Properties

Label 45.4.l.a.2.6
Level $45$
Weight $4$
Character 45.2
Analytic conductor $2.655$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,4,Mod(2,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.l (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: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 45.2
Dual form 45.4.l.a.23.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.689083 - 2.57169i) q^{2} +(5.10395 + 0.974542i) q^{3} +(0.789441 - 0.455784i) q^{4} +(6.87382 + 8.81763i) q^{5} +(-1.01082 - 13.7973i) q^{6} +(1.49332 - 0.400135i) q^{7} +(-16.7770 - 16.7770i) q^{8} +(25.1005 + 9.94802i) q^{9} +O(q^{10})\) \(q+(-0.689083 - 2.57169i) q^{2} +(5.10395 + 0.974542i) q^{3} +(0.789441 - 0.455784i) q^{4} +(6.87382 + 8.81763i) q^{5} +(-1.01082 - 13.7973i) q^{6} +(1.49332 - 0.400135i) q^{7} +(-16.7770 - 16.7770i) q^{8} +(25.1005 + 9.94802i) q^{9} +(17.9396 - 23.7534i) q^{10} +(-61.6602 - 35.5995i) q^{11} +(4.47344 - 1.55695i) q^{12} +(38.6262 + 10.3499i) q^{13} +(-2.05805 - 3.56464i) q^{14} +(26.4905 + 51.7035i) q^{15} +(-27.9383 + 48.3905i) q^{16} +(-45.8839 + 45.8839i) q^{17} +(8.28689 - 71.4058i) q^{18} +3.05396i q^{19} +(9.44540 + 3.82802i) q^{20} +(8.01179 - 0.586960i) q^{21} +(-49.0620 + 183.102i) q^{22} +(-37.6487 + 140.507i) q^{23} +(-69.2790 - 101.979i) q^{24} +(-30.5012 + 121.222i) q^{25} -106.467i q^{26} +(118.417 + 75.2357i) q^{27} +(0.996515 - 0.996515i) q^{28} +(91.6343 - 158.715i) q^{29} +(114.711 - 103.753i) q^{30} +(-89.3086 - 154.687i) q^{31} +(-39.6453 - 10.6229i) q^{32} +(-280.017 - 241.788i) q^{33} +(149.617 + 86.3814i) q^{34} +(13.7931 + 10.4171i) q^{35} +(24.3495 - 3.58705i) q^{36} +(-26.4034 - 26.4034i) q^{37} +(7.85383 - 2.10443i) q^{38} +(187.060 + 90.4680i) q^{39} +(32.6113 - 263.255i) q^{40} +(79.5097 - 45.9049i) q^{41} +(-7.03027 - 20.1994i) q^{42} +(12.9952 + 48.4988i) q^{43} -64.9027 q^{44} +(84.8186 + 289.708i) q^{45} +387.283 q^{46} +(38.3375 + 143.078i) q^{47} +(-189.754 + 219.755i) q^{48} +(-294.977 + 170.305i) q^{49} +(332.762 - 5.09194i) q^{50} +(-278.905 + 189.473i) q^{51} +(35.2104 - 9.43460i) q^{52} +(182.516 + 182.516i) q^{53} +(111.884 - 356.376i) q^{54} +(-109.937 - 788.401i) q^{55} +(-31.7665 - 18.3404i) q^{56} +(-2.97621 + 15.5872i) q^{57} +(-471.310 - 126.287i) q^{58} +(-128.795 - 223.079i) q^{59} +(44.4783 + 28.7430i) q^{60} +(152.085 - 263.419i) q^{61} +(-336.266 + 336.266i) q^{62} +(41.4638 + 4.81201i) q^{63} +556.288i q^{64} +(174.248 + 411.735i) q^{65} +(-428.851 + 886.730i) q^{66} +(62.0292 - 231.496i) q^{67} +(-15.3095 + 57.1357i) q^{68} +(-329.086 + 680.448i) q^{69} +(17.2850 - 42.6498i) q^{70} -470.304i q^{71} +(-254.214 - 588.009i) q^{72} +(445.386 - 445.386i) q^{73} +(-49.7072 + 86.0954i) q^{74} +(-273.812 + 588.984i) q^{75} +(1.39194 + 2.41092i) q^{76} +(-106.323 - 28.4892i) q^{77} +(103.756 - 543.400i) q^{78} +(-134.691 - 77.7637i) q^{79} +(-618.732 + 86.2781i) q^{80} +(531.074 + 499.401i) q^{81} +(-172.842 - 172.842i) q^{82} +(806.421 - 216.080i) q^{83} +(6.05730 - 4.11501i) q^{84} +(-719.985 - 89.1897i) q^{85} +(115.769 - 66.8393i) q^{86} +(622.371 - 720.773i) q^{87} +(437.220 + 1631.73i) q^{88} +1352.69 q^{89} +(686.593 - 417.760i) q^{90} +61.8228 q^{91} +(34.3193 + 128.081i) q^{92} +(-305.077 - 876.550i) q^{93} +(341.534 - 197.184i) q^{94} +(-26.9287 + 20.9923i) q^{95} +(-191.995 - 92.8548i) q^{96} +(287.595 - 77.0607i) q^{97} +(641.235 + 641.235i) q^{98} +(-1193.56 - 1506.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.689083 2.57169i −0.243628 0.909230i −0.974068 0.226254i \(-0.927352\pi\)
0.730441 0.682976i \(-0.239315\pi\)
\(3\) 5.10395 + 0.974542i 0.982255 + 0.187551i
\(4\) 0.789441 0.455784i 0.0986801 0.0569730i
\(5\) 6.87382 + 8.81763i 0.614813 + 0.788673i
\(6\) −1.01082 13.7973i −0.0687776 0.938788i
\(7\) 1.49332 0.400135i 0.0806319 0.0216052i −0.218278 0.975887i \(-0.570044\pi\)
0.298909 + 0.954281i \(0.403377\pi\)
\(8\) −16.7770 16.7770i −0.741445 0.741445i
\(9\) 25.1005 + 9.94802i 0.929650 + 0.368445i
\(10\) 17.9396 23.7534i 0.567300 0.751149i
\(11\) −61.6602 35.5995i −1.69011 0.975787i −0.954417 0.298475i \(-0.903522\pi\)
−0.735696 0.677312i \(-0.763145\pi\)
\(12\) 4.47344 1.55695i 0.107614 0.0374545i
\(13\) 38.6262 + 10.3499i 0.824076 + 0.220810i 0.646128 0.763229i \(-0.276387\pi\)
0.177948 + 0.984040i \(0.443054\pi\)
\(14\) −2.05805 3.56464i −0.0392883 0.0680493i
\(15\) 26.4905 + 51.7035i 0.455987 + 0.889986i
\(16\) −27.9383 + 48.3905i −0.436535 + 0.756101i
\(17\) −45.8839 + 45.8839i −0.654616 + 0.654616i −0.954101 0.299485i \(-0.903185\pi\)
0.299485 + 0.954101i \(0.403185\pi\)
\(18\) 8.28689 71.4058i 0.108513 0.935029i
\(19\) 3.05396i 0.0368750i 0.999830 + 0.0184375i \(0.00586918\pi\)
−0.999830 + 0.0184375i \(0.994131\pi\)
\(20\) 9.44540 + 3.82802i 0.105603 + 0.0427986i
\(21\) 8.01179 0.586960i 0.0832531 0.00609930i
\(22\) −49.0620 + 183.102i −0.475457 + 1.77443i
\(23\) −37.6487 + 140.507i −0.341317 + 1.27381i 0.555540 + 0.831490i \(0.312512\pi\)
−0.896856 + 0.442322i \(0.854155\pi\)
\(24\) −69.2790 101.979i −0.589230 0.867347i
\(25\) −30.5012 + 121.222i −0.244010 + 0.969773i
\(26\) 106.467i 0.803070i
\(27\) 118.417 + 75.2357i 0.844051 + 0.536263i
\(28\) 0.996515 0.996515i 0.00672584 0.00672584i
\(29\) 91.6343 158.715i 0.586761 1.01630i −0.407893 0.913030i \(-0.633736\pi\)
0.994653 0.103269i \(-0.0329304\pi\)
\(30\) 114.711 103.753i 0.698112 0.631422i
\(31\) −89.3086 154.687i −0.517429 0.896214i −0.999795 0.0202438i \(-0.993556\pi\)
0.482366 0.875970i \(-0.339778\pi\)
\(32\) −39.6453 10.6229i −0.219011 0.0586839i
\(33\) −280.017 241.788i −1.47711 1.27545i
\(34\) 149.617 + 86.3814i 0.754679 + 0.435714i
\(35\) 13.7931 + 10.4171i 0.0666130 + 0.0503090i
\(36\) 24.3495 3.58705i 0.112729 0.0166067i
\(37\) −26.4034 26.4034i −0.117316 0.117316i 0.646012 0.763328i \(-0.276436\pi\)
−0.763328 + 0.646012i \(0.776436\pi\)
\(38\) 7.85383 2.10443i 0.0335279 0.00898377i
\(39\) 187.060 + 90.4680i 0.768039 + 0.371448i
\(40\) 32.6113 263.255i 0.128908 1.04061i
\(41\) 79.5097 45.9049i 0.302862 0.174857i −0.340866 0.940112i \(-0.610720\pi\)
0.643728 + 0.765255i \(0.277387\pi\)
\(42\) −7.03027 20.1994i −0.0258284 0.0742103i
\(43\) 12.9952 + 48.4988i 0.0460872 + 0.172000i 0.985133 0.171791i \(-0.0549555\pi\)
−0.939046 + 0.343791i \(0.888289\pi\)
\(44\) −64.9027 −0.222374
\(45\) 84.8186 + 289.708i 0.280978 + 0.959714i
\(46\) 387.283 1.24134
\(47\) 38.3375 + 143.078i 0.118981 + 0.444043i 0.999554 0.0298680i \(-0.00950868\pi\)
−0.880573 + 0.473911i \(0.842842\pi\)
\(48\) −189.754 + 219.755i −0.570596 + 0.660812i
\(49\) −294.977 + 170.305i −0.859991 + 0.496516i
\(50\) 332.762 5.09194i 0.941194 0.0144022i
\(51\) −278.905 + 189.473i −0.765774 + 0.520226i
\(52\) 35.2104 9.43460i 0.0939001 0.0251605i
\(53\) 182.516 + 182.516i 0.473029 + 0.473029i 0.902893 0.429865i \(-0.141439\pi\)
−0.429865 + 0.902893i \(0.641439\pi\)
\(54\) 111.884 356.376i 0.281953 0.898085i
\(55\) −109.937 788.401i −0.269527 1.93287i
\(56\) −31.7665 18.3404i −0.0758032 0.0437650i
\(57\) −2.97621 + 15.5872i −0.00691594 + 0.0362207i
\(58\) −471.310 126.287i −1.06700 0.285902i
\(59\) −128.795 223.079i −0.284197 0.492243i 0.688217 0.725505i \(-0.258394\pi\)
−0.972414 + 0.233261i \(0.925060\pi\)
\(60\) 44.4783 + 28.7430i 0.0957020 + 0.0618450i
\(61\) 152.085 263.419i 0.319221 0.552906i −0.661105 0.750293i \(-0.729912\pi\)
0.980326 + 0.197387i \(0.0632455\pi\)
\(62\) −336.266 + 336.266i −0.688805 + 0.688805i
\(63\) 41.4638 + 4.81201i 0.0829197 + 0.00962311i
\(64\) 556.288i 1.08650i
\(65\) 174.248 + 411.735i 0.332505 + 0.785684i
\(66\) −428.851 + 886.730i −0.799816 + 1.65377i
\(67\) 62.0292 231.496i 0.113106 0.422116i −0.886033 0.463623i \(-0.846549\pi\)
0.999138 + 0.0415072i \(0.0132160\pi\)
\(68\) −15.3095 + 57.1357i −0.0273021 + 0.101893i
\(69\) −329.086 + 680.448i −0.574164 + 1.18719i
