Properties

Label 690.2.r.a.49.12
Level $690$
Weight $2$
Character 690.49
Analytic conductor $5.510$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,2,Mod(49,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.r (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(12\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 49.12
Character \(\chi\) \(=\) 690.49
Dual form 690.2.r.a.169.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(2.13321 + 0.670378i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.684801 - 1.06557i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\) \(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(2.13321 + 0.670378i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.684801 - 1.06557i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(2.20690 + 0.359967i) q^{10} +(-0.581246 + 4.04265i) q^{11} +(0.989821 + 0.142315i) q^{12} +(-1.45662 + 2.26654i) q^{13} +(-0.829477 - 0.957267i) q^{14} +(1.66195 + 1.49597i) q^{15} +(0.841254 - 0.540641i) q^{16} +(1.00253 - 3.41431i) q^{17} +(0.755750 + 0.654861i) q^{18} +(6.99364 - 2.05352i) q^{19} +(2.23567 + 0.0422279i) q^{20} +(-0.180263 - 1.25375i) q^{21} +4.08422i q^{22} +(-4.79059 + 0.224064i) q^{23} +1.00000 q^{24} +(4.10119 + 2.86012i) q^{25} +(-1.11923 + 2.45077i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-0.957267 - 0.829477i) q^{28} +(-4.95259 - 1.45421i) q^{29} +(1.85793 + 1.24422i) q^{30} +(-3.25180 - 7.12046i) q^{31} +(0.755750 - 0.654861i) q^{32} +(-2.20810 + 3.43587i) q^{33} +(0.506421 - 3.52223i) q^{34} +(-0.746490 - 2.73216i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-1.82428 + 1.58074i) q^{37} +(6.63021 - 3.02792i) q^{38} +(-2.26654 + 1.45662i) q^{39} +(2.21892 - 0.276371i) q^{40} +(5.06625 - 5.84677i) q^{41} +(-0.356855 - 1.21534i) q^{42} +(-9.49633 - 4.33683i) q^{43} +(0.581246 + 4.04265i) q^{44} +(0.890319 + 2.05118i) q^{45} +(-4.70995 + 0.903556i) q^{46} +10.6070i q^{47} +(0.989821 - 0.142315i) q^{48} +(2.24142 - 4.90802i) q^{49} +(4.46648 + 2.24735i) q^{50} +(2.33029 - 2.68930i) q^{51} +(-0.759055 + 2.58510i) q^{52} +(0.343990 + 0.535259i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-3.95003 + 8.23418i) q^{55} +(-1.06557 - 0.684801i) q^{56} +(7.21470 + 1.03732i) q^{57} +(-5.10913 - 0.734582i) q^{58} +(6.02106 + 3.86950i) q^{59} +(2.01609 + 0.967142i) q^{60} +(5.25295 + 11.5024i) q^{61} +(-4.23205 - 6.58520i) q^{62} +(0.356855 - 1.21534i) q^{63} +(0.654861 - 0.755750i) q^{64} +(-4.62671 + 3.85852i) q^{65} +(-1.69665 + 3.71514i) q^{66} +(-7.81904 + 1.12421i) q^{67} -3.55845i q^{68} +(-4.45076 - 1.78627i) q^{69} +(-1.12772 - 2.59812i) q^{70} +(-0.584110 - 4.06257i) q^{71} +(0.909632 + 0.415415i) q^{72} +(-2.57822 - 8.78061i) q^{73} +(-1.58074 + 1.82428i) q^{74} +(2.54243 + 4.30535i) q^{75} +(6.13181 - 3.94067i) q^{76} +(4.70577 - 2.14905i) q^{77} +(-2.03617 + 1.76435i) q^{78} +(-11.4370 - 7.35012i) q^{79} +(2.15701 - 0.589343i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(4.18260 - 6.50826i) q^{82} +(-3.44158 + 2.98214i) q^{83} +(-0.526184 - 1.15218i) q^{84} +(4.42749 - 6.61137i) q^{85} +(-10.0169 - 2.94122i) q^{86} +(-3.90093 - 3.38018i) q^{87} +(1.15066 + 3.91878i) q^{88} +(5.16414 - 11.3079i) q^{89} +(1.17317 + 1.90359i) q^{90} +3.41265 q^{91} +(-4.53342 + 1.56465i) q^{92} -7.82784i q^{93} +(1.50954 + 10.4991i) q^{94} +(16.2956 + 0.307795i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-3.41172 - 2.95627i) q^{97} +(1.52012 - 5.17705i) q^{98} +(-3.43587 + 2.20810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{8}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.989821 0.142315i 0.699909 0.100632i
\(3\) 0.909632 + 0.415415i 0.525176 + 0.239840i
\(4\) 0.959493 0.281733i 0.479746 0.140866i
\(5\) 2.13321 + 0.670378i 0.954001 + 0.299802i
\(6\) 0.959493 + 0.281733i 0.391711 + 0.115017i
\(7\) −0.684801 1.06557i −0.258830 0.402748i 0.687381 0.726297i \(-0.258760\pi\)
−0.946211 + 0.323549i \(0.895124\pi\)
\(8\) 0.909632 0.415415i 0.321603 0.146871i
\(9\) 0.654861 + 0.755750i 0.218287 + 0.251917i
\(10\) 2.20690 + 0.359967i 0.697884 + 0.113832i
\(11\) −0.581246 + 4.04265i −0.175252 + 1.21891i 0.692319 + 0.721592i \(0.256589\pi\)
−0.867571 + 0.497314i \(0.834320\pi\)
\(12\) 0.989821 + 0.142315i 0.285737 + 0.0410828i
\(13\) −1.45662 + 2.26654i −0.403992 + 0.628624i −0.982326 0.187176i \(-0.940067\pi\)
0.578334 + 0.815800i \(0.303703\pi\)
\(14\) −0.829477 0.957267i −0.221687 0.255840i
\(15\) 1.66195 + 1.49597i 0.429114 + 0.386257i
\(16\) 0.841254 0.540641i 0.210313 0.135160i
\(17\) 1.00253 3.41431i 0.243150 0.828092i −0.743984 0.668197i \(-0.767066\pi\)
0.987134 0.159895i \(-0.0511156\pi\)
\(18\) 0.755750 + 0.654861i 0.178132 + 0.154352i
\(19\) 6.99364 2.05352i 1.60445 0.471110i 0.647671 0.761920i \(-0.275743\pi\)
0.956781 + 0.290811i \(0.0939249\pi\)
\(20\) 2.23567 + 0.0422279i 0.499911 + 0.00944244i
\(21\) −0.180263 1.25375i −0.0393365 0.273591i
\(22\) 4.08422i 0.870759i
\(23\) −4.79059 + 0.224064i −0.998908 + 0.0467207i
\(24\) 1.00000 0.204124
\(25\) 4.10119 + 2.86012i 0.820237 + 0.572023i
\(26\) −1.11923 + 2.45077i −0.219498 + 0.480635i
\(27\) 0.281733 + 0.959493i 0.0542195 + 0.184655i
\(28\) −0.957267 0.829477i −0.180907 0.156756i
\(29\) −4.95259 1.45421i −0.919672 0.270040i −0.212565 0.977147i \(-0.568182\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(30\) 1.85793 + 1.24422i 0.339211 + 0.227162i
\(31\) −3.25180 7.12046i −0.584041 1.27887i −0.938977 0.343981i \(-0.888224\pi\)
0.354935 0.934891i \(-0.384503\pi\)
\(32\) 0.755750 0.654861i 0.133599 0.115764i
\(33\) −2.20810 + 3.43587i −0.384380 + 0.598108i
\(34\) 0.506421 3.52223i 0.0868504 0.604058i
\(35\) −0.746490 2.73216i −0.126180 0.461820i
\(36\) 0.841254 + 0.540641i 0.140209 + 0.0901068i
\(37\) −1.82428 + 1.58074i −0.299909 + 0.259873i −0.791795 0.610787i \(-0.790853\pi\)
0.491886 + 0.870660i \(0.336308\pi\)
\(38\) 6.63021 3.02792i 1.07556 0.491193i
\(39\) −2.26654 + 1.45662i −0.362936 + 0.233245i
\(40\) 2.21892 0.276371i 0.350843 0.0436981i
\(41\) 5.06625 5.84677i 0.791216 0.913111i −0.206650 0.978415i \(-0.566256\pi\)
0.997865 + 0.0653035i \(0.0208015\pi\)
\(42\) −0.356855 1.21534i −0.0550640 0.187531i
\(43\) −9.49633 4.33683i −1.44818 0.661360i −0.472652 0.881249i \(-0.656703\pi\)
−0.975525 + 0.219889i \(0.929430\pi\)
\(44\) 0.581246 + 4.04265i 0.0876261 + 0.609453i
\(45\) 0.890319 + 2.05118i 0.132721 + 0.305772i
\(46\) −4.70995 + 0.903556i −0.694444 + 0.133222i
\(47\) 10.6070i 1.54719i 0.633678 + 0.773597i \(0.281544\pi\)
−0.633678 + 0.773597i \(0.718456\pi\)
\(48\) 0.989821 0.142315i 0.142868 0.0205414i
\(49\) 2.24142 4.90802i 0.320202 0.701145i
\(50\) 4.46648 + 2.24735i 0.631656 + 0.317823i
\(51\) 2.33029 2.68930i 0.326306 0.376577i
\(52\) −0.759055 + 2.58510i −0.105262 + 0.358489i
\(53\) 0.343990 + 0.535259i 0.0472507 + 0.0735235i 0.864075 0.503363i \(-0.167904\pi\)
−0.816825 + 0.576886i \(0.804268\pi\)
\(54\) 0.415415 + 0.909632i 0.0565308 + 0.123785i
\(55\) −3.95003 + 8.23418i −0.532621 + 1.11030i
\(56\) −1.06557 0.684801i −0.142393 0.0915103i
\(57\) 7.21470 + 1.03732i 0.955611 + 0.137396i
\(58\) −5.10913 0.734582i −0.670862 0.0964554i
\(59\) 6.02106 + 3.86950i 0.783875 + 0.503766i 0.870318 0.492491i \(-0.163914\pi\)
−0.0864426 + 0.996257i \(0.527550\pi\)
\(60\) 2.01609 + 0.967142i 0.260277 + 0.124858i
\(61\) 5.25295 + 11.5024i 0.672572 + 1.47273i 0.870326 + 0.492475i \(0.163908\pi\)
−0.197754 + 0.980252i \(0.563365\pi\)
\(62\) −4.23205 6.58520i −0.537471 0.836322i
\(63\) 0.356855 1.21534i 0.0449596 0.153118i
\(64\) 0.654861 0.755750i 0.0818576 0.0944687i
\(65\) −4.62671 + 3.85852i −0.573872 + 0.478591i
\(66\) −1.69665 + 3.71514i −0.208843 + 0.457302i
\(67\) −7.81904 + 1.12421i −0.955248 + 0.137344i −0.602274 0.798289i \(-0.705739\pi\)
−0.352974 + 0.935633i \(0.614830\pi\)
\(68\) 3.55845i 0.431526i
\(69\) −4.45076 1.78627i −0.535808 0.215041i
