Properties

Label 690.2.m.f.541.1
Level $690$
Weight $2$
Character 690.541
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: \( x^{20} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + 63837 x^{12} - 154607 x^{11} + 334467 x^{10} - 664202 x^{9} + \cdots + 123904 \) 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 541.1
Root \(-0.245245 + 0.0720105i\) of defining polynomial
Character \(\chi\) \(=\) 690.541
Dual form 690.2.m.f.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.525067 - 0.605959i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(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} +(-0.525067 - 0.605959i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-3.81286 - 2.45038i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(1.33714 - 1.54314i) q^{13} +(0.769321 + 0.225893i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.27417 - 4.97974i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-1.39854 + 3.06237i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-0.674516 + 0.433485i) q^{21} +4.53236 q^{22} +(0.259300 + 4.78882i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.290588 + 2.02109i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-0.769321 + 0.225893i) q^{28} +(-2.36151 - 5.17098i) q^{29} +(0.654861 + 0.755750i) q^{30} +(-1.15750 - 8.05059i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-2.96807 + 3.42533i) q^{33} +(4.60541 + 2.95971i) q^{34} +(-0.674516 - 0.433485i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(4.13446 + 1.21399i) q^{37} +(-0.479117 - 3.33233i) q^{38} +(-1.33714 - 1.54314i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-5.00816 + 1.47053i) q^{41} +(0.333079 - 0.729342i) q^{42} +(-1.78576 + 12.4202i) q^{43} +(-3.81286 + 2.45038i) q^{44} -1.00000 q^{45} +(-2.80717 - 3.88842i) q^{46} -5.18694 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.904712 - 6.29241i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(-5.25270 + 1.54233i) q^{51} +(-0.848224 - 1.85735i) q^{52} +(-6.06642 - 7.00102i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-4.34877 - 1.27691i) q^{55} +(0.525067 - 0.605959i) q^{56} +(2.83217 + 1.82012i) q^{57} +(4.78227 + 3.07338i) q^{58} +(1.99897 - 2.30693i) q^{59} +(-0.959493 - 0.281733i) q^{60} +(-2.18047 - 15.1655i) q^{61} +(5.32623 + 6.14679i) q^{62} +(0.333079 + 0.729342i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.848224 - 1.85735i) q^{65} +(0.645022 - 4.48623i) q^{66} +(11.4849 - 7.38088i) q^{67} -5.47446 q^{68} +(4.77698 + 0.424859i) q^{69} +0.801799 q^{70} +(-4.84158 + 3.11150i) q^{71} +(0.142315 - 0.989821i) q^{72} +(1.55454 - 3.40396i) q^{73} +(-4.13446 + 1.21399i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(2.20465 + 2.54431i) q^{76} +(0.517178 + 3.59705i) q^{77} +(1.95916 + 0.575261i) q^{78} +(1.29853 - 1.49859i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(3.41810 - 3.94470i) q^{82} +(2.51187 + 0.737551i) q^{83} +(0.114108 + 0.793638i) q^{84} +(-3.58501 - 4.13732i) q^{85} +(-5.21261 - 11.4140i) q^{86} +(-5.45443 + 1.60156i) q^{87} +(1.88281 - 4.12278i) q^{88} +(-0.999078 + 6.94874i) q^{89} +(0.841254 - 0.540641i) q^{90} -1.63717 q^{91} +(4.46378 + 1.75348i) q^{92} -8.13337 q^{93} +(4.36354 - 2.80427i) q^{94} +(-0.479117 + 3.33233i) q^{95} +(0.415415 - 0.909632i) q^{96} +(0.760874 - 0.223413i) q^{97} +(2.64084 + 5.78264i) q^{98} +(2.96807 + 3.42533i) 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 \( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\)

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
\(7\) −0.525067 0.605959i −0.198457 0.229031i 0.647795 0.761815i \(-0.275691\pi\)
−0.846251 + 0.532784i \(0.821146\pi\)
\(8\) 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
\(11\) −3.81286 2.45038i −1.14962 0.738817i −0.180058 0.983656i \(-0.557629\pi\)
−0.969564 + 0.244839i \(0.921265\pi\)
\(12\) −0.841254 0.540641i −0.242849 0.156070i
\(13\) 1.33714 1.54314i 0.370856 0.427991i −0.539391 0.842055i \(-0.681346\pi\)
0.910248 + 0.414064i \(0.135891\pi\)
\(14\) 0.769321 + 0.225893i 0.205610 + 0.0603724i
\(15\) −0.142315 0.989821i −0.0367455 0.255571i
\(16\) −0.654861 0.755750i −0.163715 0.188937i
\(17\) −2.27417 4.97974i −0.551568 1.20776i −0.956046 0.293217i \(-0.905274\pi\)
0.404478 0.914548i \(-0.367453\pi\)
\(18\) 0.959493 0.281733i 0.226155 0.0664050i
\(19\) −1.39854 + 3.06237i −0.320846 + 0.702555i −0.999491 0.0319116i \(-0.989841\pi\)
0.678644 + 0.734467i \(0.262568\pi\)
\(20\) 0.142315 0.989821i 0.0318226 0.221331i
\(21\) −0.674516 + 0.433485i −0.147192 + 0.0945943i
\(22\) 4.53236 0.966303
\(23\) 0.259300 + 4.78882i 0.0540677 + 0.998537i
\(24\) 1.00000 0.204124
\(25\) 0.841254 0.540641i 0.168251 0.108128i
\(26\) −0.290588 + 2.02109i −0.0569891 + 0.396368i
\(27\) −0.415415 + 0.909632i −0.0799467 + 0.175059i
\(28\) −0.769321 + 0.225893i −0.145388 + 0.0426898i
\(29\) −2.36151 5.17098i −0.438521 0.960227i −0.991867 0.127276i \(-0.959377\pi\)
0.553346 0.832951i \(-0.313351\pi\)
\(30\) 0.654861 + 0.755750i 0.119561 + 0.137980i
\(31\) −1.15750 8.05059i −0.207893 1.44593i −0.780016 0.625760i \(-0.784789\pi\)
0.572123 0.820168i \(-0.306120\pi\)
\(32\) 0.959493 + 0.281733i 0.169616 + 0.0498038i
\(33\) −2.96807 + 3.42533i −0.516674 + 0.596273i
\(34\) 4.60541 + 2.95971i 0.789821 + 0.507587i
\(35\) −0.674516 0.433485i −0.114014 0.0732724i
\(36\) −0.654861 + 0.755750i −0.109143 + 0.125958i
\(37\) 4.13446 + 1.21399i 0.679700 + 0.199578i 0.603318 0.797501i \(-0.293845\pi\)
0.0763822 + 0.997079i \(0.475663\pi\)
\(38\) −0.479117 3.33233i −0.0777231 0.540576i
\(39\) −1.33714 1.54314i −0.214114 0.247101i
\(40\) 0.415415 + 0.909632i 0.0656829 + 0.143825i
\(41\) −5.00816 + 1.47053i −0.782143 + 0.229658i −0.648341 0.761350i \(-0.724537\pi\)
−0.133802 + 0.991008i \(0.542719\pi\)
\(42\) 0.333079 0.729342i 0.0513953 0.112540i
\(43\) −1.78576 + 12.4202i −0.272326 + 1.89407i 0.151715 + 0.988424i \(0.451520\pi\)
−0.424041 + 0.905643i \(0.639389\pi\)
\(44\) −3.81286 + 2.45038i −0.574811 + 0.369409i
\(45\) −1.00000 −0.149071
\(46\) −2.80717 3.88842i −0.413894 0.573316i
\(47\) −5.18694 −0.756594 −0.378297 0.925684i \(-0.623490\pi\)
−0.378297 + 0.925684i \(0.623490\pi\)
\(48\) −0.841254 + 0.540641i −0.121424 + 0.0780348i
\(49\) 0.904712 6.29241i 0.129245 0.898916i
\(50\) −0.415415 + 0.909632i −0.0587486 + 0.128641i
\(51\) −5.25270 + 1.54233i −0.735525 + 0.215970i
\(52\) −0.848224 1.85735i −0.117627 0.257568i
\(53\) −6.06642 7.00102i −0.833287 0.961664i 0.166416 0.986056i \(-0.446781\pi\)
−0.999702 + 0.0243914i \(0.992235\pi\)
\(54\) −0.142315 0.989821i −0.0193666 0.134698i
\(55\) −4.34877 1.27691i −0.586388 0.172179i
\(56\) 0.525067 0.605959i 0.0701650 0.0809747i
\(57\) 2.83217 + 1.82012i 0.375129 + 0.241081i
\(58\) 4.78227 + 3.07338i 0.627943 + 0.403555i
\(59\) 1.99897 2.30693i 0.260243 0.300337i −0.610558 0.791971i \(-0.709055\pi\)
0.870802 + 0.491634i \(0.163600\pi\)
\(60\) −0.959493 0.281733i −0.123870 0.0363715i
\(61\) −2.18047 15.1655i −0.279180 1.94174i −0.332355 0.943155i \(-0.607843\pi\)
0.0531745 0.998585i \(-0.483066\pi\)
\(62\) 5.32623 + 6.14679i 0.676432 + 0.780644i
\(63\) 0.333079 + 0.729342i 0.0419641 + 0.0918885i
\(64\) −0.959493 + 0.281733i −0.119937 + 0.0352166i
\(65\) 0.848224 1.85735i 0.105209 0.230376i
\(66\) 0.645022 4.48623i 0.0793968 0.552217i
\(67\) 11.4849 7.38088i 1.40310 0.901718i 0.403190 0.915116i \(-0.367901\pi\)
0.999910 + 0.0133985i \(0.00426501\pi\)
\(68\) −5.47446 −0.663875
\(69\) 4.77698 + 0.424859i 0.575080 + 0.0511471i
\(70\) 0.801799 0.0958333
\(71\) −4.84158 + 3.11150i −0.574590 + 0.369267i −0.795432 0.606043i \(-0.792756\pi\)
0.220842 + 0.975310i \(0.429120\pi\)
\(72\) 0.142315 0.989821i 0.0167720 0.116652i
\(73\) 1.55454 3.40396i 0.181945 0.398403i −0.796580 0.604533i \(-0.793360\pi\)