\(70\) 17.2850 42.6498i 0.0295137 0.0728232i
\(71\) 470.304i 0.786124i −0.919512 0.393062i \(-0.871416\pi\)
0.919512 0.393062i \(-0.128584\pi\)
\(72\) −254.214 588.009i −0.416102 0.962466i
\(73\) 445.386 445.386i 0.714089 0.714089i −0.253299 0.967388i \(-0.581516\pi\)
0.967388 + 0.253299i \(0.0815157\pi\)
\(74\) −49.7072 + 86.0954i −0.0780858 + 0.135249i
\(75\) −273.812 + 588.984i −0.421561 + 0.906800i
\(76\) 1.39194 + 2.41092i 0.00210088 + 0.00363883i
\(77\) −106.323 28.4892i −0.157359 0.0421642i
\(78\) 103.756 543.400i 0.150616 0.788820i
\(79\) −134.691 77.7637i −0.191821 0.110748i 0.401014 0.916072i \(-0.368658\pi\)
−0.592835 + 0.805324i \(0.701991\pi\)
\(80\) −618.732 + 86.2781i −0.864704 + 0.120577i
\(81\) 531.074 + 499.401i 0.728496 + 0.685050i
\(82\) −172.842 172.842i −0.232771 0.232771i
\(83\) 806.421 216.080i 1.06646 0.285757i 0.317422 0.948284i \(-0.397183\pi\)
0.749038 + 0.662527i \(0.230516\pi\)
\(84\) 6.05730 4.11501i 0.00786793 0.00534506i
\(85\) −719.985 89.1897i −0.918745 0.113811i
\(86\) 115.769 66.8393i 0.145159 0.0838078i
\(87\) 622.371 720.773i 0.766956 0.888218i
\(88\) 437.220 + 1631.73i 0.529634 + 1.97662i
\(89\) 1352.69 1.61107 0.805535 0.592549i \(-0.201878\pi\)
0.805535 + 0.592549i \(0.201878\pi\)
\(90\) 686.593 417.760i 0.804147 0.489286i
\(91\) 61.8228 0.0712174
\(92\) 34.3193 + 128.081i 0.0388917 + 0.145146i
\(93\) −305.077 876.550i −0.340162 0.977354i
\(94\) 341.534 197.184i 0.374750 0.216362i
\(95\) −26.9287 + 20.9923i −0.0290823 + 0.0226712i
\(96\) −191.995 92.8548i −0.204119 0.0987183i
\(97\) 287.595 77.0607i 0.301039 0.0806632i −0.105138 0.994458i \(-0.533528\pi\)
0.406177 + 0.913794i \(0.366862\pi\)
\(98\) 641.235 + 641.235i 0.660965 + 0.660965i
\(99\) −1193.56 1506.96i −1.21169 1.52985i
\(100\) 31.1719 + 109.599i 0.0311719 + 0.109599i
\(101\) −1036.67 598.524i −1.02132 0.589657i −0.106831 0.994277i \(-0.534070\pi\)
−0.914485 + 0.404620i \(0.867404\pi\)
\(102\) 679.455 + 586.694i 0.659569 + 0.569523i
\(103\) −459.029 122.996i −0.439121 0.117662i 0.0324837 0.999472i \(-0.489658\pi\)
−0.471604 + 0.881810i \(0.656325\pi\)
\(104\) −474.392 821.672i −0.447288 0.774726i
\(105\) 60.2472 + 66.6103i 0.0559955 + 0.0619096i
\(106\) 343.607 595.144i 0.314849 0.545335i
\(107\) 1085.11 1085.11i 0.980391 0.980391i −0.0194207 0.999811i \(-0.506182\pi\)
0.999811 + 0.0194207i \(0.00618219\pi\)
\(108\) 127.774 + 5.42153i 0.113843 + 0.00483044i
\(109\) 838.547i 0.736865i 0.929655 + 0.368432i \(0.120105\pi\)
−0.929655 + 0.368432i \(0.879895\pi\)
\(110\) −1951.77 + 825.999i −1.69176 + 0.715963i
\(111\) −109.030 160.493i −0.0932314 0.137237i
\(112\) −22.3581 + 83.4417i −0.0188629 + 0.0703973i
\(113\) −32.8629 + 122.646i −0.0273582 + 0.102102i −0.978255 0.207406i \(-0.933498\pi\)
0.950897 + 0.309508i \(0.100164\pi\)
\(114\) 42.1364 3.08700i 0.0346178 0.00253618i
\(115\) −1497.73 + 633.846i −1.21447 + 0.513969i
\(116\) 167.062i 0.133718i
\(117\) 866.578 + 644.042i 0.684745 + 0.508903i
\(118\) −484.939 + 484.939i −0.378324 + 0.378324i
\(119\) −50.1597 + 86.8792i −0.0386398 + 0.0669261i
\(120\) 423.000 1311.86i 0.321787 0.997966i
\(121\) 1869.15 + 3237.47i 1.40432 + 2.43236i
\(122\) −782.230 209.598i −0.580490 0.155542i
\(123\) 450.549 156.811i 0.330282 0.114952i
\(124\) −141.008 81.4108i −0.102120 0.0589589i
\(125\) −1278.55 + 564.307i −0.914854 + 0.403785i
\(126\) −16.1970 109.948i −0.0114519 0.0777376i
\(127\) −1460.03 1460.03i −1.02013 1.02013i −0.999793 0.0203375i \(-0.993526\pi\)
−0.0203375 0.999793i \(-0.506474\pi\)
\(128\) 1113.44 298.345i 0.768867 0.206017i
\(129\) 19.0628 + 260.199i 0.0130107 + 0.177591i
\(130\) 938.784 731.832i 0.633360 0.493738i
\(131\) −1319.03 + 761.541i −0.879725 + 0.507909i −0.870568 0.492049i \(-0.836248\pi\)
−0.00915702 + 0.999958i \(0.502915\pi\)
\(132\) −331.260 63.2504i −0.218428 0.0417064i
\(133\) 1.22199 + 4.56054i 0.000796694 + 0.00297330i
\(134\) −638.080 −0.411356
\(135\) 150.577 + 1561.31i 0.0959970 + 0.995382i
\(136\) 1539.59 0.970724
\(137\) 310.102 + 1157.32i 0.193385 + 0.721724i 0.992679 + 0.120783i \(0.0385406\pi\)
−0.799293 + 0.600941i \(0.794793\pi\)
\(138\) 1976.67 + 377.423i 1.21931 + 0.232815i
\(139\) 261.821 151.163i 0.159765 0.0922406i −0.417986 0.908454i \(-0.637264\pi\)
0.577751 + 0.816213i \(0.303930\pi\)
\(140\) 15.6368 + 1.93704i 0.00943963 + 0.00116935i
\(141\) 56.2375 + 767.621i 0.0335890 + 0.458478i
\(142\) −1209.48 + 324.078i −0.714768 + 0.191521i
\(143\) −2013.25 2013.25i −1.17732 1.17732i
\(144\) −1182.65 + 936.697i −0.684407 + 0.542070i
\(145\) 2029.37 282.982i 1.16228 0.162072i
\(146\) −1452.30 838.488i −0.823243 0.475299i
\(147\) −1671.52 + 581.760i −0.937852 + 0.326413i
\(148\) −32.8781 8.80967i −0.0182606 0.00489291i
\(149\) 1115.11 + 1931.43i 0.613110 + 1.06194i 0.990713 + 0.135970i \(0.0434151\pi\)
−0.377603 + 0.925968i \(0.623252\pi\)
\(150\) 1703.36 + 298.302i 0.927194 + 0.162375i
\(151\) 837.917 1451.32i 0.451581 0.782161i −0.546903 0.837196i \(-0.684194\pi\)
0.998484 + 0.0550344i \(0.0175268\pi\)
\(152\) 51.2362 51.2362i 0.0273408 0.0273408i
\(153\) −1608.16 + 695.256i −0.849754 + 0.367374i
\(154\) 293.062i 0.153348i
\(155\) 750.082 1850.78i 0.388697 0.959086i
\(156\) 188.906 13.8397i 0.0969527 0.00710296i
\(157\) 125.573 468.645i 0.0638333 0.238229i −0.926637 0.375958i \(-0.877314\pi\)
0.990470 + 0.137729i \(0.0439803\pi\)
\(158\) −107.171 + 399.969i −0.0539626 + 0.201391i
\(159\) 753.683 + 1109.42i 0.375918 + 0.553352i
\(160\) −178.845 422.598i −0.0883686 0.208808i
\(161\) 224.886i 0.110084i
\(162\) 918.352 1709.89i 0.445386 0.829268i
\(163\) −2513.57 + 2513.57i −1.20784 + 1.20784i −0.236117 + 0.971725i \(0.575875\pi\)
−0.971725 + 0.236117i \(0.924125\pi\)
\(164\) 41.8454 72.4784i 0.0199243 0.0345098i
\(165\) 207.215 4131.10i 0.0977678 1.94912i
\(166\) −1111.38 1924.97i −0.519638 0.900039i
\(167\) 1629.84 + 436.714i 0.755213 + 0.202359i 0.615829 0.787880i \(-0.288821\pi\)
0.139384 + 0.990238i \(0.455488\pi\)
\(168\) −144.261 124.566i −0.0662500 0.0572054i
\(169\) −517.792 298.948i −0.235682 0.136071i
\(170\) 266.761 + 1913.04i 0.120351 + 0.863078i
\(171\) −30.3808 + 76.6559i −0.0135864 + 0.0342808i
\(172\) 32.3639 + 32.3639i 0.0143472 + 0.0143472i
\(173\) 1316.26 352.691i 0.578460 0.154998i 0.0422861 0.999106i \(-0.486536\pi\)
0.536174 + 0.844108i \(0.319869\pi\)
\(174\) −2282.47 1103.87i −0.994446 0.480945i
\(175\) 2.95677 + 193.228i 0.00127721 + 0.0834665i
\(176\) 3445.36 1989.18i 1.47559 0.851931i
\(177\) −439.961 1264.10i −0.186833 0.536810i
\(178\) −932.117 3478.71i −0.392501 1.46483i
\(179\) 2448.92 1.02257 0.511287 0.859410i \(-0.329169\pi\)
0.511287 + 0.859410i \(0.329169\pi\)
\(180\) 199.003 + 190.048i 0.0824047 + 0.0786965i
\(181\) −2882.13 −1.18357 −0.591787 0.806095i \(-0.701577\pi\)
−0.591787 + 0.806095i \(0.701577\pi\)
\(182\) −42.6010 158.989i −0.0173505 0.0647531i
\(183\) 1032.95 1196.26i 0.417254 0.483225i
\(184\) 2988.91 1725.65i 1.19753 0.691394i
\(185\) 51.3232 414.307i 0.0203965 0.164651i
\(186\) −2043.99 + 1388.58i −0.805767 + 0.547396i
\(187\) 4462.65 1195.76i 1.74514 0.467609i
\(188\) 95.4776 + 95.4776i 0.0370395 + 0.0370395i
\(189\) 206.939 + 64.9684i 0.0796435 + 0.0250040i
\(190\) 72.5419 + 54.7867i 0.0276986 + 0.0209192i
\(191\) 1454.82 + 839.943i 0.551138 + 0.318200i 0.749581 0.661913i \(-0.230255\pi\)
−0.198443 + 0.980112i \(0.563588\pi\)
\(192\) −542.125 + 2839.26i −0.203774 + 1.06722i
\(193\) −188.144 50.4130i −0.0701705 0.0188021i 0.223563 0.974689i \(-0.428231\pi\)
−0.293733 + 0.955887i \(0.594898\pi\)
\(194\) −396.353 686.503i −0.146683 0.254062i
\(195\) 488.101 + 2271.29i 0.179250 + 0.834103i
\(196\) −155.244 + 268.891i −0.0565760 + 0.0979924i
\(197\) −3351.77 + 3351.77i −1.21220 + 1.21220i −0.241900 + 0.970301i \(0.577770\pi\)
−0.970301 + 0.241900i \(0.922230\pi\)
\(198\) −3052.99 + 4107.89i −1.09579 + 1.47442i
