Properties

Label 252.2.o.a.95.4
Level $252$
Weight $2$
Character 252.95
Analytic conductor $2.012$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(95,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.95");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.o (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 95.4
Character \(\chi\) \(=\) 252.95
Dual form 252.2.o.a.191.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33435 + 0.468511i) q^{2} +(-0.316645 + 1.70286i) q^{3} +(1.56099 - 1.25032i) q^{4} -2.87282i q^{5} +(-0.375293 - 2.42057i) q^{6} +(-2.24795 + 1.39525i) q^{7} +(-1.49713 + 2.39971i) q^{8} +(-2.79947 - 1.07841i) q^{9} +O(q^{10})\) \(q+(-1.33435 + 0.468511i) q^{2} +(-0.316645 + 1.70286i) q^{3} +(1.56099 - 1.25032i) q^{4} -2.87282i q^{5} +(-0.375293 - 2.42057i) q^{6} +(-2.24795 + 1.39525i) q^{7} +(-1.49713 + 2.39971i) q^{8} +(-2.79947 - 1.07841i) q^{9} +(1.34595 + 3.83335i) q^{10} -3.53765 q^{11} +(1.63484 + 3.05406i) q^{12} +(-3.15869 + 5.47102i) q^{13} +(2.34587 - 2.91494i) q^{14} +(4.89201 + 0.909664i) q^{15} +(0.873407 - 3.90348i) q^{16} +(-3.21678 - 1.85721i) q^{17} +(4.24073 + 0.127390i) q^{18} +(1.82312 - 1.05258i) q^{19} +(-3.59194 - 4.48445i) q^{20} +(-1.66411 - 4.26975i) q^{21} +(4.72047 - 1.65743i) q^{22} -5.49191 q^{23} +(-3.61231 - 3.30926i) q^{24} -3.25308 q^{25} +(1.65158 - 8.78015i) q^{26} +(2.72282 - 4.42564i) q^{27} +(-1.76454 + 4.98863i) q^{28} +(2.32201 - 1.34061i) q^{29} +(-6.95385 + 1.07815i) q^{30} +(-0.222354 + 0.128376i) q^{31} +(0.663392 + 5.61782i) q^{32} +(1.12018 - 6.02413i) q^{33} +(5.16245 + 0.971075i) q^{34} +(4.00829 + 6.45796i) q^{35} +(-5.71831 + 1.81685i) q^{36} +(-0.720918 - 1.24867i) q^{37} +(-1.93954 + 2.25866i) q^{38} +(-8.31620 - 7.11119i) q^{39} +(6.89393 + 4.30098i) q^{40} +(5.24333 + 3.02724i) q^{41} +(4.22093 + 4.91770i) q^{42} +(-4.79832 + 2.77031i) q^{43} +(-5.52225 + 4.42319i) q^{44} +(-3.09806 + 8.04237i) q^{45} +(7.32814 - 2.57302i) q^{46} +(-1.02078 + 1.76804i) q^{47} +(6.37052 + 2.72331i) q^{48} +(3.10658 - 6.27289i) q^{49} +(4.34076 - 1.52411i) q^{50} +(4.18115 - 4.88966i) q^{51} +(1.90981 + 12.4896i) q^{52} +(-1.96139 - 1.13241i) q^{53} +(-1.55973 + 7.18103i) q^{54} +10.1630i q^{55} +(0.0172906 - 7.48329i) q^{56} +(1.21511 + 3.43781i) q^{57} +(-2.47028 + 2.87673i) q^{58} +(3.55424 + 6.15612i) q^{59} +(8.77377 - 4.69659i) q^{60} +(-2.83535 + 4.91097i) q^{61} +(0.236553 - 0.275474i) q^{62} +(7.79772 - 1.48174i) q^{63} +(-3.51721 - 7.18535i) q^{64} +(15.7172 + 9.07435i) q^{65} +(1.32766 + 8.56313i) q^{66} +(6.36193 - 3.67306i) q^{67} +(-7.34348 + 1.12291i) q^{68} +(1.73899 - 9.35196i) q^{69} +(-8.37409 - 6.73927i) q^{70} -9.04391 q^{71} +(6.77903 - 5.10341i) q^{72} +(5.86192 - 10.1531i) q^{73} +(1.54697 + 1.32840i) q^{74} +(1.03007 - 5.53955i) q^{75} +(1.52982 - 3.92255i) q^{76} +(7.95247 - 4.93589i) q^{77} +(14.4284 + 5.59260i) q^{78} +(-10.7238 - 6.19137i) q^{79} +(-11.2140 - 2.50914i) q^{80} +(6.67408 + 6.03793i) q^{81} +(-8.41474 - 1.58284i) q^{82} +(5.49556 + 9.51858i) q^{83} +(-7.93621 - 4.58439i) q^{84} +(-5.33543 + 9.24123i) q^{85} +(5.10473 - 5.94464i) q^{86} +(1.54762 + 4.37855i) q^{87} +(5.29632 - 8.48934i) q^{88} +(-7.32424 + 4.22865i) q^{89} +(0.365969 - 12.1828i) q^{90} +(-0.532818 - 16.7057i) q^{91} +(-8.57284 + 6.86663i) q^{92} +(-0.148199 - 0.419288i) q^{93} +(0.533732 - 2.83744i) q^{94} +(-3.02387 - 5.23749i) q^{95} +(-9.77643 - 0.649192i) q^{96} +(4.95593 + 8.58392i) q^{97} +(-1.20636 + 9.82572i) q^{98} +(9.90355 + 3.81502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 3 q^{2} + q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 3 q^{2} + q^{4} - 6 q^{6} - 2 q^{9} + 2 q^{10} + 3 q^{12} - 4 q^{13} - 3 q^{14} + q^{16} + 5 q^{18} - 6 q^{20} - 6 q^{22} - 14 q^{24} - 60 q^{25} - 6 q^{26} - 24 q^{29} + 22 q^{30} + 27 q^{32} - 26 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} + 8 q^{40} - 12 q^{41} - 13 q^{42} - 57 q^{44} + 42 q^{45} - 6 q^{46} - 43 q^{48} - 2 q^{49} + 9 q^{50} + 14 q^{52} - 22 q^{54} - 66 q^{56} - 28 q^{57} - 10 q^{58} + 32 q^{60} + 2 q^{61} - 8 q^{64} + 18 q^{65} - 93 q^{66} - 6 q^{69} + 30 q^{70} + 53 q^{72} - 4 q^{73} - 6 q^{76} - 30 q^{77} + 55 q^{78} + 87 q^{80} + 26 q^{81} - 4 q^{82} - 7 q^{84} - 14 q^{85} - 18 q^{88} + 60 q^{89} + 41 q^{90} + 24 q^{92} - 30 q^{93} + 9 q^{94} - 20 q^{96} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33435 + 0.468511i −0.943530 + 0.331288i
\(3\) −0.316645 + 1.70286i −0.182815 + 0.983147i
\(4\) 1.56099 1.25032i 0.780497 0.625159i
\(5\) 2.87282i 1.28476i −0.766385 0.642382i \(-0.777946\pi\)
0.766385 0.642382i \(-0.222054\pi\)
\(6\) −0.375293 2.42057i −0.153213 0.988193i
\(7\) −2.24795 + 1.39525i −0.849646 + 0.527353i
\(8\) −1.49713 + 2.39971i −0.529315 + 0.848425i
\(9\) −2.79947 1.07841i −0.933157 0.359469i
\(10\) 1.34595 + 3.83335i 0.425626 + 1.21221i
\(11\) −3.53765 −1.06664 −0.533321 0.845913i \(-0.679056\pi\)
−0.533321 + 0.845913i \(0.679056\pi\)
\(12\) 1.63484 + 3.05406i 0.471937 + 0.881632i
\(13\) −3.15869 + 5.47102i −0.876064 + 1.51739i −0.0204391 + 0.999791i \(0.506506\pi\)
−0.855625 + 0.517596i \(0.826827\pi\)
\(14\) 2.34587 2.91494i 0.626961 0.779051i
\(15\) 4.89201 + 0.909664i 1.26311 + 0.234874i
\(16\) 0.873407 3.90348i 0.218352 0.975870i
\(17\) −3.21678 1.85721i −0.780184 0.450440i 0.0563112 0.998413i \(-0.482066\pi\)
−0.836496 + 0.547974i \(0.815399\pi\)
\(18\) 4.24073 + 0.127390i 0.999549 + 0.0300261i
\(19\) 1.82312 1.05258i 0.418252 0.241478i −0.276077 0.961136i \(-0.589034\pi\)
0.694329 + 0.719657i \(0.255701\pi\)
\(20\) −3.59194 4.48445i −0.803182 1.00275i
\(21\) −1.66411 4.26975i −0.363137 0.931736i
\(22\) 4.72047 1.65743i 1.00641 0.353365i
\(23\) −5.49191 −1.14514 −0.572571 0.819855i \(-0.694054\pi\)
−0.572571 + 0.819855i \(0.694054\pi\)
\(24\) −3.61231 3.30926i −0.737360 0.675500i
\(25\) −3.25308 −0.650617
\(26\) 1.65158 8.78015i 0.323901 1.72193i
\(27\) 2.72282 4.42564i 0.524006 0.851715i
\(28\) −1.76454 + 4.98863i −0.333467 + 0.942762i
\(29\) 2.32201 1.34061i 0.431186 0.248945i −0.268666 0.963233i \(-0.586583\pi\)
0.699852 + 0.714288i \(0.253249\pi\)
\(30\) −6.95385 + 1.07815i −1.26959 + 0.196842i
\(31\) −0.222354 + 0.128376i −0.0399360 + 0.0230570i −0.519835 0.854267i \(-0.674007\pi\)
0.479899 + 0.877324i \(0.340673\pi\)
\(32\) 0.663392 + 5.61782i 0.117272 + 0.993100i
\(33\) 1.12018 6.02413i 0.194998 1.04867i
\(34\) 5.16245 + 0.971075i 0.885352 + 0.166538i
\(35\) 4.00829 + 6.45796i 0.677524 + 1.09159i
\(36\) −5.71831 + 1.81685i −0.953052 + 0.302808i
\(37\) −0.720918 1.24867i −0.118518 0.205280i 0.800662 0.599116i \(-0.204481\pi\)
−0.919181 + 0.393836i \(0.871148\pi\)
\(38\) −1.93954 + 2.25866i −0.314635 + 0.366404i
\(39\) −8.31620 7.11119i −1.33166 1.13870i
\(40\) 6.89393 + 4.30098i 1.09003 + 0.680044i
\(41\) 5.24333 + 3.02724i 0.818870 + 0.472775i 0.850027 0.526740i \(-0.176586\pi\)
−0.0311565 + 0.999515i \(0.509919\pi\)
\(42\) 4.22093 + 4.91770i 0.651303 + 0.758817i
\(43\) −4.79832 + 2.77031i −0.731737 + 0.422469i −0.819057 0.573712i \(-0.805503\pi\)
0.0873202 + 0.996180i \(0.472170\pi\)
\(44\) −5.52225 + 4.42319i −0.832511 + 0.666821i
\(45\) −3.09806 + 8.04237i −0.461832 + 1.19889i
\(46\) 7.32814 2.57302i 1.08048 0.379371i
\(47\) −1.02078 + 1.76804i −0.148896 + 0.257895i −0.930820 0.365479i \(-0.880905\pi\)
0.781924 + 0.623374i \(0.214239\pi\)
\(48\) 6.37052 + 2.72331i 0.919506 + 0.393076i
\(49\) 3.10658 6.27289i 0.443797 0.896127i
\(50\) 4.34076 1.52411i 0.613876 0.215541i
\(51\) 4.18115 4.88966i 0.585478 0.684689i
\(52\) 1.90981 + 12.4896i 0.264843 + 1.73200i
\(53\) −1.96139 1.13241i −0.269417 0.155548i 0.359206 0.933258i \(-0.383048\pi\)
−0.628623 + 0.777710i \(0.716381\pi\)
\(54\) −1.55973 + 7.18103i −0.212253 + 0.977215i
\(55\) 10.1630i 1.37038i
\(56\) 0.0172906 7.48329i 0.00231055 0.999997i
\(57\) 1.21511 + 3.43781i 0.160946 + 0.455350i
\(58\) −2.47028 + 2.87673i −0.324364 + 0.377734i