0.978525 + 0.206130i \(0.0660870\pi\)
\(74\) −4.13446 + 1.21399i −0.480621 + 0.141123i
\(75\) −0.415415 0.909632i −0.0479680 0.105035i
\(76\) 2.20465 + 2.54431i 0.252891 + 0.291852i
\(77\) 0.517178 + 3.59705i 0.0589379 + 0.409922i
\(78\) 1.95916 + 0.575261i 0.221831 + 0.0651355i
\(79\) 1.29853 1.49859i 0.146097 0.168604i −0.677985 0.735076i \(-0.737146\pi\)
0.824081 + 0.566472i \(0.191692\pi\)
\(80\) −0.841254 0.540641i −0.0940550 0.0604455i
\(81\) 0.841254 + 0.540641i 0.0934726 + 0.0600712i
\(82\) 3.41810 3.94470i 0.377466 0.435620i
\(83\) 2.51187 + 0.737551i 0.275713 + 0.0809568i 0.416666 0.909060i \(-0.363198\pi\)
−0.140953 + 0.990016i \(0.545017\pi\)
\(84\) 0.114108 + 0.793638i 0.0124502 + 0.0865930i
\(85\) −3.58501 4.13732i −0.388849 0.448755i
\(86\) −5.21261 11.4140i −0.562090 1.23081i
\(87\) −5.45443 + 1.60156i −0.584776 + 0.171706i
\(88\) 1.88281 4.12278i 0.200708 0.439490i
\(89\) −0.999078 + 6.94874i −0.105902 + 0.736565i 0.865806 + 0.500380i \(0.166806\pi\)
−0.971708 + 0.236185i \(0.924103\pi\)
\(90\) 0.841254 0.540641i 0.0886759 0.0569885i
\(91\) −1.63717 −0.171622
\(92\) 4.46378 + 1.75348i 0.465381 + 0.182813i
\(93\) −8.13337 −0.843392
\(94\) 4.36354 2.80427i 0.450064 0.289239i
\(95\) −0.479117 + 3.33233i −0.0491564 + 0.341890i
\(96\) 0.415415 0.909632i 0.0423981 0.0928389i
\(97\) 0.760874 0.223413i 0.0772551 0.0226841i −0.242877 0.970057i \(-0.578091\pi\)
0.320132 + 0.947373i \(0.396273\pi\)
\(98\) 2.64084 + 5.78264i 0.266765 + 0.584135i
\(99\) 2.96807 + 3.42533i 0.298302 + 0.344259i
\(100\) −0.142315 0.989821i −0.0142315 0.0989821i
\(101\) −8.19154 2.40525i −0.815089 0.239332i −0.152489 0.988305i \(-0.548729\pi\)
−0.662600 + 0.748974i \(0.730547\pi\)
\(102\) 3.58501 4.13732i 0.354969 0.409656i
\(103\) 16.3723 + 10.5219i 1.61321 + 1.03675i 0.960165 + 0.279433i \(0.0901464\pi\)
0.653048 + 0.757317i \(0.273490\pi\)
\(104\) 1.71773 + 1.10392i 0.168437 + 0.108248i
\(105\) −0.525067 + 0.605959i −0.0512413 + 0.0591356i
\(106\) 8.88844 + 2.60988i 0.863321 + 0.253494i
\(107\) 0.0557577 + 0.387804i 0.00539030 + 0.0374904i 0.992339 0.123544i \(-0.0394260\pi\)
−0.986949 + 0.161035i \(0.948517\pi\)
\(108\) 0.654861 + 0.755750i 0.0630140 + 0.0727220i
\(109\) 3.06282 + 6.70663i 0.293365 + 0.642379i 0.997721 0.0674671i \(-0.0214918\pi\)
−0.704357 + 0.709846i \(0.748765\pi\)
\(110\) 4.34877 1.27691i 0.414639 0.121749i
\(111\) 1.79002 3.91960i 0.169902 0.372032i
\(112\) −0.114108 + 0.793638i −0.0107822 + 0.0749917i
\(113\) 13.9531 8.96710i 1.31260 0.843554i 0.318072 0.948066i \(-0.396964\pi\)
0.994524 + 0.104512i \(0.0333281\pi\)
\(114\) −3.36660 −0.315311
\(115\) 1.59796 + 4.52178i 0.149011 + 0.421658i
\(116\) −5.68470 −0.527811
\(117\) −1.71773 + 1.10392i −0.158804 + 0.102057i
\(118\) −0.434417 + 3.02144i −0.0399913 + 0.278146i
\(119\) −1.82343 + 3.99275i −0.167153 + 0.366015i
\(120\) 0.959493 0.281733i 0.0875893 0.0257185i
\(121\) 3.96401 + 8.67998i 0.360365 + 0.789089i
\(122\) 10.0334 + 11.5792i 0.908381 + 1.04833i
\(123\) 0.742825 + 5.16646i 0.0669783 + 0.465844i
\(124\) −7.80391 2.29144i −0.700812 0.205777i
\(125\) 0.654861 0.755750i 0.0585725 0.0675963i
\(126\) −0.674516 0.433485i −0.0600907 0.0386179i
\(127\) −6.94227 4.46152i −0.616026 0.395896i 0.195086 0.980786i \(-0.437501\pi\)
−0.811113 + 0.584890i \(0.801138\pi\)
\(128\) 0.654861 0.755750i 0.0578821 0.0667995i
\(129\) 12.0397 + 3.53517i 1.06003 + 0.311254i
\(130\) 0.290588 + 2.02109i 0.0254863 + 0.177261i
\(131\) −7.70990 8.89769i −0.673617 0.777395i 0.311321 0.950305i \(-0.399229\pi\)
−0.984938 + 0.172910i \(0.944683\pi\)
\(132\) 1.88281 + 4.12278i 0.163878 + 0.358842i
\(133\) 2.59000 0.760491i 0.224581 0.0659430i
\(134\) −5.67128 + 12.4184i −0.489924 + 1.07278i
\(135\) −0.142315 + 0.989821i −0.0122485 + 0.0851903i
\(136\) 4.60541 2.95971i 0.394910 0.253793i
\(137\) 7.30745 0.624317 0.312159 0.950030i \(-0.398948\pi\)
0.312159 + 0.950030i \(0.398948\pi\)
\(138\) −4.24834 + 2.22521i −0.361643 + 0.189423i
\(139\) −0.283114 −0.0240134 −0.0120067 0.999928i \(-0.503822\pi\)
−0.0120067 + 0.999928i \(0.503822\pi\)
\(140\) −0.674516 + 0.433485i −0.0570070 + 0.0366362i
\(141\) −0.738179 + 5.13415i −0.0621659 + 0.432373i
\(142\) 2.39080 5.23512i 0.200631 0.439321i
\(143\) −8.87962 + 2.60729i −0.742551 + 0.218033i
\(144\) 0.415415 + 0.909632i 0.0346179 + 0.0758027i
\(145\) −3.72269 4.29621i −0.309152 0.356781i
\(146\) 0.532560 + 3.70404i 0.0440750 + 0.306548i
\(147\) −6.09961 1.79101i −0.503087 0.147720i
\(148\) 2.82180 3.25653i 0.231950 0.267685i
\(149\) 1.79233 + 1.15186i 0.146834 + 0.0943642i 0.611995 0.790862i \(-0.290367\pi\)
−0.465161 + 0.885226i \(0.654004\pi\)
\(150\) 0.841254 + 0.540641i 0.0686881 + 0.0441431i
\(151\) 9.25100 10.6762i 0.752835 0.868818i −0.242005 0.970275i \(-0.577805\pi\)
0.994840 + 0.101457i \(0.0323504\pi\)
\(152\) −3.23023 0.948481i −0.262006 0.0769320i
\(153\) 0.779096 + 5.41873i 0.0629862 + 0.438079i
\(154\) −2.37979 2.74643i −0.191769 0.221313i
\(155\) −3.37873 7.39838i −0.271386 0.594252i
\(156\) −1.95916 + 0.575261i −0.156858 + 0.0460578i
\(157\) −9.68705 + 21.2117i −0.773111 + 1.69288i −0.0534308 + 0.998572i \(0.517016\pi\)
−0.719680 + 0.694306i \(0.755712\pi\)
\(158\) −0.282199 + 1.96273i −0.0224505 + 0.156147i
\(159\) −7.79310 + 5.00832i −0.618033 + 0.397186i
\(160\) 1.00000 0.0790569
\(161\) 2.76568 2.67157i 0.217966 0.210550i
\(162\) −1.00000 −0.0785674
\(163\) −12.3115 + 7.91210i −0.964308 + 0.619723i −0.925187 0.379511i \(-0.876092\pi\)
−0.0391212 + 0.999234i \(0.512456\pi\)
\(164\) −0.742825 + 5.16646i −0.0580049 + 0.403433i
\(165\) −1.88281 + 4.12278i −0.146577 + 0.320958i
\(166\) −2.51187 + 0.737551i −0.194959 + 0.0572451i
\(167\) 4.18410 + 9.16191i 0.323776 + 0.708970i 0.999605 0.0280881i \(-0.00894189\pi\)
−0.675830 + 0.737058i \(0.736215\pi\)
\(168\) −0.525067 0.605959i −0.0405098 0.0467508i
\(169\) 1.25675 + 8.74088i 0.0966730 + 0.672375i
\(170\) 5.25270 + 1.54233i 0.402864 + 0.118292i
\(171\) 2.20465 2.54431i 0.168594 0.194568i
\(172\) 10.5560 + 6.78393i 0.804888 + 0.517270i
\(173\) 18.8599 + 12.1205i 1.43389 + 0.921507i 0.999787 + 0.0206450i \(0.00657197\pi\)
0.434106 + 0.900862i \(0.357064\pi\)
\(174\) 3.72269 4.29621i 0.282216 0.325695i
\(175\) −0.769321 0.225893i −0.0581552 0.0170759i
\(176\) 0.645022 + 4.48623i 0.0486204 + 0.338162i
\(177\) −1.99897 2.30693i −0.150252 0.173400i
\(178\) −2.91629 6.38579i −0.218586 0.478636i
\(179\) 17.5304 5.14739i 1.31028 0.384734i 0.449307 0.893377i \(-0.351671\pi\)
0.860978 + 0.508643i \(0.169853\pi\)
\(180\) −0.415415 + 0.909632i −0.0309632 + 0.0678000i
\(181\) 0.917790 6.38337i 0.0682188 0.474472i −0.926862 0.375403i \(-0.877504\pi\)
0.995081 0.0990692i \(-0.0315865\pi\)
\(182\) 1.37728 0.885121i 0.102090 0.0656095i
\(183\) −15.3214 −1.13259
\(184\) −4.70317 + 0.938180i −0.346722 + 0.0691635i
\(185\) 4.30900 0.316804
\(186\) 6.84223 4.39723i 0.501697 0.322421i
\(187\) −3.53115 + 24.5597i −0.258223 + 1.79598i
\(188\) −2.15473 + 4.71821i −0.157150 + 0.344111i
\(189\) 0.769321 0.225893i 0.0559598 0.0164313i
\(190\) −1.39854 3.06237i −0.101461 0.222168i
\(191\) 14.2975 + 16.5001i 1.03453 + 1.19391i 0.980732 + 0.195356i \(0.0625864\pi\)
0.0537953 + 0.998552i \(0.482868\pi\)
\(192\) 0.142315 + 0.989821i 0.0102707 + 0.0714342i
\(193\) 13.8448 + 4.06521i 0.996572 + 0.292620i 0.739049 0.673652i \(-0.235275\pi\)
0.257524 + 0.966272i \(0.417093\pi\)
\(194\) −0.519302 + 0.599307i −0.0372837 + 0.0430277i
\(195\) −1.71773 1.10392i −0.123009 0.0790533i
\(196\) −5.34795 3.43692i −0.381996 0.245494i
\(197\) 3.06054 3.53205i 0.218054 0.251648i −0.636175 0.771545i \(-0.719484\pi\)
0.854229 + 0.519897i \(0.174030\pi\)
\(198\) −4.34877 1.27691i −0.309054 0.0907463i
\(199\) 0.554202 + 3.85456i 0.0392863 + 0.273242i 0.999991 0.00433145i \(-0.00137875\pi\)