\(199\) 1702.11i 0.606327i 0.952939 + 0.303163i \(0.0980428\pi\)
−0.952939 + 0.303163i \(0.901957\pi\)
\(200\) 2545.45 1522.02i 0.899954 0.538114i
\(201\) 542.196 1121.09i 0.190267 0.393412i
\(202\) −824.865 + 3078.44i −0.287313 + 1.07227i
\(203\) 73.3321 273.679i 0.0253542 0.0946232i
\(204\) −133.820 + 276.698i −0.0459278 + 0.0949644i
\(205\) 951.308 + 385.545i 0.324108 + 0.131354i
\(206\) 1265.23i 0.427928i
\(207\) −2342.76 + 3152.26i −0.786635 + 1.05844i
\(208\) −1579.98 + 1579.98i −0.526693 + 0.526693i
\(209\) 108.719 188.307i 0.0359822 0.0623230i
\(210\) 129.786 200.837i 0.0426480 0.0659956i
\(211\) −629.684 1090.65i −0.205447 0.355844i 0.744828 0.667256i \(-0.232531\pi\)
−0.950275 + 0.311412i \(0.899198\pi\)
\(212\) 227.274 + 60.8978i 0.0736283 + 0.0197287i
\(213\) 458.331 2400.41i 0.147438 0.772174i
\(214\) −3538.31 2042.84i −1.13025 0.652551i
\(215\) −338.317 + 447.959i −0.107317 + 0.142095i
\(216\) −724.454 3248.91i −0.228207 1.02343i
\(217\) −195.262 195.262i −0.0610842 0.0610842i
\(218\) 2156.48 577.828i 0.669980 0.179520i
\(219\) 2707.27 1839.18i 0.835345 0.567489i
\(220\) −446.130 572.288i −0.136718 0.175380i
\(221\) −2247.21 + 1297.43i −0.684000 + 0.394907i
\(222\) −337.607 + 390.985i −0.102066 + 0.118203i
\(223\) 78.0142 + 291.153i 0.0234270 + 0.0874307i 0.976650 0.214839i \(-0.0689225\pi\)
−0.953223 + 0.302269i \(0.902256\pi\)
\(224\) −63.4538 −0.0189272
\(225\) −1971.51 + 2739.30i −0.584152 + 0.811645i
\(226\) 338.053 0.0994996
\(227\) 1227.54 + 4581.23i 0.358918 + 1.33950i 0.875481 + 0.483252i \(0.160545\pi\)
−0.516563 + 0.856249i \(0.672789\pi\)
\(228\) 4.75486 + 13.6617i 0.00138113 + 0.00396828i
\(229\) 832.697 480.758i 0.240289 0.138731i −0.375021 0.927017i \(-0.622364\pi\)
0.615310 + 0.788286i \(0.289031\pi\)
\(230\) 2662.11 + 3414.92i 0.763193 + 0.979013i
\(231\) −514.904 249.024i −0.146659 0.0709288i
\(232\) −4200.11 + 1125.42i −1.18858 + 0.318479i
\(233\) −3014.81 3014.81i −0.847668 0.847668i 0.142174 0.989842i \(-0.454591\pi\)
−0.989842 + 0.142174i \(0.954591\pi\)
\(234\) 1059.13 2672.37i 0.295887 0.746574i
\(235\) −998.080 + 1321.53i −0.277053 + 0.366840i
\(236\) −203.351 117.405i −0.0560891 0.0323831i
\(237\) −611.670 528.164i −0.167647 0.144759i
\(238\) 257.991 + 69.1284i 0.0702649 + 0.0188274i
\(239\) −2780.59 4816.13i −0.752559 1.30347i −0.946579 0.322472i \(-0.895486\pi\)
0.194020 0.980998i \(-0.437847\pi\)
\(240\) −3242.06 162.621i −0.871974 0.0437381i
\(241\) 1313.39 2274.85i 0.351049 0.608034i −0.635385 0.772196i \(-0.719158\pi\)
0.986433 + 0.164161i \(0.0524918\pi\)
\(242\) 7037.77 7037.77i 1.86944 1.86944i
\(243\) 2223.89 + 3066.47i 0.587088 + 0.809523i
\(244\) 277.271i 0.0727478i
\(245\) −3529.30 1430.35i −0.920322 0.372987i
\(246\) −713.735 1050.62i −0.184984 0.272297i
\(247\) −31.6080 + 117.963i −0.00814239 + 0.0303878i
\(248\) −1096.85 + 4093.52i −0.280848 + 1.04814i
\(249\) 4326.51 316.969i 1.10113 0.0806710i
\(250\) 2332.25 + 2899.18i 0.590017 + 0.733440i
\(251\) 1692.12i 0.425520i 0.977104 + 0.212760i \(0.0682453\pi\)
−0.977104 + 0.212760i \(0.931755\pi\)
\(252\) 34.9264 15.0997i 0.00873078 0.00377457i
\(253\) 7323.39 7323.39i 1.81983 1.81983i
\(254\) −2748.66 + 4760.82i −0.679002 + 1.17607i
\(255\) −3587.84 1156.87i −0.881096 0.284103i
\(256\) 690.649 + 1196.24i 0.168615 + 0.292051i
\(257\) −6449.89 1728.24i −1.56550 0.419474i −0.631099 0.775702i \(-0.717396\pi\)
−0.934399 + 0.356228i \(0.884063\pi\)
\(258\) 656.017 228.322i 0.158302 0.0550959i
\(259\) −49.9937 28.8639i −0.0119940 0.00692476i
\(260\) 325.221 + 245.621i 0.0775744 + 0.0585875i
\(261\) 3878.97 3072.26i 0.919932 0.728613i
\(262\) 2867.37 + 2867.37i 0.676132 + 0.676132i
\(263\) −4539.56 + 1216.37i −1.06434 + 0.285189i −0.748165 0.663513i \(-0.769065\pi\)
−0.316174 + 0.948701i \(0.602398\pi\)
\(264\) 641.360 + 8754.33i 0.149519 + 2.04088i
\(265\) −354.777 + 2863.94i −0.0822407 + 0.663889i
\(266\) 10.8863 6.28518i 0.00250932 0.00144876i
\(267\) 6904.07 + 1318.26i 1.58248 + 0.302157i
\(268\) −56.5438 211.024i −0.0128879 0.0480983i
\(269\) −143.325 −0.0324859 −0.0162429 0.999868i \(-0.505171\pi\)
−0.0162429 + 0.999868i \(0.505171\pi\)
\(270\) 3911.46 1463.11i 0.881644 0.329786i
\(271\) −7451.06 −1.67018 −0.835091 0.550111i \(-0.814585\pi\)
−0.835091 + 0.550111i \(0.814585\pi\)
\(272\) −938.427 3502.26i −0.209193 0.780719i
\(273\) 315.540 + 60.2489i 0.0699537 + 0.0133569i
\(274\) 2762.58 1594.97i 0.609100 0.351664i
\(275\) 6196.14 6388.72i 1.35870 1.40092i
\(276\) 50.3432 + 687.166i 0.0109794 + 0.149864i
\(277\) 2126.37 569.759i 0.461232 0.123587i −0.0207183 0.999785i \(-0.506595\pi\)
0.481950 + 0.876199i \(0.339929\pi\)
\(278\) −569.160 569.160i −0.122791 0.122791i
\(279\) −702.865 4771.17i −0.150822 1.02381i
\(280\) −56.6384 406.174i −0.0120885 0.0866913i
\(281\) −1756.49 1014.11i −0.372894 0.215291i 0.301828 0.953362i \(-0.402403\pi\)
−0.674722 + 0.738072i \(0.735737\pi\)
\(282\) 1935.33 673.580i 0.408679 0.142238i
\(283\) 5600.82 + 1500.74i 1.17645 + 0.315228i 0.793516 0.608549i \(-0.208248\pi\)
0.382930 + 0.923777i \(0.374915\pi\)
\(284\) −214.357 371.277i −0.0447878 0.0775748i
\(285\) −157.900 + 80.9007i −0.0328183 + 0.0168145i
\(286\) −3790.16 + 6564.75i −0.783626 + 1.35728i
\(287\) 100.365 100.365i 0.0206425 0.0206425i
\(288\) −889.441 661.033i −0.181982 0.135249i
\(289\) 702.339i 0.142955i
\(290\) −2126.15 5023.91i −0.430523 1.01729i
\(291\) 1542.97 113.041i 0.310826 0.0227717i
\(292\) 148.606 554.605i 0.0297826 0.111150i
\(293\) −1732.92 + 6467.33i −0.345522 + 1.28951i 0.546478 + 0.837473i \(0.315968\pi\)
−0.892001 + 0.452034i \(0.850699\pi\)
\(294\) 2647.92 + 3897.74i 0.525271 + 0.773200i
\(295\) 1081.71 2669.06i 0.213491 0.526776i
\(296\) 885.939i 0.173967i
\(297\) −4623.26 8854.64i −0.903262 1.72996i
\(298\) 4198.63 4198.63i 0.816175 0.816175i
\(299\) −2908.45 + 5037.58i −0.562542 + 0.974351i
\(300\) 52.2908 + 589.767i 0.0100634 + 0.113501i
\(301\) 38.8121 + 67.2245i 0.00743220 + 0.0128729i
\(302\) −4309.73 1154.79i −0.821182 0.220035i
\(303\) −4707.84 4065.12i −0.892602 0.770742i
\(304\) −147.782 85.3222i −0.0278812 0.0160972i
\(305\) 3368.13 469.664i 0.632323 0.0881734i
\(306\) 2896.14 + 3656.61i 0.541051 + 0.683120i
\(307\) 934.416 + 934.416i 0.173713 + 0.173713i 0.788609 0.614895i \(-0.210802\pi\)
−0.614895 + 0.788609i \(0.710802\pi\)
\(308\) −96.9207 + 25.9698i −0.0179304 + 0.00480444i
\(309\) −2222.99 1075.11i −0.409261 0.197932i
\(310\) −5276.51 653.639i −0.966727 0.119755i
\(311\) 7156.17 4131.61i 1.30479 0.753320i 0.323566 0.946205i \(-0.395118\pi\)
0.981221 + 0.192886i \(0.0617847\pi\)
\(312\) −1620.52 4656.08i −0.294051 0.844868i
\(313\) 2109.01 + 7870.92i 0.380856 + 1.42138i 0.844596 + 0.535404i \(0.179841\pi\)
−0.463740 + 0.885972i \(0.653493\pi\)
\(314\) −1291.74 −0.232157
\(315\) 242.584 + 398.689i 0.0433906 + 0.0713130i
\(316\) −141.774 −0.0252386
\(317\) −1684.33 6286.01i −0.298427 1.11375i −0.938457 0.345396i \(-0.887745\pi\)
0.640030 0.768350i \(-0.278922\pi\)
\(318\) 2333.74 2702.72i 0.411540 0.476608i
\(319\) −11300.4 + 6524.27i −1.98338 + 1.14511i
\(320\) −4905.14 + 3823.82i −0.856892 + 0.667994i
\(321\) 6595.84 4480.87i 1.14687 0.779121i
\(322\) 578.338 154.965i 0.100092 0.0268195i
\(323\) −140.127 140.127i −0.0241390 0.0241390i
\(324\) 646.870 + 152.193i 0.110917 + 0.0260961i
\(325\) −2432.77 + 4366.65i −0.415219 + 0.745286i
\(326\) 8196.19 + 4732.07i 1.39247 + 0.803943i
\(327\) −817.199 + 4279.90i −0.138199 + 0.723789i
\(328\) −2104.08 563.787i −0.354202 0.0949082i
\(329\) 114.501 + 198.321i 0.0191873 + 0.0332334i
\(330\) −10766.7 + 2313.77i −1.79602 + 0.385967i
\(331\) −4213.66 + 7298.28i −0.699710 + 1.21193i 0.268857 + 0.963180i \(0.413354\pi\)
−0.968567 + 0.248753i \(0.919979\pi\)
\(332\) 538.135 538.135i 0.0889579 0.0889579i
\(333\) −400.078 925.400i −0.0658382 0.152287i