\(59\) 3.55424 + 6.15612i 0.462722 + 0.801458i 0.999096 0.0425227i \(-0.0135395\pi\)
−0.536373 + 0.843981i \(0.680206\pi\)
\(60\) 8.77377 4.69659i 1.13269 0.606327i
\(61\) −2.83535 + 4.91097i −0.363029 + 0.628785i −0.988458 0.151496i \(-0.951591\pi\)
0.625428 + 0.780282i \(0.284924\pi\)
\(62\) 0.236553 0.275474i 0.0300423 0.0349853i
\(63\) 7.79772 1.48174i 0.982420 0.186682i
\(64\) −3.51721 7.18535i −0.439652 0.898168i
\(65\) 15.7172 + 9.07435i 1.94948 + 1.12553i
\(66\) 1.32766 + 8.56313i 0.163423 + 1.05405i
\(67\) 6.36193 3.67306i 0.777234 0.448736i −0.0582151 0.998304i \(-0.518541\pi\)
0.835449 + 0.549568i \(0.185208\pi\)
\(68\) −7.34348 + 1.12291i −0.890528 + 0.136173i
\(69\) 1.73899 9.35196i 0.209349 1.12584i
\(70\) −8.37409 6.73927i −1.00090 0.805496i
\(71\) −9.04391 −1.07331 −0.536657 0.843800i \(-0.680313\pi\)
−0.536657 + 0.843800i \(0.680313\pi\)
\(72\) 6.77903 5.10341i 0.798916 0.601442i
\(73\) 5.86192 10.1531i 0.686085 1.18833i −0.287009 0.957928i \(-0.592661\pi\)
0.973094 0.230407i \(-0.0740057\pi\)
\(74\) 1.54697 + 1.32840i 0.179832 + 0.154424i
\(75\) 1.03007 5.53955i 0.118943 0.639652i
\(76\) 1.52982 3.92255i 0.175482 0.449947i
\(77\) 7.95247 4.93589i 0.906268 0.562497i
\(78\) 14.4284 + 5.59260i 1.63370 + 0.633237i
\(79\) −10.7238 6.19137i −1.20652 0.696584i −0.244521 0.969644i \(-0.578631\pi\)
−0.961997 + 0.273060i \(0.911964\pi\)
\(80\) −11.2140 2.50914i −1.25376 0.280530i
\(81\) 6.67408 + 6.03793i 0.741565 + 0.670882i
\(82\) −8.41474 1.58284i −0.929253 0.174796i
\(83\) 5.49556 + 9.51858i 0.603216 + 1.04480i 0.992331 + 0.123611i \(0.0394475\pi\)
−0.389115 + 0.921189i \(0.627219\pi\)
\(84\) −7.93621 4.58439i −0.865911 0.500198i
\(85\) −5.33543 + 9.24123i −0.578708 + 1.00235i
\(86\) 5.10473 5.94464i 0.550457 0.641027i
\(87\) 1.54762 + 4.37855i 0.165922 + 0.469430i
\(88\) 5.29632 8.48934i 0.564589 0.904966i
\(89\) −7.32424 + 4.22865i −0.776368 + 0.448236i −0.835142 0.550035i \(-0.814614\pi\)
0.0587737 + 0.998271i \(0.481281\pi\)
\(90\) 0.365969 12.1828i 0.0385765 1.28418i
\(91\) −0.532818 16.7057i −0.0558545 1.75124i
\(92\) −8.57284 + 6.86663i −0.893780 + 0.715896i
\(93\) −0.148199 0.419288i −0.0153676 0.0434781i
\(94\) 0.533732 2.83744i 0.0550503 0.292659i
\(95\) −3.02387 5.23749i −0.310242 0.537355i
\(96\) −9.77643 0.649192i −0.997803 0.0662579i
\(97\) 4.95593 + 8.58392i 0.503198 + 0.871565i 0.999993 + 0.00369720i \(0.00117686\pi\)
−0.496795 + 0.867868i \(0.665490\pi\)
\(98\) −1.20636 + 9.82572i −0.121860 + 0.992547i
\(99\) 9.90355 + 3.81502i 0.995345 + 0.383424i
\(100\) −5.07804 + 4.06739i −0.507804 + 0.406739i
\(101\) 15.0826i 1.50078i 0.660996 + 0.750389i \(0.270134\pi\)
−0.660996 + 0.750389i \(0.729866\pi\)
\(102\) −3.28827 + 8.48344i −0.325587 + 0.839986i
\(103\) 1.44210i 0.142094i −0.997473 0.0710472i \(-0.977366\pi\)
0.997473 0.0710472i \(-0.0226341\pi\)
\(104\) −8.39988 15.7708i −0.823676 1.54645i
\(105\) −12.2662 + 4.78067i −1.19706 + 0.466546i
\(106\) 3.14773 + 0.592099i 0.305734 + 0.0575097i
\(107\) 1.82752 + 3.16536i 0.176673 + 0.306007i 0.940739 0.339131i \(-0.110133\pi\)
−0.764066 + 0.645138i \(0.776800\pi\)
\(108\) −1.28316 10.3128i −0.123472 0.992348i
\(109\) −7.28399 + 12.6162i −0.697680 + 1.20842i 0.271589 + 0.962413i \(0.412451\pi\)
−0.969269 + 0.246003i \(0.920883\pi\)
\(110\) −4.76149 13.5611i −0.453991 1.29300i
\(111\) 2.35458 0.832239i 0.223487 0.0789926i
\(112\) 3.48294 + 9.99346i 0.329107 + 0.944293i
\(113\) −12.2439 7.06904i −1.15181 0.664999i −0.202484 0.979286i \(-0.564901\pi\)
−0.949328 + 0.314286i \(0.898235\pi\)
\(114\) −3.23204 4.01796i −0.302709 0.376317i
\(115\) 15.7773i 1.47124i
\(116\) 1.94845 4.99594i 0.180909 0.463861i
\(117\) 14.7427 11.9096i 1.36296 1.10104i
\(118\) −7.62681 6.54923i −0.702105 0.602906i
\(119\) 9.82244 0.313280i 0.900422 0.0287183i
\(120\) −9.50690 + 10.3775i −0.867857 + 0.947333i
\(121\) 1.51498 0.137725
\(122\) 1.48251 7.88136i 0.134220 0.713545i
\(123\) −6.81524 + 7.97010i −0.614509 + 0.718640i
\(124\) −0.186582 + 0.478408i −0.0167556 + 0.0429623i
\(125\) 5.01857i 0.448875i
\(126\) −9.71070 + 5.63049i −0.865097 + 0.501604i
\(127\) 16.9477i 1.50386i −0.659242 0.751931i \(-0.729123\pi\)
0.659242 0.751931i \(-0.270877\pi\)
\(128\) 8.05962 + 7.93993i 0.712376 + 0.701798i
\(129\) −3.19809 9.04808i −0.281576 0.796639i
\(130\) −25.2238 4.74468i −2.21227 0.416136i
\(131\) 5.20164 0.454470 0.227235 0.973840i \(-0.427032\pi\)
0.227235 + 0.973840i \(0.427032\pi\)
\(132\) −5.78348 10.8042i −0.503388 0.940386i
\(133\) −2.62968 + 4.90985i −0.228022 + 0.425738i
\(134\) −6.76819 + 7.88180i −0.584683 + 0.680884i
\(135\) −12.7141 7.82215i −1.09425 0.673224i
\(136\) 9.27270 4.93886i 0.795128 0.423504i
\(137\) 13.1000i 1.11921i −0.828760 0.559604i \(-0.810953\pi\)
0.828760 0.559604i \(-0.189047\pi\)
\(138\) 2.06107 + 13.2935i 0.175450 + 1.13162i
\(139\) −3.88147 2.24097i −0.329222 0.190076i 0.326274 0.945275i \(-0.394207\pi\)
−0.655496 + 0.755199i \(0.727540\pi\)
\(140\) 14.3314 + 5.06920i 1.21123 + 0.428426i
\(141\) −2.68750 2.29809i −0.226329 0.193534i
\(142\) 12.0678 4.23717i 1.01270 0.355576i
\(143\) 11.1744 19.3546i 0.934447 1.61851i
\(144\) −6.65461 + 9.98580i −0.554551 + 0.832150i
\(145\) −3.85133 6.67070i −0.319836 0.553972i
\(146\) −3.06500 + 16.2942i −0.253662 + 1.34852i
\(147\) 9.69818 + 7.27636i 0.799892 + 0.600144i
\(148\) −2.68658 1.04778i −0.220836 0.0861273i
\(149\) 8.44492i 0.691834i 0.938265 + 0.345917i \(0.112432\pi\)
−0.938265 + 0.345917i \(0.887568\pi\)
\(150\) 1.22086 + 7.87431i 0.0996828 + 0.642935i
\(151\) 6.29204i 0.512039i −0.966672 0.256020i \(-0.917589\pi\)
0.966672 0.256020i \(-0.0824112\pi\)
\(152\) −0.203562 + 5.95080i −0.0165110 + 0.482674i
\(153\) 7.00246 + 8.66821i 0.566116 + 0.700783i
\(154\) −8.29888 + 10.3120i −0.668743 + 0.830968i
\(155\) 0.368801 + 0.638783i 0.0296228 + 0.0513083i
\(156\) −21.8728 0.702628i −1.75122 0.0562553i
\(157\) 4.99807 + 8.65691i 0.398889 + 0.690897i 0.993589 0.113051i \(-0.0360624\pi\)
−0.594700 + 0.803948i \(0.702729\pi\)
\(158\) 17.2100 + 3.23727i 1.36916 + 0.257543i
\(159\) 2.54940 2.98140i 0.202180 0.236440i
\(160\) 16.1390 1.90581i 1.27590 0.150667i
\(161\) 12.3455 7.66256i 0.972965 0.603894i
\(162\) −11.7344 4.92985i −0.921943 0.387326i
\(163\) −10.9225 + 6.30608i −0.855513 + 0.493930i −0.862507 0.506045i \(-0.831107\pi\)
0.00699437 + 0.999976i \(0.497774\pi\)
\(164\) 11.9698 1.83033i 0.934686 0.142925i
\(165\) −17.3062 3.21808i −1.34729 0.250527i
\(166\) −11.7926 10.1264i −0.915281 0.785962i
\(167\) 4.48097 7.76126i 0.346748 0.600585i −0.638922 0.769272i \(-0.720619\pi\)
0.985670 + 0.168687i \(0.0539527\pi\)
\(168\) 12.7375 + 2.39899i 0.982722 + 0.185086i
\(169\) −13.4547 23.3042i −1.03498 1.79263i
\(170\) 2.78972 14.8308i 0.213962 1.13747i
\(171\) −6.23888 + 0.980600i −0.477099 + 0.0749884i
\(172\) −4.02638 + 10.3239i −0.307009 + 0.787188i
\(173\) −5.45971 3.15217i −0.415094 0.239655i 0.277882 0.960615i \(-0.410368\pi\)
−0.692976 + 0.720961i \(0.743701\pi\)
\(174\) −4.11648 5.11746i −0.312069 0.387953i
\(175\) 7.31278 4.53885i 0.552794 0.343105i
\(176\) −3.08981 + 13.8092i −0.232903 + 1.04090i
\(177\) −11.6084 + 4.10306i −0.872544 + 0.308405i
\(178\) 7.79195 9.07400i 0.584031 0.680125i
\(179\) 7.19492 12.4620i 0.537773 0.931451i −0.461250 0.887270i \(-0.652599\pi\)
0.999024 0.0441806i \(-0.0140677\pi\)
\(180\) 5.21947 + 16.4277i 0.389036 + 1.22445i
\(181\) 23.8306 1.77132 0.885658 0.464338i \(-0.153708\pi\)
0.885658 + 0.464338i \(0.153708\pi\)
\(182\) 8.53780 + 22.0417i 0.632864 + 1.63384i
\(183\) −7.46490 6.38324i −0.551821 0.471863i
\(184\) 8.22209 13.1790i 0.606141 0.971568i
\(185\) −3.58719 + 2.07107i −0.263736 + 0.152268i
\(186\) 0.394191 + 0.490045i 0.0289035 + 0.0359318i
\(187\) 11.3799 + 6.57016i 0.832177 + 0.480458i
\(188\) 0.617185 + 4.03620i 0.0450128 + 0.294370i
\(189\) 0.0540915 + 13.7476i 0.00393458 + 0.999992i
\(190\) 6.48873 + 5.57194i 0.470742 + 0.404231i
