Properties

Label 690.2.m.d.301.2
Level $690$
Weight $2$
Character 690.301
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: \( x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + 24088 x^{12} - 93423 x^{11} + 318055 x^{10} - 798006 x^{9} + 1869818 x^{8} + \cdots + 7921 \) 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 \(-0.0296794 + 0.00871465i\) of defining polynomial
Character \(\chi\) \(=\) 690.301
Dual form 690.2.m.d.541.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.25922 - 2.60728i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\) \(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} +(2.25922 - 2.60728i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.654861 + 0.755750i) q^{10} +(3.00554 - 1.93155i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(1.91026 + 2.20456i) q^{13} +(3.31018 - 0.971955i) q^{14} +(-0.142315 + 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.831833 - 1.82146i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(-0.366972 - 0.803556i) q^{19} +(0.142315 + 0.989821i) q^{20} +(2.90226 + 1.86517i) q^{21} +3.57270 q^{22} +(-4.56059 + 1.48358i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.415140 + 2.88736i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(3.31018 + 0.971955i) q^{28} +(-1.83516 + 4.01845i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(-0.254124 + 1.76747i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(2.33962 + 2.70006i) q^{33} +(1.68454 - 1.08259i) q^{34} +(2.90226 - 1.86517i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.67890 - 0.786596i) q^{37} +(0.125719 - 0.874394i) q^{38} +(-1.91026 + 2.20456i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-7.69951 - 2.26078i) q^{41} +(1.43315 + 3.13816i) q^{42} +(0.474462 + 3.29995i) q^{43} +(3.00554 + 1.93155i) q^{44} -1.00000 q^{45} +(-4.63870 - 1.21757i) q^{46} -6.66271 q^{47} +(-0.841254 - 0.540641i) q^{48} +(-0.697621 - 4.85206i) q^{49} +(0.415415 + 0.909632i) q^{50} +(1.92130 + 0.564145i) q^{51} +(-1.21179 + 2.65345i) q^{52} +(-2.06575 + 2.38401i) q^{53} +(0.142315 - 0.989821i) q^{54} +(3.42798 - 1.00654i) q^{55} +(2.25922 + 2.60728i) q^{56} +(0.743151 - 0.477594i) q^{57} +(-3.71638 + 2.38837i) q^{58} +(-1.49817 - 1.72898i) q^{59} +(-0.959493 + 0.281733i) q^{60} +(-0.0614036 + 0.427072i) q^{61} +(-1.16935 + 1.34950i) q^{62} +(-1.43315 + 3.13816i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.21179 + 2.65345i) q^{65} +(0.508448 + 3.53633i) q^{66} +(-4.69226 - 3.01553i) q^{67} +2.00241 q^{68} +(-2.11752 - 4.30303i) q^{69} +3.44992 q^{70} +(3.86069 + 2.48112i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-0.637855 - 1.39671i) q^{73} +(2.67890 + 0.786596i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(0.578494 - 0.667618i) q^{76} +(1.75410 - 12.2001i) q^{77} +(-2.79889 + 0.821829i) q^{78} +(-3.67678 - 4.24323i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-5.25497 - 6.06456i) q^{82} +(16.0001 - 4.69805i) q^{83} +(-0.490975 + 3.41481i) q^{84} +(1.31130 - 1.51332i) q^{85} +(-1.38495 + 3.03261i) q^{86} +(-4.23872 - 1.24460i) q^{87} +(1.48415 + 3.24984i) q^{88} +(1.55693 + 10.8287i) q^{89} +(-0.841254 - 0.540641i) q^{90} +10.0636 q^{91} +(-3.24405 - 3.53216i) q^{92} -1.78565 q^{93} +(-5.60503 - 3.60214i) q^{94} +(-0.125719 - 0.874394i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(-3.16425 - 0.929106i) q^{97} +(2.03635 - 4.45898i) q^{98} +(-2.33962 + 2.70006i) 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 \( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(7\) 2.25922 2.60728i 0.853904 0.985458i −0.146089 0.989272i \(-0.546668\pi\)
0.999993 + 0.00381361i \(0.00121391\pi\)
\(8\) −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
\(11\) 3.00554 1.93155i 0.906205 0.582383i −0.00241910 0.999997i \(-0.500770\pi\)
0.908624 + 0.417614i \(0.137134\pi\)
\(12\) −0.841254 + 0.540641i −0.242849 + 0.156070i
\(13\) 1.91026 + 2.20456i 0.529812 + 0.611436i 0.956060 0.293171i \(-0.0947104\pi\)
−0.426248 + 0.904606i \(0.640165\pi\)
\(14\) 3.31018 0.971955i 0.884682 0.259766i
\(15\) −0.142315 + 0.989821i −0.0367455 + 0.255571i
\(16\) −0.654861 + 0.755750i −0.163715 + 0.188937i
\(17\) 0.831833 1.82146i 0.201749 0.441769i −0.781531 0.623866i \(-0.785561\pi\)
0.983281 + 0.182097i \(0.0582885\pi\)
\(18\) −0.959493 0.281733i −0.226155 0.0664050i
\(19\) −0.366972 0.803556i −0.0841891 0.184348i 0.862855 0.505451i \(-0.168674\pi\)
−0.947044 + 0.321103i \(0.895947\pi\)
\(20\) 0.142315 + 0.989821i 0.0318226 + 0.221331i
\(21\) 2.90226 + 1.86517i 0.633325 + 0.407013i
\(22\) 3.57270 0.761701
\(23\) −4.56059 + 1.48358i −0.950949 + 0.309348i
\(24\) −1.00000 −0.204124
\(25\) 0.841254 + 0.540641i 0.168251 + 0.108128i
\(26\) 0.415140 + 2.88736i 0.0814157 + 0.566259i
\(27\) −0.415415 0.909632i −0.0799467 0.175059i
\(28\) 3.31018 + 0.971955i 0.625564 + 0.183682i
\(29\) −1.83516 + 4.01845i −0.340782 + 0.746207i −0.999983 0.00575855i \(-0.998167\pi\)
0.659202 + 0.751966i \(0.270894\pi\)
\(30\) −0.654861 + 0.755750i −0.119561 + 0.137980i
\(31\) −0.254124 + 1.76747i −0.0456421 + 0.317448i 0.954191 + 0.299197i \(0.0967188\pi\)
−0.999833 + 0.0182507i \(0.994190\pi\)
\(32\) −0.959493 + 0.281733i −0.169616 + 0.0498038i
\(33\) 2.33962 + 2.70006i 0.407275 + 0.470021i
\(34\) 1.68454 1.08259i 0.288896 0.185662i
\(35\) 2.90226 1.86517i 0.490571 0.315271i
\(36\) −0.654861 0.755750i −0.109143 0.125958i
\(37\) 2.67890 0.786596i 0.440408 0.129316i −0.0540085 0.998540i \(-0.517200\pi\)
0.494417 + 0.869225i \(0.335382\pi\)
\(38\) 0.125719 0.874394i 0.0203943 0.141845i
\(39\) −1.91026 + 2.20456i −0.305887 + 0.353013i
\(40\) −0.415415 + 0.909632i −0.0656829 + 0.143825i
\(41\) −7.69951 2.26078i −1.20246 0.353074i −0.381668 0.924300i \(-0.624650\pi\)
−0.820793 + 0.571225i \(0.806468\pi\)
\(42\) 1.43315 + 3.13816i 0.221140 + 0.484228i
\(43\) 0.474462 + 3.29995i 0.0723547 + 0.503238i 0.993483 + 0.113979i \(0.0363598\pi\)
−0.921128 + 0.389259i \(0.872731\pi\)
\(44\) 3.00554 + 1.93155i 0.453103 + 0.291191i
\(45\) −1.00000 −0.149071
\(46\) −4.63870 1.21757i −0.683939 0.179521i
\(47\) −6.66271 −0.971857 −0.485928 0.873999i \(-0.661518\pi\)
−0.485928 + 0.873999i \(0.661518\pi\)
\(48\) −0.841254 0.540641i −0.121424 0.0780348i
\(49\) −0.697621 4.85206i −0.0996602 0.693152i
\(50\) 0.415415 + 0.909632i 0.0587486 + 0.128641i
\(51\) 1.92130 + 0.564145i 0.269036 + 0.0789961i
\(52\) −1.21179 + 2.65345i −0.168045 + 0.367967i
\(53\) −2.06575 + 2.38401i −0.283753 + 0.327469i −0.879676 0.475573i \(-0.842241\pi\)
0.595923 + 0.803041i \(0.296786\pi\)
\(54\) 0.142315 0.989821i 0.0193666 0.134698i
\(55\) 3.42798 1.00654i 0.462228 0.135722i
\(56\) 2.25922 + 2.60728i 0.301901 + 0.348412i
\(57\) 0.743151 0.477594i 0.0984328 0.0632589i
\(58\) −3.71638 + 2.38837i −0.487984 + 0.313608i
\(59\) −1.49817 1.72898i −0.195045 0.225094i 0.649800 0.760105i \(-0.274853\pi\)
−0.844845 + 0.535012i \(0.820307\pi\)
\(60\) −0.959493 + 0.281733i −0.123870 + 0.0363715i
\(61\) −0.0614036 + 0.427072i −0.00786193 + 0.0546809i −0.993375 0.114920i \(-0.963339\pi\)
0.985513 + 0.169601i \(0.0542479\pi\)
\(62\) −1.16935 + 1.34950i −0.148508 + 0.171387i
\(63\) −1.43315 + 3.13816i −0.180560 + 0.395371i
\(64\) −0.959493 0.281733i −0.119937 0.0352166i
\(65\) 1.21179 + 2.65345i 0.150304 + 0.329120i
\(66\) 0.508448 + 3.53633i 0.0625856 + 0.435292i
\(67\) −4.69226 3.01553i −0.573250 0.368406i 0.221668 0.975122i \(-0.428850\pi\)
−0.794918 + 0.606717i \(0.792486\pi\)
\(68\) 2.00241 0.242828
\(69\) −2.11752 4.30303i −0.254919 0.518025i
\(70\) 3.44992 0.412344
\(71\) 3.86069 + 2.48112i 0.458180 + 0.294454i 0.749298 0.662233i \(-0.230391\pi\)
−0.291118 + 0.956687i \(0.594027\pi\)
\(72\) −0.142315 0.989821i −0.0167720 0.116652i
\(73\) −0.637855 1.39671i −0.0746553 0.163472i 0.868625 0.495471i \(-0.165004\pi\)
