Properties

Label 93.2.p.b.11.4
Level $93$
Weight $2$
Character 93.11
Analytic conductor $0.743$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [93,2,Mod(11,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 23]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.p (of order \(30\), degree \(8\), 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: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 93.11
Dual form 93.2.p.b.17.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13134 + 0.367594i) q^{2} +(1.09350 + 1.34323i) q^{3} +(-0.473233 + 0.343824i) q^{4} +(-3.25867 + 1.88139i) q^{5} +(-1.73088 - 1.11768i) q^{6} +(-0.121266 - 1.15377i) q^{7} +(1.80741 - 2.48769i) q^{8} +(-0.608530 + 2.93763i) q^{9} +O(q^{10})\) \(q+(-1.13134 + 0.367594i) q^{2} +(1.09350 + 1.34323i) q^{3} +(-0.473233 + 0.343824i) q^{4} +(-3.25867 + 1.88139i) q^{5} +(-1.73088 - 1.11768i) q^{6} +(-0.121266 - 1.15377i) q^{7} +(1.80741 - 2.48769i) q^{8} +(-0.608530 + 2.93763i) q^{9} +(2.99507 - 3.32636i) q^{10} +(1.44229 + 0.642148i) q^{11} +(-0.979313 - 0.259690i) q^{12} +(1.12113 + 5.27450i) q^{13} +(0.561310 + 1.26072i) q^{14} +(-6.09049 - 2.31984i) q^{15} +(-0.768816 + 2.36617i) q^{16} +(3.70486 - 1.64951i) q^{17} +(-0.391404 - 3.54715i) q^{18} +(2.07066 + 0.440133i) q^{19} +(0.895241 - 2.01075i) q^{20} +(1.41717 - 1.42453i) q^{21} +(-1.86777 - 0.196310i) q^{22} +(1.05297 + 0.765029i) q^{23} +(5.31793 - 0.292511i) q^{24} +(4.57928 - 7.93155i) q^{25} +(-3.20725 - 5.55512i) q^{26} +(-4.61134 + 2.39490i) q^{27} +(0.454079 + 0.504306i) q^{28} +(-0.285528 - 0.878764i) q^{29} +(7.74316 + 0.385699i) q^{30} +(1.59217 - 5.33526i) q^{31} +3.19035i q^{32} +(0.714585 + 2.63951i) q^{33} +(-3.58510 + 3.22804i) q^{34} +(2.56585 + 3.53159i) q^{35} +(-0.722052 - 1.59941i) q^{36} +(-7.98383 - 4.60947i) q^{37} +(-2.50441 + 0.263224i) q^{38} +(-5.85891 + 7.27358i) q^{39} +(-1.20943 + 11.5070i) q^{40} +(-2.74468 - 2.47132i) q^{41} +(-1.07965 + 2.13256i) q^{42} +(-1.64332 + 7.73123i) q^{43} +(-0.903324 + 0.192007i) q^{44} +(-3.54385 - 10.7177i) q^{45} +(-1.47249 - 0.478441i) q^{46} +(7.19341 + 2.33728i) q^{47} +(-4.01901 + 1.55470i) q^{48} +(5.53056 - 1.17556i) q^{49} +(-2.26513 + 10.6566i) q^{50} +(6.26693 + 3.17274i) q^{51} +(-2.34405 - 2.11059i) q^{52} +(-0.927089 + 8.82066i) q^{53} +(4.33664 - 4.40454i) q^{54} +(-5.90807 + 0.620963i) q^{55} +(-3.08938 - 1.78366i) q^{56} +(1.67306 + 3.26266i) q^{57} +(0.646057 + 0.889222i) q^{58} +(7.74731 - 6.97571i) q^{59} +(3.67984 - 0.996229i) q^{60} -4.86376i q^{61} +(0.159922 + 6.62126i) q^{62} +(3.46313 + 0.345867i) q^{63} +(-2.71038 - 8.34170i) q^{64} +(-13.5768 - 15.0786i) q^{65} +(-1.77871 - 2.72350i) q^{66} +(1.87847 + 3.25360i) q^{67} +(-1.18612 + 2.05442i) q^{68} +(0.123812 + 2.25094i) q^{69} +(-4.20104 - 3.05223i) q^{70} +(-7.89756 - 0.830067i) q^{71} +(6.20805 + 6.82334i) q^{72} +(0.894859 - 2.00989i) q^{73} +(10.7268 + 2.28006i) q^{74} +(15.6613 - 2.52210i) q^{75} +(-1.13123 + 0.503658i) q^{76} +(0.565988 - 1.74193i) q^{77} +(3.95468 - 10.3826i) q^{78} +(1.85553 + 4.16759i) q^{79} +(-1.94638 - 9.15701i) q^{80} +(-8.25938 - 3.57528i) q^{81} +(4.01360 + 1.78697i) q^{82} +(3.43714 - 3.81733i) q^{83} +(-0.180864 + 1.16139i) q^{84} +(-8.96954 + 12.3455i) q^{85} +(-0.982800 - 9.35072i) q^{86} +(0.868158 - 1.34446i) q^{87} +(4.20427 - 2.42734i) q^{88} +(-2.01575 + 1.46453i) q^{89} +(7.94904 + 10.8226i) q^{90} +(5.94958 - 1.93314i) q^{91} -0.761337 q^{92} +(8.90751 - 3.69543i) q^{93} -8.99735 q^{94} +(-7.57567 + 2.46148i) q^{95} +(-4.28537 + 3.48863i) q^{96} +(8.65013 - 6.28469i) q^{97} +(-5.82481 + 3.36296i) q^{98} +(-2.76407 + 3.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 10 q^{3} + 12 q^{4} - 9 q^{6} - 26 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 10 q^{3} + 12 q^{4} - 9 q^{6} - 26 q^{7} - 8 q^{9} - 36 q^{10} + 15 q^{12} - 32 q^{13} - 20 q^{15} - 24 q^{16} - 6 q^{18} + 5 q^{21} - 24 q^{22} - 48 q^{24} + 38 q^{25} + 5 q^{27} + 76 q^{28} + 30 q^{31} - 7 q^{33} - 4 q^{34} - 5 q^{36} + 48 q^{37} - 7 q^{39} + 8 q^{40} + 15 q^{42} - 92 q^{43} - 63 q^{45} - 70 q^{46} + 12 q^{48} - 2 q^{49} + 58 q^{51} + 72 q^{52} + 100 q^{54} + 10 q^{55} + 93 q^{57} + 50 q^{58} + 85 q^{60} - 18 q^{63} + 46 q^{64} + 6 q^{66} - 46 q^{67} + 110 q^{69} - 158 q^{70} + 163 q^{72} - 30 q^{73} + 55 q^{75} + 34 q^{76} - 11 q^{78} + 24 q^{79} - 108 q^{81} - 116 q^{82} - 80 q^{84} - 130 q^{85} - 9 q^{87} - 222 q^{88} - 93 q^{90} - 20 q^{91} - 121 q^{93} + 128 q^{94} - 122 q^{96} + 18 q^{97} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(-1\) \(e\left(\frac{23}{30}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13134 + 0.367594i −0.799977 + 0.259928i −0.680347 0.732890i \(-0.738171\pi\)
−0.119630 + 0.992819i \(0.538171\pi\)
\(3\) 1.09350 + 1.34323i 0.631331 + 0.775514i
\(4\) −0.473233 + 0.343824i −0.236616 + 0.171912i
\(5\) −3.25867 + 1.88139i −1.45732 + 0.841385i −0.998879 0.0473395i \(-0.984926\pi\)
−0.458442 + 0.888724i \(0.651592\pi\)
\(6\) −1.73088 1.11768i −0.706628 0.456293i
\(7\) −0.121266 1.15377i −0.0458341 0.436082i −0.993243 0.116056i \(-0.962975\pi\)
0.947409 0.320027i \(-0.103692\pi\)
\(8\) 1.80741 2.48769i 0.639016 0.879530i
\(9\) −0.608530 + 2.93763i −0.202843 + 0.979211i
\(10\) 2.99507 3.32636i 0.947124 1.05189i
\(11\) 1.44229 + 0.642148i 0.434866 + 0.193615i 0.612481 0.790485i \(-0.290172\pi\)
−0.177615 + 0.984100i \(0.556838\pi\)
\(12\) −0.979313 0.259690i −0.282703 0.0749661i
\(13\) 1.12113 + 5.27450i 0.310945 + 1.46288i 0.804908 + 0.593399i \(0.202215\pi\)
−0.493963 + 0.869483i \(0.664452\pi\)
\(14\) 0.561310 + 1.26072i 0.150016 + 0.336942i
\(15\) −6.09049 2.31984i −1.57256 0.598981i
\(16\) −0.768816 + 2.36617i −0.192204 + 0.591543i
\(17\) 3.70486 1.64951i 0.898561 0.400065i 0.0951312 0.995465i \(-0.469673\pi\)
0.803430 + 0.595400i \(0.203006\pi\)
\(18\) −0.391404 3.54715i −0.0922547 0.836071i
\(19\) 2.07066 + 0.440133i 0.475043 + 0.100973i 0.439210 0.898384i \(-0.355258\pi\)
0.0358327 + 0.999358i \(0.488592\pi\)
\(20\) 0.895241 2.01075i 0.200182 0.449616i
\(21\) 1.41717 1.42453i 0.309251 0.310857i
\(22\) −1.86777 0.196310i −0.398209 0.0418534i
\(23\) 1.05297 + 0.765029i 0.219560 + 0.159520i 0.692129 0.721774i \(-0.256673\pi\)
−0.472569 + 0.881294i \(0.656673\pi\)
\(24\) 5.31793 0.292511i 1.08552 0.0597085i
\(25\) 4.57928 7.93155i 0.915856 1.58631i
\(26\) −3.20725 5.55512i −0.628994 1.08945i
\(27\) −4.61134 + 2.39490i −0.887453 + 0.460898i
\(28\) 0.454079 + 0.504306i 0.0858129 + 0.0953048i
\(29\) −0.285528 0.878764i −0.0530212 0.163182i 0.921040 0.389469i \(-0.127341\pi\)
−0.974061 + 0.226286i \(0.927341\pi\)
\(30\) 7.74316 + 0.385699i 1.41370 + 0.0704188i
\(31\) 1.59217 5.33526i 0.285963 0.958241i
\(32\) 3.19035i 0.563979i
\(33\) 0.714585 + 2.63951i 0.124393 + 0.459480i
\(34\) −3.58510 + 3.22804i −0.614840 + 0.553604i
\(35\) 2.56585 + 3.53159i 0.433708 + 0.596948i
\(36\) −0.722052 1.59941i −0.120342 0.266569i
\(37\) −7.98383 4.60947i −1.31253 0.757792i −0.330019 0.943974i \(-0.607055\pi\)
−0.982515 + 0.186183i \(0.940388\pi\)
\(38\) −2.50441 + 0.263224i −0.406269 + 0.0427006i
\(39\) −5.85891 + 7.27358i −0.938176 + 1.16470i
\(40\) −1.20943 + 11.5070i −0.191228 + 1.81942i
\(41\) −2.74468 2.47132i −0.428647 0.385955i 0.426376 0.904546i \(-0.359790\pi\)
−0.855022 + 0.518591i \(0.826457\pi\)
\(42\) −1.07965 + 2.13256i −0.166593 + 0.329062i
\(43\) −1.64332 + 7.73123i −0.250605 + 1.17900i 0.655250 + 0.755412i \(0.272563\pi\)
−0.905854 + 0.423590i \(0.860770\pi\)
\(44\) −0.903324 + 0.192007i −0.136181 + 0.0289462i
\(45\) −3.54385 10.7177i −0.528286 1.59769i
\(46\) −1.47249 0.478441i −0.217107 0.0705422i
\(47\) 7.19341 + 2.33728i 1.04927 + 0.340928i 0.782381 0.622801i \(-0.214005\pi\)
0.266886 + 0.963728i \(0.414005\pi\)
\(48\) −4.01901 + 1.55470i −0.580094 + 0.224402i
\(49\) 5.53056 1.17556i 0.790081 0.167937i
\(50\) −2.26513 + 10.6566i −0.320337 + 1.50707i
\(51\) 6.26693 + 3.17274i 0.877545 + 0.444273i
\(52\) −2.34405 2.11059i −0.325062 0.292687i
