Properties

Label 105.3.v.a.88.12
Level $105$
Weight $3$
Character 105.88
Analytic conductor $2.861$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(37,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.v (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: \(2.86104277578\)
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 88.12
Character \(\chi\) \(=\) 105.88
Dual form 105.3.v.a.37.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.13226 + 0.571337i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.756006 + 0.436480i) q^{4} +(2.78563 - 4.15214i) q^{5} +3.82346 q^{6} +(2.73668 + 6.44287i) q^{7} +(-4.88107 - 4.88107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(2.13226 + 0.571337i) q^{2} +(1.67303 - 0.448288i) q^{3} +(0.756006 + 0.436480i) q^{4} +(2.78563 - 4.15214i) q^{5} +3.82346 q^{6} +(2.73668 + 6.44287i) q^{7} +(-4.88107 - 4.88107i) q^{8} +(2.59808 - 1.50000i) q^{9} +(8.31195 - 7.26192i) q^{10} +(-4.69282 + 8.12820i) q^{11} +(1.46049 + 0.391337i) q^{12} +(-0.405222 - 0.405222i) q^{13} +(2.15427 + 15.3014i) q^{14} +(2.79909 - 8.19543i) q^{15} +(-9.36489 - 16.2205i) q^{16} +(2.82961 + 10.5602i) q^{17} +(6.39678 - 1.71401i) q^{18} +(-23.8500 + 13.7698i) q^{19} +(3.91828 - 1.92317i) q^{20} +(7.46682 + 9.55231i) q^{21} +(-14.6503 + 14.6503i) q^{22} +(1.02354 - 3.81990i) q^{23} +(-10.3543 - 5.97806i) q^{24} +(-9.48058 - 23.1326i) q^{25} +(-0.632520 - 1.09556i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-0.743235 + 6.06535i) q^{28} -34.6601i q^{29} +(10.6507 - 15.8756i) q^{30} +(-11.8284 + 20.4874i) q^{31} +(-3.55465 - 13.2661i) q^{32} +(-4.20747 + 15.7025i) q^{33} +24.1338i q^{34} +(34.3751 + 6.58431i) q^{35} +2.61888 q^{36} +(25.6130 + 6.86297i) q^{37} +(-58.7215 + 15.7344i) q^{38} +(-0.859605 - 0.496293i) q^{39} +(-33.8637 + 6.67007i) q^{40} +54.6731 q^{41} +(10.4636 + 24.6341i) q^{42} +(-47.3942 - 47.3942i) q^{43} +(-7.09560 + 4.09664i) q^{44} +(1.00905 - 14.9660i) q^{45} +(4.36491 - 7.56024i) q^{46} +(-16.9830 - 4.55058i) q^{47} +(-22.9392 - 22.9392i) q^{48} +(-34.0211 + 35.2642i) q^{49} +(-6.99854 - 54.7414i) q^{50} +(9.46805 + 16.3992i) q^{51} +(-0.129479 - 0.483221i) q^{52} +(14.7503 - 3.95234i) q^{53} +(9.93365 - 5.73520i) q^{54} +(20.6770 + 42.1274i) q^{55} +(18.0901 - 44.8060i) q^{56} +(-33.7289 + 33.7289i) q^{57} +(19.8026 - 73.9044i) q^{58} +(90.3630 + 52.1711i) q^{59} +(5.69327 - 4.97405i) q^{60} +(-12.5803 - 21.7897i) q^{61} +(-36.9264 + 36.9264i) q^{62} +(16.7744 + 12.6340i) q^{63} +44.6014i q^{64} +(-2.81133 + 0.553743i) q^{65} +(-17.9428 + 31.0779i) q^{66} +(0.364564 + 1.36057i) q^{67} +(-2.47014 + 9.21867i) q^{68} -6.84966i q^{69} +(69.5348 + 33.6792i) q^{70} +86.5935 q^{71} +(-20.0030 - 5.35978i) q^{72} +(-84.9471 + 22.7615i) q^{73} +(50.6924 + 29.2673i) q^{74} +(-26.2314 - 34.4516i) q^{75} -24.0409 q^{76} +(-65.2117 - 7.99089i) q^{77} +(-1.54935 - 1.54935i) q^{78} +(128.353 - 74.1049i) q^{79} +(-93.4368 - 6.29977i) q^{80} +(4.50000 - 7.79423i) q^{81} +(116.577 + 31.2368i) q^{82} +(35.5711 + 35.5711i) q^{83} +(1.47557 + 10.4807i) q^{84} +(51.7299 + 17.6679i) q^{85} +(-73.9787 - 128.135i) q^{86} +(-15.5377 - 57.9875i) q^{87} +(62.5803 - 16.7683i) q^{88} +(130.143 - 75.1382i) q^{89} +(10.7022 - 31.3349i) q^{90} +(1.50183 - 3.71975i) q^{91} +(2.44111 - 2.44111i) q^{92} +(-10.6050 + 39.5786i) q^{93} +(-33.6122 - 19.4060i) q^{94} +(-9.26295 + 137.386i) q^{95} +(-11.8941 - 20.6011i) q^{96} +(74.8462 - 74.8462i) q^{97} +(-92.6896 + 55.7549i) q^{98} +28.1569i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8} - 16 q^{10} + 16 q^{11} - 48 q^{15} + 80 q^{16} + 56 q^{17} + 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 288 q^{26} - 380 q^{28} - 48 q^{30} - 136 q^{31} - 48 q^{32} - 72 q^{33} + 76 q^{35} + 384 q^{36} - 28 q^{37} - 68 q^{38} + 164 q^{40} + 128 q^{41} - 12 q^{42} + 344 q^{43} + 240 q^{46} + 412 q^{47} - 288 q^{48} - 72 q^{50} - 24 q^{51} + 388 q^{52} - 40 q^{53} - 8 q^{55} - 864 q^{56} - 192 q^{57} + 56 q^{58} - 180 q^{60} - 216 q^{61} - 912 q^{62} - 84 q^{63} + 20 q^{65} - 72 q^{66} - 368 q^{67} - 492 q^{68} + 416 q^{70} + 784 q^{71} + 36 q^{72} - 316 q^{73} + 96 q^{75} - 32 q^{76} + 844 q^{77} + 624 q^{78} + 908 q^{80} + 288 q^{81} + 556 q^{82} + 1408 q^{83} - 536 q^{85} + 1024 q^{86} + 108 q^{87} + 372 q^{88} + 216 q^{90} - 1064 q^{91} - 1704 q^{92} + 144 q^{93} + 260 q^{95} + 352 q^{97} + 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13226 + 0.571337i 1.06613 + 0.285669i 0.748902 0.662681i \(-0.230581\pi\)
0.317228 + 0.948349i \(0.397248\pi\)
\(3\) 1.67303 0.448288i 0.557678 0.149429i
\(4\) 0.756006 + 0.436480i 0.189001 + 0.109120i
\(5\) 2.78563 4.15214i 0.557125 0.830429i
\(6\) 3.82346 0.637244
\(7\) 2.73668 + 6.44287i 0.390955 + 0.920410i
\(8\) −4.88107 4.88107i −0.610133 0.610133i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) 8.31195 7.26192i 0.831195 0.726192i
\(11\) −4.69282 + 8.12820i −0.426620 + 0.738927i −0.996570 0.0827519i \(-0.973629\pi\)
0.569950 + 0.821679i \(0.306962\pi\)
\(12\) 1.46049 + 0.391337i 0.121708 + 0.0326114i
\(13\) −0.405222 0.405222i −0.0311709 0.0311709i 0.691350 0.722520i \(-0.257016\pi\)
−0.722520 + 0.691350i \(0.757016\pi\)
\(14\) 2.15427 + 15.3014i 0.153877 + 1.09296i
\(15\) 2.79909 8.19543i 0.186606 0.546362i
\(16\) −9.36489 16.2205i −0.585306 1.01378i
\(17\) 2.82961 + 10.5602i 0.166448 + 0.621191i 0.997851 + 0.0655217i \(0.0208712\pi\)
−0.831404 + 0.555669i \(0.812462\pi\)
\(18\) 6.39678 1.71401i 0.355377 0.0952229i
\(19\) −23.8500 + 13.7698i −1.25526 + 0.724725i −0.972149 0.234362i \(-0.924700\pi\)
−0.283111 + 0.959087i \(0.591367\pi\)
\(20\) 3.91828 1.92317i 0.195914 0.0961587i
\(21\) 7.46682 + 9.55231i 0.355563 + 0.454872i
\(22\) −14.6503 + 14.6503i −0.665921 + 0.665921i
\(23\) 1.02354 3.81990i 0.0445017 0.166083i −0.940099 0.340902i \(-0.889268\pi\)
0.984601 + 0.174819i \(0.0559342\pi\)
\(24\) −10.3543 5.97806i −0.431430 0.249086i
\(25\) −9.48058 23.1326i −0.379223 0.925305i
\(26\) −0.632520 1.09556i −0.0243277 0.0421368i
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −0.743235 + 6.06535i −0.0265441 + 0.216620i
\(29\) 34.6601i 1.19518i −0.801803 0.597588i \(-0.796126\pi\)
0.801803 0.597588i \(-0.203874\pi\)
\(30\) 10.6507 15.8756i 0.355025 0.529186i
\(31\) −11.8284 + 20.4874i −0.381561 + 0.660883i −0.991286 0.131730i \(-0.957947\pi\)
0.609724 + 0.792613i \(0.291280\pi\)
\(32\) −3.55465 13.2661i −0.111083 0.414566i
\(33\) −4.20747 + 15.7025i −0.127499 + 0.475833i
\(34\) 24.1338i 0.709819i
\(35\) 34.3751 + 6.58431i 0.982145 + 0.188123i
\(36\) 2.61888 0.0727467
\(37\) 25.6130 + 6.86297i 0.692242 + 0.185486i 0.587753 0.809040i \(-0.300013\pi\)
0.104489 + 0.994526i \(0.466679\pi\)
\(38\) −58.7215 + 15.7344i −1.54530 + 0.414063i
\(39\) −0.859605 0.496293i −0.0220411 0.0127255i
\(40\) −33.8637 + 6.67007i −0.846593 + 0.166752i
\(41\) 54.6731 1.33349 0.666745 0.745286i \(-0.267687\pi\)
0.666745 + 0.745286i \(0.267687\pi\)
\(42\) 10.4636 + 24.6341i 0.249134 + 0.586526i
\(43\) −47.3942 47.3942i −1.10219 1.10219i −0.994146 0.108044i \(-0.965541\pi\)
−0.108044 0.994146i \(-0.534459\pi\)
\(44\) −7.09560 + 4.09664i −0.161264 + 0.0931055i
\(45\) 1.00905 14.9660i 0.0224234 0.332578i
\(46\) 4.36491 7.56024i 0.0948893 0.164353i
\(47\) −16.9830 4.55058i −0.361340 0.0968208i 0.0735811 0.997289i \(-0.476557\pi\)
−0.434921 + 0.900468i \(0.643224\pi\)
\(48\) −22.9392 22.9392i −0.477900 0.477900i
\(49\) −34.0211 + 35.2642i −0.694308 + 0.719678i
\(50\) −6.99854 54.7414i −0.139971 1.09483i
\(51\) 9.46805 + 16.3992i 0.185648 + 0.321552i
\(52\) −0.129479 0.483221i −0.00248997 0.00929271i
\(53\) 14.7503 3.95234i 0.278308 0.0745725i −0.116965 0.993136i \(-0.537317\pi\)
0.395273 + 0.918564i \(0.370650\pi\)
\(54\) 9.93365 5.73520i 0.183957 0.106207i
\(55\) 20.6770 + 42.1274i 0.375946 + 0.765952i
\(56\) 18.0901 44.8060i 0.323038 0.800108i