\(191\) −2.74949 + 4.76226i −0.198946 + 0.344585i −0.948187 0.317713i \(-0.897085\pi\)
0.749241 + 0.662298i \(0.230419\pi\)
\(192\) 13.3494 3.71412i 0.963407 0.268043i
\(193\) 6.02207 + 10.4305i 0.433478 + 0.750807i 0.997170 0.0751787i \(-0.0239527\pi\)
−0.563692 + 0.825985i \(0.690619\pi\)
\(194\) −10.6346 9.13207i −0.763521 0.655644i
\(195\) −20.4292 + 23.8909i −1.46296 + 1.71086i
\(196\) −2.99376 13.6762i −0.213840 0.976869i
\(197\) 11.2108i 0.798738i 0.916790 + 0.399369i \(0.130771\pi\)
−0.916790 + 0.399369i \(0.869229\pi\)
\(198\) −15.0022 0.450662i −1.06616 0.0320271i
\(199\) −15.7110 9.07074i −1.11372 0.643008i −0.173931 0.984758i \(-0.555647\pi\)
−0.939791 + 0.341750i \(0.888980\pi\)
\(200\) 4.87028 7.80645i 0.344381 0.552000i
\(201\) 4.24024 + 11.9965i 0.299084 + 0.846171i
\(202\) −7.06638 20.1256i −0.497189 1.41603i
\(203\) −3.34928 + 6.25340i −0.235073 + 0.438903i
\(204\) 0.413123 12.8605i 0.0289244 0.900415i
\(205\) 8.69670 15.0631i 0.607404 1.05205i
\(206\) 0.675640 + 1.92427i 0.0470741 + 0.134070i
\(207\) 15.3744 + 5.92251i 1.06860 + 0.411643i
\(208\) 18.5972 + 17.1083i 1.28948 + 1.18625i
\(209\) −6.44956 + 3.72366i −0.446125 + 0.257571i
\(210\) 14.1277 12.1260i 0.974901 0.836771i
\(211\) 1.59074 + 0.918416i 0.109511 + 0.0632264i 0.553755 0.832679i \(-0.313194\pi\)
−0.444244 + 0.895906i \(0.646528\pi\)
\(212\) −4.47758 + 0.684677i −0.307522 + 0.0470238i
\(213\) 2.86371 15.4005i 0.196218 1.05523i
\(214\) −3.92157 3.36749i −0.268073 0.230197i
\(215\) 7.95860 + 13.7847i 0.542772 + 0.940109i
\(216\) 6.54384 + 13.1597i 0.445252 + 0.895405i
\(217\) 0.320725 0.598822i 0.0217722 0.0406507i
\(218\) 3.80856 20.2471i 0.257948 1.37131i
\(219\) 15.4332 + 13.1970i 1.04288 + 0.891769i
\(220\) 12.7070 + 15.8644i 0.856707 + 1.06958i
\(221\) 20.3217 11.7327i 1.36698 0.789228i
\(222\) −2.75193 + 2.21365i −0.184697 + 0.148570i
\(223\) −4.03987 + 2.33242i −0.270530 + 0.156190i −0.629128 0.777301i \(-0.716588\pi\)
0.358599 + 0.933492i \(0.383255\pi\)
\(224\) −9.32951 11.7030i −0.623354 0.781940i
\(225\) 9.10691 + 3.50814i 0.607128 + 0.233876i
\(226\) 19.6496 + 3.69617i 1.30708 + 0.245866i
\(227\) −13.2152 −0.877125 −0.438563 0.898701i \(-0.644512\pi\)
−0.438563 + 0.898701i \(0.644512\pi\)
\(228\) 6.19515 + 3.84713i 0.410284 + 0.254782i
\(229\) −15.1957 −1.00416 −0.502081 0.864821i \(-0.667432\pi\)
−0.502081 + 0.864821i \(0.667432\pi\)
\(230\) −7.39182 21.0524i −0.487402 1.38816i
\(231\) 5.88702 + 15.1049i 0.387338 + 0.993828i
\(232\) −0.259265 + 7.57921i −0.0170216 + 0.497599i
\(233\) −5.56063 + 3.21043i −0.364289 + 0.210322i −0.670961 0.741493i \(-0.734118\pi\)
0.306671 + 0.951815i \(0.400785\pi\)
\(234\) −14.0921 + 22.7987i −0.921230 + 1.49040i
\(235\) 5.07926 + 2.93251i 0.331335 + 0.191296i
\(236\) 13.2452 + 5.16574i 0.862192 + 0.336261i
\(237\) 13.9387 16.3006i 0.905414 1.05884i
\(238\) −12.9598 + 5.01995i −0.840061 + 0.325395i
\(239\) −5.51439 + 9.55121i −0.356696 + 0.617816i −0.987407 0.158202i \(-0.949430\pi\)
0.630710 + 0.776018i \(0.282764\pi\)
\(240\) 7.82357 18.3014i 0.505009 1.18135i
\(241\) −4.12034 −0.265414 −0.132707 0.991155i \(-0.542367\pi\)
−0.132707 + 0.991155i \(0.542367\pi\)
\(242\) −2.02151 + 0.709783i −0.129948 + 0.0456266i
\(243\) −12.3951 + 9.45315i −0.795145 + 0.606420i
\(244\) 1.71431 + 11.2111i 0.109748 + 0.717716i
\(245\) −18.0209 8.92464i −1.15131 0.570174i
\(246\) 5.35985 13.8279i 0.341732 0.881637i
\(247\) 13.2991i 0.846201i
\(248\) 0.0248271 0.725781i 0.00157652 0.0460871i
\(249\) −17.9490 + 6.34415i −1.13747 + 0.402044i
\(250\) 2.35126 + 6.69655i 0.148707 + 0.423527i
\(251\) −12.6369 −0.797636 −0.398818 0.917030i \(-0.630579\pi\)
−0.398818 + 0.917030i \(0.630579\pi\)
\(252\) 10.3195 12.0626i 0.650070 0.759874i
\(253\) 19.4285 1.22146
\(254\) 7.94017 + 22.6142i 0.498210 + 1.41894i
\(255\) −14.0471 12.0117i −0.879663 0.752201i
\(256\) −14.4743 6.81865i −0.904645 0.426166i
\(257\) 16.3541i 1.02014i 0.860133 + 0.510070i \(0.170381\pi\)
−0.860133 + 0.510070i \(0.829619\pi\)
\(258\) 8.50651 + 10.5750i 0.529592 + 0.658370i
\(259\) 3.36279 + 1.80109i 0.208953 + 0.111914i
\(260\) 35.8804 5.48655i 2.22521 0.340261i
\(261\) −7.94612 + 1.24894i −0.491852 + 0.0773072i
\(262\) −6.94083 + 2.43703i −0.428806 + 0.150560i
\(263\) −17.8573 −1.10113 −0.550564 0.834793i \(-0.685587\pi\)
−0.550564 + 0.834793i \(0.685587\pi\)
\(264\) 12.7791 + 11.7070i 0.786499 + 0.720516i
\(265\) −3.25320 + 5.63471i −0.199842 + 0.346137i
\(266\) 1.20860 7.78350i 0.0741043 0.477237i
\(267\) −4.88162 13.8111i −0.298750 0.845228i
\(268\) 5.33844 13.6881i 0.326097 0.836132i
\(269\) −8.25228 4.76446i −0.503150 0.290494i 0.226863 0.973927i \(-0.427153\pi\)
−0.730014 + 0.683433i \(0.760486\pi\)
\(270\) 20.6298 + 4.48083i 1.25549 + 0.272695i
\(271\) −1.00748 + 0.581671i −0.0612002 + 0.0353340i −0.530288 0.847818i \(-0.677916\pi\)
0.469088 + 0.883152i \(0.344583\pi\)
\(272\) −10.0591 + 10.9345i −0.609925 + 0.663004i
\(273\) 28.6163 + 4.38248i 1.73194 + 0.265240i
\(274\) 6.13749 + 17.4800i 0.370779 + 1.05601i
\(275\) 11.5083 0.693975
\(276\) −8.97838 16.7726i −0.540435 1.00959i
\(277\) −23.7404 −1.42642 −0.713212 0.700949i \(-0.752760\pi\)
−0.713212 + 0.700949i \(0.752760\pi\)
\(278\) 6.22917 + 1.17173i 0.373601 + 0.0702756i
\(279\) 0.760915 0.119597i 0.0455548 0.00716011i
\(280\) −21.4981 0.0496727i −1.28476 0.00296851i
\(281\) 6.09203 3.51723i 0.363420 0.209821i −0.307160 0.951658i \(-0.599379\pi\)
0.670580 + 0.741837i \(0.266045\pi\)
\(282\) 4.66276 + 1.80733i 0.277663 + 0.107625i
\(283\) 16.4873 9.51893i 0.980067 0.565842i 0.0777765 0.996971i \(-0.475218\pi\)
0.902290 + 0.431129i \(0.141885\pi\)
\(284\) −14.1175 + 11.3078i −0.837719 + 0.670993i
\(285\) 9.87621 3.49080i 0.585016 0.206777i
\(286\) −5.84271 + 31.0611i −0.345486 + 1.83668i
\(287\) −16.0105 + 0.510644i −0.945069 + 0.0301424i
\(288\) 4.20114 16.4423i 0.247555 0.968874i
\(289\) −1.60154 2.77395i −0.0942082 0.163173i
\(290\) 8.26434 + 7.09668i 0.485298 + 0.416731i
\(291\) −16.1865 + 5.72120i −0.948869 + 0.335383i
\(292\) −3.54424 23.1783i −0.207411 1.35640i
\(293\) −13.1105 7.56934i −0.765923 0.442206i 0.0654953 0.997853i \(-0.479137\pi\)
−0.831418 + 0.555647i \(0.812471\pi\)
\(294\) −16.3498 5.16552i −0.953542 0.301259i
\(295\) 17.6854 10.2107i 1.02968 0.594488i
\(296\) 4.07574 + 0.139421i 0.236898 + 0.00810366i
\(297\) −9.63237 + 15.6564i −0.558927 + 0.908474i
\(298\) −3.95654 11.2685i −0.229196 0.652766i
\(299\) 17.3473 30.0463i 1.00322 1.73762i
\(300\) −5.31826 9.93512i −0.307050 0.573605i
\(301\) 6.92113 12.9224i 0.398928 0.744833i
\(302\) 2.94789 + 8.39580i 0.169632 + 0.483124i
\(303\) −25.6836 4.77585i −1.47549 0.274365i
\(304\) −2.51640 8.03584i −0.144325 0.460887i
\(305\) 14.1083 + 8.14544i 0.807840 + 0.466407i
\(306\) −13.4049 8.28571i −0.766308 0.473663i
\(307\) 14.8488i 0.847463i 0.905788 + 0.423732i \(0.139280\pi\)
−0.905788 + 0.423732i \(0.860720\pi\)
\(308\) 6.24233 17.6480i 0.355690 1.00559i
\(309\) 2.45570 + 0.456634i 0.139700 + 0.0259770i
\(310\) −0.791388 0.679574i −0.0449478 0.0385972i
\(311\) 3.23069 + 5.59572i 0.183195 + 0.317304i 0.942967 0.332886i \(-0.108023\pi\)
−0.759771 + 0.650190i \(0.774689\pi\)
\(312\) 29.5152 9.31010i 1.67097 0.527080i
\(313\) 6.11528 10.5920i 0.345656 0.598694i −0.639817 0.768528i \(-0.720990\pi\)
0.985473 + 0.169834i \(0.0543230\pi\)
\(314\) −10.7250 9.20972i −0.605250 0.519735i
\(315\) −4.25678 22.4014i −0.239842 1.26218i
\(316\) −24.4809 + 3.74343i −1.37716 + 0.210585i
\(317\) −17.3463 10.0149i −0.974264 0.562492i −0.0737308 0.997278i \(-0.523491\pi\)
−0.900534 + 0.434786i \(0.856824\pi\)
\(318\) −2.00497 + 5.17266i −0.112433 + 0.290068i
\(319\) −8.21445 + 4.74261i −0.459921 + 0.265535i
\(320\) −20.6422 + 10.1043i −1.15393 + 0.564848i
\(321\) −5.96885 + 2.10972i −0.333149 + 0.117753i
\(322\) −12.8833 + 16.0086i −0.717959 + 0.892123i
\(323\) −7.81944 −0.435085
\(324\) 17.9675 + 1.08045i 0.998197 + 0.0600252i
\(325\) 10.2755 17.7977i 0.569982 0.987237i