−0.960704 + 0.277574i \(0.910470\pi\)
\(200\) 0.654861 + 0.755750i 0.0463056 + 0.0534396i
\(201\) −5.67128 12.4184i −0.400022 0.875925i
\(202\) 8.19154 2.40525i 0.576355 0.169233i
\(203\) −1.89346 + 4.14609i −0.132895 + 0.290998i
\(204\) −0.779096 + 5.41873i −0.0545477 + 0.379387i
\(205\) −4.39100 + 2.82192i −0.306681 + 0.197092i
\(206\) −19.4618 −1.35597
\(207\) 1.10037 4.66789i 0.0764810 0.324441i
\(208\) −2.04187 −0.141578
\(209\) 12.8364 8.24945i 0.887912 0.570626i
\(210\) 0.114108 0.793638i 0.00787419 0.0547662i
\(211\) −3.12818 + 6.84977i −0.215353 + 0.471557i −0.986220 0.165439i \(-0.947096\pi\)
0.770867 + 0.636996i \(0.219823\pi\)
\(212\) −8.88844 + 2.60988i −0.610460 + 0.179247i
\(213\) 2.39080 + 5.23512i 0.163815 + 0.358704i
\(214\) −0.256569 0.296096i −0.0175387 0.0202407i
\(215\) 1.78576 + 12.4202i 0.121788 + 0.847053i
\(216\) −0.959493 0.281733i −0.0652852 0.0191695i
\(217\) −4.27056 + 4.92849i −0.289905 + 0.334568i
\(218\) −6.20248 3.98609i −0.420085 0.269972i
\(219\) −3.14808 2.02315i −0.212727 0.136712i
\(220\) −2.96807 + 3.42533i −0.200107 + 0.230936i
\(221\) −10.7253 3.14924i −0.721464 0.211841i
\(222\) 0.613235 + 4.26514i 0.0411576 + 0.286258i
\(223\) −5.87713 6.78257i −0.393562 0.454194i 0.524041 0.851693i \(-0.324424\pi\)
−0.917603 + 0.397499i \(0.869878\pi\)
\(224\) −0.333079 0.729342i −0.0222548 0.0487312i
\(225\) −0.959493 + 0.281733i −0.0639662 + 0.0187822i
\(226\) −6.89010 + 15.0872i −0.458323 + 1.00359i
\(227\) −0.167872 + 1.16757i −0.0111420 + 0.0774946i −0.994634 0.103458i \(-0.967009\pi\)
0.983492 + 0.180953i \(0.0579182\pi\)
\(228\) 2.83217 1.82012i 0.187565 0.120541i
\(229\) 17.8320 1.17837 0.589186 0.807998i \(-0.299449\pi\)
0.589186 + 0.807998i \(0.299449\pi\)
\(230\) −3.78895 2.94004i −0.249836 0.193861i
\(231\) 3.63404 0.239103
\(232\) 4.78227 3.07338i 0.313972 0.201777i
\(233\) 4.07310 28.3290i 0.266837 1.85590i −0.211052 0.977475i \(-0.567689\pi\)
0.477889 0.878420i \(-0.341402\pi\)
\(234\) 0.848224 1.85735i 0.0554501 0.121419i
\(235\) −4.97684 + 1.46133i −0.324653 + 0.0953267i
\(236\) −1.26806 2.77666i −0.0825435 0.180745i
\(237\) −1.29853 1.49859i −0.0843489 0.0973438i
\(238\) −0.624679 4.34474i −0.0404919 0.281627i
\(239\) 18.9148 + 5.55389i 1.22350 + 0.359252i 0.828793 0.559556i \(-0.189028\pi\)
0.394706 + 0.918808i \(0.370846\pi\)
\(240\) −0.654861 + 0.755750i −0.0422711 + 0.0487834i
\(241\) −10.0484 6.45769i −0.647272 0.415976i 0.175397 0.984498i \(-0.443879\pi\)
−0.822668 + 0.568522i \(0.807516\pi\)
\(242\) −8.02749 5.15896i −0.516027 0.331630i
\(243\) 0.654861 0.755750i 0.0420093 0.0484814i
\(244\) −14.7008 4.31654i −0.941122 0.276338i
\(245\) −0.904712 6.29241i −0.0577999 0.402007i
\(246\) −3.41810 3.94470i −0.217930 0.251505i
\(247\) 2.85563 + 6.25296i 0.181699 + 0.397866i
\(248\) 7.80391 2.29144i 0.495549 0.145506i
\(249\) 1.08752 2.38134i 0.0689188 0.150911i
\(250\) −0.142315 + 0.989821i −0.00900078 + 0.0626018i
\(251\) −0.187467 + 0.120478i −0.0118328 + 0.00760450i −0.546544 0.837430i \(-0.684057\pi\)
0.534711 + 0.845035i \(0.320420\pi\)
\(252\) 0.801799 0.0505086
\(253\) 10.7457 18.8945i 0.675579 1.18789i
\(254\) 8.25229 0.517795
\(255\) −4.60541 + 2.95971i −0.288402 + 0.185345i
\(256\) −0.142315 + 0.989821i −0.00889468 + 0.0618638i
\(257\) −7.60579 + 16.6544i −0.474436 + 1.03887i 0.509520 + 0.860459i \(0.329823\pi\)
−0.983956 + 0.178411i \(0.942904\pi\)
\(258\) −12.0397 + 3.53517i −0.749557 + 0.220090i
\(259\) −1.43524 3.14274i −0.0891814 0.195280i
\(260\) −1.33714 1.54314i −0.0829260 0.0957017i
\(261\) 0.809017 + 5.62684i 0.0500769 + 0.348292i
\(262\) 11.2964 + 3.31693i 0.697896 + 0.204921i
\(263\) 10.4734 12.0869i 0.645816 0.745312i −0.334576 0.942369i \(-0.608593\pi\)
0.980392 + 0.197057i \(0.0631384\pi\)
\(264\) −3.81286 2.45038i −0.234666 0.150810i
\(265\) −7.79310 5.00832i −0.478727 0.307659i
\(266\) −1.76769 + 2.04002i −0.108384 + 0.125082i
\(267\) 6.73583 + 1.97782i 0.412226 + 0.121040i
\(268\) −1.94290 13.5131i −0.118681 0.825446i
\(269\) −15.1193 17.4486i −0.921842 1.06386i −0.997770 0.0667492i \(-0.978737\pi\)
0.0759276 0.997113i \(-0.475808\pi\)
\(270\) −0.415415 0.909632i −0.0252814 0.0553584i
\(271\) 2.32878 0.683792i 0.141464 0.0415374i −0.210234 0.977651i \(-0.567423\pi\)
0.351698 + 0.936114i \(0.385604\pi\)
\(272\) −2.27417 + 4.97974i −0.137892 + 0.301941i
\(273\) −0.232994 + 1.62051i −0.0141014 + 0.0980775i
\(274\) −6.14741 + 3.95070i −0.371379 + 0.238671i
\(275\) −4.53236 −0.273312
\(276\) 2.37089 4.16880i 0.142711 0.250932i
\(277\) 7.10519 0.426909 0.213455 0.976953i \(-0.431528\pi\)
0.213455 + 0.976953i \(0.431528\pi\)
\(278\) 0.238170 0.153063i 0.0142845 0.00918009i
\(279\) −1.15750 + 8.05059i −0.0692977 + 0.481976i
\(280\) 0.333079 0.729342i 0.0199053 0.0435865i
\(281\) −1.82321 + 0.535341i −0.108763 + 0.0319358i −0.335661 0.941983i \(-0.608960\pi\)
0.226898 + 0.973919i \(0.427142\pi\)
\(282\) −2.15473 4.71821i −0.128313 0.280965i
\(283\) −10.0756 11.6279i −0.598932 0.691205i 0.372632 0.927979i \(-0.378455\pi\)
−0.971565 + 0.236774i \(0.923910\pi\)
\(284\) 0.819051 + 5.69662i 0.0486017 + 0.338032i
\(285\) 3.23023 + 0.948481i 0.191342 + 0.0561832i
\(286\) 6.06041 6.99408i 0.358359 0.413569i
\(287\) 3.52070 + 2.26262i 0.207820 + 0.133558i
\(288\) −0.841254 0.540641i −0.0495713 0.0318576i
\(289\) −8.49333 + 9.80182i −0.499608 + 0.576578i
\(290\) 5.45443 + 1.60156i 0.320295 + 0.0940471i
\(291\) −0.112855 0.784925i −0.00661568 0.0460131i
\(292\) −2.45057 2.82811i −0.143409 0.165503i
\(293\) 1.33818 + 2.93020i 0.0781771 + 0.171184i 0.944685 0.327980i \(-0.106368\pi\)
−0.866508 + 0.499164i \(0.833641\pi\)
\(294\) 6.09961 1.79101i 0.355736 0.104454i
\(295\) 1.26806 2.77666i 0.0738291 0.161663i
\(296\) −0.613235 + 4.26514i −0.0356435 + 0.247906i
\(297\) 3.81286 2.45038i 0.221245 0.142185i
\(298\) −2.13055 −0.123419
\(299\) 7.73655 + 6.00319i 0.447416 + 0.347173i
\(300\) −1.00000 −0.0577350
\(301\) 8.46380 5.43935i 0.487845 0.313519i
\(302\) −2.01043 + 13.9829i −0.115687 + 0.804624i
\(303\) −3.54655 + 7.76586i −0.203744 + 0.446137i
\(304\) 3.23023 0.948481i 0.185266 0.0543991i
\(305\) −6.36475 13.9369i −0.364444 0.798022i
\(306\) −3.58501 4.13732i −0.204941 0.236515i
\(307\) −3.05645 21.2581i −0.174441 1.21326i −0.869362 0.494176i \(-0.835470\pi\)
0.694921 0.719086i \(-0.255439\pi\)
\(308\) 3.48684 + 1.02383i 0.198681 + 0.0583380i
\(309\) 12.7448 14.7083i 0.725025 0.836724i
\(310\) 6.84223 + 4.39723i 0.388613 + 0.249746i
\(311\) −17.9716 11.5496i −1.01907 0.654919i −0.0793473 0.996847i \(-0.525284\pi\)
−0.939726 + 0.341928i \(0.888920\pi\)
\(312\) 1.33714 1.54314i 0.0757007 0.0873633i
\(313\) 24.5917 + 7.22077i 1.39000 + 0.408142i 0.889240 0.457441i \(-0.151234\pi\)
0.500765 + 0.865584i \(0.333052\pi\)
\(314\) −3.31864 23.0816i −0.187282 1.30257i
\(315\) 0.525067 + 0.605959i 0.0295842 + 0.0341419i
\(316\) −0.823734 1.80372i −0.0463386 0.101467i
\(317\) 29.4491 8.64703i 1.65403 0.485666i 0.684165 0.729327i \(-0.260167\pi\)
0.969860 + 0.243662i \(0.0783487\pi\)
\(318\) 3.84827 8.42654i 0.215800 0.472537i
\(319\) −3.66676 + 25.5029i −0.205299 + 1.42789i
\(320\) −0.841254 + 0.540641i −0.0470275 + 0.0302227i
\(321\) 0.391791 0.0218677
\(322\) −0.882275 + 3.74271i −0.0491673 + 0.208573i
\(323\) 18.4303 1.02549
\(324\) 0.841254 0.540641i 0.0467363 0.0300356i
\(325\) 0.290588 2.02109i 0.0161189 0.112110i
\(326\) 6.07946 13.3122i 0.336710 0.737292i
\(327\) 7.07425 2.07719i 0.391207 0.114869i
\(328\) −2.16830 4.74791i −0.119724 0.262159i
\(329\) 2.72349 + 3.14308i 0.150151 + 0.173283i
\(330\) −0.645022 4.48623i −0.0355073 0.246959i
\(331\) −24.1421 7.08875i −1.32697 0.389633i −0.459965 0.887937i \(-0.652138\pi\)
−0.867002 + 0.498304i \(0.833956\pi\)
\(332\) 1.71437 1.97849i 0.0940882 0.108584i