−0.943280 + 0.331998i \(0.892277\pi\)
\(74\) 2.67890 + 0.786596i 0.311416 + 0.0914399i
\(75\) −0.415415 + 0.909632i −0.0479680 + 0.105035i
\(76\) 0.578494 0.667618i 0.0663579 0.0765811i
\(77\) 1.75410 12.2001i 0.199899 1.39033i
\(78\) −2.79889 + 0.821829i −0.316912 + 0.0930539i
\(79\) −3.67678 4.24323i −0.413670 0.477400i 0.510228 0.860039i \(-0.329561\pi\)
−0.923898 + 0.382639i \(0.875015\pi\)
\(80\) −0.841254 + 0.540641i −0.0940550 + 0.0604455i
\(81\) 0.841254 0.540641i 0.0934726 0.0600712i
\(82\) −5.25497 6.06456i −0.580314 0.669718i
\(83\) 16.0001 4.69805i 1.75624 0.515678i 0.764576 0.644534i \(-0.222949\pi\)
0.991663 + 0.128856i \(0.0411304\pi\)
\(84\) −0.490975 + 3.41481i −0.0535698 + 0.372586i
\(85\) 1.31130 1.51332i 0.142231 0.164143i
\(86\) −1.38495 + 3.03261i −0.149343 + 0.327015i
\(87\) −4.23872 1.24460i −0.454438 0.133435i
\(88\) 1.48415 + 3.24984i 0.158211 + 0.346434i
\(89\) 1.55693 + 10.8287i 0.165034 + 1.14784i 0.888968 + 0.457970i \(0.151423\pi\)
−0.723934 + 0.689870i \(0.757668\pi\)
\(90\) −0.841254 0.540641i −0.0886759 0.0569885i
\(91\) 10.0636 1.05495
\(92\) −3.24405 3.53216i −0.338216 0.368253i
\(93\) −1.78565 −0.185163
\(94\) −5.60503 3.60214i −0.578115 0.371532i
\(95\) −0.125719 0.874394i −0.0128985 0.0897109i
\(96\) −0.415415 0.909632i −0.0423981 0.0928389i
\(97\) −3.16425 0.929106i −0.321280 0.0943365i 0.117116 0.993118i \(-0.462635\pi\)
−0.438396 + 0.898782i \(0.644453\pi\)
\(98\) 2.03635 4.45898i 0.205702 0.450425i
\(99\) −2.33962 + 2.70006i −0.235140 + 0.271367i
\(100\) −0.142315 + 0.989821i −0.0142315 + 0.0989821i
\(101\) −14.1575 + 4.15703i −1.40873 + 0.413640i −0.895672 0.444716i \(-0.853305\pi\)
−0.513055 + 0.858355i \(0.671486\pi\)
\(102\) 1.31130 + 1.51332i 0.129838 + 0.149841i
\(103\) 13.1280 8.43685i 1.29354 0.831307i 0.301047 0.953609i \(-0.402664\pi\)
0.992493 + 0.122302i \(0.0390277\pi\)
\(104\) −2.45398 + 1.57708i −0.240633 + 0.154645i
\(105\) 2.25922 + 2.60728i 0.220477 + 0.254444i
\(106\) −3.02671 + 0.888723i −0.293980 + 0.0863205i
\(107\) 1.25180 8.70647i 0.121016 0.841686i −0.835392 0.549654i \(-0.814759\pi\)
0.956408 0.292032i \(-0.0943314\pi\)
\(108\) 0.654861 0.755750i 0.0630140 0.0727220i
\(109\) 6.12051 13.4020i 0.586239 1.28368i −0.351450 0.936207i \(-0.614311\pi\)
0.937689 0.347477i \(-0.112961\pi\)
\(110\) 3.42798 + 1.00654i 0.326845 + 0.0959703i
\(111\) 1.15984 + 2.53969i 0.110087 + 0.241057i
\(112\) 0.490975 + 3.41481i 0.0463928 + 0.322669i
\(113\) −15.4704 9.94222i −1.45533 0.935285i −0.998965 0.0454943i \(-0.985514\pi\)
−0.456368 0.889791i \(-0.650850\pi\)
\(114\) 0.883386 0.0827366
\(115\) −4.79383 + 0.138618i −0.447027 + 0.0129262i
\(116\) −4.41767 −0.410170
\(117\) −2.45398 1.57708i −0.226871 0.145801i
\(118\) −0.325583 2.26448i −0.0299724 0.208462i
\(119\) −2.86976 6.28389i −0.263070 0.576044i
\(120\) −0.959493 0.281733i −0.0875893 0.0257185i
\(121\) 0.732857 1.60473i 0.0666233 0.145885i
\(122\) −0.282548 + 0.326078i −0.0255807 + 0.0295217i
\(123\) 1.14201 7.94288i 0.102972 0.716186i
\(124\) −1.71332 + 0.503076i −0.153860 + 0.0451775i
\(125\) 0.654861 + 0.755750i 0.0585725 + 0.0675963i
\(126\) −2.90226 + 1.86517i −0.258554 + 0.166162i
\(127\) 16.9584 10.8985i 1.50482 0.967087i 0.510585 0.859827i \(-0.329429\pi\)
0.994231 0.107260i \(-0.0342076\pi\)
\(128\) −0.654861 0.755750i −0.0578821 0.0667995i
\(129\) −3.19884 + 0.939265i −0.281642 + 0.0826977i
\(130\) −0.415140 + 2.88736i −0.0364102 + 0.253239i
\(131\) −8.00078 + 9.23340i −0.699032 + 0.806726i −0.988621 0.150425i \(-0.951936\pi\)
0.289590 + 0.957151i \(0.406481\pi\)
\(132\) −1.48415 + 3.24984i −0.129179 + 0.282862i
\(133\) −2.92416 0.858611i −0.253557 0.0744510i
\(134\) −2.31706 5.07365i −0.200163 0.438297i
\(135\) −0.142315 0.989821i −0.0122485 0.0851903i
\(136\) 1.68454 + 1.08259i 0.144448 + 0.0928310i
\(137\) −14.6636 −1.25280 −0.626399 0.779502i \(-0.715472\pi\)
−0.626399 + 0.779502i \(0.715472\pi\)
\(138\) 0.545025 4.76476i 0.0463956 0.405603i
\(139\) 8.25897 0.700517 0.350258 0.936653i \(-0.386094\pi\)
0.350258 + 0.936653i \(0.386094\pi\)
\(140\) 2.90226 + 1.86517i 0.245286 + 0.157635i
\(141\) −0.948203 6.59490i −0.0798531 0.555391i
\(142\) 1.90643 + 4.17449i 0.159984 + 0.350316i
\(143\) 9.99960 + 2.93615i 0.836208 + 0.245533i
\(144\) 0.415415 0.909632i 0.0346179 0.0758027i
\(145\) −2.89296 + 3.33865i −0.240247 + 0.277260i
\(146\) 0.218519 1.51984i 0.0180848 0.125783i
\(147\) 4.70339 1.38104i 0.387929 0.113906i
\(148\) 1.82837 + 2.11005i 0.150291 + 0.173445i
\(149\) −16.6276 + 10.6859i −1.36219 + 0.875426i −0.998427 0.0560651i \(-0.982145\pi\)
−0.363763 + 0.931492i \(0.618508\pi\)
\(150\) −0.841254 + 0.540641i −0.0686881 + 0.0441431i
\(151\) 6.27561 + 7.24244i 0.510702 + 0.589381i 0.951278 0.308334i \(-0.0997714\pi\)
−0.440577 + 0.897715i \(0.645226\pi\)
\(152\) 0.847602 0.248878i 0.0687496 0.0201867i
\(153\) −0.284973 + 1.98203i −0.0230387 + 0.160238i
\(154\) 8.07150 9.31501i 0.650420 0.750625i
\(155\) −0.741785 + 1.62428i −0.0595816 + 0.130466i
\(156\) −2.79889 0.821829i −0.224091 0.0657990i
\(157\) −5.41793 11.8636i −0.432398 0.946819i −0.992932 0.118687i \(-0.962131\pi\)
0.560534 0.828131i \(-0.310596\pi\)
\(158\) −0.799040 5.55744i −0.0635682 0.442126i
\(159\) −2.65373 1.70545i −0.210454 0.135251i
\(160\) −1.00000 −0.0790569
\(161\) −6.43526 + 15.2425i −0.507170 + 1.20127i
\(162\) 1.00000 0.0785674
\(163\) −4.37597 2.81226i −0.342752 0.220273i 0.357928 0.933749i \(-0.383483\pi\)
−0.700680 + 0.713476i \(0.747120\pi\)
\(164\) −1.14201 7.94288i −0.0891763 0.620235i
\(165\) 1.48415 + 3.24984i 0.115541 + 0.253000i
\(166\) 16.0001 + 4.69805i 1.24185 + 0.364640i
\(167\) −0.0607807 + 0.133091i −0.00470335 + 0.0102989i −0.911969 0.410259i \(-0.865438\pi\)
0.907266 + 0.420558i \(0.138166\pi\)
\(168\) −2.25922 + 2.60728i −0.174302 + 0.201156i
\(169\) 0.639106 4.44508i 0.0491620 0.341929i
\(170\) 1.92130 0.564145i 0.147357 0.0432680i
\(171\) 0.578494 + 0.667618i 0.0442386 + 0.0510540i
\(172\) −2.80465 + 1.80244i −0.213852 + 0.137434i
\(173\) 15.2612 9.80780i 1.16029 0.745673i 0.188628 0.982049i \(-0.439596\pi\)
0.971662 + 0.236375i \(0.0759595\pi\)
\(174\) −2.89296 3.33865i −0.219314 0.253102i
\(175\) 3.31018 0.971955i 0.250226 0.0734729i
\(176\) −0.508448 + 3.53633i −0.0383257 + 0.266561i
\(177\) 1.49817 1.72898i 0.112609 0.129958i
\(178\) −4.54466 + 9.95142i −0.340637 + 0.745890i
\(179\) −0.962409 0.282589i −0.0719338 0.0211217i 0.245568 0.969379i \(-0.421026\pi\)
−0.317501 + 0.948258i \(0.602844\pi\)
\(180\) −0.415415 0.909632i −0.0309632 0.0678000i
\(181\) 1.70529 + 11.8606i 0.126753 + 0.881588i 0.949631 + 0.313370i \(0.101458\pi\)
−0.822878 + 0.568218i \(0.807633\pi\)
\(182\) 8.46605 + 5.44080i 0.627545 + 0.403299i
\(183\) −0.431463 −0.0318947
\(184\) −0.819440 4.72531i −0.0604099 0.348354i
\(185\) 2.79200 0.205272
\(186\) −1.50218 0.965395i −0.110145 0.0707862i
\(187\) −1.01812 7.08120i −0.0744525 0.517829i
\(188\) −2.76779 6.06062i −0.201862 0.442016i
\(189\) −3.31018 0.971955i −0.240780 0.0706993i
\(190\) 0.366972 0.803556i 0.0266229 0.0582961i
\(191\) −11.5452 + 13.3238i −0.835380 + 0.964080i −0.999751 0.0223188i \(-0.992895\pi\)
0.164371 + 0.986399i \(0.447441\pi\)
\(192\) 0.142315 0.989821i 0.0102707 0.0714342i
\(193\) −15.2647 + 4.48213i −1.09878 + 0.322631i −0.780367 0.625322i \(-0.784968\pi\)
−0.318412 + 0.947952i \(0.603150\pi\)
\(194\) −2.15962 2.49233i −0.155052 0.178939i
\(195\) −2.45398 + 1.57708i −0.175733 + 0.112937i
\(196\) 4.12379 2.65020i 0.294556 0.189300i
\(197\) −13.3507 15.4075i −0.951196 1.09774i −0.995117 0.0987041i \(-0.968530\pi\)
0.0439205 0.999035i \(-0.486015\pi\)
\(198\) −3.42798 + 1.00654i −0.243616 + 0.0715320i
\(199\) 0.586462 4.07893i 0.0415732 0.289148i −0.958420 0.285363i \(-0.907886\pi\)
