Properties

Label 370.2.ba.b.163.4
Level $370$
Weight $2$
Character 370.163
Analytic conductor $2.954$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [370,2,Mod(17,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([9, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.ba (of order \(36\), degree \(12\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 163.4
Character \(\chi\) \(=\) 370.163
Dual form 370.2.ba.b.227.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(-0.217829 + 0.467137i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.08799 - 1.95353i) q^{5} +(-0.364463 + 0.364463i) q^{6} +(-2.39725 - 3.42363i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.75760 + 2.09462i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(-0.217829 + 0.467137i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.08799 - 1.95353i) q^{5} +(-0.364463 + 0.364463i) q^{6} +(-2.39725 - 3.42363i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.75760 + 2.09462i) q^{9} +(1.69052 - 1.46360i) q^{10} +(5.07492 - 2.93001i) q^{11} +(-0.467137 + 0.217829i) q^{12} +(-0.0922595 - 0.0774149i) q^{13} +(-1.08173 - 4.03707i) q^{14} +(0.675569 + 0.933776i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.06503 + 2.46101i) q^{17} +(0.935197 + 2.56943i) q^{18} +(-1.63404 - 0.761964i) q^{19} +(2.08915 - 0.797144i) q^{20} +(2.12150 - 0.374077i) q^{21} +(5.77098 - 1.01758i) q^{22} +(-4.25632 + 7.37216i) q^{23} +(-0.513467 + 0.0449225i) q^{24} +(-2.63256 - 4.25084i) q^{25} +(-0.0602181 - 0.104301i) q^{26} +(-2.85493 + 0.764975i) q^{27} +(0.364266 - 4.16358i) q^{28} +(3.51490 + 0.941816i) q^{29} +(0.315457 + 1.10852i) q^{30} +(-1.44493 - 1.44493i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(0.263246 + 3.00892i) q^{33} +(1.09878 + 3.01888i) q^{34} +(-9.29635 + 0.958228i) q^{35} +2.73433i q^{36} +(-6.08262 - 0.0422597i) q^{37} +(-1.27489 - 1.27489i) q^{38} +(0.0562602 - 0.0262346i) q^{39} +(2.23580 - 0.0345381i) q^{40} +(-4.18660 + 4.98939i) q^{41} +(2.12150 + 0.374077i) q^{42} +11.2578 q^{43} +(5.77098 + 1.01758i) q^{44} +(6.00415 - 1.15459i) q^{45} +(-6.52106 + 5.47182i) q^{46} +(-2.71264 - 10.1237i) q^{47} +(-0.497865 - 0.133403i) q^{48} +(-3.58029 + 9.83678i) q^{49} +(-1.01992 - 4.89487i) q^{50} +(-1.59945 + 0.428572i) q^{51} +(-0.0209135 - 0.118607i) q^{52} +(-2.08418 + 2.97652i) q^{53} +(-2.94439 - 0.257601i) q^{54} +(-0.202393 - 13.1018i) q^{55} +(1.76633 - 3.78790i) q^{56} +(0.711882 - 0.597340i) q^{57} +(2.98081 + 2.08719i) q^{58} +(7.04443 - 10.0605i) q^{59} +(-0.0827037 + 1.14956i) q^{60} +(0.638144 + 7.29402i) q^{61} +(-0.863595 - 1.85199i) q^{62} +(2.95781 - 11.0387i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.251610 + 0.0960051i) q^{65} +(-0.781741 + 2.91750i) q^{66} +(-6.86037 + 4.80368i) q^{67} +3.21262i q^{68} +(-2.51665 - 3.59416i) q^{69} +(-9.06345 - 2.27910i) q^{70} +(-10.0833 + 3.67002i) q^{71} +(-0.935197 + 2.56943i) q^{72} +(-3.30299 + 3.30299i) q^{73} +(-5.70134 - 2.12009i) q^{74} +(2.55917 - 0.303806i) q^{75} +(-0.761964 - 1.63404i) q^{76} +(-22.1971 - 10.3507i) q^{77} +(0.0618400 - 0.00541030i) q^{78} +(-4.23243 + 2.96358i) q^{79} +(2.11278 + 0.732234i) q^{80} +(-1.15990 + 6.57811i) q^{81} +(-5.64059 + 3.25660i) q^{82} +(-5.71345 - 0.499862i) q^{83} +(1.86561 + 1.07711i) q^{84} +(7.05440 - 1.35655i) q^{85} +(10.5789 + 3.85039i) q^{86} +(-1.20561 + 1.43679i) q^{87} +(5.07492 + 2.93001i) q^{88} +(8.86691 + 6.20868i) q^{89} +(6.03695 + 0.968582i) q^{90} +(-0.0438708 + 0.501446i) q^{91} +(-7.99926 + 2.91149i) q^{92} +(0.989728 - 0.360231i) q^{93} +(0.913465 - 10.4410i) q^{94} +(-3.26633 + 2.36313i) q^{95} +(-0.422214 - 0.295637i) q^{96} +(6.68330 + 3.85860i) q^{97} +(-6.72875 + 8.01902i) q^{98} +(15.0569 + 5.48027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 6 q^{3} - 6 q^{5} + 60 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 6 q^{3} - 6 q^{5} + 60 q^{8} + 12 q^{10} - 36 q^{11} - 6 q^{12} - 6 q^{13} + 12 q^{14} - 24 q^{15} - 12 q^{19} + 12 q^{20} + 42 q^{21} + 6 q^{22} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 6 q^{27} - 36 q^{30} - 18 q^{33} - 30 q^{35} + 12 q^{37} - 48 q^{38} - 12 q^{40} - 30 q^{41} + 42 q^{42} + 6 q^{44} - 30 q^{45} - 6 q^{46} + 12 q^{47} - 60 q^{49} - 48 q^{50} + 12 q^{51} - 6 q^{52} + 12 q^{53} + 18 q^{54} + 36 q^{57} + 6 q^{58} - 24 q^{59} + 54 q^{60} - 72 q^{61} + 6 q^{62} + 96 q^{63} - 60 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 90 q^{73} + 24 q^{74} - 60 q^{75} + 18 q^{76} + 6 q^{77} + 24 q^{78} - 18 q^{79} + 6 q^{80} - 108 q^{81} - 36 q^{82} + 48 q^{83} + 36 q^{85} + 24 q^{86} + 108 q^{87} - 36 q^{88} + 54 q^{89} - 6 q^{90} + 42 q^{91} - 12 q^{92} - 12 q^{93} - 18 q^{94} - 198 q^{95} - 12 q^{96} - 72 q^{97} + 48 q^{98} + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) −0.217829 + 0.467137i −0.125764 + 0.269701i −0.959101 0.283063i \(-0.908649\pi\)
0.833337 + 0.552765i \(0.186427\pi\)
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 1.08799 1.95353i 0.486564 0.873645i
\(6\) −0.364463 + 0.364463i −0.148791 + 0.148791i
\(7\) −2.39725 3.42363i −0.906077 1.29401i −0.955426 0.295230i \(-0.904604\pi\)
0.0493497 0.998782i \(-0.484285\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) 1.75760 + 2.09462i 0.585865 + 0.698207i
\(10\) 1.69052 1.46360i 0.534590 0.462832i
\(11\) 5.07492 2.93001i 1.53015 0.883430i 0.530791 0.847503i \(-0.321895\pi\)
0.999354 0.0359271i \(-0.0114384\pi\)
\(12\) −0.467137 + 0.217829i −0.134851 + 0.0628819i
\(13\) −0.0922595 0.0774149i −0.0255882 0.0214710i 0.629904 0.776673i \(-0.283094\pi\)
−0.655492 + 0.755202i \(0.727539\pi\)
\(14\) −1.08173 4.03707i −0.289104 1.07895i
\(15\) 0.675569 + 0.933776i 0.174431 + 0.241100i
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) 2.06503 + 2.46101i 0.500844 + 0.596883i 0.955941 0.293559i \(-0.0948397\pi\)
−0.455097 + 0.890442i \(0.650395\pi\)
\(18\) 0.935197 + 2.56943i 0.220428 + 0.605621i
\(19\) −1.63404 0.761964i −0.374874 0.174807i 0.226045 0.974117i \(-0.427421\pi\)
−0.600918 + 0.799310i \(0.705198\pi\)
\(20\) 2.08915 0.797144i 0.467149 0.178247i
\(21\) 2.12150 0.374077i 0.462948 0.0816303i
\(22\) 5.77098 1.01758i 1.23038 0.216949i
\(23\) −4.25632 + 7.37216i −0.887504 + 1.53720i −0.0446872 + 0.999001i \(0.514229\pi\)
−0.842817 + 0.538201i \(0.819104\pi\)
\(24\) −0.513467 + 0.0449225i −0.104811 + 0.00916977i
\(25\) −2.63256 4.25084i −0.526511 0.850168i
\(26\) −0.0602181 0.104301i −0.0118097 0.0204551i
\(27\) −2.85493 + 0.764975i −0.549431 + 0.147220i
\(28\) 0.364266 4.16358i 0.0688398 0.786843i
\(29\) 3.51490 + 0.941816i 0.652701 + 0.174891i 0.569950 0.821679i \(-0.306963\pi\)
0.0827514 + 0.996570i \(0.473629\pi\)
\(30\) 0.315457 + 1.10852i 0.0575943 + 0.202387i
\(31\) −1.44493 1.44493i −0.259517 0.259517i 0.565341 0.824858i \(-0.308745\pi\)
−0.824858 + 0.565341i \(0.808745\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) 0.263246 + 3.00892i 0.0458253 + 0.523786i
\(34\) 1.09878 + 3.01888i 0.188440 + 0.517733i
\(35\) −9.29635 + 0.958228i −1.57137 + 0.161970i
\(36\) 2.73433i 0.455722i
\(37\) −6.08262 0.0422597i −0.999976 0.00694745i
\(38\) −1.27489 1.27489i −0.206814 0.206814i
\(39\) 0.0562602 0.0262346i 0.00900884 0.00420089i
\(40\) 2.23580 0.0345381i 0.353511 0.00546095i
\(41\) −4.18660 + 4.98939i −0.653837 + 0.779213i −0.986487 0.163838i \(-0.947613\pi\)
0.332650 + 0.943050i \(0.392057\pi\)
\(42\) 2.12150 + 0.374077i 0.327354 + 0.0577213i
\(43\) 11.2578 1.71680 0.858399 0.512982i \(-0.171459\pi\)
0.858399 + 0.512982i \(0.171459\pi\)
\(44\) 5.77098 + 1.01758i 0.870009 + 0.153406i
\(45\) 6.00415 1.15459i 0.895046 0.172116i
\(46\) −6.52106 + 5.47182i −0.961478 + 0.806776i
\(47\) −2.71264 10.1237i −0.395679 1.47669i −0.820620 0.571474i \(-0.806372\pi\)
0.424941 0.905221i \(-0.360295\pi\)
\(48\) −0.497865 0.133403i −0.0718607 0.0192550i
\(49\) −3.58029 + 9.83678i −0.511471 + 1.40525i
\(50\) −1.01992 4.89487i −0.144239 0.692239i
\(51\) −1.59945 + 0.428572i −0.223968 + 0.0600121i
\(52\) −0.0209135 0.118607i −0.00290019 0.0164478i
\(53\) −2.08418 + 2.97652i −0.286284 + 0.408856i −0.936375 0.351000i \(-0.885842\pi\)
