Properties

Label 731.2.k.a.35.6
Level $731$
Weight $2$
Character 731.35
Analytic conductor $5.837$
Analytic rank $0$
Dimension $180$
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] = [731,2,Mod(35,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.k (of order \(7\), degree \(6\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(180\)
Relative dimension: \(30\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 35.6
Character \(\chi\) \(=\) 731.35
Dual form 731.2.k.a.188.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.455706 + 1.99658i) q^{2} +(-0.326366 - 1.42990i) q^{3} +(-1.97672 - 0.951940i) q^{4} +(1.20644 - 1.51282i) q^{5} +3.00364 q^{6} +3.96037 q^{7} +(0.247708 - 0.310617i) q^{8} +(0.764797 - 0.368307i) q^{9} +O(q^{10})\) \(q+(-0.455706 + 1.99658i) q^{2} +(-0.326366 - 1.42990i) q^{3} +(-1.97672 - 0.951940i) q^{4} +(1.20644 - 1.51282i) q^{5} +3.00364 q^{6} +3.96037 q^{7} +(0.247708 - 0.310617i) q^{8} +(0.764797 - 0.368307i) q^{9} +(2.47069 + 3.09815i) q^{10} +(-3.98195 + 1.91761i) q^{11} +(-0.716047 + 3.13721i) q^{12} +(3.59697 - 4.51046i) q^{13} +(-1.80477 + 7.90720i) q^{14} +(-2.55693 - 1.23135i) q^{15} +(-2.22858 - 2.79455i) q^{16} +(0.623490 + 0.781831i) q^{17} +(0.386831 + 1.69482i) q^{18} +(-7.14305 - 3.43991i) q^{19} +(-3.82491 + 1.84198i) q^{20} +(-1.29253 - 5.66295i) q^{21} +(-2.01406 - 8.82416i) q^{22} +(8.22417 - 3.96055i) q^{23} +(-0.524995 - 0.252824i) q^{24} +(0.279458 + 1.22438i) q^{25} +(7.36632 + 9.23708i) q^{26} +(-3.51962 - 4.41346i) q^{27} +(-7.82856 - 3.77004i) q^{28} +(-1.43808 + 6.30065i) q^{29} +(3.62371 - 4.54398i) q^{30} +(0.940181 - 4.11920i) q^{31} +(7.31103 - 3.52080i) q^{32} +(4.04157 + 5.06797i) q^{33} +(-1.84512 + 0.888561i) q^{34} +(4.77794 - 5.99135i) q^{35} -1.86240 q^{36} -5.14400 q^{37} +(10.1232 - 12.6941i) q^{38} +(-7.62345 - 3.67126i) q^{39} +(-0.171064 - 0.749479i) q^{40} +(0.534035 - 2.33976i) q^{41} +11.8955 q^{42} +(6.38922 - 1.47575i) q^{43} +9.69667 q^{44} +(0.365496 - 1.60134i) q^{45} +(4.15975 + 18.2251i) q^{46} +(3.65600 + 1.76064i) q^{47} +(-3.26861 + 4.09871i) q^{48} +8.68455 q^{49} -2.57193 q^{50} +(0.914458 - 1.14669i) q^{51} +(-11.4039 + 5.49183i) q^{52} +(5.20008 + 6.52070i) q^{53} +(10.4157 - 5.01596i) q^{54} +(-1.90297 + 8.33747i) q^{55} +(0.981018 - 1.23016i) q^{56} +(-2.58749 + 11.3365i) q^{57} +(-11.9244 - 5.74249i) q^{58} +(2.55905 + 3.20895i) q^{59} +(3.88218 + 4.86809i) q^{60} +(0.967360 + 4.23828i) q^{61} +(7.79587 + 3.75429i) q^{62} +(3.02888 - 1.45863i) q^{63} +(2.10714 + 9.23199i) q^{64} +(-2.48401 - 10.8832i) q^{65} +(-11.9604 + 5.75981i) q^{66} +(0.569233 + 0.274128i) q^{67} +(-0.488210 - 2.13899i) q^{68} +(-8.34730 - 10.4672i) q^{69} +(9.78487 + 12.2698i) q^{70} +(-3.09044 - 1.48828i) q^{71} +(0.0750445 - 0.328791i) q^{72} +(6.33585 - 7.94491i) q^{73} +(2.34415 - 10.2704i) q^{74} +(1.65955 - 0.799196i) q^{75} +(10.8453 + 13.5995i) q^{76} +(-15.7700 + 7.59444i) q^{77} +(10.8040 - 13.5478i) q^{78} -5.38735 q^{79} -6.91631 q^{80} +(-3.57438 + 4.48212i) q^{81} +(4.42815 + 2.13249i) q^{82} +(-3.45826 - 15.1516i) q^{83} +(-2.83581 + 12.4245i) q^{84} +1.93497 q^{85} +(0.0348369 + 13.4291i) q^{86} +9.47867 q^{87} +(-0.390723 + 1.71187i) q^{88} +(1.31043 + 5.74137i) q^{89} +(3.03065 + 1.45948i) q^{90} +(14.2453 - 17.8631i) q^{91} -20.0271 q^{92} -6.19691 q^{93} +(-5.18132 + 6.49717i) q^{94} +(-13.8216 + 6.65614i) q^{95} +(-7.42048 - 9.30499i) q^{96} +(-10.6693 + 5.13807i) q^{97} +(-3.95761 + 17.3394i) q^{98} +(-2.33912 + 2.93316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.455706 + 1.99658i −0.322233 + 1.41179i 0.511337 + 0.859381i \(0.329151\pi\)
−0.833570 + 0.552414i \(0.813707\pi\)
\(3\) −0.326366 1.42990i −0.188428 0.825555i −0.977446 0.211186i \(-0.932268\pi\)
0.789018 0.614370i \(-0.210590\pi\)
\(4\) −1.97672 0.951940i −0.988362 0.475970i
\(5\) 1.20644 1.51282i 0.539535 0.676556i −0.435093 0.900385i \(-0.643285\pi\)
0.974628 + 0.223830i \(0.0718560\pi\)
\(6\) 3.00364 1.22623
\(7\) 3.96037 1.49688 0.748440 0.663202i \(-0.230803\pi\)
0.748440 + 0.663202i \(0.230803\pi\)
\(8\) 0.247708 0.310617i 0.0875782 0.109820i
\(9\) 0.764797 0.368307i 0.254932 0.122769i
\(10\) 2.47069 + 3.09815i 0.781302 + 0.979721i
\(11\) −3.98195 + 1.91761i −1.20060 + 0.578181i −0.923848 0.382759i \(-0.874974\pi\)
−0.276756 + 0.960940i \(0.589260\pi\)
\(12\) −0.716047 + 3.13721i −0.206705 + 0.905633i
\(13\) 3.59697 4.51046i 0.997620 1.25098i 0.0297411 0.999558i \(-0.490532\pi\)
0.967879 0.251418i \(-0.0808968\pi\)
\(14\) −1.80477 + 7.90720i −0.482344 + 2.11329i
\(15\) −2.55693 1.23135i −0.660197 0.317934i
\(16\) −2.22858 2.79455i −0.557146 0.698638i
\(17\) 0.623490 + 0.781831i 0.151218 + 0.189622i
\(18\) 0.386831 + 1.69482i 0.0911770 + 0.399472i
\(19\) −7.14305 3.43991i −1.63873 0.789170i −0.999802 0.0199025i \(-0.993664\pi\)
−0.638927 0.769268i \(-0.720621\pi\)
\(20\) −3.82491 + 1.84198i −0.855276 + 0.411879i
\(21\) −1.29253 5.66295i −0.282054 1.23576i
\(22\) −2.01406 8.82416i −0.429398 1.88132i
\(23\) 8.22417 3.96055i 1.71486 0.825832i 0.724180 0.689611i \(-0.242219\pi\)
0.990678 0.136221i \(-0.0434957\pi\)
\(24\) −0.524995 0.252824i −0.107164 0.0516076i
\(25\) 0.279458 + 1.22438i 0.0558916 + 0.244877i
\(26\) 7.36632 + 9.23708i 1.44465 + 1.81154i
\(27\) −3.51962 4.41346i −0.677351 0.849372i
\(28\) −7.82856 3.77004i −1.47946 0.712470i
\(29\) −1.43808 + 6.30065i −0.267045 + 1.17000i 0.646387 + 0.763010i \(0.276279\pi\)
−0.913432 + 0.406992i \(0.866578\pi\)
\(30\) 3.62371 4.54398i 0.661595 0.829614i
\(31\) 0.940181 4.11920i 0.168862 0.739831i −0.817593 0.575796i \(-0.804692\pi\)
0.986455 0.164034i \(-0.0524508\pi\)
\(32\) 7.31103 3.52080i 1.29242 0.622396i
\(33\) 4.04157 + 5.06797i 0.703547 + 0.882220i
\(34\) −1.84512 + 0.888561i −0.316435 + 0.152387i
\(35\) 4.77794 5.99135i 0.807619 1.01272i
\(36\) −1.86240 −0.310400
\(37\) −5.14400 −0.845669 −0.422835 0.906207i \(-0.638965\pi\)
−0.422835 + 0.906207i \(0.638965\pi\)
\(38\) 10.1232 12.6941i 1.64220 2.05925i
\(39\) −7.62345 3.67126i −1.22073 0.587872i
\(40\) −0.171064 0.749479i −0.0270475 0.118503i
\(41\) 0.534035 2.33976i 0.0834022 0.365409i −0.915954 0.401283i \(-0.868564\pi\)
0.999356 + 0.0358740i \(0.0114215\pi\)
\(42\) 11.8955 1.83552
\(43\) 6.38922 1.47575i 0.974347 0.225049i
\(44\) 9.69667 1.46183
\(45\) 0.365496 1.60134i 0.0544849 0.238714i
\(46\) 4.15975 + 18.2251i 0.613322 + 2.68714i
\(47\) 3.65600 + 1.76064i 0.533283 + 0.256816i 0.681089 0.732201i \(-0.261507\pi\)
−0.147806 + 0.989016i \(0.547221\pi\)
\(48\) −3.26861 + 4.09871i −0.471783 + 0.591597i
\(49\) 8.68455 1.24065
\(50\) −2.57193 −0.363726
\(51\) 0.914458 1.14669i 0.128050 0.160569i
\(52\) −11.4039 + 5.49183i −1.58144 + 0.761580i
\(53\) 5.20008 + 6.52070i 0.714286 + 0.895687i 0.997999 0.0632223i \(-0.0201377\pi\)
−0.283713 + 0.958909i \(0.591566\pi\)
\(54\) 10.4157 5.01596i 1.41740 0.682586i
\(55\) −1.90297 + 8.33747i −0.256597 + 1.12422i
\(56\) 0.981018 1.23016i 0.131094 0.164387i
\(57\) −2.58749 + 11.3365i −0.342722 + 1.50156i
\(58\) −11.9244 5.74249i −1.56575 0.754026i
\(59\) 2.55905 + 3.20895i 0.333160 + 0.417769i 0.919991 0.391940i \(-0.128196\pi\)
−0.586831 + 0.809710i \(0.699625\pi\)
\(60\) 3.88218 + 4.86809i 0.501187 + 0.628468i
\(61\) 0.967360 + 4.23828i 0.123858 + 0.542656i 0.998340 + 0.0575983i \(0.0183443\pi\)
−0.874482 + 0.485058i \(0.838799\pi\)
\(62\) 7.79587 + 3.75429i 0.990076 + 0.476796i
\(63\) 3.02888 1.45863i 0.381603 0.183770i
\(64\) 2.10714 + 9.23199i 0.263393 + 1.15400i
\(65\) −2.48401 10.8832i −0.308104 1.34989i
\(66\) −11.9604 + 5.75981i −1.47222 + 0.708984i