\(333\) −3.62496 2.32962i −0.198647 0.127662i
\(334\) −8.47319 5.44539i −0.463632 0.297958i
\(335\) 8.94022 10.3176i 0.488456 0.563709i
\(336\) 0.769321 + 0.225893i 0.0419699 + 0.0123235i
\(337\) −3.52925 24.5465i −0.192251 1.33713i −0.826033 0.563621i \(-0.809408\pi\)
0.633783 0.773511i \(-0.281501\pi\)
\(338\) −5.78292 6.67385i −0.314549 0.363009i
\(339\) −6.89010 15.0872i −0.374219 0.819425i
\(340\) −5.25270 + 1.54233i −0.284868 + 0.0836447i
\(341\) −15.3136 + 33.5321i −0.829278 + 1.81587i
\(342\) −0.479117 + 3.33233i −0.0259077 + 0.180192i
\(343\) −9.00960 + 5.79012i −0.486472 + 0.312637i
\(344\) −12.5480 −0.676540
\(345\) 4.70317 0.938180i 0.253210 0.0505099i
\(346\) −22.4188 −1.20524
\(347\) −15.4542 + 9.93180i −0.829624 + 0.533167i −0.885158 0.465290i \(-0.845950\pi\)
0.0555344 + 0.998457i \(0.482314\pi\)
\(348\) −0.809017 + 5.62684i −0.0433679 + 0.301630i
\(349\) 5.67353 12.4233i 0.303697 0.665004i −0.694835 0.719169i \(-0.744523\pi\)
0.998532 + 0.0541654i \(0.0172498\pi\)
\(350\) 0.769321 0.225893i 0.0411219 0.0120745i
\(351\) 0.848224 + 1.85735i 0.0452748 + 0.0991381i
\(352\) −2.96807 3.42533i −0.158198 0.182571i
\(353\) −1.81371 12.6146i −0.0965339 0.671408i −0.979422 0.201824i \(-0.935313\pi\)
0.882888 0.469584i \(-0.155596\pi\)
\(354\) 2.92886 + 0.859991i 0.155667 + 0.0457080i
\(355\) −3.76886 + 4.34949i −0.200030 + 0.230847i
\(356\) 5.90576 + 3.79540i 0.313005 + 0.201156i
\(357\) 3.69261 + 2.37310i 0.195434 + 0.125598i
\(358\) −11.9646 + 13.8079i −0.632350 + 0.729771i
\(359\) 5.32255 + 1.56284i 0.280913 + 0.0824836i 0.419154 0.907915i \(-0.362327\pi\)
−0.138241 + 0.990399i \(0.544145\pi\)
\(360\) −0.142315 0.989821i −0.00750065 0.0521682i
\(361\) 5.02016 + 5.79357i 0.264219 + 0.304925i
\(362\) 2.67902 + 5.86622i 0.140806 + 0.308322i
\(363\) 9.15577 2.68838i 0.480553 0.141103i
\(364\) −0.680105 + 1.48922i −0.0356472 + 0.0780565i
\(365\) 0.532560 3.70404i 0.0278755 0.193878i
\(366\) 12.8892 8.28339i 0.673729 0.432980i
\(367\) −20.6544 −1.07815 −0.539075 0.842258i \(-0.681226\pi\)
−0.539075 + 0.842258i \(0.681226\pi\)
\(368\) 3.44934 3.33197i 0.179809 0.173691i
\(369\) 5.21959 0.271721
\(370\) −3.62496 + 2.32962i −0.188453 + 0.121111i
\(371\) −1.05706 + 7.35201i −0.0548798 + 0.381697i
\(372\) −3.37873 + 7.39838i −0.175179 + 0.383588i
\(373\) −16.7161 + 4.90830i −0.865529 + 0.254142i −0.684213 0.729283i \(-0.739854\pi\)
−0.181316 + 0.983425i \(0.558036\pi\)
\(374\) −10.3074 22.5700i −0.532981 1.16707i
\(375\) −0.654861 0.755750i −0.0338169 0.0390267i
\(376\) −0.738179 5.13415i −0.0380687 0.264773i
\(377\) −11.1372 3.27019i −0.573597 0.168423i
\(378\) −0.525067 + 0.605959i −0.0270065 + 0.0311672i
\(379\) −23.7006 15.2314i −1.21742 0.782386i −0.235532 0.971867i \(-0.575683\pi\)
−0.981884 + 0.189480i \(0.939320\pi\)
\(380\) 2.83217 + 1.82012i 0.145287 + 0.0933703i
\(381\) −5.40410 + 6.23666i −0.276860 + 0.319514i
\(382\) −20.9484 6.15102i −1.07182 0.314713i
\(383\) −3.54819 24.6782i −0.181304 1.26100i −0.853684 0.520792i \(-0.825637\pi\)
0.672379 0.740207i \(-0.265272\pi\)
\(384\) −0.654861 0.755750i −0.0334182 0.0385667i
\(385\) 1.50964 + 3.30564i 0.0769382 + 0.168471i
\(386\) −13.8448 + 4.06521i −0.704683 + 0.206914i
\(387\) 5.21261 11.4140i 0.264972 0.580207i
\(388\) 0.112855 0.784925i 0.00572935 0.0398485i
\(389\) 8.07380 5.18872i 0.409358 0.263078i −0.319716 0.947513i \(-0.603587\pi\)
0.729074 + 0.684435i \(0.239951\pi\)
\(390\) 2.04187 0.103394
\(391\) 23.2574 12.1818i 1.17618 0.616062i
\(392\) 6.35712 0.321083
\(393\) −9.90436 + 6.36515i −0.499609 + 0.321079i
\(394\) −0.665118 + 4.62600i −0.0335082 + 0.233054i
\(395\) 0.823734 1.80372i 0.0414465 0.0907553i
\(396\) 4.34877 1.27691i 0.218534 0.0641673i
\(397\) 1.97167 + 4.31736i 0.0989554 + 0.216682i 0.952635 0.304117i \(-0.0983614\pi\)
−0.853679 + 0.520799i \(0.825634\pi\)
\(398\) −2.55016 2.94304i −0.127828 0.147521i
\(399\) −0.384156 2.67186i −0.0192318 0.133760i
\(400\) −0.959493 0.281733i −0.0479746 0.0140866i
\(401\) 11.0065 12.7021i 0.549636 0.634314i −0.411162 0.911562i \(-0.634877\pi\)
0.960798 + 0.277248i \(0.0894224\pi\)
\(402\) 11.4849 + 7.38088i 0.572813 + 0.368125i
\(403\) −13.9709 8.97858i −0.695942 0.447255i
\(404\) −5.59078 + 6.45211i −0.278152 + 0.321004i
\(405\) 0.959493 + 0.281733i 0.0476776 + 0.0139994i
\(406\) −0.648669 4.51159i −0.0321929 0.223907i
\(407\) −12.7894 14.7597i −0.633947 0.731614i
\(408\) −2.27417 4.97974i −0.112588 0.246534i
\(409\) 14.5689 4.27782i 0.720387 0.211525i 0.0990662 0.995081i \(-0.468414\pi\)
0.621321 + 0.783556i \(0.286596\pi\)
\(410\) 2.16830 4.74791i 0.107084 0.234482i
\(411\) 1.03996 7.23307i 0.0512973 0.356781i
\(412\) 16.3723 10.5219i 0.806607 0.518375i
\(413\) −2.44750 −0.120433
\(414\) 1.59796 + 4.52178i 0.0785355 + 0.222233i
\(415\) 2.61791 0.128508
\(416\) 1.71773 1.10392i 0.0842187 0.0541241i
\(417\) −0.0402913 + 0.280232i −0.00197307 + 0.0137230i
\(418\) −6.33867 + 13.8798i −0.310035 + 0.678881i
\(419\) 13.4881 3.96046i 0.658936 0.193481i 0.0648656 0.997894i \(-0.479338\pi\)
0.594071 + 0.804413i \(0.297520\pi\)
\(420\) 0.333079 + 0.729342i 0.0162526 + 0.0355883i
\(421\) 18.0401 + 20.8194i 0.879221 + 1.01468i 0.999759 + 0.0219669i \(0.00699284\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(422\) −1.07167 7.45361i −0.0521680 0.362836i
\(423\) 4.97684 + 1.46133i 0.241982 + 0.0710523i
\(424\) 6.06642 7.00102i 0.294611 0.340000i
\(425\) −4.60541 2.95971i −0.223395 0.143567i
\(426\) −4.84158 3.11150i −0.234576 0.150753i
\(427\) −8.04477 + 9.28416i −0.389314 + 0.449292i
\(428\) 0.375921 + 0.110380i 0.0181708 + 0.00533544i
\(429\) 1.31705 + 9.16030i 0.0635879 + 0.442263i
\(430\) −8.21716 9.48311i −0.396267 0.457316i
\(431\) 9.79465 + 21.4473i 0.471792 + 1.03308i 0.984639 + 0.174600i \(0.0558633\pi\)
−0.512848 + 0.858480i \(0.671409\pi\)
\(432\) 0.959493 0.281733i 0.0461636 0.0135549i
\(433\) −5.48636 + 12.0134i −0.263658 + 0.577330i −0.994443 0.105278i \(-0.966427\pi\)
0.730785 + 0.682607i \(0.239154\pi\)
\(434\) 0.928082 6.45495i 0.0445494 0.309848i
\(435\) −4.78227 + 3.07338i −0.229292 + 0.147357i
\(436\) 7.37291 0.353098
\(437\) −15.0278 5.90326i −0.718875 0.282391i
\(438\) 3.74213 0.178806
\(439\) −23.7535 + 15.2654i −1.13369 + 0.728579i −0.966327 0.257316i \(-0.917162\pi\)
−0.167364 + 0.985895i \(0.553525\pi\)
\(440\) 0.645022 4.48623i 0.0307502 0.213873i
\(441\) −2.64084 + 5.78264i −0.125754 + 0.275364i
\(442\) 10.7253 3.14924i 0.510152 0.149794i
\(443\) −1.97524 4.32516i −0.0938463 0.205495i 0.856887 0.515504i \(-0.172395\pi\)
−0.950734 + 0.310009i \(0.899668\pi\)
\(444\) −2.82180 3.25653i −0.133916 0.154548i
\(445\) 0.999078 + 6.94874i 0.0473608 + 0.329402i
\(446\) 8.61109 + 2.52844i 0.407747 + 0.119725i
\(447\) 1.39521 1.61016i 0.0659913 0.0761580i
\(448\) 0.674516 + 0.433485i 0.0318679 + 0.0204803i
\(449\) −2.15313 1.38374i −0.101613 0.0653025i 0.488848 0.872369i \(-0.337417\pi\)
−0.590460 + 0.807067i \(0.701054\pi\)
\(450\) 0.654861 0.755750i 0.0308704 0.0356264i
\(451\) 22.6988 + 6.66497i 1.06884 + 0.313841i
\(452\) −2.36044 16.4172i −0.111026 0.772202i
\(453\) −9.25100 10.6762i −0.434650 0.501612i
\(454\) −0.490016 1.07298i −0.0229976 0.0503577i
\(455\) −1.57085 + 0.461244i −0.0736427 + 0.0216235i
\(456\) −1.39854 + 3.06237i −0.0654925 + 0.143409i
\(457\) −2.85183 + 19.8349i −0.133403 + 0.927839i 0.807670 + 0.589635i \(0.200728\pi\)
−0.941073 + 0.338204i \(0.890181\pi\)
\(458\) −15.0012 + 9.64070i −0.700961 + 0.450480i
\(459\) 5.47446 0.255526
\(460\) 4.77698 + 0.424859i 0.222728 + 0.0198092i
\(461\) −12.6646 −0.589849 −0.294925 0.955521i \(-0.595295\pi\)
−0.294925 + 0.955521i \(0.595295\pi\)
\(462\) −3.05715 + 1.96471i −0.142232 + 0.0914067i
\(463\) −2.29032 + 15.9295i −0.106440 + 0.740308i 0.864785 + 0.502143i \(0.167455\pi\)
