Properties

Label 98.2.g.b.39.1
Level $98$
Weight $2$
Character 98.39
Analytic conductor $0.783$
Analytic rank $0$
Dimension $24$
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] = [98,2,Mod(9,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.g (of order \(21\), degree \(12\), 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: \(0.782533939809\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 39.1
Character \(\chi\) \(=\) 98.39
Dual form 98.2.g.b.93.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.988831 - 0.149042i) q^{2} +(-0.934966 + 0.637449i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0772188 + 1.03041i) q^{5} +(1.01953 - 0.490980i) q^{6} +(1.36748 + 2.26495i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.628203 + 1.60064i) q^{9} +O(q^{10})\) \(q+(-0.988831 - 0.149042i) q^{2} +(-0.934966 + 0.637449i) q^{3} +(0.955573 + 0.294755i) q^{4} +(0.0772188 + 1.03041i) q^{5} +(1.01953 - 0.490980i) q^{6} +(1.36748 + 2.26495i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.628203 + 1.60064i) q^{9} +(0.0772188 - 1.03041i) q^{10} +(1.68646 + 4.29704i) q^{11} +(-1.08132 + 0.333543i) q^{12} +(2.85987 - 3.58616i) q^{13} +(-1.01463 - 2.44347i) q^{14} +(-0.729032 - 0.914177i) q^{15} +(0.826239 + 0.563320i) q^{16} +(-4.77961 - 4.43483i) q^{17} +(0.859749 - 1.48913i) q^{18} +(-0.366097 - 0.634099i) q^{19} +(-0.229931 + 1.00740i) q^{20} +(-2.72234 - 1.24595i) q^{21} +(-1.02719 - 4.50040i) q^{22} +(-1.65499 + 1.53561i) q^{23} +(1.11895 - 0.168655i) q^{24} +(3.88837 - 0.586077i) q^{25} +(-3.36241 + 3.11986i) q^{26} +(-1.18838 - 5.20665i) q^{27} +(0.639120 + 2.56740i) q^{28} +(1.30379 - 5.71227i) q^{29} +(0.584638 + 1.01262i) q^{30} +(-1.69503 + 2.93589i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-4.31593 - 2.94255i) q^{33} +(4.06525 + 5.09766i) q^{34} +(-2.22824 + 1.58396i) q^{35} +(-1.07209 + 1.34436i) q^{36} +(3.26378 - 1.00674i) q^{37} +(0.267501 + 0.681581i) q^{38} +(-0.387884 + 5.17596i) q^{39} +(0.377508 - 0.961874i) q^{40} +(6.33962 + 3.05300i) q^{41} +(2.50623 + 1.63778i) q^{42} +(3.51133 - 1.69097i) q^{43} +(0.344964 + 4.60323i) q^{44} +(-1.69783 - 0.523710i) q^{45} +(1.86538 - 1.27179i) q^{46} +(2.70562 + 0.407807i) q^{47} -1.13159 q^{48} +(-3.26000 + 6.19455i) q^{49} -3.93229 q^{50} +(7.29574 + 1.09966i) q^{51} +(3.78985 - 2.58388i) q^{52} +(-4.46580 - 1.37752i) q^{53} +(0.399100 + 5.32562i) q^{54} +(-4.29750 + 2.06957i) q^{55} +(-0.249331 - 2.63398i) q^{56} +(0.746494 + 0.359493i) q^{57} +(-2.14060 + 5.45415i) q^{58} +(0.433778 - 5.78836i) q^{59} +(-0.427185 - 1.08845i) q^{60} +(1.36572 - 0.421270i) q^{61} +(2.11367 - 2.65046i) q^{62} +(-4.48442 + 0.765987i) q^{63} +(0.623490 + 0.781831i) q^{64} +(3.91606 + 2.66993i) q^{65} +(3.82916 + 3.55294i) q^{66} +(4.84418 - 8.39037i) q^{67} +(-3.26007 - 5.64661i) q^{68} +(0.568489 - 2.49071i) q^{69} +(2.43943 - 1.23417i) q^{70} +(3.41285 + 14.9527i) q^{71} +(1.26048 - 1.16956i) q^{72} +(-6.08937 + 0.917826i) q^{73} +(-3.37737 + 0.509056i) q^{74} +(-3.26189 + 3.02660i) q^{75} +(-0.162929 - 0.713837i) q^{76} +(-7.42638 + 9.69587i) q^{77} +(1.15499 - 5.06033i) q^{78} +(-7.53693 - 13.0544i) q^{79} +(-0.516651 + 0.894866i) q^{80} +(0.648625 + 0.601836i) q^{81} +(-5.81379 - 3.96377i) q^{82} +(-3.09838 - 3.88525i) q^{83} +(-2.23414 - 1.99302i) q^{84} +(4.20063 - 5.26742i) q^{85} +(-3.72414 + 1.14874i) q^{86} +(2.42228 + 6.17188i) q^{87} +(0.344964 - 4.60323i) q^{88} +(6.46588 - 16.4748i) q^{89} +(1.60081 + 0.770908i) q^{90} +(12.0333 + 1.57346i) q^{91} +(-2.03409 + 0.979568i) q^{92} +(-0.286678 - 3.82545i) q^{93} +(-2.61462 - 0.806504i) q^{94} +(0.625114 - 0.426196i) q^{95} +(1.11895 + 0.168655i) q^{96} -16.8307 q^{97} +(4.14684 - 5.63948i) q^{98} -7.93744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{17}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.988831 0.149042i −0.699209 0.105389i
\(3\) −0.934966 + 0.637449i −0.539803 + 0.368031i −0.802318 0.596897i \(-0.796400\pi\)
0.262516 + 0.964928i \(0.415448\pi\)
\(4\) 0.955573 + 0.294755i 0.477786 + 0.147378i
\(5\) 0.0772188 + 1.03041i 0.0345333 + 0.460815i 0.987487 + 0.157699i \(0.0504077\pi\)
−0.952954 + 0.303115i \(0.901973\pi\)
\(6\) 1.01953 0.490980i 0.416221 0.200442i
\(7\) 1.36748 + 2.26495i 0.516859 + 0.856071i
\(8\) −0.900969 0.433884i −0.318541 0.153401i
\(9\) −0.628203 + 1.60064i −0.209401 + 0.533545i
\(10\) 0.0772188 1.03041i 0.0244187 0.325845i
\(11\) 1.68646 + 4.29704i 0.508488 + 1.29561i 0.922733 + 0.385441i \(0.125951\pi\)
−0.414245 + 0.910166i \(0.635954\pi\)
\(12\) −1.08132 + 0.333543i −0.312150 + 0.0962855i
\(13\) 2.85987 3.58616i 0.793185 0.994622i −0.206684 0.978408i \(-0.566267\pi\)
0.999869 0.0162142i \(-0.00516137\pi\)
\(14\) −1.01463 2.44347i −0.271172 0.653044i
\(15\) −0.729032 0.914177i −0.188235 0.236040i
\(16\) 0.826239 + 0.563320i 0.206560 + 0.140830i
\(17\) −4.77961 4.43483i −1.15922 1.07560i −0.996031 0.0890094i \(-0.971630\pi\)
−0.163194 0.986594i \(-0.552180\pi\)
\(18\) 0.859749 1.48913i 0.202645 0.350991i
\(19\) −0.366097 0.634099i −0.0839885 0.145472i 0.820971 0.570970i \(-0.193433\pi\)
−0.904960 + 0.425497i \(0.860099\pi\)
\(20\) −0.229931 + 1.00740i −0.0514142 + 0.225260i
\(21\) −2.72234 1.24595i −0.594062 0.271889i
\(22\) −1.02719 4.50040i −0.218997 0.959488i
\(23\) −1.65499 + 1.53561i −0.345090 + 0.320196i −0.833607 0.552358i \(-0.813728\pi\)
0.488518 + 0.872554i \(0.337538\pi\)
\(24\) 1.11895 0.168655i 0.228405 0.0344266i
\(25\) 3.88837 0.586077i 0.777673 0.117215i
\(26\) −3.36241 + 3.11986i −0.659424 + 0.611856i
\(27\) −1.18838 5.20665i −0.228705 1.00202i
\(28\) 0.639120 + 2.56740i 0.120782 + 0.485192i
\(29\) 1.30379 5.71227i 0.242108 1.06074i −0.696987 0.717084i \(-0.745477\pi\)
0.939095 0.343659i \(-0.111666\pi\)
\(30\) 0.584638 + 1.01262i 0.106740 + 0.184879i
\(31\) −1.69503 + 2.93589i −0.304437 + 0.527301i −0.977136 0.212616i \(-0.931802\pi\)
0.672699 + 0.739917i \(0.265135\pi\)
\(32\) −0.733052 0.680173i −0.129586 0.120239i
\(33\) −4.31593 2.94255i −0.751307 0.512232i
\(34\) 4.06525 + 5.09766i 0.697184 + 0.874241i
\(35\) −2.22824 + 1.58396i −0.376641 + 0.267739i
\(36\) −1.07209 + 1.34436i −0.178682 + 0.224060i
\(37\) 3.26378 1.00674i 0.536561 0.165507i −0.0146193 0.999893i \(-0.504654\pi\)
0.551181 + 0.834386i \(0.314177\pi\)
\(38\) 0.267501 + 0.681581i 0.0433944 + 0.110567i
\(39\) −0.387884 + 5.17596i −0.0621112 + 0.828816i
\(40\) 0.377508 0.961874i 0.0596892 0.152086i
\(41\) 6.33962 + 3.05300i 0.990083 + 0.476799i 0.857561 0.514381i \(-0.171978\pi\)
0.132521 + 0.991180i \(0.457693\pi\)
\(42\) 2.50623 + 1.63778i 0.386720 + 0.252715i
\(43\) 3.51133 1.69097i 0.535473 0.257870i −0.146547 0.989204i \(-0.546816\pi\)
0.682020 + 0.731334i \(0.261102\pi\)
\(44\) 0.344964 + 4.60323i 0.0520053 + 0.693963i
\(45\) −1.69783 0.523710i −0.253097 0.0780700i
\(46\) 1.86538 1.27179i 0.275035 0.187516i
\(47\) 2.70562 + 0.407807i 0.394655 + 0.0594847i 0.343372 0.939199i \(-0.388431\pi\)
0.0512832 + 0.998684i \(0.483669\pi\)
\(48\) −1.13159 −0.163331
\(49\) −3.26000 + 6.19455i −0.465714 + 0.884935i
\(50\) −3.93229 −0.556109
\(51\) 7.29574 + 1.09966i 1.02161 + 0.153983i
\(52\) 3.78985 2.58388i 0.525558 0.358319i
\(53\) −4.46580 1.37752i −0.613424 0.189216i −0.0275529 0.999620i \(-0.508771\pi\)
−0.585871 + 0.810404i \(0.699248\pi\)
\(54\) 0.399100 + 5.32562i 0.0543106 + 0.724724i
\(55\) −4.29750 + 2.06957i −0.579475 + 0.279060i
\(56\) −0.249331 2.63398i −0.0333183 0.351980i
\(57\) 0.746494 + 0.359493i 0.0988756 + 0.0476160i
\(58\) −2.14060 + 5.45415i −0.281074 + 0.716165i
\(59\) 0.433778 5.78836i 0.0564731 0.753581i −0.895043 0.445981i \(-0.852855\pi\)
0.951516 0.307600i \(-0.0995259\pi\)
\(60\) −0.427185 1.08845i −0.0551493 0.140518i
\(61\) 1.36572 0.421270i 0.174863 0.0539381i −0.206087 0.978534i \(-0.566073\pi\)
0.380950 + 0.924595i \(0.375597\pi\)
\(62\) 2.11367 2.65046i 0.268437 0.336609i
\(63\) −4.48442 + 0.765987i −0.564983 + 0.0965053i
\(64\) 0.623490 + 0.781831i 0.0779362 + 0.0977289i
\(65\) 3.91606 + 2.66993i 0.485728 + 0.331163i
\(66\) 3.82916 + 3.55294i 0.471337 + 0.437337i