\(67\) 0.569233 + 0.274128i 0.0695428 + 0.0334901i 0.468332 0.883553i \(-0.344855\pi\)
−0.398789 + 0.917043i \(0.630569\pi\)
\(68\) −0.488210 2.13899i −0.0592042 0.259391i
\(69\) −8.34730 10.4672i −1.00490 1.26010i
\(70\) 9.78487 + 12.2698i 1.16952 + 1.46653i
\(71\) −3.09044 1.48828i −0.366768 0.176626i 0.241417 0.970421i \(-0.422388\pi\)
−0.608185 + 0.793795i \(0.708102\pi\)
\(72\) 0.0750445 0.328791i 0.00884408 0.0387484i
\(73\) 6.33585 7.94491i 0.741556 0.929881i −0.257785 0.966202i \(-0.582992\pi\)
0.999340 + 0.0363211i \(0.0115639\pi\)
\(74\) 2.34415 10.2704i 0.272502 1.19391i
\(75\) 1.65955 0.799196i 0.191628 0.0922832i
\(76\) 10.8453 + 13.5995i 1.24404 + 1.55997i
\(77\) −15.7700 + 7.59444i −1.79716 + 0.865467i
\(78\) 10.8040 13.5478i 1.22331 1.53399i
\(79\) −5.38735 −0.606124 −0.303062 0.952971i \(-0.598009\pi\)
−0.303062 + 0.952971i \(0.598009\pi\)
\(80\) −6.91631 −0.773267
\(81\) −3.57438 + 4.48212i −0.397153 + 0.498014i
\(82\) 4.42815 + 2.13249i 0.489008 + 0.235494i
\(83\) −3.45826 15.1516i −0.379593 1.66311i −0.698721 0.715394i \(-0.746247\pi\)
0.319128 0.947711i \(-0.396610\pi\)
\(84\) −2.83581 + 12.4245i −0.309412 + 1.35562i
\(85\) 1.93497 0.209877
\(86\) 0.0348369 + 13.4291i 0.00375656 + 1.44810i
\(87\) 9.47867 1.01622
\(88\) −0.390723 + 1.71187i −0.0416512 + 0.182486i
\(89\) 1.31043 + 5.74137i 0.138905 + 0.608584i 0.995677 + 0.0928875i \(0.0296097\pi\)
−0.856771 + 0.515697i \(0.827533\pi\)
\(90\) 3.03065 + 1.45948i 0.319459 + 0.153843i
\(91\) 14.2453 17.8631i 1.49332 1.87256i
\(92\) −20.0271 −2.08797
\(93\) −6.19691 −0.642589
\(94\) −5.18132 + 6.49717i −0.534412 + 0.670132i
\(95\) −13.8216 + 6.65614i −1.41807 + 0.682906i
\(96\) −7.42048 9.30499i −0.757350 0.949687i
\(97\) −10.6693 + 5.13807i −1.08330 + 0.521692i −0.888372 0.459125i \(-0.848163\pi\)
−0.194932 + 0.980817i \(0.562449\pi\)
\(98\) −3.95761 + 17.3394i −0.399779 + 1.75154i
\(99\) −2.33912 + 2.93316i −0.235090 + 0.294794i
\(100\) 0.613130 2.68630i 0.0613130 0.268630i
\(101\) 7.90933 + 3.80893i 0.787008 + 0.379003i 0.783817 0.620992i \(-0.213270\pi\)
0.00319106 + 0.999995i \(0.498984\pi\)
\(102\) 1.87274 + 2.34834i 0.185429 + 0.232521i
\(103\) −0.436928 0.547891i −0.0430518 0.0539853i 0.759839 0.650111i \(-0.225278\pi\)
−0.802891 + 0.596125i \(0.796706\pi\)
\(104\) −0.510023 2.23456i −0.0500119 0.219116i
\(105\) −10.1264 4.87662i −0.988236 0.475910i
\(106\) −15.3888 + 7.41086i −1.49469 + 0.719806i
\(107\) 0.492891 + 2.15950i 0.0476495 + 0.208766i 0.993149 0.116859i \(-0.0372825\pi\)
−0.945499 + 0.325625i \(0.894425\pi\)
\(108\) 2.75596 + 12.0747i 0.265193 + 1.16189i
\(109\) 0.327914 0.157915i 0.0314084 0.0151255i −0.418114 0.908395i \(-0.637309\pi\)
0.449522 + 0.893269i \(0.351594\pi\)
\(110\) −15.7792 7.59888i −1.50449 0.724524i
\(111\) 1.67883 + 7.35543i 0.159347 + 0.698147i
\(112\) −8.82602 11.0675i −0.833980 1.04578i
\(113\) 10.3243 + 12.9463i 0.971228 + 1.21788i 0.975973 + 0.217892i \(0.0699182\pi\)
−0.00474506 + 0.999989i \(0.501510\pi\)
\(114\) −21.4552 10.3323i −2.00946 0.967706i
\(115\) 3.93033 17.2199i 0.366505 1.60576i
\(116\) 8.84053 11.0857i 0.820823 1.02928i
\(117\) 1.08972 4.77437i 0.100745 0.441391i
\(118\) −7.57309 + 3.64701i −0.697160 + 0.335734i
\(119\) 2.46925 + 3.09634i 0.226356 + 0.283841i
\(120\) −1.01585 + 0.489209i −0.0927343 + 0.0446585i
\(121\) 5.32035 6.67151i 0.483669 0.606501i
\(122\) −8.90289 −0.806030
\(123\) −3.51992 −0.317381
\(124\) −5.77971 + 7.24753i −0.519034 + 0.650848i
\(125\) 10.9062 + 5.25214i 0.975479 + 0.469766i
\(126\) 1.53200 + 6.71211i 0.136481 + 0.597963i
\(127\) −2.80651 + 12.2961i −0.249037 + 1.09110i 0.683477 + 0.729972i \(0.260467\pi\)
−0.932515 + 0.361132i \(0.882390\pi\)
\(128\) −3.16340 −0.279607
\(129\) −4.19540 8.65434i −0.369385 0.761972i
\(130\) 22.8611 2.00505
\(131\) 3.07800 13.4856i 0.268926 1.17824i −0.642338 0.766422i \(-0.722035\pi\)
0.911264 0.411822i \(-0.135108\pi\)
\(132\) −3.16467 13.8653i −0.275449 1.20682i
\(133\) −28.2892 13.6233i −2.45298 1.18129i
\(134\) −0.806721 + 1.01160i −0.0696901 + 0.0873886i
\(135\) −10.9230 −0.940102
\(136\) 0.397294 0.0340676
\(137\) −2.34703 + 2.94308i −0.200520 + 0.251445i −0.871917 0.489654i \(-0.837123\pi\)
0.671397 + 0.741098i \(0.265695\pi\)
\(138\) 24.7025 11.8961i 2.10281 1.01266i
\(139\) −1.68604 2.11423i −0.143008 0.179327i 0.705169 0.709039i \(-0.250871\pi\)
−0.848177 + 0.529713i \(0.822300\pi\)
\(140\) −15.1481 + 7.29493i −1.28025 + 0.616534i
\(141\) 1.32435 5.80235i 0.111530 0.488646i
\(142\) 4.37980 5.49210i 0.367545 0.460886i
\(143\) −5.67368 + 24.8580i −0.474457 + 2.07873i
\(144\) −2.73367 1.31646i −0.227806 0.109705i
\(145\) 7.79682 + 9.77691i 0.647491 + 0.811928i
\(146\) 12.9754 + 16.2706i 1.07385 + 1.34656i
\(147\) −2.83434 12.4181i −0.233773 1.02423i
\(148\) 10.1683 + 4.89678i 0.835827 + 0.402513i
\(149\) −21.6567 + 10.4293i −1.77418 + 0.854402i −0.811235 + 0.584720i \(0.801204\pi\)
−0.962949 + 0.269683i \(0.913081\pi\)
\(150\) 0.839392 + 3.67762i 0.0685361 + 0.300276i
\(151\) 2.53255 + 11.0958i 0.206096 + 0.902966i 0.967136 + 0.254261i \(0.0818321\pi\)
−0.761040 + 0.648705i \(0.775311\pi\)
\(152\) −2.83789 + 1.36666i −0.230183 + 0.110850i
\(153\) 0.764797 + 0.368307i 0.0618302 + 0.0297759i
\(154\) −7.97641 34.9469i −0.642758 2.81611i
\(155\) −5.09736 6.39189i −0.409430 0.513409i
\(156\) 11.5746 + 14.5141i 0.926712 + 1.16206i
\(157\) 15.2769 + 7.35698i 1.21923 + 0.587151i 0.929097 0.369836i \(-0.120586\pi\)
0.290134 + 0.956986i \(0.406300\pi\)
\(158\) 2.45505 10.7563i 0.195313 0.855723i
\(159\) 7.62684 9.56375i 0.604848 0.758455i
\(160\) 3.49393 15.3079i 0.276220 1.21020i
\(161\) 32.5708 15.6853i 2.56694 1.23617i
\(162\) −7.32005 9.17906i −0.575118 0.721175i
\(163\) −6.92557 + 3.33518i −0.542452 + 0.261231i −0.684983 0.728559i \(-0.740190\pi\)
0.142531 + 0.989790i \(0.454476\pi\)
\(164\) −3.28295 + 4.11669i −0.256355 + 0.321459i
\(165\) 12.5428 0.976459
\(166\) 31.8273 2.47028
\(167\) −10.0347 + 12.5832i −0.776512 + 0.973715i −1.00000 0.000991906i \(-0.999684\pi\)
0.223488 + 0.974707i \(0.428256\pi\)
\(168\) −2.07918 1.00128i −0.160412 0.0772504i
\(169\) −4.51326 19.7739i −0.347174 1.52107i
\(170\) −0.881780 + 3.86333i −0.0676294 + 0.296304i
\(171\) −6.72993 −0.514651
\(172\) −14.0346 3.16501i −1.07012 0.241330i
\(173\) −13.1974 −1.00338 −0.501690 0.865048i \(-0.667288\pi\)
−0.501690 + 0.865048i \(0.667288\pi\)
\(174\) −4.31949 + 18.9249i −0.327459 + 1.43469i
\(175\) 1.10676 + 4.84902i 0.0836630 + 0.366552i
\(176\) 14.2330 + 6.85424i 1.07285 + 0.516658i
\(177\) 3.75330 4.70649i 0.282115 0.353761i
\(178\) −12.0603 −0.903956
\(179\) −7.67669 −0.573783 −0.286891 0.957963i \(-0.592622\pi\)
−0.286891 + 0.957963i \(0.592622\pi\)
\(180\) −2.24687 + 2.81748i −0.167472 + 0.210003i
\(181\) 15.0698 7.25725i 1.12013 0.539427i 0.220199 0.975455i \(-0.429329\pi\)
0.899933 + 0.436028i \(0.143615\pi\)
\(182\) 29.1734 + 36.5823i 2.16248 + 2.71166i
\(183\) 5.74462 2.76646i 0.424654 0.204503i
\(184\) 0.806984 3.53563i 0.0594916 0.260650i
\(185\) −6.20592 + 7.78197i −0.456268 + 0.572142i
\(186\) 2.82397 12.3726i 0.207063 0.907204i
\(187\) −3.98195 1.91761i −0.291189 0.140229i
\(188\) −5.55089 6.96059i −0.404840 0.507653i
\(189\) −13.9390 17.4790i −1.01391 1.27141i
\(190\) −6.99092 30.6292i −0.507175 2.22208i
\(191\) −18.9334 9.11785i −1.36997 0.659745i −0.403137 0.915140i \(-0.632080\pi\)
−0.966837 + 0.255395i \(0.917795\pi\)
\(192\) 12.5132 6.02602i 0.903060 0.434891i
\(193\) −1.45120 6.35811i −0.104459 0.457667i −0.999922 0.0125290i \(-0.996012\pi\)
