Properties

Label 108.2.l.a.95.14
Level $108$
Weight $2$
Character 108.95
Analytic conductor $0.862$
Analytic rank $0$
Dimension $96$
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] = [108,2,Mod(11,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.l (of order \(18\), degree \(6\), 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: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 95.14
Character \(\chi\) \(=\) 108.95
Dual form 108.2.l.a.83.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24471 + 0.671335i) q^{2} +(-0.528973 - 1.64930i) q^{3} +(1.09862 + 1.67124i) q^{4} +(0.546554 - 0.651358i) q^{5} +(0.448814 - 2.40802i) q^{6} +(0.348909 - 0.958618i) q^{7} +(0.245503 + 2.81775i) q^{8} +(-2.44038 + 1.74487i) q^{9} +O(q^{10})\) \(q+(1.24471 + 0.671335i) q^{2} +(-0.528973 - 1.64930i) q^{3} +(1.09862 + 1.67124i) q^{4} +(0.546554 - 0.651358i) q^{5} +(0.448814 - 2.40802i) q^{6} +(0.348909 - 0.958618i) q^{7} +(0.245503 + 2.81775i) q^{8} +(-2.44038 + 1.74487i) q^{9} +(1.11758 - 0.443832i) q^{10} +(-1.57259 + 1.31956i) q^{11} +(2.17523 - 2.69599i) q^{12} +(-0.374417 + 2.12343i) q^{13} +(1.07784 - 0.958970i) q^{14} +(-1.36340 - 0.556881i) q^{15} +(-1.58608 + 3.67211i) q^{16} +(-6.34902 - 3.66561i) q^{17} +(-4.20896 + 0.533549i) q^{18} +(4.39109 - 2.53520i) q^{19} +(1.68903 + 0.197828i) q^{20} +(-1.76561 - 0.0683717i) q^{21} +(-2.84329 + 0.586739i) q^{22} +(-5.20278 + 1.89366i) q^{23} +(4.51745 - 1.89542i) q^{24} +(0.742695 + 4.21203i) q^{25} +(-1.89157 + 2.39170i) q^{26} +(4.16870 + 3.10192i) q^{27} +(1.98540 - 0.470046i) q^{28} +(3.64198 - 0.642180i) q^{29} +(-1.32318 - 1.60845i) q^{30} +(-1.60292 - 4.40400i) q^{31} +(-4.43942 + 3.50593i) q^{32} +(3.00821 + 1.89566i) q^{33} +(-5.44185 - 8.82495i) q^{34} +(-0.433706 - 0.751201i) q^{35} +(-5.59713 - 2.16151i) q^{36} +(5.33157 - 9.23455i) q^{37} +(7.16761 - 0.207699i) q^{38} +(3.70022 - 0.505708i) q^{39} +(1.96955 + 1.38014i) q^{40} +(4.00006 + 0.705319i) q^{41} +(-2.15178 - 1.27042i) q^{42} +(3.51843 + 4.19310i) q^{43} +(-3.93298 - 1.17848i) q^{44} +(-0.197264 + 2.54322i) q^{45} +(-7.74725 - 1.13575i) q^{46} +(-4.10423 - 1.49382i) q^{47} +(6.89539 + 0.673469i) q^{48} +(4.56510 + 3.83057i) q^{49} +(-1.90324 + 5.74137i) q^{50} +(-2.68723 + 12.4104i) q^{51} +(-3.96009 + 1.70709i) q^{52} -5.55975i q^{53} +(3.10641 + 6.65960i) q^{54} +1.74553i q^{55} +(2.78681 + 0.747794i) q^{56} +(-6.50406 - 5.90117i) q^{57} +(4.96434 + 1.64566i) q^{58} +(9.24583 + 7.75817i) q^{59} +(-0.567171 - 2.89036i) q^{60} +(-0.502750 - 0.182986i) q^{61} +(0.961378 - 6.55781i) q^{62} +(0.821195 + 2.94819i) q^{63} +(-7.87946 + 1.38353i) q^{64} +(1.17847 + 1.40445i) q^{65} +(2.47173 + 4.37907i) q^{66} +(-6.40223 - 1.12889i) q^{67} +(-0.849045 - 14.6378i) q^{68} +(5.87534 + 7.57925i) q^{69} +(-0.0355318 - 1.22619i) q^{70} +(5.86015 - 10.1501i) q^{71} +(-5.51573 - 6.44800i) q^{72} +(-0.769587 - 1.33296i) q^{73} +(12.8357 - 7.91509i) q^{74} +(6.55404 - 3.45298i) q^{75} +(9.06105 + 4.55334i) q^{76} +(0.716265 + 1.96792i) q^{77} +(4.94521 + 1.85463i) q^{78} +(-14.2516 + 2.51294i) q^{79} +(1.52498 + 3.04011i) q^{80} +(2.91087 - 8.51627i) q^{81} +(4.50542 + 3.56330i) q^{82} +(-0.916197 - 5.19601i) q^{83} +(-1.82547 - 3.02587i) q^{84} +(-5.85770 + 2.13203i) q^{85} +(1.56446 + 7.58125i) q^{86} +(-2.98566 - 5.66703i) q^{87} +(-4.10428 - 4.10722i) q^{88} +(-3.41168 + 1.96973i) q^{89} +(-1.95289 + 3.03315i) q^{90} +(1.90492 + 1.09981i) q^{91} +(-8.88063 - 6.61468i) q^{92} +(-6.41561 + 4.97330i) q^{93} +(-4.10573 - 4.61468i) q^{94} +(0.748647 - 4.24579i) q^{95} +(8.13066 + 5.46739i) q^{96} +(3.35056 - 2.81145i) q^{97} +(3.11064 + 7.83267i) q^{98} +(1.53526 - 5.96420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24471 + 0.671335i 0.880145 + 0.474706i
\(3\) −0.528973 1.64930i −0.305402 0.952223i
\(4\) 1.09862 + 1.67124i 0.549309 + 0.835619i
\(5\) 0.546554 0.651358i 0.244426 0.291296i −0.629858 0.776710i \(-0.716887\pi\)
0.874284 + 0.485414i \(0.161331\pi\)
\(6\) 0.448814 2.40802i 0.183227 0.983071i
\(7\) 0.348909 0.958618i 0.131875 0.362324i −0.856127 0.516766i \(-0.827136\pi\)
0.988002 + 0.154442i \(0.0493580\pi\)
\(8\) 0.245503 + 2.81775i 0.0867985 + 0.996226i
\(9\) −2.44038 + 1.74487i −0.813459 + 0.581623i
\(10\) 1.11758 0.443832i 0.353410 0.140352i
\(11\) −1.57259 + 1.31956i −0.474155 + 0.397863i −0.848307 0.529504i \(-0.822378\pi\)
0.374153 + 0.927367i \(0.377934\pi\)
\(12\) 2.17523 2.69599i 0.627936 0.778265i
\(13\) −0.374417 + 2.12343i −0.103845 + 0.588933i 0.887831 + 0.460170i \(0.152212\pi\)
−0.991675 + 0.128762i \(0.958900\pi\)
\(14\) 1.07784 0.958970i 0.288066 0.256295i
\(15\) −1.36340 0.556881i −0.352027 0.143786i
\(16\) −1.58608 + 3.67211i −0.396519 + 0.918027i
\(17\) −6.34902 3.66561i −1.53986 0.889041i −0.998846 0.0480291i \(-0.984706\pi\)
−0.541017 0.841011i \(-0.681961\pi\)
\(18\) −4.20896 + 0.533549i −0.992061 + 0.125759i
\(19\) 4.39109 2.53520i 1.00738 0.581614i 0.0969597 0.995288i \(-0.469088\pi\)
0.910425 + 0.413675i \(0.135755\pi\)
\(20\) 1.68903 + 0.197828i 0.377678 + 0.0442358i
\(21\) −1.76561 0.0683717i −0.385288 0.0149199i
\(22\) −2.84329 + 0.586739i −0.606192 + 0.125093i
\(23\) −5.20278 + 1.89366i −1.08486 + 0.394855i −0.821713 0.569902i \(-0.806981\pi\)
−0.263142 + 0.964757i \(0.584759\pi\)
\(24\) 4.51745 1.89542i 0.922121 0.386901i
\(25\) 0.742695 + 4.21203i 0.148539 + 0.842407i
\(26\) −1.89157 + 2.39170i −0.370968 + 0.469050i
\(27\) 4.16870 + 3.10192i 0.802267 + 0.596965i
\(28\) 1.98540 0.470046i 0.375205 0.0888304i
\(29\) 3.64198 0.642180i 0.676300 0.119250i 0.175059 0.984558i \(-0.443988\pi\)
0.501240 + 0.865308i \(0.332877\pi\)
\(30\) −1.32318 1.60845i −0.241579 0.293662i
\(31\) −1.60292 4.40400i −0.287894 0.790981i −0.996361 0.0852374i \(-0.972835\pi\)
0.708467 0.705744i \(-0.249387\pi\)
\(32\) −4.43942 + 3.50593i −0.784786 + 0.619767i
\(33\) 3.00821 + 1.89566i 0.523662 + 0.329993i
\(34\) −5.44185 8.82495i −0.933270 1.51347i
\(35\) −0.433706 0.751201i −0.0733097 0.126976i
\(36\) −5.59713 2.16151i −0.932855 0.360251i
\(37\) 5.33157 9.23455i 0.876504 1.51815i 0.0213528 0.999772i \(-0.493203\pi\)