\(57\) −33.7289 + 33.7289i −0.591735 + 0.591735i
\(58\) 19.8026 73.9044i 0.341424 1.27421i
\(59\) 90.3630 + 52.1711i 1.53158 + 0.884256i 0.999289 + 0.0376927i \(0.0120008\pi\)
0.532288 + 0.846564i \(0.321333\pi\)
\(60\) 5.69327 4.97405i 0.0948878 0.0829008i
\(61\) −12.5803 21.7897i −0.206235 0.357209i 0.744291 0.667856i \(-0.232788\pi\)
−0.950525 + 0.310647i \(0.899454\pi\)
\(62\) −36.9264 + 36.9264i −0.595587 + 0.595587i
\(63\) 16.7744 + 12.6340i 0.266261 + 0.200540i
\(64\) 44.6014i 0.696897i
\(65\) −2.81133 + 0.553743i −0.0432513 + 0.00851912i
\(66\) −17.9428 + 31.0779i −0.271861 + 0.470877i
\(67\) 0.364564 + 1.36057i 0.00544126 + 0.0203071i 0.968593 0.248651i \(-0.0799873\pi\)
−0.963152 + 0.268958i \(0.913321\pi\)
\(68\) −2.47014 + 9.21867i −0.0363255 + 0.135569i
\(69\) 6.84966i 0.0992704i
\(70\) 69.5348 + 33.6792i 0.993354 + 0.481132i
\(71\) 86.5935 1.21963 0.609813 0.792545i \(-0.291244\pi\)
0.609813 + 0.792545i \(0.291244\pi\)
\(72\) −20.0030 5.35978i −0.277819 0.0744414i
\(73\) −84.9471 + 22.7615i −1.16366 + 0.311802i −0.788427 0.615129i \(-0.789104\pi\)
−0.375233 + 0.926931i \(0.622437\pi\)
\(74\) 50.6924 + 29.2673i 0.685033 + 0.395504i
\(75\) −26.2314 34.4516i −0.349752 0.459355i
\(76\) −24.0409 −0.316328
\(77\) −65.2117 7.99089i −0.846905 0.103778i
\(78\) −1.54935 1.54935i −0.0198635 0.0198635i
\(79\) 128.353 74.1049i 1.62473 0.938036i 0.639095 0.769128i \(-0.279309\pi\)
0.985632 0.168909i \(-0.0540243\pi\)
\(80\) −93.4368 6.29977i −1.16796 0.0787472i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 116.577 + 31.2368i 1.42167 + 0.380936i
\(83\) 35.5711 + 35.5711i 0.428567 + 0.428567i 0.888140 0.459573i \(-0.151998\pi\)
−0.459573 + 0.888140i \(0.651998\pi\)
\(84\) 1.47557 + 10.4807i 0.0175663 + 0.124770i
\(85\) 51.7299 + 17.6679i 0.608587 + 0.207858i
\(86\) −73.9787 128.135i −0.860217 1.48994i
\(87\) −15.5377 57.9875i −0.178594 0.666523i
\(88\) 62.5803 16.7683i 0.711139 0.190549i
\(89\) 130.143 75.1382i 1.46228 0.844250i 0.463166 0.886271i \(-0.346713\pi\)
0.999117 + 0.0420218i \(0.0133799\pi\)
\(90\) 10.7022 31.3349i 0.118913 0.348166i
\(91\) 1.50183 3.71975i 0.0165036 0.0408764i
\(92\) 2.44111 2.44111i 0.0265338 0.0265338i
\(93\) −10.6050 + 39.5786i −0.114033 + 0.425576i
\(94\) −33.6122 19.4060i −0.357577 0.206447i
\(95\) −9.26295 + 137.386i −0.0975047 + 1.44617i
\(96\) −11.8941 20.6011i −0.123897 0.214595i
\(97\) 74.8462 74.8462i 0.771610 0.771610i −0.206778 0.978388i \(-0.566298\pi\)
0.978388 + 0.206778i \(0.0662977\pi\)
\(98\) −92.6896 + 55.7549i −0.945812 + 0.568928i
\(99\) 28.1569i 0.284413i
\(100\) 2.92956 21.6265i 0.0292956 0.216265i
\(101\) −65.3840 + 113.248i −0.647366 + 1.12127i 0.336384 + 0.941725i \(0.390796\pi\)
−0.983750 + 0.179546i \(0.942537\pi\)
\(102\) 10.8189 + 40.3767i 0.106068 + 0.395850i
\(103\) 9.95292 37.1448i 0.0966303 0.360629i −0.900631 0.434584i \(-0.856895\pi\)
0.997262 + 0.0739549i \(0.0235621\pi\)
\(104\) 3.95583i 0.0380368i
\(105\) 60.4623 4.39417i 0.575832 0.0418492i
\(106\) 33.7097 0.318016
\(107\) −193.691 51.8993i −1.81019 0.485040i −0.814701 0.579881i \(-0.803099\pi\)
−0.995492 + 0.0948408i \(0.969766\pi\)
\(108\) 4.38147 1.17401i 0.0405692 0.0108705i
\(109\) −126.264 72.8985i −1.15838 0.668793i −0.207468 0.978242i \(-0.566522\pi\)
−0.950916 + 0.309449i \(0.899856\pi\)
\(110\) 20.0198 + 101.640i 0.181998 + 0.924001i
\(111\) 45.9279 0.413765
\(112\) 78.8776 104.727i 0.704264 0.935063i
\(113\) −50.0612 50.0612i −0.443020 0.443020i 0.450006 0.893026i \(-0.351422\pi\)
−0.893026 + 0.450006i \(0.851422\pi\)
\(114\) −91.1894 + 52.6482i −0.799907 + 0.461827i
\(115\) −13.0096 14.8907i −0.113127 0.129484i
\(116\) 15.1284 26.2032i 0.130418 0.225890i
\(117\) −1.66063 0.444964i −0.0141934 0.00380311i
\(118\) 162.870 + 162.870i 1.38026 + 1.38026i
\(119\) −60.2945 + 47.1308i −0.506677 + 0.396058i
\(120\) −53.6650 + 26.3399i −0.447208 + 0.219499i
\(121\) 16.4549 + 28.5007i 0.135991 + 0.235543i
\(122\) −14.3752 53.6490i −0.117830 0.439746i
\(123\) 91.4699 24.5093i 0.743658 0.199262i
\(124\) −17.8847 + 10.3257i −0.144231 + 0.0832719i
\(125\) −122.459 25.0741i −0.979675 0.200593i
\(126\) 28.5491 + 36.5229i 0.226580 + 0.289864i
\(127\) −120.362 + 120.362i −0.947736 + 0.947736i −0.998700 0.0509644i \(-0.983771\pi\)
0.0509644 + 0.998700i \(0.483771\pi\)
\(128\) −39.7010 + 148.166i −0.310164 + 1.15755i
\(129\) −100.538 58.0458i −0.779366 0.449967i
\(130\) −6.31087 0.425497i −0.0485451 0.00327305i
\(131\) −61.7290 106.918i −0.471214 0.816166i 0.528244 0.849093i \(-0.322851\pi\)
−0.999458 + 0.0329263i \(0.989517\pi\)
\(132\) −10.0347 + 10.0347i −0.0760204 + 0.0760204i
\(133\) −153.987 115.979i −1.15779 0.872019i
\(134\) 3.10939i 0.0232044i
\(135\) −5.02091 25.4910i −0.0371919 0.188822i
\(136\) 37.7337 65.3568i 0.277454 0.480564i
\(137\) −38.7216 144.511i −0.282639 1.05482i −0.950547 0.310581i \(-0.899477\pi\)
0.667908 0.744244i \(-0.267190\pi\)
\(138\) 3.91347 14.6053i 0.0283585 0.105835i
\(139\) 86.7413i 0.624038i 0.950076 + 0.312019i \(0.101005\pi\)
−0.950076 + 0.312019i \(0.898995\pi\)
\(140\) 23.1138 + 19.9818i 0.165099 + 0.142727i
\(141\) −30.4531 −0.215979
\(142\) 184.640 + 49.4741i 1.30028 + 0.348409i
\(143\) 5.19535 1.39209i 0.0363311 0.00973490i
\(144\) −48.6614 28.0947i −0.337926 0.195102i
\(145\) −143.914 96.5501i −0.992508 0.665863i
\(146\) −194.134 −1.32968
\(147\) −41.1099 + 74.2494i −0.279659 + 0.505098i
\(148\) 16.3680 + 16.3680i 0.110595 + 0.110595i
\(149\) −21.7762 + 12.5725i −0.146149 + 0.0843791i −0.571291 0.820747i \(-0.693557\pi\)
0.425142 + 0.905126i \(0.360224\pi\)
\(150\) −36.2487 88.4468i −0.241658 0.589645i
\(151\) −100.832 + 174.647i −0.667765 + 1.15660i 0.310763 + 0.950487i \(0.399415\pi\)
−0.978528 + 0.206115i \(0.933918\pi\)
\(152\) 183.624 + 49.2020i 1.20806 + 0.323697i
\(153\) 23.1919 + 23.1919i 0.151581 + 0.151581i
\(154\) −134.483 54.2965i −0.873265 0.352575i
\(155\) 52.1171 + 106.183i 0.336239 + 0.685054i
\(156\) −0.433244 0.750401i −0.00277721 0.00481026i
\(157\) 7.52733 + 28.0924i 0.0479448 + 0.178932i 0.985746 0.168240i \(-0.0538084\pi\)
−0.937801 + 0.347173i \(0.887142\pi\)
\(158\) 316.022 84.6778i 2.00014 0.535935i
\(159\) 22.9060 13.2248i 0.144063 0.0831748i
\(160\) −64.9847 22.1950i −0.406155 0.138719i
\(161\) 27.4122 3.85934i 0.170262 0.0239710i
\(162\) 14.0483 14.0483i 0.0867179 0.0867179i
\(163\) −21.9253 + 81.8264i −0.134511 + 0.502003i 0.865488 + 0.500929i \(0.167008\pi\)
−0.999999 + 0.00107335i \(0.999658\pi\)
\(164\) 41.3332 + 23.8637i 0.252032 + 0.145510i
\(165\) 53.4785 + 61.2112i 0.324112 + 0.370977i
\(166\) 55.5237 + 96.1699i 0.334480 + 0.579336i
\(167\) 147.643 147.643i 0.884091 0.884091i −0.109856 0.993947i \(-0.535039\pi\)
0.993947 + 0.109856i \(0.0350391\pi\)
\(168\) 10.1794 83.0715i 0.0605916 0.494473i
\(169\) 168.672i 0.998057i
\(170\) 100.207 + 67.2279i 0.589454 + 0.395458i
\(171\) −41.3093 + 71.5499i −0.241575 + 0.418420i
\(172\) −15.1437 56.5169i −0.0880445 0.328587i
\(173\) −18.0662 + 67.4239i −0.104429 + 0.389733i −0.998280 0.0586307i \(-0.981327\pi\)
0.893851 + 0.448364i \(0.147993\pi\)
\(174\) 132.522i 0.761619i
\(175\) 123.095 124.389i 0.703401 0.710794i
\(176\) 175.791 0.998812
\(177\) 174.568 + 46.7753i 0.986260 + 0.264268i
\(178\) 320.428 85.8585i 1.80016 0.482351i
\(179\) −10.7449 6.20357i −0.0600273 0.0346568i 0.469686 0.882834i \(-0.344367\pi\)
−0.529713 + 0.848177i \(0.677700\pi\)
\(180\) 7.29522 10.8740i 0.0405290 0.0604109i
\(181\) −163.979 −0.905964 −0.452982 0.891520i \(-0.649640\pi\)
−0.452982 + 0.891520i \(0.649640\pi\)
\(182\) 5.32752 7.07343i 0.0292721 0.0388650i
\(183\) −30.8153 30.8153i −0.168390 0.168390i
\(184\) −23.6412 + 13.6492i −0.128485 + 0.0741806i
\(185\) 99.8441 87.2310i 0.539698 0.471519i
\(186\) −45.2254 + 78.3328i −0.243148 + 0.421144i
\(187\) −99.1146 26.5577i −0.530025 0.142020i
\(188\) −10.8530 10.8530i −0.0577287 0.0577287i