0.895462 0.445138i \(-0.146845\pi\)
\(194\) −5.39649 23.6436i −0.387445 1.69751i
\(195\) −14.7512 + 7.10379i −1.05635 + 0.508713i
\(196\) −17.1670 8.26718i −1.22621 0.590513i
\(197\) −0.371986 1.62978i −0.0265029 0.116117i 0.959946 0.280184i \(-0.0903956\pi\)
−0.986449 + 0.164068i \(0.947538\pi\)
\(198\) −4.79034 6.00690i −0.340435 0.426892i
\(199\) 3.77864 + 4.73826i 0.267861 + 0.335887i 0.897511 0.440992i \(-0.145373\pi\)
−0.629650 + 0.776879i \(0.716802\pi\)
\(200\) 0.449538 + 0.216486i 0.0317872 + 0.0153079i
\(201\) 0.206198 0.903414i 0.0145441 0.0637219i
\(202\) −11.2092 + 14.0559i −0.788675 + 0.988967i
\(203\) −5.69534 + 24.9529i −0.399735 + 1.75135i
\(204\) −2.89921 + 1.39619i −0.202986 + 0.0977527i
\(205\) −2.89537 3.63067i −0.202221 0.253577i
\(206\) 1.29302 0.622685i 0.0900889 0.0433845i
\(207\) 4.83112 6.05804i 0.335786 0.421063i
\(208\) −20.6209 −1.42980
\(209\) 35.0397 2.42375
\(210\) 14.3512 17.9959i 0.990329 1.24183i
\(211\) −2.69582 1.29824i −0.185588 0.0893746i 0.338782 0.940865i \(-0.389985\pi\)
−0.524370 + 0.851490i \(0.675699\pi\)
\(212\) −4.07182 17.8398i −0.279653 1.22524i
\(213\) −1.11948 + 4.90476i −0.0767054 + 0.336068i
\(214\) −4.53622 −0.310089
\(215\) 5.47565 11.4462i 0.373436 0.780622i
\(216\) −2.24274 −0.152599
\(217\) 3.72347 16.3136i 0.252765 1.10744i
\(218\) 0.165857 + 0.726669i 0.0112333 + 0.0492162i
\(219\) −13.4283 6.46671i −0.907398 0.436980i
\(220\) 11.6984 14.6694i 0.788708 0.989008i
\(221\) 5.76909 0.388071
\(222\) −15.4508 −1.03699
\(223\) 3.97683 4.98679i 0.266308 0.333940i −0.630640 0.776075i \(-0.717208\pi\)
0.896948 + 0.442136i \(0.145779\pi\)
\(224\) 28.9544 13.9437i 1.93460 0.931653i
\(225\) 0.664678 + 0.833480i 0.0443119 + 0.0555653i
\(226\) −30.5531 + 14.7136i −2.03236 + 0.978733i
\(227\) −1.05162 + 4.60746i −0.0697986 + 0.305808i −0.997762 0.0668633i \(-0.978701\pi\)
0.927964 + 0.372671i \(0.121558\pi\)
\(228\) 15.9065 19.9461i 1.05343 1.32096i
\(229\) −0.209251 + 0.916788i −0.0138277 + 0.0605831i −0.981371 0.192122i \(-0.938463\pi\)
0.967543 + 0.252705i \(0.0813202\pi\)
\(230\) 32.5898 + 15.6944i 2.14891 + 1.03486i
\(231\) 16.0061 + 20.0710i 1.05313 + 1.32058i
\(232\) 1.60086 + 2.00742i 0.105102 + 0.131793i
\(233\) 0.548508 + 2.40317i 0.0359339 + 0.157437i 0.989712 0.143076i \(-0.0456993\pi\)
−0.953778 + 0.300513i \(0.902842\pi\)
\(234\) 9.03582 + 4.35142i 0.590690 + 0.284461i
\(235\) 7.07428 3.40679i 0.461475 0.222235i
\(236\) −2.00381 8.77926i −0.130437 0.571481i
\(237\) 1.75825 + 7.70339i 0.114211 + 0.500389i
\(238\) −7.30735 + 3.51903i −0.473665 + 0.228105i
\(239\) 14.3635 + 6.91711i 0.929099 + 0.447430i 0.836311 0.548255i \(-0.184708\pi\)
0.0927879 + 0.995686i \(0.470422\pi\)
\(240\) 2.25725 + 9.88966i 0.145705 + 0.638375i
\(241\) −1.53741 1.92786i −0.0990335 0.124184i 0.729845 0.683612i \(-0.239592\pi\)
−0.828879 + 0.559428i \(0.811021\pi\)
\(242\) 10.8957 + 13.6628i 0.700401 + 0.878276i
\(243\) −7.68243 3.69967i −0.492828 0.237334i
\(244\) 2.12238 9.29878i 0.135872 0.595293i
\(245\) 10.4774 13.1382i 0.669375 0.839369i
\(246\) 1.60405 7.02780i 0.102271 0.448076i
\(247\) −41.2089 + 19.8452i −2.62206 + 1.26272i
\(248\) −1.04660 1.31240i −0.0664593 0.0833373i
\(249\) −20.5367 + 9.88995i −1.30146 + 0.626750i
\(250\) −15.4563 + 19.3816i −0.977545 + 1.22580i
\(251\) −19.7788 −1.24843 −0.624214 0.781254i \(-0.714581\pi\)
−0.624214 + 0.781254i \(0.714581\pi\)
\(252\) −7.37580 −0.464631
\(253\) −25.1535 + 31.5415i −1.58139 + 1.98300i
\(254\) −23.2712 11.2068i −1.46017 0.703179i
\(255\) −0.631510 2.76683i −0.0395467 0.173265i
\(256\) −2.77271 + 12.1480i −0.173294 + 0.759251i
\(257\) −18.5575 −1.15758 −0.578791 0.815476i \(-0.696475\pi\)
−0.578791 + 0.815476i \(0.696475\pi\)
\(258\) 19.1909 4.43262i 1.19478 0.275963i
\(259\) −20.3722 −1.26587
\(260\) −5.44992 + 23.8776i −0.337989 + 1.48083i
\(261\) 1.22073 + 5.34838i 0.0755614 + 0.331056i
\(262\) 25.5224 + 12.2910i 1.57678 + 0.759338i
\(263\) −5.09210 + 6.38529i −0.313992 + 0.393734i −0.913636 0.406533i \(-0.866738\pi\)
0.599644 + 0.800267i \(0.295309\pi\)
\(264\) 2.57533 0.158500
\(265\) 16.1382 0.991365
\(266\) 40.0916 50.2733i 2.45818 3.08245i
\(267\) 7.78193 3.74758i 0.476246 0.229348i
\(268\) −0.864262 1.08375i −0.0527932 0.0662006i
\(269\) −13.2231 + 6.36789i −0.806224 + 0.388257i −0.791144 0.611629i \(-0.790514\pi\)
−0.0150794 + 0.999886i \(0.504800\pi\)
\(270\) 4.97768 21.8086i 0.302932 1.32723i
\(271\) −15.0959 + 18.9297i −0.917011 + 1.14990i 0.0713013 + 0.997455i \(0.477285\pi\)
−0.988313 + 0.152441i \(0.951287\pi\)
\(272\) 0.795372 3.48475i 0.0482265 0.211294i
\(273\) −30.1917 14.5396i −1.82728 0.879974i
\(274\) −4.80654 6.02722i −0.290374 0.364117i
\(275\) −3.46068 4.33955i −0.208687 0.261685i
\(276\) 6.53618 + 28.6369i 0.393432 + 1.72374i
\(277\) −6.40557 3.08476i −0.384873 0.185345i 0.231435 0.972850i \(-0.425658\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(278\) 4.98957 2.40285i 0.299255 0.144113i
\(279\) −0.798083 3.49663i −0.0477800 0.209338i
\(280\) −0.677476 2.96822i −0.0404869 0.177385i
\(281\) 2.09584 1.00930i 0.125027 0.0602099i −0.370325 0.928902i \(-0.620754\pi\)
0.495352 + 0.868693i \(0.335039\pi\)
\(282\) 10.9813 + 5.28833i 0.653929 + 0.314915i
\(283\) −0.559659 2.45203i −0.0332683 0.145758i 0.955566 0.294777i \(-0.0952455\pi\)
−0.988834 + 0.149019i \(0.952388\pi\)
\(284\) 4.69220 + 5.88383i 0.278431 + 0.349141i
\(285\) 14.0286 + 17.5913i 0.830980 + 1.04202i
\(286\) −47.0455 22.6559i −2.78186 1.33967i
\(287\) 2.11498 9.26632i 0.124843 0.546974i
\(288\) 4.29472 5.38540i 0.253069 0.317338i
\(289\) −0.222521 + 0.974928i −0.0130895 + 0.0573487i
\(290\) −23.0734 + 11.1116i −1.35492 + 0.652494i
\(291\) 10.8290 + 13.5792i 0.634810 + 0.796026i
\(292\) −20.0873 + 9.67354i −1.17552 + 0.566101i
\(293\) −8.67796 + 10.8818i −0.506972 + 0.635722i −0.967786 0.251774i \(-0.918986\pi\)
0.460814 + 0.887497i \(0.347557\pi\)
\(294\) 26.0853 1.52133
\(295\) 7.94191 0.462396
\(296\) −1.27421 + 1.59781i −0.0740622 + 0.0928710i
\(297\) 22.4783 + 10.8250i 1.30432 + 0.628128i
\(298\) −10.9539 47.9920i −0.634540 2.78010i
\(299\) 11.7182 51.3407i 0.677680 2.96911i
\(300\) −4.04125 −0.233322
\(301\) 25.3037 5.84451i 1.45848 0.336872i
\(302\) −23.3078 −1.34121
\(303\) 2.86507 12.5527i 0.164594 0.721133i
\(304\) 6.30586 + 27.6278i 0.361666 + 1.58456i
\(305\) 7.57883 + 3.64977i 0.433963 + 0.208985i
\(306\) −1.08388 + 1.35914i −0.0619611 + 0.0776968i
\(307\) 10.8839 0.621176 0.310588 0.950545i \(-0.399474\pi\)
0.310588 + 0.950545i \(0.399474\pi\)
\(308\) 38.4024 2.18818
\(309\) −0.640833 + 0.803579i −0.0364557 + 0.0457140i
\(310\) 15.0848 7.26446i 0.856760 0.412594i
\(311\) 15.8110 + 19.8263i 0.896558 + 1.12425i 0.991673 + 0.128781i \(0.0411066\pi\)
−0.0951154 + 0.995466i \(0.530322\pi\)
\(312\) −3.02875 + 1.45857i −0.171469 + 0.0825751i
\(313\) −1.72989 + 7.57912i −0.0977789 + 0.428397i −0.999996 0.00288513i \(-0.999082\pi\)
0.902217 + 0.431283i \(0.141939\pi\)
\(314\) −21.6506 + 27.1490i −1.22181 + 1.53210i
\(315\) 1.44750 6.34192i 0.0815574 0.357326i
\(316\) 10.6493 + 5.12843i 0.599070 + 0.288497i
\(317\) 8.72927 + 10.9462i 0.490285 + 0.614797i 0.964007 0.265877i \(-0.0856614\pi\)
−0.473722 + 0.880674i \(0.657090\pi\)
\(318\) 15.6192 + 19.5859i 0.875881 + 1.09832i
\(319\) −6.35580 27.8466i −0.355857 1.55911i
\(320\) 16.5085 + 7.95008i 0.922854 + 0.444423i
\(321\) 2.92701 1.40957i 0.163370 0.0786747i
\(322\) 16.4742 + 72.1780i 0.918069 + 4.02232i
\(323\) −1.76419 7.72941i −0.0981621 0.430076i
\(324\) 11.3323 5.45733i 0.629570 0.303185i
\(325\) 6.52774 + 3.14359i 0.362094 + 0.174375i
