Properties

Label 315.2.cb.a.13.2
Level $315$
Weight $2$
Character 315.13
Analytic conductor $2.515$
Analytic rank $0$
Dimension $176$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(13,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.cb (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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(44\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 315.13
Dual form 315.2.cb.a.97.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.62442 - 0.703211i) q^{2} +(1.23789 - 1.21146i) q^{3} +(4.66101 + 2.69104i) q^{4} +(1.95271 - 1.08946i) q^{5} +(-4.10064 + 2.30889i) q^{6} +(-2.50777 + 0.843251i) q^{7} +(-6.49767 - 6.49767i) q^{8} +(0.0647207 - 2.99930i) q^{9} +O(q^{10})\) \(q+(-2.62442 - 0.703211i) q^{2} +(1.23789 - 1.21146i) q^{3} +(4.66101 + 2.69104i) q^{4} +(1.95271 - 1.08946i) q^{5} +(-4.10064 + 2.30889i) q^{6} +(-2.50777 + 0.843251i) q^{7} +(-6.49767 - 6.49767i) q^{8} +(0.0647207 - 2.99930i) q^{9} +(-5.89084 + 1.48604i) q^{10} +(-0.924101 - 1.60059i) q^{11} +(9.02989 - 2.31544i) q^{12} +(-0.249485 - 0.931092i) q^{13} +(7.17443 - 0.449551i) q^{14} +(1.09739 - 3.71426i) q^{15} +(7.10129 + 12.2998i) q^{16} +(-3.17307 - 3.17307i) q^{17} +(-2.27900 + 7.82591i) q^{18} +4.59786 q^{19} +(12.0334 + 0.176806i) q^{20} +(-2.08277 + 4.08192i) q^{21} +(1.29968 + 4.85046i) q^{22} +(4.58351 - 1.22815i) q^{23} +(-15.9150 - 0.171692i) q^{24} +(2.62614 - 4.25481i) q^{25} +2.61902i q^{26} +(-3.55342 - 3.79120i) q^{27} +(-13.9580 - 2.81811i) q^{28} +(-0.575505 + 0.332268i) q^{29} +(-5.49191 + 8.97608i) q^{30} +(-5.02022 - 2.89843i) q^{31} +(-5.23079 - 19.5216i) q^{32} +(-3.08299 - 0.861834i) q^{33} +(6.09613 + 10.5588i) q^{34} +(-3.97826 + 4.37875i) q^{35} +(8.37290 - 13.8056i) q^{36} +(4.47787 - 4.47787i) q^{37} +(-12.0667 - 3.23327i) q^{38} +(-1.43682 - 0.850344i) q^{39} +(-19.7670 - 5.60908i) q^{40} +(-3.16075 - 1.82486i) q^{41} +(8.33651 - 9.24804i) q^{42} +(-0.763478 + 2.84934i) q^{43} -9.94716i q^{44} +(-3.14125 - 5.92727i) q^{45} -12.8927 q^{46} +(-1.62868 + 6.07833i) q^{47} +(23.6913 + 6.62280i) q^{48} +(5.57785 - 4.22937i) q^{49} +(-9.88411 + 9.31967i) q^{50} +(-7.77196 - 0.0838442i) q^{51} +(1.34275 - 5.01121i) q^{52} +(6.88237 + 6.88237i) q^{53} +(6.65966 + 12.4485i) q^{54} +(-3.54828 - 2.11871i) q^{55} +(21.7738 + 10.8155i) q^{56} +(5.69163 - 5.57013i) q^{57} +(1.74402 - 0.467309i) q^{58} +(-5.45237 + 9.44378i) q^{59} +(15.1101 - 14.3591i) q^{60} +(1.06448 - 0.614578i) q^{61} +(11.1370 + 11.1370i) q^{62} +(2.36686 + 7.57614i) q^{63} +26.5059i q^{64} +(-1.50156 - 1.54635i) q^{65} +(7.48499 + 4.42980i) q^{66} +(0.117576 + 0.438800i) q^{67} +(-6.25088 - 23.3286i) q^{68} +(4.18600 - 7.07305i) q^{69} +(13.5198 - 8.69412i) q^{70} +0.841193 q^{71} +(-19.9090 + 19.0679i) q^{72} +(2.75264 - 2.75264i) q^{73} +(-14.9007 + 8.60291i) q^{74} +(-1.90368 - 8.44843i) q^{75} +(21.4307 + 12.3730i) q^{76} +(3.66714 + 3.23467i) q^{77} +(3.17284 + 3.24204i) q^{78} +(11.0510 - 6.38032i) q^{79} +(27.2669 + 16.2813i) q^{80} +(-8.99162 - 0.388234i) q^{81} +(7.01188 + 7.01188i) q^{82} +(0.153202 + 0.0410503i) q^{83} +(-20.6924 + 13.4211i) q^{84} +(-9.65303 - 2.73914i) q^{85} +(4.00737 - 6.94097i) q^{86} +(-0.309879 + 1.10851i) q^{87} +(-4.39560 + 16.4046i) q^{88} -10.5728 q^{89} +(4.07583 + 17.7646i) q^{90} +(1.41080 + 2.12459i) q^{91} +(24.6688 + 6.60998i) q^{92} +(-9.72579 + 2.49389i) q^{93} +(8.54869 - 14.8068i) q^{94} +(8.97828 - 5.00920i) q^{95} +(-30.1247 - 17.8286i) q^{96} +(-1.15352 + 4.30501i) q^{97} +(-17.6128 + 7.17722i) q^{98} +(-4.86046 + 2.66807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176 q - 4 q^{2} - 2 q^{7} - 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 176 q - 4 q^{2} - 2 q^{7} - 32 q^{8} - 12 q^{11} - 20 q^{15} + 56 q^{16} - 8 q^{18} + 12 q^{22} - 12 q^{23} - 4 q^{25} - 32 q^{28} - 56 q^{30} + 48 q^{32} - 8 q^{35} - 80 q^{36} - 16 q^{37} + 38 q^{42} - 4 q^{43} - 80 q^{46} - 76 q^{50} - 28 q^{51} + 64 q^{53} - 52 q^{56} - 112 q^{57} - 44 q^{58} - 40 q^{60} + 24 q^{63} + 20 q^{65} - 4 q^{67} + 18 q^{70} - 64 q^{71} - 20 q^{72} + 26 q^{77} + 76 q^{78} - 64 q^{81} - 4 q^{85} + 80 q^{86} - 60 q^{88} - 16 q^{91} - 68 q^{92} + 88 q^{93} + 40 q^{95} - 120 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62442 0.703211i −1.85574 0.497245i −0.855940 0.517074i \(-0.827021\pi\)
−0.999803 + 0.0198294i \(0.993688\pi\)
\(3\) 1.23789 1.21146i 0.714693 0.699438i
\(4\) 4.66101 + 2.69104i 2.33051 + 1.34552i
\(5\) 1.95271 1.08946i 0.873278 0.487223i
\(6\) −4.10064 + 2.30889i −1.67408 + 0.942600i
\(7\) −2.50777 + 0.843251i −0.947849 + 0.318719i
\(8\) −6.49767 6.49767i −2.29727 2.29727i
\(9\) 0.0647207 2.99930i 0.0215736 0.999767i
\(10\) −5.89084 + 1.48604i −1.86285 + 0.469928i
\(11\) −0.924101 1.60059i −0.278627 0.482596i 0.692417 0.721498i \(-0.256546\pi\)
−0.971044 + 0.238902i \(0.923213\pi\)
\(12\) 9.02989 2.31544i 2.60670 0.668411i
\(13\) −0.249485 0.931092i −0.0691948 0.258239i 0.922660 0.385616i \(-0.126011\pi\)
−0.991854 + 0.127377i \(0.959344\pi\)
\(14\) 7.17443 0.449551i 1.91745 0.120148i
\(15\) 1.09739 3.71426i 0.283344 0.959018i
\(16\) 7.10129 + 12.2998i 1.77532 + 3.07495i
\(17\) −3.17307 3.17307i −0.769583 0.769583i 0.208450 0.978033i \(-0.433158\pi\)
−0.978033 + 0.208450i \(0.933158\pi\)
\(18\) −2.27900 + 7.82591i −0.537164 + 1.84458i
\(19\) 4.59786 1.05482 0.527411 0.849610i \(-0.323163\pi\)
0.527411 + 0.849610i \(0.323163\pi\)
\(20\) 12.0334 + 0.176806i 2.69075 + 0.0395351i
\(21\) −2.08277 + 4.08192i −0.454497 + 0.890748i
\(22\) 1.29968 + 4.85046i 0.277092 + 1.03412i
\(23\) 4.58351 1.22815i 0.955728 0.256086i 0.252937 0.967483i \(-0.418604\pi\)
0.702791 + 0.711396i \(0.251937\pi\)
\(24\) −15.9150 0.171692i −3.24864 0.0350465i
\(25\) 2.62614 4.25481i 0.525228 0.850962i
\(26\) 2.61902i 0.513631i
\(27\) −3.55342 3.79120i −0.683857 0.729617i
\(28\) −13.9580 2.81811i −2.63781 0.532572i
\(29\) −0.575505 + 0.332268i −0.106869 + 0.0617006i −0.552482 0.833525i \(-0.686319\pi\)
0.445613 + 0.895226i \(0.352986\pi\)
\(30\) −5.49191 + 8.97608i −1.00268 + 1.63880i
\(31\) −5.02022 2.89843i −0.901658 0.520573i −0.0239205 0.999714i \(-0.507615\pi\)
−0.877738 + 0.479141i \(0.840948\pi\)
\(32\) −5.23079 19.5216i −0.924681 3.45096i
\(33\) −3.08299 0.861834i −0.536679 0.150026i
\(34\) 6.09613 + 10.5588i 1.04548 + 1.81082i
\(35\) −3.97826 + 4.37875i −0.672448 + 0.740144i
\(36\) 8.37290 13.8056i 1.39548 2.30094i
\(37\) 4.47787 4.47787i 0.736157 0.736157i −0.235675 0.971832i \(-0.575730\pi\)
0.971832 + 0.235675i \(0.0757302\pi\)
\(38\) −12.0667 3.23327i −1.95748 0.524505i
\(39\) −1.43682 0.850344i −0.230075 0.136164i
\(40\) −19.7670 5.60908i −3.12544 0.886873i
\(41\) −3.16075 1.82486i −0.493627 0.284996i 0.232451 0.972608i \(-0.425325\pi\)
−0.726078 + 0.687612i \(0.758659\pi\)
\(42\) 8.33651 9.24804i 1.28635 1.42700i
\(43\) −0.763478 + 2.84934i −0.116429 + 0.434520i −0.999390 0.0349270i \(-0.988880\pi\)
0.882960 + 0.469447i \(0.155547\pi\)
\(44\) 9.94716i 1.49959i
\(45\) −3.14125 5.92727i −0.468270 0.883586i
\(46\) −12.8927 −1.90092
\(47\) −1.62868 + 6.07833i −0.237568 + 0.886615i 0.739407 + 0.673259i \(0.235106\pi\)
−0.976974 + 0.213356i \(0.931561\pi\)
\(48\) 23.6913 + 6.62280i 3.41955 + 0.955918i
\(49\) 5.57785 4.22937i 0.796836 0.604195i
\(50\) −9.88411 + 9.31967i −1.39782 + 1.31800i
\(51\) −7.77196 0.0838442i −1.08829 0.0117405i
\(52\) 1.34275 5.01121i 0.186206 0.694930i
\(53\) 6.88237 + 6.88237i 0.945367 + 0.945367i 0.998583 0.0532162i \(-0.0169472\pi\)
−0.0532162 + 0.998583i \(0.516947\pi\)
\(54\) 6.65966 + 12.4485i 0.906264 + 1.69403i
\(55\) −3.54828 2.11871i −0.478451 0.285687i
\(56\) 21.7738 + 10.8155i 2.90965 + 1.44528i
\(57\) 5.69163 5.57013i 0.753874 0.737782i
\(58\) 1.74402 0.467309i 0.229001 0.0613606i
\(59\) −5.45237 + 9.44378i −0.709838 + 1.22947i 0.255079 + 0.966920i \(0.417898\pi\)
−0.964917 + 0.262555i \(0.915435\pi\)
\(60\) 15.1101 14.3591i 1.95071 1.85375i