\(189\) 33.7278 + 13.6174i 0.178454 + 0.0720497i
\(190\) −98.2447 + 287.650i −0.517077 + 1.51395i
\(191\) 63.0093 + 109.135i 0.329892 + 0.571389i 0.982490 0.186315i \(-0.0596545\pi\)
−0.652598 + 0.757704i \(0.726321\pi\)
\(192\) 19.9943 + 74.6196i 0.104137 + 0.388644i
\(193\) 53.1737 14.2479i 0.275512 0.0738231i −0.118418 0.992964i \(-0.537782\pi\)
0.393929 + 0.919141i \(0.371115\pi\)
\(194\) 202.354 116.829i 1.04306 0.602212i
\(195\) −4.45522 + 2.18672i −0.0228473 + 0.0112139i
\(196\) −41.1123 + 11.8104i −0.209757 + 0.0602571i
\(197\) 62.0394 62.0394i 0.314921 0.314921i −0.531892 0.846812i \(-0.678519\pi\)
0.846812 + 0.531892i \(0.178519\pi\)
\(198\) −16.0871 + 60.0379i −0.0812480 + 0.303222i
\(199\) 242.793 + 140.177i 1.22007 + 0.704405i 0.964932 0.262501i \(-0.0845472\pi\)
0.255134 + 0.966906i \(0.417880\pi\)
\(200\) −66.6366 + 159.187i −0.333183 + 0.795937i
\(201\) 1.21986 + 2.11285i 0.00606894 + 0.0105117i
\(202\) −204.119 + 204.119i −1.01049 + 1.01049i
\(203\) 223.311 94.8538i 1.10005 0.467260i
\(204\) 16.5305i 0.0810317i
\(205\) 152.299 227.011i 0.742921 1.10737i
\(206\) 42.4444 73.5159i 0.206041 0.356873i
\(207\) −3.07062 11.4597i −0.0148339 0.0553609i
\(208\) −2.77803 + 10.3677i −0.0133559 + 0.0498449i
\(209\) 258.476i 1.23673i
\(210\) 131.432 + 25.1749i 0.625866 + 0.119880i
\(211\) 215.254 1.02016 0.510081 0.860126i \(-0.329615\pi\)
0.510081 + 0.860126i \(0.329615\pi\)
\(212\) 12.8765 + 3.45024i 0.0607380 + 0.0162747i
\(213\) 144.874 38.8188i 0.680158 0.182248i
\(214\) −383.347 221.326i −1.79134 1.03423i
\(215\) −328.810 + 64.7650i −1.52935 + 0.301233i
\(216\) −35.8684 −0.166057
\(217\) −164.368 20.1413i −0.757457 0.0928170i
\(218\) −227.578 227.578i −1.04393 1.04393i
\(219\) −131.916 + 76.1615i −0.602354 + 0.347769i
\(220\) −2.75582 + 40.8736i −0.0125264 + 0.185789i
\(221\) 3.13262 5.42586i 0.0141747 0.0245514i
\(222\) 97.9302 + 26.2403i 0.441127 + 0.118200i
\(223\) 129.293 + 129.293i 0.579788 + 0.579788i 0.934845 0.355057i \(-0.115538\pi\)
−0.355057 + 0.934845i \(0.615538\pi\)
\(224\) 75.7439 59.2073i 0.338142 0.264318i
\(225\) −59.3302 45.8795i −0.263690 0.203909i
\(226\) −78.1417 135.345i −0.345760 0.598874i
\(227\) −12.3978 46.2690i −0.0546156 0.203828i 0.933227 0.359289i \(-0.116981\pi\)
−0.987842 + 0.155460i \(0.950314\pi\)
\(228\) −40.2213 + 10.7773i −0.176409 + 0.0472687i
\(229\) −275.307 + 158.949i −1.20221 + 0.694099i −0.961047 0.276384i \(-0.910864\pi\)
−0.241168 + 0.970483i \(0.577530\pi\)
\(230\) −19.2322 39.1837i −0.0836183 0.170364i
\(231\) −112.683 + 15.8646i −0.487807 + 0.0686778i
\(232\) −169.178 + 169.178i −0.729217 + 0.729217i
\(233\) −70.2155 + 262.048i −0.301354 + 1.12467i 0.634685 + 0.772771i \(0.281130\pi\)
−0.936039 + 0.351897i \(0.885537\pi\)
\(234\) −3.28667 1.89756i −0.0140456 0.00810923i
\(235\) −66.2029 + 57.8396i −0.281715 + 0.246126i
\(236\) 45.5433 + 78.8833i 0.192980 + 0.334251i
\(237\) 181.519 181.519i 0.765904 0.765904i
\(238\) −155.491 + 66.0467i −0.653324 + 0.277507i
\(239\) 18.7596i 0.0784918i 0.999230 + 0.0392459i \(0.0124956\pi\)
−0.999230 + 0.0392459i \(0.987504\pi\)
\(240\) −159.147 + 31.3468i −0.663112 + 0.130612i
\(241\) −39.4000 + 68.2427i −0.163485 + 0.283165i −0.936116 0.351690i \(-0.885607\pi\)
0.772631 + 0.634855i \(0.218940\pi\)
\(242\) 18.8026 + 70.1723i 0.0776968 + 0.289968i
\(243\) 4.03459 15.0573i 0.0166032 0.0619642i
\(244\) 21.9642i 0.0900173i
\(245\) 51.6519 + 239.493i 0.210824 + 0.977524i
\(246\) 209.041 0.849759
\(247\) 15.2443 + 4.08470i 0.0617179 + 0.0165373i
\(248\) 157.735 42.2651i 0.636030 0.170424i
\(249\) 75.4576 + 43.5655i 0.303043 + 0.174962i
\(250\) −246.789 123.430i −0.987158 0.493720i
\(251\) −86.2825 −0.343755 −0.171877 0.985118i \(-0.554983\pi\)
−0.171877 + 0.985118i \(0.554983\pi\)
\(252\) 7.16705 + 16.8731i 0.0284407 + 0.0669568i
\(253\) 26.2456 + 26.2456i 0.103738 + 0.103738i
\(254\) −325.412 + 187.877i −1.28115 + 0.739671i
\(255\) 94.4661 + 6.36917i 0.370455 + 0.0249771i
\(256\) −80.1031 + 138.743i −0.312903 + 0.541963i
\(257\) −241.586 64.7328i −0.940024 0.251879i −0.243900 0.969800i \(-0.578427\pi\)
−0.696124 + 0.717922i \(0.745094\pi\)
\(258\) −181.210 181.210i −0.702364 0.702364i
\(259\) 25.8774 + 183.803i 0.0999126 + 0.709663i
\(260\) −2.36708 0.808459i −0.00910416 0.00310946i
\(261\) −51.9902 90.0496i −0.199196 0.345018i
\(262\) −70.5362 263.245i −0.269222 1.00475i
\(263\) −350.527 + 93.9235i −1.33280 + 0.357123i −0.853759 0.520668i \(-0.825683\pi\)
−0.479043 + 0.877791i \(0.659016\pi\)
\(264\) 97.1818 56.1079i 0.368113 0.212530i
\(265\) 24.6782 72.2553i 0.0931254 0.272661i
\(266\) −262.077 335.275i −0.985251 1.26043i
\(267\) 184.050 184.050i 0.689327 0.689327i
\(268\) −0.318250 + 1.18773i −0.00118750 + 0.00443181i
\(269\) 255.637 + 147.592i 0.950323 + 0.548669i 0.893181 0.449697i \(-0.148468\pi\)
0.0571419 + 0.998366i \(0.481801\pi\)
\(270\) 3.85807 57.2221i 0.0142892 0.211934i
\(271\) 208.489 + 361.113i 0.769332 + 1.33252i 0.937926 + 0.346836i \(0.112744\pi\)
−0.168594 + 0.985686i \(0.553923\pi\)
\(272\) 144.793 144.793i 0.532328 0.532328i
\(273\) 0.845084 6.89652i 0.00309554 0.0252620i
\(274\) 330.258i 1.20532i
\(275\) 232.517 + 31.4971i 0.845517 + 0.114535i
\(276\) 2.98974 5.17838i 0.0108324 0.0187623i
\(277\) −65.5326 244.571i −0.236580 0.882927i −0.977430 0.211258i \(-0.932244\pi\)
0.740851 0.671670i \(-0.234423\pi\)
\(278\) −49.5586 + 184.955i −0.178268 + 0.665306i
\(279\) 70.9704i 0.254374i
\(280\) −135.649 199.926i −0.484460 0.714020i
\(281\) 235.018 0.836363 0.418181 0.908363i \(-0.362668\pi\)
0.418181 + 0.908363i \(0.362668\pi\)
\(282\) −64.9339 17.3990i −0.230262 0.0616985i
\(283\) 45.4761 12.1853i 0.160693 0.0430576i −0.177576 0.984107i \(-0.556825\pi\)
0.338269 + 0.941050i \(0.390159\pi\)
\(284\) 65.4652 + 37.7963i 0.230511 + 0.133086i
\(285\) 46.0912 + 234.003i 0.161723 + 0.821065i
\(286\) 11.8732 0.0415147
\(287\) 149.623 + 352.252i 0.521335 + 1.22736i
\(288\) −29.1344 29.1344i −0.101161 0.101161i
\(289\) 146.769 84.7373i 0.507852 0.293209i
\(290\) −251.699 288.093i −0.867927 0.993425i
\(291\) 91.6675 158.773i 0.315009 0.545611i
\(292\) −74.1555 19.8699i −0.253957 0.0680476i
\(293\) −12.1766 12.1766i −0.0415584 0.0415584i 0.686022 0.727581i \(-0.259355\pi\)
−0.727581 + 0.686022i \(0.759355\pi\)
\(294\) −130.079 + 134.831i −0.442444 + 0.458610i
\(295\) 468.340 229.871i 1.58759 0.779224i
\(296\) −91.5200 158.517i −0.309189 0.535531i
\(297\) 12.6224 + 47.1074i 0.0424997 + 0.158611i
\(298\) −53.6156 + 14.3663i −0.179918 + 0.0482089i
\(299\) −1.96267 + 1.13315i −0.00656410 + 0.00378979i
\(300\) −4.79365 37.4951i −0.0159788 0.124984i
\(301\) 175.652 435.058i 0.583560 1.44537i
\(302\) −314.783 + 314.783i −1.04233 + 1.04233i
\(303\) −58.6217 + 218.779i −0.193471 + 0.722043i
\(304\) 446.704 + 257.905i 1.46942 + 0.848371i
\(305\) −125.518 8.46279i −0.411535 0.0277468i
\(306\) 36.2008 + 62.7016i 0.118303 + 0.204907i
\(307\) −104.260 + 104.260i −0.339609 + 0.339609i −0.856220 0.516611i \(-0.827193\pi\)
0.516611 + 0.856220i \(0.327193\pi\)
\(308\) −45.8125 34.5048i −0.148742 0.112028i
\(309\) 66.6062i 0.215554i
\(310\) 50.4606 + 256.187i 0.162776 + 0.826410i
\(311\) −16.5632 + 28.6884i −0.0532580 + 0.0922455i −0.891425 0.453168i \(-0.850294\pi\)
0.838167 + 0.545413i \(0.183627\pi\)
\(312\) 1.77335 + 6.61823i 0.00568381 + 0.0212123i
\(313\) −112.285 + 419.052i −0.358737 + 1.33882i 0.516980 + 0.855998i \(0.327056\pi\)
−0.875716 + 0.482826i \(0.839610\pi\)
\(314\) 64.2009i 0.204462i
\(315\) 99.1856 34.4561i 0.314875 0.109384i
\(316\) 129.381 0.409434
\(317\) 270.012 + 72.3496i 0.851774 + 0.228232i 0.658190 0.752852i \(-0.271322\pi\)
0.193584 + 0.981084i \(0.437989\pi\)
\(318\) 56.3974 15.1116i 0.177350 0.0475209i
\(319\) 281.724 + 162.654i 0.883148 + 0.509886i
\(320\) 185.191 + 124.243i 0.578723 + 0.388259i
