Properties

Label 690.2.m.e.301.2
Level $690$
Weight $2$
Character 690.301
Analytic conductor $5.510$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 301.2
Root \(-2.21104 - 0.649220i\) of defining polynomial
Character \(\chi\) \(=\) 690.301
Dual form 690.2.m.e.541.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.988122 - 1.14035i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(0.988122 - 1.14035i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.654861 + 0.755750i) q^{10} +(-3.77903 + 2.42863i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(1.59204 + 1.83732i) q^{13} +(-1.44778 + 0.425107i) q^{14} +(0.142315 - 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.823348 + 1.80288i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-0.110643 - 0.242274i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(1.26937 + 0.815775i) q^{21} +4.49214 q^{22} +(-0.877569 + 4.71486i) q^{23} +1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.345984 - 2.40637i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(1.44778 + 0.425107i) q^{28} +(-1.31308 + 2.87525i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(0.838056 - 5.82881i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.94172 - 3.39493i) q^{33} +(1.66735 - 1.07154i) q^{34} +(-1.26937 + 0.815775i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-11.2307 + 3.29764i) q^{37} +(-0.0379046 + 0.263632i) q^{38} +(-1.59204 + 1.83732i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(7.39839 + 2.17236i) q^{41} +(-0.626821 - 1.37255i) q^{42} +(1.74154 + 12.1127i) q^{43} +(-3.77903 - 2.42863i) q^{44} +1.00000 q^{45} +(3.28730 - 3.49194i) q^{46} -9.15991 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.672183 + 4.67513i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-1.90170 - 0.558391i) q^{51} +(-1.00992 + 2.21142i) q^{52} +(-8.83527 + 10.1964i) q^{53} +(-0.142315 + 0.989821i) q^{54} +(4.31017 - 1.26558i) q^{55} +(-0.988122 - 1.14035i) q^{56} +(0.224062 - 0.143996i) q^{57} +(2.65911 - 1.70891i) q^{58} +(-9.60937 - 11.0898i) q^{59} +(0.959493 - 0.281733i) q^{60} +(0.873883 - 6.07799i) q^{61} +(-3.85631 + 4.45042i) q^{62} +(-0.626821 + 1.37255i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.00992 - 2.21142i) q^{65} +(0.639298 + 4.44641i) q^{66} +(0.869412 + 0.558737i) q^{67} -1.98199 q^{68} +(-4.79176 - 0.197643i) q^{69} +1.50890 q^{70} +(5.47877 + 3.52099i) q^{71} +(0.142315 + 0.989821i) q^{72} +(-0.679674 - 1.48828i) q^{73} +(11.2307 + 3.29764i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(0.174418 - 0.201289i) q^{76} +(-0.964639 + 6.70921i) q^{77} +(2.33264 - 0.684925i) q^{78} +(5.79056 + 6.68266i) q^{79} +(0.841254 - 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-5.04946 - 5.82738i) q^{82} +(7.15379 - 2.10054i) q^{83} +(-0.214739 + 1.49355i) q^{84} +(1.29793 - 1.49789i) q^{85} +(5.08354 - 11.1314i) q^{86} +(-3.03285 - 0.890526i) q^{87} +(1.86610 + 4.08619i) q^{88} +(0.948091 + 6.59412i) q^{89} +(-0.841254 - 0.540641i) q^{90} +3.66832 q^{91} +(-4.65334 + 1.16036i) q^{92} +5.88874 q^{93} +(7.70580 + 4.95222i) q^{94} +(0.0379046 + 0.263632i) q^{95} +(0.415415 + 0.909632i) q^{96} +(11.4555 + 3.36363i) q^{97} +(1.96209 - 4.29638i) q^{98} +(2.94172 - 3.39493i) 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841254 0.540641i −0.594856 0.382291i
\(3\) 0.142315 + 0.989821i 0.0821655 + 0.571474i
\(4\) 0.415415 + 0.909632i 0.207708 + 0.454816i
\(5\) −0.959493 0.281733i −0.429098 0.125995i
\(6\) 0.415415 0.909632i 0.169592 0.371356i
\(7\) 0.988122 1.14035i 0.373475 0.431013i −0.537634 0.843178i \(-0.680682\pi\)
0.911109 + 0.412165i \(0.135227\pi\)
\(8\) 0.142315 0.989821i 0.0503159 0.349955i
\(9\) −0.959493 + 0.281733i −0.319831 + 0.0939109i
\(10\) 0.654861 + 0.755750i 0.207085 + 0.238989i
\(11\) −3.77903 + 2.42863i −1.13942 + 0.732260i −0.967505 0.252852i \(-0.918631\pi\)
−0.171914 + 0.985112i \(0.554995\pi\)
\(12\) −0.841254 + 0.540641i −0.242849 + 0.156070i
\(13\) 1.59204 + 1.83732i 0.441553 + 0.509580i 0.932282 0.361733i \(-0.117815\pi\)
−0.490729 + 0.871313i \(0.663269\pi\)
\(14\) −1.44778 + 0.425107i −0.386936 + 0.113615i
\(15\) 0.142315 0.989821i 0.0367455 0.255571i
\(16\) −0.654861 + 0.755750i −0.163715 + 0.188937i
\(17\) −0.823348 + 1.80288i −0.199691 + 0.437263i −0.982813 0.184606i \(-0.940899\pi\)
0.783121 + 0.621869i \(0.213626\pi\)
\(18\) 0.959493 + 0.281733i 0.226155 + 0.0664050i
\(19\) −0.110643 0.242274i −0.0253832 0.0555815i 0.896516 0.443012i \(-0.146090\pi\)
−0.921899 + 0.387430i \(0.873363\pi\)
\(20\) −0.142315 0.989821i −0.0318226 0.221331i
\(21\) 1.26937 + 0.815775i 0.276999 + 0.178017i
\(22\) 4.49214 0.957727
\(23\) −0.877569 + 4.71486i −0.182986 + 0.983116i
\(24\) 1.00000 0.204124
\(25\) 0.841254 + 0.540641i 0.168251 + 0.108128i
\(26\) −0.345984 2.40637i −0.0678530 0.471928i
\(27\) −0.415415 0.909632i −0.0799467 0.175059i
\(28\) 1.44778 + 0.425107i 0.273605 + 0.0803377i
\(29\) −1.31308 + 2.87525i −0.243833 + 0.533920i −0.991493 0.130162i \(-0.958450\pi\)
0.747660 + 0.664082i \(0.231178\pi\)
\(30\) −0.654861 + 0.755750i −0.119561 + 0.137980i
\(31\) 0.838056 5.82881i 0.150519 1.04688i −0.764833 0.644229i \(-0.777178\pi\)
0.915352 0.402655i \(-0.131913\pi\)
\(32\) 0.959493 0.281733i 0.169616 0.0498038i
\(33\) −2.94172 3.39493i −0.512088 0.590981i
\(34\) 1.66735 1.07154i 0.285949 0.183768i
\(35\) −1.26937 + 0.815775i −0.214563 + 0.137891i
\(36\) −0.654861 0.755750i −0.109143 0.125958i
\(37\) −11.2307 + 3.29764i −1.84632 + 0.542129i −0.846367 + 0.532600i \(0.821215\pi\)
−0.999955 + 0.00952929i \(0.996967\pi\)
\(38\) −0.0379046 + 0.263632i −0.00614894 + 0.0427668i
\(39\) −1.59204 + 1.83732i −0.254931 + 0.294206i
\(40\) −0.415415 + 0.909632i −0.0656829 + 0.143825i
\(41\) 7.39839 + 2.17236i 1.15543 + 0.339266i 0.802657 0.596441i \(-0.203419\pi\)
0.352778 + 0.935707i \(0.385237\pi\)
\(42\) −0.626821 1.37255i −0.0967206 0.211789i
\(43\) 1.74154 + 12.1127i 0.265583 + 1.84717i 0.488794 + 0.872399i \(0.337437\pi\)
−0.223212 + 0.974770i \(0.571654\pi\)
\(44\) −3.77903 2.42863i −0.569710 0.366130i
\(45\) 1.00000 0.149071
\(46\) 3.28730 3.49194i 0.484686 0.514858i
\(47\) −9.15991 −1.33611 −0.668055 0.744112i \(-0.732873\pi\)
−0.668055 + 0.744112i \(0.732873\pi\)
\(48\) −0.841254 0.540641i −0.121424 0.0780348i
\(49\) 0.672183 + 4.67513i 0.0960261 + 0.667876i
\(50\) −0.415415 0.909632i −0.0587486 0.128641i
\(51\) −1.90170 0.558391i −0.266292 0.0781903i
\(52\) −1.00992 + 2.21142i −0.140051 + 0.306669i
\(53\) −8.83527 + 10.1964i −1.21362 + 1.40059i −0.322654 + 0.946517i \(0.604575\pi\)
−0.890964 + 0.454073i \(0.849971\pi\)
\(54\) −0.142315 + 0.989821i −0.0193666 + 0.134698i
\(55\) 4.31017 1.26558i 0.581184 0.170651i
\(56\) −0.988122 1.14035i −0.132043 0.152386i
\(57\) 0.224062 0.143996i 0.0296778 0.0190727i
\(58\) 2.65911 1.70891i 0.349159 0.224391i
\(59\) −9.60937 11.0898i −1.25103 1.44377i −0.849213 0.528051i \(-0.822923\pi\)
−0.401821 0.915718i \(-0.631622\pi\)
\(60\) 0.959493 0.281733i 0.123870 0.0363715i
\(61\) 0.873883 6.07799i 0.111889 0.778207i −0.854190 0.519961i \(-0.825946\pi\)
0.966079 0.258246i \(-0.0831444\pi\)
\(62\) −3.85631 + 4.45042i −0.489752 + 0.565203i
\(63\) −0.626821 + 1.37255i −0.0789721 + 0.172925i
\(64\) −0.959493 0.281733i −0.119937 0.0352166i
\(65\) −1.00992 2.21142i −0.125265 0.274293i
\(66\) 0.639298 + 4.44641i 0.0786921 + 0.547316i
\(67\) 0.869412 + 0.558737i 0.106216 + 0.0682606i 0.592670 0.805445i \(-0.298074\pi\)
−0.486455 + 0.873706i \(0.661710\pi\)
\(68\) −1.98199 −0.240351
\(69\) −4.79176 0.197643i −0.576860 0.0237934i
\(70\) 1.50890 0.180348
\(71\) 5.47877 + 3.52099i 0.650210 + 0.417865i 0.823743 0.566963i \(-0.191882\pi\)
−0.173533 + 0.984828i \(0.555518\pi\)
\(72\) 0.142315 + 0.989821i 0.0167720 + 0.116652i