\(67\) 4.84418 8.39037i 0.591811 1.02505i −0.402177 0.915562i \(-0.631746\pi\)
0.993988 0.109485i \(-0.0349202\pi\)
\(68\) −3.26007 5.64661i −0.395342 0.684752i
\(69\) 0.568489 2.49071i 0.0684380 0.299847i
\(70\) 2.43943 1.23417i 0.291568 0.147512i
\(71\) 3.41285 + 14.9527i 0.405031 + 1.77456i 0.606521 + 0.795067i \(0.292564\pi\)
−0.201490 + 0.979491i \(0.564578\pi\)
\(72\) 1.26048 1.16956i 0.148549 0.137834i
\(73\) −6.08937 + 0.917826i −0.712707 + 0.107423i −0.495381 0.868676i \(-0.664972\pi\)
−0.217326 + 0.976099i \(0.569734\pi\)
\(74\) −3.37737 + 0.509056i −0.392611 + 0.0591766i
\(75\) −3.26189 + 3.02660i −0.376651 + 0.349481i
\(76\) −0.162929 0.713837i −0.0186892 0.0818827i
\(77\) −7.42638 + 9.69587i −0.846314 + 1.10495i
\(78\) 1.15499 5.06033i 0.130777 0.572970i
\(79\) −7.53693 13.0544i −0.847971 1.46873i −0.883016 0.469344i \(-0.844491\pi\)
0.0350442 0.999386i \(-0.488843\pi\)
\(80\) −0.516651 + 0.894866i −0.0577633 + 0.100049i
\(81\) 0.648625 + 0.601836i 0.0720695 + 0.0668707i
\(82\) −5.81379 3.96377i −0.642025 0.437726i
\(83\) −3.09838 3.88525i −0.340092 0.426462i 0.582146 0.813084i \(-0.302213\pi\)
−0.922238 + 0.386622i \(0.873642\pi\)
\(84\) −2.23414 1.99302i −0.243765 0.217456i
\(85\) 4.20063 5.26742i 0.455622 0.571332i
\(86\) −3.72414 + 1.14874i −0.401584 + 0.123872i
\(87\) 2.42228 + 6.17188i 0.259696 + 0.661695i
\(88\) 0.344964 4.60323i 0.0367733 0.490706i
\(89\) 6.46588 16.4748i 0.685381 1.74632i 0.0200229 0.999800i \(-0.493626\pi\)
0.665359 0.746524i \(-0.268279\pi\)
\(90\) 1.60081 + 0.770908i 0.168740 + 0.0812608i
\(91\) 12.0333 + 1.57346i 1.26143 + 0.164943i
\(92\) −2.03409 + 0.979568i −0.212069 + 0.102127i
\(93\) −0.286678 3.82545i −0.0297271 0.396681i
\(94\) −2.61462 0.806504i −0.269678 0.0831845i
\(95\) 0.625114 0.426196i 0.0641354 0.0437268i
\(96\) 1.11895 + 0.168655i 0.114203 + 0.0172133i
\(97\) −16.8307 −1.70890 −0.854451 0.519532i \(-0.826106\pi\)
−0.854451 + 0.519532i \(0.826106\pi\)
\(98\) 4.14684 5.63948i 0.418894 0.569673i
\(99\) −7.93744 −0.797743
\(100\) 3.88837 + 0.586077i 0.388837 + 0.0586077i
\(101\) 7.94630 5.41770i 0.790686 0.539081i −0.0993056 0.995057i \(-0.531662\pi\)
0.889992 + 0.455976i \(0.150710\pi\)
\(102\) −7.05036 2.17475i −0.698090 0.215332i
\(103\) 0.638239 + 8.51671i 0.0628876 + 0.839177i 0.936077 + 0.351795i \(0.114429\pi\)
−0.873189 + 0.487381i \(0.837952\pi\)
\(104\) −4.13263 + 1.99017i −0.405238 + 0.195152i
\(105\) 1.07363 2.90134i 0.104776 0.283142i
\(106\) 4.21061 + 2.02772i 0.408971 + 0.196950i
\(107\) 2.70322 6.88769i 0.261330 0.665858i −0.738636 0.674105i \(-0.764530\pi\)
0.999966 + 0.00824627i \(0.00262490\pi\)
\(108\) 0.399100 5.32562i 0.0384034 0.512458i
\(109\) 6.42308 + 16.3657i 0.615219 + 1.56755i 0.809825 + 0.586671i \(0.199562\pi\)
−0.194606 + 0.980881i \(0.562343\pi\)
\(110\) 4.55795 1.40594i 0.434584 0.134051i
\(111\) −2.40977 + 3.02176i −0.228725 + 0.286813i
\(112\) −0.146028 + 2.64172i −0.0137983 + 0.249619i
\(113\) 4.50521 + 5.64936i 0.423815 + 0.531447i 0.947197 0.320651i \(-0.103902\pi\)
−0.523383 + 0.852098i \(0.675330\pi\)
\(114\) −0.684577 0.466737i −0.0641165 0.0437139i
\(115\) −1.71011 1.58675i −0.159468 0.147965i
\(116\) 2.92959 5.07419i 0.272005 0.471127i
\(117\) 3.94356 + 6.83045i 0.364582 + 0.631475i
\(118\) −1.29164 + 5.65906i −0.118905 + 0.520959i
\(119\) 3.50865 16.8901i 0.321637 1.54831i
\(120\) 0.260189 + 1.13996i 0.0237519 + 0.104064i
\(121\) −7.55682 + 7.01170i −0.686984 + 0.637428i
\(122\) −1.41326 + 0.213014i −0.127950 + 0.0192854i
\(123\) −7.87346 + 1.18673i −0.709926 + 0.107004i
\(124\) −2.48510 + 2.30583i −0.223168 + 0.207070i
\(125\) 2.05381 + 8.99834i 0.183699 + 0.804836i
\(126\) 4.54849 0.0890640i 0.405212 0.00793445i
\(127\) −2.49193 + 10.9178i −0.221123 + 0.968803i 0.735512 + 0.677512i \(0.236942\pi\)
−0.956635 + 0.291291i \(0.905915\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.20507 + 3.81929i −0.194145 + 0.336270i
\(130\) −3.47439 3.22376i −0.304724 0.282743i
\(131\) 8.33818 + 5.68488i 0.728510 + 0.496690i 0.869878 0.493267i \(-0.164198\pi\)
−0.141367 + 0.989957i \(0.545150\pi\)
\(132\) −3.25685 4.08396i −0.283473 0.355463i
\(133\) 0.935573 1.69631i 0.0811245 0.147089i
\(134\) −6.04060 + 7.57467i −0.521828 + 0.654352i
\(135\) 5.27323 1.62658i 0.453848 0.139993i
\(136\) 2.38208 + 6.06943i 0.204261 + 0.520450i
\(137\) −0.138542 + 1.84872i −0.0118365 + 0.157947i 0.988154 + 0.153469i \(0.0490444\pi\)
−0.999990 + 0.00447796i \(0.998575\pi\)
\(138\) −0.933361 + 2.37817i −0.0794530 + 0.202443i
\(139\) −4.54586 2.18917i −0.385575 0.185683i 0.231047 0.972943i \(-0.425785\pi\)
−0.616622 + 0.787259i \(0.711499\pi\)
\(140\) −2.59613 + 0.856809i −0.219413 + 0.0724136i
\(141\) −2.78962 + 1.34341i −0.234928 + 0.113135i
\(142\) −1.14615 15.2943i −0.0961830 1.28347i
\(143\) 20.2329 + 6.24103i 1.69196 + 0.521902i
\(144\) −1.42072 + 0.968628i −0.118393 + 0.0807190i
\(145\) 5.98668 + 0.902346i 0.497166 + 0.0749358i
\(146\) 6.15816 0.509653
\(147\) −0.900716 7.86977i −0.0742898 0.649088i
\(148\) 3.41552 0.280754
\(149\) −4.62471 0.697063i −0.378871 0.0571056i −0.0431538 0.999068i \(-0.513741\pi\)
−0.335717 + 0.941963i \(0.608979\pi\)
\(150\) 3.67655 2.50663i 0.300189 0.204666i
\(151\) −19.2281 5.93107i −1.56476 0.482664i −0.613147 0.789969i \(-0.710096\pi\)
−0.951611 + 0.307305i \(0.900573\pi\)
\(152\) 0.0547170 + 0.730147i 0.00443813 + 0.0592228i
\(153\) 10.1011 4.86444i 0.816626 0.393266i
\(154\) 8.78853 8.48073i 0.708200 0.683397i
\(155\) −3.15606 1.51988i −0.253501 0.122080i
\(156\) −1.89629 + 4.83167i −0.151825 + 0.386843i
\(157\) −0.417045 + 5.56507i −0.0332838 + 0.444141i 0.955521 + 0.294924i \(0.0952944\pi\)
−0.988804 + 0.149217i \(0.952325\pi\)
\(158\) 5.50710 + 14.0319i 0.438122 + 1.11632i
\(159\) 5.05346 1.55879i 0.400766 0.123620i
\(160\) 0.644253 0.807868i 0.0509327 0.0638676i
\(161\) −5.74124 1.64856i −0.452473 0.129925i
\(162\) −0.551682 0.691787i −0.0433442 0.0543519i
\(163\) −14.1335 9.63603i −1.10702 0.754752i −0.135279 0.990808i \(-0.543193\pi\)
−0.971740 + 0.236055i \(0.924145\pi\)
\(164\) 5.15808 + 4.78600i 0.402779 + 0.373724i
\(165\) 2.69877 4.67441i 0.210099 0.363902i
\(166\) 2.48471 + 4.30365i 0.192851 + 0.334028i
\(167\) −1.84525 + 8.08458i −0.142790 + 0.625604i 0.851990 + 0.523559i \(0.175396\pi\)
−0.994780 + 0.102045i \(0.967461\pi\)
\(168\) 1.91214 + 2.30374i 0.147525 + 0.177738i
\(169\) −1.78893 7.83783i −0.137610 0.602910i
\(170\) −4.93878 + 4.58252i −0.378787 + 0.351463i
\(171\) 1.24495 0.187645i 0.0952034 0.0143496i
\(172\) 3.85375 0.580860i 0.293846 0.0442901i
\(173\) −9.84632 + 9.13605i −0.748602 + 0.694601i −0.959123 0.282988i \(-0.908674\pi\)
0.210522 + 0.977589i \(0.432484\pi\)
\(174\) −1.47536 6.46396i −0.111847 0.490032i
\(175\) 6.64470 + 8.00551i 0.502292 + 0.605160i
\(176\) −1.02719 + 4.50040i −0.0774271 + 0.339230i
\(177\) 3.28422 + 5.68843i 0.246857 + 0.427569i
\(178\) −8.84910 + 15.3271i −0.663268 + 1.14881i
\(179\) −8.43368 7.82531i −0.630363 0.584891i 0.298912 0.954281i \(-0.403376\pi\)
−0.929275 + 0.369389i \(0.879567\pi\)
\(180\) −1.46803 1.00089i −0.109420 0.0746016i
\(181\) 4.07010 + 5.10374i 0.302528 + 0.379358i 0.909738 0.415184i \(-0.136283\pi\)
−0.607210 + 0.794542i \(0.707711\pi\)
\(182\) −11.6644 3.34935i −0.864621 0.248271i
\(183\) −1.00837 + 1.26445i −0.0745407 + 0.0934710i
\(184\) 2.15737 0.665461i 0.159044 0.0490584i
\(185\) 1.28938 + 3.28530i 0.0947974 + 0.241540i
\(186\) −0.286678 + 3.82545i −0.0210202 + 0.280496i
\(187\) 10.9960 28.0173i 0.804107 2.04883i
\(188\) 2.46521 + 1.18718i 0.179794 + 0.0865843i
\(189\) 10.1677 9.81162i 0.739592 0.713690i
\(190\) −0.681654 + 0.328267i −0.0494524 + 0.0238150i
\(191\) −0.462309 6.16908i −0.0334515 0.446379i −0.988632 0.150355i \(-0.951958\pi\)
0.955181 0.296024i \(-0.0956608\pi\)
\(192\) −1.08132 0.333543i −0.0780375 0.0240714i
\(193\) 13.7296 9.36066i 0.988276 0.673795i 0.0426630 0.999090i \(-0.486416\pi\)
0.945613 + 0.325295i \(0.105463\pi\)
\(194\) 16.6428 + 2.50849i 1.19488 + 0.180099i
\(195\) −5.36332 −0.384076
\(196\) −4.94104 + 4.95844i −0.352932 + 0.354174i
