Properties

Label 138.3.h.a.7.1
Level $138$
Weight $3$
Character 138.7
Analytic conductor $3.760$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [138,3,Mod(7,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 138.h (of order \(22\), degree \(10\), 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: \(3.76022764817\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 7.1
Character \(\chi\) \(=\) 138.7
Dual form 138.3.h.a.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.926113 + 1.06879i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(1.12201 - 0.512407i) q^{5} +(0.348599 - 2.42456i) q^{6} +(2.20763 + 7.51851i) q^{7} +(2.37942 + 1.52916i) q^{8} +(1.24625 - 2.72890i) q^{9} +O(q^{10})\) \(q+(-0.926113 + 1.06879i) q^{2} +(-1.45709 + 0.936417i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(1.12201 - 0.512407i) q^{5} +(0.348599 - 2.42456i) q^{6} +(2.20763 + 7.51851i) q^{7} +(2.37942 + 1.52916i) q^{8} +(1.24625 - 2.72890i) q^{9} +(-0.491456 + 1.67375i) q^{10} +(-15.5963 + 13.5143i) q^{11} +(2.26850 + 2.61799i) q^{12} +(-14.5601 - 4.27524i) q^{13} +(-10.0802 - 4.60349i) q^{14} +(-1.15505 + 1.79730i) q^{15} +(-3.83797 + 1.12693i) q^{16} +(-19.6785 - 2.82935i) q^{17} +(1.76246 + 3.85924i) q^{18} +(32.9814 - 4.74201i) q^{19} +(-1.33374 - 2.07534i) q^{20} +(-10.2572 - 8.88791i) q^{21} -29.1850i q^{22} +(-20.9466 + 9.49950i) q^{23} -4.89898 q^{24} +(-15.3752 + 17.7439i) q^{25} +(18.0536 - 11.6024i) q^{26} +(0.739490 + 5.14326i) q^{27} +(14.2556 - 6.51032i) q^{28} +(-3.31586 + 23.0623i) q^{29} +(-0.851227 - 2.89901i) q^{30} +(14.5557 + 9.35437i) q^{31} +(2.34994 - 5.14566i) q^{32} +(10.0703 - 34.2963i) q^{33} +(21.2485 - 18.4120i) q^{34} +(6.32953 + 7.30467i) q^{35} +(-5.75696 - 1.69040i) q^{36} +(30.6081 + 13.9782i) q^{37} +(-25.4763 + 39.6419i) q^{38} +(25.2189 - 7.40493i) q^{39} +(3.45330 + 0.496510i) q^{40} +(25.2644 + 55.3213i) q^{41} +(18.9986 - 2.73159i) q^{42} +(-28.8157 - 44.8382i) q^{43} +(31.1927 + 27.0286i) q^{44} -3.70044i q^{45} +(9.24592 - 31.1851i) q^{46} +57.1118 q^{47} +(4.53701 - 5.23599i) q^{48} +(-10.4329 + 6.70483i) q^{49} +(-4.72537 - 32.8657i) q^{50} +(31.3229 - 14.3047i) q^{51} +(-4.31920 + 30.0407i) q^{52} +(-27.9070 - 95.0424i) q^{53} +(-6.18193 - 3.97288i) q^{54} +(-10.5745 + 23.1549i) q^{55} +(-6.24413 + 21.2656i) q^{56} +(-43.6165 + 37.7939i) q^{57} +(-21.5779 - 24.9023i) q^{58} +(11.8679 + 3.48473i) q^{59} +(3.88677 + 1.77503i) q^{60} +(22.3943 - 34.8462i) q^{61} +(-23.4781 + 6.89378i) q^{62} +(23.2685 + 3.34550i) q^{63} +(3.32332 + 7.27706i) q^{64} +(-18.5273 + 2.66383i) q^{65} +(27.3293 + 42.5253i) q^{66} +(65.1245 + 56.4307i) q^{67} +39.7618i q^{68} +(21.6256 - 33.4564i) q^{69} -13.6690 q^{70} +(17.9626 - 20.7300i) q^{71} +(7.13827 - 4.58749i) q^{72} +(3.45579 + 24.0355i) q^{73} +(-43.2864 + 19.7682i) q^{74} +(5.78737 - 40.2521i) q^{75} +(-18.7750 - 63.9417i) q^{76} +(-136.038 - 87.4266i) q^{77} +(-15.4412 + 33.8115i) q^{78} +(-15.9200 + 54.2184i) q^{79} +(-3.72881 + 3.23103i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(-82.5246 - 24.2314i) q^{82} +(30.1087 + 13.7502i) q^{83} +(-14.6754 + 22.8353i) q^{84} +(-23.5294 + 6.90885i) q^{85} +(74.6093 + 10.7272i) q^{86} +(-16.7644 - 36.7090i) q^{87} +(-57.7759 + 8.30692i) q^{88} +(-2.22338 - 3.45964i) q^{89} +(3.95500 + 3.42703i) q^{90} -118.909i q^{91} +(24.7676 + 38.7629i) q^{92} -29.9686 q^{93} +(-52.8920 + 61.0406i) q^{94} +(34.5758 - 22.2205i) q^{95} +(1.39439 + 9.69823i) q^{96} +(-103.894 + 47.4466i) q^{97} +(2.49600 - 17.3600i) q^{98} +(17.4423 + 59.4029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 16 q^{4} - 24 q^{9} - 16 q^{13} - 32 q^{16} + 220 q^{17} + 132 q^{19} + 88 q^{20} - 104 q^{23} - 336 q^{25} - 208 q^{26} - 264 q^{28} - 164 q^{29} - 268 q^{31} + 552 q^{35} - 48 q^{36} + 352 q^{37} + 216 q^{39} + 192 q^{41} + 88 q^{43} + 80 q^{46} - 64 q^{47} - 40 q^{49} + 160 q^{50} - 264 q^{51} - 32 q^{52} - 352 q^{53} + 196 q^{55} - 528 q^{57} + 312 q^{58} - 696 q^{59} + 616 q^{61} + 96 q^{62} - 64 q^{64} + 44 q^{67} + 72 q^{69} - 32 q^{70} - 32 q^{71} - 284 q^{73} - 48 q^{75} - 224 q^{77} + 144 q^{78} - 440 q^{79} - 72 q^{81} - 616 q^{82} + 352 q^{83} - 532 q^{85} - 96 q^{87} + 88 q^{89} - 32 q^{92} - 192 q^{93} + 16 q^{94} + 372 q^{95} - 264 q^{97} + 1184 q^{98} + 660 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.926113 + 1.06879i −0.463056 + 0.534396i
\(3\) −1.45709 + 0.936417i −0.485698 + 0.312139i
\(4\) −0.284630 1.97964i −0.0711574 0.494911i
\(5\) 1.12201 0.512407i 0.224403 0.102481i −0.300041 0.953926i \(-0.597000\pi\)
0.524444 + 0.851445i \(0.324273\pi\)
\(6\) 0.348599 2.42456i 0.0580998 0.404093i
\(7\) 2.20763 + 7.51851i 0.315376 + 1.07407i 0.952810 + 0.303568i \(0.0981778\pi\)
−0.637434 + 0.770505i \(0.720004\pi\)
\(8\) 2.37942 + 1.52916i 0.297428 + 0.191145i
\(9\) 1.24625 2.72890i 0.138472 0.303211i
\(10\) −0.491456 + 1.67375i −0.0491456 + 0.167375i
\(11\) −15.5963 + 13.5143i −1.41785 + 1.22857i −0.482000 + 0.876171i \(0.660089\pi\)
−0.935849 + 0.352401i \(0.885365\pi\)
\(12\) 2.26850 + 2.61799i 0.189042 + 0.218166i
\(13\) −14.5601 4.27524i −1.12001 0.328864i −0.331235 0.943548i \(-0.607465\pi\)
−0.788774 + 0.614684i \(0.789284\pi\)
\(14\) −10.0802 4.60349i −0.720017 0.328821i
\(15\) −1.15505 + 1.79730i −0.0770035 + 0.119820i
\(16\) −3.83797 + 1.12693i −0.239873 + 0.0704331i
\(17\) −19.6785 2.82935i −1.15756 0.166432i −0.463331 0.886185i \(-0.653346\pi\)
−0.694230 + 0.719753i \(0.744255\pi\)
\(18\) 1.76246 + 3.85924i 0.0979143 + 0.214402i
\(19\) 32.9814 4.74201i 1.73586 0.249580i 0.799514 0.600647i \(-0.205090\pi\)
0.936350 + 0.351067i \(0.114181\pi\)
\(20\) −1.33374 2.07534i −0.0666870 0.103767i
\(21\) −10.2572 8.88791i −0.488438 0.423234i
\(22\) 29.1850i 1.32659i
\(23\) −20.9466 + 9.49950i −0.910721 + 0.413022i
\(24\) −4.89898 −0.204124
\(25\) −15.3752 + 17.7439i −0.615007 + 0.709755i
\(26\) 18.0536 11.6024i 0.694371 0.446245i
\(27\) 0.739490 + 5.14326i 0.0273885 + 0.190491i
\(28\) 14.2556 6.51032i 0.509129 0.232511i
\(29\) −3.31586 + 23.0623i −0.114340 + 0.795252i 0.849273 + 0.527953i \(0.177040\pi\)
−0.963614 + 0.267299i \(0.913869\pi\)
\(30\) −0.851227 2.89901i −0.0283742 0.0966337i
\(31\) 14.5557 + 9.35437i 0.469538 + 0.301754i 0.753931 0.656954i \(-0.228156\pi\)
−0.284392 + 0.958708i \(0.591792\pi\)
\(32\) 2.34994 5.14566i 0.0734357 0.160802i
\(33\) 10.0703 34.2963i 0.305161 1.03928i
\(34\) 21.2485 18.4120i 0.624957 0.541528i
\(35\) 6.32953 + 7.30467i 0.180844 + 0.208705i
\(36\) −5.75696 1.69040i −0.159915 0.0469554i
\(37\) 30.6081 + 13.9782i 0.827245 + 0.377790i 0.783607 0.621257i \(-0.213378\pi\)
0.0436385 + 0.999047i \(0.486105\pi\)
\(38\) −25.4763 + 39.6419i −0.670429 + 1.04321i
\(39\) 25.2189 7.40493i 0.646637 0.189870i
\(40\) 3.45330 + 0.496510i 0.0863325 + 0.0124127i
\(41\) 25.2644 + 55.3213i 0.616205 + 1.34930i 0.918248 + 0.396006i \(0.129604\pi\)
−0.302043 + 0.953294i \(0.597669\pi\)
\(42\) 18.9986 2.73159i 0.452348 0.0650379i
\(43\) −28.8157 44.8382i −0.670133 1.04275i −0.995276 0.0970831i \(-0.969049\pi\)
0.325143 0.945665i \(-0.394588\pi\)
\(44\) 31.1927 + 27.0286i 0.708924 + 0.614286i
\(45\) 3.70044i 0.0822321i
\(46\) 9.24592 31.1851i 0.200998 0.677938i
\(47\) 57.1118 1.21515 0.607573 0.794264i \(-0.292143\pi\)
0.607573 + 0.794264i \(0.292143\pi\)
\(48\) 4.53701 5.23599i 0.0945210 0.109083i
\(49\) −10.4329 + 6.70483i −0.212917 + 0.136833i
\(50\) −4.72537 32.8657i −0.0945074 0.657314i
\(51\) 31.3229 14.3047i 0.614175 0.280484i
\(52\) −4.31920 + 30.0407i −0.0830615 + 0.577706i
\(53\) −27.9070 95.0424i −0.526547 1.79325i −0.604869 0.796325i \(-0.706774\pi\)
0.0783220 0.996928i \(-0.475044\pi\)
\(54\) −6.18193 3.97288i −0.114480 0.0735719i
\(55\) −10.5745 + 23.1549i −0.192263 + 0.420998i
\(56\) −6.24413 + 21.2656i −0.111502 + 0.379742i
\(57\) −43.6165 + 37.7939i −0.765202 + 0.663052i
\(58\) −21.5779 24.9023i −0.372034 0.429350i