\(73\) −0.679674 1.48828i −0.0795498 0.174190i 0.865678 0.500601i \(-0.166888\pi\)
−0.945228 + 0.326412i \(0.894160\pi\)
\(74\) 11.2307 + 3.29764i 1.30555 + 0.383343i
\(75\) −0.415415 + 0.909632i −0.0479680 + 0.105035i
\(76\) 0.174418 0.201289i 0.0200071 0.0230894i
\(77\) −0.964639 + 6.70921i −0.109931 + 0.764585i
\(78\) 2.33264 0.684925i 0.264119 0.0775524i
\(79\) 5.79056 + 6.68266i 0.651489 + 0.751858i 0.981362 0.192167i \(-0.0615515\pi\)
−0.329873 + 0.944025i \(0.607006\pi\)
\(80\) 0.841254 0.540641i 0.0940550 0.0604455i
\(81\) 0.841254 0.540641i 0.0934726 0.0600712i
\(82\) −5.04946 5.82738i −0.557619 0.643527i
\(83\) 7.15379 2.10054i 0.785231 0.230565i 0.135549 0.990771i \(-0.456720\pi\)
0.649682 + 0.760206i \(0.274902\pi\)
\(84\) −0.214739 + 1.49355i −0.0234300 + 0.162959i
\(85\) 1.29793 1.49789i 0.140780 0.162469i
\(86\) 5.08354 11.1314i 0.548172 1.20033i
\(87\) −3.03285 0.890526i −0.325156 0.0954744i
\(88\) 1.86610 + 4.08619i 0.198927 + 0.435589i
\(89\) 0.948091 + 6.59412i 0.100497 + 0.698975i 0.976318 + 0.216339i \(0.0694115\pi\)
−0.875821 + 0.482636i \(0.839679\pi\)
\(90\) −0.841254 0.540641i −0.0886759 0.0569885i
\(91\) 3.66832 0.384544
\(92\) −4.65334 + 1.16036i −0.485144 + 0.120976i
\(93\) 5.88874 0.610634
\(94\) 7.70580 + 4.95222i 0.794793 + 0.510782i
\(95\) 0.0379046 + 0.263632i 0.00388893 + 0.0270481i
\(96\) 0.415415 + 0.909632i 0.0423981 + 0.0928389i
\(97\) 11.4555 + 3.36363i 1.16313 + 0.341525i 0.805647 0.592396i \(-0.201818\pi\)
0.357480 + 0.933921i \(0.383636\pi\)
\(98\) 1.96209 4.29638i 0.198201 0.434000i
\(99\) 2.94172 3.39493i 0.295654 0.341203i
\(100\) −0.142315 + 0.989821i −0.0142315 + 0.0989821i
\(101\) 0.917554 0.269418i 0.0913001 0.0268081i −0.235763 0.971810i \(-0.575759\pi\)
0.327064 + 0.945002i \(0.393941\pi\)
\(102\) 1.29793 + 1.49789i 0.128514 + 0.148313i
\(103\) −6.32611 + 4.06554i −0.623330 + 0.400590i −0.813835 0.581096i \(-0.802624\pi\)
0.190505 + 0.981686i \(0.438988\pi\)
\(104\) 2.04519 1.31436i 0.200547 0.128884i
\(105\) −0.988122 1.14035i −0.0964308 0.111287i
\(106\) 12.9453 3.80109i 1.25736 0.369194i
\(107\) 1.18625 8.25054i 0.114679 0.797609i −0.848586 0.529057i \(-0.822546\pi\)
0.963265 0.268552i \(-0.0865452\pi\)
\(108\) 0.654861 0.755750i 0.0630140 0.0727220i
\(109\) −1.35450 + 2.96594i −0.129738 + 0.284086i −0.963342 0.268276i \(-0.913546\pi\)
0.833604 + 0.552362i \(0.186273\pi\)
\(110\) −4.31017 1.26558i −0.410959 0.120668i
\(111\) −4.86238 10.6471i −0.461516 1.01058i
\(112\) 0.214739 + 1.49355i 0.0202910 + 0.141127i
\(113\) −11.2424 7.22504i −1.05759 0.679675i −0.108317 0.994116i \(-0.534546\pi\)
−0.949277 + 0.314442i \(0.898183\pi\)
\(114\) −0.266343 −0.0249453
\(115\) 2.17035 4.27663i 0.202386 0.398798i
\(116\) −3.16089 −0.293482
\(117\) −2.04519 1.31436i −0.189077 0.121513i
\(118\) 2.08832 + 14.5246i 0.192245 + 1.33709i
\(119\) 1.24235 + 2.72037i 0.113886 + 0.249376i
\(120\) −0.959493 0.281733i −0.0875893 0.0257185i
\(121\) 3.81321 8.34977i 0.346656 0.759070i
\(122\) −4.02117 + 4.64067i −0.364059 + 0.420147i
\(123\) −1.09735 + 7.63225i −0.0989449 + 0.688177i
\(124\) 5.65021 1.65905i 0.507404 0.148987i
\(125\) −0.654861 0.755750i −0.0585725 0.0675963i
\(126\) 1.26937 0.815775i 0.113085 0.0726750i
\(127\) 4.09035 2.62871i 0.362960 0.233260i −0.346431 0.938075i \(-0.612607\pi\)
0.709391 + 0.704815i \(0.248970\pi\)
\(128\) 0.654861 + 0.755750i 0.0578821 + 0.0667995i
\(129\) −11.7416 + 3.44763i −1.03379 + 0.303547i
\(130\) −0.345984 + 2.40637i −0.0303448 + 0.211053i
\(131\) 9.62604 11.1090i 0.841031 0.970601i −0.158830 0.987306i \(-0.550772\pi\)
0.999860 + 0.0167048i \(0.00531756\pi\)
\(132\) 1.86610 4.08619i 0.162423 0.355657i
\(133\) −0.385607 0.113224i −0.0334364 0.00981781i
\(134\) −0.429320 0.940079i −0.0370876 0.0812105i
\(135\) 0.142315 + 0.989821i 0.0122485 + 0.0851903i
\(136\) 1.66735 + 1.07154i 0.142975 + 0.0918841i
\(137\) 15.5526 1.32875 0.664374 0.747401i \(-0.268698\pi\)
0.664374 + 0.747401i \(0.268698\pi\)
\(138\) 3.92423 + 2.75689i 0.334053 + 0.234682i
\(139\) −5.64348 −0.478673 −0.239337 0.970937i \(-0.576930\pi\)
−0.239337 + 0.970937i \(0.576930\pi\)
\(140\) −1.26937 0.815775i −0.107281 0.0689456i
\(141\) −1.30359 9.06667i −0.109782 0.763552i
\(142\) −2.70544 5.92409i −0.227036 0.497139i
\(143\) −10.4785 3.07677i −0.876259 0.257293i
\(144\) 0.415415 0.909632i 0.0346179 0.0758027i
\(145\) 2.06994 2.38884i 0.171900 0.198383i
\(146\) −0.232846 + 1.61948i −0.0192705 + 0.134029i
\(147\) −4.53189 + 1.33068i −0.373784 + 0.109753i
\(148\) −7.66506 8.84595i −0.630064 0.727132i
\(149\) 3.32180 2.13479i 0.272133 0.174889i −0.397456 0.917621i \(-0.630107\pi\)
0.669589 + 0.742732i \(0.266470\pi\)
\(150\) 0.841254 0.540641i 0.0686881 0.0441431i
\(151\) −9.60453 11.0842i −0.781606 0.902021i 0.215618 0.976478i \(-0.430823\pi\)
−0.997224 + 0.0744565i \(0.976278\pi\)
\(152\) −0.255554 + 0.0750376i −0.0207282 + 0.00608635i
\(153\) 0.282066 1.96181i 0.0228037 0.158603i
\(154\) 4.43878 5.12262i 0.357687 0.412793i
\(155\) −2.44627 + 5.35659i −0.196489 + 0.430252i
\(156\) −2.33264 0.684925i −0.186761 0.0548379i
\(157\) 8.76610 + 19.1951i 0.699611 + 1.53193i 0.840442 + 0.541901i \(0.182295\pi\)
−0.140831 + 0.990034i \(0.544977\pi\)
\(158\) −1.25841 8.75243i −0.100114 0.696306i
\(159\) −11.3501 7.29424i −0.900118 0.578471i
\(160\) −1.00000 −0.0790569
\(161\) 4.50946 + 5.65959i 0.355395 + 0.446038i
\(162\) −1.00000 −0.0785674
\(163\) −10.5463 6.77769i −0.826049 0.530870i 0.0579711 0.998318i \(-0.481537\pi\)
−0.884020 + 0.467449i \(0.845173\pi\)
\(164\) 1.09735 + 7.63225i 0.0856888 + 0.595978i
\(165\) 1.86610 + 4.08619i 0.145276 + 0.318110i
\(166\) −7.15379 2.10054i −0.555242 0.163034i
\(167\) 2.12148 4.64540i 0.164165 0.359472i −0.809615 0.586961i \(-0.800324\pi\)
0.973781 + 0.227489i \(0.0730516\pi\)
\(168\) 0.988122 1.14035i 0.0762353 0.0879802i
\(169\) 1.00897 7.01751i 0.0776127 0.539808i
\(170\) −1.90170 + 0.558391i −0.145854 + 0.0428266i
\(171\) 0.174418 + 0.201289i 0.0133381 + 0.0153929i
\(172\) −10.2946 + 6.61596i −0.784959 + 0.504462i
\(173\) 11.2085 7.20328i 0.852168 0.547655i −0.0400820 0.999196i \(-0.512762\pi\)
0.892250 + 0.451541i \(0.149126\pi\)
\(174\) 2.06994 + 2.38884i 0.156922 + 0.181098i
\(175\) 1.44778 0.425107i 0.109442 0.0321351i
\(176\) 0.639298 4.44641i 0.0481889 0.335161i
\(177\) 9.60937 11.0898i 0.722284 0.833561i
\(178\) 2.76746 6.05990i 0.207430 0.454209i
\(179\) −5.77778 1.69651i −0.431851 0.126803i 0.0585802 0.998283i \(-0.481343\pi\)
−0.490432 + 0.871480i \(0.663161\pi\)
\(180\) 0.415415 + 0.909632i 0.0309632 + 0.0678000i
\(181\) 1.22742 + 8.53689i 0.0912334 + 0.634542i 0.983212 + 0.182465i \(0.0584077\pi\)
−0.891979 + 0.452077i \(0.850683\pi\)
\(182\) −3.08599 1.98324i −0.228749 0.147008i
\(183\) 6.14049 0.453918
\(184\) 4.54197 + 1.53963i 0.334839 + 0.113503i
\(185\) 11.7049 0.860559
\(186\) −4.95393 3.18370i −0.363240 0.233440i
\(187\) −1.26708 8.81274i −0.0926581 0.644451i
\(188\) −3.80516 8.33215i −0.277520 0.607684i
\(189\) −1.44778 0.425107i −0.105311 0.0309220i
\(190\) 0.110643 0.242274i 0.00802689 0.0175764i
\(191\) 14.4943 16.7273i 1.04877 1.21035i 0.0717033 0.997426i \(-0.477157\pi\)
0.977069 0.212922i \(-0.0682980\pi\)
\(192\) 0.142315 0.989821i 0.0102707 0.0714342i
\(193\) 20.5087 6.02191i 1.47625 0.433466i 0.558126 0.829756i \(-0.311521\pi\)
0.918125 + 0.396290i \(0.129703\pi\)
\(194\) −7.81844 9.02296i −0.561331 0.647811i
\(195\) 2.04519 1.31436i 0.146459 0.0941233i
\(196\) −3.97342 + 2.55356i −0.283815 + 0.182397i
\(197\) −0.515432 0.594841i −0.0367230 0.0423806i 0.737091 0.675794i \(-0.236199\pi\)
−0.773814 + 0.633413i \(0.781653\pi\)
\(198\) −4.31017 + 1.26558i −0.306311 + 0.0899409i
\(199\) 1.43309 9.96738i 0.101589 0.706569i −0.873833 0.486226i \(-0.838373\pi\)
0.975422 0.220343i \(-0.0707177\pi\)