\(326\) 11.6199 13.5318i 0.643569 0.749459i
\(327\) −19.1773 16.3985i −1.06050 0.906839i
\(328\) −15.1144 + 8.05030i −0.834555 + 0.444504i
\(329\) −0.172188 5.39871i −0.00949305 0.297641i
\(330\) 24.6003 3.81411i 1.35420 0.209960i
\(331\) 23.8292 + 13.7578i 1.30977 + 0.756198i 0.982058 0.188579i \(-0.0603881\pi\)
0.327715 + 0.944777i \(0.393721\pi\)
\(332\) 20.4798 + 7.98726i 1.12397 + 0.438358i
\(333\) 0.671620 + 4.27305i 0.0368045 + 0.234162i
\(334\) −2.34295 + 12.4556i −0.128201 + 0.681543i
\(335\) −10.5520 18.2767i −0.576520 0.998562i
\(336\) −18.1203 + 2.76658i −0.988545 + 0.150929i
\(337\) 7.03073 12.1776i 0.382988 0.663355i −0.608500 0.793554i \(-0.708228\pi\)
0.991488 + 0.130199i \(0.0415616\pi\)
\(338\) 28.8716 + 24.7924i 1.57041 + 1.34853i
\(339\) 15.9146 18.6113i 0.864361 1.01083i
\(340\) 3.22591 + 21.0965i 0.174950 + 1.14412i
\(341\) 0.786611 0.454150i 0.0425974 0.0245936i
\(342\) 7.86544 4.23145i 0.425314 0.228811i
\(343\) 1.76877 + 18.4356i 0.0955048 + 0.995429i
\(344\) 0.535760 15.6621i 0.0288862 0.844443i
\(345\) −26.8665 4.99579i −1.44644 0.268964i
\(346\) 8.76200 + 1.64816i 0.471048 + 0.0886059i
\(347\) −8.41428 14.5740i −0.451702 0.782371i 0.546790 0.837270i \(-0.315850\pi\)
−0.998492 + 0.0548988i \(0.982516\pi\)
\(348\) 7.89042 + 4.89988i 0.422971 + 0.262661i
\(349\) 0.669636 + 1.15984i 0.0358448 + 0.0620850i 0.883391 0.468636i \(-0.155254\pi\)
−0.847546 + 0.530721i \(0.821921\pi\)
\(350\) −7.63132 + 9.48254i −0.407911 + 0.506863i
\(351\) 15.6122 + 28.8758i 0.833318 + 1.54128i
\(352\) −2.34685 19.8739i −0.125088 1.05928i
\(353\) 1.45611i 0.0775010i −0.999249 0.0387505i \(-0.987662\pi\)
0.999249 0.0387505i \(-0.0123378\pi\)
\(354\) 13.5674 10.9136i 0.721100 0.580052i
\(355\) 25.9815i 1.37896i
\(356\) −6.14593 + 15.7585i −0.325734 + 0.835201i
\(357\) −2.57676 + 16.8254i −0.136376 + 0.890497i
\(358\) −3.76199 + 19.9996i −0.198827 + 1.05701i
\(359\) 0.574142 + 0.994443i 0.0303021 + 0.0524847i 0.880779 0.473528i \(-0.157020\pi\)
−0.850477 + 0.526013i \(0.823686\pi\)
\(360\) −14.6612 19.4749i −0.772711 1.02642i
\(361\) −7.28416 + 12.6165i −0.383377 + 0.664028i
\(362\) −31.7985 + 11.1649i −1.67129 + 0.586815i
\(363\) −0.479710 + 2.57979i −0.0251782 + 0.135404i
\(364\) −21.7192 25.4114i −1.13840 1.33192i
\(365\) −29.1681 16.8402i −1.52673 0.881457i
\(366\) 12.9514 + 5.02011i 0.676982 + 0.262405i
\(367\) 2.51626i 0.131348i 0.997841 + 0.0656738i \(0.0209197\pi\)
−0.997841 + 0.0656738i \(0.979080\pi\)
\(368\) −4.79667 + 21.4376i −0.250044 + 1.11751i
\(369\) −11.4140 14.1291i −0.594187 0.735532i
\(370\) 3.81626 4.44417i 0.198398 0.231042i
\(371\) 5.98909 0.191018i 0.310938 0.00991716i
\(372\) −0.755582 0.469209i −0.0391751 0.0243274i
\(373\) −3.95758 −0.204916 −0.102458 0.994737i \(-0.532671\pi\)
−0.102458 + 0.994737i \(0.532671\pi\)
\(374\) −18.2629 3.43532i −0.944354 0.177636i
\(375\) 8.54594 + 1.58911i 0.441310 + 0.0820612i
\(376\) −2.71455 5.09656i −0.139992 0.262835i
\(377\) 16.9383i 0.872368i
\(378\) −6.51309 18.3188i −0.334997 0.942219i
\(379\) 5.59867i 0.287584i 0.989608 + 0.143792i \(0.0459297\pi\)
−0.989608 + 0.143792i \(0.954070\pi\)
\(380\) −11.2688 4.39490i −0.578076 0.225453i
\(381\) 28.8595 + 5.36640i 1.47852 + 0.274929i
\(382\) 1.43762 7.64270i 0.0735550 0.391034i
\(383\) 26.0879 1.33303 0.666516 0.745491i \(-0.267785\pi\)
0.666516 + 0.745491i \(0.267785\pi\)
\(384\) −16.0726 + 11.2103i −0.820204 + 0.572071i
\(385\) −14.1799 22.8460i −0.722675 1.16434i
\(386\) −12.9224 11.0966i −0.657733 0.564802i
\(387\) 16.4203 2.58087i 0.834690 0.131193i
\(388\) 18.4688 + 7.20296i 0.937612 + 0.365675i
\(389\) 6.40736i 0.324866i 0.986720 + 0.162433i \(0.0519342\pi\)
−0.986720 + 0.162433i \(0.948066\pi\)
\(390\) 16.0665 41.4502i 0.813560 2.09891i
\(391\) 17.6663 + 10.1996i 0.893422 + 0.515817i
\(392\) 10.4022 + 16.8462i 0.525389 + 0.850862i
\(393\) −1.64708 + 8.85767i −0.0830840 + 0.446811i
\(394\) −5.25240 14.9592i −0.264612 0.753633i
\(395\) −17.7867 + 30.8074i −0.894945 + 1.55009i
\(396\) 20.2294 6.42737i 1.01656 0.322987i
\(397\) −11.5465 19.9991i −0.579500 1.00372i −0.995537 0.0943761i \(-0.969914\pi\)
0.416036 0.909348i \(-0.363419\pi\)
\(398\) 25.2137 + 4.74280i 1.26385 + 0.237735i
\(399\) −7.52811 6.03266i −0.376877 0.302011i
\(400\) −2.84126 + 12.6983i −0.142063 + 0.634917i
\(401\) 32.8384i 1.63987i 0.572455 + 0.819936i \(0.305991\pi\)
−0.572455 + 0.819936i \(0.694009\pi\)
\(402\) −11.2785 14.0210i −0.562520 0.699305i
\(403\) 1.62200i 0.0807978i
\(404\) 18.8581 + 23.5439i 0.938225 + 1.17135i
\(405\) 17.3459 19.1734i 0.861924 0.952735i
\(406\) 1.53933 9.91342i 0.0763958 0.491995i
\(407\) 2.55036 + 4.41735i 0.126416 + 0.218960i
\(408\) 5.47404 + 17.3540i 0.271005 + 0.859151i
\(409\) 3.65396 + 6.32885i 0.180677 + 0.312941i 0.942111 0.335301i \(-0.108838\pi\)
−0.761434 + 0.648242i \(0.775505\pi\)
\(410\) −4.54722 + 24.1740i −0.224571 + 1.19387i
\(411\) 22.3075 + 4.14805i 1.10035 + 0.204608i
\(412\) −1.80308 2.25111i −0.0888316 0.110904i
\(413\) −16.5790 8.87963i −0.815801 0.436938i
\(414\) −23.2897 0.699615i −1.14463 0.0343842i
\(415\) 27.3452 15.7877i 1.34232 0.774989i
\(416\) −32.8307 14.1155i −1.60966 0.692071i
\(417\) 5.04510 5.90001i 0.247060 0.288925i
\(418\) 6.86141 7.99036i 0.335603 0.390821i
\(419\) 4.39689 7.61563i 0.214802 0.372048i −0.738409 0.674353i \(-0.764423\pi\)
0.953211 + 0.302305i \(0.0977561\pi\)
\(420\) −13.1701 + 22.7993i −0.642636 + 1.11249i
\(421\) 18.6580 + 32.3165i 0.909334 + 1.57501i 0.814992 + 0.579472i \(0.196741\pi\)
0.0943413 + 0.995540i \(0.469926\pi\)
\(422\) −2.55290 0.480210i −0.124273 0.0233762i
\(423\) 4.76431 3.84877i 0.231649 0.187134i
\(424\) 5.65390 3.01140i 0.274577 0.146246i
\(425\) 10.4645 + 6.04166i 0.507601 + 0.293064i
\(426\) 3.39412 + 21.8914i 0.164445 + 1.06064i
\(427\) −0.478276 14.9956i −0.0231454 0.725690i
\(428\) 6.81046 + 2.65613i 0.329196 + 0.128389i
\(429\) 29.4198 + 25.1569i 1.42040 + 1.21459i
\(430\) −17.0779 14.6650i −0.823568 0.707207i
\(431\) 11.2054 19.4082i 0.539743 0.934862i −0.459175 0.888346i \(-0.651855\pi\)
0.998918 0.0465160i \(-0.0148118\pi\)
\(432\) −14.8973 14.4938i −0.716745 0.697335i
\(433\) −41.0490 −1.97269 −0.986343 0.164702i \(-0.947334\pi\)
−0.986343 + 0.164702i \(0.947334\pi\)
\(434\) −0.147406 + 0.949303i −0.00707569 + 0.0455680i
\(435\) 12.5788 4.44604i 0.603107 0.213171i
\(436\) 4.40405 + 28.8012i 0.210916 + 1.37933i
\(437\) −10.0124 + 5.78066i −0.478958 + 0.276527i
\(438\) −26.7763 10.3788i −1.27942 0.495917i
\(439\) −33.7983 19.5135i −1.61310 0.931326i −0.988645 0.150269i \(-0.951986\pi\)
−0.624460 0.781057i \(-0.714681\pi\)
\(440\) −24.3883 15.2154i −1.16267 0.725364i
\(441\) −15.4615 + 14.2106i −0.736262 + 0.676696i
\(442\) −21.6194 + 25.1765i −1.02833 + 1.19752i
\(443\) 7.31109 12.6632i 0.347360 0.601646i −0.638419 0.769689i \(-0.720411\pi\)
0.985780 + 0.168043i \(0.0537447\pi\)
\(444\) 2.63492 4.24310i 0.125048 0.201368i
\(445\) 12.1481 + 21.0412i 0.575877 + 0.997449i
\(446\) 4.29785 5.00500i 0.203509 0.236993i
\(447\) −14.3805 2.67404i −0.680175 0.126478i
\(448\) 17.9318 + 11.2449i 0.847200 + 0.531274i
\(449\) 4.89587i 0.231051i 0.993305 + 0.115525i \(0.0368551\pi\)
−0.993305 + 0.115525i \(0.963145\pi\)
\(450\) −13.7954 0.414411i −0.650323 0.0195355i
\(451\) −18.5491 10.7093i −0.873441 0.504282i
\(452\) −27.9513 + 4.27409i −1.31472 + 0.201036i
\(453\) 10.7145 + 1.99235i 0.503410 + 0.0936086i
\(454\) 17.6338 6.19148i 0.827594 0.290581i
\(455\) −47.9926 + 1.53069i −2.24993 + 0.0717599i
\(456\) −10.0689 2.23093i −0.471521 0.104473i
\(457\) 14.5077 25.1280i 0.678639 1.17544i −0.296752 0.954955i \(-0.595903\pi\)
0.975391 0.220483i \(-0.0707633\pi\)
\(458\) 20.2765 7.11937i 0.947457 0.332666i
\(459\) −16.9780 + 9.17948i −0.792467 + 0.428461i
\(460\) 19.7266 + 24.6282i 0.919757 + 1.14830i
\(461\) −6.60037 + 3.81073i −0.307410 + 0.177483i −0.645767 0.763535i \(-0.723462\pi\)