0.855152 0.518378i \(-0.173464\pi\)
\(38\) 7.16761 0.207699i 1.16274 0.0336932i
\(39\) 3.70022 0.505708i 0.592510 0.0809781i
\(40\) 1.96955 + 1.38014i 0.311412 + 0.218220i
\(41\) 4.00006 + 0.705319i 0.624705 + 0.110152i 0.477035 0.878884i \(-0.341712\pi\)
0.147670 + 0.989037i \(0.452823\pi\)
\(42\) −2.15178 1.27042i −0.332027 0.196030i
\(43\) 3.51843 + 4.19310i 0.536555 + 0.639441i 0.964412 0.264405i \(-0.0851756\pi\)
−0.427857 + 0.903847i \(0.640731\pi\)
\(44\) −3.93298 1.17848i −0.592919 0.177663i
\(45\) −0.197264 + 2.54322i −0.0294064 + 0.379121i
\(46\) −7.74725 1.13575i −1.14227 0.167457i
\(47\) −4.10423 1.49382i −0.598663 0.217896i 0.0248724 0.999691i \(-0.492082\pi\)
−0.623535 + 0.781795i \(0.714304\pi\)
\(48\) 6.89539 + 0.673469i 0.995264 + 0.0972068i
\(49\) 4.56510 + 3.83057i 0.652157 + 0.547225i
\(50\) −1.90324 + 5.74137i −0.269159 + 0.811952i
\(51\) −2.68723 + 12.4104i −0.376287 + 1.73781i
\(52\) −3.96009 + 1.70709i −0.549166 + 0.236731i
\(53\) 5.55975i 0.763690i −0.924226 0.381845i \(-0.875289\pi\)
0.924226 0.381845i \(-0.124711\pi\)
\(54\) 3.10641 + 6.65960i 0.422728 + 0.906256i
\(55\) 1.74553i 0.235368i
\(56\) 2.78681 + 0.747794i 0.372403 + 0.0999282i
\(57\) −6.50406 5.90117i −0.861484 0.781629i
\(58\) 4.96434 + 1.64566i 0.651850 + 0.216086i
\(59\) 9.24583 + 7.75817i 1.20370 + 1.01003i 0.999516 + 0.0310964i \(0.00989987\pi\)
0.204188 + 0.978932i \(0.434545\pi\)
\(60\) −0.567171 2.89036i −0.0732215 0.373144i
\(61\) −0.502750 0.182986i −0.0643705 0.0234290i 0.309634 0.950856i \(-0.399793\pi\)
−0.374005 + 0.927427i \(0.622016\pi\)
\(62\) 0.961378 6.55781i 0.122095 0.832843i
\(63\) 0.821195 + 2.94819i 0.103461 + 0.371437i
\(64\) −7.87946 + 1.38353i −0.984932 + 0.172942i
\(65\) 1.17847 + 1.40445i 0.146171 + 0.174200i
\(66\) 2.47173 + 4.37907i 0.304249 + 0.539027i
\(67\) −6.40223 1.12889i −0.782157 0.137915i −0.231709 0.972785i \(-0.574432\pi\)
−0.550448 + 0.834870i \(0.685543\pi\)
\(68\) −0.849045 14.6378i −0.102962 1.77510i
\(69\) 5.87534 + 7.57925i 0.707308 + 0.912435i
\(70\) −0.0355318 1.22619i −0.00424687 0.146558i
\(71\) 5.86015 10.1501i 0.695472 1.20459i −0.274550 0.961573i \(-0.588529\pi\)
0.970021 0.243019i \(-0.0781379\pi\)
\(72\) −5.51573 6.44800i −0.650035 0.759905i
\(73\) −0.769587 1.33296i −0.0900734 0.156012i 0.817468 0.575973i \(-0.195377\pi\)
−0.907542 + 0.419962i \(0.862043\pi\)
\(74\) 12.8357 7.91509i 1.49212 0.920110i
\(75\) 6.55404 3.45298i 0.756795 0.398716i
\(76\) 9.06105 + 4.55334i 1.03937 + 0.522304i
\(77\) 0.716265 + 1.96792i 0.0816260 + 0.224266i
\(78\) 4.94521 + 1.85463i 0.559935 + 0.209995i
\(79\) −14.2516 + 2.51294i −1.60343 + 0.282728i −0.902560 0.430563i \(-0.858315\pi\)
−0.700868 + 0.713291i \(0.747204\pi\)
\(80\) 1.52498 + 3.04011i 0.170498 + 0.339894i
\(81\) 2.91087 8.51627i 0.323430 0.946252i
\(82\) 4.50542 + 3.56330i 0.497541 + 0.393501i
\(83\) −0.916197 5.19601i −0.100566 0.570337i −0.992899 0.118960i \(-0.962044\pi\)
0.892333 0.451377i \(-0.149067\pi\)
\(84\) −1.82547 3.02587i −0.199175 0.330150i
\(85\) −5.85770 + 2.13203i −0.635357 + 0.231251i
\(86\) 1.56446 + 7.58125i 0.168700 + 0.817507i
\(87\) −2.98566 5.66703i −0.320096 0.607569i
\(88\) −4.10428 4.10722i −0.437517 0.437831i
\(89\) −3.41168 + 1.96973i −0.361637 + 0.208791i −0.669799 0.742543i \(-0.733620\pi\)
0.308162 + 0.951334i \(0.400286\pi\)
\(90\) −1.95289 + 3.03315i −0.205853 + 0.319722i
\(91\) 1.90492 + 1.09981i 0.199690 + 0.115291i
\(92\) −8.88063 6.61468i −0.925869 0.689628i
\(93\) −6.41561 + 4.97330i −0.665267 + 0.515707i
\(94\) −4.10573 4.61468i −0.423474 0.475968i
\(95\) 0.748647 4.24579i 0.0768096 0.435609i
\(96\) 8.13066 + 5.46739i 0.829832 + 0.558014i
\(97\) 3.35056 2.81145i 0.340198 0.285460i −0.456642 0.889651i \(-0.650948\pi\)
0.796840 + 0.604191i \(0.206503\pi\)
\(98\) 3.11064 + 7.83267i 0.314222 + 0.791219i
\(99\) 1.53526 5.96420i 0.154299 0.599424i
\(100\) −6.22337 + 5.86864i −0.622337 + 0.586864i
\(101\) −2.06720 + 5.67959i −0.205694 + 0.565140i −0.999048 0.0436206i \(-0.986111\pi\)
0.793354 + 0.608760i \(0.208333\pi\)
\(102\) −11.6764 + 13.6434i −1.15613 + 1.35090i
\(103\) 0.110043 0.131145i 0.0108429 0.0129221i −0.760596 0.649226i \(-0.775093\pi\)
0.771439 + 0.636304i \(0.219537\pi\)
\(104\) −6.07521 0.533707i −0.595723 0.0523343i
\(105\) −1.00954 + 1.11268i −0.0985207 + 0.108586i
\(106\) 3.73245 6.92028i 0.362528 0.672157i
\(107\) 8.17263 0.790078 0.395039 0.918664i \(-0.370731\pi\)
0.395039 + 0.918664i \(0.370731\pi\)
\(108\) −0.604239 + 10.3747i −0.0581429 + 0.998308i
\(109\) −19.1819 −1.83729 −0.918646 0.395082i \(-0.870716\pi\)
−0.918646 + 0.395082i \(0.870716\pi\)
\(110\) −1.17184 + 2.17269i −0.111730 + 0.207158i
\(111\) −18.0508 3.90853i −1.71330 0.370981i
\(112\) 2.96675 + 2.80167i 0.280332 + 0.264733i
\(113\) −3.19731 + 3.81040i −0.300777 + 0.358452i −0.895172 0.445721i \(-0.852947\pi\)
0.594395 + 0.804174i \(0.297392\pi\)
\(114\) −4.13402 11.7117i −0.387187 1.09690i
\(115\) −1.61015 + 4.42386i −0.150148 + 0.412527i
\(116\) 5.07439 + 5.38111i 0.471145 + 0.499624i
\(117\) −2.79138 5.83527i −0.258063 0.539471i
\(118\) 6.30007 + 15.8637i 0.579968 + 1.46038i
\(119\) −5.72915 + 4.80732i −0.525190 + 0.440687i
\(120\) 1.23443 3.97843i 0.112688 0.363179i
\(121\) −1.17833 + 6.68262i −0.107121 + 0.607511i
\(122\) −0.502934 0.565279i −0.0455335 0.0511779i
\(123\) −0.952641 6.97039i −0.0858968 0.628499i
\(124\) 5.59913 7.51718i 0.502817 0.675063i
\(125\) 6.83132 + 3.94406i 0.611011 + 0.352768i
\(126\) −0.957071 + 4.22094i −0.0852627 + 0.376032i
\(127\) 12.8653 7.42778i 1.14161 0.659109i 0.194781 0.980847i \(-0.437600\pi\)
0.946829 + 0.321738i \(0.104267\pi\)
\(128\) −10.7365 3.56765i −0.948979 0.315339i
\(129\) 5.05452 8.02097i 0.445026 0.706207i
\(130\) 0.524003 + 2.53928i 0.0459581 + 0.222710i
\(131\) −2.94977 + 1.07363i −0.257722 + 0.0938032i −0.467650 0.883914i \(-0.654899\pi\)
0.209928 + 0.977717i \(0.432677\pi\)
\(132\) 0.136770 + 7.11005i 0.0119043 + 0.618850i
\(133\) −0.898197 5.09393i −0.0778836 0.441700i
\(134\) −7.21108 5.70318i −0.622942 0.492680i
\(135\) 4.29888 1.01995i 0.369989 0.0877831i