−0.971225 + 0.238165i \(0.923454\pi\)
\(464\) −2.36151 + 5.17098i −0.109630 + 0.240057i
\(465\) −7.80391 + 2.29144i −0.361898 + 0.106263i
\(466\) 11.8893 + 26.0340i 0.550762 + 1.20600i
\(467\) −14.3314 16.5393i −0.663177 0.765347i 0.320116 0.947378i \(-0.396278\pi\)
−0.983293 + 0.182031i \(0.941733\pi\)
\(468\) 0.290588 + 2.02109i 0.0134325 + 0.0934248i
\(469\) −10.5028 3.08391i −0.484976 0.142402i
\(470\) 3.39673 3.92003i 0.156679 0.180818i
\(471\) 19.6172 + 12.6072i 0.903912 + 0.580909i
\(472\) 2.56793 + 1.65031i 0.118199 + 0.0759617i
\(473\) 37.2431 42.9809i 1.71244 1.97626i
\(474\) 1.90260 + 0.558652i 0.0873891 + 0.0256598i
\(475\) 0.479117 + 3.33233i 0.0219834 + 0.152898i
\(476\) 2.87446 + 3.31730i 0.131750 + 0.152048i
\(477\) 3.84827 + 8.42654i 0.176200 + 0.385825i
\(478\) −18.9148 + 5.55389i −0.865144 + 0.254029i
\(479\) −10.3040 + 22.5627i −0.470803 + 1.03091i 0.514088 + 0.857738i \(0.328131\pi\)
−0.984891 + 0.173177i \(0.944597\pi\)
\(480\) 0.142315 0.989821i 0.00649575 0.0451790i
\(481\) 7.40170 4.75679i 0.337489 0.216891i
\(482\) 11.9445 0.544057
\(483\) −2.25078 3.11773i −0.102414 0.141862i
\(484\) 9.54230 0.433741
\(485\) 0.667111 0.428726i 0.0302919 0.0194674i
\(486\) −0.142315 + 0.989821i −0.00645553 + 0.0448992i
\(487\) 7.56252 16.5596i 0.342690 0.750387i −0.657304 0.753625i \(-0.728303\pi\)
0.999995 + 0.00323794i \(0.00103067\pi\)
\(488\) 14.7008 4.31654i 0.665474 0.195401i
\(489\) 6.07946 + 13.3122i 0.274923 + 0.601997i
\(490\) 4.16303 + 4.80439i 0.188066 + 0.217040i
\(491\) 0.788382 + 5.48332i 0.0355792 + 0.247459i 0.999847 0.0174693i \(-0.00556093\pi\)
−0.964268 + 0.264928i \(0.914652\pi\)
\(492\) 5.00816 + 1.47053i 0.225785 + 0.0662965i
\(493\) −20.3797 + 23.5194i −0.917855 + 1.05926i
\(494\) −5.78291 3.71645i −0.260186 0.167211i
\(495\) 3.81286 + 2.45038i 0.171376 + 0.110136i
\(496\) −5.32623 + 6.14679i −0.239155 + 0.275999i
\(497\) 4.42760 + 1.30006i 0.198605 + 0.0583156i
\(498\) 0.372568 + 2.59127i 0.0166952 + 0.116117i
\(499\) −14.2523 16.4481i −0.638023 0.736318i 0.341001 0.940063i \(-0.389234\pi\)
−0.979024 + 0.203745i \(0.934689\pi\)
\(500\) −0.415415 0.909632i −0.0185779 0.0406800i
\(501\) 9.66411 2.83764i 0.431761 0.126776i
\(502\) 0.0925722 0.202705i 0.00413170 0.00904716i
\(503\) −5.49060 + 38.1879i −0.244814 + 1.70272i 0.382505 + 0.923953i \(0.375061\pi\)
−0.627319 + 0.778762i \(0.715848\pi\)
\(504\) −0.674516 + 0.433485i −0.0300453 + 0.0193090i
\(505\) −8.53736 −0.379908
\(506\) 1.17524 + 21.7046i 0.0522458 + 0.964889i
\(507\) 8.83076 0.392188
\(508\) −6.94227 + 4.46152i −0.308013 + 0.197948i
\(509\) −1.68890 + 11.7465i −0.0748590 + 0.520656i 0.917545 + 0.397632i \(0.130168\pi\)
−0.992404 + 0.123023i \(0.960741\pi\)
\(510\) 2.27417 4.97974i 0.100702 0.220507i
\(511\) −2.87889 + 0.845320i −0.127355 + 0.0373947i
\(512\) −0.415415 0.909632i −0.0183589 0.0402004i
\(513\) −2.20465 2.54431i −0.0973379 0.112334i
\(514\) −2.60563 18.1225i −0.114929 0.799351i
\(515\) 18.6735 + 5.48303i 0.822852 + 0.241611i
\(516\) 8.21716 9.48311i 0.361740 0.417471i
\(517\) 19.7771 + 12.7100i 0.869797 + 0.558984i
\(518\) 2.90649 + 1.86789i 0.127704 + 0.0820703i
\(519\) 14.6812 16.9430i 0.644433 0.743716i
\(520\) 1.95916 + 0.575261i 0.0859149 + 0.0252269i
\(521\) −0.491137 3.41593i −0.0215171 0.149655i 0.976230 0.216735i \(-0.0695407\pi\)
−0.997748 + 0.0670803i \(0.978632\pi\)
\(522\) −3.72269 4.29621i −0.162938 0.188040i
\(523\) −17.8385 39.0609i −0.780023 1.70801i −0.703227 0.710966i \(-0.748258\pi\)
−0.0767966 0.997047i \(-0.524469\pi\)
\(524\) −11.2964 + 3.31693i −0.493487 + 0.144901i
\(525\) −0.333079 + 0.729342i −0.0145368 + 0.0318311i
\(526\) −2.27608 + 15.8305i −0.0992419 + 0.690243i
\(527\) −37.4575 + 24.0725i −1.63167 + 1.04861i
\(528\) 4.53236 0.197246
\(529\) −22.8655 + 2.48348i −0.994153 + 0.107977i
\(530\) 9.26368 0.402389
\(531\) −2.56793 + 1.65031i −0.111439 + 0.0716173i
\(532\) 0.384156 2.67186i 0.0166553 0.115840i
\(533\) −4.42738 + 9.69461i −0.191771 + 0.419920i
\(534\) −6.73583 + 1.97782i −0.291488 + 0.0855885i
\(535\) 0.162756 + 0.356386i 0.00703656 + 0.0154079i
\(536\) 8.94022 + 10.3176i 0.386159 + 0.445651i
\(537\) −2.60016 18.0845i −0.112205 0.780405i
\(538\) 22.1526 + 6.50460i 0.955068 + 0.280433i
\(539\) −18.8683 + 21.7752i −0.812717 + 0.937925i
\(540\) 0.841254 + 0.540641i 0.0362018 + 0.0232655i
\(541\) −18.0400 11.5936i −0.775602 0.498449i 0.0919695 0.995762i \(-0.470684\pi\)
−0.867571 + 0.497313i \(0.834320\pi\)
\(542\) −1.58941 + 1.83428i −0.0682711 + 0.0787890i
\(543\) −6.18778 1.81690i −0.265543 0.0779705i
\(544\) −0.779096 5.41873i −0.0334035 0.232326i
\(545\) 4.82823 + 5.57207i 0.206819 + 0.238681i
\(546\) −0.680105 1.48922i −0.0291058 0.0637328i
\(547\) −24.5662 + 7.21330i −1.05038 + 0.308418i −0.760969 0.648788i \(-0.775276\pi\)
−0.289407 + 0.957206i \(0.593458\pi\)
\(548\) 3.03562 6.64709i 0.129675 0.283949i
\(549\) −2.18047 + 15.1655i −0.0930600 + 0.647247i
\(550\) 3.81286 2.45038i 0.162581 0.104485i
\(551\) 19.1381 0.815311
\(552\) 0.259300 + 4.78882i 0.0110365 + 0.203826i
\(553\) −1.58990 −0.0676095
\(554\) −5.97726 + 3.84135i −0.253950 + 0.163203i
\(555\) 0.613235 4.26514i 0.0260304 0.181045i
\(556\) −0.117610 + 0.257529i −0.00498776 + 0.0109217i
\(557\) −31.6666 + 9.29816i −1.34176 + 0.393976i −0.872296 0.488977i \(-0.837370\pi\)
−0.469461 + 0.882953i \(0.655552\pi\)
\(558\) −3.37873 7.39838i −0.143033 0.313198i
\(559\) 16.7784 + 19.3633i 0.709650 + 0.818979i
\(560\) 0.114108 + 0.793638i 0.00482194 + 0.0335373i
\(561\) 23.8071 + 6.99041i 1.00514 + 0.295135i
\(562\) 1.24435 1.43606i 0.0524898 0.0605764i
\(563\) 2.04050 + 1.31135i 0.0859967 + 0.0552667i 0.582933 0.812521i \(-0.301905\pi\)
−0.496936 + 0.867787i \(0.665542\pi\)
\(564\) 4.36354 + 2.80427i 0.183738 + 0.118081i
\(565\) 10.8616 12.5349i 0.456949 0.527348i
\(566\) 14.7626 + 4.33470i 0.620520 + 0.182201i
\(567\) −0.114108 0.793638i −0.00479208 0.0333297i
\(568\) −3.76886 4.34949i −0.158138 0.182501i
\(569\) 7.04411 + 15.4245i 0.295305 + 0.646627i 0.997887 0.0649756i \(-0.0206970\pi\)
−0.702582 + 0.711603i \(0.747970\pi\)
\(570\) −3.23023 + 0.948481i −0.135299 + 0.0397275i
\(571\) 12.5158 27.4059i 0.523772 1.14690i −0.444220 0.895918i \(-0.646519\pi\)
0.967992 0.250983i \(-0.0807537\pi\)
\(572\) −1.31705 + 9.16030i −0.0550687 + 0.383011i
\(573\) 18.3669 11.8037i 0.767290 0.493107i
\(574\) −4.18506 −0.174681
\(575\) 2.80717 + 3.88842i 0.117067 + 0.162158i
\(576\) 1.00000 0.0416667
\(577\) −16.4260 + 10.5564i −0.683824 + 0.439467i −0.835885 0.548904i \(-0.815045\pi\)
0.152062 + 0.988371i \(0.451409\pi\)
\(578\) 1.84578 12.8377i 0.0767742 0.533976i
\(579\) 5.99415 13.1254i 0.249109 0.545472i
\(580\) −5.45443 + 1.60156i −0.226483 + 0.0665013i
\(581\) −0.871973 1.90935i −0.0361755 0.0792134i
\(582\) 0.519302 + 0.599307i 0.0215258 + 0.0248421i
\(583\) 5.97528 + 41.5590i 0.247471 + 1.72120i
\(584\) 3.59054 + 1.05428i 0.148578 + 0.0436264i
\(585\) −1.33714 + 1.54314i −0.0552840 + 0.0638011i
\(586\) −2.70993 1.74157i −0.111946 0.0719435i
\(587\) 5.12688 + 3.29484i 0.211609 + 0.135993i 0.642152 0.766577i \(-0.278042\pi\)
−0.430543 + 0.902570i \(0.641678\pi\)
\(588\) −4.16303 + 4.80439i −0.171680 + 0.198130i
\(589\) 26.2727 + 7.71435i 1.08255 + 0.317864i
\(590\) 0.434417 + 3.02144i 0.0178847 + 0.124391i
\(591\) −3.06054 3.53205i −0.125894 0.145289i
\(592\) −1.79002 3.91960i −0.0735695 0.161095i
\(593\) 26.7550 7.85599i 1.09870 0.322607i 0.318363 0.947969i \(-0.396867\pi\)
0.780335 + 0.625362i \(0.215049\pi\)
\(594\) −1.88281 + 4.12278i −0.0772527 + 0.169160i
\(595\) −0.624679 + 4.34474i −0.0256093 + 0.178117i
\(596\) 1.79233 1.15186i 0.0734168 0.0471821i
\(597\) 3.89420 0.159379
\(598\) −9.75397 0.867508i −0.398869 0.0354750i
\(599\) 19.7629 0.807489 0.403745 0.914872i \(-0.367708\pi\)