\(61\) 1.06448 0.614578i 0.136293 0.0786887i −0.430303 0.902684i \(-0.641593\pi\)
0.566596 + 0.823996i \(0.308260\pi\)
\(62\) 11.1370 + 11.1370i 1.41439 + 1.41439i
\(63\) 2.36686 + 7.57614i 0.298196 + 0.954505i
\(64\) 26.5059i 3.31324i
\(65\) −1.50156 1.54635i −0.186246 0.191801i
\(66\) 7.48499 + 4.42980i 0.921339 + 0.545271i
\(67\) 0.117576 + 0.438800i 0.0143642 + 0.0536080i 0.972736 0.231915i \(-0.0744993\pi\)
−0.958372 + 0.285523i \(0.907833\pi\)
\(68\) −6.25088 23.3286i −0.758030 2.82901i
\(69\) 4.18600 7.07305i 0.503936 0.851495i
\(70\) 13.5198 8.69412i 1.61592 1.03915i
\(71\) 0.841193 0.0998313 0.0499156 0.998753i \(-0.484105\pi\)
0.0499156 + 0.998753i \(0.484105\pi\)
\(72\) −19.9090 + 19.0679i −2.34630 + 2.24718i
\(73\) 2.75264 2.75264i 0.322172 0.322172i −0.527428 0.849600i \(-0.676843\pi\)
0.849600 + 0.527428i \(0.176843\pi\)
\(74\) −14.9007 + 8.60291i −1.73217 + 1.00007i
\(75\) −1.90368 8.44843i −0.219818 0.975541i
\(76\) 21.4307 + 12.3730i 2.45827 + 1.41928i
\(77\) 3.66714 + 3.23467i 0.417909 + 0.368625i
\(78\) 3.17284 + 3.24204i 0.359253 + 0.367089i
\(79\) 11.0510 6.38032i 1.24334 0.717842i 0.273567 0.961853i \(-0.411797\pi\)
0.969772 + 0.244011i \(0.0784633\pi\)
\(80\) 27.2669 + 16.2813i 3.04854 + 1.82031i
\(81\) −8.99162 0.388234i −0.999069 0.0431371i
\(82\) 7.01188 + 7.01188i 0.774332 + 0.774332i
\(83\) 0.153202 + 0.0410503i 0.0168161 + 0.00450585i 0.267217 0.963636i \(-0.413896\pi\)
−0.250401 + 0.968142i \(0.580563\pi\)
\(84\) −20.6924 + 13.4211i −2.25773 + 1.46436i
\(85\) −9.65303 2.73914i −1.04702 0.297101i
\(86\) 4.00737 6.94097i 0.432126 0.748465i
\(87\) −0.309879 + 1.10851i −0.0332225 + 0.118845i
\(88\) −4.39560 + 16.4046i −0.468573 + 1.74874i
\(89\) −10.5728 −1.12071 −0.560357 0.828251i \(-0.689336\pi\)
−0.560357 + 0.828251i \(0.689336\pi\)
\(90\) 4.07583 + 17.7646i 0.429630 + 1.87255i
\(91\) 1.41080 + 2.12459i 0.147892 + 0.222718i
\(92\) 24.6688 + 6.60998i 2.57190 + 0.689138i
\(93\) −9.72579 + 2.49389i −1.00852 + 0.258604i
\(94\) 8.54869 14.8068i 0.881730 1.52720i
\(95\) 8.97828 5.00920i 0.921152 0.513933i
\(96\) −30.1247 17.8286i −3.07459 1.81962i
\(97\) −1.15352 + 4.30501i −0.117122 + 0.437107i −0.999437 0.0335533i \(-0.989318\pi\)
0.882314 + 0.470660i \(0.155984\pi\)
\(98\) −17.6128 + 7.17722i −1.77916 + 0.725009i
\(99\) −4.86046 + 2.66807i −0.488495 + 0.268151i
\(100\) 23.6903 12.7647i 2.36903 1.27647i
\(101\) 6.09879 3.52114i 0.606852 0.350366i −0.164880 0.986314i \(-0.552724\pi\)
0.771732 + 0.635947i \(0.219390\pi\)
\(102\) 20.3379 + 5.68537i 2.01375 + 0.562935i
\(103\) 4.88957 + 18.2481i 0.481784 + 1.79804i 0.594126 + 0.804372i \(0.297498\pi\)
−0.112343 + 0.993670i \(0.535835\pi\)
\(104\) −4.42886 + 7.67100i −0.434285 + 0.752204i
\(105\) 0.380063 + 10.2399i 0.0370904 + 0.999312i
\(106\) −13.2225 22.9020i −1.28428 2.22444i
\(107\) −1.52495 + 1.52495i −0.147423 + 0.147423i −0.776966 0.629543i \(-0.783242\pi\)
0.629543 + 0.776966i \(0.283242\pi\)
\(108\) −6.36029 27.2332i −0.612020 2.62052i
\(109\) 5.57444i 0.533935i 0.963706 + 0.266967i \(0.0860216\pi\)
−0.963706 + 0.266967i \(0.913978\pi\)
\(110\) 7.82228 + 8.05557i 0.745825 + 0.768069i
\(111\) 0.118322 10.9678i 0.0112306 1.04102i
\(112\) −28.1803 24.8569i −2.66278 2.34876i
\(113\) 9.42835 2.52632i 0.886945 0.237656i 0.213544 0.976934i \(-0.431499\pi\)
0.673401 + 0.739277i \(0.264833\pi\)
\(114\) −18.8542 + 10.6159i −1.76586 + 0.994275i
\(115\) 7.61223 7.39178i 0.709844 0.689287i
\(116\) −3.57658 −0.332077
\(117\) −2.80877 + 0.688021i −0.259671 + 0.0636076i
\(118\) 20.9503 20.9503i 1.92863 1.92863i
\(119\) 10.6330 + 5.28165i 0.974730 + 0.484168i
\(120\) −31.2645 + 17.0036i −2.85404 + 1.55221i
\(121\) 3.79207 6.56806i 0.344734 0.597097i
\(122\) −3.22582 + 0.864356i −0.292052 + 0.0782551i
\(123\) −6.12340 + 1.57016i −0.552129 + 0.141577i
\(124\) −15.5995 27.0192i −1.40088 2.42640i
\(125\) 0.492622 11.1695i 0.0440615 0.999029i
\(126\) −0.884006 21.5474i −0.0787535 1.91959i
\(127\) −0.704793 + 0.704793i −0.0625403 + 0.0625403i −0.737685 0.675145i \(-0.764081\pi\)
0.675145 + 0.737685i \(0.264081\pi\)
\(128\) 8.17767 30.5195i 0.722810 2.69756i
\(129\) 2.50677 + 4.45208i 0.220709 + 0.391984i
\(130\) 2.85332 + 5.11418i 0.250253 + 0.448543i
\(131\) 18.4050 + 10.6261i 1.60805 + 0.928410i 0.989805 + 0.142428i \(0.0454910\pi\)
0.618249 + 0.785982i \(0.287842\pi\)
\(132\) −12.0506 12.3134i −1.04887 1.07175i
\(133\) −11.5304 + 3.87715i −0.999812 + 0.336192i
\(134\) 1.23428i 0.106625i
\(135\) −11.0692 3.53178i −0.952682 0.303967i
\(136\) 41.2352i 3.53588i
\(137\) −2.60652 0.698414i −0.222690 0.0596695i 0.145749 0.989322i \(-0.453441\pi\)
−0.368439 + 0.929652i \(0.620107\pi\)
\(138\) −15.9597 + 15.6190i −1.35858 + 1.32958i
\(139\) −7.50438 + 12.9980i −0.636514 + 1.10247i 0.349679 + 0.936870i \(0.386291\pi\)
−0.986192 + 0.165604i \(0.947043\pi\)
\(140\) −30.3261 + 9.70378i −2.56302 + 0.820119i
\(141\) 5.34754 + 9.49736i 0.450344 + 0.799822i
\(142\) −2.20764 0.591536i −0.185261 0.0496406i
\(143\) −1.25975 + 1.25975i −0.105345 + 0.105345i
\(144\) 37.3504 20.5029i 3.11253 1.70857i
\(145\) −0.761799 + 1.27581i −0.0632640 + 0.105951i
\(146\) −9.15977 + 5.28840i −0.758068 + 0.437671i
\(147\) 1.78103 11.9928i 0.146897 0.989152i
\(148\) 32.9215 8.82129i 2.70613 0.725105i
\(149\) 3.16716 + 1.82856i 0.259464 + 0.149802i 0.624090 0.781352i \(-0.285470\pi\)
−0.364626 + 0.931154i \(0.618803\pi\)
\(150\) −0.944975 + 23.5109i −0.0771569 + 1.91966i
\(151\) 4.25259 + 7.36570i 0.346071 + 0.599412i 0.985548 0.169398i \(-0.0541824\pi\)
−0.639477 + 0.768810i \(0.720849\pi\)
\(152\) −29.8754 29.8754i −2.42321 2.42321i
\(153\) −9.72237 + 9.31164i −0.786007 + 0.752802i
\(154\) −7.34945 11.0679i −0.592235 0.891876i
\(155\) −12.9608 0.190432i −1.04103 0.0152959i
\(156\) −4.40872 7.82999i −0.352980 0.626901i
\(157\) −9.38278 + 2.51411i −0.748827 + 0.200648i −0.612998 0.790085i \(-0.710037\pi\)
−0.135829 + 0.990732i \(0.543370\pi\)
\(158\) −33.4893 + 8.97342i −2.66426 + 0.713887i
\(159\) 16.8573 + 0.181858i 1.33687 + 0.0144222i
\(160\) −31.4822 32.4212i −2.48889 2.56312i
\(161\) −10.4588 + 6.94497i −0.824266 + 0.547340i
\(162\) 23.3248 + 7.34189i 1.83257 + 0.576834i
\(163\) 2.06258 + 2.06258i 0.161553 + 0.161553i 0.783255 0.621701i \(-0.213558\pi\)
−0.621701 + 0.783255i \(0.713558\pi\)
\(164\) −9.82155 17.0114i −0.766934 1.32837i
\(165\) −6.95911 + 1.67589i −0.541766 + 0.130468i
\(166\) −0.373198 0.215466i −0.0289658 0.0167234i
\(167\) 15.2322 4.08145i 1.17870 0.315832i 0.384291 0.923212i \(-0.374446\pi\)
0.794412 + 0.607380i \(0.207779\pi\)
\(168\) 40.0561 12.9898i 3.09040 1.00219i
\(169\) 10.4536 6.03541i 0.804126 0.464262i
\(170\) 23.4074 + 13.9768i 1.79527 + 1.07197i
\(171\) 0.297577 13.7904i 0.0227563 1.05458i
\(172\) −11.2263 + 11.2263i −0.855995 + 0.855995i
\(173\) 5.98267 + 1.60305i 0.454854 + 0.121878i 0.478970 0.877831i \(-0.341010\pi\)
−0.0241157 + 0.999709i \(0.507677\pi\)
\(174\) 1.59277 2.69129i 0.120748 0.204026i
\(175\) −2.99789 + 12.8846i −0.226619 + 0.973984i
\(176\) 13.1246 22.7325i 0.989306 1.71353i
\(177\) 4.69137 + 18.2956i 0.352625 + 1.37519i
\(178\) 27.7474 + 7.43490i 2.07976 + 0.557269i
\(179\) 21.5287i 1.60913i −0.593863 0.804566i \(-0.702398\pi\)
0.593863 0.804566i \(-0.297602\pi\)
\(180\) 1.30910 36.0803i 0.0975749 2.68927i
\(181\) 2.02784i 0.150728i −0.997156 0.0753641i \(-0.975988\pi\)
0.997156 0.0753641i \(-0.0240119\pi\)
\(182\) −2.20849 6.56790i −0.163704 0.486845i
\(183\) 0.573167 2.05036i 0.0423697 0.151567i
\(184\) −37.7622 21.8020i −2.78387 1.60727i
\(185\) 3.86549 13.6224i 0.284197 1.00154i
\(186\) 27.2783 + 0.294279i 2.00014 + 0.0215776i
\(187\) −2.14655 + 8.01103i −0.156971 + 0.585825i
\(188\) −23.9483 + 23.9483i −1.74661 + 1.74661i
\(189\) 12.1081 + 6.51104i 0.880736 + 0.473608i
\(190\) −27.0853 + 6.83262i −1.96497 + 0.495690i
\(191\) 9.62038 + 16.6630i 0.696106 + 1.20569i 0.969806 + 0.243877i \(0.0784192\pi\)
−0.273700 + 0.961815i \(0.588248\pi\)