\(53\) −0.927089 + 8.82066i −0.127345 + 1.21161i 0.725043 + 0.688703i \(0.241820\pi\)
−0.852389 + 0.522908i \(0.824847\pi\)
\(54\) 4.33664 4.40454i 0.590142 0.599382i
\(55\) −5.90807 + 0.620963i −0.796644 + 0.0837307i
\(56\) −3.08938 1.78366i −0.412836 0.238351i
\(57\) 1.67306 + 3.26266i 0.221603 + 0.432150i
\(58\) 0.646057 + 0.889222i 0.0848315 + 0.116761i
\(59\) 7.74731 6.97571i 1.00861 0.908160i 0.0128323 0.999918i \(-0.495915\pi\)
0.995781 + 0.0917578i \(0.0292486\pi\)
\(60\) 3.67984 0.996229i 0.475065 0.128613i
\(61\) 4.86376i 0.622741i −0.950289 0.311371i \(-0.899212\pi\)
0.950289 0.311371i \(-0.100788\pi\)
\(62\) 0.159922 + 6.62126i 0.0203101 + 0.840900i
\(63\) 3.46313 + 0.345867i 0.436314 + 0.0435751i
\(64\) −2.71038 8.34170i −0.338798 1.04271i
\(65\) −13.5768 15.0786i −1.68399 1.87026i
\(66\) −1.77871 2.72350i −0.218944 0.335240i
\(67\) 1.87847 + 3.25360i 0.229491 + 0.397491i 0.957657 0.287910i \(-0.0929604\pi\)
−0.728166 + 0.685401i \(0.759627\pi\)
\(68\) −1.18612 + 2.05442i −0.143838 + 0.249135i
\(69\) 0.123812 + 2.25094i 0.0149052 + 0.270981i
\(70\) −4.20104 3.05223i −0.502120 0.364812i
\(71\) −7.89756 0.830067i −0.937267 0.0985108i −0.376438 0.926442i \(-0.622851\pi\)
−0.560830 + 0.827931i \(0.689518\pi\)
\(72\) 6.20805 + 6.82334i 0.731626 + 0.804138i
\(73\) 0.894859 2.00989i 0.104735 0.235239i −0.853574 0.520971i \(-0.825570\pi\)
0.958310 + 0.285732i \(0.0922366\pi\)
\(74\) 10.7268 + 2.28006i 1.24697 + 0.265051i
\(75\) 15.6613 2.52210i 1.80841 0.291227i
\(76\) −1.13123 + 0.503658i −0.129761 + 0.0577735i
\(77\) 0.565988 1.74193i 0.0645003 0.198512i
\(78\) 3.95468 10.3826i 0.447780 1.17560i
\(79\) 1.85553 + 4.16759i 0.208764 + 0.468891i 0.987332 0.158669i \(-0.0507204\pi\)
−0.778568 + 0.627560i \(0.784054\pi\)
\(80\) −1.94638 9.15701i −0.217612 1.02379i
\(81\) −8.25938 3.57528i −0.917709 0.397253i
\(82\) 4.01360 + 1.78697i 0.443228 + 0.197338i
\(83\) 3.43714 3.81733i 0.377276 0.419007i −0.524365 0.851494i \(-0.675697\pi\)
0.901640 + 0.432487i \(0.142364\pi\)
\(84\) −0.180864 + 1.16139i −0.0197339 + 0.126718i
\(85\) −8.96954 + 12.3455i −0.972883 + 1.33906i
\(86\) −0.982800 9.35072i −0.105978 1.00831i
\(87\) 0.868158 1.34446i 0.0930763 0.144141i
\(88\) 4.20427 2.42734i 0.448177 0.258755i
\(89\) −2.01575 + 1.46453i −0.213669 + 0.155240i −0.689472 0.724312i \(-0.742158\pi\)
0.475803 + 0.879552i \(0.342158\pi\)
\(90\) 7.94904 + 10.8226i 0.837902 + 1.14080i
\(91\) 5.94958 1.93314i 0.623685 0.202648i
\(92\) −0.761337 −0.0793748
\(93\) 8.90751 3.69543i 0.923666 0.383198i
\(94\) −8.99735 −0.928006
\(95\) −7.57567 + 2.46148i −0.777247 + 0.252543i
\(96\) −4.28537 + 3.48863i −0.437373 + 0.356057i
\(97\) 8.65013 6.28469i 0.878288 0.638114i −0.0545100 0.998513i \(-0.517360\pi\)
0.932798 + 0.360400i \(0.117360\pi\)
\(98\) −5.82481 + 3.36296i −0.588395 + 0.339710i
\(99\) −2.76407 + 3.84615i −0.277800 + 0.386552i
\(100\) 0.559989 + 5.32794i 0.0559989 + 0.532794i
\(101\) 5.24637 7.22101i 0.522033 0.718517i −0.463857 0.885910i \(-0.653535\pi\)
0.985890 + 0.167393i \(0.0535348\pi\)
\(102\) −8.25630 1.28576i −0.817495 0.127309i
\(103\) −9.21813 + 10.2378i −0.908289 + 1.00876i 0.0916269 + 0.995793i \(0.470793\pi\)
−0.999916 + 0.0129638i \(0.995873\pi\)
\(104\) 15.1476 + 6.74416i 1.48535 + 0.661320i
\(105\) −1.93799 + 7.30831i −0.189128 + 0.713218i
\(106\) −2.19357 10.3199i −0.213059 1.00236i
\(107\) 5.11120 + 11.4799i 0.494119 + 1.10981i 0.972763 + 0.231800i \(0.0744615\pi\)
−0.478645 + 0.878009i \(0.658872\pi\)
\(108\) 1.35882 2.71883i 0.130752 0.261620i
\(109\) 3.12175 9.60775i 0.299009 0.920256i −0.682836 0.730572i \(-0.739254\pi\)
0.981845 0.189684i \(-0.0607464\pi\)
\(110\) 6.45577 2.87429i 0.615533 0.274053i
\(111\) −2.53872 15.7646i −0.240965 1.49631i
\(112\) 2.82324 + 0.600098i 0.266771 + 0.0567039i
\(113\) 2.49342 5.60030i 0.234561 0.526832i −0.757464 0.652877i \(-0.773562\pi\)
0.992025 + 0.126045i \(0.0402284\pi\)
\(114\) −3.09214 3.07616i −0.289605 0.288109i
\(115\) −4.87061 0.511922i −0.454187 0.0477370i
\(116\) 0.437261 + 0.317689i 0.0405987 + 0.0294967i
\(117\) −16.1768 + 0.0837769i −1.49554 + 0.00774518i
\(118\) −6.20060 + 10.7398i −0.570811 + 0.988674i
\(119\) −2.35242 4.07451i −0.215646 0.373510i
\(120\) −16.7790 + 10.9583i −1.53171 + 1.00035i
\(121\) −5.69260 6.32227i −0.517509 0.574752i
\(122\) 1.78789 + 5.50256i 0.161868 + 0.498179i
\(123\) 0.318252 6.38911i 0.0286958 0.576087i
\(124\) 1.08092 + 3.07225i 0.0970695 + 0.275896i
\(125\) 15.6478i 1.39958i
\(126\) −4.04512 + 0.881735i −0.360368 + 0.0785512i
\(127\) 13.1249 11.8177i 1.16465 1.04865i 0.166609 0.986023i \(-0.446718\pi\)
0.998037 0.0626292i \(-0.0199485\pi\)
\(128\) 2.38225 + 3.27888i 0.210563 + 0.289815i
\(129\) −12.1818 + 6.24672i −1.07255 + 0.549993i
\(130\) 20.9027 + 12.0682i 1.83329 + 1.05845i
\(131\) −2.68613 + 0.282323i −0.234688 + 0.0246667i −0.221142 0.975242i \(-0.570979\pi\)
−0.0135456 + 0.999908i \(0.504312\pi\)
\(132\) −1.24569 1.00341i −0.108424 0.0873358i
\(133\) 0.256710 2.44243i 0.0222596 0.211786i
\(134\) −3.32119 2.99041i −0.286907 0.258332i
\(135\) 10.5211 16.4799i 0.905511 1.41837i
\(136\) 2.59274 12.1979i 0.222326 1.04596i
\(137\) −1.46614 + 0.311639i −0.125261 + 0.0266251i −0.270116 0.962828i \(-0.587062\pi\)
0.144854 + 0.989453i \(0.453729\pi\)
\(138\) −0.967506 2.50106i −0.0823596 0.212905i
\(139\) 9.59427 + 3.11737i 0.813775 + 0.264412i 0.686196 0.727417i \(-0.259279\pi\)
0.127579 + 0.991828i \(0.459279\pi\)
\(140\) −2.42849 0.789064i −0.205245 0.0666881i
\(141\) 4.72647 + 12.2182i 0.398040 + 1.02896i
\(142\) 9.23994 1.96401i 0.775398 0.164816i
\(143\) −1.77002 + 8.32728i −0.148016 + 0.696362i
\(144\) −6.48310 3.69838i −0.540258 0.308199i
\(145\) 2.58374 + 2.32641i 0.214568 + 0.193198i
\(146\) −0.273566 + 2.60281i −0.0226405 + 0.215410i
\(147\) 7.62670 + 6.14335i 0.629039 + 0.506695i
\(148\) 5.36306 0.563680i 0.440841 0.0463342i
\(149\) −14.2926 8.25182i −1.17089 0.676016i −0.217003 0.976171i \(-0.569628\pi\)
−0.953890 + 0.300155i \(0.902961\pi\)
\(150\) −16.7911 + 8.61035i −1.37099 + 0.703033i
\(151\) 5.96820 + 8.21452i 0.485685 + 0.668488i 0.979585 0.201031i \(-0.0644291\pi\)
−0.493900 + 0.869519i \(0.664429\pi\)
\(152\) 4.83745 4.35566i 0.392369 0.353291i
\(153\) 2.59114 + 11.8873i 0.209481 + 0.961031i
\(154\) 2.17877i 0.175570i
\(155\) 4.84935 + 20.3813i 0.389509 + 1.63707i
\(156\) 0.271799 5.45653i 0.0217613 0.436872i
\(157\) 3.99077 + 12.2823i 0.318498 + 0.980235i 0.974291 + 0.225295i \(0.0723344\pi\)
−0.655793 + 0.754941i \(0.727666\pi\)
\(158\) −3.63122 4.03287i −0.288884 0.320838i
\(159\) −12.8619 + 8.40007i −1.02002 + 0.666169i
\(160\) −6.00230 10.3963i −0.474523 0.821898i
\(161\) 0.754975 1.30766i 0.0595004 0.103058i
\(162\) 10.6584 + 1.00875i 0.837404 + 0.0792546i
\(163\) −10.5737 7.68227i −0.828199 0.601722i 0.0908502 0.995865i \(-0.471042\pi\)
−0.919049 + 0.394143i \(0.871042\pi\)
\(164\) 2.14857 + 0.225824i 0.167775 + 0.0176339i
\(165\) −7.29455 7.25687i −0.567880 0.564947i
\(166\) −2.48534 + 5.58217i −0.192900 + 0.433261i
\(167\) −13.9748 2.97044i −1.08140 0.229859i −0.367443 0.930046i \(-0.619767\pi\)
−0.713960 + 0.700187i \(0.753100\pi\)
\(168\) −0.982371 6.10017i −0.0757916 0.470639i
\(169\) −14.6873 + 6.53921i −1.12979 + 0.503016i
\(170\) 5.60945 17.2641i 0.430225 1.32410i
\(171\) −2.55301 + 5.81502i −0.195234 + 0.444685i
\(172\) −1.88051 4.22369i −0.143387 0.322053i
\(173\) −1.12821 5.30779i −0.0857759 0.403544i 0.914223 0.405212i \(-0.132802\pi\)
−0.999999 + 0.00166815i \(0.999469\pi\)
\(174\) −0.487967 + 1.84016i −0.0369927 + 0.139502i
\(175\) −9.70646 4.32159i −0.733739 0.326682i
\(176\) −2.62829 + 2.91901i −0.198114 + 0.220028i
\(177\) 17.8416 + 2.77850i 1.34106 + 0.208845i
\(178\) 1.74215 2.39786i 0.130579 0.179727i
\(179\) −0.0625795 0.595405i −0.00467741 0.0445026i 0.991934 0.126754i \(-0.0404558\pi\)
−0.996612 + 0.0822510i \(0.973789\pi\)
\(180\) 5.36205 + 3.85349i 0.399664 + 0.287222i
\(181\) 2.80488 1.61940i 0.208485 0.120369i −0.392122 0.919913i \(-0.628259\pi\)
0.600607 + 0.799544i \(0.294926\pi\)