0.999993 0.00378534i \(-0.00120492\pi\)
\(200\) −0.654861 + 0.755750i −0.0463056 + 0.0534396i
\(201\) 2.31706 5.07365i 0.163433 0.357868i
\(202\) −14.1575 4.15703i −0.996120 0.292487i
\(203\) 6.33117 + 13.8633i 0.444361 + 0.973015i
\(204\) 0.284973 + 1.98203i 0.0199521 + 0.138770i
\(205\) −6.75069 4.33840i −0.471489 0.303007i
\(206\) 15.6053 1.08727
\(207\) 3.95788 2.70835i 0.275092 0.188243i
\(208\) −2.91706 −0.202261
\(209\) −2.65505 1.70630i −0.183654 0.118027i
\(210\) 0.490975 + 3.41481i 0.0338805 + 0.235644i
\(211\) 4.76636 + 10.4369i 0.328130 + 0.718503i 0.999749 0.0223926i \(-0.00712838\pi\)
−0.671620 + 0.740896i \(0.734401\pi\)
\(212\) −3.02671 0.888723i −0.207876 0.0610378i
\(213\) −1.90643 + 4.17449i −0.130626 + 0.286032i
\(214\) 5.76016 6.64758i 0.393756 0.454419i
\(215\) −0.474462 + 3.29995i −0.0323580 + 0.225055i
\(216\) 0.959493 0.281733i 0.0652852 0.0191695i
\(217\) 4.03417 + 4.65568i 0.273857 + 0.316048i
\(218\) 12.3946 7.96552i 0.839468 0.539493i
\(219\) 1.29172 0.830135i 0.0872861 0.0560953i
\(220\) 2.33962 + 2.70006i 0.157737 + 0.182038i
\(221\) 5.60454 1.64564i 0.377002 0.110698i
\(222\) −0.397342 + 2.76358i −0.0266679 + 0.185479i
\(223\) 2.74294 3.16552i 0.183681 0.211979i −0.656440 0.754378i \(-0.727939\pi\)
0.840121 + 0.542399i \(0.182484\pi\)
\(224\) −1.43315 + 3.13816i −0.0957563 + 0.209677i
\(225\) −0.959493 0.281733i −0.0639662 0.0187822i
\(226\) −7.63936 16.7279i −0.508162 1.11272i
\(227\) −2.31335 16.0897i −0.153543 1.06791i −0.910220 0.414125i \(-0.864088\pi\)
0.756677 0.653788i \(-0.226821\pi\)
\(228\) 0.743151 + 0.477594i 0.0492164 + 0.0316295i
\(229\) 5.86649 0.387668 0.193834 0.981034i \(-0.437908\pi\)
0.193834 + 0.981034i \(0.437908\pi\)
\(230\) −4.10777 2.47513i −0.270858 0.163205i
\(231\) 12.3255 0.810960
\(232\) −3.71638 2.38837i −0.243992 0.156804i
\(233\) 3.14011 + 21.8399i 0.205715 + 1.43078i 0.786935 + 0.617035i \(0.211666\pi\)
−0.581220 + 0.813746i \(0.697424\pi\)
\(234\) −1.21179 2.65345i −0.0792171 0.173461i
\(235\) −6.39283 1.87710i −0.417022 0.122449i
\(236\) 0.950372 2.08103i 0.0618640 0.135463i
\(237\) 3.67678 4.24323i 0.238832 0.275627i
\(238\) 0.983135 6.83786i 0.0637272 0.443232i
\(239\) −6.00657 + 1.76369i −0.388533 + 0.114084i −0.470164 0.882579i \(-0.655805\pi\)
0.0816311 + 0.996663i \(0.473987\pi\)
\(240\) −0.654861 0.755750i −0.0422711 0.0487834i
\(241\) 0.270609 0.173910i 0.0174315 0.0112025i −0.531896 0.846810i \(-0.678520\pi\)
0.549328 + 0.835607i \(0.314884\pi\)
\(242\) 1.48410 0.953774i 0.0954017 0.0613109i
\(243\) 0.654861 + 0.755750i 0.0420093 + 0.0484814i
\(244\) −0.413986 + 0.121557i −0.0265027 + 0.00778190i
\(245\) 0.697621 4.85206i 0.0445694 0.309987i
\(246\) 5.25497 6.06456i 0.335045 0.386662i
\(247\) 1.07048 2.34402i 0.0681128 0.149146i
\(248\) −1.71332 0.503076i −0.108796 0.0319453i
\(249\) 6.92728 + 15.1686i 0.438999 + 0.961273i
\(250\) 0.142315 + 0.989821i 0.00900078 + 0.0626018i
\(251\) 8.02082 + 5.15467i 0.506270 + 0.325360i 0.768720 0.639586i \(-0.220894\pi\)
−0.262450 + 0.964946i \(0.584531\pi\)
\(252\) −3.44992 −0.217325
\(253\) −10.8414 + 13.2680i −0.681596 + 0.834149i
\(254\) 20.1585 1.26486
\(255\) 1.68454 + 1.08259i 0.105490 + 0.0677942i
\(256\) −0.142315 0.989821i −0.00889468 0.0618638i
\(257\) 4.76678 + 10.4378i 0.297343 + 0.651091i 0.998054 0.0623542i \(-0.0198608\pi\)
−0.700711 + 0.713446i \(0.747134\pi\)
\(258\) −3.19884 0.939265i −0.199151 0.0584761i
\(259\) 4.00135 8.76172i 0.248631 0.544427i
\(260\) −1.91026 + 2.20456i −0.118470 + 0.136721i
\(261\) 0.628699 4.37270i 0.0389155 0.270663i
\(262\) −11.7226 + 3.44208i −0.724227 + 0.212652i
\(263\) 10.9849 + 12.6773i 0.677360 + 0.781715i 0.985509 0.169623i \(-0.0542551\pi\)
−0.308149 + 0.951338i \(0.599710\pi\)
\(264\) −3.00554 + 1.93155i −0.184978 + 0.118878i
\(265\) −2.65373 + 1.70545i −0.163017 + 0.104765i
\(266\) −1.99576 2.30323i −0.122368 0.141220i
\(267\) −10.4969 + 3.08217i −0.642400 + 0.188626i
\(268\) 0.793789 5.52092i 0.0484884 0.337244i
\(269\) −5.43013 + 6.26670i −0.331081 + 0.382088i −0.896745 0.442548i \(-0.854075\pi\)
0.565664 + 0.824636i \(0.308620\pi\)
\(270\) 0.415415 0.909632i 0.0252814 0.0553584i
\(271\) −10.5618 3.10122i −0.641584 0.188386i −0.0552717 0.998471i \(-0.517602\pi\)
−0.586312 + 0.810085i \(0.699421\pi\)
\(272\) 0.831833 + 1.82146i 0.0504373 + 0.110442i
\(273\) 1.43220 + 9.96118i 0.0866808 + 0.602878i
\(274\) −12.3358 7.92776i −0.745235 0.478933i
\(275\) 3.57270 0.215442
\(276\) 3.03453 3.71371i 0.182657 0.223539i
\(277\) 17.1728 1.03181 0.515906 0.856645i \(-0.327455\pi\)
0.515906 + 0.856645i \(0.327455\pi\)
\(278\) 6.94789 + 4.46514i 0.416707 + 0.267801i
\(279\) −0.254124 1.76747i −0.0152140 0.105816i
\(280\) 1.43315 + 3.13816i 0.0856470 + 0.187541i
\(281\) 8.09556 + 2.37707i 0.482941 + 0.141804i 0.514135 0.857709i \(-0.328113\pi\)
−0.0311944 + 0.999513i \(0.509931\pi\)
\(282\) 2.76779 6.06062i 0.164820 0.360905i
\(283\) −14.5793 + 16.8254i −0.866646 + 1.00016i 0.133312 + 0.991074i \(0.457439\pi\)
−0.999959 + 0.00908927i \(0.997107\pi\)
\(284\) −0.653113 + 4.54250i −0.0387551 + 0.269548i
\(285\) 0.847602 0.248878i 0.0502076 0.0147423i
\(286\) 6.82480 + 7.87623i 0.403559 + 0.465731i
\(287\) −23.2893 + 14.9672i −1.37473 + 0.883483i
\(288\) 0.841254 0.540641i 0.0495713 0.0318576i
\(289\) 8.50686 + 9.81744i 0.500404 + 0.577497i
\(290\) −4.23872 + 1.24460i −0.248906 + 0.0730854i
\(291\) 0.469330 3.26426i 0.0275126 0.191355i
\(292\) 1.00552 1.16043i 0.0588434 0.0679089i
\(293\) 4.83241 10.5815i 0.282312 0.618178i −0.714352 0.699786i \(-0.753279\pi\)
0.996664 + 0.0816087i \(0.0260058\pi\)
\(294\) 4.70339 + 1.38104i 0.274307 + 0.0805439i
\(295\) −0.950372 2.08103i −0.0553328 0.121162i
\(296\) 0.397342 + 2.76358i 0.0230951 + 0.160630i
\(297\) −3.00554 1.93155i −0.174399 0.112080i
\(298\) −19.7653 −1.14497
\(299\) −11.9826 7.22008i −0.692971 0.417548i
\(300\) −1.00000 −0.0577350
\(301\) 9.67581 + 6.21826i 0.557704 + 0.358415i
\(302\) 1.36382 + 9.48557i 0.0784790 + 0.545833i
\(303\) −6.12954 13.4218i −0.352133 0.771064i
\(304\) 0.847602 + 0.248878i 0.0486133 + 0.0142742i
\(305\) −0.179236 + 0.392473i −0.0102630 + 0.0224729i
\(306\) −1.31130 + 1.51332i −0.0749622 + 0.0865109i
\(307\) 3.30356 22.9768i 0.188544 1.31135i −0.647237 0.762289i \(-0.724075\pi\)
0.835781 0.549063i \(-0.185015\pi\)
\(308\) 11.8262 3.47250i 0.673863 0.197864i
\(309\) 10.2193 + 11.7937i 0.581355 + 0.670919i
\(310\) −1.50218 + 0.965395i −0.0853183 + 0.0548307i
\(311\) 11.6288 7.47339i 0.659410 0.423777i −0.167684 0.985841i \(-0.553629\pi\)
0.827094 + 0.562064i \(0.189993\pi\)
\(312\) −1.91026 2.20456i −0.108147 0.124809i
\(313\) −27.3925 + 8.04316i −1.54832 + 0.454627i −0.940597 0.339526i \(-0.889733\pi\)
−0.607719 + 0.794152i \(0.707915\pi\)
\(314\) 1.85610 12.9095i 0.104746 0.728523i
\(315\) −2.25922 + 2.60728i −0.127293 + 0.146903i
\(316\) 2.33239 5.10721i 0.131207 0.287303i
\(317\) −3.41259 1.00203i −0.191670 0.0562794i 0.184489 0.982835i \(-0.440937\pi\)
−0.376159 + 0.926555i \(0.622755\pi\)
\(318\) −1.31042 2.86943i −0.0734849 0.160910i
\(319\) 2.24615 + 15.6223i 0.125760 + 0.874682i
\(320\) −0.841254 0.540641i −0.0470275 0.0302227i
\(321\) 8.79600 0.490945
\(322\) −13.6544 + 9.34360i −0.760929 + 0.520699i
\(323\) −1.76890 −0.0984244
\(324\) 0.841254 + 0.540641i 0.0467363 + 0.0300356i
\(325\) 0.415140 + 2.88736i 0.0230278 + 0.160162i
\(326\) −2.16087 4.73165i −0.119680 0.262062i
\(327\) 14.1367 + 4.15090i 0.781760 + 0.229545i
\(328\) 3.33352 7.29940i 0.184063 0.403042i
\(329\) −15.0525 + 17.3715i −0.829872 + 0.957724i
\(330\) −0.508448 + 3.53633i −0.0279891 + 0.194669i
\(331\) −11.4186 + 3.35282i −0.627625 + 0.184287i −0.580051 0.814580i \(-0.696967\pi\)
−0.0475744 + 0.998868i \(0.515149\pi\)