\(136\) 8.77007 18.7899i 0.752027 1.61122i
\(137\) −11.8307 + 2.08607i −1.01077 + 0.178225i −0.654422 0.756130i \(-0.727088\pi\)
−0.356344 + 0.934355i \(0.615977\pi\)
\(138\) 2.22489 + 13.3783i 0.189395 + 1.13884i
\(139\) −0.983129 2.70112i −0.0833879 0.229106i 0.890990 0.454022i \(-0.150011\pi\)
−0.974378 + 0.224916i \(0.927789\pi\)
\(140\) 0.778958 1.55011i 0.0658340 0.131008i
\(141\) −0.292727 + 7.55929i −0.0246520 + 0.636607i
\(142\) 14.1083 8.69980i 1.18394 0.730071i
\(143\) −2.21319 3.83335i −0.185076 0.320561i
\(144\) −2.53672 11.7288i −0.211394 0.977401i
\(145\) 1.57225 2.72322i 0.130568 0.226151i
\(146\) −0.0630493 2.17581i −0.00521799 0.180071i
\(147\) 3.90295 9.55548i 0.321910 0.788123i
\(148\) 21.2905 1.23492i 1.75007 0.101510i
\(149\) 10.9239 + 1.92617i 0.894918 + 0.157798i 0.602148 0.798385i \(-0.294312\pi\)
0.292770 + 0.956183i \(0.405423\pi\)
\(150\) 10.4760 + 0.101992i 0.855362 + 0.00832763i
\(151\) 3.78495 + 4.51073i 0.308015 + 0.367078i 0.897740 0.440527i \(-0.145208\pi\)
−0.589725 + 0.807604i \(0.700764\pi\)
\(152\) 8.22158 + 11.7506i 0.666858 + 0.953099i
\(153\) 21.8900 2.13274i 1.76970 0.172422i
\(154\) −0.429591 + 2.93035i −0.0346174 + 0.236135i
\(155\) −3.74466 1.36295i −0.300779 0.109474i
\(156\) 4.91029 + 5.62837i 0.393138 + 0.450631i
\(157\) −13.5896 11.4030i −1.08456 0.910058i −0.0882726 0.996096i \(-0.528135\pi\)
−0.996292 + 0.0860388i \(0.972579\pi\)
\(158\) −19.4261 6.43970i −1.54546 0.512315i
\(159\) −9.16968 + 2.94095i −0.727203 + 0.233233i
\(160\) −0.142770 + 4.80783i −0.0112869 + 0.380092i
\(161\) 5.64820i 0.445140i
\(162\) 9.34047 8.64614i 0.733856 0.679305i
\(163\) 18.0395i 1.41296i 0.707732 + 0.706481i \(0.249718\pi\)
−0.707732 + 0.706481i \(0.750282\pi\)
\(164\) 3.21579 + 7.45993i 0.251111 + 0.582523i
\(165\) 2.87891 0.923339i 0.224123 0.0718818i
\(166\) 2.34786 7.08262i 0.182230 0.549718i
\(167\) 12.3127 + 10.3316i 0.952789 + 0.799485i 0.979765 0.200151i \(-0.0641433\pi\)
−0.0269759 + 0.999636i \(0.508588\pi\)
\(168\) −0.240809 4.99184i −0.0185788 0.385129i
\(169\) 7.84725 + 2.85617i 0.603635 + 0.219705i
\(170\) −8.72246 1.27872i −0.668982 0.0980732i
\(171\) −6.29232 + 13.8487i −0.481186 + 1.05904i
\(172\) −3.14226 + 10.4867i −0.239595 + 0.799607i
\(173\) 3.51165 + 4.18502i 0.266986 + 0.318181i 0.882835 0.469683i \(-0.155632\pi\)
−0.615850 + 0.787864i \(0.711187\pi\)
\(174\) 0.0881888 9.05820i 0.00668557 0.686700i
\(175\) 4.29687 + 0.757653i 0.324813 + 0.0572732i
\(176\) −2.35132 7.86765i −0.177238 0.593047i
\(177\) 7.90476 19.3530i 0.594158 1.45466i
\(178\) −5.56891 + 0.161372i −0.417407 + 0.0120954i
\(179\) −6.73827 + 11.6710i −0.503642 + 0.872333i 0.496349 + 0.868123i \(0.334674\pi\)
−0.999991 + 0.00421032i \(0.998660\pi\)
\(180\) −4.46705 + 2.46436i −0.332954 + 0.183682i
\(181\) 7.16955 + 12.4180i 0.532909 + 0.923025i 0.999261 + 0.0384262i \(0.0122345\pi\)
−0.466353 + 0.884599i \(0.654432\pi\)
\(182\) 1.63274 + 2.64778i 0.121027 + 0.196266i
\(183\) −0.0358577 + 0.925980i −0.00265068 + 0.0684504i
\(184\) −6.61316 14.1953i −0.487529 1.04649i
\(185\) −3.10100 8.51994i −0.227990 0.626398i
\(186\) −11.3243 + 1.88330i −0.830340 + 0.138090i
\(187\) 14.8214 2.61342i 1.08385 0.191112i
\(188\) −2.01246 8.50028i −0.146773 0.619946i
\(189\) 4.42806 2.91391i 0.322094 0.211956i
\(190\) 3.78220 4.78219i 0.274390 0.346937i
\(191\) 1.45788 + 8.26803i 0.105488 + 0.598254i 0.991024 + 0.133683i \(0.0426803\pi\)
−0.885536 + 0.464571i \(0.846209\pi\)
\(192\) 6.44988 + 12.2637i 0.465480 + 0.885058i
\(193\) −1.16115 + 0.422623i −0.0835812 + 0.0304211i −0.383472 0.923552i \(-0.625272\pi\)
0.299891 + 0.953973i \(0.403050\pi\)
\(194\) 6.05791 1.25010i 0.434933 0.0897522i
\(195\) 1.69297 2.68657i 0.121236 0.192389i
\(196\) −1.38650 + 11.8377i −0.0990356 + 0.845550i
\(197\) 2.53158 1.46161i 0.180368 0.104135i −0.407098 0.913385i \(-0.633459\pi\)
0.587466 + 0.809249i \(0.300126\pi\)
\(198\) 5.91493 6.39304i 0.420355 0.454333i
\(199\) −12.5012 7.21757i −0.886186 0.511640i −0.0134930 0.999909i \(-0.504295\pi\)
−0.872693 + 0.488269i \(0.837628\pi\)
\(200\) −11.6861 + 3.12680i −0.826335 + 0.221098i
\(201\) 1.52473 + 11.1563i 0.107546 + 0.786908i
\(202\) −6.38597 + 5.68167i −0.449316 + 0.399761i
\(203\) 0.655114 3.71534i 0.0459800 0.260765i
\(204\) −23.6930 + 9.14334i −1.65884 + 0.640162i
\(205\) 2.64567 2.21998i 0.184781 0.155050i
\(206\) 0.225014 0.0893613i 0.0156775 0.00622610i
\(207\) 9.39256 13.6994i 0.652828 0.952175i
\(208\) −7.20359 4.74281i −0.499479 0.328855i
\(209\) −3.56005 + 9.78114i −0.246253 + 0.676576i
\(210\) −2.00356 + 0.707224i −0.138259 + 0.0488031i
\(211\) 3.58544 4.27296i 0.246832 0.294163i −0.628376 0.777910i \(-0.716280\pi\)
0.875208 + 0.483747i \(0.160724\pi\)
\(212\) 9.29166 6.10804i 0.638154 0.419502i
\(213\) −19.8404 4.29603i −1.35944 0.294359i
\(214\) 10.1726 + 5.48657i 0.695383 + 0.375055i
\(215\) 4.65422 0.317415
\(216\) −7.71702 + 12.5079i −0.525077 + 0.851055i
\(217\) −4.78103 −0.324557
\(218\) −23.8759 12.8775i −1.61708 0.872173i
\(219\) −1.79137 + 1.97438i −0.121049 + 0.133416i
\(220\) −2.91720 + 1.91767i −0.196678 + 0.129290i
\(221\) 10.1608 12.1092i 0.683492 0.814554i
\(222\) −19.8441 16.9831i −1.33185 1.13983i
\(223\) −4.64768 + 12.7694i −0.311231 + 0.855102i 0.681177 + 0.732119i \(0.261468\pi\)
−0.992409 + 0.122983i \(0.960754\pi\)
\(224\) 1.81190 + 5.47896i 0.121062 + 0.366078i
\(225\) −9.16190 8.98304i −0.610793 0.598869i
\(226\) −6.53778 + 2.59639i −0.434887 + 0.172709i
\(227\) 13.7746 11.5582i 0.914249 0.767146i −0.0586732 0.998277i \(-0.518687\pi\)
0.972923 + 0.231131i \(0.0742426\pi\)
\(228\) 2.71678 17.3530i 0.179923 1.14923i
\(229\) 2.41193 13.6787i 0.159385 0.903916i −0.795282 0.606240i \(-0.792677\pi\)
0.954667 0.297676i \(-0.0962117\pi\)
\(230\) −4.97407 + 4.42548i −0.327980 + 0.291808i
\(231\) 2.86681 2.22231i 0.188622 0.146217i
\(232\) 2.70362 + 10.1046i 0.177502 + 0.663396i
\(233\) 2.12007 + 1.22403i 0.138891 + 0.0801886i 0.567835 0.823142i \(-0.307781\pi\)
−0.428945 + 0.903331i \(0.641114\pi\)
\(234\) 0.442954 9.13718i 0.0289568 0.597316i
\(235\) −3.21619 + 1.85687i −0.209801 + 0.121129i