0.650091 + 0.759856i \(0.274731\pi\)
\(54\) −2.94439 0.257601i −0.400681 0.0350550i
\(55\) −0.202393 13.1018i −0.0272907 1.76665i
\(56\) 1.76633 3.78790i 0.236035 0.506179i
\(57\) 0.711882 0.597340i 0.0942911 0.0791196i
\(58\) 2.98081 + 2.08719i 0.391399 + 0.274061i
\(59\) 7.04443 10.0605i 0.917106 1.30976i −0.0335239 0.999438i \(-0.510673\pi\)
0.950630 0.310326i \(-0.100438\pi\)
\(60\) −0.0827037 + 1.14956i −0.0106770 + 0.148408i
\(61\) 0.638144 + 7.29402i 0.0817059 + 0.933903i 0.920830 + 0.389964i \(0.127512\pi\)
−0.839124 + 0.543940i \(0.816932\pi\)
\(62\) −0.863595 1.85199i −0.109677 0.235202i
\(63\) 2.95781 11.0387i 0.372649 1.39075i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −0.251610 + 0.0960051i −0.0312084 + 0.0119080i
\(66\) −0.781741 + 2.91750i −0.0962256 + 0.359119i
\(67\) −6.86037 + 4.80368i −0.838127 + 0.586863i −0.911900 0.410412i \(-0.865385\pi\)
0.0737728 + 0.997275i \(0.476496\pi\)
\(68\) 3.21262i 0.389588i
\(69\) −2.51665 3.59416i −0.302970 0.432685i
\(70\) −9.06345 2.27910i −1.08329 0.272405i
\(71\) −10.0833 + 3.67002i −1.19667 + 0.435552i −0.862060 0.506806i \(-0.830826\pi\)
−0.334608 + 0.942357i \(0.608604\pi\)
\(72\) −0.935197 + 2.56943i −0.110214 + 0.302811i
\(73\) −3.30299 + 3.30299i −0.386586 + 0.386586i −0.873468 0.486882i \(-0.838134\pi\)
0.486882 + 0.873468i \(0.338134\pi\)
\(74\) −5.70134 2.12009i −0.662767 0.246455i
\(75\) 2.55917 0.303806i 0.295508 0.0350804i
\(76\) −0.761964 1.63404i −0.0874033 0.187437i
\(77\) −22.1971 10.3507i −2.52960 1.17957i
\(78\) 0.0618400 0.00541030i 0.00700200 0.000612596i
\(79\) −4.23243 + 2.96358i −0.476185 + 0.333429i −0.786906 0.617073i \(-0.788318\pi\)
0.310721 + 0.950501i \(0.399430\pi\)
\(80\) 2.11278 + 0.732234i 0.236216 + 0.0818662i
\(81\) −1.15990 + 6.57811i −0.128877 + 0.730901i
\(82\) −5.64059 + 3.25660i −0.622899 + 0.359631i
\(83\) −5.71345 0.499862i −0.627132 0.0548670i −0.230841 0.972992i \(-0.574148\pi\)
−0.396292 + 0.918125i \(0.629703\pi\)
\(84\) 1.86561 + 1.07711i 0.203555 + 0.117523i
\(85\) 7.05440 1.35655i 0.765157 0.147138i
\(86\) 10.5789 + 3.85039i 1.14075 + 0.415199i
\(87\) −1.20561 + 1.43679i −0.129255 + 0.154040i
\(88\) 5.07492 + 2.93001i 0.540988 + 0.312340i
\(89\) 8.86691 + 6.20868i 0.939890 + 0.658118i 0.939743 0.341882i \(-0.111064\pi\)
0.000147385 1.00000i \(0.499953\pi\)
\(90\) 6.03695 + 0.968582i 0.636350 + 0.102097i
\(91\) −0.0438708 + 0.501446i −0.00459891 + 0.0525658i
\(92\) −7.99926 + 2.91149i −0.833981 + 0.303544i
\(93\) 0.989728 0.360231i 0.102630 0.0373543i
\(94\) 0.913465 10.4410i 0.0942167 1.07690i
\(95\) −3.26633 + 2.36313i −0.335119 + 0.242452i
\(96\) −0.422214 0.295637i −0.0430920 0.0301734i
\(97\) 6.68330 + 3.85860i 0.678586 + 0.391782i 0.799322 0.600903i \(-0.205192\pi\)
−0.120736 + 0.992685i \(0.538525\pi\)
\(98\) −6.72875 + 8.01902i −0.679707 + 0.810043i
\(99\) 15.0569 + 5.48027i 1.51328 + 0.550787i
\(100\) 0.715732 4.94851i 0.0715732 0.494851i
\(101\) −3.61027 2.08439i −0.359235 0.207404i 0.309510 0.950896i \(-0.399835\pi\)
−0.668745 + 0.743492i \(0.733168\pi\)
\(102\) −1.64958 0.144319i −0.163332 0.0142897i
\(103\) −7.69016 + 4.43992i −0.757734 + 0.437478i −0.828482 0.560016i \(-0.810795\pi\)
0.0707473 + 0.997494i \(0.477462\pi\)
\(104\) 0.0209135 0.118607i 0.00205074 0.0116303i
\(105\) 1.57740 4.55140i 0.153938 0.444171i
\(106\) −2.97652 + 2.08418i −0.289105 + 0.202433i
\(107\) 1.13918 0.0996655i 0.110129 0.00963502i −0.0319581 0.999489i \(-0.510174\pi\)
0.142087 + 0.989854i \(0.454619\pi\)
\(108\) −2.67872 1.24911i −0.257760 0.120195i
\(109\) −0.653121 1.40062i −0.0625577 0.134155i 0.872543 0.488537i \(-0.162469\pi\)
−0.935101 + 0.354381i \(0.884691\pi\)
\(110\) 4.29090 12.3809i 0.409121 1.18047i
\(111\) 1.34471 2.83221i 0.127635 0.268821i
\(112\) 2.95534 2.95534i 0.279253 0.279253i
\(113\) −0.339096 + 0.931658i −0.0318994 + 0.0876430i −0.954620 0.297827i \(-0.903738\pi\)
0.922721 + 0.385470i \(0.125961\pi\)
\(114\) 0.873253 0.317838i 0.0817876 0.0297683i
\(115\) 9.77090 + 16.3357i 0.911141 + 1.52331i
\(116\) 2.08719 + 2.98081i 0.193790 + 0.276761i
\(117\) 0.329313i 0.0304450i
\(118\) 10.0605 7.04443i 0.926143 0.648492i
\(119\) 3.47519 12.9696i 0.318570 1.18892i
\(120\) −0.470889 + 1.05195i −0.0429861 + 0.0960293i
\(121\) 11.6699 20.2128i 1.06090 1.83753i
\(122\) −1.89504 + 7.07239i −0.171569 + 0.640304i
\(123\) −1.41876 3.04255i −0.127926 0.274337i
\(124\) −0.178097 2.03566i −0.0159936 0.182808i
\(125\) −11.1683 + 0.517906i −0.998927 + 0.0463229i
\(126\) 6.55489 9.36135i 0.583956 0.833976i
\(127\) 9.30413 + 6.51482i 0.825608 + 0.578097i 0.908224 0.418485i \(-0.137439\pi\)
−0.0826161 + 0.996581i \(0.526328\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) −2.45228 + 5.25893i −0.215911 + 0.463023i
\(130\) −0.269272 + 0.00415964i −0.0236167 + 0.000364824i
\(131\) −9.02275 0.789389i −0.788322 0.0689692i −0.314117 0.949384i \(-0.601709\pi\)
−0.474204 + 0.880415i \(0.657264\pi\)
\(132\) −1.73244 + 2.47418i −0.150789 + 0.215350i
\(133\) 1.30852 + 7.42096i 0.113463 + 0.643479i
\(134\) −8.08959 + 2.16760i −0.698834 + 0.187252i
\(135\) −1.61173 + 6.40947i −0.138716 + 0.551639i
\(136\) −1.09878 + 3.01888i −0.0942198 + 0.258867i
\(137\) 17.6421 + 4.72718i 1.50726 + 0.403870i 0.915526 0.402260i \(-0.131775\pi\)
0.591739 + 0.806130i \(0.298442\pi\)
\(138\) −1.13561 4.23815i −0.0966694 0.360775i
\(139\) −3.15125 + 2.64421i −0.267285 + 0.224279i −0.766573 0.642157i \(-0.778040\pi\)
0.499287 + 0.866436i \(0.333595\pi\)
\(140\) −7.73736 5.24154i −0.653926 0.442991i
\(141\) 5.32005 + 0.938068i 0.448029 + 0.0789996i
\(142\) −10.7304 −0.900478
\(143\) −0.695036 0.122554i −0.0581218 0.0102484i
\(144\) −1.75760 + 2.09462i −0.146466 + 0.174552i
\(145\) 5.66404 5.84178i 0.470373 0.485134i
\(146\) −4.23348 + 1.97411i −0.350366 + 0.163378i
\(147\) −3.81523 3.81523i −0.314675 0.314675i
\(148\) −4.63239 3.94220i −0.380780 0.324047i
\(149\) 1.97337i 0.161665i 0.996728 + 0.0808324i \(0.0257579\pi\)
−0.996728 + 0.0808324i \(0.974242\pi\)
\(150\) 2.50874 + 0.589804i 0.204838 + 0.0481573i
\(151\) 6.68436 + 18.3651i 0.543965 + 1.49453i 0.841733 + 0.539894i \(0.181536\pi\)
−0.297768 + 0.954638i \(0.596242\pi\)
\(152\) −0.157138 1.79610i −0.0127456 0.145683i
\(153\) −1.52539 + 8.65093i −0.123321 + 0.699386i
\(154\) −17.3183 17.3183i −1.39555 1.39555i
\(155\) −4.39478 + 1.25064i −0.352997 + 0.100454i
\(156\) 0.0599610 + 0.0160665i 0.00480073 + 0.00128635i
\(157\) 0.371284 4.24379i 0.0296317 0.338691i −0.966880 0.255233i \(-0.917848\pi\)
0.996511 0.0834585i \(-0.0265966\pi\)
\(158\) −4.99079 + 1.33728i −0.397046 + 0.106388i
\(159\) −0.936444 1.62197i −0.0742649 0.128631i
\(160\) 1.73492 + 1.41069i 0.137158 + 0.111525i
\(161\) 35.4430 3.10086i 2.79330 0.244382i
\(162\) −3.33979 + 5.78469i −0.262399 + 0.454488i
\(163\) 0.947301 0.167035i 0.0741984 0.0130832i −0.136426 0.990650i \(-0.543562\pi\)
0.210624 + 0.977567i \(0.432450\pi\)
\(164\) −6.41424 + 1.13100i −0.500868 + 0.0883166i
\(165\) 6.16443 + 2.75942i 0.479900 + 0.214820i
\(166\) −5.19792 2.42383i −0.403437 0.188126i
\(167\) −8.52249 23.4154i −0.659490 1.81194i −0.579235 0.815161i \(-0.696649\pi\)
−0.0802556 0.996774i \(-0.525574\pi\)
\(168\) 1.38471 + 1.65023i 0.106833 + 0.127318i
\(169\) −2.25491 12.7882i −0.173454 0.983709i
\(170\) 7.09293 + 1.13801i 0.544003 + 0.0872810i
\(171\) −1.27595 4.76191i −0.0975744 0.364153i
\(172\) 8.62398 + 7.23637i 0.657572 + 0.551768i
\(173\) 0.397286 0.185258i 0.0302051 0.0140849i −0.407457 0.913224i \(-0.633584\pi\)
0.437662 + 0.899140i \(0.355807\pi\)
\(174\) −1.62431 + 0.937795i −0.123138 + 0.0710940i
\(175\) −8.24241 + 19.2032i −0.623068 + 1.45163i
\(176\) 3.76674 + 4.48903i 0.283929 + 0.338373i
\(177\) 3.16514 + 5.48218i 0.237906 + 0.412066i
\(178\) 6.20868 + 8.86691i 0.465360 + 0.664603i
\(179\) 5.04279 5.04279i 0.376916 0.376916i −0.493072 0.869988i \(-0.664126\pi\)
0.869988 + 0.493072i \(0.164126\pi\)
\(180\) 5.34160 + 2.97493i 0.398140 + 0.221738i
\(181\) −4.36158 3.65980i −0.324194 0.272031i 0.466135 0.884713i \(-0.345646\pi\)
−0.790329 + 0.612683i \(0.790090\pi\)