\(326\) −3.50292 15.3473i −0.194009 0.850009i
\(327\) −0.332823 0.417347i −0.0184052 0.0230793i
\(328\) −0.594483 0.745458i −0.0328248 0.0411611i
\(329\) 14.4791 + 6.97279i 0.798261 + 0.384422i
\(330\) −5.71585 + 25.0428i −0.314647 + 1.37856i
\(331\) −8.25301 + 10.3489i −0.453626 + 0.568829i −0.955077 0.296357i \(-0.904228\pi\)
0.501451 + 0.865186i \(0.332800\pi\)
\(332\) −7.58741 + 33.2426i −0.416413 + 1.82443i
\(333\) −3.93412 + 1.89457i −0.215588 + 0.103822i
\(334\) −20.5504 25.7694i −1.12447 1.41004i
\(335\) 1.10145 0.530431i 0.0601787 0.0289805i
\(336\) −12.9449 + 16.2324i −0.706203 + 0.885550i
\(337\) −3.22964 −0.175930 −0.0879648 0.996124i \(-0.528036\pi\)
−0.0879648 + 0.996124i \(0.528036\pi\)
\(338\) 41.5368 2.25931
\(339\) 15.1424 18.9880i 0.822422 1.03128i
\(340\) −3.82491 1.84198i −0.207435 0.0998954i
\(341\) 4.15526 + 18.2054i 0.225020 + 0.985877i
\(342\) 3.06687 13.4368i 0.165837 0.726581i
\(343\) 6.67146 0.360225
\(344\) 1.12427 2.35015i 0.0606168 0.126712i
\(345\) −25.9055 −1.39471
\(346\) 6.01413 26.3496i 0.323322 1.41657i
\(347\) 4.80688 + 21.0603i 0.258047 + 1.13058i 0.923337 + 0.383992i \(0.125451\pi\)
−0.665290 + 0.746585i \(0.731692\pi\)
\(348\) −18.7367 9.02312i −1.00439 0.483690i
\(349\) −10.9922 + 13.7837i −0.588397 + 0.737826i −0.983519 0.180802i \(-0.942131\pi\)
0.395123 + 0.918628i \(0.370702\pi\)
\(350\) −10.1858 −0.544455
\(351\) −32.5667 −1.73828
\(352\) −22.3607 + 28.0394i −1.19183 + 1.49450i
\(353\) 26.7908 12.9017i 1.42593 0.686691i 0.447692 0.894188i \(-0.352246\pi\)
0.978236 + 0.207497i \(0.0665318\pi\)
\(354\) 7.68647 + 9.63853i 0.408531 + 0.512282i
\(355\) −5.97993 + 2.87978i −0.317382 + 0.152843i
\(356\) 2.87508 12.5966i 0.152379 0.667616i
\(357\) 3.62159 4.54133i 0.191675 0.240353i
\(358\) 3.49832 15.3271i 0.184892 0.810064i
\(359\) −20.2613 9.75733i −1.06935 0.514972i −0.185454 0.982653i \(-0.559375\pi\)
−0.883897 + 0.467681i \(0.845090\pi\)
\(360\) −0.406867 0.510195i −0.0214438 0.0268897i
\(361\) 27.3439 + 34.2882i 1.43915 + 1.80464i
\(362\) 7.62226 + 33.3953i 0.400617 + 1.75522i
\(363\) −11.2760 5.43024i −0.591837 0.285014i
\(364\) −45.1637 + 21.7497i −2.36722 + 1.13999i
\(365\) −4.37544 19.1701i −0.229021 1.00341i
\(366\) 2.90560 + 12.7303i 0.151878 + 0.665422i
\(367\) 20.5775 9.90959i 1.07414 0.517276i 0.188698 0.982035i \(-0.439573\pi\)
0.885437 + 0.464759i \(0.153859\pi\)
\(368\) −29.3962 14.1565i −1.53238 0.737957i
\(369\) −0.453321 1.98613i −0.0235990 0.103394i
\(370\) −12.7093 15.9369i −0.660723 0.828520i
\(371\) 20.5943 + 25.8244i 1.06920 + 1.34074i
\(372\) 12.2496 + 5.89908i 0.635111 + 0.305853i
\(373\) −3.42429 + 15.0028i −0.177303 + 0.776815i 0.805566 + 0.592507i \(0.201862\pi\)
−0.982869 + 0.184308i \(0.940996\pi\)
\(374\) 5.64326 7.07642i 0.291806 0.365913i
\(375\) 3.95065 17.3089i 0.204011 0.893829i
\(376\) 1.45251 0.699490i 0.0749073 0.0360735i
\(377\) 23.2461 + 29.1497i 1.19723 + 1.50128i
\(378\) 41.2502 19.8651i 2.12168 1.02175i
\(379\) 8.80883 11.0459i 0.452479 0.567391i −0.502305 0.864690i \(-0.667515\pi\)
0.954784 + 0.297300i \(0.0960860\pi\)
\(380\) 33.6578 1.72661
\(381\) 18.4982 0.947692
\(382\) 26.8326 33.6470i 1.37287 1.72153i
\(383\) −3.49090 1.68113i −0.178377 0.0859016i 0.342564 0.939494i \(-0.388705\pi\)
−0.520941 + 0.853593i \(0.674419\pi\)
\(384\) 1.03243 + 4.52335i 0.0526857 + 0.230831i
\(385\) −7.53649 + 33.0195i −0.384095 + 1.68283i
\(386\) 13.3558 0.679792
\(387\) 4.34293 3.48184i 0.220764 0.176992i
\(388\) 25.9814 1.31901
\(389\) 3.25732 14.2713i 0.165153 0.723582i −0.822737 0.568423i \(-0.807554\pi\)
0.987889 0.155159i \(-0.0495890\pi\)
\(390\) −7.46108 32.6891i −0.377807 1.65528i
\(391\) 8.22417 + 3.96055i 0.415914 + 0.200294i
\(392\) 2.15124 2.69757i 0.108654 0.136248i
\(393\) −20.2877 −1.02338
\(394\) 3.42350 0.172473
\(395\) −6.49950 + 8.15011i −0.327025 + 0.410077i
\(396\) 7.41599 3.57135i 0.372667 0.179467i
\(397\) 3.59379 + 4.50647i 0.180367 + 0.226173i 0.863793 0.503846i \(-0.168082\pi\)
−0.683426 + 0.730020i \(0.739511\pi\)
\(398\) −11.1823 + 5.38510i −0.560516 + 0.269930i
\(399\) −10.2474 + 44.8970i −0.513014 + 2.24766i
\(400\) 2.79881 3.50960i 0.139941 0.175480i
\(401\) 2.80958 12.3096i 0.140304 0.614711i −0.855060 0.518529i \(-0.826480\pi\)
0.995364 0.0961817i \(-0.0306630\pi\)
\(402\) 1.70977 + 0.823383i 0.0852757 + 0.0410666i
\(403\) −15.1977 19.0573i −0.757051 0.949311i
\(404\) −12.0087 15.0584i −0.597455 0.749185i
\(405\) 2.46841 + 10.8148i 0.122656 + 0.537392i
\(406\) −47.2251 22.7424i −2.34374 1.12869i
\(407\) 20.4832 9.86419i 1.01531 0.488950i
\(408\) −0.129663 0.568091i −0.00641928 0.0281247i
\(409\) 7.82317 + 34.2755i 0.386831 + 1.69482i 0.675477 + 0.737381i \(0.263938\pi\)
−0.288647 + 0.957436i \(0.593205\pi\)
\(410\) 8.56836 4.12631i 0.423161 0.203784i
\(411\) 4.97432 + 2.39551i 0.245365 + 0.118162i
\(412\) 0.342128 + 1.49896i 0.0168554 + 0.0738484i
\(413\) 10.1348 + 12.7086i 0.498700 + 0.625351i
\(414\) 9.89378 + 12.4064i 0.486253 + 0.609742i
\(415\) −27.0939 13.0477i −1.32999 0.640488i
\(416\) 10.4171 45.6403i 0.510740 2.23770i
\(417\) −2.47288 + 3.10089i −0.121097 + 0.151851i
\(418\) −15.9678 + 69.9596i −0.781012 + 3.42184i
\(419\) 3.02503 1.45678i 0.147782 0.0711682i −0.358531 0.933518i \(-0.616722\pi\)
0.506313 + 0.862350i \(0.331008\pi\)
\(420\) 15.3749 + 19.2795i 0.750217 + 0.940742i
\(421\) 34.2748 16.5059i 1.67045 0.804448i 0.672528 0.740072i \(-0.265208\pi\)
0.997926 0.0643764i \(-0.0205058\pi\)
\(422\) 3.82054 4.79081i 0.185981 0.233213i
\(423\) 3.44456 0.167480
\(424\) 3.31354 0.160920
\(425\) −0.783024 + 0.981880i −0.0379822 + 0.0476282i
\(426\) −9.28259 4.47026i −0.449743 0.216585i
\(427\) 3.83110 + 16.7852i 0.185400 + 0.812291i
\(428\) 1.08140 4.73793i 0.0522715 0.229016i
\(429\) 37.3963 1.80551
\(430\) 20.3579 + 16.1487i 0.981745 + 0.778758i
\(431\) −19.5020 −0.939379 −0.469689 0.882832i \(-0.655634\pi\)
−0.469689 + 0.882832i \(0.655634\pi\)
\(432\) −4.48990 + 19.6715i −0.216020 + 0.946447i
\(433\) 2.23479 + 9.79125i 0.107397 + 0.470538i 0.999813 + 0.0193243i \(0.00615149\pi\)
−0.892416 + 0.451213i \(0.850991\pi\)
\(434\) 30.8746 + 14.8684i 1.48203 + 0.713706i
\(435\) 11.4354 14.3396i 0.548286 0.687529i
\(436\) −0.798520 −0.0382422
\(437\) −72.3696 −3.46191
\(438\) 19.0306 23.8637i 0.909319 1.14025i
\(439\) −5.35122 + 2.57701i −0.255400 + 0.122994i −0.557203 0.830376i \(-0.688126\pi\)
0.301803 + 0.953370i \(0.402411\pi\)
\(440\) 2.11837 + 2.65636i 0.100990 + 0.126637i
\(441\) 6.64192 3.19858i 0.316282 0.152313i
\(442\) −2.62901 + 11.5184i −0.125049 + 0.547877i
\(443\) 2.57766 3.23229i 0.122469 0.153571i −0.716817 0.697261i \(-0.754402\pi\)
0.839286 + 0.543690i \(0.182973\pi\)
\(444\) 3.68335 16.1378i 0.174804 0.765866i
\(445\) 10.2666 + 4.94415i 0.486685 + 0.234375i
\(446\) 8.14425 + 10.2126i 0.385641 + 0.483579i
\(447\) 21.9809 + 27.5632i 1.03966 + 1.30369i
\(448\) 8.34507 + 36.5621i 0.394268 + 1.72740i
\(449\) −5.34205 2.57259i −0.252107 0.121408i 0.303563 0.952811i \(-0.401824\pi\)
−0.555670 + 0.831403i \(0.687538\pi\)
\(450\) −1.96701 + 0.947261i −0.0927256 + 0.0446543i
\(451\) 2.36024 + 10.3409i 0.111139 + 0.486933i
\(452\) −8.08422 35.4193i −0.380250 1.66598i
\(453\) 15.0394 7.24261i 0.706614 0.340287i
\(454\) −8.71993 4.19930i −0.409246 0.197083i
\(455\) −9.83761 43.1014i −0.461194 2.02062i
\(456\) 2.88038 + 3.61188i 0.134886 + 0.169142i
\(457\) −20.9118 26.2226i −0.978213 1.22664i −0.973976 0.226649i \(-0.927223\pi\)
−0.00423647 0.999991i \(-0.501349\pi\)
\(458\) −1.73508 0.835572i −0.0810751 0.0390437i