\(70\) −1.12772 2.59812i −0.134788 0.310534i
\(71\) −0.584110 4.06257i −0.0693211 0.482139i −0.994677 0.103040i \(-0.967143\pi\)
0.925356 0.379099i \(-0.123766\pi\)
\(72\) 0.909632 + 0.415415i 0.107201 + 0.0489571i
\(73\) −2.57822 8.78061i −0.301758 1.02769i −0.961181 0.275920i \(-0.911017\pi\)
0.659423 0.751772i \(-0.270801\pi\)
\(74\) −1.58074 + 1.82428i −0.183758 + 0.212068i
\(75\) 2.54243 + 4.30535i 0.293575 + 0.497139i
\(76\) 6.13181 3.94067i 0.703367 0.452026i
\(77\) 4.70577 2.14905i 0.536272 0.244907i
\(78\) −2.03617 + 1.76435i −0.230551 + 0.199773i
\(79\) −11.4370 7.35012i −1.28676 0.826953i −0.295058 0.955479i \(-0.595339\pi\)
−0.991706 + 0.128527i \(0.958975\pi\)
\(80\) 2.15701 0.589343i 0.241161 0.0658906i
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 4.18260 6.50826i 0.461891 0.718717i
\(83\) −3.44158 + 2.98214i −0.377762 + 0.327333i −0.822960 0.568100i \(-0.807679\pi\)
0.445198 + 0.895432i \(0.353133\pi\)
\(84\) −0.526184 1.15218i −0.0574114 0.125713i
\(85\) 4.42749 6.61137i 0.480229 0.717104i
\(86\) −10.0169 2.94122i −1.08015 0.317160i
\(87\) −3.90093 3.38018i −0.418224 0.362393i
\(88\) 1.15066 + 3.91878i 0.122661 + 0.417744i
\(89\) 5.16414 11.3079i 0.547397 1.19863i −0.410589 0.911820i \(-0.634677\pi\)
0.957987 0.286813i \(-0.0925957\pi\)
\(90\) 1.17317 + 1.90359i 0.123663 + 0.200657i
\(91\) 3.41265 0.357743
\(92\) −4.53342 + 1.56465i −0.472641 + 0.163127i
\(93\) 7.82784i 0.811710i
\(94\) 1.50954 + 10.4991i 0.155697 + 1.08290i
\(95\) 16.2956 + 0.307795i 1.67189 + 0.0315791i
\(96\) 0.959493 0.281733i 0.0979278 0.0287542i
\(97\) −3.41172 2.95627i −0.346408 0.300164i 0.464227 0.885716i \(-0.346332\pi\)
−0.810635 + 0.585552i \(0.800878\pi\)
\(98\) 1.52012 5.17705i 0.153555 0.522961i
\(99\) −3.43587 + 2.20810i −0.345318 + 0.221922i
\(100\) 4.74085 + 1.58882i 0.474085 + 0.158882i
\(101\) 9.22744 + 10.6490i 0.918164 + 1.05962i 0.998025 + 0.0628122i \(0.0200069\pi\)
−0.0798610 + 0.996806i \(0.525448\pi\)
\(102\) 1.92385 2.99356i 0.190489 0.296407i
\(103\) −11.5150 1.65560i −1.13460 0.163131i −0.450680 0.892686i \(-0.648818\pi\)
−0.683923 + 0.729555i \(0.739727\pi\)
\(104\) −0.383430 + 2.66681i −0.0375984 + 0.261503i
\(105\) 0.455951 2.79537i 0.0444962 0.272800i
\(106\) 0.416664 + 0.480856i 0.0404700 + 0.0467049i
\(107\) −2.63967 + 1.20550i −0.255186 + 0.116540i −0.538901 0.842369i \(-0.681160\pi\)
0.283715 + 0.958909i \(0.408433\pi\)
\(108\) 0.540641 + 0.841254i 0.0520232 + 0.0809497i
\(109\) −12.9306 3.79677i −1.23853 0.363664i −0.404066 0.914730i \(-0.632403\pi\)
−0.834462 + 0.551066i \(0.814221\pi\)
\(110\) −2.73797 + 8.71251i −0.261056 + 0.830706i
\(111\) −2.31609 + 0.680064i −0.219833 + 0.0645488i
\(112\) −1.15218 0.526184i −0.108871 0.0497197i
\(113\) −3.89061 + 0.559385i −0.365998 + 0.0526225i −0.322860 0.946447i \(-0.604644\pi\)
−0.0431374 + 0.999069i \(0.513735\pi\)
\(114\) 7.28889 0.682667
\(115\) −10.3696 2.73353i −0.966967 0.254903i
\(116\) −5.16167 −0.479249
\(117\) −2.66681 + 0.383430i −0.246547 + 0.0354481i
\(118\) 6.51046 + 2.97323i 0.599336 + 0.273708i
\(119\) −4.32472 + 1.26985i −0.396447 + 0.116407i
\(120\) 2.13321 + 0.670378i 0.194735 + 0.0611969i
\(121\) −5.45076 1.60049i −0.495524 0.145499i
\(122\) 6.83644 + 10.6377i 0.618943 + 0.963093i
\(123\) 7.03726 3.21381i 0.634528 0.289779i
\(124\) −5.12615 5.91589i −0.460342 0.531263i
\(125\) 6.83134 + 8.85058i 0.611014 + 0.791620i
\(126\) 0.180263 1.25375i 0.0160591 0.111693i
\(127\) 22.1763 + 3.18847i 1.96783 + 0.282931i 0.999440 + 0.0334733i \(0.0106569\pi\)
0.968386 + 0.249457i \(0.0802522\pi\)
\(128\) 0.540641 0.841254i 0.0477863 0.0743570i
\(129\) −6.83658 7.88984i −0.601927 0.694661i
\(130\) −4.03049 + 4.47770i −0.353497 + 0.392720i
\(131\) −10.3545 + 6.65445i −0.904679 + 0.581402i −0.908174 0.418592i \(-0.862524\pi\)
0.00349565 + 0.999994i \(0.498887\pi\)
\(132\) −1.15066 + 3.91878i −0.100152 + 0.341086i
\(133\) −6.97742 6.04597i −0.605019 0.524252i
\(134\) −7.57947 + 2.22553i −0.654766 + 0.192257i
\(135\) −0.0422279 + 2.23567i −0.00363440 + 0.192416i
\(136\) −0.506421 3.52223i −0.0434252 0.302029i
\(137\) 0.824598i 0.0704502i −0.999379 0.0352251i \(-0.988785\pi\)
0.999379 0.0352251i \(-0.0112148\pi\)
\(138\) −4.65967 1.13468i −0.396657 0.0965902i
\(139\) −4.75065 −0.402945 −0.201472 0.979494i \(-0.564573\pi\)
−0.201472 + 0.979494i \(0.564573\pi\)
\(140\) −1.48599 2.41118i −0.125589 0.203782i
\(141\) −4.40632 + 9.64849i −0.371079 + 0.812549i
\(142\) −1.15633 3.93810i −0.0970370 0.330478i
\(143\) −8.31617 7.20600i −0.695433 0.602596i
\(144\) 0.959493 + 0.281733i 0.0799577 + 0.0234777i
\(145\) −9.59005 6.42225i −0.796410 0.533338i
\(146\) −3.80159 8.32431i −0.314622 0.688925i
\(147\) 4.07773 3.53337i 0.336325 0.291428i
\(148\) −1.30503 + 2.03067i −0.107273 + 0.166920i
\(149\) −1.30572 + 9.08145i −0.106968 + 0.743981i 0.863778 + 0.503873i \(0.168092\pi\)
−0.970746 + 0.240108i \(0.922817\pi\)
\(150\) 3.12927 + 3.89970i 0.255504 + 0.318409i
\(151\) −6.19039 3.97832i −0.503767 0.323751i 0.263954 0.964535i \(-0.414973\pi\)
−0.767721 + 0.640784i \(0.778610\pi\)
\(152\) 5.50858 4.77321i 0.446805 0.387158i
\(153\) 3.23688 1.47824i 0.261687 0.119508i
\(154\) 4.35203 2.79688i 0.350696 0.225379i
\(155\) −2.16339 17.3694i −0.173768 1.39514i
\(156\) −1.76435 + 2.03617i −0.141261 + 0.163024i
\(157\) 3.08284 + 10.4992i 0.246037 + 0.837925i 0.986209 + 0.165507i \(0.0529261\pi\)
−0.740171 + 0.672418i \(0.765256\pi\)
\(158\) −12.3666 5.64765i −0.983836 0.449303i
\(159\) 0.0905498 + 0.629787i 0.00718106 + 0.0499454i
\(160\) 2.05118 0.890319i 0.162160 0.0703859i
\(161\) 3.51936 + 4.95128i 0.277364 + 0.390215i
\(162\) 1.00000i 0.0785674i
\(163\) −20.3871 + 2.93123i −1.59684 + 0.229591i −0.882537 0.470243i \(-0.844166\pi\)
−0.714305 + 0.699834i \(0.753257\pi\)
\(164\) 3.21381 7.03726i 0.250956 0.549518i
\(165\) −7.01367 + 5.84917i −0.546014 + 0.455357i
\(166\) −2.98214 + 3.44158i −0.231459 + 0.267118i
\(167\) 1.59585 5.43496i 0.123490 0.420570i −0.874421 0.485168i \(-0.838758\pi\)
0.997911 + 0.0645982i \(0.0205766\pi\)
\(168\) −0.684801 1.06557i −0.0528335 0.0822105i
\(169\) 2.38493 + 5.22227i 0.183456 + 0.401713i
\(170\) 3.44153 7.17418i 0.263953 0.550234i
\(171\) 6.13181 + 3.94067i 0.468911 + 0.301351i
\(172\) −10.3335 1.48573i −0.787921 0.113286i
\(173\) 9.87692 + 1.42009i 0.750928 + 0.107967i 0.507143 0.861862i \(-0.330702\pi\)
0.243785 + 0.969829i \(0.421611\pi\)
\(174\) −4.34227 2.79061i −0.329187 0.211556i
\(175\) 0.239162 6.32871i 0.0180790 0.478406i
\(176\) 1.69665 + 3.71514i 0.127890 + 0.280039i
\(177\) 3.86950 + 6.02106i 0.290849 + 0.452570i
\(178\) 3.50229 11.9277i 0.262508 0.894020i
\(179\) −5.26654 + 6.07791i −0.393640 + 0.454284i −0.917628 0.397441i \(-0.869898\pi\)
0.523988 + 0.851726i \(0.324444\pi\)
\(180\) 1.43214 + 1.71726i 0.106745 + 0.127997i
\(181\) −5.25275 + 11.5019i −0.390434 + 0.854931i 0.607717 + 0.794153i \(0.292085\pi\)
−0.998151 + 0.0607777i \(0.980642\pi\)
\(182\) 3.37791 0.485670i 0.250387 0.0360003i
\(183\) 12.6451i 0.934751i
\(184\) −4.26460 + 2.19390i −0.314390 + 0.161737i
\(185\) −4.95127 + 2.14911i −0.364024 + 0.158006i
\(186\) −1.11402 7.74817i −0.0816838 0.568123i
\(187\) 13.2202 + 6.03744i 0.966753 + 0.441502i
\(188\) 2.98834 + 10.1774i 0.217947 + 0.742261i
\(189\) 0.829477 0.957267i 0.0603356 0.0696309i
\(190\) 16.1735 2.01444i 1.17335 0.146143i
\(191\) 13.6933 8.80014i 0.990811 0.636756i 0.0584526 0.998290i \(-0.481383\pi\)
0.932359 + 0.361534i \(0.117747\pi\)
\(192\) 0.909632 0.415415i 0.0656470 0.0299800i
\(193\) 13.5655 11.7546i 0.976470 0.846116i −0.0116299 0.999932i \(-0.503702\pi\)
0.988099 + 0.153817i \(0.0491565\pi\)
\(194\) −3.79772 2.44064i −0.272660 0.175228i
\(195\) −5.81149 + 1.58783i −0.416169 + 0.113707i
\(196\) 0.767875 5.34069i 0.0548482 0.381478i
\(197\) 7.20479 11.2109i 0.513320 0.798741i −0.483753 0.875205i \(-0.660727\pi\)