\(332\) 10.9202 + 12.6026i 0.599323 + 0.691655i
\(333\) −2.34878 + 1.50947i −0.128712 + 0.0827183i
\(334\) −0.123087 + 0.0791029i −0.00673500 + 0.00432832i
\(335\) −3.65261 4.21534i −0.199564 0.230309i
\(336\) −3.31018 + 0.971955i −0.180585 + 0.0530245i
\(337\) −4.36046 + 30.3277i −0.237529 + 1.65205i 0.426603 + 0.904439i \(0.359710\pi\)
−0.664133 + 0.747615i \(0.731199\pi\)
\(338\) 2.94084 3.39391i 0.159961 0.184605i
\(339\) 7.63936 16.7279i 0.414913 0.908532i
\(340\) 1.92130 + 0.564145i 0.104197 + 0.0305951i
\(341\) 2.65017 + 5.80307i 0.143515 + 0.314254i
\(342\) 0.125719 + 0.874394i 0.00679810 + 0.0472818i
\(343\) 6.08906 + 3.91320i 0.328779 + 0.211293i
\(344\) −3.33389 −0.179751
\(345\) −0.819440 4.72531i −0.0441172 0.254402i
\(346\) 18.1411 0.975270
\(347\) 16.3505 + 10.5078i 0.877739 + 0.564089i 0.900111 0.435661i \(-0.143485\pi\)
−0.0223714 + 0.999750i \(0.507122\pi\)
\(348\) −0.628699 4.37270i −0.0337018 0.234401i
\(349\) 3.93021 + 8.60596i 0.210379 + 0.460666i 0.985177 0.171543i \(-0.0548754\pi\)
−0.774797 + 0.632210i \(0.782148\pi\)
\(350\) 3.31018 + 0.971955i 0.176936 + 0.0519532i
\(351\) 1.21179 2.65345i 0.0646805 0.141631i
\(352\) −2.33962 + 2.70006i −0.124702 + 0.143914i
\(353\) 4.96524 34.5340i 0.264273 1.83806i −0.235463 0.971883i \(-0.575661\pi\)
0.499737 0.866177i \(-0.333430\pi\)
\(354\) 2.19510 0.644538i 0.116668 0.0342568i
\(355\) 3.00530 + 3.46830i 0.159505 + 0.184078i
\(356\) −9.20335 + 5.91464i −0.487777 + 0.313475i
\(357\) 5.81152 3.73484i 0.307578 0.197669i
\(358\) −0.656851 0.758046i −0.0347157 0.0400640i
\(359\) 18.4440 5.41566i 0.973439 0.285827i 0.243925 0.969794i \(-0.421565\pi\)
0.729513 + 0.683967i \(0.239747\pi\)
\(360\) 0.142315 0.989821i 0.00750065 0.0521682i
\(361\) 11.9313 13.7695i 0.627964 0.724709i
\(362\) −4.97772 + 10.8997i −0.261623 + 0.572875i
\(363\) 1.69269 + 0.497020i 0.0888434 + 0.0260868i
\(364\) 4.18057 + 9.15418i 0.219122 + 0.479809i
\(365\) −0.218519 1.51984i −0.0114378 0.0795519i
\(366\) −0.362970 0.233267i −0.0189727 0.0121930i
\(367\) 22.9467 1.19781 0.598905 0.800820i \(-0.295603\pi\)
0.598905 + 0.800820i \(0.295603\pi\)
\(368\) 1.86534 4.41820i 0.0972374 0.230315i
\(369\) 8.02456 0.417742
\(370\) 2.34878 + 1.50947i 0.122107 + 0.0784734i
\(371\) 1.54878 + 10.7720i 0.0804085 + 0.559253i
\(372\) −0.741785 1.62428i −0.0384598 0.0842152i
\(373\) −17.2684 5.07045i −0.894122 0.262538i −0.197778 0.980247i \(-0.563373\pi\)
−0.696343 + 0.717709i \(0.745191\pi\)
\(374\) 2.97189 6.50752i 0.153673 0.336496i
\(375\) −0.654861 + 0.755750i −0.0338169 + 0.0390267i
\(376\) 0.948203 6.59490i 0.0488998 0.340106i
\(377\) −12.3646 + 3.63057i −0.636808 + 0.186984i
\(378\) −2.25922 2.60728i −0.116202 0.134104i
\(379\) −26.8009 + 17.2239i −1.37667 + 0.884731i −0.999148 0.0412703i \(-0.986860\pi\)
−0.377520 + 0.926001i \(0.623223\pi\)
\(380\) 0.743151 0.477594i 0.0381229 0.0245001i
\(381\) 13.2010 + 15.2348i 0.676309 + 0.780502i
\(382\) −16.9158 + 4.96694i −0.865490 + 0.254131i
\(383\) 1.32646 9.22570i 0.0677787 0.471411i −0.927458 0.373927i \(-0.878011\pi\)
0.995237 0.0974848i \(-0.0310797\pi\)
\(384\) 0.654861 0.755750i 0.0334182 0.0385667i
\(385\) 5.12021 11.2117i 0.260950 0.571400i
\(386\) −15.2647 4.48213i −0.776955 0.228134i
\(387\) −1.38495 3.03261i −0.0704008 0.154156i
\(388\) −0.469330 3.26426i −0.0238266 0.165718i
\(389\) 19.4127 + 12.4758i 0.984264 + 0.632548i 0.930610 0.366012i \(-0.119277\pi\)
0.0536535 + 0.998560i \(0.482913\pi\)
\(390\) −2.91706 −0.147711
\(391\) −1.09137 + 9.54102i −0.0551928 + 0.482510i
\(392\) 4.90196 0.247586
\(393\) −10.2780 6.60530i −0.518459 0.333193i
\(394\) −2.90138 20.1795i −0.146169 1.01663i
\(395\) −2.33239 5.10721i −0.117355 0.256972i
\(396\) −3.42798 1.00654i −0.172262 0.0505808i
\(397\) 7.77143 17.0170i 0.390037 0.854061i −0.608147 0.793824i \(-0.708087\pi\)
0.998184 0.0602371i \(-0.0191857\pi\)
\(398\) 2.69860 3.11435i 0.135269 0.156108i
\(399\) 0.433720 3.01659i 0.0217132 0.151018i
\(400\) −0.959493 + 0.281733i −0.0479746 + 0.0140866i
\(401\) −12.6891 14.6440i −0.633661 0.731284i 0.344579 0.938757i \(-0.388022\pi\)
−0.978241 + 0.207473i \(0.933476\pi\)
\(402\) 4.69226 3.01553i 0.234028 0.150401i
\(403\) −4.38195 + 2.81611i −0.218281 + 0.140280i
\(404\) −9.66262 11.1513i −0.480733 0.554796i
\(405\) 0.959493 0.281733i 0.0476776 0.0139994i
\(406\) −2.16896 + 15.0855i −0.107644 + 0.748679i
\(407\) 6.53220 7.53856i 0.323789 0.373673i
\(408\) −0.831833 + 1.82146i −0.0411819 + 0.0901757i
\(409\) 15.0320 + 4.41380i 0.743286 + 0.218248i 0.631383 0.775471i \(-0.282487\pi\)
0.111902 + 0.993719i \(0.464306\pi\)
\(410\) −3.33352 7.29940i −0.164631 0.360491i
\(411\) −2.08685 14.5144i −0.102937 0.715941i
\(412\) 13.1280 + 8.43685i 0.646770 + 0.415654i
\(413\) −7.89261 −0.388370
\(414\) 4.79383 0.138618i 0.235604 0.00681272i
\(415\) 16.6756 0.818572
\(416\) −2.45398 1.57708i −0.120316 0.0773227i
\(417\) 1.17537 + 8.17490i 0.0575583 + 0.400327i
\(418\) −1.31108 2.87086i −0.0641269 0.140418i
\(419\) −0.259147 0.0760924i −0.0126601 0.00371735i 0.275396 0.961331i \(-0.411191\pi\)
−0.288056 + 0.957613i \(0.593009\pi\)
\(420\) −1.43315 + 3.13816i −0.0699305 + 0.153126i
\(421\) −11.7970 + 13.6144i −0.574948 + 0.663526i −0.966511 0.256626i \(-0.917389\pi\)
0.391562 + 0.920152i \(0.371935\pi\)
\(422\) −1.63288 + 11.3569i −0.0794874 + 0.552847i
\(423\) 6.39283 1.87710i 0.310830 0.0912679i
\(424\) −2.06575 2.38401i −0.100322 0.115778i
\(425\) 1.68454 1.08259i 0.0817121 0.0525132i
\(426\) −3.86069 + 2.48112i −0.187051 + 0.120210i
\(427\) 0.974769 + 1.12494i 0.0471724 + 0.0544399i
\(428\) 8.43970 2.47812i 0.407948 0.119784i
\(429\) −1.48317 + 10.3157i −0.0716081 + 0.498045i
\(430\) −2.18323 + 2.51958i −0.105285 + 0.121505i
\(431\) −9.47823 + 20.7544i −0.456550 + 0.999706i 0.531710 + 0.846926i \(0.321550\pi\)
−0.988260 + 0.152779i \(0.951178\pi\)
\(432\) 0.959493 + 0.281733i 0.0461636 + 0.0135549i
\(433\) 8.04525 + 17.6166i 0.386630 + 0.846602i 0.998453 + 0.0556068i \(0.0177093\pi\)
−0.611823 + 0.790995i \(0.709563\pi\)
\(434\) 0.876709 + 6.09765i 0.0420834 + 0.292696i
\(435\) −3.71638 2.38837i −0.178187 0.114514i
\(436\) 14.7335 0.705606
\(437\) 2.86575 + 3.12026i 0.137087 + 0.149262i
\(438\) 1.53547 0.0733674
\(439\) 30.9917 + 19.9171i 1.47915 + 0.950593i 0.997230 + 0.0743777i \(0.0236970\pi\)
0.481921 + 0.876215i \(0.339939\pi\)
\(440\) 0.508448 + 3.53633i 0.0242393 + 0.168588i
\(441\) 2.03635 + 4.45898i 0.0969689 + 0.212332i
\(442\) 5.60454 + 1.64564i 0.266581 + 0.0782752i
\(443\) 14.2737 31.2551i 0.678165 1.48497i −0.186411 0.982472i \(-0.559685\pi\)
0.864576 0.502502i \(-0.167587\pi\)
\(444\) −1.82837 + 2.11005i −0.0867705 + 0.100138i
\(445\) −1.55693 + 10.8287i −0.0738056 + 0.513329i
\(446\) 4.01891 1.18006i 0.190301 0.0558774i
\(447\) −12.9435 14.9376i −0.612208 0.706526i
\(448\) −2.90226 + 1.86517i −0.137119 + 0.0881209i
\(449\) −22.6309 + 14.5440i −1.06802 + 0.686375i −0.951760 0.306844i \(-0.900727\pi\)
−0.116260 + 0.993219i \(0.537091\pi\)
\(450\) −0.654861 0.755750i −0.0308704 0.0356264i
\(451\) −27.5080 + 8.07708i −1.29530 + 0.380335i
\(452\) 2.61713 18.2025i 0.123099 0.856174i
\(453\) −6.27561 + 7.24244i −0.294854 + 0.340279i
\(454\) 6.75265 14.7862i 0.316918 0.693953i
\(455\) 9.65596 + 2.83525i 0.452679 + 0.132918i
\(456\) 0.366972 + 0.803556i 0.0171850 + 0.0376299i
\(457\) 3.96111 + 27.5501i 0.185293 + 1.28874i 0.844001 + 0.536341i \(0.180194\pi\)
−0.658709 + 0.752398i \(0.728897\pi\)
\(458\) 4.93520 + 3.17166i 0.230607 + 0.148202i
\(459\) −2.00241 −0.0934647
\(460\) −2.11752 4.30303i −0.0987299 0.200630i
\(461\) 13.8343 0.644327 0.322163 0.946684i \(-0.395590\pi\)
0.322163 + 0.946684i \(0.395590\pi\)
\(462\) 10.3689 + 6.66368i 0.482404 + 0.310022i