\(459\) 1.25614 5.50350i 0.0586315 0.256881i
\(460\) −24.1615 + 30.2975i −1.12653 + 1.41263i
\(461\) 1.69864 7.44221i 0.0791134 0.346618i −0.919843 0.392286i \(-0.871684\pi\)
0.998957 + 0.0456676i \(0.0145415\pi\)
\(462\) −47.3675 + 22.8110i −2.20374 + 1.06126i
\(463\) 9.53784 + 11.9601i 0.443261 + 0.555832i 0.952399 0.304853i \(-0.0986072\pi\)
−0.509138 + 0.860685i \(0.670036\pi\)
\(464\) 20.8124 10.0227i 0.966191 0.465293i
\(465\) −7.47618 + 9.37483i −0.346699 + 0.434747i
\(466\) −5.04808 −0.233848
\(467\) −4.47020 −0.206856 −0.103428 0.994637i \(-0.532981\pi\)
−0.103428 + 0.994637i \(0.532981\pi\)
\(468\) −6.69899 + 8.40027i −0.309661 + 0.388303i
\(469\) 2.25437 + 1.08565i 0.104097 + 0.0501306i
\(470\) 3.57814 + 15.6768i 0.165047 + 0.723119i
\(471\) 5.53390 24.2456i 0.254989 1.11718i
\(472\) 1.63065 0.0750568
\(473\) −22.6117 + 18.1284i −1.03969 + 0.833544i
\(474\) −16.1817 −0.743249
\(475\) 2.21560 9.70716i 0.101658 0.445395i
\(476\) −1.93350 8.47120i −0.0886216 0.388277i
\(477\) 6.37863 + 3.07179i 0.292057 + 0.140647i
\(478\) −20.3561 + 25.5257i −0.931066 + 1.16752i
\(479\) 37.1768 1.69865 0.849327 0.527868i \(-0.177008\pi\)
0.849327 + 0.527868i \(0.177008\pi\)
\(480\) −23.0292 −1.05113
\(481\) −18.5028 + 23.2018i −0.843656 + 1.05791i
\(482\) 4.54973 2.19103i 0.207234 0.0997988i
\(483\) −33.0584 41.4539i −1.50421 1.88622i
\(484\) −16.8678 + 8.12308i −0.766716 + 0.369231i
\(485\) −5.09885 + 22.3395i −0.231527 + 1.01439i
\(486\) 10.8876 13.6526i 0.493872 0.619296i
\(487\) 9.17013 40.1770i 0.415538 1.82059i −0.141294 0.989968i \(-0.545126\pi\)
0.556832 0.830625i \(-0.312017\pi\)
\(488\) 1.55610 + 0.749380i 0.0704415 + 0.0339228i
\(489\) 7.02925 + 8.81440i 0.317874 + 0.398601i
\(490\) 21.4569 + 26.9061i 0.969323 + 1.21549i
\(491\) 9.59233 + 42.0267i 0.432896 + 1.89664i 0.442662 + 0.896688i \(0.354034\pi\)
−0.00976659 + 0.999952i \(0.503109\pi\)
\(492\) 6.95791 + 3.35075i 0.313687 + 0.151064i
\(493\) −5.82268 + 2.80405i −0.262240 + 0.126288i
\(494\) −20.8433 91.3204i −0.937784 4.10870i
\(495\) 1.61536 + 7.07735i 0.0726050 + 0.318103i
\(496\) −13.6066 + 6.55260i −0.610955 + 0.294220i
\(497\) −12.2393 5.89414i −0.549008 0.264388i
\(498\) −10.3874 45.5100i −0.465469 2.03935i
\(499\) −17.5508 22.0080i −0.785681 0.985213i −0.999964 0.00844135i \(-0.997313\pi\)
0.214283 0.976772i \(-0.431258\pi\)
\(500\) −16.5588 20.7641i −0.740532 0.928598i
\(501\) 21.2677 + 10.2420i 0.950172 + 0.457579i
\(502\) 9.01333 39.4900i 0.402284 1.76252i
\(503\) 0.339633 0.425886i 0.0151435 0.0189893i −0.774202 0.632938i \(-0.781849\pi\)
0.789346 + 0.613949i \(0.210420\pi\)
\(504\) 0.297204 1.30214i 0.0132385 0.0580018i
\(505\) 15.3044 7.37019i 0.681035 0.327969i
\(506\) −51.5125 64.5946i −2.29001 2.87158i
\(507\) −26.8018 + 12.9071i −1.19031 + 0.573222i
\(508\) 17.2529 21.6344i 0.765472 0.959871i
\(509\) 23.3239 1.03382 0.516908 0.856041i \(-0.327083\pi\)
0.516908 + 0.856041i \(0.327083\pi\)
\(510\) 5.81197 0.257359
\(511\) 25.0923 31.4648i 1.11002 1.39192i
\(512\) −28.6912 13.8169i −1.26798 0.610629i
\(513\) 9.95890 + 43.6328i 0.439696 + 1.92643i
\(514\) 8.45675 37.0514i 0.373011 1.63427i
\(515\) −1.35599 −0.0597520
\(516\) 0.0547389 + 21.1010i 0.00240975 + 0.928920i
\(517\) −17.9343 −0.788748
\(518\) 9.28373 40.6747i 0.407904 1.78714i
\(519\) 4.30718 + 18.8710i 0.189064 + 0.828345i
\(520\) −3.99580 1.92428i −0.175228 0.0843851i
\(521\) 6.51445 8.16886i 0.285403 0.357884i −0.618377 0.785882i \(-0.712209\pi\)
0.903780 + 0.427998i \(0.140781\pi\)
\(522\) −11.2348 −0.491732
\(523\) 2.42786 0.106163 0.0530815 0.998590i \(-0.483096\pi\)
0.0530815 + 0.998590i \(0.483096\pi\)
\(524\) −18.9219 + 23.7273i −0.826605 + 1.03653i
\(525\) 6.57242 3.16511i 0.286844 0.138137i
\(526\) −10.4282 13.0766i −0.454693 0.570167i
\(527\) 3.80672 1.83322i 0.165823 0.0798562i
\(528\) 5.15574 22.5888i 0.224375 0.983050i
\(529\) 37.6108 47.1624i 1.63525 2.05054i
\(530\) −7.35430 + 32.2213i −0.319450 + 1.39960i
\(531\) 3.13903 + 1.51168i 0.136222 + 0.0656012i
\(532\) 42.9512 + 53.8592i 1.86217 + 2.33509i
\(533\) −8.63248 10.8248i −0.373914 0.468873i
\(534\) 3.93607 + 17.2450i 0.170330 + 0.746265i
\(535\) 3.86158 + 1.85964i 0.166951 + 0.0803992i
\(536\) 0.226152 0.108909i 0.00976830 0.00470417i
\(537\) 2.50541 + 10.9769i 0.108116 + 0.473689i
\(538\) −6.68817 29.3028i −0.288347 1.26333i
\(539\) −34.5815 + 16.6536i −1.48953 + 0.717320i
\(540\) 21.5917 + 10.3980i 0.929161 + 0.447460i
\(541\) −1.96930 8.62806i −0.0846668 0.370949i 0.914789 0.403932i \(-0.132357\pi\)
−0.999456 + 0.0329822i \(0.989500\pi\)
\(542\) −30.9153 38.7666i −1.32793 1.66517i
\(543\) −15.2955 19.1799i −0.656391 0.823088i
\(544\) 7.31103 + 3.52080i 0.313458 + 0.150953i
\(545\) 0.156710 0.686590i 0.00671271 0.0294103i
\(546\) 42.7879 53.6544i 1.83115 2.29619i
\(547\) −9.46809 + 41.4824i −0.404826 + 1.77366i 0.202577 + 0.979266i \(0.435068\pi\)
−0.607403 + 0.794394i \(0.707789\pi\)
\(548\) 7.44107 3.58343i 0.317867 0.153077i
\(549\) 2.30082 + 2.88514i 0.0981967 + 0.123135i
\(550\) 10.2413 4.93196i 0.436691 0.210299i
\(551\) 31.9460 40.0590i 1.36094 1.70657i
\(552\) −5.31898 −0.226391
\(553\) −21.3359 −0.907295
\(554\) 9.07803 11.3835i 0.385688 0.483638i
\(555\) 13.1529 + 6.33409i 0.558308 + 0.268867i
\(556\) 1.32022 + 5.78426i 0.0559898 + 0.245307i
\(557\) −4.68314 + 20.5182i −0.198431 + 0.869384i 0.773440 + 0.633870i \(0.218534\pi\)
−0.971871 + 0.235514i \(0.924323\pi\)
\(558\) 7.34499 0.310938
\(559\) 16.3255 34.1265i 0.690497 1.44340i
\(560\) −27.3912 −1.15749
\(561\) −1.44242 + 6.31965i −0.0608990 + 0.266816i
\(562\) 1.06007 + 4.64445i 0.0447161 + 0.195914i
\(563\) −3.19615 1.53919i −0.134702 0.0648690i 0.365319 0.930882i \(-0.380960\pi\)
−0.500021 + 0.866013i \(0.666674\pi\)
\(564\) −8.14136 + 10.2089i −0.342813 + 0.429874i
\(565\) 32.0410 1.34798
\(566\) 5.15071 0.216500
\(567\) −14.1559 + 17.7509i −0.594490 + 0.745467i
\(568\) −1.22781 + 0.591283i −0.0515179 + 0.0248097i
\(569\) 6.04913 + 7.58538i 0.253593 + 0.317995i 0.892290 0.451463i \(-0.149098\pi\)
−0.638697 + 0.769458i \(0.720526\pi\)
\(570\) −41.5152 + 19.9927i −1.73888 + 0.837401i
\(571\) 1.89576 8.30585i 0.0793350 0.347589i −0.919645 0.392751i \(-0.871523\pi\)
0.998980 + 0.0451622i \(0.0143805\pi\)
\(572\) 34.8786 43.7364i 1.45835 1.82871i
\(573\) −6.85842 + 30.0487i −0.286515 + 1.25530i
\(574\) 17.5371 + 8.44544i 0.731986 + 0.352506i
\(575\) 7.14755 + 8.96274i 0.298073 + 0.373772i
\(576\) 5.01174 + 6.28453i 0.208823 + 0.261855i
\(577\) −3.57627 15.6686i −0.148882 0.652294i −0.993197 0.116447i \(-0.962849\pi\)
0.844315 0.535847i \(-0.180008\pi\)
\(578\) −1.84512 0.888561i −0.0767467 0.0369593i
\(579\) −8.61786 + 4.15014i −0.358146 + 0.172474i
\(580\) −6.10514 26.7484i −0.253502 1.11066i
\(581\) −13.6960 60.0060i −0.568205 2.48947i
\(582\) −32.0468 + 15.4329i −1.32838 + 0.639715i
\(583\) −33.2106 15.9934i −1.37544 0.662379i
\(584\) −0.898376 3.93604i −0.0371751 0.162875i
\(585\) −5.90811 7.40853i −0.244270 0.306305i
\(586\) −17.7718 22.2851i −0.734147 0.920591i
\(587\) −26.3255 12.6777i −1.08657 0.523264i −0.197158 0.980372i \(-0.563171\pi\)
−0.889411 + 0.457108i \(0.848885\pi\)
\(588\) −6.21855 + 27.2452i −0.256449 + 1.12357i
\(589\) −20.8855 + 26.1895i −0.860571 + 1.07912i
\(590\) −3.61918 + 15.8566i −0.148999 + 0.652808i
\(591\) −2.20902 + 1.06381i −0.0908670 + 0.0437593i
\(592\) 11.4638 + 14.3752i 0.471161 + 0.590817i
\(593\) 18.6638 8.98800i 0.766429 0.369093i −0.00946564 0.999955i \(-0.503013\pi\)
0.775895 + 0.630862i \(0.217299\pi\)
\(594\) −31.8564 + 39.9466i −1.30708 + 1.63903i