\(334\) 4492.37i 0.735963i
\(335\) 2467.62 1044.31i 0.402450 0.170319i
\(336\) −195.432 + 404.093i −0.0317312 + 0.0656103i
\(337\) 133.160 496.961i 0.0215243 0.0803299i −0.954328 0.298760i \(-0.903427\pi\)
0.975853 + 0.218430i \(0.0700936\pi\)
\(338\) −411.999 + 1537.60i −0.0663012 + 0.247439i
\(339\) −287.254 + 593.952i −0.0460221 + 0.0951594i
\(340\) −609.036 + 257.747i −0.0971460 + 0.0411127i
\(341\) 12717.4i 2.01960i
\(342\) 218.070 + 25.3078i 0.0344792 + 0.00400143i
\(343\) −747.314 + 747.314i −0.117642 + 0.117642i
\(344\) 595.643 1031.68i 0.0933573 0.161700i
\(345\) −8262.02 + 1775.52i −1.28931 + 0.277074i
\(346\) −1814.03 3141.99i −0.281857 0.488191i
\(347\) −808.744 216.702i −0.125117 0.0335251i 0.195717 0.980660i \(-0.437297\pi\)
−0.320834 + 0.947135i \(0.603963\pi\)
\(348\) 162.809 852.674i 0.0250789 0.131345i
\(349\) 3705.03 + 2139.10i 0.568269 + 0.328090i 0.756458 0.654043i \(-0.226928\pi\)
−0.188189 + 0.982133i \(0.560262\pi\)
\(350\) 494.884 140.754i 0.0755791 0.0214960i
\(351\) 3795.32 + 4131.67i 0.577149 + 0.628297i
\(352\) 2066.36 + 2066.36i 0.312891 + 0.312891i
\(353\) 3611.88 967.800i 0.544592 0.145923i 0.0239736 0.999713i \(-0.492368\pi\)
0.520618 + 0.853790i \(0.325702\pi\)
\(354\) −2947.70 + 2002.51i −0.442566 + 0.300656i
\(355\) 4146.97 3232.78i 0.619995 0.483319i
\(356\) 1067.87 616.535i 0.158980 0.0917874i
\(357\) −340.680 + 394.544i −0.0505062 + 0.0584916i
\(358\) −1687.51 6297.86i −0.249127 0.929755i
\(359\) 325.208 0.0478102 0.0239051 0.999714i \(-0.492390\pi\)
0.0239051 + 0.999714i \(0.492390\pi\)
\(360\) 3437.43 6283.43i 0.503246 0.919906i
\(361\) 6849.67 0.998640
\(362\) 1986.02 + 7411.94i 0.288351 + 1.07614i
\(363\) 6385.01 + 18345.4i 0.923212 + 2.65258i
\(364\) 48.8054 28.1778i 0.00702774 0.00405747i
\(365\) 6988.75 + 865.747i 1.00221 + 0.124151i
\(366\) −3788.20 1832.09i −0.541017 0.261653i
\(367\) 3038.52 814.170i 0.432179 0.115802i −0.0361698 0.999346i \(-0.511516\pi\)
0.468349 + 0.883544i \(0.344849\pi\)
\(368\) −5747.35 5747.35i −0.814134 0.814134i
\(369\) 2452.40 361.275i 0.345980 0.0509680i
\(370\) −1100.84 + 153.504i −0.154675 + 0.0215684i
\(371\) 345.587 + 199.525i 0.0483611 + 0.0279213i
\(372\) −640.357 552.934i −0.0892500 0.0770654i
\(373\) −1752.69 469.631i −0.243299 0.0651918i 0.135109 0.990831i \(-0.456862\pi\)
−0.378408 + 0.925639i \(0.623528\pi\)
\(374\) −6150.27 10652.6i −0.850329 1.47281i
\(375\) −7075.58 + 1634.19i −0.974350 + 0.225038i
\(376\) 1757.22 3043.60i 0.241016 0.417451i
\(377\) 5182.17 5182.17i 0.707945 0.707945i
\(378\) 24.4804 576.953i 0.00333105 0.0785059i
\(379\) 12501.2i 1.69431i −0.531345 0.847155i \(-0.678313\pi\)
0.531345 0.847155i \(-0.321687\pi\)
\(380\) −11.6906 + 28.8458i −0.00157820 + 0.00389411i
\(381\) −6029.05 8874.77i −0.810702 1.19335i
\(382\) 1157.58 4320.15i 0.155044 0.578633i
\(383\) −319.753 + 1193.34i −0.0426596 + 0.159208i −0.983970 0.178335i \(-0.942929\pi\)
0.941310 + 0.337543i \(0.109596\pi\)
\(384\) 5973.68 437.644i 0.793862 0.0581600i
\(385\) −479.639 1133.35i −0.0634926 0.150028i
\(386\) 518.587i 0.0683818i
\(387\) −156.280 + 1346.62i −0.0205275 + 0.176880i
\(388\) 191.916 191.916i 0.0251110 0.0251110i
\(389\) −1415.73 + 2452.12i −0.184526 + 0.319608i −0.943417 0.331610i \(-0.892408\pi\)
0.758891 + 0.651218i \(0.225742\pi\)
\(390\) 5504.70 2820.35i 0.714722 0.366190i
\(391\) −4719.53 8174.46i −0.610426 1.05729i
\(392\) 7806.03 + 2091.62i 1.00578 + 0.269497i
\(393\) −7474.40 + 2601.42i −0.959373 + 0.333903i
\(394\) 10929.4 + 6310.07i 1.39750 + 0.806844i
\(395\) −240.148 1722.19i −0.0305902 0.219374i
\(396\) −1629.09 645.654i −0.206730 0.0819326i
\(397\) −3719.83 3719.83i −0.470260 0.470260i 0.431739 0.901999i \(-0.357900\pi\)
−0.901999 + 0.431739i \(0.857900\pi\)
\(398\) 4377.29 1172.89i 0.551291 0.147718i
\(399\) 1.79255 + 24.4676i 0.000224912 + 0.00306996i
\(400\) −5013.82 4862.69i −0.626727 0.607836i
\(401\) −3644.58 + 2104.20i −0.453870 + 0.262042i −0.709463 0.704743i \(-0.751062\pi\)
0.255593 + 0.966784i \(0.417729\pi\)
\(402\) −3256.72 621.835i −0.404056 0.0771501i
\(403\) −1848.66 6899.31i −0.228508 0.852802i
\(404\) −1091.19 −0.134378
\(405\) −753.030 + 8115.61i −0.0923910 + 0.995723i
\(406\) −754.350 −0.0922113
\(407\) 688.089 + 2567.98i 0.0838018 + 0.312752i
\(408\) 7857.97 + 1500.39i 0.953499 + 0.182060i
\(409\) −8758.07 + 5056.47i −1.05882 + 0.611312i −0.925106 0.379708i \(-0.876024\pi\)
−0.133716 + 0.991020i \(0.542691\pi\)
\(410\) 335.972 2712.14i 0.0404695 0.326691i
\(411\) 454.891 + 6209.09i 0.0545939 + 0.745187i
\(412\) −418.436 + 112.119i −0.0500360 + 0.0134071i
\(413\) −281.593 281.593i −0.0335504 0.0335504i
\(414\) 9721.01 + 3852.70i 1.15401 + 0.457366i
\(415\) 7448.50 + 5625.43i 0.881042 + 0.665401i
\(416\) −1421.40 820.647i −0.167524 0.0967200i
\(417\) 1483.64 516.370i 0.174230 0.0606397i
\(418\) −559.185 149.833i −0.0654322 0.0175325i
\(419\) 6057.57 + 10492.0i 0.706281 + 1.22331i 0.966227 + 0.257691i \(0.0829618\pi\)
−0.259946 + 0.965623i \(0.583705\pi\)
\(420\) 77.9215 + 25.1252i 0.00905281 + 0.00291901i
\(421\) 4457.66 7720.89i 0.516040 0.893808i −0.483786 0.875186i \(-0.660739\pi\)
0.999827 0.0186217i \(-0.00592782\pi\)
\(422\) −2370.90 + 2370.90i −0.273492 + 0.273492i
\(423\) −461.046 + 3972.70i −0.0529948 + 0.456642i
\(424\) 6124.15i 0.701450i
\(425\) −4162.60 6961.63i −0.475096 0.794562i
\(426\) −6488.93 + 475.393i −0.738004 + 0.0540677i
\(427\) 121.709 454.223i 0.0137937 0.0514787i
\(428\) 362.055 1351.21i 0.0408893 0.152601i
\(429\) −8313.52 12237.5i −0.935619 1.37723i
\(430\) 1385.14 + 561.368i 0.155343 + 0.0629571i
\(431\) 11279.2i 1.26056i −0.776368 0.630279i \(-0.782940\pi\)
0.776368 0.630279i \(-0.217060\pi\)
\(432\) −6949.05 + 3628.30i −0.773927 + 0.404090i
\(433\) 1968.81 1968.81i 0.218510 0.218510i −0.589360 0.807870i \(-0.700620\pi\)
0.807870 + 0.589360i \(0.200620\pi\)
\(434\) −367.603 + 636.706i −0.0406578 + 0.0704214i
\(435\) 10633.6 + 533.378i 1.17205 + 0.0587897i
\(436\) 382.196 + 661.983i 0.0419814 + 0.0727138i
\(437\) −429.101 114.977i −0.0469718 0.0125861i
\(438\) −6595.34 5694.93i −0.719492 0.621265i
\(439\) −4264.82 2462.29i −0.463664 0.267697i 0.249919 0.968267i \(-0.419596\pi\)
−0.713584 + 0.700570i \(0.752929\pi\)
\(440\) −11382.6 + 15071.4i −1.23328 + 1.63296i
\(441\) −9098.27 + 1340.31i −0.982429 + 0.144726i
\(442\) 4885.10 + 4885.10i 0.525703 + 0.525703i
\(443\) 8764.22 2348.37i 0.939957 0.251861i 0.243861 0.969810i \(-0.421586\pi\)
0.696095 + 0.717949i \(0.254919\pi\)
\(444\) −159.223 77.0052i −0.0170189 0.00823086i
\(445\) 9298.17 + 11927.5i 0.990506 + 1.27061i
\(446\) 694.997 401.257i 0.0737872 0.0426010i
\(447\) 3809.21 + 10944.6i 0.403063 + 1.15808i
\(448\) 222.590 + 830.717i 0.0234741 + 0.0876065i
\(449\) 5958.93 0.626323 0.313162 0.949700i \(-0.398612\pi\)
0.313162 + 0.949700i \(0.398612\pi\)
\(450\) 8403.17 + 3182.52i 0.880287 + 0.333389i
\(451\) −6536.77 −0.682494
\(452\) 29.9567 + 111.800i 0.00311736 + 0.0116341i
\(453\) 5691.05 6590.85i 0.590263 0.683588i
\(454\) 10935.6 6313.69i 1.13047 0.652679i
\(455\) 424.959 + 545.130i 0.0437854 + 0.0561673i
\(456\) 311.439 211.575i 0.0319834 0.0217279i
\(457\) −13853.7 + 3712.09i −1.41805 + 0.379966i −0.884792 0.465986i \(-0.845700\pi\)
−0.533259 + 0.845952i \(0.679033\pi\)
\(458\) −1810.16 1810.16i −0.184679 0.184679i
\(459\) −8885.54 + 1981.33i −0.903576 + 0.201483i
\(460\) −893.469 + 1183.02i −0.0905613 + 0.119910i
\(461\) −681.107 393.237i −0.0688120 0.0397286i 0.465199 0.885206i \(-0.345983\pi\)
−0.534011 + 0.845477i \(0.679316\pi\)
\(462\) −285.601 + 1495.77i −0.0287605 + 0.150627i
\(463\) −4093.92 1096.96i −0.410930 0.110108i 0.0474312 0.998875i \(-0.484897\pi\)
−0.458361 + 0.888766i \(0.651563\pi\)
\(464\) 5120.20 + 8868.45i 0.512283 + 0.887301i
\(465\) 5632.04 8715.30i 0.561677 0.869167i