\(463\) 3.60814 + 25.0952i 0.167685 + 1.16627i 0.883654 + 0.468140i \(0.155076\pi\)
−0.715970 + 0.698131i \(0.754015\pi\)
\(464\) −1.83516 4.01845i −0.0851954 0.186552i
\(465\) −1.71332 0.503076i −0.0794532 0.0233296i
\(466\) −9.16593 + 20.0706i −0.424604 + 0.929752i
\(467\) −11.7828 + 13.5981i −0.545245 + 0.629246i −0.959769 0.280792i \(-0.909403\pi\)
0.414524 + 0.910039i \(0.363948\pi\)
\(468\) 0.415140 2.88736i 0.0191899 0.133468i
\(469\) −18.4631 + 5.42127i −0.852549 + 0.250331i
\(470\) −4.36315 5.03534i −0.201257 0.232263i
\(471\) 10.9718 7.05115i 0.505554 0.324900i
\(472\) 1.92459 1.23686i 0.0885865 0.0569311i
\(473\) 7.80003 + 9.00171i 0.358646 + 0.413899i
\(474\) 5.38716 1.58181i 0.247441 0.0726551i
\(475\) 0.125719 0.874394i 0.00576838 0.0401199i
\(476\) 4.52389 5.22085i 0.207352 0.239297i
\(477\) 1.31042 2.86943i 0.0600002 0.131382i
\(478\) −6.00657 1.76369i −0.274734 0.0806693i
\(479\) 7.02663 + 15.3862i 0.321055 + 0.703012i 0.999499 0.0316398i \(-0.0100729\pi\)
−0.678445 + 0.734652i \(0.737346\pi\)
\(480\) −0.142315 0.989821i −0.00649575 0.0451790i
\(481\) 6.85151 + 4.40320i 0.312402 + 0.200768i
\(482\) 0.321674 0.0146518
\(483\) −16.0031 4.20053i −0.728168 0.191131i
\(484\) 1.76416 0.0801889
\(485\) −2.77431 1.78294i −0.125975 0.0809592i
\(486\) 0.142315 + 0.989821i 0.00645553 + 0.0448992i
\(487\) −13.2410 28.9938i −0.600009 1.31384i −0.929202 0.369573i \(-0.879504\pi\)
0.329193 0.944263i \(-0.393223\pi\)
\(488\) −0.413986 0.121557i −0.0187403 0.00550264i
\(489\) 2.16087 4.73165i 0.0977181 0.213973i
\(490\) 3.21010 3.70465i 0.145017 0.167359i
\(491\) −3.09971 + 21.5590i −0.139888 + 0.972942i 0.792084 + 0.610412i \(0.208996\pi\)
−0.931972 + 0.362530i \(0.881913\pi\)
\(492\) 7.69951 2.26078i 0.347121 0.101924i
\(493\) 5.79290 + 6.68536i 0.260899 + 0.301093i
\(494\) 2.16781 1.39317i 0.0975345 0.0626816i
\(495\) −3.00554 + 1.93155i −0.135089 + 0.0868165i
\(496\) −1.16935 1.34950i −0.0525054 0.0605945i
\(497\) 15.1911 4.46051i 0.681414 0.200081i
\(498\) −2.37318 + 16.5058i −0.106345 + 0.739645i
\(499\) −5.34372 + 6.16699i −0.239218 + 0.276072i −0.862646 0.505809i \(-0.831194\pi\)
0.623428 + 0.781881i \(0.285740\pi\)
\(500\) −0.415415 + 0.909632i −0.0185779 + 0.0406800i
\(501\) −0.140387 0.0412212i −0.00627201 0.00184163i
\(502\) 3.96072 + 8.67276i 0.176775 + 0.387084i
\(503\) −0.132378 0.920708i −0.00590243 0.0410523i 0.986657 0.162810i \(-0.0520559\pi\)
−0.992560 + 0.121758i \(0.961147\pi\)
\(504\) −2.90226 1.86517i −0.129277 0.0830812i
\(505\) −14.7552 −0.656599
\(506\) −16.2936 + 5.30038i −0.724339 + 0.235631i
\(507\) 4.49079 0.199443
\(508\) 16.9584 + 10.8985i 0.752408 + 0.483543i
\(509\) −3.04140 21.1534i −0.134807 0.937607i −0.939166 0.343463i \(-0.888400\pi\)
0.804359 0.594144i \(-0.202509\pi\)
\(510\) 0.831833 + 1.82146i 0.0368342 + 0.0806556i
\(511\) −5.08266 1.49240i −0.224844 0.0660200i
\(512\) 0.415415 0.909632i 0.0183589 0.0402004i
\(513\) −0.578494 + 0.667618i −0.0255412 + 0.0294761i
\(514\) −1.63303 + 11.3579i −0.0720297 + 0.500977i
\(515\) 14.9732 4.39651i 0.659796 0.193734i
\(516\) −2.18323 2.51958i −0.0961115 0.110919i
\(517\) −20.0251 + 12.8693i −0.880702 + 0.565993i
\(518\) 8.10309 5.20754i 0.356029 0.228806i
\(519\) 11.8799 + 13.7101i 0.521468 + 0.601807i
\(520\) −2.79889 + 0.821829i −0.122740 + 0.0360396i
\(521\) 0.446868 3.10803i 0.0195776 0.136165i −0.977688 0.210060i \(-0.932634\pi\)
0.997266 + 0.0738951i \(0.0235430\pi\)
\(522\) 2.89296 3.33865i 0.126621 0.146129i
\(523\) 13.6560 29.9025i 0.597136 1.30755i −0.333897 0.942610i \(-0.608364\pi\)
0.931033 0.364936i \(-0.118909\pi\)
\(524\) −11.7226 3.44208i −0.512106 0.150368i
\(525\) 1.43315 + 3.13816i 0.0625478 + 0.136960i
\(526\) 2.38725 + 16.6037i 0.104089 + 0.723956i
\(527\) 3.00799 + 1.93312i 0.131030 + 0.0842080i
\(528\) −3.57270 −0.155482
\(529\) 18.5980 13.5320i 0.808608 0.588348i
\(530\) −3.15449 −0.137022
\(531\) 1.92459 + 1.23686i 0.0835202 + 0.0536751i
\(532\) −0.433720 3.01659i −0.0188042 0.130786i
\(533\) −9.72407 21.2927i −0.421196 0.922291i
\(534\) −10.4969 3.08217i −0.454245 0.133378i
\(535\) 3.65399 8.00113i 0.157976 0.345919i
\(536\) 3.65261 4.21534i 0.157769 0.182075i
\(537\) 0.142747 0.992830i 0.00616000 0.0428438i
\(538\) −7.95615 + 2.33614i −0.343014 + 0.100718i
\(539\) −11.4687 13.2356i −0.493992 0.570097i
\(540\) 0.841254 0.540641i 0.0362018 0.0232655i
\(541\) −16.0471 + 10.3129i −0.689921 + 0.443385i −0.838058 0.545582i \(-0.816309\pi\)
0.148137 + 0.988967i \(0.452672\pi\)
\(542\) −7.20850 8.31905i −0.309632 0.357334i
\(543\) −11.4971 + 3.37587i −0.493390 + 0.144872i
\(544\) −0.284973 + 1.98203i −0.0122181 + 0.0849789i
\(545\) 9.64838 11.1348i 0.413291 0.476963i
\(546\) −4.18057 + 9.15418i −0.178912 + 0.391763i
\(547\) −1.10924 0.325702i −0.0474276 0.0139260i 0.257933 0.966163i \(-0.416959\pi\)
−0.305360 + 0.952237i \(0.598777\pi\)
\(548\) −6.09149 13.3385i −0.260216 0.569793i
\(549\) −0.0614036 0.427072i −0.00262064 0.0182270i
\(550\) 3.00554 + 1.93155i 0.128157 + 0.0823614i
\(551\) 3.90250 0.166252
\(552\) 4.56059 1.48358i 0.194112 0.0631454i
\(553\) −19.3699 −0.823692
\(554\) 14.4466 + 9.28430i 0.613779 + 0.394452i
\(555\) 0.397342 + 2.76358i 0.0168662 + 0.117307i
\(556\) 3.43090 + 7.51262i 0.145503 + 0.318606i
\(557\) 19.4224 + 5.70293i 0.822954 + 0.241641i 0.665987 0.745963i \(-0.268010\pi\)
0.156966 + 0.987604i \(0.449829\pi\)
\(558\) 0.741785 1.62428i 0.0314023 0.0687614i
\(559\) −6.36861 + 7.34977i −0.269364 + 0.310862i
\(560\) −0.490975 + 3.41481i −0.0207475 + 0.144302i
\(561\) 6.86423 2.01552i 0.289808 0.0850953i
\(562\) 5.52528 + 6.37651i 0.233070 + 0.268977i
\(563\) 33.5785 21.5796i 1.41517 0.909473i 0.415167 0.909745i \(-0.363723\pi\)
1.00000 0.000272706i \(8.68051e-5\pi\)
\(564\) 5.60503 3.60214i 0.236014 0.151677i
\(565\) −12.0427 13.8980i −0.506640 0.584693i
\(566\) −21.3613 + 6.27225i −0.897883 + 0.263642i
\(567\) 0.490975 3.41481i 0.0206190 0.143408i
\(568\) −3.00530 + 3.46830i −0.126099 + 0.145526i
\(569\) 10.5859 23.1800i 0.443785 0.971754i −0.547103 0.837066i \(-0.684269\pi\)
0.990888 0.134689i \(-0.0430035\pi\)
\(570\) 0.847602 + 0.248878i 0.0355021 + 0.0104244i
\(571\) −18.0824 39.5950i −0.756727 1.65700i −0.753887 0.657004i \(-0.771823\pi\)
−0.00283969 0.999996i \(-0.500904\pi\)
\(572\) 1.48317 + 10.3157i 0.0620144 + 0.431320i
\(573\) −14.8313 9.53149i −0.619586 0.398184i
\(574\) −27.6841 −1.15551
\(575\) −4.63870 1.21757i −0.193447 0.0507763i
\(576\) 1.00000 0.0416667
\(577\) 31.4207 + 20.1928i 1.30806 + 0.840639i 0.994065 0.108786i \(-0.0346962\pi\)
0.313995 + 0.949425i \(0.398333\pi\)
\(578\) 1.84872 + 12.8581i 0.0768965 + 0.534827i
\(579\) −6.60891 14.4715i −0.274657 0.601414i
\(580\) −4.23872 1.24460i −0.176003 0.0516792i
\(581\) 23.8986 52.3306i 0.991480 2.17104i
\(582\) 2.15962 2.49233i 0.0895191 0.103311i
\(583\) −1.60389 + 11.1553i −0.0664265 + 0.462007i
\(584\) 1.47327 0.432591i 0.0609643 0.0179007i
\(585\) −1.91026 2.20456i −0.0789797 0.0911475i
\(586\) 9.78607 6.28912i 0.404259 0.259801i
\(587\) 6.11634 3.93073i 0.252448 0.162239i −0.408296 0.912849i \(-0.633877\pi\)
0.660745 + 0.750611i \(0.270241\pi\)
\(588\) 3.21010 + 3.70465i 0.132382 + 0.152777i
\(589\) 1.51352 0.444410i 0.0623635 0.0183116i
\(590\) 0.325583 2.26448i 0.0134040 0.0932272i
\(591\) 13.3507 15.4075i 0.549173 0.633780i
\(592\) −1.15984 + 2.53969i −0.0476690 + 0.104381i
\(593\) −39.1398 11.4925i −1.60728 0.471940i −0.649719 0.760174i \(-0.725113\pi\)
−0.957560 + 0.288235i \(0.906932\pi\)
\(594\) −1.48415 3.24984i −0.0608955 0.133342i
\(595\) −0.983135 6.83786i −0.0403046 0.280325i
\(596\) −16.6276 10.6859i −0.681095 0.437713i
\(597\) 4.12088 0.168656
\(598\) −6.17692 12.5522i −0.252593 0.513297i
\(599\) 45.3874 1.85448 0.927239 0.374470i \(-0.122175\pi\)
0.927239 + 0.374470i \(0.122175\pi\)
