(646\) −1.22854 2.12790i −0.0483363 0.0837209i
\(647\) −22.9610 + 6.15237i −0.902689 + 0.241875i −0.680171 0.733054i \(-0.738094\pi\)
−0.222518 + 0.974929i \(0.571428\pi\)
\(648\) 5.78825 9.18064i 0.227384 0.360650i
\(649\) 5.07783 2.93169i 0.199322 0.115079i
\(650\) −2.40969 + 4.33408i −0.0945160 + 0.169996i
\(651\) −27.1320 1.37237i −1.06339 0.0537874i
\(652\) 3.64616 3.64616i 0.142794 0.142794i
\(653\) 21.0505 + 5.64046i 0.823769 + 0.220728i 0.645994 0.763343i \(-0.276443\pi\)
0.177775 + 0.984071i \(0.443110\pi\)
\(654\) 1.26030 0.0702921i 0.0492817 0.00274864i
\(655\) 3.42597 + 3.37102i 0.133864 + 0.131717i
\(656\) 12.9759 7.49163i 0.506623 0.292499i
\(657\) −1.51800 3.87653i −0.0592227 0.151238i
\(658\) 2.20058 + 2.72604i 0.0857876 + 0.106272i
\(659\) −42.6184 −1.66018 −0.830088 0.557632i \(-0.811710\pi\)
−0.830088 + 0.557632i \(0.811710\pi\)
\(660\) −5.61293 + 0.358598i −0.218483 + 0.0139584i
\(661\) −22.7467 + 39.3985i −0.884744 + 1.53242i −0.0387381 + 0.999249i \(0.512334\pi\)
−0.846006 + 0.533173i \(0.821000\pi\)
\(662\) −1.85511 + 0.497076i −0.0721010 + 0.0193194i
\(663\) −8.44027 25.6828i −0.327793 0.997439i
\(664\) 8.61819i 0.334451i
\(665\) −3.99674 8.82087i −0.154987 0.342059i
\(666\) −3.00210 1.31254i −0.116329 0.0508601i
\(667\) −36.5253 9.78693i −1.41427 0.378951i
\(668\) −2.68783 10.0311i −0.103995 0.388115i
\(669\) −2.10809 37.7971i −0.0815035 1.46132i
\(670\) 0.00898467 + 0.0324786i 0.000347108 + 0.00125476i
\(671\) 3.35026i 0.129335i
\(672\) 10.6715 + 11.8086i 0.411664 + 0.455527i
\(673\) −32.1249 32.1249i −1.23832 1.23832i −0.960686 0.277636i \(-0.910449\pi\)
−0.277636 0.960686i \(-0.589551\pi\)
\(674\) 3.28666 + 5.69266i 0.126597 + 0.219273i
\(675\) 2.03690 25.9008i 0.0784004 0.996922i
\(676\) 2.55910 4.43248i 0.0984268 0.170480i
\(677\) −11.0202 + 41.1280i −0.423542 + 1.58068i 0.343545 + 0.939136i \(0.388372\pi\)
−0.767087 + 0.641543i \(0.778295\pi\)
\(678\) −1.84809 + 8.84036i −0.0709753 + 0.339512i
\(679\) −12.7606 + 5.65793i −0.489706 + 0.217131i
\(680\) 12.6861 + 3.28953i 0.486489 + 0.126148i
\(681\) −19.8615 10.0361i −0.761094 0.384584i
\(682\) −0.361305 1.34841i −0.0138351 0.0516332i
\(683\) −0.603360 2.25177i −0.0230869 0.0861617i 0.953421 0.301642i \(-0.0975348\pi\)
−0.976508 + 0.215481i \(0.930868\pi\)
\(684\) −1.04008 9.29507i −0.0397685 0.355406i
\(685\) −9.99568 16.9942i −0.381915 0.649316i
\(686\) 5.60017 1.16343i 0.213815 0.0444201i
\(687\) −25.9409 5.42298i −0.989708 0.206899i
\(688\) −3.38438 + 12.6307i −0.129028 + 0.481540i
\(689\) 11.1600 19.3297i 0.425163 0.736404i
\(690\) −5.07158 7.61731i −0.193072 0.289986i
\(691\) 8.27824 + 14.3383i 0.314919 + 0.545456i 0.979420 0.201831i \(-0.0646893\pi\)
−0.664501 + 0.747287i \(0.731356\pi\)
\(692\) −1.78210 1.78210i −0.0677454 0.0677454i