\(595\) 7.66322 0.314161
\(596\) 52.7374 2.16021
\(597\) 5.54204 6.94950i 0.226821 0.284424i
\(598\) 97.1658 + 46.7926i 3.97341 + 1.91349i
\(599\) 0.648234 + 2.84010i 0.0264861 + 0.116043i 0.986443 0.164105i \(-0.0524735\pi\)
−0.959957 + 0.280148i \(0.909616\pi\)
\(600\) 0.162840 0.713450i 0.00664793 0.0291265i
\(601\) −28.1432 −1.14799 −0.573993 0.818860i \(-0.694606\pi\)
−0.573993 + 0.818860i \(0.694606\pi\)
\(602\) 0.137967 + 53.1842i 0.00562313 + 2.16763i
\(603\) 0.536311 0.0218403
\(604\) 5.55641 24.3442i 0.226087 0.990553i
\(605\) −3.67415 16.0975i −0.149376 0.654457i
\(606\) 23.7568 + 11.4407i 0.965055 + 0.464746i
\(607\) 26.3521 33.0444i 1.06960 1.34123i 0.132885 0.991131i \(-0.457576\pi\)
0.936712 0.350101i \(-0.113853\pi\)
\(608\) −64.3343 −2.60910
\(609\) 37.5391 1.52116
\(610\) −10.7408 + 13.4685i −0.434881 + 0.545324i
\(611\) 21.0918 10.1573i 0.853284 0.410920i
\(612\) −1.16119 1.45608i −0.0469382 0.0588586i
\(613\) 35.6836 17.1843i 1.44125 0.694068i 0.460197 0.887817i \(-0.347779\pi\)
0.981051 + 0.193749i \(0.0620646\pi\)
\(614\) −4.95985 + 21.7305i −0.200163 + 0.876973i
\(615\) −4.24656 + 5.32502i −0.171238 + 0.214726i
\(616\) −1.54741 + 6.77964i −0.0623469 + 0.273160i
\(617\) −17.4303 8.39400i −0.701719 0.337930i 0.0487729 0.998810i \(-0.484469\pi\)
−0.750492 + 0.660880i \(0.770183\pi\)
\(618\) −1.31238 1.64567i −0.0527916 0.0661985i
\(619\) −5.42144 6.79827i −0.217906 0.273246i 0.660849 0.750519i \(-0.270197\pi\)
−0.878755 + 0.477274i \(0.841625\pi\)
\(620\) 3.99138 + 17.4874i 0.160298 + 0.702310i
\(621\) −46.4257 22.3574i −1.86300 0.897173i
\(622\) −46.7900 + 22.5329i −1.87611 + 0.903486i
\(623\) 5.18979 + 22.7380i 0.207925 + 0.910978i
\(624\) 6.72995 + 29.4858i 0.269414 + 1.18038i
\(625\) 15.4457 7.43825i 0.617828 0.297530i
\(626\) −14.3440 6.90771i −0.573302 0.276088i
\(627\) −11.4358 50.1034i −0.456701 2.00094i
\(628\) −23.1948 29.0854i −0.925575 1.16063i
\(629\) −3.20723 4.02174i −0.127881 0.160357i
\(630\) 12.0025 + 5.78010i 0.478191 + 0.230285i
\(631\) −2.85471 + 12.5073i −0.113644 + 0.497908i 0.885784 + 0.464098i \(0.153621\pi\)
−0.999428 + 0.0338105i \(0.989236\pi\)
\(632\) −1.33449 + 1.67340i −0.0530833 + 0.0665643i
\(633\) −0.976533 + 4.27847i −0.0388137 + 0.170054i
\(634\) −25.8329 + 12.4404i −1.02595 + 0.494073i
\(635\) 15.2160 + 19.0802i 0.603828 + 0.757176i
\(636\) −24.1803 + 11.6446i −0.958810 + 0.461739i
\(637\) 31.2381 39.1713i 1.23770 1.55202i
\(638\) 58.4943 2.31581
\(639\) −2.91170 −0.115185
\(640\) −3.81644 + 4.78566i −0.150858 + 0.189170i
\(641\) 34.1098 + 16.4264i 1.34726 + 0.648805i 0.961757 0.273903i \(-0.0883147\pi\)
0.385500 + 0.922708i \(0.374029\pi\)
\(642\) 1.48047 + 6.48635i 0.0584294 + 0.255996i
\(643\) 9.10914 39.9097i 0.359229 1.57389i −0.395889 0.918298i \(-0.629564\pi\)
0.755119 0.655588i \(-0.227579\pi\)
\(644\) −79.3149 −3.12544
\(645\) −18.1540 4.09401i −0.714812 0.161201i
\(646\) 16.2363 0.638810
\(647\) −2.99730 + 13.1320i −0.117836 + 0.516274i 0.881215 + 0.472716i \(0.156726\pi\)
−0.999051 + 0.0435576i \(0.986131\pi\)
\(648\) 0.506819 + 2.22052i 0.0199097 + 0.0872303i
\(649\) −16.3435 7.87063i −0.641539 0.308949i
\(650\) −9.25116 + 11.6006i −0.362860 + 0.455013i
\(651\) −24.5421 −0.961879
\(652\) 16.8648 0.660477
\(653\) −0.338321 + 0.424241i −0.0132395 + 0.0166018i −0.788407 0.615154i \(-0.789094\pi\)
0.775168 + 0.631756i \(0.217665\pi\)
\(654\) 0.984936 0.474320i 0.0385140 0.0185474i
\(655\) −16.6880 20.9260i −0.652052 0.817648i
\(656\) −7.72872 + 3.72196i −0.301756 + 0.145318i
\(657\) 1.91948 8.40978i 0.0748860 0.328097i
\(658\) −20.5200 + 25.7312i −0.799951 + 1.00311i
\(659\) −7.74191 + 33.9195i −0.301582 + 1.32132i 0.566157 + 0.824297i \(0.308429\pi\)
−0.867739 + 0.497019i \(0.834428\pi\)
\(660\) −24.7937 11.9400i −0.965095 0.464765i
\(661\) −7.44958 9.34148i −0.289755 0.363341i 0.615554 0.788095i \(-0.288932\pi\)
−0.905309 + 0.424753i \(0.860361\pi\)
\(662\) −16.9015 21.1939i −0.656897 0.823723i
\(663\) −1.88284 8.24924i −0.0731233 0.320374i
\(664\) −5.56298 2.67899i −0.215886 0.103965i
\(665\) −54.7388 + 26.3608i −2.12268 + 1.02223i
\(666\) −1.98986 8.71815i −0.0771056 0.337822i
\(667\) 13.1270 + 57.5132i 0.508280 + 2.22692i
\(668\) 31.8143 15.3210i 1.23093 0.592786i
\(669\) −8.42853 4.05896i −0.325866 0.156929i
\(670\) 0.557109 + 2.44086i 0.0215230 + 0.0942985i
\(671\) −11.9793 15.0216i −0.462457 0.579903i
\(672\) −29.3879 36.8512i −1.13366 1.42157i
\(673\) −16.3650 7.88097i −0.630825 0.303789i 0.0910149 0.995850i \(-0.470989\pi\)
−0.721840 + 0.692060i \(0.756703\pi\)
\(674\) 1.47177 6.44823i 0.0566903 0.248376i
\(675\) 4.42019 5.54275i 0.170133 0.213340i
\(676\) −9.90208 + 43.3839i −0.380849 + 1.66861i
\(677\) 23.3412 11.2405i 0.897074 0.432008i 0.0722425 0.997387i \(-0.476984\pi\)
0.824831 + 0.565379i \(0.191270\pi\)
\(678\) 31.0105 + 38.8859i 1.19095 + 1.49341i
\(679\) −42.2544 + 20.3487i −1.62158 + 0.780910i
\(680\) 0.479310 0.601035i 0.0183807 0.0230487i
\(681\) 6.93144 0.265613
\(682\) −38.2421 −1.46436
\(683\) −4.54362 + 5.69752i −0.173857 + 0.218009i −0.861124 0.508396i \(-0.830239\pi\)
0.687267 + 0.726405i \(0.258810\pi\)
\(684\) 13.3032 + 6.40649i 0.508661 + 0.244958i
\(685\) 1.62082 + 7.10129i 0.0619285 + 0.271326i
\(686\) −3.04023 + 13.3201i −0.116076 + 0.508564i
\(687\) 1.37921 0.0526202
\(688\) −18.3630 14.5662i −0.700081 0.555331i
\(689\) 48.1159 1.83307
\(690\) 11.8053 51.7224i 0.449420 1.96904i
\(691\) −4.50487 19.7371i −0.171373 0.750835i −0.985434 0.170056i \(-0.945605\pi\)
0.814061 0.580779i \(-0.197252\pi\)
\(692\) 26.0876 + 12.5631i 0.991702 + 0.477578i
\(693\) −9.26379 + 11.6164i −0.351902 + 0.441271i
\(694\) −44.2391 −1.67929
\(695\) −5.23256 −0.198482
\(696\) 2.34795 2.94423i 0.0889987 0.111601i
\(697\) 2.16226 1.04129i 0.0819015 0.0394417i
\(698\) −22.5111 28.2281i −0.852059 1.06845i
\(699\) 3.25729 1.56863i 0.123202 0.0593309i
\(700\) 2.42822 10.6387i 0.0917782 0.402107i
\(701\) −17.1557 + 21.5126i −0.647962 + 0.812519i −0.991973 0.126446i \(-0.959643\pi\)
0.344011 + 0.938966i \(0.388214\pi\)
\(702\) 14.8409 65.0220i 0.560132 2.45410i
\(703\) 36.7439 + 17.6949i 1.38582 + 0.667377i
\(704\) −26.0939 32.7207i −0.983451 1.23321i
\(705\) −7.18019 9.00367i −0.270422 0.339098i
\(706\) 13.5506 + 59.3693i 0.509985 + 2.23439i
\(707\) 31.3239 + 15.0848i 1.17806 + 0.567322i
\(708\) −11.8995 + 5.73051i −0.447212 + 0.215366i
\(709\) −2.81532 12.3347i −0.105731 0.463240i −0.999880 0.0154699i \(-0.995076\pi\)
0.894149 0.447770i \(-0.147782\pi\)
\(710\) −3.02462 13.2517i −0.113512 0.497329i
\(711\) −4.12023 + 1.98420i −0.154521 + 0.0744133i
\(712\) 2.10797 + 1.01514i 0.0789995 + 0.0380442i
\(713\) −8.58211 37.6007i −0.321402 1.40816i
\(714\) 7.41675 + 9.30031i 0.277565 + 0.348056i
\(715\) 30.7609 + 38.5729i 1.15039 + 1.44254i
\(716\) 15.1747 + 7.30775i 0.567105 + 0.273103i
\(717\) 5.20303 22.7960i 0.194311 0.851331i
\(718\) 28.7145 36.0068i 1.07162 1.34376i
\(719\) −5.31737 + 23.2969i −0.198304 + 0.868828i 0.773641 + 0.633624i \(0.218433\pi\)
−0.971946 + 0.235205i \(0.924424\pi\)
\(720\) −5.28958 + 2.54733i −0.197131 + 0.0949332i
\(721\) −1.73040 2.16985i −0.0644435 0.0808095i
\(722\) −80.9198 + 38.9689i −3.01152 + 1.45027i
\(723\) −2.25489 + 2.82754i −0.0838602 + 0.105157i
\(724\) −36.6974 −1.36385
\(725\) −8.11631 −0.301432
\(726\) 15.9804 20.0388i 0.593090 0.743711i
\(727\) −26.3515 12.6902i −0.977323 0.470654i −0.124139 0.992265i \(-0.539617\pi\)
−0.853183 + 0.521611i \(0.825331\pi\)
\(728\) −2.01988 8.84968i −0.0748618 0.327991i
\(729\) −6.60992 + 28.9599i −0.244812 + 1.07259i