\(466\) −5675.70 + 9830.60i −0.564210 + 0.977240i
\(467\) −10534.2 + 10534.2i −1.04383 + 1.04383i −0.0448309 + 0.998995i \(0.514275\pi\)
−0.998995 + 0.0448309i \(0.985725\pi\)
\(468\) 977.656 + 113.460i 0.0965644 + 0.0112066i
\(469\) 370.518i 0.0364796i
\(470\) 4086.34 + 1656.11i 0.401040 + 0.162533i
\(471\) 1097.63 2269.56i 0.107381 0.222030i
\(472\) −1581.80 + 5903.37i −0.154255 + 0.575688i
\(473\) 925.246 3453.07i 0.0899426 0.335670i
\(474\) −936.783 + 1936.98i −0.0907761 + 0.187697i
\(475\) −370.205 93.1494i −0.0357604 0.00899787i
\(476\) 91.4479i 0.00880569i
\(477\) 2765.58 + 6396.93i 0.265466 + 0.614036i
\(478\) −10469.5 + 10469.5i −1.00181 + 1.00181i
\(479\) 4528.85 7844.19i 0.432001 0.748247i −0.565045 0.825060i \(-0.691141\pi\)
0.997045 + 0.0768132i \(0.0244745\pi\)
\(480\) −500.979 2331.21i −0.0476384 0.221676i
\(481\) −746.591 1293.13i −0.0707726 0.122582i
\(482\) −6755.26 1810.07i −0.638368 0.171050i
\(483\) −219.161 + 1147.81i −0.0206463 + 0.108131i
\(484\) 2951.17 + 1703.86i 0.277157 + 0.160017i
\(485\) 2656.37 + 2006.20i 0.248700 + 0.187829i
\(486\) 6353.58 7832.20i 0.593012 0.731020i
\(487\) −1647.82 1647.82i −0.153326 0.153326i 0.626276 0.779602i \(-0.284578\pi\)
−0.779602 + 0.626276i \(0.784578\pi\)
\(488\) −6970.90 + 1867.85i −0.646635 + 0.173265i
\(489\) −15278.7 + 10379.6i −1.41294 + 0.959877i
\(490\) −1246.44 + 10061.9i −0.114915 + 0.927655i
\(491\) −3966.40 + 2290.00i −0.364564 + 0.210481i −0.671081 0.741384i \(-0.734170\pi\)
0.306517 + 0.951865i \(0.400836\pi\)
\(492\) 284.210 329.146i 0.0260430 0.0301606i
\(493\) 3077.93 + 11487.0i 0.281183 + 1.04939i
\(494\) 325.144 0.0296132
\(495\) 5083.54 20883.0i 0.461592 1.89620i
\(496\) 9980.51 0.903504
\(497\) −188.185 702.316i −0.0169844 0.0633867i
\(498\) −3796.47 10908.0i −0.341614 0.981526i
\(499\) 2616.51 1510.64i 0.234731 0.135522i −0.378022 0.925797i \(-0.623395\pi\)
0.612753 + 0.790275i \(0.290062\pi\)
\(500\) −752.135 + 1028.23i −0.0672730 + 0.0919675i
\(501\) 7893.01 + 3817.31i 0.703859 + 0.340409i
\(502\) 4351.61 1166.01i 0.386896 0.103668i
\(503\) −4876.93 4876.93i −0.432310 0.432310i 0.457104 0.889413i \(-0.348887\pi\)
−0.889413 + 0.457104i \(0.848887\pi\)
\(504\) −614.906 776.368i −0.0543454 0.0686155i
\(505\) −1848.35 13255.2i −0.162872 1.16801i
\(506\) −23879.9 13787.1i −2.09801 1.21129i
\(507\) −2351.45 2030.42i −0.205979 0.177858i
\(508\) −1818.06 487.149i −0.158786 0.0425467i
\(509\) −5209.57 9023.23i −0.453654 0.785752i 0.544956 0.838465i \(-0.316547\pi\)
−0.998610 + 0.0527129i \(0.983213\pi\)
\(510\) −502.803 + 10024.0i −0.0436559 + 0.870335i
\(511\) 486.891 843.320i 0.0421503 0.0730064i
\(512\) 9121.19 9121.19i 0.787311 0.787311i
\(513\) −229.766 + 361.640i −0.0197747 + 0.0311244i
\(514\) 17778.0i 1.52559i
\(515\) −2070.74 4893.00i −0.177180 0.418663i
\(516\) 133.644 + 196.723i 0.0114018 + 0.0167835i
\(517\) 2729.59 10187.0i 0.232200 0.866582i
\(518\) −39.7792 + 148.458i −0.00337412 + 0.0125924i
\(519\) 7061.84 517.365i 0.597265 0.0437569i
\(520\) 3984.31 9831.04i 0.336007 0.829076i
\(521\) 523.372i 0.0440102i 0.999758 + 0.0220051i \(0.00700501\pi\)
−0.999758 + 0.0220051i \(0.992995\pi\)
\(522\) −10573.8 7858.48i −0.886598 0.658920i
\(523\) −14550.3 + 14550.3i −1.21652 + 1.21652i −0.247683 + 0.968841i \(0.579669\pi\)
−0.968841 + 0.247683i \(0.920331\pi\)
\(524\) −694.196 + 1202.38i −0.0578742 + 0.100241i
\(525\) −173.217 + 989.105i −0.0143997 + 0.0822249i
\(526\) 6256.26 + 10836.2i 0.518604 + 0.898249i
\(527\) 11195.5 + 2999.82i 0.925393 + 0.247958i
\(528\) 19523.4 6795.01i 1.60918 0.560066i
\(529\) −7787.77 4496.27i −0.640074 0.369547i
\(530\) 7609.65 1061.12i 0.623664 0.0869659i
\(531\) −1013.62 6880.64i −0.0828388 0.562325i
\(532\) 3.04331 + 3.04331i 0.000248016 + 0.000248016i
\(533\) 3546.27 950.220i 0.288191 0.0772206i
\(534\) −1367.33 18663.5i −0.110805 1.51245i
\(535\) 17027.0 + 2109.26i 1.37596 + 0.170451i
\(536\) −4924.47 + 2843.14i −0.396837 + 0.229114i
\(537\) 12499.1 + 2386.57i 1.00443 + 0.191784i
\(538\) 98.7630 + 368.588i 0.00791445 + 0.0295371i
\(539\) 24251.1 1.93798
\(540\) 830.493 + 1163.93i 0.0661828 + 0.0927551i
\(541\) 19374.8 1.53972 0.769858 0.638216i \(-0.220327\pi\)
0.769858 + 0.638216i \(0.220327\pi\)
\(542\) 5134.39 + 19161.8i 0.406902 + 1.51858i
\(543\) −14710.2 2808.75i −1.16257 0.221980i
\(544\) 2306.50 1331.66i 0.181784 0.104953i
\(545\) −7394.00 + 5764.02i −0.581145 + 0.453034i
\(546\) −62.4917 852.988i −0.00489817 0.0668581i
\(547\) −10194.1 + 2731.50i −0.796832 + 0.213511i −0.634193 0.773175i \(-0.718667\pi\)
−0.162640 + 0.986686i \(0.552001\pi\)
\(548\) 772.293 + 772.293i 0.0602021 + 0.0602021i
\(549\) 6437.90 5099.01i 0.500479 0.396394i
\(550\) −20699.5 11532.2i −1.60478 0.894064i
\(551\) 484.709 + 279.847i 0.0374761 + 0.0216368i
\(552\) 16937.0 5894.80i 1.30595 0.454528i
\(553\) −232.253 62.2319i −0.0178597 0.00478548i
\(554\) −2930.49 5075.76i −0.224737 0.389257i
\(555\) 665.711 2064.59i 0.0509150 0.157904i
\(556\) 137.795 238.668i 0.0105104 0.0182046i
\(557\) −935.942 + 935.942i −0.0711977 + 0.0711977i −0.741809 0.670611i \(-0.766032\pi\)
0.670611 + 0.741809i \(0.266032\pi\)
\(558\) −11785.7 + 5095.28i −0.894133 + 0.386560i
\(559\) 2007.82i 0.151917i
\(560\) −889.444 + 376.417i −0.0671176 + 0.0284045i
\(561\) 23942.5 1754.07i 1.80187 0.132009i
\(562\) −1397.61 + 5215.95i −0.104901 + 0.391498i
\(563\) −21.9336 + 81.8572i −0.00164190 + 0.00612765i −0.966742 0.255754i \(-0.917676\pi\)
0.965100 + 0.261882i \(0.0843430\pi\)
\(564\) 394.266 + 580.359i 0.0294354 + 0.0433290i
\(565\) −1307.34 + 553.273i −0.0973454 + 0.0411971i
\(566\) 15437.7i 1.14646i
\(567\) 992.893 + 533.266i 0.0735407 + 0.0394975i
\(568\) −7890.29 + 7890.29i −0.582868 + 0.582868i
\(569\) −4295.92 + 7440.75i −0.316510 + 0.548212i −0.979757 0.200189i \(-0.935845\pi\)
0.663247 + 0.748401i \(0.269178\pi\)
\(570\) 316.858 + 350.324i 0.0232837 + 0.0257429i
\(571\) 5232.69 + 9063.28i 0.383505 + 0.664249i 0.991561 0.129645i \(-0.0413837\pi\)
−0.608056 + 0.793894i \(0.708050\pi\)
\(572\) −2506.95 671.735i −0.183253 0.0491025i
\(573\) 6606.78 + 5704.81i 0.481679 + 0.415919i
\(574\) −327.269 188.949i −0.0237978 0.0137397i
\(575\) −15884.1 8849.46i −1.15202 0.641822i
\(576\) −5533.96 + 13963.1i −0.400315 + 1.01006i
\(577\) 1229.42 + 1229.42i 0.0887029 + 0.0887029i 0.750066 0.661363i \(-0.230022\pi\)
−0.661363 + 0.750066i \(0.730022\pi\)
\(578\) 1806.20 483.970i 0.129979 0.0348278i
\(579\) −911.147 440.660i −0.0653990 0.0316290i
\(580\) 1473.09 1148.35i 0.105460 0.0822115i
\(581\) 1117.79 645.354i 0.0798168 0.0460822i
\(582\) −1353.94 3890.14i −0.0964305 0.277064i
\(583\) −4756.49 17751.5i −0.337897 1.26105i
\(584\) −14944.5 −1.05892
\(585\) 277.781 + 12068.2i 0.0196322 + 0.852920i
\(586\) 17826.1 1.25664
\(587\) −4593.13 17141.8i −0.322962 1.20531i −0.916345 0.400390i \(-0.868875\pi\)
0.593383 0.804920i \(-0.297792\pi\)
\(588\) −1054.40 + 1221.11i −0.0739506 + 0.0856427i
\(589\) 472.408 272.745i 0.0330479 0.0190802i
\(590\) −7609.40 942.631i −0.530973 0.0657754i
\(591\) −20373.7 + 13840.8i −1.41804 + 0.963341i
\(592\) 2015.34 540.008i 0.139915 0.0374902i
\(593\) 4295.56 + 4295.56i 0.297466 + 0.297466i 0.840021 0.542555i \(-0.182543\pi\)
−0.542555 + 0.840021i \(0.682543\pi\)
\(594\) −19585.6 + 17991.2i −1.35287 + 1.24274i
\(595\) −1110.86 + 154.902i −0.0765390 + 0.0106729i
\(596\) 1760.63 + 1016.50i 0.121003 + 0.0698614i
\(597\) −1658.77 + 8687.46i −0.113717 + 0.595568i
\(598\) 14959.3 + 4008.33i 1.02296 + 0.274101i
\(599\) 189.493 + 328.212i 0.0129257 + 0.0223879i 0.872416 0.488764i \(-0.162552\pi\)
−0.859490 + 0.511152i \(0.829219\pi\)
\(600\) 14475.1 5287.63i 0.984907 0.359778i
\(601\) 10568.0 18304.3i 0.717267 1.24234i −0.244811 0.969571i \(-0.578726\pi\)
0.962078 0.272773i \(-0.0879407\pi\)
\(602\) 146.136 146.136i 0.00989378 0.00989378i