\(59\) 11.8679 + 3.48473i 0.201151 + 0.0590632i 0.380756 0.924676i \(-0.375664\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(60\) 3.88677 + 1.77503i 0.0647795 + 0.0295838i
\(61\) 22.3943 34.8462i 0.367119 0.571249i −0.607722 0.794150i \(-0.707916\pi\)
0.974841 + 0.222901i \(0.0715528\pi\)
\(62\) −23.4781 + 6.89378i −0.378679 + 0.111190i
\(63\) 23.2685 + 3.34550i 0.369341 + 0.0531032i
\(64\) 3.32332 + 7.27706i 0.0519269 + 0.113704i
\(65\) −18.5273 + 2.66383i −0.285036 + 0.0409819i
\(66\) 27.3293 + 42.5253i 0.414081 + 0.644322i
\(67\) 65.1245 + 56.4307i 0.972007 + 0.842249i 0.987498 0.157631i \(-0.0503857\pi\)
−0.0154909 + 0.999880i \(0.504931\pi\)
\(68\) 39.7618i 0.584733i
\(69\) 21.6256 33.4564i 0.313415 0.484876i
\(70\) −13.6690 −0.195272
\(71\) 17.9626 20.7300i 0.252995 0.291972i −0.615018 0.788513i \(-0.710851\pi\)
0.868013 + 0.496541i \(0.165397\pi\)
\(72\) 7.13827 4.58749i 0.0991427 0.0637151i
\(73\) 3.45579 + 24.0355i 0.0473396 + 0.329254i 0.999705 + 0.0242943i \(0.00773387\pi\)
−0.952365 + 0.304960i \(0.901357\pi\)
\(74\) −43.2864 + 19.7682i −0.584951 + 0.267138i
\(75\) 5.78737 40.2521i 0.0771650 0.536694i
\(76\) −18.7750 63.9417i −0.247039 0.841338i
\(77\) −136.038 87.4266i −1.76673 1.13541i
\(78\) −15.4412 + 33.8115i −0.197964 + 0.433481i
\(79\) −15.9200 + 54.2184i −0.201519 + 0.686309i 0.795272 + 0.606253i \(0.207328\pi\)
−0.996790 + 0.0800563i \(0.974490\pi\)
\(80\) −3.72881 + 3.23103i −0.0466101 + 0.0403879i
\(81\) −5.89375 6.80175i −0.0727623 0.0839722i
\(82\) −82.5246 24.2314i −1.00640 0.295505i
\(83\) 30.1087 + 13.7502i 0.362756 + 0.165665i 0.588451 0.808533i \(-0.299738\pi\)
−0.225695 + 0.974198i \(0.572465\pi\)
\(84\) −14.6754 + 22.8353i −0.174707 + 0.271849i
\(85\) −23.5294 + 6.90885i −0.276816 + 0.0812806i
\(86\) 74.6093 + 10.7272i 0.867550 + 0.124735i
\(87\) −16.7644 36.7090i −0.192695 0.421943i
\(88\) −57.7759 + 8.30692i −0.656544 + 0.0943968i
\(89\) −2.22338 3.45964i −0.0249818 0.0388724i 0.828538 0.559933i \(-0.189173\pi\)
−0.853520 + 0.521060i \(0.825537\pi\)
\(90\) 3.95500 + 3.42703i 0.0439445 + 0.0380781i
\(91\) 118.909i 1.30669i
\(92\) 24.7676 + 38.7629i 0.269213 + 0.421336i
\(93\) −29.9686 −0.322243
\(94\) −52.8920 + 61.0406i −0.562681 + 0.649369i
\(95\) 34.5758 22.2205i 0.363956 0.233900i
\(96\) 1.39439 + 9.69823i 0.0145249 + 0.101023i
\(97\) −103.894 + 47.4466i −1.07107 + 0.489140i −0.871324 0.490708i \(-0.836738\pi\)
−0.199744 + 0.979848i \(0.564011\pi\)
\(98\) 2.49600 17.3600i 0.0254694 0.177143i
\(99\) 17.4423 + 59.4029i 0.176185 + 0.600029i
\(100\) 39.5028 + 25.3869i 0.395028 + 0.253869i
\(101\) 4.62812 10.1342i 0.0458230 0.100338i −0.885336 0.464952i \(-0.846072\pi\)
0.931159 + 0.364614i \(0.118799\pi\)
\(102\) −13.7198 + 46.7255i −0.134508 + 0.458093i
\(103\) −133.447 + 115.633i −1.29560 + 1.12265i −0.310522 + 0.950566i \(0.600504\pi\)
−0.985083 + 0.172081i \(0.944951\pi\)
\(104\) −28.1072 32.4374i −0.270261 0.311898i
\(105\) −16.0629 4.71650i −0.152980 0.0449191i
\(106\) 127.426 + 58.1933i 1.20213 + 0.548993i
\(107\) −34.3937 + 53.5176i −0.321436 + 0.500165i −0.963941 0.266117i \(-0.914259\pi\)
0.642504 + 0.766282i \(0.277896\pi\)
\(108\) 9.97134 2.92785i 0.0923273 0.0271097i
\(109\) 55.2506 + 7.94384i 0.506886 + 0.0728792i 0.391014 0.920385i \(-0.372124\pi\)
0.115873 + 0.993264i \(0.463034\pi\)
\(110\) −14.9546 32.7460i −0.135951 0.297691i
\(111\) −57.6883 + 8.29433i −0.519714 + 0.0747237i
\(112\) −16.9457 26.3680i −0.151301 0.235428i
\(113\) 58.8089 + 50.9582i 0.520433 + 0.450958i 0.875035 0.484060i \(-0.160838\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(114\) 81.6184i 0.715951i
\(115\) −18.6348 + 21.3917i −0.162041 + 0.186015i
\(116\) 46.5990 0.401715
\(117\) −29.8121 + 34.4050i −0.254805 + 0.294060i
\(118\) −14.7154 + 9.45705i −0.124707 + 0.0801444i
\(119\) −22.1705 154.200i −0.186307 1.29579i
\(120\) −5.49672 + 2.51027i −0.0458060 + 0.0209189i
\(121\) 43.3892 301.779i 0.358589 2.49404i
\(122\) 16.5037 + 56.2063i 0.135276 + 0.460707i
\(123\) −88.6164 56.9503i −0.720459 0.463011i
\(124\) 14.3753 31.4776i 0.115930 0.253851i
\(125\) −16.8469 + 57.3751i −0.134775 + 0.459001i
\(126\) −25.1249 + 21.7708i −0.199404 + 0.172784i
\(127\) 52.1108 + 60.1391i 0.410322 + 0.473536i 0.922864 0.385125i \(-0.125842\pi\)
−0.512543 + 0.858662i \(0.671296\pi\)
\(128\) −10.8554 3.18744i −0.0848080 0.0249019i
\(129\) 83.9745 + 38.3499i 0.650965 + 0.297286i
\(130\) 14.3113 22.2688i 0.110087 0.171299i
\(131\) 133.348 39.1544i 1.01792 0.298888i 0.270130 0.962824i \(-0.412933\pi\)
0.747790 + 0.663935i \(0.231115\pi\)
\(132\) −70.7607 10.1739i −0.536066 0.0770746i
\(133\) 108.464 + 237.503i 0.815517 + 1.78573i
\(134\) −120.625 + 17.3433i −0.900188 + 0.129428i
\(135\) 3.46516 + 5.39189i 0.0256678 + 0.0399400i
\(136\) −42.4971 36.8239i −0.312479 0.270764i
\(137\) 47.7301i 0.348395i −0.984711 0.174197i \(-0.944267\pi\)
0.984711 0.174197i \(-0.0557331\pi\)
\(138\) 15.7301 + 54.0977i 0.113986 + 0.392012i
\(139\) 8.63722 0.0621383 0.0310691 0.999517i \(-0.490109\pi\)
0.0310691 + 0.999517i \(0.490109\pi\)
\(140\) 12.6591 14.6093i 0.0904219 0.104352i
\(141\) −83.2173 + 53.4805i −0.590194 + 0.379295i
\(142\) 5.52060 + 38.3966i 0.0388775 + 0.270399i
\(143\) 284.861 130.092i 1.99204 0.909733i
\(144\) −1.70778 + 11.8779i −0.0118596 + 0.0824851i
\(145\) 8.09684 + 27.5753i 0.0558403 + 0.190175i
\(146\) −28.8894 18.5661i −0.197873 0.127165i
\(147\) 8.92322 19.5391i 0.0607022 0.132919i
\(148\) 18.9600 64.5717i 0.128108 0.436295i
\(149\) 18.4193 15.9604i 0.123619 0.107117i −0.590857 0.806776i \(-0.701210\pi\)
0.714477 + 0.699659i \(0.246665\pi\)
\(150\) 37.6613 + 43.4635i 0.251075 + 0.289756i
\(151\) 169.673 + 49.8204i 1.12366 + 0.329937i 0.790213 0.612832i \(-0.209970\pi\)
0.333448 + 0.942769i \(0.391788\pi\)
\(152\) 85.7281 + 39.1507i 0.564001 + 0.257571i
\(153\) −32.2453 + 50.1746i −0.210754 + 0.327939i
\(154\) 219.428 64.4298i 1.42485 0.418375i
\(155\) 21.1249 + 3.03730i 0.136290 + 0.0195955i
\(156\) −21.8371 47.8167i −0.139982 0.306517i
\(157\) −57.7893 + 8.30884i −0.368084 + 0.0529226i −0.323875 0.946100i \(-0.604986\pi\)
−0.0442090 + 0.999022i \(0.514077\pi\)
\(158\) −43.2045 67.2275i −0.273446 0.425491i
\(159\) 129.662 + 112.353i 0.815487 + 0.706624i
\(160\) 6.97762i 0.0436101i
\(161\) −117.664 136.516i −0.730835 0.847924i
\(162\) 12.7279 0.0785674
\(163\) −175.017 + 201.980i −1.07372 + 1.23914i −0.104090 + 0.994568i \(0.533193\pi\)
−0.969631 + 0.244572i \(0.921352\pi\)
\(164\) 102.325 65.7606i 0.623936 0.400979i
\(165\) −6.27463 43.6410i −0.0380280 0.264491i
\(166\) −42.5802 + 19.4457i −0.256507 + 0.117143i
\(167\) −15.3613 + 106.840i −0.0919836 + 0.639760i 0.890717 + 0.454559i \(0.150203\pi\)
−0.982701 + 0.185202i \(0.940706\pi\)
\(168\) −10.8152 36.8330i −0.0643759 0.219244i
\(169\) 51.5475 + 33.1275i 0.305015 + 0.196021i
\(170\) 14.4067 31.5464i 0.0847456 0.185567i
\(171\) 28.1625 95.9126i 0.164693 0.560892i
\(172\) −80.5617 + 69.8071i −0.468382 + 0.405855i
\(173\) −69.4698 80.1724i −0.401559 0.463424i 0.518572 0.855034i \(-0.326464\pi\)
−0.920131 + 0.391610i \(0.871918\pi\)
\(174\) 54.7600 + 16.0790i 0.314713 + 0.0924080i
\(175\) −167.350 76.4263i −0.956287 0.436722i
\(176\) 44.6286 69.4435i 0.253572 0.394565i
\(177\) −20.5558 + 6.03572i −0.116134 + 0.0341001i
\(178\) 5.75673 + 0.827693i 0.0323412 + 0.00464996i
\(179\) −46.0296 100.791i −0.257149 0.563077i 0.736392 0.676555i \(-0.236528\pi\)
−0.993540 + 0.113478i \(0.963801\pi\)
\(180\) −7.32556 + 1.05326i −0.0406975 + 0.00585142i
\(181\) −77.1420 120.035i −0.426199 0.663178i 0.560048 0.828460i \(-0.310783\pi\)
−0.986246 + 0.165282i \(0.947146\pi\)
\(182\) 127.088 + 110.123i 0.698288 + 0.605070i
\(183\) 71.7445i 0.392047i
\(184\) −64.3671 9.42741i −0.349821 0.0512359i
\(185\) 41.5052 0.224353
\(186\) 27.7543 32.0302i 0.149217 0.172205i
\(187\) 345.150 221.814i 1.84572 1.18617i