\(600\) −0.841254 0.540641i −0.0343440 0.0220716i
\(601\) −4.69569 32.6593i −0.191541 1.33220i −0.827930 0.560831i \(-0.810482\pi\)
0.636389 0.771368i \(-0.280427\pi\)
\(602\) 4.77796 + 10.4623i 0.194735 + 0.426410i
\(603\) 5.35176 + 1.57142i 0.217940 + 0.0639931i
\(604\) −3.98097 + 8.71711i −0.161983 + 0.354694i
\(605\) 1.15528 1.33326i 0.0469687 0.0542047i
\(606\) 2.09989 14.6050i 0.0853021 0.593289i
\(607\) −42.3421 + 12.4328i −1.71861 + 0.504631i −0.984647 0.174555i \(-0.944151\pi\)
−0.733967 + 0.679186i \(0.762333\pi\)
\(608\) 0.578494 + 0.667618i 0.0234610 + 0.0270755i
\(609\) −12.8212 + 8.23969i −0.519542 + 0.333889i
\(610\) −0.362970 + 0.233267i −0.0146962 + 0.00944469i
\(611\) −12.7275 14.6884i −0.514901 0.594228i
\(612\) −1.92130 + 0.564145i −0.0776640 + 0.0228042i
\(613\) −3.54682 + 24.6687i −0.143255 + 0.996360i 0.783687 + 0.621155i \(0.213336\pi\)
−0.926942 + 0.375204i \(0.877573\pi\)
\(614\) 15.2013 17.5432i 0.613475 0.707987i
\(615\) 3.33352 7.29940i 0.134421 0.294340i
\(616\) 11.8262 + 3.47250i 0.476493 + 0.139911i
\(617\) −0.150510 0.329570i −0.00605929 0.0132680i 0.906578 0.422038i \(-0.138685\pi\)
−0.912637 + 0.408770i \(0.865958\pi\)
\(618\) 2.22086 + 15.4464i 0.0893362 + 0.621347i
\(619\) −19.5685 12.5759i −0.786526 0.505470i 0.0846675 0.996409i \(-0.473017\pi\)
−0.871194 + 0.490940i \(0.836654\pi\)
\(620\) −1.78565 −0.0717134
\(621\) 3.24405 + 3.53216i 0.130179 + 0.141741i
\(622\) 13.8232 0.554260
\(623\) 31.7508 + 20.4050i 1.27207 + 0.817510i
\(624\) −0.415140 2.88736i −0.0166189 0.115587i
\(625\) 0.415415 + 0.909632i 0.0166166 + 0.0363853i
\(626\) −27.3925 8.04316i −1.09482 0.321470i
\(627\) 1.31108 2.87086i 0.0523594 0.114651i
\(628\) 8.54083 9.85664i 0.340816 0.393323i
\(629\) 0.795644 5.53382i 0.0317244 0.220648i
\(630\) −3.31018 + 0.971955i −0.131881 + 0.0387236i
\(631\) −25.6469 29.5981i −1.02099 1.17828i −0.983854 0.178972i \(-0.942723\pi\)
−0.0371333 0.999310i \(-0.511823\pi\)
\(632\) 4.72329 3.03548i 0.187883 0.120745i
\(633\) −9.65231 + 6.20316i −0.383645 + 0.246554i
\(634\) −2.32912 2.68794i −0.0925010 0.106752i
\(635\) 19.3419 5.67931i 0.767562 0.225376i
\(636\) 0.448931 3.12239i 0.0178013 0.123811i
\(637\) 9.36404 10.8067i 0.371017 0.428176i
\(638\) −6.55649 + 14.3567i −0.259574 + 0.568387i
\(639\) −4.40332 1.29293i −0.174193 0.0511475i
\(640\) −0.415415 0.909632i −0.0164207 0.0359564i
\(641\) −3.23735 22.5163i −0.127868 0.889340i −0.948250 0.317525i \(-0.897148\pi\)
0.820382 0.571816i \(-0.193761\pi\)
\(642\) 7.39967 + 4.75548i 0.292042 + 0.187684i
\(643\) 0.617140 0.0243376 0.0121688 0.999926i \(-0.496126\pi\)
0.0121688 + 0.999926i \(0.496126\pi\)
\(644\) −16.5383 + 0.478223i −0.651701 + 0.0188446i
\(645\) −3.33389 −0.131272
\(646\) −1.48810 0.956341i −0.0585484 0.0376268i
\(647\) −0.753992 5.24413i −0.0296425 0.206168i 0.969618 0.244625i \(-0.0786648\pi\)
−0.999260 + 0.0384570i \(0.987756\pi\)
\(648\) 0.415415 + 0.909632i 0.0163190 + 0.0357337i
\(649\) −7.84241 2.30274i −0.307841 0.0903904i
\(650\) −1.21179 + 2.65345i −0.0475303 + 0.104077i
\(651\) −4.03417 + 4.65568i −0.158112 + 0.182471i
\(652\) 0.740282 5.14878i 0.0289917 0.201642i
\(653\) −28.6830 + 8.42208i −1.12245 + 0.329582i −0.789737 0.613446i \(-0.789783\pi\)
−0.332715 + 0.943027i \(0.607965\pi\)
\(654\) 9.64838 + 11.1348i 0.377282 + 0.435406i
\(655\) −10.2780 + 6.60530i −0.401596 + 0.258090i
\(656\) 6.75069 4.33840i 0.263570 0.169386i
\(657\) 1.00552 + 1.16043i 0.0392289 + 0.0452726i
\(658\) −22.0548 + 6.47586i −0.859784 + 0.252455i
\(659\) 1.47779 10.2782i 0.0575664 0.400383i −0.940583 0.339565i \(-0.889720\pi\)
0.998149 0.0608177i \(-0.0193708\pi\)
\(660\) −2.33962 + 2.70006i −0.0910695 + 0.105100i
\(661\) −1.23883 + 2.71266i −0.0481849 + 0.105510i −0.932193 0.361961i \(-0.882107\pi\)
0.884008 + 0.467471i \(0.154835\pi\)
\(662\) −11.4186 3.35282i −0.443798 0.130311i
\(663\) 2.42650 + 5.31330i 0.0942375 + 0.206351i
\(664\) 2.37318 + 16.5058i 0.0920973 + 0.640551i
\(665\) −2.56381 1.64766i −0.0994204 0.0638936i
\(666\) −2.79200 −0.108188
\(667\) 2.40774 21.0491i 0.0932281 0.815025i
\(668\) −0.146313 −0.00566103
\(669\) 3.52366 + 2.26452i 0.136233 + 0.0875513i
\(670\) −0.793789 5.52092i −0.0306667 0.213292i
\(671\) 0.640357 + 1.40219i 0.0247207 + 0.0541308i
\(672\) −3.31018 0.971955i −0.127693 0.0374940i
\(673\) 0.691741 1.51470i 0.0266647 0.0583875i −0.895831 0.444395i \(-0.853419\pi\)
0.922496 + 0.386007i \(0.126146\pi\)
\(674\) −20.0646 + 23.1558i −0.772861 + 0.891929i
\(675\) 0.142315 0.989821i 0.00547770 0.0380982i
\(676\) 4.30888 1.26520i 0.165726 0.0486616i
\(677\) −10.9338 12.6183i −0.420220 0.484960i 0.505684 0.862719i \(-0.331240\pi\)
−0.925904 + 0.377759i \(0.876695\pi\)
\(678\) 15.4704 9.94222i 0.594137 0.381829i
\(679\) −9.57116 + 6.15101i −0.367307 + 0.236054i
\(680\) 1.31130 + 1.51332i 0.0502861 + 0.0580333i
\(681\) 15.5967 4.57962i 0.597668 0.175491i
\(682\) −0.907909 + 6.31465i −0.0347656 + 0.241800i
\(683\) 13.1410 15.1655i 0.502825 0.580291i −0.446422 0.894823i \(-0.647302\pi\)
0.949247 + 0.314532i \(0.101847\pi\)
\(684\) −0.366972 + 0.803556i −0.0140315 + 0.0307247i
\(685\) −14.0696 4.13122i −0.537574 0.157846i
\(686\) 3.00681 + 6.58399i 0.114800 + 0.251378i
\(687\) 0.834888 + 5.80677i 0.0318530 + 0.221542i
\(688\) −2.80465 1.80244i −0.106926 0.0687172i
\(689\) −9.20183 −0.350562
\(690\) 1.86534 4.41820i 0.0710121 0.168198i
\(691\) −42.5140 −1.61731 −0.808654 0.588284i \(-0.799804\pi\)
−0.808654 + 0.588284i \(0.799804\pi\)
\(692\) 15.2612 + 9.80780i 0.580145 + 0.372837i
\(693\) 1.75410 + 12.2001i 0.0666329 + 0.463442i
\(694\) 8.07394 + 17.6795i 0.306483 + 0.671103i
\(695\) 7.92442 + 2.32682i 0.300591 + 0.0882613i
\(696\) 1.83516 4.01845i 0.0695617 0.152319i
\(697\) −10.5226 + 12.1438i −0.398573 + 0.459978i
\(698\) −1.34643 + 9.36463i −0.0509631 + 0.354456i
\(699\) −21.1708 + 6.21629i −0.800751 + 0.235122i
\(700\) 2.25922 + 2.60728i 0.0853904 + 0.0985458i
\(701\) 4.59536 2.95326i 0.173564 0.111543i −0.450974 0.892537i \(-0.648923\pi\)
0.624539 + 0.780994i \(0.285287\pi\)
\(702\) 2.45398 1.57708i 0.0926196 0.0595230i
\(703\) −1.61515 1.86399i −0.0609167 0.0703016i
\(704\) −3.42798 + 1.00654i −0.129197 + 0.0379356i
\(705\) 0.948203 6.59490i 0.0357114 0.248378i
\(706\) 22.8475 26.3675i 0.859878 0.992352i
\(707\) −21.1464 + 46.3042i −0.795293 + 1.74145i
\(708\) 2.19510 + 0.644538i 0.0824968 + 0.0242232i
\(709\) 13.7314 + 30.0676i 0.515694 + 1.12921i 0.971044 + 0.238899i \(0.0767866\pi\)
−0.455351 + 0.890312i \(0.650486\pi\)
\(710\) 0.653113 + 4.54250i 0.0245109 + 0.170477i
\(711\) 4.72329 + 3.03548i 0.177137 + 0.113839i
\(712\) −10.9400 −0.409996
\(713\) −1.46323 8.43774i −0.0547985 0.315996i
\(714\) 6.90817 0.258532
\(715\) 8.76733 + 5.63442i 0.327880 + 0.210715i
\(716\) −0.142747 0.992830i −0.00533472 0.0371038i
\(717\) −2.60056 5.69444i −0.0971198 0.212663i
\(718\) 18.4440 + 5.41566i 0.688325 + 0.202110i
\(719\) −11.8243 + 25.8916i −0.440971 + 0.965593i 0.550447 + 0.834870i \(0.314457\pi\)
−0.991419 + 0.130723i \(0.958270\pi\)
\(720\) 0.654861 0.755750i 0.0244052 0.0281651i
\(721\) 7.66180 53.2890i 0.285340 1.98459i
\(722\) 17.4816 5.13306i 0.650598 0.191033i
\(723\) 0.210652 + 0.243105i 0.00783421 + 0.00904117i
\(724\) −10.0803 + 6.47824i −0.374633 + 0.240762i
\(725\) −3.71638 + 2.38837i −0.138023 + 0.0887019i
\(726\) 1.15528 + 1.33326i 0.0428763 + 0.0494819i
\(727\) 39.9797 11.7391i 1.48276 0.435379i 0.562539 0.826771i \(-0.309824\pi\)
0.920224 + 0.391392i \(0.128006\pi\)
\(728\) −1.43220 + 9.96118i −0.0530809 + 0.369186i
\(729\) −0.654861 + 0.755750i −0.0242541 + 0.0279907i
\(730\) 0.637855 1.39671i 0.0236081 0.0516945i
\(731\) 6.40541 + 1.88080i 0.236913 + 0.0695638i
\(732\) −0.179236 0.392473i −0.00662476 0.0145062i