\(197\) 7.74907 0.552098 0.276049 0.961144i \(-0.410975\pi\)
0.276049 + 0.961144i \(0.410975\pi\)
\(198\) 7.84878 + 1.18301i 0.557789 + 0.0840731i
\(199\) −17.7783 + 12.1210i −1.26027 + 0.859237i −0.994494 0.104798i \(-0.966580\pi\)
−0.265776 + 0.964035i \(0.585628\pi\)
\(200\) −3.75759 1.15906i −0.265701 0.0819580i
\(201\) 0.819287 + 10.9326i 0.0577881 + 0.771128i
\(202\) −8.66501 + 4.17285i −0.609668 + 0.293601i
\(203\) 14.7209 4.85840i 1.03321 0.340993i
\(204\) 6.64748 + 3.20126i 0.465417 + 0.224133i
\(205\) −2.65631 + 6.76818i −0.185525 + 0.472710i
\(206\) 0.638239 8.51671i 0.0444682 0.593388i
\(207\) −1.41828 3.61371i −0.0985772 0.251171i
\(208\) 4.38309 1.35200i 0.303913 0.0937446i
\(209\) 2.10734 2.64252i 0.145768 0.182787i
\(210\) −1.49406 + 2.70892i −0.103100 + 0.186933i
\(211\) −12.0767 15.1436i −0.831391 1.04253i −0.998398 0.0565758i \(-0.981982\pi\)
0.167007 0.985956i \(-0.446590\pi\)
\(212\) −3.86136 2.63263i −0.265200 0.180810i
\(213\) −12.7225 11.8047i −0.871729 0.808847i
\(214\) −3.69958 + 6.40787i −0.252898 + 0.438033i
\(215\) 2.01353 + 3.48754i 0.137322 + 0.237849i
\(216\) −1.18838 + 5.20665i −0.0808593 + 0.354268i
\(217\) −8.96756 + 0.175594i −0.608758 + 0.0119201i
\(218\) −3.91215 17.1402i −0.264964 1.16088i
\(219\) 5.10829 4.73980i 0.345186 0.320286i
\(220\) −4.71659 + 0.710911i −0.317992 + 0.0479296i
\(221\) −29.5730 + 4.45742i −1.98930 + 0.299838i
\(222\) 2.83323 2.62885i 0.190154 0.176437i
\(223\) −1.10486 4.84070i −0.0739868 0.324157i 0.924368 0.381503i \(-0.124593\pi\)
−0.998354 + 0.0573457i \(0.981736\pi\)
\(224\) 0.538124 2.59045i 0.0359549 0.173082i
\(225\) −1.50459 + 6.59203i −0.100306 + 0.439469i
\(226\) −3.61290 6.25773i −0.240327 0.416258i
\(227\) 6.38505 11.0592i 0.423790 0.734026i −0.572516 0.819893i \(-0.694033\pi\)
0.996307 + 0.0858670i \(0.0273660\pi\)
\(228\) 0.607367 + 0.563554i 0.0402239 + 0.0373223i
\(229\) −20.7480 14.1457i −1.37106 0.934775i −0.999981 0.00617554i \(-0.998034\pi\)
−0.371083 0.928600i \(-0.621013\pi\)
\(230\) 1.45451 + 1.82390i 0.0959078 + 0.120265i
\(231\) 0.762788 13.7992i 0.0501878 0.907923i
\(232\) −3.65314 + 4.58089i −0.239840 + 0.300750i
\(233\) −0.579607 + 0.178785i −0.0379713 + 0.0117126i −0.313683 0.949528i \(-0.601563\pi\)
0.275711 + 0.961240i \(0.411087\pi\)
\(234\) −2.88149 7.34191i −0.188369 0.479956i
\(235\) −0.211285 + 2.81940i −0.0137827 + 0.183917i
\(236\) 2.12066 5.40335i 0.138043 0.351728i
\(237\) 15.3683 + 7.40096i 0.998275 + 0.480744i
\(238\) −5.98680 + 16.1785i −0.388067 + 1.04870i
\(239\) −0.219746 + 0.105824i −0.0142142 + 0.00684520i −0.440977 0.897518i \(-0.645368\pi\)
0.426763 + 0.904363i \(0.359654\pi\)
\(240\) −0.0873802 1.16601i −0.00564037 0.0752655i
\(241\) 25.5110 + 7.86909i 1.64331 + 0.506893i 0.972137 0.234412i \(-0.0753165\pi\)
0.671168 + 0.741305i \(0.265793\pi\)
\(242\) 8.51746 5.80710i 0.547523 0.373295i
\(243\) 14.8526 + 2.23867i 0.952796 + 0.143611i
\(244\) 1.42922 0.0914965
\(245\) −6.63467 2.88081i −0.423874 0.184048i
\(246\) 7.96239 0.507664
\(247\) −3.32097 0.500556i −0.211308 0.0318496i
\(248\) 2.80101 1.90969i 0.177864 0.121266i
\(249\) 5.37353 + 1.65751i 0.340534 + 0.105041i
\(250\) −0.689740 9.20394i −0.0436230 0.582108i
\(251\) 2.57608 1.24058i 0.162601 0.0783045i −0.350813 0.936445i \(-0.614095\pi\)
0.513414 + 0.858141i \(0.328380\pi\)
\(252\) −4.51097 0.589849i −0.284164 0.0371570i
\(253\) −9.38965 4.52182i −0.590323 0.284284i
\(254\) 4.09132 10.4245i 0.256712 0.654092i
\(255\) −0.569732 + 7.60254i −0.0356780 + 0.476090i
\(256\) 0.365341 + 0.930874i 0.0228338 + 0.0581796i
\(257\) −23.4780 + 7.24201i −1.46452 + 0.451744i −0.921633 0.388063i \(-0.873144\pi\)
−0.542886 + 0.839807i \(0.682668\pi\)
\(258\) 2.74967 3.44798i 0.171187 0.214662i
\(259\) 6.74337 + 6.01559i 0.419012 + 0.373791i
\(260\) 2.95511 + 3.70559i 0.183268 + 0.229811i
\(261\) 8.32423 + 5.67536i 0.515257 + 0.351296i
\(262\) −7.39777 6.86412i −0.457036 0.424067i
\(263\) 5.04046 8.73033i 0.310808 0.538335i −0.667729 0.744404i \(-0.732734\pi\)
0.978538 + 0.206069i \(0.0660670\pi\)
\(264\) 2.61179 + 4.52376i 0.160745 + 0.278418i
\(265\) 1.07457 4.70798i 0.0660101 0.289209i
\(266\) −1.17795 + 1.53792i −0.0722245 + 0.0942962i
\(267\) 4.45646 + 19.5250i 0.272731 + 1.19491i
\(268\) 7.10207 6.58976i 0.433828 0.402534i
\(269\) −22.6846 + 3.41915i −1.38310 + 0.208469i −0.798082 0.602549i \(-0.794152\pi\)
−0.585021 + 0.811018i \(0.698914\pi\)
\(270\) −5.45676 + 0.822475i −0.332088 + 0.0500542i
\(271\) −4.97344 + 4.61468i −0.302115 + 0.280322i −0.816632 0.577158i \(-0.804162\pi\)
0.514517 + 0.857480i \(0.327971\pi\)
\(272\) −1.45087 6.35667i −0.0879719 0.385430i
\(273\) −12.2537 + 6.19947i −0.741628 + 0.375209i
\(274\) 0.412532 1.80742i 0.0249220 0.109190i
\(275\) 9.07598 + 15.7201i 0.547302 + 0.947956i
\(276\) 1.27738 2.21249i 0.0768894 0.133176i
\(277\) 15.4688 + 14.3530i 0.929432 + 0.862387i 0.990746 0.135731i \(-0.0433384\pi\)
−0.0613133 + 0.998119i \(0.519529\pi\)
\(278\) 4.16881 + 2.84225i 0.250029 + 0.170467i
\(279\) −3.63446 4.55747i −0.217589 0.272848i
\(280\) 2.69483 0.460306i 0.161047 0.0275086i
\(281\) 8.49063 10.6469i 0.506508 0.635142i −0.461175 0.887309i \(-0.652572\pi\)
0.967684 + 0.252168i \(0.0811434\pi\)
\(282\) 2.95869 0.912634i 0.176187 0.0543465i
\(283\) 7.84738 + 19.9948i 0.466478 + 1.18857i 0.949726 + 0.313084i \(0.101362\pi\)
−0.483247 + 0.875484i \(0.660543\pi\)
\(284\) −1.14615 + 15.2943i −0.0680116 + 0.907552i
\(285\) −0.312783 + 0.796957i −0.0185276 + 0.0472076i
\(286\) −19.0768 9.18689i −1.12803 0.543232i
\(287\) 1.75441 + 18.5338i 0.103559 + 1.09402i
\(288\) 1.54921 0.746062i 0.0912884 0.0439622i
\(289\) 1.90654 + 25.4410i 0.112149 + 1.49653i
\(290\) −5.78532 1.78454i −0.339726 0.104792i
\(291\) 15.7362 10.7287i 0.922470 0.628929i
\(292\) −6.08937 0.917826i −0.356354 0.0537117i
\(293\) 12.0113 0.701710 0.350855 0.936430i \(-0.385891\pi\)
0.350855 + 0.936430i \(0.385891\pi\)
\(294\) −0.282273 + 7.91612i −0.0164625 + 0.461677i
\(295\) 5.99790 0.349211
\(296\) −3.37737 0.509056i −0.196306 0.0295883i
\(297\) 20.3690 13.8874i 1.18193 0.805826i
\(298\) 4.46916 + 1.37855i 0.258892 + 0.0798575i
\(299\) 0.773879 + 10.3267i 0.0447546 + 0.597209i
\(300\) −4.00908 + 1.93067i −0.231464 + 0.111467i
\(301\) 8.63162 + 5.64062i 0.497519 + 0.325120i
\(302\) 18.1293 + 8.73062i 1.04323 + 0.502391i
\(303\) −3.97601 + 10.1307i −0.228416 + 0.581995i
\(304\) 0.0547170 0.730147i 0.00313823 0.0418768i
\(305\) 0.539542 + 1.37473i 0.0308941 + 0.0787168i
\(306\) −10.7133 + 3.30461i −0.612438 + 0.188912i
\(307\) −16.9253 + 21.2236i −0.965975 + 1.21129i 0.0114328 + 0.999935i \(0.496361\pi\)
−0.977408 + 0.211360i \(0.932211\pi\)
\(308\) −9.95435 + 7.07615i −0.567202 + 0.403201i
\(309\) −6.02570 7.55599i −0.342790 0.429845i
\(310\) 2.89429 + 1.97329i 0.164384 + 0.112075i
\(311\) −7.88704 7.31811i −0.447233 0.414972i 0.424137 0.905598i \(-0.360578\pi\)
−0.871370 + 0.490626i \(0.836768\pi\)
\(312\) 2.59523 4.49508i 0.146926 0.254484i
\(313\) −2.30193 3.98706i −0.130113 0.225362i 0.793607 0.608431i \(-0.208201\pi\)
−0.923720 + 0.383069i \(0.874867\pi\)
\(314\) 1.24182 5.44076i 0.0700798 0.307040i
\(315\) −1.13556 4.56165i −0.0639818 0.257020i
\(316\) −3.35425 14.6959i −0.188691 0.826711i
\(317\) 1.42092 1.31842i 0.0798070 0.0740501i −0.639261 0.768990i \(-0.720760\pi\)
0.719068 + 0.694940i \(0.244569\pi\)
\(318\) −5.22934 + 0.788197i −0.293247 + 0.0441999i
\(319\) 26.7447 4.03111i 1.49741 0.225699i
\(320\) −0.757464 + 0.702824i −0.0423435 + 0.0392891i
\(321\) 1.86313 + 8.16292i 0.103990 + 0.455610i
\(322\) 5.43141 + 2.48584i 0.302681 + 0.138530i
\(323\) −1.06232 + 4.65432i −0.0591090 + 0.258973i
\(324\) 0.442414 + 0.766284i 0.0245786 + 0.0425713i
\(325\) 9.01845 15.6204i 0.500253 0.866464i
\(326\) 12.5394 + 11.6349i 0.694495 + 0.644397i
\(327\) −16.4377 11.2070i −0.909005 0.619749i
\(328\) −4.38715 5.50132i −0.242240 0.303759i
\(329\) 2.77622 + 6.68576i 0.153058 + 0.368598i
\(330\) −3.36531 + 4.21997i −0.185254 + 0.232302i
\(331\) −8.17936 + 2.52300i −0.449578 + 0.138676i −0.511273 0.859419i \(-0.670826\pi\)