\(236\) −2.80812 + 23.9753i −0.182793 + 1.56066i
\(237\) 11.6833 + 22.1759i 0.758911 + 1.44048i
\(238\) −10.3585 + 2.13756i −0.671440 + 0.138557i
\(239\) −14.4768 + 5.26911i −0.936424 + 0.340831i −0.764753 0.644324i \(-0.777139\pi\)
−0.171671 + 0.985154i \(0.554917\pi\)
\(240\) 4.20737 4.12328i 0.271585 0.266157i
\(241\) 2.02973 + 11.5112i 0.130747 + 0.741501i 0.977728 + 0.209878i \(0.0673067\pi\)
−0.846981 + 0.531623i \(0.821582\pi\)
\(242\) −5.95295 + 7.52688i −0.382670 + 0.483846i
\(243\) −15.5856 0.296022i −0.999820 0.0189898i
\(244\) −0.246517 1.04125i −0.0157816 0.0666590i
\(245\) 4.99015 0.879897i 0.318809 0.0562146i
\(246\) 3.49371 9.31568i 0.222751 0.593946i
\(247\) 3.73920 + 10.2734i 0.237920 + 0.653679i
\(248\) 12.0159 5.59784i 0.763007 0.355463i
\(249\) −8.08514 + 4.25963i −0.512375 + 0.269943i
\(250\) 5.85524 + 9.49532i 0.370318 + 0.600537i
\(251\) 1.74376 + 3.02028i 0.110065 + 0.190639i 0.915796 0.401643i \(-0.131561\pi\)
−0.805731 + 0.592281i \(0.798227\pi\)
\(252\) −4.02495 + 4.61135i −0.253548 + 0.290488i
\(253\) 5.68306 9.84335i 0.357291 0.618846i
\(254\) 21.0001 0.608528i 1.31766 0.0381825i
\(255\) 6.61492 + 8.53332i 0.414242 + 0.534377i
\(256\) −10.9687 11.6485i −0.685546 0.728030i
\(257\) −17.5820 3.10019i −1.09674 0.193385i −0.404132 0.914701i \(-0.632426\pi\)
−0.692606 + 0.721316i \(0.743537\pi\)
\(258\) 11.6762 6.59053i 0.726928 0.410308i
\(259\) −6.99218 8.33295i −0.434473 0.517784i
\(260\) −1.05248 + 3.51246i −0.0652718 + 0.217833i
\(261\) −7.76729 + 7.92194i −0.480783 + 0.490356i
\(262\) −4.39237 0.643924i −0.271362 0.0397818i
\(263\) 6.92028 + 2.51878i 0.426723 + 0.155314i 0.546449 0.837493i \(-0.315979\pi\)
−0.119726 + 0.992807i \(0.538202\pi\)
\(264\) −4.60299 + 8.94179i −0.283294 + 0.550329i
\(265\) −3.62138 3.03870i −0.222460 0.186666i
\(266\) 2.30174 6.94347i 0.141128 0.425731i
\(267\) 5.05336 + 4.58494i 0.309261 + 0.280594i
\(268\) −5.14697 11.9399i −0.314401 0.729344i
\(269\) 0.906912i 0.0552954i −0.999618 0.0276477i \(-0.991198\pi\)
0.999618 0.0276477i \(-0.00880165\pi\)
\(270\) 6.03560 + 1.61645i 0.367315 + 0.0983739i
\(271\) 6.71551i 0.407938i −0.978977 0.203969i \(-0.934616\pi\)
0.978977 0.203969i \(-0.0653842\pi\)
\(272\) 23.5305 17.5003i 1.42675 1.06111i
\(273\) 0.806258 3.72355i 0.0487970 0.225359i
\(274\) −16.1263 5.34581i −0.974224 0.322952i
\(275\) −6.72600 5.64378i −0.405593 0.340333i
\(276\) −6.21198 + 18.1458i −0.373917 + 1.09225i
\(277\) 1.68312 + 0.612607i 0.101129 + 0.0368080i 0.392089 0.919927i \(-0.371752\pi\)
−0.290960 + 0.956735i \(0.593975\pi\)
\(278\) 0.589647 4.02213i 0.0353647 0.241231i
\(279\) 11.5961 + 7.95052i 0.694242 + 0.475985i
\(280\) 2.01022 1.40650i 0.120134 0.0840544i
\(281\) −3.69638 4.40517i −0.220508 0.262791i 0.644438 0.764657i \(-0.277091\pi\)
−0.864945 + 0.501866i \(0.832647\pi\)
\(282\) −5.43917 + 9.21262i −0.323898 + 0.548604i
\(283\) −10.1948 1.79762i −0.606019 0.106858i −0.137785 0.990462i \(-0.543998\pi\)
−0.468234 + 0.883605i \(0.655110\pi\)
\(284\) 23.4013 1.35735i 1.38861 0.0805442i
\(285\) −7.39859 + 1.01116i −0.438255 + 0.0598961i
\(286\) −0.181318 6.25721i −0.0107215 0.369997i
\(287\) 2.07179 3.58844i 0.122294 0.211819i
\(288\) 4.71647 16.3020i 0.277921 0.960604i
\(289\) 18.3734 + 31.8236i 1.08079 + 1.87198i
\(290\) 3.78520 2.33412i 0.222274 0.137064i
\(291\) −6.40928 4.03890i −0.375719 0.236764i
\(292\) 1.38222 2.75058i 0.0808882 0.160966i
\(293\) −4.28880 11.7834i −0.250555 0.688393i −0.999663 0.0259461i \(-0.991740\pi\)
0.749109 0.662447i \(-0.230482\pi\)
\(294\) 11.2730 9.27364i 0.657454 0.540850i
\(295\) 10.1067 1.78208i 0.588434 0.103757i
\(296\) 27.3296 + 12.7559i 1.58850 + 0.741423i
\(297\) −10.6489 + 0.622800i −0.617909 + 0.0361385i
\(298\) 12.3040 + 9.73111i 0.712750 + 0.563708i
\(299\) −2.07303 11.7567i −0.119886 0.679910i
\(300\) 12.9711 + 7.15986i 0.748889 + 0.413375i
\(301\) 5.24719 1.90982i 0.302443 0.110080i
\(302\) 1.68296 + 8.15553i 0.0968437 + 0.469298i
\(303\) 10.4608 + 0.405086i 0.600959 + 0.0232716i
\(304\) 2.34491 + 20.1456i 0.134490 + 1.15543i
\(305\) −0.393969 + 0.227458i −0.0225586 + 0.0130242i
\(306\) 28.6785 + 12.0409i 1.63944 + 0.688331i
\(307\) −23.0184 13.2897i −1.31373 0.758482i −0.331017 0.943625i \(-0.607392\pi\)
−0.982712 + 0.185143i \(0.940725\pi\)
\(308\) −2.50197 + 3.35905i −0.142563 + 0.191399i
\(309\) −0.274507 0.112123i −0.0156161 0.00637843i
\(310\) −3.74604 4.21040i −0.212760 0.239135i
\(311\) 3.84093 21.7830i 0.217799 1.23520i −0.658184 0.752857i \(-0.728675\pi\)
0.875983 0.482342i \(-0.160214\pi\)
\(312\) 2.33338 + 10.3022i 0.132101 + 0.583245i
\(313\) −4.20542 + 3.52877i −0.237705 + 0.199458i −0.753856 0.657039i \(-0.771809\pi\)
0.516152 + 0.856497i \(0.327364\pi\)
\(314\) −9.25986 23.3166i −0.522564 1.31583i
\(315\) 2.36915 + 1.07645i 0.133487 + 0.0606512i
\(316\) −19.8568 21.0570i −1.11703 1.18455i
\(317\) 6.85935 18.8459i 0.385260 1.05849i −0.583850 0.811862i \(-0.698454\pi\)
0.969110 0.246631i \(-0.0793235\pi\)
\(318\) −13.3880 2.49529i −0.750761 0.139929i
\(319\) −4.87996 + 5.81571i −0.273225 + 0.325617i
\(320\) −3.40537 + 5.88852i −0.190366 + 0.329178i
\(321\) −4.32310 13.4791i −0.241292 0.752331i
\(322\) −3.79183 + 7.03038i −0.211311 + 0.391788i
\(323\) −37.1721 −2.06831
\(324\) 17.4307 4.49137i 0.968369 0.249521i
\(325\) −9.22202 −0.511546
\(326\) −12.1105 + 22.4540i −0.670740 + 1.24361i
\(327\) 10.1467 + 31.6367i 0.561114 + 1.74951i
\(328\) −1.00539 + 11.4443i −0.0555131 + 0.631908i
\(329\) −2.86400 + 3.41318i −0.157897 + 0.188175i
\(330\) 4.20328 + 0.783419i 0.231383 + 0.0431258i
\(331\) 7.99263 21.9596i 0.439315 1.20701i −0.500624 0.865665i \(-0.666896\pi\)
0.939939 0.341343i \(-0.110882\pi\)
\(332\) 7.67723 7.23962i 0.421343 0.397326i
\(333\) 3.10204 + 31.8386i 0.169991 + 1.74475i
\(334\) 8.38985 + 21.1259i 0.459072 + 1.15596i
\(335\) −4.23448 + 3.55315i −0.231354 + 0.194129i
\(336\) 3.05146 6.37507i 0.166471 0.347789i
\(337\) 1.10728 6.27969i 0.0603173 0.342076i −0.939683 0.342047i \(-0.888880\pi\)
1.00000 2.90332e-5i \(-9.24155e-6\pi\)
\(338\) 7.85013 + 8.82324i 0.426991 + 0.479921i