\(188\) −16.2557 113.061i −0.0864666 0.601389i
\(189\) −37.0372 + 16.9143i −0.195964 + 0.0894937i
\(190\) −8.27200 + 57.5330i −0.0435368 + 0.302805i
\(191\) 31.0959 + 105.903i 0.162806 + 0.554465i 0.999972 + 0.00751639i \(0.00239256\pi\)
−0.837166 + 0.546949i \(0.815789\pi\)
\(192\) −11.6568 7.49134i −0.0607122 0.0390174i
\(193\) 121.080 265.129i 0.627359 1.37373i −0.282684 0.959213i \(-0.591225\pi\)
0.910044 0.414513i \(-0.136048\pi\)
\(194\) 45.5067 154.982i 0.234571 0.798874i
\(195\) 24.5016 21.2307i 0.125649 0.108876i
\(196\) 16.2427 + 18.7451i 0.0828708 + 0.0956380i
\(197\) 194.327 + 57.0596i 0.986433 + 0.289643i 0.734877 0.678200i \(-0.237240\pi\)
0.251556 + 0.967843i \(0.419058\pi\)
\(198\) −79.6428 36.3717i −0.402236 0.183695i
\(199\) −149.403 + 232.475i −0.750768 + 1.16822i 0.230029 + 0.973184i \(0.426118\pi\)
−0.980797 + 0.195033i \(0.937518\pi\)
\(200\) −63.7173 + 18.7091i −0.318587 + 0.0935455i
\(201\) −147.735 21.2411i −0.735001 0.105677i
\(202\) 6.54515 + 14.3319i 0.0324017 + 0.0709499i
\(203\) −180.714 + 25.9828i −0.890219 + 0.127994i
\(204\) −37.2337 57.9367i −0.182518 0.284003i
\(205\) 56.6940 + 49.1256i 0.276556 + 0.239637i
\(206\) 249.716i 1.21221i
\(207\) −0.181433 + 68.9998i −0.000876486 + 0.333332i
\(208\) 60.6992 0.291823
\(209\) −450.304 + 519.679i −2.15457 + 2.48650i
\(210\) 19.9171 12.7999i 0.0948431 0.0609520i
\(211\) −19.9013 138.417i −0.0943190 0.656003i −0.981055 0.193728i \(-0.937942\pi\)
0.886736 0.462275i \(-0.152967\pi\)
\(212\) −180.207 + 82.2977i −0.850033 + 0.388197i
\(213\) −6.76132 + 47.0260i −0.0317433 + 0.220780i
\(214\) −25.3467 86.3231i −0.118443 0.403379i
\(215\) −55.3070 35.5437i −0.257242 0.165319i
\(216\) −6.10533 + 13.3688i −0.0282654 + 0.0618926i
\(217\) −38.1973 + 130.088i −0.176024 + 0.599484i
\(218\) −59.6586 + 51.6945i −0.273663 + 0.237131i
\(219\) −27.5427 31.7860i −0.125766 0.145141i
\(220\) 48.8482 + 14.3431i 0.222037 + 0.0651961i
\(221\) 274.426 + 125.326i 1.24175 + 0.567086i
\(222\) 44.5610 69.3382i 0.200725 0.312334i
\(223\) −165.560 + 48.6129i −0.742423 + 0.217995i −0.631005 0.775778i \(-0.717357\pi\)
−0.111418 + 0.993774i \(0.535539\pi\)
\(224\) 43.8755 + 6.30834i 0.195873 + 0.0281622i
\(225\) 29.2600 + 64.0705i 0.130044 + 0.284758i
\(226\) −108.927 + 15.6614i −0.481980 + 0.0692982i
\(227\) 99.0833 + 154.177i 0.436490 + 0.679192i 0.987909 0.155036i \(-0.0495495\pi\)
−0.551418 + 0.834229i \(0.685913\pi\)
\(228\) 87.2331 + 75.5879i 0.382601 + 0.331526i
\(229\) 12.0670i 0.0526945i 0.999653 + 0.0263473i \(0.00838756\pi\)
−0.999653 + 0.0263473i \(0.991612\pi\)
\(230\) −5.60542 39.7278i −0.0243714 0.172730i
\(231\) 280.088 1.21250
\(232\) −43.1559 + 49.8046i −0.186017 + 0.214675i
\(233\) 11.3707 7.30748i 0.0488011 0.0313626i −0.516013 0.856581i \(-0.672584\pi\)
0.564814 + 0.825218i \(0.308948\pi\)
\(234\) −9.16240 63.7259i −0.0391556 0.272333i
\(235\) 64.0803 29.2645i 0.272682 0.124530i
\(236\) 3.52056 24.4860i 0.0149176 0.103754i
\(237\) −27.5742 93.9091i −0.116347 0.396241i
\(238\) 185.340 + 119.110i 0.778738 + 0.500464i
\(239\) −24.9463 + 54.6247i −0.104378 + 0.228555i −0.954614 0.297846i \(-0.903732\pi\)
0.850236 + 0.526401i \(0.176459\pi\)
\(240\) 2.40763 8.19964i 0.0100318 0.0341652i
\(241\) −176.554 + 152.985i −0.732589 + 0.634792i −0.939097 0.343653i \(-0.888336\pi\)
0.206508 + 0.978445i \(0.433790\pi\)
\(242\) 282.355 + 325.855i 1.16676 + 1.34651i
\(243\) 14.9570 + 4.39178i 0.0615515 + 0.0180732i
\(244\) −75.3570 34.4144i −0.308840 0.141043i
\(245\) −8.27028 + 12.8688i −0.0337562 + 0.0525257i
\(246\) 142.937 41.9700i 0.581044 0.170610i
\(247\) −500.487 71.9591i −2.02626 0.291332i
\(248\) 20.3298 + 44.5160i 0.0819749 + 0.179500i
\(249\) −56.7472 + 8.15901i −0.227900 + 0.0327671i
\(250\) −45.7200 71.1416i −0.182880 0.284567i
\(251\) −152.678 132.297i −0.608281 0.527078i 0.295351 0.955389i \(-0.404563\pi\)
−0.903632 + 0.428311i \(0.859109\pi\)
\(252\) 47.0155i 0.186570i
\(253\) 198.311 431.236i 0.783837 1.70449i
\(254\) −112.537 −0.443058
\(255\) 27.8150 32.1002i 0.109078 0.125883i
\(256\) 13.4601 8.65025i 0.0525783 0.0337901i
\(257\) −26.5736 184.823i −0.103399 0.719156i −0.973898 0.226986i \(-0.927113\pi\)
0.870499 0.492170i \(-0.163796\pi\)
\(258\) −118.758 + 54.2349i −0.460302 + 0.210213i
\(259\) −37.5241 + 260.986i −0.144881 + 1.00767i
\(260\) 10.5468 + 35.9193i 0.0405648 + 0.138151i
\(261\) 58.8023 + 37.7899i 0.225296 + 0.144789i
\(262\) −81.6470 + 178.782i −0.311630 + 0.682374i
\(263\) −129.689 + 441.679i −0.493113 + 1.67939i 0.217708 + 0.976014i \(0.430142\pi\)
−0.710820 + 0.703374i \(0.751676\pi\)
\(264\) 76.4061 66.2063i 0.289417 0.250781i
\(265\) −80.0124 92.3392i −0.301934 0.348450i
\(266\) −354.290 104.029i −1.33192 0.391087i
\(267\) 6.47933 + 2.95901i 0.0242672 + 0.0110824i
\(268\) 93.1762 144.985i 0.347673 0.540989i
\(269\) 26.5004 7.78122i 0.0985145 0.0289265i −0.232104 0.972691i \(-0.574561\pi\)
0.330618 + 0.943765i \(0.392743\pi\)
\(270\) −8.97194 1.28997i −0.0332294 0.00477767i
\(271\) 7.38977 + 16.1813i 0.0272685 + 0.0597097i 0.922776 0.385336i \(-0.125915\pi\)
−0.895508 + 0.445046i \(0.853187\pi\)
\(272\) 78.7142 11.3174i 0.289390 0.0416081i
\(273\) 111.348 + 173.261i 0.407868 + 0.634655i
\(274\) 51.0135 + 44.2035i 0.186181 + 0.161326i
\(275\) 484.524i 1.76191i
\(276\) −72.3870 33.2884i −0.262272 0.120610i
\(277\) 90.0526 0.325100 0.162550 0.986700i \(-0.448028\pi\)
0.162550 + 0.986700i \(0.448028\pi\)
\(278\) −7.99904 + 9.23138i −0.0287735 + 0.0332064i
\(279\) 43.6670 28.0631i 0.156513 0.100585i
\(280\) 3.89061 + 27.0598i 0.0138950 + 0.0966421i
\(281\) 51.7835 23.6487i 0.184283 0.0841592i −0.321137 0.947033i \(-0.604065\pi\)
0.505420 + 0.862874i \(0.331338\pi\)
\(282\) 19.9091 138.471i 0.0705997 0.491032i
\(283\) −80.3945 273.799i −0.284080 0.967486i −0.970665 0.240437i \(-0.922709\pi\)
0.686585 0.727049i \(-0.259109\pi\)
\(284\) −46.1507 29.6592i −0.162502 0.104434i
\(285\) −29.5725 + 64.7547i −0.103763 + 0.227210i
\(286\) −124.773 + 424.937i −0.436268 + 1.48579i
\(287\) −360.159 + 312.080i −1.25491 + 1.08739i
\(288\) −11.1134 12.8255i −0.0385880 0.0445330i
\(289\) 101.947 + 29.9342i 0.352756 + 0.103579i
\(290\) −36.9709 16.8840i −0.127486 0.0582208i
\(291\) 106.953 166.422i 0.367536 0.571897i
\(292\) 46.5981 13.6825i 0.159583 0.0468577i
\(293\) −145.057 20.8560i −0.495074 0.0711809i −0.109744 0.993960i \(-0.535003\pi\)
−0.385330 + 0.922779i \(0.625912\pi\)
\(294\) 12.6193 + 27.6325i 0.0429229 + 0.0939881i
\(295\) 15.1015 2.17127i 0.0511916 0.00736025i
\(296\) 51.4546 + 80.0649i 0.173833 + 0.270490i
\(297\) −81.0409 70.2224i −0.272865 0.236439i
\(298\) 34.4675i 0.115663i
\(299\) 345.597 48.7622i 1.15584 0.163084i
\(300\) −81.3320 −0.271107
\(301\) 273.502 315.638i 0.908643 1.04863i
\(302\) −210.384 + 135.205i −0.696635 + 0.447700i
\(303\) 2.74621 + 19.1003i 0.00906339 + 0.0630373i
\(304\) −121.238 + 55.3675i −0.398809 + 0.182130i
\(305\) 7.27128 50.5729i 0.0238403 0.165813i
\(306\) −23.7634 80.9309i −0.0776583 0.264480i
\(307\) −422.807 271.722i −1.37722 0.885087i −0.378051 0.925785i \(-0.623406\pi\)
−0.999172 + 0.0406977i \(0.987042\pi\)
\(308\) −134.353 + 294.192i −0.436210 + 0.955168i
\(309\) 86.1647 293.450i 0.278850 0.949677i
\(310\) −22.8103 + 19.7652i −0.0735816 + 0.0637588i
\(311\) 351.881 + 406.092i 1.13145 + 1.30576i 0.946387 + 0.323035i \(0.104703\pi\)
0.185062 + 0.982727i \(0.440752\pi\)
\(312\) 71.3297 + 20.9443i 0.228621 + 0.0671291i
\(313\) 323.070 + 147.541i 1.03217 + 0.471378i 0.858169 0.513367i \(-0.171602\pi\)
0.174004 + 0.984745i \(0.444329\pi\)
\(314\) 44.6390 69.4596i 0.142162 0.221209i
\(315\) 27.8218 8.16922i 0.0883232 0.0259340i
\(316\) 111.864 + 16.0837i 0.354001 + 0.0508977i
\(317\) 62.4279 + 136.698i 0.196933 + 0.431224i 0.982176 0.187965i \(-0.0601890\pi\)
−0.785242 + 0.619188i \(0.787462\pi\)
\(318\) −240.164 + 34.5304i −0.755233 + 0.108586i