\(192\) 32.1109 + 32.8113i 2.31740 + 2.36795i
\(193\) 3.31857 0.889207i 0.238876 0.0640065i −0.137395 0.990516i \(-0.543873\pi\)
0.376271 + 0.926510i \(0.377206\pi\)
\(194\) 6.05465 10.4870i 0.434699 0.752920i
\(195\) −3.73210 0.0951128i −0.267261 0.00681117i
\(196\) 37.3798 4.70292i 2.66999 0.335923i
\(197\) 0.441048 0.441048i 0.0314234 0.0314234i −0.691221 0.722644i \(-0.742927\pi\)
0.722644 + 0.691221i \(0.242927\pi\)
\(198\) 14.6321 3.58419i 1.03986 0.254718i
\(199\) 7.80790 0.553487 0.276744 0.960944i \(-0.410745\pi\)
0.276744 + 0.960944i \(0.410745\pi\)
\(200\) −44.7101 + 10.5826i −3.16148 + 0.748300i
\(201\) 0.677135 + 0.400745i 0.0477614 + 0.0282664i
\(202\) −18.4819 + 4.95220i −1.30038 + 0.348436i
\(203\) 1.16305 1.31855i 0.0816301 0.0925439i
\(204\) −35.9996 21.3054i −2.52047 1.49168i
\(205\) −8.16015 0.119897i −0.569930 0.00837396i
\(206\) 51.3291i 3.57627i
\(207\) −3.38694 13.8268i −0.235408 0.961030i
\(208\) 9.68058 9.68058i 0.671227 0.671227i
\(209\) −4.24889 7.35929i −0.293902 0.509053i
\(210\) 6.20336 27.1410i 0.428073 1.87291i
\(211\) −9.22048 + 15.9703i −0.634764 + 1.09944i 0.351801 + 0.936075i \(0.385569\pi\)
−0.986565 + 0.163369i \(0.947764\pi\)
\(212\) 13.5581 + 50.5996i 0.931175 + 3.47519i
\(213\) 1.04130 1.01907i 0.0713488 0.0698258i
\(214\) 5.07447 2.92975i 0.346884 0.200273i
\(215\) 1.61340 + 6.39571i 0.110033 + 0.436184i
\(216\) −1.54499 + 47.7229i −0.105123 + 3.24713i
\(217\) 15.0337 + 3.03529i 1.02055 + 0.206049i
\(218\) 3.92001 14.6297i 0.265496 0.990846i
\(219\) 0.0727349 6.74218i 0.00491497 0.455594i
\(220\) −10.8371 19.4239i −0.730635 1.30956i
\(221\) −2.16279 + 3.74606i −0.145485 + 0.251987i
\(222\) −8.02323 + 28.7010i −0.538484 + 1.92629i
\(223\) −19.0379 5.10119i −1.27487 0.341601i −0.442976 0.896533i \(-0.646077\pi\)
−0.831895 + 0.554932i \(0.812744\pi\)
\(224\) 29.5792 + 44.5448i 1.97634 + 2.97627i
\(225\) −12.5915 8.15196i −0.839433 0.543464i
\(226\) −26.5205 −1.76412
\(227\) −6.16334 + 23.0019i −0.409075 + 1.52669i 0.387338 + 0.921938i \(0.373395\pi\)
−0.796413 + 0.604753i \(0.793272\pi\)
\(228\) 41.5182 10.6461i 2.74961 0.705055i
\(229\) 10.8542 18.8000i 0.717265 1.24234i −0.244815 0.969570i \(-0.578727\pi\)
0.962080 0.272769i \(-0.0879394\pi\)
\(230\) −25.1757 + 14.0461i −1.66003 + 0.926173i
\(231\) 8.45817 0.438447i 0.556507 0.0288477i
\(232\) 5.89840 + 1.58047i 0.387249 + 0.103763i
\(233\) 15.3200 + 15.3200i 1.00365 + 1.00365i 0.999993 + 0.00365459i \(0.00116330\pi\)
0.00365459 + 0.999993i \(0.498837\pi\)
\(234\) 7.85522 + 0.169505i 0.513512 + 0.0110809i
\(235\) 3.44177 + 13.6436i 0.224517 + 0.890010i
\(236\) −50.8271 + 29.3450i −3.30856 + 1.91020i
\(237\) 5.95041 21.2860i 0.386520 1.38268i
\(238\) −24.1914 21.3385i −1.56810 1.38317i
\(239\) 9.11536 + 5.26276i 0.589624 + 0.340419i 0.764949 0.644091i \(-0.222764\pi\)
−0.175325 + 0.984511i \(0.556098\pi\)
\(240\) 53.4775 12.8784i 3.45196 0.831300i
\(241\) −15.5209 + 8.96102i −0.999791 + 0.577230i −0.908187 0.418566i \(-0.862533\pi\)
−0.0916048 + 0.995795i \(0.529200\pi\)
\(242\) −14.5707 + 14.5707i −0.936641 + 0.936641i
\(243\) −11.6009 + 10.4124i −0.744200 + 0.667957i
\(244\) 6.61541 0.423508
\(245\) 6.28418 14.3356i 0.401482 0.915867i
\(246\) 17.1745 + 0.185279i 1.09501 + 0.0118130i
\(247\) −1.14710 4.28103i −0.0729882 0.272396i
\(248\) 13.7867 + 51.4527i 0.875458 + 3.26725i
\(249\) 0.239377 0.134782i 0.0151699 0.00854149i
\(250\) −9.14735 + 28.9670i −0.578529 + 1.83203i
\(251\) 6.53469i 0.412466i −0.978503 0.206233i \(-0.933880\pi\)
0.978503 0.206233i \(-0.0661204\pi\)
\(252\) −9.35572 + 41.6818i −0.589355 + 2.62571i
\(253\) −6.20139 6.20139i −0.389878 0.389878i
\(254\) 2.34529 1.35405i 0.147157 0.0849609i
\(255\) −15.2677 + 8.30354i −0.956101 + 0.519988i
\(256\) −16.4173 + 28.4356i −1.02608 + 1.77723i
\(257\) 5.72261 1.53337i 0.356967 0.0956489i −0.0758789 0.997117i \(-0.524176\pi\)
0.432845 + 0.901468i \(0.357510\pi\)
\(258\) −3.44806 13.4469i −0.214667 0.837168i
\(259\) −7.45351 + 15.0054i −0.463138 + 0.932393i
\(260\) −2.83753 11.2483i −0.175976 0.697590i
\(261\) 0.959324 + 1.74762i 0.0593807 + 0.108175i
\(262\) −40.8301 40.8301i −2.52249 2.52249i
\(263\) 0.574999 2.14593i 0.0354560 0.132324i −0.945929 0.324373i \(-0.894847\pi\)
0.981385 + 0.192049i \(0.0615134\pi\)
\(264\) 14.4323 + 25.6321i 0.888247 + 1.57755i
\(265\) 20.9374 + 5.94117i 1.28617 + 0.364963i
\(266\) 32.9870 2.06697i 2.02256 0.126734i
\(267\) −13.0879 + 12.8085i −0.800967 + 0.783870i
\(268\) −0.632804 + 2.36166i −0.0386546 + 0.144261i
\(269\) −23.2623 −1.41832 −0.709162 0.705045i \(-0.750927\pi\)
−0.709162 + 0.705045i \(0.750927\pi\)
\(270\) 26.5665 + 17.0528i 1.61679 + 1.03780i
\(271\) 7.00818i 0.425717i −0.977083 0.212858i \(-0.931723\pi\)
0.977083 0.212858i \(-0.0682773\pi\)
\(272\) 16.4952 61.5611i 1.00017 3.73269i
\(273\) 4.32027 + 0.920871i 0.261474 + 0.0557336i
\(274\) 6.34945 + 3.66586i 0.383584 + 0.221463i
\(275\) −9.23702 0.271497i −0.557013 0.0163719i
\(276\) 38.5449 21.7029i 2.32013 1.30636i
\(277\) 10.1150 + 2.71032i 0.607754 + 0.162847i 0.549555 0.835458i \(-0.314797\pi\)
0.0581994 + 0.998305i \(0.481464\pi\)
\(278\) 28.8350 28.8350i 1.72941 1.72941i
\(279\) −9.01817 + 14.8696i −0.539904 + 0.890218i
\(280\) 54.3011 2.60228i 3.24511 0.155516i
\(281\) −8.57764 14.8569i −0.511699 0.886289i −0.999908 0.0135620i \(-0.995683\pi\)
0.488209 0.872727i \(-0.337650\pi\)
\(282\) −7.35553 28.6855i −0.438016 1.70820i
\(283\) −1.31537 4.90902i −0.0781905 0.291811i 0.915747 0.401755i \(-0.131600\pi\)
−0.993938 + 0.109944i \(0.964933\pi\)
\(284\) 3.92081 + 2.26368i 0.232658 + 0.134325i
\(285\) 5.04563 17.0777i 0.298877 1.01159i
\(286\) 4.19197 2.42024i 0.247877 0.143112i
\(287\) 9.46527 + 1.91103i 0.558717 + 0.112805i
\(288\) −58.8896 + 14.4253i −3.47010 + 0.850016i
\(289\) 3.13679i 0.184517i
\(290\) 2.89645 2.81256i 0.170085 0.165159i
\(291\) 3.78742 + 6.72655i 0.222023 + 0.394318i
\(292\) 20.2376 5.42264i 1.18431 0.317336i
\(293\) −0.990116 3.69516i −0.0578432 0.215874i 0.930955 0.365135i \(-0.118977\pi\)
−0.988798 + 0.149261i \(0.952310\pi\)
\(294\) −13.1076 + 30.2218i −0.764454 + 1.76257i
\(295\) −0.358231 + 24.3811i −0.0208570 + 1.41952i
\(296\) −58.1914 −3.38230
\(297\) −2.78443 + 9.19102i −0.161569 + 0.533317i
\(298\) −7.02609 7.02609i −0.407010 0.407010i
\(299\) −2.28704 3.96127i −0.132263 0.229086i
\(300\) 13.8620 44.5011i 0.800321 2.56927i
\(301\) −0.488079 7.78930i −0.0281324 0.448968i
\(302\) −5.98093 22.3211i −0.344164 1.28444i
\(303\) 3.28388 11.7472i 0.188654 0.674860i
\(304\) 32.6508 + 56.5528i 1.87265 + 3.24352i
\(305\) 1.40906 2.35980i 0.0806825 0.135122i
\(306\) 32.0636 17.6008i 1.83295 1.00617i
\(307\) −6.56783 6.56783i −0.374846 0.374846i 0.494393 0.869239i \(-0.335390\pi\)
−0.869239 + 0.494393i \(0.835390\pi\)
\(308\) 8.38796 + 24.9452i 0.477948 + 1.42139i
\(309\) 28.1596 + 16.6656i 1.60195 + 0.948071i
\(310\) 33.8805 + 9.61392i 1.92428 + 0.546034i
\(311\) −8.11941 4.68775i −0.460410 0.265818i 0.251807 0.967778i \(-0.418975\pi\)
−0.712217 + 0.701960i \(0.752309\pi\)
\(312\) 3.81071 + 14.8612i 0.215739 + 0.841351i
\(313\) −2.23751 0.599538i −0.126471 0.0338879i 0.195028 0.980798i \(-0.437520\pi\)
−0.321500 + 0.946910i \(0.604187\pi\)
\(314\) 26.3923 1.48940
\(315\) 12.8757 + 12.2154i 0.725465 + 0.688259i
\(316\) 68.6787 3.86348
\(317\) −4.75897 1.27516i −0.267291 0.0716203i 0.122684 0.992446i \(-0.460850\pi\)
−0.389975 + 0.920825i \(0.627516\pi\)
\(318\) −44.1128 12.3315i −2.47372 0.691517i
\(319\) 1.06365 + 0.614098i 0.0595529 + 0.0343829i
\(320\) 28.8772 + 51.7583i 1.61429 + 2.89338i
\(321\) −0.0402948 + 3.73513i −0.00224904 + 0.208475i
\(322\) 32.3319 10.8718i 1.80179 0.605860i
\(323\) −14.5894 14.5894i −0.811773 0.811773i
\(324\) −40.8653 26.0064i −2.27030 1.44480i
\(325\) −4.61680 1.38366i −0.256094 0.0767519i
\(326\) −3.96264 6.86349i −0.219470 0.380134i
\(327\) 6.75322 + 6.90052i 0.373454 + 0.381600i