\(339\) 7.97578 + 3.25772i 0.433185 + 0.176935i
\(340\) −9.99851 7.44733i −0.542245 0.403888i
\(341\) 8.33210 + 4.81054i 0.451208 + 0.260505i
\(342\) −17.1292 + 13.0134i −0.926244 + 0.703684i
\(343\) 11.4491 6.61016i 0.618195 0.356915i
\(344\) −10.9513 + 10.9435i −0.590456 + 0.590033i
\(345\) 8.14799 + 0.315524i 0.438673 + 0.0169872i
\(346\) 1.56144 + 7.56664i 0.0839436 + 0.406785i
\(347\) 15.1793 5.52480i 0.814866 0.296587i 0.0992334 0.995064i \(-0.468361\pi\)
0.715632 + 0.698477i \(0.246139\pi\)
\(348\) 6.19085 11.2156i 0.331865 0.601222i
\(349\) −3.65392 20.7224i −0.195590 1.10925i −0.911576 0.411132i \(-0.865134\pi\)
0.715986 0.698115i \(-0.245978\pi\)
\(350\) 4.83972 + 3.82770i 0.258694 + 0.204599i
\(351\) −8.14754 + 7.69052i −0.434884 + 0.410490i
\(352\) 2.35511 11.3715i 0.125528 0.606103i
\(353\) −9.47086 + 1.66997i −0.504083 + 0.0888834i −0.419906 0.907567i \(-0.637937\pi\)
−0.0841766 + 0.996451i \(0.526826\pi\)
\(354\) 22.8315 18.7822i 1.21348 0.998262i
\(355\) −3.40844 9.36462i −0.180901 0.497022i
\(356\) −7.04002 3.53774i −0.373120 0.187500i
\(357\) 10.9593 + 6.90613i 0.580027 + 0.365511i
\(358\) −16.2224 + 10.0034i −0.857379 + 0.528698i
\(359\) 7.01604 + 12.1521i 0.370292 + 0.641365i 0.989610 0.143775i \(-0.0459242\pi\)
−0.619318 + 0.785140i \(0.712591\pi\)
\(360\) −7.21460 + 0.0685286i −0.380243 + 0.00361177i
\(361\) 3.35443 5.81005i 0.176549 0.305792i
\(362\) 0.587373 + 20.2701i 0.0308717 + 1.06537i
\(363\) 11.6449 1.59151i 0.611201 0.0835326i
\(364\) 0.254742 + 4.39184i 0.0133521 + 0.230195i
\(365\) −1.28886 0.227260i −0.0674619 0.0118954i
\(366\) −0.666275 + 1.12851i −0.0348268 + 0.0589880i
\(367\) −23.8419 28.4137i −1.24454 1.48318i −0.814276 0.580478i \(-0.802866\pi\)
−0.430261 0.902704i \(-0.641579\pi\)
\(368\) 1.29829 22.1087i 0.0676780 1.15249i
\(369\) −10.9923 + 5.25834i −0.572239 + 0.273738i
\(370\) 1.85987 12.6867i 0.0966903 0.659549i
\(371\) −5.32967 1.93984i −0.276703 0.100712i
\(372\) −15.3599 5.25825i −0.796372 0.272628i
\(373\) 21.7187 + 18.2242i 1.12455 + 0.943611i 0.998825 0.0484536i \(-0.0154293\pi\)
0.125727 + 0.992065i \(0.459874\pi\)
\(374\) 20.2029 + 6.69719i 1.04467 + 0.346303i
\(375\) 2.89136 13.3532i 0.149309 0.689555i
\(376\) 3.20160 11.9314i 0.165110 0.615317i
\(377\) 7.97393i 0.410678i
\(378\) 7.46786 0.654267i 0.384105 0.0336519i
\(379\) 15.3245i 0.787168i 0.919289 + 0.393584i \(0.128765\pi\)
−0.919289 + 0.393584i \(0.871235\pi\)
\(380\) 7.91820 3.41334i 0.406195 0.175100i
\(381\) −19.0560 17.2896i −0.976269 0.885774i
\(382\) −3.73598 + 11.2700i −0.191149 + 0.576626i
\(383\) −28.1952 23.6586i −1.44071 1.20890i −0.939028 0.343841i \(-0.888272\pi\)
−0.501678 0.865055i \(-0.667284\pi\)
\(384\) −0.204826 + 19.5948i −0.0104525 + 0.999945i
\(385\) 1.67330 + 0.609031i 0.0852792 + 0.0310391i
\(386\) −1.72902 0.253475i −0.0880046 0.0129015i
\(387\) −15.9027 4.09354i −0.808379 0.208087i
\(388\) 8.37960 + 2.51087i 0.425410 + 0.127470i
\(389\) −5.77806 6.88602i −0.292959 0.349135i 0.599409 0.800443i \(-0.295402\pi\)
−0.892369 + 0.451307i \(0.850958\pi\)
\(390\) 3.91085 2.20745i 0.198034 0.111778i
\(391\) 39.9740 + 7.04849i 2.02157 + 0.356457i
\(392\) −9.67286 + 13.8037i −0.488553 + 0.697194i
\(393\) 3.33108 + 4.29713i 0.168031 + 0.216761i
\(394\) 4.13232 0.119744i 0.208184 0.00603262i
\(395\) −6.15244 + 10.6563i −0.309563 + 0.536178i
\(396\) 11.6543 3.98660i 0.585648 0.200334i
\(397\) −2.35735 4.08305i −0.118312 0.204922i 0.800787 0.598949i \(-0.204415\pi\)
−0.919099 + 0.394027i \(0.871082\pi\)
\(398\) −10.7150 17.3763i −0.537094 0.870994i
\(399\) −7.92629 + 4.17594i −0.396811 + 0.209059i
\(400\) −16.6450 3.95335i −0.832250 0.197667i
\(401\) 5.87724 + 16.1476i 0.293495 + 0.806372i 0.995549 + 0.0942475i \(0.0300445\pi\)
−0.702053 + 0.712124i \(0.747733\pi\)
\(402\) −5.59179 + 14.9101i −0.278893 + 0.743646i
\(403\) 9.95173 1.75476i 0.495731 0.0874107i
\(404\) −11.7630 + 2.78491i −0.585231 + 0.138555i
\(405\) −3.95619 6.55062i −0.196585 0.325503i
\(406\) 3.30966 4.18472i 0.164256 0.207684i
\(407\) 3.80117 + 21.5575i 0.188417 + 1.06857i
\(408\) −35.6293 4.52514i −1.76391 0.224028i
\(409\) 18.1511 6.60646i 0.897514 0.326668i 0.148258 0.988949i \(-0.452633\pi\)
0.749256 + 0.662280i \(0.230411\pi\)
\(410\) 4.78344 0.987105i 0.236237 0.0487496i
\(411\) 9.69868 + 18.4089i 0.478400 + 0.908044i
\(412\) 0.340070 + 0.0398308i 0.0167540 + 0.00196233i
\(413\) 10.6631 6.15633i 0.524696 0.302933i
\(414\) 20.8879 10.7463i 1.02659 0.528150i
\(415\) −3.88522 2.24313i −0.190718 0.110111i
\(416\) −5.78239 10.7395i −0.283505 0.526546i
\(417\) −3.93491 + 3.05029i −0.192694 + 0.149374i
\(418\) −10.9977 + 9.78473i −0.537913 + 0.478587i
\(419\) −2.66451 + 15.1112i −0.130170 + 0.738230i 0.847932 + 0.530105i \(0.177847\pi\)
−0.978102 + 0.208126i \(0.933264\pi\)
\(420\) −2.96864 0.464770i −0.144855 0.0226785i
\(421\) −17.8213 + 14.9539i −0.868558 + 0.728807i −0.963794 0.266648i \(-0.914084\pi\)
0.0952359 + 0.995455i \(0.469639\pi\)
\(422\) 7.33143 2.91158i 0.356889 0.141733i
\(423\) 12.6224 3.51586i 0.613721 0.170947i
\(424\) 15.6660 1.36494i 0.760808 0.0662871i
\(425\) 10.7243 29.4647i 0.520204 1.42925i
\(426\) −21.8115 18.6669i −1.05677 0.904412i
\(427\) −0.350828 + 0.418100i −0.0169777 + 0.0202333i
\(428\) 8.97860 + 13.6584i 0.433997 + 0.660204i
\(429\) −5.15163 + 5.67795i −0.248723 + 0.274134i
\(430\) 5.79316 + 3.12454i 0.279371 + 0.150679i
\(431\) 16.8732 0.812754 0.406377 0.913706i \(-0.366792\pi\)
0.406377 + 0.913706i \(0.366792\pi\)
\(432\) −18.0025 + 10.3880i −0.866144 + 0.499795i
\(433\) −2.79450 −0.134295 −0.0671475 0.997743i \(-0.521390\pi\)
−0.0671475 + 0.997743i \(0.521390\pi\)
\(434\) −5.95100 3.20967i −0.285657 0.154069i
\(435\) −5.32309 1.15261i −0.255222 0.0552632i
\(436\) −21.0736 32.0575i −1.00924 1.53528i
\(437\) −18.0451 + 21.5053i −0.863213 + 1.02874i
\(438\) −3.55521 + 1.25493i −0.169874 + 0.0599629i
\(439\) −1.92679 + 5.29380i −0.0919605 + 0.252659i −0.977142 0.212586i \(-0.931812\pi\)
0.885182 + 0.465245i \(0.154034\pi\)
\(440\) −4.91848 + 0.428534i −0.234479 + 0.0204296i
\(441\) −17.8244 1.38254i −0.848781 0.0658353i