\(730\) 40.2685 1.49040
\(731\) 5.13740 + 4.07518i 0.190014 + 0.150726i
\(732\) −13.9890 −0.517049
\(733\) −4.04085 + 17.7041i −0.149252 + 0.653916i 0.843842 + 0.536592i \(0.180289\pi\)
−0.993094 + 0.117324i \(0.962568\pi\)
\(734\) 10.4080 + 45.6004i 0.384166 + 1.68314i
\(735\) −22.2058 10.6938i −0.819074 0.394445i
\(736\) 46.1828 57.9114i 1.70232 2.13464i
\(737\) −2.79233 −0.102857
\(738\) 4.17205 0.153575
\(739\) 16.8997 21.1916i 0.621667 0.779546i −0.366911 0.930256i \(-0.619585\pi\)
0.988578 + 0.150710i \(0.0481560\pi\)
\(740\) 19.6754 9.47515i 0.723281 0.348314i
\(741\) 41.8259 + 52.4480i 1.53651 + 1.92672i
\(742\) −60.9454 + 29.3498i −2.23738 + 1.07746i
\(743\) 7.47647 32.7566i 0.274285 1.20172i −0.630614 0.776096i \(-0.717197\pi\)
0.904899 0.425626i \(-0.139946\pi\)
\(744\) −1.53503 + 1.92486i −0.0562768 + 0.0705689i
\(745\) −10.3497 + 45.3451i −0.379184 + 1.66131i
\(746\) −28.3938 13.6737i −1.03957 0.500631i
\(747\) −8.22531 10.3142i −0.300948 0.377377i
\(748\) 6.04578 + 7.58116i 0.221056 + 0.277195i
\(749\) 1.95203 + 8.55241i 0.0713257 + 0.312498i
\(750\) 32.7583 + 15.7756i 1.19616 + 0.576042i
\(751\) 31.9943 15.4076i 1.16749 0.562232i 0.253246 0.967402i \(-0.418502\pi\)
0.914242 + 0.405170i \(0.132788\pi\)
\(752\) −3.22751 14.1406i −0.117695 0.515656i
\(753\) 6.45513 + 28.2818i 0.235238 + 1.03065i
\(754\) −68.7930 + 33.1290i −2.50529 + 1.20649i
\(755\) 19.8414 + 9.55512i 0.722103 + 0.347746i
\(756\) 10.9146 + 47.8202i 0.396962 + 1.73920i
\(757\) −3.15619 3.95774i −0.114714 0.143846i 0.721159 0.692769i \(-0.243610\pi\)
−0.835873 + 0.548923i \(0.815038\pi\)
\(758\) 18.0398 + 22.6212i 0.655236 + 0.821640i
\(759\) 53.3105 + 25.6730i 1.93505 + 0.931871i
\(760\) −1.35623 + 5.94201i −0.0491955 + 0.215539i
\(761\) −23.5175 + 29.4900i −0.852507 + 1.06901i 0.144329 + 0.989530i \(0.453898\pi\)
−0.996836 + 0.0794803i \(0.974674\pi\)
\(762\) −8.42975 + 36.9331i −0.305378 + 1.33795i
\(763\) 1.29866 0.625402i 0.0470147 0.0226411i
\(764\) 28.7465 + 36.0470i 1.04001 + 1.30413i
\(765\) 1.47986 0.712665i 0.0535046 0.0257664i
\(766\) 4.94733 6.20376i 0.178754 0.224151i
\(767\) 23.6786 0.854986
\(768\) 18.2754 0.659457
\(769\) 31.6612 39.7019i 1.14173 1.43169i 0.256499 0.966545i \(-0.417431\pi\)
0.885235 0.465144i \(-0.153998\pi\)
\(770\) −62.4916 30.0944i −2.25204 1.08453i
\(771\) 6.05653 + 26.5354i 0.218120 + 0.955648i
\(772\) −3.18392 + 13.9497i −0.114592 + 0.502060i
\(773\) 13.8342 0.497582 0.248791 0.968557i \(-0.419967\pi\)
0.248791 + 0.968557i \(0.419967\pi\)
\(774\) 4.97267 + 10.2577i 0.178739 + 0.368706i
\(775\) 5.30623 0.190605
\(776\) −1.04691 + 4.58681i −0.0375818 + 0.164657i
\(777\) 6.64879 + 29.1302i 0.238524 + 1.04504i
\(778\) 27.0093 + 13.0070i 0.968332 + 0.466324i
\(779\) −11.8632 + 14.8760i −0.425044 + 0.532988i
\(780\) 35.9214 1.28619
\(781\) 15.1599 0.542465
\(782\) −11.6554 + 14.6154i −0.416795 + 0.522644i
\(783\) 32.8692 15.8290i 1.17465 0.565681i
\(784\) −19.3542 24.2695i −0.691223 0.866766i
\(785\) 29.5605 14.2356i 1.05506 0.508089i
\(786\) 9.24523 40.5060i 0.329766 1.44480i
\(787\) 4.10630 5.14914i 0.146374 0.183547i −0.703240 0.710953i \(-0.748264\pi\)
0.849613 + 0.527406i \(0.176835\pi\)
\(788\) −0.816137 + 3.57573i −0.0290737 + 0.127380i
\(789\) 10.7922 + 5.19727i 0.384214 + 0.185028i
\(790\) −13.3105 16.6908i −0.473566 0.593833i
\(791\) 40.8881 + 51.2720i 1.45381 + 1.82302i
\(792\) 0.331669 + 1.45314i 0.0117854 + 0.0516350i
\(793\) 22.5961 + 10.8817i 0.802412 + 0.386421i
\(794\) −10.6352 + 5.12166i −0.377431 + 0.181761i
\(795\) −5.26698 23.0761i −0.186800 0.818426i
\(796\) −2.95878 12.9633i −0.104871 0.459471i
\(797\) −0.523021 + 0.251874i −0.0185264 + 0.00892182i −0.443124 0.896460i \(-0.646130\pi\)
0.424598 + 0.905382i \(0.360416\pi\)
\(798\) −84.9705 40.9196i −3.00792 1.44854i
\(799\) 0.902958 + 3.95612i 0.0319444 + 0.139957i
\(800\) 6.35394 + 7.96759i 0.224646 + 0.281697i
\(801\) 3.11680 + 3.90834i 0.110127 + 0.138095i
\(802\) 23.2967 + 11.2191i 0.822635 + 0.396160i
\(803\) −9.99386 + 43.7860i −0.352676 + 1.54517i
\(804\) −1.26759 + 1.58951i −0.0447046 + 0.0560578i
\(805\) 15.5656 68.1972i 0.548614 2.40363i
\(806\) 44.9751 21.6589i 1.58418 0.762901i
\(807\) 13.4210 + 16.8294i 0.472442 + 0.592424i
\(808\) 3.14233 1.51327i 0.110547 0.0532365i
\(809\) −25.8731 + 32.4438i −0.909649 + 1.14066i 0.0799478 + 0.996799i \(0.474525\pi\)
−0.989597 + 0.143865i \(0.954047\pi\)
\(810\) −22.7175 −0.798211
\(811\) −4.11380 −0.144455 −0.0722275 0.997388i \(-0.523011\pi\)
−0.0722275 + 0.997388i \(0.523011\pi\)
\(812\) 35.0118 43.9034i 1.22867 1.54071i
\(813\) 31.9944 + 15.4077i 1.12209 + 0.540371i
\(814\) 10.3603 + 45.3915i 0.363129 + 1.59097i
\(815\) −3.30972 + 14.5008i −0.115935 + 0.507943i
\(816\) −5.24244 −0.183522
\(817\) −50.7150 11.4370i −1.77429 0.400131i
\(818\) −71.9989 −2.51738
\(819\) 4.31570 18.9083i 0.150803 0.660709i
\(820\) 2.26715 + 9.93305i 0.0791725 + 0.346877i
\(821\) −45.5031 21.9132i −1.58807 0.764774i −0.589010 0.808125i \(-0.700482\pi\)
−0.999060 + 0.0433512i \(0.986197\pi\)
\(822\) −7.04964 + 8.83997i −0.245885 + 0.308330i
\(823\) 36.0625 1.25706 0.628531 0.777785i \(-0.283657\pi\)
0.628531 + 0.777785i \(0.283657\pi\)
\(824\) −0.278415 −0.00969904
\(825\) −5.07570 + 6.36472i −0.176713 + 0.221591i
\(826\) −29.9923 + 14.4435i −1.04356 + 0.502554i
\(827\) −20.3914 25.5700i −0.709079 0.889157i 0.288586 0.957454i \(-0.406815\pi\)
−0.997665 + 0.0682974i \(0.978243\pi\)
\(828\) −15.3167 + 7.37613i −0.532292 + 0.256338i
\(829\) −3.14965 + 13.7995i −0.109392 + 0.479277i 0.890321 + 0.455333i \(0.150480\pi\)
−0.999713 + 0.0239446i \(0.992377\pi\)
\(830\) 38.3977 48.1492i 1.33280 1.67128i
\(831\) −2.32035 + 10.1661i −0.0804920 + 0.352658i
\(832\) 49.2198 + 23.7030i 1.70639 + 0.821755i
\(833\) 5.41473 + 6.78986i 0.187609 + 0.235255i
\(834\) −5.06427 6.35040i −0.175361 0.219896i
\(835\) 6.92984 + 30.3616i 0.239817 + 1.05071i
\(836\) −69.2639 33.3557i −2.39554 1.15363i
\(837\) −21.4890 + 10.3486i −0.742770 + 0.357699i
\(838\) 1.53005 + 6.70357i 0.0528546 + 0.231571i
\(839\) −4.91414 21.5303i −0.169655 0.743307i −0.986137 0.165936i \(-0.946936\pi\)
0.816482 0.577372i \(-0.195922\pi\)
\(840\) −4.02316 + 1.93745i −0.138812 + 0.0668484i
\(841\) −11.5020 5.53908i −0.396622 0.191003i
\(842\) 17.3361 + 75.9543i 0.597440 + 2.61756i
\(843\) −2.12721 2.66744i −0.0732651 0.0918716i
\(844\) 4.09305 + 5.13253i 0.140889 + 0.176669i
\(845\) −35.3594 17.0282i −1.21640 0.585787i
\(846\) −1.56971 + 6.87733i −0.0539676 + 0.236448i
\(847\) 21.0706 26.4217i 0.723994 0.907860i
\(848\) 6.63363 29.0638i 0.227800 0.998056i
\(849\) −3.32351 + 1.60052i −0.114063 + 0.0549296i
\(850\) −1.60357 2.01082i −0.0550021 0.0689705i
\(851\) −42.3052 + 20.3731i −1.45020 + 0.698381i
\(852\) 6.88194 8.62968i 0.235771 0.295648i
\(853\) −32.9693 −1.12885 −0.564424 0.825485i \(-0.690902\pi\)
−0.564424 + 0.825485i \(0.690902\pi\)
\(854\) −35.2588 −1.20653
\(855\) −8.11924 + 10.1812i −0.277672 + 0.348190i
\(856\) 0.792868 + 0.381825i 0.0270997 + 0.0130505i
\(857\) −6.63902 29.0874i −0.226785 0.993608i −0.952243 0.305342i \(-0.901229\pi\)
0.725458 0.688266i \(-0.241628\pi\)
\(858\) −17.0417 + 74.6646i −0.581794 + 2.54901i
\(859\) 12.2621 0.418376 0.209188 0.977875i \(-0.432918\pi\)
0.209188 + 0.977875i \(0.432918\pi\)
\(860\) −21.7199 + 17.4134i −0.740643 + 0.593793i
\(861\) −13.9402 −0.475081
\(862\) 8.88719 38.9373i 0.302699 1.32621i
\(863\) 8.60011 + 37.6796i 0.292751 + 1.28263i 0.880679 + 0.473714i \(0.157087\pi\)
−0.587928 + 0.808913i \(0.700056\pi\)
\(864\) −41.2710 19.8751i −1.40407 0.676163i