\(693\) −4.25711 + 4.30143i −0.161714 + 0.163398i
\(694\) 5.94884i 0.225815i
\(695\) 22.3326 6.17796i 0.847125 0.234343i
\(696\) −10.3072 + 0.574875i −0.390694 + 0.0217906i
\(697\) −5.48418 20.4672i −0.207728 0.775252i
\(698\) −2.75752 0.738875i −0.104374 0.0279668i
\(699\) 6.50607 + 9.94523i 0.246082 + 0.376163i
\(700\) 23.6519 + 8.68414i 0.893957 + 0.328230i
\(701\) 26.5973i 1.00457i −0.864703 0.502284i \(-0.832493\pi\)
0.864703 0.502284i \(-0.167507\pi\)
\(702\) −0.487050 + 5.13039i −0.0183825 + 0.193634i
\(703\) −5.59148 + 1.49823i −0.210886 + 0.0565069i
\(704\) 2.21152 3.83047i 0.0833500 0.144366i
\(705\) 12.4668 + 10.9695i 0.469525 + 0.413134i
\(706\) −3.64717 −0.137263
\(707\) 31.5562 + 39.0912i 1.18679 + 1.47017i
\(708\) −24.8318 5.19111i −0.933235 0.195094i
\(709\) −13.7850 + 7.95880i −0.517708 + 0.298899i −0.735997 0.676985i \(-0.763286\pi\)
0.218288 + 0.975884i \(0.429953\pi\)
\(710\) 0.0693280 + 8.57481i 0.00260184 + 0.321807i
\(711\) 7.53760 + 10.2295i 0.282682 + 0.383636i
\(712\) −1.05671 0.283144i −0.0396018 0.0106113i
\(713\) −32.0712 + 32.0712i −1.20108 + 1.20108i
\(714\) 6.12324 3.13401i 0.229156 0.117287i
\(715\) 4.71930 2.77580i 0.176492 0.103809i
\(716\) −0.398625 + 0.230146i −0.0148973 + 0.00860096i
\(717\) 24.1532 + 21.6013i 0.902018 + 0.806715i
\(718\) −4.16523 + 1.11607i −0.155445 + 0.0416514i
\(719\) 10.6906 + 18.5167i 0.398694 + 0.690558i 0.993565 0.113263i \(-0.0361302\pi\)
−0.594871 + 0.803821i \(0.702797\pi\)
\(720\) 18.1297 + 14.2422i 0.675655 + 0.530775i
\(721\) 19.6848 27.0065i 0.733099 1.00577i
\(722\) −3.56409 3.56409i −0.132642 0.132642i
\(723\) 3.24508 1.06644i 0.120686 0.0396615i
\(724\) 30.8223 + 17.7952i 1.14550 + 0.661355i
\(725\) −21.1991 + 12.7007i −0.787315 + 0.471692i
\(726\) 4.97418 + 2.51348i 0.184609 + 0.0932840i
\(727\) 7.43836 7.43836i 0.275873 0.275873i −0.555586 0.831459i \(-0.687506\pi\)
0.831459 + 0.555586i \(0.187506\pi\)
\(728\) −9.55960 3.68643i −0.354302 0.136628i
\(729\) −8.85885 25.5053i −0.328106 0.944641i
\(730\) −0.923641 + 0.255510i −0.0341855 + 0.00945685i
\(731\) 16.0148 + 9.24617i 0.592330 + 0.341982i
\(732\) 9.66302 10.8046i 0.357156 0.399349i
\(733\) 9.45077 35.2708i 0.349072 1.30276i −0.538710 0.842491i \(-0.681088\pi\)
0.887782 0.460264i \(-0.152245\pi\)
\(734\) 4.65810 0.171934
\(735\) 25.2280 9.92723i 0.930547 0.366171i
\(736\) 26.5725 0.979475
\(737\) 0.00962968 0.0359385i 0.000354714 0.00132381i
\(738\) −0.605083 + 3.99367i −0.0222734 + 0.147009i
\(739\) 33.2198 + 19.1794i 1.22201 + 0.705527i 0.965346 0.260974i \(-0.0840437\pi\)
0.256663 + 0.966501i \(0.417377\pi\)
\(740\) 7.42475 13.1036i 0.272939 0.481697i
\(741\) 4.98446 + 7.61928i 0.183109 + 0.279901i
\(742\) 5.29885 + 2.04337i 0.194527 + 0.0750146i
\(743\) −30.8182 + 30.8182i −1.13061 + 1.13061i −0.140534 + 0.990076i \(0.544882\pi\)