0.338357 + 0.941018i \(0.390129\pi\)
\(462\) −14.9322 17.3971i −0.694708 0.809386i
\(463\) −11.4432 6.60672i −0.531810 0.307040i 0.209943 0.977714i \(-0.432672\pi\)
−0.741753 + 0.670673i \(0.766005\pi\)
\(464\) −3.20499 10.2348i −0.148788 0.475139i
\(465\) −1.20454 + 0.425750i −0.0558591 + 0.0197437i
\(466\) 5.91572 6.88907i 0.274040 0.319130i
\(467\) −4.71551 8.16751i −0.218208 0.377947i 0.736052 0.676925i \(-0.236688\pi\)
−0.954260 + 0.298977i \(0.903354\pi\)
\(468\) 8.12240 37.0238i 0.375458 1.71143i
\(469\) −9.17650 + 17.1333i −0.423731 + 0.791144i
\(470\) −8.15144 1.53332i −0.375998 0.0707266i
\(471\) −16.3241 + 5.76985i −0.752176 + 0.265861i
\(472\) −20.0940 0.687365i −0.924903 0.0316385i
\(473\) 16.9748 9.80040i 0.780502 0.450623i
\(474\) −10.9621 + 28.2812i −0.503505 + 1.29900i
\(475\) −5.93076 + 3.42413i −0.272122 + 0.157110i
\(476\) 14.9411 12.7702i 0.684823 0.585321i
\(477\) 4.26965 + 5.28531i 0.195494 + 0.241998i
\(478\) 2.88330 15.3282i 0.131879 0.701097i
\(479\) −3.94024 −0.180034 −0.0900170 0.995940i \(-0.528692\pi\)
−0.0900170 + 0.995940i \(0.528692\pi\)
\(480\) −1.86501 + 28.0859i −0.0851257 + 1.28194i
\(481\) 9.10864 0.415318
\(482\) 5.49798 1.93042i 0.250426 0.0879284i
\(483\) 9.13911 + 23.4491i 0.415844 + 1.06697i
\(484\) 2.36487 1.89420i 0.107494 0.0861001i
\(485\) 24.6600 14.2375i 1.11976 0.646491i
\(486\) 12.1105 18.4211i 0.549343 0.835597i
\(487\) 29.7489 + 17.1756i 1.34805 + 0.778299i 0.987974 0.154623i \(-0.0494162\pi\)
0.360079 + 0.932922i \(0.382750\pi\)
\(488\) −7.54002 14.1564i −0.341321 0.640829i
\(489\) −7.27984 20.5962i −0.329206 0.931393i
\(490\) 28.2275 + 3.46564i 1.27519 + 0.156562i
\(491\) 15.4355 26.7350i 0.696592 1.20653i −0.273049 0.962000i \(-0.588032\pi\)
0.969641 0.244533i \(-0.0786346\pi\)
\(492\) −0.673387 + 20.9625i −0.0303586 + 0.945062i
\(493\) −9.95919 −0.448539
\(494\) −6.23078 17.7457i −0.280336 0.798416i
\(495\) 10.9599 28.4511i 0.492610 1.27878i
\(496\) 0.306908 + 0.980079i 0.0137806 + 0.0440069i
\(497\) 20.3303 12.6185i 0.911938 0.566016i
\(498\) 20.9779 16.8746i 0.940044 0.756170i
\(499\) 5.12747i 0.229537i −0.993392 0.114768i \(-0.963387\pi\)
0.993392 0.114768i \(-0.0366126\pi\)
\(500\) −6.27482 7.83397i −0.280618 0.350346i
\(501\) 11.7975 + 10.0880i 0.527072 + 0.450700i
\(502\) 16.8621 5.92054i 0.752593 0.264247i
\(503\) 6.16708 0.274976 0.137488 0.990503i \(-0.456097\pi\)
0.137488 + 0.990503i \(0.456097\pi\)
\(504\) −8.11844 + 20.9306i −0.361624 + 0.932324i
\(505\) 43.3297 1.92814
\(506\) −25.9244 + 9.10245i −1.15248 + 0.404653i
\(507\) 43.9442 15.5323i 1.95163 0.689814i
\(508\) −21.1900 26.4552i −0.940153 1.17376i
\(509\) 9.99588i 0.443059i −0.975154 0.221530i \(-0.928895\pi\)
0.975154 0.221530i \(-0.0711050\pi\)
\(510\) 24.3714 + 9.44660i 1.07918 + 0.418303i
\(511\) 0.988806 + 31.0026i 0.0437422 + 1.37147i
\(512\) 22.5085 + 2.31710i 0.994743 + 0.102402i
\(513\) 0.305686 10.9344i 0.0134964 0.482768i
\(514\) −7.66208 21.8221i −0.337960 0.962533i
\(515\) −4.14289 −0.182558
\(516\) −16.3052 10.1254i −0.717796 0.445745i
\(517\) 3.61116 6.25472i 0.158819 0.275082i
\(518\) −5.33097 0.827781i −0.234229 0.0363706i
\(519\) 7.09649 8.29901i 0.311501 0.364286i
\(520\) −45.3065 + 24.1313i −1.98682 + 1.05823i
\(521\) −10.2779 5.93396i −0.450284 0.259971i 0.257666 0.966234i \(-0.417046\pi\)
−0.707950 + 0.706263i \(0.750380\pi\)
\(522\) 10.0178 5.38937i 0.438466 0.235886i
\(523\) −13.5741 + 7.83700i −0.593553 + 0.342688i −0.766501 0.642243i \(-0.778004\pi\)
0.172948 + 0.984931i \(0.444671\pi\)
\(524\) 8.11973 6.50371i 0.354712 0.284116i
\(525\) 5.41347 + 13.8898i 0.236263 + 0.606203i
\(526\) 23.8279 8.36634i 1.03895 0.364790i
\(527\) 0.953686 0.0415432
\(528\) −22.5367 9.63412i −0.980784 0.419271i
\(529\) 7.16105 0.311350
\(530\) 1.70099 9.04285i 0.0738863 0.392796i
\(531\) −3.31119 21.0668i −0.143693 0.914220i
\(532\) 2.03395 + 10.9522i 0.0881831 + 0.474837i
\(533\) −33.1241 + 19.1242i −1.43477 + 0.828362i
\(534\) 12.9845 + 16.1418i 0.561893 + 0.698526i
\(535\) 9.09351 5.25014i 0.393147 0.226983i
\(536\) −0.710346 + 20.7658i −0.0306823 + 0.896948i
\(537\) 18.9428 + 16.1980i 0.817440 + 0.698994i
\(538\) 13.2437 + 2.49118i 0.570974 + 0.107402i
\(539\) −10.9900 + 22.1913i −0.473373 + 0.955847i
\(540\) −29.6267 + 3.68628i −1.27493 + 0.158632i
\(541\) 16.2898 + 28.2148i 0.700354 + 1.21305i 0.968342 + 0.249627i \(0.0803079\pi\)
−0.267988 + 0.963422i \(0.586359\pi\)
\(542\) 1.07182 1.24817i 0.0460386 0.0536135i
\(543\) −7.54586 + 40.5802i −0.323824 + 1.74146i
\(544\) 8.29949 19.3034i 0.355838 0.827625i
\(545\) 36.2442 + 20.9256i 1.55253 + 0.896353i
\(546\) −40.2374 + 7.55927i −1.72200 + 0.323507i
\(547\) −14.3949 + 8.31091i −0.615482 + 0.355349i −0.775108 0.631829i \(-0.782305\pi\)
0.159626 + 0.987178i \(0.448971\pi\)
\(548\) −16.3792 20.4490i −0.699683 0.873538i
\(549\) 13.2335 10.6905i 0.564792 0.456258i
\(550\) −15.3561 + 5.39176i −0.654786 + 0.229905i
\(551\) 2.82220 4.88819i 0.120230 0.208244i
\(552\) 19.8385 + 18.1741i 0.844382 + 0.773543i
\(553\) 32.7450 1.04438i 1.39246 0.0444116i
\(554\) 31.6781 11.1227i 1.34587 0.472556i
\(555\) −2.39087 6.76428i −0.101487 0.287128i
\(556\) −8.86087 + 1.35494i −0.375785 + 0.0574621i
\(557\) 9.30728 + 5.37356i 0.394362 + 0.227685i 0.684049 0.729436i \(-0.260218\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(558\) −0.959297 + 0.516083i −0.0406103 + 0.0218475i
\(559\) 35.0023i 1.48044i
\(560\) 28.7094 10.0058i 1.21319 0.422824i
\(561\) −14.7915 + 17.2979i −0.624496 + 0.730318i
\(562\) −6.48105 + 7.54741i −0.273387 + 0.318368i
\(563\) 0.348722 + 0.604004i 0.0146969 + 0.0254557i 0.873280 0.487218i \(-0.161988\pi\)
−0.858583 + 0.512674i \(0.828655\pi\)
\(564\) −7.06852 0.227065i −0.297638 0.00956116i
\(565\) −20.3081 + 35.1746i −0.854366 + 1.47981i
\(566\) −17.5401 + 20.4261i −0.737266 + 0.858573i
\(567\) −23.4274 4.26101i −0.983859 0.178946i
\(568\) 13.5399 21.7028i 0.568121 0.910627i
\(569\) 5.08845 + 2.93782i 0.213319 + 0.123160i 0.602853 0.797852i \(-0.294031\pi\)
−0.389534 + 0.921012i \(0.627364\pi\)
\(570\) −11.5429 + 9.28507i −0.483478 + 0.388909i
\(571\) 31.1397 17.9785i 1.30316 0.752378i 0.322213 0.946667i \(-0.395573\pi\)
0.980944 + 0.194289i \(0.0622401\pi\)
\(572\) −6.75625 44.1839i −0.282493 1.84742i
\(573\) −7.23885 6.18994i −0.302407 0.258589i
\(574\) 21.1244 8.18247i 0.881715 0.341530i
\(575\) 17.8656 0.745048
\(576\) 2.09761 + 23.9082i 0.0874005 + 0.996173i
\(577\) −15.0558 + 26.0774i −0.626782 + 1.08562i 0.361411 + 0.932406i \(0.382295\pi\)
−0.988193 + 0.153212i \(0.951038\pi\)
\(578\) 3.43664 + 2.95108i 0.142946 + 0.122749i
\(579\) −19.6686 + 6.95197i −0.817400 + 0.288914i
\(580\) −14.3524 5.59754i −0.595951 0.232425i
\(581\) −25.6345 13.7297i −1.06350 0.569603i
\(582\) 18.9181 15.2177i 0.784178 0.630792i
\(583\) 6.93870 + 4.00606i 0.287372 + 0.165914i
\(584\) 15.5885 + 29.2674i 0.645058 + 1.21110i
\(585\) −34.2141 42.3530i −1.41458 1.75108i
\(586\) 21.0403 + 3.95776i 0.869168 + 0.163494i
\(587\) 16.3434 + 28.3076i 0.674563 + 1.16838i 0.976596 + 0.215080i \(0.0690014\pi\)
−0.302033 + 0.953297i \(0.597665\pi\)
\(588\) 24.2366 0.767457i 0.999499 0.0316494i
\(589\) −0.270252 + 0.468090i −0.0111355 + 0.0192873i
\(590\) −18.8147 + 21.9104i −0.774591 + 0.902039i
\(591\) −19.0905 3.54985i −0.785277 0.146022i
\(592\) −5.50380 + 1.72350i −0.226205 + 0.0708352i
\(593\) 23.5045 13.5704i 0.965216 0.557268i 0.0674416 0.997723i \(-0.478516\pi\)
0.897774 + 0.440455i \(0.145183\pi\)
\(594\) 5.51780 25.4040i 0.226398 1.04234i
\(595\) −0.899997 28.2181i −0.0368963 1.15683i
\(596\) 10.5588 + 13.1825i 0.432507 + 0.539975i
\(597\) 20.4210 23.8814i 0.835777 0.977401i
\(598\) −9.07031 + 48.2198i −0.370913 + 1.97185i
\(599\) 23.5306 + 40.7562i 0.961433 + 1.66525i 0.718907 + 0.695107i \(0.244643\pi\)
0.242527 + 0.970145i \(0.422024\pi\)
\(600\) 11.7512 + 10.7653i 0.479739 + 0.439491i
\(601\) 6.84978 + 11.8642i 0.279408 + 0.483950i 0.971238 0.238111i \(-0.0765283\pi\)