\(603\) 3859.89 5193.61i 0.260675 0.350746i
\(604\) 1527.64i 0.102912i
\(605\) −15698.6 + 38735.3i −1.05494 + 2.60299i
\(606\) −7210.13 + 14908.3i −0.483320 + 0.999355i
\(607\) 5611.20 20941.3i 0.375209 1.40030i −0.477831 0.878452i \(-0.658577\pi\)
0.853040 0.521846i \(-0.174756\pi\)
\(608\) 32.4419 121.075i 0.00216397 0.00807605i
\(609\) 640.995 1325.38i 0.0426509 0.0881889i
\(610\) −3528.75 8338.16i −0.234221 0.553446i
\(611\) 5923.33i 0.392197i
\(612\) −952.663 + 1281.84i −0.0629234 + 0.0846654i
\(613\) 9303.05 9303.05i 0.612964 0.612964i −0.330754 0.943717i \(-0.607303\pi\)
0.943717 + 0.330754i \(0.107303\pi\)
\(614\) 1759.14 3046.92i 0.115624 0.200267i
\(615\) 4479.69 + 2894.89i 0.293721 + 0.189810i
\(616\) 1305.82 + 2261.75i 0.0854107 + 0.147936i
\(617\) −19370.4 5190.29i −1.26390 0.338660i −0.436207 0.899846i \(-0.643679\pi\)
−0.827690 + 0.561186i \(0.810345\pi\)
\(618\) −1233.02 + 6457.69i −0.0802581 + 0.420334i
\(619\) 11987.0 + 6920.68i 0.778347 + 0.449379i 0.835844 0.548967i \(-0.184979\pi\)
−0.0574971 + 0.998346i \(0.518312\pi\)
\(620\) −251.411 1802.96i −0.0162853 0.116788i
\(621\) −15029.4 + 13805.9i −0.971187 + 0.892126i
\(622\) −15556.4 15556.4i −1.00282 1.00282i
\(623\) 2020.01 541.259i 0.129904 0.0348075i
\(624\) −9603.91 + 6524.39i −0.616129 + 0.418565i
\(625\) −13764.3 7394.82i −0.880918 0.473268i
\(626\) 18788.3 10847.4i 1.19957 0.692572i
\(627\) 738.411 855.160i 0.0470324 0.0544686i
\(628\) −114.468 427.202i −0.00727354 0.0271452i
\(629\) 2422.98 0.153594
\(630\) 858.145 898.581i 0.0542687 0.0568259i
\(631\) −27232.2 −1.71806 −0.859032 0.511922i \(-0.828934\pi\)
−0.859032 + 0.511922i \(0.828934\pi\)
\(632\) 955.064 + 3564.35i 0.0601114 + 0.224339i
\(633\) −2151.00 6180.25i −0.135062 0.388061i
\(634\) −15005.0 + 8663.16i −0.939946 + 0.542678i
\(635\) 2838.02 22910.0i 0.177360 1.43174i
\(636\) 1100.64 + 532.306i 0.0686217 + 0.0331876i
\(637\) −13156.5 + 3525.27i −0.818334 + 0.219272i
\(638\) 24565.3 + 24565.3i 1.52437 + 1.52437i
\(639\) 4678.59 11804.9i 0.289644 0.730820i
\(640\) 10284.3 + 7767.12i 0.635189 + 0.479722i
\(641\) 10303.5 + 5948.74i 0.634891 + 0.366554i 0.782644 0.622470i \(-0.213871\pi\)
−0.147753 + 0.989024i \(0.547204\pi\)
\(642\) −16068.5 13874.8i −0.987808 0.852951i
\(643\) 7499.52 + 2009.49i 0.459957 + 0.123245i 0.481355 0.876526i \(-0.340145\pi\)
−0.0213976 + 0.999771i \(0.506812\pi\)
\(644\) 102.500 + 177.534i 0.00627181 + 0.0108631i
\(645\) −2163.31 + 1956.65i −0.132062 + 0.119447i
\(646\) −263.805 + 456.924i −0.0160670 + 0.0278288i
\(647\) −1793.65 + 1793.65i −0.108989 + 0.108989i −0.759498 0.650509i \(-0.774555\pi\)
0.650509 + 0.759498i \(0.274555\pi\)
\(648\) −531.373 17288.3i −0.0322134 1.04807i
\(649\) 18340.1i 1.10926i
\(650\) 12906.1 + 3247.36i 0.778796 + 0.195957i
\(651\) −806.317 1186.90i −0.0485439 0.0714566i
\(652\) −838.671 + 3129.96i −0.0503756 + 0.188004i
\(653\) 2589.01 9662.33i 0.155155 0.579045i −0.843938 0.536441i \(-0.819768\pi\)
0.999092 0.0426031i \(-0.0135651\pi\)
\(654\) 11569.7 847.620i 0.691760 0.0506798i
\(655\) −15781.7 6396.00i −0.941440 0.381546i
\(656\) 5130.01i 0.305325i
\(657\) 15610.1 6748.72i 0.926955 0.400750i
\(658\) 431.120 431.120i 0.0255422 0.0255422i
\(659\) 2314.59 4008.99i 0.136819 0.236977i −0.789472 0.613787i \(-0.789646\pi\)
0.926291 + 0.376810i \(0.122979\pi\)
\(660\) −1719.30 3355.70i −0.101400 0.197910i
\(661\) −6085.01 10539.6i −0.358063 0.620183i 0.629574 0.776940i \(-0.283229\pi\)
−0.987637 + 0.156757i \(0.949896\pi\)
\(662\) 21672.5 + 5807.13i 1.27239 + 0.340937i
\(663\) −12734.1 + 4432.01i −0.745927 + 0.259615i
\(664\) −17154.5 9904.15i −1.00259 0.578848i
\(665\) −31.8134 + 42.1234i −0.00185515 + 0.00245636i
\(666\) −2104.16 + 1666.55i −0.122424 + 0.0969634i
\(667\) 18850.6 + 18850.6i 1.09430 + 1.09430i
\(668\) 1485.71 398.094i 0.0860535 0.0230580i
\(669\) 114.440 + 1562.06i 0.00661359 + 0.0902730i
\(670\) −4386.04 5626.35i −0.252907 0.324425i
\(671\) −18755.2 + 10828.3i −1.07904 + 0.622983i
\(672\) −323.865 61.8384i −0.0185913 0.00354980i
\(673\) 2016.19 + 7524.51i 0.115480 + 0.430978i 0.999322 0.0368070i \(-0.0117187\pi\)
−0.883842 + 0.467785i \(0.845052\pi\)
\(674\) −1369.79 −0.0782823
\(675\) −12732.1 + 12059.9i −0.726010 + 0.687684i
\(676\) −545.022 −0.0310094
\(677\) 2421.22 + 9036.11i 0.137452 + 0.512978i 0.999976 + 0.00696137i \(0.00221589\pi\)
−0.862524 + 0.506017i \(0.831117\pi\)
\(678\) 1725.40 + 329.446i 0.0977340 + 0.0186612i
\(679\) 398.637 230.153i 0.0225306 0.0130081i
\(680\) 10582.8 + 13575.5i 0.596814 + 0.765584i
\(681\) 1800.68 + 24578.6i 0.101325 + 1.38305i
\(682\) 32705.2 8763.33i 1.83628 0.492031i
\(683\) 15632.3 + 15632.3i 0.875775 + 0.875775i 0.993094 0.117320i \(-0.0374302\pi\)
−0.117320 + 0.993094i \(0.537430\pi\)
\(684\) 10.9547 + 74.3624i 0.000612372 + 0.00415690i
\(685\) −8073.21 + 10689.6i −0.450309 + 0.596243i
\(686\) 2436.82 + 1406.90i 0.135624 + 0.0783028i
\(687\) 4718.56 1642.27i 0.262044 0.0912028i
\(688\) −2709.94 726.126i −0.150168 0.0402374i
\(689\) 5160.89 + 8938.93i 0.285362 + 0.494261i
\(690\) 10259.3 + 20023.9i 0.566036 + 1.10478i
\(691\) 5115.78 8860.78i 0.281640 0.487815i −0.690149 0.723667i \(-0.742455\pi\)
0.971789 + 0.235853i \(0.0757883\pi\)
\(692\) 878.360 878.360i 0.0482518 0.0482518i
\(693\) −2385.36 1772.80i −0.130754 0.0971762i
\(694\) 2229.17i 0.121928i
\(695\) 3132.61 + 1269.58i 0.170973 + 0.0692919i
\(696\) −22533.9 + 1650.88i −1.22722 + 0.0899088i
\(697\) −1541.92 + 5754.51i −0.0837937 + 0.312722i
\(698\) 2948.03 11002.2i 0.159864 0.596619i
\(699\) −12449.4 18325.5i −0.673645 0.991606i
\(700\) 90.4042 + 151.194i 0.00488137 + 0.00816371i
\(701\) 24579.9i 1.32435i −0.749348 0.662176i \(-0.769633\pi\)
0.749348 0.662176i \(-0.230367\pi\)
\(702\) 8010.09 12607.5i 0.430657 0.677832i
\(703\) 80.6347 80.6347i 0.00432603 0.00432603i
\(704\) 19803.6 34300.8i 1.06019 1.83631i
\(705\) −6382.04 + 5772.37i −0.340938 + 0.308369i
\(706\) −4977.76 8621.74i −0.265355 0.459608i
\(707\) −1787.58 478.980i −0.0950903 0.0254794i
\(708\) −923.478 797.402i −0.0490204 0.0423280i
\(709\) 29697.0 + 17145.6i 1.57305 + 0.908203i 0.995792 + 0.0916440i \(0.0292122\pi\)
0.577262 + 0.816559i \(0.304121\pi\)
\(710\) −11171.3 8437.06i −0.590496 0.445968i
\(711\) −2607.21 3291.82i −0.137522 0.173633i
\(712\) −22694.1 22694.1i −1.19452 1.19452i
\(713\) 25096.9 6724.70i 1.31821 0.353215i
\(714\) 1249.40 + 604.250i 0.0654870 + 0.0316716i
\(715\) 3913.38 31590.8i 0.204688 1.65235i
\(716\) 1933.28 1116.18i 0.100908 0.0582591i
\(717\) −9498.47 27291.1i −0.494738 1.42148i
\(718\) −224.095 836.336i −0.0116479 0.0434704i
\(719\) −24579.6 −1.27492 −0.637459 0.770485i \(-0.720014\pi\)
−0.637459 + 0.770485i \(0.720014\pi\)
\(720\) −16388.8 3989.53i −0.848298 0.206501i
\(721\) −734.693 −0.0379492
\(722\) −4719.99 17615.2i −0.243296 0.907994i
\(723\) 8920.40 10330.8i 0.458857 0.531405i
\(724\) −2275.27 + 1313.63i −0.116795 + 0.0674317i
\(725\) 16444.8 + 15949.1i 0.842404 + 0.817011i
\(726\) 42779.0 29061.8i 2.18688 1.48565i
\(727\) 744.411 199.464i 0.0379761 0.0101757i −0.239781 0.970827i \(-0.577076\pi\)
0.277757 + 0.960651i \(0.410409\pi\)
\(728\) −1037.20 1037.20i −0.0528039 0.0528039i
\(729\) 8362.19 + 17818.4i 0.424843 + 0.905267i
\(730\) −2589.39 18569.5i −0.131285 0.941490i
\(731\) −2821.58 1629.04i −0.142763 0.0824244i
\(732\) 270.212 1415.18i 0.0136439 0.0714569i
\(733\) −6172.97 1654.04i −0.311056 0.0833471i 0.0999142 0.994996i \(-0.468143\pi\)
−0.410970 + 0.911649i \(0.634810\pi\)
\(734\) −4187.59 7253.12i −0.210581 0.364738i
\(735\) −16619.4 10739.9i −0.834037 0.538975i
\(736\) 2985.18 5170.49i 0.149504 0.258949i
\(737\) −12065.9 + 12065.9i −0.603056 + 0.603056i
\(738\) −2618.99 6057.86i −0.130632 0.302159i
\(739\) 11521.7i 0.573521i 0.958002 + 0.286760i \(0.0925784\pi\)
−0.958002 + 0.286760i \(0.907422\pi\)