\(182\) −6.02038 + 4.37406i −0.446260 + 0.324227i
\(183\) 6.53315 5.31851i 0.482944 0.393156i
\(184\) 3.80631 1.23674i 0.280605 0.0911740i
\(185\) 34.6889 2.55038
\(186\) −8.71899 + 7.45513i −0.639307 + 0.546637i
\(187\) 6.40271 0.468212
\(188\) −4.20777 + 1.36719i −0.306883 + 0.0997124i
\(189\) 3.32235 + 5.02999i 0.241665 + 0.365878i
\(190\) 7.66582 5.56954i 0.556137 0.404057i
\(191\) −1.82620 + 1.05436i −0.132139 + 0.0762907i −0.564613 0.825356i \(-0.690974\pi\)
0.432473 + 0.901647i \(0.357641\pi\)
\(192\) 8.24103 12.7623i 0.594745 0.921039i
\(193\) −0.379362 3.60939i −0.0273071 0.259810i −0.999655 0.0262719i \(-0.991636\pi\)
0.972348 0.233538i \(-0.0750302\pi\)
\(194\) −7.47601 + 10.2898i −0.536746 + 0.738768i
\(195\) 5.40778 34.7251i 0.387259 2.48672i
\(196\) −2.21306 + 2.45785i −0.158076 + 0.175561i
\(197\) 2.19081 + 0.975409i 0.156088 + 0.0694950i 0.483294 0.875458i \(-0.339440\pi\)
−0.327205 + 0.944953i \(0.606107\pi\)
\(198\) 1.71328 5.36735i 0.121757 0.381441i
\(199\) 2.00691 + 9.44178i 0.142266 + 0.669310i 0.990252 + 0.139290i \(0.0444821\pi\)
−0.847985 + 0.530020i \(0.822185\pi\)
\(200\) −11.4546 25.7274i −0.809960 1.81920i
\(201\) −2.31623 + 6.08102i −0.163375 + 0.428922i
\(202\) −3.28102 + 10.0979i −0.230852 + 0.710489i
\(203\) −0.979263 + 0.435996i −0.0687308 + 0.0306009i
\(204\) −4.05658 + 0.653271i −0.284017 + 0.0457381i
\(205\) 13.5935 + 2.88939i 0.949412 + 0.201804i
\(206\) 6.66548 14.9709i 0.464406 1.04307i
\(207\) −2.88814 + 2.62770i −0.200740 + 0.182638i
\(208\) −13.3423 1.40233i −0.925123 0.0972343i
\(209\) 2.70386 + 1.96447i 0.187030 + 0.135885i
\(210\) −0.493973 8.98057i −0.0340874 0.619718i
\(211\) −2.15453 + 3.73176i −0.148324 + 0.256905i −0.930608 0.366017i \(-0.880721\pi\)
0.782284 + 0.622922i \(0.214055\pi\)
\(212\) −2.59403 4.49298i −0.178158 0.308579i
\(213\) −7.52098 11.5159i −0.515329 0.789057i
\(214\) −10.0025 11.1089i −0.683754 0.759386i
\(215\) −9.19044 28.2853i −0.626783 1.92904i
\(216\) −2.37683 + 15.8001i −0.161723 + 1.07506i
\(217\) −6.34871 1.19001i −0.430979 0.0807833i
\(218\) 12.0172i 0.813905i
\(219\) 3.67827 0.995804i 0.248554 0.0672902i
\(220\) 2.58239 2.32520i 0.174105 0.156765i
\(221\) 12.8540 + 17.6920i 0.864651 + 1.19009i
\(222\) 8.66711 + 16.9018i 0.581698 + 1.13438i
\(223\) 5.90105 + 3.40697i 0.395163 + 0.228148i 0.684395 0.729111i \(-0.260066\pi\)
−0.289232 + 0.957259i \(0.593400\pi\)
\(224\) 3.68091 0.386879i 0.245941 0.0258495i
\(225\) 20.5134 + 18.2788i 1.36756 + 1.21859i
\(226\) −0.762259 + 7.25241i −0.0507047 + 0.482423i
\(227\) 4.05339 + 3.64969i 0.269033 + 0.242239i 0.792594 0.609750i \(-0.208730\pi\)
−0.523561 + 0.851988i \(0.675397\pi\)
\(228\) −1.91353 0.968759i −0.126727 0.0641576i
\(229\) 4.22707 19.8868i 0.279333 1.31416i −0.584917 0.811093i \(-0.698873\pi\)
0.864250 0.503063i \(-0.167794\pi\)
\(230\) 5.69849 1.21125i 0.375747 0.0798675i
\(231\) 2.95872 1.14455i 0.194670 0.0753056i
\(232\) −2.70216 0.877984i −0.177405 0.0576425i
\(233\) 8.76839 + 2.84902i 0.574437 + 0.186646i 0.581807 0.813327i \(-0.302346\pi\)
−0.00737018 + 0.999973i \(0.502346\pi\)
\(234\) 18.2706 6.04127i 1.19439 0.394930i
\(235\) −27.8383 + 5.91721i −1.81597 + 0.385996i
\(236\) −1.26787 + 5.96484i −0.0825311 + 0.388278i
\(237\) −3.56901 + 7.04965i −0.231832 + 0.457924i
\(238\) 4.15915 + 3.74492i 0.269598 + 0.242747i
\(239\) 0.458427 4.36164i 0.0296532 0.282131i −0.969640 0.244537i \(-0.921364\pi\)
0.999293 0.0375939i \(-0.0119693\pi\)
\(240\) 10.1716 12.6276i 0.656574 0.815108i
\(241\) 10.1009 1.06165i 0.650657 0.0683868i 0.226551 0.973999i \(-0.427255\pi\)
0.424106 + 0.905613i \(0.360588\pi\)
\(242\) 8.76428 + 5.06006i 0.563389 + 0.325273i
\(243\) −4.22919 15.0038i −0.271303 0.962494i
\(244\) 1.67228 + 2.30169i 0.107057 + 0.147351i
\(245\) −15.8106 + 14.2359i −1.01010 + 0.909500i
\(246\) 1.98855 + 7.34523i 0.126785 + 0.468315i
\(247\) 11.4152i 0.726329i
\(248\) −10.3947 13.6038i −0.660067 0.863844i
\(249\) 8.88606 + 0.442629i 0.563131 + 0.0280505i
\(250\) −5.75204 17.7029i −0.363791 1.11963i
\(251\) −2.88906 3.20863i −0.182356 0.202527i 0.645035 0.764153i \(-0.276843\pi\)
−0.827391 + 0.561626i \(0.810176\pi\)
\(252\) −1.75779 + 1.02703i −0.110730 + 0.0646970i
\(253\) 1.02743 + 1.77956i 0.0645938 + 0.111880i
\(254\) −10.5046 + 18.1945i −0.659116 + 1.14162i
\(255\) −26.3910 + 1.45163i −1.65267 + 0.0909045i
\(256\) 10.2913 + 7.47709i 0.643208 + 0.467318i
\(257\) −27.4716 2.88738i −1.71363 0.180110i −0.803745 0.594974i \(-0.797162\pi\)
−0.909883 + 0.414864i \(0.863829\pi\)
\(258\) 11.4855 11.5451i 0.715054 0.718767i
\(259\) −4.35008 + 9.77044i −0.270301 + 0.607106i
\(260\) 11.6094 + 2.46764i 0.719981 + 0.153037i
\(261\) 2.75524 0.304022i 0.170545 0.0188185i
\(262\) 2.93514 1.30681i 0.181333 0.0807348i
\(263\) −5.83384 + 17.9547i −0.359730 + 1.10713i 0.593486 + 0.804844i \(0.297751\pi\)
−0.953216 + 0.302290i \(0.902249\pi\)
\(264\) 7.85782 + 2.99301i 0.483616 + 0.184207i
\(265\) −13.5741 30.4878i −0.833848 1.87285i
\(266\) 0.607398 + 2.85758i 0.0372420 + 0.175210i
\(267\) −4.17142 1.10616i −0.255287 0.0676959i
\(268\) −2.00762 0.893849i −0.122635 0.0546005i
\(269\) 18.5110 20.5586i 1.12864 1.25348i 0.164991 0.986295i \(-0.447240\pi\)
0.963646 0.267183i \(-0.0860930\pi\)
\(270\) −5.84499 + 22.5119i −0.355715 + 1.37003i
\(271\) −2.84575 + 3.91684i −0.172867 + 0.237931i −0.886656 0.462430i \(-0.846978\pi\)
0.713789 + 0.700361i \(0.246978\pi\)
\(272\) 1.05467 + 10.0345i 0.0639487 + 0.608431i
\(273\) 9.10249 + 5.87777i 0.550908 + 0.355739i
\(274\) 1.54415 0.891515i 0.0932855 0.0538584i
\(275\) 11.6979 8.49900i 0.705408 0.512509i
\(276\) −0.832519 1.02265i −0.0501118 0.0615563i
\(277\) −26.7266 + 8.68400i −1.60585 + 0.521771i −0.968544 0.248843i \(-0.919950\pi\)
−0.637302 + 0.770614i \(0.719950\pi\)
\(278\) −12.0003 −0.719729
\(279\) 14.7041 + 7.92389i 0.880314 + 0.474391i
\(280\) 13.4230 0.802180
\(281\) −3.30079 + 1.07249i −0.196908 + 0.0639794i −0.405811 0.913957i \(-0.633011\pi\)
0.208903 + 0.977936i \(0.433011\pi\)
\(282\) −9.83858 12.0855i −0.585879 0.719682i
\(283\) −18.6877 + 13.5774i −1.11087 + 0.807093i −0.982800 0.184672i \(-0.940878\pi\)
−0.128068 + 0.991765i \(0.540878\pi\)
\(284\) 4.02278 2.32255i 0.238708 0.137818i
\(285\) −11.5903 7.48424i −0.686551 0.443328i
\(286\) −1.05857 10.0716i −0.0625945 0.595547i
\(287\) −2.51849 + 3.46640i −0.148662 + 0.204615i
\(288\) −9.37207 1.94142i −0.552255 0.114399i
\(289\) −0.370106 + 0.411044i −0.0217709 + 0.0241791i
\(290\) −3.77826 1.68219i −0.221867 0.0987816i
\(291\) 17.9007 + 4.74683i 1.04936 + 0.278264i
\(292\) 0.267570 + 1.25882i 0.0156584 + 0.0736668i
\(293\) 4.71099 + 10.5811i 0.275219 + 0.618152i 0.997282 0.0736750i \(-0.0234728\pi\)
−0.722063 + 0.691827i \(0.756806\pi\)
\(294\) −10.8866 4.14668i −0.634921 0.241839i
\(295\) −12.1219 + 37.3073i −0.705762 + 2.17211i
\(296\) −25.8970 + 11.5301i −1.50523 + 0.670172i
\(297\) −8.18876 + 0.492969i −0.475160 + 0.0286049i
\(298\) 19.2031 + 4.08174i 1.11240 + 0.236449i
\(299\) −2.85463 + 6.41160i −0.165087 + 0.370792i
\(300\) −6.54429 + 6.57827i −0.377835 + 0.379797i
\(301\) 9.11931 + 0.958478i 0.525628 + 0.0552458i
\(302\) −9.77166 7.09953i −0.562296 0.408532i
\(303\) 15.4364 0.849072i 0.886796 0.0487779i
\(304\) −2.63339 + 4.56116i −0.151035 + 0.261601i
\(305\) 9.15065 + 15.8494i 0.523965 + 0.907534i
\(306\) −7.30116 12.4961i −0.417379 0.714353i
\(307\) −12.5264 13.9120i −0.714919 0.793998i 0.270757 0.962648i \(-0.412726\pi\)
−0.985676 + 0.168650i \(0.946059\pi\)
\(308\) 0.331074 + 1.01894i 0.0188647 + 0.0580595i
\(309\) −23.8317 1.18709i −1.35574 0.0675314i
\(310\) −12.9783 21.2756i −0.737119 1.20837i
\(311\) 23.1382i 1.31205i −0.754740 0.656024i \(-0.772237\pi\)
0.754740 0.656024i \(-0.227763\pi\)
\(312\) 7.50493 + 27.7215i 0.424883 + 1.56942i
\(313\) −2.87354 + 2.58735i −0.162422 + 0.146245i −0.746334 0.665571i \(-0.768188\pi\)
0.583912 + 0.811817i \(0.301521\pi\)
\(314\) −9.02981 12.4285i −0.509582 0.701379i
\(315\) −11.9359 + 5.38845i −0.672513 + 0.303605i