\(200\) 0.654861 0.755750i 0.0463056 0.0534396i
\(201\) −0.429320 + 0.940079i −0.0302819 + 0.0663081i
\(202\) −0.917554 0.269418i −0.0645589 0.0189562i
\(203\) 1.98131 + 4.33847i 0.139061 + 0.304501i
\(204\) −0.282066 1.96181i −0.0197486 0.137355i
\(205\) −6.48668 4.16874i −0.453049 0.291157i
\(206\) 7.51986 0.523933
\(207\) −0.486307 4.77111i −0.0338007 0.331615i
\(208\) −2.43112 −0.168568
\(209\) 1.00652 + 0.646850i 0.0696223 + 0.0447435i
\(210\) 0.214739 + 1.49355i 0.0148184 + 0.103064i
\(211\) −4.96612 10.8743i −0.341882 0.748617i 0.658109 0.752923i \(-0.271357\pi\)
−0.999991 + 0.00430607i \(0.998629\pi\)
\(212\) −12.9453 3.80109i −0.889088 0.261060i
\(213\) −2.70544 + 5.92409i −0.185374 + 0.405912i
\(214\) −5.45851 + 6.29946i −0.373136 + 0.430622i
\(215\) 1.74154 12.1127i 0.118772 0.826079i
\(216\) −0.959493 + 0.281733i −0.0652852 + 0.0191695i
\(217\) −5.81880 6.71525i −0.395006 0.455861i
\(218\) 2.74299 1.76281i 0.185779 0.119393i
\(219\) 1.37640 0.884560i 0.0930087 0.0597730i
\(220\) 2.94172 + 3.39493i 0.198331 + 0.228886i
\(221\) −4.62326 + 1.35751i −0.310994 + 0.0913162i
\(222\) −1.66578 + 11.5857i −0.111800 + 0.777583i
\(223\) 3.83051 4.42064i 0.256510 0.296028i −0.612859 0.790193i \(-0.709980\pi\)
0.869368 + 0.494164i \(0.164526\pi\)
\(224\) 0.626821 1.37255i 0.0418813 0.0917072i
\(225\) −0.959493 0.281733i −0.0639662 0.0187822i
\(226\) 5.55154 + 12.1562i 0.369283 + 0.808617i
\(227\) 3.59763 + 25.0220i 0.238783 + 1.66077i 0.658099 + 0.752931i \(0.271361\pi\)
−0.419316 + 0.907840i \(0.637730\pi\)
\(228\) 0.224062 + 0.143996i 0.0148389 + 0.00953637i
\(229\) 9.38548 0.620210 0.310105 0.950702i \(-0.399636\pi\)
0.310105 + 0.950702i \(0.399636\pi\)
\(230\) −4.13794 + 2.42435i −0.272847 + 0.159857i
\(231\) −6.77820 −0.445973
\(232\) 2.65911 + 1.70891i 0.174579 + 0.112195i
\(233\) 1.21905 + 8.47869i 0.0798627 + 0.555458i 0.989991 + 0.141131i \(0.0450738\pi\)
−0.910128 + 0.414327i \(0.864017\pi\)
\(234\) 1.00992 + 2.21142i 0.0660207 + 0.144565i
\(235\) 8.78887 + 2.58064i 0.573322 + 0.168343i
\(236\) 6.09576 13.3479i 0.396800 0.868872i
\(237\) −5.79056 + 6.68266i −0.376137 + 0.434086i
\(238\) 0.425611 2.96019i 0.0275883 0.191881i
\(239\) −9.40863 + 2.76262i −0.608594 + 0.178699i −0.571486 0.820612i \(-0.693633\pi\)
−0.0371079 + 0.999311i \(0.511815\pi\)
\(240\) 0.654861 + 0.755750i 0.0422711 + 0.0487834i
\(241\) −3.88935 + 2.49953i −0.250535 + 0.161009i −0.659881 0.751370i \(-0.729393\pi\)
0.409346 + 0.912379i \(0.365757\pi\)
\(242\) −7.72211 + 4.96270i −0.496396 + 0.319014i
\(243\) 0.654861 + 0.755750i 0.0420093 + 0.0484814i
\(244\) 5.89176 1.72998i 0.377181 0.110750i
\(245\) 0.672183 4.67513i 0.0429442 0.298683i
\(246\) 5.04946 5.82738i 0.321942 0.371540i
\(247\) 0.268986 0.588997i 0.0171152 0.0374770i
\(248\) −5.65021 1.65905i −0.358789 0.105350i
\(249\) 3.09725 + 6.78204i 0.196280 + 0.429794i
\(250\) 0.142315 + 0.989821i 0.00900078 + 0.0626018i
\(251\) 1.45132 + 0.932704i 0.0916062 + 0.0588717i 0.585642 0.810570i \(-0.300842\pi\)
−0.494036 + 0.869442i \(0.664479\pi\)
\(252\) −1.50890 −0.0950520
\(253\) −8.13430 19.9489i −0.511399 1.25417i
\(254\) −4.86221 −0.305082
\(255\) 1.66735 + 1.07154i 0.104414 + 0.0671027i
\(256\) −0.142315 0.989821i −0.00889468 0.0618638i
\(257\) 12.2871 + 26.9050i 0.766447 + 1.67829i 0.734322 + 0.678802i \(0.237500\pi\)
0.0321259 + 0.999484i \(0.489772\pi\)
\(258\) 11.7416 + 3.44763i 0.730998 + 0.214640i
\(259\) −7.33686 + 16.0655i −0.455890 + 0.998260i
\(260\) 1.59204 1.83732i 0.0987343 0.113945i
\(261\) 0.449842 3.12872i 0.0278445 0.193663i
\(262\) −14.1039 + 4.14129i −0.871344 + 0.255850i
\(263\) −10.8522 12.5241i −0.669175 0.772269i 0.315072 0.949068i \(-0.397971\pi\)
−0.984247 + 0.176799i \(0.943426\pi\)
\(264\) −3.77903 + 2.42863i −0.232583 + 0.149472i
\(265\) 11.3501 7.29424i 0.697228 0.448081i
\(266\) 0.263180 + 0.303725i 0.0161366 + 0.0186226i
\(267\) −6.39207 + 1.87688i −0.391188 + 0.114863i
\(268\) −0.147078 + 1.02295i −0.00898424 + 0.0624868i
\(269\) −4.50291 + 5.19664i −0.274547 + 0.316845i −0.876232 0.481889i \(-0.839951\pi\)
0.601685 + 0.798734i \(0.294496\pi\)
\(270\) 0.415415 0.909632i 0.0252814 0.0553584i
\(271\) −22.2486 6.53277i −1.35150 0.396838i −0.475744 0.879584i \(-0.657821\pi\)
−0.875760 + 0.482746i \(0.839639\pi\)
\(272\) −0.823348 1.80288i −0.0499228 0.109316i
\(273\) 0.522056 + 3.63098i 0.0315963 + 0.219757i
\(274\) −13.0837 8.40836i −0.790413 0.507968i
\(275\) −4.49214 −0.270886
\(276\) −1.81079 4.44084i −0.108996 0.267307i
\(277\) 5.20907 0.312983 0.156491 0.987679i \(-0.449982\pi\)
0.156491 + 0.987679i \(0.449982\pi\)
\(278\) 4.74759 + 3.05109i 0.284742 + 0.182992i
\(279\) 0.838056 + 5.82881i 0.0501731 + 0.348961i
\(280\) 0.626821 + 1.37255i 0.0374597 + 0.0820254i
\(281\) 26.6505 + 7.82529i 1.58984 + 0.466818i 0.952695 0.303929i \(-0.0982986\pi\)
0.637141 + 0.770747i \(0.280117\pi\)
\(282\) −3.80516 + 8.33215i −0.226594 + 0.496172i
\(283\) −12.6365 + 14.5833i −0.751162 + 0.866888i −0.994680 0.103009i \(-0.967153\pi\)
0.243518 + 0.969896i \(0.421699\pi\)
\(284\) −0.926843 + 6.44633i −0.0549980 + 0.382520i
\(285\) −0.255554 + 0.0750376i −0.0151377 + 0.00444484i
\(286\) 7.15167 + 8.25347i 0.422887 + 0.488038i
\(287\) 9.78778 6.29022i 0.577754 0.371300i
\(288\) −0.841254 + 0.540641i −0.0495713 + 0.0318576i
\(289\) 8.56016 + 9.87895i 0.503539 + 0.581115i
\(290\) −3.03285 + 0.890526i −0.178095 + 0.0522935i
\(291\) −1.69911 + 11.8176i −0.0996035 + 0.692758i
\(292\) 1.07144 1.23651i 0.0627012 0.0723611i
\(293\) 5.63013 12.3283i 0.328915 0.720224i −0.670856 0.741587i \(-0.734073\pi\)
0.999772 + 0.0213629i \(0.00680054\pi\)
\(294\) 4.53189 + 1.33068i 0.264305 + 0.0776069i
\(295\) 6.09576 + 13.3479i 0.354909 + 0.777142i
\(296\) 1.66578 + 11.5857i 0.0968213 + 0.673407i
\(297\) 3.77903 + 2.42863i 0.219281 + 0.140924i
\(298\) −3.94863 −0.228738
\(299\) −10.0598 + 5.89388i −0.581774 + 0.340852i
\(300\) −1.00000 −0.0577350
\(301\) 15.5336 + 9.98285i 0.895342 + 0.575402i
\(302\) 2.08726 + 14.5172i 0.120109 + 0.835374i
\(303\) 0.397258 + 0.869873i 0.0228219 + 0.0499729i
\(304\) 0.255554 + 0.0750376i 0.0146571 + 0.00430370i
\(305\) −2.55085 + 5.58559i −0.146061 + 0.319830i
\(306\) −1.29793 + 1.49789i −0.0741975 + 0.0856285i
\(307\) −2.77904 + 19.3287i −0.158608 + 1.10314i 0.742593 + 0.669743i \(0.233596\pi\)
−0.901201 + 0.433401i \(0.857313\pi\)
\(308\) −6.50364 + 1.90964i −0.370579 + 0.108812i
\(309\) −4.92446 5.68313i −0.280143 0.323302i
\(310\) 4.95393 3.18370i 0.281364 0.180822i
\(311\) 7.76527 4.99043i 0.440328 0.282982i −0.301634 0.953424i \(-0.597532\pi\)
0.741962 + 0.670442i \(0.233896\pi\)
\(312\) 1.59204 + 1.83732i 0.0901317 + 0.104017i
\(313\) −17.6962 + 5.19606i −1.00025 + 0.293699i −0.740557 0.671994i \(-0.765438\pi\)
−0.259689 + 0.965692i \(0.583620\pi\)
\(314\) 3.00313 20.8872i 0.169477 1.17874i
\(315\) 0.988122 1.14035i 0.0556744 0.0642516i
\(316\) −3.67328 + 8.04336i −0.206638 + 0.452474i
\(317\) −12.7371 3.73994i −0.715385 0.210056i −0.0962687 0.995355i \(-0.530691\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(318\) 5.60471 + 12.2726i 0.314297 + 0.688214i
\(319\) −2.02075 14.0546i −0.113140 0.786908i
\(320\) 0.841254 + 0.540641i 0.0470275 + 0.0302227i
\(321\) 8.33538 0.465235
\(322\) −0.733790 7.19915i −0.0408925 0.401193i
\(323\) 0.527889 0.0293725
\(324\) 0.841254 + 0.540641i 0.0467363 + 0.0300356i
\(325\) 0.345984 + 2.40637i 0.0191917 + 0.133481i
\(326\) 5.20781 + 11.4035i 0.288434 + 0.631582i
\(327\) −3.12852 0.918616i −0.173007 0.0507996i
\(328\) 3.20315 7.01393i 0.176865 0.387279i
\(329\) −9.05110 + 10.4455i −0.499004 + 0.575881i
\(330\) 0.639298 4.44641i 0.0351922 0.244767i
\(331\) −18.6948 + 5.48928i −1.02756 + 0.301718i −0.751717 0.659486i \(-0.770774\pi\)
−0.275840 + 0.961204i \(0.588956\pi\)