0.0616945 + 0.998095i \(0.480350\pi\)
\(332\) −1.81553 4.62590i −0.0996404 0.253880i
\(333\) −0.438888 + 5.85656i −0.0240509 + 0.320937i
\(334\) 3.02959 7.71927i 0.165772 0.422379i
\(335\) 9.01961 + 4.34361i 0.492794 + 0.237317i
\(336\) −1.54743 2.56300i −0.0844192 0.139823i
\(337\) 13.6463 6.57170i 0.743360 0.357983i −0.0235629 0.999722i \(-0.507501\pi\)
0.766923 + 0.641739i \(0.221787\pi\)
\(338\) 0.600784 + 8.01691i 0.0326784 + 0.436062i
\(339\) −7.81340 2.41011i −0.424365 0.130899i
\(340\) 5.56660 3.79525i 0.301891 0.205826i
\(341\) −15.4742 2.33237i −0.837977 0.126305i
\(342\) −1.25901 −0.0680794
\(343\) −18.4883 + 1.08717i −0.998276 + 0.0587017i
\(344\) −3.89728 −0.210127
\(345\) 2.61036 + 0.393449i 0.140537 + 0.0211826i
\(346\) 11.0980 7.56649i 0.596632 0.406777i
\(347\) −27.7231 8.55145i −1.48825 0.459066i −0.559207 0.829028i \(-0.688894\pi\)
−0.929047 + 0.369962i \(0.879371\pi\)
\(348\) 0.495475 + 6.61166i 0.0265603 + 0.354422i
\(349\) 21.1722 10.1960i 1.13332 0.545779i 0.229339 0.973347i \(-0.426344\pi\)
0.903983 + 0.427567i \(0.140629\pi\)
\(350\) −5.37732 8.90643i −0.287430 0.476069i
\(351\) −22.0705 10.6286i −1.17804 0.567312i
\(352\) 1.68646 4.29704i 0.0898888 0.229033i
\(353\) 2.21704 29.5844i 0.118001 1.57462i −0.553013 0.833173i \(-0.686522\pi\)
0.671014 0.741445i \(-0.265859\pi\)
\(354\) −2.39972 6.11438i −0.127544 0.324976i
\(355\) −15.1439 + 4.67128i −0.803755 + 0.247926i
\(356\) 11.0346 13.8370i 0.584835 0.733360i
\(357\) 7.48611 + 18.0282i 0.396207 + 0.954156i
\(358\) 7.17318 + 8.99488i 0.379114 + 0.475394i
\(359\) 13.4898 + 9.19717i 0.711963 + 0.485408i 0.864336 0.502915i \(-0.167739\pi\)
−0.152373 + 0.988323i \(0.548692\pi\)
\(360\) 1.30246 + 1.20850i 0.0686456 + 0.0636938i
\(361\) 9.23195 15.9902i 0.485892 0.841589i
\(362\) −3.26396 5.65335i −0.171550 0.297134i
\(363\) 2.59576 11.3728i 0.136242 0.596916i
\(364\) 11.0349 + 5.05043i 0.578386 + 0.264714i
\(365\) −1.41595 6.20370i −0.0741144 0.324716i
\(366\) 1.18556 1.10004i 0.0619703 0.0575000i
\(367\) 2.60485 0.392619i 0.135972 0.0204945i −0.0807034 0.996738i \(-0.525717\pi\)
0.216676 + 0.976244i \(0.430479\pi\)
\(368\) −2.23246 + 0.336489i −0.116375 + 0.0175407i
\(369\) −8.86932 + 8.22952i −0.461718 + 0.428412i
\(370\) −0.785335 3.44078i −0.0408276 0.178877i
\(371\) −2.98688 11.9985i −0.155071 0.622933i
\(372\) 0.853629 3.74000i 0.0442586 0.193910i
\(373\) −3.13197 5.42473i −0.162167 0.280882i 0.773479 0.633822i \(-0.218515\pi\)
−0.935646 + 0.352941i \(0.885182\pi\)
\(374\) −15.0489 + 26.0655i −0.778162 + 1.34782i
\(375\) −7.65623 7.10394i −0.395366 0.366846i
\(376\) −2.26074 1.54135i −0.116589 0.0794889i
\(377\) −16.7565 21.0119i −0.863002 1.08217i
\(378\) −11.5165 + 8.18661i −0.592345 + 0.421074i
\(379\) 10.4673 13.1256i 0.537669 0.674215i −0.436587 0.899662i \(-0.643813\pi\)
0.974255 + 0.225447i \(0.0723842\pi\)
\(380\) 0.722966 0.223005i 0.0370874 0.0114399i
\(381\) −4.62970 11.7963i −0.237187 0.604342i
\(382\) −0.462309 + 6.16908i −0.0236538 + 0.315638i
\(383\) −11.7483 + 29.9341i −0.600308 + 1.52956i 0.230541 + 0.973063i \(0.425950\pi\)
−0.830849 + 0.556498i \(0.812145\pi\)
\(384\) 1.01953 + 0.490980i 0.0520276 + 0.0250552i
\(385\) −10.5642 6.90353i −0.538402 0.351837i
\(386\) −14.9714 + 7.20982i −0.762022 + 0.366970i
\(387\) 0.500794 + 6.68263i 0.0254568 + 0.339697i
\(388\) −16.0830 4.96095i −0.816490 0.251854i
\(389\) 1.80846 1.23299i 0.0916928 0.0625151i −0.516606 0.856223i \(-0.672805\pi\)
0.608299 + 0.793708i \(0.291852\pi\)
\(390\) 5.30342 + 0.799362i 0.268549 + 0.0404773i
\(391\) 14.7204 0.744441
\(392\) 5.62487 4.16663i 0.284099 0.210447i
\(393\) −11.4197 −0.576049
\(394\) −7.66252 1.15494i −0.386032 0.0581850i
\(395\) 12.8694 8.77419i 0.647529 0.441478i
\(396\) −7.58480 2.33960i −0.381151 0.117569i
\(397\) −0.449806 6.00225i −0.0225751 0.301244i −0.997050 0.0767493i \(-0.975546\pi\)
0.974475 0.224495i \(-0.0720732\pi\)
\(398\) 19.3863 9.33593i 0.971745 0.467968i
\(399\) 0.206582 + 2.18237i 0.0103420 + 0.109255i
\(400\) 3.54287 + 1.70616i 0.177143 + 0.0853078i
\(401\) 0.299577 0.763309i 0.0149601 0.0381178i −0.923199 0.384323i \(-0.874435\pi\)
0.938159 + 0.346206i \(0.112530\pi\)
\(402\) 0.819287 10.9326i 0.0408623 0.545270i
\(403\) 5.68098 + 14.4749i 0.282990 + 0.721047i
\(404\) 9.19016 2.83479i 0.457228 0.141036i
\(405\) −0.570054 + 0.714825i −0.0283262 + 0.0355199i
\(406\) −15.2806 + 2.61009i −0.758364 + 0.129537i
\(407\) 9.83025 + 12.3267i 0.487267 + 0.611014i
\(408\) −6.09611 4.15626i −0.301803 0.205766i
\(409\) −11.1498 10.3455i −0.551322 0.511552i 0.354588 0.935023i \(-0.384621\pi\)
−0.905910 + 0.423471i \(0.860812\pi\)
\(410\) 3.63539 6.29668i 0.179539 0.310971i
\(411\) −1.04893 1.81680i −0.0517399 0.0896162i
\(412\) −1.90046 + 8.32646i −0.0936290 + 0.410215i
\(413\) 13.7035 6.93298i 0.674307 0.341150i
\(414\) 0.863841 + 3.78474i 0.0424555 + 0.186010i
\(415\) 3.76416 3.49263i 0.184775 0.171446i
\(416\) −4.53564 + 0.683638i −0.222378 + 0.0335181i
\(417\) 5.64571 0.850954i 0.276472 0.0416714i
\(418\) −2.47765 + 2.29892i −0.121186 + 0.112444i
\(419\) 5.33972 + 23.3948i 0.260862 + 1.14291i 0.920318 + 0.391170i \(0.127930\pi\)
−0.659456 + 0.751743i \(0.729213\pi\)
\(420\) 1.88112 2.45598i 0.0917891 0.119840i
\(421\) 2.02648 8.87858i 0.0987645 0.432715i −0.901235 0.433330i \(-0.857338\pi\)
1.00000 0.000614544i \(0.000195615\pi\)
\(422\) 9.68472 + 16.7744i 0.471445 + 0.816567i
\(423\) −2.35243 + 4.07453i −0.114379 + 0.198110i
\(424\) 3.42586 + 3.17874i 0.166375 + 0.154373i
\(425\) −21.1840 14.4430i −1.02758 0.700589i
\(426\) 10.8210 + 13.5691i 0.524278 + 0.657423i
\(427\) 2.82176 + 2.51722i 0.136554 + 0.121817i
\(428\) 4.61331 5.78490i 0.222993 0.279624i
\(429\) −22.8954 + 7.06231i −1.10540 + 0.340971i
\(430\) −1.47125 3.74869i −0.0709501 0.180778i
\(431\) 1.20981 16.1439i 0.0582747 0.777622i −0.889144 0.457627i \(-0.848700\pi\)
0.947419 0.319995i \(-0.103681\pi\)
\(432\) 1.95112 4.97138i 0.0938734 0.239185i
\(433\) −18.7415 9.02544i −0.900660 0.433735i −0.0745325 0.997219i \(-0.523746\pi\)
−0.826127 + 0.563484i \(0.809461\pi\)
\(434\) 8.89357 + 1.16291i 0.426905 + 0.0558216i
\(435\) −6.17254 + 2.97254i −0.295950 + 0.142522i
\(436\) 1.31383 + 17.5319i 0.0629212 + 0.839625i
\(437\) 1.57962 + 0.487247i 0.0755633 + 0.0233082i
\(438\) −5.75766 + 3.92551i −0.275112 + 0.187568i
\(439\) 24.5005 + 3.69285i 1.16934 + 0.176250i 0.704870 0.709336i \(-0.251005\pi\)
0.464474 + 0.885587i \(0.346243\pi\)
\(440\) 4.76986 0.227394
\(441\) −7.86727 9.10951i −0.374632 0.433786i
\(442\) 29.9071 1.42253
\(443\) 4.72285 + 0.711855i 0.224389 + 0.0338213i 0.260275 0.965535i \(-0.416187\pi\)
−0.0358851 + 0.999356i \(0.511425\pi\)
\(444\) −3.19339 + 2.17722i −0.151552 + 0.103326i
\(445\) 17.4751 + 5.39036i 0.828400 + 0.255528i
\(446\) 0.371049 + 4.95131i 0.0175697 + 0.234451i
\(447\) 4.76829 2.29629i 0.225532 0.108611i
\(448\) −0.918200 + 2.48131i −0.0433809 + 0.117231i
\(449\) −20.8541 10.0428i −0.984168 0.473950i −0.128631 0.991693i \(-0.541058\pi\)
−0.855537 + 0.517742i \(0.826773\pi\)
\(450\) 2.47028 6.29416i 0.116450 0.296710i
\(451\) −2.42732 + 32.3904i −0.114298 + 1.52520i
\(452\) 2.63988 + 6.72631i 0.124170 + 0.316379i
\(453\) 21.7583 6.71156i 1.02230 0.315336i
\(454\) −7.96202 + 9.98406i −0.373676 + 0.468575i
\(455\) −0.692116 + 12.5208i −0.0324469 + 0.586982i
\(456\) −0.516590 0.647783i −0.0241915 0.0303352i
\(457\) 9.14445 + 6.23458i 0.427759 + 0.291641i 0.757999 0.652256i \(-0.226177\pi\)
−0.330240 + 0.943897i \(0.607130\pi\)
\(458\) 18.4079 + 17.0800i 0.860145 + 0.798098i
\(459\) −17.4106 + 30.1560i −0.812656 + 1.40756i
\(460\) −1.16643 2.02032i −0.0543851 0.0941977i
\(461\) 0.266299 1.16673i 0.0124028 0.0543402i −0.968348 0.249605i \(-0.919699\pi\)
0.980751 + 0.195264i \(0.0625565\pi\)
\(462\) −2.81094 + 13.5314i −0.130777 + 0.629539i
\(463\) −2.63550 11.5469i −0.122482 0.536629i −0.998520 0.0543866i \(-0.982680\pi\)
0.876038 0.482242i \(-0.160177\pi\)
\(464\) 4.29508 3.98525i 0.199394 0.185011i
\(465\) 3.91966 0.590793i 0.181770 0.0273974i
\(466\) 0.599780 0.0904023i 0.0277843 0.00418781i