−0.990076 + 0.140534i \(0.955118\pi\)
\(744\) −5.58432 + 11.0514i −0.204731 + 0.405164i
\(745\) −27.3737 + 27.8199i −1.00289 + 1.01924i
\(746\) −9.31740 5.37940i −0.341134 0.196954i
\(747\) 16.7524 + 13.3806i 0.612938 + 0.489571i
\(748\) −4.99090 4.99090i −0.182485 0.182485i
\(749\) −3.39837 + 4.66239i −0.124174 + 0.170360i
\(750\) −5.88201 1.08146i −0.214781 0.0394894i
\(751\) −19.9356 34.5294i −0.727459 1.26000i −0.957954 0.286923i \(-0.907368\pi\)
0.230495 0.973074i \(-0.425966\pi\)
\(752\) −14.2335 + 3.81385i −0.519042 + 0.139077i
\(753\) 20.6699 23.1118i 0.753254 0.842242i
\(754\) 4.24517 2.45095i 0.154600 0.0892583i
\(755\) −32.9342 8.53991i −1.19860 0.310799i
\(756\) 26.1357 1.59349i 0.950545 0.0579545i
\(757\) 0.798673 0.798673i 0.0290283 0.0290283i −0.692444 0.721472i \(-0.743466\pi\)
0.721472 + 0.692444i \(0.243466\pi\)
\(758\) 5.68591 + 1.52354i 0.206522 + 0.0553373i
\(759\) 0.562653 + 10.0881i 0.0204230 + 0.366175i
\(760\) −4.41371 + 0.0356852i −0.160102 + 0.00129444i
\(761\) 37.3941 21.5895i 1.35554 0.782619i 0.366518 0.930411i \(-0.380550\pi\)
0.989019 + 0.147791i \(0.0472164\pi\)
\(762\) −0.690601 + 3.30350i −0.0250178 + 0.119673i
\(763\) 3.92153 + 4.85791i 0.141969 + 0.175868i
\(764\) 27.1236 0.981299
\(765\) 26.0908 19.5524i 0.943314 0.706918i
\(766\) 1.56829 2.71637i 0.0566648 0.0981463i
\(767\) 23.8538 6.39162i 0.861312 0.230788i
\(768\) −14.6502 + 4.81457i −0.528644 + 0.173731i
\(769\) 44.1875i 1.59344i 0.604348 + 0.796720i \(0.293434\pi\)
−0.604348 + 0.796720i \(0.706566\pi\)
\(770\) 0.883782 + 1.07688i 0.0318493 + 0.0388081i
\(771\) 28.5812 18.6975i 1.02933 0.673376i
\(772\) −12.5397 3.36001i −0.451315 0.120929i
\(773\) −5.66214 21.1314i −0.203653 0.760043i −0.989856 0.142075i \(-0.954623\pi\)
0.786203 0.617968i \(-0.212044\pi\)
\(774\) −2.09113 2.83793i −0.0751640 0.102007i
\(775\) 0.479274 + 29.6375i 0.0172160 + 1.06461i
\(776\) 6.36214i 0.228388i
\(777\) −3.39822 15.8454i −0.121911 0.568450i
\(778\) 8.13643 + 8.13643i 0.291705 + 0.291705i
\(779\) 3.56817 + 6.18024i 0.127843 + 0.221430i
\(780\) −23.2259 4.65973i −0.831620 0.166845i
\(781\) 4.73385 8.19927i 0.169391 0.293393i
\(782\) 2.97231 11.0928i 0.106289 0.396678i
\(783\) −14.8856 + 20.9281i −0.531966 + 0.747911i
\(784\) −5.07407 + 23.5165i −0.181217 + 0.839876i
\(785\) 17.6095 10.3576i 0.628512 0.369679i
\(786\) 0.518555 1.02622i 0.0184962 0.0366041i
\(787\) 0.0780372 + 0.291239i 0.00278173 + 0.0103815i 0.967303 0.253625i \(-0.0816228\pi\)
−0.964521 + 0.264006i \(0.914956\pi\)
\(788\) 5.33748 + 19.9197i 0.190140 + 0.709612i
\(789\) −4.33425 + 8.57748i −0.154303 + 0.305367i
\(790\) 2.52120 1.48292i 0.0897003 0.0527600i
\(791\) −40.8360 + 18.1063i −1.45196 + 0.643787i
\(792\) 1.00577 + 2.56845i 0.0357385 + 0.0912659i
\(793\) −3.65209 + 13.6298i −0.129689 + 0.484007i