\(316\) −2.31102 1.33427i −0.130005 0.0750583i
\(317\) 16.1318 1.69553i 0.906055 0.0952302i 0.359974 0.932963i \(-0.382786\pi\)
0.546081 + 0.837732i \(0.316119\pi\)
\(318\) 11.4634 14.2313i 0.642835 0.798052i
\(319\) 0.152483 1.45078i 0.00853743 0.0812282i
\(320\) 24.5263 + 22.0836i 1.37106 + 1.23451i
\(321\) −9.83112 + 19.4188i −0.548720 + 1.08385i
\(322\) −0.373446 + 1.75693i −0.0208113 + 0.0979096i
\(323\) 8.39753 1.78495i 0.467251 0.0993172i
\(324\) 5.13788 1.14783i 0.285438 0.0637686i
\(325\) 46.9689 + 15.2611i 2.60537 + 0.846535i
\(326\) 14.7864 + 4.80440i 0.818945 + 0.266091i
\(327\) 16.3190 6.31282i 0.902445 0.349100i
\(328\) −11.1086 + 2.36121i −0.613371 + 0.130376i
\(329\) 1.82436 8.58294i 0.100580 0.473193i
\(330\) 10.9202 + 5.52855i 0.601137 + 0.304336i
\(331\) −6.97956 6.28442i −0.383631 0.345423i 0.454641 0.890675i \(-0.349767\pi\)
−0.838272 + 0.545252i \(0.816434\pi\)
\(332\) −0.314079 + 2.98826i −0.0172373 + 0.164002i
\(333\) 18.3993 20.6486i 1.00828 1.13153i
\(334\) 16.9022 1.77649i 0.924845 0.0972051i
\(335\) −12.2426 7.06827i −0.668885 0.386181i
\(336\) 2.28113 + 4.44846i 0.124446 + 0.242683i
\(337\) −6.47827 8.91658i −0.352894 0.485717i 0.595258 0.803535i \(-0.297050\pi\)
−0.948152 + 0.317818i \(0.897050\pi\)
\(338\) 14.2125 12.7970i 0.773060 0.696066i
\(339\) 10.2490 2.77469i 0.556651 0.150700i
\(340\) 8.92624i 0.484094i
\(341\) 5.72240 6.67257i 0.309885 0.361340i
\(342\) 0.750753 7.51722i 0.0405961 0.406485i
\(343\) −4.53646 13.9618i −0.244946 0.753866i
\(344\) 16.2627 + 18.0616i 0.876827 + 0.973815i
\(345\) −4.63837 7.10213i −0.249721 0.382366i
\(346\) 3.22750 + 5.59019i 0.173511 + 0.300530i
\(347\) 12.1402 21.0275i 0.651722 1.12882i −0.330983 0.943637i \(-0.607380\pi\)
0.982705 0.185179i \(-0.0592865\pi\)
\(348\) 0.0514147 + 0.934734i 0.00275612 + 0.0501070i
\(349\) 14.6202 + 10.6222i 0.782602 + 0.568594i 0.905759 0.423793i \(-0.139302\pi\)
−0.123156 + 0.992387i \(0.539302\pi\)
\(350\) 12.5699 + 1.32115i 0.671888 + 0.0706183i
\(351\) −17.8018 21.6375i −0.950189 1.15493i
\(352\) −2.04867 + 4.60140i −0.109195 + 0.245255i
\(353\) −19.9436 4.23914i −1.06149 0.225627i −0.356102 0.934447i \(-0.615894\pi\)
−0.705389 + 0.708820i \(0.749228\pi\)
\(354\) −21.2063 + 3.41506i −1.12710 + 0.181508i
\(355\) 27.2972 12.1535i 1.44879 0.645041i
\(356\) 0.450380 1.38613i 0.0238701 0.0734646i
\(357\) 2.90064 7.61531i 0.153518 0.403045i
\(358\) 0.289666 + 0.650600i 0.0153093 + 0.0343853i
\(359\) −2.68755 12.6439i −0.141843 0.667321i −0.990402 0.138219i \(-0.955862\pi\)
0.848558 0.529102i \(-0.177471\pi\)
\(360\) −33.0674 10.5552i −1.74280 0.556309i
\(361\) −13.2634 5.90526i −0.698075 0.310803i
\(362\) −2.57798 + 2.86314i −0.135496 + 0.150483i
\(363\) 2.26742 14.5598i 0.119009 0.764194i
\(364\) −2.15088 + 2.96043i −0.112737 + 0.155169i
\(365\) 0.865338 + 8.23314i 0.0452939 + 0.430942i
\(366\) −5.43615 + 8.41858i −0.284152 + 0.440046i
\(367\) 25.2920 14.6023i 1.32023 0.762236i 0.336466 0.941695i \(-0.390768\pi\)
0.983765 + 0.179459i \(0.0574348\pi\)
\(368\) −2.61973 + 1.90335i −0.136563 + 0.0992188i
\(369\) 8.93005 6.55898i 0.464880 0.341447i
\(370\) −39.2449 + 12.7514i −2.04024 + 0.662915i
\(371\) 10.2894 0.534199
\(372\) −2.94475 + 4.81142i −0.152678 + 0.249460i
\(373\) −26.5286 −1.37360 −0.686800 0.726847i \(-0.740985\pi\)
−0.686800 + 0.726847i \(0.740985\pi\)
\(374\) −7.24363 + 2.35360i −0.374559 + 0.121702i
\(375\) −21.0186 + 17.1108i −1.08539 + 0.883598i
\(376\) 18.8159 13.6705i 0.970354 0.705004i
\(377\) 4.31493 2.49122i 0.222230 0.128305i
\(378\) −5.60769 4.46934i −0.288429 0.229878i
\(379\) −0.781797 7.43830i −0.0401582 0.382080i −0.996080 0.0884581i \(-0.971806\pi\)
0.955922 0.293622i \(-0.0948606\pi\)
\(380\) 2.73874 3.76955i 0.140494 0.193374i
\(381\) 30.2259 + 4.70712i 1.54852 + 0.241153i
\(382\) 1.67848 1.86414i 0.0858784 0.0953776i
\(383\) −4.60563 2.05056i −0.235336 0.104779i 0.285680 0.958325i \(-0.407780\pi\)
−0.521017 + 0.853546i \(0.674447\pi\)
\(384\) −1.79931 + 6.78535i −0.0918206 + 0.346263i
\(385\) 1.43289 + 6.74123i 0.0730270 + 0.343565i
\(386\) 1.75598 + 3.94399i 0.0893769 + 0.200744i
\(387\) −21.7115 9.53217i −1.10366 0.484547i
\(388\) −1.93270 + 5.94824i −0.0981181 + 0.301976i
\(389\) −9.56419 + 4.25825i −0.484924 + 0.215902i −0.634612 0.772831i \(-0.718840\pi\)
0.149688 + 0.988733i \(0.452173\pi\)
\(390\) 6.64671 + 41.2737i 0.336569 + 2.08998i
\(391\) 5.16304 + 1.09744i 0.261106 + 0.0554999i
\(392\) 7.07158 15.8830i 0.357169 0.802214i
\(393\) −3.31649 3.29936i −0.167295 0.166431i
\(394\) −2.83710 0.298191i −0.142931 0.0150226i
\(395\) −13.8874 10.0898i −0.698753 0.507674i
\(396\) −0.0143478 2.77048i −0.000721006 0.139222i
\(397\) 7.43511 12.8780i 0.373157 0.646328i −0.616892 0.787048i \(-0.711608\pi\)
0.990049 + 0.140720i \(0.0449418\pi\)
\(398\) −5.74124 9.94411i −0.287782 0.498453i
\(399\) 3.56146 2.32597i 0.178296 0.116444i
\(400\) 15.2468 + 16.9333i 0.762339 + 0.846663i
\(401\) 10.9221 + 33.6149i 0.545426 + 1.67865i 0.719976 + 0.693999i \(0.244153\pi\)
−0.174550 + 0.984648i \(0.555847\pi\)
\(402\) 0.385100 7.73112i 0.0192070 0.385593i
\(403\) 29.9258 + 2.41641i 1.49071 + 0.120370i
\(404\) 5.22105i 0.259757i
\(405\) 33.6411 3.88851i 1.67164 0.193221i
\(406\) 0.947609 0.853231i 0.0470290 0.0423451i
\(407\) −8.55502 11.7750i −0.424057 0.583664i
\(408\) 19.2197 9.85570i 0.951517 0.487930i
\(409\) −5.95500 3.43812i −0.294456 0.170004i 0.345494 0.938421i \(-0.387711\pi\)
−0.639950 + 0.768417i \(0.721045\pi\)
\(410\) −16.4410 + 1.72802i −0.811963 + 0.0853407i
\(411\) −2.02183 1.62859i −0.0997294 0.0803326i
\(412\) 0.842333 8.01426i 0.0414988 0.394834i
\(413\) −8.98781 8.09266i −0.442261 0.398214i
\(414\) 2.30154 4.03449i 0.113114 0.198284i
\(415\) −4.01861 + 18.9061i −0.197266 + 0.928062i
\(416\) −16.8275 + 3.57679i −0.825035 + 0.175367i
\(417\) 6.30396 + 16.2961i 0.308706 + 0.798025i
\(418\) −3.78111 1.22856i −0.184940 0.0600907i
\(419\) −27.2477 8.85330i −1.33113 0.432512i −0.444830 0.895615i \(-0.646736\pi\)
−0.886305 + 0.463103i \(0.846736\pi\)
\(420\) −1.59565 4.12486i −0.0778598 0.201273i
\(421\) 7.34131 1.56044i 0.357793 0.0760513i −0.0255081 0.999675i \(-0.508120\pi\)
0.383302 + 0.923623i \(0.374787\pi\)
\(422\) 1.06573 5.01387i 0.0518790 0.244072i
\(423\) −11.2435 + 19.7093i −0.546677 + 0.958299i
\(424\) 20.2674 + 18.2489i 0.984273 + 0.886243i
\(425\) 3.88243 36.9389i 0.188326 1.79180i
\(426\) 12.7420 + 10.2637i 0.617350 + 0.497279i
\(427\) −5.61164 + 0.589808i −0.271566 + 0.0285428i
\(428\) −6.36587 3.67534i −0.307706 0.177654i
\(429\) −13.1209 + 6.72831i −0.633485 + 0.324846i
\(430\) 20.7950 + 28.6219i 1.00282 + 1.38027i
\(431\) −28.3644 + 25.5394i −1.36627 + 1.23019i −0.419706 + 0.907660i \(0.637867\pi\)
−0.946559 + 0.322531i \(0.895466\pi\)
\(432\) −2.12147 12.7525i −0.102069 0.613553i
\(433\) 12.8928i 0.619589i 0.950804 + 0.309794i \(0.100260\pi\)
−0.950804 + 0.309794i \(0.899740\pi\)
\(434\) 7.61998 0.987443i 0.365771 0.0473988i
\(435\) −0.299591 + 6.01448i −0.0143643 + 0.288372i
\(436\) 1.82606 + 5.62004i 0.0874525 + 0.269151i
\(437\) 1.84364 + 2.04757i 0.0881931 + 0.0979484i
\(438\) −3.79531 + 2.47870i −0.181347 + 0.118437i
\(439\) −6.69314 11.5929i −0.319446 0.553297i 0.660926 0.750451i \(-0.270164\pi\)
−0.980373 + 0.197154i \(0.936830\pi\)
\(440\) −9.13355 + 15.8198i −0.435425 + 0.754178i
\(441\) 0.0878441 + 16.9621i 0.00418305 + 0.807721i
\(442\) −21.0457 15.2906i −1.00104 0.727298i
\(443\) 36.1618 + 3.80076i 1.71810 + 0.180580i 0.911719 0.410815i \(-0.134756\pi\)
0.806382 + 0.591395i \(0.201422\pi\)
\(444\) 6.62164 + 6.58743i 0.314249 + 0.312626i
\(445\) 3.81331 8.56484i 0.180768 0.406013i
\(446\) −7.92847 1.68525i −0.375424 0.0797988i
\(447\) −4.54479 28.2215i −0.214961 1.33483i
\(448\) −9.29569 + 4.13871i −0.439180 + 0.195536i
\(449\) −0.663659 + 2.04253i −0.0313200 + 0.0963931i −0.965495 0.260423i \(-0.916138\pi\)
0.934175 + 0.356816i \(0.116138\pi\)
\(450\) −29.9267 13.1390i −1.41076 0.619377i
\(451\) −2.37166 5.32684i −0.111677 0.250831i