\(467\) 15.3577 14.2498i 0.710667 0.659403i −0.239588 0.970875i \(-0.577012\pi\)
0.950255 + 0.311472i \(0.100822\pi\)
\(468\) 1.75505 + 7.68937i 0.0811272 + 0.355441i
\(469\) 25.6281 0.501823i 1.18340 0.0231720i
\(470\) 0.629134 2.75642i 0.0290198 0.127144i
\(471\) −3.15753 5.46900i −0.145491 0.251998i
\(472\) −2.90230 + 5.02693i −0.133589 + 0.231383i
\(473\) 13.1879 + 12.2366i 0.606379 + 0.562638i
\(474\) −14.0935 9.60882i −0.647338 0.441348i
\(475\) −1.79515 2.25105i −0.0823672 0.103285i
\(476\) 8.33122 15.1055i 0.381861 0.692361i
\(477\) 5.01033 6.28276i 0.229407 0.287668i
\(478\) 0.233064 0.0718908i 0.0106601 0.00328821i
\(479\) −1.71123 4.36015i −0.0781882 0.199220i 0.886435 0.462854i \(-0.153174\pi\)
−0.964623 + 0.263633i \(0.915079\pi\)
\(480\) −0.0873802 + 1.16601i −0.00398834 + 0.0532207i
\(481\) 5.72363 14.5836i 0.260975 0.664954i
\(482\) −24.0532 11.5834i −1.09559 0.527610i
\(483\) 6.41874 2.11840i 0.292063 0.0963905i
\(484\) −9.28783 + 4.47278i −0.422174 + 0.203308i
\(485\) −1.29965 17.3426i −0.0590140 0.787487i
\(486\) −14.3531 4.42733i −0.651068 0.200828i
\(487\) 3.70806 2.52812i 0.168028 0.114560i −0.476386 0.879236i \(-0.658054\pi\)
0.644415 + 0.764676i \(0.277101\pi\)
\(488\) −1.41326 0.213014i −0.0639752 0.00964271i
\(489\) 19.3568 0.875344
\(490\) 6.13121 + 3.83748i 0.276980 + 0.173360i
\(491\) −31.9992 −1.44410 −0.722051 0.691840i \(-0.756801\pi\)
−0.722051 + 0.691840i \(0.756801\pi\)
\(492\) −7.87346 1.18673i −0.354963 0.0535021i
\(493\) −31.5645 + 21.5203i −1.42160 + 0.969227i
\(494\) 3.20928 + 0.989930i 0.144392 + 0.0445391i
\(495\) −0.612919 8.17884i −0.0275487 0.367611i
\(496\) −3.05435 + 1.47090i −0.137144 + 0.0660452i
\(497\) −29.2001 + 28.1774i −1.30980 + 1.26393i
\(498\) −5.06647 2.43988i −0.227034 0.109334i
\(499\) 2.81759 7.17910i 0.126133 0.321381i −0.853833 0.520547i \(-0.825728\pi\)
0.979966 + 0.199166i \(0.0638234\pi\)
\(500\) −0.689740 + 9.20394i −0.0308461 + 0.411613i
\(501\) −3.42826 8.73506i −0.153163 0.390254i
\(502\) −2.73221 + 0.842775i −0.121944 + 0.0376149i
\(503\) −4.23268 + 5.30761i −0.188726 + 0.236655i −0.867188 0.497980i \(-0.834075\pi\)
0.678463 + 0.734635i \(0.262647\pi\)
\(504\) 4.37267 + 1.25558i 0.194774 + 0.0559282i
\(505\) 6.19607 + 7.76962i 0.275721 + 0.345744i
\(506\) 8.61084 + 5.87077i 0.382798 + 0.260988i
\(507\) 6.66880 + 6.18774i 0.296172 + 0.274807i
\(508\) −5.59931 + 9.69829i −0.248429 + 0.430292i
\(509\) 17.2950 + 29.9558i 0.766586 + 1.32777i 0.939404 + 0.342812i \(0.111379\pi\)
−0.172818 + 0.984954i \(0.555287\pi\)
\(510\) 1.69647 7.43271i 0.0751209 0.329126i
\(511\) −10.4059 12.5370i −0.460331 0.554605i
\(512\) −0.222521 0.974928i −0.00983413 0.0430861i
\(513\) −2.86647 + 2.65969i −0.126558 + 0.117428i
\(514\) 24.2952 3.66191i 1.07161 0.161520i
\(515\) −8.72645 + 1.31530i −0.384533 + 0.0579591i
\(516\) −3.23286 + 2.99965i −0.142319 + 0.132052i
\(517\) 2.81057 + 12.3139i 0.123609 + 0.541565i
\(518\) −5.77147 6.95345i −0.253584 0.305517i
\(519\) 3.38221 14.8184i 0.148462 0.650456i
\(520\) −2.36981 4.10463i −0.103923 0.180000i
\(521\) −3.04859 + 5.28032i −0.133561 + 0.231335i −0.925047 0.379853i \(-0.875975\pi\)
0.791486 + 0.611188i \(0.209308\pi\)
\(522\) −7.38538 6.85263i −0.323249 0.299932i
\(523\) 29.5059 + 20.1168i 1.29020 + 0.879644i 0.997075 0.0764294i \(-0.0243520\pi\)
0.293126 + 0.956074i \(0.405304\pi\)
\(524\) 6.29209 + 7.89004i 0.274871 + 0.344678i
\(525\) −11.3157 3.24922i −0.493856 0.141808i
\(526\) −6.28535 + 7.88158i −0.274054 + 0.343653i
\(527\) 21.1217 6.51519i 0.920077 0.283806i
\(528\) −1.90839 4.86250i −0.0830520 0.211613i
\(529\) −1.33789 + 17.8528i −0.0581690 + 0.776211i
\(530\) −1.76425 + 4.49524i −0.0766343 + 0.195261i
\(531\) 8.99256 + 4.33059i 0.390244 + 0.187932i
\(532\) 1.39400 1.34518i 0.0604377 0.0583211i
\(533\) 29.0790 14.0037i 1.25955 0.606569i
\(534\) −1.49663 19.9711i −0.0647655 0.864236i
\(535\) 7.30591 + 2.25357i 0.315862 + 0.0974305i
\(536\) −8.00490 + 5.45765i −0.345759 + 0.235735i
\(537\) 12.8734 + 1.94036i 0.555530 + 0.0837326i
\(538\) 22.9408 0.989049
\(539\) −32.1161 3.56148i −1.38334 0.153404i
\(540\) 5.51840 0.237474
\(541\) −29.5304 4.45100i −1.26961 0.191363i −0.520532 0.853842i \(-0.674266\pi\)
−0.749081 + 0.662479i \(0.769504\pi\)
\(542\) 5.60568 3.82189i 0.240784 0.164164i
\(543\) −7.05877 2.17734i −0.302921 0.0934387i
\(544\) 0.487251 + 6.50192i 0.0208907 + 0.278767i
\(545\) −16.3675 + 7.88216i −0.701106 + 0.337635i
\(546\) 13.0408 4.30391i 0.558096 0.184190i
\(547\) 18.3375 + 8.83086i 0.784054 + 0.377580i 0.782684 0.622419i \(-0.213850\pi\)
0.00136926 + 0.999999i \(0.499564\pi\)
\(548\) −0.677307 + 1.72575i −0.0289331 + 0.0737203i
\(549\) −0.183652 + 2.45067i −0.00783810 + 0.104592i
\(550\) −6.63166 16.8972i −0.282775 0.720499i
\(551\) −4.09946 + 1.26452i −0.174643 + 0.0538702i
\(552\) −1.59287 + 1.99740i −0.0677971 + 0.0850149i
\(553\) 19.2609 34.9223i 0.819055 1.48505i
\(554\) −13.1569 16.4982i −0.558981 0.700941i
\(555\) −3.29974 2.24972i −0.140066 0.0954954i
\(556\) −3.69863 3.43183i −0.156857 0.145542i
\(557\) 4.23486 7.33500i 0.179437 0.310794i −0.762251 0.647282i \(-0.775906\pi\)
0.941688 + 0.336488i \(0.109239\pi\)
\(558\) 2.91461 + 5.04825i 0.123385 + 0.213710i
\(559\) 3.97786 17.4281i 0.168245 0.737131i
\(560\) −2.73334 + 0.0535214i −0.115505 + 0.00226169i
\(561\) 7.57874 + 33.2046i 0.319975 + 1.40190i
\(562\) −9.98264 + 9.26253i −0.421092 + 0.390716i
\(563\) −8.98177 + 1.35378i −0.378536 + 0.0570552i −0.335555 0.942021i \(-0.608924\pi\)
−0.0429816 + 0.999076i \(0.513686\pi\)
\(564\) −3.06166 + 0.461471i −0.128919 + 0.0194314i
\(565\) −5.47329 + 5.07847i −0.230263 + 0.213653i
\(566\) −4.77966 20.9411i −0.200904 0.880219i
\(567\) −0.476148 + 2.29210i −0.0199963 + 0.0962593i
\(568\) 3.41285 14.9527i 0.143200 0.627401i
\(569\) 1.64013 + 2.84079i 0.0687578 + 0.119092i 0.898355 0.439271i \(-0.144763\pi\)
−0.829597 + 0.558363i \(0.811430\pi\)
\(570\) 0.428069 0.741438i 0.0179298 0.0310554i
\(571\) −13.2381 12.2831i −0.553996 0.514033i 0.352746 0.935719i \(-0.385248\pi\)
−0.906742 + 0.421686i \(0.861438\pi\)
\(572\) 17.4945 + 11.9275i 0.731480 + 0.498715i
\(573\) 4.36472 + 5.47318i 0.182339 + 0.228645i
\(574\) 1.02752 18.5883i 0.0428877 0.775861i
\(575\) −5.53523 + 6.94096i −0.230835 + 0.289458i
\(576\) −1.64311 + 0.506831i −0.0684628 + 0.0211180i
\(577\) 11.5968 + 29.5481i 0.482780 + 1.23010i 0.940130 + 0.340817i \(0.110704\pi\)
−0.457349 + 0.889287i \(0.651201\pi\)
\(578\) 1.90654 25.4410i 0.0793015 1.05821i
\(579\) −6.86973 + 17.5038i −0.285496 + 0.727433i
\(580\) 5.45473 + 2.62686i 0.226495 + 0.109074i
\(581\) 4.56293 12.3307i 0.189302 0.511563i
\(582\) −17.1594 + 8.26355i −0.711281 + 0.342535i
\(583\) −1.61216 21.5128i −0.0667690 0.890971i
\(584\) 5.88457 + 1.81515i 0.243505 + 0.0751114i
\(585\) −6.73366 + 4.59093i −0.278403 + 0.189812i
\(586\) −11.8772 1.79020i −0.490642 0.0739524i
\(587\) −24.4886 −1.01075 −0.505377 0.862899i \(-0.668647\pi\)
−0.505377 + 0.862899i \(0.668647\pi\)
\(588\) 1.45896 7.78563i 0.0601663 0.321074i
\(589\) 2.48219 0.102277
\(590\) −5.93091 0.893941i −0.244172 0.0368030i
\(591\) −7.24511 + 4.93963i −0.298024 + 0.203189i
\(592\) 3.26378 + 1.00674i 0.134140 + 0.0413768i
\(593\) −1.90959 25.4818i −0.0784176 1.04641i −0.888133 0.459587i \(-0.847997\pi\)
0.809715 0.586823i \(-0.199622\pi\)
\(594\) −22.2113 + 10.6964i −0.911341 + 0.438879i
\(595\) 17.6747 + 2.31113i 0.724593 + 0.0947469i
\(596\) −4.21378 2.02925i −0.172603 0.0831214i
\(597\) 8.89555 22.6655i 0.364071 0.927637i
\(598\) 0.773879 10.3267i 0.0316463 0.422290i
\(599\) 4.47191 + 11.3942i 0.182717 + 0.465556i 0.992658 0.120956i \(-0.0385959\pi\)
−0.809941 + 0.586512i \(0.800501\pi\)
\(600\) 4.25206 1.31159i 0.173589 0.0535453i
\(601\) 2.51975 3.15966i 0.102783 0.128885i −0.727780 0.685811i \(-0.759448\pi\)
0.830562 + 0.556926i \(0.188019\pi\)
\(602\) −7.69453 6.86410i −0.313605 0.279760i
\(603\) 10.3868 + 13.0246i 0.422983 + 0.530404i
\(604\) −16.6256 11.3351i −0.676486 0.461220i
\(605\) −7.80848 7.24521i −0.317460 0.294560i