\(319\) −259.956 404.499i −0.814909 1.26802i
\(320\) 7.45762 + 6.46207i 0.0233051 + 0.0201940i
\(321\) 110.187i 0.343262i
\(322\) 254.877 + 0.670192i 0.791545 + 0.00208134i
\(323\) −662.443 −2.05091
\(324\) −11.7875 + 13.6035i −0.0363812 + 0.0419861i
\(325\) 299.723 192.621i 0.922226 0.592679i
\(326\) −53.7892 374.112i −0.164998 1.14758i
\(327\) −87.9441 + 40.1627i −0.268942 + 0.122822i
\(328\) −24.4806 + 170.266i −0.0746359 + 0.519104i
\(329\) 126.082 + 429.396i 0.383228 + 1.30515i
\(330\) 52.4541 + 33.7102i 0.158952 + 0.102152i
\(331\) 114.927 251.655i 0.347212 0.760288i −0.652784 0.757544i \(-0.726399\pi\)
0.999996 0.00274414i \(-0.000873488\pi\)
\(332\) 18.6506 63.5183i 0.0561766 0.191320i
\(333\) 76.2903 66.1059i 0.229100 0.198516i
\(334\) −99.9634 115.364i −0.299292 0.345401i
\(335\) 101.986 + 29.9458i 0.304436 + 0.0893904i
\(336\) 49.3829 + 22.5524i 0.146973 + 0.0671202i
\(337\) 175.912 273.724i 0.521993 0.812237i −0.475737 0.879588i \(-0.657818\pi\)
0.997729 + 0.0673512i \(0.0214548\pi\)
\(338\) −83.1452 + 24.4136i −0.245992 + 0.0722297i
\(339\) −133.408 19.1812i −0.393535 0.0565818i
\(340\) 20.3742 + 44.6133i 0.0599242 + 0.131216i
\(341\) −353.433 + 50.8160i −1.03646 + 0.149021i
\(342\) 76.4289 + 118.926i 0.223476 + 0.347736i
\(343\) 216.735 + 187.802i 0.631881 + 0.547528i
\(344\) 150.753i 0.438235i
\(345\) 7.12099 48.6197i 0.0206406 0.140927i
\(346\) 150.024 0.433597
\(347\) 347.469 401.000i 1.00135 1.15562i 0.0135484 0.999908i \(-0.495687\pi\)
0.987802 0.155712i \(-0.0497673\pi\)
\(348\) −67.8991 + 43.6361i −0.195112 + 0.125391i
\(349\) 52.7365 + 366.790i 0.151107 + 1.05097i 0.914368 + 0.404884i \(0.132688\pi\)
−0.763261 + 0.646091i \(0.776403\pi\)
\(350\) 236.669 108.083i 0.676197 0.308809i
\(351\) 11.2216 78.0480i 0.0319704 0.222359i
\(352\) 32.8895 + 112.011i 0.0934359 + 0.318214i
\(353\) −182.366 117.200i −0.516618 0.332011i 0.256215 0.966620i \(-0.417525\pi\)
−0.772833 + 0.634609i \(0.781161\pi\)
\(354\) 12.5860 27.5596i 0.0355538 0.0778520i
\(355\) 9.53214 32.4635i 0.0268511 0.0914465i
\(356\) −6.21601 + 5.38621i −0.0174607 + 0.0151298i
\(357\) 176.700 + 203.922i 0.494957 + 0.571211i
\(358\) 150.353 + 44.1476i 0.419980 + 0.123317i
\(359\) 372.177 + 169.968i 1.03670 + 0.473447i 0.859720 0.510766i \(-0.170638\pi\)
0.176985 + 0.984214i \(0.443366\pi\)
\(360\) 5.65858 8.80493i 0.0157183 0.0244581i
\(361\) 718.911 211.091i 1.99144 0.584740i
\(362\) 199.735 + 28.7175i 0.551754 + 0.0793302i
\(363\) 219.369 + 480.350i 0.604321 + 1.32328i
\(364\) −235.396 + 33.8449i −0.646693 + 0.0929805i
\(365\) 16.1934 + 25.1974i 0.0443655 + 0.0690341i
\(366\) −76.6799 66.4435i −0.209508 0.181540i
\(367\) 13.3631i 0.0364117i 0.999834 + 0.0182059i \(0.00579543\pi\)
−0.999834 + 0.0182059i \(0.994205\pi\)
\(368\) 69.6871 60.0642i 0.189367 0.163218i
\(369\) 182.452 0.494449
\(370\) −38.4385 + 44.3604i −0.103888 + 0.119893i
\(371\) 652.969 419.638i 1.76002 1.13110i
\(372\) 8.52995 + 59.3271i 0.0229300 + 0.159481i
\(373\) 110.798 50.5998i 0.297046 0.135656i −0.261317 0.965253i \(-0.584157\pi\)
0.558363 + 0.829597i \(0.311430\pi\)
\(374\) −82.5745 + 574.318i −0.220787 + 1.53561i
\(375\) −29.1796 99.3767i −0.0778123 0.265004i
\(376\) 135.893 + 87.3333i 0.361418 + 0.232270i
\(377\) 146.876 321.614i 0.389592 0.853087i
\(378\) 16.2227 55.2495i 0.0429173 0.146163i
\(379\) −272.809 + 236.390i −0.719812 + 0.623720i −0.935741 0.352689i \(-0.885267\pi\)
0.215929 + 0.976409i \(0.430722\pi\)
\(380\) −53.8300 62.1231i −0.141658 0.163482i
\(381\) −132.246 38.8308i −0.347102 0.101918i
\(382\) −141.986 64.8430i −0.371692 0.169746i
\(383\) 52.4983 81.6889i 0.137071 0.213287i −0.765931 0.642923i \(-0.777722\pi\)
0.903002 + 0.429636i \(0.141358\pi\)
\(384\) 18.8021 5.52081i 0.0489639 0.0143771i
\(385\) −197.435 28.3869i −0.512818 0.0737321i
\(386\) 171.234 + 374.949i 0.443610 + 0.971371i
\(387\) −158.270 + 22.7558i −0.408967 + 0.0588006i
\(388\) 123.499 + 192.168i 0.318295 + 0.495277i
\(389\) −395.925 343.071i −1.01780 0.881930i −0.0247597 0.999693i \(-0.507882\pi\)
−0.993042 + 0.117764i \(0.962428\pi\)
\(390\) 45.8491i 0.117562i
\(391\) 439.076 127.671i 1.12296 0.326525i
\(392\) −35.0771 −0.0894824
\(393\) −157.635 + 181.921i −0.401107 + 0.462902i
\(394\) −240.954 + 154.852i −0.611558 + 0.393025i
\(395\) 9.91946 + 68.9914i 0.0251126 + 0.174662i
\(396\) 112.632 51.4373i 0.284424 0.129892i
\(397\) −84.0141 + 584.331i −0.211623 + 1.47187i 0.556117 + 0.831104i \(0.312291\pi\)
−0.767739 + 0.640763i \(0.778618\pi\)
\(398\) −110.104 374.979i −0.276642 0.942157i
\(399\) −380.443 244.496i −0.953492 0.612772i
\(400\) 39.0133 85.4273i 0.0975333 0.213568i
\(401\) 40.4973 137.921i 0.100991 0.343943i −0.893460 0.449142i \(-0.851730\pi\)
0.994451 + 0.105199i \(0.0335479\pi\)
\(402\) 159.522 138.226i 0.396820 0.343847i
\(403\) −171.940 198.430i −0.426651 0.492381i
\(404\) −21.3793 6.27754i −0.0529192 0.0155385i
\(405\) −10.0981 4.61166i −0.0249336 0.0113868i
\(406\) 139.592 217.209i 0.343822 0.534998i
\(407\) −666.280 + 195.637i −1.63705 + 0.480682i
\(408\) 96.4048 + 13.8609i 0.236286 + 0.0339728i
\(409\) 153.125 + 335.297i 0.374389 + 0.819798i 0.999237 + 0.0390516i \(0.0124337\pi\)
−0.624848 + 0.780746i \(0.714839\pi\)
\(410\) −105.010 + 15.0982i −0.256122 + 0.0368248i
\(411\) 44.6953 + 69.5472i 0.108748 + 0.169215i
\(412\) 266.895 + 231.265i 0.647802 + 0.561324i
\(413\) 96.9218i 0.234678i
\(414\) −73.5783 64.0955i −0.177725 0.154820i
\(415\) 40.8281 0.0983810
\(416\) −56.2143 + 64.8748i −0.135131 + 0.155949i
\(417\) −12.5852 + 8.08804i −0.0301804 + 0.0193958i
\(418\) −138.396 962.563i −0.331090 2.30278i
\(419\) −113.425 + 51.7994i −0.270704 + 0.123626i −0.546142 0.837692i \(-0.683904\pi\)
0.275439 + 0.961319i \(0.411177\pi\)
\(420\) −4.76500 + 33.1413i −0.0113452 + 0.0789079i
\(421\) 99.4373 + 338.652i 0.236193 + 0.804400i 0.989223 + 0.146414i \(0.0467732\pi\)
−0.753030 + 0.657986i \(0.771409\pi\)
\(422\) 166.369 + 106.919i 0.394240 + 0.253363i
\(423\) 71.1754 155.852i 0.168263 0.368445i
\(424\) 78.9328 268.821i 0.186162 0.634011i
\(425\) 352.765 305.672i 0.830034 0.719229i
\(426\) −43.9993 50.7779i −0.103285 0.119197i
\(427\) 311.430 + 91.4440i 0.729343 + 0.214155i
\(428\) 115.735 + 52.8545i 0.270410 + 0.123492i
\(429\) −293.249 + 456.305i −0.683565 + 1.06365i
\(430\) 89.2093 26.1942i 0.207464 0.0609168i
\(431\) −466.648 67.0938i −1.08271 0.155670i −0.422211 0.906498i \(-0.638746\pi\)
−0.660498 + 0.750827i \(0.729655\pi\)
\(432\) −8.63424 18.9063i −0.0199867 0.0437647i
\(433\) 100.245 14.4130i 0.231512 0.0332865i −0.0255821 0.999673i \(-0.508144\pi\)
0.257094 + 0.966386i \(0.417235\pi\)
\(434\) −103.662 161.301i −0.238852 0.371662i
\(435\) −37.6199 32.5978i −0.0864825 0.0749375i
\(436\) 111.638i 0.256049i
\(437\) −645.802 + 412.636i −1.47781 + 0.944247i
\(438\) 59.4802 0.135800
\(439\) −307.971 + 355.418i −0.701529 + 0.809608i −0.988958 0.148194i \(-0.952654\pi\)
0.287429 + 0.957802i \(0.407199\pi\)
\(440\) −60.5688 + 38.9252i −0.137656 + 0.0884664i
\(441\) 5.29481 + 36.8262i 0.0120064 + 0.0835061i
\(442\) −388.097 + 177.238i −0.878047 + 0.400991i
\(443\) 77.7339 540.651i 0.175472 1.22043i −0.691612 0.722269i \(-0.743099\pi\)
0.867084 0.498163i \(-0.165992\pi\)
\(444\) 32.8396 + 111.841i 0.0739631 + 0.251895i
\(445\) −4.26740 2.74249i −0.00958967 0.00616290i
\(446\) 101.371 221.971i 0.227288 0.497692i
\(447\) −11.8930 + 40.5040i −0.0266064 + 0.0906129i
\(448\) −47.3759 + 41.0515i −0.105750 + 0.0916328i
\(449\) 232.374 + 268.173i 0.517536 + 0.597268i 0.953012 0.302932i \(-0.0979655\pi\)
−0.435476 + 0.900200i \(0.643420\pi\)
\(450\) −95.5760 28.0636i −0.212391 0.0623637i
\(451\) −1141.66 521.379i −2.53140 1.15605i
\(452\) 84.1403 130.925i 0.186151 0.289657i
\(453\) −293.882 + 86.2915i −0.648746 + 0.190489i
\(454\) −256.545 36.8856i −0.565077 0.0812458i
\(455\) −60.9295 133.417i −0.133911 0.293224i
