Properties

Label 690.2.m.e.331.2
Level $690$
Weight $2$
Character 690.331
Analytic conductor $5.510$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,2,Mod(31,690)]
 
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, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\), 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: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + 2670 x^{12} - 12826 x^{11} + 18393 x^{10} - 2728 x^{9} - 12654 x^{8} - 6818 x^{7} + \cdots + 1849 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 331.2
Root \(0.121066 + 0.842031i\) of defining polynomial
Character \(\chi\) \(=\) 690.331
Dual form 690.2.m.e.271.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(1.22647 - 2.68560i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.959493 - 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.841254 + 0.540641i) q^{6} +(1.22647 - 2.68560i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-0.332740 - 0.0977012i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-2.39074 - 5.23499i) q^{13} +(0.420170 - 2.92235i) q^{14} +(0.654861 - 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(3.39875 + 2.18424i) q^{17} +(0.142315 + 0.989821i) q^{18} +(0.353661 - 0.227284i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(2.83281 - 0.831787i) q^{21} -0.346787 q^{22} +(4.27109 - 2.18123i) q^{23} +1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-3.76876 - 4.34939i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.420170 - 2.92235i) q^{28} +(3.21798 + 2.06807i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-6.38358 + 7.36705i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.144061 - 0.315449i) q^{33} +(3.87645 + 1.13823i) q^{34} +(-2.83281 - 0.831787i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.02158 + 7.10522i) q^{37} +(0.275302 - 0.317716i) q^{38} +(2.39074 - 5.23499i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.0904755 + 0.629271i) q^{41} +(2.48372 - 1.59619i) q^{42} +(-0.142051 - 0.163936i) q^{43} +(-0.332740 + 0.0977012i) q^{44} +1.00000 q^{45} +(3.48356 - 3.29618i) q^{46} +5.27458 q^{47} +(0.959493 - 0.281733i) q^{48} +(-1.12417 - 1.29737i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.574966 + 3.99898i) q^{51} +(-4.84147 - 3.11142i) q^{52} +(1.84214 - 4.03373i) q^{53} +(-0.654861 + 0.755750i) q^{54} +(-0.0493529 + 0.343257i) q^{55} +(-1.22647 - 2.68560i) q^{56} +(0.403369 + 0.118440i) q^{57} +(3.67027 + 1.07769i) q^{58} +(-3.02769 - 6.62972i) q^{59} +(0.142315 - 0.989821i) q^{60} +(-0.141270 + 0.163034i) q^{61} +(-4.04947 + 8.86709i) q^{62} +(2.48372 + 1.59619i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-4.84147 + 3.11142i) q^{65} +(-0.227097 - 0.262084i) q^{66} +(-1.64642 + 0.483433i) q^{67} +4.04010 q^{68} +(4.44543 + 1.79948i) q^{69} -2.95240 q^{70} +(3.18335 - 0.934716i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-3.03256 + 1.94891i) q^{73} +(1.02158 + 7.10522i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(0.174640 - 0.382407i) q^{76} +(-0.670482 + 0.773777i) q^{77} +(0.819031 - 5.69648i) q^{78} +(4.64031 + 10.1609i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.264097 + 0.578291i) q^{82} +(-2.32955 + 16.2024i) q^{83} +(1.93341 - 2.23127i) q^{84} +(1.67832 - 3.67500i) q^{85} +(-0.182483 - 0.117275i) q^{86} +(0.544385 + 3.78628i) q^{87} +(-0.291736 + 0.187487i) q^{88} +(-0.189805 - 0.219047i) q^{89} +(0.959493 - 0.281733i) q^{90} -16.9912 q^{91} +(2.41381 - 4.14409i) q^{92} -9.74800 q^{93} +(5.06092 - 1.48602i) q^{94} +(-0.275302 - 0.317716i) q^{95} +(0.841254 - 0.540641i) q^{96} +(1.46491 + 10.1887i) q^{97} +(-1.44415 - 0.928098i) q^{98} +(0.144061 - 0.315449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.959493 0.281733i 0.678464 0.199215i
\(3\) 0.654861 + 0.755750i 0.378084 + 0.436332i
\(4\) 0.841254 0.540641i 0.420627 0.270320i
\(5\) −0.142315 0.989821i −0.0636451 0.442662i
\(6\) 0.841254 + 0.540641i 0.343440 + 0.220716i
\(7\) 1.22647 2.68560i 0.463562 1.01506i −0.523099 0.852272i \(-0.675224\pi\)
0.986661 0.162788i \(-0.0520487\pi\)
\(8\) 0.654861 0.755750i 0.231528 0.267198i
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) −0.415415 0.909632i −0.131366 0.287651i
\(11\) −0.332740 0.0977012i −0.100325 0.0294580i 0.231185 0.972910i \(-0.425740\pi\)
−0.331510 + 0.943452i \(0.607558\pi\)
\(12\) 0.959493 + 0.281733i 0.276982 + 0.0813292i
\(13\) −2.39074 5.23499i −0.663072 1.45192i −0.879632 0.475655i \(-0.842211\pi\)
0.216560 0.976269i \(-0.430516\pi\)
\(14\) 0.420170 2.92235i 0.112295 0.781030i
\(15\) 0.654861 0.755750i 0.169084 0.195134i
\(16\) 0.415415 0.909632i 0.103854 0.227408i
\(17\) 3.39875 + 2.18424i 0.824317 + 0.529756i 0.883467 0.468493i \(-0.155203\pi\)
−0.0591502 + 0.998249i \(0.518839\pi\)
\(18\) 0.142315 + 0.989821i 0.0335439 + 0.233303i
\(19\) 0.353661 0.227284i 0.0811354 0.0521426i −0.499444 0.866346i \(-0.666462\pi\)
0.580580 + 0.814204i \(0.302826\pi\)
\(20\) −0.654861 0.755750i −0.146431 0.168991i
\(21\) 2.83281 0.831787i 0.618169 0.181511i
\(22\) −0.346787 −0.0739353
\(23\) 4.27109 2.18123i 0.890585 0.454817i
\(24\) 1.00000 0.204124
\(25\) −0.959493 + 0.281733i −0.191899 + 0.0563465i
\(26\) −3.76876 4.34939i −0.739116 0.852985i
\(27\) −0.841254 + 0.540641i −0.161899 + 0.104046i
\(28\) −0.420170 2.92235i −0.0794047 0.552272i
\(29\) 3.21798 + 2.06807i 0.597563 + 0.384031i 0.804175 0.594392i \(-0.202607\pi\)
−0.206612 + 0.978423i \(0.566244\pi\)
\(30\) 0.415415 0.909632i 0.0758441 0.166075i
\(31\) −6.38358 + 7.36705i −1.14653 + 1.32316i −0.207929 + 0.978144i \(0.566672\pi\)
−0.938596 + 0.345017i \(0.887873\pi\)
\(32\) 0.142315 0.989821i 0.0251579 0.174977i
\(33\) −0.144061 0.315449i −0.0250777 0.0549126i
\(34\) 3.87645 + 1.13823i 0.664805 + 0.195204i
\(35\) −2.83281 0.831787i −0.478832 0.140598i
\(36\) 0.415415 + 0.909632i 0.0692358 + 0.151605i
\(37\) −1.02158 + 7.10522i −0.167946 + 1.16809i 0.715175 + 0.698946i \(0.246347\pi\)
−0.883121 + 0.469146i \(0.844562\pi\)
\(38\) 0.275302 0.317716i 0.0446599 0.0515403i
\(39\) 2.39074 5.23499i 0.382825 0.838269i
\(40\) −0.841254 0.540641i −0.133014 0.0854828i
\(41\) 0.0904755 + 0.629271i 0.0141299 + 0.0982756i 0.995666 0.0930016i \(-0.0296462\pi\)
−0.981536 + 0.191277i \(0.938737\pi\)
\(42\) 2.48372 1.59619i 0.383246 0.246297i
\(43\) −0.142051 0.163936i −0.0216626 0.0250000i 0.744815 0.667271i \(-0.232538\pi\)
−0.766478 + 0.642271i \(0.777992\pi\)
\(44\) −0.332740 + 0.0977012i −0.0501624 + 0.0147290i
\(45\) 1.00000 0.149071
\(46\) 3.48356 3.29618i 0.513623 0.485995i
\(47\) 5.27458 0.769377 0.384688 0.923046i \(-0.374309\pi\)
0.384688 + 0.923046i \(0.374309\pi\)
\(48\) 0.959493 0.281733i 0.138491 0.0406646i
\(49\) −1.12417 1.29737i −0.160596 0.185338i
\(50\) −0.841254 + 0.540641i −0.118971 + 0.0764582i
\(51\) 0.574966 + 3.99898i 0.0805113 + 0.559969i
\(52\) −4.84147 3.11142i −0.671391 0.431477i
\(53\) 1.84214 4.03373i 0.253038 0.554075i −0.739899 0.672717i \(-0.765127\pi\)
0.992937 + 0.118642i \(0.0378542\pi\)
\(54\) −0.654861 + 0.755750i −0.0891153 + 0.102844i
\(55\) −0.0493529 + 0.343257i −0.00665475 + 0.0462848i
\(56\) −1.22647 2.68560i −0.163894 0.358878i
\(57\) 0.403369 + 0.118440i 0.0534275 + 0.0156877i
\(58\) 3.67027 + 1.07769i 0.481930 + 0.141507i
\(59\) −3.02769 6.62972i −0.394172 0.863116i −0.997828 0.0658715i \(-0.979017\pi\)
0.603656 0.797245i \(-0.293710\pi\)
\(60\) 0.142315 0.989821i 0.0183728 0.127785i
\(61\) −0.141270 + 0.163034i −0.0180877 + 0.0208744i −0.764721 0.644361i \(-0.777123\pi\)
0.746634 + 0.665235i \(0.231669\pi\)
\(62\) −4.04947 + 8.86709i −0.514283 + 1.12612i
\(63\) 2.48372 + 1.59619i 0.312919 + 0.201101i
\(64\) −0.142315 0.989821i −0.0177894 0.123728i
\(65\) −4.84147 + 3.11142i −0.600510 + 0.385924i
\(66\) −0.227097 0.262084i −0.0279537 0.0322603i
\(67\) −1.64642 + 0.483433i −0.201142 + 0.0590607i −0.380752 0.924677i \(-0.624335\pi\)