\(452\) 0.745552 + 3.50754i 0.0350678 + 0.164981i
\(453\) −4.50778 + 16.9992i −0.211794 + 0.798692i
\(454\) −5.92737 2.63903i −0.278185 0.123856i
\(455\) −15.7507 + 17.4929i −0.738405 + 0.820082i
\(456\) 11.1404 + 1.73491i 0.521697 + 0.0812444i
\(457\) −22.6609 + 31.1900i −1.06003 + 1.45901i −0.180254 + 0.983620i \(0.557692\pi\)
−0.879777 + 0.475387i \(0.842308\pi\)
\(458\) 2.52802 + 24.0525i 0.118127 + 1.12390i
\(459\) −13.1340 + 16.4792i −0.613041 + 0.769184i
\(460\) 2.48094 1.43237i 0.115675 0.0667848i
\(461\) −4.48062 + 3.25536i −0.208683 + 0.151617i −0.687218 0.726451i \(-0.741168\pi\)
0.478534 + 0.878069i \(0.341168\pi\)
\(462\) −2.92659 + 2.38248i −0.136157 + 0.110843i
\(463\) 30.0642 9.76847i 1.39720 0.453979i 0.488918 0.872330i \(-0.337392\pi\)
0.908286 + 0.418350i \(0.137392\pi\)
\(464\) 2.29883 0.106720
\(465\) −22.0741 + 28.8007i −1.02366 + 1.33560i
\(466\) −10.9673 −0.508051
\(467\) 13.6624 4.43919i 0.632222 0.205421i 0.0246628 0.999696i \(-0.492149\pi\)
0.607559 + 0.794274i \(0.292149\pi\)
\(468\) 7.62658 5.60161i 0.352539 0.258934i
\(469\) 3.52610 2.56186i 0.162820 0.118296i
\(470\) 29.3194 16.9276i 1.35240 0.780810i
\(471\) −12.1341 + 18.7912i −0.559109 + 0.865852i
\(472\) −3.35081 31.8808i −0.154234 1.46743i
\(473\) −7.33474 + 10.0954i −0.337252 + 0.464187i
\(474\) 1.44635 9.28749i 0.0664331 0.426588i
\(475\) 12.9731 14.4081i 0.595246 0.661088i
\(476\) 2.51416 + 1.11938i 0.115236 + 0.0513065i
\(477\) −25.3477 8.09109i −1.16059 0.370465i
\(478\) 1.08468 + 5.10301i 0.0496120 + 0.233406i
\(479\) 4.68489 + 10.5224i 0.214058 + 0.480783i 0.988379 0.152011i \(-0.0485749\pi\)
−0.774321 + 0.632794i \(0.781908\pi\)
\(480\) 7.40110 19.4308i 0.337812 0.886889i
\(481\) 15.3617 47.2785i 0.700434 2.15571i
\(482\) −11.0373 + 4.91412i −0.502735 + 0.223832i
\(483\) 2.58204 0.415812i 0.117487 0.0189201i
\(484\) 4.86767 + 1.03466i 0.221258 + 0.0470298i
\(485\) −16.3639 + 36.7540i −0.743049 + 1.66891i
\(486\) 10.3000 + 15.4197i 0.467215 + 0.699454i
\(487\) 6.00968 + 0.631643i 0.272325 + 0.0286225i 0.239706 0.970845i \(-0.422949\pi\)
0.0326182 + 0.999468i \(0.489615\pi\)
\(488\) −12.0995 8.79082i −0.547720 0.397942i
\(489\) −1.24330 22.6035i −0.0562238 1.02217i
\(490\) 12.6541 21.9175i 0.571653 0.990133i
\(491\) 19.6959 + 34.1143i 0.888864 + 1.53956i 0.841220 + 0.540693i \(0.181838\pi\)
0.0476440 + 0.998864i \(0.484829\pi\)
\(492\) 2.04612 + 3.13296i 0.0922462 + 0.141245i
\(493\) −2.50737 2.78472i −0.112926 0.125417i
\(494\) −4.19614 12.9144i −0.188793 0.581047i
\(495\) 1.77108 17.7336i 0.0796039 0.797067i
\(496\) 11.4000 + 7.86919i 0.511877 + 0.353337i
\(497\) 9.21259i 0.413241i
\(498\) −10.2159 + 2.76570i −0.457783 + 0.123934i
\(499\) −1.64665 + 1.48265i −0.0737142 + 0.0663726i −0.705164 0.709044i \(-0.749127\pi\)
0.631450 + 0.775417i \(0.282460\pi\)
\(500\) −5.38008 7.40505i −0.240605 0.331164i
\(501\) −11.2914 22.0195i −0.504464 0.983760i
\(502\) 4.44798 + 2.56804i 0.198523 + 0.114617i
\(503\) 32.0705 3.37075i 1.42995 0.150294i 0.642320 0.766437i \(-0.277972\pi\)
0.787635 + 0.616143i \(0.211306\pi\)
\(504\) 7.11971 7.99007i 0.317137 0.355906i
\(505\) −3.51063 + 33.4014i −0.156221 + 1.48634i
\(506\) −1.81652 1.63560i −0.0807543 0.0727115i
\(507\) −24.8442 12.5778i −1.10337 0.558600i
\(508\) −2.14792 + 10.1052i −0.0952987 + 0.448345i
\(509\) 5.32357 1.13156i 0.235963 0.0501555i −0.0884121 0.996084i \(-0.528179\pi\)
0.324375 + 0.945928i \(0.394846\pi\)
\(510\) 29.3236 11.3435i 1.29847 0.502297i
\(511\) −2.42745 0.788728i −0.107384 0.0348913i
\(512\) −22.1006 7.18093i −0.976719 0.317355i
\(513\) −10.6026 + 2.92942i −0.468117 + 0.129337i
\(514\) 32.1410 6.83178i 1.41768 0.301337i
\(515\) 10.7776 50.7044i 0.474916 2.23430i
\(516\) 3.61705 7.14454i 0.159232 0.314521i
\(517\) 8.87409 + 7.99027i 0.390282 + 0.351412i
\(518\) 1.32986 12.6527i 0.0584305 0.555929i
\(519\) 5.89589 7.31949i 0.258801 0.321290i
\(520\) −62.0496 + 6.52167i −2.72105 + 0.285994i
\(521\) 15.7757 + 9.10813i 0.691148 + 0.399034i 0.804042 0.594573i \(-0.202679\pi\)
−0.112894 + 0.993607i \(0.536012\pi\)
\(522\) −3.00535 + 1.35676i −0.131541 + 0.0593838i
\(523\) 20.8880 + 28.7498i 0.913368 + 1.25714i 0.966003 + 0.258529i \(0.0832378\pi\)
−0.0526358 + 0.998614i \(0.516762\pi\)
\(524\) 1.17409 1.05716i 0.0512905 0.0461822i
\(525\) −4.80909 17.7636i −0.209886 0.775269i
\(526\) 22.4573i 0.979186i
\(527\) −2.90178 22.3927i −0.126404 0.975441i
\(528\) −6.79492 0.338466i −0.295711 0.0147298i
\(529\) −6.58391 20.2632i −0.286257 0.881008i
\(530\) 26.5640 + 29.5023i 1.15387 + 1.28150i
\(531\) 15.7776 + 27.0037i 0.684690 + 1.17186i
\(532\) 0.718283 + 1.24410i 0.0311415 + 0.0539387i
\(533\) 9.95782 17.2475i 0.431321 0.747070i
\(534\) 5.12590 0.281949i 0.221820 0.0122011i
\(535\) −38.2540 27.7932i −1.65387 1.20160i
\(536\) 11.4891 + 1.20755i 0.496254 + 0.0521584i
\(537\) 0.731334 0.735132i 0.0315594 0.0317233i
\(538\) −13.3850 + 30.0632i −0.577069 + 1.29612i
\(539\) 8.73155 + 1.85595i 0.376094 + 0.0799413i
\(540\) 0.687265 + 11.4162i 0.0295752 + 0.491277i
\(541\) −24.1718 + 10.7620i −1.03923 + 0.462694i −0.854148 0.520030i \(-0.825921\pi\)
−0.185079 + 0.982724i \(0.559254\pi\)
\(542\) 1.77970 5.47736i 0.0764447 0.235273i
\(543\) 5.24234 + 1.99679i 0.224970 + 0.0856904i
\(544\) 5.26251 + 11.8198i 0.225628 + 0.506769i
\(545\) 7.90322 + 37.1817i 0.338537 + 1.59269i
\(546\) −12.4586 3.30373i −0.533180 0.141386i
\(547\) 16.1841 + 7.20564i 0.691984 + 0.308091i 0.722429 0.691445i \(-0.243026\pi\)
−0.0304449 + 0.999536i \(0.509692\pi\)
\(548\) 0.586679 0.651573i 0.0250617 0.0278338i
\(549\) 14.2880 + 2.95975i 0.609795 + 0.126319i
\(550\) −10.1101 + 13.9153i −0.431095 + 0.593351i
\(551\) −0.204459 1.94530i −0.00871024 0.0828724i
\(552\) 5.82342 + 3.76037i 0.247861 + 0.160052i
\(553\) 4.58341 2.64623i 0.194906 0.112529i
\(554\) 27.0446 19.6491i 1.14902 0.834810i
\(555\) 37.9322 + 46.5951i 1.61013 + 1.97785i
\(556\) −5.61215 + 1.82350i −0.238008 + 0.0773335i
\(557\) −41.1621 −1.74410 −0.872048 0.489421i \(-0.837208\pi\)
−0.872048 + 0.489421i \(0.837208\pi\)
\(558\) −19.5481 3.55944i −0.827539 0.150683i
\(559\) −42.6207 −1.80267
\(560\) −10.3290 + 3.35610i −0.436481 + 0.141821i
\(561\) 7.00134 + 8.60030i 0.295597 + 0.363105i
\(562\) 3.34007 2.42670i 0.140892 0.102364i
\(563\) −12.5443 + 7.24244i −0.528678 + 0.305232i −0.740478 0.672081i \(-0.765401\pi\)
0.211800 + 0.977313i \(0.432067\pi\)
\(564\) −6.43763 4.15699i −0.271073 0.175041i
\(565\) 2.41116 + 22.9406i 0.101438 + 0.965120i
\(566\) 16.1511 22.2301i 0.678883 0.934402i
\(567\) −3.12345 + 9.96295i −0.131173 + 0.418405i
\(568\) −16.3391 + 18.1464i −0.685572 + 0.761405i
\(569\) −23.1127 10.2904i −0.968933 0.431397i −0.139635 0.990203i \(-0.544593\pi\)
−0.829298 + 0.558806i \(0.811259\pi\)
\(570\) 15.8637 + 4.20668i 0.664458 + 0.176198i
\(571\) −0.416666 1.96026i −0.0174369 0.0820343i 0.968569 0.248746i \(-0.0800184\pi\)
−0.986006 + 0.166712i \(0.946685\pi\)
\(572\) −2.02549 4.54931i −0.0846898 0.190216i
\(573\) −3.41319 1.30007i −0.142588 0.0543113i
\(574\) 1.57503 4.84745i 0.0657406 0.202329i
\(575\) 10.8897 4.84842i 0.454133 0.202193i
\(576\) 26.1542 2.88594i 1.08976 0.120247i
\(577\) −21.9391 4.66330i −0.913337 0.194136i −0.272807 0.962069i \(-0.587952\pi\)
−0.640530 + 0.767933i \(0.721285\pi\)
\(578\) 0.267617 0.601079i 0.0111314 0.0250016i
\(579\) 4.43341 4.45643i 0.184246 0.185203i
\(580\) −2.02259 0.212583i −0.0839834 0.00882701i
\(581\) −4.82112 3.50275i −0.200014 0.145318i
\(582\) −21.9966 + 1.20992i −0.911789 + 0.0501526i
\(583\) −7.00130 + 12.1266i −0.289964 + 0.502233i
\(584\) −3.38259 5.85882i −0.139973 0.242440i
\(585\) 52.5572 30.7079i 2.17297 1.26962i
\(586\) −9.21926 10.2390i −0.380844 0.422970i
\(587\) −4.48610 13.8068i −0.185161 0.569867i 0.814790 0.579756i \(-0.196852\pi\)
−0.999951 + 0.00988889i \(0.996852\pi\)
\(588\) −5.72143 0.284994i −0.235948 0.0117529i
\(589\) 5.64508 10.3468i 0.232602 0.426331i
\(590\) 46.6631i 1.92109i
\(591\) 1.08544 + 4.00936i 0.0446490 + 0.164923i
\(592\) 17.0449 15.3473i 0.700540 0.630769i