\(328\) 8.68018 + 32.3949i 0.479283 + 1.78871i
\(329\) −1.04119 16.6165i −0.0574027 0.916095i
\(330\) 19.4421 + 0.495483i 1.07025 + 0.0272755i
\(331\) −16.6004 28.7527i −0.912438 1.58039i −0.810609 0.585588i \(-0.800864\pi\)
−0.101829 0.994802i \(-0.532470\pi\)
\(332\) 0.603607 + 0.603607i 0.0331273 + 0.0331273i
\(333\) −13.1407 13.7203i −0.720104 0.751867i
\(334\) −42.8458 −2.34442
\(335\) 0.707649 + 0.728754i 0.0386630 + 0.0398161i
\(336\) −64.9971 + 3.36927i −3.54589 + 0.183809i
\(337\) −1.61938 6.04361i −0.0882133 0.329217i 0.907690 0.419641i \(-0.137844\pi\)
−0.995903 + 0.0904249i \(0.971177\pi\)
\(338\) −31.6789 + 8.48833i −1.72310 + 0.461704i
\(339\) 8.61068 14.5494i 0.467668 0.790214i
\(340\) −37.6218 38.7438i −2.04033 2.10118i
\(341\) 10.7138i 0.580182i
\(342\) −10.4785 + 35.9824i −0.566613 + 1.94571i
\(343\) −10.4216 + 15.3098i −0.562712 + 0.826653i
\(344\) 23.4749 13.5532i 1.26568 0.730742i
\(345\) 0.468214 18.3721i 0.0252078 0.989121i
\(346\) −14.5737 8.41416i −0.783490 0.452348i
\(347\) −2.35383 8.78461i −0.126360 0.471583i 0.873524 0.486780i \(-0.161829\pi\)
−0.999885 + 0.0151979i \(0.995162\pi\)
\(348\) −4.42740 + 4.33289i −0.237333 + 0.232267i
\(349\) −15.1545 26.2484i −0.811204 1.40505i −0.912022 0.410141i \(-0.865479\pi\)
0.100818 0.994905i \(-0.467854\pi\)
\(350\) 16.9283 31.7064i 0.904855 1.69478i
\(351\) −2.64343 + 4.25441i −0.141096 + 0.227084i
\(352\) −26.4122 + 26.4122i −1.40778 + 1.40778i
\(353\) 11.3280 + 3.03533i 0.602930 + 0.161555i 0.547356 0.836900i \(-0.315634\pi\)
0.0555740 + 0.998455i \(0.482301\pi\)
\(354\) 0.553582 51.3144i 0.0294226 2.72733i
\(355\) 1.64261 0.916450i 0.0871804 0.0486401i
\(356\) −49.2799 28.4518i −2.61183 1.50794i
\(357\) 19.5610 6.34345i 1.03528 0.335731i
\(358\) −15.1392 + 56.5003i −0.800133 + 2.98614i
\(359\) 16.6314i 0.877773i −0.898543 0.438886i \(-0.855373\pi\)
0.898543 0.438886i \(-0.144627\pi\)
\(360\) −18.1026 + 58.9242i −0.954093 + 3.10558i
\(361\) 2.14033 0.112649
\(362\) −1.42600 + 5.32190i −0.0749488 + 0.279713i
\(363\) −3.26281 12.7245i −0.171253 0.667861i
\(364\) 0.858398 + 13.6993i 0.0449923 + 0.718036i
\(365\) 2.37620 8.37401i 0.124376 0.438316i
\(366\) −2.94606 + 4.97793i −0.153993 + 0.260201i
\(367\) 2.74138 10.2310i 0.143099 0.534052i −0.856734 0.515759i \(-0.827510\pi\)
0.999833 0.0182935i \(-0.00582332\pi\)
\(368\) 47.6548 + 47.6548i 2.48418 + 2.48418i
\(369\) −5.67788 + 9.36195i −0.295579 + 0.487364i
\(370\) −19.7241 + 33.0327i −1.02541 + 1.71729i
\(371\) −23.0630 11.4559i −1.19737 0.594759i
\(372\) −52.0432 14.5484i −2.69831 0.754301i
\(373\) 30.5624 8.18916i 1.58246 0.424019i 0.642773 0.766057i \(-0.277784\pi\)
0.939686 + 0.342038i \(0.111117\pi\)
\(374\) 11.2669 19.5148i 0.582597 1.00909i
\(375\) −12.9216 14.4233i −0.667268 0.744818i
\(376\) 50.0776 28.9123i 2.58256 1.49104i
\(377\) 0.452952 + 0.452952i 0.0233282 + 0.0233282i
\(378\) −27.1981 25.6022i −1.39892 1.31684i
\(379\) 32.2804i 1.65813i 0.559151 + 0.829066i \(0.311127\pi\)
−0.559151 + 0.829066i \(0.688873\pi\)
\(380\) 55.3278 + 0.812930i 2.83826 + 0.0417025i
\(381\) −0.0186232 + 1.72628i −0.000954096 + 0.0884402i
\(382\) −13.5303 50.4958i −0.692271 2.58359i
\(383\) −0.955322 3.56531i −0.0488147 0.182179i 0.937214 0.348755i \(-0.113395\pi\)
−0.986029 + 0.166576i \(0.946729\pi\)
\(384\) −26.8501 47.6865i −1.37019 2.43349i
\(385\) 10.6849 + 2.32115i 0.544553 + 0.118297i
\(386\) −9.33461 −0.475119
\(387\) 8.49662 + 2.47431i 0.431907 + 0.125776i
\(388\) −16.9615 + 16.9615i −0.861091 + 0.861091i
\(389\) −3.23475 + 1.86758i −0.164008 + 0.0946903i −0.579758 0.814789i \(-0.696853\pi\)
0.415749 + 0.909479i \(0.363519\pi\)
\(390\) 9.72772 + 2.87407i 0.492582 + 0.145534i
\(391\) −18.4408 10.6468i −0.932592 0.538432i
\(392\) −63.7241 8.76202i −3.21855 0.442549i
\(393\) 35.6565 9.14303i 1.79863 0.461205i
\(394\) −1.46764 + 0.847345i −0.0739389 + 0.0426886i
\(395\) 14.6283 24.4986i 0.736031 1.23266i
\(396\) −29.8345 0.643788i −1.49924 0.0323515i
\(397\) 4.37221 + 4.37221i 0.219435 + 0.219435i 0.808260 0.588825i \(-0.200409\pi\)
−0.588825 + 0.808260i \(0.700409\pi\)
\(398\) −20.4912 5.49060i −1.02713 0.275219i
\(399\) −9.57628 + 18.7681i −0.479414 + 0.939580i
\(400\) 70.9823 + 2.08633i 3.54911 + 0.104317i
\(401\) −11.3985 + 19.7428i −0.569214 + 0.985908i 0.427429 + 0.904049i \(0.359419\pi\)
−0.996644 + 0.0818596i \(0.973914\pi\)
\(402\) −1.49528 1.52789i −0.0745777 0.0762043i
\(403\) −1.44623 + 5.39741i −0.0720419 + 0.268864i
\(404\) 37.9021 1.88570
\(405\) −17.9810 + 9.03794i −0.893482 + 0.449099i
\(406\) −3.97955 + 2.64255i −0.197502 + 0.131148i
\(407\) −11.3052 3.02923i −0.560379 0.150153i
\(408\) 49.9548 + 51.0444i 2.47313 + 2.52707i
\(409\) −6.34057 + 10.9822i −0.313521 + 0.543034i −0.979122 0.203273i \(-0.934842\pi\)
0.665601 + 0.746308i \(0.268175\pi\)
\(410\) 21.3313 + 6.05297i 1.05348 + 0.298935i
\(411\) −4.07267 + 2.29314i −0.200890 + 0.113112i
\(412\) −26.3160 + 98.2128i −1.29650 + 4.83860i
\(413\) 5.70982 28.2806i 0.280962 1.39160i
\(414\) −0.834424 + 38.6691i −0.0410097 + 1.90048i
\(415\) 0.343881 0.0867485i 0.0168805 0.00425832i
\(416\) −16.8714 + 9.74069i −0.827187 + 0.477577i
\(417\) 6.45698 + 25.1813i 0.316200 + 1.23313i
\(418\) 5.97573 + 22.3017i 0.292282 + 1.09081i
\(419\) −12.4249 + 21.5205i −0.606995 + 1.05135i 0.384737 + 0.923026i \(0.374292\pi\)
−0.991733 + 0.128321i \(0.959041\pi\)
\(420\) −25.7845 + 48.7511i −1.25815 + 2.37881i
\(421\) 18.8246 + 32.6052i 0.917455 + 1.58908i 0.803266 + 0.595620i \(0.203094\pi\)
0.114189 + 0.993459i \(0.463573\pi\)
\(422\) 35.4289 35.4289i 1.72465 1.72465i
\(423\) 18.1253 + 5.27831i 0.881284 + 0.256640i
\(424\) 89.4388i 4.34353i
\(425\) −21.8337 + 5.16789i −1.05909 + 0.250680i
\(426\) −3.44943 + 1.94222i −0.167126 + 0.0941009i
\(427\) −2.15123 + 2.43885i −0.104105 + 0.118024i
\(428\) −11.2115 + 3.00412i −0.541929 + 0.145209i
\(429\) −0.0332871 + 3.08556i −0.00160712 + 0.148972i
\(430\) 0.263292 17.9196i 0.0126971 0.864159i
\(431\) 20.2933 0.977496 0.488748 0.872425i \(-0.337454\pi\)
0.488748 + 0.872425i \(0.337454\pi\)
\(432\) 21.3971 70.6288i 1.02947 3.39813i
\(433\) 13.5264 13.5264i 0.650039 0.650039i −0.302963 0.953002i \(-0.597976\pi\)
0.953002 + 0.302963i \(0.0979760\pi\)
\(434\) −37.3202 18.5377i −1.79143 0.889838i
\(435\) 0.602579 + 2.50220i 0.0288915 + 0.119971i
\(436\) −15.0010 + 25.9825i −0.718419 + 1.24434i
\(437\) 21.0743 5.64685i 1.00812 0.270126i
\(438\) −4.93206 + 17.6431i −0.235663 + 0.843022i
\(439\) −7.22100 12.5071i −0.344640 0.596933i 0.640649 0.767834i \(-0.278666\pi\)
−0.985288 + 0.170901i \(0.945332\pi\)
\(440\) 9.28889 + 36.8223i 0.442831 + 1.75543i
\(441\) −12.3241 17.0034i −0.586864 0.809685i
\(442\) 8.31033 8.31033i 0.395282 0.395282i
\(443\) −3.44903 + 12.8720i −0.163868 + 0.611565i 0.834313 + 0.551290i \(0.185864\pi\)
−0.998182 + 0.0602748i \(0.980802\pi\)
\(444\) 30.0664 50.8029i 1.42689 2.41100i
\(445\) −20.6456 + 11.5187i −0.978694 + 0.546037i
\(446\) 46.3762 + 26.7753i 2.19598 + 1.26785i
\(447\) 6.13581 1.57334i 0.290214 0.0744167i
\(448\) −22.3511 66.4708i −1.05599 3.14045i
\(449\) 7.14525i 0.337205i −0.985684 0.168603i \(-0.946075\pi\)
0.985684 0.168603i \(-0.0539255\pi\)
\(450\) 27.3128 + 30.2486i 1.28754 + 1.42593i
\(451\) 6.74543i 0.317630i
\(452\) 50.7441 + 13.5968i 2.38680 + 0.639542i
\(453\) 14.1875 + 3.96604i 0.666586 + 0.186341i
\(454\) 32.3504 56.0325i 1.51828 2.62974i
\(455\) 5.06954 + 2.61169i 0.237664 + 0.122438i
\(456\) −73.1752 0.789417i −3.42674 0.0369678i
\(457\) −40.4652 10.8426i −1.89288 0.507197i −0.998164 0.0605682i \(-0.980709\pi\)
−0.894720 0.446628i \(-0.852625\pi\)
\(458\) −41.7063 + 41.7063i −1.94881 + 1.94881i
\(459\) −0.754481 + 23.3050i −0.0352161 + 1.08779i
\(460\) 55.3723 13.9684i 2.58175 0.651279i
\(461\) −0.581473 + 0.335714i −0.0270819 + 0.0156357i −0.513480 0.858102i \(-0.671644\pi\)
0.486398 + 0.873737i \(0.338311\pi\)
\(462\) −22.5061 4.79721i −1.04708 0.223186i