0.179609 + 0.983738i \(0.442517\pi\)
\(68\) 4.04010 0.489934
\(69\) 4.44543 + 1.79948i 0.535167 + 0.216632i
\(70\) −2.95240 −0.352879
\(71\) 3.18335 0.934716i 0.377794 0.110930i −0.0873217 0.996180i \(-0.527831\pi\)
0.465116 + 0.885250i \(0.346013\pi\)
\(72\) 0.654861 + 0.755750i 0.0771761 + 0.0890659i
\(73\) −3.03256 + 1.94891i −0.354934 + 0.228103i −0.705941 0.708270i \(-0.749476\pi\)
0.351007 + 0.936373i \(0.385839\pi\)
\(74\) 1.02158 + 7.10522i 0.118756 + 0.825965i
\(75\) −0.841254 0.540641i −0.0971396 0.0624278i
\(76\) 0.174640 0.382407i 0.0200325 0.0438651i
\(77\) −0.670482 + 0.773777i −0.0764085 + 0.0881801i
\(78\) 0.819031 5.69648i 0.0927370 0.645000i
\(79\) 4.64031 + 10.1609i 0.522076 + 1.14319i 0.968648 + 0.248439i \(0.0799175\pi\)
−0.446572 + 0.894748i \(0.647355\pi\)
\(80\) −0.959493 0.281733i −0.107275 0.0314987i
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0.264097 + 0.578291i 0.0291646 + 0.0638615i
\(83\) −2.32955 + 16.2024i −0.255701 + 1.77844i 0.306930 + 0.951732i \(0.400698\pi\)
−0.562631 + 0.826708i \(0.690211\pi\)
\(84\) 1.93341 2.23127i 0.210952 0.243452i
\(85\) 1.67832 3.67500i 0.182039 0.398610i
\(86\) −0.182483 0.117275i −0.0196777 0.0126461i
\(87\) 0.544385 + 3.78628i 0.0583642 + 0.405932i
\(88\) −0.291736 + 0.187487i −0.0310991 + 0.0199862i
\(89\) −0.189805 0.219047i −0.0201193 0.0232189i 0.745601 0.666393i \(-0.232163\pi\)
−0.765720 + 0.643174i \(0.777617\pi\)
\(90\) 0.959493 0.281733i 0.101139 0.0296972i
\(91\) −16.9912 −1.78117
\(92\) 2.41381 4.14409i 0.251657 0.432052i
\(93\) −9.74800 −1.01082
\(94\) 5.06092 1.48602i 0.521995 0.153271i
\(95\) −0.275302 0.317716i −0.0282454 0.0325969i
\(96\) 0.841254 0.540641i 0.0858601 0.0551789i
\(97\) 1.46491 + 10.1887i 0.148739 + 1.03450i 0.918287 + 0.395915i \(0.129572\pi\)
−0.769548 + 0.638589i \(0.779518\pi\)
\(98\) −1.44415 0.928098i −0.145881 0.0937520i
\(99\) 0.144061 0.315449i 0.0144786 0.0317038i
\(100\) −0.654861 + 0.755750i −0.0654861 + 0.0755750i
\(101\) 2.53633 17.6406i 0.252374 1.75530i −0.331498 0.943456i \(-0.607554\pi\)
0.583872 0.811846i \(-0.301537\pi\)
\(102\) 1.67832 + 3.67500i 0.166178 + 0.363879i
\(103\) −9.41007 2.76305i −0.927202 0.272251i −0.216937 0.976186i \(-0.569607\pi\)
−0.710265 + 0.703935i \(0.751425\pi\)
\(104\) −5.52194 1.62139i −0.541471 0.158990i
\(105\) −1.22647 2.68560i −0.119691 0.262087i
\(106\) 0.631089 4.38932i 0.0612968 0.426329i
\(107\) −4.58998 + 5.29712i −0.443730 + 0.512092i −0.932919 0.360086i \(-0.882747\pi\)
0.489189 + 0.872178i \(0.337293\pi\)
\(108\) −0.415415 + 0.909632i −0.0399733 + 0.0875294i
\(109\) −4.02790 2.58857i −0.385803 0.247940i 0.333334 0.942809i \(-0.391826\pi\)
−0.719137 + 0.694868i \(0.755463\pi\)
\(110\) 0.0493529 + 0.343257i 0.00470562 + 0.0327283i
\(111\) −6.03876 + 3.88088i −0.573174 + 0.368356i
\(112\) −1.93341 2.23127i −0.182690 0.210836i
\(113\) −12.0928 + 3.55076i −1.13759 + 0.334028i −0.795688 0.605707i \(-0.792891\pi\)
−0.341906 + 0.939734i \(0.611072\pi\)
\(114\) 0.420398 0.0393739
\(115\) −2.76687 3.91720i −0.258012 0.365281i
\(116\) 3.82522 0.355162
\(117\) 5.52194 1.62139i 0.510504 0.149897i
\(118\) −4.77286 5.50817i −0.439377 0.507068i
\(119\) 10.0345 6.44875i 0.919857 0.591156i
\(120\) −0.142315 0.989821i −0.0129915 0.0903579i
\(121\) −9.15262 5.88203i −0.832056 0.534730i
\(122\) −0.0896154 + 0.196230i −0.00811340 + 0.0177659i
\(123\) −0.416322 + 0.480461i −0.0375385 + 0.0433217i
\(124\) −1.38729 + 9.64878i −0.124582 + 0.866486i
\(125\) 0.415415 + 0.909632i 0.0371558 + 0.0813600i
\(126\) 2.83281 + 0.831787i 0.252366 + 0.0741015i
\(127\) 16.8686 + 4.95306i 1.49684 + 0.439513i 0.924718 0.380653i \(-0.124301\pi\)
0.572126 + 0.820166i \(0.306119\pi\)
\(128\) −0.415415 0.909632i −0.0367178 0.0804009i
\(129\) 0.0308707 0.214711i 0.00271802 0.0189042i
\(130\) −3.76876 + 4.34939i −0.330543 + 0.381466i
\(131\) −5.41130 + 11.8491i −0.472787 + 1.03526i 0.511597 + 0.859226i \(0.329054\pi\)
−0.984384 + 0.176034i \(0.943673\pi\)
\(132\) −0.291736 0.187487i −0.0253923 0.0163187i
\(133\) −0.176639 1.22855i −0.0153165 0.106529i
\(134\) −1.44353 + 0.927701i −0.124702 + 0.0801412i
\(135\) 0.654861 + 0.755750i 0.0563614 + 0.0650446i
\(136\) 3.87645 1.13823i 0.332402 0.0976022i
\(137\) 11.3999 0.973959 0.486979 0.873413i \(-0.338099\pi\)
0.486979 + 0.873413i \(0.338099\pi\)
\(138\) 4.77233 + 0.474163i 0.406248 + 0.0403635i
\(139\) −18.5308 −1.57176 −0.785880 0.618379i \(-0.787790\pi\)
−0.785880 + 0.618379i \(0.787790\pi\)
\(140\) −2.83281 + 0.831787i −0.239416 + 0.0702988i
\(141\) 3.45412 + 3.98626i 0.290889 + 0.335704i
\(142\) 2.79106 1.79371i 0.234221 0.150525i
\(143\) 0.284029 + 1.97547i 0.0237517 + 0.165197i
\(144\) 0.841254 + 0.540641i 0.0701045 + 0.0450534i
\(145\) 1.58905 3.47954i 0.131964 0.288960i
\(146\) −2.36065 + 2.72434i −0.195369 + 0.225468i
\(147\) 0.244307 1.69919i 0.0201501 0.140147i
\(148\) 2.98197 + 6.52960i 0.245116 + 0.536730i
\(149\) 7.06196 + 2.07358i 0.578539 + 0.169874i 0.557893 0.829913i \(-0.311610\pi\)
0.0206452 + 0.999787i \(0.493428\pi\)
\(150\) −0.959493 0.281733i −0.0783423 0.0230034i
\(151\) −2.86104 6.26481i −0.232828 0.509823i 0.756770 0.653681i \(-0.226776\pi\)
−0.989598 + 0.143858i \(0.954049\pi\)
\(152\) 0.0598289 0.416119i 0.00485276 0.0337517i
\(153\) −2.64570 + 3.05330i −0.213892 + 0.246845i
\(154\) −0.425324 + 0.931330i −0.0342736 + 0.0750487i
\(155\) 8.20054 + 5.27017i 0.658683 + 0.423310i
\(156\) −0.819031 5.69648i −0.0655749 0.456084i
\(157\) 3.97870 2.55696i 0.317535 0.204067i −0.372158 0.928170i \(-0.621382\pi\)
0.689693 + 0.724102i \(0.257746\pi\)
\(158\) 7.31499 + 8.44195i 0.581950 + 0.671606i
\(159\) 4.25483 1.24933i 0.337430 0.0990785i
\(160\) −1.00000 −0.0790569
\(161\) −0.619522 14.1457i −0.0488252 1.11483i
\(162\) −1.00000 −0.0785674
\(163\) −11.8711 + 3.48568i −0.929819 + 0.273020i −0.711361 0.702827i \(-0.751921\pi\)
−0.218458 + 0.975846i \(0.570103\pi\)
\(164\) 0.416322 + 0.480461i 0.0325093 + 0.0375177i
\(165\) −0.291736 + 0.187487i −0.0227116 + 0.0145959i
\(166\) 2.32955 + 16.2024i 0.180808 + 1.25755i
\(167\) 6.69283 + 4.30122i 0.517907 + 0.332838i 0.773343 0.633987i \(-0.218583\pi\)
−0.255437 + 0.966826i \(0.582219\pi\)
\(168\) 1.22647 2.68560i 0.0946243 0.207198i
\(169\) −13.1763 + 15.2062i −1.01356 + 1.16971i
\(170\) 0.574966 3.99898i 0.0440979 0.306707i
\(171\) 0.174640 + 0.382407i 0.0133550 + 0.0292434i
\(172\) −0.208132 0.0611130i −0.0158699 0.00465982i
\(173\) 0.590686 + 0.173441i 0.0449090 + 0.0131865i 0.304110 0.952637i \(-0.401641\pi\)
−0.259201 + 0.965823i \(0.583459\pi\)
\(174\) 1.58905 + 3.47954i 0.120466 + 0.263783i
\(175\) −0.420170 + 2.92235i −0.0317619 + 0.220909i
\(176\) −0.227097 + 0.262084i −0.0171181 + 0.0197553i
\(177\) 3.02769 6.62972i 0.227575 0.498320i
\(178\) −0.243829 0.156700i −0.0182758 0.0117451i
\(179\) −0.483864 3.36535i −0.0361657 0.251538i 0.963716 0.266930i \(-0.0860094\pi\)
−0.999882 + 0.0153923i \(0.995100\pi\)
\(180\) 0.841254 0.540641i 0.0627033 0.0402970i
\(181\) −4.40472 5.08332i −0.327401 0.377840i 0.568056 0.822990i \(-0.307696\pi\)
−0.895456 + 0.445150i \(0.853150\pi\)
\(182\) −16.3030 + 4.78699i −1.20846 + 0.354835i
\(183\) −0.215725 −0.0159468
\(184\) 1.14851 4.65628i 0.0846694 0.343265i
\(185\) 7.17829 0.527758
\(186\) −9.35314 + 2.74633i −0.685805 + 0.201371i
\(187\) −0.917495 1.05885i −0.0670939 0.0774305i
\(188\) 4.43726 2.85165i 0.323621 0.207978i
\(189\) 0.420170 + 2.92235i 0.0305629 + 0.212570i
\(190\) −0.353661 0.227284i −0.0256573 0.0164889i
\(191\) −7.54901 + 16.5300i −0.546227 + 1.19607i 0.412294 + 0.911051i \(0.364728\pi\)
−0.958521 + 0.285020i \(0.908000\pi\)
\(192\) 0.654861 0.755750i 0.0472605 0.0545415i
\(193\) 2.63740 18.3435i 0.189844 1.32040i −0.642563 0.766233i \(-0.722129\pi\)
0.832408 0.554164i \(-0.186962\pi\)
\(194\) 4.27606 + 9.36325i 0.307003 + 0.672243i
\(195\) −5.52194 1.62139i −0.395434 0.116110i