\(332\) 4.88251 + 5.63472i 0.267963 + 0.309246i
\(333\) 9.84676 6.32813i 0.539599 0.346779i
\(334\) −4.29619 + 2.76100i −0.235077 + 0.151075i
\(335\) −0.676780 0.781046i −0.0369765 0.0426731i
\(336\) −1.44778 + 0.425107i −0.0789830 + 0.0231915i
\(337\) −1.21884 + 8.47720i −0.0663943 + 0.461783i 0.929318 + 0.369280i \(0.120396\pi\)
−0.995712 + 0.0925025i \(0.970513\pi\)
\(338\) −4.64275 + 5.35802i −0.252532 + 0.291438i
\(339\) 5.55154 12.1562i 0.301518 0.660233i
\(340\) 1.90170 + 0.558391i 0.103134 + 0.0302830i
\(341\) 10.9890 + 24.0625i 0.595087 + 1.30306i
\(342\) −0.0379046 0.263632i −0.00204965 0.0142556i
\(343\) 14.8811 + 9.56350i 0.803504 + 0.516380i
\(344\) 12.2373 0.659789
\(345\) 4.54197 + 1.53963i 0.244532 + 0.0828909i
\(346\) −13.3236 −0.716281
\(347\) 11.5623 + 7.43066i 0.620699 + 0.398899i 0.812855 0.582466i \(-0.197912\pi\)
−0.192157 + 0.981364i \(0.561548\pi\)
\(348\) −0.449842 3.12872i −0.0241141 0.167717i
\(349\) −1.26274 2.76500i −0.0675927 0.148007i 0.872820 0.488042i \(-0.162289\pi\)
−0.940413 + 0.340034i \(0.889561\pi\)
\(350\) −1.44778 0.425107i −0.0773872 0.0227229i
\(351\) 1.00992 2.21142i 0.0539057 0.118037i
\(352\) −2.94172 + 3.39493i −0.156794 + 0.180950i
\(353\) −1.94823 + 13.5502i −0.103694 + 0.721206i 0.869951 + 0.493138i \(0.164150\pi\)
−0.973645 + 0.228068i \(0.926759\pi\)
\(354\) −14.0795 + 4.13412i −0.748318 + 0.219726i
\(355\) −4.26486 4.92191i −0.226355 0.261228i
\(356\) −5.60437 + 3.60171i −0.297031 + 0.190890i
\(357\) −2.51588 + 1.61686i −0.133154 + 0.0855731i
\(358\) 3.94337 + 4.55090i 0.208414 + 0.240522i
\(359\) −3.02720 + 0.888865i −0.159769 + 0.0469125i −0.360639 0.932705i \(-0.617441\pi\)
0.200870 + 0.979618i \(0.435623\pi\)
\(360\) 0.142315 0.989821i 0.00750065 0.0521682i
\(361\) 12.3959 14.3056i 0.652416 0.752928i
\(362\) 3.58282 7.84528i 0.188309 0.412339i
\(363\) 8.80746 + 2.58610i 0.462272 + 0.135735i
\(364\) 1.52388 + 3.33682i 0.0798728 + 0.174897i
\(365\) 0.232846 + 1.61948i 0.0121877 + 0.0847674i
\(366\) −5.16571 3.31980i −0.270016 0.173529i
\(367\) −13.0715 −0.682328 −0.341164 0.940004i \(-0.610821\pi\)
−0.341164 + 0.940004i \(0.610821\pi\)
\(368\) −2.98857 3.75080i −0.155790 0.195524i
\(369\) −7.71073 −0.401405
\(370\) −9.84676 6.32813i −0.511909 0.328984i
\(371\) 2.89723 + 20.1507i 0.150417 + 1.04617i
\(372\) 2.44627 + 5.35659i 0.126833 + 0.277726i
\(373\) −24.5823 7.21801i −1.27282 0.373734i −0.425570 0.904925i \(-0.639927\pi\)
−0.847252 + 0.531191i \(0.821745\pi\)
\(374\) −3.69859 + 8.09878i −0.191250 + 0.418778i
\(375\) 0.654861 0.755750i 0.0338169 0.0390267i
\(376\) −1.30359 + 9.06667i −0.0672276 + 0.467578i
\(377\) −7.37322 + 2.16497i −0.379740 + 0.111502i
\(378\) 0.988122 + 1.14035i 0.0508235 + 0.0586534i
\(379\) −17.0813 + 10.9775i −0.877407 + 0.563875i −0.900010 0.435869i \(-0.856441\pi\)
0.0226030 + 0.999745i \(0.492805\pi\)
\(380\) −0.224062 + 0.143996i −0.0114941 + 0.00738684i
\(381\) 3.18407 + 3.67461i 0.163125 + 0.188256i
\(382\) −21.2369 + 6.23571i −1.08657 + 0.319047i
\(383\) 2.56391 17.8324i 0.131010 0.911193i −0.813232 0.581940i \(-0.802294\pi\)
0.944242 0.329253i \(-0.106797\pi\)
\(384\) −0.654861 + 0.755750i −0.0334182 + 0.0385667i
\(385\) 2.81577 6.16567i 0.143505 0.314232i
\(386\) −20.5087 6.02191i −1.04387 0.306507i
\(387\) −5.08354 11.1314i −0.258411 0.565841i
\(388\) 1.69911 + 11.8176i 0.0862592 + 0.599946i
\(389\) 32.2171 + 20.7047i 1.63347 + 1.04977i 0.946309 + 0.323262i \(0.104780\pi\)
0.687161 + 0.726505i \(0.258857\pi\)
\(390\) −2.43112 −0.123104
\(391\) −7.77778 5.46412i −0.393339 0.276332i
\(392\) 4.72321 0.238558
\(393\) 12.3659 + 7.94708i 0.623777 + 0.400877i
\(394\) 0.112014 + 0.779076i 0.00564319 + 0.0392493i
\(395\) −3.67328 8.04336i −0.184823 0.404705i
\(396\) 4.31017 + 1.26558i 0.216594 + 0.0635978i
\(397\) 4.05992 8.88998i 0.203762 0.446176i −0.779971 0.625816i \(-0.784766\pi\)
0.983732 + 0.179640i \(0.0574934\pi\)
\(398\) −6.59437 + 7.61031i −0.330546 + 0.381470i
\(399\) 0.0571944 0.397796i 0.00286330 0.0199147i
\(400\) −0.959493 + 0.281733i −0.0479746 + 0.0140866i
\(401\) 6.70181 + 7.73430i 0.334672 + 0.386232i 0.897996 0.440004i \(-0.145023\pi\)
−0.563324 + 0.826236i \(0.690478\pi\)
\(402\) 0.869412 0.558737i 0.0433623 0.0278673i
\(403\) 12.0436 7.73993i 0.599933 0.385554i
\(404\) 0.626237 + 0.722716i 0.0311565 + 0.0359565i
\(405\) −0.959493 + 0.281733i −0.0476776 + 0.0139994i
\(406\) 0.678768 4.72094i 0.0336867 0.234296i
\(407\) 34.4325 39.7372i 1.70675 1.96970i
\(408\) −0.823348 + 1.80288i −0.0407618 + 0.0892559i
\(409\) −17.0281 4.99991i −0.841986 0.247229i −0.167828 0.985816i \(-0.553675\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(410\) 3.20315 + 7.01393i 0.158192 + 0.346393i
\(411\) 2.21336 + 15.3943i 0.109177 + 0.759344i
\(412\) −6.32611 4.06554i −0.311665 0.200295i
\(413\) −22.1415 −1.08951
\(414\) −2.17035 + 4.27663i −0.106667 + 0.210185i
\(415\) −7.45581 −0.365991
\(416\) 2.04519 + 1.31436i 0.100273 + 0.0644418i
\(417\) −0.803150 5.58603i −0.0393304 0.273549i
\(418\) −0.497023 1.08833i −0.0243102 0.0532319i
\(419\) 30.7112 + 9.01762i 1.50034 + 0.440540i 0.925824 0.377954i \(-0.123372\pi\)
0.574516 + 0.818494i \(0.305190\pi\)
\(420\) 0.626821 1.37255i 0.0305857 0.0669734i
\(421\) 14.6937 16.9575i 0.716129 0.826457i −0.274707 0.961528i \(-0.588581\pi\)
0.990836 + 0.135071i \(0.0431263\pi\)
\(422\) −1.70132 + 11.8329i −0.0828188 + 0.576017i
\(423\) 8.78887 2.58064i 0.427329 0.125475i
\(424\) 8.83527 + 10.1964i 0.429079 + 0.495183i
\(425\) −1.66735 + 1.07154i −0.0808786 + 0.0519775i
\(426\) 5.47877 3.52099i 0.265447 0.170593i
\(427\) −6.06755 7.00233i −0.293629 0.338866i
\(428\) 7.99774 2.34835i 0.386585 0.113512i
\(429\) 1.55421 10.8097i 0.0750378 0.521899i
\(430\) −8.01370 + 9.24830i −0.386455 + 0.445993i
\(431\) −8.63717 + 18.9128i −0.416038 + 0.910996i 0.579351 + 0.815078i \(0.303306\pi\)
−0.995389 + 0.0959178i \(0.969421\pi\)
\(432\) 0.959493 + 0.281733i 0.0461636 + 0.0135549i
\(433\) 7.64285 + 16.7355i 0.367292 + 0.804257i 0.999564 + 0.0295111i \(0.00939503\pi\)
−0.632273 + 0.774746i \(0.717878\pi\)
\(434\) 1.26455 + 8.79511i 0.0607001 + 0.422179i
\(435\) 2.65911 + 1.70891i 0.127495 + 0.0819358i
\(436\) −3.26060 −0.156154
\(437\) 1.23939 0.309053i 0.0592879 0.0147840i
\(438\) −1.63613 −0.0781775
\(439\) −3.58155 2.30172i −0.170938 0.109855i 0.452374 0.891828i \(-0.350577\pi\)
−0.623312 + 0.781973i \(0.714213\pi\)
\(440\) −0.639298 4.44641i −0.0304773 0.211974i
\(441\) −1.96209 4.29638i −0.0934330 0.204590i
\(442\) 4.62326 + 1.35751i 0.219906 + 0.0645703i
\(443\) 6.98828 15.3022i 0.332023 0.727029i −0.667827 0.744316i \(-0.732776\pi\)
0.999851 + 0.0172868i \(0.00550284\pi\)
\(444\) 7.66506 8.84595i 0.363768 0.419810i
\(445\) 0.948091 6.59412i 0.0449438 0.312591i
\(446\) −5.61241 + 1.64795i −0.265755 + 0.0780328i
\(447\) 2.58580 + 2.98418i 0.122304 + 0.141147i
\(448\) −1.26937 + 0.815775i −0.0599721 + 0.0385417i
\(449\) −14.0529 + 9.03126i −0.663198 + 0.426212i −0.828468 0.560037i \(-0.810787\pi\)
0.165270 + 0.986248i \(0.447151\pi\)
\(450\) 0.654861 + 0.755750i 0.0308704 + 0.0356264i
\(451\) −33.2346 + 9.75856i −1.56496 + 0.459512i
\(452\) 1.90187 13.2278i 0.0894566 0.622184i
\(453\) 9.60453 11.0842i 0.451260 0.520782i
\(454\) 10.5014 22.9949i 0.492856 1.07920i
\(455\) −3.51973 1.03349i −0.165007 0.0484505i
\(456\) −0.110643 0.242274i −0.00518133 0.0113455i
\(457\) −0.411520 2.86219i −0.0192501 0.133888i 0.977930 0.208933i \(-0.0669990\pi\)
−0.997180 + 0.0750452i \(0.976090\pi\)
\(458\) −7.89557 5.07417i −0.368936 0.237101i
\(459\) 1.98199 0.0925113
\(460\) 4.79176 + 0.197643i 0.223417 + 0.00921515i
\(461\) −1.88975 −0.0880145 −0.0440073 0.999031i \(-0.514012\pi\)
−0.0440073 + 0.999031i \(0.514012\pi\)
\(462\) 5.70219 + 3.66457i 0.265290 + 0.170491i