\(463\) −15.3977 + 4.12580i −0.715592 + 0.191742i −0.598204 0.801344i \(-0.704119\pi\)
−0.117388 + 0.993086i \(0.537452\pi\)
\(464\) −8.17365 4.71906i −0.379452 0.219077i
\(465\) −16.2746 + 15.4657i −0.754718 + 0.717206i
\(466\) −29.4329 50.9793i −1.36345 2.36157i
\(467\) −10.6717 10.6717i −0.493825 0.493825i 0.415684 0.909509i \(-0.363542\pi\)
−0.909509 + 0.415684i \(0.863542\pi\)
\(468\) −14.9432 4.35164i −0.690751 0.201155i
\(469\) −0.664873 1.00126i −0.0307010 0.0462341i
\(470\) 0.561665 38.2268i 0.0259077 1.76327i
\(471\) −8.56906 + 14.4791i −0.394841 + 0.667159i
\(472\) 96.7902 25.9349i 4.45513 1.19375i
\(473\) 5.26616 1.41106i 0.242138 0.0648807i
\(474\) −30.5849 + 51.6790i −1.40481 + 2.37370i
\(475\) 12.0746 19.5630i 0.554022 0.897613i
\(476\) 35.3477 + 53.2318i 1.62016 + 2.43987i
\(477\) 21.0878 20.1969i 0.965542 0.924752i
\(478\) −20.2217 20.2217i −0.924919 0.924919i
\(479\) 14.9790 + 25.9443i 0.684406 + 1.18543i 0.973623 + 0.228163i \(0.0732719\pi\)
−0.289217 + 0.957264i \(0.593395\pi\)
\(480\) −78.2484 1.99416i −3.57153 0.0910207i
\(481\) −5.28647 3.05214i −0.241042 0.139166i
\(482\) 47.0349 12.6030i 2.14238 0.574049i
\(483\) −4.53319 + 21.2675i −0.206267 + 0.967703i
\(484\) 35.3498 20.4092i 1.60681 0.927692i
\(485\) 2.43765 + 9.66314i 0.110688 + 0.438781i
\(486\) 37.7678 19.1686i 1.71318 0.869507i
\(487\) −17.9327 + 17.9327i −0.812607 + 0.812607i −0.985024 0.172417i \(-0.944842\pi\)
0.172417 + 0.985024i \(0.444842\pi\)
\(488\) −10.9100 2.92332i −0.493871 0.132332i
\(489\) 5.05197 + 0.0545008i 0.228458 + 0.00246461i
\(490\) −26.5733 + 33.2035i −1.20046 + 1.49998i
\(491\) −20.2361 + 35.0499i −0.913241 + 1.58178i −0.103786 + 0.994600i \(0.533096\pi\)
−0.809456 + 0.587181i \(0.800238\pi\)
\(492\) −32.7666 9.15976i −1.47723 0.412954i
\(493\) 2.88043 + 0.771809i 0.129728 + 0.0347605i
\(494\) 12.0419i 0.541790i
\(495\) −6.58430 + 10.5053i −0.295942 + 0.472176i
\(496\) 82.3303i 3.69674i
\(497\) −2.10952 + 0.709338i −0.0946250 + 0.0318181i
\(498\) −0.723006 + 0.185393i −0.0323987 + 0.00830766i
\(499\) 12.8480 + 7.41778i 0.575154 + 0.332066i 0.759205 0.650851i \(-0.225588\pi\)
−0.184051 + 0.982917i \(0.558921\pi\)
\(500\) 32.3536 50.7354i 1.44690 2.26896i
\(501\) 13.9112 23.5056i 0.621506 1.05015i
\(502\) −4.59526 + 17.1497i −0.205097 + 0.765431i
\(503\) 9.32634 9.32634i 0.415841 0.415841i −0.467926 0.883767i \(-0.654999\pi\)
0.883767 + 0.467926i \(0.154999\pi\)
\(504\) 33.8482 64.6063i 1.50772 2.87780i
\(505\) 8.07300 13.5202i 0.359244 0.601639i
\(506\) 11.9141 + 20.6359i 0.529648 + 0.917378i
\(507\) 5.62874 20.1353i 0.249981 0.894242i
\(508\) −5.18167 + 1.38843i −0.229900 + 0.0616014i
\(509\) −7.59457 + 13.1542i −0.336624 + 0.583049i −0.983795 0.179295i \(-0.942618\pi\)
0.647172 + 0.762344i \(0.275952\pi\)
\(510\) 45.9080 11.0555i 2.03284 0.489548i
\(511\) −4.58183 + 9.22417i −0.202688 + 0.408053i
\(512\) 18.3985 18.3985i 0.813109 0.813109i
\(513\) −16.3381 17.4314i −0.721347 0.769615i
\(514\) −16.0968 −0.710000
\(515\) 29.4286 + 30.3063i 1.29678 + 1.33545i
\(516\) −0.296639 + 27.4970i −0.0130588 + 1.21049i
\(517\) 11.2340 3.01014i 0.494070 0.132386i
\(518\) 30.1131 34.1392i 1.32309 1.49999i
\(519\) 9.34790 5.26338i 0.410327 0.231037i
\(520\) −0.290984 + 19.8043i −0.0127605 + 0.868476i
\(521\) 30.2895i 1.32701i 0.748174 + 0.663503i \(0.230931\pi\)
−0.748174 + 0.663503i \(0.769069\pi\)
\(522\) −1.28873 5.26109i −0.0564060 0.230271i
\(523\) −12.2063 + 12.2063i −0.533746 + 0.533746i −0.921685 0.387939i \(-0.873187\pi\)
0.387939 + 0.921685i \(0.373187\pi\)
\(524\) 57.1907 + 99.0572i 2.49839 + 4.32733i
\(525\) 11.8982 + 19.5815i 0.519278 + 0.854605i
\(526\) −3.01808 + 5.22746i −0.131594 + 0.227928i
\(527\) 6.73261 + 25.1264i 0.293277 + 1.09453i
\(528\) −11.2928 44.0402i −0.491456 1.91661i
\(529\) −0.418382 + 0.241553i −0.0181905 + 0.0105023i
\(530\) −50.7705 30.3155i −2.20533 1.31682i
\(531\) 27.9719 + 16.9645i 1.21388 + 0.736197i
\(532\) −64.1769 12.9573i −2.78242 0.561768i
\(533\) −0.910553 + 3.39823i −0.0394404 + 0.147194i
\(534\) 43.3552 24.4114i 1.87616 1.05638i
\(535\) −1.31641 + 4.63916i −0.0569132 + 0.200568i
\(536\) 2.08721 3.61515i 0.0901536 0.156151i
\(537\) −26.0812 26.6501i −1.12549 1.15004i
\(538\) 61.0499 + 16.3583i 2.63205 + 0.705255i
\(539\) −11.9240 5.01950i −0.513602 0.216205i
\(540\) −42.0894 46.2492i −1.81124 1.99025i
\(541\) 34.6353 1.48909 0.744543 0.667574i \(-0.232667\pi\)
0.744543 + 0.667574i \(0.232667\pi\)
\(542\) −4.92823 + 18.3924i −0.211685 + 0.790021i
\(543\) −2.45665 2.51023i −0.105425 0.107724i
\(544\) −45.3457 + 78.5410i −1.94418 + 3.36742i
\(545\) 6.07315 + 10.8853i 0.260145 + 0.466273i
\(546\) −10.6906 5.45481i −0.457516 0.233444i
\(547\) −26.8603 7.19719i −1.14846 0.307730i −0.366114 0.930570i \(-0.619312\pi\)
−0.782349 + 0.622840i \(0.785979\pi\)
\(548\) −10.2695 10.2695i −0.438693 0.438693i
\(549\) −1.77441 3.23247i −0.0757300 0.137959i
\(550\) 24.0509 + 7.20810i 1.02553 + 0.307354i
\(551\) −2.64609 + 1.52772i −0.112727 + 0.0650831i
\(552\) −73.1576 + 18.7591i −3.11379 + 0.798439i
\(553\) −22.3333 + 25.3192i −0.949708 + 1.07668i
\(554\) −24.6402 14.2260i −1.04686 0.604405i
\(555\) −11.7180 21.5459i −0.497402 0.914573i
\(556\) −69.9561 + 40.3892i −2.96680 + 1.71288i
\(557\) 3.28310 3.28310i 0.139109 0.139109i −0.634123 0.773232i \(-0.718639\pi\)
0.773232 + 0.634123i \(0.218639\pi\)
\(558\) 34.1239 32.6823i 1.44458 1.38355i
\(559\) 2.84348 0.120266
\(560\) −82.1085 17.8370i −3.46972 0.753750i
\(561\) 7.04788 + 12.5172i 0.297562 + 0.528477i
\(562\) 12.0638 + 45.0226i 0.508880 + 1.89916i
\(563\) −9.83388 36.7005i −0.414448 1.54674i −0.785938 0.618306i \(-0.787819\pi\)
0.371489 0.928437i \(-0.378847\pi\)
\(564\) −0.632802 + 58.6578i −0.0266458 + 2.46994i
\(565\) 15.6585 15.2050i 0.658757 0.639680i
\(566\) 13.8083i 0.580406i
\(567\) 22.8763 6.60860i 0.960716 0.277535i
\(568\) −5.46580 5.46580i −0.229340 0.229340i
\(569\) −32.7045 + 18.8820i −1.37104 + 0.791573i −0.991060 0.133420i \(-0.957404\pi\)
−0.379985 + 0.924993i \(0.624071\pi\)
\(570\) −25.2510 + 41.2708i −1.05765 + 1.72864i
\(571\) 10.1577 17.5937i 0.425089 0.736275i −0.571340 0.820713i \(-0.693576\pi\)
0.996429 + 0.0844384i \(0.0269096\pi\)
\(572\) −9.26173 + 2.48167i −0.387252 + 0.103764i
\(573\) 32.0955 + 8.97215i 1.34081 + 0.374817i
\(574\) −23.4970 11.6714i −0.980745 0.487156i
\(575\) 6.81139 22.7272i 0.284055 0.947791i
\(576\) 79.4992 + 1.71548i 3.31247 + 0.0714784i
\(577\) 17.0063 + 17.0063i 0.707981 + 0.707981i 0.966110 0.258130i \(-0.0831062\pi\)
−0.258130 + 0.966110i \(0.583106\pi\)
\(578\) 2.20582 8.23224i 0.0917501 0.342416i
\(579\) 3.03076 5.12105i 0.125954 0.212824i
\(580\) −6.98402 + 3.89655i −0.289996 + 0.161796i
\(581\) −0.418811 + 0.0262428i −0.0173752 + 0.00108873i
\(582\) −5.20959 20.3166i −0.215945 0.842152i
\(583\) 4.65585 17.3759i 0.192826 0.719635i
\(584\) −35.7715 −1.48024
\(585\) −4.73514 + 4.40356i −0.195774 + 0.182065i
\(586\) 10.3939i 0.429369i
\(587\) 9.30842 34.7395i 0.384199 1.43385i −0.455225 0.890376i \(-0.650441\pi\)
0.839425 0.543476i \(-0.182892\pi\)
\(588\) 40.5745 51.1059i 1.67327 2.10757i
\(589\) −23.0823 13.3266i −0.951089 0.549111i
\(590\) 18.0852 63.7343i 0.744556 2.62390i
\(591\) 0.0116541 1.08028i 0.000479386 0.0444368i
\(592\) 86.8755 + 23.2782i 3.57056 + 0.956729i
\(593\) 27.4760 27.4760i 1.12830 1.12830i 0.137849 0.990453i \(-0.455981\pi\)
0.990453 0.137849i \(-0.0440189\pi\)
\(594\) 13.7707 22.1630i 0.565020 0.909361i
\(595\) 26.5174 1.27080i 1.08711 0.0520976i
\(596\) 9.84145 + 17.0459i 0.403122 + 0.698227i
\(597\) 9.66528 9.45897i 0.395574 0.387130i
\(598\) 3.21654 + 12.0043i 0.131534 + 0.490892i
\(599\) −26.1595 15.1032i −1.06885 0.617099i −0.140981 0.990012i \(-0.545026\pi\)
−0.927866 + 0.372913i \(0.878359\pi\)
\(600\) −42.5256 + 67.2646i −1.73610 + 2.74607i
\(601\) −22.7129 + 13.1133i −0.926480 + 0.534903i −0.885696 0.464265i \(-0.846319\pi\)
−0.0407831 + 0.999168i \(0.512985\pi\)