\(794\) −1.37270 + 2.37759i −0.0487153 + 0.0843774i
\(795\) 26.3927 + 5.29509i 0.936054 + 0.187798i
\(796\) −15.5988 27.0180i −0.552886 0.957626i
\(797\) −8.45240 8.45240i −0.299399 0.299399i 0.541379 0.840779i \(-0.317902\pi\)
−0.840779 + 0.541379i \(0.817902\pi\)
\(798\) −1.71879 + 1.55329i −0.0608446 + 0.0549858i
\(799\) 20.8390i 0.737231i
\(800\) 12.0795 12.4766i 0.427073 0.441113i
\(801\) −2.19103 + 1.61446i −0.0774163 + 0.0570441i
\(802\) 0.371808 + 1.38761i 0.0131290 + 0.0489981i
\(803\) 1.02203 + 0.273853i 0.0360668 + 0.00966407i
\(804\) −0.134712 + 0.0881271i −0.00475092 + 0.00310800i
\(805\) 15.9434 42.3613i 0.561932 1.49304i
\(806\) 5.87955i 0.207098i
\(807\) −16.5311 + 5.43269i −0.581922 + 0.191240i
\(808\) 22.1177 5.92642i 0.778098 0.208491i
\(809\) −18.5676 + 32.1600i −0.652801 + 1.13068i 0.329640 + 0.944107i \(0.393073\pi\)
−0.982440 + 0.186577i \(0.940261\pi\)
\(810\) −6.05021 + 1.42268i −0.212583 + 0.0499878i
\(811\) 23.5491 0.826921 0.413461 0.910522i \(-0.364320\pi\)
0.413461 + 0.910522i \(0.364320\pi\)
\(812\) −15.6442 19.3797i −0.549003 0.680093i
\(813\) −1.99915 + 9.56300i −0.0701134 + 0.335389i
\(814\) 0.721171 0.416368i 0.0252770 0.0145937i
\(815\) −6.05359 + 0.0489438i −0.212048 + 0.00171442i
\(816\) 1.61116 + 28.8874i 0.0564019 + 1.01126i
\(817\) −6.01583 1.61194i −0.210467 0.0563945i
\(818\) 5.79994 5.79994i 0.202790 0.202790i
\(819\) −22.0081 + 12.8588i −0.769024 + 0.449322i
\(820\) −17.9727 4.66036i −0.627633 0.162747i
\(821\) −35.4996 + 20.4957i −1.23895 + 0.715306i −0.968879 0.247536i \(-0.920379\pi\)
−0.270067 + 0.962842i \(0.587046\pi\)
\(822\) −3.14419 + 3.51563i −0.109666 + 0.122622i
\(823\) 24.8888 6.66893i 0.867568 0.232464i 0.202532 0.979276i \(-0.435083\pi\)
0.665036 + 0.746812i \(0.268416\pi\)
\(824\) −7.61596 13.1912i −0.265315 0.459538i
\(825\) 4.99243 + 4.32172i 0.173814 + 0.150463i
\(826\) 2.54694 + 5.74423i 0.0886195 + 0.199867i
\(827\) 19.5668 + 19.5668i 0.680404 + 0.680404i 0.960091 0.279687i \(-0.0902308\pi\)
−0.279687 + 0.960091i \(0.590231\pi\)
\(828\) 27.2822 34.1570i 0.948121 1.18704i
\(829\) 21.9279 + 12.6601i 0.761588 + 0.439703i 0.829866 0.557963i \(-0.188417\pi\)
−0.0682778 + 0.997666i \(0.521750\pi\)
\(830\) 3.46153 3.51796i 0.120151 0.122110i
\(831\) −8.78391 + 17.3834i −0.304710 + 0.603023i
\(832\) 13.1727 13.1727i 0.456680 0.456680i
\(833\) 30.2665 + 15.5388i 1.04867 + 0.538386i
\(834\) −3.03461 4.63873i −0.105080 0.160626i
\(835\) −6.01053 + 10.6077i −0.208003 + 0.367094i
\(836\) 2.05866 + 1.18857i 0.0712002 + 0.0411075i
\(837\) 12.8119 + 28.0134i 0.442844 + 0.968286i
\(838\) 2.06449 7.70479i 0.0713167 0.266157i
\(839\) 50.7484 1.75203 0.876014 0.482286i \(-0.160193\pi\)
0.876014 + 0.482286i \(0.160193\pi\)
\(840\) 0.524423 12.3456i 0.0180943 0.425963i
\(841\) −4.57160 −0.157641