\(463\) 4.30213 + 29.9220i 0.199937 + 1.39059i 0.804462 + 0.594005i \(0.202454\pi\)
−0.604525 + 0.796586i \(0.706637\pi\)
\(464\) −1.31308 2.87525i −0.0609583 0.133480i
\(465\) −5.65021 1.65905i −0.262022 0.0769366i
\(466\) 3.55839 7.79180i 0.164839 0.360948i
\(467\) −6.24854 + 7.21120i −0.289148 + 0.333695i −0.881676 0.471855i \(-0.843584\pi\)
0.592528 + 0.805550i \(0.298130\pi\)
\(468\) 0.345984 2.40637i 0.0159931 0.111235i
\(469\) 1.49624 0.439336i 0.0690901 0.0202867i
\(470\) −5.99846 6.92260i −0.276689 0.319316i
\(471\) −17.7522 + 11.4086i −0.817976 + 0.525682i
\(472\) −12.3445 + 7.93332i −0.568201 + 0.365160i
\(473\) −35.9986 41.5446i −1.65522 1.91022i
\(474\) 8.48425 2.49120i 0.389694 0.114425i
\(475\) 0.0379046 0.263632i 0.00173918 0.0120963i
\(476\) −1.95845 + 2.26017i −0.0897652 + 0.103595i
\(477\) 5.60471 12.2726i 0.256622 0.561924i
\(478\) 9.40863 + 2.76262i 0.430341 + 0.126359i
\(479\) −3.31305 7.25457i −0.151377 0.331470i 0.818718 0.574196i \(-0.194685\pi\)
−0.970095 + 0.242727i \(0.921958\pi\)
\(480\) −0.142315 0.989821i −0.00649575 0.0451790i
\(481\) −23.9386 15.3844i −1.09151 0.701469i
\(482\) 4.62328 0.210585
\(483\) −4.96022 + 5.26900i −0.225698 + 0.239748i
\(484\) 9.17929 0.417240
\(485\) −10.0438 6.45476i −0.456065 0.293095i
\(486\) −0.142315 0.989821i −0.00645553 0.0448992i
\(487\) 4.36703 + 9.56245i 0.197889 + 0.433316i 0.982398 0.186802i \(-0.0598121\pi\)
−0.784509 + 0.620118i \(0.787085\pi\)
\(488\) −5.89176 1.72998i −0.266707 0.0783123i
\(489\) 5.20781 11.4035i 0.235505 0.515684i
\(490\) −3.09304 + 3.56956i −0.139730 + 0.161256i
\(491\) −3.62930 + 25.2423i −0.163788 + 1.13917i 0.727624 + 0.685977i \(0.240625\pi\)
−0.891412 + 0.453194i \(0.850284\pi\)
\(492\) −7.39839 + 2.17236i −0.333545 + 0.0979377i
\(493\) −4.10261 4.73466i −0.184772 0.213238i
\(494\) −0.544721 + 0.350071i −0.0245082 + 0.0157504i
\(495\) −3.77903 + 2.42863i −0.169855 + 0.109159i
\(496\) 3.85631 + 4.45042i 0.173153 + 0.199830i
\(497\) 9.42886 2.76856i 0.422942 0.124187i
\(498\) 1.06107 7.37992i 0.0475478 0.330702i
\(499\) 14.9772 17.2846i 0.670472 0.773766i −0.313978 0.949430i \(-0.601662\pi\)
0.984450 + 0.175665i \(0.0562074\pi\)
\(500\) 0.415415 0.909632i 0.0185779 0.0406800i
\(501\) 4.90003 + 1.43878i 0.218917 + 0.0642799i
\(502\) −0.716666 1.56928i −0.0319864 0.0700404i
\(503\) −2.57583 17.9153i −0.114850 0.798802i −0.963088 0.269187i \(-0.913245\pi\)
0.848238 0.529616i \(-0.177664\pi\)
\(504\) 1.26937 + 0.815775i 0.0565423 + 0.0363375i
\(505\) −0.956291 −0.0425544
\(506\) −3.94216 + 21.1798i −0.175250 + 0.941556i
\(507\) 7.08967 0.314863
\(508\) 4.09035 + 2.62871i 0.181480 + 0.116630i
\(509\) −2.05382 14.2846i −0.0910340 0.633155i −0.983347 0.181738i \(-0.941828\pi\)
0.892313 0.451417i \(-0.149081\pi\)
\(510\) −0.823348 1.80288i −0.0364585 0.0798329i
\(511\) −2.36876 0.695532i −0.104788 0.0307685i
\(512\) −0.415415 + 0.909632i −0.0183589 + 0.0402004i
\(513\) −0.174418 + 0.201289i −0.00770073 + 0.00888712i
\(514\) 4.20937 29.2768i 0.185667 1.29134i
\(515\) 7.21525 2.11859i 0.317942 0.0933562i
\(516\) −8.01370 9.24830i −0.352783 0.407134i
\(517\) 34.6155 22.2460i 1.52239 0.978380i
\(518\) 14.8578 9.54854i 0.652815 0.419539i
\(519\) 8.72510 + 10.0693i 0.382989 + 0.441993i
\(520\) −2.33264 + 0.684925i −0.102293 + 0.0300359i
\(521\) 2.62454 18.2541i 0.114983 0.799726i −0.847967 0.530048i \(-0.822174\pi\)
0.962951 0.269678i \(-0.0869171\pi\)
\(522\) −2.06994 + 2.38884i −0.0905990 + 0.104557i
\(523\) −11.4827 + 25.1436i −0.502103 + 1.09945i 0.473677 + 0.880698i \(0.342926\pi\)
−0.975780 + 0.218753i \(0.929801\pi\)
\(524\) 14.1039 + 4.14129i 0.616133 + 0.180913i
\(525\) 0.626821 + 1.37255i 0.0273567 + 0.0599029i
\(526\) 2.35841 + 16.4031i 0.102831 + 0.715208i
\(527\) 9.81863 + 6.31005i 0.427706 + 0.274870i
\(528\) 4.49214 0.195495
\(529\) −21.4597 8.27523i −0.933032 0.359792i
\(530\) −13.4918 −0.586048
\(531\) 12.3445 + 7.93332i 0.535705 + 0.344277i
\(532\) −0.0571944 0.397796i −0.00247969 0.0172466i
\(533\) 7.78724 + 17.0517i 0.337303 + 0.738590i
\(534\) 6.39207 + 1.87688i 0.276612 + 0.0812206i
\(535\) −3.46264 + 7.58213i −0.149703 + 0.327804i
\(536\) 0.676780 0.781046i 0.0292325 0.0337361i
\(537\) 0.856977 5.96041i 0.0369813 0.257211i
\(538\) 6.59761 1.93723i 0.284443 0.0835200i
\(539\) −13.8944 16.0350i −0.598473 0.690675i
\(540\) −0.841254 + 0.540641i −0.0362018 + 0.0232655i
\(541\) −27.5396 + 17.6986i −1.18402 + 0.760924i −0.976121 0.217226i \(-0.930299\pi\)
−0.207899 + 0.978150i \(0.566663\pi\)
\(542\) 15.1848 + 17.5242i 0.652243 + 0.752729i
\(543\) −8.27532 + 2.42985i −0.355128 + 0.104275i
\(544\) −0.282066 + 1.96181i −0.0120935 + 0.0841121i
\(545\) 2.13524 2.46419i 0.0914634 0.105554i
\(546\) 1.52388 3.33682i 0.0652158 0.142803i
\(547\) −11.7363 3.44609i −0.501808 0.147344i 0.0210258 0.999779i \(-0.493307\pi\)
−0.522833 + 0.852435i \(0.675125\pi\)
\(548\) 6.46078 + 14.1471i 0.275991 + 0.604335i
\(549\) 0.873883 + 6.07799i 0.0372964 + 0.259402i
\(550\) 3.77903 + 2.42863i 0.161138 + 0.103557i
\(551\) 0.841882 0.0358654
\(552\) −0.877569 + 4.71486i −0.0373518 + 0.200678i
\(553\) 13.3424 0.567375
\(554\) −4.38215 2.81624i −0.186180 0.119650i
\(555\) 1.66578 + 11.5857i 0.0707083 + 0.491787i
\(556\) −2.34438 5.13349i −0.0994240 0.217708i
\(557\) −6.65762 1.95485i −0.282092 0.0828297i 0.137626 0.990484i \(-0.456053\pi\)
−0.419718 + 0.907655i \(0.637871\pi\)
\(558\) 2.44627 5.35659i 0.103559 0.226763i
\(559\) −19.4822 + 22.4837i −0.824011 + 0.950959i
\(560\) 0.214739 1.49355i 0.00907440 0.0631138i
\(561\) 8.54271 2.50837i 0.360674 0.105903i
\(562\) −18.1892 20.9914i −0.767263 0.885469i
\(563\) −14.4649 + 9.29601i −0.609622 + 0.391780i −0.808715 0.588200i \(-0.799837\pi\)
0.199093 + 0.979981i \(0.436200\pi\)
\(564\) 7.70580 4.95222i 0.324473 0.208526i
\(565\) 8.75146 + 10.0997i 0.368177 + 0.424898i
\(566\) 18.5148 5.43645i 0.778237 0.228511i
\(567\) 0.214739 1.49355i 0.00901821 0.0627230i
\(568\) 4.26486 4.92191i 0.178950 0.206519i
\(569\) −7.17424 + 15.7094i −0.300760 + 0.658573i −0.998319 0.0579546i \(-0.981542\pi\)
0.697559 + 0.716527i \(0.254269\pi\)
\(570\) 0.255554 + 0.0750376i 0.0107040 + 0.00314298i
\(571\) −3.63709 7.96411i −0.152207 0.333288i 0.818134 0.575028i \(-0.195009\pi\)
−0.970341 + 0.241741i \(0.922282\pi\)
\(572\) −1.55421 10.8097i −0.0649847 0.451978i
\(573\) 18.6198 + 11.9662i 0.777855 + 0.499897i
\(574\) −11.6348 −0.485625
\(575\) −3.28730 + 3.49194i −0.137090 + 0.145624i
\(576\) 1.00000 0.0416667
\(577\) −11.7747 7.56714i −0.490187 0.315024i 0.272093 0.962271i \(-0.412284\pi\)
−0.762281 + 0.647247i \(0.775920\pi\)
\(578\) −1.86030 12.9387i −0.0773783 0.538178i
\(579\) 8.87931 + 19.4430i 0.369012 + 0.808023i
\(580\) 3.03285 + 0.890526i 0.125932 + 0.0369771i
\(581\) 4.67346 10.2334i 0.193888 0.424555i
\(582\) 7.81844 9.02296i 0.324085 0.374014i
\(583\) 8.62530 59.9903i 0.357223 2.48454i
\(584\) −1.56986 + 0.460952i −0.0649612 + 0.0190743i
\(585\) 1.59204 + 1.83732i 0.0658229 + 0.0759636i
\(586\) −11.4015 + 7.32731i −0.470993 + 0.302689i
\(587\) 9.14073 5.87439i 0.377278 0.242462i −0.338234 0.941062i \(-0.609830\pi\)
0.715513 + 0.698600i \(0.246193\pi\)
\(588\) −3.09304 3.56956i −0.127555 0.147206i
\(589\) −1.50489 + 0.441877i −0.0620081 + 0.0182072i
\(590\) 2.08832 14.5246i 0.0859746 0.597966i
\(591\) 0.515432 0.594841i 0.0212021 0.0244685i
\(592\) 4.86238 10.6471i 0.199842 0.437594i
\(593\) −35.2755 10.3578i −1.44859 0.425345i −0.539516 0.841975i \(-0.681393\pi\)
−0.909076 + 0.416630i \(0.863211\pi\)
\(594\) −1.86610 4.08619i −0.0765670 0.167658i
\(595\) −0.425611 2.96019i −0.0174484 0.121356i
\(596\) 3.32180 + 2.13479i 0.136066 + 0.0874445i
\(597\) 10.0699 0.412133
\(598\) 11.6493 + 0.480493i 0.476376 + 0.0196488i
\(599\) −11.4056 −0.466021 −0.233010 0.972474i \(-0.574858\pi\)