\(321\) −347.317 −1.08198
\(322\) 60.6550 + 7.43252i 0.188370 + 0.0230824i
\(323\) −212.898 212.898i −0.659128 0.659128i
\(324\) 6.80405 3.92832i 0.0210002 0.0121244i
\(325\) −5.53210 + 13.2156i −0.0170219 + 0.0406633i
\(326\) −93.5010 + 161.948i −0.286813 + 0.496774i
\(327\) −243.923 65.3590i −0.745942 0.199875i
\(328\) −266.863 266.863i −0.813607 0.813607i
\(329\) −17.1583 121.873i −0.0521529 0.370434i
\(330\) 79.0578 + 161.073i 0.239569 + 0.488099i
\(331\) −125.181 216.820i −0.378191 0.655047i 0.612608 0.790387i \(-0.290121\pi\)
−0.990799 + 0.135340i \(0.956787\pi\)
\(332\) 11.3659 + 42.4180i 0.0342345 + 0.127765i
\(333\) 76.8389 20.5889i 0.230747 0.0618286i
\(334\) 399.168 230.460i 1.19511 0.689999i
\(335\) 6.66483 + 2.27632i 0.0198950 + 0.00679499i
\(336\) 85.0169 210.572i 0.253027 0.626701i
\(337\) −7.57759 + 7.57759i −0.0224854 + 0.0224854i −0.718260 0.695775i \(-0.755061\pi\)
0.695775 + 0.718260i \(0.255061\pi\)
\(338\) 96.3684 359.652i 0.285114 1.06406i
\(339\) −106.196 61.3122i −0.313262 0.180862i
\(340\) 31.3964 + 35.9361i 0.0923423 + 0.105694i
\(341\) −111.017 192.287i −0.325563 0.563892i
\(342\) −128.961 + 128.961i −0.377080 + 0.377080i
\(343\) −320.308 122.687i −0.933842 0.357687i
\(344\) 462.669i 1.34497i
\(345\) −28.4408 19.0806i −0.0824370 0.0553060i
\(346\) −77.0436 + 133.443i −0.222669 + 0.385675i
\(347\) −80.6472 300.979i −0.232413 0.867376i −0.979298 0.202423i \(-0.935118\pi\)
0.746885 0.664953i \(-0.231548\pi\)
\(348\) 13.5638 50.6208i 0.0389764 0.145462i
\(349\) 396.973i 1.13746i 0.822525 + 0.568729i \(0.192565\pi\)
−0.822525 + 0.568729i \(0.807435\pi\)
\(350\) 333.539 194.901i 0.952968 0.556859i
\(351\) −2.97776 −0.00848364
\(352\) 124.511 + 33.3626i 0.353724 + 0.0947802i
\(353\) −127.946 + 34.2831i −0.362454 + 0.0971193i −0.435450 0.900213i \(-0.643411\pi\)
0.0729959 + 0.997332i \(0.476744\pi\)
\(354\) 345.500 + 199.474i 0.975988 + 0.563487i
\(355\) 241.217 359.548i 0.679484 1.01281i
\(356\) 131.185 0.368498
\(357\) −79.7465 + 105.881i −0.223380 + 0.296585i
\(358\) −19.3666 19.3666i −0.0540966 0.0540966i
\(359\) −66.6339 + 38.4711i −0.185610 + 0.107162i −0.589926 0.807458i \(-0.700843\pi\)
0.404316 + 0.914619i \(0.367510\pi\)
\(360\) −77.9754 + 68.1249i −0.216598 + 0.189236i
\(361\) 198.713 344.182i 0.550453 0.953412i
\(362\) −349.647 93.6876i −0.965875 0.258805i
\(363\) 40.3061 + 40.3061i 0.111036 + 0.111036i
\(364\) 2.75899 2.15664i 0.00757963 0.00592483i
\(365\) −142.122 + 416.118i −0.389375 + 1.14005i
\(366\) −48.1004 83.3123i −0.131422 0.227629i
\(367\) 60.6221 + 226.245i 0.165183 + 0.616471i 0.998017 + 0.0629479i \(0.0200502\pi\)
−0.832834 + 0.553523i \(0.813283\pi\)
\(368\) −71.5459 + 19.1707i −0.194418 + 0.0520942i
\(369\) 142.045 82.0096i 0.384945 0.222248i
\(370\) 262.732 128.955i 0.710087 0.348526i
\(371\) 65.8315 + 84.2182i 0.177443 + 0.227003i
\(372\) −25.2927 + 25.2927i −0.0679912 + 0.0679912i
\(373\) −98.3605 + 367.087i −0.263701 + 0.984146i 0.699339 + 0.714790i \(0.253478\pi\)
−0.963041 + 0.269356i \(0.913189\pi\)
\(374\) −196.165 113.256i −0.524505 0.302823i
\(375\) −216.119 + 12.9472i −0.576317 + 0.0345260i
\(376\) 60.6835 + 105.107i 0.161392 + 0.279539i
\(377\) −14.0450 + 14.0450i −0.0372547 + 0.0372547i
\(378\) 64.1364 + 48.3058i 0.169673 + 0.127793i
\(379\) 369.290i 0.974379i −0.873296 0.487190i \(-0.838022\pi\)
0.873296 0.487190i \(-0.161978\pi\)
\(380\) −66.9690 + 99.8214i −0.176234 + 0.262688i
\(381\) −147.413 + 255.327i −0.386912 + 0.670151i
\(382\) 71.9991 + 268.704i 0.188479 + 0.703415i
\(383\) 187.821 700.956i 0.490393 1.83017i −0.0640459 0.997947i \(-0.520400\pi\)
0.554439 0.832224i \(-0.312933\pi\)
\(384\) 265.685i 0.691887i
\(385\) −214.835 + 248.509i −0.558012 + 0.645477i
\(386\) 121.521 0.314820
\(387\) −194.225 52.0424i −0.501873 0.134477i
\(388\) 89.2530 23.9153i 0.230034 0.0616373i
\(389\) 135.464 + 78.2101i 0.348236 + 0.201054i 0.663908 0.747814i \(-0.268897\pi\)
−0.315672 + 0.948868i \(0.602230\pi\)
\(390\) −10.7490 + 2.11721i −0.0275616 + 0.00542876i
\(391\) 43.2353 0.110576
\(392\) 338.186 6.06760i 0.862720 0.0154786i
\(393\) −151.205 151.205i −0.384745 0.384745i
\(394\) 167.730 96.8387i 0.425710 0.245784i
\(395\) 49.8504 739.370i 0.126204 1.87182i
\(396\) −12.2899 + 21.2868i −0.0310352 + 0.0537545i
\(397\) 608.327 + 163.001i 1.53231 + 0.410581i 0.923772 0.382944i \(-0.125090\pi\)
0.608538 + 0.793525i \(0.291756\pi\)
\(398\) 437.610 + 437.610i 1.09952 + 1.09952i
\(399\) −309.616 125.006i −0.775981 0.313297i
\(400\) −286.437 + 370.414i −0.716093 + 0.926035i
\(401\) 175.823 + 304.535i 0.438463 + 0.759439i 0.997571 0.0696551i \(-0.0221899\pi\)
−0.559109 + 0.829094i \(0.688857\pi\)
\(402\) 1.39390 + 5.20210i 0.00346741 + 0.0129406i
\(403\) 13.0950 3.50881i 0.0324939 0.00870672i
\(404\) −98.8613 + 57.0776i −0.244706 + 0.141281i
\(405\) −19.8274 40.3964i −0.0489566 0.0997443i
\(406\) 530.350 74.6673i 1.30628 0.183910i
\(407\) −175.981 + 175.981i −0.432385 + 0.432385i
\(408\) 33.8312 126.260i 0.0829195 0.309460i
\(409\) 63.4064 + 36.6077i 0.155028 + 0.0895055i 0.575507 0.817797i \(-0.304805\pi\)
−0.420479 + 0.907302i \(0.638138\pi\)
\(410\) 454.440 397.032i 1.10839 0.968370i
\(411\) −129.565 224.413i −0.315243 0.546018i
\(412\) 23.7374 23.7374i 0.0576151 0.0576151i
\(413\) −88.8365 + 724.973i −0.215101 + 1.75538i
\(414\) 26.1894i 0.0632595i
\(415\) 246.784 48.6085i 0.594660 0.117129i
\(416\) −3.93530 + 6.81614i −0.00945985 + 0.0163849i
\(417\) 38.8851 + 145.121i 0.0932495 + 0.348012i
\(418\) 147.677 551.139i 0.353295 1.31851i
\(419\) 19.8543i 0.0473849i −0.999719 0.0236925i \(-0.992458\pi\)
0.999719 0.0236925i \(-0.00754225\pi\)
\(420\) 47.6278 + 23.0686i 0.113400 + 0.0549252i
\(421\) −19.3162 −0.0458817 −0.0229408 0.999737i \(-0.507303\pi\)
−0.0229408 + 0.999737i \(0.507303\pi\)
\(422\) 458.978 + 122.983i 1.08763 + 0.291429i
\(423\) −50.9490 + 13.6517i −0.120447 + 0.0322736i
\(424\) −91.2891 52.7058i −0.215304 0.124306i
\(425\) 217.460 165.574i 0.511670 0.389585i
\(426\) 331.087 0.777200
\(427\) 105.960 140.685i 0.248150 0.329473i
\(428\) −123.778 123.778i −0.289202 0.289202i
\(429\) 8.06794 4.65803i 0.0188064 0.0108579i
\(430\) −738.111 49.7655i −1.71654 0.115734i
\(431\) −129.158 + 223.709i −0.299671 + 0.519046i −0.976061 0.217498i \(-0.930210\pi\)
0.676389 + 0.736544i \(0.263544\pi\)
\(432\) −94.0066 25.1890i −0.217608 0.0583079i
\(433\) −307.927 307.927i −0.711147 0.711147i 0.255628 0.966775i \(-0.417718\pi\)
−0.966775 + 0.255628i \(0.917718\pi\)
\(434\) −338.968 136.856i −0.781032 0.315337i
\(435\) −284.055 97.0167i −0.652999 0.223027i
\(436\) −63.6375 110.223i −0.145957 0.252806i
\(437\) 28.1878 + 105.198i 0.0645030 + 0.240729i
\(438\) −324.792 + 87.0279i −0.741535 + 0.198694i
\(439\) −544.482 + 314.357i −1.24028 + 0.716074i −0.969151 0.246469i \(-0.920730\pi\)
−0.271127 + 0.962544i \(0.587396\pi\)
\(440\) 104.701 306.552i 0.237956 0.696710i
\(441\) −35.4931 + 142.651i −0.0804833 + 0.323471i
\(442\) 9.77955 9.77955i 0.0221257 0.0221257i
\(443\) 173.821 648.708i 0.392372 1.46435i −0.433839 0.900990i \(-0.642841\pi\)
0.826211 0.563361i \(-0.190492\pi\)
\(444\) 34.7218 + 20.0466i 0.0782022 + 0.0451500i
\(445\) 50.5456 749.680i 0.113586 1.68467i
\(446\) 201.816 + 349.556i 0.452502 + 0.783757i
\(447\) −30.7962 + 30.7962i −0.0688952 + 0.0688952i
\(448\) −287.361 + 122.060i −0.641431 + 0.272455i
\(449\) 36.1975i 0.0806181i 0.999187 + 0.0403091i \(0.0128342\pi\)
−0.999187 + 0.0403091i \(0.987166\pi\)
\(450\) −100.295 131.725i −0.222877 0.292721i
\(451\) −256.571 + 444.394i −0.568893 + 0.985352i
\(452\) −15.9958 59.6973i −0.0353890 0.132074i
\(453\) −90.4039 + 337.392i −0.199567 + 0.744795i
\(454\) 105.741i 0.232910i
\(455\) −11.2614 16.5976i −0.0247504 0.0364783i
\(456\) 329.266 0.722075
\(457\) −628.547 168.419i −1.37538 0.368531i −0.505937 0.862570i \(-0.668853\pi\)