\(602\) −4.19660 + 20.7856i −0.171041 + 0.847158i
\(603\) 1.32370 0.324247i 0.0539054 0.0132044i
\(604\) 45.7755i 1.86258i
\(605\) 0.249146 16.9568i 0.0101292 0.689394i
\(606\) −16.8790 + 28.5203i −0.685664 + 1.15856i
\(607\) −38.5839 + 10.3385i −1.56607 + 0.419628i −0.934580 0.355754i \(-0.884224\pi\)
−0.631493 + 0.775382i \(0.717557\pi\)
\(608\) −24.0504 89.7574i −0.975374 3.64014i
\(609\) −0.157647 3.04120i −0.00638819 0.123236i
\(610\) −5.35740 + 5.20225i −0.216915 + 0.210633i
\(611\) 6.06582 0.245397
\(612\) −70.3741 + 17.2384i −2.84470 + 0.696822i
\(613\) −7.95610 7.95610i −0.321344 0.321344i 0.527939 0.849282i \(-0.322965\pi\)
−0.849282 + 0.527939i \(0.822965\pi\)
\(614\) 12.6182 + 21.8553i 0.509227 + 0.882008i
\(615\) −10.2466 + 9.73729i −0.413182 + 0.392646i
\(616\) −2.81004 44.8456i −0.113220 1.80688i
\(617\) −6.37378 23.7873i −0.256599 0.957640i −0.967194 0.254039i \(-0.918241\pi\)
0.710595 0.703601i \(-0.248426\pi\)
\(618\) −62.1833 63.5396i −2.50138 2.55594i
\(619\) 6.26054 + 10.8436i 0.251633 + 0.435840i 0.963975 0.265991i \(-0.0856992\pi\)
−0.712343 + 0.701832i \(0.752366\pi\)
\(620\) −59.8978 35.7655i −2.40555 1.43638i
\(621\) −20.9433 13.0129i −0.840425 0.522188i
\(622\) 18.0123 + 18.0123i 0.722226 + 0.722226i
\(623\) 26.5142 8.91552i 1.06227 0.357193i
\(624\) 0.255796 23.7111i 0.0102401 0.949204i
\(625\) −11.2068 22.3474i −0.448272 0.893897i
\(626\) 5.45055 + 3.14688i 0.217848 + 0.125775i
\(627\) −14.1751 3.96259i −0.566101 0.158251i
\(628\) −50.4988 13.5311i −2.01512 0.539950i
\(629\) −28.4172 −1.13307
\(630\) −25.2013 41.1126i −1.00404 1.63797i
\(631\) −29.9315 −1.19156 −0.595778 0.803149i \(-0.703156\pi\)
−0.595778 + 0.803149i \(0.703156\pi\)
\(632\) −113.263 30.3488i −4.50537 1.20721i
\(633\) 7.93356 + 30.9397i 0.315331 + 1.22974i
\(634\) 11.5928 + 6.69312i 0.460410 + 0.265818i
\(635\) −0.608409 + 2.14410i −0.0241440 + 0.0850861i
\(636\) 78.0828 + 46.2113i 3.09619 + 1.83240i
\(637\) −5.32953 4.13833i −0.211163 0.163967i
\(638\) −2.35962 2.35962i −0.0934182 0.0934182i
\(639\) 0.0544426 2.52299i 0.00215372 0.0998081i
\(640\) −17.2812 68.5049i −0.683101 2.70789i
\(641\) −10.6677 18.4770i −0.421348 0.729796i 0.574724 0.818348i \(-0.305110\pi\)
−0.996072 + 0.0885516i \(0.971776\pi\)
\(642\) 2.73234 9.77422i 0.107837 0.385758i
\(643\) 7.48426 + 27.9316i 0.295150 + 1.10152i 0.941098 + 0.338134i \(0.109796\pi\)
−0.645948 + 0.763382i \(0.723538\pi\)
\(644\) −67.4376 + 4.22565i −2.65741 + 0.166514i
\(645\) 9.74537 + 5.96258i 0.383723 + 0.234777i
\(646\) 28.0292 + 48.5479i 1.10279 + 1.91009i
\(647\) 8.50021 + 8.50021i 0.334178 + 0.334178i 0.854171 0.519993i \(-0.174065\pi\)
−0.519993 + 0.854171i \(0.674065\pi\)
\(648\) 55.9020 + 60.9472i 2.19604 + 2.39423i
\(649\) 20.1542 0.791120
\(650\) 11.1434 + 6.87790i 0.437081 + 0.269773i
\(651\) 22.2871 14.4554i 0.873501 0.566551i
\(652\) 4.06323 + 15.1642i 0.159128 + 0.593875i
\(653\) 3.12038 0.836104i 0.122110 0.0327193i −0.197246 0.980354i \(-0.563200\pi\)
0.319357 + 0.947635i \(0.396533\pi\)
\(654\) −12.8708 22.8588i −0.503286 0.893849i
\(655\) 47.5164 + 0.698157i 1.85662 + 0.0272793i
\(656\) 51.8355i 2.02384i
\(657\) −8.07785 8.43416i −0.315147 0.329048i
\(658\) −8.95235 + 44.3407i −0.348999 + 1.72858i
\(659\) 39.3257 22.7047i 1.53191 0.884450i 0.532638 0.846343i \(-0.321201\pi\)
0.999274 0.0381066i \(-0.0121326\pi\)
\(660\) −36.9464 10.9159i −1.43814 0.424900i
\(661\) 26.5745 + 15.3428i 1.03363 + 0.596766i 0.918022 0.396529i \(-0.129785\pi\)
0.115607 + 0.993295i \(0.463119\pi\)
\(662\) 23.3471 + 87.1326i 0.907411 + 3.38650i
\(663\) 1.86092 + 7.25733i 0.0722723 + 0.281851i
\(664\) −0.728723 1.26218i −0.0282799 0.0489823i
\(665\) −18.2915 + 20.1329i −0.709313 + 0.780720i
\(666\) 24.8383 + 45.2484i 0.962466 + 1.75334i
\(667\) −2.22976 + 2.22976i −0.0863365 + 0.0863365i
\(668\) 81.9808 + 21.9667i 3.17193 + 0.849917i
\(669\) −29.7466 + 16.7490i −1.15007 + 0.647554i
\(670\) −1.34470 2.41018i −0.0519502 0.0931134i
\(671\) −1.96738 1.13586i −0.0759497 0.0438496i
\(672\) 90.5800 + 19.3072i 3.49420 + 0.744793i
\(673\) 6.20707 23.1651i 0.239265 0.892948i −0.736915 0.675985i \(-0.763718\pi\)
0.976180 0.216963i \(-0.0696151\pi\)
\(674\) 16.9997i 0.654805i
\(675\) −25.4626 + 5.16292i −0.980056 + 0.198721i
\(676\) 64.9661 2.49870
\(677\) 4.62252 17.2515i 0.177658 0.663028i −0.818426 0.574612i \(-0.805153\pi\)
0.996084 0.0884161i \(-0.0281805\pi\)
\(678\) −32.8293 + 32.1285i −1.26080 + 1.23389i
\(679\) −0.737429 11.7687i −0.0282999 0.451641i
\(680\) 44.9242 + 80.5202i 1.72276 + 3.08781i
\(681\) 20.2364 + 35.9404i 0.775461 + 1.37724i
\(682\) 7.53403 28.1174i 0.288493 1.07667i
\(683\) 3.78937 + 3.78937i 0.144996 + 0.144996i 0.775879 0.630882i \(-0.217307\pi\)
−0.630882 + 0.775879i \(0.717307\pi\)
\(684\) 38.4974 63.4763i 1.47199 2.42708i
\(685\) −5.85066 + 1.47591i −0.223542 + 0.0563914i
\(686\) 38.1166 32.8508i 1.45530 1.25425i
\(687\) −9.33924 36.4217i −0.356314 1.38957i
\(688\) −40.4680 + 10.8434i −1.54283 + 0.413399i
\(689\) 4.69107 8.12518i 0.178716 0.309545i
\(690\) −14.1482 + 47.8868i −0.538615 + 1.82302i
\(691\) 21.7524 12.5587i 0.827500 0.477757i −0.0254960 0.999675i \(-0.508116\pi\)
0.852996 + 0.521918i \(0.174783\pi\)
\(692\) 23.5714 + 23.5714i 0.896052 + 0.896052i
\(693\) 9.93908 10.7895i 0.377555 0.409859i
\(694\) 24.7097i 0.937968i
\(695\) −0.493052 + 33.5570i −0.0187025 + 1.27289i
\(696\) 9.21623 5.18925i 0.349340 0.196698i
\(697\) 4.23888 + 15.8197i 0.160559 + 0.599215i
\(698\) 21.3137 + 79.5437i 0.806734 + 3.01077i
\(699\) 37.5240 + 0.404811i 1.41929 + 0.0153114i
\(700\) −48.6461 + 51.9878i −1.83865 + 1.96496i
\(701\) −4.01390 −0.151603 −0.0758014 0.997123i \(-0.524151\pi\)
−0.0758014 + 0.997123i \(0.524151\pi\)
\(702\) 9.92921 9.30647i 0.374754 0.351250i
\(703\) 20.5886 20.5886i 0.776514 0.776514i
\(704\) 42.4251 24.4941i 1.59896 0.923158i
\(705\) 20.7892 + 12.7196i 0.782967 + 0.479049i
\(706\) −27.5950 15.9320i −1.03855 0.599608i
\(707\) −12.3252 + 13.9730i −0.463536 + 0.525510i
\(708\) −27.3677 + 97.9009i −1.02854 + 3.67934i
\(709\) 13.5214 7.80657i 0.507806 0.293182i −0.224125 0.974560i \(-0.571952\pi\)
0.731931 + 0.681378i \(0.238619\pi\)
\(710\) −4.95534 + 1.25005i −0.185971 + 0.0469135i
\(711\) −18.4213 33.5583i −0.690852 1.25854i
\(712\) 68.6985 + 68.6985i 2.57458 + 2.57458i
\(713\) −26.5699 7.11939i −0.995051 0.266623i
\(714\) −55.7971 + 2.89236i −2.08815 + 0.108244i
\(715\) −1.08747 + 3.83237i −0.0406691 + 0.143322i
\(716\) 57.9346 100.346i 2.16512 3.75009i
\(717\) 17.6594 4.52822i 0.659502 0.169110i
\(718\) −11.6954 + 43.6478i −0.436468 + 1.62892i
\(719\) −5.56765 −0.207638 −0.103819 0.994596i \(-0.533106\pi\)
−0.103819 + 0.994596i \(0.533106\pi\)
\(720\) 50.5973 80.7280i 1.88565 3.00856i
\(721\) −27.6497 41.6390i −1.02973 1.55072i
\(722\) −5.61712 1.50510i −0.209048 0.0560142i
\(723\) −8.35721 + 29.8957i −0.310808 + 1.11183i
\(724\) 5.45699 9.45179i 0.202808 0.351273i
\(725\) −0.0976189 + 3.32124i −0.00362548 + 0.123348i
\(726\) −0.385012 + 35.6888i −0.0142891 + 1.32453i
\(727\) 6.77214 25.2740i 0.251165 0.937360i −0.719019 0.694990i \(-0.755409\pi\)
0.970184 0.242370i \(-0.0779247\pi\)
\(728\) 4.63798 22.9718i 0.171895 0.851391i
\(729\) −1.74637 + 26.9435i −0.0646806 + 0.997906i
\(730\) −12.1248 + 20.3059i −0.448761 + 0.751556i
\(731\) 11.4637 6.61859i 0.424002 0.244797i
\(732\) 8.18912 8.01432i 0.302679 0.296218i
\(733\) −2.62706 9.80432i −0.0970327 0.362131i 0.900287 0.435297i \(-0.143356\pi\)
−0.997320 + 0.0731657i \(0.976690\pi\)
\(734\) −14.3891 + 24.9226i −0.531110 + 0.919909i
\(735\) −9.58792 25.3589i −0.353656 0.935376i
\(736\) −47.9507 83.0530i −1.76749 3.06138i
\(737\) 0.593687 0.593687i 0.0218687 0.0218687i
\(738\) 21.4846 20.5769i 0.790857 0.757447i
\(739\) 1.54566i 0.0568579i −0.999596 0.0284289i \(-0.990950\pi\)
0.999596 0.0284289i \(-0.00905043\pi\)
\(740\) 54.6756 53.0922i 2.00992 1.95171i
\(741\) −6.60629 3.90976i −0.242688 0.143629i