\(865\) −15.9218 + 19.9653i −0.541358 + 0.678842i
\(866\) −20.5674 −0.698909
\(867\) 1.46668 0.0498109
\(868\) −22.8898 + 28.7029i −0.776931 + 0.974241i
\(869\) 21.4522 10.3308i 0.727716 0.350449i
\(870\) 23.4189 + 29.3663i 0.793974 + 0.995612i
\(871\) 3.28395 1.58147i 0.111273 0.0535860i
\(872\) 0.0321760 0.140972i 0.00108962 0.00477392i
\(873\) −6.26747 + 7.85916i −0.212122 + 0.265992i
\(874\) 32.9793 144.492i 1.11554 4.88751i
\(875\) 43.1926 + 20.8004i 1.46018 + 0.703183i
\(876\) 20.3880 + 25.5658i 0.688848 + 0.863788i
\(877\) 26.0682 + 32.6885i 0.880262 + 1.10381i 0.993899 + 0.110291i \(0.0351784\pi\)
−0.113637 + 0.993522i \(0.536250\pi\)
\(878\) −2.70663 11.8585i −0.0913442 0.400205i
\(879\) 18.3921 + 8.85719i 0.620351 + 0.298746i
\(880\) 27.5404 13.2628i 0.928388 0.447088i
\(881\) −8.93232 39.1350i −0.300937 1.31849i −0.868716 0.495311i \(-0.835054\pi\)
0.567778 0.823182i \(-0.307803\pi\)
\(882\) 3.35946 + 14.7187i 0.113119 + 0.495606i
\(883\) 9.36247 4.50873i 0.315072 0.151731i −0.269664 0.962955i \(-0.586912\pi\)
0.584736 + 0.811224i \(0.301198\pi\)
\(884\) −11.4039 5.49183i −0.383555 0.184710i
\(885\) −2.59197 11.3562i −0.0871281 0.381733i
\(886\) 5.27886 + 6.61948i 0.177347 + 0.222386i
\(887\) −13.8468 17.3633i −0.464930 0.583003i 0.492992 0.870034i \(-0.335903\pi\)
−0.957921 + 0.287031i \(0.907332\pi\)
\(888\) 2.70058 + 1.30053i 0.0906255 + 0.0436429i
\(889\) −11.1148 + 48.6972i −0.372779 + 1.63325i
\(890\) −14.5500 + 18.2451i −0.487716 + 0.611576i
\(891\) 5.63804 24.7019i 0.188881 0.827544i
\(892\) −12.6082 + 6.07180i −0.422154 + 0.203299i
\(893\) −20.0586 25.1527i −0.671235 0.841702i
\(894\) −65.0490 + 31.3259i −2.17556 + 1.04770i
\(895\) −9.26144 + 11.6135i −0.309576 + 0.388196i
\(896\) −12.5282 −0.418539
\(897\) −77.2367 −2.57886
\(898\) 7.57079 9.49347i 0.252641 0.316801i
\(899\) 24.6016 + 11.8475i 0.820509 + 0.395137i
\(900\) −0.520462 2.28029i −0.0173487 0.0760098i
\(901\) −1.85589 + 8.13118i −0.0618286 + 0.270889i
\(902\) −21.7220 −0.723263
\(903\) −16.6154 34.2744i −0.552924 1.14058i
\(904\) 6.57874 0.218806
\(905\) 7.20187 31.5534i 0.239398 1.04887i
\(906\) 7.60688 + 33.3279i 0.252722 + 1.10725i
\(907\) 21.9983 + 10.5938i 0.730442 + 0.351762i 0.761858 0.647744i \(-0.224287\pi\)
−0.0314160 + 0.999506i \(0.510002\pi\)
\(908\) 6.46479 8.10659i 0.214542 0.269027i
\(909\) 7.45189 0.247164
\(910\) 90.5384 3.00132
\(911\) 6.13721 7.69582i 0.203335 0.254974i −0.669700 0.742632i \(-0.733577\pi\)
0.873035 + 0.487658i \(0.162149\pi\)
\(912\) 37.4470 18.0335i 1.24000 0.597150i
\(913\) 42.8255 + 53.7015i 1.41732 + 1.77726i
\(914\) 61.8851 29.8023i 2.04698 0.985772i
\(915\) 2.74535 12.0282i 0.0907584 0.397639i
\(916\) 1.28636 1.61304i 0.0425025 0.0532964i
\(917\) 12.1900 53.4081i 0.402551 1.76369i
\(918\) 10.4157 + 5.01596i 0.343771 + 0.165551i
\(919\) 18.8639 + 23.6545i 0.622261 + 0.780291i 0.988661 0.150167i \(-0.0479811\pi\)
−0.366400 + 0.930458i \(0.619410\pi\)
\(920\) −4.37521 5.48634i −0.144246 0.180879i
\(921\) −3.55213 15.5629i −0.117047 0.512815i
\(922\) 14.0849 + 6.78292i 0.463861 + 0.223384i
\(923\) −17.8290 + 8.58601i −0.586850 + 0.282612i
\(924\) −12.5333 54.9118i −0.412314 1.80647i
\(925\) −1.43753 6.29824i −0.0472658 0.207085i
\(926\) −28.2257 + 13.5928i −0.927554 + 0.446687i
\(927\) −0.535954 0.258102i −0.0176030 0.00847717i
\(928\) 11.6695 + 51.1274i 0.383070 + 1.67834i
\(929\) 2.65824 + 3.33333i 0.0872140 + 0.109363i 0.823524 0.567282i \(-0.192005\pi\)
−0.736310 + 0.676644i \(0.763433\pi\)
\(930\) −15.3107 19.1990i −0.502056 0.629558i
\(931\) −62.0342 29.8741i −2.03309 0.979084i
\(932\) 1.20342 5.27255i 0.0394195 0.172708i
\(933\) 23.1896 29.0788i 0.759192 0.951997i
\(934\) 2.03710 8.92511i 0.0666559 0.292039i
\(935\) −7.70498 + 3.71052i −0.251980 + 0.121347i
\(936\) −1.21307 1.52114i −0.0396503 0.0497199i
\(937\) 29.7169 14.3109i 0.970810 0.467517i 0.119875 0.992789i \(-0.461751\pi\)
0.850935 + 0.525272i \(0.176036\pi\)
\(938\) −3.19492 + 4.00630i −0.104318 + 0.130810i
\(939\) 11.4020 0.372090
\(940\) −17.2270 −0.561881
\(941\) 15.5547 19.5050i 0.507068 0.635844i −0.460739 0.887536i \(-0.652416\pi\)
0.967807 + 0.251692i \(0.0809870\pi\)
\(942\) 45.8864 + 22.0977i 1.49506 + 0.719983i
\(943\) −4.87475 21.3577i −0.158744 0.695501i
\(944\) 3.26452 14.3028i 0.106251 0.465517i
\(945\) −43.2591 −1.40722
\(946\) −25.8905 53.4073i −0.841772 1.73642i
\(947\) −1.90507 −0.0619063 −0.0309532 0.999521i \(-0.509854\pi\)
−0.0309532 + 0.999521i \(0.509854\pi\)
\(948\) 3.85759 16.9012i 0.125289 0.548926i
\(949\) −13.0453 57.1552i −0.423468 1.85534i
\(950\) 18.3714 + 8.84722i 0.596049 + 0.287042i
\(951\) 12.8030 16.0545i 0.415166 0.520602i
\(952\) 1.57343 0.0509952
\(953\) −20.2321 −0.655380 −0.327690 0.944785i \(-0.606270\pi\)
−0.327690 + 0.944785i \(0.606270\pi\)
\(954\) −9.03985 + 11.3356i −0.292676 + 0.367004i
\(955\) −36.6357 + 17.6428i −1.18550 + 0.570908i
\(956\) −21.8080 27.3464i −0.705322 0.884446i
\(957\) −37.7436 + 18.1764i −1.22008 + 0.587559i
\(958\) −16.9417 + 74.2265i −0.547362 + 2.39815i
\(959\) −9.29512 + 11.6557i −0.300155 + 0.376383i
\(960\) 5.98003 26.2002i 0.193005 0.845609i
\(961\) 11.8461 + 5.70480i 0.382134 + 0.184026i
\(962\) −37.8924 47.5156i −1.22170 1.53196i
\(963\) 1.17232 + 1.47004i 0.0377774 + 0.0473714i
\(964\) 1.20384 + 5.27436i 0.0387731 + 0.169876i
\(965\) −11.3695 5.47525i −0.365997 0.176255i
\(966\) 97.8310 47.1129i 3.14766 1.51583i
\(967\) 7.03921 + 30.8408i 0.226366 + 0.991773i 0.952576 + 0.304300i \(0.0984226\pi\)
−0.726211 + 0.687472i \(0.758720\pi\)
\(968\) −0.754386 3.30518i −0.0242469 0.106233i
\(969\) −10.4765 + 5.04524i −0.336555 + 0.162076i
\(970\) −42.2791 20.3605i −1.35750 0.653737i
\(971\) −9.31822 40.8258i −0.299036 1.31016i −0.871566 0.490278i \(-0.836895\pi\)
0.572530 0.819884i \(-0.305962\pi\)
\(972\) 11.6642 + 14.6264i 0.374129 + 0.469143i
\(973\) −6.67736 8.37314i −0.214066 0.268431i
\(974\) 76.0376 + 36.6178i 2.43640 + 1.17331i
\(975\) 2.36460 10.3600i 0.0757279 0.331785i
\(976\) 9.68826 12.1487i 0.310114 0.388870i
\(977\) 1.31366 5.75552i 0.0420277 0.184135i −0.949557 0.313594i \(-0.898467\pi\)
0.991585 + 0.129459i \(0.0413240\pi\)
\(978\) −20.8019 + 10.0177i −0.665173 + 0.320330i
\(979\) −16.2278 20.3490i −0.518642 0.650356i
\(980\) −33.2176 + 15.9968i −1.06110 + 0.510998i
\(981\) 0.192626 0.241546i 0.00615009 0.00771196i
\(982\) −88.2810 −2.81716
\(983\) −12.4499 −0.397091 −0.198546 0.980092i \(-0.563622\pi\)
−0.198546 + 0.980092i \(0.563622\pi\)
\(984\) −0.871914 + 1.09335i −0.0277956 + 0.0348546i
\(985\) −2.91435 1.40348i −0.0928588 0.0447184i
\(986\) −2.94509 12.9033i −0.0937906 0.410924i
\(987\) 5.24491 22.9795i 0.166947 0.731444i
\(988\) 100.350 3.19256
\(989\) 46.7013 37.4416i 1.48501 1.19058i
\(990\) −14.8666 −0.472492
\(991\) −10.3876 + 45.5111i −0.329973 + 1.44571i 0.489205 + 0.872169i \(0.337287\pi\)
−0.819178 + 0.573539i \(0.805570\pi\)
\(992\) −7.62922 33.4258i −0.242228 1.06127i
\(993\) 17.4915 + 8.42346i 0.555076 + 0.267310i
\(994\) 17.3456 21.7507i 0.550170 0.689892i
\(995\) 11.7268 0.371766
\(996\) 50.0100 1.58463
\(997\) −24.2809 + 30.4473i −0.768985 + 0.964276i −0.999962 0.00868292i \(-0.997236\pi\)
0.230978 + 0.972959i \(0.425808\pi\)
\(998\) 51.9387 25.0124i 1.64409 0.791752i
\(999\) 18.1049 + 22.7029i 0.572815 + 0.718287i
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 731.2.k.a.35.6 180
43.16 even 7 inner 731.2.k.a.188.6 yes 180
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.k.a.35.6 180 1.1 even 1 trivial
731.2.k.a.188.6 yes 180 43.16 even 7 inner