\(442\) 20.7767 8.25116i 0.988245 0.392468i
\(443\) −4.19281 + 3.51819i −0.199206 + 0.167154i −0.736934 0.675964i \(-0.763727\pi\)
0.537728 + 0.843119i \(0.319283\pi\)
\(444\) −13.2988 34.4611i −0.631135 1.63545i
\(445\) −0.581665 + 3.29879i −0.0275736 + 0.156377i
\(446\) −14.3576 + 12.7741i −0.679850 + 0.604870i
\(447\) −2.60159 19.0356i −0.123051 0.900354i
\(448\) −1.42293 + 8.03612i −0.0672270 + 0.379671i
\(449\) −21.3460 12.3241i −1.00738 0.581612i −0.0969581 0.995288i \(-0.530911\pi\)
−0.910424 + 0.413676i \(0.864245\pi\)
\(450\) −5.37330 17.3320i −0.253300 0.817039i
\(451\) −7.22118 + 4.16915i −0.340032 + 0.196318i
\(452\) −9.88071 1.15728i −0.464749 0.0544340i
\(453\) 5.43740 8.62856i 0.255471 0.405405i
\(454\) 24.9048 5.13932i 1.16884 0.241200i
\(455\) 1.75751 0.639680i 0.0823932 0.0299887i
\(456\) 15.0313 19.7756i 0.703903 0.926077i
\(457\) −1.98007 11.2295i −0.0926236 0.525294i −0.995450 0.0952886i \(-0.969623\pi\)
0.902826 0.430006i \(-0.141489\pi\)
\(458\) 12.1852 15.4069i 0.569376 0.719916i
\(459\) −15.0967 34.9750i −0.704655 1.63249i
\(460\) −9.16227 + 2.16918i −0.427193 + 0.101139i
\(461\) 18.4150 3.24705i 0.857670 0.151230i 0.272515 0.962152i \(-0.412145\pi\)
0.585155 + 0.810921i \(0.301034\pi\)
\(462\) 5.06027 0.841552i 0.235425 0.0391525i
\(463\) 12.1162 + 33.2889i 0.563086 + 1.54707i 0.815086 + 0.579340i \(0.196690\pi\)
−0.252000 + 0.967727i \(0.581088\pi\)
\(464\) −3.41831 + 14.3923i −0.158691 + 0.668146i
\(465\) −0.267081 + 6.89703i −0.0123856 + 0.319842i
\(466\) 1.81715 + 2.94684i 0.0841779 + 0.136510i
\(467\) −1.62531 2.81512i −0.0752103 0.130268i 0.825967 0.563718i \(-0.190629\pi\)
−0.901178 + 0.433450i \(0.857296\pi\)
\(468\) 6.68546 11.0758i 0.309036 0.511979i
\(469\) −3.31596 + 5.74342i −0.153117 + 0.265206i
\(470\) −5.24981 + 0.152126i −0.242156 + 0.00701705i
\(471\) −11.6184 + 28.4451i −0.535349 + 1.31068i
\(472\) −19.5907 + 27.9571i −0.901736 + 1.28683i
\(473\) −11.0661 1.95125i −0.508820 0.0897187i
\(474\) −0.345095 + 35.4460i −0.0158507 + 1.62809i
\(475\) 13.9396 + 16.6125i 0.639591 + 0.762235i
\(476\) −14.3283 4.29335i −0.656738 0.196786i
\(477\) 9.70102 + 13.5679i 0.444179 + 0.621230i
\(478\) −21.5568 3.16023i −0.985983 0.144546i
\(479\) 36.5463 + 13.3018i 1.66984 + 0.607774i 0.991864 0.127306i \(-0.0406329\pi\)
0.677981 + 0.735079i \(0.262855\pi\)
\(480\) 8.00507 2.30774i 0.365380 0.105333i
\(481\) 17.6126 + 14.7788i 0.803068 + 0.673854i
\(482\) −5.20143 + 15.6908i −0.236919 + 0.714695i
\(483\) 9.31556 2.98774i 0.423873 0.135947i
\(484\) −12.4628 + 5.37238i −0.566490 + 0.244199i
\(485\) 3.71903i 0.168872i
\(486\) −19.2009 10.8317i −0.870971 0.491334i
\(487\) 14.4854i 0.656395i 0.944609 + 0.328198i \(0.106441\pi\)
−0.944609 + 0.328198i \(0.893559\pi\)
\(488\) 0.392183 1.46155i 0.0177533 0.0661612i
\(489\) 29.7525 9.54239i 1.34545 0.431522i
\(490\) 6.80200 + 2.25484i 0.307283 + 0.101863i
\(491\) 5.58619 + 4.68737i 0.252101 + 0.211538i 0.760076 0.649834i \(-0.225161\pi\)
−0.507975 + 0.861372i \(0.669606\pi\)
\(492\) 10.6026 9.24989i 0.478002 0.417017i
\(493\) −25.4770 9.27287i −1.14743 0.417629i
\(494\) −2.24264 + 15.2977i −0.100901 + 0.688274i
\(495\) −3.04572 4.25976i −0.136895 0.191462i
\(496\) 18.7143 + 1.09896i 0.840297 + 0.0493449i
\(497\) −7.68539 9.15909i −0.344737 0.410842i
\(498\) −12.9233 0.125819i −0.579108 0.00563807i
\(499\) −14.1578 2.49639i −0.633788 0.111754i −0.152482 0.988306i \(-0.548726\pi\)
−0.481307 + 0.876552i \(0.659838\pi\)
\(500\) 0.913542 + 15.7498i 0.0408548 + 0.704351i
\(501\) 10.5268 25.7726i 0.470304 1.15143i
\(502\) 0.142859 + 4.93003i 0.00637613 + 0.220038i
\(503\) −9.08769 + 15.7403i −0.405200 + 0.701827i −0.994345 0.106200i \(-0.966132\pi\)
0.589145 + 0.808028i \(0.299465\pi\)
\(504\) −8.10566 + 3.03771i −0.361055 + 0.135310i
\(505\) 2.56961 + 4.45069i 0.114346 + 0.198053i
\(506\) 13.6820 8.43690i 0.608237 0.375066i
\(507\) 0.559691 14.4533i 0.0248568 0.641894i
\(508\) 26.5476 + 13.3407i 1.17786 + 0.591896i
\(509\) 6.60337 + 18.1426i 0.292689 + 0.804157i 0.995671 + 0.0929491i \(0.0296294\pi\)
−0.702982 + 0.711208i \(0.748148\pi\)
\(510\) 2.50496 + 15.0624i 0.110921 + 0.666973i
\(511\) −1.54632 + 0.272658i −0.0684052 + 0.0120617i
\(512\) −5.83289 21.8627i −0.257780 0.966204i
\(513\) 26.1691 + 3.05234i 1.15539 + 0.134764i
\(514\) −19.8033 15.6623i −0.873487 0.690834i
\(515\) −0.0252774 0.143355i −0.00111386 0.00631699i
\(516\) 18.9579 0.364678i 0.834577 0.0160541i
\(517\) 8.42546 3.06662i 0.370551 0.134870i
\(518\) −3.10905 15.0662i −0.136604 0.661972i
\(519\) 5.04478 8.00552i 0.221441 0.351403i
\(520\) −3.66807 + 3.66544i −0.160855 + 0.160740i
\(521\) 24.7853 14.3098i 1.08586 0.626924i 0.153392 0.988165i \(-0.450980\pi\)
0.932472 + 0.361241i \(0.117647\pi\)
\(522\) −14.9863 + 4.64609i −0.655934 + 0.203354i
\(523\) 10.5509 + 6.09156i 0.461359 + 0.266365i 0.712615 0.701555i \(-0.247511\pi\)
−0.251257 + 0.967920i \(0.580844\pi\)
\(524\) −5.03495 3.75025i −0.219953 0.163831i
\(525\) −1.02333 7.48760i −0.0446617 0.326785i
\(526\) 6.92282 + 7.78098i 0.301849 + 0.339267i
\(527\) −5.96633 + 33.8368i −0.259898 + 1.47395i
\(528\) −11.7323 + 8.03981i −0.510584 + 0.349888i
\(529\) 5.86398 4.92046i 0.254956 0.213933i
\(530\) −2.46759 6.21347i −0.107185 0.269896i
\(531\) −36.1003 2.80010i −1.56662 0.121514i
\(532\) 7.52639 7.09738i 0.326310 0.307711i
\(533\) −2.99539 + 8.22975i −0.129745 + 0.356470i
\(534\) 3.21195 + 9.09943i 0.138995 + 0.393771i
\(535\) 4.46679 5.32331i 0.193116 0.230147i
\(536\) 1.60915 18.3171i 0.0695048 0.791176i
\(537\) 22.8134 + 4.93977i 0.984470 + 0.213167i
\(538\) 0.608842 1.12884i 0.0262490 0.0486679i
\(539\) −12.2337 −0.526944
\(540\) 6.42741 + 6.06392i 0.276592 + 0.260950i
\(541\) 6.27951 0.269977 0.134989 0.990847i \(-0.456900\pi\)
0.134989 + 0.990847i \(0.456900\pi\)
\(542\) 4.50836 8.35888i 0.193651 0.359045i
\(543\) 16.6886 18.3935i 0.716174 0.789342i
\(544\) 41.0373 5.98603i 1.75946 0.256649i
\(545\) −10.4839 + 12.4943i −0.449083 + 0.535196i
\(546\) 3.50331 4.09348i 0.149928 0.175185i
\(547\) 8.59471 23.6138i 0.367483 1.00965i −0.608832 0.793299i \(-0.708362\pi\)