\(742\) 52.4711 + 46.2831i 1.92627 + 1.69911i
\(743\) 51.2472 13.7316i 1.88008 0.503765i 0.880520 0.474009i \(-0.157194\pi\)
0.999557 0.0297559i \(-0.00947298\pi\)
\(744\) 79.3994 + 46.9905i 2.91092 + 1.72276i
\(745\) 8.17669 + 0.120140i 0.299571 + 0.00440158i
\(746\) −85.9671 −3.14748
\(747\) 0.133037 0.456841i 0.00486759 0.0167150i
\(748\) −31.5631 + 31.5631i −1.15406 + 1.15406i
\(749\) 2.53831 5.11015i 0.0927480 0.186721i
\(750\) 23.7690 + 46.9395i 0.867922 + 1.71399i
\(751\) 15.9634 27.6494i 0.582513 1.00894i −0.412668 0.910882i \(-0.635403\pi\)
0.995180 0.0980603i \(-0.0312638\pi\)
\(752\) −86.3280 + 23.1315i −3.14806 + 0.843519i
\(753\) −7.91652 8.08919i −0.288494 0.294787i
\(754\) −0.870215 1.50726i −0.0316914 0.0548910i
\(755\) 16.3287 + 9.75002i 0.594263 + 0.354839i
\(756\) 38.9146 + 62.9314i 1.41531 + 2.28879i
\(757\) 26.0899 26.0899i 0.948255 0.948255i −0.0504705 0.998726i \(-0.516072\pi\)
0.998726 + 0.0504705i \(0.0160721\pi\)
\(758\) 22.6999 84.7172i 0.824497 3.07707i
\(759\) −15.1893 0.163863i −0.551338 0.00594786i
\(760\) −90.8860 25.7898i −3.29678 0.935493i
\(761\) −25.9576 14.9866i −0.940963 0.543265i −0.0507010 0.998714i \(-0.516146\pi\)
−0.890262 + 0.455449i \(0.849479\pi\)
\(762\) 1.26282 4.51739i 0.0457470 0.163648i
\(763\) −4.70065 13.9794i −0.170175 0.506089i
\(764\) 103.555i 3.74650i
\(765\) −8.84025 + 28.7751i −0.319620 + 1.04037i
\(766\) 10.0287i 0.362350i
\(767\) 10.1533 + 2.72057i 0.366615 + 0.0982342i
\(768\) 14.1259 + 55.0890i 0.509725 + 1.98785i
\(769\) −0.240526 + 0.416604i −0.00867360 + 0.0150231i −0.870330 0.492470i \(-0.836094\pi\)
0.861656 + 0.507493i \(0.169428\pi\)
\(770\) −26.4094 13.6054i −0.951728 0.490305i
\(771\) 5.22632 8.83086i 0.188221 0.318036i
\(772\) 17.8608 + 4.78578i 0.642823 + 0.172244i
\(773\) −18.9180 + 18.9180i −0.680432 + 0.680432i −0.960098 0.279665i \(-0.909776\pi\)
0.279665 + 0.960098i \(0.409776\pi\)
\(774\) −20.5587 12.4685i −0.738968 0.448173i
\(775\) −25.5160 + 13.7484i −0.916563 + 0.493858i
\(776\) 35.4677 20.4773i 1.27322 0.735092i
\(777\) 8.95193 + 27.6047i 0.321149 + 0.990311i
\(778\) 9.80264 2.62661i 0.351442 0.0941685i
\(779\) −14.5327 8.39047i −0.520688 0.300620i
\(780\) −17.1394 10.4866i −0.613690 0.375479i
\(781\) −0.777348 1.34641i −0.0278157 0.0481782i
\(782\) 40.9094 + 40.9094i 1.46292 + 1.46292i
\(783\) 3.30471 + 1.00116i 0.118101 + 0.0357787i
\(784\) 91.6303 + 38.5725i 3.27251 + 1.37759i
\(785\) −15.5828 + 15.1315i −0.556174 + 0.540067i
\(786\) −100.007 1.07888i −3.56713 0.0384824i
\(787\) −45.8857 + 12.2950i −1.63565 + 0.438270i −0.955545 0.294846i \(-0.904732\pi\)
−0.680103 + 0.733117i \(0.738065\pi\)
\(788\) 3.24261 0.868854i 0.115513 0.0309517i
\(789\) −1.88793 3.35300i −0.0672119 0.119370i
\(790\) −55.6185 + 54.0078i −1.97882 + 1.92151i
\(791\) −21.5138 + 14.2859i −0.764944 + 0.507948i
\(792\) 48.9179 + 14.2455i 1.73822 + 0.506190i
\(793\) −0.837802 0.837802i −0.0297512 0.0297512i
\(794\) −8.39992 14.5491i −0.298102 0.516328i
\(795\) 33.1156 18.0103i 1.17449 0.638760i
\(796\) 36.3927 + 21.0113i 1.28991 + 0.744727i
\(797\) −48.8495 + 13.0892i −1.73034 + 0.463643i −0.980261 0.197708i \(-0.936650\pi\)
−0.750077 + 0.661351i \(0.769983\pi\)
\(798\) 38.3301 42.5212i 1.35687 1.50523i
\(799\) 24.4549 14.1190i 0.865153 0.499496i
\(800\) −96.7973 29.0103i −3.42230 1.02567i
\(801\) −0.684279 + 31.7110i −0.0241778 + 1.12045i
\(802\) 43.7978 43.7978i 1.54655 1.54655i
\(803\) −6.94957 1.86213i −0.245245 0.0657132i
\(804\) 2.07772 + 3.69008i 0.0732754 + 0.130139i
\(805\) −12.8566 + 24.9559i −0.453136 + 0.879581i
\(806\) 7.59103 13.1480i 0.267383 0.463120i
\(807\) −28.7960 + 28.1813i −1.01367 + 0.992030i
\(808\) −62.5071 16.7487i −2.19899 0.589218i
\(809\) 44.3393i 1.55889i 0.626473 + 0.779443i \(0.284498\pi\)
−0.626473 + 0.779443i \(0.715502\pi\)
\(810\) 53.5452 11.0749i 1.88139 0.389133i
\(811\) 15.9073i 0.558582i −0.960207 0.279291i \(-0.909901\pi\)
0.960207 0.279291i \(-0.0900994\pi\)
\(812\) 8.96925 3.01596i 0.314759 0.105839i
\(813\) −8.49014 8.67532i −0.297762 0.304257i
\(814\) 27.5395 + 15.8999i 0.965258 + 0.557292i
\(815\) 6.27471 + 1.78051i 0.219794 + 0.0623685i
\(816\) −54.1597 96.1889i −1.89597 3.36729i
\(817\) −3.51037 + 13.1009i −0.122812 + 0.458342i
\(818\) 24.3631 24.3631i 0.851836 0.851836i
\(819\) 6.46359 4.09390i 0.225856 0.143053i
\(820\) −37.7119 22.5181i −1.31696 0.786367i
\(821\) 9.06589 + 15.7026i 0.316402 + 0.548024i 0.979734 0.200301i \(-0.0641919\pi\)
−0.663333 + 0.748325i \(0.730859\pi\)
\(822\) 12.3009 3.15421i 0.429045 0.110016i
\(823\) −4.58956 + 1.22977i −0.159982 + 0.0428670i −0.337921 0.941174i \(-0.609724\pi\)
0.177939 + 0.984042i \(0.443057\pi\)
\(824\) 86.7995 150.341i 3.02380 5.23738i
\(825\) −11.7633 + 10.8542i −0.409545 + 0.377895i
\(826\) −34.8722 + 70.2048i −1.21336 + 2.44274i
\(827\) −0.938044 + 0.938044i −0.0326190 + 0.0326190i −0.723228 0.690609i \(-0.757343\pi\)
0.690609 + 0.723228i \(0.257343\pi\)
\(828\) 21.4219 73.5613i 0.744463 2.55643i
\(829\) −19.4893 −0.676893 −0.338446 0.940986i \(-0.609901\pi\)
−0.338446 + 0.940986i \(0.609901\pi\)
\(830\) −0.963490 0.0141565i −0.0334432 0.000491380i
\(831\) 15.8047 8.89893i 0.548259 0.308700i
\(832\) 24.6795 6.61284i 0.855606 0.229259i
\(833\) −31.1190 4.27885i −1.07821 0.148253i
\(834\) 0.761925 70.6268i 0.0263833 2.44561i
\(835\) 25.2974 24.5648i 0.875454 0.850100i
\(836\) 45.7357i 1.58180i
\(837\) 6.85046 + 29.3320i 0.236786 + 1.01386i
\(838\) 47.7416 47.7416i 1.64920 1.64920i
\(839\) −20.6306 35.7333i −0.712249 1.23365i −0.964011 0.265862i \(-0.914343\pi\)
0.251762 0.967789i \(-0.418990\pi\)
\(840\) 64.0659 69.0050i 2.21049 2.38090i
\(841\) −14.2792 + 24.7323i −0.492386 + 0.852838i
\(842\) −26.4753 98.8073i −0.912400 3.40512i
\(843\) −28.6167 7.99967i −0.985612 0.275523i
\(844\) −85.9536 + 49.6253i −2.95864 + 1.70817i
\(845\) 13.8375 23.1743i 0.476026 0.797219i
\(846\) −43.8567 26.5984i −1.50782 0.914472i
\(847\) −3.97113 + 19.6689i −0.136450 + 0.675831i
\(848\) −35.7781 + 133.526i −1.22862 + 4.58529i
\(849\) −7.57536 4.48328i −0.259986 0.153866i
\(850\) 60.9350 + 1.79102i 2.09005 + 0.0614314i
\(851\) 15.0249 26.0238i 0.515045 0.892085i
\(852\) 7.59588 1.94774i 0.260231 0.0667283i
\(853\) 23.1236 + 6.19595i 0.791737 + 0.212145i 0.631953 0.775007i \(-0.282254\pi\)
0.159784 + 0.987152i \(0.448920\pi\)
\(854\) 7.36076 4.88779i 0.251880 0.167257i
\(855\) −14.4430 27.2528i −0.493941 0.932025i
\(856\) 19.8172 0.677340
\(857\) −7.72966 + 28.8475i −0.264040 + 0.985411i 0.698795 + 0.715322i \(0.253720\pi\)
−0.962835 + 0.270089i \(0.912947\pi\)
\(858\) 2.25716 8.07439i 0.0770581 0.275655i
\(859\) 9.50953 16.4710i 0.324461 0.561983i −0.656942 0.753941i \(-0.728150\pi\)
0.981403 + 0.191958i \(0.0614837\pi\)
\(860\) −9.69101 + 34.1522i −0.330461 + 1.16458i
\(861\) 14.0321 9.10118i 0.478212 0.310167i
\(862\) −53.2582 14.2705i −1.81398 0.486055i
\(863\) 29.0505 + 29.0505i 0.988890 + 0.988890i 0.999939 0.0110485i \(-0.00351692\pi\)
−0.0110485 + 0.999939i \(0.503517\pi\)
\(864\) −55.4229 + 89.1993i −1.88553 + 3.03462i
\(865\) 13.4289 3.38761i 0.456596 0.115182i
\(866\) −45.0109 + 25.9871i −1.52953 + 0.883077i
\(867\) 3.80010 + 3.88298i 0.129058 + 0.131873i
\(868\) 61.9041 + 54.6037i 2.10116 + 1.85337i
\(869\) −20.4246 11.7921i −0.692856 0.400020i
\(870\) 0.178155 6.99056i 0.00604002 0.237002i
\(871\) 0.379230 0.218949i 0.0128497 0.00741879i
\(872\) 36.2209 36.2209i 1.22659 1.22659i
\(873\) 12.8374 + 3.73839i 0.434479 + 0.126525i
\(874\) −59.2788 −2.00514
\(875\) 8.18330 + 28.4259i 0.276646 + 0.960972i
\(876\) 18.4825 31.2296i 0.624465 1.05515i
\(877\) 2.54092 + 9.48284i 0.0858007 + 0.320213i 0.995465 0.0951325i \(-0.0303275\pi\)
−0.909664 + 0.415345i \(0.863661\pi\)
\(878\) 10.1558 + 37.9018i 0.342741 + 1.27913i
\(879\) −5.70220 3.37470i −0.192330 0.113826i
\(880\) 0.862312 58.6888i 0.0290685 1.97840i
\(881\) 20.3578i 0.685872i 0.939359 + 0.342936i \(0.111421\pi\)