\(456\) −161.575 + 23.2310i −0.354332 + 0.0509452i
\(457\) −96.9901 150.920i −0.212232 0.330240i 0.718774 0.695244i \(-0.244704\pi\)
−0.931006 + 0.365005i \(0.881067\pi\)
\(458\) −12.8972 11.1754i −0.0281597 0.0244005i
\(459\) 103.304i 0.225064i
\(460\) 47.6520 + 30.8014i 0.103591 + 0.0669596i
\(461\) 684.915 1.48572 0.742858 0.669449i \(-0.233470\pi\)
0.742858 + 0.669449i \(0.233470\pi\)
\(462\) −259.394 + 299.356i −0.561458 + 0.647957i
\(463\) −733.980 + 471.700i −1.58527 + 1.01879i −0.611502 + 0.791243i \(0.709434\pi\)
−0.973767 + 0.227548i \(0.926929\pi\)
\(464\) −13.2634 92.2493i −0.0285850 0.198813i
\(465\) −33.6252 + 15.3561i −0.0723122 + 0.0330239i
\(466\) −2.72035 + 18.9204i −0.00583765 + 0.0406018i
\(467\) 54.9895 + 187.277i 0.117751 + 0.401022i 0.997183 0.0750012i \(-0.0238961\pi\)
−0.879433 + 0.476023i \(0.842078\pi\)
\(468\) 76.5951 + 49.2247i 0.163665 + 0.105181i
\(469\) −280.504 + 614.217i −0.598089 + 1.30963i
\(470\) −28.0680 + 95.5907i −0.0597191 + 0.203384i
\(471\) 76.4238 66.2216i 0.162259 0.140598i
\(472\) 22.9100 + 26.4396i 0.0485382 + 0.0560161i
\(473\) 1055.38 + 309.886i 2.23124 + 0.655151i
\(474\) 125.906 + 57.4994i 0.265625 + 0.121307i
\(475\) −422.953 + 658.128i −0.890427 + 1.38553i
\(476\) −298.950 + 87.7795i −0.628045 + 0.184411i
\(477\) −294.140 42.2909i −0.616645 0.0886602i
\(478\) −35.2793 77.2510i −0.0738061 0.161613i
\(479\) −65.5621 + 9.42640i −0.136873 + 0.0196793i −0.210411 0.977613i \(-0.567480\pi\)
0.0735379 + 0.997292i \(0.476571\pi\)
\(480\) 6.53397 + 10.1671i 0.0136124 + 0.0211814i
\(481\) −385.897 334.382i −0.802280 0.695180i
\(482\) 330.381i 0.685437i
\(483\) 299.284 + 88.7331i 0.619635 + 0.183712i
\(484\) −609.764 −1.25984
\(485\) −92.2581 + 106.472i −0.190223 + 0.219529i
\(486\) −18.5458 + 11.9186i −0.0381600 + 0.0245240i
\(487\) 13.2837 + 92.3900i 0.0272766 + 0.189713i 0.998904 0.0468035i \(-0.0149035\pi\)
−0.971628 + 0.236516i \(0.923994\pi\)
\(488\) 106.571 48.6693i 0.218383 0.0997322i
\(489\) 65.8781 458.192i 0.134720 0.936998i
\(490\) −6.09486 20.7572i −0.0124385 0.0423616i
\(491\) −424.738 272.963i −0.865048 0.555932i 0.0311866 0.999514i \(-0.490071\pi\)
−0.896234 + 0.443581i \(0.853708\pi\)
\(492\) −87.5184 + 191.639i −0.177883 + 0.389509i
\(493\) 130.503 444.451i 0.264711 0.901524i
\(494\) 540.416 468.273i 1.09396 0.947922i
\(495\) 50.0089 + 57.7134i 0.101028 + 0.116593i
\(496\) −66.4060 19.4986i −0.133883 0.0393116i
\(497\) 195.513 + 89.2880i 0.393387 + 0.179654i
\(498\) 43.8340 68.2071i 0.0880201 0.136962i
\(499\) 346.544 101.755i 0.694477 0.203917i 0.0846024 0.996415i \(-0.473038\pi\)
0.609875 + 0.792498i \(0.291220\pi\)
\(500\) 118.377 + 17.0201i 0.236755 + 0.0340402i
\(501\) −77.6640 170.060i −0.155018 0.339442i
\(502\) 282.795 40.6598i 0.563336 0.0809956i
\(503\) −163.983 255.162i −0.326009 0.507280i 0.639101 0.769122i \(-0.279306\pi\)
−0.965111 + 0.261842i \(0.915670\pi\)
\(504\) 50.2498 + 43.5417i 0.0997019 + 0.0863922i
\(505\) 13.7422i 0.0272122i
\(506\) 277.243 + 611.326i 0.547911 + 1.20815i
\(507\) −106.131 −0.209331
\(508\) 104.222 120.278i 0.205161 0.236768i
\(509\) 308.141 198.030i 0.605385 0.389058i −0.201739 0.979439i \(-0.564659\pi\)
0.807124 + 0.590382i \(0.201023\pi\)
\(510\) 8.54859 + 59.4568i 0.0167619 + 0.116582i
\(511\) −173.082 + 79.0440i −0.338713 + 0.154685i
\(512\) −3.22022 + 22.3971i −0.00628949 + 0.0437443i
\(513\) 48.7788 + 166.125i 0.0950855 + 0.323831i
\(514\) 222.148 + 142.766i 0.432194 + 0.277754i
\(515\) −90.4787 + 198.121i −0.175687 + 0.384701i
\(516\) 52.0174 177.155i 0.100809 0.343324i
\(517\) −890.735 + 771.827i −1.72289 + 1.49289i
\(518\) −244.188 281.808i −0.471405 0.544031i
\(519\) 176.299 + 51.7660i 0.339689 + 0.0997418i
\(520\) −48.1578 21.9929i −0.0926111 0.0422941i
\(521\) −354.276 + 551.264i −0.679992 + 1.05809i 0.314083 + 0.949395i \(0.398303\pi\)
−0.994075 + 0.108693i \(0.965333\pi\)
\(522\) −94.8471 + 27.8496i −0.181699 + 0.0533518i
\(523\) 755.135 + 108.572i 1.44385 + 0.207595i 0.819290 0.573380i \(-0.194368\pi\)
0.624563 + 0.780975i \(0.285277\pi\)
\(524\) −115.466 252.836i −0.220356 0.482511i
\(525\) 315.412 45.3494i 0.600785 0.0863798i
\(526\) −351.956 547.655i −0.669118 1.04117i
\(527\) −259.968 225.263i −0.493298 0.427445i
\(528\) 142.977i 0.270789i
\(529\) 348.519 397.964i 0.658826 0.752295i
\(530\) 172.792 0.326022
\(531\) 24.2998 28.0434i 0.0457622 0.0528124i
\(532\) 439.298 282.320i 0.825748 0.530676i
\(533\) −131.341 913.496i −0.246418 1.71388i
\(534\) −9.16316 + 4.18468i −0.0171595 + 0.00783647i
\(535\) −11.1674 + 77.6711i −0.0208737 + 0.145180i
\(536\) 68.6670 + 233.858i 0.128110 + 0.436303i
\(537\) 161.452 + 103.759i 0.300655 + 0.193219i
\(538\) −16.2259 + 35.5297i −0.0301596 + 0.0660403i
\(539\) 72.1042 245.564i 0.133774 0.455592i
\(540\) 9.68774 8.39447i 0.0179403 0.0155453i
\(541\) −227.356 262.383i −0.420252 0.484997i 0.505662 0.862732i \(-0.331248\pi\)
−0.925914 + 0.377735i \(0.876703\pi\)
\(542\) −24.1382 7.08762i −0.0445355 0.0130768i
\(543\) 224.806 + 102.666i 0.414008 + 0.189071i
\(544\) −60.8023 + 94.6102i −0.111769 + 0.173916i
\(545\) 66.0624 19.3977i 0.121215 0.0355921i
\(546\) −288.301 41.4514i −0.528023 0.0759182i
\(547\) 116.653 + 255.435i 0.213260 + 0.466975i 0.985785 0.168009i \(-0.0537339\pi\)
−0.772525 + 0.634984i \(0.781007\pi\)
\(548\) −94.4885 + 13.5854i −0.172424 + 0.0247909i
\(549\) −67.1828 104.539i −0.122373 0.190416i
\(550\) 517.855 + 448.724i 0.941555 + 0.815862i
\(551\) 776.352i 1.40899i
\(552\) 102.617 46.5379i 0.185900 0.0843077i
\(553\) −442.787 −0.800700
\(554\) −83.3989 + 96.2475i −0.150540 + 0.173732i
\(555\) −60.4770 + 38.8662i −0.108968 + 0.0700292i
\(556\) −2.45841 17.0986i −0.00442160 0.0307529i
\(557\) 586.949 268.051i 1.05377 0.481240i 0.188252 0.982121i \(-0.439718\pi\)
0.865516 + 0.500881i \(0.166990\pi\)
\(558\) −10.4470 + 72.6606i −0.0187222 + 0.130216i
\(559\) 227.867 + 776.043i 0.407633 + 1.38827i
\(560\) −32.5244 20.9022i −0.0580793 0.0373253i
\(561\) −295.205 + 646.409i −0.526212 + 1.15224i
\(562\) −22.6818 + 77.2471i −0.0403591 + 0.137450i
\(563\) 535.566 464.071i 0.951273 0.824282i −0.0332667 0.999447i \(-0.510591\pi\)
0.984539 + 0.175164i \(0.0560456\pi\)
\(564\) 129.558 + 149.518i 0.229714 + 0.265104i
\(565\) 92.0958 + 27.0418i 0.163001 + 0.0478615i
\(566\) 367.088 + 167.643i 0.648565 + 0.296190i
\(567\) 38.1278 59.3280i 0.0672447 0.104635i
\(568\) 74.4402 21.8576i 0.131057 0.0384817i
\(569\) −223.499 32.1344i −0.392793 0.0564751i −0.0569113 0.998379i \(-0.518125\pi\)
−0.335882 + 0.941904i \(0.609034\pi\)
\(570\) −41.8218 91.5770i −0.0733716 0.160661i
\(571\) −237.085 + 34.0876i −0.415210 + 0.0596982i −0.346754 0.937956i \(-0.612716\pi\)
−0.0684555 + 0.997654i \(0.521807\pi\)
\(572\) −338.615 526.896i −0.591985 0.921146i
\(573\) −144.479 125.192i −0.252145 0.218485i
\(574\) 673.956i 1.17414i
\(575\) 153.499 517.730i 0.266955 0.900400i
\(576\) 24.0000 0.0416667
\(577\) 462.034 533.215i 0.800751 0.924116i −0.197671 0.980268i \(-0.563338\pi\)
0.998422 + 0.0561520i \(0.0178832\pi\)
\(578\) −126.407 + 81.2371i −0.218698 + 0.140549i
\(579\) 71.8460 + 499.700i 0.124086 + 0.863039i
\(580\) 52.2847 23.8776i 0.0901460 0.0411683i
\(581\) −36.9119 + 256.728i −0.0635318 + 0.441873i
\(582\) 78.8199 + 268.436i 0.135429 + 0.461230i
\(583\) 1719.68 + 1105.17i 2.94971 + 1.89566i
\(584\) −28.5315 + 62.4752i −0.0488552 + 0.106978i
\(585\) −15.8203 + 53.8789i −0.0270432 + 0.0921007i
\(586\) 156.629 135.720i 0.267286 0.231604i
\(587\) 490.172 + 565.689i 0.835047 + 0.963695i 0.999743 0.0226490i \(-0.00721002\pi\)
−0.164697 + 0.986344i \(0.552665\pi\)
\(588\) −41.2203 12.1034i −0.0701026 0.0205840i
\(589\) 524.426 + 239.497i 0.890366 + 0.406617i
\(590\) −11.6651 + 18.1512i −0.0197713 + 0.0307648i
\(591\) −336.585 + 98.8302i −0.569517 + 0.167225i
\(592\) −133.225 19.1549i −0.225043 0.0323563i