0.997072 + 0.0764637i \(0.0243629\pi\)
\(198\) −3.08665 + 2.67460i −0.219359 + 0.190075i
\(199\) −4.51814 9.89335i −0.320283 0.701321i 0.679184 0.733968i \(-0.262334\pi\)
−0.999467 + 0.0326467i \(0.989606\pi\)
\(200\) 4.91871 + 0.897960i 0.347805 + 0.0634954i
\(201\) −7.57947 2.22553i −0.534614 0.156977i
\(202\) 10.6490 + 9.22744i 0.749263 + 0.649240i
\(203\) 1.84197 + 6.27317i 0.129281 + 0.440291i
\(204\) 1.47824 3.23688i 0.103497 0.226627i
\(205\) 14.7269 9.07609i 1.02857 0.633901i
\(206\) −11.6334 −0.810535
\(207\) −3.30651 3.47376i −0.229818 0.241443i
\(208\) 2.69424i 0.186812i
\(209\) 4.23664 + 29.4665i 0.293054 + 2.03824i
\(210\) 0.0534878 2.83180i 0.00369101 0.195413i
\(211\) 24.3271 7.14309i 1.67475 0.491750i 0.699829 0.714310i \(-0.253259\pi\)
0.974919 + 0.222560i \(0.0714413\pi\)
\(212\) 0.480856 + 0.416664i 0.0330253 + 0.0286166i
\(213\) 1.15633 3.93810i 0.0792304 0.269834i
\(214\) −2.44124 + 1.56889i −0.166880 + 0.107247i
\(215\) −17.3504 15.6175i −1.18329 1.06511i
\(216\) 0.654861 + 0.755750i 0.0445576 + 0.0514222i
\(217\) −5.36051 + 8.34112i −0.363895 + 0.566232i
\(218\) −13.3393 1.91791i −0.903453 0.129897i
\(219\) 1.30237 9.05815i 0.0880057 0.612093i
\(220\) −1.47019 + 9.01349i −0.0991199 + 0.607689i
\(221\) 6.27836 + 7.24562i 0.422328 + 0.487393i
\(222\) −2.19573 + 1.00276i −0.147368 + 0.0673005i
\(223\) −11.0368 17.1736i −0.739077 1.15003i −0.983597 0.180382i \(-0.942266\pi\)
0.244519 0.969644i \(-0.421370\pi\)
\(224\) −1.21534 0.356855i −0.0812032 0.0238434i
\(225\) 0.524173 + 4.97245i 0.0349449 + 0.331497i
\(226\) −3.77140 + 1.10738i −0.250870 + 0.0736620i
\(227\) 0.286068 + 0.130643i 0.0189870 + 0.00867109i 0.424886 0.905247i \(-0.360314\pi\)
−0.405899 + 0.913918i \(0.633041\pi\)
\(228\) 7.21470 1.03732i 0.477805 0.0686980i
\(229\) −17.3533 −1.14674 −0.573368 0.819298i \(-0.694364\pi\)
−0.573368 + 0.819298i \(0.694364\pi\)
\(230\) −10.6530 1.22997i −0.702440 0.0811016i
\(231\) 5.17327 0.340376
\(232\) −5.10913 + 0.734582i −0.335431 + 0.0482277i
\(233\) 0.959990 + 0.438413i 0.0628910 + 0.0287214i 0.446612 0.894728i \(-0.352630\pi\)
−0.383721 + 0.923449i \(0.625358\pi\)
\(234\) −2.58510 + 0.759055i −0.168993 + 0.0496210i
\(235\) −7.11072 + 22.6270i −0.463852 + 1.47602i
\(236\) 6.86733 + 2.01643i 0.447025 + 0.131258i
\(237\) −7.35012 11.4370i −0.477441 0.742913i
\(238\) −4.09999 + 1.87240i −0.265763 + 0.121370i
\(239\) 19.3210 + 22.2976i 1.24977 + 1.44231i 0.850916 + 0.525302i \(0.176047\pi\)
0.398857 + 0.917013i \(0.369407\pi\)
\(240\) 2.20690 + 0.359967i 0.142455 + 0.0232358i
\(241\) 1.33639 9.29483i 0.0860847 0.598732i −0.900423 0.435016i \(-0.856743\pi\)
0.986507 0.163716i \(-0.0523482\pi\)
\(242\) −5.62306 0.808473i −0.361464 0.0519706i
\(243\) −0.540641 + 0.841254i −0.0346821 + 0.0539664i
\(244\) 8.28076 + 9.55651i 0.530122 + 0.611793i
\(245\) 8.07164 8.96724i 0.515678 0.572896i
\(246\) 6.50826 4.18260i 0.414951 0.266673i
\(247\) −5.53267 + 18.8425i −0.352035 + 1.19892i
\(248\) −5.91589 5.12615i −0.375659 0.325511i
\(249\) −4.36939 + 1.28297i −0.276899 + 0.0813049i
\(250\) 8.02138 + 7.78830i 0.507316 + 0.492575i
\(251\) 0.570550 + 3.96826i 0.0360128 + 0.250474i 0.999873 0.0159339i \(-0.00507213\pi\)
−0.963860 + 0.266408i \(0.914163\pi\)
\(252\) 1.26665i 0.0797912i
\(253\) 1.87870 19.4969i 0.118113 1.22576i
\(254\) 22.4043 1.40577
\(255\) 6.77385 4.17467i 0.424195 0.261428i
\(256\) 0.415415 0.909632i 0.0259634 0.0568520i
\(257\) 1.36119 + 4.63578i 0.0849085 + 0.289172i 0.990991 0.133930i \(-0.0427596\pi\)
−0.906082 + 0.423101i \(0.860941\pi\)
\(258\) −7.88984 6.83658i −0.491200 0.425627i
\(259\) 2.93366 + 0.861400i 0.182289 + 0.0535248i
\(260\) −3.35222 + 5.00572i −0.207896 + 0.310441i
\(261\) −2.14424 4.69522i −0.132725 0.290627i
\(262\) −9.30210 + 8.06032i −0.574686 + 0.497968i
\(263\) −8.08405 + 12.5790i −0.498484 + 0.775657i −0.995765 0.0919330i \(-0.970695\pi\)
0.497281 + 0.867590i \(0.334332\pi\)
\(264\) −0.581246 + 4.04265i −0.0357732 + 0.248808i
\(265\) 0.374978 + 1.37242i 0.0230347 + 0.0843074i
\(266\) −7.76683 4.99144i −0.476215 0.306045i
\(267\) 9.39493 8.14075i 0.574960 0.498206i
\(268\) −7.18559 + 3.28155i −0.438930 + 0.200453i
\(269\) 16.9646 10.9025i 1.03435 0.664736i 0.0907662 0.995872i \(-0.471068\pi\)
0.943583 + 0.331136i \(0.107432\pi\)
\(270\) 0.276371 + 2.21892i 0.0168194 + 0.135039i
\(271\) 0.0391892 0.0452268i 0.00238058 0.00274733i −0.754558 0.656233i \(-0.772149\pi\)
0.756939 + 0.653486i \(0.226694\pi\)
\(272\) −1.00253 3.41431i −0.0607874 0.207023i
\(273\) 3.10425 + 1.41766i 0.187878 + 0.0858010i
\(274\) −0.117353 0.816205i −0.00708953 0.0493087i
\(275\) −13.9463 + 14.9172i −0.840991 + 0.899543i
\(276\) −4.77372 0.459989i −0.287344 0.0276881i
\(277\) 5.88242i 0.353440i −0.984261 0.176720i \(-0.943451\pi\)
0.984261 0.176720i \(-0.0565487\pi\)
\(278\) −4.70230 + 0.676088i −0.282025 + 0.0405491i
\(279\) 3.25180 7.12046i 0.194680 0.426291i
\(280\) −1.81401 2.17516i −0.108408 0.129991i
\(281\) 8.29639 9.57454i 0.494921 0.571169i −0.452253 0.891890i \(-0.649380\pi\)
0.947174 + 0.320720i \(0.103925\pi\)
\(282\) −2.98834 + 10.1774i −0.177953 + 0.606053i
\(283\) −2.33833 3.63851i −0.138999 0.216287i 0.764774 0.644299i \(-0.222851\pi\)
−0.903773 + 0.428012i \(0.859214\pi\)
\(284\) −1.70501 3.73345i −0.101174 0.221539i
\(285\) 14.6951 + 7.04940i 0.870462 + 0.417570i
\(286\) −9.25705 5.94914i −0.547381 0.351780i
\(287\) −9.69951 1.39458i −0.572544 0.0823194i
\(288\) 0.989821 + 0.142315i 0.0583258 + 0.00838598i
\(289\) 3.64886 + 2.34498i 0.214639 + 0.137940i
\(290\) −10.4064 4.99207i −0.611086 0.293144i
\(291\) −1.87533 4.10640i −0.109934 0.240722i
\(292\) −4.94757 7.69856i −0.289534 0.450524i
\(293\) −2.77510 + 9.45112i −0.162123 + 0.552140i 0.837857 + 0.545889i \(0.183808\pi\)
−0.999980 + 0.00625131i \(0.998010\pi\)
\(294\) 3.53337 4.07773i 0.206070 0.237818i
\(295\) 10.2502 + 12.2908i 0.596788 + 0.715601i
\(296\) −1.00276 + 2.19573i −0.0582840 + 0.127624i
\(297\) −4.04265 + 0.581246i −0.234578 + 0.0337273i
\(298\) 9.17483i 0.531484i
\(299\) 6.47020 11.1844i 0.374181 0.646813i
\(300\) 3.65240 + 3.41467i 0.210872 + 0.197146i
\(301\) 1.88190 + 13.0889i 0.108471 + 0.754430i
\(302\) −6.69356 3.05685i −0.385171 0.175902i
\(303\) 3.96981 + 13.5199i 0.228059 + 0.776699i
\(304\) 4.77321 5.50858i 0.273762 0.315939i
\(305\) 3.49473 + 28.0584i 0.200108 + 1.60662i
\(306\) 2.99356 1.92385i 0.171131 0.109979i
\(307\) −3.04913 + 1.39249i −0.174023 + 0.0794738i −0.500522 0.865724i \(-0.666858\pi\)
0.326498 + 0.945198i \(0.394131\pi\)
\(308\) 3.90969 3.38777i 0.222775 0.193036i
\(309\) −9.78661 6.28947i −0.556741 0.357796i
\(310\) −4.61329 16.8847i −0.262017 0.958987i
\(311\) −1.05765 + 7.35612i −0.0599739 + 0.417128i 0.937612 + 0.347684i \(0.113032\pi\)
−0.997586 + 0.0694441i \(0.977877\pi\)
\(312\) −1.45662 + 2.26654i −0.0824646 + 0.128317i
\(313\) 12.9806 11.2477i 0.733705 0.635759i −0.205681 0.978619i \(-0.565941\pi\)
0.939387 + 0.342860i \(0.111396\pi\)
\(314\) 4.54565 + 9.95358i 0.256526 + 0.561713i
\(315\) 1.57598 2.35335i 0.0887967 0.132596i
\(316\) −13.0445 3.83021i −0.733810 0.215466i
\(317\) 19.7859 + 17.1446i 1.11128 + 0.962934i 0.999526 0.0308014i \(-0.00980593\pi\)
0.111759 + 0.993735i \(0.464351\pi\)
\(318\) 0.179256 + 0.610491i 0.0100522 + 0.0342346i
\(319\) 8.75754 19.1763i 0.490328 1.07367i
\(320\) 1.90359 1.17317i 0.106414 0.0655822i
\(321\) −2.90191 −0.161969
\(322\) 4.18818 + 4.40002i 0.233398 + 0.245204i
\(323\) 25.9372i 1.44318i
\(324\) 0.142315 + 0.989821i 0.00790638 + 0.0549901i
\(325\) −12.4564 + 5.12940i −0.690958 + 0.284528i
\(326\) −19.7625 + 5.80278i −1.09454 + 0.321386i
\(327\) −10.1849 8.82523i −0.563224 0.488036i
\(328\) 2.17959 7.42300i 0.120348 0.409867i
\(329\) 11.3025 7.26370i 0.623129 0.400461i
\(330\) −6.10986 + 6.78779i −0.336337 + 0.373655i