\(182\) −0.212730 + 0.456200i −0.0157686 + 0.0338158i
\(183\) −3.54631 1.29075i −0.262151 0.0954150i
\(184\) −8.51264 −0.627560
\(185\) −6.70038 + 11.8366i −0.492622 + 0.870244i
\(186\) 1.05325 0.0772278
\(187\) 17.6907 + 6.43887i 1.29367 + 0.470857i
\(188\) 4.42939 9.49886i 0.323047 0.692776i
\(189\) 9.46297 + 7.94038i 0.688330 + 0.577578i
\(190\) −3.87759 + 1.10346i −0.281310 + 0.0800537i
\(191\) 12.3650 12.3650i 0.894701 0.894701i −0.100260 0.994961i \(-0.531967\pi\)
0.994961 + 0.100260i \(0.0319675\pi\)
\(192\) −0.295637 0.422214i −0.0213358 0.0304707i
\(193\) −5.99567 10.3848i −0.431578 0.747515i 0.565432 0.824795i \(-0.308710\pi\)
−0.997009 + 0.0772806i \(0.975376\pi\)
\(194\) 4.96052 + 5.91172i 0.356145 + 0.424437i
\(195\) 0.00996052 0.138449i 0.000713288 0.00991453i
\(196\) −9.06562 + 5.23404i −0.647545 + 0.373860i
\(197\) 5.26969 2.45730i 0.375450 0.175075i −0.225728 0.974190i \(-0.572476\pi\)
0.601178 + 0.799115i \(0.294698\pi\)
\(198\) 12.2745 + 10.2995i 0.872311 + 0.731956i
\(199\) −3.02952 11.3063i −0.214757 0.801483i −0.986252 0.165248i \(-0.947158\pi\)
0.771495 0.636235i \(-0.219509\pi\)
\(200\) 2.36506 4.40528i 0.167235 0.311500i
\(201\) −0.749586 4.25111i −0.0528717 0.299850i
\(202\) −2.67964 3.19347i −0.188539 0.224692i
\(203\) −5.20168 14.2915i −0.365087 1.00307i
\(204\) −1.50073 0.699803i −0.105072 0.0489960i
\(205\) 5.19195 + 13.6071i 0.362622 + 0.950358i
\(206\) −8.74493 + 1.54197i −0.609288 + 0.107434i
\(207\) −22.9228 + 4.04190i −1.59324 + 0.280932i
\(208\) 0.0602181 0.104301i 0.00417538 0.00723196i
\(209\) −10.5252 + 0.920832i −0.728041 + 0.0636953i
\(210\) 3.03894 3.73741i 0.209707 0.257906i
\(211\) 8.14188 + 14.1021i 0.560510 + 0.970832i 0.997452 + 0.0713421i \(0.0227282\pi\)
−0.436942 + 0.899490i \(0.643938\pi\)
\(212\) −3.50984 + 0.940460i −0.241057 + 0.0645910i
\(213\) 0.482038 5.50972i 0.0330287 0.377520i
\(214\) 1.10457 + 0.295968i 0.0755067 + 0.0202320i
\(215\) 12.2484 21.9924i 0.835332 1.49987i
\(216\) −2.08995 2.08995i −0.142203 0.142203i
\(217\) −1.48305 + 8.41077i −0.100676 + 0.570960i
\(218\) −0.134692 1.53954i −0.00912249 0.104271i
\(219\) −0.823459 2.26244i −0.0556442 0.152881i
\(220\) 8.26664 10.1667i 0.557337 0.685437i
\(221\) 0.386916i 0.0260268i
\(222\) 2.23229 2.20148i 0.149821 0.147754i
\(223\) 7.18479 + 7.18479i 0.481129 + 0.481129i 0.905492 0.424363i \(-0.139502\pi\)
−0.424363 + 0.905492i \(0.639502\pi\)
\(224\) 3.78790 1.76633i 0.253090 0.118018i
\(225\) 4.27693 12.9855i 0.285129 0.865698i
\(226\) −0.637291 + 0.759494i −0.0423920 + 0.0505208i
\(227\) −11.9450 2.10622i −0.792816 0.139795i −0.237449 0.971400i \(-0.576311\pi\)
−0.555367 + 0.831605i \(0.687422\pi\)
\(228\) 0.929296 0.0615442
\(229\) 26.1210 + 4.60584i 1.72612 + 0.304362i 0.946696 0.322129i \(-0.104398\pi\)
0.779428 + 0.626491i \(0.215510\pi\)
\(230\) 3.59451 + 18.6924i 0.237015 + 1.23254i
\(231\) 9.67037 8.11440i 0.636264 0.533889i
\(232\) 0.941816 + 3.51490i 0.0618332 + 0.230765i
\(233\) 2.49237 + 0.667828i 0.163281 + 0.0437509i 0.339533 0.940594i \(-0.389731\pi\)
−0.176253 + 0.984345i \(0.556398\pi\)
\(234\) 0.112632 0.309453i 0.00736296 0.0202296i
\(235\) −22.7283 5.71527i −1.48263 0.372823i
\(236\) 11.8631 3.17871i 0.772222 0.206916i
\(237\) −0.462449 2.62268i −0.0300393 0.170361i
\(238\) 7.70147 10.9988i 0.499212 0.712949i
\(239\) 3.56618 + 0.312000i 0.230677 + 0.0201816i 0.201908 0.979404i \(-0.435286\pi\)
0.0287688 + 0.999586i \(0.490841\pi\)
\(240\) −0.802278 + 0.827454i −0.0517868 + 0.0534119i
\(241\) 0.306053 0.656334i 0.0197146 0.0422782i −0.896204 0.443642i \(-0.853686\pi\)
0.915919 + 0.401364i \(0.131464\pi\)
\(242\) 17.8793 15.0025i 1.14932 0.964396i
\(243\) −10.0836 7.06059i −0.646861 0.452937i
\(244\) −4.19966 + 5.99773i −0.268855 + 0.383965i
\(245\) 15.3211 + 17.6965i 0.978830 + 1.13059i
\(246\) −0.292589 3.34431i −0.0186548 0.213225i
\(247\) 0.0917681 + 0.196797i 0.00583906 + 0.0125219i
\(248\) 0.528881 1.97381i 0.0335840 0.125337i
\(249\) 1.47806 2.56008i 0.0936682 0.162238i
\(250\) −10.6719 3.33312i −0.674953 0.210805i
\(251\) −5.93286 + 22.1417i −0.374479 + 1.39757i 0.479626 + 0.877473i \(0.340772\pi\)
−0.854105 + 0.520101i \(0.825894\pi\)
\(252\) 9.36135 6.55489i 0.589710 0.412919i
\(253\) 49.8842i 3.13619i
\(254\) 6.51482 + 9.30413i 0.408776 + 0.583793i
\(255\) −0.902960 + 3.59086i −0.0565456 + 0.224869i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 9.32640 25.6241i 0.581765 1.59839i −0.203397 0.979096i \(-0.565198\pi\)
0.785162 0.619290i \(-0.212579\pi\)
\(258\) −4.10305 + 4.10305i −0.255445 + 0.255445i
\(259\) 14.4369 + 20.9259i 0.897065 + 1.30028i
\(260\) −0.254455 0.0881875i −0.0157806 0.00546916i
\(261\) 4.20503 + 9.01772i 0.260285 + 0.558183i
\(262\) −8.20863 3.82775i −0.507131 0.236479i
\(263\) −13.9167 + 1.21755i −0.858139 + 0.0750774i −0.507727 0.861518i \(-0.669514\pi\)
−0.350412 + 0.936596i \(0.613959\pi\)
\(264\) −2.47418 + 1.73244i −0.152275 + 0.106624i
\(265\) 3.54715 + 7.30993i 0.217900 + 0.449045i
\(266\) −1.30852 + 7.42096i −0.0802303 + 0.455008i
\(267\) −4.83177 + 2.78962i −0.295700 + 0.170722i
\(268\) −8.34309 0.729926i −0.509636 0.0445873i
\(269\) −3.25099 1.87696i −0.198216 0.114440i 0.397607 0.917556i \(-0.369841\pi\)
−0.595823 + 0.803116i \(0.703174\pi\)
\(270\) −3.70670 + 5.47169i −0.225582 + 0.332996i
\(271\) 1.87128 + 0.681091i 0.113672 + 0.0413733i 0.398230 0.917286i \(-0.369625\pi\)
−0.284558 + 0.958659i \(0.591847\pi\)
\(272\) −2.06503 + 2.46101i −0.125211 + 0.149221i
\(273\) −0.224687 0.129723i −0.0135987 0.00785121i
\(274\) 14.9613 + 10.4760i 0.903847 + 0.632881i
\(275\) −25.8150 13.8593i −1.55670 0.835745i
\(276\) 0.382409 4.37096i 0.0230183 0.263101i
\(277\) 6.11756 2.22661i 0.367569 0.133784i −0.151631 0.988437i \(-0.548452\pi\)
0.519199 + 0.854653i \(0.326230\pi\)
\(278\) −3.86558 + 1.40696i −0.231842 + 0.0843836i
\(279\) 0.486978 5.56618i 0.0291546 0.333239i
\(280\) −5.47803 7.57177i −0.327375 0.452500i
\(281\) −21.2654 14.8902i −1.26859 0.888276i −0.271346 0.962482i \(-0.587469\pi\)
−0.997243 + 0.0742061i \(0.976358\pi\)
\(282\) 4.67837 + 2.70106i 0.278593 + 0.160846i
\(283\) 18.0793 21.5461i 1.07470 1.28078i 0.116968 0.993136i \(-0.462682\pi\)
0.957736 0.287647i \(-0.0928731\pi\)
\(284\) −10.0833 3.67002i −0.598334 0.217776i
\(285\) −0.392401 2.04058i −0.0232438 0.120874i
\(286\) −0.611204 0.352879i −0.0361413 0.0208662i
\(287\) 27.1182 + 2.37253i 1.60074 + 0.140046i
\(288\) −2.36800 + 1.36717i −0.139536 + 0.0805611i
\(289\) 1.15981 6.57759i 0.0682239 0.386917i
\(290\) 7.32047 3.55226i 0.429873 0.208596i
\(291\) −3.25831 + 2.28149i −0.191006 + 0.133744i
\(292\) −4.65336 + 0.407116i −0.272317 + 0.0238247i
\(293\) 2.67782 + 1.24869i 0.156440 + 0.0729491i 0.499261 0.866451i \(-0.333605\pi\)
−0.342821 + 0.939401i \(0.611383\pi\)
\(294\) −2.28026 4.89002i −0.132987 0.285192i
\(295\) −11.9892 24.7072i −0.698038 1.43851i
\(296\) −3.00471 5.28883i −0.174645 0.307407i
\(297\) −12.2471 + 12.2471i −0.710651 + 0.710651i
\(298\) −0.674933 + 1.85436i −0.0390978 + 0.107420i
\(299\) 0.963401 0.350649i 0.0557149 0.0202786i
\(300\) 2.15572 + 1.41227i 0.124461 + 0.0815377i
\(301\) −26.9878 38.5426i −1.55555 2.22156i
\(302\) 19.5438i 1.12462i
\(303\) 1.76012 1.23245i 0.101116 0.0708022i
\(304\) 0.466640 1.74153i 0.0267637 0.0998834i
\(305\) 14.9434 + 6.68918i 0.855655 + 0.383021i
\(306\) −4.39219 + 7.60750i −0.251085 + 0.434892i
\(307\) −1.33245 + 4.97277i −0.0760469 + 0.283811i −0.993469 0.114105i \(-0.963600\pi\)
0.917422 + 0.397916i \(0.130267\pi\)
\(308\) −10.3507 22.1971i −0.589785 1.26480i
\(309\) −0.398905 4.55950i −0.0226929 0.259381i
\(310\) −4.55749 0.327883i −0.258848 0.0186225i
\(311\) 3.19498 4.56290i 0.181171 0.258739i −0.718287 0.695747i \(-0.755073\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(312\) 0.0508499 + 0.0356055i 0.00287881 + 0.00201576i
\(313\) 6.82741 5.72888i 0.385908 0.323815i −0.429108 0.903253i \(-0.641172\pi\)
0.815017 + 0.579438i \(0.196728\pi\)
\(314\) 1.80035 3.86087i 0.101600 0.217882i
\(315\) −18.3464 17.7882i −1.03370 1.00225i
\(316\) −5.14718 0.450320i −0.289552 0.0253325i