−0.233010 + 0.972474i \(0.574858\pi\)
\(600\) 0.841254 + 0.540641i 0.0343440 + 0.0220716i
\(601\) 0.726756 + 5.05470i 0.0296450 + 0.206186i 0.999261 0.0384480i \(-0.0122414\pi\)
−0.969616 + 0.244634i \(0.921332\pi\)
\(602\) −7.67057 16.7962i −0.312629 0.684562i
\(603\) −0.991609 0.291163i −0.0403814 0.0118571i
\(604\) 6.09270 13.3411i 0.247908 0.542843i
\(605\) −6.01115 + 6.93724i −0.244388 + 0.282039i
\(606\) 0.136094 0.946557i 0.00552846 0.0384513i
\(607\) 39.9415 11.7279i 1.62117 0.476020i 0.659841 0.751405i \(-0.270624\pi\)
0.961334 + 0.275385i \(0.0888055\pi\)
\(608\) −0.174418 0.201289i −0.00707357 0.00816334i
\(609\) −4.01234 + 2.57858i −0.162588 + 0.104489i
\(610\) 5.16571 3.31980i 0.209153 0.134415i
\(611\) −14.5830 16.8296i −0.589964 0.680854i
\(612\) 1.90170 0.558391i 0.0768718 0.0225716i
\(613\) 2.29246 15.9444i 0.0925915 0.643988i −0.889688 0.456568i \(-0.849078\pi\)
0.982280 0.187420i \(-0.0600125\pi\)
\(614\) 12.7877 14.7578i 0.516071 0.595578i
\(615\) 3.20315 7.01393i 0.129164 0.282829i
\(616\) 6.50364 + 1.90964i 0.262039 + 0.0769416i
\(617\) 0.598069 + 1.30959i 0.0240774 + 0.0527221i 0.921289 0.388880i \(-0.127138\pi\)
−0.897211 + 0.441602i \(0.854410\pi\)
\(618\) 1.07019 + 7.44332i 0.0430493 + 0.299414i
\(619\) −6.58051 4.22904i −0.264493 0.169979i 0.401672 0.915784i \(-0.368429\pi\)
−0.666165 + 0.745804i \(0.732065\pi\)
\(620\) −5.88874 −0.236498
\(621\) 4.65334 1.16036i 0.186732 0.0465635i
\(622\) −9.23059 −0.370113
\(623\) 8.45645 + 5.43463i 0.338801 + 0.217734i
\(624\) −0.345984 2.40637i −0.0138504 0.0963319i
\(625\) 0.415415 + 0.909632i 0.0166166 + 0.0363853i
\(626\) 17.6962 + 5.19606i 0.707280 + 0.207676i
\(627\) −0.497023 + 1.08833i −0.0198492 + 0.0434637i
\(628\) −13.8189 + 15.9479i −0.551434 + 0.636389i
\(629\) 3.30155 22.9628i 0.131641 0.915586i
\(630\) −1.44778 + 0.425107i −0.0576810 + 0.0169367i
\(631\) −29.8129 34.4059i −1.18683 1.36968i −0.913030 0.407893i \(-0.866264\pi\)
−0.273803 0.961786i \(-0.588282\pi\)
\(632\) 7.43873 4.78058i 0.295897 0.190161i
\(633\) 10.0568 6.46314i 0.399724 0.256887i
\(634\) 8.69314 + 10.0324i 0.345249 + 0.398438i
\(635\) −4.66526 + 1.36984i −0.185135 + 0.0543605i
\(636\) 1.92009 13.3545i 0.0761365 0.529541i
\(637\) −7.51955 + 8.67803i −0.297935 + 0.343836i
\(638\) −5.89854 + 12.9160i −0.233526 + 0.511350i
\(639\) −6.24882 1.83482i −0.247199 0.0725843i
\(640\) −0.415415 0.909632i −0.0164207 0.0359564i
\(641\) 4.57846 + 31.8439i 0.180838 + 1.25776i 0.854787 + 0.518979i \(0.173688\pi\)
−0.673948 + 0.738778i \(0.735403\pi\)
\(642\) −7.01217 4.50645i −0.276748 0.177855i
\(643\) 26.4239 1.04206 0.521028 0.853539i \(-0.325549\pi\)
0.521028 + 0.853539i \(0.325549\pi\)
\(644\) −3.27485 + 6.45303i −0.129047 + 0.254285i
\(645\) 12.2373 0.481841
\(646\) −0.444089 0.285398i −0.0174724 0.0112289i
\(647\) −6.01302 41.8215i −0.236396 1.64417i −0.669488 0.742823i \(-0.733486\pi\)
0.433091 0.901350i \(-0.357423\pi\)
\(648\) −0.415415 0.909632i −0.0163190 0.0357337i
\(649\) 63.2471 + 18.5710i 2.48267 + 0.728976i
\(650\) 1.00992 2.21142i 0.0396124 0.0867391i
\(651\) 5.81880 6.71525i 0.228057 0.263191i
\(652\) 1.78412 12.4088i 0.0698714 0.485966i
\(653\) 0.808083 0.237275i 0.0316227 0.00928527i −0.265883 0.964005i \(-0.585663\pi\)
0.297506 + 0.954720i \(0.403845\pi\)
\(654\) 2.13524 + 2.46419i 0.0834943 + 0.0963576i
\(655\) −12.3659 + 7.94708i −0.483175 + 0.310518i
\(656\) −6.48668 + 4.16874i −0.253262 + 0.162762i
\(657\) 1.07144 + 1.23651i 0.0418008 + 0.0482407i
\(658\) 13.2616 3.89394i 0.516989 0.151802i
\(659\) 1.88262 13.0939i 0.0733366 0.510067i −0.919733 0.392543i \(-0.871595\pi\)
0.993070 0.117524i \(-0.0374957\pi\)
\(660\) −2.94172 + 3.39493i −0.114506 + 0.132147i
\(661\) 1.09699 2.40208i 0.0426681 0.0934300i −0.887098 0.461582i \(-0.847282\pi\)
0.929766 + 0.368152i \(0.120009\pi\)
\(662\) 18.6948 + 5.48928i 0.726592 + 0.213347i
\(663\) −2.00165 4.38301i −0.0777378 0.170222i
\(664\) −1.06107 7.37992i −0.0411776 0.286396i
\(665\) 0.338088 + 0.217276i 0.0131105 + 0.00842561i
\(666\) −11.7049 −0.453554
\(667\) −12.4041 8.71422i −0.480287 0.337416i
\(668\) 5.10690 0.197592
\(669\) 4.92079 + 3.16240i 0.190249 + 0.122265i
\(670\) 0.147078 + 1.02295i 0.00568213 + 0.0395201i
\(671\) 11.4588 + 25.0912i 0.442361 + 0.968636i
\(672\) 1.44778 + 0.425107i 0.0558494 + 0.0163989i
\(673\) −11.8554 + 25.9598i −0.456993 + 1.00068i 0.531169 + 0.847266i \(0.321753\pi\)
−0.988163 + 0.153410i \(0.950974\pi\)
\(674\) 5.60847 6.47252i 0.216030 0.249312i
\(675\) 0.142315 0.989821i 0.00547770 0.0380982i
\(676\) 6.80249 1.99739i 0.261634 0.0768228i
\(677\) 16.0227 + 18.4912i 0.615802 + 0.710673i 0.974904 0.222625i \(-0.0714625\pi\)
−0.359102 + 0.933298i \(0.616917\pi\)
\(678\) −11.2424 + 7.22504i −0.431761 + 0.277476i
\(679\) 15.1551 9.73960i 0.581600 0.373772i
\(680\) −1.29793 1.49789i −0.0497732 0.0574413i
\(681\) −24.2554 + 7.12202i −0.929468 + 0.272916i
\(682\) 3.76466 26.1838i 0.144156 1.00263i
\(683\) 17.2624 19.9219i 0.660528 0.762289i −0.322336 0.946625i \(-0.604468\pi\)
0.982863 + 0.184336i \(0.0590135\pi\)
\(684\) −0.110643 + 0.242274i −0.00423054 + 0.00926359i
\(685\) −14.9226 4.38167i −0.570163 0.167415i
\(686\) −7.34836 16.0907i −0.280562 0.614344i
\(687\) 1.33569 + 9.28995i 0.0509599 + 0.354434i
\(688\) −10.2946 6.61596i −0.392479 0.252231i
\(689\) −32.8002 −1.24959
\(690\) −2.98857 3.75080i −0.113773 0.142790i
\(691\) 37.7620 1.43653 0.718267 0.695767i \(-0.244936\pi\)
0.718267 + 0.695767i \(0.244936\pi\)
\(692\) 11.2085 + 7.20328i 0.426084 + 0.273828i
\(693\) −0.964639 6.70921i −0.0366436 0.254862i
\(694\) −5.70953 12.5021i −0.216731 0.474575i
\(695\) 5.41488 + 1.58995i 0.205398 + 0.0603103i
\(696\) −1.31308 + 2.87525i −0.0497723 + 0.108986i
\(697\) −10.0080 + 11.5498i −0.379079 + 0.437480i
\(698\) −0.432594 + 3.00876i −0.0163739 + 0.113883i
\(699\) −8.21890 + 2.41329i −0.310867 + 0.0912789i
\(700\) 0.988122 + 1.14035i 0.0373475 + 0.0431013i
\(701\) −2.93273 + 1.88475i −0.110768 + 0.0711862i −0.594852 0.803835i \(-0.702789\pi\)
0.484084 + 0.875022i \(0.339153\pi\)
\(702\) −2.04519 + 1.31436i −0.0771905 + 0.0496074i
\(703\) 2.04154 + 2.35606i 0.0769980 + 0.0888604i
\(704\) 4.31017 1.26558i 0.162446 0.0476984i
\(705\) −1.30359 + 9.06667i −0.0490961 + 0.341471i
\(706\) 8.96476 10.3459i 0.337393 0.389373i
\(707\) 0.599423 1.31255i 0.0225436 0.0493637i
\(708\) 14.0795 + 4.13412i 0.529141 + 0.155370i
\(709\) −3.94794 8.64478i −0.148268 0.324662i 0.820896 0.571077i \(-0.193474\pi\)
−0.969164 + 0.246416i \(0.920747\pi\)
\(710\) 0.926843 + 6.44633i 0.0347838 + 0.241927i
\(711\) −7.43873 4.78058i −0.278974 0.179286i
\(712\) 6.66192 0.249666
\(713\) 26.7465 + 9.06649i 1.00167 + 0.339543i
\(714\) 2.99063 0.111922
\(715\) 9.18725 + 5.90429i 0.343584 + 0.220808i
\(716\) −0.856977 5.96041i −0.0320267 0.222751i
\(717\) −4.07349 8.91970i −0.152127 0.333112i
\(718\) 3.02720 + 0.888865i 0.112974 + 0.0331721i
\(719\) 3.79737 8.31509i 0.141618 0.310100i −0.825511 0.564386i \(-0.809113\pi\)
0.967129 + 0.254286i \(0.0818403\pi\)
\(720\) −0.654861 + 0.755750i −0.0244052 + 0.0281651i
\(721\) −1.61481 + 11.2313i −0.0601387 + 0.418274i
\(722\) −18.1623 + 5.33293i −0.675931 + 0.198471i
\(723\) −3.02760 3.49404i −0.112598 0.129945i
\(724\) −7.25554 + 4.66285i −0.269650 + 0.173294i
\(725\) −2.65911 + 1.70891i −0.0987569 + 0.0634672i
\(726\) −6.01115 6.93724i −0.223095 0.257465i
\(727\) −7.93850 + 2.33095i −0.294423 + 0.0864503i −0.425608 0.904908i \(-0.639940\pi\)
0.131185 + 0.991358i \(0.458122\pi\)
\(728\) 0.522056 3.63098i 0.0193487 0.134573i
\(729\) −0.654861 + 0.755750i −0.0242541 + 0.0279907i
\(730\) 0.679674 1.48828i 0.0251559 0.0550837i
\(731\) −23.2716 6.83317i −0.860733 0.252734i
\(732\) 2.55085 + 5.58559i 0.0942822 + 0.206449i