\(593\) −7.22644 9.94634i −0.296754 0.408447i 0.634439 0.772973i \(-0.281231\pi\)
−0.931193 + 0.364526i \(0.881231\pi\)
\(594\) 9.08305 3.56785i 0.372682 0.146391i
\(595\) 15.3315 + 8.85166i 0.628531 + 0.362883i
\(596\) 9.60089 1.00909i 0.393268 0.0413341i
\(597\) −10.4879 + 13.0203i −0.429242 + 0.532885i
\(598\) 0.872684 8.30303i 0.0356867 0.339536i
\(599\) 1.16949 + 1.05302i 0.0477843 + 0.0430251i 0.692677 0.721248i \(-0.256431\pi\)
−0.644893 + 0.764273i \(0.723098\pi\)
\(600\) 22.0322 43.5189i 0.899462 1.77665i
\(601\) 6.58757 30.9921i 0.268713 1.26419i −0.612120 0.790765i \(-0.709683\pi\)
0.880832 0.473428i \(-0.156984\pi\)
\(602\) −10.6694 + 2.26784i −0.434850 + 0.0924303i
\(603\) −10.7010 + 3.53834i −0.435778 + 0.144092i
\(604\) −5.64870 1.83537i −0.229842 0.0746802i
\(605\) 30.4450 + 9.89217i 1.23776 + 0.402174i
\(606\) −17.1516 + 6.63490i −0.696737 + 0.269524i
\(607\) 6.49501 1.38056i 0.263624 0.0560350i −0.0742032 0.997243i \(-0.523641\pi\)
0.337827 + 0.941208i \(0.390308\pi\)
\(608\) −1.40418 + 6.60614i −0.0569469 + 0.267914i
\(609\) −1.65646 0.838615i −0.0671233 0.0339824i
\(610\) −16.1786 14.5673i −0.655054 0.589813i
\(611\) −4.26324 + 40.5620i −0.172472 + 1.64096i
\(612\) −5.31335 4.73457i −0.214779 0.191384i
\(613\) 29.1975 3.06878i 1.17928 0.123947i 0.505463 0.862848i \(-0.331322\pi\)
0.673814 + 0.738901i \(0.264655\pi\)
\(614\) 19.2855 + 11.1345i 0.778301 + 0.449353i
\(615\) 10.9833 + 21.4187i 0.442891 + 0.863687i
\(616\) −3.31041 4.55639i −0.133380 0.183582i
\(617\) 17.0541 15.3556i 0.686571 0.618192i −0.250175 0.968201i \(-0.580488\pi\)
0.936746 + 0.350009i \(0.113822\pi\)
\(618\) 27.3980 7.41737i 1.10211 0.298371i
\(619\) 0.513624i 0.0206443i 0.999947 + 0.0103221i \(0.00328570\pi\)
−0.999947 + 0.0103221i \(0.996714\pi\)
\(620\) −9.30247 7.97780i −0.373596 0.320396i
\(621\) −6.68778 1.00605i −0.268372 0.0403714i
\(622\) 8.50547 + 26.1772i 0.341038 + 1.04961i
\(623\) 1.93417 + 2.14811i 0.0774907 + 0.0860622i
\(624\) −12.7061 19.4552i −0.508652 0.778832i
\(625\) −6.54324 11.3332i −0.261730 0.453329i
\(626\) 2.29985 3.98346i 0.0919206 0.159211i
\(627\) 0.317930 + 5.78005i 0.0126969 + 0.230833i
\(628\) −6.11151 4.44027i −0.243876 0.177186i
\(629\) −37.1824 3.90802i −1.48256 0.155823i
\(630\) 11.5228 10.4837i 0.459079 0.417682i
\(631\) 4.98255 11.1910i 0.198352 0.445506i −0.786796 0.617213i \(-0.788262\pi\)
0.985148 + 0.171707i \(0.0549282\pi\)
\(632\) 13.7214 + 2.91657i 0.545807 + 0.116015i
\(633\) −7.36858 + 1.18664i −0.292875 + 0.0471645i
\(634\) −17.6273 + 7.84818i −0.700070 + 0.311691i
\(635\) −20.5359 + 63.2031i −0.814944 + 2.50814i
\(636\) 3.19855 8.39743i 0.126831 0.332980i
\(637\) 12.4010 + 27.8530i 0.491344 + 1.10358i
\(638\) 0.360789 + 1.69738i 0.0142838 + 0.0671998i
\(639\) 7.24433 22.6950i 0.286581 0.897801i
\(640\) −13.9318 6.20284i −0.550703 0.245189i
\(641\) −4.94245 + 5.48915i −0.195215 + 0.216808i −0.832803 0.553569i \(-0.813266\pi\)
0.637588 + 0.770377i \(0.279932\pi\)
\(642\) 3.98409 25.5831i 0.157239 1.00968i
\(643\) 0.593177 0.816439i 0.0233926 0.0321972i −0.797160 0.603767i \(-0.793666\pi\)
0.820553 + 0.571570i \(0.193666\pi\)
\(644\) 0.0923240 + 0.878404i 0.00363807 + 0.0346140i
\(645\) 27.9439 43.2747i 1.10029 1.70394i
\(646\) −8.84431 + 5.10626i −0.347975 + 0.200903i
\(647\) 22.3539 16.2410i 0.878821 0.638501i −0.0541185 0.998535i \(-0.517235\pi\)
0.932939 + 0.360034i \(0.117235\pi\)
\(648\) −23.8223 + 14.0848i −0.935827 + 0.553302i
\(649\) 15.6533 5.08606i 0.614445 0.199645i
\(650\) −58.7476 −2.30427
\(651\) −5.34384 9.82905i −0.209442 0.385231i
\(652\) 7.64519 0.299409
\(653\) 28.5427 9.27408i 1.11696 0.362923i 0.308354 0.951272i \(-0.400222\pi\)
0.808607 + 0.588349i \(0.200222\pi\)
\(654\) −16.1418 + 13.1407i −0.631194 + 0.513843i
\(655\) 8.22203 5.97366i 0.321261 0.233410i
\(656\) 7.95771 4.59439i 0.310696 0.179381i
\(657\) 5.35976 + 3.85185i 0.209104 + 0.150275i
\(658\) 1.09107 + 10.3808i 0.0425343 + 0.404687i
\(659\) −12.5455 + 17.2674i −0.488702 + 0.672641i −0.980148 0.198267i \(-0.936469\pi\)
0.491446 + 0.870908i \(0.336469\pi\)
\(660\) 5.94711 + 0.926150i 0.231491 + 0.0360503i
\(661\) −13.8296 + 15.3593i −0.537908 + 0.597407i −0.949425 0.313995i \(-0.898332\pi\)
0.411517 + 0.911402i \(0.364999\pi\)
\(662\) 10.2064 + 4.54416i 0.396681 + 0.176614i
\(663\) −9.70860 + 36.6119i −0.377051 + 1.42189i
\(664\) −3.28400 15.4500i −0.127444 0.599577i
\(665\) 3.75865 + 8.44206i 0.145754 + 0.327369i
\(666\) −13.2256 + 30.1240i −0.512480 + 1.16728i
\(667\) 0.371628 1.14375i 0.0143895 0.0442863i
\(668\) 7.63465 3.39916i 0.295393 0.131518i
\(669\) 1.87643 + 11.6520i 0.0725471 + 0.450491i
\(670\) 16.4488 + 3.49630i 0.635472 + 0.135074i
\(671\) 3.12326 7.01495i 0.120572 0.270809i
\(672\) 4.54473 + 4.52126i 0.175317 + 0.174411i
\(673\) −22.5759 2.37283i −0.870238 0.0914657i −0.341126 0.940018i \(-0.610808\pi\)
−0.529112 + 0.848552i \(0.677475\pi\)
\(674\) 10.6068 + 7.70629i 0.408559 + 0.296835i
\(675\) −2.12138 + 47.5420i −0.0816521 + 1.82989i
\(676\) 4.70218 8.14441i 0.180853 0.313247i
\(677\) −11.1447 19.3032i −0.428325 0.741881i 0.568399 0.822753i \(-0.307563\pi\)
−0.996725 + 0.0808716i \(0.974230\pi\)
\(678\) −10.5752 + 6.90659i −0.406137 + 0.265246i
\(679\) −8.30002 9.21811i −0.318526 0.353759i
\(680\) 14.5001 + 44.6268i 0.556055 + 1.71136i
\(681\) −0.470001 + 9.43557i −0.0180105 + 0.361572i
\(682\) −4.02117 + 9.65245i −0.153979 + 0.369611i
\(683\) 10.0595i 0.384917i −0.981305 0.192459i \(-0.938354\pi\)
0.981305 0.192459i \(-0.0616461\pi\)
\(684\) −0.791173 3.62964i −0.0302512 0.138783i
\(685\) 4.19137 3.77392i 0.160144 0.144194i
\(686\) 10.2646 + 14.1279i 0.391902 + 0.539407i
\(687\) 31.3348 16.0682i 1.19550 0.613041i
\(688\) −17.0300 9.83228i −0.649263 0.374852i
\(689\) −47.5640 + 4.99917i −1.81204 + 0.190453i
\(690\) 7.85827 + 6.32988i 0.299159 + 0.240974i
\(691\) −3.88931 + 37.0043i −0.147956 + 1.40771i 0.628632 + 0.777703i \(0.283615\pi\)
−0.776588 + 0.630008i \(0.783051\pi\)
\(692\) 2.35885 + 2.12392i 0.0896700 + 0.0807392i
\(693\) 4.77274 + 2.72268i 0.181301 + 0.103426i
\(694\) −6.00513 + 28.2519i −0.227952 + 1.07243i
\(695\) −37.1295 + 7.89213i −1.40840 + 0.299365i
\(696\) −1.77547 4.58969i −0.0672988 0.173972i
\(697\) −14.2451 4.62852i −0.539572 0.175318i
\(698\) −20.4451 6.64301i −0.773858 0.251442i
\(699\) 5.76132 + 14.8934i 0.217913 + 0.563319i
\(700\) 6.07928 1.29219i 0.229775 0.0488402i
\(701\) 6.84460 32.2013i 0.258517 1.21623i −0.636882 0.770961i \(-0.719776\pi\)
0.895399 0.445265i \(-0.146891\pi\)
\(702\) 28.0937 + 17.9355i 1.06033 + 0.676933i
\(703\) −14.5031 13.0586i −0.546993 0.492515i
\(704\) 1.44745 13.7716i 0.0545530 0.519037i
\(705\) −38.3893 30.9228i −1.44582 1.16462i
\(706\) 24.1213 2.53525i 0.907815 0.0954152i
\(707\) −8.96756 5.17742i −0.337260 0.194717i
\(708\) −9.39856 + 4.81950i −0.353220 + 0.181128i
\(709\) −10.5187 14.4777i −0.395038 0.543723i 0.564452 0.825466i \(-0.309088\pi\)
−0.959490 + 0.281743i \(0.909088\pi\)
\(710\) −26.4148 + 23.7840i −0.991330 + 0.892598i
\(711\) −13.3720 + 2.91477i −0.501489 + 0.109312i
\(712\) 7.66157i 0.287129i
\(713\) 5.75815 4.39982i 0.215644 0.164775i
\(714\) −0.482264 + 9.68175i −0.0180483 + 0.362330i
\(715\) −9.89898 30.4659i −0.370201 1.13936i
\(716\) 0.234329 + 0.260249i 0.00875728 + 0.00972595i
\(717\) 6.35997 4.15367i 0.237517 0.155122i
\(718\) 7.68836 + 13.3166i 0.286927 + 0.496972i
\(719\) 3.67007 6.35676i 0.136871 0.237067i −0.789440 0.613828i \(-0.789629\pi\)
0.926311 + 0.376761i \(0.122962\pi\)
\(720\) 28.0844 0.145444i 1.04664 0.00542039i
\(721\) 12.9298 + 9.39407i 0.481532 + 0.349853i
\(722\) 17.1762 + 1.80529i 0.639231 + 0.0671859i
\(723\) 12.4713 + 12.4069i 0.463814 + 0.461419i
\(724\) −0.770573 + 1.73073i −0.0286381 + 0.0643222i
\(725\) −8.27748 1.75943i −0.307418 0.0653437i
\(726\) 2.78689 + 17.3056i 0.103431 + 0.642271i
\(727\) 26.7877 11.9267i 0.993501 0.442335i 0.155401 0.987852i \(-0.450333\pi\)
0.838100 + 0.545517i \(0.183666\pi\)
\(728\) 5.94429 18.2947i 0.220310 0.678045i