\(317\) −5.78155 + 8.25691i −0.324724 + 0.463754i −0.948010 0.318240i \(-0.896908\pi\)
0.623286 + 0.781994i \(0.285797\pi\)
\(318\) −0.325224 1.84444i −0.0182376 0.103431i
\(319\) 20.5974 5.51905i 1.15323 0.309007i
\(320\) 1.14781 + 1.91899i 0.0641646 + 0.107275i
\(321\) −0.201590 + 0.553863i −0.0112516 + 0.0309136i
\(322\) 34.3661 + 9.20838i 1.91515 + 0.513163i
\(323\) −1.49914 5.59487i −0.0834144 0.311307i
\(324\) −5.11686 + 4.29355i −0.284270 + 0.238531i
\(325\) −0.0862001 + 0.595980i −0.00478152 + 0.0330590i
\(326\) 0.947301 + 0.167035i 0.0524662 + 0.00925120i
\(327\) 0.796551 0.0440494
\(328\) −6.41424 1.13100i −0.354167 0.0624492i
\(329\) −28.1570 + 33.5562i −1.55234 + 1.85001i
\(330\) 4.84889 + 4.70136i 0.266923 + 0.258801i
\(331\) 3.92890 1.83208i 0.215952 0.100700i −0.311632 0.950203i \(-0.600876\pi\)
0.527584 + 0.849503i \(0.323098\pi\)
\(332\) −4.05545 4.05545i −0.222572 0.222572i
\(333\) −10.6023 12.8151i −0.581000 0.702261i
\(334\) 24.9181i 1.36346i
\(335\) 1.92012 + 18.6283i 0.104908 + 1.01777i
\(336\) 0.736788 + 2.02431i 0.0401951 + 0.110435i
\(337\) 0.0562217 + 0.642617i 0.00306259 + 0.0350056i 0.997572 0.0696395i \(-0.0221849\pi\)
−0.994510 + 0.104645i \(0.966629\pi\)
\(338\) 2.25491 12.7882i 0.122651 0.695587i
\(339\) −0.361346 0.361346i −0.0196256 0.0196256i
\(340\) 6.27595 + 3.49530i 0.340361 + 0.189559i
\(341\) −11.5666 3.09925i −0.626364 0.167834i
\(342\) 0.429669 4.91114i 0.0232338 0.265564i
\(343\) 14.0009 3.75153i 0.755977 0.202563i
\(344\) 5.62890 + 9.74954i 0.303490 + 0.525660i
\(345\) −9.75938 + 1.00596i −0.525428 + 0.0541588i
\(346\) 0.436689 0.0382053i 0.0234765 0.00205393i
\(347\) −10.4024 + 18.0174i −0.558428 + 0.967226i 0.439200 + 0.898389i \(0.355262\pi\)
−0.997628 + 0.0688364i \(0.978071\pi\)
\(348\) −1.84710 + 0.325693i −0.0990147 + 0.0174590i
\(349\) −23.6280 + 4.16625i −1.26478 + 0.223014i −0.765504 0.643431i \(-0.777510\pi\)
−0.499272 + 0.866445i \(0.666399\pi\)
\(350\) −14.3132 + 15.2261i −0.765074 + 0.813868i
\(351\) 0.322615 + 0.150438i 0.0172199 + 0.00802977i
\(352\) 2.00424 + 5.50661i 0.106826 + 0.293503i
\(353\) −13.0497 15.5521i −0.694568 0.827754i 0.297332 0.954774i \(-0.403903\pi\)
−0.991900 + 0.127021i \(0.959459\pi\)
\(354\) 1.09924 + 6.23410i 0.0584240 + 0.331339i
\(355\) −3.80103 + 23.6910i −0.201738 + 1.25739i
\(356\) 2.80159 + 10.4557i 0.148484 + 0.554149i
\(357\) 5.30157 + 4.44854i 0.280589 + 0.235442i
\(358\) 6.46341 3.01394i 0.341602 0.159292i
\(359\) −13.7835 + 7.95788i −0.727463 + 0.420001i −0.817493 0.575938i \(-0.804637\pi\)
0.0900303 + 0.995939i \(0.471304\pi\)
\(360\) 4.00198 + 4.62245i 0.210923 + 0.243625i
\(361\) −10.1235 12.0647i −0.532815 0.634984i
\(362\) −2.84682 4.93083i −0.149625 0.259159i
\(363\) 6.90010 + 9.85436i 0.362161 + 0.517220i
\(364\) −0.355930 + 0.355930i −0.0186558 + 0.0186558i
\(365\) 2.85887 + 10.0461i 0.149640 + 0.525837i
\(366\) −2.89098 2.42582i −0.151114 0.126800i
\(367\) 6.31697 13.5468i 0.329743 0.707136i −0.669624 0.742700i \(-0.733545\pi\)
0.999367 + 0.0355637i \(0.0113227\pi\)
\(368\) −7.99926 2.91149i −0.416990 0.151772i
\(369\) −17.8092 −0.927112
\(370\) −10.3446 + 8.83109i −0.537793 + 0.459107i
\(371\) 15.1868 0.788460
\(372\) 0.989728 + 0.360231i 0.0513150 + 0.0186771i
\(373\) −6.17661 + 13.2458i −0.319813 + 0.685840i −0.998834 0.0482781i \(-0.984627\pi\)
0.679021 + 0.734119i \(0.262404\pi\)
\(374\) 14.4216 + 12.1011i 0.745721 + 0.625734i
\(375\) 2.19086 5.32995i 0.113135 0.275238i
\(376\) 7.41107 7.41107i 0.382197 0.382197i
\(377\) −0.251373 0.358998i −0.0129464 0.0184893i
\(378\) 6.17652 + 10.6980i 0.317686 + 0.550248i
\(379\) 5.56450 + 6.63151i 0.285829 + 0.340638i 0.889785 0.456380i \(-0.150854\pi\)
−0.603956 + 0.797018i \(0.706410\pi\)
\(380\) −4.02115 0.289296i −0.206281 0.0148406i
\(381\) −5.07002 + 2.92718i −0.259745 + 0.149964i
\(382\) 15.8484 7.39023i 0.810875 0.378117i
\(383\) 4.52795 + 3.79940i 0.231368 + 0.194141i 0.751100 0.660189i \(-0.229524\pi\)
−0.519732 + 0.854329i \(0.673968\pi\)
\(384\) −0.133403 0.497865i −0.00680767 0.0254066i
\(385\) −44.3706 + 32.1013i −2.26134 + 1.63603i
\(386\) −2.08227 11.8092i −0.105985 0.601071i
\(387\) 19.7867 + 23.5808i 1.00581 + 1.19868i
\(388\) 2.63944 + 7.25180i 0.133997 + 0.368154i
\(389\) −14.2517 6.64566i −0.722588 0.336948i 0.0262918 0.999654i \(-0.491630\pi\)
−0.748880 + 0.662706i \(0.769408\pi\)
\(390\) 0.0567121 0.126693i 0.00287173 0.00641533i
\(391\) −26.9324 + 4.74891i −1.36203 + 0.240163i
\(392\) −10.3090 + 1.81776i −0.520686 + 0.0918109i
\(393\) 2.33417 4.04291i 0.117743 0.203938i
\(394\) 5.79233 0.506763i 0.291813 0.0255304i
\(395\) 1.18460 + 11.4925i 0.0596037 + 0.578251i
\(396\) 8.01161 + 13.8765i 0.402599 + 0.697321i
\(397\) 23.8409 6.38814i 1.19654 0.320611i 0.395071 0.918650i \(-0.370720\pi\)
0.801467 + 0.598039i \(0.204053\pi\)
\(398\) 1.02017 11.6606i 0.0511366 0.584493i
\(399\) −3.75164 1.00525i −0.187817 0.0503253i
\(400\) 3.72912 3.33071i 0.186456 0.166536i
\(401\) −14.2306 14.2306i −0.710641 0.710641i 0.256028 0.966669i \(-0.417586\pi\)
−0.966669 + 0.256028i \(0.917586\pi\)
\(402\) 0.749586 4.25111i 0.0373859 0.212026i
\(403\) 0.0214494 + 0.245168i 0.00106847 + 0.0122127i
\(404\) −1.42581 3.91737i −0.0709365 0.194896i
\(405\) 11.5886 + 9.42281i 0.575841 + 0.468223i
\(406\) 15.2087i 0.754796i
\(407\) −30.9926 + 17.6076i −1.53625 + 0.872778i
\(408\) −1.17088 1.17088i −0.0579673 0.0579673i
\(409\) −4.66030 + 2.17313i −0.230437 + 0.107455i −0.534408 0.845227i \(-0.679465\pi\)
0.303971 + 0.952681i \(0.401688\pi\)
\(410\) 0.224953 + 14.5622i 0.0111096 + 0.719176i
\(411\) −6.05120 + 7.21154i −0.298484 + 0.355719i
\(412\) −8.74493 1.54197i −0.430832 0.0759673i
\(413\) −51.3307 −2.52582
\(414\) −22.9228 4.04190i −1.12659 0.198649i
\(415\) −7.19267 + 10.6175i −0.353074 + 0.521195i
\(416\) 0.0922595 0.0774149i 0.00452340 0.00379558i
\(417\) −0.548773 2.04805i −0.0268735 0.100293i
\(418\) −10.2054 2.73452i −0.499160 0.133750i
\(419\) −4.08952 + 11.2359i −0.199786 + 0.548908i −0.998613 0.0526531i \(-0.983232\pi\)
0.798827 + 0.601561i \(0.205454\pi\)
\(420\) 4.13394 2.47264i 0.201715 0.120653i
\(421\) 8.42718 2.25806i 0.410716 0.110051i −0.0475442 0.998869i \(-0.515140\pi\)
0.458260 + 0.888818i \(0.348473\pi\)
\(422\) 2.82764 + 16.0364i 0.137648 + 0.780638i
\(423\) 16.4376 23.4753i 0.799224 1.14141i
\(424\) −3.61983 0.316694i −0.175794 0.0153800i
\(425\) 5.02505 15.2569i 0.243751 0.740068i
\(426\) 2.33740 5.01258i 0.113248 0.242860i
\(427\) 23.4422 19.6704i 1.13445 0.951916i
\(428\) 0.936727 + 0.655904i 0.0452784 + 0.0317043i
\(429\) 0.208648 0.297981i 0.0100736 0.0143866i
\(430\) 19.0316 16.4770i 0.917784 0.794589i
\(431\) −3.12695 35.7412i −0.150620 1.72159i −0.576742 0.816927i \(-0.695676\pi\)
0.426122 0.904666i \(-0.359879\pi\)
\(432\) −1.24911 2.67872i −0.0600976 0.128880i
\(433\) 2.98928 11.1561i 0.143655 0.536129i −0.856156 0.516717i \(-0.827154\pi\)
0.999812 0.0194122i \(-0.00617948\pi\)
\(434\) −4.27026 + 7.39631i −0.204979 + 0.355034i
\(435\) 1.49512 + 3.91839i 0.0716853 + 0.187873i
\(436\) 0.399983 1.49276i 0.0191557 0.0714901i
\(437\) 12.5723 8.80322i 0.601415 0.421115i
\(438\) 2.40763i 0.115041i
\(439\) −11.2245 16.0303i −0.535717 0.765083i 0.456484 0.889732i \(-0.349108\pi\)
−0.992201 + 0.124649i \(0.960220\pi\)
\(440\) 11.2453 6.72619i 0.536099 0.320658i
\(441\) −26.8970 + 9.78972i −1.28081 + 0.466177i
\(442\) 0.132333 0.363582i 0.00629445 0.0172939i
\(443\) 9.23821 9.23821i 0.438921 0.438921i −0.452728 0.891649i \(-0.649549\pi\)
0.891649 + 0.452728i \(0.149549\pi\)
\(444\) 2.85062 1.30523i 0.135284 0.0619435i
\(445\) 21.7759 10.5668i 1.03228 0.500914i
\(446\) 4.29415 + 9.20884i 0.203334 + 0.436051i
\(447\) −0.921834 0.429858i −0.0436012 0.0203316i
\(448\) 4.16358 0.364266i 0.196711 0.0172100i
\(449\) −15.3293 + 10.7337i −0.723435 + 0.506554i −0.876344 0.481686i \(-0.840025\pi\)
0.152909 + 0.988240i \(0.451136\pi\)
\(450\) 8.46029 10.7396i 0.398822 0.506267i
\(451\) −6.62770 + 37.5875i −0.312086 + 1.76993i
\(452\) −0.858620 + 0.495725i −0.0403861 + 0.0233169i
\(453\) −10.0351 0.877955i −0.471489 0.0412499i