\(331\) 6.34806 + 7.32605i 0.348921 + 0.402676i 0.902897 0.429856i \(-0.141436\pi\)
−0.553976 + 0.832532i \(0.686890\pi\)
\(332\) −2.46200 + 3.83095i −0.135120 + 0.210251i
\(333\) −2.38929 0.343529i −0.130933 0.0188253i
\(334\) 0.806129 5.60675i 0.0441094 0.306788i
\(335\) −17.4333 2.84354i −0.952484 0.155359i
\(336\) −0.829477 0.957267i −0.0452517 0.0522232i
\(337\) 31.7032 14.4784i 1.72698 0.788687i 0.732868 0.680371i \(-0.238181\pi\)
0.994116 0.108317i \(-0.0345461\pi\)
\(338\) 3.10386 + 4.82970i 0.168828 + 0.262701i
\(339\) −3.77140 1.10738i −0.204834 0.0601448i
\(340\) 2.38551 7.59094i 0.129372 0.411676i
\(341\) 30.6756 9.00718i 1.66118 0.487766i
\(342\) 6.63021 + 3.02792i 0.358521 + 0.163731i
\(343\) −15.5410 + 2.23446i −0.839137 + 0.120650i
\(344\) −10.4397 −0.562874
\(345\) −8.29693 6.79418i −0.446692 0.365786i
\(346\) 9.97848 0.536447
\(347\) −1.22048 + 0.175479i −0.0655190 + 0.00942021i −0.174996 0.984569i \(-0.555991\pi\)
0.109477 + 0.993989i \(0.465082\pi\)
\(348\) −4.69522 2.14424i −0.251690 0.114943i
\(349\) 1.86909 0.548815i 0.100050 0.0293774i −0.231324 0.972877i \(-0.574306\pi\)
0.331375 + 0.943499i \(0.392488\pi\)
\(350\) −0.663942 6.29833i −0.0354892 0.336660i
\(351\) −2.58510 0.759055i −0.137983 0.0405153i
\(352\) 2.20810 + 3.43587i 0.117692 + 0.183132i
\(353\) −3.09167 + 1.41192i −0.164553 + 0.0751488i −0.495989 0.868329i \(-0.665194\pi\)
0.331436 + 0.943478i \(0.392467\pi\)
\(354\) 4.68700 + 5.40908i 0.249111 + 0.287490i
\(355\) 1.47743 9.05791i 0.0784139 0.480744i
\(356\) 1.76915 12.3047i 0.0937650 0.652150i
\(357\) −4.46142 0.641456i −0.236124 0.0339494i
\(358\) −4.34796 + 6.76555i −0.229797 + 0.357571i
\(359\) 13.1509 + 15.1770i 0.694078 + 0.801009i 0.987940 0.154839i \(-0.0494859\pi\)
−0.293862 + 0.955848i \(0.594940\pi\)
\(360\) 1.66195 + 1.49597i 0.0875926 + 0.0788443i
\(361\) 28.7103 18.4510i 1.51107 0.971104i
\(362\) −3.56239 + 12.1324i −0.187235 + 0.637664i
\(363\) −4.29332 3.72018i −0.225341 0.195259i
\(364\) 3.27441 0.961454i 0.171626 0.0503939i
\(365\) 0.386440 20.4593i 0.0202272 1.07089i
\(366\) 1.79958 + 12.5164i 0.0940657 + 0.654241i
\(367\) 28.8414i 1.50551i 0.658302 + 0.752754i \(0.271275\pi\)
−0.658302 + 0.752754i \(0.728725\pi\)
\(368\) −3.90897 + 2.77849i −0.203769 + 0.144839i
\(369\) 7.73638 0.402740
\(370\) −4.59502 + 2.83187i −0.238884 + 0.147222i
\(371\) 0.334792 0.733091i 0.0173815 0.0380602i
\(372\) −2.20536 7.51076i −0.114343 0.389415i
\(373\) 23.4105 + 20.2853i 1.21215 + 1.05033i 0.997281 + 0.0736888i \(0.0234771\pi\)
0.214867 + 0.976643i \(0.431068\pi\)
\(374\) 13.9448 + 4.09457i 0.721069 + 0.211725i
\(375\) 2.53734 + 10.8886i 0.131028 + 0.562286i
\(376\) 4.40632 + 9.64849i 0.227238 + 0.497583i
\(377\) 10.5100 9.10700i 0.541294 0.469034i
\(378\) 0.684801 1.06557i 0.0352223 0.0548070i
\(379\) −4.26686 + 29.6767i −0.219174 + 1.52439i 0.521925 + 0.852991i \(0.325214\pi\)
−0.741099 + 0.671396i \(0.765695\pi\)
\(380\) 15.7222 4.29566i 0.806531 0.220363i
\(381\) 18.8477 + 12.1127i 0.965597 + 0.620552i
\(382\) 12.3015 10.6593i 0.629400 0.545379i
\(383\) 11.3111 5.16559i 0.577968 0.263949i −0.104910 0.994482i \(-0.533455\pi\)
0.682878 + 0.730532i \(0.260728\pi\)
\(384\) 0.841254 0.540641i 0.0429300 0.0275895i
\(385\) 11.4791 1.42974i 0.585028 0.0728663i
\(386\) 11.7546 13.5655i 0.598294 0.690468i
\(387\) −2.94122 10.0169i −0.149510 0.509186i
\(388\) −4.10640 1.87533i −0.208471 0.0952055i
\(389\) 2.69077 + 18.7147i 0.136427 + 0.948873i 0.936923 + 0.349535i \(0.113660\pi\)
−0.800496 + 0.599338i \(0.795430\pi\)
\(390\) −5.52636 + 2.39873i −0.279838 + 0.121464i
\(391\) −4.03770 + 16.5812i −0.204195 + 0.838548i
\(392\) 5.39561i 0.272519i
\(393\) −12.1832 + 1.75167i −0.614559 + 0.0883603i
\(394\) 5.53598 12.1221i 0.278899 0.610703i
\(395\) −19.4702 23.3465i −0.979652 1.17469i
\(396\) −2.67460 + 3.08665i −0.134404 + 0.155110i
\(397\) −1.46148 + 4.97733i −0.0733494 + 0.249805i −0.988003 0.154433i \(-0.950645\pi\)
0.914654 + 0.404238i \(0.132463\pi\)
\(398\) −5.88012 9.14965i −0.294744 0.458631i
\(399\) −3.83530 8.39813i −0.192005 0.420432i
\(400\) 4.99643 + 0.188815i 0.249822 + 0.00944076i
\(401\) −14.1043 9.06425i −0.704333 0.452647i 0.138823 0.990317i \(-0.455668\pi\)
−0.843155 + 0.537670i \(0.819305\pi\)
\(402\) −7.81904 1.12421i −0.389978 0.0560704i
\(403\) 20.8754 + 3.00143i 1.03988 + 0.149512i
\(404\) 11.8538 + 7.61800i 0.589751 + 0.379010i
\(405\) −0.967142 + 2.01609i −0.0480577 + 0.100181i
\(406\) 2.71599 + 5.94718i 0.134792 + 0.295154i
\(407\) −5.33005 8.29372i −0.264201 0.411104i
\(408\) 1.00253 3.41431i 0.0496327 0.169034i
\(409\) −9.43089 + 10.8838i −0.466328 + 0.538171i −0.939386 0.342860i \(-0.888604\pi\)
0.473059 + 0.881031i \(0.343150\pi\)
\(410\) 13.2854 11.0796i 0.656118 0.547181i
\(411\) 0.342550 0.750081i 0.0168968 0.0369988i
\(412\) −11.5150 + 1.65560i −0.567301 + 0.0815656i
\(413\) 9.06570i 0.446094i
\(414\) −3.76722 2.96784i −0.185149 0.145861i
\(415\) −9.34077 + 4.05438i −0.458521 + 0.199022i
\(416\) 0.383430 + 2.66681i 0.0187992 + 0.130751i
\(417\) −4.32134 1.97349i −0.211617 0.0966423i
\(418\) 8.38703 + 28.5636i 0.410223 + 1.39709i
\(419\) 1.99300 2.30005i 0.0973647 0.112365i −0.704976 0.709231i \(-0.749042\pi\)
0.802341 + 0.596866i \(0.203588\pi\)
\(420\) −0.350064 2.81059i −0.0170814 0.137143i
\(421\) −18.8368 + 12.1057i −0.918049 + 0.589994i −0.912091 0.409988i \(-0.865533\pi\)
−0.00595790 + 0.999982i \(0.501896\pi\)
\(422\) 23.0629 10.5325i 1.12269 0.512714i
\(423\) −8.01625 + 6.94612i −0.389764 + 0.337732i
\(424\) 0.535259 + 0.343990i 0.0259945 + 0.0167056i
\(425\) 13.8769 11.1354i 0.673129 0.540145i
\(426\) 0.584110 4.06257i 0.0283002 0.196832i
\(427\) 8.65935 13.4742i 0.419056 0.652063i
\(428\) −2.19311 + 1.90034i −0.106008 + 0.0918566i
\(429\) −4.57117 10.0095i −0.220698 0.483262i
\(430\) −19.3964 12.9893i −0.935376 0.626401i
\(431\) 11.7913 + 3.46224i 0.567967 + 0.166770i 0.553093 0.833119i \(-0.313447\pi\)
0.0148733 + 0.999889i \(0.495266\pi\)
\(432\) 0.755750 + 0.654861i 0.0363610 + 0.0315070i
\(433\) 1.02899 + 3.50443i 0.0494503 + 0.168412i 0.980516 0.196439i \(-0.0629379\pi\)
−0.931066 + 0.364852i \(0.881120\pi\)
\(434\) −4.11889 + 9.01910i −0.197713 + 0.432931i
\(435\) −6.05552 9.82573i −0.290340 0.471108i
\(436\) −13.4765 −0.645407
\(437\) −33.0436 + 11.4046i −1.58069 + 0.545556i
\(438\) 9.15130i 0.437266i
\(439\) −0.116094 0.807454i −0.00554088 0.0385377i 0.986863 0.161557i \(-0.0516515\pi\)
−0.992404 + 0.123019i \(0.960742\pi\)
\(440\) −0.172468 + 9.13097i −0.00822210 + 0.435302i
\(441\) 5.17705 1.52012i 0.246526 0.0723866i
\(442\) 7.24562 + 6.27836i 0.344639 + 0.298631i
\(443\) −11.3745 + 38.7379i −0.540417 + 1.84049i 0.00140475 + 0.999999i \(0.499553\pi\)
−0.541822 + 0.840493i \(0.682265\pi\)
\(444\) −2.03067 + 1.30503i −0.0963714 + 0.0619341i
\(445\) 18.5968 20.6602i 0.881571 0.979387i
\(446\) −13.3685 15.4281i −0.633016 0.730540i
\(447\) −4.96029 + 7.71836i −0.234614 + 0.365066i
\(448\) −1.25375 0.180263i −0.0592343 0.00851660i
\(449\) 0.269571 1.87491i 0.0127219 0.0884825i −0.982471 0.186414i \(-0.940313\pi\)
0.995193 + 0.0979314i \(0.0312226\pi\)
\(450\) 1.22649 + 4.84724i 0.0578173 + 0.228501i
\(451\) 20.6917 + 23.8795i 0.974334 + 1.12444i
\(452\) −3.57541 + 1.63284i −0.168173 + 0.0768022i
\(453\) −3.97832 6.19039i −0.186918 0.290850i
\(454\) 0.301749 + 0.0886015i 0.0141618 + 0.00415828i
\(455\) 7.27990 + 2.28776i 0.341287 + 0.107252i
\(456\) 6.99364 2.05352i 0.327507 0.0961648i
\(457\) 22.6588 + 10.3479i 1.05993 + 0.484055i 0.867594 0.497274i \(-0.165666\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(458\) −17.1766 + 2.46963i −0.802612 + 0.115398i
\(459\) 3.55845 0.166094
\(460\) −10.7196 + 0.298637i −0.499806 + 0.0139240i
\(461\) 4.06186 0.189180 0.0945899 0.995516i \(-0.469846\pi\)
0.0945899 + 0.995516i \(0.469846\pi\)
\(462\) 5.12061 0.736232i 0.238232 0.0342526i