−0.939359 + 0.342936i \(0.888579\pi\)
\(882\) 20.3867 + 53.2905i 0.686457 + 1.79438i
\(883\) −33.9789 33.9789i −1.14348 1.14348i −0.987809 0.155672i \(-0.950246\pi\)
−0.155672 0.987809i \(-0.549754\pi\)
\(884\) −20.1616 + 11.6403i −0.678107 + 0.391505i
\(885\) 29.0933 + 30.6150i 0.977961 + 1.02911i
\(886\) 18.1034 31.3560i 0.608195 1.05343i
\(887\) −9.56274 + 2.56233i −0.321086 + 0.0860346i −0.415762 0.909473i \(-0.636485\pi\)
0.0946764 + 0.995508i \(0.469818\pi\)
\(888\) −72.0342 + 70.4966i −2.41731 + 2.36571i
\(889\) 1.17314 2.36178i 0.0393460 0.0792115i
\(890\) 62.2827 15.7116i 2.08772 0.526655i
\(891\) 7.68777 + 14.7507i 0.257550 + 0.494166i
\(892\) −75.0084 75.0084i −2.51147 2.51147i
\(893\) −7.48846 + 27.9473i −0.250592 + 0.935221i
\(894\) −17.2093 0.185655i −0.575566 0.00620923i
\(895\) −23.4548 42.0393i −0.784006 1.40522i
\(896\) 5.22785 + 83.4317i 0.174650 + 2.78726i
\(897\) −7.63001 2.13293i −0.254759 0.0712166i
\(898\) −5.02462 + 18.7521i −0.167674 + 0.625766i
\(899\) 3.85221 0.128479
\(900\) −36.7519 71.8806i −1.22506 2.39602i
\(901\) 43.6766i 1.45508i
\(902\) 4.74346 17.7028i 0.157940 0.589440i
\(903\) −10.0406 9.05098i −0.334131 0.301198i
\(904\) −77.6775 44.8471i −2.58351 1.49159i
\(905\) −2.20926 3.95978i −0.0734382 0.131627i
\(906\) −34.4449 20.3853i −1.14436 0.677257i
\(907\) −5.72684 1.53450i −0.190156 0.0509523i 0.162484 0.986711i \(-0.448049\pi\)
−0.352640 + 0.935759i \(0.614716\pi\)
\(908\) −90.6264 + 90.6264i −3.00754 + 3.00754i
\(909\) −10.1662 18.5200i −0.337193 0.614270i
\(910\) −11.4680 10.4191i −0.380161 0.345391i
\(911\) 5.02116 + 8.69690i 0.166358 + 0.288141i 0.937137 0.348962i \(-0.113466\pi\)
−0.770778 + 0.637103i \(0.780132\pi\)
\(912\) 108.929 + 30.4507i 3.60701 + 1.00832i
\(913\) −0.0758692 0.283148i −0.00251090 0.00937082i
\(914\) 98.5730 + 56.9112i 3.26051 + 1.88245i
\(915\) −1.11456 4.62819i −0.0368462 0.153003i
\(916\) 101.183 58.4180i 3.34318 1.93019i
\(917\) −55.1161 11.1279i −1.82009 0.367476i
\(918\) 18.3684 60.6316i 0.606248 2.00114i
\(919\) 12.9193i 0.426168i 0.977034 + 0.213084i \(0.0683508\pi\)
−0.977034 + 0.213084i \(0.931649\pi\)
\(920\) −97.4911 1.43243i −3.21419 0.0472259i
\(921\) −16.0869 0.173546i −0.530081 0.00571854i
\(922\) 1.76211 0.472155i 0.0580318 0.0155496i
\(923\) −0.209866 0.783229i −0.00690781 0.0257803i
\(924\) 40.6035 + 20.7176i 1.33576 + 0.681561i
\(925\) −7.29297 30.8120i −0.239791 1.01309i
\(926\) 43.3113 1.42330
\(927\) 55.0481 13.4843i 1.80802 0.442881i
\(928\) 9.49673 + 9.49673i 0.311745 + 0.311745i
\(929\) −15.1575 26.2535i −0.497301 0.861350i 0.502695 0.864464i \(-0.332342\pi\)
−0.999995 + 0.00311426i \(0.999009\pi\)
\(930\) 53.5871 29.1440i 1.75719 0.955671i
\(931\) 25.6462 19.4460i 0.840520 0.637318i
\(932\) 30.1801 + 112.634i 0.988581 + 3.68944i
\(933\) −15.7299 + 4.03347i −0.514975 + 0.132050i
\(934\) 20.5025 + 35.5113i 0.670861 + 1.16197i
\(935\) 4.53614 + 17.9818i 0.148348 + 0.588067i
\(936\) 22.7210 + 13.7799i 0.742660 + 0.450412i
\(937\) 36.0958 + 36.0958i 1.17920 + 1.17920i 0.979949 + 0.199249i \(0.0638504\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(938\) 1.04080 + 3.09528i 0.0339835 + 0.101065i
\(939\) −3.49609 + 1.96849i −0.114091 + 0.0642394i
\(940\) −20.6733 + 72.8549i −0.674287 + 2.37627i
\(941\) 13.7585 + 7.94345i 0.448513 + 0.258949i 0.707202 0.707012i \(-0.249957\pi\)
−0.258689 + 0.965961i \(0.583290\pi\)
\(942\) 32.6706 31.9732i 1.06447 1.04174i
\(943\) −16.7285 4.48240i −0.544756 0.145967i
\(944\) −154.875 −5.04076
\(945\) 30.7371 0.477190i 0.999880 0.0155230i
\(946\) −14.8129 −0.481608
\(947\) 1.35890 + 0.364115i 0.0441582 + 0.0118322i 0.280831 0.959757i \(-0.409390\pi\)
−0.236672 + 0.971590i \(0.576057\pi\)
\(948\) 85.0164 83.2017i 2.76120 2.70226i
\(949\) −3.24971 1.87622i −0.105490 0.0609047i
\(950\) −45.4458 + 42.8505i −1.47446 + 1.39026i
\(951\) −7.43587 + 4.18681i −0.241125 + 0.135767i
\(952\) −34.7716 103.408i −1.12695 3.35149i
\(953\) −14.7841 14.7841i −0.478903 0.478903i 0.425878 0.904781i \(-0.359965\pi\)
−0.904781 + 0.425878i \(0.859965\pi\)
\(954\) −69.5457 + 38.1759i −2.25163 + 1.23599i
\(955\) 36.9395 + 22.0569i 1.19533 + 0.713745i
\(956\) 28.3245 + 49.0596i 0.916081 + 1.58670i
\(957\) 2.06063 0.528387i 0.0666108 0.0170803i
\(958\) −21.0667 78.6221i −0.680635 2.54017i
\(959\) 7.12549 0.446485i 0.230094 0.0144177i
\(960\) 98.4499 + 29.0872i 3.17746 + 0.938785i
\(961\) 1.30175 + 2.25469i 0.0419918 + 0.0727320i
\(962\) 11.7276 + 11.7276i 0.378113 + 0.378113i
\(963\) 4.47509 + 4.67248i 0.144208 + 0.150569i
\(964\) −96.4577 −3.10669
\(965\) 5.51143 5.35182i 0.177419 0.172281i
\(966\) 26.8525 52.6269i 0.863965 1.69324i
\(967\) 2.29603 + 8.56889i 0.0738352 + 0.275557i 0.992967 0.118394i \(-0.0377746\pi\)
−0.919131 + 0.393951i \(0.871108\pi\)
\(968\) −67.3167 + 18.0375i −2.16364 + 0.579746i
\(969\) −35.7344 0.385504i −1.14795 0.0123842i
\(970\) 0.397802 27.0743i 0.0127727 0.869304i
\(971\) 0.877499i 0.0281603i 0.999901 + 0.0140801i \(0.00448200\pi\)
−0.999901 + 0.0140801i \(0.995518\pi\)
\(972\) −82.0923 + 17.3139i −2.63311 + 0.555343i
\(973\) 7.85873 38.9241i 0.251939 1.24785i
\(974\) 59.6732 34.4524i 1.91205 1.10393i
\(975\) −7.39133 + 3.88026i −0.236712 + 0.124268i
\(976\) 15.1184 + 8.72860i 0.483927 + 0.279396i
\(977\) 4.22411 + 15.7646i 0.135141 + 0.504354i 0.999997 + 0.00233386i \(0.000742890\pi\)
−0.864856 + 0.502020i \(0.832590\pi\)
\(978\) −13.2201 3.69563i −0.422734 0.118173i
\(979\) 9.77033 + 16.9227i 0.312261 + 0.540852i
\(980\) 67.8683 49.9074i 2.16797 1.59423i
\(981\) 16.7194 + 0.360782i 0.533810 + 0.0115189i
\(982\) 77.7554 77.7554i 2.48127 2.48127i
\(983\) −20.7249 5.55322i −0.661022 0.177120i −0.0873149 0.996181i \(-0.527829\pi\)
−0.573707 + 0.819060i \(0.694495\pi\)
\(984\) 49.9902 + 29.5854i 1.59363 + 0.943150i
\(985\) 0.380732 1.34174i 0.0121311 0.0427515i
\(986\) −7.01671 4.05110i −0.223457 0.129013i
\(987\) −21.4191 19.3079i −0.681777 0.614578i
\(988\) 6.17378 23.0408i 0.196414 0.733027i
\(989\) 13.9976i 0.445099i
\(990\) 24.6674 22.9400i 0.783980 0.729082i
\(991\) −24.5273 −0.779134 −0.389567 0.920998i \(-0.627375\pi\)
−0.389567 + 0.920998i \(0.627375\pi\)
\(992\) −30.3221 + 113.164i −0.962727 + 3.59295i
\(993\) −55.3821 15.4818i −1.75750 0.491300i
\(994\) 6.03508 0.378160i 0.191421 0.0119945i
\(995\) 15.2465 8.50642i 0.483348 0.269672i
\(996\) 1.47844 + 0.0159495i 0.0468463 + 0.000505380i
\(997\) −0.501151 + 1.87032i −0.0158716 + 0.0592337i −0.973407 0.229080i \(-0.926428\pi\)
0.957536 + 0.288314i \(0.0930948\pi\)
\(998\) −28.5022 28.5022i −0.902221 0.902221i
\(999\) −32.8882 1.06473i −1.04054 0.0336865i
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 315.2.cb.a.13.2 yes 176
3.2 odd 2 945.2.ce.a.118.43 176
5.2 odd 4 inner 315.2.cb.a.202.43 yes 176
7.6 odd 2 inner 315.2.cb.a.13.1 176
9.2 odd 6 945.2.ce.a.748.2 176
9.7 even 3 inner 315.2.cb.a.223.44 yes 176
15.2 even 4 945.2.ce.a.307.1 176
21.20 even 2 945.2.ce.a.118.44 176
35.27 even 4 inner 315.2.cb.a.202.44 yes 176
45.2 even 12 945.2.ce.a.937.44 176
45.7 odd 12 inner 315.2.cb.a.97.1 yes 176
63.20 even 6 945.2.ce.a.748.1 176
63.34 odd 6 inner 315.2.cb.a.223.43 yes 176
105.62 odd 4 945.2.ce.a.307.2 176
315.97 even 12 inner 315.2.cb.a.97.2 yes 176
315.272 odd 12 945.2.ce.a.937.43 176
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.cb.a.13.1 176 7.6 odd 2 inner
315.2.cb.a.13.2 yes 176 1.1 even 1 trivial
315.2.cb.a.97.1 yes 176 45.7 odd 12 inner
315.2.cb.a.97.2 yes 176 315.97 even 12 inner
315.2.cb.a.202.43 yes 176 5.2 odd 4 inner
315.2.cb.a.202.44 yes 176 35.27 even 4 inner
315.2.cb.a.223.43 yes 176 63.34 odd 6 inner
315.2.cb.a.223.44 yes 176 9.7 even 3 inner
945.2.ce.a.118.43 176 3.2 odd 2
945.2.ce.a.118.44 176 21.20 even 2
945.2.ce.a.307.1 176 15.2 even 4
945.2.ce.a.307.2 176 105.62 odd 4
945.2.ce.a.748.1 176 63.20 even 6
945.2.ce.a.748.2 176 9.2 odd 6
945.2.ce.a.937.43 176 315.272 odd 12
945.2.ce.a.937.44 176 45.2 even 12