0.976315 0.216353i \(-0.0694162\pi\)
\(548\) −16.4838 17.4801i −0.704151 0.746714i
\(549\) 1.54619 0.430678i 0.0659896 0.0183809i
\(550\) −4.58307 11.5403i −0.195423 0.492079i
\(551\) 14.3642 12.0530i 0.611936 0.513476i
\(552\) −19.9140 + 18.4160i −0.847598 + 0.783836i
\(553\) −2.56355 + 14.5386i −0.109013 + 0.618245i
\(554\) 1.68374 + 1.89246i 0.0715353 + 0.0804029i
\(555\) −12.4116 + 9.62130i −0.526842 + 0.408401i
\(556\) 3.43414 4.61055i 0.145640 0.195531i
\(557\) 17.6052 + 10.1644i 0.745958 + 0.430679i 0.824232 0.566253i \(-0.191607\pi\)
−0.0782737 + 0.996932i \(0.524941\pi\)
\(558\) 9.09639 + 17.6810i 0.385081 + 0.748496i
\(559\) −10.2211 + 5.90115i −0.432306 + 0.249592i
\(560\) 3.44638 0.401154i 0.145636 0.0169518i
\(561\) −12.1504 23.0625i −0.512992 0.973701i
\(562\) −1.64358 7.96468i −0.0693303 0.335970i
\(563\) 33.7274 12.2758i 1.42144 0.517362i 0.486976 0.873416i \(-0.338100\pi\)
0.934466 + 0.356053i \(0.115878\pi\)
\(564\) −12.9550 + 7.81556i −0.545502 + 0.329094i
\(565\) 0.734434 + 4.16518i 0.0308979 + 0.175230i
\(566\) −11.4828 9.08166i −0.482659 0.381731i
\(567\) −7.14822 5.76181i −0.300197 0.241973i
\(568\) 30.0391 + 14.0206i 1.26041 + 0.588290i
\(569\) 37.1364 6.54816i 1.55684 0.274513i 0.672051 0.740505i \(-0.265413\pi\)
0.884789 + 0.465992i \(0.154302\pi\)
\(570\) −9.88795 3.70833i −0.414161 0.155325i
\(571\) −4.67247 12.8375i −0.195537 0.537233i 0.802713 0.596365i \(-0.203389\pi\)
−0.998250 + 0.0591320i \(0.981167\pi\)
\(572\) 3.97500 7.91016i 0.166203 0.330740i
\(573\) 12.8653 6.77804i 0.537455 0.283157i
\(574\) 4.98783 3.07571i 0.208188 0.128378i
\(575\) −11.8402 20.5079i −0.493772 0.855238i
\(576\) 16.8148 17.1250i 0.700615 0.713540i
\(577\) 8.52845 14.7717i 0.355044 0.614954i −0.632082 0.774902i \(-0.717799\pi\)
0.987125 + 0.159948i \(0.0511326\pi\)
\(578\) 1.50526 + 51.9459i 0.0626104 + 2.16067i
\(579\) 1.31125 + 1.69152i 0.0544935 + 0.0702973i
\(580\) 6.27846 0.364172i 0.260699 0.0151214i
\(581\) −5.30066 0.934650i −0.219909 0.0387758i
\(582\) −5.26626 9.33004i −0.218294 0.386743i
\(583\) 7.33643 + 8.74322i 0.303844 + 0.362107i
\(584\) 3.56703 2.49575i 0.147605 0.103275i
\(585\) −5.32649 1.37110i −0.220223 0.0566881i
\(586\) 2.57228 17.5462i 0.106260 0.724825i
\(587\) −5.94463 2.16367i −0.245361 0.0893041i 0.216412 0.976302i \(-0.430564\pi\)
−0.461773 + 0.886998i \(0.652787\pi\)
\(588\) 20.2573 3.97507i 0.835399 0.163929i
\(589\) −18.2036 15.2746i −0.750065 0.629379i
\(590\) 13.7763 + 4.56680i 0.567161 + 0.188012i
\(591\) −3.74977 3.40219i −0.154245 0.139947i
\(592\) 25.4540 + 34.2248i 1.04615 + 1.40663i
\(593\) 28.7935i 1.18241i 0.806523 + 0.591203i \(0.201347\pi\)
−0.806523 + 0.591203i \(0.798653\pi\)
\(594\) −13.6729 6.37374i −0.561004 0.261518i
\(595\) 6.35919i 0.260701i
\(596\) 8.78207 + 20.3725i 0.359728 + 0.834491i
\(597\) −5.29114 + 24.4361i −0.216552 + 1.00010i
\(598\) 5.31239 16.0255i 0.217240 0.655330i
\(599\) −36.9656 31.0178i −1.51037 1.26735i −0.863024 0.505163i \(-0.831433\pi\)
−0.647351 0.762192i \(-0.724123\pi\)
\(600\) 11.3387 + 17.6199i 0.462899 + 0.719331i
\(601\) −41.1432 14.9749i −1.67827 0.610839i −0.685196 0.728358i \(-0.740284\pi\)
−0.993071 + 0.117519i \(0.962506\pi\)
\(602\) 7.81337 + 1.14544i 0.318449 + 0.0466848i
\(603\) 17.5936 8.41615i 0.716467 0.342732i
\(604\) −3.38028 + 11.2811i −0.137542 + 0.459022i
\(605\) 3.70876 + 4.41992i 0.150782 + 0.179695i
\(606\) 12.7488 + 7.52694i 0.517884 + 0.305761i
\(607\) 1.37632 + 0.242682i 0.0558630 + 0.00985015i 0.201510 0.979486i \(-0.435415\pi\)
−0.145647 + 0.989337i \(0.546526\pi\)
\(608\) −10.6057 + 26.6496i −0.430117 + 1.08079i
\(609\) −6.47424 + 0.884832i −0.262349 + 0.0358552i
\(610\) −0.643079 + 0.0186348i −0.0260375 + 0.000754500i
\(611\) 4.70870 8.15571i 0.190494 0.329945i
\(612\) 27.6131 + 34.2403i 1.11619 + 1.38408i
\(613\) −9.57422 16.5830i −0.386699 0.669782i 0.605304 0.795994i \(-0.293051\pi\)
−0.992003 + 0.126212i \(0.959718\pi\)
\(614\) −19.7295 31.9949i −0.796216 1.29121i
\(615\) −5.06089 3.18919i −0.204075 0.128600i
\(616\) −5.36927 + 2.50139i −0.216334 + 0.100784i
\(617\) 2.45052 + 6.73275i 0.0986543 + 0.271050i 0.979195 0.202919i \(-0.0650429\pi\)
−0.880541 + 0.473970i \(0.842821\pi\)
\(618\) −0.266410 0.323846i −0.0107166 0.0130270i
\(619\) −0.559347 + 0.0986280i −0.0224821 + 0.00396419i −0.184878 0.982761i \(-0.559189\pi\)
0.162396 + 0.986726i \(0.448078\pi\)
\(620\) −1.83615 7.75558i −0.0737415 0.311472i
\(621\) −27.5628 8.24453i −1.10606 0.330842i
\(622\) 19.4045 24.5350i 0.778051 0.983764i
\(623\) 0.697858 + 3.95775i 0.0279591 + 0.158564i
\(624\) −4.01182 + 14.3897i −0.160601 + 0.576049i
\(625\) −13.7927 + 5.02013i −0.551708 + 0.200805i
\(626\) −7.60353 + 1.56906i −0.303898 + 0.0627121i
\(627\) 18.0152 + 0.697623i 0.719458 + 0.0278604i
\(628\) 4.12738 35.2389i 0.164700 1.40619i
\(629\) −67.7005 + 39.0869i −2.69939 + 1.55850i
\(630\) 2.22625 + 2.93037i 0.0886961 + 0.116749i
\(631\) −16.0510 9.26705i −0.638980 0.368915i 0.145242 0.989396i \(-0.453604\pi\)
−0.784222 + 0.620481i \(0.786937\pi\)
\(632\) −10.5796 39.5405i −0.420836 1.57284i
\(633\) −8.94399 3.65319i −0.355492 0.145201i
\(634\) 21.1899 18.8528i 0.841557 0.748741i
\(635\) 2.19343 12.4396i 0.0870438 0.493650i
\(636\) −14.9890 12.0937i −0.594353 0.479548i
\(637\) −9.84319 + 8.25942i −0.390002 + 0.327250i
\(638\) −9.97844 + 3.96280i −0.395050 + 0.156889i
\(639\) 3.40958 + 34.9952i 0.134881 + 1.38439i
\(640\) −8.19188 + 5.04337i −0.323813 + 0.199357i
\(641\) −8.67287 + 23.8285i −0.342558 + 0.941170i 0.642092 + 0.766628i \(0.278067\pi\)
−0.984650 + 0.174542i \(0.944155\pi\)
\(642\) 3.66799 19.6799i 0.144764 0.776703i
\(643\) −18.0729 + 21.5384i −0.712725 + 0.849392i −0.993902 0.110263i \(-0.964831\pi\)
0.281178 + 0.959656i \(0.409275\pi\)
\(644\) −9.43948 + 6.20521i −0.371968 + 0.244520i
\(645\) −2.46195 7.67620i −0.0969393 0.302250i
\(646\) −46.2686 24.9550i −1.82041 0.981840i
\(647\) 26.2892 1.03353 0.516767 0.856126i \(-0.327135\pi\)
0.516767 + 0.856126i \(0.327135\pi\)
\(648\) 24.7114 + 6.11134i 0.970754 + 0.240076i
\(649\) −24.7773 −0.972595
\(650\) −11.4788 6.19107i −0.450234 0.242834i