−0.691829 + 0.722061i \(0.743195\pi\)
\(602\) −3.18096 + 20.4856i −0.129646 + 0.834932i
\(603\) −21.7711 + 3.42189i −0.886588 + 0.139350i
\(604\) −7.86706 9.82184i −0.320106 0.399645i
\(605\) 4.35225i 0.176944i
\(606\) 36.5086 5.66041i 1.48306 0.229938i
\(607\) 44.1997i 1.79401i 0.442021 + 0.897005i \(0.354262\pi\)
−0.442021 + 0.897005i \(0.645738\pi\)
\(608\) 7.12264 + 9.54369i 0.288861 + 0.387048i
\(609\) −9.58814 7.68347i −0.388531 0.311350i
\(610\) −22.6417 4.25899i −0.916736 0.172441i
\(611\) −6.44866 11.1694i −0.260885 0.451866i
\(612\) 21.7688 + 4.77571i 0.879953 + 0.193047i
\(613\) 15.3894 26.6553i 0.621573 1.07660i −0.367620 0.929976i \(-0.619827\pi\)
0.989193 0.146620i \(-0.0468394\pi\)
\(614\) −6.95681 19.8135i −0.280754 0.799607i
\(615\) 22.8966 + 19.5789i 0.923282 + 0.789499i
\(616\) −0.0611680 + 26.4733i −0.00246453 + 1.06664i
\(617\) 6.67742 + 3.85521i 0.268823 + 0.155205i 0.628353 0.777929i \(-0.283730\pi\)
−0.359530 + 0.933134i \(0.617063\pi\)
\(618\) −3.49070 + 0.541210i −0.140417 + 0.0217707i
\(619\) 13.6833i 0.549978i −0.961447 0.274989i \(-0.911326\pi\)
0.961447 0.274989i \(-0.0886743\pi\)
\(620\) 1.37438 + 0.536017i 0.0551964 + 0.0215270i
\(621\) −14.9535 + 24.3052i −0.600061 + 0.975334i
\(622\) −6.93253 5.95304i −0.277969 0.238695i
\(623\) 10.5645 19.7249i 0.423259 0.790262i
\(624\) −35.0218 + 26.2512i −1.40199 + 1.05089i
\(625\) −30.6829 −1.22731
\(626\) −3.19748 + 16.9985i −0.127797 + 0.679397i
\(627\) −4.29864 12.1618i −0.171671 0.485695i
\(628\) 18.6259 + 7.26421i 0.743253 + 0.289874i
\(629\) 5.35559i 0.213541i
\(630\) 16.1754 + 27.8971i 0.644442 + 1.11145i
\(631\) 7.14717i 0.284524i 0.989829 + 0.142262i \(0.0454376\pi\)
−0.989829 + 0.142262i \(0.954562\pi\)
\(632\) 30.9124 16.4647i 1.22963 0.654929i
\(633\) −2.06764 + 2.41800i −0.0821811 + 0.0961069i
\(634\) 27.8381 + 5.23645i 1.10559 + 0.207966i
\(635\) −48.6875 −1.93211
\(636\) 0.251896 7.84150i 0.00998831 0.310936i
\(637\) 24.5064 + 36.8103i 0.970977 + 1.45848i
\(638\) 8.73901 10.1769i 0.345981 0.402907i
\(639\) 25.3182 + 9.75301i 1.00157 + 0.385823i
\(640\) 22.8100 23.1538i 0.901644 0.915235i
\(641\) 45.7652i 1.80762i −0.427937 0.903809i \(-0.640759\pi\)
0.427937 0.903809i \(-0.359241\pi\)
\(642\) 6.97612 5.61158i 0.275325 0.221471i
\(643\) 7.64287 + 4.41261i 0.301405 + 0.174016i 0.643074 0.765804i \(-0.277659\pi\)
−0.341669 + 0.939820i \(0.610992\pi\)
\(644\) 9.69069 27.3971i 0.381867 1.07960i
\(645\) −25.9935 + 9.18753i −1.02349 + 0.361759i
\(646\) 10.4339 3.66350i 0.410516 0.144138i
\(647\) 9.24938 16.0204i 0.363630 0.629826i −0.624925 0.780685i \(-0.714870\pi\)
0.988555 + 0.150858i \(0.0482037\pi\)
\(648\) −24.4812 + 6.97629i −0.961714 + 0.274055i
\(649\) −12.5736 21.7782i −0.493559 0.854869i
\(650\) −5.37272 + 28.5626i −0.210735 + 1.12032i
\(651\) 0.918155 + 0.735765i 0.0359853 + 0.0288369i
\(652\) −9.16528 + 23.5003i −0.358940 + 0.920343i
\(653\) 15.5423i 0.608218i 0.952637 + 0.304109i \(0.0983586\pi\)
−0.952637 + 0.304109i \(0.901641\pi\)
\(654\) 33.2721 + 12.8966i 1.30104 + 0.504297i
\(655\) 14.9434i 0.583886i
\(656\) 16.3963 17.8232i 0.640169 0.695880i
\(657\) −27.3595 + 22.1019i −1.06739 + 0.862277i
\(658\) 2.75912 + 7.12311i 0.107562 + 0.277688i
\(659\) 24.9174 + 43.1582i 0.970644 + 1.68120i 0.693619 + 0.720342i \(0.256015\pi\)
0.277025 + 0.960863i \(0.410652\pi\)
\(660\) −31.0385 + 16.6149i −1.20817 + 0.646734i
\(661\) −17.4624 30.2458i −0.679209 1.17643i −0.975219 0.221240i \(-0.928989\pi\)
0.296010 0.955185i \(-0.404344\pi\)
\(662\) −38.2423 7.19351i −1.48633 0.279584i
\(663\) 13.5444 + 38.3201i 0.526022 + 1.48823i
\(664\) −31.0694 1.06280i −1.20573 0.0412448i
\(665\) 14.1051 + 7.55460i 0.546972 + 0.292955i
\(666\) −2.89815 5.38709i −0.112301 0.208746i
\(667\) −12.7522 + 7.36251i −0.493769 + 0.285078i
\(668\) −2.70929 17.7179i −0.104825 0.685527i
\(669\) −2.69258 7.61789i −0.104101 0.294525i
\(670\) 22.6430 + 19.4438i 0.874775 + 0.751179i
\(671\) 10.0305 17.3733i 0.387222 0.670689i
\(672\) 22.8827 12.1812i 0.882720 0.469899i
\(673\) −17.4451 30.2158i −0.672459 1.16473i −0.977205 0.212300i \(-0.931905\pi\)
0.304745 0.952434i \(-0.401429\pi\)
\(674\) −3.67614 + 19.5432i −0.141600 + 0.752775i
\(675\) −8.85754 + 14.3970i −0.340927 + 0.554140i
\(676\) −50.1404 19.5551i −1.92848 0.752119i
\(677\) 22.1167 + 12.7691i 0.850015 + 0.490757i 0.860656 0.509187i \(-0.170054\pi\)
−0.0106407 + 0.999943i \(0.503387\pi\)
\(678\) −12.5160 + 32.2902i −0.480675 + 1.24010i
\(679\) −23.1174 12.3815i −0.887163 0.475159i
\(680\) −14.1885 26.6388i −0.544102 1.02155i
\(681\) 4.18454 22.5037i 0.160352 0.862343i
\(682\) −0.836842 + 0.974533i −0.0320443 + 0.0373168i
\(683\) −0.707620 + 1.22563i −0.0270763 + 0.0468976i −0.879246 0.476368i \(-0.841953\pi\)
0.852170 + 0.523265i \(0.175286\pi\)
\(684\) −8.51279 + 9.33130i −0.325495 + 0.356791i
\(685\) −37.6339 −1.43792
\(686\) −10.9975 23.7709i −0.419885 0.907577i
\(687\) 4.81166 25.8762i 0.183576 0.987239i
\(688\) 6.62298 + 21.1498i 0.252499 + 0.806327i
\(689\) 12.3908 7.15385i 0.472053 0.272540i
\(690\) 38.1899 5.92109i 1.45387 0.225412i
\(691\) −25.7347 14.8580i −0.978996 0.565223i −0.0770289 0.997029i \(-0.524543\pi\)
−0.901967 + 0.431805i \(0.857877\pi\)
\(692\) −12.4638 + 1.90587i −0.473802 + 0.0724501i
\(693\) −27.5856 + 5.24189i −1.04789 + 0.199123i
\(694\) 18.0557 + 15.5046i 0.685384 + 0.588547i
\(695\) −6.43789 + 11.1508i −0.244203 + 0.422972i
\(696\) −12.8242 2.84141i −0.486102 0.107704i
\(697\) −11.2444 19.4759i −0.425913 0.737703i
\(698\) −1.43693 1.23391i −0.0543886 0.0467041i
\(699\) −3.70617 10.4856i −0.140180 0.396600i
\(700\) 5.74019 16.2284i 0.216959 0.613377i
\(701\) 37.7345i 1.42521i −0.701565 0.712605i \(-0.747515\pi\)
0.701565 0.712605i \(-0.252485\pi\)
\(702\) −34.3608 31.2160i −1.29687 1.17817i
\(703\) −2.62864 1.51765i −0.0991410 0.0572391i
\(704\) 12.4427 + 25.4193i 0.468951 + 0.958024i
\(705\) −6.60199 + 7.72071i −0.248645 + 0.290779i
\(706\) 0.682205 + 1.94297i 0.0256751 + 0.0731245i
\(707\) −21.0440 33.9050i −0.791440 1.27513i
\(708\) −12.9906 + 20.9191i −0.488216 + 0.786188i
\(709\) −2.19013 + 3.79342i −0.0822521 + 0.142465i −0.904217 0.427073i \(-0.859545\pi\)
0.821965 + 0.569538i \(0.192878\pi\)
\(710\) −12.1726 34.6685i −0.456831 1.30109i
\(711\) 23.3441 + 28.8971i 0.875471 + 1.08373i
\(712\) 0.817792 23.9069i 0.0306481 0.895948i
\(713\) 1.22115 0.705030i 0.0457324 0.0264036i
\(714\) −4.44461 23.6583i −0.166335 0.885390i
\(715\) −55.6021 32.1019i −2.07940 1.20054i
\(716\) −4.35020 28.4490i −0.162575 1.06319i
\(717\) −14.5183 12.4146i −0.542195 0.463631i
\(718\) −1.23202 1.05795i −0.0459784 0.0394822i
\(719\) 21.7265 + 37.6314i 0.810261 + 1.40341i 0.912681 + 0.408672i \(0.134008\pi\)
−0.102421 + 0.994741i \(0.532659\pi\)
\(720\) 28.6874 + 19.1175i 1.06912 + 0.712467i
\(721\) 2.01208 + 3.24177i 0.0749339 + 0.120730i
\(722\) 3.80865 20.2476i 0.141743 0.753538i
\(723\) 1.30469 7.01636i 0.0485218 0.260941i
\(724\) 37.1995 29.7959i 1.38251 1.10735i
\(725\) −7.55368 + 4.36112i −0.280537 + 0.161968i
\(726\) −0.568560 3.66710i −0.0211012 0.136099i
\(727\) 21.6003 12.4710i 0.801112 0.462522i −0.0427480 0.999086i \(-0.513611\pi\)
0.843860 + 0.536564i \(0.180278\pi\)
\(728\) 40.8866 + 23.7320i 1.51536 + 0.879568i
\(729\) −12.1726 24.1004i −0.450835 0.892607i
\(730\) 46.8104 + 8.80520i 1.73253 + 0.325895i
\(731\) 20.5802 0.761187
\(732\) −19.6338 0.630703i −0.725684 0.0233115i
\(733\) −15.0009 −0.554070 −0.277035 0.960860i \(-0.589352\pi\)
−0.277035 + 0.960860i \(0.589352\pi\)
\(734\) −1.17890 3.35758i −0.0435139 0.123930i
\(735\) 20.9037 27.8611i 0.771043 1.02767i
\(736\) −3.64329 30.8526i −0.134293 1.13724i
\(737\) −22.5063 + 12.9940i −0.829030 + 0.478641i
\(738\) 21.8499 + 13.5056i 0.804305 + 0.497149i
\(739\) 3.08238 + 1.77962i 0.113387 + 0.0654642i 0.555621 0.831436i \(-0.312481\pi\)
−0.442234 + 0.896900i \(0.645814\pi\)