\(842\) −0.0345654 + 0.129000i −0.00119120 + 0.00444563i
\(843\) −2.22651 + 2.48954i −0.0766851 + 0.0857444i
\(844\) −42.0656 24.2866i −1.44796 0.835978i
\(845\) −5.79137 + 1.60209i −0.199229 + 0.0551134i
\(846\) 1.59136 3.63981i 0.0547120 0.125139i
\(847\) 4.27036 + 27.2324i 0.146731 + 0.935715i
\(848\) −16.8908 + 16.8908i −0.580031 + 0.580031i
\(849\) 40.7578 + 20.5951i 1.39880 + 0.706823i
\(850\) −3.85723 6.43820i −0.132302 0.220829i
\(851\) −23.4310 13.5279i −0.803204 0.463730i
\(852\) −38.9155 + 12.7890i −1.33322 + 0.438143i
\(853\) −18.8448 18.8448i −0.645233 0.645233i 0.306604 0.951837i \(-0.400807\pi\)
−0.951837 + 0.306604i \(0.900807\pi\)
\(854\) −3.57009 0.380772i −0.122166 0.0130297i
\(855\) −6.78337 + 8.63495i −0.231986 + 0.295309i
\(856\) 1.31482 + 2.27733i 0.0449395 + 0.0778375i
\(857\) 12.0212 3.22108i 0.410637 0.110030i −0.0475860 0.998867i \(-0.515153\pi\)
0.458223 + 0.888837i \(0.348486\pi\)
\(858\) −0.976291 0.873141i −0.0333300 0.0298085i
\(859\) 3.33705 1.92665i 0.113859 0.0657364i −0.441989 0.897020i \(-0.645727\pi\)
0.555848 + 0.831284i \(0.312394\pi\)
\(860\) 13.9670 8.21515i 0.476272 0.280134i
\(861\) −17.7843 + 9.10240i −0.606087 + 0.310209i
\(862\) 3.56217 3.56217i 0.121328 0.121328i
\(863\) −48.2127 12.9186i −1.64118 0.439753i −0.684056 0.729429i \(-0.739786\pi\)
−0.957125 + 0.289676i \(0.906452\pi\)
\(864\) 6.29759 16.9128i 0.214248 0.575387i
\(865\) 0.0239219 + 2.95877i 0.000813368 + 0.100601i
\(866\) 0.194509 0.112300i 0.00660967 0.00381610i
\(867\) 11.2282 + 2.34727i 0.381331 + 0.0797176i
\(868\) −29.5128 + 4.62795i −1.00173 + 0.157083i
\(869\) −3.22945 −0.109552
\(870\) 4.43832 + 3.90527i 0.150473 + 0.132401i
\(871\) 0.0783524 0.135710i 0.00265487 0.00459837i
\(872\) 2.74860 0.736484i 0.0930793 0.0249405i
\(873\) 12.3670 + 9.87787i 0.418559 + 0.334315i
\(874\) 3.86774i 0.130828i
\(875\) −12.6422 26.7427i −0.427386 0.904069i
\(876\) −2.50620 3.83099i −0.0846765 0.129437i
\(877\) 43.6713 + 11.7017i 1.47467 + 0.395138i 0.904531 0.426408i \(-0.140221\pi\)
0.570143 + 0.821546i \(0.306888\pi\)
\(878\) 1.22284 + 4.56370i 0.0412689 + 0.154018i
\(879\) −19.1579 + 1.06851i −0.646179 + 0.0360399i
\(880\) −5.64741 + 1.56226i −0.190374 + 0.0526639i
\(881\) 25.2055i 0.849195i −0.905382 0.424597i \(-0.860416\pi\)
0.905382 0.424597i \(-0.139584\pi\)
\(882\) −4.09984 5.02534i −0.138049 0.169212i
\(883\) −14.2942 14.2942i −0.481039 0.481039i 0.424424 0.905463i \(-0.360476\pi\)
−0.905463 + 0.424424i \(0.860476\pi\)
\(884\) −14.8638 25.7449i −0.499925 0.865895i
\(885\) 16.5059 + 24.7912i 0.554839 + 0.833346i
\(886\) −1.40912 + 2.44067i −0.0473403 + 0.0819958i
\(887\) 10.0709 37.5853i 0.338149 1.26199i −0.562266 0.826957i \(-0.690070\pi\)
0.900415 0.435033i \(-0.143263\pi\)
\(888\) −7.23000 1.51144i −0.242623 0.0507206i