\(733\) 1.99104 + 13.8480i 0.0735408 + 0.511487i 0.992983 + 0.118261i \(0.0377320\pi\)
−0.919442 + 0.393226i \(0.871359\pi\)
\(734\) 10.9965 + 7.06700i 0.405887 + 0.260848i
\(735\) 4.72321 0.174218
\(736\) 0.486307 + 4.77111i 0.0179255 + 0.175866i
\(737\) −4.64250 −0.171009
\(738\) 6.48668 + 4.16874i 0.238778 + 0.153453i
\(739\) 6.62107 + 46.0505i 0.243560 + 1.69400i 0.633972 + 0.773356i \(0.281424\pi\)
−0.390412 + 0.920640i \(0.627667\pi\)
\(740\) 4.86238 + 10.6471i 0.178745 + 0.391396i
\(741\) 0.621283 + 0.182425i 0.0228234 + 0.00670155i
\(742\) 8.45697 18.5182i 0.310465 0.679824i
\(743\) −31.1322 + 35.9285i −1.14213 + 1.31809i −0.201177 + 0.979555i \(0.564477\pi\)
−0.940954 + 0.338534i \(0.890069\pi\)
\(744\) 0.838056 5.82881i 0.0307246 0.213694i
\(745\) −3.78869 + 1.11246i −0.138807 + 0.0407573i
\(746\) 16.7776 + 19.3624i 0.614271 + 0.708906i
\(747\) −6.27222 + 4.03091i −0.229489 + 0.147483i
\(748\) 7.48999 4.81352i 0.273861 0.176000i
\(749\) −8.23637 9.50528i −0.300950 0.347315i
\(750\) −0.959493 + 0.281733i −0.0350357 + 0.0102874i
\(751\) 0.134564 0.935913i 0.00491031 0.0341519i −0.987219 0.159370i \(-0.949054\pi\)
0.992129 + 0.125218i \(0.0399629\pi\)
\(752\) 5.99846 6.92260i 0.218741 0.252441i
\(753\) −0.716666 + 1.56928i −0.0261168 + 0.0571878i
\(754\) 7.37322 + 2.16497i 0.268517 + 0.0788437i
\(755\) 6.09270 + 13.3411i 0.221736 + 0.485534i
\(756\) −0.214739 1.49355i −0.00781000 0.0543197i
\(757\) −28.3898 18.2450i −1.03185 0.663127i −0.0888889 0.996042i \(-0.528332\pi\)
−0.942957 + 0.332914i \(0.891968\pi\)
\(758\) 20.3046 0.737495
\(759\) 18.5882 10.8905i 0.674708 0.395301i
\(760\) 0.266343 0.00966128
\(761\) 43.5888 + 28.0128i 1.58009 + 1.01546i 0.975790 + 0.218708i \(0.0701844\pi\)
0.604302 + 0.796755i \(0.293452\pi\)
\(762\) −0.691964 4.81272i −0.0250672 0.174346i
\(763\) 2.04381 + 4.47532i 0.0739909 + 0.162017i
\(764\) 21.2369 + 6.23571i 0.768324 + 0.225600i
\(765\) −0.823348 + 1.80288i −0.0297682 + 0.0651833i
\(766\) −11.7978 + 13.6154i −0.426272 + 0.491945i
\(767\) 5.07694 35.3109i 0.183318 1.27500i
\(768\) 0.959493 0.281733i 0.0346227 0.0101661i
\(769\) −0.279205 0.322220i −0.0100684 0.0116196i 0.750693 0.660651i \(-0.229720\pi\)
−0.760761 + 0.649032i \(0.775174\pi\)
\(770\) −5.70219 + 3.66457i −0.205492 + 0.132062i
\(771\) −24.8825 + 15.9910i −0.896121 + 0.575902i
\(772\) 13.9974 + 16.1538i 0.503776 + 0.581388i
\(773\) −50.5455 + 14.8415i −1.81800 + 0.533812i −0.999189 0.0402577i \(-0.987182\pi\)
−0.818807 + 0.574070i \(0.805364\pi\)
\(774\) −1.74154 + 12.1127i −0.0625985 + 0.435382i
\(775\) 3.85631 4.45042i 0.138523 0.159864i
\(776\) 4.95967 10.8602i 0.178042 0.389857i
\(777\) −16.9461 4.97582i −0.607938 0.178507i
\(778\) −15.9089 34.8357i −0.570363 1.24892i
\(779\) −0.292272 2.03280i −0.0104717 0.0728325i
\(780\) 2.04519 + 1.31436i 0.0732294 + 0.0470617i
\(781\) −29.2556 −1.04685
\(782\) 3.58896 + 8.80169i 0.128341 + 0.314748i
\(783\) 3.16089 0.112961
\(784\) −3.97342 2.55356i −0.141908 0.0911986i
\(785\) −3.00313 20.8872i −0.107186 0.745498i
\(786\) −6.10634 13.3710i −0.217806 0.476928i
\(787\) 49.4364 + 14.5158i 1.76222 + 0.517434i 0.992638 0.121118i \(-0.0386480\pi\)
0.769579 + 0.638552i \(0.220466\pi\)
\(788\) 0.326968 0.715959i 0.0116477 0.0255050i
\(789\) 10.8522 12.5241i 0.386348 0.445870i
\(790\) −1.25841 + 8.75243i −0.0447722 + 0.311397i
\(791\) −19.3479 + 5.68107i −0.687933 + 0.201995i
\(792\) −2.94172 3.39493i −0.104530 0.120634i
\(793\) 12.5584 8.07082i 0.445963 0.286603i
\(794\) −8.22171 + 5.28377i −0.291778 + 0.187514i
\(795\) 8.83527 + 10.1964i 0.313355 + 0.361631i
\(796\) 9.66198 2.83701i 0.342460 0.100555i
\(797\) −0.870382 + 6.05364i −0.0308305 + 0.214431i −0.999413 0.0342621i \(-0.989092\pi\)
0.968582 + 0.248693i \(0.0800010\pi\)
\(798\) −0.263180 + 0.303725i −0.00931646 + 0.0107518i
\(799\) 7.54179 16.5142i 0.266809 0.584231i
\(800\) 0.959493 + 0.281733i 0.0339232 + 0.00996075i
\(801\) −2.76746 6.05990i −0.0977835 0.214116i
\(802\) −1.45644 10.1298i −0.0514288 0.357695i
\(803\) 6.18299 + 3.97356i 0.218193 + 0.140224i
\(804\) −1.03347 −0.0364477
\(805\) −2.73230 6.70080i −0.0963010 0.236172i
\(806\) −14.3162 −0.504267
\(807\) −5.78458 3.71752i −0.203627 0.130863i
\(808\) −0.136094 0.946557i −0.00478778 0.0332998i
\(809\) 18.0175 + 39.4529i 0.633462 + 1.38709i 0.905311 + 0.424749i \(0.139638\pi\)
−0.271849 + 0.962340i \(0.587635\pi\)
\(810\) 0.959493 + 0.281733i 0.0337131 + 0.00989907i
\(811\) 0.612312 1.34078i 0.0215012 0.0470810i −0.898577 0.438816i \(-0.855398\pi\)
0.920078 + 0.391735i \(0.128125\pi\)
\(812\) −3.12335 + 3.60453i −0.109608 + 0.126494i
\(813\) 3.29997 22.9518i 0.115735 0.804956i
\(814\) −50.4500 + 14.8135i −1.76827 + 0.519211i
\(815\) 8.20959 + 9.47438i 0.287570 + 0.331873i
\(816\) 1.66735 1.07154i 0.0583691 0.0375115i
\(817\) 2.74191 1.76212i 0.0959272 0.0616486i
\(818\) 11.6218 + 13.4123i 0.406347 + 0.468949i
\(819\) −3.51973 + 1.03349i −0.122989 + 0.0361129i
\(820\) 1.09735 7.63225i 0.0383212 0.266530i
\(821\) −29.0901 + 33.5717i −1.01525 + 1.17166i −0.0301743 + 0.999545i \(0.509606\pi\)
−0.985076 + 0.172117i \(0.944939\pi\)
\(822\) 6.46078 14.1471i 0.225345 0.493438i
\(823\) 28.5859 + 8.39357i 0.996441 + 0.292581i 0.738995 0.673711i \(-0.235301\pi\)
0.257446 + 0.966293i \(0.417119\pi\)
\(824\) 3.12386 + 6.84031i 0.108825 + 0.238293i
\(825\) −0.639298 4.44641i −0.0222575 0.154804i
\(826\) 18.6266 + 11.9706i 0.648103 + 0.416511i
\(827\) −21.4101 −0.744504 −0.372252 0.928132i \(-0.621414\pi\)
−0.372252 + 0.928132i \(0.621414\pi\)
\(828\) 4.13794 2.42435i 0.143803 0.0842520i
\(829\) 24.5944 0.854199 0.427099 0.904205i \(-0.359535\pi\)
0.427099 + 0.904205i \(0.359535\pi\)
\(830\) 6.27222 + 4.03091i 0.217712 + 0.139915i
\(831\) 0.741328 + 5.15605i 0.0257164 + 0.178861i
\(832\) −1.00992 2.21142i −0.0350128 0.0766672i
\(833\) −8.98215 2.63740i −0.311213 0.0913804i
\(834\) −2.34438 + 5.13349i −0.0811794 + 0.177758i
\(835\) −3.34431 + 3.85953i −0.115734 + 0.133565i
\(836\) −0.170273 + 1.18427i −0.00588900 + 0.0409589i
\(837\) −5.65021 + 1.65905i −0.195300 + 0.0573452i
\(838\) −20.9606 24.1898i −0.724072 0.835624i
\(839\) 28.0493 18.0262i 0.968369 0.622333i 0.0420667 0.999115i \(-0.486606\pi\)
0.926302 + 0.376782i \(0.122969\pi\)
\(840\) −1.26937 + 0.815775i −0.0437974 + 0.0281469i
\(841\) 12.4481 + 14.3659i 0.429244 + 0.495375i
\(842\) −21.5291 + 6.32150i −0.741940 + 0.217853i
\(843\) −3.95288 + 27.4929i −0.136144 + 0.946906i
\(844\) 7.82860 9.03468i 0.269471 0.310987i
\(845\) −2.94516 + 6.44899i −0.101316 + 0.221852i
\(846\) −8.78887 2.58064i −0.302167 0.0887244i
\(847\) −5.75377 12.5990i −0.197702 0.432907i
\(848\) −1.92009 13.3545i −0.0659361 0.458596i
\(849\) −16.2332 10.4325i −0.557123 0.358041i
\(850\) 1.98199 0.0679816
\(851\) −5.69216 55.8452i −0.195125 1.91435i
\(852\) −6.51262 −0.223119
\(853\) 32.1760 + 20.6782i 1.10168 + 0.708009i 0.959466 0.281826i \(-0.0909400\pi\)
0.142219 + 0.989835i \(0.454576\pi\)
\(854\) 1.31861 + 9.17110i 0.0451217 + 0.313829i
\(855\) −0.110643 0.242274i −0.00378391 0.00828561i
\(856\) −7.99774 2.34835i −0.273357 0.0802649i
\(857\) 19.0893 41.7998i 0.652078 1.42785i −0.237645 0.971352i \(-0.576375\pi\)
0.889723 0.456501i \(-0.150897\pi\)
\(858\) −7.15167 + 8.25347i −0.244154 + 0.281769i
\(859\) −5.23947 + 36.4413i −0.178768 + 1.24336i 0.680849 + 0.732424i \(0.261611\pi\)
−0.859617 + 0.510938i \(0.829298\pi\)
\(860\) 11.7416 3.44763i 0.400384 0.117563i
\(861\) 7.61914 + 8.79296i 0.259660 + 0.299663i
\(862\) 17.4911 11.2408i 0.595748 0.382864i
\(863\) 21.6818 13.9340i 0.738056 0.474320i −0.116819 0.993153i \(-0.537270\pi\)
0.854875 + 0.518833i \(0.173633\pi\)
\(864\) −0.654861 0.755750i −0.0222788 0.0257111i
\(865\) −12.7839 + 3.75369i −0.434666 + 0.127629i
\(866\) 2.61832 18.2108i 0.0889743 0.618830i