\(196\) −1.64713 0.483640i −0.117652 0.0345457i
\(197\) −3.27278 7.16639i −0.233176 0.510584i 0.756485 0.654011i \(-0.226915\pi\)
−0.989661 + 0.143427i \(0.954188\pi\)
\(198\) 0.0493529 0.343257i 0.00350736 0.0243942i
\(199\) −12.4117 + 14.3239i −0.879844 + 1.01539i 0.119900 + 0.992786i \(0.461742\pi\)
−0.999744 + 0.0226081i \(0.992803\pi\)
\(200\) −0.415415 + 0.909632i −0.0293743 + 0.0643207i
\(201\) −1.44353 0.927701i −0.101819 0.0654350i
\(202\) −2.53633 17.6406i −0.178456 1.24119i
\(203\) 9.50075 6.10576i 0.666822 0.428540i
\(204\) 2.64570 + 3.05330i 0.185236 + 0.213774i
\(205\) 0.609990 0.179109i 0.0426035 0.0125095i
\(206\) −9.80734 −0.683310
\(207\) 1.55118 + 4.53804i 0.107815 + 0.315416i
\(208\) −5.75506 −0.399042
\(209\) −0.139883 + 0.0410734i −0.00967592 + 0.00284111i
\(210\) −1.93341 2.23127i −0.133418 0.153973i
\(211\) 10.5747 6.79596i 0.727993 0.467853i −0.123416 0.992355i \(-0.539385\pi\)
0.851409 + 0.524502i \(0.175748\pi\)
\(212\) −0.631089 4.38932i −0.0433434 0.301460i
\(213\) 2.79106 + 1.79371i 0.191240 + 0.122903i
\(214\) −2.91168 + 6.37569i −0.199038 + 0.435833i
\(215\) −0.142051 + 0.163936i −0.00968783 + 0.0111803i
\(216\) −0.142315 + 0.989821i −0.00968330 + 0.0673488i
\(217\) 11.9556 + 26.1792i 0.811602 + 1.77716i
\(218\) −4.59403 1.34893i −0.311147 0.0913609i
\(219\) −3.45879 1.01559i −0.233724 0.0686274i
\(220\) 0.144061 + 0.315449i 0.00971256 + 0.0212675i
\(221\) 3.30896 23.0144i 0.222585 1.54811i
\(222\) −4.70078 + 5.42499i −0.315496 + 0.364101i
\(223\) 8.74038 19.1388i 0.585299 1.28163i −0.352943 0.935645i \(-0.614819\pi\)
0.938242 0.345981i \(-0.112454\pi\)
\(224\) −2.48372 1.59619i −0.165950 0.106650i
\(225\) −0.142315 0.989821i −0.00948766 0.0659881i
\(226\) −10.6026 + 6.81386i −0.705273 + 0.453251i
\(227\) 14.5093 + 16.7446i 0.963017 + 1.11138i 0.993725 + 0.111852i \(0.0356784\pi\)
−0.0307079 + 0.999528i \(0.509776\pi\)
\(228\) 0.403369 0.118440i 0.0267138 0.00784386i
\(229\) 19.9430 1.31787 0.658936 0.752199i \(-0.271007\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(230\) −3.75839 2.97901i −0.247821 0.196430i
\(231\) −1.02385 −0.0673646
\(232\) 3.67027 1.07769i 0.240965 0.0707537i
\(233\) 9.97082 + 11.5069i 0.653210 + 0.753845i 0.981652 0.190679i \(-0.0610691\pi\)
−0.328442 + 0.944524i \(0.606524\pi\)
\(234\) 4.84147 3.11142i 0.316497 0.203400i
\(235\) −0.750651 5.22089i −0.0489671 0.340574i
\(236\) −6.13136 3.94038i −0.399117 0.256497i
\(237\) −4.64031 + 10.1609i −0.301421 + 0.660019i
\(238\) 7.81117 9.01457i 0.506323 0.584328i
\(239\) −2.92470 + 20.3417i −0.189183 + 1.31580i 0.644946 + 0.764228i \(0.276880\pi\)
−0.834129 + 0.551569i \(0.814029\pi\)
\(240\) −0.415415 0.909632i −0.0268149 0.0587165i
\(241\) −21.3434 6.26697i −1.37485 0.403691i −0.490874 0.871231i \(-0.663322\pi\)
−0.883972 + 0.467539i \(0.845141\pi\)
\(242\) −10.4390 3.06518i −0.671046 0.197037i
\(243\) −0.415415 0.909632i −0.0266489 0.0583529i
\(244\) −0.0307009 + 0.213529i −0.00196542 + 0.0136698i
\(245\) −1.12417 + 1.29737i −0.0718209 + 0.0828857i
\(246\) −0.264097 + 0.578291i −0.0168382 + 0.0368705i
\(247\) −2.03534 1.30804i −0.129506 0.0832283i
\(248\) 1.38729 + 9.64878i 0.0880927 + 0.612698i
\(249\) −13.7705 + 8.84974i −0.872667 + 0.560829i
\(250\) 0.654861 + 0.755750i 0.0414170 + 0.0477978i
\(251\) 13.7477 4.03668i 0.867746 0.254793i 0.182590 0.983189i \(-0.441552\pi\)
0.685156 + 0.728396i \(0.259734\pi\)
\(252\) 2.95240 0.185984
\(253\) −1.63427 + 0.308490i −0.102746 + 0.0193946i
\(254\) 17.5807 1.10311
\(255\) 3.87645 1.13823i 0.242752 0.0712786i
\(256\) −0.654861 0.755750i −0.0409288 0.0472343i
\(257\) 16.3367 10.4990i 1.01906 0.654909i 0.0793362 0.996848i \(-0.474720\pi\)
0.939722 + 0.341939i \(0.111084\pi\)
\(258\) −0.0308707 0.214711i −0.00192193 0.0133673i
\(259\) 17.8288 + 11.4579i 1.10783 + 0.711959i
\(260\) −2.39074 + 5.23499i −0.148267 + 0.324660i
\(261\) −2.50498 + 2.89090i −0.155055 + 0.178943i
\(262\) −1.85383 + 12.8937i −0.114530 + 0.796572i
\(263\) 9.42067 + 20.6284i 0.580904 + 1.27200i 0.940785 + 0.339004i \(0.110090\pi\)
−0.359881 + 0.932998i \(0.617183\pi\)
\(264\) −0.332740 0.0977012i −0.0204787 0.00601309i
\(265\) −4.25483 1.24933i −0.261372 0.0767458i
\(266\) −0.515606 1.12902i −0.0316138 0.0692246i
\(267\) 0.0412486 0.286890i 0.00252437 0.0175574i
\(268\) −1.12369 + 1.29681i −0.0686406 + 0.0792154i
\(269\) 12.4780 27.3231i 0.760798 1.66592i 0.0148703 0.999889i \(-0.495266\pi\)
0.745928 0.666027i \(-0.232006\pi\)
\(270\) 0.841254 + 0.540641i 0.0511971 + 0.0329024i
\(271\) 0.822521 + 5.72076i 0.0499646 + 0.347511i 0.999434 + 0.0336507i \(0.0107134\pi\)
−0.949469 + 0.313861i \(0.898378\pi\)
\(272\) 3.39875 2.18424i 0.206079 0.132439i
\(273\) −11.1269 12.8411i −0.673430 0.777180i
\(274\) 10.9381 3.21172i 0.660796 0.194027i
\(275\) 0.346787 0.0209120
\(276\) 4.71261 0.889565i 0.283666 0.0535455i
\(277\) 4.35921 0.261919 0.130960 0.991388i \(-0.458194\pi\)
0.130960 + 0.991388i \(0.458194\pi\)
\(278\) −17.7801 + 5.22072i −1.06638 + 0.313118i
\(279\) −6.38358 7.36705i −0.382175 0.441054i
\(280\) −2.48372 + 1.59619i −0.148430 + 0.0953905i
\(281\) −2.82007 19.6140i −0.168231 1.17007i −0.882538 0.470240i \(-0.844167\pi\)
0.714307 0.699832i \(-0.246742\pi\)
\(282\) 4.43726 + 2.85165i 0.264235 + 0.169814i
\(283\) −2.99166 + 6.55083i −0.177836 + 0.389406i −0.977468 0.211084i \(-0.932301\pi\)
0.799632 + 0.600490i \(0.205028\pi\)
\(284\) 2.17266 2.50738i 0.128924 0.148786i
\(285\) 0.0598289 0.416119i 0.00354396 0.0246488i
\(286\) 0.829078 + 1.81543i 0.0490244 + 0.107348i
\(287\) 1.80093 + 0.528802i 0.106306 + 0.0312142i
\(288\) 0.959493 + 0.281733i 0.0565387 + 0.0166013i
\(289\) −0.281488 0.616373i −0.0165581 0.0362572i
\(290\) 0.544385 3.78628i 0.0319674 0.222338i
\(291\) −6.74078 + 7.77927i −0.395151 + 0.456029i
\(292\) −1.49749 + 3.27905i −0.0876342 + 0.191892i
\(293\) 9.03805 + 5.80840i 0.528009 + 0.339330i 0.777333 0.629090i \(-0.216572\pi\)
−0.249324 + 0.968420i \(0.580209\pi\)
\(294\) −0.244307 1.69919i −0.0142482 0.0990987i
\(295\) −6.13136 + 3.94038i −0.356981 + 0.229418i
\(296\) 4.70078 + 5.42499i 0.273227 + 0.315321i
\(297\) 0.332740 0.0977012i 0.0193075 0.00566920i
\(298\) 7.36010 0.426359
\(299\) −21.6298 17.1444i −1.25088 0.991486i
\(300\) −1.00000 −0.0577350
\(301\) −0.614488 + 0.180430i −0.0354185 + 0.0103998i
\(302\) −4.51015 5.20499i −0.259530 0.299514i
\(303\) 14.9928 9.63528i 0.861313 0.553532i
\(304\) −0.0598289 0.416119i −0.00343142 0.0238661i
\(305\) 0.181479 + 0.116630i 0.0103915 + 0.00667820i
\(306\) −1.67832 + 3.67500i −0.0959430 + 0.210086i
\(307\) 6.63438 7.65648i 0.378644 0.436979i −0.534156 0.845386i \(-0.679370\pi\)
0.912800 + 0.408408i \(0.133916\pi\)
\(308\) −0.145710 + 1.01343i −0.00830258 + 0.0577457i
\(309\) −4.07412 8.92107i −0.231768 0.507502i
\(310\) 9.35314 + 2.74633i 0.531223 + 0.155981i
\(311\) −18.6805 5.48508i −1.05927 0.311030i −0.294714 0.955586i \(-0.595224\pi\)
−0.764558 + 0.644555i \(0.777043\pi\)
\(312\) −2.39074 5.23499i −0.135349 0.296373i
\(313\) 4.69396 32.6472i 0.265319 1.84533i −0.225719 0.974193i \(-0.572473\pi\)
0.491037 0.871139i \(-0.336618\pi\)
\(314\) 3.09716 3.57431i 0.174783 0.201710i
\(315\) 1.22647 2.68560i 0.0691038 0.151316i
\(316\) 9.39706 + 6.03912i 0.528626 + 0.339727i
\(317\) −1.89175 13.1574i −0.106252 0.738996i −0.971395 0.237471i \(-0.923682\pi\)
0.865143 0.501525i \(-0.167227\pi\)
\(318\) 3.73051 2.39745i 0.209196 0.134442i
\(319\) −0.868696 1.00253i −0.0486376 0.0561308i
\(320\) −0.959493 + 0.281733i −0.0536373 + 0.0157493i
\(321\) −7.00909 −0.391209
\(322\) −4.57972 13.3981i −0.255218 0.746648i
\(323\) 1.69845 0.0945042
\(324\) −0.959493 + 0.281733i −0.0533052 + 0.0156518i
\(325\) 3.76876 + 4.34939i 0.209053 + 0.241261i
\(326\) −10.4082 + 6.68897i −0.576459 + 0.370468i
\(327\) −0.681399 4.73924i −0.0376815 0.262080i
\(328\) 0.534820 + 0.343708i 0.0295305 + 0.0189781i