−0.869440 + 0.494039i \(0.835520\pi\)
\(458\) −677.840 + 181.627i −1.48000 + 0.396565i
\(459\) 49.1975 + 28.4042i 0.107184 + 0.0618827i
\(460\) −3.33582 16.9359i −0.00725179 0.0368171i
\(461\) −224.604 −0.487210 −0.243605 0.969875i \(-0.578330\pi\)
−0.243605 + 0.969875i \(0.578330\pi\)
\(462\) −249.335 30.5529i −0.539685 0.0661318i
\(463\) 36.7738 + 36.7738i 0.0794250 + 0.0794250i 0.745703 0.666278i \(-0.232114\pi\)
−0.666278 + 0.745703i \(0.732114\pi\)
\(464\) −562.203 + 324.588i −1.21164 + 0.699543i
\(465\) 134.794 + 154.285i 0.289880 + 0.331795i
\(466\) −299.435 + 518.637i −0.642565 + 1.11296i
\(467\) −249.401 66.8267i −0.534049 0.143098i −0.0182915 0.999833i \(-0.505823\pi\)
−0.515757 + 0.856735i \(0.672489\pi\)
\(468\) −1.06123 1.06123i −0.00226758 0.00226758i
\(469\) −7.76830 + 6.07230i −0.0165635 + 0.0129473i
\(470\) −174.208 + 85.5049i −0.370655 + 0.181925i
\(471\) 25.1870 + 43.6251i 0.0534755 + 0.0926223i
\(472\) −186.417 695.719i −0.394952 1.47398i
\(473\) 607.642 162.817i 1.28465 0.344222i
\(474\) 490.755 283.337i 1.03535 0.597758i
\(475\) 544.643 + 421.167i 1.14662 + 0.886666i
\(476\) −66.1547 + 9.31384i −0.138980 + 0.0195669i
\(477\) 32.3940 32.3940i 0.0679120 0.0679120i
\(478\) −10.7180 + 40.0002i −0.0224227 + 0.0836825i
\(479\) −633.380 365.682i −1.32230 0.763429i −0.338202 0.941073i \(-0.609819\pi\)
−0.984095 + 0.177645i \(0.943152\pi\)
\(480\) −118.671 8.00116i −0.247232 0.0166691i
\(481\) −7.59790 13.1599i −0.0157960 0.0273596i
\(482\) −123.001 + 123.001i −0.255188 + 0.255188i
\(483\) 44.1315 18.7454i 0.0913695 0.0388103i
\(484\) 28.7290i 0.0593574i
\(485\) −102.279 519.266i −0.210884 1.07065i
\(486\) 17.2056 29.8010i 0.0354024 0.0613188i
\(487\) 194.148 + 724.570i 0.398661 + 1.48782i 0.815454 + 0.578823i \(0.196488\pi\)
−0.416792 + 0.909002i \(0.636846\pi\)
\(488\) −44.9518 + 167.762i −0.0921144 + 0.343776i
\(489\) 146.727i 0.300055i
\(490\) −26.6961 + 540.173i −0.0544819 + 1.10239i
\(491\) −114.225 −0.232638 −0.116319 0.993212i \(-0.537109\pi\)
−0.116319 + 0.993212i \(0.537109\pi\)
\(492\) 79.8496 + 21.3956i 0.162296 + 0.0434870i
\(493\) 366.019 98.0745i 0.742432 0.198934i
\(494\) 30.1711 + 17.4193i 0.0610751 + 0.0352618i
\(495\) 116.912 + 78.4346i 0.236185 + 0.158454i
\(496\) 443.087 0.893320
\(497\) 236.979 + 557.910i 0.476819 + 1.12256i
\(498\) 136.005 + 136.005i 0.273102 + 0.273102i
\(499\) −326.723 + 188.633i −0.654755 + 0.378023i −0.790275 0.612752i \(-0.790063\pi\)
0.135521 + 0.990775i \(0.456729\pi\)
\(500\) −81.6356 72.4072i −0.163271 0.144814i
\(501\) 180.825 313.199i 0.360929 0.625147i
\(502\) −183.977 49.2964i −0.366487 0.0982000i
\(503\) −29.7057 29.7057i −0.0590572 0.0590572i 0.676961 0.736019i \(-0.263296\pi\)
−0.736019 + 0.676961i \(0.763296\pi\)
\(504\) −20.2095 143.545i −0.0400982 0.284811i
\(505\) 288.088 + 586.951i 0.570472 + 1.16228i
\(506\) 40.9674 + 70.9576i 0.0809633 + 0.140233i
\(507\) −75.6134 282.193i −0.149139 0.556594i
\(508\) −143.531 + 38.4589i −0.282540 + 0.0757065i
\(509\) −147.952 + 85.4202i −0.290672 + 0.167820i −0.638245 0.769833i \(-0.720339\pi\)
0.347573 + 0.937653i \(0.387006\pi\)
\(510\) 197.787 + 67.5527i 0.387818 + 0.132456i
\(511\) −379.123 485.012i −0.741924 0.949143i
\(512\) 183.792 183.792i 0.358968 0.358968i
\(513\) −37.0369 + 138.224i −0.0721967 + 0.269442i
\(514\) −478.141 276.055i −0.930234 0.537071i
\(515\) −126.505 144.797i −0.245642 0.281160i
\(516\) −50.6717 87.7659i −0.0982009 0.170089i
\(517\) 116.686 116.686i 0.225699 0.225699i
\(518\) −49.8361 + 406.700i −0.0962087 + 0.785135i
\(519\) 120.901i 0.232950i
\(520\) 16.4252 + 11.0195i 0.0315869 + 0.0211913i
\(521\) −75.4299 + 130.648i −0.144779 + 0.250765i −0.929291 0.369350i \(-0.879580\pi\)
0.784511 + 0.620114i \(0.212914\pi\)
\(522\) −59.4078 221.713i −0.113808 0.424738i
\(523\) 210.608 786.001i 0.402693 1.50287i −0.405579 0.914060i \(-0.632930\pi\)
0.808271 0.588810i \(-0.200403\pi\)
\(524\) 107.774i 0.205676i
\(525\) 150.180 263.289i 0.286057 0.501502i
\(526\) −801.077 −1.52296
\(527\) −249.821 66.9395i −0.474044 0.127020i
\(528\) 294.104 78.8049i 0.557015 0.149252i
\(529\) 444.583 + 256.680i 0.840422 + 0.485218i
\(530\) 93.9026 139.967i 0.177175 0.264090i
\(531\) 313.027 0.589504
\(532\) −65.7925 154.893i −0.123670 0.291151i
\(533\) −22.1547 22.1547i −0.0415661 0.0415661i
\(534\) 497.598 287.288i 0.931831 0.537993i
\(535\) −755.043 + 659.660i −1.41130 + 1.23301i
\(536\) 4.86159 8.42051i 0.00907012 0.0157099i
\(537\) −20.7575 5.56197i −0.0386546 0.0103575i
\(538\) 460.760 + 460.760i 0.856431 + 0.856431i
\(539\) −126.980 442.019i −0.235584 0.820072i
\(540\) 7.33048 21.4629i 0.0135750 0.0397460i
\(541\) −525.462 910.127i −0.971280 1.68231i −0.691702 0.722183i \(-0.743139\pi\)
−0.279577 0.960123i \(-0.590194\pi\)
\(542\) 238.235 + 889.105i 0.439548 + 1.64042i
\(543\) −274.343 + 73.5100i −0.505236 + 0.135377i
\(544\) 130.035 75.0758i 0.239035 0.138007i
\(545\) −654.409 + 321.198i −1.20075 + 0.589354i
\(546\) 5.74218 14.2223i 0.0105168 0.0260482i
\(547\) 332.845 332.845i 0.608492 0.608492i −0.334060 0.942552i \(-0.608419\pi\)
0.942552 + 0.334060i \(0.108419\pi\)
\(548\) 33.8024 126.152i 0.0616833 0.230205i
\(549\) −65.3692 37.7409i −0.119070 0.0687448i
\(550\) 477.792 + 200.006i 0.868712 + 0.363647i
\(551\) 477.262 + 826.642i 0.866174 + 1.50026i
\(552\) −33.4337 + 33.4337i −0.0605682 + 0.0605682i
\(553\) 828.711 + 624.163i 1.49857 + 1.12868i
\(554\) 558.930i 1.00890i
\(555\) 127.938 190.699i 0.230519 0.343602i
\(556\) −37.8609 + 65.5769i −0.0680951 + 0.117944i
\(557\) 177.542 + 662.596i 0.318747 + 1.18958i 0.920450 + 0.390860i \(0.127823\pi\)
−0.601703 + 0.798720i \(0.705511\pi\)
\(558\) −40.5480 + 151.327i −0.0726667 + 0.271196i
\(559\) 38.4103i 0.0687125i
\(560\) −215.118 619.241i −0.384140 1.10579i
\(561\) −177.727 −0.316805
\(562\) 501.120 + 134.275i 0.891672 + 0.238923i
\(563\) 451.611 121.009i 0.802152 0.214936i 0.165623 0.986189i \(-0.447036\pi\)
0.636528 + 0.771253i \(0.280370\pi\)
\(564\) −23.0227 13.2922i −0.0408204 0.0235677i
\(565\) −347.313 + 68.4096i −0.614714 + 0.121079i
\(566\) 103.929 0.183620
\(567\) 62.5323 + 7.66256i 0.110286 + 0.0135142i
\(568\) −422.669 422.669i −0.744135 0.744135i
\(569\) 492.294 284.226i 0.865192 0.499519i −0.000555696 1.00000i \(-0.500177\pi\)
0.865747 + 0.500481i \(0.166844\pi\)
\(570\) −35.4165 + 525.290i −0.0621343 + 0.921561i
\(571\) 377.172 653.280i 0.660546 1.14410i −0.319927 0.947442i \(-0.603658\pi\)
0.980472 0.196657i \(-0.0630084\pi\)
\(572\) 4.53534 + 1.21524i 0.00792891 + 0.00212455i
\(573\) 154.341 + 154.341i 0.269355 + 0.269355i
\(574\) 117.781 + 836.577i 0.205193 + 1.45745i
\(575\) −98.0681 + 12.5377i −0.170553 + 0.0218048i
\(576\) 66.9021 + 115.878i 0.116149 + 0.201177i
\(577\) −146.947 548.414i −0.254675 0.950458i −0.968271 0.249902i \(-0.919602\pi\)
0.713597 0.700557i \(-0.247065\pi\)
\(578\) 361.364 96.8272i 0.625197 0.167521i
\(579\) 82.5743 47.6743i 0.142615 0.0823390i
\(580\) −66.6574 135.808i −0.114927 0.234152i
\(581\) −131.833 + 326.527i −0.226907 + 0.562008i
\(582\) 286.172 286.172i 0.491704 0.491704i
\(583\) −37.0953 + 138.441i −0.0636282 + 0.237464i
\(584\) 525.733 + 303.532i 0.900228 + 0.519747i
\(585\) −6.47344 + 5.65567i −0.0110657 + 0.00966780i
\(586\) −19.0067 32.9206i −0.0324347 0.0561786i
\(587\) 191.752 191.752i 0.326665 0.326665i −0.524652 0.851317i \(-0.675805\pi\)
0.851317 + 0.524652i \(0.175805\pi\)
\(588\) −63.4877 + 38.1893i −0.107972 + 0.0649478i
\(589\) 651.497i 1.10611i
\(590\) 1129.96 222.565i 1.91518 0.377229i
\(591\) 75.9824 131.605i 0.128566 0.222683i
\(592\) −128.542 479.725i −0.217132 0.810346i
\(593\) 158.838 592.793i 0.267856 0.999651i −0.692623 0.721299i \(-0.743545\pi\)
0.960479 0.278352i \(-0.0897881\pi\)
\(594\) 107.657i 0.181241i
\(595\) 27.7361 + 381.640i 0.0466154 + 0.641412i
\(596\) −21.9506 −0.0368298