0.403745 + 0.914872i \(0.367708\pi\)
\(600\) 0.841254 0.540641i 0.0343440 0.0220716i
\(601\) −0.728737 + 5.06848i −0.0297258 + 0.206748i −0.999272 0.0381628i \(-0.987849\pi\)
0.969546 + 0.244910i \(0.0787586\pi\)
\(602\) −4.17946 + 9.15175i −0.170342 + 0.372997i
\(603\) −13.0991 + 3.84624i −0.533436 + 0.156631i
\(604\) −5.86843 12.8501i −0.238783 0.522862i
\(605\) 6.24888 + 7.21159i 0.254053 + 0.293193i
\(606\) −1.21499 8.45047i −0.0493557 0.343277i
\(607\) −29.1790 8.56772i −1.18434 0.347753i −0.370493 0.928835i \(-0.620811\pi\)
−0.813845 + 0.581082i \(0.802629\pi\)
\(608\) −2.20465 + 2.54431i −0.0894106 + 0.103185i
\(609\) 3.83442 + 2.46423i 0.155379 + 0.0998558i
\(610\) 12.8892 + 8.28339i 0.521868 + 0.335385i
\(611\) −6.93567 + 8.00420i −0.280587 + 0.323815i
\(612\) 5.25270 + 1.54233i 0.212328 + 0.0623451i
\(613\) 2.65371 + 18.4570i 0.107182 + 0.745470i 0.970551 + 0.240896i \(0.0774413\pi\)
−0.863369 + 0.504574i \(0.831650\pi\)
\(614\) 14.0642 + 16.2310i 0.567586 + 0.655029i
\(615\) 2.16830 + 4.74791i 0.0874341 + 0.191454i
\(616\) −3.48684 + 1.02383i −0.140489 + 0.0412512i
\(617\) 10.9254 23.9234i 0.439841 0.963118i −0.551786 0.833986i \(-0.686053\pi\)
0.991627 0.129133i \(-0.0412193\pi\)
\(618\) −2.76971 + 19.2637i −0.111414 + 0.774901i
\(619\) 29.0034 18.6394i 1.16575 0.749180i 0.193034 0.981192i \(-0.438167\pi\)
0.972713 + 0.232012i \(0.0745309\pi\)
\(620\) −8.13337 −0.326644
\(621\) −4.46378 1.75348i −0.179125 0.0703647i
\(622\) 21.3628 0.856571
\(623\) 4.73524 3.04315i 0.189713 0.121921i
\(624\) −0.290588 + 2.02109i −0.0116328 + 0.0809082i
\(625\) 0.415415 0.909632i 0.0166166 0.0363853i
\(626\) −24.5917 + 7.22077i −0.982882 + 0.288600i
\(627\) −6.33867 13.8798i −0.253142 0.554304i
\(628\) 15.2707 + 17.6233i 0.609367 + 0.703247i
\(629\) −3.35713 23.3493i −0.133857 0.930999i
\(630\) −0.769321 0.225893i −0.0306505 0.00899979i
\(631\) 8.11573 9.36605i 0.323082 0.372857i −0.570854 0.821052i \(-0.693388\pi\)
0.893936 + 0.448195i \(0.147933\pi\)
\(632\) 1.66814 + 1.07205i 0.0663549 + 0.0426437i
\(633\) 6.33486 + 4.07117i 0.251788 + 0.161814i
\(634\) −20.0992 + 23.1957i −0.798241 + 0.921220i
\(635\) −7.91801 2.32494i −0.314217 0.0922623i
\(636\) 1.31836 + 9.16939i 0.0522763 + 0.363590i
\(637\) −8.50036 9.80994i −0.336797 0.388684i
\(638\) −10.7032 23.4368i −0.423744 0.927870i
\(639\) 5.52208 1.62143i 0.218450 0.0641427i
\(640\) 0.415415 0.909632i 0.0164207 0.0359564i
\(641\) −4.91519 + 34.1859i −0.194138 + 1.35026i 0.626771 + 0.779203i \(0.284376\pi\)
−0.820910 + 0.571058i \(0.806533\pi\)
\(642\) −0.329596 + 0.211818i −0.0130081 + 0.00835981i
\(643\) 9.77223 0.385379 0.192690 0.981260i \(-0.438279\pi\)
0.192690 + 0.981260i \(0.438279\pi\)
\(644\) −1.28124 3.62556i −0.0504881 0.142867i
\(645\) 12.5480 0.494075
\(646\) −15.5046 + 9.96418i −0.610019 + 0.392035i
\(647\) −0.724304 + 5.03764i −0.0284753 + 0.198050i −0.999093 0.0425758i \(-0.986444\pi\)
0.970618 + 0.240626i \(0.0773527\pi\)
\(648\) −0.415415 + 0.909632i −0.0163190 + 0.0357337i
\(649\) −13.2746 + 3.89779i −0.521075 + 0.153002i
\(650\) 0.848224 + 1.85735i 0.0332701 + 0.0728513i
\(651\) 4.27056 + 4.92849i 0.167377 + 0.193163i
\(652\) 2.08273 + 14.4857i 0.0815660 + 0.567304i
\(653\) −13.0462 3.83071i −0.510537 0.149907i 0.0163104 0.999867i \(-0.494808\pi\)
−0.526848 + 0.849960i \(0.676626\pi\)
\(654\) −4.82823 + 5.57207i −0.188799 + 0.217885i
\(655\) −9.90436 6.36515i −0.386995 0.248707i
\(656\) 4.39100 + 2.82192i 0.171440 + 0.110178i
\(657\) −2.45057 + 2.82811i −0.0956059 + 0.110335i
\(658\) −3.99042 1.17169i −0.155563 0.0456774i
\(659\) −1.92160 13.3651i −0.0748551 0.520628i −0.992406 0.123009i \(-0.960746\pi\)
0.917550 0.397619i \(-0.130164\pi\)
\(660\) 2.96807 + 3.42533i 0.115532 + 0.133331i
\(661\) 4.07611 + 8.92543i 0.158542 + 0.347159i 0.972188 0.234202i \(-0.0752477\pi\)
−0.813646 + 0.581361i \(0.802520\pi\)
\(662\) 24.1421 7.08875i 0.938308 0.275512i
\(663\) −4.64356 + 10.1680i −0.180341 + 0.394892i
\(664\) −0.372568 + 2.59127i −0.0144584 + 0.100561i
\(665\) 2.27083 1.45937i 0.0880589 0.0565920i
\(666\) 4.30900 0.166970
\(667\) 24.1506 12.6497i 0.935113 0.489797i
\(668\) 10.0721 0.389701
\(669\) −7.54993 + 4.85205i −0.291897 + 0.187591i
\(670\) −1.94290 + 13.5131i −0.0750606 + 0.522058i
\(671\) −28.8473 + 63.1669i −1.11364 + 2.43853i
\(672\) −0.769321 + 0.225893i −0.0296772 + 0.00871401i
\(673\) −1.89115 4.14103i −0.0728983 0.159625i 0.869675 0.493625i \(-0.164329\pi\)
−0.942573 + 0.334000i \(0.891601\pi\)
\(674\) 16.2398 + 18.7418i 0.625535 + 0.721906i
\(675\) 0.142315 + 0.989821i 0.00547770 + 0.0380982i
\(676\) 8.47306 + 2.48791i 0.325887 + 0.0956890i
\(677\) 25.9019 29.8924i 0.995491 1.14886i 0.00663569 0.999978i \(-0.497888\pi\)
0.988855 0.148880i \(-0.0475668\pi\)
\(678\) 13.9531 + 8.96710i 0.535865 + 0.344380i
\(679\) −0.534889 0.343752i −0.0205272 0.0131920i
\(680\) 3.58501 4.13732i 0.137479 0.158659i
\(681\) 1.13180 + 0.332326i 0.0433707 + 0.0127348i
\(682\) −5.24621 36.4882i −0.200888 1.39720i
\(683\) −14.1390 16.3173i −0.541014 0.624364i 0.417751 0.908561i \(-0.362818\pi\)
−0.958766 + 0.284197i \(0.908273\pi\)
\(684\) −1.39854 3.06237i −0.0534744 0.117093i
\(685\) 7.01144 2.05875i 0.267893 0.0786606i
\(686\) 4.44898 9.74191i 0.169863 0.371948i
\(687\) 2.53776 17.6505i 0.0968215 0.673408i
\(688\) 10.5560 6.78393i 0.402444 0.258635i
\(689\) −18.9152 −0.720613
\(690\) −3.44934 + 3.33197i −0.131314 + 0.126846i
\(691\) 21.0492 0.800749 0.400374 0.916352i \(-0.368880\pi\)
0.400374 + 0.916352i \(0.368880\pi\)
\(692\) 18.8599 12.1205i 0.716946 0.460753i
\(693\) 0.517178 3.59705i 0.0196460 0.136641i
\(694\) 7.63135 16.7103i 0.289682 0.634315i
\(695\) −0.271645 + 0.0797623i −0.0103041 + 0.00302556i
\(696\) −2.36151 5.17098i −0.0895128 0.196006i
\(697\) 18.7123 + 21.5951i 0.708777 + 0.817973i
\(698\) 1.94366 + 13.5185i 0.0735688 + 0.511682i
\(699\) −27.4610 8.06328i −1.03867 0.304981i
\(700\) −0.525067 + 0.605959i −0.0198457 + 0.0229031i
\(701\) −38.1647 24.5270i −1.44146 0.926372i −0.999571 0.0293036i \(-0.990671\pi\)
−0.441892 0.897068i \(-0.645693\pi\)
\(702\) −1.71773 1.10392i −0.0648316 0.0416647i
\(703\) −9.49986 + 10.9634i −0.358294 + 0.413493i
\(704\) 4.34877 + 1.27691i 0.163900 + 0.0481255i
\(705\) 0.738179 + 5.13415i 0.0278014 + 0.193363i
\(706\) 8.34576 + 9.63152i 0.314097 + 0.362487i
\(707\) 2.84362 + 6.22666i 0.106945 + 0.234178i
\(708\) −2.92886 + 0.859991i −0.110073 + 0.0323204i
\(709\) −9.24002 + 20.2328i −0.347016 + 0.759860i 0.652981 + 0.757375i \(0.273518\pi\)
−0.999997 + 0.00248519i \(0.999209\pi\)
\(710\) 0.819051 5.69662i 0.0307384 0.213790i
\(711\) −1.66814 + 1.07205i −0.0625600 + 0.0402049i
\(712\) −7.02020 −0.263093
\(713\) 38.2526 7.63057i 1.43257 0.285767i
\(714\) −4.38941 −0.164270
\(715\) −7.78538 + 5.00336i −0.291157 + 0.187115i
\(716\) 2.60016 18.0845i 0.0971727 0.675851i
\(717\) 8.18922 17.9319i 0.305832 0.669679i
\(718\) −5.32255 + 1.56284i −0.198636 + 0.0583247i
\(719\) −14.1594 31.0047i −0.528055 1.15628i −0.966299 0.257423i \(-0.917127\pi\)
0.438244 0.898856i \(-0.355601\pi\)
\(720\) 0.654861 + 0.755750i 0.0244052 + 0.0281651i
\(721\) −2.22075 15.4456i −0.0827050 0.575226i
\(722\) −7.35547 2.15976i −0.273742 0.0803780i
\(723\) −7.82199 + 9.02706i −0.290903 + 0.335720i
\(724\) −5.42525 3.48660i −0.201628 0.129578i
\(725\) −4.78227 3.07338i −0.177609 0.114142i
\(726\) −6.24888 + 7.21159i −0.231918 + 0.267647i
\(727\) 24.7683 + 7.27264i 0.918607 + 0.269727i 0.706659 0.707554i \(-0.250201\pi\)
0.211947 + 0.977281i \(0.432019\pi\)
\(728\) −0.232994 1.62051i −0.00863532 0.0600600i
\(729\) −0.654861 0.755750i −0.0242541 0.0279907i
\(730\) 1.55454 + 3.40396i 0.0575359 + 0.125986i
\(731\) 65.9106 19.3531i 2.43779 0.715801i
\(732\) −6.36475 + 13.9369i −0.235248 + 0.515121i