\(889\) −15.2598 + 6.76605i −0.511796 + 0.226926i
\(890\) 0.317623 + 0.540010i 0.0106468 + 0.0181012i
\(891\) 6.55421 + 2.03273i 0.219574 + 0.0680989i
\(892\) −10.7740 40.2091i −0.360740 1.34630i
\(893\) −1.81649 6.77923i −0.0607865 0.226858i
\(894\) 8.33323 + 4.21082i 0.278705 + 0.140831i
\(895\) 0.523094 + 0.135639i 0.0174851 + 0.00453393i
\(896\) 18.6823 + 13.6174i 0.624133 + 0.454924i
\(897\) −8.70792 + 41.6545i −0.290749 + 1.39080i
\(898\) 0.752081 2.80681i 0.0250973 0.0936643i
\(899\) 14.6503 25.3750i 0.488613 0.846303i
\(900\) −3.63562 28.3370i −0.121187 0.944567i
\(901\) 16.8905 + 29.2553i 0.562705 + 0.974634i
\(902\) −0.725914 0.725914i −0.0241703 0.0241703i
\(903\) 5.35767 16.5920i 0.178292 0.552147i
\(904\) 20.3599i 0.677161i
\(905\) −11.1405 40.2716i −0.370322 1.33867i
\(906\) 0.453252 + 8.12659i 0.0150583 + 0.269988i
\(907\) 0.623721 + 2.32776i 0.0207103 + 0.0772920i 0.975508 0.219966i \(-0.0705946\pi\)
−0.954797 + 0.297258i \(0.903928\pi\)
\(908\) −23.6365 6.33337i −0.784404 0.210180i
\(909\) 22.8200 52.1946i 0.756891 1.73119i
\(910\) 2.42157 + 5.34445i 0.0802744 + 0.177167i
\(911\) 19.3662i 0.641631i −0.947142 0.320815i \(-0.896043\pi\)
0.947142 0.320815i \(-0.103957\pi\)
\(912\) −3.04218 9.25703i −0.100737 0.306531i
\(913\) −5.26347 + 1.41034i −0.174196 + 0.0466755i
\(914\) −5.33185 + 9.23503i −0.176362 + 0.305468i
\(915\) −16.9832 + 1.08502i −0.561446 + 0.0358696i
\(916\) −29.1421 −0.962883
\(917\) 5.61830 0.881015i 0.185533 0.0290937i
\(918\) −6.35591 4.52077i −0.209776 0.149208i
\(919\) 29.5591 17.0659i 0.975063 0.562953i 0.0742872 0.997237i \(-0.476332\pi\)
0.900776 + 0.434284i \(0.142998\pi\)
\(920\) −14.7050 14.4691i −0.484808 0.477031i
\(921\) −41.7647 + 2.32938i −1.37619 + 0.0767558i
\(922\) −11.0175 2.95213i −0.362842 0.0972231i
\(923\) 28.1966 28.1966i 0.928102 0.928102i
\(924\) −3.61432 + 5.58782i −0.118902 + 0.183826i
\(925\) −17.0031 + 4.85196i −0.559059 + 0.159531i
\(926\) −9.97388 + 5.75842i −0.327762 + 0.189233i
\(927\) −37.4662 5.67652i −1.23055 0.186441i
\(928\) −16.5814 + 4.44297i −0.544311 + 0.145848i
\(929\) 9.86232 + 17.0820i 0.323572 + 0.560443i 0.981222 0.192880i \(-0.0617828\pi\)
−0.657650 + 0.753323i \(0.728450\pi\)
\(930\) 6.71836 2.26823i 0.220304 0.0743782i
\(931\) −11.2006 2.41672i −0.367085 0.0792047i
\(932\) 9.24073 + 9.24073i 0.302690 + 0.302690i
\(933\) 12.7878 + 38.9120i 0.418655 + 1.27392i
\(934\) −2.72793 1.57497i −0.0892606 0.0515346i
\(935\) 0.0669948 + 8.28622i 0.00219096 + 0.270988i
\(936\) 1.29190 + 11.5456i 0.0422271 + 0.377378i
\(937\) −17.3041 + 17.3041i −0.565300 + 0.565300i −0.930808 0.365508i \(-0.880895\pi\)
0.365508 + 0.930808i \(0.380895\pi\)
\(938\) 0.0372022 + 0.0143461i 0.00121470 + 0.000468418i
\(939\) −17.9436 + 11.7385i −0.585568 + 0.383072i
\(940\) 15.8871 + 9.00194i 0.518179 + 0.293611i