\(597\) 469.040 + 125.679i 0.785662 + 0.210517i
\(598\) −4.83233 + 1.29482i −0.00808081 + 0.00216525i
\(599\) −649.805 375.165i −1.08482 0.626319i −0.152625 0.988284i \(-0.548773\pi\)
−0.932192 + 0.361965i \(0.882106\pi\)
\(600\) −40.1234 + 296.198i −0.0668724 + 0.493663i
\(601\) −592.685 −0.986165 −0.493083 0.869982i \(-0.664130\pi\)
−0.493083 + 0.869982i \(0.664130\pi\)
\(602\) 623.100 827.300i 1.03505 1.37425i
\(603\) 2.98803 + 2.98803i 0.00495527 + 0.00495527i
\(604\) −152.460 + 88.0227i −0.252417 + 0.145733i
\(605\) 164.176 + 11.0692i 0.271366 + 0.0182963i
\(606\) −249.993 + 433.001i −0.412530 + 0.714523i
\(607\) 387.642 + 103.868i 0.638619 + 0.171117i 0.563578 0.826063i \(-0.309425\pi\)
0.0750410 + 0.997180i \(0.476091\pi\)
\(608\) 267.450 + 267.450i 0.439884 + 0.439884i
\(609\) 331.084 258.801i 0.543652 0.424960i
\(610\) −262.802 89.7581i −0.430823 0.147144i
\(611\) 5.03788 + 8.72587i 0.00824531 + 0.0142813i
\(612\) 7.41041 + 27.6560i 0.0121085 + 0.0451896i
\(613\) −212.730 + 57.0009i −0.347031 + 0.0929868i −0.428125 0.903720i \(-0.640826\pi\)
0.0810932 + 0.996707i \(0.474159\pi\)
\(614\) −281.877 + 162.742i −0.459084 + 0.265052i
\(615\) 153.035 448.070i 0.248837 0.728569i
\(616\) 279.299 + 357.307i 0.453407 + 0.580043i
\(617\) 338.020 338.020i 0.547844 0.547844i −0.377973 0.925817i \(-0.623379\pi\)
0.925817 + 0.377973i \(0.123379\pi\)
\(618\) 38.0546 142.022i 0.0615771 0.229809i
\(619\) 266.400 + 153.806i 0.430371 + 0.248475i 0.699505 0.714628i \(-0.253404\pi\)
−0.269134 + 0.963103i \(0.586737\pi\)
\(620\) −6.94612 + 103.023i −0.0112034 + 0.166167i
\(621\) −10.2745 17.7959i −0.0165451 0.0286569i
\(622\) −51.7078 + 51.7078i −0.0831316 + 0.0831316i
\(623\) 840.266 + 632.866i 1.34874 + 1.01584i
\(624\) 18.5909i 0.0297931i
\(625\) −445.237 + 438.622i −0.712379 + 0.701795i
\(626\) −478.840 + 829.375i −0.764920 + 1.32488i
\(627\) −115.872 432.439i −0.184803 0.689696i
\(628\) −6.57106 + 24.5235i −0.0104635 + 0.0390502i
\(629\) 289.899i 0.460888i
\(630\) 231.176 16.8009i 0.366945 0.0266682i
\(631\) −219.545 −0.347931 −0.173966 0.984752i \(-0.555658\pi\)
−0.173966 + 0.984752i \(0.555658\pi\)
\(632\) −988.213 264.791i −1.56363 0.418973i
\(633\) 360.128 96.4959i 0.568922 0.152442i
\(634\) 534.401 + 308.536i 0.842903 + 0.486650i
\(635\) 164.477 + 835.047i 0.259020 + 1.31503i
\(636\) 23.0894 0.0363042
\(637\) 28.0759 0.503726i 0.0440752 0.000790779i
\(638\) 507.779 + 507.779i 0.795892 + 0.795892i
\(639\) 224.976 129.890i 0.352076 0.203271i
\(640\) 504.615 + 577.580i 0.788462 + 0.902469i
\(641\) 417.537 723.194i 0.651383 1.12823i −0.331404 0.943489i \(-0.607522\pi\)
0.982787 0.184740i \(-0.0591442\pi\)
\(642\) −740.570 198.435i −1.15354 0.309089i
\(643\) −649.916 649.916i −1.01076 1.01076i −0.999942 0.0108149i \(-0.996557\pi\)
−0.0108149 0.999942i \(-0.503443\pi\)
\(644\) 22.4083 + 9.04721i 0.0347955 + 0.0140485i
\(645\) −521.076 + 255.755i −0.807870 + 0.396520i
\(646\) −332.318 575.591i −0.514424 0.891008i
\(647\) 95.3328 + 355.787i 0.147346 + 0.549902i 0.999640 + 0.0268391i \(0.00854417\pi\)
−0.852294 + 0.523063i \(0.824789\pi\)
\(648\) −60.0090 + 16.0794i −0.0926064 + 0.0248138i
\(649\) −848.115 + 489.659i −1.30680 + 0.754483i
\(650\) −19.3464 + 25.0184i −0.0297637 + 0.0384898i
\(651\) −284.022 + 39.9872i −0.436286 + 0.0614242i
\(652\) −52.2913 + 52.2913i −0.0802014 + 0.0802014i
\(653\) 117.038 436.792i 0.179232 0.668901i −0.816561 0.577260i \(-0.804122\pi\)
0.995792 0.0916414i \(-0.0292113\pi\)
\(654\) −482.765 278.725i −0.738173 0.426185i
\(655\) −615.892 41.5252i −0.940293 0.0633972i
\(656\) −512.008 886.823i −0.780499 1.35186i
\(657\) −186.557 + 186.557i −0.283953 + 0.283953i
\(658\) 33.0444 269.668i 0.0502195 0.409829i
\(659\) 395.881i 0.600730i −0.953824 0.300365i \(-0.902892\pi\)
0.953824 0.300365i \(-0.0971085\pi\)
\(660\) 13.7126 + 69.6183i 0.0207766 + 0.105482i
\(661\) −41.2693 + 71.4804i −0.0624346 + 0.108140i −0.895553 0.444955i \(-0.853220\pi\)
0.833119 + 0.553094i \(0.186553\pi\)
\(662\) −143.042 533.838i −0.216075 0.806403i
\(663\) 2.80863 10.4819i 0.00423624 0.0158099i
\(664\) 347.250i 0.522966i
\(665\) −910.509 + 316.302i −1.36919 + 0.475642i
\(666\) 175.604 0.263669
\(667\) −132.398 35.4760i −0.198498 0.0531874i
\(668\) 176.062 47.1758i 0.263567 0.0706225i
\(669\) 274.271 + 158.351i 0.409972 + 0.236698i
\(670\) 12.9106 + 8.66158i 0.0192696 + 0.0129277i
\(671\) 236.148 0.351935
\(672\) 100.180 133.011i 0.149078 0.197933i
\(673\) 923.540 + 923.540i 1.37227 + 1.37227i 0.857066 + 0.515207i \(0.172285\pi\)
0.515207 + 0.857066i \(0.327715\pi\)
\(674\) −20.4868 + 11.8280i −0.0303958 + 0.0175490i
\(675\) −119.829 50.1608i −0.177524 0.0743123i
\(676\) 73.6218 127.517i 0.108908 0.188634i
\(677\) −242.099 64.8703i −0.357606 0.0958203i 0.0755429 0.997143i \(-0.475931\pi\)
−0.433149 + 0.901322i \(0.642598\pi\)
\(678\) −191.407 191.407i −0.282312 0.282312i
\(679\) 687.055 + 277.394i 1.01186 + 0.408533i
\(680\) −166.259 338.735i −0.244498 0.498140i
\(681\) −41.4837 71.8518i −0.0609158 0.105509i
\(682\) −126.856 473.434i −0.186006 0.694185i
\(683\) −1283.82 + 344.000i −1.87968 + 0.503660i −0.880101 + 0.474787i \(0.842525\pi\)
−0.999583 + 0.0288723i \(0.990808\pi\)
\(684\) −62.4602 + 36.0614i −0.0913161 + 0.0527213i
\(685\) −707.894 241.776i −1.03342 0.352957i
\(686\) −612.884 444.603i −0.893417 0.648110i
\(687\) −389.343 + 389.343i −0.566729 + 0.566729i
\(688\) −324.914 + 1212.60i −0.472259 + 1.76250i
\(689\) −7.57873 4.37558i −0.0109996 0.00635063i
\(690\) −49.7417 56.9341i −0.0720894 0.0825131i
\(691\) 161.274 + 279.335i 0.233392 + 0.404247i 0.958804 0.284068i \(-0.0916840\pi\)
−0.725412 + 0.688315i \(0.758351\pi\)
\(692\) −43.0873 + 43.0873i −0.0622649 + 0.0622649i
\(693\) −181.411 + 77.0566i −0.261777 + 0.111193i
\(694\) 687.843i 0.991129i
\(695\) 360.162 + 241.629i 0.518219 + 0.347667i
\(696\) −207.200 + 358.881i −0.297702 + 0.515634i
\(697\) 154.703 + 577.361i 0.221956 + 0.828352i
\(698\) −226.805 + 846.449i −0.324936 + 1.21268i
\(699\) 469.891i 0.672233i
\(700\) 147.354 40.3101i 0.210506 0.0575859i
\(701\) 993.695 1.41754 0.708769 0.705440i \(-0.249251\pi\)
0.708769 + 0.705440i \(0.249251\pi\)
\(702\) −6.34936 1.70130i −0.00904467 0.00242351i
\(703\) −705.369 + 189.003i −1.00337 + 0.268852i
\(704\) −362.529 209.306i −0.514956 0.297310i
\(705\) −84.8309 + 126.446i −0.120327 + 0.179355i
\(706\) −292.402 −0.414167
\(707\) −908.580 111.335i −1.28512 0.157476i
\(708\) 111.558 + 111.558i 0.157568 + 0.157568i
\(709\) 594.099 343.003i 0.837940 0.483785i −0.0186238 0.999827i \(-0.505928\pi\)
0.856563 + 0.516042i \(0.172595\pi\)
\(710\) 719.761 628.835i 1.01375 0.885683i
\(711\) 222.315 385.060i 0.312679 0.541576i
\(712\) −1001.99 268.483i −1.40729 0.377083i
\(713\) 66.1530 + 66.1530i 0.0927811 + 0.0927811i
\(714\) −230.534 + 180.203i −0.322877 + 0.252385i
\(715\) 8.69215 25.4497i 0.0121568 0.0355940i
\(716\) −5.41547 9.37986i −0.00756350 0.0131004i
\(717\) 8.40968 + 31.3853i 0.0117290 + 0.0437731i
\(718\) −164.061 + 43.9599i −0.228497 + 0.0612255i
\(719\) 258.622 149.315i 0.359696 0.207671i −0.309251 0.950980i \(-0.600078\pi\)
0.668948 + 0.743310i \(0.266745\pi\)
\(720\) −252.206 + 123.788i −0.350285 + 0.171928i
\(721\) 266.557 37.5282i 0.369705 0.0520503i
\(722\) 620.353 620.353i 0.859214 0.859214i
\(723\) −35.3250 + 131.835i −0.0488590 + 0.182344i
\(724\) −123.969 71.5738i −0.171228 0.0988588i
\(725\) −801.779 + 328.598i −1.10590 + 0.453239i
\(726\) 62.9148 + 108.972i 0.0866595 + 0.150099i
\(727\) 427.959 427.959i 0.588665 0.588665i −0.348605 0.937270i \(-0.613344\pi\)
0.937270 + 0.348605i \(0.113344\pi\)
\(728\) −25.4869 + 10.8259i −0.0350094 + 0.0148707i
\(729\) 27.0000i 0.0370370i
\(730\) −540.784 + 806.072i −0.740800 + 1.10421i
\(731\) 366.387 634.601i 0.501214 0.868127i
\(732\) −9.84629 36.7469i −0.0134512 0.0502006i