\(329\) 6.46912 14.1654i 0.356654 0.780964i
\(330\) −0.227097 + 0.262084i −0.0125013 + 0.0144273i
\(331\) 3.98739 27.7329i 0.219167 1.52434i −0.521959 0.852971i \(-0.674799\pi\)
0.741125 0.671367i \(-0.234292\pi\)
\(332\) 6.79992 + 14.8897i 0.373194 + 0.817181i
\(333\) −6.88752 2.02236i −0.377434 0.110824i
\(334\) 7.63351 + 2.24140i 0.417687 + 0.122644i
\(335\) 0.712823 + 1.56086i 0.0389457 + 0.0852791i
\(336\) 0.420170 2.92235i 0.0229222 0.159427i
\(337\) 4.87231 5.62295i 0.265412 0.306302i −0.607363 0.794424i \(-0.707773\pi\)
0.872775 + 0.488123i \(0.162318\pi\)
\(338\) −8.35846 + 18.3025i −0.454640 + 0.995523i
\(339\) −10.6026 6.81386i −0.575853 0.370078i
\(340\) −0.574966 3.99898i −0.0311819 0.216875i
\(341\) 2.84384 1.82763i 0.154003 0.0989715i
\(342\) 0.275302 + 0.317716i 0.0148866 + 0.0171801i
\(343\) 14.9667 4.39461i 0.808124 0.237287i
\(344\) −0.216919 −0.0116955
\(345\) 1.14851 4.65628i 0.0618338 0.250686i
\(346\) 0.615623 0.0330961
\(347\) 19.9581 5.86022i 1.07141 0.314593i 0.301970 0.953317i \(-0.402356\pi\)
0.769436 + 0.638724i \(0.220538\pi\)
\(348\) 2.50498 + 2.89090i 0.134281 + 0.154969i
\(349\) −24.8810 + 15.9901i −1.33185 + 0.855928i −0.996287 0.0860896i \(-0.972563\pi\)
−0.335563 + 0.942018i \(0.608926\pi\)
\(350\) 0.420170 + 2.92235i 0.0224590 + 0.156206i
\(351\) 4.84147 + 3.11142i 0.258418 + 0.166075i
\(352\) −0.144061 + 0.315449i −0.00767845 + 0.0168135i
\(353\) −21.0906 + 24.3398i −1.12254 + 1.29548i −0.171921 + 0.985111i \(0.554997\pi\)
−0.950617 + 0.310367i \(0.899548\pi\)
\(354\) 1.03724 7.21417i 0.0551288 0.383429i
\(355\) −1.37824 3.01793i −0.0731494 0.160175i
\(356\) −0.278100 0.0816575i −0.0147393 0.00432784i
\(357\) 11.4448 + 3.36050i 0.605724 + 0.177857i
\(358\) −1.41239 3.09271i −0.0746473 0.163455i
\(359\) −0.967592 + 6.72975i −0.0510676 + 0.355183i 0.948226 + 0.317597i \(0.102876\pi\)
−0.999293 + 0.0375859i \(0.988033\pi\)
\(360\) 0.654861 0.755750i 0.0345142 0.0398315i
\(361\) −7.81947 + 17.1222i −0.411551 + 0.901171i
\(362\) −5.65844 3.63646i −0.297401 0.191128i
\(363\) −1.54835 10.7690i −0.0812672 0.565226i
\(364\) −14.2939 + 9.18616i −0.749206 + 0.481486i
\(365\) 2.36065 + 2.72434i 0.123562 + 0.142598i
\(366\) −0.206987 + 0.0607767i −0.0108194 + 0.00317685i
\(367\) −0.567641 −0.0296306 −0.0148153 0.999890i \(-0.504716\pi\)
−0.0148153 + 0.999890i \(0.504716\pi\)
\(368\) −0.209837 4.79124i −0.0109385 0.249761i
\(369\) −0.635742 −0.0330954
\(370\) 6.88752 2.02236i 0.358065 0.105137i
\(371\) −8.57363 9.89450i −0.445121 0.513697i
\(372\) −8.20054 + 5.27017i −0.425178 + 0.273245i
\(373\) −1.93369 13.4491i −0.100122 0.696367i −0.976622 0.214964i \(-0.931037\pi\)
0.876499 0.481403i \(-0.159873\pi\)
\(374\) −1.17864 0.757467i −0.0609461 0.0391677i
\(375\) −0.415415 + 0.909632i −0.0214519 + 0.0469732i
\(376\) 3.45412 3.98626i 0.178132 0.205576i
\(377\) 3.13297 21.7903i 0.161356 1.12226i
\(378\) 1.22647 + 2.68560i 0.0630829 + 0.138132i
\(379\) 11.0344 + 3.24000i 0.566801 + 0.166428i 0.552563 0.833471i \(-0.313650\pi\)
0.0142373 + 0.999899i \(0.495468\pi\)
\(380\) −0.403369 0.118440i −0.0206924 0.00607583i
\(381\) 7.30329 + 15.9920i 0.374159 + 0.819294i
\(382\) −2.58618 + 17.9873i −0.132320 + 0.920308i
\(383\) −12.0395 + 13.8944i −0.615191 + 0.709969i −0.974786 0.223140i \(-0.928369\pi\)
0.359595 + 0.933108i \(0.382915\pi\)
\(384\) 0.415415 0.909632i 0.0211991 0.0464195i
\(385\) 0.861321 + 0.553537i 0.0438970 + 0.0282109i
\(386\) −2.63740 18.3435i −0.134240 0.933661i
\(387\) 0.182483 0.117275i 0.00927616 0.00596142i
\(388\) 6.74078 + 7.77927i 0.342211 + 0.394933i
\(389\) −8.36837 + 2.45717i −0.424293 + 0.124584i −0.486906 0.873454i \(-0.661875\pi\)
0.0626132 + 0.998038i \(0.480057\pi\)
\(390\) −5.75506 −0.291419
\(391\) 19.2807 + 1.91567i 0.975067 + 0.0968794i
\(392\) −1.71666 −0.0867045
\(393\) −12.4986 + 3.66992i −0.630470 + 0.185123i
\(394\) −5.15921 5.95405i −0.259917 0.299961i
\(395\) 9.39706 6.03912i 0.472817 0.303861i
\(396\) −0.0493529 0.343257i −0.00248008 0.0172493i
\(397\) −12.1959 7.83784i −0.612095 0.393370i 0.197547 0.980293i \(-0.436703\pi\)
−0.809642 + 0.586924i \(0.800339\pi\)
\(398\) −7.87346 + 17.2405i −0.394661 + 0.864186i
\(399\) 0.812802 0.938023i 0.0406910 0.0469599i
\(400\) −0.142315 + 0.989821i −0.00711574 + 0.0494911i
\(401\) 2.31828 + 5.07632i 0.115769 + 0.253499i 0.958643 0.284613i \(-0.0918650\pi\)
−0.842873 + 0.538112i \(0.819138\pi\)
\(402\) −1.64642 0.483433i −0.0821160 0.0241114i
\(403\) 53.8279 + 15.8053i 2.68136 + 0.787318i
\(404\) −7.40351 16.2114i −0.368338 0.806549i
\(405\) −0.142315 + 0.989821i −0.00707168 + 0.0491846i
\(406\) 7.39571 8.53511i 0.367043 0.423590i
\(407\) 1.03411 2.26438i 0.0512588 0.112241i
\(408\) 3.39875 + 2.18424i 0.168263 + 0.108136i
\(409\) −5.16417 35.9176i −0.255352 1.77601i −0.564934 0.825136i \(-0.691098\pi\)
0.309582 0.950873i \(-0.399811\pi\)
\(410\) 0.534820 0.343708i 0.0264129 0.0169745i
\(411\) 7.46534 + 8.61547i 0.368238 + 0.424970i
\(412\) −9.41007 + 2.76305i −0.463601 + 0.136126i
\(413\) −21.5181 −1.05884
\(414\) 2.76687 + 3.91720i 0.135984 + 0.192520i
\(415\) 16.3690 0.803521
\(416\) −5.52194 + 1.62139i −0.270735 + 0.0794951i
\(417\) −12.1351 14.0046i −0.594257 0.685809i
\(418\) −0.122645 + 0.0788192i −0.00599877 + 0.00385517i
\(419\) −3.48059 24.2081i −0.170038 1.18264i −0.878799 0.477192i \(-0.841655\pi\)
0.708761 0.705449i \(-0.249255\pi\)
\(420\) −2.48372 1.59619i −0.121193 0.0778860i
\(421\) 10.5510 23.1034i 0.514222 1.12599i −0.457358 0.889282i \(-0.651204\pi\)
0.971581 0.236708i \(-0.0760684\pi\)
\(422\) 8.23172 9.49991i 0.400714 0.462449i
\(423\) −0.750651 + 5.22089i −0.0364979 + 0.253849i
\(424\) −1.84214 4.03373i −0.0894623 0.195895i
\(425\) −3.87645 1.13823i −0.188035 0.0552121i
\(426\) 3.18335 + 0.934716i 0.154234 + 0.0452871i
\(427\) 0.264580 + 0.579350i 0.0128039 + 0.0280367i
\(428\) −0.997498 + 6.93775i −0.0482159 + 0.335349i
\(429\) −1.30696 + 1.50831i −0.0631006 + 0.0728219i
\(430\) −0.0901112 + 0.197316i −0.00434555 + 0.00951542i
\(431\) −20.1669 12.9605i −0.971405 0.624284i −0.0442731 0.999019i \(-0.514097\pi\)
−0.927132 + 0.374735i \(0.877734\pi\)
\(432\) 0.142315 + 0.989821i 0.00684713 + 0.0476228i
\(433\) −18.2945 + 11.7572i −0.879178 + 0.565014i −0.900547 0.434758i \(-0.856834\pi\)
0.0213689 + 0.999772i \(0.493198\pi\)
\(434\) 18.8469 + 21.7505i 0.904680 + 1.04406i
\(435\) 3.67027 1.07769i 0.175976 0.0516712i
\(436\) −4.78797 −0.229302
\(437\) 1.01476 1.74217i 0.0485426 0.0833392i
\(438\) −3.60481 −0.172245
\(439\) 28.3812 8.33348i 1.35456 0.397735i 0.477719 0.878513i \(-0.341464\pi\)
0.876843 + 0.480778i \(0.159646\pi\)
\(440\) 0.227097 + 0.262084i 0.0108264 + 0.0124944i
\(441\) 1.44415 0.928098i 0.0687690 0.0441951i
\(442\) −3.30896 23.0144i −0.157391 1.09468i
\(443\) 26.6149 + 17.1043i 1.26451 + 0.812651i 0.988895 0.148617i \(-0.0474821\pi\)
0.275615 + 0.961268i \(0.411118\pi\)
\(444\) −2.98197 + 6.52960i −0.141518 + 0.309881i
\(445\) −0.189805 + 0.219047i −0.00899763 + 0.0103838i
\(446\) 2.99432 20.8260i 0.141785 0.986137i
\(447\) 3.05750 + 6.69498i 0.144615 + 0.316662i
\(448\) −2.83281 0.831787i −0.133838 0.0392982i
\(449\) 11.0865 + 3.25529i 0.523205 + 0.153627i 0.532661 0.846329i \(-0.321192\pi\)
−0.00945661 + 0.999955i \(0.503010\pi\)
\(450\) −0.415415 0.909632i −0.0195829 0.0428805i
\(451\) 0.0313757 0.218223i 0.00147742 0.0102757i
\(452\) −8.25341 + 9.52495i −0.388208 + 0.448016i
\(453\) 2.86104 6.26481i 0.134423 0.294346i
\(454\) 18.6391 + 11.9786i 0.874776 + 0.562184i
\(455\) 2.41811 + 16.8183i 0.113363 + 0.788454i
\(456\) 0.353661 0.227284i 0.0165617 0.0106436i
\(457\) 16.6005 + 19.1580i 0.776539 + 0.896173i 0.996854 0.0792552i \(-0.0252542\pi\)
−0.220316 + 0.975429i \(0.570709\pi\)
\(458\) 19.1352 5.61860i 0.894129 0.262540i
\(459\) −4.04010 −0.188576
\(460\) −4.44543 1.79948i −0.207269 0.0839011i
\(461\) −11.6638 −0.543237 −0.271619 0.962405i \(-0.587559\pi\)