\(606\) 5.44151 9.42497i 0.221046 0.382863i
\(607\) −16.2822 28.2016i −0.660874 1.14467i −0.980386 0.197085i \(-0.936852\pi\)
0.319513 0.947582i \(-0.396481\pi\)
\(608\) −0.162929 + 0.713837i −0.00660763 + 0.0289499i
\(609\) −10.6666 + 13.9263i −0.432231 + 0.564321i
\(610\) −0.328623 1.43979i −0.0133055 0.0582954i
\(611\) 9.20018 8.53652i 0.372199 0.345351i
\(612\) 11.0862 1.67097i 0.448132 0.0675450i
\(613\) −41.4028 + 6.24047i −1.67225 + 0.252050i −0.915692 0.401882i \(-0.868356\pi\)
−0.756553 + 0.653932i \(0.773118\pi\)
\(614\) 19.8994 18.4640i 0.803076 0.745145i
\(615\) −1.83080 8.02128i −0.0738251 0.323449i
\(616\) 10.8978 5.51349i 0.439086 0.222145i
\(617\) −7.72239 + 33.8340i −0.310892 + 1.36210i 0.542159 + 0.840276i \(0.317607\pi\)
−0.853050 + 0.521829i \(0.825250\pi\)
\(618\) 4.83224 + 8.36968i 0.194381 + 0.336678i
\(619\) 12.1917 21.1167i 0.490027 0.848751i −0.509908 0.860229i \(-0.670320\pi\)
0.999934 + 0.0114783i \(0.00365372\pi\)
\(620\) −2.56786 2.38262i −0.103128 0.0956884i
\(621\) 9.96214 + 6.79207i 0.399767 + 0.272556i
\(622\) 6.70824 + 8.41187i 0.268976 + 0.337285i
\(623\) 46.1565 7.88403i 1.84922 0.315867i
\(624\) −3.23620 + 4.05807i −0.129552 + 0.162453i
\(625\) 9.67452 2.98419i 0.386981 0.119368i
\(626\) 1.68198 + 4.28561i 0.0672254 + 0.171287i
\(627\) −0.285819 + 3.81399i −0.0114145 + 0.152316i
\(628\) −2.03885 + 5.19491i −0.0813590 + 0.207299i
\(629\) −20.0643 9.66245i −0.800016 0.385267i
\(630\) 0.443002 + 4.67995i 0.0176496 + 0.186454i
\(631\) 11.3963 5.48815i 0.453678 0.218480i −0.193068 0.981185i \(-0.561844\pi\)
0.646746 + 0.762706i \(0.276129\pi\)
\(632\) 1.12647 + 15.0317i 0.0448086 + 0.597930i
\(633\) 20.9446 + 6.46054i 0.832471 + 0.256783i
\(634\) −1.60155 + 1.09192i −0.0636058 + 0.0433657i
\(635\) −11.4423 1.72465i −0.454074 0.0684407i
\(636\) 5.28841 0.209699
\(637\) 12.8915 + 29.4065i 0.510778 + 1.16513i
\(638\) −27.0467 −1.07079
\(639\) −26.0778 3.93059i −1.03162 0.155492i
\(640\) 0.853754 0.582080i 0.0337476 0.0230087i
\(641\) 7.60648 + 2.34629i 0.300438 + 0.0926728i 0.441309 0.897355i \(-0.354514\pi\)
−0.140871 + 0.990028i \(0.544990\pi\)
\(642\) −0.625703 8.34943i −0.0246945 0.329526i
\(643\) −36.1913 + 17.4288i −1.42725 + 0.687325i −0.978483 0.206326i \(-0.933849\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(644\) −5.00025 3.26758i −0.197038 0.128761i
\(645\) −4.10572 1.97721i −0.161662 0.0778525i
\(646\) 1.74414 4.44401i 0.0686225 0.174847i
\(647\) −0.277072 + 3.69727i −0.0108928 + 0.145355i −0.999998 0.00185399i \(-0.999410\pi\)
0.989105 + 0.147209i \(0.0470289\pi\)
\(648\) −0.323264 0.823664i −0.0126990 0.0323566i
\(649\) 25.6044 7.89791i 1.00506 0.310020i
\(650\) −11.2458 + 14.1018i −0.441097 + 0.553119i
\(651\) 8.27243 5.88053i 0.324222 0.230476i
\(652\) −10.6653 13.3738i −0.417685 0.523760i
\(653\) −30.6748 20.9137i −1.20040 0.818418i −0.213060 0.977039i \(-0.568343\pi\)
−0.987340 + 0.158621i \(0.949295\pi\)
\(654\) 14.5838 + 13.5317i 0.570270 + 0.529133i
\(655\) −5.21391 + 9.03075i −0.203724 + 0.352861i
\(656\) 3.51823 + 6.09374i 0.137364 + 0.237921i
\(657\) 2.35626 10.3235i 0.0919265 0.402756i
\(658\) −1.74875 7.02486i −0.0681733 0.273858i
\(659\) 1.63589 + 7.16731i 0.0637253 + 0.279199i 0.996744 0.0806286i \(-0.0256928\pi\)
−0.933019 + 0.359827i \(0.882836\pi\)
\(660\) 3.95668 3.67126i 0.154013 0.142904i
\(661\) 20.7083 3.12127i 0.805460 0.121404i 0.266609 0.963805i \(-0.414097\pi\)
0.538851 + 0.842401i \(0.318859\pi\)
\(662\) 8.46403 1.27575i 0.328964 0.0495833i
\(663\) 24.8084 23.0188i 0.963478 0.893977i
\(664\) 1.10580 + 4.84483i 0.0429134 + 0.188016i
\(665\) 1.82014 + 0.833039i 0.0705821 + 0.0323039i
\(666\) 1.30686 5.72573i 0.0506398 0.221868i
\(667\) 6.61405 + 11.4559i 0.256097 + 0.443573i
\(668\) −4.14625 + 7.18151i −0.160423 + 0.277861i
\(669\) 4.11870 + 3.82160i 0.159238 + 0.147752i
\(670\) −8.27148 5.63940i −0.319555 0.217869i
\(671\) 4.11346 + 5.15812i 0.158798 + 0.199127i
\(672\) 1.14815 + 2.76501i 0.0442909 + 0.106662i
\(673\) −28.6471 + 35.9223i −1.10426 + 1.38470i −0.188938 + 0.981989i \(0.560505\pi\)
−0.915326 + 0.402714i \(0.868067\pi\)
\(674\) −14.4733 + 4.46443i −0.557492 + 0.171963i
\(675\) −7.67237 19.5489i −0.295310 0.752437i
\(676\) 0.600784 8.01691i 0.0231071 0.308343i
\(677\) −10.3127 + 26.2763i −0.396349 + 1.00988i 0.583849 + 0.811862i \(0.301546\pi\)
−0.980198 + 0.198019i \(0.936549\pi\)
\(678\) 7.36692 + 3.54772i 0.282925 + 0.136249i
\(679\) −23.0157 38.1208i −0.883261 1.46294i
\(680\) −6.07008 + 2.92320i −0.232777 + 0.112099i
\(681\) 1.07989 + 14.4101i 0.0413815 + 0.552197i
\(682\) 14.9538 + 4.61263i 0.572610 + 0.176627i
\(683\) −4.18446 + 2.85291i −0.160114 + 0.109164i −0.640726 0.767769i \(-0.721367\pi\)
0.480613 + 0.876933i \(0.340414\pi\)
\(684\) 1.24495 + 0.187645i 0.0476017 + 0.00717480i
\(685\) −1.91564 −0.0731929
\(686\) 18.4439 + 1.68051i 0.704190 + 0.0641623i
\(687\) 28.4158 1.08413
\(688\) 3.85375 + 0.580860i 0.146923 + 0.0221451i
\(689\) −17.7116 + 12.0756i −0.674757 + 0.460042i
\(690\) −2.52257 0.778108i −0.0960324 0.0296221i
\(691\) −1.13591 15.1577i −0.0432122 0.576626i −0.976222 0.216775i \(-0.930446\pi\)
0.933009 0.359852i \(-0.117173\pi\)
\(692\) −12.1018 + 5.82791i −0.460040 + 0.221544i
\(693\) −10.8543 17.9779i −0.412320 0.682924i
\(694\) 26.1389 + 12.5878i 0.992220 + 0.477828i
\(695\) 1.90473 4.85316i 0.0722504 0.184091i
\(696\) 0.495475 6.61166i 0.0187809 0.250614i
\(697\) −16.7614 42.7073i −0.634882 1.61765i
\(698\) −22.4554 + 6.92656i −0.849948 + 0.262174i
\(699\) 0.427947 0.536628i 0.0161864 0.0202971i
\(700\) 3.98982 + 9.60840i 0.150801 + 0.363164i
\(701\) 20.0757 + 25.1741i 0.758248 + 0.950813i 0.999808 0.0195726i \(-0.00623054\pi\)
−0.241560 + 0.970386i \(0.577659\pi\)
\(702\) 20.2399 + 13.7993i 0.763905 + 0.520822i
\(703\) −1.83323 1.70099i −0.0691417 0.0641541i
\(704\) −2.30807 + 3.99769i −0.0869886 + 0.150669i
\(705\) −1.59968 2.77072i −0.0602473 0.104351i
\(706\) −6.60160 + 28.9235i −0.248455 + 1.08855i
\(707\) 23.1372 + 10.5894i 0.870164 + 0.398255i
\(708\) 1.46161 + 6.40375i 0.0549308 + 0.240668i
\(709\) 16.1338 14.9700i 0.605918 0.562210i −0.316407 0.948623i \(-0.602477\pi\)
0.922326 + 0.386413i \(0.126286\pi\)
\(710\) 15.6710 2.36202i 0.588121 0.0886450i
\(711\) 25.6300 3.86310i 0.961200 0.144878i
\(712\) −12.9737 + 12.0378i −0.486210 + 0.451137i
\(713\) −1.70310 7.46178i −0.0637817 0.279446i
\(714\) −4.71552 18.9426i −0.176474 0.708910i
\(715\) −4.86848 + 21.3302i −0.182071 + 0.797704i
\(716\) −5.75244 9.96353i −0.214979 0.372354i
\(717\) 0.137998 0.239019i 0.00515362 0.00892633i
\(718\) −11.9683 11.1050i −0.446654 0.414435i
\(719\) 14.3030 + 9.75165i 0.533414 + 0.363675i 0.799872 0.600171i \(-0.204901\pi\)
−0.266458 + 0.963847i \(0.585853\pi\)
\(720\) −1.10779 1.38913i −0.0412850 0.0517697i
\(721\) −18.4172 + 13.0920i −0.685891 + 0.487572i
\(722\) −11.5120 + 14.4357i −0.428434 + 0.537239i
\(723\) −28.8680 + 8.90460i −1.07361 + 0.331166i
\(724\) 2.38492 + 6.07668i 0.0886348 + 0.225838i
\(725\) 1.72178 22.9755i 0.0639452 0.853290i
\(726\) −4.26180 + 10.8589i −0.158170 + 0.403011i
\(727\) −20.3186 9.78494i −0.753577 0.362903i 0.0173315 0.999850i \(-0.494483\pi\)
−0.770908 + 0.636946i \(0.780197\pi\)
\(728\) −10.1589 6.63868i −0.376515 0.246046i
\(729\) −17.7053 + 8.52644i −0.655753 + 0.315794i
\(730\) 0.475525 + 6.34544i 0.0176000 + 0.234855i
\(731\) −24.2819 7.48998i −0.898099 0.277027i
\(732\) −1.33627 + 0.911055i −0.0493901 + 0.0336736i
\(733\) 5.93565 + 0.894655i 0.219238 + 0.0330448i 0.257743 0.966214i \(-0.417021\pi\)
−0.0385045 + 0.999258i \(0.512259\pi\)
\(734\) −2.63428 −0.0972329
\(735\) 8.03956 1.53580i 0.296544 0.0566490i
\(736\) 2.25767 0.0832190
\(737\) 44.2233 + 6.66559i 1.62899 + 0.245530i
\(738\) 9.99680 6.81570i 0.367987 0.250889i
\(739\) 28.8139 + 8.88792i 1.05994 + 0.326948i 0.775238 0.631669i \(-0.217630\pi\)
0.284700 + 0.958617i \(0.408106\pi\)
\(740\) 0.263742 + 3.51939i 0.00969535 + 0.129375i
\(741\) 3.42407 1.64895i 0.125786 0.0605756i
\(742\) 1.16523 + 12.3097i 0.0427769 + 0.451903i