\(733\) 112.025 418.082i 0.152830 0.570370i −0.846451 0.532466i \(-0.821265\pi\)
0.999281 0.0379039i \(-0.0120681\pi\)
\(734\) 517.048i 0.704426i
\(735\) 193.777 + 377.525i 0.263643 + 0.513640i
\(736\) −54.3136 −0.0737956
\(737\) −12.7698 3.42167i −0.0173268 0.00464270i
\(738\) 349.732 93.7104i 0.473891 0.126979i
\(739\) −160.126 92.4489i −0.216680 0.125100i 0.387732 0.921772i \(-0.373259\pi\)
−0.604412 + 0.796672i \(0.706592\pi\)
\(740\) 113.557 22.3672i 0.153456 0.0302259i
\(741\) 27.3354 0.0368898
\(742\) 92.2528 + 217.187i 0.124330 + 0.292705i
\(743\) −576.263 576.263i −0.775589 0.775589i 0.203488 0.979077i \(-0.434772\pi\)
−0.979077 + 0.203488i \(0.934772\pi\)
\(744\) 244.950 141.422i 0.329233 0.190083i
\(745\) −8.45753 + 125.440i −0.0113524 + 0.168376i
\(746\) −419.461 + 726.527i −0.562280 + 0.973897i
\(747\) 145.773 + 39.0597i 0.195145 + 0.0522888i
\(748\) −63.3393 63.3393i −0.0846782 0.0846782i
\(749\) −195.690 1389.96i −0.261269 1.85575i
\(750\) −468.219 95.8699i −0.624292 0.127827i
\(751\) 710.061 + 1229.86i 0.945487 + 1.63763i 0.754772 + 0.655987i \(0.227747\pi\)
0.190715 + 0.981645i \(0.438919\pi\)
\(752\) 85.2314 + 318.088i 0.113340 + 0.422989i
\(753\) −144.353 + 38.6794i −0.191704 + 0.0513670i
\(754\) −37.9721 + 21.9232i −0.0503609 + 0.0290759i
\(755\) 444.278 + 905.172i 0.588447 + 1.19890i
\(756\) 19.5547 + 25.0164i 0.0258660 + 0.0330904i
\(757\) −316.057 + 316.057i −0.417512 + 0.417512i −0.884345 0.466833i \(-0.845395\pi\)
0.466833 + 0.884345i \(0.345395\pi\)
\(758\) 210.989 787.422i 0.278350 1.03882i
\(759\) 55.6754 + 32.1442i 0.0733536 + 0.0423507i
\(760\) 715.803 625.377i 0.941846 0.822864i
\(761\) 393.410 + 681.407i 0.516965 + 0.895409i 0.999806 + 0.0197013i \(0.00627154\pi\)
−0.482841 + 0.875708i \(0.660395\pi\)
\(762\) −460.202 + 460.202i −0.603939 + 0.603939i
\(763\) 124.131 1013.00i 0.162688 1.32766i
\(764\) 110.009i 0.143991i
\(765\) 160.900 31.6921i 0.210327 0.0414276i
\(766\) 800.964 1387.31i 1.04565 1.81111i
\(767\) −15.4762 57.7579i −0.0201776 0.0753037i
\(768\) −71.8184 + 268.030i −0.0935136 + 0.348998i
\(769\) 1512.03i 1.96622i −0.183008 0.983111i \(-0.558583\pi\)
0.183008 0.983111i \(-0.441417\pi\)
\(770\) −600.066 + 407.142i −0.779306 + 0.528756i
\(771\) −433.201 −0.561869
\(772\) 46.4186 + 12.4378i 0.0601277 + 0.0161112i
\(773\) −228.469 + 61.2182i −0.295562 + 0.0791956i −0.403553 0.914956i \(-0.632225\pi\)
0.107991 + 0.994152i \(0.465558\pi\)
\(774\) −384.404 221.936i −0.496647 0.286739i
\(775\) 586.067 + 79.3895i 0.756216 + 0.102438i
\(776\) −730.659 −0.941570
\(777\) 125.690 + 295.907i 0.161763 + 0.380833i
\(778\) 244.160 + 244.160i 0.313830 + 0.313830i
\(779\) −1303.95 + 752.836i −1.67388 + 0.966414i
\(780\) −4.32263 0.291444i −0.00554183 0.000373646i
\(781\) −406.367 + 703.849i −0.520317 + 0.901215i
\(782\) 92.1889 + 24.7019i 0.117889 + 0.0315882i
\(783\) −127.349 127.349i −0.162643 0.162643i
\(784\) 890.606 + 221.593i 1.13598 + 0.282644i
\(785\) 137.612 + 47.0003i 0.175302 + 0.0598730i
\(786\) −236.019 408.796i −0.300278 0.520097i
\(787\) −154.380 576.154i −0.196163 0.732090i −0.991963 0.126530i \(-0.959616\pi\)
0.795800 0.605560i \(-0.207051\pi\)
\(788\) 73.9811 19.8232i 0.0938847 0.0251563i
\(789\) −544.339 + 314.274i −0.689909 + 0.398319i
\(790\) 528.724 1548.05i 0.669271 1.95955i
\(791\) 185.536 459.540i 0.234559 0.580961i
\(792\) 137.436 137.436i 0.173530 0.173530i
\(793\) −3.73186 + 13.9275i −0.00470600 + 0.0175630i
\(794\) 1203.98 + 695.120i 1.51635 + 0.875466i
\(795\) 8.89634 131.948i 0.0111904 0.165973i
\(796\) 122.369 + 211.949i 0.153729 + 0.266267i
\(797\) 650.745 650.745i 0.816493 0.816493i −0.169105 0.985598i \(-0.554088\pi\)
0.985598 + 0.169105i \(0.0540876\pi\)
\(798\) −588.762 443.440i −0.737798 0.555689i
\(799\) 192.221i 0.240577i
\(800\) −273.180 + 207.999i −0.341475 + 0.259999i
\(801\) 225.415 390.430i 0.281417 0.487428i
\(802\) 200.909 + 749.803i 0.250510 + 0.934916i
\(803\) 213.631 797.283i 0.266041 0.992880i
\(804\) 2.12977i 0.00264897i
\(805\) 60.3357 124.570i 0.0749512 0.154746i
\(806\) 29.9268 0.0371300
\(807\) 493.853 + 132.327i 0.611961 + 0.163974i
\(808\) 871.917 233.629i 1.07910 0.289145i
\(809\) 1022.42 + 590.294i 1.26381 + 0.729659i 0.973809 0.227368i \(-0.0730120\pi\)
0.289998 + 0.957027i \(0.406345\pi\)
\(810\) −19.1973 97.4639i −0.0237003 0.120326i
\(811\) 919.216 1.13344 0.566718 0.823912i \(-0.308213\pi\)
0.566718 + 0.823912i \(0.308213\pi\)
\(812\) 210.226 + 25.7606i 0.258899 + 0.0317249i
\(813\) 510.691 + 510.691i 0.628157 + 0.628157i
\(814\) −475.781 + 274.692i −0.584497 + 0.337460i
\(815\) 278.679 + 318.975i 0.341938 + 0.391380i
\(816\) 177.335 307.153i 0.217322 0.376412i
\(817\) 1782.96 + 477.742i 2.18232 + 0.584751i
\(818\) 114.284 + 114.284i 0.139711 + 0.139711i
\(819\) −1.67777 11.9169i −0.00204856 0.0145506i
\(820\) 214.224 105.146i 0.261249 0.128227i
\(821\) 390.979 + 677.195i 0.476222 + 0.824842i 0.999629 0.0272416i \(-0.00867236\pi\)
−0.523406 + 0.852083i \(0.675339\pi\)
\(822\) −148.051 552.533i −0.180110 0.672181i
\(823\) 343.971 92.1667i 0.417947 0.111989i −0.0437157 0.999044i \(-0.513920\pi\)
0.461663 + 0.887055i \(0.347253\pi\)
\(824\) −229.887 + 132.725i −0.278989 + 0.161074i
\(825\) 403.129 51.5389i 0.488641 0.0624714i
\(826\) −603.627 + 1495.08i −0.730783 + 1.81002i
\(827\) −953.358 + 953.358i −1.15279 + 1.15279i −0.166800 + 0.985991i \(0.553344\pi\)
−0.985991 + 0.166800i \(0.946656\pi\)
\(828\) 2.68053 10.0039i 0.00323735 0.0120820i
\(829\) −230.809 133.258i −0.278419 0.160745i 0.354288 0.935136i \(-0.384723\pi\)
−0.632708 + 0.774391i \(0.718056\pi\)
\(830\) 553.979 + 37.3509i 0.667445 + 0.0450010i
\(831\) −219.276 379.798i −0.263870 0.457037i
\(832\) 18.0735 18.0735i 0.0217229 0.0217229i
\(833\) −468.665 259.487i −0.562623 0.311509i
\(834\) 331.652i 0.397665i
\(835\) −201.757 1024.31i −0.241625 1.22672i
\(836\) 112.820 195.410i 0.134952 0.233743i
\(837\) 31.8151 + 118.736i 0.0380109 + 0.141859i
\(838\) 11.3435 42.3345i 0.0135364 0.0505185i
\(839\) 709.681i 0.845866i 0.906161 + 0.422933i \(0.138999\pi\)
−0.906161 + 0.422933i \(0.861001\pi\)
\(840\) −316.569 273.672i −0.376868 0.325801i
\(841\) −360.323 −0.428446
\(842\) −41.1871 11.0361i −0.0489158 0.0131070i
\(843\) 393.193 105.356i 0.466421 0.124977i
\(844\) 162.734 + 93.9543i 0.192812 + 0.111320i
\(845\) −700.349 469.856i −0.828815 0.556042i
\(846\) −116.436 −0.137631
\(847\) −138.595 + 184.014i −0.163630 + 0.217254i
\(848\) −202.244 202.244i −0.238496 0.238496i
\(849\) 70.6205 40.7728i 0.0831809 0.0480245i
\(850\) 558.279 228.803i 0.656799 0.269180i
\(851\) 52.4318 90.8145i 0.0616119 0.106715i
\(852\) 126.469 + 33.8873i 0.148438 + 0.0397738i
\(853\) −2.10021 2.10021i −0.00246214 0.00246214i 0.705875 0.708337i \(-0.250554\pi\)
−0.708337 + 0.705875i \(0.750554\pi\)
\(854\) 306.313 239.438i 0.358680 0.280372i
\(855\) 182.013 + 370.833i 0.212881 + 0.433723i
\(856\) 692.094 + 1198.74i 0.808521 + 1.40040i
\(857\) 9.61382 + 35.8793i 0.0112180 + 0.0418661i 0.971308 0.237825i \(-0.0764345\pi\)
−0.960090 + 0.279691i \(0.909768\pi\)
\(858\) 19.8642 5.32261i 0.0231518 0.00620351i
\(859\) 83.8106 48.3881i 0.0975677 0.0563307i −0.450422 0.892816i \(-0.648727\pi\)
0.547990 + 0.836485i \(0.315393\pi\)
\(860\) −276.851 94.5563i −0.321920 0.109949i
\(861\) 408.234 + 522.254i 0.474140 + 0.606567i
\(862\) −403.212 + 403.212i −0.467764 + 0.467764i
\(863\) −33.9627 + 126.751i −0.0393543 + 0.146872i −0.982807 0.184634i \(-0.940890\pi\)
0.943453 + 0.331506i \(0.107557\pi\)
\(864\) −61.8034 35.6822i −0.0715318 0.0412989i
\(865\) 229.628 + 262.831i 0.265466 + 0.303851i
\(866\) −480.650 832.510i −0.555023 0.961328i
\(867\) 207.563 207.563i 0.239404 0.239404i
\(868\) −115.472 86.9703i −0.133032 0.100196i
\(869\) 1391.04i 1.60074i
\(870\) −550.249 369.156i −0.632470 0.424317i
\(871\) 0.403604 0.699063i 0.000463380 0.000802598i