\(463\) 15.5823 + 7.11620i 0.724171 + 0.330718i 0.743171 0.669102i \(-0.233321\pi\)
−0.0189997 + 0.999819i \(0.506048\pi\)
\(464\) −4.95259 + 1.45421i −0.229918 + 0.0675100i
\(465\) 5.24762 16.6985i 0.243352 0.774372i
\(466\) 1.01261 + 0.297330i 0.0469083 + 0.0137735i
\(467\) −13.5647 21.1071i −0.627700 0.976721i −0.998840 0.0481439i \(-0.984669\pi\)
0.371140 0.928577i \(-0.378967\pi\)
\(468\) −2.45077 + 1.11923i −0.113287 + 0.0517363i
\(469\) 6.55241 + 7.56188i 0.302562 + 0.349175i
\(470\) −3.81818 + 23.4087i −0.176119 + 1.07976i
\(471\) −1.55727 + 10.8310i −0.0717552 + 0.499068i
\(472\) 7.08439 + 1.01858i 0.326086 + 0.0468840i
\(473\) 23.0520 35.8696i 1.05993 1.64929i
\(474\) −8.90296 10.2746i −0.408926 0.471926i
\(475\) 34.5555 + 11.5808i 1.58552 + 0.531362i
\(476\) −3.79178 + 2.43683i −0.173796 + 0.111692i
\(477\) −0.179256 + 0.610491i −0.00820758 + 0.0279524i
\(478\) 22.2976 + 19.3210i 1.01987 + 0.883723i
\(479\) −13.5821 + 3.98806i −0.620581 + 0.182219i −0.576884 0.816826i \(-0.695732\pi\)
−0.0436967 + 0.999045i \(0.513914\pi\)
\(480\) 2.23567 + 0.0422279i 0.102044 + 0.00192743i
\(481\) −0.925548 6.43733i −0.0422014 0.293517i
\(482\) 9.39041i 0.427721i
\(483\) 1.14449 + 5.96583i 0.0520759 + 0.271455i
\(484\) −5.68088 −0.258222
\(485\) −5.29611 8.59350i −0.240484 0.390211i
\(486\) −0.415415 + 0.909632i −0.0188436 + 0.0412617i
\(487\) −2.09173 7.12376i −0.0947851 0.322808i 0.898427 0.439122i \(-0.144710\pi\)
−0.993213 + 0.116314i \(0.962892\pi\)
\(488\) 9.55651 + 8.28076i 0.432603 + 0.374853i
\(489\) −19.7625 5.80278i −0.893689 0.262411i
\(490\) 6.71331 10.0247i 0.303277 0.452869i
\(491\) −15.8472 34.7006i −0.715176 1.56602i −0.820544 0.571583i \(-0.806329\pi\)
0.105368 0.994433i \(-0.466398\pi\)
\(492\) 5.84677 5.06625i 0.263593 0.228404i
\(493\) −9.93026 + 15.4518i −0.447236 + 0.695913i
\(494\) −2.79478 + 19.4381i −0.125743 + 0.874563i
\(495\) −8.80969 + 2.40701i −0.395966 + 0.108187i
\(496\) −6.58520 4.23205i −0.295684 0.190025i
\(497\) −3.92896 + 3.40446i −0.176238 + 0.152711i
\(498\) −4.14233 + 1.89174i −0.185622 + 0.0847709i
\(499\) 16.2211 10.4247i 0.726157 0.466673i −0.124617 0.992205i \(-0.539770\pi\)
0.850774 + 0.525532i \(0.176134\pi\)
\(500\) 9.04812 + 6.56746i 0.404644 + 0.293706i
\(501\) 3.70940 4.28087i 0.165724 0.191255i
\(502\) 1.12948 + 3.84667i 0.0504114 + 0.171685i
\(503\) 18.2705 + 8.34384i 0.814640 + 0.372033i 0.778759 0.627323i \(-0.215849\pi\)
0.0358801 + 0.999356i \(0.488577\pi\)
\(504\) −0.180263 1.25375i −0.00802953 0.0558466i
\(505\) 12.5452 + 28.9025i 0.558254 + 1.28614i
\(506\) −0.915129 19.5659i −0.0406824 0.869808i
\(507\) 5.74108i 0.254970i
\(508\) 22.1763 3.18847i 0.983913 0.141465i
\(509\) −10.8169 + 23.6856i −0.479448 + 1.04985i 0.503166 + 0.864190i \(0.332168\pi\)
−0.982615 + 0.185656i \(0.940559\pi\)
\(510\) 6.11079 5.09620i 0.270590 0.225663i
\(511\) −7.59079 + 8.76024i −0.335797 + 0.387530i
\(512\) 0.281733 0.959493i 0.0124509 0.0424040i
\(513\) 3.94067 + 6.13181i 0.173985 + 0.270726i
\(514\) 2.00707 + 4.39487i 0.0885281 + 0.193850i
\(515\) −23.4540 11.2511i −1.03350 0.495784i
\(516\) −8.78248 5.64415i −0.386627 0.248470i
\(517\) −42.8805 6.16529i −1.88588 0.271149i
\(518\) 3.02639 + 0.435129i 0.132972 + 0.0191185i
\(519\) 8.39443 + 5.39478i 0.368475 + 0.236804i
\(520\) −2.60571 + 5.43184i −0.114268 + 0.238202i
\(521\) −8.11650 17.7727i −0.355591 0.778635i −0.999904 0.0138730i \(-0.995584\pi\)
0.644313 0.764762i \(-0.277143\pi\)
\(522\) −2.79061 4.34227i −0.122142 0.190056i
\(523\) −4.00862 + 13.6521i −0.175285 + 0.596964i 0.824243 + 0.566236i \(0.191601\pi\)
−0.999528 + 0.0307284i \(0.990217\pi\)
\(524\) −8.06032 + 9.30210i −0.352117 + 0.406364i
\(525\) 2.84659 5.65745i 0.124235 0.246911i
\(526\) −6.21159 + 13.6015i −0.270838 + 0.593053i
\(527\) −27.5715 + 3.96418i −1.20103 + 0.172683i
\(528\) 4.08422i 0.177743i
\(529\) 22.8996 2.14680i 0.995634 0.0933393i
\(530\) 0.566477 + 1.30509i 0.0246062 + 0.0566895i
\(531\) 1.01858 + 7.08439i 0.0442027 + 0.307437i
\(532\) −8.39813 3.83530i −0.364105 0.166281i
\(533\) 5.87234 + 19.9993i 0.254359 + 0.866268i
\(534\) 8.14075 9.39493i 0.352285 0.406558i
\(535\) −6.43910 + 0.802002i −0.278387 + 0.0346736i
\(536\) −6.64544 + 4.27076i −0.287039 + 0.184469i
\(537\) −7.31547 + 3.34086i −0.315686 + 0.144169i
\(538\) 15.2403 13.2058i 0.657057 0.569343i
\(539\) 18.5386 + 11.9140i 0.798514 + 0.513174i
\(540\) 0.589343 + 2.15701i 0.0253613 + 0.0928228i
\(541\) 0.974609 6.77855i 0.0419017 0.291433i −0.958086 0.286481i \(-0.907515\pi\)
0.999988 0.00495211i \(-0.00157631\pi\)
\(542\) 0.0323539 0.0503436i 0.00138972 0.00216244i
\(543\) −9.55614 + 8.28044i −0.410093 + 0.355348i
\(544\) −1.47824 3.23688i −0.0633788 0.138780i
\(545\) −25.0385 16.7677i −1.07253 0.718250i
\(546\) 3.27441 + 0.961454i 0.140132 + 0.0411464i
\(547\) −16.7878 14.5467i −0.717794 0.621972i 0.217411 0.976080i \(-0.430239\pi\)
−0.935204 + 0.354108i \(0.884784\pi\)
\(548\) −0.232316 0.791196i −0.00992405 0.0337982i
\(549\) −5.25295 + 11.5024i −0.224191 + 0.490909i
\(550\) −11.6814 + 16.7502i −0.498095 + 0.714229i
\(551\) −37.6229 −1.60279
\(552\) −4.79059 + 0.224064i −0.203901 + 0.00953681i
\(553\) 17.2203i 0.732282i
\(554\) −0.837155 5.82254i −0.0355673 0.247376i
\(555\) −5.39660 0.101932i −0.229073 0.00432679i
\(556\) −4.55822 + 1.33841i −0.193311 + 0.0567614i
\(557\) −22.4129 19.4209i −0.949667 0.822891i 0.0346323 0.999400i \(-0.488974\pi\)
−0.984299 + 0.176509i \(0.943519\pi\)
\(558\) 2.20536 7.51076i 0.0933603 0.317956i
\(559\) 23.6621 15.2067i 1.00080 0.643175i
\(560\) −2.10511 1.89486i −0.0889570 0.0800724i
\(561\) 9.51743 + 10.9837i 0.401826 + 0.463732i
\(562\) 6.84934 10.6578i 0.288922 0.449572i
\(563\) 22.0874 + 3.17568i 0.930872 + 0.133839i 0.591036 0.806646i \(-0.298719\pi\)
0.339836 + 0.940485i \(0.389628\pi\)
\(564\) −1.50954 + 10.4991i −0.0635630 + 0.442090i
\(565\) −8.67449 1.41489i −0.364939 0.0595250i
\(566\) −2.83234 3.26870i −0.119052 0.137394i
\(567\) 1.15218 0.526184i 0.0483871 0.0220976i
\(568\) −2.21898 3.45280i −0.0931063 0.144876i
\(569\) −8.70407 2.55575i −0.364894 0.107142i 0.0941456 0.995558i \(-0.469988\pi\)
−0.459039 + 0.888416i \(0.651806\pi\)
\(570\) 15.5488 + 4.88632i 0.651266 + 0.204665i
\(571\) −19.0562 + 5.59541i −0.797477 + 0.234160i −0.654991 0.755636i \(-0.727328\pi\)
−0.142486 + 0.989797i \(0.545510\pi\)
\(572\) −10.0095 4.57117i −0.418517 0.191130i
\(573\) 16.1116 2.31649i 0.673070 0.0967729i
\(574\) −9.79926 −0.409013
\(575\) −20.2880 12.7827i −0.846067 0.533077i
\(576\) 1.00000 0.0416667
\(577\) 28.2020 4.05484i 1.17407 0.168805i 0.472448 0.881359i \(-0.343370\pi\)
0.701618 + 0.712553i \(0.252461\pi\)
\(578\) 3.94544 + 1.80182i 0.164109 + 0.0749460i
\(579\) 17.2227 5.05704i 0.715751 0.210163i
\(580\) −11.0109 3.46027i −0.457204 0.143680i
\(581\) 5.53448 + 1.62507i 0.229609 + 0.0674192i
\(582\) −2.44064 3.79772i −0.101168 0.157420i
\(583\) −2.36381 + 1.07952i −0.0978990 + 0.0447090i
\(584\) −5.99283 6.91609i −0.247985 0.286190i
\(585\) −5.94592 0.969837i −0.245834 0.0400978i
\(586\) −1.40182 + 9.74986i −0.0579086 + 0.402763i
\(587\) 32.4960 + 4.67222i 1.34125 + 0.192843i 0.775299 0.631594i \(-0.217599\pi\)
0.565953 + 0.824437i \(0.308508\pi\)
\(588\) 2.91709 4.53907i 0.120299 0.187188i
\(589\) −37.3640 43.1203i −1.53955 1.77674i
\(590\) 11.8950 + 10.7070i 0.489709 + 0.440800i
\(591\) 11.2109 7.20479i 0.461153 0.296365i
\(592\) −0.680064 + 2.31609i −0.0279505 + 0.0951905i
\(593\) 1.90565 + 1.65126i 0.0782557 + 0.0678090i 0.693110 0.720832i \(-0.256240\pi\)
−0.614855 + 0.788640i \(0.710785\pi\)
\(594\) −3.91878 + 1.15066i −0.160790 + 0.0472121i
\(595\) −10.0768 0.190334i −0.413110 0.00780293i
\(596\) 1.30572 + 9.08145i 0.0534842 + 0.371991i
\(597\) 10.8762i 0.445134i
\(598\) 4.81263 11.9914i 0.196803 0.490365i
\(599\) −16.2966 −0.665859 −0.332930 0.942952i \(-0.608037\pi\)