\(941\) 3.89269 + 2.24744i 0.126898 + 0.0732646i 0.562105 0.827066i \(-0.309992\pi\)
−0.435207 + 0.900330i \(0.643325\pi\)
\(942\) −3.64292 3.25803i −0.118693 0.106152i
\(943\) −8.63274 + 32.2178i −0.281121 + 1.04916i
\(944\) −26.4292 −0.860196
\(945\) −23.1836 20.1872i −0.754162 0.656688i
\(946\) 0.895935 0.0291294
\(947\) −3.88234 + 14.4891i −0.126159 + 0.470832i −0.999878 0.0155984i \(-0.995035\pi\)
0.873719 + 0.486431i \(0.161701\pi\)
\(948\) 10.4150 + 9.31460i 0.338263 + 0.302524i
\(949\) 3.85939 + 2.22822i 0.125281 + 0.0723311i
\(950\) 1.81602 + 1.75822i 0.0589193 + 0.0570440i
\(951\) −6.36658 + 4.16495i −0.206451 + 0.135058i
\(952\) 12.0660 9.74025i 0.391062 0.315683i
\(953\) 21.6181 21.6181i 0.700277 0.700277i −0.264193 0.964470i \(-0.585105\pi\)
0.964470 + 0.264193i \(0.0851054\pi\)
\(954\) −0.716096 6.39966i −0.0231845 0.207197i
\(955\) −22.6983 22.3342i −0.734499 0.722717i
\(956\) 30.8583 + 17.8160i 0.998028 + 0.576212i
\(957\) −2.03785 6.20096i −0.0658743 0.200448i
\(958\) −2.99334 2.99334i −0.0967106 0.0967106i
\(959\) −23.1966 2.47406i −0.749058 0.0798915i
\(960\) 20.1337 + 9.97015i 0.649813 + 0.321785i
\(961\) −2.07218 3.58912i −0.0668444 0.115778i
\(962\) 3.38780 0.907759i 0.109227 0.0292673i
\(963\) 6.46814 + 0.979992i 0.208433 + 0.0315798i
\(964\) 3.25292 1.87807i 0.104769 0.0604887i
\(965\) 7.72710 + 13.1373i 0.248744 + 0.422904i
\(966\) −10.8140 0.546985i −0.347935 0.0175989i
\(967\) 16.1911 16.1911i 0.520672 0.520672i −0.397102 0.917774i \(-0.629984\pi\)
0.917774 + 0.397102i \(0.129984\pi\)
\(968\) 12.1357 + 3.25174i 0.390055 + 0.104515i
\(969\) −13.7587 + 0.767375i −0.441992 + 0.0246517i
\(970\) 2.55538 2.59703i 0.0820482 0.0833857i
\(971\) 15.8437 9.14738i 0.508450 0.293553i −0.223747 0.974647i \(-0.571829\pi\)
0.732196 + 0.681094i \(0.238495\pi\)
\(972\) −15.2744 25.4596i −0.489928 0.816618i
\(973\) 9.86456 25.5807i 0.316243 0.820078i
\(974\) 7.06004 0.226218
\(975\) 15.5995 + 23.0241i 0.499584 + 0.737363i
\(976\) 7.55064 13.0781i 0.241690 0.418619i
\(977\) −14.3951 + 3.85716i −0.460540 + 0.123401i −0.481627 0.876376i \(-0.659954\pi\)
0.0210868 + 0.999778i \(0.493287\pi\)
\(978\) 0.452142 + 1.37582i 0.0144579 + 0.0439939i
\(979\) 0.691709i 0.0221071i
\(980\) 24.9207 16.3620i 0.796063 0.522665i
\(981\) 2.83587 6.48630i 0.0905423 0.207092i
\(982\) −7.08425 1.89822i −0.226067 0.0605746i
\(983\) −3.04352 11.3586i −0.0970733 0.362283i 0.900252 0.435368i \(-0.143382\pi\)
−0.997326 + 0.0730860i \(0.976715\pi\)
\(984\) 0.507079 + 9.09168i 0.0161651 + 0.289832i
\(985\) 11.9357 21.0647i 0.380303 0.671178i
\(986\) 7.41895i 0.236267i
\(987\) 19.2113 4.12008i 0.611502 0.131144i
\(988\) 7.07955 + 7.07955i 0.225230 + 0.225230i
\(989\) −14.5546 25.2092i −0.462808 0.801607i
\(990\) 0.621071 1.45242i 0.0197389 0.0461608i