\(743\) 12.9716 + 6.24681i 0.475883 + 0.229173i 0.656421 0.754395i \(-0.272069\pi\)
−0.180538 + 0.983568i \(0.557784\pi\)
\(744\) −1.40151 + 3.57100i −0.0513819 + 0.130919i
\(745\) 0.361148 4.81919i 0.0132314 0.176561i
\(746\) 2.28847 + 5.83093i 0.0837869 + 0.213486i
\(747\) 8.16529 2.51866i 0.298752 0.0921529i
\(748\) 18.7657 23.5315i 0.686143 0.860396i
\(749\) 19.2969 3.29612i 0.705093 0.120437i
\(750\) 6.51192 + 8.16570i 0.237782 + 0.298169i
\(751\) −0.577392 0.393659i −0.0210693 0.0143648i 0.552740 0.833354i \(-0.313582\pi\)
−0.573809 + 0.818989i \(0.694535\pi\)
\(752\) 2.00576 + 1.86108i 0.0731427 + 0.0678665i
\(753\) −1.61775 + 2.80202i −0.0589539 + 0.102111i
\(754\) 13.4376 + 23.2747i 0.489370 + 0.847614i
\(755\) 4.62669 20.2708i 0.168382 0.737731i
\(756\) 12.6080 6.37873i 0.458549 0.231992i
\(757\) −0.0310433 0.136009i −0.00112829 0.00494335i 0.974361 0.224992i \(-0.0722356\pi\)
−0.975489 + 0.220049i \(0.929378\pi\)
\(758\) −12.3066 + 11.4189i −0.446998 + 0.414753i
\(759\) 11.6614 1.75768i 0.423283 0.0637997i
\(760\) −0.748128 + 0.112762i −0.0271375 + 0.00409031i
\(761\) 18.6896 17.3414i 0.677497 0.628625i −0.264445 0.964401i \(-0.585189\pi\)
0.941942 + 0.335776i \(0.108998\pi\)
\(762\) 2.81985 + 12.3546i 0.102152 + 0.447558i
\(763\) −28.2841 + 36.9277i −1.02395 + 1.33687i
\(764\) 1.37660 6.03128i 0.0498036 0.218204i
\(765\) 5.79237 + 10.0327i 0.209424 + 0.362733i
\(766\) 16.0785 27.8488i 0.580939 1.00622i
\(767\) −19.5175 18.1096i −0.704735 0.653898i
\(768\) −0.934966 0.637449i −0.0337377 0.0230019i
\(769\) 18.0488 + 22.6324i 0.650855 + 0.816146i 0.992313 0.123750i \(-0.0394922\pi\)
−0.341458 + 0.939897i \(0.610921\pi\)
\(770\) 9.41729 + 8.40094i 0.339376 + 0.302749i
\(771\) 17.3347 21.7371i 0.624295 0.782841i
\(772\) 15.8787 4.89793i 0.571487 0.176280i
\(773\) 8.29243 + 21.1288i 0.298258 + 0.759949i 0.998920 + 0.0464557i \(0.0147926\pi\)
−0.700663 + 0.713493i \(0.747112\pi\)
\(774\) 0.500794 6.68263i 0.0180007 0.240202i
\(775\) −4.87026 + 12.4092i −0.174945 + 0.445752i
\(776\) 15.1640 + 7.30258i 0.544355 + 0.262147i
\(777\) −10.1394 1.32582i −0.363751 0.0475636i
\(778\) −1.97203 + 0.949681i −0.0707008 + 0.0340477i
\(779\) −0.385013 5.13765i −0.0137945 0.184075i
\(780\) −5.12505 1.58087i −0.183506 0.0566041i
\(781\) −58.4966 + 39.8823i −2.09317 + 1.42710i
\(782\) −14.5560 2.19396i −0.520520 0.0784557i
\(783\) −31.2912 −1.11826
\(784\) −6.18305 + 3.28175i −0.220823 + 0.117205i
\(785\) −5.76653 −0.205816
\(786\) 11.2922 + 1.70202i 0.402779 + 0.0607091i
\(787\) −5.57140 + 3.79852i −0.198599 + 0.135402i −0.658536 0.752549i \(-0.728824\pi\)
0.459938 + 0.887951i \(0.347872\pi\)
\(788\) 7.40480 + 2.28408i 0.263785 + 0.0813669i
\(789\) 0.852483 + 11.3756i 0.0303492 + 0.404982i
\(790\) −14.0334 + 6.75811i −0.499285 + 0.240443i
\(791\) −6.63473 + 17.9295i −0.235904 + 0.637498i
\(792\) 7.15139 + 3.44393i 0.254113 + 0.122375i
\(793\) 2.39505 6.10249i 0.0850507 0.216706i
\(794\) −0.449806 + 6.00225i −0.0159630 + 0.213012i
\(795\) 1.99642 + 5.08678i 0.0708056 + 0.180410i
\(796\) −20.5612 + 6.34228i −0.728772 + 0.224796i
\(797\) −12.5335 + 15.7165i −0.443959 + 0.556707i −0.952582 0.304283i \(-0.901583\pi\)
0.508623 + 0.860989i \(0.330155\pi\)
\(798\) 0.120991 2.18879i 0.00428302 0.0774822i
\(799\) −11.1233 13.9481i −0.393512 0.493449i
\(800\) −3.24901 2.21514i −0.114870 0.0783169i
\(801\) 22.3082 + 20.6990i 0.788223 + 0.731364i
\(802\) −0.409996 + 0.710134i −0.0144775 + 0.0250757i
\(803\) −14.2134 24.6184i −0.501581 0.868765i
\(804\) −2.43956 + 10.6884i −0.0860366 + 0.376951i
\(805\) 1.25537 6.04315i 0.0442459 0.212993i
\(806\) −3.46016 15.1599i −0.121879 0.533986i
\(807\) 19.0298 17.6570i 0.669880 0.621558i
\(808\) −9.51002 + 1.43340i −0.334561 + 0.0504270i
\(809\) 24.9698 3.76359i 0.877891 0.132321i 0.305392 0.952227i \(-0.401212\pi\)
0.572498 + 0.819906i \(0.305974\pi\)
\(810\) 0.670226 0.621879i 0.0235493 0.0218506i
\(811\) −4.52257 19.8147i −0.158809 0.695788i −0.990148 0.140023i \(-0.955282\pi\)
0.831339 0.555765i \(-0.187575\pi\)
\(812\) 15.4989 0.303485i 0.543906 0.0106502i
\(813\) 1.70838 7.48488i 0.0599154 0.262506i
\(814\) −7.88325 13.6542i −0.276308 0.478579i
\(815\) 8.83772 15.3074i 0.309572 0.536194i
\(816\) 5.40857 + 5.01842i 0.189338 + 0.175680i
\(817\) −2.35773 1.60747i −0.0824865 0.0562383i
\(818\) 9.48334 + 11.8917i 0.331577 + 0.415785i
\(819\) −10.0779 + 18.2725i −0.352150 + 0.638491i
\(820\) −4.53326 + 5.68452i −0.158308 + 0.198512i
\(821\) 19.8167 6.11265i 0.691609 0.213333i 0.0710264 0.997474i \(-0.477373\pi\)
0.620582 + 0.784141i \(0.286896\pi\)
\(822\) 0.766435 + 1.95284i 0.0267325 + 0.0681133i
\(823\) −1.39303 + 18.5887i −0.0485581 + 0.647963i 0.918828 + 0.394658i \(0.129137\pi\)
−0.967386 + 0.253305i \(0.918482\pi\)
\(824\) 3.12023 7.95022i 0.108698 0.276959i
\(825\) −18.5065 8.91225i −0.644313 0.310285i
\(826\) −14.5838 + 4.81314i −0.507435 + 0.167471i
\(827\) 7.90249 3.80564i 0.274797 0.132335i −0.291410 0.956598i \(-0.594125\pi\)
0.566207 + 0.824263i \(0.308410\pi\)
\(828\) −0.290107 3.87121i −0.0100819 0.134534i
\(829\) −33.0731 10.2017i −1.14868 0.354320i −0.338765 0.940871i \(-0.610009\pi\)
−0.809912 + 0.586551i \(0.800485\pi\)
\(830\) −4.24267 + 2.89260i −0.147265 + 0.100404i
\(831\) −23.6121 3.55895i −0.819095 0.123459i
\(832\) 4.58687 0.159021
\(833\) 43.0533 15.1499i 1.49171 0.524915i
\(834\) −5.70948 −0.197703
\(835\) −8.47295 1.27709i −0.293218 0.0441956i
\(836\) 2.79261 1.90397i 0.0965846 0.0658502i
\(837\) 17.3005 + 5.33649i 0.597992 + 0.184456i
\(838\) −1.79326 23.9294i −0.0619471 0.826627i
\(839\) 46.6215 22.4517i 1.60955 0.775119i 0.609705 0.792629i \(-0.291288\pi\)
0.999847 + 0.0175095i \(0.00557372\pi\)
\(840\) −2.22615 + 2.14819i −0.0768095 + 0.0741195i
\(841\) −4.80210 2.31257i −0.165589 0.0797437i
\(842\) −3.32713 + 8.47738i −0.114660 + 0.292150i
\(843\) −1.15159 + 15.3668i −0.0396627 + 0.529262i
\(844\) −7.07645 18.0305i −0.243582 0.620636i
\(845\) 7.93806 2.44857i 0.273077 0.0842332i
\(846\) 2.93343 3.67841i 0.100853 0.126466i
\(847\) −26.2150 7.52746i −0.900757 0.258647i
\(848\) −2.91383 3.65383i −0.100061 0.125473i
\(849\) −20.0827 13.6921i −0.689236 0.469913i
\(850\) 18.7948 + 17.4390i 0.644656 + 0.598153i
\(851\) −3.85556 + 6.67803i −0.132167 + 0.228920i
\(852\) −8.67774 15.0303i −0.297295 0.514929i
\(853\) −3.14524 + 13.7802i −0.107691 + 0.471825i 0.892109 + 0.451820i \(0.149225\pi\)
−0.999800 + 0.0200044i \(0.993632\pi\)
\(854\) −2.41507 2.90967i −0.0826419 0.0995667i
\(855\) 0.289485 + 1.26832i 0.00990019 + 0.0433756i
\(856\) −5.42398 + 5.03271i −0.185388 + 0.172015i
\(857\) −16.6017 + 2.50231i −0.567104 + 0.0854771i −0.426335 0.904565i \(-0.640195\pi\)
−0.140769 + 0.990043i \(0.544957\pi\)
\(858\) 23.6923 3.57104i 0.808842 0.121913i
\(859\) 5.56685 5.16528i 0.189939 0.176237i −0.579471 0.814993i \(-0.696741\pi\)
0.769410 + 0.638755i \(0.220550\pi\)
\(860\) 0.896107 + 3.92610i 0.0305570 + 0.133879i
\(861\) −13.4547 16.2102i −0.458534 0.552441i
\(862\) −3.60242 + 15.7832i −0.122699 + 0.537579i
\(863\) −4.34851 7.53184i −0.148025 0.256387i 0.782473 0.622685i \(-0.213958\pi\)
−0.930497 + 0.366298i \(0.880625\pi\)
\(864\) −2.67027 + 4.62505i −0.0908446 + 0.157347i
\(865\) −10.1742 9.44030i −0.345934 0.320980i
\(866\) 17.1870 + 11.7179i 0.584039 + 0.398191i
\(867\) −17.9999 22.5711i −0.611308 0.766556i
\(868\) −8.62091 2.47544i −0.292613 0.0840220i
\(869\) 43.3843 54.4022i 1.47171 1.84547i
\(870\) 6.54663 2.01937i 0.221951 0.0684629i
\(871\) −16.2355 41.3674i −0.550119 1.40168i
\(872\) 1.31383 17.5319i 0.0444920 0.593704i
\(873\) 10.5731 26.9399i 0.357846 0.911777i
\(874\) −1.48935 0.717235i −0.0503781 0.0242608i
\(875\) −17.5723 + 16.9568i −0.594051 + 0.573245i
\(876\) 6.27842 3.02353i 0.212128 0.102156i
\(877\) −0.0576947 0.769883i −0.00194821 0.0259971i 0.996145 0.0877223i \(-0.0279588\pi\)
−0.998093 + 0.0617252i \(0.980340\pi\)
\(878\) −23.6764 7.30321i −0.799041 0.246472i
\(879\) −11.2302 + 7.65661i −0.378785 + 0.258251i
\(880\) −4.71659 0.710911i −0.158996 0.0239648i
\(881\) −57.1026 −1.92384 −0.961918 0.273339i \(-0.911872\pi\)