\(733\) 3.40548 23.6856i 0.125784 0.874848i −0.825031 0.565088i \(-0.808842\pi\)
0.950815 0.309760i \(-0.100249\pi\)
\(734\) 17.3756 11.1666i 0.641344 0.412167i
\(735\) −6.35712 −0.234486
\(736\) −1.10037 + 4.66789i −0.0405602 + 0.172061i
\(737\) −61.8762 −2.27924
\(738\) −4.39100 + 2.82192i −0.161635 + 0.103876i
\(739\) −5.16632 + 35.9325i −0.190046 + 1.32180i 0.641834 + 0.766844i \(0.278174\pi\)
−0.831880 + 0.554955i \(0.812735\pi\)
\(740\) 1.79002 3.91960i 0.0658026 0.144088i
\(741\) 6.59571 1.93668i 0.242300 0.0711456i
\(742\) −3.08554 6.75639i −0.113274 0.248035i
\(743\) 8.56759 + 9.88752i 0.314314 + 0.362738i 0.890821 0.454354i \(-0.150130\pi\)
−0.576507 + 0.817092i \(0.695585\pi\)
\(744\) −1.15750 8.05059i −0.0424360 0.295149i
\(745\) 2.04425 + 0.600245i 0.0748954 + 0.0219913i
\(746\) 11.4089 13.1666i 0.417709 0.482062i
\(747\) −2.20233 1.41535i −0.0805790 0.0517850i
\(748\) 20.8734 + 13.4145i 0.763206 + 0.490483i
\(749\) 0.205717 0.237410i 0.00751672 0.00867476i
\(750\) 0.959493 + 0.281733i 0.0350357 + 0.0102874i
\(751\) 0.608522 + 4.23236i 0.0222053 + 0.154441i 0.997907 0.0646605i \(-0.0205964\pi\)
−0.975702 + 0.219102i \(0.929687\pi\)
\(752\) 3.39673 + 3.92003i 0.123866 + 0.142949i
\(753\) 0.0925722 + 0.202705i 0.00337352 + 0.00738698i
\(754\) 11.1372 3.27019i 0.405594 0.119093i
\(755\) 5.86843 12.8501i 0.213574 0.467662i
\(756\) 0.114108 0.793638i 0.00415007 0.0288643i
\(757\) −8.09072 + 5.19959i −0.294062 + 0.188982i −0.679350 0.733814i \(-0.737738\pi\)
0.385288 + 0.922796i \(0.374102\pi\)
\(758\) 28.1729 1.02329
\(759\) −17.1729 13.3253i −0.623337 0.483679i
\(760\) −3.36660 −0.122119
\(761\) −8.81295 + 5.66374i −0.319469 + 0.205310i −0.690540 0.723294i \(-0.742627\pi\)
0.371071 + 0.928605i \(0.378991\pi\)
\(762\) 1.17442 8.16829i 0.0425449 0.295906i
\(763\) 2.45576 5.37737i 0.0889046 0.194674i
\(764\) 20.9484 6.15102i 0.757888 0.222536i
\(765\) 2.27417 + 4.97974i 0.0822228 + 0.180043i
\(766\) 16.3270 + 18.8424i 0.589918 + 0.680802i
\(767\) −0.887023 6.16938i −0.0320286 0.222763i
\(768\) 0.959493 + 0.281733i 0.0346227 + 0.0101661i
\(769\) 34.5477 39.8702i 1.24582 1.43776i 0.389735 0.920927i \(-0.372566\pi\)
0.856088 0.516830i \(-0.172888\pi\)
\(770\) −3.05715 1.96471i −0.110172 0.0708033i
\(771\) 15.4024 + 9.89853i 0.554704 + 0.356487i
\(772\) 9.44919 10.9049i 0.340084 0.392478i
\(773\) −1.05860 0.310834i −0.0380753 0.0111799i 0.262639 0.964894i \(-0.415407\pi\)
−0.300715 + 0.953714i \(0.597225\pi\)
\(774\) 1.78576 + 12.4202i 0.0641878 + 0.446436i
\(775\) −5.32623 6.14679i −0.191324 0.220799i
\(776\) 0.329423 + 0.721335i 0.0118256 + 0.0258944i
\(777\) −3.31500 + 0.973373i −0.118925 + 0.0349196i
\(778\) −3.98688 + 8.73005i −0.142937 + 0.312988i
\(779\) 2.50080 17.3934i 0.0896003 0.623184i
\(780\) −1.71773 + 1.10392i −0.0615046 + 0.0395266i
\(781\) 26.0847 0.933382
\(782\) −12.9793 + 22.8219i −0.464141 + 0.816109i
\(783\) 5.68470 0.203155
\(784\) −5.34795 + 3.43692i −0.190998 + 0.122747i
\(785\) −3.31864 + 23.0816i −0.118447 + 0.823819i
\(786\) 4.89082 10.7094i 0.174450 0.381992i
\(787\) −0.228252 + 0.0670208i −0.00813630 + 0.00238903i −0.285798 0.958290i \(-0.592259\pi\)
0.277662 + 0.960679i \(0.410441\pi\)
\(788\) −1.94147 4.25123i −0.0691620 0.151444i
\(789\) −10.4734 12.0869i −0.372862 0.430306i
\(790\) 0.282199 + 1.96273i 0.0100402 + 0.0698309i
\(791\) −12.7600 3.74668i −0.453694 0.133216i
\(792\) −2.96807 + 3.42533i −0.105466 + 0.121714i
\(793\) −26.3181 16.9136i −0.934582 0.600620i
\(794\) −3.99282 2.56603i −0.141700 0.0910649i
\(795\) −6.06642 + 7.00102i −0.215154 + 0.248301i
\(796\) 3.73645 + 1.09712i 0.132435 + 0.0388865i
\(797\) −2.52654 17.5725i −0.0894948 0.622450i −0.984367 0.176128i \(-0.943643\pi\)
0.894872 0.446322i \(-0.147266\pi\)
\(798\) 1.76769 + 2.04002i 0.0625756 + 0.0722161i
\(799\) 11.7960 + 25.8296i 0.417312 + 0.913787i
\(800\) 0.959493 0.281733i 0.0339232 0.00996075i
\(801\) 2.91629 6.38579i 0.103042 0.225631i
\(802\) −2.39193 + 16.6363i −0.0844621 + 0.587447i
\(803\) −14.2682 + 9.16963i −0.503515 + 0.323589i
\(804\) −13.6521 −0.481472
\(805\) 1.90098 3.34254i 0.0670007 0.117809i
\(806\) 16.6073 0.584967
\(807\) −19.4227 + 12.4822i −0.683713 + 0.439396i
\(808\) 1.21499 8.45047i 0.0427433 0.297286i
\(809\) −14.6059 + 31.9824i −0.513514 + 1.12444i 0.458323 + 0.888786i \(0.348450\pi\)
−0.971837 + 0.235654i \(0.924277\pi\)
\(810\) −0.959493 + 0.281733i −0.0337131 + 0.00989907i
\(811\) −14.7911 32.3879i −0.519384 1.13729i −0.969672 0.244410i \(-0.921406\pi\)
0.450288 0.892884i \(-0.351321\pi\)
\(812\) 2.98485 + 3.44470i 0.104748 + 0.120885i
\(813\) −0.345412 2.40239i −0.0121141 0.0842556i
\(814\) 18.7388 + 5.50222i 0.656796 + 0.192853i
\(815\) −9.58367 + 11.0601i −0.335701 + 0.387420i
\(816\) 4.60541 + 2.95971i 0.161221 + 0.103611i
\(817\) −35.5379 22.8388i −1.24331 0.799029i
\(818\) −9.94340 + 11.4753i −0.347663 + 0.401224i
\(819\) 1.57085 + 0.461244i 0.0548901 + 0.0161172i
\(820\) 0.742825 + 5.16646i 0.0259406 + 0.180421i
\(821\) −3.24866 3.74915i −0.113379 0.130846i 0.696223 0.717826i \(-0.254862\pi\)
−0.809602 + 0.586979i \(0.800317\pi\)
\(822\) 3.03562 + 6.64709i 0.105880 + 0.231844i
\(823\) 5.14456 1.51058i 0.179328 0.0526555i −0.190836 0.981622i \(-0.561120\pi\)
0.370164 + 0.928967i \(0.379302\pi\)
\(824\) −8.08473 + 17.7031i −0.281645 + 0.616717i
\(825\) −0.645022 + 4.48623i −0.0224568 + 0.156190i
\(826\) 2.05897 1.32322i 0.0716406 0.0460406i
\(827\) 14.5268 0.505145 0.252572 0.967578i \(-0.418723\pi\)
0.252572 + 0.967578i \(0.418723\pi\)
\(828\) −3.78895 2.94004i −0.131675 0.102174i
\(829\) −42.9182 −1.49061 −0.745305 0.666723i \(-0.767696\pi\)
−0.745305 + 0.666723i \(0.767696\pi\)
\(830\) −2.20233 + 1.41535i −0.0764440 + 0.0491275i
\(831\) 1.01117 7.03287i 0.0350772 0.243967i
\(832\) −0.848224 + 1.85735i −0.0294069 + 0.0643921i
\(833\) −33.3920 + 9.80479i −1.15697 + 0.339716i
\(834\) −0.117610 0.257529i −0.00407249 0.00891751i
\(835\) 6.59582 + 7.61199i 0.228258 + 0.263424i
\(836\) −2.17153 15.1033i −0.0751040 0.522360i
\(837\) 7.80391 + 2.29144i 0.269743 + 0.0792036i
\(838\) −9.20572 + 10.6240i −0.318006 + 0.366999i
\(839\) 8.34492 + 5.36295i 0.288099 + 0.185150i 0.676705 0.736254i \(-0.263407\pi\)
−0.388607 + 0.921404i \(0.627043\pi\)
\(840\) −0.674516 0.433485i −0.0232730 0.0149567i
\(841\) −2.17138 + 2.50591i −0.0748752 + 0.0864105i
\(842\) −26.4321 7.76117i −0.910911 0.267468i
\(843\) 0.270423 + 1.88083i 0.00931387 + 0.0647794i
\(844\) 4.93127 + 5.69099i 0.169741 + 0.195892i
\(845\) 3.66843 + 8.03275i 0.126198 + 0.276335i
\(846\) −4.97684 + 1.46133i −0.171107 + 0.0502416i
\(847\) 3.17834 6.95960i 0.109209 0.239135i
\(848\) −1.31836 + 9.16939i −0.0452726 + 0.314878i
\(849\) −12.9434 + 8.31823i −0.444217 + 0.285481i
\(850\) 5.47446 0.187772
\(851\) −4.74149 + 20.1139i −0.162536 + 0.689497i
\(852\) 5.75520 0.197170
\(853\) 9.94524 6.39142i 0.340519 0.218838i −0.359193 0.933263i \(-0.616948\pi\)
0.699712 + 0.714425i \(0.253312\pi\)
\(854\) 1.74830 12.1597i 0.0598254 0.416095i
\(855\) 1.39854 3.06237i 0.0478289 0.104731i
\(856\) −0.375921 + 0.110380i −0.0128487 + 0.00377272i
\(857\) −18.0629 39.5523i −0.617018 1.35108i −0.917669 0.397346i \(-0.869931\pi\)
0.300651 0.953734i \(-0.402796\pi\)
\(858\) −6.06041 6.99408i −0.206899 0.238774i
\(859\) −6.36242 44.2516i −0.217083 1.50985i −0.748727 0.662878i \(-0.769335\pi\)
0.531644 0.846968i \(-0.321574\pi\)
\(860\) 12.0397 + 3.53517i 0.410549 + 0.120548i
\(861\) 2.74063 3.16286i 0.0934005 0.107790i
\(862\) −19.8351 12.7472i −0.675585 0.434172i
\(863\) 34.5930 + 22.2315i 1.17756 + 0.756771i 0.974936 0.222486i \(-0.0714173\pi\)
0.202622 + 0.979257i \(0.435054\pi\)
\(864\) −0.654861 + 0.755750i −0.0222788 + 0.0257111i
\(865\) 21.5107 + 6.31611i 0.731386 + 0.214754i
\(866\) −1.87954 13.0725i −0.0638695 0.444222i