\(872\) 260.480 + 972.125i 0.298716 + 1.11482i
\(873\) 82.1868 306.725i 0.0941430 0.351346i
\(874\) 240.415i 0.275074i
\(875\) −173.584 857.609i −0.198381 0.980125i
\(876\) −132.972 −0.151794
\(877\) −636.168 170.461i −0.725391 0.194368i −0.122815 0.992430i \(-0.539192\pi\)
−0.602576 + 0.798062i \(0.705859\pi\)
\(878\) −1340.58 + 359.207i −1.52686 + 0.409120i
\(879\) −25.8305 14.9132i −0.0293862 0.0169661i
\(880\) 489.688 729.909i 0.556463 0.829442i
\(881\) −1005.81 −1.14167 −0.570834 0.821066i \(-0.693380\pi\)
−0.570834 + 0.821066i \(0.693380\pi\)
\(882\) −157.182 + 283.890i −0.178211 + 0.321871i
\(883\) 571.004 + 571.004i 0.646664 + 0.646664i 0.952185 0.305522i \(-0.0988308\pi\)
−0.305522 + 0.952185i \(0.598831\pi\)
\(884\) 4.73656 2.73465i 0.00535810 0.00309350i
\(885\) 680.499 594.533i 0.768925 0.671788i
\(886\) 741.262 1283.90i 0.836639 1.44910i
\(887\) 708.127 + 189.742i 0.798339 + 0.213914i 0.634855 0.772632i \(-0.281060\pi\)
0.163484 + 0.986546i \(0.447727\pi\)
\(888\) −224.177 224.177i −0.252452 0.252452i
\(889\) −1104.87 446.085i −1.24283 0.501783i
\(890\) 536.097 1569.63i 0.602356 1.76363i
\(891\) 42.2354 + 73.1538i 0.0474022 + 0.0821030i
\(892\) 41.3123 + 154.180i 0.0463143 + 0.172847i
\(893\) 467.704 125.321i 0.523745 0.140337i
\(894\) −83.2605 + 48.0705i −0.0931325 + 0.0537701i
\(895\) −55.6893 + 27.3335i −0.0622227 + 0.0305402i
\(896\) −1063.27 + 149.696i −1.18668 + 0.167071i
\(897\) −2.77563 + 2.77563i −0.00309435 + 0.00309435i
\(898\) −20.6810 + 77.1826i −0.0230301 + 0.0859494i
\(899\) 710.095 + 409.973i 0.789872 + 0.456033i
\(900\) −24.8285 60.5816i −0.0275872 0.0673129i
\(901\) 83.4754 + 144.584i 0.0926475 + 0.160470i
\(902\) −800.975 + 800.975i −0.887999 + 0.887999i
\(903\) 98.8399 806.608i 0.109457 0.893253i
\(904\) 488.705i 0.540602i
\(905\) −456.785 + 680.866i −0.504735 + 0.752338i
\(906\) −385.529 + 667.756i −0.425529 + 0.737038i
\(907\) 63.8934 + 238.454i 0.0704448 + 0.262904i 0.992162 0.124959i \(-0.0398800\pi\)
−0.921717 + 0.387863i \(0.873213\pi\)
\(908\) 10.8227 40.3910i 0.0119193 0.0444835i
\(909\) 392.304i 0.431577i
\(910\) −14.5294 41.8245i −0.0159664 0.0459610i
\(911\) −322.782 −0.354316 −0.177158 0.984182i \(-0.556690\pi\)
−0.177158 + 0.984182i \(0.556690\pi\)
\(912\) 862.967 + 231.231i 0.946235 + 0.253543i
\(913\) −456.057 + 122.200i −0.499515 + 0.133845i
\(914\) −1244.00 718.225i −1.36105 0.785804i
\(915\) −213.790 + 42.1097i −0.233650 + 0.0460215i
\(916\) −277.512 −0.302960
\(917\) 519.924 690.312i 0.566984 0.752794i
\(918\) 88.6734 + 88.6734i 0.0965941 + 0.0965941i
\(919\) −355.096 + 205.015i −0.386394 + 0.223084i −0.680596 0.732659i \(-0.738279\pi\)
0.294203 + 0.955743i \(0.404946\pi\)
\(920\) −9.18186 + 136.183i −0.00998028 + 0.148025i
\(921\) −127.692 + 221.169i −0.138645 + 0.240140i
\(922\) −478.914 128.325i −0.519429 0.139181i
\(923\) −35.0895 35.0895i −0.0380168 0.0380168i
\(924\) −92.1139 37.1904i −0.0996904 0.0402493i
\(925\) −84.0672 657.560i −0.0908835 0.710876i
\(926\) 57.4010 + 99.4215i 0.0619881 + 0.107367i
\(927\) −29.8587 111.434i −0.0322101 0.120210i
\(928\) −459.805 + 123.204i −0.495480 + 0.132763i
\(929\) 392.860 226.818i 0.422884 0.244152i −0.273426 0.961893i \(-0.588157\pi\)
0.696311 + 0.717741i \(0.254824\pi\)
\(930\) 199.268 + 405.988i 0.214266 + 0.436547i
\(931\) 325.822 1309.51i 0.349970 1.40657i
\(932\) −167.462 + 167.462i −0.179680 + 0.179680i
\(933\) −14.8502 + 55.4216i −0.0159166 + 0.0594015i
\(934\) −493.607 284.984i −0.528487 0.305122i
\(935\) −386.367 + 337.558i −0.413227 + 0.361025i
\(936\) 5.93374 + 10.2775i 0.00633947 + 0.0109803i
\(937\) −699.175 + 699.175i −0.746184 + 0.746184i −0.973760 0.227576i \(-0.926920\pi\)
0.227576 + 0.973760i \(0.426920\pi\)
\(938\) −20.0334 + 8.50941i −0.0213575 + 0.00907186i
\(939\) 751.423i 0.800238i
\(940\) −75.2956 + 14.8308i −0.0801017 + 0.0157775i
\(941\) 401.325 695.115i 0.426488 0.738698i −0.570070 0.821596i \(-0.693084\pi\)
0.996558 + 0.0828975i \(0.0264174\pi\)
\(942\) 28.7805 + 107.410i 0.0305525 + 0.114024i
\(943\) 55.9601 208.846i 0.0593426 0.221470i
\(944\) 1954.31i 2.07024i
\(945\) 150.494 102.110i 0.159253 0.108053i
\(946\) 1388.67 1.46794
\(947\) −110.716 29.6662i −0.116912 0.0313265i 0.199889 0.979819i \(-0.435942\pi\)
−0.316801 + 0.948492i \(0.602609\pi\)
\(948\) 216.459 58.0000i 0.228332 0.0611815i
\(949\) 43.6459 + 25.1990i 0.0459914 + 0.0265532i
\(950\) 920.692 + 1209.21i 0.969149 + 1.27285i
\(951\) 484.173 0.509120
\(952\) 524.350 + 64.2527i 0.550788 + 0.0674923i
\(953\) 45.8367 + 45.8367i 0.0480973 + 0.0480973i 0.730746 0.682649i \(-0.239172\pi\)
−0.682649 + 0.730746i \(0.739172\pi\)
\(954\) 87.5804 50.5645i 0.0918033 0.0530027i
\(955\) 628.666 + 42.3864i 0.658289 + 0.0443837i
\(956\) −8.18817 + 14.1823i −0.00856503 + 0.0148351i
\(957\) 544.249 + 145.831i 0.568704 + 0.152384i
\(958\) −1141.60 1141.60i −1.19165 1.19165i
\(959\) 825.097 644.959i 0.860372 0.672533i
\(960\) 365.528 + 124.843i 0.380758 + 0.130045i
\(961\) 200.678 + 347.585i 0.208822 + 0.361691i
\(962\) −8.68193 32.4014i −0.00902487 0.0336813i
\(963\) −581.072 + 155.698i −0.603398 + 0.161680i
\(964\) −59.5732 + 34.3946i −0.0617979 + 0.0356790i
\(965\) 88.9629 260.474i 0.0921896 0.269921i
\(966\) 104.810 14.7560i 0.108499 0.0152754i
\(967\) −464.416 + 464.416i −0.480265 + 0.480265i −0.905216 0.424951i \(-0.860291\pi\)
0.424951 + 0.905216i \(0.360291\pi\)
\(968\) 58.7965 219.432i 0.0607402 0.226686i
\(969\) −451.625 260.746i −0.466074 0.269088i
\(970\) 78.5911 1165.64i 0.0810218 1.20170i
\(971\) −515.699 893.217i −0.531101 0.919894i −0.999341 0.0362930i \(-0.988445\pi\)
0.468240 0.883601i \(-0.344888\pi\)
\(972\) 9.62238 9.62238i 0.00989957 0.00989957i
\(973\) −558.863 + 237.384i −0.574371 + 0.243971i
\(974\) 1655.90i 1.70010i
\(975\) −3.33101 + 24.5901i −0.00341642 + 0.0252206i
\(976\) −235.626 + 408.117i −0.241421 + 0.418153i
\(977\) −36.2844 135.415i −0.0371386 0.138603i 0.944867 0.327454i \(-0.106191\pi\)
−0.982006 + 0.188850i \(0.939524\pi\)
\(978\) −83.8307 + 312.860i −0.0857165 + 0.319898i
\(979\) 1410.44i 1.44069i
\(980\) −65.4849 + 203.603i −0.0668214 + 0.207759i
\(981\) −437.391 −0.445862
\(982\) −243.558 65.2611i −0.248022 0.0664574i
\(983\) −456.919 + 122.431i −0.464821 + 0.124549i −0.483626 0.875275i \(-0.660681\pi\)
0.0188048 + 0.999823i \(0.494014\pi\)
\(984\) −566.102 326.839i −0.575307 0.332154i
\(985\) −84.7780 430.415i −0.0860690 0.436970i
\(986\) 836.482 0.848359
\(987\) −83.3405 196.205i −0.0844382 0.198789i
\(988\) 9.74190 + 9.74190i 0.00986023 + 0.00986023i
\(989\) −229.551 + 132.531i −0.232104 + 0.134005i
\(990\) 204.473 + 234.039i 0.206539 + 0.236403i
\(991\) −423.672 + 733.822i −0.427520 + 0.740486i −0.996652 0.0817597i \(-0.973946\pi\)
0.569132 + 0.822246i \(0.307279\pi\)
\(992\) 313.834 + 84.0915i 0.316365 + 0.0847697i
\(993\) −306.630 306.630i −0.308792 0.308792i
\(994\) 186.546 + 1325.00i 0.187672 + 1.33300i
\(995\) 1258.36 617.632i 1.26469 0.620736i
\(996\) 38.0309 + 65.8715i 0.0381837 + 0.0661361i
\(997\) −62.9660 234.992i −0.0631554 0.235699i 0.927132 0.374735i \(-0.122266\pi\)
−0.990287 + 0.139036i \(0.955600\pi\)
\(998\) −804.431 + 215.547i −0.806043 + 0.215979i
\(999\) 119.324 68.8919i 0.119444 0.0689608i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 105.3.v.a.88.12 yes 64
3.2 odd 2 315.3.ca.b.298.5 64
5.2 odd 4 inner 105.3.v.a.67.5 yes 64
7.2 even 3 inner 105.3.v.a.58.5 yes 64
15.2 even 4 315.3.ca.b.172.12 64
21.2 odd 6 315.3.ca.b.163.12 64
35.2 odd 12 inner 105.3.v.a.37.12 64
105.2 even 12 315.3.ca.b.37.5 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.12 64 35.2 odd 12 inner
105.3.v.a.58.5 yes 64 7.2 even 3 inner
105.3.v.a.67.5 yes 64 5.2 odd 4 inner
105.3.v.a.88.12 yes 64 1.1 even 1 trivial
315.3.ca.b.37.5 64 105.2 even 12
315.3.ca.b.163.12 64 21.2 odd 6
315.3.ca.b.172.12 64 15.2 even 4
315.3.ca.b.298.5 64 3.2 odd 2