\(593\) −124.897 273.487i −0.210619 0.461192i 0.774608 0.632441i \(-0.217947\pi\)
−0.985228 + 0.171249i \(0.945220\pi\)
\(594\) 150.106 21.5820i 0.252704 0.0363333i
\(595\) −103.889 161.654i −0.174603 0.271687i
\(596\) −36.8386 31.9208i −0.0618097 0.0535584i
\(597\) 478.642i 0.801745i
\(598\) −267.946 + 414.531i −0.448069 + 0.693195i
\(599\) 934.470 1.56005 0.780025 0.625749i \(-0.215206\pi\)
0.780025 + 0.625749i \(0.215206\pi\)
\(600\) 75.3226 86.9269i 0.125538 0.144878i
\(601\) −379.062 + 243.608i −0.630718 + 0.405338i −0.816575 0.577239i \(-0.804130\pi\)
0.185857 + 0.982577i \(0.440494\pi\)
\(602\) 84.0574 + 584.632i 0.139630 + 0.971150i
\(603\) 235.155 107.391i 0.389974 0.178095i
\(604\) 50.3327 350.072i 0.0833323 0.579589i
\(605\) −105.950 360.833i −0.175124 0.596418i
\(606\) −22.9575 14.7539i −0.0378837 0.0243464i
\(607\) 279.578 612.191i 0.460590 1.00855i −0.526762 0.850013i \(-0.676594\pi\)
0.987353 0.158539i \(-0.0506785\pi\)
\(608\) 53.1037 180.855i 0.0873416 0.297458i
\(609\) 238.987 207.084i 0.392426 0.340039i
\(610\) 47.3178 + 54.6077i 0.0775702 + 0.0895208i
\(611\) −831.555 244.167i −1.36097 0.399618i
\(612\) 108.506 + 49.5530i 0.177297 + 0.0809689i
\(613\) −363.009 + 564.853i −0.592184 + 0.921457i 0.407781 + 0.913080i \(0.366303\pi\)
−0.999965 + 0.00837691i \(0.997334\pi\)
\(614\) 681.981 200.248i 1.11072 0.326136i
\(615\) −128.611 18.4914i −0.209123 0.0300673i
\(616\) −190.004 416.050i −0.308447 0.675405i
\(617\) −264.243 + 37.9924i −0.428270 + 0.0615760i −0.353080 0.935593i \(-0.614866\pi\)
−0.0751905 + 0.997169i \(0.523956\pi\)
\(618\) 233.839 + 363.860i 0.378380 + 0.588770i
\(619\) −712.241 617.160i −1.15063 0.997027i −0.999964 0.00844273i \(-0.997313\pi\)
−0.150667 0.988585i \(-0.548142\pi\)
\(620\) 42.6843i 0.0688456i
\(621\) −64.3482 100.709i −0.103620 0.162172i
\(622\) −759.909 −1.22172
\(623\) 21.1029 24.3541i 0.0338731 0.0390916i
\(624\) −88.4444 + 56.8398i −0.141738 + 0.0910894i
\(625\) −73.0366 507.981i −0.116859 0.812769i
\(626\) −456.890 + 208.655i −0.729857 + 0.333314i
\(627\) 169.499 1178.89i 0.270334 1.88021i
\(628\) 32.8971 + 112.037i 0.0523839 + 0.178403i
\(629\) −562.773 361.672i −0.894711 0.574996i
\(630\) −17.0350 + 37.3013i −0.0270396 + 0.0592085i
\(631\) −27.1714 + 92.5373i −0.0430608 + 0.146652i −0.978217 0.207583i \(-0.933440\pi\)
0.935157 + 0.354235i \(0.115259\pi\)
\(632\) −120.789 + 104.664i −0.191122 + 0.165608i
\(633\) 158.614 + 183.050i 0.250575 + 0.289179i
\(634\) −203.917 59.8754i −0.321635 0.0944407i
\(635\) 89.2848 + 40.7750i 0.140606 + 0.0642126i
\(636\) 185.513 288.664i 0.291688 0.453875i
\(637\) 180.569 53.0199i 0.283468 0.0832338i
\(638\) 673.074 + 96.7734i 1.05497 + 0.151682i
\(639\) −34.1841 74.8528i −0.0534963 0.117140i
\(640\) −13.8132 + 1.98604i −0.0215831 + 0.00310319i
\(641\) −341.328 531.116i −0.532492 0.828574i 0.465924 0.884825i \(-0.345722\pi\)
−0.998417 + 0.0562502i \(0.982086\pi\)
\(642\) 117.767 + 102.046i 0.183438 + 0.158950i
\(643\) 657.200i 1.02208i 0.859556 + 0.511042i \(0.170740\pi\)
−0.859556 + 0.511042i \(0.829260\pi\)
\(644\) −236.762 + 271.790i −0.367642 + 0.422034i
\(645\) 113.871 0.176545
\(646\) 613.497 708.014i 0.949686 1.09600i
\(647\) 236.547 152.020i 0.365607 0.234961i −0.344919 0.938632i \(-0.612094\pi\)
0.710526 + 0.703671i \(0.248457\pi\)
\(648\) −3.62274 25.1967i −0.00559065 0.0388839i
\(649\) −232.189 + 106.037i −0.357765 + 0.163386i
\(650\) −71.7066 + 498.730i −0.110318 + 0.767277i
\(651\) −66.1597 225.319i −0.101628 0.346112i
\(652\) 449.663 + 288.981i 0.689667 + 0.443222i
\(653\) −195.591 + 428.285i −0.299527 + 0.655872i −0.998226 0.0595436i \(-0.981035\pi\)
0.698699 + 0.715416i \(0.253763\pi\)
\(654\) 38.5206 131.189i 0.0589000 0.200595i
\(655\) 129.555 112.260i 0.197794 0.171389i
\(656\) −159.307 183.850i −0.242846 0.280260i
\(657\) 69.8972 + 20.5237i 0.106388 + 0.0312385i
\(658\) −575.701 262.914i −0.874925 0.399565i
\(659\) 478.963 745.282i 0.726803 1.13093i −0.259461 0.965754i \(-0.583545\pi\)
0.986264 0.165175i \(-0.0528188\pi\)
\(660\) −84.6076 + 24.8430i −0.128193 + 0.0376410i
\(661\) 1097.64 + 157.817i 1.66058 + 0.238755i 0.907765 0.419479i \(-0.137787\pi\)
0.752813 + 0.658234i \(0.228696\pi\)
\(662\) 162.531 + 355.894i 0.245516 + 0.537605i
\(663\) −517.222 + 74.3652i −0.780123 + 0.112165i
\(664\) 50.6152 + 78.7587i 0.0762277 + 0.118613i
\(665\) 243.396 + 210.904i 0.366009 + 0.317148i
\(666\) 142.760i 0.214354i
\(667\) −149.625 514.576i −0.224325 0.771478i
\(668\) 215.877 0.323170
\(669\) 195.715 225.867i 0.292549 0.337619i
\(670\) −126.456 + 81.2686i −0.188741 + 0.121296i
\(671\) 121.653 + 846.115i 0.181301 + 1.26098i
\(672\) −69.8379 + 31.8939i −0.103925 + 0.0474612i
\(673\) 1.01670 7.07130i 0.00151070 0.0105071i −0.989052 0.147566i \(-0.952856\pi\)
0.990563 + 0.137059i \(0.0437651\pi\)
\(674\) 129.640 + 441.512i 0.192344 + 0.655062i
\(675\) −102.631 65.9571i −0.152046 0.0977142i
\(676\) 50.9088 111.475i 0.0753088 0.164903i
\(677\) −17.8802 + 60.8945i −0.0264110 + 0.0899476i −0.971644 0.236449i \(-0.924016\pi\)
0.945233 + 0.326397i \(0.105835\pi\)
\(678\) 144.052 124.822i 0.212466 0.184103i
\(679\) −586.087 676.380i −0.863162 0.996142i
\(680\) −66.5511 19.5412i −0.0978693 0.0287370i
\(681\) −288.747 131.867i −0.424005 0.193637i
\(682\) 273.007 424.807i 0.400304 0.622885i
\(683\) −645.179 + 189.442i −0.944625 + 0.277367i −0.717547 0.696510i \(-0.754735\pi\)
−0.227078 + 0.973877i \(0.572917\pi\)
\(684\) −197.889 28.4521i −0.289311 0.0415966i
\(685\) −24.4572 53.5538i −0.0357040 0.0781808i
\(686\) −401.443 + 57.7187i −0.585193 + 0.0841381i
\(687\) −11.2998 17.5828i −0.0164480 0.0255936i
\(688\) 161.123 + 139.614i 0.234191 + 0.202928i
\(689\) 1503.14i 2.18162i
\(690\) 45.3695 + 52.6382i 0.0657528 + 0.0762872i
\(691\) 399.989 0.578856 0.289428 0.957200i \(-0.406535\pi\)
0.289428 + 0.957200i \(0.406535\pi\)
\(692\) −138.940 + 160.345i −0.200780 + 0.231712i
\(693\) −408.115 + 262.280i −0.588911 + 0.378470i
\(694\) 106.790 + 742.743i 0.153877 + 1.07024i
\(695\) 9.69108 4.42577i 0.0139440 0.00636801i
\(696\) 16.2443 112.982i 0.0233396 0.162330i
\(697\) −340.643 1160.12i −0.488728 1.66445i
\(698\) −440.862 283.325i −0.631607 0.405909i
\(699\) −9.72527 + 21.2954i −0.0139131 + 0.0304655i
\(700\) −103.664 + 353.047i −0.148091 + 0.504353i
\(701\) −230.230 + 199.496i −0.328431 + 0.284587i −0.803430 0.595399i \(-0.796994\pi\)
0.474999 + 0.879986i \(0.342449\pi\)
\(702\) 73.0245 + 84.2748i 0.104024 + 0.120050i
\(703\) 1075.78 + 315.878i 1.53027 + 0.449329i
\(704\) −150.176 68.5830i −0.213318 0.0974191i
\(705\) −65.9672 + 102.647i −0.0935705 + 0.145599i
\(706\) 294.154 86.3714i 0.416648 0.122339i
\(707\) 86.4111 + 12.4240i 0.122222 + 0.0175729i
\(708\) 17.7994 + 38.9752i 0.0251403 + 0.0550497i
\(709\) 1062.22 152.725i 1.49820 0.215408i 0.656076 0.754695i \(-0.272215\pi\)
0.842122 + 0.539286i \(0.181306\pi\)
\(710\) 25.8689 + 40.2527i 0.0364350 + 0.0566940i
\(711\) 128.116 + 111.013i 0.180192 + 0.156137i
\(712\) 11.6319i 0.0163369i
\(713\) −393.754 57.6704i −0.552249 0.0808841i
\(714\) −381.594 −0.534446
\(715\) 252.958 291.930i 0.353788 0.408293i
\(716\) −186.428 + 119.810i −0.260375 + 0.167333i
\(717\) −14.8025 102.953i −0.0206450 0.143589i
\(718\) −526.338 + 240.370i −0.733061 + 0.334778i
\(719\) −32.5524 + 226.407i −0.0452746 + 0.314892i 0.954582 + 0.297949i \(0.0963024\pi\)
−0.999856 + 0.0169429i \(0.994607\pi\)
\(720\) 4.17014 + 14.2022i 0.00579186 + 0.0197253i
\(721\) −1163.99 748.050i −1.61441 1.03752i
\(722\) −440.180 + 963.860i −0.609668 + 1.33499i
\(723\) 113.998 388.242i 0.157674 0.536987i
\(724\) −215.670 + 186.879i −0.297887 + 0.258120i
\(725\) −358.233 413.423i −0.494115 0.570239i
\(726\) −716.554 210.399i −0.986989 0.289806i
\(727\) 256.992 + 117.364i 0.353496 + 0.161436i 0.584246 0.811577i \(-0.301390\pi\)
−0.230749 + 0.973013i \(0.574118\pi\)
\(728\) 181.831 282.934i 0.249767 0.388645i