\(740\) −3.01009 + 7.71805i −0.110653 + 0.283721i
\(741\) −22.6465 4.21110i −0.831940 0.154698i
\(742\) −7.90206 + 3.06084i −0.290094 + 0.112367i
\(743\) −24.3308 + 42.1422i −0.892610 + 1.54605i −0.0558753 + 0.998438i \(0.517795\pi\)
−0.836735 + 0.547608i \(0.815538\pi\)
\(744\) 1.22804 + 0.272092i 0.0450222 + 0.00997538i
\(745\) 24.2607 0.888844
\(746\) 5.28081 1.85417i 0.193344 0.0678861i
\(747\) −5.11975 32.5734i −0.187322 1.19180i
\(748\) 25.9787 3.97246i 0.949875 0.145247i
\(749\) −8.52464 4.56574i −0.311484 0.166829i
\(750\) −12.1478 + 1.88344i −0.443575 + 0.0687734i
\(751\) 21.4737i 0.783588i −0.920053 0.391794i \(-0.871855\pi\)
0.920053 0.391794i \(-0.128145\pi\)
\(752\) 6.00996 + 5.52881i 0.219161 + 0.201615i
\(753\) 4.00143 21.5189i 0.145820 0.784194i
\(754\) −7.93580 22.6017i −0.289005 0.823105i
\(755\) −18.0759 −0.657849
\(756\) 17.2733 + 21.3923i 0.628225 + 0.778031i
\(757\) 2.47427 0.0899289 0.0449645 0.998989i \(-0.485683\pi\)
0.0449645 + 0.998989i \(0.485683\pi\)
\(758\) −2.62304 7.47060i −0.0952731 0.271344i
\(759\) −6.15193 + 33.0840i −0.223301 + 1.20087i
\(760\) 17.0956 + 0.584795i 0.620122 + 0.0212128i
\(761\) 45.0235i 1.63210i 0.577980 + 0.816051i \(0.303841\pi\)
−0.577980 + 0.816051i \(0.696159\pi\)
\(762\) −41.0230 + 6.36034i −1.48611 + 0.230411i
\(763\) −1.22869 38.5237i −0.0444814 1.39465i
\(764\) 1.66240 + 10.8716i 0.0601435 + 0.393320i
\(765\) 24.9022 20.1168i 0.900340 0.727325i
\(766\) −34.8105 + 12.2225i −1.25775 + 0.441617i
\(767\) −44.9070 −1.62150
\(768\) 16.1944 22.4887i 0.584367 0.811490i
\(769\) −7.14970 + 12.3836i −0.257825 + 0.446566i −0.965659 0.259813i \(-0.916339\pi\)
0.707834 + 0.706379i \(0.249672\pi\)
\(770\) 29.6246 + 23.8412i 1.06760 + 0.859176i
\(771\) −27.8488 5.17845i −1.00295 0.186497i
\(772\) 22.4419 + 8.75250i 0.807702 + 0.315009i
\(773\) 42.1150 + 24.3151i 1.51477 + 0.874553i 0.999850 + 0.0173147i \(0.00551170\pi\)
0.514920 + 0.857238i \(0.327822\pi\)
\(774\) −20.7013 + 11.1369i −0.744092 + 0.400307i
\(775\) 0.723336 0.417618i 0.0259830 0.0150013i
\(776\) −28.0186 0.958443i −1.00581 0.0344061i
\(777\) −4.13181 + 5.15605i −0.148228 + 0.184972i
\(778\) −3.00192 8.54968i −0.107624 0.306521i
\(779\) 12.7456 0.456659
\(780\) −2.01852 + 62.8365i −0.0722747 + 2.24991i
\(781\) 31.9942 1.14484
\(782\) −28.3517 5.33305i −1.01385 0.190710i
\(783\) 0.389335 13.9266i 0.0139137 0.497696i
\(784\) −21.7728 17.6053i −0.777600 0.628759i
\(785\) 24.8697 14.3585i 0.887639 0.512478i
\(786\) −1.95214 12.5909i −0.0696305 0.449104i
\(787\) −33.7450 + 19.4827i −1.20288 + 0.694482i −0.961194 0.275873i \(-0.911033\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(788\) 14.0171 + 17.5000i 0.499338 + 0.623413i
\(789\) 5.65443 30.4085i 0.201303 1.08257i
\(790\) 9.30008 49.4413i 0.330882 1.75904i
\(791\) 37.3868 1.19243i 1.32932 0.0423978i
\(792\) −23.9818 + 18.0541i −0.852158 + 0.641523i
\(793\) −17.9120 31.0245i −0.636074 1.10171i
\(794\) 24.7768 + 21.2762i 0.879297 + 0.755062i
\(795\) −8.56501 7.32395i −0.303770 0.259754i
\(796\) −35.8661 + 5.48436i −1.27124 + 0.194388i
\(797\) −26.8665 15.5114i −0.951662 0.549442i −0.0580649 0.998313i \(-0.518493\pi\)
−0.893597 + 0.448871i \(0.851826\pi\)
\(798\) 12.8715 + 4.52269i 0.455647 + 0.160102i
\(799\) 6.56725 3.79161i 0.232333 0.134137i
\(800\) −2.15807 18.2752i −0.0762993 0.646127i
\(801\) 25.0642 3.93949i 0.885600 0.139195i
\(802\) −15.3852 43.8180i −0.543269 1.54727i
\(803\) −20.7374 + 35.9183i −0.731807 + 1.26753i
\(804\) 21.6185 + 13.4249i 0.762426 + 0.473459i
\(805\) −22.0131 35.4665i −0.775861 1.25003i
\(806\) 0.759927 + 2.16433i 0.0267673 + 0.0762351i
\(807\) 10.7263 12.5438i 0.377582 0.441564i
\(808\) −36.1939 22.5806i −1.27330 0.794384i
\(809\) 5.35787 + 3.09337i 0.188373 + 0.108757i 0.591221 0.806510i \(-0.298646\pi\)
−0.402848 + 0.915267i \(0.631980\pi\)
\(810\) −14.1626 + 33.7108i −0.497622 + 1.18448i
\(811\) 6.48257i 0.227634i −0.993502 0.113817i \(-0.963692\pi\)
0.993502 0.113817i \(-0.0363077\pi\)
\(812\) 2.59054 + 13.9492i 0.0909100 + 0.489521i
\(813\) −0.671490 1.89979i −0.0235502 0.0666285i
\(814\) −5.47265 4.69943i −0.191816 0.164715i
\(815\) 18.1162 + 31.3782i 0.634584 + 1.09913i
\(816\) −15.4348 20.5917i −0.540327 0.720854i
\(817\) −5.83194 + 10.1012i −0.204034 + 0.353397i
\(818\) −7.84081 6.73299i −0.274148 0.235414i
\(819\) −16.5240 + 47.3418i −0.577394 + 1.65426i
\(820\) −5.25821 34.3871i −0.183625 1.20085i
\(821\) −22.9617 13.2569i −0.801369 0.462670i 0.0425809 0.999093i \(-0.486442\pi\)
−0.843949 + 0.536423i \(0.819775\pi\)
\(822\) −31.7094 + 4.91633i −1.10599 + 0.171477i
\(823\) −22.3440 + 12.9003i −0.778862 + 0.449676i −0.836027 0.548688i \(-0.815127\pi\)
0.0571645 + 0.998365i \(0.481794\pi\)
\(824\) 3.46062 + 2.15901i 0.120556 + 0.0752126i
\(825\) −3.64404 + 19.5970i −0.126869 + 0.682280i
\(826\) 26.2825 + 4.08108i 0.914485 + 0.141999i
\(827\) 40.3698 1.40379 0.701897 0.712278i \(-0.252337\pi\)
0.701897 + 0.712278i \(0.252337\pi\)
\(828\) 31.4044 9.97795i 1.09138 0.346758i
\(829\) −13.9633 + 24.1851i −0.484965 + 0.839984i −0.999851 0.0172749i \(-0.994501\pi\)
0.514886 + 0.857259i \(0.327834\pi\)
\(830\) −29.0913 + 33.8779i −1.00978 + 1.17592i
\(831\) 7.51729 40.4266i 0.260772 1.40238i
\(832\) 50.4210 + 3.45358i 1.74803 + 0.119731i
\(833\) −21.6433 + 14.4090i −0.749895 + 0.499241i
\(834\) −3.96773 + 10.2364i −0.137391 + 0.354457i
\(835\) −22.2967 12.8730i −0.771609 0.445489i
\(836\) −5.41197 + 13.8766i −0.187177 + 0.479933i
\(837\) −0.0372825 + 1.33360i −0.00128867 + 0.0460961i
\(838\) −2.29899 + 12.2219i −0.0794172 + 0.422200i
\(839\) 6.10301 + 10.5707i 0.210699 + 0.364942i 0.951934 0.306305i \(-0.0990926\pi\)
−0.741234 + 0.671246i \(0.765759\pi\)
\(840\) 6.89187 36.5926i 0.237792 1.26257i
\(841\) −10.9055 + 18.8889i −0.376053 + 0.651342i
\(842\) −40.0370 34.3802i −1.37977 1.18482i
\(843\) 4.06035 + 11.4876i 0.139846 + 0.395654i
\(844\) 3.63145 0.555294i 0.125000 0.0191140i
\(845\) −66.9488 + 38.6529i −2.30311 + 1.32970i
\(846\) −4.55408 + 7.36775i −0.156572 + 0.253308i
\(847\) −3.40559 + 2.11376i −0.117018 + 0.0726297i
\(848\) −6.13342 + 6.66718i −0.210622 + 0.228952i
\(849\) 10.9888 + 31.0897i 0.377135 + 1.06699i
\(850\) −16.7939 3.15899i −0.576025 0.108352i
\(851\) 3.95921 + 6.85756i 0.135720 + 0.235074i
\(852\) −14.7853 27.6207i −0.506537 0.946269i
\(853\) −4.47707 7.75452i −0.153292 0.265510i 0.779144 0.626845i \(-0.215654\pi\)
−0.932436 + 0.361336i \(0.882321\pi\)
\(854\) 7.66381 + 19.7854i 0.262250 + 0.677042i
\(855\) 2.81709 + 17.9232i 0.0963423 + 0.612959i
\(856\) −10.3320 0.353430i −0.353140 0.0120800i
\(857\) 16.2364i 0.554626i 0.960780 + 0.277313i \(0.0894439\pi\)
−0.960780 + 0.277313i \(0.910556\pi\)
\(858\) −51.0427 19.7847i −1.74257 0.675438i
\(859\) 33.8234i 1.15404i 0.816731 + 0.577019i \(0.195784\pi\)
−0.816731 + 0.577019i \(0.804216\pi\)
\(860\) 29.6586 + 11.5671i 1.01135 + 0.394433i
\(861\) 4.20009 27.4253i 0.143139 0.934653i
\(862\) −5.85891 + 31.1473i −0.199555 + 1.06088i
\(863\) −10.1074 17.5066i −0.344062 0.595932i 0.641121 0.767440i \(-0.278470\pi\)
−0.985183 + 0.171507i \(0.945136\pi\)
\(864\) 26.6687 + 12.3604i 0.907289 + 0.420508i
\(865\) −9.05560 + 15.6848i −0.307900 + 0.533298i
\(866\) 54.7738 19.2319i 1.86129 0.653527i
\(867\) 5.23077 1.84884i 0.177646 0.0627899i
\(868\) −0.248068 1.33577i −0.00841998 0.0453389i
\(869\) 37.9370 + 21.9029i 1.28692 + 0.743005i
\(870\) −14.7015 + 11.8259i −0.498428 + 0.400935i
\(871\) 46.4083i 1.57249i
\(872\) −19.3702 36.3676i −0.655959 1.23156i
\(873\) −4.61703 29.3750i −0.156263 0.994191i
\(874\) 10.6518 12.4044i 0.360302 0.419584i
\(875\) 7.00214 + 11.2815i 0.236716 + 0.381385i
\(876\) 40.5916 + 1.30394i 1.37146 + 0.0440561i
\(877\) −22.3432 −0.754475 −0.377237 0.926117i \(-0.623126\pi\)
−0.377237 + 0.926117i \(0.623126\pi\)
\(878\) 54.2411 + 10.2029i 1.83055 + 0.344333i
\(879\) 17.0409 19.9285i 0.574776 0.672173i
\(880\) 39.6712 + 8.87645i 1.33732 + 0.299225i