\(454\) −10.5042 6.06462i −0.492988 0.284627i
\(455\) 0.931858 + 0.631271i 0.0436862 + 0.0295944i
\(456\) 0.873253 + 0.317838i 0.0408938 + 0.0148841i
\(457\) 12.0868 14.4045i 0.565397 0.673814i −0.405282 0.914192i \(-0.632827\pi\)
0.970680 + 0.240377i \(0.0772712\pi\)
\(458\) 22.9704 + 13.2620i 1.07334 + 0.619692i
\(459\) −7.77813 5.44631i −0.363052 0.254212i
\(460\) −3.01543 + 18.7945i −0.140595 + 0.876297i
\(461\) 0.829351 9.47953i 0.0386267 0.441506i −0.952114 0.305742i \(-0.901096\pi\)
0.990741 0.135764i \(-0.0433489\pi\)
\(462\) 11.8625 4.31758i 0.551892 0.200872i
\(463\) −1.62388 + 0.591045i −0.0754682 + 0.0274682i −0.379478 0.925201i \(-0.623897\pi\)
0.304010 + 0.952669i \(0.401674\pi\)
\(464\) −0.317151 + 3.62505i −0.0147234 + 0.168289i
\(465\) 0.373091 2.32539i 0.0173017 0.107837i
\(466\) 2.11365 + 1.47999i 0.0979130 + 0.0685594i
\(467\) −34.1584 19.7214i −1.58066 0.912597i −0.994762 0.102215i \(-0.967407\pi\)
−0.585902 0.810382i \(-0.699260\pi\)
\(468\) 0.211678 0.252268i 0.00978483 0.0116611i
\(469\) 32.8921 + 11.9717i 1.51882 + 0.552804i
\(470\) −19.4029 13.1441i −0.894988 0.606293i
\(471\) 1.90155 + 1.09786i 0.0876190 + 0.0505868i
\(472\) 12.2349 + 1.07041i 0.563155 + 0.0492696i
\(473\) 57.1324 32.9854i 2.62695 1.51667i
\(474\) 0.462449 2.62268i 0.0212410 0.120464i
\(475\) 1.06271 + 8.95194i 0.0487604 + 0.410743i
\(476\) 10.9988 7.70147i 0.504131 0.352996i
\(477\) −9.89782 + 0.865947i −0.453190 + 0.0396490i
\(478\) 3.24440 + 1.51289i 0.148395 + 0.0691979i
\(479\) 1.20633 + 2.58699i 0.0551188 + 0.118203i 0.931938 0.362617i \(-0.118117\pi\)
−0.876819 + 0.480820i \(0.840339\pi\)
\(480\) −1.03690 + 0.503157i −0.0473278 + 0.0229659i
\(481\) 0.557908 + 0.474784i 0.0254384 + 0.0216483i
\(482\) 0.512076 0.512076i 0.0233244 0.0233244i
\(483\) −6.27201 + 17.2322i −0.285386 + 0.784092i
\(484\) 21.9322 7.98266i 0.996917 0.362848i
\(485\) 14.8093 8.85790i 0.672454 0.402216i
\(486\) −7.06059 10.0836i −0.320275 0.457400i
\(487\) 27.9379i 1.26599i −0.774156 0.632994i \(-0.781826\pi\)
0.774156 0.632994i \(-0.218174\pi\)
\(488\) −5.99773 + 4.19966i −0.271505 + 0.190110i
\(489\) −0.128322 + 0.478904i −0.00580292 + 0.0216568i
\(490\) 8.34457 + 21.8694i 0.376969 + 0.987960i
\(491\) −9.61627 + 16.6559i −0.433976 + 0.751668i −0.997211 0.0746280i \(-0.976223\pi\)
0.563235 + 0.826296i \(0.309556\pi\)
\(492\) 0.868877 3.24269i 0.0391720 0.146192i
\(493\) 4.94058 + 10.5951i 0.222512 + 0.477179i
\(494\) 0.0189252 + 0.216316i 0.000851483 + 0.00973249i
\(495\) 27.0876 23.4516i 1.21750 1.05407i
\(496\) 1.17207 1.67389i 0.0526274 0.0751598i
\(497\) 36.7370 + 25.7236i 1.64788 + 1.15386i
\(498\) 2.26452 1.90016i 0.101476 0.0851481i
\(499\) −4.63194 + 9.93323i −0.207354 + 0.444673i −0.982290 0.187368i \(-0.940004\pi\)
0.774936 + 0.632040i \(0.217782\pi\)
\(500\) −8.88835 6.78213i −0.397499 0.303306i
\(501\) 12.7946 + 1.11938i 0.571621 + 0.0500104i
\(502\) −13.1480 + 18.7773i −0.586823 + 0.838071i
\(503\) 2.53165 + 14.3577i 0.112881 + 0.640179i 0.987778 + 0.155870i \(0.0498179\pi\)
−0.874897 + 0.484309i \(0.839071\pi\)
\(504\) 11.0387 2.95781i 0.491703 0.131751i
\(505\) −7.99985 + 4.78497i −0.355989 + 0.212928i
\(506\) −17.0614 + 46.8758i −0.758471 + 2.08388i
\(507\) 6.46503 + 1.73230i 0.287122 + 0.0769341i
\(508\) 2.93973 + 10.9712i 0.130429 + 0.486769i
\(509\) 32.7132 27.4497i 1.44999 1.21669i 0.517401 0.855743i \(-0.326900\pi\)
0.932588 0.360942i \(-0.117545\pi\)
\(510\) −2.07665 + 3.06548i −0.0919557 + 0.135742i
\(511\) 19.2263 + 3.39012i 0.850523 + 0.149970i
\(512\) −1.00000 −0.0441942
\(513\) 5.24794 + 0.925353i 0.231702 + 0.0408553i
\(514\) 17.5279 20.8889i 0.773123 0.921372i
\(515\) 0.306692 + 19.8535i 0.0135145 + 0.874852i
\(516\) −5.25893 + 2.45228i −0.231511 + 0.107956i
\(517\) −43.4289 43.4289i −1.91000 1.91000i
\(518\) 6.40914 + 24.6017i 0.281602 + 1.08094i
\(519\) 0.225941i 0.00991773i
\(520\) −0.208948 0.169898i −0.00916296 0.00745052i
\(521\) −12.9750 35.6484i −0.568443 1.56179i −0.806935 0.590641i \(-0.798875\pi\)
0.238491 0.971145i \(-0.423347\pi\)
\(522\) 0.867196 + 9.91210i 0.0379561 + 0.433841i
\(523\) 2.32143 13.1655i 0.101509 0.575687i −0.891048 0.453909i \(-0.850029\pi\)
0.992557 0.121778i \(-0.0388597\pi\)
\(524\) −6.40442 6.40442i −0.279778 0.279778i
\(525\) −7.17510 8.03336i −0.313147 0.350605i
\(526\) −13.4938 3.61566i −0.588359 0.157650i
\(527\) 0.572160 6.53982i 0.0249237 0.284879i
\(528\) −2.91750 + 0.781741i −0.126968 + 0.0340209i
\(529\) −24.7325 42.8380i −1.07533 1.86252i
\(530\) 0.833087 + 8.08228i 0.0361870 + 0.351072i
\(531\) 33.4542 2.92686i 1.45179 0.127015i
\(532\) −3.76772 + 6.52588i −0.163351 + 0.282933i
\(533\) 0.772507 0.136214i 0.0334610 0.00590008i
\(534\) −5.49449 + 0.968827i −0.237770 + 0.0419252i
\(535\) 1.04472 2.33386i 0.0451671 0.100902i
\(536\) −7.59029 3.53941i −0.327851 0.152879i
\(537\) 1.25720 + 3.45414i 0.0542524 + 0.149057i
\(538\) −2.41297 2.87567i −0.104031 0.123979i
\(539\) 10.6521 + 60.4111i 0.458819 + 2.60209i
\(540\) −5.35458 + 3.87394i −0.230425 + 0.166708i
\(541\) 2.72667 + 10.1761i 0.117229 + 0.437504i 0.999444 0.0333424i \(-0.0106152\pi\)
−0.882215 + 0.470847i \(0.843949\pi\)
\(542\) 1.52548 + 1.28003i 0.0655251 + 0.0549821i
\(543\) 2.65971 1.24024i 0.114139 0.0532238i
\(544\) −2.78221 + 1.60631i −0.119286 + 0.0688700i
\(545\) −3.44675 0.247972i −0.147642 0.0106219i
\(546\) −0.166769 0.198748i −0.00713706 0.00850561i
\(547\) 17.7620 + 30.7647i 0.759450 + 1.31541i 0.943132 + 0.332420i \(0.107865\pi\)
−0.183682 + 0.982986i \(0.558802\pi\)
\(548\) 10.4760 + 14.9613i 0.447514 + 0.639117i
\(549\) −14.1566 + 14.1566i −0.604189 + 0.604189i
\(550\) −19.5180 21.8527i −0.832251 0.931802i
\(551\) −5.02585 4.21719i −0.214109 0.179658i
\(552\) 1.85430 3.97656i 0.0789243 0.169254i
\(553\) 20.2924 + 7.38583i 0.862921 + 0.314078i
\(554\) 6.51017 0.276591
\(555\) −4.06977 5.70835i −0.172752 0.242306i
\(556\) −4.11366 −0.174458
\(557\) 34.6599 + 12.6152i 1.46859 + 0.534522i 0.947716 0.319114i \(-0.103385\pi\)
0.520870 + 0.853636i \(0.325608\pi\)
\(558\) 2.36136 5.06395i 0.0999642 0.214374i
\(559\) −1.03864 0.871522i −0.0439298 0.0368614i
\(560\) −2.55797 8.98873i −0.108094 0.379843i
\(561\) −6.86138 + 6.86138i −0.289688 + 0.289688i
\(562\) −14.8902 21.2654i −0.628106 0.897028i
\(563\) −6.89828 11.9482i −0.290728 0.503555i 0.683254 0.730180i \(-0.260564\pi\)
−0.973982 + 0.226625i \(0.927231\pi\)
\(564\) 3.47241 + 4.13826i 0.146215 + 0.174252i
\(565\) 1.45109 + 1.67607i 0.0610478 + 0.0705127i
\(566\) 24.3582 14.0632i 1.02385 0.591121i
\(567\) 25.3016 11.7983i 1.06257 0.495483i
\(568\) −8.21999 6.89739i −0.344903 0.289408i
\(569\) 8.14974 + 30.4152i 0.341655 + 1.27507i 0.896472 + 0.443101i \(0.146122\pi\)
−0.554817 + 0.831972i \(0.687212\pi\)
\(570\) 0.329184 2.05173i 0.0137880 0.0859375i
\(571\) −0.398417 2.25953i −0.0166732 0.0945586i 0.975336 0.220727i \(-0.0708431\pi\)
−0.992009 + 0.126169i \(0.959732\pi\)
\(572\) −0.453652 0.540642i −0.0189682 0.0226054i
\(573\) 3.08269 + 8.46962i 0.128781 + 0.353823i
\(574\) 24.6713 + 11.5044i 1.02976 + 0.480185i
\(575\) 42.5429 1.31470i 1.77416 0.0548266i
\(576\) −2.69279 + 0.474812i −0.112200 + 0.0197838i
\(577\) 26.6815 4.70468i 1.11077 0.195858i 0.411984 0.911191i \(-0.364836\pi\)
0.698784 + 0.715333i \(0.253725\pi\)
\(578\) 3.33953 5.78423i 0.138906 0.240592i
\(579\) 6.15715 0.538681i 0.255883 0.0223868i
\(580\) 8.09394 0.834288i 0.336082 0.0346419i
\(581\) 11.9852 + 20.7590i 0.497231 + 0.861230i
\(582\) −3.84213 + 1.02950i −0.159261 + 0.0426740i
\(583\) −1.85583 + 21.2122i −0.0768606 + 0.878521i
\(584\) −4.51197 1.20898i −0.186707 0.0500279i
\(585\) −0.643323 0.358289i −0.0265981 0.0148134i
\(586\) 2.08925 + 2.08925i 0.0863062 + 0.0863062i
\(587\) 1.35983 7.71200i 0.0561263 0.318308i −0.943799 0.330520i \(-0.892776\pi\)
0.999925 + 0.0122114i \(0.00388710\pi\)
\(588\) −0.470253 5.37501i −0.0193929 0.221662i
\(589\) 1.26008 + 3.46205i 0.0519209 + 0.142651i
\(590\) −2.81579 27.3177i −0.115924 1.12465i
\(591\) 2.99693i 0.123277i
\(592\) −1.01462 5.99755i −0.0417005 0.246498i