−0.271619 + 0.962405i \(0.587559\pi\)
\(462\) −0.982381 + 0.288453i −0.0457045 + 0.0134200i
\(463\) 3.09152 + 3.56780i 0.143675 + 0.165810i 0.823026 0.568004i \(-0.192284\pi\)
−0.679351 + 0.733813i \(0.737739\pi\)
\(464\) 3.21798 2.06807i 0.149391 0.0960076i
\(465\) 1.38729 + 9.64878i 0.0643338 + 0.447451i
\(466\) 12.8088 + 8.23172i 0.593357 + 0.381327i
\(467\) 4.83077 10.5779i 0.223541 0.489488i −0.764318 0.644840i \(-0.776924\pi\)
0.987859 + 0.155352i \(0.0496513\pi\)
\(468\) 3.76876 4.34939i 0.174211 0.201050i
\(469\) −0.720982 + 5.01454i −0.0332919 + 0.231550i
\(470\) −2.19114 4.79793i −0.101070 0.221312i
\(471\) 4.53792 + 1.33245i 0.209096 + 0.0613962i
\(472\) −6.99313 2.05337i −0.321885 0.0945139i
\(473\) 0.0312494 + 0.0684267i 0.00143685 + 0.00314626i
\(474\) −1.58970 + 11.0566i −0.0730173 + 0.507847i
\(475\) −0.275302 + 0.317716i −0.0126317 + 0.0145778i
\(476\) 4.95506 10.8501i 0.227115 0.497312i
\(477\) 3.73051 + 2.39745i 0.170808 + 0.109772i
\(478\) 2.92470 + 20.3417i 0.133773 + 0.930409i
\(479\) −21.0079 + 13.5010i −0.959876 + 0.616875i −0.923964 0.382480i \(-0.875070\pi\)
−0.0359125 + 0.999355i \(0.511434\pi\)
\(480\) −0.654861 0.755750i −0.0298902 0.0344951i
\(481\) 39.6381 11.6388i 1.80734 0.530683i
\(482\) −22.2444 −1.01321
\(483\) 10.2849 9.73163i 0.467978 0.442805i
\(484\) −10.8797 −0.494534
\(485\) 9.87650 2.90000i 0.448469 0.131682i
\(486\) −0.654861 0.755750i −0.0297051 0.0342815i
\(487\) 12.8251 8.24216i 0.581159 0.373488i −0.216786 0.976219i \(-0.569557\pi\)
0.797944 + 0.602731i \(0.205921\pi\)
\(488\) 0.0307009 + 0.213529i 0.00138976 + 0.00966601i
\(489\) −10.4082 6.68897i −0.470677 0.302486i
\(490\) −0.713127 + 1.56153i −0.0322158 + 0.0705428i
\(491\) −19.6154 + 22.6374i −0.885230 + 1.02161i 0.114373 + 0.993438i \(0.463514\pi\)
−0.999603 + 0.0281721i \(0.991031\pi\)
\(492\) −0.0904755 + 0.629271i −0.00407895 + 0.0283697i
\(493\) 6.41993 + 14.0577i 0.289139 + 0.633126i
\(494\) −2.32141 0.681628i −0.104445 0.0306679i
\(495\) −0.332740 0.0977012i −0.0149555 0.00439134i
\(496\) 4.04947 + 8.86709i 0.181826 + 0.398144i
\(497\) 1.39402 9.69560i 0.0625302 0.434907i
\(498\) −10.7194 + 12.3708i −0.480348 + 0.554351i
\(499\) −0.526653 + 1.15321i −0.0235762 + 0.0516247i −0.921054 0.389435i \(-0.872670\pi\)
0.897478 + 0.441060i \(0.145397\pi\)
\(500\) 0.841254 + 0.540641i 0.0376220 + 0.0241782i
\(501\) 1.13223 + 7.87480i 0.0505841 + 0.351820i
\(502\) 12.0535 7.74634i 0.537976 0.345736i
\(503\) 8.11695 + 9.36746i 0.361917 + 0.417675i 0.907281 0.420525i \(-0.138154\pi\)
−0.545364 + 0.838199i \(0.683609\pi\)
\(504\) 2.83281 0.831787i 0.126183 0.0370507i
\(505\) −17.8220 −0.793067
\(506\) −1.48116 + 0.756421i −0.0658456 + 0.0336270i
\(507\) −20.1207 −0.893594
\(508\) 16.8686 4.95306i 0.748422 0.219757i
\(509\) −11.3842 13.1381i −0.504598 0.582337i 0.445110 0.895476i \(-0.353165\pi\)
−0.949707 + 0.313139i \(0.898619\pi\)
\(510\) 3.39875 2.18424i 0.150499 0.0967199i
\(511\) 1.51463 + 10.5345i 0.0670035 + 0.466020i
\(512\) −0.841254 0.540641i −0.0371785 0.0238932i
\(513\) −0.174640 + 0.382407i −0.00771053 + 0.0168837i
\(514\) 12.7171 14.6763i 0.560927 0.647344i
\(515\) −1.39573 + 9.70751i −0.0615032 + 0.427764i
\(516\) −0.0901112 0.197316i −0.00396693 0.00868635i
\(517\) −1.75506 0.515333i −0.0771876 0.0226643i
\(518\) 20.3347 + 5.97081i 0.893455 + 0.262342i
\(519\) 0.255739 + 0.559990i 0.0112257 + 0.0245809i
\(520\) −0.819031 + 5.69648i −0.0359169 + 0.249807i
\(521\) 7.77442 8.97216i 0.340604 0.393078i −0.559445 0.828868i \(-0.688986\pi\)
0.900048 + 0.435790i \(0.143531\pi\)
\(522\) −1.58905 + 3.47954i −0.0695509 + 0.152295i
\(523\) −26.2445 16.8663i −1.14759 0.737513i −0.178435 0.983952i \(-0.557103\pi\)
−0.969158 + 0.246438i \(0.920740\pi\)
\(524\) 1.85383 + 12.8937i 0.0809848 + 0.563262i
\(525\) −2.48372 + 1.59619i −0.108398 + 0.0696633i
\(526\) 14.8508 + 17.1387i 0.647524 + 0.747283i
\(527\) −37.7876 + 11.0954i −1.64605 + 0.483325i
\(528\) −0.346787 −0.0150920
\(529\) 13.4845 18.6325i 0.586283 0.810107i
\(530\) −4.43446 −0.192621
\(531\) 6.99313 2.05337i 0.303476 0.0891086i
\(532\) −0.812802 0.938023i −0.0352394 0.0406685i
\(533\) 3.07792 1.97806i 0.133320 0.0856793i
\(534\) −0.0412486 0.286890i −0.00178500 0.0124150i
\(535\) 5.89642 + 3.78940i 0.254925 + 0.163830i
\(536\) −0.712823 + 1.56086i −0.0307892 + 0.0674190i
\(537\) 2.22650 2.56952i 0.0960805 0.110883i
\(538\) 4.27478 29.7317i 0.184299 1.28183i
\(539\) 0.247303 + 0.541519i 0.0106521 + 0.0233249i
\(540\) 0.959493 + 0.281733i 0.0412900 + 0.0121238i
\(541\) 23.6122 + 6.93317i 1.01517 + 0.298080i 0.746666 0.665199i \(-0.231653\pi\)
0.268502 + 0.963279i \(0.413471\pi\)
\(542\) 2.40093 + 5.25730i 0.103129 + 0.225820i
\(543\) 0.957238 6.65774i 0.0410790 0.285711i
\(544\) 2.64570 3.05330i 0.113434 0.130909i
\(545\) −1.98900 + 4.35529i −0.0851992 + 0.186560i
\(546\) −14.2939 9.18616i −0.611724 0.393131i
\(547\) 5.33379 + 37.0973i 0.228056 + 1.58617i 0.706282 + 0.707930i \(0.250371\pi\)
−0.478226 + 0.878237i \(0.658720\pi\)
\(548\) 9.59020 6.16325i 0.409673 0.263281i
\(549\) −0.141270 0.163034i −0.00602925 0.00695812i
\(550\) 0.332740 0.0977012i 0.0141881 0.00416599i
\(551\) 1.60811 0.0685079
\(552\) 4.27109 2.18123i 0.181790 0.0928392i
\(553\) 32.9792 1.40242
\(554\) 4.18263 1.22813i 0.177703 0.0521783i
\(555\) 4.70078 + 5.42499i 0.199537 + 0.230278i
\(556\) −15.5891 + 10.0185i −0.661124 + 0.424879i
\(557\) −5.34586 37.1813i −0.226512 1.57542i −0.712637 0.701533i \(-0.752499\pi\)
0.486125 0.873889i \(-0.338410\pi\)
\(558\) −8.20054 5.27017i −0.347157 0.223104i
\(559\) −0.518596 + 1.13557i −0.0219343 + 0.0480293i
\(560\) −1.93341 + 2.23127i −0.0817015 + 0.0942886i
\(561\) 0.199391 1.38679i 0.00841828 0.0585505i
\(562\) −8.23173 18.0250i −0.347235 0.760338i
\(563\) −30.2456 8.88091i −1.27470 0.374286i −0.426754 0.904368i \(-0.640343\pi\)
−0.847947 + 0.530082i \(0.822161\pi\)
\(564\) 5.06092 + 1.48602i 0.213103 + 0.0625728i
\(565\) 5.23560 + 11.4644i 0.220264 + 0.482310i
\(566\) −1.02490 + 7.12832i −0.0430797 + 0.299626i
\(567\) −1.93341 + 2.23127i −0.0811956 + 0.0937047i
\(568\) 1.37824 3.01793i 0.0578297 0.126629i
\(569\) −1.13699 0.730700i −0.0476652 0.0306326i 0.516591 0.856232i \(-0.327201\pi\)
−0.564256 + 0.825600i \(0.690837\pi\)
\(570\) −0.0598289 0.416119i −0.00250595 0.0174293i
\(571\) −13.9278 + 8.95086i −0.582861 + 0.374582i −0.798594 0.601871i \(-0.794422\pi\)
0.215733 + 0.976452i \(0.430786\pi\)
\(572\) 1.30696 + 1.50831i 0.0546467 + 0.0630656i
\(573\) −17.4361 + 5.11971i −0.728404 + 0.213879i
\(574\) 1.87696 0.0783429
\(575\) −3.48356 + 3.29618i −0.145275 + 0.137460i
\(576\) 1.00000 0.0416667
\(577\) −36.6055 + 10.7484i −1.52391 + 0.447460i −0.933179 0.359411i \(-0.882978\pi\)
−0.590728 + 0.806870i \(0.701160\pi\)
\(578\) −0.443738 0.512101i −0.0184571 0.0213006i
\(579\) 15.5903 10.0192i 0.647909 0.416386i
\(580\) −0.544385 3.78628i −0.0226044 0.157217i
\(581\) 40.6559 + 26.1280i 1.68669 + 1.08397i
\(582\) −4.27606 + 9.36325i −0.177248 + 0.388119i
\(583\) −1.00705 + 1.16220i −0.0417079 + 0.0481335i
\(584\) −0.513018 + 3.56812i −0.0212288 + 0.147650i
\(585\) −2.39074 5.23499i −0.0988449 0.216440i
\(586\) 10.3084 + 3.02681i 0.425834 + 0.125036i
\(587\) −22.8381 6.70588i −0.942631 0.276781i −0.225915 0.974147i \(-0.572537\pi\)
−0.716716 + 0.697365i \(0.754355\pi\)
\(588\) −0.713127 1.56153i −0.0294089 0.0643964i
\(589\) −0.583212 + 4.05633i −0.0240308 + 0.167138i
\(590\) −4.77286 + 5.50817i −0.196495 + 0.226768i
\(591\) 3.27278 7.16639i 0.134624 0.294786i
\(592\) 6.03876 + 3.88088i 0.248191 + 0.159503i
\(593\) −0.0159378 0.110850i −0.000654485 0.00455204i 0.989492 0.144590i \(-0.0461865\pi\)
−0.990146 + 0.140038i \(0.955277\pi\)
\(594\) 0.291736 0.187487i 0.0119701 0.00769269i
\(595\) −7.81117 9.01457i −0.320227 0.369561i
\(596\) 7.06196 2.07358i 0.289269 0.0849371i
\(597\) −18.9532 −0.775704