−0.332930 + 0.942952i \(0.608037\pi\)
\(600\) 4.10119 + 2.86012i 0.167430 + 0.116764i
\(601\) −7.78717 + 17.0515i −0.317645 + 0.695546i −0.999349 0.0360822i \(-0.988512\pi\)
0.681703 + 0.731629i \(0.261239\pi\)
\(602\) 3.72548 + 12.6878i 0.151839 + 0.517117i
\(603\) −5.97000 5.17304i −0.243117 0.210662i
\(604\) −7.06046 2.07314i −0.287286 0.0843548i
\(605\) −10.5547 7.06825i −0.429110 0.287365i
\(606\) 5.85348 + 12.8173i 0.237781 + 0.520669i
\(607\) 18.2591 15.8216i 0.741114 0.642179i −0.200183 0.979759i \(-0.564154\pi\)
0.941297 + 0.337580i \(0.109608\pi\)
\(608\) 3.94067 6.13181i 0.159815 0.248678i
\(609\) −0.930456 + 6.47146i −0.0377040 + 0.262237i
\(610\) 7.45229 + 27.2755i 0.301734 + 1.10435i
\(611\) −24.0412 15.4504i −0.972604 0.625054i
\(612\) 2.68930 2.33029i 0.108709 0.0941965i
\(613\) 21.2017 9.68251i 0.856330 0.391073i 0.0616474 0.998098i \(-0.480365\pi\)
0.794683 + 0.607025i \(0.207637\pi\)
\(614\) −2.81993 + 1.81226i −0.113803 + 0.0731367i
\(615\) 17.1664 2.13811i 0.692217 0.0862169i
\(616\) 3.38777 3.90969i 0.136497 0.157526i
\(617\) 8.00452 + 27.2609i 0.322250 + 1.09748i 0.948215 + 0.317631i \(0.102887\pi\)
−0.625965 + 0.779851i \(0.715295\pi\)
\(618\) −10.5821 4.83267i −0.425674 0.194399i
\(619\) −4.53502 31.5417i −0.182278 1.26777i −0.851360 0.524582i \(-0.824222\pi\)
0.669082 0.743188i \(-0.266687\pi\)
\(620\) −6.96928 16.0563i −0.279893 0.644837i
\(621\) −1.56465 4.53342i −0.0627874 0.181920i
\(622\) 7.43177i 0.297987i
\(623\) −15.5857 + 2.24089i −0.624430 + 0.0897794i
\(624\) −1.11923 + 2.45077i −0.0448049 + 0.0981091i
\(625\) 8.63946 + 23.4597i 0.345578 + 0.938390i
\(626\) 11.2477 12.9806i 0.449550 0.518808i
\(627\) −8.38703 + 28.5636i −0.334946 + 1.14072i
\(628\) 5.91592 + 9.20535i 0.236071 + 0.367333i
\(629\) 3.56826 + 7.81340i 0.142276 + 0.311540i
\(630\) 1.22503 2.55368i 0.0488062 0.101741i
\(631\) −12.9083 8.29568i −0.513872 0.330246i 0.257871 0.966179i \(-0.416979\pi\)
−0.771744 + 0.635934i \(0.780615\pi\)
\(632\) −13.4568 1.93480i −0.535283 0.0769621i
\(633\) 25.0961 + 3.60827i 0.997479 + 0.143416i
\(634\) 22.0244 + 14.1542i 0.874701 + 0.562136i
\(635\) 45.1692 + 21.6682i 1.79248 + 0.859875i
\(636\) 0.264313 + 0.578766i 0.0104807 + 0.0229496i
\(637\) 7.85932 + 12.2293i 0.311398 + 0.484544i
\(638\) 5.93932 20.2275i 0.235140 0.800813i
\(639\) 2.68778 3.10186i 0.106327 0.122708i
\(640\) 1.71726 1.43214i 0.0678806 0.0566102i
\(641\) 0.117167 0.256560i 0.00462782 0.0101335i −0.907304 0.420475i \(-0.861863\pi\)
0.911932 + 0.410342i \(0.134591\pi\)
\(642\) −2.87237 + 0.412984i −0.113363 + 0.0162992i
\(643\) 30.0196i 1.18386i −0.805991 0.591928i \(-0.798367\pi\)
0.805991 0.591928i \(-0.201633\pi\)
\(644\) 4.77174 + 3.75920i 0.188033 + 0.148133i
\(645\) −9.29470 21.4138i −0.365979 0.843167i
\(646\) −3.69125 25.6732i −0.145230 1.01010i
\(647\) −37.3180 17.0426i −1.46712 0.670012i −0.487918 0.872889i \(-0.662244\pi\)
−0.979204 + 0.202877i \(0.934971\pi\)
\(648\) 0.281733 + 0.959493i 0.0110675 + 0.0376924i
\(649\) −19.1427 + 22.0919i −0.751419 + 0.867183i
\(650\) −11.5996 + 6.84992i −0.454975 + 0.268676i
\(651\) −8.34112 + 5.36051i −0.326914 + 0.210095i
\(652\) −18.7355 + 8.55620i −0.733738 + 0.335087i
\(653\) 11.3776 9.85875i 0.445240 0.385803i −0.403185 0.915119i \(-0.632097\pi\)
0.848425 + 0.529316i \(0.177551\pi\)
\(654\) −11.3372 7.28595i −0.443318 0.284903i
\(655\) −26.5494 + 7.25390i −1.03737 + 0.283433i
\(656\) 1.10100 7.65764i 0.0429869 0.298980i
\(657\) 4.94757 7.69856i 0.193023 0.300350i
\(658\) 10.1538 8.79828i 0.395835 0.342993i
\(659\) 7.74501 + 16.9592i 0.301703 + 0.660637i 0.998389 0.0567389i \(-0.0180702\pi\)
−0.696686 + 0.717376i \(0.745343\pi\)
\(660\) −5.08167 + 7.58822i −0.197804 + 0.295371i
\(661\) −12.7220 3.73551i −0.494827 0.145294i 0.0247915 0.999693i \(-0.492108\pi\)
−0.519619 + 0.854398i \(0.673926\pi\)
\(662\) 7.32605 + 6.34806i 0.284735 + 0.246724i
\(663\) 2.70106 + 9.19897i 0.104901 + 0.357258i
\(664\) −1.89174 + 4.14233i −0.0734138 + 0.160754i
\(665\) −10.8312 17.5748i −0.420017 0.681523i
\(666\) −2.41386 −0.0935353
\(667\) 24.0517 + 5.85684i 0.931284 + 0.226778i
\(668\) 5.66441i 0.219163i
\(669\) −2.90525 20.2065i −0.112323 0.781227i
\(670\) −17.6606 0.333577i −0.682287 0.0128872i
\(671\) −49.5533 + 14.5502i −1.91298 + 0.561703i
\(672\) −0.957267 0.829477i −0.0369274 0.0319978i
\(673\) 2.62191 8.92941i 0.101067 0.344203i −0.893398 0.449265i \(-0.851686\pi\)
0.994466 + 0.105062i \(0.0335040\pi\)
\(674\) 29.3200 18.8428i 1.12937 0.725799i
\(675\) −1.58882 + 4.74085i −0.0611539 + 0.182475i
\(676\) 3.75961 + 4.33882i 0.144600 + 0.166878i
\(677\) 6.40628 9.96836i 0.246213 0.383115i −0.696047 0.717996i \(-0.745060\pi\)
0.942261 + 0.334881i \(0.108696\pi\)
\(678\) −3.89061 0.559385i −0.149418 0.0214831i
\(679\) −0.813769 + 5.65989i −0.0312296 + 0.217207i
\(680\) 1.28093 7.85316i 0.0491213 0.301155i
\(681\) 0.205946 + 0.237674i 0.00789187 + 0.00910770i
\(682\) 29.0815 13.2811i 1.11359 0.508559i
\(683\) −12.5655 19.5522i −0.480804 0.748145i 0.513108 0.858324i \(-0.328494\pi\)
−0.993912 + 0.110179i \(0.964858\pi\)
\(684\) 6.99364 + 2.05352i 0.267409 + 0.0785183i
\(685\) 0.552792 1.75904i 0.0211211 0.0672095i
\(686\) −15.0649 + 4.42344i −0.575179 + 0.168888i
\(687\) −15.7851 7.20881i −0.602239 0.275033i
\(688\) −10.3335 + 1.48573i −0.393961 + 0.0566430i
\(689\) −1.71425 −0.0653076
\(690\) −9.17940 5.54425i −0.349454 0.211066i
\(691\) 17.4927 0.665452 0.332726 0.943023i \(-0.392031\pi\)
0.332726 + 0.943023i \(0.392031\pi\)
\(692\) 9.87692 1.42009i 0.375464 0.0539836i
\(693\) 4.70577 + 2.14905i 0.178757 + 0.0816357i
\(694\) −1.18309 + 0.347386i −0.0449094 + 0.0131866i
\(695\) −10.1341 3.18473i −0.384410 0.120804i
\(696\) −4.95259 1.45421i −0.187727 0.0551217i
\(697\) −14.8836 23.1593i −0.563757 0.877222i
\(698\) 1.77196 0.809229i 0.0670699 0.0306298i
\(699\) 0.691114 + 0.797589i 0.0261403 + 0.0301676i
\(700\) −1.55353 6.13974i −0.0587179 0.232060i
\(701\) 4.24730 29.5406i 0.160418 1.11573i −0.737428 0.675426i \(-0.763960\pi\)
0.897846 0.440309i \(-0.145131\pi\)
\(702\) −2.66681 0.383430i −0.100652 0.0144716i
\(703\) −9.51225 + 14.8013i −0.358761 + 0.558243i
\(704\) 2.67460 + 3.08665i 0.100803 + 0.116332i
\(705\) −15.8677 + 17.6284i −0.597614 + 0.663923i
\(706\) −2.85926 + 1.83754i −0.107610 + 0.0691566i
\(707\) 5.02834 17.1249i 0.189110 0.644050i
\(708\) 5.40908 + 4.68700i 0.203286 + 0.176148i
\(709\) −26.0196 + 7.64006i −0.977188 + 0.286928i −0.731063 0.682310i \(-0.760976\pi\)
−0.246125 + 0.969238i \(0.579157\pi\)
\(710\) 0.173318 9.17597i 0.00650451 0.344368i
\(711\) −1.93480 13.4568i −0.0725606 0.504670i
\(712\) 12.4313i 0.465882i
\(713\) 17.1735 + 33.3826i 0.643153 + 1.25019i
\(714\) −4.50730 −0.168682
\(715\) −12.9094 20.9469i −0.482784 0.783370i
\(716\) −3.34086 + 7.31547i −0.124854 + 0.273392i
\(717\) 8.31224 + 28.3089i 0.310426 + 1.05722i
\(718\) 15.1770 + 13.1509i 0.566399 + 0.490787i
\(719\) −32.0320 9.40546i −1.19459 0.350764i −0.376810 0.926290i \(-0.622979\pi\)
−0.817783 + 0.575526i \(0.804797\pi\)
\(720\) 1.85793 + 1.24422i 0.0692411 + 0.0463693i
\(721\) 6.12129 + 13.4038i 0.227969 + 0.499182i
\(722\) 25.7922 22.3491i 0.959886 0.831746i
\(723\) 5.07684 7.89971i 0.188810 0.293793i
\(724\) −1.79951 + 12.5159i −0.0668783 + 0.465149i
\(725\) −16.1523 20.1290i −0.599880 0.747571i
\(726\) −4.77906 3.07132i −0.177368 0.113987i
\(727\) −26.2325 + 22.7306i −0.972911 + 0.843032i −0.987621 0.156859i \(-0.949863\pi\)
0.0147097 + 0.999892i \(0.495318\pi\)
\(728\) 3.10425 1.41766i 0.115051 0.0525421i
\(729\) −0.841254 + 0.540641i −0.0311575 + 0.0200237i
\(730\) −2.52915 20.3060i −0.0936081 0.751560i
\(731\) −24.3277 + 28.0756i −0.899791 + 1.03841i
\(732\) 3.56253 + 12.1329i 0.131675 + 0.448443i
\(733\) −34.5166 15.7632i −1.27490 0.582228i −0.341102 0.940026i \(-0.610800\pi\)