\(593\) 31.2809 + 31.2809i 1.28455 + 1.28455i 0.938049 + 0.346502i \(0.112631\pi\)
0.346502 + 0.938049i \(0.387369\pi\)
\(594\) −15.6973 + 7.31978i −0.644068 + 0.300334i
\(595\) −21.5555 20.8997i −0.883689 0.856803i
\(596\) −1.26846 + 1.51169i −0.0519581 + 0.0619212i
\(597\) 5.94151 + 1.04765i 0.243170 + 0.0428774i
\(598\) 1.02523 0.0419248
\(599\) 34.8542 + 6.14574i 1.42410 + 0.251108i 0.832010 0.554761i \(-0.187190\pi\)
0.592094 + 0.805869i \(0.298301\pi\)
\(600\) 1.54269 + 2.06440i 0.0629800 + 0.0842790i
\(601\) −28.0523 + 23.5387i −1.14428 + 0.960164i −0.999570 0.0293108i \(-0.990669\pi\)
−0.144708 + 0.989474i \(0.546224\pi\)
\(602\) −12.1779 45.4485i −0.496334 1.85234i
\(603\) −22.1197 5.92694i −0.900782 0.241364i
\(604\) −6.68436 + 18.3651i −0.271983 + 0.747266i
\(605\) −26.7896 44.7887i −1.08915 1.82092i
\(606\) 2.07549 0.556126i 0.0843110 0.0225911i
\(607\) 3.25867 + 18.4808i 0.132265 + 0.750114i 0.976725 + 0.214495i \(0.0688106\pi\)
−0.844460 + 0.535619i \(0.820078\pi\)
\(608\) 1.03414 1.47690i 0.0419397 0.0598961i
\(609\) 7.80917 + 0.683214i 0.316443 + 0.0276852i
\(610\) 11.7543 + 11.3967i 0.475919 + 0.461439i
\(611\) −0.533459 + 1.14401i −0.0215815 + 0.0462816i
\(612\) −6.72923 + 5.64649i −0.272013 + 0.228246i
\(613\) 20.3049 + 14.2177i 0.820108 + 0.574246i 0.906592 0.422007i \(-0.138674\pi\)
−0.0864842 + 0.996253i \(0.527563\pi\)
\(614\) −2.95288 + 4.21715i −0.119168 + 0.170190i
\(615\) −7.48731 0.538665i −0.301918 0.0217211i
\(616\) −2.13460 24.3986i −0.0860056 0.983048i
\(617\) 0.979983 + 2.10158i 0.0394526 + 0.0846064i 0.925046 0.379854i \(-0.124026\pi\)
−0.885594 + 0.464461i \(0.846248\pi\)
\(618\) 1.18459 4.42096i 0.0476513 0.177837i
\(619\) −20.4695 + 35.4541i −0.822737 + 1.42502i 0.0809002 + 0.996722i \(0.474220\pi\)
−0.903637 + 0.428299i \(0.859113\pi\)
\(620\) −4.17050 1.86686i −0.167491 0.0749750i
\(621\) 6.51196 24.3030i 0.261316 0.975244i
\(622\) 4.56290 3.19498i 0.182956 0.128107i
\(623\) 45.2408i 1.81253i
\(624\) 0.0356055 + 0.0508499i 0.00142536 + 0.00203562i
\(625\) −11.1393 + 22.3812i −0.445572 + 0.895246i
\(626\) 8.37506 3.04827i 0.334735 0.121833i
\(627\) 1.86253 5.11727i 0.0743825 0.204364i
\(628\) 3.01228 3.01228i 0.120203 0.120203i
\(629\) −12.4568 15.0567i −0.496685 0.600348i
\(630\) −11.1560 22.9902i −0.444467 0.915953i
\(631\) −6.90172 14.8008i −0.274753 0.589210i 0.719713 0.694272i \(-0.244274\pi\)
−0.994466 + 0.105062i \(0.966496\pi\)
\(632\) −4.68275 2.18360i −0.186270 0.0868590i
\(633\) −8.36117 + 0.731507i −0.332327 + 0.0290748i
\(634\) −8.25691 + 5.78155i −0.327924 + 0.229615i
\(635\) 22.8497 11.0878i 0.906762 0.440007i
\(636\) 0.325224 1.84444i 0.0128960 0.0731366i
\(637\) 1.09183 0.630368i 0.0432599 0.0249761i
\(638\) 21.2428 + 1.85851i 0.841012 + 0.0735790i
\(639\) −25.4097 14.6703i −1.00519 0.580348i
\(640\) 0.422256 + 2.19584i 0.0166911 + 0.0867981i
\(641\) −13.4246 4.88615i −0.530240 0.192991i 0.0630057 0.998013i \(-0.479931\pi\)
−0.593245 + 0.805022i \(0.702154\pi\)
\(642\) −0.378865 + 0.451514i −0.0149526 + 0.0178198i
\(643\) 10.9372 + 6.31462i 0.431323 + 0.249024i 0.699910 0.714231i \(-0.253223\pi\)
−0.268587 + 0.963255i \(0.586557\pi\)
\(644\) 29.1441 + 20.4069i 1.14844 + 0.804146i
\(645\) 7.60542 + 10.5123i 0.299463 + 0.413920i
\(646\) 0.504826 5.77019i 0.0198621 0.227025i
\(647\) 20.9009 7.60731i 0.821699 0.299074i 0.103252 0.994655i \(-0.467075\pi\)
0.718448 + 0.695581i \(0.244853\pi\)
\(648\) −6.27675 + 2.28455i −0.246574 + 0.0897457i
\(649\) 6.27262 71.6964i 0.246222 2.81433i
\(650\) −0.284839 + 0.530556i −0.0111723 + 0.0208101i
\(651\) −3.60593 2.52490i −0.141327 0.0989586i
\(652\) 0.833043 + 0.480957i 0.0326245 + 0.0188357i
\(653\) 1.47155 1.75373i 0.0575864 0.0686287i −0.736482 0.676457i \(-0.763515\pi\)
0.794069 + 0.607828i \(0.207959\pi\)
\(654\) 0.748513 + 0.272437i 0.0292692 + 0.0106531i
\(655\) −11.3588 + 16.7674i −0.443823 + 0.655155i
\(656\) −5.64059 3.25660i −0.220228 0.127149i
\(657\) −12.7238 1.11319i −0.496404 0.0434297i
\(658\) −37.9358 + 21.9022i −1.47889 + 0.853838i
\(659\) 7.56560 42.9067i 0.294714 1.67141i −0.373648 0.927571i \(-0.621893\pi\)
0.668362 0.743836i \(-0.266996\pi\)
\(660\) 2.94851 + 6.07625i 0.114770 + 0.236518i
\(661\) −0.616154 + 0.431435i −0.0239656 + 0.0167809i −0.585498 0.810674i \(-0.699101\pi\)
0.561532 + 0.827455i \(0.310212\pi\)
\(662\) 4.31857 0.377826i 0.167846 0.0146846i
\(663\) 0.180743 + 0.0842817i 0.00701947 + 0.00327323i
\(664\) −2.42383 5.19792i −0.0940629 0.201718i
\(665\) 15.9207 + 5.51771i 0.617379 + 0.213967i
\(666\) −5.57986 15.6684i −0.216215 0.607138i
\(667\) −21.9038 + 21.9038i −0.848117 + 0.848117i
\(668\) 8.52249 23.4154i 0.329745 0.905968i
\(669\) −4.92134 + 1.79122i −0.190270 + 0.0692526i
\(670\) −4.56692 + 18.1616i −0.176436 + 0.701643i
\(671\) 24.6100 + 35.1468i 0.950060 + 1.35683i
\(672\) 2.15422i 0.0831010i
\(673\) −31.4721 + 22.0370i −1.21316 + 0.849465i −0.992058 0.125785i \(-0.959855\pi\)
−0.221104 + 0.975250i \(0.570966\pi\)
\(674\) −0.166957 + 0.623092i −0.00643094 + 0.0240006i
\(675\) 10.7675 + 10.1220i 0.414443 + 0.389596i
\(676\) 6.49275 11.2458i 0.249721 0.432530i
\(677\) −10.4726 + 39.0843i −0.402495 + 1.50213i 0.406134 + 0.913814i \(0.366877\pi\)
−0.808629 + 0.588319i \(0.799790\pi\)
\(678\) −0.215967 0.463142i −0.00829415 0.0177869i
\(679\) −2.81112 32.1312i −0.107881 1.23308i
\(680\) 4.70200 + 5.43101i 0.180314 + 0.208270i
\(681\) 3.58586 5.12114i 0.137410 0.196242i
\(682\) −9.80900 6.86834i −0.375606 0.263002i
\(683\) −21.7289 + 18.2327i −0.831434 + 0.697656i −0.955620 0.294603i \(-0.904813\pi\)
0.124185 + 0.992259i \(0.460368\pi\)
\(684\) 2.08346 4.46800i 0.0796632 0.170838i
\(685\) 28.4291 29.3212i 1.08622 1.12031i
\(686\) 14.4396 + 1.26330i 0.551308 + 0.0482332i
\(687\) −7.84147 + 11.1988i −0.299171 + 0.427260i
\(688\) 1.95490 + 11.0868i 0.0745297 + 0.422679i
\(689\) 0.422712 0.113265i 0.0161041 0.00431507i
\(690\) −9.51488 2.39262i −0.362225 0.0910854i
\(691\) −1.48807 + 4.08844i −0.0566088 + 0.155531i −0.964774 0.263081i \(-0.915261\pi\)
0.908165 + 0.418613i \(0.137484\pi\)
\(692\) 0.423420 + 0.113455i 0.0160960 + 0.00431292i
\(693\) −17.3328 64.6869i −0.658419 2.45725i
\(694\) −15.9373 + 13.3730i −0.604973 + 0.507633i
\(695\) 1.73702 + 9.03293i 0.0658889 + 0.342639i
\(696\) −1.84710 0.325693i −0.0700140 0.0123454i
\(697\) −20.9244 −0.792569
\(698\) −23.6280 4.16625i −0.894332 0.157695i
\(699\) −0.854878 + 1.01880i −0.0323345 + 0.0385347i
\(700\) −18.6577 + 9.41242i −0.705193 + 0.355756i
\(701\) −28.1367 + 13.1204i −1.06271 + 0.495549i −0.873720 0.486430i \(-0.838299\pi\)
−0.188989 + 0.981979i \(0.560521\pi\)
\(702\) 0.251706 + 0.251706i 0.00950003 + 0.00950003i
\(703\) 9.90702 + 4.70379i 0.373650 + 0.177407i
\(704\) 5.86001i 0.220857i
\(705\) 7.62070 9.37226i 0.287012 0.352980i
\(706\) −6.94362 19.0774i −0.261327 0.717989i
\(707\) 1.51854 + 17.3570i 0.0571107 + 0.652779i
\(708\) −1.09924 + 6.23410i −0.0413120 + 0.234292i
\(709\) 0.0353863 + 0.0353863i 0.00132896 + 0.00132896i 0.707771 0.706442i \(-0.249701\pi\)
−0.706442 + 0.707771i \(0.749701\pi\)
\(710\) −11.6746 + 20.9622i −0.438140 + 0.786698i
\(711\) −13.6465 3.65656i −0.511783 0.137132i
\(712\) −0.943417 + 10.7833i −0.0353560 + 0.404121i
\(713\) 16.8023 4.50217i 0.629253 0.168608i
\(714\) 3.46035 + 5.99351i 0.129500 + 0.224301i
\(715\) −0.995604 + 1.22444i −0.0372335 + 0.0457913i
\(716\) 7.10444 0.621558i 0.265506 0.0232287i
\(717\) −0.922565 + 1.59793i −0.0344538 + 0.0596758i
\(718\) −15.6740 + 2.76374i −0.584947 + 0.103142i
\(719\) −19.6408 + 3.46320i −0.732478 + 0.129156i −0.527433 0.849597i \(-0.676845\pi\)
−0.205045 + 0.978752i \(0.565734\pi\)
\(720\) 2.17966 + 5.71244i 0.0812311 + 0.212890i
\(721\) 33.6359 + 15.6847i 1.25267 + 0.584128i
\(722\) −5.38659 14.7995i −0.200468 0.550782i
\(723\) 0.239930 + 0.285938i 0.00892310 + 0.0106341i
\(724\) −0.988689 5.60714i −0.0367444 0.208388i
\(725\) −5.24968 17.4207i −0.194968 0.646988i
\(726\) 3.11358 + 11.6200i 0.115556 + 0.431260i
\(727\) 20.0922 + 16.8594i 0.745179 + 0.625279i 0.934223 0.356689i \(-0.116095\pi\)
−0.189044 + 0.981969i \(0.560539\pi\)