\(740\) −148.318 350.463i −0.00736794 0.0174098i
\(741\) −276.285 + 571.272i −0.0136972 + 0.0283215i
\(742\) 274.978 1026.23i 0.0136048 0.0507738i
\(743\) −6256.61 + 23350.0i −0.308927 + 1.15293i 0.620585 + 0.784139i \(0.286895\pi\)
−0.929512 + 0.368792i \(0.879771\pi\)
\(744\) −9587.59 + 19824.2i −0.472443 + 0.976866i
\(745\) −9365.55 + 23108.9i −0.460573 + 1.13644i
\(746\) 4830.98i 0.237098i
\(747\) 22391.2 + 2598.57i 1.09672 + 0.127278i
\(748\) 2977.99 2977.99i 0.145570 0.145570i
\(749\) 1186.23 2054.62i 0.0578692 0.100232i
\(750\) 9078.30 + 17070.1i 0.441990 + 0.831083i
\(751\) 14058.2 + 24349.5i 0.683077 + 1.18312i 0.974037 + 0.226388i \(0.0726918\pi\)
−0.290961 + 0.956735i \(0.593975\pi\)
\(752\) −7994.67 2142.17i −0.387680 0.103879i
\(753\) −1649.04 + 8636.48i −0.0798066 + 0.417969i
\(754\) −16897.9 9755.99i −0.816160 0.471210i
\(755\) 18556.9 2587.63i 0.894507 0.124733i
\(756\) 192.978 43.0309i 0.00928378 0.00207013i
\(757\) 8806.75 + 8806.75i 0.422836 + 0.422836i 0.886179 0.463343i \(-0.153350\pi\)
−0.463343 + 0.886179i \(0.653350\pi\)
\(758\) −32149.2 + 8614.36i −1.54052 + 0.412781i
\(759\) 44515.2 30241.3i 2.12885 1.44623i
\(760\) 803.970 + 99.5936i 0.0383725 + 0.00475347i
\(761\) 9352.07 5399.42i 0.445483 0.257200i −0.260438 0.965491i \(-0.583867\pi\)
0.705920 + 0.708291i \(0.250534\pi\)
\(762\) −18668.7 + 21620.3i −0.887525 + 1.02785i
\(763\) 335.532 + 1252.22i 0.0159201 + 0.0594148i
\(764\) 1531.33 0.0725151
\(765\) −17184.7 9401.13i −0.812177 0.444312i
\(766\) 3289.23 0.155150
\(767\) −2666.01 9949.69i −0.125507 0.468400i
\(768\) 2359.25 + 6778.61i 0.110849 + 0.318492i
\(769\) −9203.05 + 5313.38i −0.431561 + 0.249162i −0.700011 0.714132i \(-0.746822\pi\)
0.268450 + 0.963293i \(0.413488\pi\)
\(770\) −2584.11 + 2014.45i −0.120941 + 0.0942804i
\(771\) −31235.6 15106.5i −1.45905 0.705641i
\(772\) −171.506 + 45.9549i −0.00799564 + 0.00214243i
\(773\) −25837.0 25837.0i −1.20219 1.20219i −0.973499 0.228691i \(-0.926556\pi\)
−0.228691 0.973499i \(-0.573444\pi\)
\(774\) 3570.78 526.030i 0.165826 0.0244286i
\(775\) 21475.4 6107.99i 0.995381 0.283104i
\(776\) −6117.82 3532.13i −0.283012 0.163397i
\(777\) −227.036 196.041i −0.0104825 0.00905137i
\(778\) 7281.66 + 1951.12i 0.335553 + 0.0899112i
\(779\) 140.192 + 242.819i 0.00644786 + 0.0111680i
\(780\) 1420.54 + 1570.58i 0.0652097 + 0.0720970i
\(781\) −16742.6 + 28999.0i −0.767090 + 1.32864i
\(782\) −17770.0 + 17770.0i −0.812603 + 0.812603i
\(783\) 22792.1 11900.4i 1.04026 0.543150i
\(784\) 19032.1i 0.866987i
\(785\) 4995.51 2114.12i 0.227130 0.0961227i
\(786\) 11840.5 + 17429.3i 0.537325 + 0.790943i
\(787\) −8655.36 + 32302.3i −0.392034 + 1.46309i 0.434741 + 0.900556i \(0.356840\pi\)
−0.826774 + 0.562534i \(0.809827\pi\)
\(788\) −1118.34 + 4173.70i −0.0505574 + 0.188683i
\(789\) −24355.1 + 1784.30i −1.09894 + 0.0805106i
\(790\) −4263.45 + 1804.32i −0.192009 + 0.0812591i
\(791\) 196.299i 0.00882377i
\(792\) −5257.99 + 45306.7i −0.235902 + 2.03270i
\(793\) 8600.81 8600.81i 0.385150 0.385150i
\(794\) −7002.99 + 12129.5i −0.313006 + 0.542142i
\(795\) −4601.80 + 14271.7i −0.205294 + 0.636684i
\(796\) 775.792 + 1343.71i 0.0345442 + 0.0598324i
\(797\) 26392.0 + 7071.71i 1.17296 + 0.314295i 0.792132 0.610350i \(-0.208971\pi\)
0.380831 + 0.924645i \(0.375638\pi\)
\(798\) 61.6880 21.4701i 0.00273651 0.000952424i
\(799\) −8324.02 4805.88i −0.368564 0.212791i
\(800\) 2496.96 4481.85i 0.110351 0.198072i
\(801\) 33953.3 + 13456.6i 1.49773 + 0.593591i
\(802\) 7922.77 + 7922.77i 0.348831 + 0.348831i
\(803\) −43318.1 + 11607.1i −1.90369 + 0.510092i
\(804\) −82.9444 1132.16i −0.00363834 0.0496620i
\(805\) −1982.97 + 1545.83i −0.0868203 + 0.0676811i
\(806\) −16469.0 + 9508.39i −0.719723 + 0.415532i
\(807\) −731.524 139.676i −0.0319094 0.00609274i
\(808\) 7350.84 + 27433.7i 0.320052 + 1.19445i
\(809\) −4530.67 −0.196897 −0.0984486 0.995142i \(-0.531388\pi\)
−0.0984486 + 0.995142i \(0.531388\pi\)
\(810\) 21389.7 3655.76i 0.927850 0.158581i
\(811\) 13005.2 0.563100 0.281550 0.959547i \(-0.409151\pi\)
0.281550 + 0.959547i \(0.409151\pi\)
\(812\) −66.8472 249.477i −0.00288901 0.0107819i
\(813\) −38029.8 7261.37i −1.64055 0.313244i
\(814\) 6129.91 3539.11i 0.263948 0.152390i
\(815\) −39441.6 4885.91i −1.69519 0.209995i
\(816\) −1376.59 18789.9i −0.0590565 0.806099i
\(817\) −148.113 + 39.6868i −0.00634250 + 0.00169947i
\(818\) 19038.7 + 19038.7i 0.813781 + 0.813781i
\(819\) 1551.78 + 615.014i 0.0662073 + 0.0262397i
\(820\) 926.726 129.226i 0.0394667 0.00550337i
\(821\) 7911.52 + 4567.72i 0.336314 + 0.194171i 0.658641 0.752457i \(-0.271132\pi\)
−0.322327 + 0.946628i \(0.604465\pi\)
\(822\) 15654.4 5448.41i 0.664246 0.231186i
\(823\) −11842.5 3173.19i −0.501584 0.134399i −0.000849174 1.00000i \(-0.500270\pi\)
−0.500735 + 0.865601i \(0.666937\pi\)
\(824\) 5637.61 + 9764.63i 0.238344 + 0.412824i
\(825\) 37850.9 26569.3i 1.59733 1.12124i
\(826\) −530.130 + 918.212i −0.0223312 + 0.0386788i
\(827\) 2547.55 2547.55i 0.107118 0.107118i −0.651516 0.758635i \(-0.725867\pi\)
0.758635 + 0.651516i \(0.225867\pi\)
\(828\) −412.723 + 3556.32i −0.0173226 + 0.149264i
\(829\) 19833.8i 0.830950i −0.909605 0.415475i \(-0.863615\pi\)
0.909605 0.415475i \(-0.136385\pi\)
\(830\) 9334.23 23031.6i 0.390356 0.963180i
\(831\) 11408.1 835.784i 0.476226 0.0348893i
\(832\) −5757.50 + 21487.3i −0.239910 + 0.895358i
\(833\) 5720.43 21348.9i 0.237937 0.887991i
\(834\) −2350.29 3459.63i −0.0975826 0.143642i
\(835\) 7352.43 + 17373.2i 0.304720 + 0.720029i
\(836\) 198.210i 0.00820005i
\(837\) 1062.32 25036.8i 0.0438701 1.03393i
\(838\) 22808.1 22808.1i 0.940205 0.940205i
\(839\) −10560.8 + 18291.9i −0.434565 + 0.752689i −0.997260 0.0739757i \(-0.976431\pi\)
0.562695 + 0.826665i \(0.309765\pi\)
\(840\) 106.755 2128.29i 0.00438498 0.0874201i
\(841\) −4599.18 7966.01i −0.188576 0.326623i
\(842\) −22927.4 6143.39i −0.938399 0.251443i
\(843\) −7976.73 6887.73i −0.325899 0.281407i
\(844\) −994.197 574.000i −0.0405470 0.0234098i
\(845\) −923.202 6620.61i −0.0375847 0.269534i
\(846\) 10534.3 1551.85i 0.428104 0.0630660i
\(847\) 4086.67 + 4086.67i 0.165785 + 0.165785i
\(848\) −13931.2 + 3732.86i −0.564151 + 0.151164i
\(849\) 27123.8 + 13117.9i 1.09645 + 0.530277i
\(850\) −15034.8 + 15502.1i −0.606693 + 0.625549i
\(851\) 4703.90 2715.80i 0.189480 0.109396i
\(852\) −732.241 2103.88i −0.0294439 0.0845982i
\(853\) 2546.69 + 9504.36i 0.102224 + 0.381504i 0.998015 0.0629700i \(-0.0200572\pi\)
−0.895792 + 0.444474i \(0.853391\pi\)
\(854\) −1251.99 −0.0501665
\(855\) −884.756 + 259.032i −0.0353895 + 0.0103611i
\(856\) −36409.9 −1.45381
\(857\) −8927.04 33316.2i −0.355825 1.32796i −0.879444 0.476003i \(-0.842085\pi\)
0.523619 0.851953i \(-0.324582\pi\)
\(858\) −25742.4 + 29812.5i −1.02428 + 1.18623i
\(859\) 22284.7 12866.1i 0.885151 0.511042i 0.0127979 0.999918i \(-0.495926\pi\)
0.872353 + 0.488876i \(0.162593\pi\)
\(860\) −62.9093 + 507.836i −0.00249441 + 0.0201361i
\(861\) 610.070 414.450i 0.0241477 0.0164047i
\(862\) −29006.7 + 7772.31i −1.14614 + 0.307107i
\(863\) −16350.7 16350.7i −0.644942 0.644942i 0.306824 0.951766i \(-0.400734\pi\)
−0.951766 + 0.306824i \(0.900734\pi\)
\(864\) −3895.45 4240.67i −0.153387 0.166980i
\(865\) 12157.6 + 9181.98i 0.477887 + 0.360921i
\(866\) −6419.83 3706.49i −0.251911 0.145441i
\(867\) −684.459 + 3584.70i −0.0268113 + 0.140418i
\(868\) −243.145 65.1506i −0.00950794 0.00254764i
\(869\) 5536.70 + 9589.85i 0.216133 + 0.374354i
\(870\) −5955.73 27713.8i −0.232090 1.07998i
\(871\) 4791.91 8299.82i 0.186415 0.322880i
\(872\) 14068.3 14068.3i 0.546345 0.546345i
\(873\) 7985.38 + 926.730i 0.309581 + 0.0359279i
\(874\) 1182.74i 0.0457745i
\(875\) −1683.49 + 1354.28i −0.0650425 + 0.0523236i
\(876\) 1298.96 2685.85i 0.0501004 0.103592i
\(877\) 6354.23 23714.3i 0.244660 0.913085i −0.728894 0.684627i \(-0.759965\pi\)