\(729\) −25.9063 + 7.60678i −0.0355368 + 0.0104345i
\(730\) −41.9277 6.02830i −0.0574352 0.00825794i
\(731\) 440.189 + 963.880i 0.602174 + 1.31858i
\(732\) 142.029 20.4206i 0.194028 0.0278970i
\(733\) 160.470 + 249.696i 0.218922 + 0.340650i 0.933292 0.359119i \(-0.116923\pi\)
−0.714369 + 0.699769i \(0.753286\pi\)
\(734\) −14.2824 12.3757i −0.0194583 0.0168607i
\(735\) 26.4955i 0.0360483i
\(736\) −0.342113 + 130.107i −0.000464827 + 0.176776i
\(737\) −1778.32 −2.41292
\(738\) −168.971 + 195.003i −0.228958 + 0.264231i
\(739\) 1078.73 693.258i 1.45972 0.938103i 0.461003 0.887399i \(-0.347490\pi\)
0.998714 0.0507039i \(-0.0161465\pi\)
\(740\) −11.8136 82.1655i −0.0159644 0.111035i
\(741\) 796.640 363.813i 1.07509 0.490976i
\(742\) −156.218 + 1086.52i −0.210536 + 1.46431i
\(743\) −328.752 1119.63i −0.442465 1.50690i −0.815321 0.579009i \(-0.803440\pi\)
0.372856 0.927889i \(-0.378379\pi\)
\(744\) −71.3080 45.8269i −0.0958441 0.0615952i
\(745\) 12.4885 27.3460i 0.0167631 0.0367060i
\(746\) −48.5309 + 165.281i −0.0650548 + 0.221556i
\(747\) 75.0457 65.0275i 0.100463 0.0870515i
\(748\) −537.353 620.139i −0.718386 0.829062i
\(749\) −478.302 140.442i −0.638587 0.187506i
\(750\) 133.237 + 60.8471i 0.177649 + 0.0811294i
\(751\) −50.2911 + 78.2545i −0.0669655 + 0.104200i −0.873121 0.487503i \(-0.837908\pi\)
0.806156 + 0.591703i \(0.201544\pi\)
\(752\) −219.194 + 64.3611i −0.291481 + 0.0855865i
\(753\) 346.352 + 49.7978i 0.459962 + 0.0661326i
\(754\) 207.714 + 454.831i 0.275483 + 0.603224i
\(755\) 215.904 31.0422i 0.285965 0.0411156i
\(756\) 44.0261 + 68.5060i 0.0582356 + 0.0906164i
\(757\) −56.5385 48.9909i −0.0746876 0.0647171i 0.616717 0.787185i \(-0.288462\pi\)
−0.691405 + 0.722468i \(0.743008\pi\)
\(758\) 510.499i 0.673482i
\(759\) 114.859 + 814.053i 0.151330 + 1.07253i
\(760\) 116.249 0.152960
\(761\) 542.377 625.937i 0.712717 0.822519i −0.277694 0.960669i \(-0.589570\pi\)
0.990411 + 0.138150i \(0.0441158\pi\)
\(762\) 163.977 105.381i 0.215192 0.138296i
\(763\) 62.2473 + 432.939i 0.0815823 + 0.567417i
\(764\) 200.799 91.7018i 0.262826 0.120029i
\(765\) −10.4698 + 72.8194i −0.0136861 + 0.0951887i
\(766\) 38.6891 + 131.763i 0.0505079 + 0.172014i
\(767\) −157.900 101.476i −0.205867 0.132303i
\(768\) −11.5123 + 25.2085i −0.0149900 + 0.0328235i
\(769\) −393.617 + 1340.54i −0.511855 + 1.74322i 0.145225 + 0.989399i \(0.453610\pi\)
−0.657080 + 0.753821i \(0.728209\pi\)
\(770\) 213.187 184.727i 0.276866 0.239906i
\(771\) 211.792 + 244.421i 0.274698 + 0.317018i
\(772\) −559.324 164.232i −0.724513 0.212736i
\(773\) −476.037 217.399i −0.615831 0.281241i 0.0829752 0.996552i \(-0.473558\pi\)
−0.698806 + 0.715311i \(0.746285\pi\)
\(774\) 122.255 190.232i 0.157952 0.245778i
\(775\) −389.779 + 114.449i −0.502940 + 0.147677i
\(776\) −319.761 45.9746i −0.412063 0.0592457i
\(777\) −189.716 415.419i −0.244164 0.534645i
\(778\) 733.342 105.439i 0.942599 0.135525i
\(779\) 1095.59 + 1704.77i 1.40641 + 2.18841i
\(780\) −49.0032 42.4615i −0.0628246 0.0544378i
\(781\) 566.064i 0.724794i
\(782\) −270.180 + 587.518i −0.345499 + 0.751302i
\(783\) −121.068 −0.154620
\(784\) 32.4854 37.4901i 0.0414354 0.0478190i
\(785\) −60.5828 + 38.9342i −0.0771756 + 0.0495977i
\(786\) −48.4472 336.958i −0.0616377 0.428700i
\(787\) −237.982 + 108.683i −0.302391 + 0.138097i −0.560832 0.827930i \(-0.689519\pi\)
0.258441 + 0.966027i \(0.416791\pi\)
\(788\) 57.6464 400.940i 0.0731553 0.508807i
\(789\) −224.627 765.010i −0.284699 0.969595i
\(790\) −82.9239 53.2920i −0.104967 0.0674582i
\(791\) −253.301 + 554.653i −0.320229 + 0.701204i
\(792\) −49.3342 + 168.017i −0.0622906 + 0.212142i
\(793\) −475.039 + 411.623i −0.599040 + 0.519071i
\(794\) −546.721 630.950i −0.688566 0.794648i
\(795\) 203.054 + 59.6219i 0.255413 + 0.0749961i
\(796\) 502.742 + 229.595i 0.631586 + 0.288436i
\(797\) −321.647 + 500.493i −0.403572 + 0.627971i −0.982248 0.187587i \(-0.939933\pi\)
0.578676 + 0.815558i \(0.303570\pi\)
\(798\) 613.649 180.184i 0.768984 0.225794i
\(799\) −1123.88 161.589i −1.40661 0.202239i
\(800\) 55.1732 + 120.812i 0.0689665 + 0.151015i
\(801\) −12.2119 + 1.75580i −0.0152458 + 0.00219201i
\(802\) 109.904 + 171.014i 0.137037 + 0.213234i
\(803\) −378.721 328.164i −0.471633 0.408672i
\(804\) 298.509i 0.371279i
\(805\) −201.973 92.8805i −0.250898 0.115379i
\(806\) 371.316 0.460690
\(807\) −31.3271 + 36.1534i −0.0388192 + 0.0447998i
\(808\) 26.5091 17.0363i 0.0328082 0.0210846i
\(809\) −44.9502 312.635i −0.0555626 0.386447i −0.998560 0.0536464i \(-0.982916\pi\)
0.942997 0.332800i \(-0.107993\pi\)
\(810\) 14.2809 6.52187i 0.0176307 0.00805169i
\(811\) 13.6402 94.8695i 0.0168190 0.116978i −0.979682 0.200555i \(-0.935725\pi\)
0.996501 + 0.0835769i \(0.0266344\pi\)
\(812\) 102.873 + 350.355i 0.126691 + 0.431471i
\(813\) −25.9201 16.6578i −0.0318820 0.0204893i
\(814\) 407.955 893.297i 0.501173 1.09742i
\(815\) −92.8752 + 316.304i −0.113957 + 0.388103i
\(816\) −104.096 + 90.1998i −0.127569 + 0.110539i
\(817\) −1163.01 1342.18i −1.42351 1.64282i
\(818\) −500.174 146.864i −0.611460 0.179541i
\(819\) −324.489 148.189i −0.396201 0.180939i
\(820\) 81.1144 126.216i 0.0989200 0.153923i
\(821\) 270.108 79.3108i 0.328999 0.0966027i −0.113062 0.993588i \(-0.536066\pi\)
0.442060 + 0.896985i \(0.354248\pi\)
\(822\) −115.724 16.6386i −0.140784 0.0202417i
\(823\) −250.679 548.911i −0.304592 0.666964i 0.694002 0.719973i \(-0.255846\pi\)
−0.998594 + 0.0530093i \(0.983119\pi\)
\(824\) −494.349 + 71.0767i −0.599938 + 0.0862581i
\(825\) 453.717 + 705.997i 0.549960 + 0.855754i
\(826\) −103.589 89.7606i −0.125411 0.108669i
\(827\) 249.338i 0.301497i 0.988572 + 0.150749i \(0.0481684\pi\)
−0.988572 + 0.150749i \(0.951832\pi\)
\(828\) 136.647 19.2802i 0.165032 0.0232853i
\(829\) −746.897 −0.900962 −0.450481 0.892786i \(-0.648747\pi\)
−0.450481 + 0.892786i \(0.648747\pi\)
\(830\) −37.8114 + 43.6367i −0.0455560 + 0.0525744i
\(831\) −131.215 + 84.3268i −0.157900 + 0.101476i
\(832\) −17.2768 120.163i −0.0207654 0.144426i
\(833\) 224.275 102.423i 0.269238 0.122957i
\(834\) 3.01092 20.9414i 0.00361022 0.0251096i
\(835\) 37.5100 + 127.747i 0.0449221 + 0.152991i
\(836\) 1156.95 + 743.526i 1.38391 + 0.889385i
\(837\) −37.3482 + 81.7812i −0.0446215 + 0.0977075i
\(838\) 49.6814 169.199i 0.0592857 0.201909i
\(839\) 539.470 467.454i 0.642992 0.557156i −0.271156 0.962535i \(-0.587406\pi\)
0.914149 + 0.405379i \(0.132861\pi\)
\(840\) −31.0082 35.7854i −0.0369146 0.0426017i
\(841\) 286.058 + 83.9942i 0.340140 + 0.0998741i
\(842\) −454.039 207.353i −0.539239 0.246262i
\(843\) −53.3083 + 82.9494i −0.0632364 + 0.0983978i
\(844\) −268.351 + 78.7950i −0.317951 + 0.0933590i
\(845\) 74.8117 + 10.7563i 0.0885346 + 0.0127294i
\(846\) 100.657 + 220.408i 0.118980 + 0.260530i
\(847\) 2364.71 339.994i 2.79187 0.401410i
\(848\) 214.212 + 333.321i 0.252609 + 0.393067i
\(849\) 373.532 + 323.667i 0.439967 + 0.381234i
\(850\) 660.119i 0.776610i
\(851\) −773.921 2.03500i −0.909425 0.00239131i
\(852\) 95.0192 0.111525
\(853\) 687.963 793.952i 0.806522 0.930776i −0.192198 0.981356i \(-0.561562\pi\)
0.998720 + 0.0505802i \(0.0161070\pi\)
\(854\) −386.154 + 248.166i −0.452170 + 0.290592i
\(855\) −17.5476 122.046i −0.0205235 0.142744i
\(856\) −163.674 + 74.7476i −0.191208 + 0.0873220i
\(857\) 120.755 839.869i 0.140904 0.980010i −0.789572 0.613658i \(-0.789697\pi\)
0.930476 0.366352i \(-0.119394\pi\)
\(858\) −216.113 736.012i −0.251880 0.857823i
\(859\) 1161.24 + 746.283i 1.35185 + 0.868781i 0.997790 0.0664426i \(-0.0211649\pi\)
0.354059 + 0.935223i \(0.384801\pi\)
\(860\) −54.6218 + 119.605i −0.0635137 + 0.139076i
\(861\) 232.549 791.989i 0.270092 0.919848i
\(862\) 503.878 436.613i 0.584545 0.506511i
\(863\) 953.945 + 1100.91i 1.10538 + 1.27568i 0.958053 + 0.286591i \(0.0925221\pi\)
0.147329 + 0.989088i \(0.452932\pi\)
\(864\) 28.2032 + 8.28121i 0.0326426 + 0.00958474i
\(865\) −119.027 54.3578i −0.137603 0.0628414i