\(728\) −0.456200 + 0.212730i −0.0169079 + 0.00788429i
\(729\) −11.8593 + 6.84698i −0.439234 + 0.253592i
\(730\) −0.749513 + 10.4180i −0.0277407 + 0.385589i
\(731\) 23.2477 + 27.7056i 0.859849 + 1.02473i
\(732\) −1.88695 3.26830i −0.0697437 0.120800i
\(733\) −10.7795 15.3947i −0.398149 0.568615i 0.569157 0.822229i \(-0.307270\pi\)
−0.967306 + 0.253614i \(0.918381\pi\)
\(734\) 10.5693 10.5693i 0.390119 0.390119i
\(735\) −11.6041 + 3.30223i −0.428023 + 0.121805i
\(736\) −6.52106 5.47182i −0.240369 0.201694i
\(737\) −20.7410 + 44.4792i −0.764004 + 1.63841i
\(738\) −16.7352 6.09112i −0.616032 0.224217i
\(739\) −2.98215 −0.109700 −0.0548501 0.998495i \(-0.517468\pi\)
−0.0548501 + 0.998495i \(0.517468\pi\)
\(740\) −12.7412 + 4.76044i −0.468376 + 0.174997i
\(741\) −0.111921 −0.00411152
\(742\) 14.2709 + 5.19419i 0.523902 + 0.190685i
\(743\) −16.8005 + 36.0287i −0.616349 + 1.32176i 0.312010 + 0.950079i \(0.398998\pi\)
−0.928359 + 0.371686i \(0.878780\pi\)
\(744\) 0.806833 + 0.677014i 0.0295799 + 0.0248205i
\(745\) 3.85504 + 2.14701i 0.141238 + 0.0786603i
\(746\) −10.3344 + 10.3344i −0.378371 + 0.378371i
\(747\) −8.99491 12.8461i −0.329107 0.470013i
\(748\) 9.41300 + 16.3038i 0.344173 + 0.596126i
\(749\) −3.07212 3.66122i −0.112253 0.133778i
\(750\) 3.88169 4.25920i 0.141739 0.155524i
\(751\) 15.5748 8.99213i 0.568334 0.328128i −0.188150 0.982140i \(-0.560249\pi\)
0.756483 + 0.654013i \(0.226916\pi\)
\(752\) 9.49886 4.42939i 0.346388 0.161523i
\(753\) −9.05086 7.59458i −0.329832 0.276762i
\(754\) −0.113429 0.423322i −0.00413083 0.0154165i
\(755\) 43.1493 + 6.92297i 1.57036 + 0.251953i
\(756\) 2.14508 + 12.1654i 0.0780159 + 0.442450i
\(757\) −1.74737 2.08243i −0.0635091 0.0756872i 0.733355 0.679846i \(-0.237954\pi\)
−0.796864 + 0.604159i \(0.793509\pi\)
\(758\) 2.96081 + 8.13475i 0.107541 + 0.295467i
\(759\) −23.3027 10.8662i −0.845835 0.394419i
\(760\) −3.67970 1.64716i −0.133477 0.0597489i
\(761\) 28.3640 5.00133i 1.02819 0.181298i 0.365987 0.930620i \(-0.380732\pi\)
0.662206 + 0.749322i \(0.269620\pi\)
\(762\) −5.76542 + 1.01660i −0.208859 + 0.0368275i
\(763\) −3.22952 + 5.59369i −0.116917 + 0.202505i
\(764\) 17.4202 1.52407i 0.630242 0.0551390i
\(765\) 15.2402 + 12.3920i 0.551012 + 0.448034i
\(766\) 2.95541 + 5.11892i 0.106783 + 0.184954i
\(767\) −1.42875 + 0.382832i −0.0515891 + 0.0138233i
\(768\) 0.0449225 0.513467i 0.00162100 0.0185281i
\(769\) −3.59012 0.961971i −0.129463 0.0346896i 0.193506 0.981099i \(-0.438014\pi\)
−0.322969 + 0.946410i \(0.604681\pi\)
\(770\) −52.6740 + 14.9897i −1.89824 + 0.540192i
\(771\) 9.93838 + 9.93838i 0.357922 + 0.357922i
\(772\) 2.08227 11.8092i 0.0749427 0.425021i
\(773\) −1.73250 19.8026i −0.0623137 0.712249i −0.961522 0.274728i \(-0.911412\pi\)
0.899208 0.437521i \(-0.144143\pi\)
\(774\) 10.5283 + 28.9262i 0.378431 + 1.03973i
\(775\) −2.33831 + 9.94603i −0.0839945 + 0.357272i
\(776\) 7.71721i 0.277032i
\(777\) −12.9201 + 2.18571i −0.463504 + 0.0784120i
\(778\) −11.1192 11.1192i −0.398644 0.398644i
\(779\) 10.6428 4.96282i 0.381318 0.177811i
\(780\) 0.0966234 0.0996555i 0.00345967 0.00356824i
\(781\) −40.4188 + 48.1692i −1.44630 + 1.72363i
\(782\) −26.9324 4.74891i −0.963101 0.169821i
\(783\) −10.7553 −0.384362
\(784\) −10.3090 1.81776i −0.368180 0.0649201i
\(785\) −7.88642 5.34252i −0.281478 0.190683i
\(786\) 3.57616 3.00075i 0.127557 0.107033i
\(787\) 3.96017 + 14.7796i 0.141165 + 0.526835i 0.999896 + 0.0144086i \(0.00458655\pi\)
−0.858731 + 0.512426i \(0.828747\pi\)
\(788\) 5.61633 + 1.50489i 0.200074 + 0.0536096i
\(789\) 2.46270 6.76621i 0.0876744 0.240883i
\(790\) −2.81751 + 11.2046i −0.100243 + 0.398641i
\(791\) 4.00255 1.07248i 0.142314 0.0381330i
\(792\) 2.78240 + 15.7798i 0.0988684 + 0.560711i
\(793\) 0.505791 0.722344i 0.0179612 0.0256512i
\(794\) 24.5879 + 2.15117i 0.872594 + 0.0763420i
\(795\) −4.18741 + 0.0646860i −0.148512 + 0.00229417i
\(796\) 4.94681 10.6085i 0.175335 0.376007i
\(797\) −8.05769 + 6.76120i −0.285418 + 0.239494i −0.774244 0.632887i \(-0.781870\pi\)
0.488826 + 0.872381i \(0.337425\pi\)
\(798\) −3.18157 2.22776i −0.112626 0.0788618i
\(799\) 19.3129 27.5816i 0.683240 0.975768i
\(800\) 4.64340 1.85441i 0.164169 0.0655633i
\(801\) 2.57962 + 29.4852i 0.0911463 + 1.04181i
\(802\) −8.50522 18.2395i −0.300330 0.644059i
\(803\) −7.08463 + 26.4402i −0.250011 + 0.933054i
\(804\) 2.15835 3.73836i 0.0761190 0.131842i
\(805\) 32.5040 72.6127i 1.14562 2.55926i
\(806\) −0.0636965 + 0.237718i −0.00224361 + 0.00837327i
\(807\) 1.58496 1.10980i 0.0557931 0.0390667i
\(808\) 4.16878i 0.146657i
\(809\) 13.6434 + 19.4848i 0.479677 + 0.685050i 0.983940 0.178500i \(-0.0571246\pi\)
−0.504263 + 0.863550i \(0.668236\pi\)
\(810\) 7.66690 + 12.8181i 0.269387 + 0.450381i
\(811\) 4.67860 1.70287i 0.164288 0.0597959i −0.258567 0.965993i \(-0.583250\pi\)
0.422855 + 0.906197i \(0.361028\pi\)
\(812\) 5.20168 14.2915i 0.182543 0.501534i
\(813\) −0.725782 + 0.725782i −0.0254543 + 0.0254543i
\(814\) −35.1457 + 5.94567i −1.23186 + 0.208396i
\(815\) 0.704347 2.03231i 0.0246722 0.0711888i
\(816\) −0.699803 1.50073i −0.0244980 0.0525362i
\(817\) −18.3957 8.57804i −0.643583 0.300108i
\(818\) −5.12251 + 0.448161i −0.179104 + 0.0156696i
\(819\) −1.12745 + 0.789447i −0.0393962 + 0.0275855i
\(820\) −4.76918 + 13.7609i −0.166547 + 0.480553i
\(821\) 7.84053 44.4658i 0.273636 1.55187i −0.469624 0.882866i \(-0.655611\pi\)
0.743261 0.669002i \(-0.233278\pi\)
\(822\) −8.15276 + 4.70700i −0.284360 + 0.164175i
\(823\) 27.5191 + 2.40761i 0.959256 + 0.0839240i 0.556017 0.831171i \(-0.312329\pi\)
0.403239 + 0.915095i \(0.367884\pi\)
\(824\) −7.69016 4.43992i −0.267900 0.154672i
\(825\) 12.0974 9.04017i 0.421179 0.314738i
\(826\) −48.2351 17.5561i −1.67831 0.610856i
\(827\) 1.11537 1.32925i 0.0387853 0.0462225i −0.746303 0.665606i \(-0.768173\pi\)
0.785088 + 0.619384i \(0.212617\pi\)
\(828\) −20.1579 11.6382i −0.700537 0.404455i
\(829\) −23.9472 16.7680i −0.831720 0.582377i 0.0783050 0.996929i \(-0.475049\pi\)
−0.910025 + 0.414553i \(0.863938\pi\)
\(830\) −10.3903 + 7.51719i −0.360653 + 0.260925i
\(831\) −0.292453 + 3.34276i −0.0101451 + 0.115959i
\(832\) 0.113173 0.0411916i 0.00392357 0.00142806i
\(833\) −31.6019 + 11.5021i −1.09494 + 0.398525i
\(834\) 0.184796 2.11223i 0.00639897 0.0731405i
\(835\) −55.0150 8.82673i −1.90387 0.305461i
\(836\) −8.65464 6.06005i −0.299327 0.209591i
\(837\) 5.23050 + 3.01983i 0.180793 + 0.104381i
\(838\) −7.68579 + 9.15957i −0.265501 + 0.316412i
\(839\) 51.6994 + 18.8170i 1.78486 + 0.649637i 0.999533 + 0.0305581i \(0.00972846\pi\)
0.785329 + 0.619079i \(0.212494\pi\)
\(840\) 4.73032 0.909634i 0.163212 0.0313854i
\(841\) −13.6472 7.87922i −0.470593 0.271697i
\(842\) 8.69126 + 0.760387i 0.299521 + 0.0262047i
\(843\) 11.5880 6.69033i 0.399112 0.230427i
\(844\) −2.82764 + 16.0364i −0.0973315 + 0.551995i
\(845\) −27.4355 9.50842i −0.943809 0.327100i
\(846\) 23.4753 16.4376i 0.807099 0.565137i
\(847\) −97.1768 + 8.50187i −3.33903 + 0.292128i
\(848\) −3.29321 1.53565i −0.113089 0.0527344i
\(849\) 6.12676 + 13.1389i 0.210270 + 0.450925i
\(850\) 9.94016 12.6181i 0.340945 0.432798i
\(851\) 26.2011 44.6622i 0.898162 1.53100i
\(852\) 3.91084 3.91084i 0.133983 0.133983i
\(853\) 3.64178 10.0057i 0.124692 0.342589i −0.861602 0.507584i \(-0.830539\pi\)
0.986294 + 0.164995i \(0.0527609\pi\)
\(854\) 28.7562 10.4664i 0.984016 0.358152i
\(855\) −10.6908 2.68831i −0.365616 0.0919381i
\(856\) 0.655904 + 0.936727i 0.0224183 + 0.0320167i
\(857\) 2.93877i 0.100386i −0.998740 0.0501932i \(-0.984016\pi\)
0.998740 0.0501932i \(-0.0159837\pi\)
\(858\) 0.297981 0.208648i 0.0101729 0.00712314i
\(859\) −2.86608 + 10.6964i −0.0977895 + 0.364955i −0.997428 0.0716810i \(-0.977164\pi\)
0.899638 + 0.436636i \(0.143830\pi\)
\(860\) 23.5193 8.97409i 0.802000 0.306014i
\(861\) −7.01544 + 12.1511i −0.239085 + 0.414108i
\(862\) 9.28583 34.6552i 0.316277 1.18036i
\(863\) 3.15451 + 6.76487i 0.107381 + 0.230279i 0.952655 0.304055i \(-0.0983405\pi\)
−0.845274 + 0.534333i \(0.820563\pi\)
\(864\) −0.257601 2.94439i −0.00876375 0.100170i
\(865\) 0.0703371 0.977669i 0.00239153 0.0332417i