\(881\) 50.5729i 1.70384i −0.523669 0.851922i \(-0.675437\pi\)
0.523669 0.851922i \(-0.324563\pi\)
\(882\) 13.9733 26.2059i 0.470504 0.882398i
\(883\) 48.7254i 1.63974i 0.572549 + 0.819870i \(0.305954\pi\)
−0.572549 + 0.819870i \(0.694046\pi\)
\(884\) 17.0524 43.7233i 0.573533 1.47057i
\(885\) 11.7874 + 33.3489i 0.396228 + 1.12101i
\(886\) −3.82273 + 20.3225i −0.128427 + 0.682747i
\(887\) 28.4596 0.955581 0.477791 0.878474i \(-0.341438\pi\)
0.477791 + 0.878474i \(0.341438\pi\)
\(888\) −1.52798 + 6.89628i −0.0512756 + 0.231424i
\(889\) 23.6461 + 38.0975i 0.793066 + 1.27775i
\(890\) −26.0680 22.3848i −0.873800 0.750342i
\(891\) −23.6106 21.3601i −0.790984 0.715590i
\(892\) −3.38995 + 8.69202i −0.113504 + 0.291030i
\(893\) 4.29780i 0.143821i
\(894\) 20.4415 3.16932i 0.683666 0.105998i
\(895\) −35.8009 20.6697i −1.19669 0.690911i
\(896\) −29.1958 6.60345i −0.975363 0.220606i
\(897\) 45.6718 + 39.0540i 1.52494 + 1.30397i
\(898\) −2.29377 6.53282i −0.0765442 0.218003i
\(899\) −0.344205 + 0.596181i −0.0114799 + 0.0198837i
\(900\) 18.6021 5.91035i 0.620071 0.197012i
\(901\) 4.20624 + 7.28541i 0.140130 + 0.242712i
\(902\) 29.7684 + 5.59955i 0.991180 + 0.186445i
\(903\) 19.8134 + 15.8775i 0.659350 + 0.528371i
\(904\) 35.2944 18.7986i 1.17387 0.625233i
\(905\) 68.4610i 2.27572i
\(906\) −15.2303 + 2.36136i −0.505994 + 0.0784509i
\(907\) 16.6344i 0.552337i 0.961109 + 0.276168i \(0.0890647\pi\)
−0.961109 + 0.276168i \(0.910935\pi\)
\(908\) −20.6289 + 16.5232i −0.684594 + 0.548343i
\(909\) 16.2652 42.2234i 0.539483 1.40046i
\(910\) 63.3218 24.5275i 2.09910 0.813080i
\(911\) −20.7017 35.8564i −0.685877 1.18797i −0.973160 0.230129i \(-0.926085\pi\)
0.287283 0.957846i \(-0.407248\pi\)
\(912\) 14.4807 1.74056i 0.479505 0.0576357i
\(913\) −19.4414 33.6734i −0.643415 1.11443i
\(914\) −7.58558 + 40.3266i −0.250909 + 1.33389i
\(915\) −18.3379 + 21.4453i −0.606232 + 0.708960i
\(916\) −23.7204 + 18.9995i −0.783746 + 0.627761i
\(917\) −11.6930 + 7.25757i −0.386138 + 0.239666i
\(918\) 18.3540 20.2031i 0.605773 0.666801i
\(919\) −32.1594 + 18.5672i −1.06084 + 0.612476i −0.925664 0.378346i \(-0.876493\pi\)
−0.135175 + 0.990822i \(0.543160\pi\)
\(920\) −37.8608 23.6206i −1.24823 0.778747i
\(921\) −25.2854 4.70179i −0.833181 0.154929i
\(922\) 7.02186 8.17720i 0.231253 0.269302i
\(923\) 28.5669 49.4794i 0.940292 1.62863i
\(924\) 28.0755 + 16.2180i 0.923617 + 0.533532i
\(925\) 2.34521 + 4.06202i 0.0771099 + 0.133558i
\(926\) 18.3646 + 3.45444i 0.603497 + 0.113520i
\(927\) −1.55517 + 4.03712i −0.0510785 + 0.132596i
\(928\) 9.07172 + 12.1553i 0.297794 + 0.399016i
\(929\) 29.0451 + 16.7692i 0.952939 + 0.550180i 0.893993 0.448081i \(-0.147893\pi\)
0.0589466 + 0.998261i \(0.481226\pi\)
\(930\) 1.40781 1.13244i 0.0461639 0.0371342i
\(931\) −0.939041 14.7062i −0.0307758 0.481975i
\(932\) −4.66605 + 11.9640i −0.152842 + 0.391895i
\(933\) −10.5517 + 3.72956i −0.345447 + 0.122100i
\(934\) 10.1187 + 8.68907i 0.331095 + 0.284315i
\(935\) 18.8749 32.6923i 0.617275 1.06915i
\(936\) 6.50795 + 53.2083i 0.212719 + 1.73917i
\(937\) 20.2579 0.661796 0.330898 0.943666i \(-0.392648\pi\)
0.330898 + 0.943666i \(0.392648\pi\)
\(938\) 4.21753 27.1612i 0.137707 0.886845i
\(939\) 16.1003 + 13.7674i 0.525413 + 0.449281i
\(940\) 11.5953 1.77306i 0.378196 0.0578308i
\(941\) −6.81838 + 3.93660i −0.222273 + 0.128329i −0.607002 0.794700i \(-0.707628\pi\)
0.384729 + 0.923029i \(0.374295\pi\)
\(942\) 19.0789 15.3471i 0.621625 0.500034i
\(943\) −28.7959 16.6253i −0.937723 0.541394i
\(944\) 27.1346 8.49710i 0.883155 0.276557i
\(945\) 39.4944 0.155395i 1.28475 0.00505500i
\(946\) −18.0588 + 21.0301i −0.587141 + 0.683747i
\(947\) −17.7016 + 30.6601i −0.575225 + 0.996319i 0.420792 + 0.907157i \(0.361752\pi\)
−0.996017 + 0.0891620i \(0.971581\pi\)
\(948\) 1.37723 42.8730i 0.0447302 1.39245i
\(949\) 37.0320 + 64.1413i 1.20211 + 2.08211i
\(950\) 6.30948 7.34762i 0.204707 0.238388i
\(951\) 22.5466 26.3671i 0.731123 0.855013i
\(952\) −13.9537 + 24.0400i −0.452241 + 0.779142i
\(953\) 23.9458i 0.775681i −0.921727 0.387840i \(-0.873221\pi\)
0.921727 0.387840i \(-0.126779\pi\)
\(954\) −8.17345 5.05209i −0.264625 0.163567i
\(955\) 13.6811 + 7.89878i 0.442710 + 0.255599i
\(956\) 3.33412 + 21.8041i 0.107833 + 0.705196i
\(957\) −5.47495 15.4898i −0.176980 0.500714i
\(958\) 5.25767 1.84605i 0.169867 0.0596430i
\(959\) 18.2777 + 29.4481i 0.590217 + 0.950930i
\(960\) −10.6700 38.3503i −0.344372 1.23775i
\(961\) −15.4670 + 26.7897i −0.498937 + 0.864184i
\(962\) −12.1541 + 4.26750i −0.391865 + 0.137590i
\(963\) −1.70255 10.8322i −0.0548640 0.349061i
\(964\) −6.43182 + 5.15173i −0.207155 + 0.165926i
\(965\) 29.9650 17.3003i 0.964609 0.556917i
\(966\) −23.1810 27.0075i −0.745835 0.868954i
\(967\) −2.20834 1.27499i −0.0710154 0.0410008i 0.464072 0.885798i \(-0.346388\pi\)
−0.535087 + 0.844797i \(0.679721\pi\)
\(968\) −2.26811 + 3.63550i −0.0728999 + 0.116849i
\(969\) 2.47599 13.3154i 0.0795402 0.427753i
\(970\) −26.2348 + 30.5513i −0.842348 + 0.980944i
\(971\) −18.4002 31.8700i −0.590489 1.02276i −0.994167 0.107856i \(-0.965601\pi\)
0.403677 0.914901i \(-0.367732\pi\)
\(972\) −7.52920 + 30.2541i −0.241499 + 0.970401i
\(973\) 11.8521 0.378013i 0.379959 0.0121185i
\(974\) −47.7425 8.98054i −1.52977 0.287755i
\(975\) 27.0533 + 23.1333i 0.866398 + 0.740858i
\(976\) 16.6935 + 15.3570i 0.534345 + 0.491566i
\(977\) −13.2746 + 7.66408i −0.424691 + 0.245196i −0.697082 0.716991i \(-0.745519\pi\)
0.272391 + 0.962187i \(0.412185\pi\)
\(978\) 19.3634 + 24.0719i 0.619174 + 0.769735i
\(979\) 25.9106 14.9595i 0.828107 0.478108i
\(980\) −39.2891 + 8.60052i −1.25505 + 0.274733i
\(981\) 33.9967 27.4637i 1.08543 0.876848i
\(982\) −8.07069 + 42.9056i −0.257546 + 1.36917i
\(983\) −8.73571 −0.278626 −0.139313 0.990248i \(-0.544489\pi\)
−0.139313 + 0.990248i \(0.544489\pi\)
\(984\) −8.92263 28.2869i −0.284443 0.901752i
\(985\) 32.2066 1.02619
\(986\) 13.2891 4.66599i 0.423210 0.148595i
\(987\) 9.24778 + 1.41626i 0.294360 + 0.0450802i
\(988\) 16.6281 + 20.7598i 0.529011 + 0.660458i
\(989\) 26.3519 15.2143i 0.837943 0.483787i
\(990\) −1.29467 + 43.0986i −0.0411473 + 1.36976i
\(991\) 14.8582 + 8.57839i 0.471986 + 0.272501i 0.717071 0.697000i \(-0.245482\pi\)
−0.245084 + 0.969502i \(0.578816\pi\)
\(992\) −0.868702 1.16398i −0.0275813 0.0369564i
\(993\) −30.9731 + 36.2215i −0.982900 + 1.14946i
\(994\) −21.2159 + 26.3625i −0.672926 + 0.836166i
\(995\) −26.0586 + 45.1348i −0.826113 + 1.43087i
\(996\) −20.0860 + 32.3451i −0.636450 + 1.02489i
\(997\) 16.8766 0.534487 0.267243 0.963629i \(-0.413887\pi\)
0.267243 + 0.963629i \(0.413887\pi\)
\(998\) 2.40228 + 6.84185i 0.0760427 + 0.216575i
\(999\) −7.48907 0.209366i −0.236944 0.00662405i
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 252.2.o.a.95.4 88
3.2 odd 2 756.2.o.a.179.41 88
4.3 odd 2 inner 252.2.o.a.95.19 yes 88
7.2 even 3 252.2.bb.a.23.34 yes 88
9.2 odd 6 252.2.bb.a.11.11 yes 88
9.7 even 3 756.2.bb.a.683.34 88
12.11 even 2 756.2.o.a.179.26 88
21.2 odd 6 756.2.bb.a.611.11 88
28.23 odd 6 252.2.bb.a.23.11 yes 88
36.7 odd 6 756.2.bb.a.683.11 88
36.11 even 6 252.2.bb.a.11.34 yes 88
63.2 odd 6 inner 252.2.o.a.191.19 yes 88
63.16 even 3 756.2.o.a.359.26 88
84.23 even 6 756.2.bb.a.611.34 88
252.79 odd 6 756.2.o.a.359.41 88
252.191 even 6 inner 252.2.o.a.191.4 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.o.a.95.4 88 1.1 even 1 trivial
252.2.o.a.95.19 yes 88 4.3 odd 2 inner
252.2.o.a.191.4 yes 88 252.191 even 6 inner
252.2.o.a.191.19 yes 88 63.2 odd 6 inner
252.2.bb.a.11.11 yes 88 9.2 odd 6
252.2.bb.a.11.34 yes 88 36.11 even 6
252.2.bb.a.23.11 yes 88 28.23 odd 6
252.2.bb.a.23.34 yes 88 7.2 even 3
756.2.o.a.179.26 88 12.11 even 2
756.2.o.a.179.41 88 3.2 odd 2
756.2.o.a.359.26 88 63.16 even 3
756.2.o.a.359.41 88 252.79 odd 6
756.2.bb.a.611.11 88 21.2 odd 6
756.2.bb.a.611.34 88 84.23 even 6
756.2.bb.a.683.11 88 36.7 odd 6
756.2.bb.a.683.34 88 9.7 even 3