\(729\) 15.5289 22.0874i 0.575146 0.818051i
\(730\) −4.00544 8.99637i −0.148248 0.332971i
\(731\) 6.66446 + 31.3538i 0.246494 + 1.15966i
\(732\) −1.26307 + 4.76315i −0.0466845 + 0.176051i
\(733\) 14.6521 + 6.52354i 0.541188 + 0.240953i 0.659079 0.752074i \(-0.270946\pi\)
−0.117890 + 0.993027i \(0.537613\pi\)
\(734\) −23.2461 + 25.8174i −0.858028 + 0.952937i
\(735\) −36.4109 5.67032i −1.34304 0.209153i
\(736\) −2.44071 + 3.35935i −0.0899657 + 0.123827i
\(737\) 0.619998 + 5.89888i 0.0228379 + 0.217288i
\(738\) −7.69186 + 10.7031i −0.283141 + 0.393985i
\(739\) −5.25564 + 3.03434i −0.193332 + 0.111620i −0.593541 0.804803i \(-0.702271\pi\)
0.400210 + 0.916424i \(0.368937\pi\)
\(740\) −16.4159 + 11.9269i −0.603461 + 0.438440i
\(741\) −15.3332 + 12.4824i −0.563278 + 0.458554i
\(742\) −11.6408 + 3.78232i −0.427347 + 0.138853i
\(743\) 3.35772 0.123183 0.0615914 0.998101i \(-0.480382\pi\)
0.0615914 + 0.998101i \(0.480382\pi\)
\(744\) 6.90645 28.8383i 0.253203 1.05726i
\(745\) 62.0997 2.27516
\(746\) 30.0128 9.75176i 1.09885 0.357037i
\(747\) 9.12233 + 12.4200i 0.333768 + 0.454425i
\(748\) −3.02997 + 2.20140i −0.110787 + 0.0804913i
\(749\) 12.6254 7.28925i 0.461320 0.266344i
\(750\) 17.4893 27.0844i 0.638618 0.988983i
\(751\) 0.333307 + 3.17120i 0.0121625 + 0.115719i 0.998919 0.0464921i \(-0.0148042\pi\)
−0.986756 + 0.162211i \(0.948138\pi\)
\(752\) −11.0608 + 15.2239i −0.403346 + 0.555159i
\(753\) 1.15074 7.38930i 0.0419355 0.269281i
\(754\) −3.96588 + 4.40456i −0.144429 + 0.160405i
\(755\) −34.9031 15.5399i −1.27025 0.565554i
\(756\) −3.30167 1.23805i −0.120081 0.0450276i
\(757\) 0.750979 + 3.53308i 0.0272948 + 0.128412i 0.989685 0.143257i \(-0.0457577\pi\)
−0.962391 + 0.271669i \(0.912424\pi\)
\(758\) 3.61875 + 8.12785i 0.131439 + 0.295217i
\(759\) −1.26686 + 3.32601i −0.0459843 + 0.120727i
\(760\) −7.56894 + 23.2948i −0.274554 + 0.844992i
\(761\) 25.3996 11.3087i 0.920736 0.409938i 0.109053 0.994036i \(-0.465218\pi\)
0.811683 + 0.584098i \(0.198552\pi\)
\(762\) −35.9261 + 5.78553i −1.30146 + 0.209588i
\(763\) −11.4637 2.43668i −0.415012 0.0882136i
\(764\) 0.501706 1.12685i 0.0181511 0.0407680i
\(765\) −30.8084 33.8618i −1.11388 1.22428i
\(766\) 5.96429 + 0.626873i 0.215499 + 0.0226498i
\(767\) 45.4791 + 33.0425i 1.64215 + 1.19310i
\(768\) 1.21009 + 21.9998i 0.0436654 + 0.793849i
\(769\) −21.1761 + 36.6781i −0.763631 + 1.32265i 0.177337 + 0.984150i \(0.443252\pi\)
−0.940968 + 0.338497i \(0.890082\pi\)
\(770\) −4.09912 7.09989i −0.147722 0.255862i
\(771\) −26.1616 40.0579i −0.942189 1.44265i
\(772\) 1.42052 + 1.57765i 0.0511257 + 0.0567808i
\(773\) −9.35080 28.7788i −0.336325 1.03510i −0.966066 0.258296i \(-0.916839\pi\)
0.629741 0.776805i \(-0.283161\pi\)
\(774\) 28.0670 + 2.80308i 1.00885 + 0.100755i
\(775\) −35.0259 37.0601i −1.25817 1.33124i
\(776\) 32.8778i 1.18025i
\(777\) −17.8807 + 4.84079i −0.641468 + 0.173662i
\(778\) 9.25503 8.33327i 0.331809 0.298762i
\(779\) −4.59559 6.32529i −0.164654 0.226627i
\(780\) 9.38018 + 18.2924i 0.335864 + 0.654972i
\(781\) −10.8575 6.26859i −0.388513 0.224308i
\(782\) −6.24456 + 0.656330i −0.223305 + 0.0234703i
\(783\) 3.42122 + 3.36847i 0.122264 + 0.120379i
\(784\) −1.47041 + 13.9900i −0.0525148 + 0.499645i
\(785\) −36.1124 32.5158i −1.28891 1.16054i
\(786\) 4.96490 + 2.51357i 0.177092 + 0.0896562i
\(787\) 5.04436 23.7318i 0.179812 0.845949i −0.792061 0.610442i \(-0.790992\pi\)
0.971873 0.235506i \(-0.0756749\pi\)
\(788\) −1.37213 + 0.291655i −0.0488801 + 0.0103898i
\(789\) −30.4966 + 11.7972i −1.08571 + 0.419993i
\(790\) 19.4204 + 6.31005i 0.690945 + 0.224502i
\(791\) −6.76380 2.19769i −0.240493 0.0781410i
\(792\) 4.57220 + 13.8277i 0.162466 + 0.491346i
\(793\) 25.6539 5.45291i 0.910997 0.193638i
\(794\) −3.67775 + 17.3025i −0.130519 + 0.614041i
\(795\) 26.1090 51.5714i 0.925990 1.82905i
\(796\) −4.19604 3.77813i −0.148725 0.133912i
\(797\) 4.25644 40.4973i 0.150771 1.43449i −0.613552 0.789654i \(-0.710260\pi\)
0.764323 0.644833i \(-0.223073\pi\)
\(798\) −3.17420 + 3.94063i −0.112366 + 0.139497i
\(799\) 30.5060 3.20631i 1.07922 0.113431i
\(800\) 25.3044 + 14.6095i 0.894645 + 0.516524i
\(801\) −3.07561 6.81275i −0.108671 0.240717i
\(802\) −24.7133 34.0149i −0.872656 1.20111i
\(803\) 2.58129 2.32420i 0.0910917 0.0820194i
\(804\) −0.994680 3.67411i −0.0350796 0.129576i
\(805\) 5.68162i 0.200251i
\(806\) −34.7445 + 8.26679i −1.22382 + 0.291185i
\(807\) 47.8566 + 2.38382i 1.68463 + 0.0839143i
\(808\) −8.48127 26.1027i −0.298370 0.918288i
\(809\) 12.3149 + 13.6771i 0.432970 + 0.480862i 0.919662 0.392712i \(-0.128463\pi\)
−0.486691 + 0.873574i \(0.661796\pi\)
\(810\) −36.6301 + 16.7655i −1.28705 + 0.589079i
\(811\) 1.69145 + 2.92968i 0.0593949 + 0.102875i 0.894194 0.447680i \(-0.147750\pi\)
−0.834799 + 0.550555i \(0.814416\pi\)
\(812\) 0.313514 0.543022i 0.0110022 0.0190563i
\(813\) −8.37304 + 0.460556i −0.293655 + 0.0161524i
\(814\) 14.0070 + 10.1767i 0.490947 + 0.356694i
\(815\) 48.9097 + 5.14061i 1.71323 + 0.180068i
\(816\) −12.3254 + 12.3894i −0.431474 + 0.433714i
\(817\) −6.80554 + 15.2855i −0.238096 + 0.534772i
\(818\) 8.00096 + 1.70066i 0.279747 + 0.0594620i
\(819\) 2.05835 + 18.6541i 0.0719245 + 0.651825i
\(820\) −7.42634 + 3.30642i −0.259339 + 0.115465i
\(821\) 7.68340 23.6471i 0.268153 0.825289i −0.722798 0.691060i \(-0.757144\pi\)
0.990950 0.134229i \(-0.0428559\pi\)
\(822\) 2.88603 + 1.09928i 0.100662 + 0.0383417i
\(823\) −4.38149 9.84099i −0.152729 0.343035i 0.820935 0.571021i \(-0.193453\pi\)
−0.973664 + 0.227986i \(0.926786\pi\)
\(824\) 8.80742 + 41.4357i 0.306821 + 1.44348i
\(825\) 24.2077 + 6.41929i 0.842804 + 0.223491i
\(826\) 13.1431 + 5.85167i 0.457306 + 0.203606i
\(827\) 16.9267 18.7990i 0.588598 0.653704i −0.373108 0.927788i \(-0.621708\pi\)
0.961706 + 0.274084i \(0.0883746\pi\)
\(828\) 0.463296 2.23653i 0.0161007 0.0777247i
\(829\) 13.6214 18.7482i 0.473090 0.651152i −0.504069 0.863663i \(-0.668164\pi\)
0.977159 + 0.212512i \(0.0681643\pi\)
\(830\) −2.40335 22.8664i −0.0834215 0.793703i
\(831\) −40.8901 26.4040i −1.41846 0.915946i
\(832\) 40.9596 23.6480i 1.42002 0.819848i
\(833\) 18.5509 13.4780i 0.642750 0.466985i
\(834\) −13.1223 16.1191i −0.454387 0.558160i
\(835\) 51.1278 16.6124i 1.76935 0.574897i
\(836\) −1.95499 −0.0676147
\(837\) 5.43534 + 28.4158i 0.187873 + 0.982193i
\(838\) 34.0807 1.17730
\(839\) 19.1991 6.23816i 0.662826 0.215365i 0.0417650 0.999127i \(-0.486702\pi\)
0.621061 + 0.783762i \(0.286702\pi\)
\(840\) 14.6780 + 18.0302i 0.506441 + 0.622102i
\(841\) 22.7708 16.5439i 0.785200 0.570481i
\(842\) −7.73189 + 4.46401i −0.266459 + 0.153840i
\(843\) −5.05000 3.26095i −0.173931 0.112313i
\(844\) −0.263472 2.50677i −0.00906909 0.0862866i
\(845\) 35.5582 48.9417i 1.22324 1.68365i
\(846\) 5.47516 26.4309i 0.188240 0.908714i
\(847\) −6.60410 + 7.33460i −0.226920 + 0.252020i
\(848\) −20.1584 8.97512i −0.692244 0.308207i
\(849\) −38.6725 10.2550i −1.32724 0.351951i
\(850\) 9.18617 + 43.2175i 0.315083 + 1.48235i
\(851\) −4.88038 10.9615i −0.167297 0.375756i
\(852\) 7.51862 + 2.86381i 0.257584 + 0.0981126i
\(853\) −14.7495 + 45.3942i −0.505012 + 1.55427i 0.295738 + 0.955269i \(0.404434\pi\)
−0.800750 + 0.598999i \(0.795566\pi\)
\(854\) 6.13186 2.73008i 0.209828 0.0934214i
\(855\) −2.62092 23.7524i −0.0896335 0.812316i
\(856\) 37.7966 + 8.03391i 1.29186 + 0.274593i
\(857\) −19.5412 + 43.8903i −0.667515 + 1.49926i 0.188370 + 0.982098i \(0.439679\pi\)
−0.855886 + 0.517165i \(0.826987\pi\)
\(858\) 12.3709 12.4352i 0.422337 0.424530i
\(859\) −36.6378 3.85079i −1.25006 0.131387i −0.543727 0.839262i \(-0.682987\pi\)
−0.706338 + 0.707875i \(0.749654\pi\)
\(860\) 14.0744 + 10.2256i 0.479932 + 0.348691i
\(861\) −7.41013 + 0.407591i −0.252536 + 0.0138907i
\(862\) 22.7016 39.3203i 0.773219 1.33926i
\(863\) 23.0792 + 39.9743i 0.785624 + 1.36074i 0.928625 + 0.371019i \(0.120991\pi\)
−0.143001 + 0.989723i \(0.545675\pi\)
\(864\) −7.64055 14.7118i −0.259937 0.500505i
\(865\) 13.6625 + 15.1737i 0.464539 + 0.515923i
\(866\) −4.73932 14.5861i −0.161049 0.495657i