−0.933799 + 0.357798i \(0.883528\pi\)
\(734\) 4.10456 + 28.5478i 0.151502 + 1.05372i
\(735\) 11.0674 4.80381i 0.408225 0.177191i
\(736\) −3.47376 + 3.30651i −0.128044 + 0.121880i
\(737\) 32.2631i 1.18843i
\(738\) 7.65764 1.10100i 0.281881 0.0405284i
\(739\) −17.4506 + 38.2116i −0.641933 + 1.40564i 0.256509 + 0.966542i \(0.417428\pi\)
−0.898441 + 0.439094i \(0.855299\pi\)
\(740\) −4.14523 + 3.45699i −0.152382 + 0.127081i
\(741\) −12.8602 + 14.8414i −0.472430 + 0.545213i
\(742\) 0.227054 0.773275i 0.00833542 0.0283878i
\(743\) −14.2382 22.1550i −0.522348 0.812789i 0.475407 0.879766i \(-0.342301\pi\)
−0.997754 + 0.0669774i \(0.978664\pi\)
\(744\) −3.25180 7.12046i −0.119217 0.261049i
\(745\) −8.87337 + 18.4973i −0.325095 + 0.677690i
\(746\) 26.0591 + 16.7472i 0.954091 + 0.613157i
\(747\) −4.50751 0.648082i −0.164921 0.0237121i
\(748\) 14.3856 + 2.06834i 0.525989 + 0.0756258i
\(749\) 3.09218 + 1.98723i 0.112986 + 0.0726117i
\(750\) 4.06112 + 10.4167i 0.148291 + 0.380363i
\(751\) −2.76868 6.06256i −0.101031 0.221226i 0.852366 0.522945i \(-0.175167\pi\)
−0.953397 + 0.301719i \(0.902439\pi\)
\(752\) 5.73459 + 8.92320i 0.209119 + 0.325396i
\(753\) −1.12948 + 3.84667i −0.0411607 + 0.140181i
\(754\) 9.10700 10.5100i 0.331657 0.382753i
\(755\) −10.5384 12.6365i −0.383533 0.459890i
\(756\) 0.526184 1.15218i 0.0191371 0.0419044i
\(757\) −31.5810 + 4.54066i −1.14783 + 0.165033i −0.689865 0.723938i \(-0.742330\pi\)
−0.457964 + 0.888971i \(0.651421\pi\)
\(758\) 29.9818i 1.08899i
\(759\) 9.80825 16.9546i 0.356017 0.615413i
\(760\) 14.9508 6.48944i 0.542323 0.235397i
\(761\) 4.48760 + 31.2119i 0.162675 + 1.13143i 0.893564 + 0.448935i \(0.148197\pi\)
−0.730889 + 0.682496i \(0.760894\pi\)
\(762\) 20.3797 + 9.30709i 0.738278 + 0.337160i
\(763\) 4.80916 + 16.3785i 0.174103 + 0.592942i
\(764\) 10.6593 12.3015i 0.385641 0.445053i
\(765\) 7.89593 0.983453i 0.285478 0.0355568i
\(766\) 10.4608 6.72274i 0.377964 0.242903i
\(767\) −17.5407 + 8.01058i −0.633359 + 0.289245i
\(768\) 0.755750 0.654861i 0.0272708 0.0236303i
\(769\) −31.2600 20.0896i −1.12726 0.724448i −0.162276 0.986745i \(-0.551884\pi\)
−0.964987 + 0.262297i \(0.915520\pi\)
\(770\) 11.1588 3.04883i 0.402134 0.109872i
\(771\) −0.687592 + 4.78231i −0.0247630 + 0.172231i
\(772\) 9.70439 15.1003i 0.349269 0.543473i
\(773\) −19.3457 + 16.7631i −0.695816 + 0.602928i −0.929253 0.369444i \(-0.879548\pi\)
0.233437 + 0.972372i \(0.425003\pi\)
\(774\) −4.33683 9.49633i −0.155884 0.341339i
\(775\) 7.02909 38.5029i 0.252492 1.38306i
\(776\) −4.33149 1.27184i −0.155492 0.0456564i
\(777\) 2.31071 + 2.00224i 0.0828964 + 0.0718301i
\(778\) 5.32676 + 18.1413i 0.190974 + 0.650396i
\(779\) 23.4251 51.2938i 0.839292 1.83779i
\(780\) −5.12874 + 3.16080i −0.183638 + 0.113175i
\(781\) 16.7631 0.599830
\(782\) −1.63685 + 16.9871i −0.0585336 + 0.607456i
\(783\) 5.16167i 0.184463i
\(784\) −0.767875 5.34069i −0.0274241 0.190739i
\(785\) −0.462075 + 24.4636i −0.0164922 + 0.873144i
\(786\) −11.8099 + 3.46769i −0.421244 + 0.123688i
\(787\) 0.695002 + 0.602222i 0.0247741 + 0.0214669i 0.667160 0.744915i \(-0.267510\pi\)
−0.642386 + 0.766382i \(0.722055\pi\)
\(788\) 3.75448 12.7866i 0.133748 0.455503i
\(789\) −12.5790 + 8.08405i −0.447825 + 0.287800i
\(790\) −22.5946 20.3379i −0.803879 0.723592i
\(791\) 3.26036 + 3.76265i 0.115925 + 0.133784i
\(792\) −2.20810 + 3.43587i −0.0784613 + 0.122088i
\(793\) −33.7221 4.84850i −1.19751 0.172175i
\(794\) −0.738252 + 5.13466i −0.0261996 + 0.182222i
\(795\) −0.229034 + 1.40417i −0.00812300 + 0.0498009i
\(796\) −7.12240 8.21969i −0.252447 0.291339i
\(797\) 13.3420 6.09310i 0.472599 0.215829i −0.164854 0.986318i \(-0.552715\pi\)
0.637453 + 0.770489i \(0.279988\pi\)
\(798\) −4.99144 7.76683i −0.176695 0.274943i
\(799\) 36.2157 + 10.6339i 1.28122 + 0.376200i
\(800\) 4.97245 0.524173i 0.175803 0.0185323i
\(801\) 11.9277 3.50229i 0.421445 0.123747i
\(802\) −15.2507 6.96475i −0.538520 0.245934i
\(803\) 36.9955 5.31915i 1.30554 0.187709i
\(804\) −7.89945 −0.278592
\(805\) 4.18831 + 12.9214i 0.147618 + 0.455420i
\(806\) 21.0901 0.742866
\(807\) 19.9606 2.86990i 0.702646 0.101025i
\(808\) 12.8173 + 5.85348i 0.450912 + 0.205925i
\(809\) −28.3315 + 8.31889i −0.996084 + 0.292477i −0.738848 0.673872i \(-0.764630\pi\)
−0.257236 + 0.966349i \(0.582812\pi\)
\(810\) −0.670378 + 2.13321i −0.0235547 + 0.0749534i
\(811\) 47.8583 + 14.0525i 1.68053 + 0.493449i 0.976282 0.216502i \(-0.0694646\pi\)
0.704251 + 0.709951i \(0.251283\pi\)
\(812\) 3.53471 + 5.50012i 0.124044 + 0.193017i
\(813\) 0.0544356 0.0248599i 0.00190914 0.000871876i
\(814\) −6.45611 7.45075i −0.226287 0.261149i
\(815\) −45.4551 7.41415i −1.59222 0.259707i
\(816\) 0.506421 3.52223i 0.0177283 0.123303i
\(817\) −75.3197 10.8293i −2.63510 0.378871i
\(818\) −7.78597 + 12.1152i −0.272230 + 0.423598i
\(819\) 2.23481 + 2.57911i 0.0780905 + 0.0901213i
\(820\) 11.5734 12.8575i 0.404159 0.449003i
\(821\) 34.2347 22.0013i 1.19480 0.767850i 0.216749 0.976227i \(-0.430455\pi\)
0.978048 + 0.208377i \(0.0668182\pi\)
\(822\) 0.232316 0.791196i 0.00810295 0.0275961i
\(823\) 21.8417 + 18.9260i 0.761355 + 0.659718i 0.946395 0.323013i \(-0.104696\pi\)
−0.185039 + 0.982731i \(0.559241\pi\)
\(824\) −11.1621 + 3.27750i −0.388851 + 0.114177i
\(825\) −18.8828 + 7.77571i −0.657415 + 0.270716i
\(826\) −1.29018 8.97342i −0.0448912 0.312225i
\(827\) 35.0288i 1.21807i 0.793144 + 0.609035i \(0.208443\pi\)
−0.793144 + 0.609035i \(0.791557\pi\)
\(828\) −4.15124 2.40150i −0.144266 0.0834578i
\(829\) −37.8144 −1.31335 −0.656674 0.754175i \(-0.728037\pi\)
−0.656674 + 0.754175i \(0.728037\pi\)
\(830\) −8.66870 + 5.34245i −0.300895 + 0.185439i
\(831\) 2.44364 5.35083i 0.0847691 0.185618i
\(832\) 0.759055 + 2.58510i 0.0263155 + 0.0896223i
\(833\) −14.5104 12.5733i −0.502756 0.435640i
\(834\) −4.55822 1.33841i −0.157838 0.0463455i
\(835\) 7.04776 10.5241i 0.243898 0.364202i
\(836\) 12.3667 + 27.0793i 0.427711 + 0.936556i
\(837\) 5.91589 5.12615i 0.204483 0.177186i
\(838\) 1.64539 2.56027i 0.0568390 0.0884432i
\(839\) −1.18237 + 8.22355i −0.0408199 + 0.283909i 0.959179 + 0.282798i \(0.0912626\pi\)
−0.999999 + 0.00111061i \(0.999646\pi\)
\(840\) −0.746490 2.73216i −0.0257563 0.0942686i
\(841\) −1.98297 1.27438i −0.0683782 0.0439440i
\(842\) −16.9222 + 14.6632i −0.583179 + 0.505327i
\(843\) 11.5241 5.26287i 0.396910 0.181263i
\(844\) 21.3293 13.7075i 0.734183 0.471831i
\(845\) 1.58667 + 12.7390i 0.0545830 + 0.438235i
\(846\) −6.94612 + 8.01625i −0.238813 + 0.275604i
\(847\) 2.02725 + 6.90419i 0.0696572 + 0.237231i
\(848\) 0.578766 + 0.264313i 0.0198749 + 0.00907656i
\(849\) −0.615527 4.28108i −0.0211248 0.146926i
\(850\) 12.1509 12.9969i 0.416773 0.445790i
\(851\) 8.38518 7.98146i 0.287440 0.273601i
\(852\) 4.10435i 0.140613i
\(853\) −21.8434 + 3.14061i −0.747905 + 0.107533i −0.505720 0.862698i \(-0.668773\pi\)
−0.242185 + 0.970230i \(0.577864\pi\)
\(854\) 6.65363 14.5694i 0.227683 0.498555i
\(855\) 10.4387 + 12.5169i 0.356996 + 0.428070i
\(856\) −1.90034 + 2.19311i −0.0649524 + 0.0749591i
\(857\) −6.55587 + 22.3272i −0.223944 + 0.762684i 0.768485 + 0.639868i \(0.221011\pi\)
−0.992429 + 0.122816i \(0.960807\pi\)
\(858\) −5.94914 9.25705i −0.203100 0.316030i
\(859\) −20.7263 45.3842i −0.707171 1.54849i −0.831055 0.556191i \(-0.812262\pi\)
0.123884 0.992297i \(-0.460465\pi\)
\(860\) −21.0475 10.0967i −0.717714 0.344295i
\(861\) −8.24366 5.29788i −0.280943 0.180551i
\(862\) 12.1640 + 1.74892i 0.414308 + 0.0595684i
\(863\) 30.2741 + 4.35275i 1.03054 + 0.148169i 0.636782 0.771044i \(-0.280265\pi\)
0.393760 + 0.919213i \(0.371174\pi\)
\(864\) 0.841254 + 0.540641i 0.0286200 + 0.0183930i
\(865\) 20.1176 + 9.65061i 0.684018 + 0.328131i
\(866\) 1.51725 + 3.32232i 0.0515583 + 0.112897i
\(867\) 2.34498 + 3.64886i 0.0796397 + 0.123922i
\(868\) −2.79341 + 9.51348i −0.0948145 + 0.322908i
\(869\) 36.3617 41.9636i 1.23349 1.42352i