0.973554 0.228458i \(-0.0733682\pi\)
\(878\) −3393.45 + 12664.5i −0.130437 + 0.486796i
\(879\) −15147.4 + 31320.1i −0.581239 + 1.20182i
\(880\) 41222.6 + 16706.6i 1.57911 + 0.639978i
\(881\) 11658.3i 0.445833i −0.974837 0.222917i \(-0.928442\pi\)
0.974837 0.222917i \(-0.0715578\pi\)
\(882\) 9716.33 + 22474.4i 0.370936 + 0.857995i
\(883\) 16684.3 16684.3i 0.635869 0.635869i −0.313665 0.949534i \(-0.601557\pi\)
0.949534 + 0.313665i \(0.101557\pi\)
\(884\) −1182.69 + 2048.49i −0.0449981 + 0.0779390i
\(885\) 8122.13 12568.6i 0.308500 0.477388i
\(886\) −12078.5 20920.7i −0.457999 0.793277i
\(887\) 15191.5 + 4070.55i 0.575063 + 0.154088i 0.534618 0.845094i \(-0.320456\pi\)
0.0404454 + 0.999182i \(0.487122\pi\)
\(888\) −863.384 + 4521.78i −0.0326276 + 0.170880i
\(889\) −2764.50 1596.09i −0.104295 0.0602149i
\(890\) 24266.8 32131.1i 0.913959 1.21015i
\(891\) −14967.7 49699.1i −0.562779 1.86867i
\(892\) 194.290 + 194.290i 0.00729296 + 0.00729296i
\(893\) −436.952 + 117.081i −0.0163741 + 0.00438742i
\(894\) 25521.3 17337.9i 0.954766 0.648618i
\(895\) 16833.4 + 21593.7i 0.628692 + 0.806476i
\(896\) 1543.34 891.050i 0.0575441 0.0332231i
\(897\) −19753.9 + 22877.2i −0.735300 + 0.851556i
\(898\) −4106.19 15324.5i −0.152590 0.569472i
\(899\) −32734.9 −1.21443
\(900\) −307.863 + 3061.10i −0.0114023 + 0.113374i
\(901\) −16749.1 −0.619305
\(902\) 4504.38 + 16810.6i 0.166274 + 0.620544i
\(903\) 132.582 + 380.934i 0.00488598 + 0.0140384i
\(904\) 2608.97 1506.29i 0.0959878 0.0554186i
\(905\) −19811.2 25413.5i −0.727676 0.933452i
\(906\) −20871.2 10094.0i −0.765343 0.370144i
\(907\) 17700.3 4742.77i 0.647991 0.173629i 0.0801705 0.996781i \(-0.474454\pi\)
0.567820 + 0.823153i \(0.307787\pi\)
\(908\) 3057.12 + 3057.12i 0.111733 + 0.111733i
\(909\) −20066.9 25336.1i −0.732210 0.924473i
\(910\) 1109.08 1468.50i 0.0404017 0.0534949i
\(911\) 46641.3 + 26928.4i 1.69626 + 0.979338i 0.949247 + 0.314532i \(0.101847\pi\)
0.747016 + 0.664806i \(0.231486\pi\)
\(912\) −671.123 579.500i −0.0243674 0.0210407i
\(913\) −57416.4 15384.7i −2.08128 0.557676i
\(914\) 19092.7 + 33069.5i 0.690953 + 1.19677i
\(915\) 17648.5 + 885.245i 0.637640 + 0.0319839i
\(916\) 438.243 759.060i 0.0158078 0.0273800i
\(917\) −1665.01 + 1665.01i −0.0599603 + 0.0599603i
\(918\) 11218.2 + 21485.6i 0.403330 + 0.772472i
\(919\) 21344.2i 0.766139i 0.923720 + 0.383069i \(0.125133\pi\)
−0.923720 + 0.383069i \(0.874867\pi\)
\(920\) 35761.4 + 14493.3i 1.28154 + 0.519381i
\(921\) 3858.58 + 5679.84i 0.138051 + 0.203211i
\(922\) −541.946 + 2022.57i −0.0193580 + 0.0722449i
\(923\) 4867.58 18166.1i 0.173584 0.647826i
\(924\) −519.987 + 38.0953i −0.0185133 + 0.00135633i
\(925\) 4005.99 2395.32i 0.142396 0.0851435i
\(926\) 11284.2i 0.400455i
\(927\) −10298.3 7653.70i −0.364876 0.271176i
\(928\) −5318.89 + 5318.89i −0.188148 + 0.188148i
\(929\) 25517.3 44197.2i 0.901178 1.56089i 0.0752112 0.997168i \(-0.476037\pi\)
0.825967 0.563719i \(-0.190630\pi\)
\(930\) −26294.0 8478.32i −0.927113 0.298941i
\(931\) −520.104 900.846i −0.0183090 0.0317122i
\(932\) −3754.11 1005.91i −0.131942 0.0353538i
\(933\) 40551.1 14113.6i 1.42292 0.495238i
\(934\) 34349.8 + 19831.9i 1.20338 + 0.694773i
\(935\) 41219.3 + 31130.6i 1.44173 + 1.08885i
\(936\) −3733.50 25343.7i −0.130377 0.885025i
\(937\) −18569.7 18569.7i −0.647433 0.647433i 0.304939 0.952372i \(-0.401364\pi\)
−0.952372 + 0.304939i \(0.901364\pi\)
\(938\) −952.859 + 255.318i −0.0331684 + 0.00888744i
\(939\) 3093.72 + 42228.1i 0.107518 + 1.46758i
\(940\) −185.590 + 1498.18i −0.00643967 + 0.0519844i
\(941\) −44953.6 + 25954.0i −1.55733 + 0.899124i −0.559817 + 0.828616i \(0.689128\pi\)
−0.997511 + 0.0705073i \(0.977538\pi\)
\(942\) −6592.98 1258.86i −0.228037 0.0435411i
\(943\) 3456.52 + 12899.9i 0.119363 + 0.445470i
\(944\) 14393.2 0.496248
\(945\) 849.596 + 2271.30i 0.0292459 + 0.0781854i
\(946\) −9517.79 −0.327114
\(947\) 2392.38 + 8928.47i 0.0820927 + 0.306374i 0.994748 0.102356i \(-0.0326382\pi\)
−0.912655 + 0.408731i \(0.865972\pi\)
\(948\) −723.606 138.164i −0.0247907 0.00473352i
\(949\) 21813.3 12593.9i 0.746142 0.430785i
\(950\) 15.5506 + 1016.24i 0.000531081 + 0.0347066i
\(951\) −2470.76 33724.9i −0.0842479 1.14995i
\(952\) 2299.10 616.042i 0.0782713 0.0209727i
\(953\) 20099.7 + 20099.7i 0.683204 + 0.683204i 0.960721 0.277517i \(-0.0895115\pi\)
−0.277517 + 0.960721i \(0.589511\pi\)
\(954\) 14545.2 11520.2i 0.493625 0.390966i
\(955\) 2593.89 + 18601.7i 0.0878913 + 0.630301i
\(956\) −4390.22 2534.70i −0.148525 0.0857510i
\(957\) −64034.7 + 22286.9i −2.16295 + 0.752802i
\(958\) −23293.6 6241.50i −0.785576 0.210494i
\(959\) 926.165 + 1604.17i 0.0311861 + 0.0540158i
\(960\) −28762.0 + 14736.3i −0.966969 + 0.495430i
\(961\) −1056.56 + 1830.02i −0.0354658 + 0.0614286i
\(962\) −2811.08 + 2811.08i −0.0942129 + 0.0942129i
\(963\) 38031.6 16442.2i 1.27264 0.550200i
\(964\) 2394.48i 0.0800012i
\(965\) −848.744 2005.51i −0.0283130 0.0669014i
\(966\) 3102.83 227.320i 0.103346 0.00757132i
\(967\) −2351.26 + 8775.02i −0.0781917 + 0.291815i −0.993938 0.109942i \(-0.964934\pi\)
0.915746 + 0.401757i \(0.131600\pi\)
\(968\) 22956.2 85673.7i 0.762232 2.84469i
\(969\) −578.642 851.762i −0.0191834 0.0282379i
\(970\) 3328.88 8213.79i 0.110189 0.271886i
\(971\) 29432.8i 0.972752i 0.873750 + 0.486376i \(0.161681\pi\)
−0.873750 + 0.486376i \(0.838319\pi\)
\(972\) 3153.27 + 1407.19i 0.104055 + 0.0464357i
\(973\) 330.498 330.498i 0.0108893 0.0108893i
\(974\) −3102.20 + 5373.17i −0.102054 + 0.176763i
\(975\) −16672.2 + 19916.3i −0.547630 + 0.654187i
\(976\) 8497.97 + 14718.9i 0.278702 + 0.482726i
\(977\) 50189.6 + 13448.3i 1.64351 + 0.440377i 0.957785 0.287484i \(-0.0928189\pi\)
0.685724 + 0.727861i \(0.259486\pi\)
\(978\) 37221.3 + 32139.8i 1.21698 + 1.05084i
\(979\) −83407.3 48155.2i −2.72289 1.57206i
\(980\) −3438.11 + 479.422i −0.112068 + 0.0156271i
\(981\) −8341.88 + 21048.0i −0.271494 + 0.685026i
\(982\) 8622.36 + 8622.36i 0.280194 + 0.280194i
\(983\) −12972.1 + 3475.88i −0.420903 + 0.112781i −0.463053 0.886331i \(-0.653246\pi\)
0.0421501 + 0.999111i \(0.486579\pi\)
\(984\) −10189.7 4928.05i −0.330117 0.159655i
\(985\) −52594.1 6515.21i −1.70131 0.210753i
\(986\) 27420.1 15831.0i 0.885632 0.511320i
\(987\) 391.133 + 1123.80i 0.0126139 + 0.0362422i
\(988\) 28.8129 + 107.531i 0.000927792 + 0.00346257i
\(989\) −7303.65 −0.234826
\(990\) −57207.5 + 1316.78i −1.83654 + 0.0422728i
\(991\) 3959.04 0.126905 0.0634526 0.997985i \(-0.479789\pi\)
0.0634526 + 0.997985i \(0.479789\pi\)
\(992\) 1897.44 + 7081.33i 0.0607295 + 0.226646i
\(993\) −28618.8 + 33143.6i −0.914592 + 1.05920i
\(994\) −1676.46 + 967.907i −0.0534952 + 0.0308855i
\(995\) −15008.5 + 11700.0i −0.478194 + 0.372778i
\(996\) 3271.05 2222.18i 0.104063 0.0706952i
\(997\) 46983.9 12589.3i 1.49247 0.399906i 0.581900 0.813260i \(-0.302309\pi\)
0.910571 + 0.413354i \(0.135643\pi\)
\(998\) −5687.89 5687.89i −0.180408 0.180408i
\(999\) −1140.13 5113.08i −0.0361083 0.161933i
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 45.4.l.a.2.6 64
3.2 odd 2 135.4.m.a.62.11 64
5.2 odd 4 225.4.p.b.218.11 64
5.3 odd 4 inner 45.4.l.a.38.6 yes 64
5.4 even 2 225.4.p.b.182.11 64
9.4 even 3 135.4.m.a.17.11 64
9.5 odd 6 inner 45.4.l.a.32.6 yes 64
15.8 even 4 135.4.m.a.8.11 64
45.13 odd 12 135.4.m.a.98.11 64
45.14 odd 6 225.4.p.b.32.11 64
45.23 even 12 inner 45.4.l.a.23.6 yes 64
45.32 even 12 225.4.p.b.68.11 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.l.a.2.6 64 1.1 even 1 trivial
45.4.l.a.23.6 yes 64 45.23 even 12 inner
45.4.l.a.32.6 yes 64 9.5 odd 6 inner
45.4.l.a.38.6 yes 64 5.3 odd 4 inner
135.4.m.a.8.11 64 15.8 even 4
135.4.m.a.17.11 64 9.4 even 3
135.4.m.a.62.11 64 3.2 odd 2
135.4.m.a.98.11 64 45.13 odd 12
225.4.p.b.32.11 64 45.14 odd 6
225.4.p.b.68.11 64 45.32 even 12
225.4.p.b.182.11 64 5.4 even 2
225.4.p.b.218.11 64 5.2 odd 4