\(991\) −5.02003 + 8.69495i −0.159467 + 0.276204i −0.934676 0.355499i \(-0.884311\pi\)
0.775210 + 0.631704i \(0.217644\pi\)
\(992\) −5.32910 + 19.8885i −0.169199 + 0.631459i
\(993\) −2.20405 + 10.5431i −0.0699434 + 0.334576i
\(994\) 8.19927 + 5.97636i 0.260065 + 0.189559i
\(995\) −9.19337 + 35.4542i −0.291449 + 1.12397i
\(996\) 21.0425 + 10.6329i 0.666757 + 0.336916i
\(997\) −3.64290 13.5955i −0.115372 0.430574i 0.883943 0.467596i \(-0.154880\pi\)
−0.999314 + 0.0370216i \(0.988213\pi\)
\(998\) −0.258609 0.965142i −0.00818612 0.0305510i
\(999\) −14.1633 + 11.7073i −0.448107 + 0.370402i
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 105.2.x.a.53.6 yes 48
3.2 odd 2 inner 105.2.x.a.53.7 yes 48
5.2 odd 4 inner 105.2.x.a.32.6 yes 48
5.3 odd 4 525.2.bf.f.32.7 48
5.4 even 2 525.2.bf.f.368.7 48
7.2 even 3 inner 105.2.x.a.23.7 yes 48
7.3 odd 6 735.2.j.e.638.6 24
7.4 even 3 735.2.j.g.638.6 24
7.5 odd 6 735.2.y.i.128.7 48
7.6 odd 2 735.2.y.i.263.6 48
15.2 even 4 inner 105.2.x.a.32.7 yes 48
15.8 even 4 525.2.bf.f.32.6 48
15.14 odd 2 525.2.bf.f.368.6 48
21.2 odd 6 inner 105.2.x.a.23.6 yes 48
21.5 even 6 735.2.y.i.128.6 48
21.11 odd 6 735.2.j.g.638.7 24
21.17 even 6 735.2.j.e.638.7 24
21.20 even 2 735.2.y.i.263.7 48
35.2 odd 12 inner 105.2.x.a.2.7 yes 48
35.9 even 6 525.2.bf.f.443.6 48
35.12 even 12 735.2.y.i.422.7 48
35.17 even 12 735.2.j.e.197.7 24
35.23 odd 12 525.2.bf.f.107.6 48
35.27 even 4 735.2.y.i.557.6 48
35.32 odd 12 735.2.j.g.197.7 24
105.2 even 12 inner 105.2.x.a.2.6 48
105.17 odd 12 735.2.j.e.197.6 24
105.23 even 12 525.2.bf.f.107.7 48
105.32 even 12 735.2.j.g.197.6 24
105.44 odd 6 525.2.bf.f.443.7 48
105.47 odd 12 735.2.y.i.422.6 48
105.62 odd 4 735.2.y.i.557.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.6 48 105.2 even 12 inner
105.2.x.a.2.7 yes 48 35.2 odd 12 inner
105.2.x.a.23.6 yes 48 21.2 odd 6 inner
105.2.x.a.23.7 yes 48 7.2 even 3 inner
105.2.x.a.32.6 yes 48 5.2 odd 4 inner
105.2.x.a.32.7 yes 48 15.2 even 4 inner
105.2.x.a.53.6 yes 48 1.1 even 1 trivial
105.2.x.a.53.7 yes 48 3.2 odd 2 inner
525.2.bf.f.32.6 48 15.8 even 4
525.2.bf.f.32.7 48 5.3 odd 4
525.2.bf.f.107.6 48 35.23 odd 12
525.2.bf.f.107.7 48 105.23 even 12
525.2.bf.f.368.6 48 15.14 odd 2
525.2.bf.f.368.7 48 5.4 even 2
525.2.bf.f.443.6 48 35.9 even 6
525.2.bf.f.443.7 48 105.44 odd 6
735.2.j.e.197.6 24 105.17 odd 12
735.2.j.e.197.7 24 35.17 even 12
735.2.j.e.638.6 24 7.3 odd 6
735.2.j.e.638.7 24 21.17 even 6
735.2.j.g.197.6 24 105.32 even 12
735.2.j.g.197.7 24 35.32 odd 12
735.2.j.g.638.6 24 7.4 even 3
735.2.j.g.638.7 24 21.11 odd 6
735.2.y.i.128.6 48 21.5 even 6
735.2.y.i.128.7 48 7.5 odd 6
735.2.y.i.263.6 48 7.6 odd 2
735.2.y.i.263.7 48 21.20 even 2
735.2.y.i.422.6 48 105.47 odd 12
735.2.y.i.422.7 48 35.12 even 12
735.2.y.i.557.6 48 35.27 even 4
735.2.y.i.557.7 48 105.62 odd 4