\(598\) −25.5837 10.3561i −1.04620 0.423493i
\(599\) −25.9804 −1.06153 −0.530766 0.847519i \(-0.678096\pi\)
−0.530766 + 0.847519i \(0.678096\pi\)
\(600\) −0.959493 + 0.281733i −0.0391711 + 0.0115017i
\(601\) 1.89211 + 2.18361i 0.0771807 + 0.0890713i 0.793027 0.609187i \(-0.208504\pi\)
−0.715846 + 0.698258i \(0.753959\pi\)
\(602\) −0.538764 + 0.346243i −0.0219584 + 0.0141118i
\(603\) −0.244202 1.69846i −0.00994468 0.0691668i
\(604\) −5.79387 3.72350i −0.235749 0.151507i
\(605\) −4.51961 + 9.89656i −0.183748 + 0.402352i
\(606\) 11.6709 13.4689i 0.474098 0.547138i
\(607\) −0.261313 + 1.81747i −0.0106063 + 0.0737688i −0.994437 0.105332i \(-0.966410\pi\)
0.983831 + 0.179100i \(0.0573187\pi\)
\(608\) −0.174640 0.382407i −0.00708257 0.0155087i
\(609\) 10.8361 + 3.18176i 0.439101 + 0.128932i
\(610\) 0.206987 + 0.0607767i 0.00838064 + 0.00246078i
\(611\) −12.6102 27.6124i −0.510152 1.11708i
\(612\) −0.574966 + 3.99898i −0.0232416 + 0.161649i
\(613\) −21.1326 + 24.3883i −0.853538 + 0.985035i −0.999991 0.00418250i \(-0.998669\pi\)
0.146454 + 0.989218i \(0.453214\pi\)
\(614\) 4.20856 9.21546i 0.169844 0.371906i
\(615\) 0.534820 + 0.343708i 0.0215660 + 0.0138596i
\(616\) 0.145710 + 1.01343i 0.00587081 + 0.0408324i
\(617\) −30.7061 + 19.7336i −1.23618 + 0.794445i −0.984842 0.173454i \(-0.944507\pi\)
−0.251339 + 0.967899i \(0.580871\pi\)
\(618\) −6.42244 7.41189i −0.258348 0.298150i
\(619\) −30.1359 + 8.84871i −1.21127 + 0.355660i −0.824150 0.566372i \(-0.808347\pi\)
−0.387115 + 0.922031i \(0.626528\pi\)
\(620\) 9.74800 0.391489
\(621\) −2.41381 + 4.14409i −0.0968630 + 0.166297i
\(622\) −19.4691 −0.780639
\(623\) −0.821062 + 0.241086i −0.0328952 + 0.00965889i
\(624\) −3.76876 4.34939i −0.150871 0.174115i
\(625\) 0.841254 0.540641i 0.0336501 0.0216256i
\(626\) −4.69396 32.6472i −0.187609 1.30485i
\(627\) −0.122645 0.0788192i −0.00489797 0.00314774i
\(628\) 1.96470 4.30210i 0.0784002 0.171672i
\(629\) −18.9916 + 21.9175i −0.757245 + 0.873907i
\(630\) 0.420170 2.92235i 0.0167400 0.116429i
\(631\) 15.0632 + 32.9837i 0.599655 + 1.31306i 0.929429 + 0.369001i \(0.120300\pi\)
−0.329774 + 0.944060i \(0.606973\pi\)
\(632\) 10.7178 + 3.14704i 0.426332 + 0.125182i
\(633\) 12.0610 + 3.54143i 0.479382 + 0.140759i
\(634\) −5.52201 12.0915i −0.219307 0.480215i
\(635\) 2.50200 17.4018i 0.0992887 0.690568i
\(636\) 2.90395 3.35134i 0.115149 0.132889i
\(637\) −4.10409 + 8.98671i −0.162610 + 0.356066i
\(638\) −1.11595 0.717179i −0.0441810 0.0283934i
\(639\) 0.472164 + 3.28397i 0.0186785 + 0.129912i
\(640\) −0.841254 + 0.540641i −0.0332535 + 0.0213707i
\(641\) 14.8484 + 17.1359i 0.586476 + 0.676829i 0.968984 0.247123i \(-0.0794852\pi\)
−0.382508 + 0.923952i \(0.624940\pi\)
\(642\) −6.72517 + 1.97469i −0.265421 + 0.0779348i
\(643\) −25.0817 −0.989125 −0.494562 0.869142i \(-0.664672\pi\)
−0.494562 + 0.869142i \(0.664672\pi\)
\(644\) −8.16889 11.5651i −0.321899 0.455730i
\(645\) −0.216919 −0.00854116
\(646\) 1.62965 0.478508i 0.0641177 0.0188267i
\(647\) −23.6910 27.3409i −0.931391 1.07488i −0.997028 0.0770391i \(-0.975453\pi\)
0.0656369 0.997844i \(-0.479092\pi\)
\(648\) −0.841254 + 0.540641i −0.0330476 + 0.0212384i
\(649\) 0.359702 + 2.50178i 0.0141195 + 0.0982035i
\(650\) 4.84147 + 3.11142i 0.189898 + 0.122040i
\(651\) −11.9556 + 26.1792i −0.468579 + 1.02604i
\(652\) −8.10214 + 9.35036i −0.317304 + 0.366189i
\(653\) 1.19079 8.28216i 0.0465994 0.324106i −0.953166 0.302448i \(-0.902196\pi\)
0.999765 0.0216584i \(-0.00689461\pi\)
\(654\) −1.98900 4.35529i −0.0777759 0.170305i
\(655\) 12.4986 + 3.66992i 0.488360 + 0.143395i
\(656\) 0.609990 + 0.179109i 0.0238161 + 0.00699304i
\(657\) −1.49749 3.27905i −0.0584228 0.127928i
\(658\) 2.21622 15.4142i 0.0863974 0.600907i
\(659\) −21.2658 + 24.5420i −0.828397 + 0.956021i −0.999573 0.0292193i \(-0.990698\pi\)
0.171176 + 0.985240i \(0.445243\pi\)
\(660\) −0.144061 + 0.315449i −0.00560755 + 0.0122788i
\(661\) 22.9952 + 14.7781i 0.894408 + 0.574801i 0.905127 0.425141i \(-0.139776\pi\)
−0.0107188 + 0.999943i \(0.503412\pi\)
\(662\) −3.98739 27.7329i −0.154974 1.07787i
\(663\) 19.5600 12.5704i 0.759647 0.488196i
\(664\) 10.7194 + 12.3708i 0.415993 + 0.480082i
\(665\) −1.19091 + 0.349681i −0.0461813 + 0.0135601i
\(666\) −7.17829 −0.278153
\(667\) 18.2552 + 1.81378i 0.706844 + 0.0702297i
\(668\) 7.95578 0.307818
\(669\) 20.1878 5.92768i 0.780507 0.229177i
\(670\) 1.12369 + 1.29681i 0.0434121 + 0.0501002i
\(671\) 0.0629347 0.0404457i 0.00242957 0.00156139i
\(672\) −0.420170 2.92235i −0.0162084 0.112732i
\(673\) 9.79822 + 6.29693i 0.377694 + 0.242729i 0.715689 0.698419i \(-0.246113\pi\)
−0.337996 + 0.941148i \(0.609749\pi\)
\(674\) 3.09078 6.76787i 0.119052 0.260689i
\(675\) 0.654861 0.755750i 0.0252056 0.0290888i
\(676\) −2.86348 + 19.9159i −0.110134 + 0.765998i
\(677\) 6.39623 + 14.0058i 0.245827 + 0.538286i 0.991816 0.127672i \(-0.0407504\pi\)
−0.745990 + 0.665958i \(0.768023\pi\)
\(678\) −12.0928 3.55076i −0.464421 0.136366i
\(679\) 29.1594 + 8.56196i 1.11903 + 0.328578i
\(680\) −1.67832 3.67500i −0.0643605 0.140930i
\(681\) −3.15317 + 21.9308i −0.120830 + 0.840391i
\(682\) 2.21374 2.55480i 0.0847686 0.0978282i
\(683\) −1.96507 + 4.30290i −0.0751913 + 0.164646i −0.943495 0.331387i \(-0.892483\pi\)
0.868304 + 0.496033i \(0.165211\pi\)
\(684\) 0.353661 + 0.227284i 0.0135226 + 0.00869043i
\(685\) −1.62237 11.2839i −0.0619877 0.431134i
\(686\) 13.1223 8.43320i 0.501012 0.321981i
\(687\) 13.0599 + 15.0719i 0.498267 + 0.575030i
\(688\) −0.208132 + 0.0611130i −0.00793495 + 0.00232991i
\(689\) −25.5206 −0.972257
\(690\) −0.209837 4.79124i −0.00798835 0.182399i
\(691\) −23.9406 −0.910744 −0.455372 0.890301i \(-0.650494\pi\)
−0.455372 + 0.890301i \(0.650494\pi\)
\(692\) 0.590686 0.173441i 0.0224545 0.00659324i
\(693\) −0.670482 0.773777i −0.0254695 0.0293934i
\(694\) 17.4986 11.2457i 0.664239 0.426880i
\(695\) 2.63720 + 18.3422i 0.100035 + 0.695758i
\(696\) 3.21798 + 2.06807i 0.121977 + 0.0783899i
\(697\) −1.06698 + 2.33635i −0.0404146 + 0.0884956i
\(698\) −19.3682 + 22.3521i −0.733099 + 0.846041i
\(699\) −2.16687 + 15.0709i −0.0819584 + 0.570033i
\(700\) 1.22647 + 2.68560i 0.0463562 + 0.101506i
\(701\) 43.9725 + 12.9115i 1.66082 + 0.487660i 0.971547 0.236845i \(-0.0761135\pi\)
0.689269 + 0.724505i \(0.257932\pi\)
\(702\) 5.52194 + 1.62139i 0.208412 + 0.0611954i
\(703\) 1.25361 + 2.74503i 0.0472809 + 0.103531i
\(704\) −0.0493529 + 0.343257i −0.00186006 + 0.0129370i
\(705\) 3.45412 3.98626i 0.130090 0.150131i
\(706\) −13.3789 + 29.2958i −0.503523 + 1.10256i
\(707\) −44.2647 28.4472i −1.66475 1.06987i
\(708\) −1.03724 7.21417i −0.0389819 0.271125i
\(709\) −29.8328 + 19.1724i −1.12040 + 0.720035i −0.963534 0.267586i \(-0.913774\pi\)
−0.156862 + 0.987621i \(0.550138\pi\)
\(710\) −2.17266 2.50738i −0.0815385 0.0941004i
\(711\) −10.7178 + 3.14704i −0.401950 + 0.118023i
\(712\) −0.289841 −0.0108622
\(713\) −11.1957 + 45.3894i −0.419282 + 1.69985i
\(714\) 11.9280 0.446394
\(715\) 1.91494 0.562277i 0.0716146 0.0210280i
\(716\) −2.22650 2.56952i −0.0832082 0.0960273i
\(717\) −17.2885 + 11.1107i −0.645652 + 0.414935i
\(718\) 0.967592 + 6.72975i 0.0361102 + 0.251152i
\(719\) 14.9429 + 9.60324i 0.557277 + 0.358140i 0.788763 0.614698i \(-0.210722\pi\)
−0.231485 + 0.972838i \(0.574358\pi\)
\(720\) 0.415415 0.909632i 0.0154816 0.0339000i
\(721\) −18.9616 + 21.8829i −0.706167 + 0.814960i
\(722\) −2.67883 + 18.6317i −0.0996957 + 0.693399i
\(723\) −9.24066 20.2342i −0.343664 0.752519i
\(724\) −6.45374 1.89499i −0.239851 0.0704267i
\(725\) −3.67027 1.07769i −0.136310 0.0400243i
\(726\) −4.51961 9.89656i −0.167738 0.367296i
\(727\) −2.43279 + 16.9204i −0.0902272 + 0.627544i 0.893659 + 0.448747i \(0.148130\pi\)
−0.983886 + 0.178797i \(0.942779\pi\)
\(728\) −11.1269 + 12.8411i −0.412390 + 0.475924i
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 3.03256 + 1.94891i 0.112240 + 0.0721323i