\(866\) −77.4335 + 120.489i −0.0894152 + 0.139133i
\(867\) −176.577 + 51.8476i −0.203664 + 0.0598011i
\(868\) 268.400 + 38.5901i 0.309217 + 0.0444586i
\(869\) −484.431 1060.76i −0.557458 1.22066i
\(870\) 69.6805 10.0185i 0.0800925 0.0115156i
\(871\) −706.965 1100.06i −0.811671 1.26298i
\(872\) 119.317 + 103.389i 0.136832 + 0.118565i
\(873\) 342.645i 0.392491i
\(874\) 157.063 1072.37i 0.179706 1.22697i
\(875\) −468.567 −0.535505
\(876\) −55.0854 + 63.5719i −0.0628829 + 0.0725707i
\(877\) −892.868 + 573.812i −1.01809 + 0.654289i −0.939476 0.342616i \(-0.888687\pi\)
−0.0786182 + 0.996905i \(0.525051\pi\)
\(878\) −94.6513 658.314i −0.107803 0.749788i
\(879\) 230.891 105.444i 0.262675 0.119959i
\(880\) 14.4906 100.785i 0.0164666 0.114528i
\(881\) 479.331 + 1632.45i 0.544076 + 1.85295i 0.521577 + 0.853204i \(0.325344\pi\)
0.0224987 + 0.999747i \(0.492838\pi\)
\(882\) −44.2631 28.4462i −0.0501849 0.0322519i
\(883\) 170.901 374.220i 0.193545 0.423805i −0.787833 0.615889i \(-0.788797\pi\)
0.981379 + 0.192083i \(0.0615244\pi\)
\(884\) 169.991 578.937i 0.192298 0.654906i
\(885\) −19.9711 + 17.3051i −0.0225663 + 0.0195538i
\(886\) 505.853 + 583.786i 0.570940 + 0.658900i
\(887\) −658.613 193.386i −0.742518 0.218023i −0.111471 0.993768i \(-0.535556\pi\)
−0.631047 + 0.775745i \(0.717374\pi\)
\(888\) −149.948 68.4791i −0.168861 0.0771161i
\(889\) −337.115 + 524.561i −0.379207 + 0.590057i
\(890\) 6.88325 2.02110i 0.00773399 0.00227090i
\(891\) 183.842 + 26.4324i 0.206332 + 0.0296660i
\(892\) 143.360 + 313.914i 0.160717 + 0.351921i
\(893\) 1883.63 270.825i 2.10933 0.303276i
\(894\) −32.2760 50.2224i −0.0361029 0.0561772i
\(895\) −103.292 89.5028i −0.115410 0.100003i
\(896\) 88.6533i 0.0989434i
\(897\) −457.906 + 394.674i −0.510486 + 0.439994i
\(898\) −501.825 −0.558826
\(899\) −263.998 + 304.670i −0.293657 + 0.338899i
\(900\) 118.508 76.1607i 0.131676 0.0846230i
\(901\) 280.261 + 1949.26i 0.311055 + 2.16344i
\(902\) 1614.55 737.341i 1.78997 0.817451i
\(903\) −102.949 + 716.025i −0.114008 + 0.792941i
\(904\) 62.0079 + 211.180i 0.0685929 + 0.233606i
\(905\) −148.061 95.1532i −0.163604 0.105142i
\(906\) 179.940 394.014i 0.198609 0.434894i
\(907\) 5.35485 18.2370i 0.00590392 0.0201069i −0.956488 0.291771i \(-0.905756\pi\)
0.962392 + 0.271664i \(0.0875738\pi\)
\(908\) 277.013 240.033i 0.305080 0.264353i
\(909\) −21.8873 25.2593i −0.0240785 0.0277880i
\(910\) 199.023 + 58.4383i 0.218706 + 0.0642179i
\(911\) −402.754 183.932i −0.442101 0.201901i 0.181912 0.983315i \(-0.441771\pi\)
−0.624013 + 0.781414i \(0.714499\pi\)
\(912\) 124.808 194.205i 0.136851 0.212944i
\(913\) −655.410 + 192.446i −0.717864 + 0.210784i
\(914\) 251.125 + 36.1064i 0.274754 + 0.0395037i
\(915\) 36.7624 + 80.4984i 0.0401775 + 0.0879764i
\(916\) 23.8884 3.43464i 0.0260791 0.00374961i
\(917\) 588.765 + 916.136i 0.642056 + 0.999058i
\(918\) 110.411 + 95.6714i 0.120273 + 0.104217i
\(919\) 1415.29i 1.54004i −0.638021 0.770019i \(-0.720247\pi\)
0.638021 0.770019i \(-0.279753\pi\)
\(920\) −77.0515 + 22.4044i −0.0837516 + 0.0243527i
\(921\) 870.515 0.945184
\(922\) −634.308 + 732.031i −0.687970 + 0.793960i
\(923\) −350.163 + 225.036i −0.379375 + 0.243810i
\(924\) −79.7215 554.475i −0.0862787 0.600081i
\(925\) −718.632 + 328.188i −0.776900 + 0.354798i
\(926\) 175.599 1221.32i 0.189632 1.31892i
\(927\) 149.242 + 508.270i 0.160994 + 0.548296i
\(928\) 110.879 + 71.2574i 0.119481 + 0.0767860i
\(929\) 371.825 814.183i 0.400242 0.876408i −0.597004 0.802238i \(-0.703642\pi\)
0.997246 0.0741691i \(-0.0236305\pi\)
\(930\) 14.7282 50.1598i 0.0158368 0.0539352i
\(931\) −312.298 + 270.608i −0.335444 + 0.290664i
\(932\) −17.7026 20.4299i −0.0189942 0.0219205i
\(933\) −892.994 262.207i −0.957122 0.281036i
\(934\) −251.087 114.667i −0.268829 0.122770i
\(935\) 273.604 425.736i 0.292624 0.455332i
\(936\) −123.547 + 36.2766i −0.131994 + 0.0387570i
\(937\) 273.343 + 39.3008i 0.291721 + 0.0419432i 0.286622 0.958044i \(-0.407468\pi\)
0.00509944 + 0.999987i \(0.498377\pi\)
\(938\) −396.692 868.634i −0.422913 0.926049i
\(939\) −608.904 + 87.5472i −0.648460 + 0.0932345i
\(940\) −76.1724 118.527i −0.0810345 0.126092i
\(941\) 177.280 + 153.614i 0.188395 + 0.163245i 0.743952 0.668234i \(-0.232949\pi\)
−0.555557 + 0.831479i \(0.687495\pi\)
\(942\) 143.010i 0.151815i
\(943\) −1054.73 918.793i −1.11848 0.974330i
\(944\) −49.4757 −0.0524107
\(945\) −32.8892 + 37.9562i −0.0348034 + 0.0401653i
\(946\) −1308.60 + 840.987i −1.38330 + 0.888993i
\(947\) 217.898 + 1515.51i 0.230092 + 1.60033i 0.697699 + 0.716391i \(0.254207\pi\)
−0.467606 + 0.883937i \(0.654883\pi\)
\(948\) −178.058 + 81.3164i −0.187825 + 0.0857768i
\(949\) 52.4409 364.734i 0.0552591 0.384336i
\(950\) −311.699 1061.55i −0.328104 1.11742i
\(951\) −218.970 140.723i −0.230252 0.147974i
\(952\) 183.043 400.808i 0.192272 0.421017i
\(953\) 122.596 417.524i 0.128642 0.438116i −0.869831 0.493350i \(-0.835772\pi\)
0.998473 + 0.0552339i \(0.0175905\pi\)
\(954\) 317.607 275.208i 0.332921 0.288478i
\(955\) 89.1553 + 102.891i 0.0933564 + 0.107739i
\(956\) 115.238 + 33.8369i 0.120542 + 0.0353942i
\(957\) 757.560 + 345.966i 0.791599 + 0.361511i
\(958\) 50.6430 78.8021i 0.0528633 0.0822569i
\(959\) 358.859 105.371i 0.374201 0.109875i
\(960\) −16.9176 2.43239i −0.0176226 0.00253374i
\(961\) −274.850 601.838i −0.286004 0.626262i
\(962\) 714.768 102.768i 0.743002 0.106828i
\(963\) 103.181 + 160.553i 0.107145 + 0.166722i
\(964\) 353.108 + 305.970i 0.366295 + 0.317396i
\(965\) 359.521i 0.372560i
\(966\) −372.008 + 237.695i −0.385101 + 0.246061i
\(967\) 1817.11 1.87912 0.939558 0.342389i \(-0.111236\pi\)
0.939558 + 0.342389i \(0.111236\pi\)
\(968\) 564.710 651.710i 0.583378 0.673255i
\(969\) 965.242 620.323i 0.996122 0.640169i
\(970\) −28.3544 197.209i −0.0292314 0.203309i
\(971\) −32.2682 + 14.7364i −0.0332319 + 0.0151765i −0.431962 0.901892i \(-0.642178\pi\)
0.398730 + 0.917068i \(0.369451\pi\)
\(972\) 4.43694 30.8596i 0.00456475 0.0317485i
\(973\) 19.0678 + 64.9390i 0.0195969 + 0.0667410i
\(974\) −111.048 71.3661i −0.114012 0.0732712i
\(975\) −256.352 + 561.332i −0.262925 + 0.575726i
\(976\) −46.6794 + 158.975i −0.0478272 + 0.162885i
\(977\) 713.384 618.151i 0.730178 0.632703i −0.208291 0.978067i \(-0.566790\pi\)
0.938469 + 0.345364i \(0.112245\pi\)
\(978\) 428.701 + 494.748i 0.438345 + 0.505877i
\(979\) 81.4311 + 23.9103i 0.0831779 + 0.0244232i
\(980\) 27.8296 + 12.7094i 0.0283976 + 0.0129687i
\(981\) 90.5337 140.873i 0.0922872 0.143602i
\(982\) 685.096 201.162i 0.697654 0.204850i
\(983\) −476.921 68.5709i −0.485169 0.0697568i −0.104610 0.994513i \(-0.533359\pi\)
−0.380559 + 0.924757i \(0.624268\pi\)
\(984\) −123.770 271.018i −0.125782 0.275425i
\(985\) 247.276 35.5529i 0.251041 0.0360943i
\(986\) 354.165 + 551.092i 0.359194 + 0.558917i
\(987\) −585.807 507.605i −0.593523 0.514291i
\(988\) 1011.27i 1.02355i
\(989\) 1029.53 + 665.471i 1.04098 + 0.672873i
\(990\) −107.997 −0.109088
\(991\) −511.694 + 590.527i −0.516341 + 0.595890i −0.952711 0.303878i \(-0.901719\pi\)
0.436370 + 0.899767i \(0.356264\pi\)
\(992\) 82.3394 52.9163i 0.0830034 0.0533430i
\(993\) 68.1948 + 474.305i 0.0686755 + 0.477649i
\(994\) −276.498 + 126.272i −0.278167 + 0.127035i
\(995\) −48.5101 + 337.395i −0.0487539 + 0.339091i
\(996\) 32.3039 + 110.017i 0.0324336 + 0.110459i
\(997\) −366.595 235.597i −0.367698 0.236305i 0.343723 0.939071i \(-0.388312\pi\)
−0.711421 + 0.702766i \(0.751948\pi\)
\(998\) −212.185 + 464.619i −0.212610 + 0.465551i
\(999\) −49.2594 + 167.762i −0.0493087 + 0.167930i
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 138.3.h.a.7.1 80
3.2 odd 2 414.3.l.b.145.6 80
23.10 odd 22 inner 138.3.h.a.79.1 yes 80
69.56 even 22 414.3.l.b.217.6 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.3.h.a.7.1 80 1.1 even 1 trivial
138.3.h.a.79.1 yes 80 23.10 odd 22 inner
414.3.l.b.145.6 80 3.2 odd 2
414.3.l.b.217.6 80 69.56 even 22