\(733\) 4.12562 + 28.6943i 0.152383 + 1.05985i 0.912210 + 0.409723i \(0.134375\pi\)
−0.759827 + 0.650126i \(0.774716\pi\)
\(734\) 19.3040 + 12.4059i 0.712524 + 0.457911i
\(735\) 4.90196 0.180811
\(736\) 3.95788 2.70835i 0.145889 0.0998312i
\(737\) −19.9274 −0.734035
\(738\) 6.75069 + 4.33840i 0.248496 + 0.159699i
\(739\) −2.14188 14.8971i −0.0787905 0.548000i −0.990537 0.137246i \(-0.956175\pi\)
0.911746 0.410753i \(-0.134734\pi\)
\(740\) 1.15984 + 2.53969i 0.0426364 + 0.0933608i
\(741\) 2.47250 + 0.725992i 0.0908296 + 0.0266700i
\(742\) −4.52086 + 9.89930i −0.165966 + 0.363415i
\(743\) −11.8152 + 13.6355i −0.433457 + 0.500237i −0.929889 0.367839i \(-0.880098\pi\)
0.496432 + 0.868076i \(0.334643\pi\)
\(744\) 0.254124 1.76747i 0.00931665 0.0647987i
\(745\) −18.9647 + 5.56854i −0.694812 + 0.204015i
\(746\) −11.7858 13.6015i −0.431508 0.497987i
\(747\) −14.0284 + 9.01550i −0.513272 + 0.329860i
\(748\) 6.01834 3.86775i 0.220052 0.141419i
\(749\) −19.8721 22.9336i −0.726110 0.837976i
\(750\) −0.959493 + 0.281733i −0.0350357 + 0.0102874i
\(751\) 3.89754 27.1080i 0.142223 0.989184i −0.786283 0.617867i \(-0.787997\pi\)
0.928506 0.371317i \(-0.121094\pi\)
\(752\) 4.36315 5.03534i 0.159108 0.183620i
\(753\) −3.96072 + 8.67276i −0.144337 + 0.316053i
\(754\) −12.3646 3.63057i −0.450291 0.132217i
\(755\) 3.98097 + 8.71711i 0.144882 + 0.317248i
\(756\) −0.490975 3.41481i −0.0178566 0.124195i
\(757\) 27.8301 + 17.8853i 1.01150 + 0.650054i 0.937782 0.347225i \(-0.112876\pi\)
0.0737214 + 0.997279i \(0.476512\pi\)
\(758\) −31.8583 −1.15714
\(759\) −14.6758 8.84287i −0.532698 0.320976i
\(760\) 0.883386 0.0320438
\(761\) −38.4969 24.7404i −1.39551 0.896840i −0.395743 0.918362i \(-0.629513\pi\)
−0.999768 + 0.0215211i \(0.993149\pi\)
\(762\) 2.86886 + 19.9533i 0.103928 + 0.722833i
\(763\) −21.1153 46.2360i −0.764424 1.67386i
\(764\) −16.9158 4.96694i −0.611994 0.179698i
\(765\) −0.831833 + 1.82146i −0.0300750 + 0.0658550i
\(766\) 6.10368 7.04402i 0.220535 0.254511i
\(767\) 0.949744 6.60561i 0.0342933 0.238515i
\(768\) 0.959493 0.281733i 0.0346227 0.0101661i
\(769\) −26.9000 31.0443i −0.970040 1.11949i −0.992805 0.119745i \(-0.961792\pi\)
0.0227642 0.999741i \(-0.492753\pi\)
\(770\) 10.3689 6.66368i 0.373669 0.240142i
\(771\) −9.65316 + 6.20371i −0.347650 + 0.223421i
\(772\) −10.4183 12.0233i −0.374962 0.432730i
\(773\) 28.6971 8.42622i 1.03216 0.303070i 0.278573 0.960415i \(-0.410139\pi\)
0.753590 + 0.657345i \(0.228321\pi\)
\(774\) 0.474462 3.29995i 0.0170542 0.118614i
\(775\) −1.16935 + 1.34950i −0.0420043 + 0.0484756i
\(776\) 1.36997 2.99981i 0.0491790 0.107687i
\(777\) 9.24199 + 2.71369i 0.331555 + 0.0973532i
\(778\) 9.58609 + 20.9906i 0.343678 + 0.752550i
\(779\) 1.00884 + 7.01663i 0.0361454 + 0.251397i
\(780\) −2.45398 1.57708i −0.0878667 0.0564685i
\(781\) 16.3959 0.586690
\(782\) −6.07638 + 7.43638i −0.217291 + 0.265925i
\(783\) 4.41767 0.157874
\(784\) 4.12379 + 2.65020i 0.147278 + 0.0946499i
\(785\) −1.85610 12.9095i −0.0662470 0.460758i
\(786\) −5.07535 11.1135i −0.181032 0.396404i
\(787\) 19.2252 + 5.64504i 0.685306 + 0.201224i 0.605808 0.795611i \(-0.292850\pi\)
0.0794980 + 0.996835i \(0.474668\pi\)
\(788\) 8.46909 18.5447i 0.301699 0.660628i
\(789\) −10.9849 + 12.6773i −0.391074 + 0.451323i
\(790\) 0.799040 5.55744i 0.0284286 0.197725i
\(791\) −60.8731 + 17.8740i −2.16440 + 0.635525i
\(792\) −2.33962 2.70006i −0.0831347 0.0959426i
\(793\) −1.05880 + 0.680452i −0.0375992 + 0.0241635i
\(794\) 15.7379 10.1141i 0.558515 0.358936i
\(795\) −2.06575 2.38401i −0.0732647 0.0845520i
\(796\) 3.95395 1.16099i 0.140144 0.0411500i
\(797\) 6.74111 46.8854i 0.238782 1.66077i −0.419320 0.907838i \(-0.637731\pi\)
0.658102 0.752928i \(-0.271359\pi\)
\(798\) 1.99576 2.30323i 0.0706492 0.0815335i
\(799\) −5.54226 + 12.1359i −0.196071 + 0.429336i
\(800\) −0.959493 0.281733i −0.0339232 0.00996075i
\(801\) −4.54466 9.95142i −0.160578 0.351616i
\(802\) −2.75760 19.1795i −0.0973741 0.677252i
\(803\) −4.61491 2.96582i −0.162857 0.104662i
\(804\) 5.57769 0.196710
\(805\) −10.4689 + 12.8120i −0.368980 + 0.451564i
\(806\) −5.20884 −0.183473
\(807\) −6.97571 4.48301i −0.245556 0.157810i
\(808\) −2.09989 14.6050i −0.0738738 0.513803i
\(809\) 17.1952 + 37.6522i 0.604550 + 1.32378i 0.926240 + 0.376935i \(0.123022\pi\)
−0.321690 + 0.946845i \(0.604251\pi\)
\(810\) 0.959493 + 0.281733i 0.0337131 + 0.00989907i
\(811\) 17.4372 38.1822i 0.612304 1.34076i −0.308683 0.951165i \(-0.599888\pi\)
0.920987 0.389593i \(-0.127384\pi\)
\(812\) −9.98047 + 11.5181i −0.350246 + 0.404205i
\(813\) 1.56656 10.8956i 0.0549416 0.382127i
\(814\) 9.57089 2.81027i 0.335460 0.0984998i
\(815\) −3.40640 3.93120i −0.119321 0.137704i
\(816\) −1.68454 + 1.08259i −0.0589706 + 0.0378981i
\(817\) 2.47758 1.59225i 0.0866797 0.0557056i
\(818\) 10.2595 + 11.8401i 0.358714 + 0.413978i
\(819\) −9.65596 + 2.83525i −0.337407 + 0.0990715i
\(820\) 1.14201 7.94288i 0.0398809 0.277377i
\(821\) 5.09320 5.87787i 0.177754 0.205139i −0.659880 0.751371i \(-0.729393\pi\)
0.837634 + 0.546232i \(0.183938\pi\)
\(822\) 6.09149 13.3385i 0.212465 0.465234i
\(823\) −0.630761 0.185208i −0.0219869 0.00645595i 0.270721 0.962658i \(-0.412738\pi\)
−0.292708 + 0.956202i \(0.594556\pi\)
\(824\) 6.48266 + 14.1951i 0.225834 + 0.494508i
\(825\) 0.508448 + 3.53633i 0.0177019 + 0.123119i
\(826\) −6.63969 4.26707i −0.231024 0.148470i
\(827\) −19.6319 −0.682669 −0.341335 0.939942i \(-0.610879\pi\)
−0.341335 + 0.939942i \(0.610879\pi\)
\(828\) 4.10777 + 2.47513i 0.142755 + 0.0860166i
\(829\) −9.62079 −0.334144 −0.167072 0.985945i \(-0.553431\pi\)
−0.167072 + 0.985945i \(0.553431\pi\)
\(830\) 14.0284 + 9.01550i 0.486932 + 0.312932i
\(831\) 2.44394 + 16.9980i 0.0847793 + 0.589653i
\(832\) −1.21179 2.65345i −0.0420112 0.0919917i
\(833\) −9.41814 2.76542i −0.326319 0.0958160i
\(834\) −3.43090 + 7.51262i −0.118802 + 0.260141i
\(835\) −0.0958148 + 0.110576i −0.00331581 + 0.00382665i
\(836\) 0.449155 3.12394i 0.0155344 0.108044i
\(837\) 1.71332 0.503076i 0.0592209 0.0173888i
\(838\) −0.176870 0.204118i −0.00610986 0.00705115i
\(839\) 29.1487 18.7327i 1.00632 0.646726i 0.0698854 0.997555i \(-0.477737\pi\)
0.936439 + 0.350829i \(0.114100\pi\)
\(840\) −2.90226 + 1.86517i −0.100137 + 0.0643544i
\(841\) 6.21085 + 7.16770i 0.214167 + 0.247162i
\(842\) −17.2847 + 5.07526i −0.595671 + 0.174905i
\(843\) −1.20076 + 8.35146i −0.0413563 + 0.287639i
\(844\) −7.51369 + 8.67126i −0.258632 + 0.298477i
\(845\) 1.86554 4.08497i 0.0641766 0.140527i
\(846\) 6.39283 + 1.87710i 0.219790 + 0.0645361i
\(847\) −2.52830 5.53620i −0.0868733 0.190226i
\(848\) −0.448931 3.12239i −0.0154164 0.107223i
\(849\) −18.7289 12.0364i −0.642775 0.413087i
\(850\) 2.00241 0.0686822
\(851\) −11.0504 + 7.56171i −0.378802 + 0.259212i
\(852\) −4.58921 −0.157224
\(853\) 41.6679 + 26.7783i 1.42668 + 0.916873i 0.999922 + 0.0125087i \(0.00398175\pi\)
0.426761 + 0.904365i \(0.359655\pi\)
\(854\) 0.211838 + 1.47336i 0.00724894 + 0.0504175i
\(855\) 0.366972 + 0.803556i 0.0125502 + 0.0274810i
\(856\) 8.43970 + 2.47812i 0.288463 + 0.0847004i
\(857\) 2.16699 4.74504i 0.0740228 0.162087i −0.869003 0.494807i \(-0.835239\pi\)
0.943026 + 0.332719i \(0.107966\pi\)
\(858\) −6.82480 + 7.87623i −0.232995 + 0.268890i
\(859\) −3.21486 + 22.3598i −0.109690 + 0.762908i 0.858522 + 0.512776i \(0.171383\pi\)
−0.968212 + 0.250131i \(0.919526\pi\)
\(860\) −3.19884 + 0.939265i −0.109080 + 0.0320287i
\(861\) −18.1292 20.9222i −0.617843 0.713028i
\(862\) −19.1943 + 12.3354i −0.653760 + 0.420146i
\(863\) 5.02987 3.23250i 0.171219 0.110036i −0.452225 0.891904i \(-0.649370\pi\)
0.623443 + 0.781868i \(0.285733\pi\)
\(864\) 0.654861 + 0.755750i 0.0222788 + 0.0257111i
\(865\) 17.4062 5.11093i 0.591829 0.173777i
\(866\) −2.75618 + 19.1697i −0.0936588 + 0.651411i