\(867\) −8.56016 + 9.87895i −0.290718 + 0.335507i
\(868\) 3.69119 8.08258i 0.125287 0.274341i
\(869\) −38.1124 11.1908i −1.29287 0.379622i
\(870\) −1.31308 2.87525i −0.0445177 0.0974801i
\(871\) 0.357565 + 2.48692i 0.0121156 + 0.0842660i
\(872\) 2.74299 + 1.76281i 0.0928893 + 0.0596963i
\(873\) −11.9391 −0.404077
\(874\) −1.20972 0.410070i −0.0409195 0.0138708i
\(875\) −1.50890 −0.0510103
\(876\) 1.37640 + 0.884560i 0.0465043 + 0.0298865i
\(877\) 7.36469 + 51.2225i 0.248688 + 1.72966i 0.605815 + 0.795606i \(0.292847\pi\)
−0.357127 + 0.934056i \(0.616244\pi\)
\(878\) 1.76859 + 3.87266i 0.0596869 + 0.130696i
\(879\) 13.0040 + 3.81833i 0.438615 + 0.128789i
\(880\) −1.86610 + 4.08619i −0.0629062 + 0.137745i
\(881\) −18.0607 + 20.8431i −0.608479 + 0.702223i −0.973477 0.228786i \(-0.926524\pi\)
0.364997 + 0.931009i \(0.381070\pi\)
\(882\) −0.672183 + 4.67513i −0.0226336 + 0.157420i
\(883\) 4.21766 1.23842i 0.141936 0.0416760i −0.209993 0.977703i \(-0.567344\pi\)
0.351929 + 0.936027i \(0.385526\pi\)
\(884\) −3.15541 3.64154i −0.106128 0.122478i
\(885\) −12.3445 + 7.93332i −0.414955 + 0.266676i
\(886\) −14.1519 + 9.09488i −0.475443 + 0.305548i
\(887\) −23.2690 26.8538i −0.781296 0.901664i 0.215906 0.976414i \(-0.430729\pi\)
−0.997202 + 0.0747503i \(0.976184\pi\)
\(888\) −11.2307 + 3.29764i −0.376879 + 0.110662i
\(889\) 1.04411 7.26193i 0.0350182 0.243557i
\(890\) −4.36263 + 5.03475i −0.146236 + 0.168765i
\(891\) −1.86610 + 4.08619i −0.0625167 + 0.136893i
\(892\) 5.61241 + 1.64795i 0.187917 + 0.0551775i
\(893\) 1.01348 + 2.21921i 0.0339148 + 0.0742630i
\(894\) −0.561949 3.90844i −0.0187944 0.130718i
\(895\) 5.06578 + 3.25558i 0.169330 + 0.108822i
\(896\) 1.50890 0.0504089
\(897\) −7.26555 9.11862i −0.242590 0.304462i
\(898\) 16.7047 0.557444
\(899\) 15.6588 + 10.0633i 0.522251 + 0.335630i
\(900\) −0.142315 0.989821i −0.00474383 0.0329940i
\(901\) −11.1085 24.3242i −0.370077 0.810355i
\(902\) 33.2346 + 9.75856i 1.10659 + 0.324924i
\(903\) −7.67057 + 16.7962i −0.255261 + 0.558943i
\(904\) −8.75146 + 10.0997i −0.291069 + 0.335912i
\(905\) 1.22742 8.53689i 0.0408008 0.283776i
\(906\) −14.0724 + 4.13204i −0.467525 + 0.137278i
\(907\) 1.90415 + 2.19750i 0.0632261 + 0.0729668i 0.786482 0.617614i \(-0.211901\pi\)
−0.723255 + 0.690581i \(0.757355\pi\)
\(908\) −21.2663 + 13.6671i −0.705749 + 0.453557i
\(909\) −0.804483 + 0.517010i −0.0266830 + 0.0171481i
\(910\) 2.40224 + 2.77233i 0.0796335 + 0.0919019i
\(911\) 15.3977 4.52116i 0.510147 0.149793i −0.0165213 0.999864i \(-0.505259\pi\)
0.526668 + 0.850071i \(0.323441\pi\)
\(912\) −0.0379046 + 0.263632i −0.00125515 + 0.00872974i
\(913\) −21.9329 + 25.3119i −0.725874 + 0.837703i
\(914\) −1.20122 + 2.63031i −0.0397329 + 0.0870029i
\(915\) −5.89176 1.72998i −0.194775 0.0571912i
\(916\) 3.89887 + 8.53733i 0.128822 + 0.282081i
\(917\) −3.15653 21.9542i −0.104238 0.724990i
\(918\) −1.66735 1.07154i −0.0550309 0.0353662i
\(919\) −34.7600 −1.14663 −0.573313 0.819336i \(-0.694342\pi\)
−0.573313 + 0.819336i \(0.694342\pi\)
\(920\) −3.92423 2.75689i −0.129378 0.0908919i
\(921\) −19.5274 −0.643450
\(922\) 1.58976 + 1.02168i 0.0523560 + 0.0336471i
\(923\) 2.25326 + 15.6718i 0.0741671 + 0.515843i
\(924\) −2.81577 6.16567i −0.0926319 0.202836i
\(925\) −11.2307 3.29764i −0.369264 0.108426i
\(926\) 12.5579 27.4979i 0.412677 0.903636i
\(927\) 4.92446 5.68313i 0.161741 0.186659i
\(928\) −0.449842 + 3.12872i −0.0147668 + 0.102705i
\(929\) 55.4855 16.2920i 1.82042 0.534524i 0.821080 0.570814i \(-0.193372\pi\)
0.999341 + 0.0362898i \(0.0115539\pi\)
\(930\) 3.85631 + 4.45042i 0.126453 + 0.145935i
\(931\) 1.05829 0.680123i 0.0346841 0.0222901i
\(932\) −7.20608 + 4.63106i −0.236043 + 0.151696i
\(933\) 6.04475 + 6.97601i 0.197896 + 0.228384i
\(934\) 9.15528 2.68823i 0.299570 0.0879616i
\(935\) −1.26708 + 8.81274i −0.0414380 + 0.288207i
\(936\) −1.59204 + 1.83732i −0.0520375 + 0.0600545i
\(937\) 4.88646 10.6999i 0.159634 0.349549i −0.812867 0.582450i \(-0.802094\pi\)
0.972501 + 0.232900i \(0.0748216\pi\)
\(938\) −1.49624 0.439336i −0.0488541 0.0143448i
\(939\) −7.66159 16.7766i −0.250027 0.547482i
\(940\) 1.30359 + 9.06667i 0.0425184 + 0.295722i
\(941\) 13.2540 + 8.51781i 0.432067 + 0.277673i 0.738544 0.674205i \(-0.235514\pi\)
−0.306477 + 0.951878i \(0.599150\pi\)
\(942\) 21.1020 0.687541
\(943\) −16.7350 + 32.9760i −0.544966 + 1.07385i
\(944\) 14.6739 0.477595
\(945\) 1.26937 + 0.815775i 0.0412926 + 0.0265372i
\(946\) 7.82325 + 54.4119i 0.254356 + 1.76908i
\(947\) 8.43513 + 18.4703i 0.274105 + 0.600206i 0.995754 0.0920531i \(-0.0293429\pi\)
−0.721649 + 0.692259i \(0.756616\pi\)
\(948\) −8.48425 2.49120i −0.275556 0.0809104i
\(949\) 1.65237 3.61818i 0.0536381 0.117451i
\(950\) −0.174418 + 0.201289i −0.00565886 + 0.00653067i
\(951\) 1.88920 13.1397i 0.0612615 0.426083i
\(952\) 2.86949 0.842558i 0.0930007 0.0273075i
\(953\) −27.7420 32.0160i −0.898651 1.03710i −0.999111 0.0421573i \(-0.986577\pi\)
0.100460 0.994941i \(-0.467969\pi\)
\(954\) −11.3501 + 7.29424i −0.367472 + 0.236160i
\(955\) −18.6198 + 11.9662i −0.602524 + 0.387219i
\(956\) −6.42145 7.41075i −0.207685 0.239681i
\(957\) 13.6240 4.00037i 0.440401 0.129313i
\(958\) −1.13500 + 7.89410i −0.0366702 + 0.255047i
\(959\) 15.3678 17.7354i 0.496254 0.572707i
\(960\) −0.415415 + 0.909632i −0.0134075 + 0.0293582i
\(961\) −3.52835 1.03602i −0.113818 0.0334199i
\(962\) 11.8210 + 25.8844i 0.381125 + 0.834546i
\(963\) 1.18625 + 8.25054i 0.0382263 + 0.265870i
\(964\) −3.88935 2.49953i −0.125268 0.0805045i
\(965\) −21.3746 −0.688071
\(966\) 7.02144 1.75087i 0.225911 0.0563332i
\(967\) 28.9145 0.929827 0.464914 0.885356i \(-0.346085\pi\)
0.464914 + 0.885356i \(0.346085\pi\)
\(968\) −7.72211 4.96270i −0.248198 0.159507i
\(969\) 0.0751265 + 0.522516i 0.00241341 + 0.0167856i
\(970\) 4.95967 + 10.8602i 0.159246 + 0.348699i
\(971\) −56.7998 16.6779i −1.82279 0.535220i −0.823317 0.567581i \(-0.807879\pi\)
−0.999476 + 0.0323610i \(0.989697\pi\)
\(972\) −0.415415 + 0.909632i −0.0133244 + 0.0291765i
\(973\) −5.57644 + 6.43556i −0.178772 + 0.206314i
\(974\) 1.49608 10.4054i 0.0479374 0.333412i
\(975\) −2.33264 + 0.684925i −0.0747042 + 0.0219351i
\(976\) 4.02117 + 4.64067i 0.128714 + 0.148544i
\(977\) 24.7057 15.8774i 0.790405 0.507962i −0.0820669 0.996627i \(-0.526152\pi\)
0.872472 + 0.488664i \(0.162516\pi\)
\(978\) −10.5463 + 6.77769i −0.337233 + 0.216727i
\(979\) −19.5975 22.6168i −0.626340 0.722835i
\(980\) 4.53189 1.33068i 0.144766 0.0425071i
\(981\) 0.464031 3.22741i 0.0148154 0.103043i
\(982\) 16.7002 19.2731i 0.532925 0.615028i
\(983\) −4.30705 + 9.43112i −0.137374 + 0.300806i −0.965798 0.259294i \(-0.916510\pi\)
0.828425 + 0.560100i \(0.189237\pi\)
\(984\) 7.39839 + 2.17236i 0.235852 + 0.0692524i
\(985\) 0.326968 + 0.715959i 0.0104181 + 0.0228124i
\(986\) 0.891582 + 6.20109i 0.0283937 + 0.197483i
\(987\) −11.6273 7.47242i −0.370102 0.237850i
\(988\) 0.647511 0.0206001
\(989\) −58.6380 2.41861i −1.86458 0.0769072i
\(990\) 4.49214 0.142769
\(991\) 27.9447 + 17.9589i 0.887692 + 0.570485i 0.903116 0.429396i \(-0.141274\pi\)
−0.0154246 + 0.999881i \(0.504910\pi\)
\(992\) −0.838056 5.82881i −0.0266083 0.185065i
\(993\) −8.09395 17.7233i −0.256854 0.562431i
\(994\) −9.42886 2.76856i −0.299065 0.0878135i
\(995\) −4.18318 + 9.15988i −0.132616 + 0.290388i
\(996\) −4.88251 + 5.63472i −0.154708 + 0.178543i
\(997\) −2.93584 + 20.4192i −0.0929790 + 0.646683i 0.889030 + 0.457849i \(0.151380\pi\)
−0.982009 + 0.188834i \(0.939529\pi\)
\(998\) −21.9444 + 6.44346i −0.694638 + 0.203964i
\(999\) 7.66506 + 8.84595i 0.242512 + 0.279873i
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.301.2 20
23.12 even 11 inner 690.2.m.e.541.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.e.301.2 20 1.1 even 1 trivial
690.2.m.e.541.2 yes 20 23.12 even 11 inner