\(731\) −0.124721 0.867452i −0.00461296 0.0320839i
\(732\) −0.181479 + 0.116630i −0.00670767 + 0.00431076i
\(733\) −12.3810 14.2884i −0.457302 0.527755i 0.479534 0.877523i \(-0.340806\pi\)
−0.936836 + 0.349768i \(0.886260\pi\)
\(734\) −0.544648 + 0.159923i −0.0201033 + 0.00590287i
\(735\) −1.71666 −0.0633200
\(736\) −1.55118 4.53804i −0.0571774 0.167274i
\(737\) 0.595062 0.0219194
\(738\) −0.609990 + 0.179109i −0.0224540 + 0.00659310i
\(739\) −7.48772 8.64129i −0.275440 0.317875i 0.601128 0.799153i \(-0.294718\pi\)
−0.876568 + 0.481278i \(0.840173\pi\)
\(740\) 6.03876 3.88088i 0.221989 0.142664i
\(741\) −0.344319 2.39479i −0.0126489 0.0879748i
\(742\) −11.0139 7.07823i −0.404334 0.259850i
\(743\) 8.33223 18.2450i 0.305680 0.669345i −0.692988 0.720949i \(-0.743706\pi\)
0.998668 + 0.0516039i \(0.0164333\pi\)
\(744\) −6.38358 + 7.36705i −0.234034 + 0.270089i
\(745\) 1.04745 7.28518i 0.0383757 0.266909i
\(746\) −5.64440 12.3595i −0.206656 0.452514i
\(747\) −15.7059 4.61167i −0.574649 0.168732i
\(748\) −1.34430 0.394722i −0.0491525 0.0144325i
\(749\) 8.59645 + 18.8236i 0.314107 + 0.687799i
\(750\) −0.142315 + 0.989821i −0.00519660 + 0.0361432i
\(751\) −1.57083 + 1.81284i −0.0573205 + 0.0661514i −0.783686 0.621158i \(-0.786663\pi\)
0.726365 + 0.687309i \(0.241208\pi\)
\(752\) 2.19114 4.79793i 0.0799027 0.174962i
\(753\) 12.0535 + 7.74634i 0.439255 + 0.282292i
\(754\) −3.13297 21.7903i −0.114096 0.793555i
\(755\) −5.79387 + 3.72350i −0.210861 + 0.135512i
\(756\) 1.93341 + 2.23127i 0.0703175 + 0.0811507i
\(757\) 42.3356 12.4308i 1.53871 0.451807i 0.601009 0.799243i \(-0.294766\pi\)
0.937704 + 0.347436i \(0.112948\pi\)
\(758\) 11.5003 0.417709
\(759\) −1.30336 1.03308i −0.0473090 0.0374985i
\(760\) −0.420398 −0.0152494
\(761\) 14.9885 4.40103i 0.543334 0.159537i 0.00146288 0.999999i \(-0.499534\pi\)
0.541871 + 0.840462i \(0.317716\pi\)
\(762\) 11.5129 + 13.2866i 0.417069 + 0.481323i
\(763\) −11.8920 + 7.64250i −0.430518 + 0.276677i
\(764\) 2.58618 + 17.9873i 0.0935646 + 0.650756i
\(765\) 3.39875 + 2.18424i 0.122882 + 0.0789714i
\(766\) −7.63735 + 16.7235i −0.275949 + 0.604244i
\(767\) −27.4681 + 31.6999i −0.991816 + 1.14462i
\(768\) 0.142315 0.989821i 0.00513534 0.0357171i
\(769\) 0.0990297 + 0.216845i 0.00357110 + 0.00781962i 0.911409 0.411501i \(-0.134995\pi\)
−0.907838 + 0.419321i \(0.862268\pi\)
\(770\) 0.982381 + 0.288453i 0.0354025 + 0.0103951i
\(771\) 18.6329 + 5.47111i 0.671048 + 0.197037i
\(772\) −7.69854 16.8575i −0.277077 0.606713i
\(773\) 6.14193 42.7180i 0.220910 1.53646i −0.513699 0.857970i \(-0.671725\pi\)
0.734609 0.678491i \(-0.237366\pi\)
\(774\) 0.142051 0.163936i 0.00510593 0.00589256i
\(775\) 4.04947 8.86709i 0.145461 0.318515i
\(776\) 8.65940 + 5.56506i 0.310854 + 0.199774i
\(777\) 3.01610 + 20.9775i 0.108202 + 0.752562i
\(778\) −7.33713 + 4.71528i −0.263049 + 0.169051i
\(779\) 0.175021 + 0.201985i 0.00627078 + 0.00723686i
\(780\) −5.52194 + 1.62139i −0.197717 + 0.0580550i
\(781\) −1.15055 −0.0411699
\(782\) 19.0394 3.59393i 0.680848 0.128519i
\(783\) −3.82522 −0.136702
\(784\) −1.64713 + 0.483640i −0.0588259 + 0.0172728i
\(785\) −3.09716 3.57431i −0.110542 0.127573i
\(786\) −10.9584 + 7.04252i −0.390872 + 0.251198i
\(787\) −7.41924 51.6019i −0.264467 1.83941i −0.498142 0.867096i \(-0.665984\pi\)
0.233674 0.972315i \(-0.424925\pi\)
\(788\) −6.62768 4.25935i −0.236101 0.151733i
\(789\) −9.42067 + 20.6284i −0.335385 + 0.734390i
\(790\) 7.31499 8.44195i 0.260256 0.300351i
\(791\) −5.29554 + 36.8313i −0.188288 + 1.30957i
\(792\) −0.144061 0.315449i −0.00511897 0.0112090i
\(793\) 1.19122 + 0.349774i 0.0423015 + 0.0124208i
\(794\) −13.9101 4.08436i −0.493650 0.144949i
\(795\) −1.84214 4.03373i −0.0653340 0.143062i
\(796\) −2.69733 + 18.7603i −0.0956042 + 0.664942i
\(797\) 14.7512 17.0238i 0.522513 0.603013i −0.431745 0.901996i \(-0.642102\pi\)
0.954258 + 0.298983i \(0.0966474\pi\)
\(798\) 0.515606 1.12902i 0.0182522 0.0399668i
\(799\) 17.9270 + 11.5210i 0.634211 + 0.407582i
\(800\) 0.142315 + 0.989821i 0.00503159 + 0.0349955i
\(801\) 0.243829 0.156700i 0.00861529 0.00553671i
\(802\) 3.65453 + 4.21756i 0.129046 + 0.148927i
\(803\) 1.19946 0.352195i 0.0423282 0.0124287i
\(804\) −1.71593 −0.0605161
\(805\) −13.9135 + 2.62635i −0.490386 + 0.0925667i
\(806\) 56.1004 1.97605
\(807\) 28.8208 8.46254i 1.01454 0.297895i
\(808\) −11.6709 13.4689i −0.410581 0.473836i
\(809\) 13.7830 8.85777i 0.484583 0.311423i −0.275441 0.961318i \(-0.588824\pi\)
0.760024 + 0.649896i \(0.225187\pi\)
\(810\) 0.142315 + 0.989821i 0.00500043 + 0.0347788i
\(811\) −43.5856 28.0107i −1.53050 0.983590i −0.989814 0.142363i \(-0.954530\pi\)
−0.540682 0.841227i \(-0.681834\pi\)
\(812\) 4.69152 10.2730i 0.164640 0.360511i
\(813\) −3.78482 + 4.36792i −0.132740 + 0.153190i
\(814\) 0.354270 2.46400i 0.0124171 0.0863631i
\(815\) 5.13964 + 11.2542i 0.180034 + 0.394219i
\(816\) 3.87645 + 1.13823i 0.135703 + 0.0398459i
\(817\) −0.0874982 0.0256918i −0.00306117 0.000898842i
\(818\) −15.0741 33.0077i −0.527054 1.15409i
\(819\) 2.41811 16.8183i 0.0844955 0.587679i
\(820\) 0.416322 0.480461i 0.0145386 0.0167784i
\(821\) −10.2203 + 22.3793i −0.356691 + 0.781044i 0.643191 + 0.765705i \(0.277610\pi\)
−0.999882 + 0.0153388i \(0.995117\pi\)
\(822\) 9.59020 + 6.16325i 0.334497 + 0.214968i
\(823\) −4.23751 29.4725i −0.147710 1.02735i −0.919955 0.392023i \(-0.871775\pi\)
0.772245 0.635325i \(-0.219134\pi\)
\(824\) −8.25046 + 5.30225i −0.287418 + 0.184713i
\(825\) 0.227097 + 0.262084i 0.00790651 + 0.00912460i
\(826\) −20.6465 + 6.06236i −0.718384 + 0.210937i
\(827\) 4.21601 0.146605 0.0733025 0.997310i \(-0.476646\pi\)
0.0733025 + 0.997310i \(0.476646\pi\)
\(828\) 3.75839 + 2.97901i 0.130613 + 0.103528i
\(829\) −49.4871 −1.71876 −0.859379 0.511339i \(-0.829150\pi\)
−0.859379 + 0.511339i \(0.829150\pi\)
\(830\) 15.7059 4.61167i 0.545160 0.160074i
\(831\) 2.85467 + 3.29447i 0.0990275 + 0.114284i
\(832\) −4.84147 + 3.11142i −0.167848 + 0.107869i
\(833\) −0.987022 6.86489i −0.0341983 0.237854i
\(834\) −15.5891 10.0185i −0.539806 0.346912i
\(835\) 3.30495 7.23683i 0.114373 0.250441i
\(836\) −0.0954712 + 0.110180i −0.00330194 + 0.00381064i
\(837\) 1.38729 9.64878i 0.0479516 0.333511i
\(838\) −10.1598 22.2469i −0.350965 0.768505i
\(839\) 4.68379 + 1.37528i 0.161702 + 0.0474801i 0.361582 0.932340i \(-0.382237\pi\)
−0.199879 + 0.979821i \(0.564055\pi\)
\(840\) −2.83281 0.831787i −0.0977411 0.0286994i
\(841\) −5.96857 13.0693i −0.205813 0.450667i
\(842\) 3.61460 25.1401i 0.124567 0.866385i
\(843\) 12.9765 14.9757i 0.446935 0.515790i
\(844\) 5.22185 11.4342i 0.179743 0.393583i
\(845\) 16.9266 + 10.8781i 0.582294 + 0.374218i
\(846\) 0.750651 + 5.22089i 0.0258079 + 0.179498i
\(847\) −27.0222 + 17.3661i −0.928493 + 0.596706i
\(848\) −2.90395 3.35134i −0.0997222 0.115086i
\(849\) −6.90991 + 2.02893i −0.237147 + 0.0696328i
\(850\) −4.04010 −0.138574
\(851\) 11.1349 + 32.5754i 0.381698 + 1.11667i
\(852\) 3.31774 0.113664
\(853\) −45.4393 + 13.3422i −1.55581 + 0.456828i −0.942831 0.333271i \(-0.891848\pi\)
−0.612980 + 0.790098i \(0.710030\pi\)
\(854\) 0.417085 + 0.481342i 0.0142724 + 0.0164712i
\(855\) 0.353661 0.227284i 0.0120950 0.00777296i
\(856\) 0.997498 + 6.93775i 0.0340938 + 0.237127i
\(857\) 18.2738 + 11.7438i 0.624220 + 0.401162i 0.814166 0.580633i \(-0.197195\pi\)
−0.189945 + 0.981795i \(0.560831\pi\)
\(858\) −0.829078 + 1.81543i −0.0283042 + 0.0619776i
\(859\) 10.0179 11.5612i 0.341806 0.394465i −0.558657 0.829399i \(-0.688683\pi\)
0.900462 + 0.434934i \(0.143228\pi\)
\(860\) −0.0308707 + 0.214711i −0.00105268 + 0.00732157i
\(861\) 0.779719 + 1.70735i 0.0265727 + 0.0581862i
\(862\) −23.0014 6.75381i −0.783430 0.230036i
\(863\) −7.09174 2.08232i −0.241406 0.0708831i 0.158792 0.987312i \(-0.449240\pi\)
−0.400197 + 0.916429i \(0.631058\pi\)
\(864\) 0.415415 + 0.909632i 0.0141327 + 0.0309463i
\(865\) 0.0876123 0.609357i 0.00297891 0.0207188i