−0.961918 + 0.273339i \(0.911872\pi\)
\(882\) 6.42170 + 10.1803i 0.216230 + 0.342789i
\(883\) −13.7570 −0.462961 −0.231480 0.972840i \(-0.574357\pi\)
−0.231480 + 0.972840i \(0.574357\pi\)
\(884\) −29.5730 4.45742i −0.994649 0.149919i
\(885\) −5.60783 + 3.82335i −0.188505 + 0.128521i
\(886\) −4.56401 1.40781i −0.153331 0.0472963i
\(887\) −0.871623 11.6310i −0.0292663 0.390531i −0.992532 0.121982i \(-0.961075\pi\)
0.963266 0.268549i \(-0.0865441\pi\)
\(888\) 3.48222 1.67695i 0.116856 0.0562747i
\(889\) −28.1360 + 9.28584i −0.943653 + 0.311437i
\(890\) −16.4765 7.93468i −0.552295 0.265971i
\(891\) −1.49223 + 3.80214i −0.0499917 + 0.127377i
\(892\) 0.371049 4.95131i 0.0124236 0.165782i
\(893\) −0.731931 1.86493i −0.0244931 0.0624075i
\(894\) −5.05727 + 1.55996i −0.169140 + 0.0521729i
\(895\) 7.41206 9.29443i 0.247758 0.310679i
\(896\) 1.27777 2.31675i 0.0426871 0.0773971i
\(897\) −7.30629 9.16180i −0.243950 0.305904i
\(898\) 19.1244 + 13.0388i 0.638190 + 0.435110i
\(899\) 14.5606 + 13.5103i 0.485624 + 0.450593i
\(900\) −3.38078 + 5.85568i −0.112693 + 0.195189i
\(901\) 15.2357 + 26.3890i 0.507575 + 0.879146i
\(902\) 7.22775 31.6668i 0.240658 1.05439i
\(903\) −11.6659 + 0.228429i −0.388216 + 0.00760165i
\(904\) −1.60789 7.04464i −0.0534777 0.234301i
\(905\) −4.94467 + 4.58798i −0.164366 + 0.152510i
\(906\) −22.5156 + 3.39368i −0.748031 + 0.112748i
\(907\) 54.2318 8.17413i 1.80074 0.271418i 0.838751 0.544515i \(-0.183286\pi\)
0.961986 + 0.273097i \(0.0880481\pi\)
\(908\) 9.36114 8.68587i 0.310660 0.288251i
\(909\) 3.67987 + 16.1226i 0.122053 + 0.534751i
\(910\) 2.55051 12.2778i 0.0845485 0.407003i
\(911\) 7.97454 34.9387i 0.264208 1.15757i −0.652429 0.757850i \(-0.726250\pi\)
0.916637 0.399721i \(-0.130893\pi\)
\(912\) 0.414273 + 0.717542i 0.0137180 + 0.0237602i
\(913\) 11.4698 19.8662i 0.379594 0.657476i
\(914\) −8.11310 7.52785i −0.268357 0.248999i
\(915\) −1.38077 0.941395i −0.0456470 0.0311216i
\(916\) −15.6567 19.6328i −0.517311 0.648687i
\(917\) −1.47367 + 26.6595i −0.0486650 + 0.880375i
\(918\) 21.7106 27.2243i 0.716558 0.898535i
\(919\) −10.2351 + 3.15710i −0.337623 + 0.104143i −0.458931 0.888472i \(-0.651767\pi\)
0.121307 + 0.992615i \(0.461291\pi\)
\(920\) 0.852289 + 2.17160i 0.0280991 + 0.0715955i
\(921\) 2.29557 30.6323i 0.0756418 1.00937i
\(922\) −0.437218 + 1.11401i −0.0143990 + 0.0366881i
\(923\) 63.3831 + 30.5237i 2.08628 + 1.00470i
\(924\) 4.79630 12.9613i 0.157787 0.426397i
\(925\) 12.1007 5.82740i 0.397869 0.191604i
\(926\) 0.885090 + 11.8107i 0.0290859 + 0.388124i
\(927\) −14.0331 4.32864i −0.460908 0.142171i
\(928\) −4.84108 + 3.30059i −0.158916 + 0.108347i
\(929\) −4.60409 0.693956i −0.151055 0.0227679i 0.0730791 0.997326i \(-0.476717\pi\)
−0.224135 + 0.974558i \(0.571956\pi\)
\(930\) −3.96393 −0.129982
\(931\) 5.12143 0.200642i 0.167848 0.00657579i
\(932\) −0.606555 −0.0198684
\(933\) 12.0390 + 1.81459i 0.394140 + 0.0594071i
\(934\) −17.3099 + 11.8017i −0.566399 + 0.386164i
\(935\) 29.7185 + 9.16695i 0.971899 + 0.299791i
\(936\) −0.589405 7.86506i −0.0192653 0.257078i
\(937\) 4.06784 1.95897i 0.132891 0.0639967i −0.366257 0.930514i \(-0.619361\pi\)
0.499148 + 0.866517i \(0.333647\pi\)
\(938\) −25.4166 3.32345i −0.829883 0.108515i
\(939\) 4.69377 + 2.26040i 0.153175 + 0.0737654i
\(940\) −1.03293 + 2.63186i −0.0336904 + 0.0858419i
\(941\) −0.976766 + 13.0340i −0.0318416 + 0.424897i 0.958390 + 0.285463i \(0.0921474\pi\)
−0.990231 + 0.139434i \(0.955472\pi\)
\(942\) 2.30715 + 5.87852i 0.0751709 + 0.191532i
\(943\) −15.1802 + 4.68248i −0.494337 + 0.152483i
\(944\) 3.61911 4.53822i 0.117792 0.147706i
\(945\) 10.8952 + 9.71930i 0.354419 + 0.316169i
\(946\) −11.2168 14.0654i −0.364690 0.457307i
\(947\) 19.0095 + 12.9605i 0.617726 + 0.421159i 0.831344 0.555759i \(-0.187572\pi\)
−0.213617 + 0.976917i \(0.568525\pi\)
\(948\) 12.5040 + 11.6020i 0.406112 + 0.376816i
\(949\) −14.1233 + 24.4623i −0.458463 + 0.794081i
\(950\) 1.43960 + 2.49346i 0.0467068 + 0.0808985i
\(951\) −0.488087 + 2.13845i −0.0158273 + 0.0693439i
\(952\) −10.4895 + 13.6951i −0.339967 + 0.443861i
\(953\) 4.08630 + 17.9033i 0.132368 + 0.579944i 0.996991 + 0.0775212i \(0.0247006\pi\)
−0.864622 + 0.502422i \(0.832442\pi\)
\(954\) −5.89077 + 5.46583i −0.190721 + 0.176963i
\(955\) 6.32100 0.952738i 0.204543 0.0308299i
\(956\) −0.241176 + 0.0363514i −0.00780019 + 0.00117569i
\(957\) −22.4357 + 20.8173i −0.725243 + 0.672928i
\(958\) 1.04227 + 4.56650i 0.0336743 + 0.147537i
\(959\) −4.37671 + 2.21429i −0.141331 + 0.0715032i
\(960\) 0.260189 1.13996i 0.00839755 0.0367921i
\(961\) 9.75372 + 16.8939i 0.314636 + 0.544966i
\(962\) −7.83327 + 13.5676i −0.252555 + 0.437438i
\(963\) 9.32652 + 8.65374i 0.300543 + 0.278863i
\(964\) 22.0581 + 15.0390i 0.710445 + 0.484373i
\(965\) 10.7055 + 13.4243i 0.344623 + 0.432144i
\(966\) −6.66278 + 1.13807i −0.214371 + 0.0366170i
\(967\) −32.3871 + 40.6121i −1.04150 + 1.30600i −0.0908050 + 0.995869i \(0.528944\pi\)
−0.950694 + 0.310130i \(0.899627\pi\)
\(968\) 9.85072 3.03855i 0.316614 0.0976626i
\(969\) −1.97366 5.02881i −0.0634031 0.161549i
\(970\) −1.29965 + 17.3426i −0.0417292 + 0.556838i
\(971\) −17.8742 + 45.5427i −0.573610 + 1.46153i 0.289828 + 0.957079i \(0.406402\pi\)
−0.863438 + 0.504455i \(0.831693\pi\)
\(972\) 13.5329 + 6.51710i 0.434068 + 0.209036i
\(973\) −1.25801 13.2898i −0.0403298 0.426052i
\(974\) −4.04344 + 1.94722i −0.129560 + 0.0623930i
\(975\) 1.52527 + 20.3533i 0.0488478 + 0.651829i
\(976\) 1.36572 + 0.421270i 0.0437158 + 0.0134845i
\(977\) −3.54412 + 2.41634i −0.113386 + 0.0773055i −0.618686 0.785639i \(-0.712335\pi\)
0.505299 + 0.862944i \(0.331382\pi\)
\(978\) −19.1406 2.88498i −0.612048 0.0922514i
\(979\) 81.6973 2.61106
\(980\) −5.49078 4.70843i −0.175396 0.150405i
\(981\) −30.2306 −0.965188
\(982\) 31.6418 + 4.76923i 1.00973 + 0.152192i
\(983\) 0.669700 0.456594i 0.0213601 0.0145631i −0.552593 0.833451i \(-0.686362\pi\)
0.573953 + 0.818888i \(0.305409\pi\)
\(984\) 7.60865 + 2.34696i 0.242555 + 0.0748182i
\(985\) 0.598374 + 7.98474i 0.0190658 + 0.254415i
\(986\) 34.4194 16.5755i 1.09614 0.527872i
\(987\) −6.85750 4.48126i −0.218277 0.142640i
\(988\) −3.02589 1.45719i −0.0962664 0.0463594i
\(989\) −3.21456 + 8.19056i −0.102217 + 0.260445i
\(990\) −0.612919 + 8.17884i −0.0194799 + 0.259941i
\(991\) 1.20520 + 3.07080i 0.0382845 + 0.0975472i 0.948737 0.316066i \(-0.102362\pi\)
−0.910453 + 0.413613i \(0.864267\pi\)
\(992\) 3.23946 0.999240i 0.102853 0.0317259i
\(993\) 6.03914 7.57284i 0.191646 0.240317i
\(994\) 33.0736 23.5107i 1.04903 0.745713i
\(995\) −13.8625 17.3830i −0.439470 0.551078i
\(996\) 4.64624 + 3.16775i 0.147222 + 0.100374i
\(997\) −33.1432 30.7524i −1.04966 0.973939i −0.0499650 0.998751i \(-0.515911\pi\)
−0.999692 + 0.0248115i \(0.992101\pi\)
\(998\) −3.85611 + 6.67897i −0.122063 + 0.211419i
\(999\) −9.12037 15.7969i −0.288556 0.499793i
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 98.2.g.b.39.1 24
3.2 odd 2 882.2.z.b.235.2 24
4.3 odd 2 784.2.bg.b.529.2 24
7.2 even 3 686.2.g.f.569.1 24
7.3 odd 6 686.2.e.d.295.1 24
7.4 even 3 686.2.e.c.295.4 24
7.5 odd 6 686.2.g.d.569.2 24
7.6 odd 2 686.2.g.e.165.2 24
49.3 odd 42 686.2.e.d.393.1 24
49.5 odd 42 686.2.g.e.79.2 24
49.8 even 7 686.2.g.f.557.1 24
49.17 odd 42 4802.2.a.l.1.10 12
49.32 even 21 4802.2.a.o.1.3 12
49.41 odd 14 686.2.g.d.557.2 24
49.44 even 21 inner 98.2.g.b.93.1 yes 24
49.46 even 21 686.2.e.c.393.4 24
147.44 odd 42 882.2.z.b.289.2 24
196.191 odd 42 784.2.bg.b.289.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.2.g.b.39.1 24 1.1 even 1 trivial
98.2.g.b.93.1 yes 24 49.44 even 21 inner
686.2.e.c.295.4 24 7.4 even 3
686.2.e.c.393.4 24 49.46 even 21
686.2.e.d.295.1 24 7.3 odd 6
686.2.e.d.393.1 24 49.3 odd 42
686.2.g.d.557.2 24 49.41 odd 14
686.2.g.d.569.2 24 7.5 odd 6
686.2.g.e.79.2 24 49.5 odd 42
686.2.g.e.165.2 24 7.6 odd 2
686.2.g.f.557.1 24 49.8 even 7
686.2.g.f.569.1 24 7.2 even 3
784.2.bg.b.289.2 24 196.191 odd 42
784.2.bg.b.529.2 24 4.3 odd 2
882.2.z.b.235.2 24 3.2 odd 2
882.2.z.b.289.2 24 147.44 odd 42
4802.2.a.l.1.10 12 49.17 odd 42
4802.2.a.o.1.3 12 49.32 even 21