\(867\) 8.49333 + 9.80182i 0.288449 + 0.332887i
\(868\) 2.70906 + 5.93201i 0.0919515 + 0.201346i
\(869\) −8.62325 + 2.53201i −0.292524 + 0.0858927i
\(870\) 2.36151 5.17098i 0.0800626 0.175313i
\(871\) 3.96714 27.5921i 0.134421 0.934922i
\(872\) −6.20248 + 3.98609i −0.210043 + 0.134986i
\(873\) −0.792996 −0.0268389
\(874\) 15.8337 3.15848i 0.535583 0.106837i
\(875\) −0.801799 −0.0271058
\(876\) −3.14808 + 2.02315i −0.106364 + 0.0683558i
\(877\) −0.264048 + 1.83649i −0.00891626 + 0.0620139i −0.993794 0.111238i \(-0.964518\pi\)
0.984878 + 0.173252i \(0.0554275\pi\)
\(878\) 11.7296 25.6842i 0.395854 0.866799i
\(879\) 3.09082 0.907545i 0.104251 0.0306107i
\(880\) 1.88281 + 4.12278i 0.0634695 + 0.138979i
\(881\) 29.6479 + 34.2155i 0.998863 + 1.15275i 0.988256 + 0.152805i \(0.0488307\pi\)
0.0106063 + 0.999944i \(0.496624\pi\)
\(882\) −0.904712 6.29241i −0.0304632 0.211877i
\(883\) −1.75246 0.514568i −0.0589749 0.0173166i 0.252112 0.967698i \(-0.418875\pi\)
−0.311087 + 0.950381i \(0.600693\pi\)
\(884\) −7.32012 + 8.44787i −0.246202 + 0.284133i
\(885\) −2.56793 1.65031i −0.0863201 0.0554746i
\(886\) 4.00003 + 2.57067i 0.134384 + 0.0863632i
\(887\) 23.6724 27.3195i 0.794843 0.917298i −0.203244 0.979128i \(-0.565148\pi\)
0.998087 + 0.0618306i \(0.0196939\pi\)
\(888\) 4.13446 + 1.21399i 0.138743 + 0.0407387i
\(889\) 0.941651 + 6.54933i 0.0315820 + 0.219657i
\(890\) −4.59725 5.30551i −0.154100 0.177841i
\(891\) −1.88281 4.12278i −0.0630765 0.138118i
\(892\) −8.61109 + 2.52844i −0.288320 + 0.0846585i
\(893\) 7.25413 15.8843i 0.242750 0.531549i
\(894\) −0.303209 + 2.10886i −0.0101408 + 0.0705309i
\(895\) 15.3701 9.87778i 0.513766 0.330178i
\(896\) −0.801799 −0.0267862
\(897\) 7.04311 6.80346i 0.235163 0.227161i
\(898\) 2.55944 0.0854095
\(899\) −38.8960 + 24.9969i −1.29725 + 0.833695i
\(900\) −0.142315 + 0.989821i −0.00474383 + 0.0329940i
\(901\) −21.0672 + 46.1307i −0.701850 + 1.53684i
\(902\) −22.6988 + 6.66497i −0.755787 + 0.221919i
\(903\) −4.17946 9.15175i −0.139084 0.304551i
\(904\) 10.8616 + 12.5349i 0.361250 + 0.416905i
\(905\) −0.917790 6.38337i −0.0305084 0.212190i
\(906\) 13.5544 + 3.97994i 0.450316 + 0.132225i
\(907\) 29.7225 34.3016i 0.986919 1.13896i −0.00337792 0.999994i \(-0.501075\pi\)
0.990297 0.138970i \(-0.0443793\pi\)
\(908\) 0.992327 + 0.637730i 0.0329315 + 0.0211638i
\(909\) 7.18209 + 4.61565i 0.238215 + 0.153091i
\(910\) 1.07212 1.23729i 0.0355404 0.0410158i
\(911\) −1.07924 0.316893i −0.0357568 0.0104991i 0.263805 0.964576i \(-0.415022\pi\)
−0.299562 + 0.954077i \(0.596841\pi\)
\(912\) −0.479117 3.33233i −0.0158652 0.110345i
\(913\) −7.77014 8.96722i −0.257154 0.296772i
\(914\) −8.32446 18.2280i −0.275349 0.602929i
\(915\) −14.7008 + 4.31654i −0.485993 + 0.142701i
\(916\) 7.40768 16.2205i 0.244757 0.535942i
\(917\) −1.34343 + 9.34377i −0.0443640 + 0.308558i
\(918\) −4.60541 + 2.95971i −0.152001 + 0.0976851i
\(919\) −11.3990 −0.376020 −0.188010 0.982167i \(-0.560204\pi\)
−0.188010 + 0.982167i \(0.560204\pi\)
\(920\) −4.24834 + 2.22521i −0.140064 + 0.0733631i
\(921\) −21.4767 −0.707680
\(922\) 10.6541 6.84700i 0.350875 0.225494i
\(923\) −1.67240 + 11.6318i −0.0550476 + 0.382864i
\(924\) 1.50964 3.30564i 0.0496634 0.108748i
\(925\) 4.13446 1.21399i 0.135940 0.0399156i
\(926\) −6.68541 14.6390i −0.219696 0.481068i
\(927\) −12.7448 14.7083i −0.418594 0.483083i
\(928\) −0.809017 5.62684i −0.0265573 0.184710i
\(929\) 0.419324 + 0.123125i 0.0137576 + 0.00403959i 0.288604 0.957449i \(-0.406809\pi\)
−0.274847 + 0.961488i \(0.588627\pi\)
\(930\) 5.32623 6.14679i 0.174654 0.201561i
\(931\) 18.0044 + 11.5707i 0.590071 + 0.379215i
\(932\) −24.0769 15.4733i −0.788667 0.506845i
\(933\) −13.9897 + 16.1449i −0.458001 + 0.528562i
\(934\) 20.9981 + 6.16561i 0.687080 + 0.201745i
\(935\) 3.53115 + 24.5597i 0.115481 + 0.803187i
\(936\) −1.33714 1.54314i −0.0437058 0.0504392i
\(937\) 2.17563 + 4.76397i 0.0710748 + 0.155632i 0.941835 0.336076i \(-0.109100\pi\)
−0.870760 + 0.491708i \(0.836373\pi\)
\(938\) 10.5028 3.08391i 0.342930 0.100693i
\(939\) 10.6470 23.3138i 0.347453 0.760816i
\(940\) −0.738179 + 5.13415i −0.0240767 + 0.167457i
\(941\) −43.9936 + 28.2730i −1.43415 + 0.921673i −0.434371 + 0.900734i \(0.643029\pi\)
−0.999781 + 0.0209391i \(0.993334\pi\)
\(942\) −23.3190 −0.759773
\(943\) −8.34070 23.6018i −0.271611 0.768582i
\(944\) −3.05251 −0.0993506
\(945\) 0.674516 0.433485i 0.0219420 0.0141013i
\(946\) −8.09371 + 56.2930i −0.263149 + 1.83024i
\(947\) 3.80191 8.32503i 0.123546 0.270527i −0.837746 0.546060i \(-0.816127\pi\)
0.961292 + 0.275533i \(0.0888543\pi\)
\(948\) −1.90260 + 0.558652i −0.0617934 + 0.0181442i
\(949\) −3.17416 6.95044i −0.103038 0.225621i
\(950\) −2.20465 2.54431i −0.0715285 0.0825482i
\(951\) −4.36797 30.3799i −0.141641 0.985137i
\(952\) −4.21161 1.23664i −0.136499 0.0400798i
\(953\) −29.2292 + 33.7323i −0.946828 + 1.09270i 0.0487553 + 0.998811i \(0.484475\pi\)
−0.995583 + 0.0938866i \(0.970071\pi\)
\(954\) −7.79310 5.00832i −0.252311 0.162150i
\(955\) 18.3669 + 11.8037i 0.594340 + 0.381959i
\(956\) 12.9095 14.8984i 0.417523 0.481847i
\(957\) 24.7214 + 7.25887i 0.799131 + 0.234646i
\(958\) −3.53000 24.5517i −0.114049 0.793230i
\(959\) −3.83690 4.42802i −0.123900 0.142988i
\(960\) 0.415415 + 0.909632i 0.0134075 + 0.0293582i
\(961\) −33.7279 + 9.90340i −1.08800 + 0.319464i
\(962\) −3.65500 + 8.00333i −0.117842 + 0.258038i
\(963\) 0.0557577 0.387804i 0.00179677 0.0124968i
\(964\) −10.0484 + 6.45769i −0.323636 + 0.207988i
\(965\) 14.4293 0.464496
\(966\) 3.57905 + 1.40594i 0.115154 + 0.0452353i
\(967\) −30.7784 −0.989767 −0.494883 0.868959i \(-0.664789\pi\)
−0.494883 + 0.868959i \(0.664789\pi\)
\(968\) −8.02749 + 5.15896i −0.258013 + 0.165815i
\(969\) 2.62291 18.2427i 0.0842599 0.586040i
\(970\) −0.329423 + 0.721335i −0.0105771 + 0.0231607i
\(971\) 11.1912 3.28603i 0.359143 0.105454i −0.0971832 0.995267i \(-0.530983\pi\)
0.456326 + 0.889813i \(0.349165\pi\)
\(972\) −0.415415 0.909632i −0.0133244 0.0291765i
\(973\) 0.148654 + 0.171555i 0.00476561 + 0.00549981i
\(974\) 2.59080 + 18.0194i 0.0830147 + 0.577380i
\(975\) −1.95916 0.575261i −0.0627434 0.0184231i
\(976\) −10.0334 + 11.5792i −0.321161 + 0.370640i
\(977\) 10.1836 + 6.54458i 0.325801 + 0.209380i 0.693308 0.720641i \(-0.256152\pi\)
−0.367507 + 0.930021i \(0.619789\pi\)
\(978\) −12.3115 7.91210i −0.393677 0.253001i
\(979\) 20.8364 24.0465i 0.665934 0.768529i
\(980\) −6.09961 1.79101i −0.194845 0.0572116i
\(981\) −1.04927 7.29786i −0.0335007 0.233003i
\(982\) −3.62773 4.18663i −0.115766 0.133601i
\(983\) 13.4326 + 29.4132i 0.428432 + 0.938135i 0.993579 + 0.113145i \(0.0360924\pi\)
−0.565146 + 0.824991i \(0.691180\pi\)
\(984\) −5.00816 + 1.47053i −0.159654 + 0.0468787i
\(985\) 1.94147 4.25123i 0.0618604 0.135455i
\(986\) 4.42893 30.8039i 0.141046 0.980995i
\(987\) 3.49868 2.24846i 0.111364 0.0715694i
\(988\) 6.87416 0.218696
\(989\) −59.9413 5.33111i −1.90602 0.169520i
\(990\) −4.53236 −0.144048
\(991\) 40.5767 26.0771i 1.28896 0.828366i 0.296997 0.954878i \(-0.404015\pi\)
0.991965 + 0.126512i \(0.0403783\pi\)
\(992\) 1.15750 8.05059i 0.0367507 0.255606i
\(993\) −10.4524 + 22.8875i −0.331696 + 0.726313i
\(994\) −4.42760 + 1.30006i −0.140435 + 0.0412354i
\(995\) 1.61771 + 3.54229i 0.0512848 + 0.112298i
\(996\) −1.71437 1.97849i −0.0543219 0.0626908i
\(997\) −1.34851 9.37909i −0.0427077 0.297039i −0.999969 0.00781576i \(-0.997512\pi\)
0.957262 0.289223i \(-0.0933970\pi\)
\(998\) 20.8823 + 6.13161i 0.661019 + 0.194093i
\(999\) −2.82180 + 3.25653i −0.0892776 + 0.103032i
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.f.541.1 yes 20
23.2 even 11 inner 690.2.m.f.301.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.f.301.1 20 23.2 even 11 inner
690.2.m.f.541.1 yes 20 1.1 even 1 trivial