\(866\) −14.2411 + 16.4351i −0.483932 + 0.558487i
\(867\) 0.281488 0.616373i 0.00955983 0.0209331i
\(868\) 24.2113 + 15.5596i 0.821784 + 0.528129i
\(869\) −0.551287 3.83429i −0.0187011 0.130069i
\(870\) 3.21798 2.06807i 0.109100 0.0701141i
\(871\) 6.46693 + 7.46324i 0.219124 + 0.252882i
\(872\) −4.59403 + 1.34893i −0.155573 + 0.0456804i
\(873\) −10.2935 −0.348381
\(874\) 0.482832 1.95749i 0.0163320 0.0662131i
\(875\) 2.95240 0.0998093
\(876\) −3.45879 + 1.01559i −0.116862 + 0.0343137i
\(877\) −14.1989 16.3864i −0.479462 0.553329i 0.463557 0.886067i \(-0.346573\pi\)
−0.943019 + 0.332738i \(0.892027\pi\)
\(878\) 24.8838 15.9918i 0.839786 0.539698i
\(879\) 1.52897 + 10.6342i 0.0515708 + 0.358683i
\(880\) 0.291736 + 0.187487i 0.00983441 + 0.00632019i
\(881\) 6.55607 14.3558i 0.220880 0.483659i −0.766458 0.642295i \(-0.777982\pi\)
0.987337 + 0.158636i \(0.0507097\pi\)
\(882\) 1.12417 1.29737i 0.0378529 0.0436846i
\(883\) 2.65271 18.4500i 0.0892709 0.620893i −0.895242 0.445580i \(-0.852997\pi\)
0.984513 0.175312i \(-0.0560935\pi\)
\(884\) −9.65882 21.1499i −0.324861 0.711347i
\(885\) −6.99313 2.05337i −0.235071 0.0690232i
\(886\) 30.3556 + 8.91321i 1.01982 + 0.299445i
\(887\) 10.1265 + 22.1740i 0.340015 + 0.744529i 0.999977 0.00677014i \(-0.00215502\pi\)
−0.659962 + 0.751299i \(0.729428\pi\)
\(888\) −1.02158 + 7.10522i −0.0342819 + 0.238436i
\(889\) 33.9907 39.2274i 1.14001 1.31564i
\(890\) −0.120404 + 0.263648i −0.00403596 + 0.00883751i
\(891\) 0.291736 + 0.187487i 0.00977352 + 0.00628106i
\(892\) −2.99432 20.8260i −0.100257 0.697304i
\(893\) 1.86542 1.19883i 0.0624237 0.0401173i
\(894\) 4.81984 + 5.56239i 0.161200 + 0.186034i
\(895\) −3.26224 + 0.957879i −0.109044 + 0.0320184i
\(896\) −2.95240 −0.0986327
\(897\) −1.20762 27.5739i −0.0403214 0.920665i
\(898\) 11.5545 0.385580
\(899\) −35.7778 + 10.5053i −1.19326 + 0.350371i
\(900\) −0.654861 0.755750i −0.0218287 0.0251917i
\(901\) 15.0716 9.68593i 0.502108 0.322685i
\(902\) −0.0313757 0.218223i −0.00104470 0.00726603i
\(903\) −0.538764 0.346243i −0.0179289 0.0115222i
\(904\) −5.23560 + 11.4644i −0.174134 + 0.381299i
\(905\) −4.40472 + 5.08332i −0.146418 + 0.168975i
\(906\) 0.980149 6.81709i 0.0325633 0.226483i
\(907\) 7.14268 + 15.6403i 0.237169 + 0.519327i 0.990367 0.138466i \(-0.0442173\pi\)
−0.753198 + 0.657793i \(0.771490\pi\)
\(908\) 21.2588 + 6.24216i 0.705500 + 0.207153i
\(909\) 17.1000 + 5.02103i 0.567173 + 0.166537i
\(910\) 7.05842 + 15.4558i 0.233984 + 0.512354i
\(911\) −0.0274808 + 0.191133i −0.000910481 + 0.00633253i −0.990272 0.139148i \(-0.955564\pi\)
0.989361 + 0.145480i \(0.0464728\pi\)
\(912\) 0.275302 0.317716i 0.00911616 0.0105206i
\(913\) 2.35812 5.16357i 0.0780425 0.170889i
\(914\) 21.3255 + 13.7051i 0.705385 + 0.453323i
\(915\) 0.0307009 + 0.213529i 0.00101494 + 0.00705906i
\(916\) 16.7771 10.7820i 0.554332 0.356248i
\(917\) 25.1851 + 29.0651i 0.831684 + 0.959815i
\(918\) −3.87645 + 1.13823i −0.127942 + 0.0375671i
\(919\) −20.4801 −0.675575 −0.337787 0.941222i \(-0.609678\pi\)
−0.337787 + 0.941222i \(0.609678\pi\)
\(920\) −4.77233 0.474163i −0.157339 0.0156327i
\(921\) 10.1310 0.333827
\(922\) −11.1913 + 3.28607i −0.368567 + 0.108221i
\(923\) −12.5038 14.4301i −0.411567 0.474974i
\(924\) −0.861321 + 0.553537i −0.0283354 + 0.0182100i
\(925\) −1.02158 7.10522i −0.0335892 0.233618i
\(926\) 3.97146 + 2.55230i 0.130510 + 0.0838738i
\(927\) 4.07412 8.92107i 0.133812 0.293006i
\(928\) 2.50498 2.89090i 0.0822301 0.0948986i
\(929\) −5.04088 + 35.0601i −0.165386 + 1.15028i 0.722886 + 0.690967i \(0.242815\pi\)
−0.888272 + 0.459318i \(0.848094\pi\)
\(930\) 4.04947 + 8.86709i 0.132787 + 0.290763i
\(931\) −0.692448 0.203321i −0.0226941 0.00666358i
\(932\) 14.6091 + 4.28962i 0.478537 + 0.140511i
\(933\) −8.08775 17.7097i −0.264781 0.579790i
\(934\) 1.65495 11.5104i 0.0541516 0.376633i
\(935\) −0.917495 + 1.05885i −0.0300053 + 0.0346280i
\(936\) 2.39074 5.23499i 0.0781438 0.171111i
\(937\) 40.0779 + 25.7565i 1.30929 + 0.841428i 0.994191 0.107631i \(-0.0343265\pi\)
0.315097 + 0.949059i \(0.397963\pi\)
\(938\) 0.720982 + 5.01454i 0.0235409 + 0.163731i
\(939\) 27.7470 17.8319i 0.905490 0.581923i
\(940\) −3.45412 3.98626i −0.112661 0.130018i
\(941\) 47.5162 13.9520i 1.54898 0.454822i 0.608186 0.793794i \(-0.291897\pi\)
0.940796 + 0.338972i \(0.110079\pi\)
\(942\) 4.72949 0.154095
\(943\) 1.75901 + 2.49033i 0.0572813 + 0.0810962i
\(944\) −7.28836 −0.237216
\(945\) 2.83281 0.831787i 0.0921512 0.0270580i
\(946\) 0.0492616 + 0.0568509i 0.00160163 + 0.00184838i
\(947\) 4.52598 2.90867i 0.147074 0.0945190i −0.465034 0.885293i \(-0.653958\pi\)
0.612109 + 0.790774i \(0.290322\pi\)
\(948\) 1.58970 + 11.0566i 0.0516310 + 0.359102i
\(949\) 17.4526 + 11.2161i 0.566535 + 0.364090i
\(950\) −0.174640 + 0.382407i −0.00566606 + 0.0124069i
\(951\) 8.70490 10.0460i 0.282276 0.325763i
\(952\) 1.69753 11.8066i 0.0550172 0.382653i
\(953\) 1.02160 + 2.23698i 0.0330927 + 0.0724630i 0.925457 0.378854i \(-0.123682\pi\)
−0.892364 + 0.451317i \(0.850954\pi\)
\(954\) 4.25483 + 1.24933i 0.137755 + 0.0404486i
\(955\) 17.4361 + 5.11971i 0.564220 + 0.165670i
\(956\) 8.53715 + 18.6938i 0.276111 + 0.604599i
\(957\) 0.188786 1.31303i 0.00610257 0.0424443i
\(958\) −16.3533 + 18.8727i −0.528351 + 0.609749i
\(959\) 13.9816 30.6155i 0.451491 0.988627i
\(960\) −0.841254 0.540641i −0.0271513 0.0174491i
\(961\) −9.11150 63.3719i −0.293919 2.04425i
\(962\) 34.7534 22.3347i 1.12050 0.720099i
\(963\) −4.58998 5.29712i −0.147910 0.170697i
\(964\) −21.3434 + 6.26697i −0.687423 + 0.201846i
\(965\) −18.5322 −0.596572
\(966\) 7.12654 12.2350i 0.229293 0.393655i
\(967\) −15.7924 −0.507848 −0.253924 0.967224i \(-0.581721\pi\)
−0.253924 + 0.967224i \(0.581721\pi\)
\(968\) −10.4390 + 3.06518i −0.335523 + 0.0985185i
\(969\) 1.11225 + 1.28360i 0.0357305 + 0.0412352i
\(970\) 8.65940 5.56506i 0.278037 0.178683i
\(971\) 0.298918 + 2.07902i 0.00959274 + 0.0667190i 0.994056 0.108875i \(-0.0347247\pi\)
−0.984463 + 0.175593i \(0.943816\pi\)
\(972\) −0.841254 0.540641i −0.0269832 0.0173411i
\(973\) −22.7275 + 49.7662i −0.728609 + 1.59543i
\(974\) 9.98346 11.5215i 0.319891 0.369174i
\(975\) −0.819031 + 5.69648i −0.0262300 + 0.182434i
\(976\) 0.0896154 + 0.196230i 0.00286852 + 0.00628118i
\(977\) −42.5005 12.4793i −1.35971 0.399247i −0.481050 0.876693i \(-0.659745\pi\)
−0.878661 + 0.477446i \(0.841563\pi\)
\(978\) −11.8711 3.48568i −0.379597 0.111460i
\(979\) 0.0417546 + 0.0914298i 0.00133448 + 0.00292211i
\(980\) −0.244307 + 1.69919i −0.00780408 + 0.0542786i
\(981\) 3.13545 3.61851i 0.100107 0.115530i
\(982\) −12.4431 + 27.2467i −0.397077 + 0.869477i
\(983\) 41.4232 + 26.6211i 1.32120 + 0.849081i 0.995348 0.0963417i \(-0.0307142\pi\)
0.325847 + 0.945422i \(0.394351\pi\)
\(984\) 0.0904755 + 0.629271i 0.00288425 + 0.0200604i
\(985\) −6.62768 + 4.25935i −0.211175 + 0.135714i
\(986\) 10.1204 + 11.6795i 0.322299 + 0.371952i
\(987\) 14.9419 4.38733i 0.475605 0.139650i
\(988\) −2.41942 −0.0769719
\(989\) −0.964297 0.390340i −0.0306629 0.0124121i
\(990\) −0.346787 −0.0110216
\(991\) 26.3034 7.72338i 0.835555 0.245341i 0.164154 0.986435i \(-0.447511\pi\)
0.671402 + 0.741094i \(0.265693\pi\)
\(992\) 6.38358 + 7.36705i 0.202679 + 0.233904i
\(993\) 23.5703 15.1477i 0.747981 0.480698i
\(994\) −1.39402 9.69560i −0.0442155 0.307526i
\(995\) 15.9445 + 10.2469i 0.505474 + 0.324848i
\(996\) −6.79992 + 14.8897i −0.215464 + 0.471800i
\(997\) −35.3607 + 40.8084i −1.11988 + 1.29242i −0.168059 + 0.985777i \(0.553750\pi\)
−0.951826 + 0.306639i \(0.900796\pi\)
\(998\) −0.180423 + 1.25487i −0.00571120 + 0.0397222i
\(999\) −2.98197 6.52960i −0.0943453 0.206587i
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.m.e.331.2 yes 20
23.18 even 11 inner 690.2.m.e.271.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.e.271.2 20 23.18 even 11 inner
690.2.m.e.331.2 yes 20 1.1 even 1 trivial