\(870\) −7.39223 8.86393i −0.250620 0.300515i
\(871\) 8.84128 19.3597i 0.299575 0.655978i
\(872\) −13.3393 + 1.91791i −0.451727 + 0.0649485i
\(873\) 4.51436i 0.152788i
\(874\) −31.0842 + 15.9911i −1.05144 + 0.540907i
\(875\) 4.75281 13.3402i 0.160674 0.450980i
\(876\) −1.30237 9.05815i −0.0440029 0.306047i
\(877\) −8.15950 3.72632i −0.275527 0.125829i 0.272860 0.962054i \(-0.412030\pi\)
−0.548387 + 0.836225i \(0.684758\pi\)
\(878\) −0.229825 0.782713i −0.00775623 0.0264153i
\(879\) −6.45046 + 7.44423i −0.217569 + 0.251087i
\(880\) 1.12876 + 9.06258i 0.0380505 + 0.305499i
\(881\) −1.21567 + 0.781265i −0.0409570 + 0.0263215i −0.560959 0.827843i \(-0.689568\pi\)
0.520002 + 0.854165i \(0.325931\pi\)
\(882\) 4.90802 2.24142i 0.165262 0.0754724i
\(883\) 33.5079 29.0348i 1.12763 0.977099i 0.127740 0.991808i \(-0.459228\pi\)
0.999892 + 0.0147089i \(0.00468215\pi\)
\(884\) 8.06537 + 5.18330i 0.271268 + 0.174333i
\(885\) 4.21808 + 15.4382i 0.141789 + 0.518950i
\(886\) −5.74572 + 39.9623i −0.193031 + 1.34256i
\(887\) 16.9293 26.3426i 0.568432 0.884497i −0.431412 0.902155i \(-0.641985\pi\)
0.999844 + 0.0176578i \(0.00562096\pi\)
\(888\) −1.82428 + 1.58074i −0.0612187 + 0.0530463i
\(889\) −11.7888 25.8138i −0.395383 0.865768i
\(890\) 15.4672 23.0965i 0.518462 0.774196i
\(891\) −3.91878 1.15066i −0.131284 0.0385485i
\(892\) −15.4281 13.3685i −0.516570 0.447610i
\(893\) 21.7817 + 74.1817i 0.728898 + 2.48240i
\(894\) −3.81136 + 8.34572i −0.127471 + 0.279123i
\(895\) −15.3091 + 9.43490i −0.511728 + 0.315374i
\(896\) −1.26665 −0.0423157
\(897\) 10.5317 7.48590i 0.351643 0.249947i
\(898\) 1.89419i 0.0632100i
\(899\) 5.75020 + 39.9935i 0.191780 + 1.33386i
\(900\) 1.90384 + 4.62335i 0.0634614 + 0.154112i
\(901\) 2.17240 0.637875i 0.0723732 0.0212507i
\(902\) 23.8795 + 20.6917i 0.795100 + 0.688958i
\(903\) −3.72548 + 12.6878i −0.123976 + 0.422224i
\(904\) −3.30665 + 2.12505i −0.109977 + 0.0706782i
\(905\) −18.9159 + 21.0147i −0.628785 + 0.698552i
\(906\) −4.81882 5.56121i −0.160094 0.184759i
\(907\) 10.2960 16.0210i 0.341875 0.531967i −0.627161 0.778890i \(-0.715783\pi\)
0.969035 + 0.246923i \(0.0794194\pi\)
\(908\) 0.311287 + 0.0447563i 0.0103304 + 0.00148529i
\(909\) −2.00531 + 13.9473i −0.0665121 + 0.462602i
\(910\) 7.53138 + 1.22844i 0.249663 + 0.0407224i
\(911\) −22.3243 25.7636i −0.739637 0.853587i 0.253884 0.967235i \(-0.418292\pi\)
−0.993521 + 0.113648i \(0.963746\pi\)
\(912\) 6.63021 3.02792i 0.219548 0.100264i
\(913\) −10.0554 15.6464i −0.332784 0.517822i
\(914\) 23.9008 + 7.01790i 0.790568 + 0.232132i
\(915\) −8.47698 + 26.9746i −0.280240 + 0.891754i
\(916\) −16.6503 + 4.88898i −0.550143 + 0.161536i
\(917\) 14.1816 + 6.47650i 0.468316 + 0.213873i
\(918\) 3.52223 0.506421i 0.116251 0.0167144i
\(919\) 5.63108 0.185752 0.0928760 0.995678i \(-0.470394\pi\)
0.0928760 + 0.995678i \(0.470394\pi\)
\(920\) −10.5680 + 1.82116i −0.348418 + 0.0600419i
\(921\) −3.35205 −0.110454
\(922\) 4.02052 0.578064i 0.132409 0.0190375i
\(923\) 10.0588 + 4.59370i 0.331089 + 0.151203i
\(924\) 4.96371 1.45748i 0.163294 0.0479475i
\(925\) −12.0028 + 1.26528i −0.394650 + 0.0416022i
\(926\) 16.4364 + 4.82618i 0.540135 + 0.158598i
\(927\) −6.28947 9.78661i −0.206573 0.321434i
\(928\) −4.69522 + 2.14424i −0.154128 + 0.0703880i
\(929\) −12.8882 14.8738i −0.422849 0.487993i 0.503854 0.863789i \(-0.331915\pi\)
−0.926703 + 0.375795i \(0.877370\pi\)
\(930\) 2.81777 17.2753i 0.0923982 0.566479i
\(931\) 5.59696 38.9277i 0.183433 1.27580i
\(932\) 1.04462 + 0.150194i 0.0342176 + 0.00491975i
\(933\) −4.01792 + 6.25200i −0.131541 + 0.204681i
\(934\) −16.4305 18.9618i −0.537623 0.620450i
\(935\) 24.1540 + 21.7416i 0.789921 + 0.711028i
\(936\) −2.26654 + 1.45662i −0.0740841 + 0.0476110i
\(937\) 1.82943 6.23047i 0.0597649 0.203541i −0.924198 0.381914i \(-0.875265\pi\)
0.983963 + 0.178373i \(0.0570834\pi\)
\(938\) 7.56188 + 6.55241i 0.246904 + 0.213944i
\(939\) 16.4800 4.83897i 0.537805 0.157914i
\(940\) −0.447912 + 23.7138i −0.0146093 + 0.773459i
\(941\) 1.85498 + 12.9017i 0.0604705 + 0.420582i 0.997460 + 0.0712250i \(0.0226908\pi\)
−0.936990 + 0.349357i \(0.886400\pi\)
\(942\) 10.9424i 0.356523i
\(943\) −22.9603 + 29.1447i −0.747690 + 0.949080i
\(944\) 7.15724 0.232948
\(945\) 2.41118 1.48599i 0.0784357 0.0483393i
\(946\) 17.7126 38.7851i 0.575886 1.26101i
\(947\) 8.39573 + 28.5932i 0.272825 + 0.929155i 0.975933 + 0.218072i \(0.0699768\pi\)
−0.703108 + 0.711083i \(0.748205\pi\)
\(948\) −10.2746 8.90296i −0.333702 0.289155i
\(949\) 23.6570 + 6.94634i 0.767940 + 0.225488i
\(950\) 35.8519 + 6.54514i 1.16319 + 0.212352i
\(951\) 10.8758 + 23.8146i 0.352670 + 0.772241i
\(952\) −3.40639 + 2.95165i −0.110402 + 0.0956637i
\(953\) −26.2613 + 40.8635i −0.850688 + 1.32370i 0.0939476 + 0.995577i \(0.470051\pi\)
−0.944636 + 0.328120i \(0.893585\pi\)
\(954\) −0.0905498 + 0.629787i −0.00293166 + 0.0203901i
\(955\) 35.1101 9.59288i 1.13614 0.310418i
\(956\) 24.8204 + 15.9511i 0.802748 + 0.515895i
\(957\) 15.9323 13.8054i 0.515017 0.446265i
\(958\) −12.8763 + 5.88040i −0.416014 + 0.189987i
\(959\) −0.878667 + 0.564685i −0.0283736 + 0.0182346i
\(960\) 2.21892 0.276371i 0.0716154 0.00891983i
\(961\) −19.8260 + 22.8804i −0.639549 + 0.738079i
\(962\) −1.83225 6.24009i −0.0590743 0.201188i
\(963\) −2.63967 1.20550i −0.0850621 0.0388465i
\(964\) −1.33639 9.29483i −0.0430424 0.299366i
\(965\) 36.8182 15.9810i 1.18522 0.514448i
\(966\) 1.98186 + 5.74223i 0.0637654 + 0.184753i
\(967\) 29.2072i 0.939240i 0.882869 + 0.469620i \(0.155609\pi\)
−0.882869 + 0.469620i \(0.844391\pi\)
\(968\) −5.62306 + 0.808473i −0.180732 + 0.0259853i
\(969\) 10.7747 23.5933i 0.346133 0.757926i
\(970\) −6.46518 7.75232i −0.207584 0.248912i
\(971\) 7.14846 8.24977i 0.229405 0.264748i −0.629364 0.777111i \(-0.716684\pi\)
0.858769 + 0.512363i \(0.171230\pi\)
\(972\) −0.281733 + 0.959493i −0.00903658 + 0.0307758i
\(973\) 3.25325 + 5.06215i 0.104294 + 0.162285i
\(974\) −3.08425 6.75357i −0.0988258 0.216398i
\(975\) −13.4616 0.508713i −0.431116 0.0162919i
\(976\) 10.6377 + 6.83644i 0.340505 + 0.218829i
\(977\) −40.1885 5.77823i −1.28574 0.184862i −0.534659 0.845068i \(-0.679560\pi\)
−0.751085 + 0.660206i \(0.770469\pi\)
\(978\) −20.3871 2.93123i −0.651908 0.0937302i
\(979\) 42.7122 + 27.4495i 1.36509 + 0.877289i
\(980\) 5.21832 10.8781i 0.166693 0.347487i
\(981\) −5.59834 12.2587i −0.178741 0.391389i
\(982\) −20.6243 32.0921i −0.658149 1.02410i
\(983\) −8.34748 + 28.4289i −0.266243 + 0.906741i 0.712504 + 0.701669i \(0.247561\pi\)
−0.978747 + 0.205073i \(0.934257\pi\)
\(984\) 5.06625 5.84677i 0.161506 0.186388i
\(985\) 22.8849 19.0852i 0.729172 0.608106i
\(986\) −7.63016 + 16.7077i −0.242994 + 0.532082i
\(987\) 13.2986 1.91205i 0.423299 0.0608612i
\(988\) 19.6380i 0.624769i
\(989\) 46.4648 + 18.6482i 1.47749 + 0.592978i
\(990\) −8.37747 + 3.63626i −0.266253 + 0.115568i
\(991\) −4.25030 29.5615i −0.135015 0.939051i −0.938881 0.344241i \(-0.888136\pi\)
0.803866 0.594810i \(-0.202773\pi\)
\(992\) −7.12046 3.25180i −0.226075 0.103245i
\(993\) 2.73105 + 9.30109i 0.0866672 + 0.295161i
\(994\) −3.40446 + 3.92896i −0.107983 + 0.124619i
\(995\) −3.00587 24.1335i −0.0952924 0.765083i
\(996\) −3.83095 + 2.46200i −0.121388 + 0.0780115i
\(997\) 2.10480 0.961228i 0.0666596 0.0304424i −0.381806 0.924242i \(-0.624698\pi\)
0.448466 + 0.893800i \(0.351971\pi\)
\(998\) 14.5724 12.6271i 0.461282 0.399703i
\(999\) −2.03067 1.30503i −0.0642476 0.0412894i
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 690.2.r.a.49.12 yes 120
5.4 even 2 inner 690.2.r.a.49.3 120
23.8 even 11 inner 690.2.r.a.169.3 yes 120
115.54 even 22 inner 690.2.r.a.169.12 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.r.a.49.3 120 5.4 even 2 inner
690.2.r.a.49.12 yes 120 1.1 even 1 trivial
690.2.r.a.169.3 yes 120 23.8 even 11 inner
690.2.r.a.169.12 yes 120 115.54 even 22 inner