\(867\) −8.50686 + 9.81744i −0.288908 + 0.333418i
\(868\) −2.55910 + 5.60365i −0.0868616 + 0.190200i
\(869\) −19.2467 5.65134i −0.652899 0.191708i
\(870\) −1.83516 4.01845i −0.0622179 0.136238i
\(871\) −2.31553 16.1048i −0.0784586 0.545691i
\(872\) 12.3946 + 7.96552i 0.419734 + 0.269747i
\(873\) 3.29783 0.111615
\(874\) 0.723882 + 4.17427i 0.0244857 + 0.141197i
\(875\) 3.44992 0.116629
\(876\) 1.29172 + 0.830135i 0.0436430 + 0.0280477i
\(877\) −0.0560459 0.389808i −0.00189254 0.0131629i 0.988853 0.148893i \(-0.0475710\pi\)
−0.990746 + 0.135730i \(0.956662\pi\)
\(878\) 15.3038 + 33.5107i 0.516479 + 1.13093i
\(879\) 11.1615 + 3.27732i 0.376469 + 0.110541i
\(880\) −1.48415 + 3.24984i −0.0500307 + 0.109552i
\(881\) −11.8955 + 13.7281i −0.400768 + 0.462511i −0.919883 0.392193i \(-0.871716\pi\)
0.519114 + 0.854705i \(0.326262\pi\)
\(882\) −0.697621 + 4.85206i −0.0234901 + 0.163377i
\(883\) −4.49392 + 1.31953i −0.151232 + 0.0444058i −0.356472 0.934306i \(-0.616021\pi\)
0.205240 + 0.978712i \(0.434202\pi\)
\(884\) 3.82514 + 4.41445i 0.128653 + 0.148474i
\(885\) 1.92459 1.23686i 0.0646944 0.0415766i
\(886\) 28.9056 18.5765i 0.971103 0.624090i
\(887\) 35.8713 + 41.3977i 1.20444 + 1.39000i 0.899094 + 0.437755i \(0.144226\pi\)
0.305345 + 0.952242i \(0.401228\pi\)
\(888\) −2.67890 + 0.786596i −0.0898980 + 0.0263964i
\(889\) 9.89732 68.8374i 0.331946 2.30873i
\(890\) −7.16421 + 8.26794i −0.240145 + 0.277142i
\(891\) 1.48415 3.24984i 0.0497209 0.108874i
\(892\) 4.01891 + 1.18006i 0.134563 + 0.0395113i
\(893\) 2.44503 + 5.35386i 0.0818197 + 0.179160i
\(894\) −2.81290 19.5641i −0.0940774 0.654323i
\(895\) −0.843810 0.542284i −0.0282055 0.0181266i
\(896\) −3.44992 −0.115254
\(897\) 5.44129 12.8881i 0.181679 0.430323i
\(898\) −26.9014 −0.897713
\(899\) −6.63615 4.26479i −0.221328 0.142239i
\(900\) −0.142315 0.989821i −0.00474383 0.0329940i
\(901\) 2.62401 + 5.74578i 0.0874185 + 0.191420i
\(902\) −27.5080 8.07708i −0.915916 0.268937i
\(903\) −4.77796 + 10.4623i −0.159001 + 0.348163i
\(904\) 12.0427 13.8980i 0.400534 0.462241i
\(905\) −1.70529 + 11.8606i −0.0566858 + 0.394258i
\(906\) −9.19493 + 2.69988i −0.305481 + 0.0896974i
\(907\) 23.3050 + 26.8954i 0.773829 + 0.893046i 0.996648 0.0818140i \(-0.0260713\pi\)
−0.222819 + 0.974860i \(0.571526\pi\)
\(908\) 13.6747 8.78822i 0.453812 0.291647i
\(909\) 12.4129 7.97728i 0.411709 0.264590i
\(910\) 6.59026 + 7.60557i 0.218465 + 0.252122i
\(911\) −23.4130 + 6.87467i −0.775707 + 0.227768i −0.645542 0.763724i \(-0.723369\pi\)
−0.130164 + 0.991492i \(0.541550\pi\)
\(912\) −0.125719 + 0.874394i −0.00416297 + 0.0289541i
\(913\) 39.0145 45.0251i 1.29119 1.49011i
\(914\) −11.5624 + 25.3182i −0.382451 + 0.837450i
\(915\) −0.413986 0.121557i −0.0136860 0.00401856i
\(916\) 2.43703 + 5.33634i 0.0805216 + 0.176318i
\(917\) 5.99850 + 41.7205i 0.198088 + 1.37773i
\(918\) −1.68454 1.08259i −0.0555980 0.0357307i
\(919\) 51.0608 1.68434 0.842170 0.539212i \(-0.181278\pi\)
0.842170 + 0.539212i \(0.181278\pi\)
\(920\) 0.545025 4.76476i 0.0179690 0.157090i
\(921\) 23.2130 0.764895
\(922\) 11.6381 + 7.47938i 0.383282 + 0.246320i
\(923\) 1.90517 + 13.2507i 0.0627093 + 0.436153i
\(924\) 5.12021 + 11.2117i 0.168442 + 0.368837i
\(925\) 2.67890 + 0.786596i 0.0880817 + 0.0258631i
\(926\) −10.5321 + 23.0621i −0.346107 + 0.757868i
\(927\) −10.2193 + 11.7937i −0.335645 + 0.387355i
\(928\) 0.628699 4.37270i 0.0206381 0.143541i
\(929\) 54.0027 15.8566i 1.77177 0.520239i 0.777667 0.628676i \(-0.216403\pi\)
0.994103 + 0.108437i \(0.0345846\pi\)
\(930\) −1.16935 1.34950i −0.0383445 0.0442520i
\(931\) −3.64289 + 2.34115i −0.119391 + 0.0767280i
\(932\) −18.5619 + 11.9290i −0.608014 + 0.390747i
\(933\) 9.05227 + 10.4469i 0.296358 + 0.342015i
\(934\) −17.2641 + 5.06918i −0.564897 + 0.165869i
\(935\) 1.01812 7.08120i 0.0332962 0.231580i
\(936\) 1.91026 2.20456i 0.0624390 0.0720584i
\(937\) −4.83808 + 10.5939i −0.158053 + 0.346088i −0.972047 0.234785i \(-0.924561\pi\)
0.813994 + 0.580873i \(0.197289\pi\)
\(938\) −18.4631 5.42127i −0.602843 0.177011i
\(939\) −11.8597 25.9690i −0.387025 0.847467i
\(940\) −0.948203 6.59490i −0.0309270 0.215102i
\(941\) 14.3111 + 9.19717i 0.466528 + 0.299819i 0.752705 0.658357i \(-0.228748\pi\)
−0.286178 + 0.958177i \(0.592385\pi\)
\(942\) 13.0422 0.424938
\(943\) 38.4684 1.11235i 1.25270 0.0362232i
\(944\) 2.28777 0.0744605
\(945\) −2.90226 1.86517i −0.0944105 0.0606739i
\(946\) 1.69511 + 11.7897i 0.0551127 + 0.383317i
\(947\) 6.58188 + 14.4123i 0.213882 + 0.468337i 0.985915 0.167245i \(-0.0534872\pi\)
−0.772033 + 0.635583i \(0.780760\pi\)
\(948\) 5.38716 + 1.58181i 0.174967 + 0.0513749i
\(949\) 1.86066 4.07428i 0.0603996 0.132257i
\(950\) 0.578494 0.667618i 0.0187688 0.0216604i
\(951\) 0.506165 3.52046i 0.0164135 0.114159i
\(952\) 6.62834 1.94626i 0.214826 0.0630785i
\(953\) 39.3764 + 45.4428i 1.27553 + 1.47204i 0.809328 + 0.587357i \(0.199832\pi\)
0.466199 + 0.884680i \(0.345623\pi\)
\(954\) 2.65373 1.70545i 0.0859176 0.0552159i
\(955\) −14.8313 + 9.53149i −0.479929 + 0.308432i
\(956\) −4.09953 4.73111i −0.132588 0.153015i
\(957\) −15.1437 + 4.44658i −0.489525 + 0.143737i
\(958\) −2.40721 + 16.7425i −0.0777736 + 0.540927i
\(959\) −33.1283 + 38.2321i −1.06977 + 1.23458i
\(960\) 0.415415 0.909632i 0.0134075 0.0293582i
\(961\) 26.6849 + 7.83539i 0.860803 + 0.252755i
\(962\) 3.38331 + 7.40841i 0.109082 + 0.238857i
\(963\) 1.25180 + 8.70647i 0.0403387 + 0.280562i
\(964\) 0.270609 + 0.173910i 0.00871574 + 0.00560126i
\(965\) −15.9092 −0.512134
\(966\) −11.1917 12.1857i −0.360088 0.392067i
\(967\) −28.5518 −0.918163 −0.459081 0.888394i \(-0.651821\pi\)
−0.459081 + 0.888394i \(0.651821\pi\)
\(968\) 1.48410 + 0.953774i 0.0477008 + 0.0306555i
\(969\) −0.251741 1.75090i −0.00808709 0.0562470i
\(970\) −1.36997 2.99981i −0.0439870 0.0963182i
\(971\) 10.9578 + 3.21749i 0.351651 + 0.103254i 0.452788 0.891618i \(-0.350430\pi\)
−0.101136 + 0.994873i \(0.532248\pi\)
\(972\) −0.415415 + 0.909632i −0.0133244 + 0.0291765i
\(973\) 18.6588 21.5334i 0.598174 0.690330i
\(974\) 4.53618 31.5498i 0.145349 1.01092i
\(975\) −2.79889 + 0.821829i −0.0896363 + 0.0263196i
\(976\) −0.282548 0.326078i −0.00904415 0.0104375i
\(977\) 3.64415 2.34195i 0.116587 0.0749257i −0.481048 0.876694i \(-0.659744\pi\)
0.597635 + 0.801769i \(0.296107\pi\)
\(978\) 4.37597 2.81226i 0.139928 0.0899263i
\(979\) 25.5955 + 29.5388i 0.818037 + 0.944065i
\(980\) 4.70339 1.38104i 0.150244 0.0441157i
\(981\) −2.09679 + 14.5835i −0.0669455 + 0.465616i
\(982\) −14.2633 + 16.4607i −0.455160 + 0.525283i
\(983\) 11.0955 24.2958i 0.353892 0.774914i −0.646041 0.763303i \(-0.723577\pi\)
0.999933 0.0116117i \(-0.00369619\pi\)
\(984\) 7.69951 + 2.26078i 0.245451 + 0.0720710i
\(985\) −8.46909 18.5447i −0.269848 0.590884i
\(986\) 1.25892 + 8.75596i 0.0400921 + 0.278846i
\(987\) −19.3369 12.4271i −0.615501 0.395558i
\(988\) 2.57688 0.0819816
\(989\) −7.05958 14.3458i −0.224481 0.456171i
\(990\) −3.57270 −0.113548
\(991\) −10.8142 6.94989i −0.343526 0.220770i 0.357489 0.933917i \(-0.383633\pi\)
−0.701015 + 0.713147i \(0.747269\pi\)
\(992\) −0.254124 1.76747i −0.00806846 0.0561174i
\(993\) −4.94373 10.8253i −0.156885 0.343529i
\(994\) 15.1911 + 4.46051i 0.481832 + 0.141479i
\(995\) 1.71187 3.74848i 0.0542701 0.118835i
\(996\) −10.9202 + 12.6026i −0.346019 + 0.399327i
\(997\) 6.11770 42.5496i 0.193750 1.34756i −0.628224 0.778032i \(-0.716218\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(998\) −7.82955 + 2.29896i −0.247840 + 0.0727724i
\(999\) −1.82837 2.11005i −0.0578470 0.0667590i
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.d.301.2 20
23.12 even 11 inner 690.2.m.d.541.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.d.301.2 20 1.1 even 1 trivial
690.2.m.d.541.2 yes 20 23.12 even 11 inner