\(866\) 6.62462 9.46094i 0.225114 0.321496i
\(867\) 2.81999 + 1.97458i 0.0957719 + 0.0670602i
\(868\) −6.54242 + 5.48974i −0.222064 + 0.186334i
\(869\) −12.7959 + 27.4410i −0.434072 + 0.930871i
\(870\) 0.0647792 + 4.19345i 0.00219622 + 0.142171i
\(871\) 1.00481 + 0.0879096i 0.0340467 + 0.00297870i
\(872\) 0.886414 1.26593i 0.0300178 0.0428698i
\(873\) 3.66422 + 20.7808i 0.124015 + 0.703325i
\(874\) 14.8250 3.97234i 0.501462 0.134366i
\(875\) 28.5465 + 36.9947i 0.965046 + 1.25065i
\(876\) 0.823459 2.26244i 0.0278221 0.0764406i
\(877\) −27.1458 7.27368i −0.916647 0.245615i −0.230495 0.973073i \(-0.574035\pi\)
−0.686152 + 0.727459i \(0.740701\pi\)
\(878\) −5.06492 18.9025i −0.170933 0.637929i
\(879\) −1.16662 + 0.978907i −0.0393490 + 0.0330177i
\(880\) 12.8676 2.47443i 0.433768 0.0834129i
\(881\) 14.8951 + 2.62641i 0.501829 + 0.0884861i 0.418832 0.908064i \(-0.362440\pi\)
0.0829973 + 0.996550i \(0.473551\pi\)
\(882\) −28.6232 −0.963794
\(883\) 16.6880 + 2.94254i 0.561596 + 0.0990244i 0.447238 0.894415i \(-0.352408\pi\)
0.114358 + 0.993440i \(0.463519\pi\)
\(884\) 0.248705 0.296395i 0.00836485 0.00996884i
\(885\) 14.1532 0.218635i 0.475756 0.00734935i
\(886\) 11.8407 5.52142i 0.397797 0.185496i
\(887\) −6.24925 6.24925i −0.209829 0.209829i 0.594366 0.804195i \(-0.297403\pi\)
−0.804195 + 0.594366i \(0.797403\pi\)
\(888\) 3.12512 0.251547i 0.104872 0.00844138i
\(889\) 47.4716i 1.59215i
\(890\) 24.0767 2.48173i 0.807054 0.0831877i
\(891\) 13.3875 + 36.7819i 0.448498 + 1.23224i
\(892\) 0.885575 + 10.1222i 0.0296512 + 0.338915i
\(893\) −3.28135 + 18.6094i −0.109806 + 0.622741i
\(894\) −0.719220 0.719220i −0.0240543 0.0240543i
\(895\) −4.36474 15.3377i −0.145897 0.512684i
\(896\) 4.03707 + 1.08173i 0.134869 + 0.0361381i
\(897\) −0.0460559 + 0.526422i −0.00153776 + 0.0175767i
\(898\) −18.0760 + 4.84344i −0.603203 + 0.161628i
\(899\) −3.71793 6.43965i −0.124000 0.214774i
\(900\) 11.6232 7.19829i 0.387441 0.239943i
\(901\) −11.6291 + 1.01742i −0.387423 + 0.0338951i
\(902\) −19.0837 + 33.0539i −0.635417 + 1.10058i
\(903\) 23.8834 4.21128i 0.794789 0.140143i
\(904\) −0.976387 + 0.172163i −0.0324742 + 0.00572607i
\(905\) −11.8949 + 4.53865i −0.395399 + 0.150870i
\(906\) −9.12960 4.25720i −0.303311 0.141436i
\(907\) −15.2257 41.8321i −0.505560 1.38901i −0.885775 0.464116i \(-0.846372\pi\)
0.380215 0.924898i \(-0.375850\pi\)
\(908\) −7.79653 9.29154i −0.258737 0.308351i
\(909\) −1.97939 11.2257i −0.0656521 0.372332i
\(910\) 0.659753 + 0.911915i 0.0218706 + 0.0302297i
\(911\) 9.02197 + 33.6704i 0.298911 + 1.11555i 0.938061 + 0.346470i \(0.112620\pi\)
−0.639150 + 0.769082i \(0.720714\pi\)
\(912\) 0.711882 + 0.597340i 0.0235728 + 0.0197799i
\(913\) −30.4599 + 14.2037i −1.00807 + 0.470073i
\(914\) 16.2845 9.40187i 0.538644 0.310986i
\(915\) −6.37987 + 5.52349i −0.210912 + 0.182601i
\(916\) 17.0493 + 20.3185i 0.563324 + 0.671343i
\(917\) 18.9272 + 32.7830i 0.625033 + 1.08259i
\(918\) −5.44631 7.77813i −0.179755 0.256717i
\(919\) −2.58829 + 2.58829i −0.0853798 + 0.0853798i −0.748507 0.663127i \(-0.769229\pi\)
0.663127 + 0.748507i \(0.269229\pi\)
\(920\) −9.26166 + 16.6297i −0.305348 + 0.548265i
\(921\) −2.03271 1.70565i −0.0669802 0.0562031i
\(922\) 4.02153 8.62419i 0.132442 0.284023i
\(923\) 1.21440 + 0.442004i 0.0399723 + 0.0145487i
\(924\) 12.6238 0.415292
\(925\) 15.8332 + 25.9675i 0.520592 + 0.853806i
\(926\) −1.72810 −0.0567889
\(927\) −22.8161 8.30440i −0.749381 0.272752i
\(928\) −1.53786 + 3.29796i −0.0504829 + 0.108261i
\(929\) −32.2196 27.0354i −1.05709 0.887003i −0.0632681 0.997997i \(-0.520152\pi\)
−0.993821 + 0.110993i \(0.964597\pi\)
\(930\) 1.14592 2.05755i 0.0375762 0.0674697i
\(931\) 13.3456 13.3456i 0.437385 0.437385i
\(932\) 1.47999 + 2.11365i 0.0484788 + 0.0692349i
\(933\) 1.43554 + 2.48643i 0.0469974 + 0.0814019i
\(934\) −25.3533 30.2149i −0.829586 0.988662i
\(935\) 31.8258 27.5538i 1.04081 0.901105i
\(936\) 0.285193 0.164656i 0.00932184 0.00538197i
\(937\) 8.16977 3.80963i 0.266895 0.124455i −0.284564 0.958657i \(-0.591849\pi\)
0.551459 + 0.834202i \(0.314071\pi\)
\(938\) 26.8139 + 22.4995i 0.875504 + 0.734635i
\(939\) 1.18896 + 4.43725i 0.0388002 + 0.144804i
\(940\) −13.7372 18.9876i −0.448057 0.619308i
\(941\) 0.954108 + 5.41102i 0.0311030 + 0.176394i 0.996402 0.0847533i \(-0.0270102\pi\)
−0.965299 + 0.261147i \(0.915899\pi\)
\(942\) 1.41138 + 1.68202i 0.0459854 + 0.0548033i
\(943\) −18.9631 52.1007i −0.617524 1.69663i
\(944\) 11.1309 + 5.19042i 0.362280 + 0.168934i
\(945\) 25.8074 9.84715i 0.839514 0.320328i
\(946\) 64.9686 11.4557i 2.11231 0.372457i
\(947\) −10.2946 + 1.81522i −0.334529 + 0.0589866i −0.338390 0.941006i \(-0.609882\pi\)
0.00386046 + 0.999993i \(0.498771\pi\)
\(948\) 1.33157 2.30634i 0.0432473 0.0749065i
\(949\) 0.560433 0.0490315i 0.0181924 0.00159163i
\(950\) −2.06313 + 8.77554i −0.0669367 + 0.284716i
\(951\) −2.59771 4.49937i −0.0842366 0.145902i
\(952\) 12.9696 3.47519i 0.420347 0.112632i
\(953\) −0.762309 + 8.71323i −0.0246936 + 0.282249i 0.973801 + 0.227401i \(0.0730229\pi\)
−0.998495 + 0.0548478i \(0.982533\pi\)
\(954\) −9.59708 2.57153i −0.310717 0.0832564i
\(955\) −10.7024 37.6084i −0.346322 1.21698i
\(956\) 2.53130 + 2.53130i 0.0818681 + 0.0818681i
\(957\) −1.90856 + 10.8240i −0.0616951 + 0.349890i
\(958\) 0.248780 + 2.84357i 0.00803771 + 0.0918715i
\(959\) −26.1084 71.7322i −0.843084 2.31635i
\(960\) −1.14646 + 0.118172i −0.0370018 + 0.00381398i
\(961\) 26.8244i 0.865302i
\(962\) 0.361876 + 0.636967i 0.0116674 + 0.0205366i
\(963\) 2.21098 + 2.21098i 0.0712479 + 0.0712479i
\(964\) 0.656334 0.306053i 0.0211391 0.00985732i
\(965\) −26.8103 + 0.414158i −0.863053 + 0.0133322i
\(966\) −11.7875 + 14.0478i −0.379257 + 0.451981i
\(967\) 23.3356 + 4.11469i 0.750422 + 0.132320i 0.535762 0.844369i \(-0.320025\pi\)
0.214660 + 0.976689i \(0.431136\pi\)
\(968\) 23.3397 0.750167
\(969\) 2.94012 + 0.518423i 0.0944504 + 0.0166541i
\(970\) 16.9457 3.25864i 0.544094 0.104629i
\(971\) −28.1301 + 23.6039i −0.902737 + 0.757487i −0.970724 0.240200i \(-0.922787\pi\)
0.0679861 + 0.997686i \(0.478343\pi\)
\(972\) −3.18600 11.8903i −0.102191 0.381382i
\(973\) 16.6071 + 4.44987i 0.532401 + 0.142656i
\(974\) 9.55534 26.2531i 0.306173 0.841203i
\(975\) −0.259627 0.170089i −0.00831472 0.00544721i
\(976\) −7.07239 + 1.89504i −0.226382 + 0.0606588i
\(977\) 3.00640 + 17.0502i 0.0961834 + 0.545483i 0.994378 + 0.105886i \(0.0337678\pi\)
−0.898195 + 0.439597i \(0.855121\pi\)
\(978\) −0.284378 + 0.406134i −0.00909341 + 0.0129867i
\(979\) 63.1903 + 5.52843i 2.01957 + 0.176690i
\(980\) 0.361547 + 23.4046i 0.0115492 + 0.747631i
\(981\) 1.78585 3.82977i 0.0570178 0.122275i
\(982\) −14.7330 + 12.3624i −0.470148 + 0.394501i
\(983\) 29.3131 + 20.5253i 0.934944 + 0.654655i 0.938478 0.345339i \(-0.112236\pi\)
−0.00353406 + 0.999994i \(0.501125\pi\)
\(984\) 1.92554 2.74996i 0.0613841 0.0876656i
\(985\) 0.932966 12.9680i 0.0297268 0.413195i
\(986\) 1.01889 + 11.6459i 0.0324479 + 0.370882i
\(987\) −9.54190 20.4627i −0.303722 0.651334i
\(988\) −0.0562004 + 0.209743i −0.00178797 + 0.00667281i
\(989\) −47.9168 + 82.9943i −1.52367 + 2.63907i
\(990\) 33.4750 12.7728i 1.06390 0.405947i
\(991\) −6.27750 + 23.4280i −0.199411 + 0.744214i 0.791669 + 0.610950i \(0.209212\pi\)
−0.991081 + 0.133264i \(0.957454\pi\)
\(992\) 1.67389 1.17207i 0.0531460 0.0372132i
\(993\) 2.23442i 0.0709070i
\(994\) 25.7236 + 36.7370i 0.815902 + 1.16523i
\(995\) −25.3833 6.38290i −0.804704 0.202351i
\(996\) 2.77784 1.01105i 0.0880194 0.0320364i
\(997\) 6.99743 19.2253i 0.221611 0.608871i −0.778206 0.628009i \(-0.783870\pi\)
0.999817 + 0.0191383i \(0.00609229\pi\)
\(998\) −7.74997 + 7.74997i −0.245321 + 0.245321i
\(999\) 17.3977 4.53240i 0.550440 0.143399i
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 370.2.ba.b.163.4 120
5.2 odd 4 370.2.bd.b.237.7 yes 120
37.5 odd 36 370.2.bd.b.153.7 yes 120
185.42 even 36 inner 370.2.ba.b.227.4 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.ba.b.163.4 120 1.1 even 1 trivial
370.2.ba.b.227.4 yes 120 185.42 even 36 inner
370.2.bd.b.153.7 yes 120 37.5 odd 36
370.2.bd.b.237.7 yes 120 5.2 odd 4