\(867\) −0.956836 0.0476615i −0.0324958 0.00161867i
\(868\) 3.41357 1.61969i 0.115864 0.0549757i
\(869\) 7.20239i 0.244324i
\(870\) −1.87195 6.91454i −0.0634650 0.234425i
\(871\) −15.0551 + 13.5557i −0.510123 + 0.459317i
\(872\) −18.2588 25.1311i −0.618321 0.851046i
\(873\) 13.1983 + 29.2353i 0.446693 + 0.989466i
\(874\) −2.83845 1.63878i −0.0960121 0.0554326i
\(875\) 18.0539 1.89754i 0.610333 0.0641486i
\(876\) −1.39830 + 1.73592i −0.0472440 + 0.0586514i
\(877\) −3.72336 + 35.4254i −0.125729 + 1.19623i 0.731699 + 0.681628i \(0.238728\pi\)
−0.857428 + 0.514604i \(0.827939\pi\)
\(878\) 11.8337 + 10.6551i 0.399367 + 0.359592i
\(879\) −9.06133 + 17.8983i −0.305631 + 0.603694i
\(880\) 3.07291 14.4569i 0.103588 0.487343i
\(881\) 35.7863 7.60662i 1.20567 0.256274i 0.439104 0.898436i \(-0.355296\pi\)
0.766568 + 0.642163i \(0.221963\pi\)
\(882\) −6.33456 19.1576i −0.213296 0.645071i
\(883\) −44.0738 14.3204i −1.48320 0.481921i −0.548133 0.836391i \(-0.684661\pi\)
−0.935067 + 0.354470i \(0.884661\pi\)
\(884\) −12.1658 3.95292i −0.409182 0.132951i
\(885\) −63.3674 + 24.5129i −2.13007 + 0.823993i
\(886\) −42.3084 + 8.99293i −1.42138 + 0.302123i
\(887\) −9.10917 + 42.8553i −0.305856 + 1.43894i 0.509745 + 0.860325i \(0.329740\pi\)
−0.815601 + 0.578614i \(0.803594\pi\)
\(888\) −43.8058 22.1775i −1.47003 0.744227i
\(889\) −15.2265 13.7100i −0.510679 0.459818i
\(890\) −1.16576 + 11.0915i −0.0390764 + 0.371788i
\(891\) −9.61655 10.4603i −0.322167 0.350434i
\(892\) −3.96397 + 0.416630i −0.132723 + 0.0139498i
\(893\) 13.8664 + 8.00578i 0.464022 + 0.267903i
\(894\) 15.5158 + 30.2575i 0.518925 + 1.01196i
\(895\) 1.32412 + 1.82249i 0.0442603 + 0.0609191i
\(896\) 3.49417 3.14617i 0.116732 0.105106i
\(897\) −11.7338 + 3.17664i −0.391779 + 0.106065i
\(898\) 2.55475i 0.0852532i
\(899\) −5.14305 + 0.124219i −0.171530 + 0.00414293i
\(900\) −15.9923 1.59717i −0.533077 0.0532389i
\(901\) 11.1150 + 34.2086i 0.370296 + 1.13965i
\(902\) 4.64127 + 5.15465i 0.154537 + 0.171631i
\(903\) 8.68448 + 13.2974i 0.289001 + 0.442510i
\(904\) −9.42518 16.3249i −0.313477 0.542958i
\(905\) −6.09344 + 10.5542i −0.202553 + 0.350832i
\(906\) −1.14899 20.8889i −0.0381725 0.693987i
\(907\) 2.65334 + 1.92776i 0.0881026 + 0.0640103i 0.630965 0.775812i \(-0.282659\pi\)
−0.542862 + 0.839822i \(0.682659\pi\)
\(908\) −3.17305 0.333501i −0.105301 0.0110676i
\(909\) 18.0201 + 19.8061i 0.597689 + 0.656927i
\(910\) 11.3891 25.5803i 0.377545 0.847979i
\(911\) −13.1742 2.80027i −0.436481 0.0927769i −0.0155699 0.999879i \(-0.504956\pi\)
−0.420911 + 0.907102i \(0.638290\pi\)
\(912\) −9.00629 + 1.45037i −0.298228 + 0.0480266i
\(913\) 7.40864 3.29854i 0.245190 0.109166i
\(914\) 14.1718 43.6165i 0.468763 1.44270i
\(915\) −11.2832 + 29.6227i −0.373010 + 0.979296i
\(916\) 4.83717 + 10.8645i 0.159824 + 0.358972i
\(917\) 0.651470 + 3.06492i 0.0215134 + 0.101213i
\(918\) 8.80130 23.4715i 0.290486 0.774676i
\(919\) 31.7855 + 14.1518i 1.04851 + 0.466825i 0.857350 0.514734i \(-0.172109\pi\)
0.191157 + 0.981559i \(0.438776\pi\)
\(920\) −10.0767 + 11.1913i −0.332219 + 0.368966i
\(921\) 4.98939 32.0385i 0.164406 1.05570i
\(922\) 3.87245 5.32996i 0.127532 0.175533i
\(923\) −4.47600 42.5863i −0.147329 1.40174i
\(924\) −1.00664 + 1.55892i −0.0331161 + 0.0512846i
\(925\) −73.1204 + 42.2161i −2.40419 + 1.38806i
\(926\) −30.4220 + 22.1029i −0.999729 + 0.726346i
\(927\) −24.4653 33.3095i −0.803546 1.09403i
\(928\) 2.80356 0.910933i 0.0920315 0.0299028i
\(929\) 12.2276 0.401176 0.200588 0.979676i \(-0.435715\pi\)
0.200588 + 0.979676i \(0.435715\pi\)
\(930\) 14.3863 40.6977i 0.471744 1.33453i
\(931\) 11.9693 0.392279
\(932\) −5.12905 + 1.66653i −0.168008 + 0.0545890i
\(933\) 31.0799 25.3016i 1.01751 0.828336i
\(934\) −13.8250 + 10.0445i −0.452368 + 0.328665i
\(935\) −20.8643 + 12.0460i −0.682336 + 0.393947i
\(936\) −29.0297 + 40.3942i −0.948864 + 1.32033i
\(937\) 0.257967 + 2.45439i 0.00842740 + 0.0801814i 0.997927 0.0643528i \(-0.0204983\pi\)
−0.989500 + 0.144534i \(0.953832\pi\)
\(938\) −3.04749 + 4.19451i −0.0995040 + 0.136955i
\(939\) −6.61760 1.03057i −0.215957 0.0336313i
\(940\) 11.1395 12.3717i 0.363331 0.403520i
\(941\) 8.46562 + 3.76914i 0.275971 + 0.122870i 0.540056 0.841629i \(-0.318403\pi\)
−0.264084 + 0.964500i \(0.585070\pi\)
\(942\) 6.82022 25.7196i 0.222215 0.837990i
\(943\) −0.999439 4.70199i −0.0325462 0.153118i
\(944\) 10.5495 + 23.6945i 0.343356 + 0.771190i
\(945\) −20.2898 10.1404i −0.660028 0.329868i
\(946\) 4.58706 14.1175i 0.149138 0.459000i
\(947\) 5.71879 2.54617i 0.185836 0.0827394i −0.311709 0.950177i \(-0.600902\pi\)
0.497545 + 0.867438i \(0.334235\pi\)
\(948\) −0.734863 4.56324i −0.0238673 0.148207i
\(949\) 11.6044 + 2.46659i 0.376695 + 0.0800689i
\(950\) −9.38063 + 21.0692i −0.304348 + 0.683577i
\(951\) 19.9176 + 19.8147i 0.645872 + 0.642536i
\(952\) −14.3879 1.51223i −0.466315 0.0490116i
\(953\) −2.83580 2.06033i −0.0918606 0.0667406i 0.540907 0.841082i \(-0.318081\pi\)
−0.632767 + 0.774342i \(0.718081\pi\)
\(954\) 31.6511 0.163916i 1.02474 0.00530697i
\(955\) 3.96733 6.87161i 0.128380 0.222360i
\(956\) 1.28269 + 2.22169i 0.0414853 + 0.0718546i
\(957\) 2.11547 1.38161i 0.0683836 0.0446610i
\(958\) −9.16819 10.1823i −0.296211 0.328975i
\(959\) 0.537351 + 1.65380i 0.0173520 + 0.0534039i
\(960\) −2.84388 + 57.0927i −0.0917858 + 1.84266i
\(961\) −25.9300 16.9893i −0.836450 0.548043i
\(962\) 59.1349i 1.90658i
\(963\) −36.8342 + 8.02895i −1.18697 + 0.258729i
\(964\) −4.41506 + 3.97534i −0.142200 + 0.128037i
\(965\) 8.02690 + 11.0481i 0.258395 + 0.355650i
\(966\) −2.76832 + 1.41957i −0.0890691 + 0.0456739i
\(967\) 37.7052 + 21.7691i 1.21252 + 0.700047i 0.963307 0.268402i \(-0.0864955\pi\)
0.249211 + 0.968449i \(0.419829\pi\)
\(968\) −26.0167 + 2.73446i −0.836208 + 0.0878890i
\(969\) 11.5803 + 9.32797i 0.372012 + 0.299658i
\(970\) 5.00260 47.5965i 0.160624 1.52823i
\(971\) −19.0331 17.1375i −0.610801 0.549968i 0.304615 0.952475i \(-0.401472\pi\)
−0.915417 + 0.402507i \(0.868139\pi\)
\(972\) 7.16006 + 5.64619i 0.229659 + 0.181102i
\(973\) 2.43325 11.4476i 0.0780066 0.366992i
\(974\) −7.03117 + 1.49452i −0.225293 + 0.0478876i
\(975\) 30.8612 + 79.7780i 0.988348 + 2.55494i
\(976\) 11.5085 + 3.73934i 0.368378 + 0.119693i
\(977\) −54.4437 17.6898i −1.74181 0.565948i −0.746739 0.665117i \(-0.768381\pi\)
−0.995071 + 0.0991693i \(0.968381\pi\)
\(978\) 9.71550 + 25.1152i 0.310667 + 0.803095i
\(979\) −3.84774 + 0.817863i −0.122974 + 0.0261390i
\(980\) 2.58744 12.1730i 0.0826528 0.388851i
\(981\) 26.3244 + 15.0172i 0.840473 + 0.479461i
\(982\) −34.8230 31.3547i −1.11125 1.00057i
\(983\) −4.92386 + 46.8474i −0.157047 + 1.49420i 0.577919 + 0.816094i \(0.303865\pi\)
−0.734965 + 0.678105i \(0.762802\pi\)
\(984\) −15.3189 12.3395i −0.488348 0.393367i
\(985\) −8.97424 + 0.943231i −0.285943 + 0.0300538i
\(986\) 3.86033 + 2.22876i 0.122938 + 0.0709783i
\(987\) 13.5238 6.93488i 0.430467 0.220740i
\(988\) −3.92480 5.40203i −0.124865 0.171861i
\(989\) −7.64500 + 6.88359i −0.243097 + 0.218885i
\(990\) 4.51509 + 20.7138i 0.143499 + 0.658327i
\(991\) 24.2125i 0.769137i 0.923097 + 0.384568i \(0.125650\pi\)
−0.923097 + 0.384568i \(0.874350\pi\)
\(992\) 17.0213 + 5.07959i 0.540428 + 0.161277i
\(993\) 0.809297 16.2471i 0.0256822 0.515588i
\(994\) −3.38649 10.4226i −0.107413 0.330583i
\(995\) −24.3036 26.9918i −0.770474 0.855699i
\(996\) −4.35736 + 2.84577i −0.138068 + 0.0901718i
\(997\) 15.9655 + 27.6531i 0.505634 + 0.875783i 0.999979 + 0.00651764i \(0.00207464\pi\)
−0.494345 + 0.869266i \(0.664592\pi\)
\(998\) 1.31791 2.28268i 0.0417176 0.0722570i
\(999\) 47.8554 + 2.13537i 1.51408 + 0.0675600i
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 93.2.p.b.11.4 64
3.2 odd 2 inner 93.2.p.b.11.5 yes 64
31.17 odd 30 inner 93.2.p.b.17.5 yes 64
93.17 even 30 inner 93.2.p.b.17.4 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.p.b.11.4 64 1.1 even 1 trivial
93.2.p.b.11.5 yes 64 3.2 odd 2 inner
93.2.p.b.17.4 yes 64 93.17 even 30 inner
93.2.p.b.17.5 yes 64 31.17 odd 30 inner