\(651\) 2.52903 + 7.88534i 0.0991206 + 0.309051i
\(652\) −30.1483 + 19.8185i −1.18070 + 0.776153i
\(653\) 3.30137 3.93442i 0.129193 0.153966i −0.697570 0.716516i \(-0.745735\pi\)
0.826763 + 0.562551i \(0.190180\pi\)
\(654\) −8.60909 + 46.1904i −0.336642 + 1.80619i
\(655\) −0.912891 + 2.50815i −0.0356696 + 0.0980014i
\(656\) −8.93440 + 13.5700i −0.348830 + 0.529818i
\(657\) 4.20393 + 1.91011i 0.164011 + 0.0745203i
\(658\) −5.85625 + 2.32573i −0.228300 + 0.0906663i
\(659\) 6.33669 5.31712i 0.246842 0.207125i −0.510969 0.859599i \(-0.670713\pi\)
0.757811 + 0.652474i \(0.226269\pi\)
\(660\) 4.70594 + 3.79694i 0.183178 + 0.147796i
\(661\) 0.914795 5.18806i 0.0355814 0.201792i −0.961835 0.273630i \(-0.911775\pi\)
0.997416 + 0.0718384i \(0.0228866\pi\)
\(662\) 24.6908 21.9676i 0.959634 0.853796i
\(663\) −25.3465 10.3528i −0.984377 0.402070i
\(664\) 14.4162 3.85726i 0.559455 0.149691i
\(665\) −3.80888 2.19906i −0.147702 0.0852759i
\(666\) −17.5133 + 41.7125i −0.678625 + 1.61633i
\(667\) −17.7324 + 10.2378i −0.686601 + 0.396409i
\(668\) −3.73959 + 31.9281i −0.144689 + 1.23533i
\(669\) 23.5190 + 0.910754i 0.909299 + 0.0352118i
\(670\) −7.65606 + 1.57989i −0.295779 + 0.0610366i
\(671\) 1.03208 0.375647i 0.0398431 0.0145017i
\(672\) 8.07800 5.88658i 0.311616 0.227080i
\(673\) 2.65489 + 15.0566i 0.102338 + 0.580390i 0.992250 + 0.124257i \(0.0396547\pi\)
−0.889912 + 0.456133i \(0.849234\pi\)
\(674\) 5.59402 7.07305i 0.215474 0.272444i
\(675\) −9.96933 + 19.8625i −0.383720 + 0.764508i
\(676\) 3.84780 + 16.2525i 0.147992 + 0.625095i
\(677\) −24.0011 + 4.23205i −0.922439 + 0.162651i −0.614647 0.788803i \(-0.710701\pi\)
−0.307792 + 0.951454i \(0.599590\pi\)
\(678\) 7.74053 + 9.40934i 0.297273 + 0.361364i
\(679\) −1.52607 4.19285i −0.0585653 0.160907i
\(680\) −7.44562 15.9821i −0.285526 0.612887i
\(681\) −26.3493 16.6044i −1.00971 0.636281i
\(682\) 7.14158 + 11.5814i 0.273465 + 0.443473i
\(683\) 12.9096 + 22.3600i 0.493971 + 0.855582i 0.999976 0.00694804i \(-0.00221165\pi\)
−0.506005 + 0.862530i \(0.668878\pi\)
\(684\) −30.0573 + 4.69847i −1.14927 + 0.179650i
\(685\) −5.10734 + 8.84617i −0.195141 + 0.337995i
\(686\) 18.6885 0.541544i 0.713531 0.0206763i
\(687\) −23.8362 + 3.25768i −0.909407 + 0.124288i
\(688\) −20.9780 + 6.26947i −0.799778 + 0.239021i
\(689\) 11.8057 + 2.08167i 0.449762 + 0.0793051i
\(690\) 9.93009 + 5.86277i 0.378032 + 0.223192i
\(691\) −6.26030 7.46074i −0.238153 0.283820i 0.633709 0.773572i \(-0.281532\pi\)
−0.871862 + 0.489752i \(0.837087\pi\)
\(692\) −3.13620 + 10.4665i −0.119221 + 0.397878i
\(693\) −5.18172 3.55268i −0.196837 0.134955i
\(694\) 22.6028 + 3.31358i 0.857991 + 0.125782i
\(695\) −2.29673 0.835942i −0.0871200 0.0317091i
\(696\) 15.2353 9.80412i 0.577492 0.371624i
\(697\) −22.8110 19.1407i −0.864030 0.725007i
\(698\) 9.36361 28.2465i 0.354418 1.06915i
\(699\) 0.897323 4.14411i 0.0339399 0.156745i
\(700\) 3.45440 + 8.01346i 0.130564 + 0.302880i
\(701\) 46.8518i 1.76957i −0.466000 0.884785i \(-0.654305\pi\)
0.466000 0.884785i \(-0.345695\pi\)
\(702\) −15.3043 + 4.10276i −0.577622 + 0.154849i
\(703\) 54.0663i 2.03915i
\(704\) 10.5655 12.5732i 0.398203 0.473869i
\(705\) 4.76381 + 4.32223i 0.179415 + 0.162785i
\(706\) −12.9096 4.27949i −0.485859 0.161061i
\(707\) 4.72329 + 3.96331i 0.177638 + 0.149056i
\(708\) 41.0278 8.05083i 1.54192 0.302569i
\(709\) 25.0301 + 9.11022i 0.940026 + 0.342142i 0.766176 0.642631i \(-0.222157\pi\)
0.173850 + 0.984772i \(0.444379\pi\)
\(710\) 2.04427 13.9445i 0.0767199 0.523326i
\(711\) 30.3945 30.9997i 1.13988 1.16258i
\(712\) −6.38779 9.12968i −0.239393 0.342149i
\(713\) 16.6793 + 19.8776i 0.624646 + 0.744424i
\(714\) 9.00482 + 15.9535i 0.336997 + 0.597045i
\(715\) −3.70651 0.653558i −0.138616 0.0244417i
\(716\) −26.9078 + 1.56075i −1.00559 + 0.0583279i
\(717\) 16.3482 + 21.0893i 0.610533 + 0.787595i
\(718\) 0.574796 + 19.8360i 0.0214512 + 0.740274i
\(719\) 19.9787 34.6042i 0.745081 1.29052i −0.205076 0.978746i \(-0.565744\pi\)
0.950157 0.311772i \(-0.100922\pi\)
\(720\) −9.02611 4.75812i −0.336383 0.177325i
\(721\) −0.0873226 0.151247i −0.00325206 0.00563274i
\(722\) 8.07579 4.97989i 0.300550 0.185332i
\(723\) 17.9117 9.43675i 0.666145 0.350956i
\(724\) −12.8769 + 25.6247i −0.478566 + 0.952335i
\(725\) 5.40977 + 14.8632i 0.200914 + 0.552006i
\(726\) 15.5630 + 5.83668i 0.577598 + 0.216620i
\(727\) −46.3051 + 8.16484i −1.71736 + 0.302817i −0.943705 0.330788i \(-0.892686\pi\)
−0.773657 + 0.633605i \(0.781574\pi\)
\(728\) −2.63131 + 5.63759i −0.0975230 + 0.208943i
\(729\) 7.75615 + 25.8620i 0.287265 + 0.957851i
\(730\) −1.45169 1.14813i −0.0537294 0.0424942i
\(731\) −6.96831 39.5192i −0.257732 1.46167i
\(732\) −1.58693 + 0.957372i −0.0586545 + 0.0353855i
\(733\) −10.6192 + 3.86508i −0.392230 + 0.142760i −0.530604 0.847620i \(-0.678035\pi\)
0.138374 + 0.990380i \(0.455812\pi\)
\(734\) −10.6012 51.3728i −0.391298 1.89620i
\(735\) −4.09087 7.76480i −0.150894 0.286409i
\(736\) 16.4583 26.6473i 0.606661 0.982234i
\(737\) 11.5577 6.67287i 0.425735 0.245798i
\(738\) −17.2124 0.834427i −0.633598 0.0307157i
\(739\) 27.1693 + 15.6862i 0.999438 + 0.577026i 0.908082 0.418793i \(-0.137547\pi\)
0.0913557 + 0.995818i \(0.470880\pi\)
\(740\) 10.8320 14.5427i 0.398193 0.534599i
\(741\) 14.9659 11.6014i 0.549787 0.426188i
\(742\) −5.33163 5.99254i −0.195730 0.219993i
\(743\) 1.81455 10.2908i 0.0665695 0.377535i −0.933262 0.359196i \(-0.883051\pi\)
0.999832 0.0183390i \(-0.00583781\pi\)
\(744\) −15.5886 16.8566i −0.571505 0.617994i
\(745\) 7.22511 6.06259i 0.264708 0.222116i
\(746\) 14.7990 + 37.2644i 0.541831 + 1.36435i
\(747\) 11.3022 + 11.0816i 0.413527 + 0.405454i
\(748\) 20.6507 + 21.8990i 0.755065 + 0.800706i
\(749\) 2.85150 7.83444i 0.104192 0.286264i
\(750\) 12.5634 14.6798i 0.458749 0.536031i
\(751\) −6.54549 + 7.80061i −0.238848 + 0.284648i −0.872131 0.489272i \(-0.837263\pi\)
0.633283 + 0.773920i \(0.281707\pi\)
\(752\) 11.9951 12.7019i 0.437415 0.463189i
\(753\) 4.05895 4.47363i 0.147916 0.163028i
\(754\) −5.35318 + 9.92525i −0.194951 + 0.361456i
\(755\) 5.00678 0.182215
\(756\) 9.73458 + 4.19906i 0.354043 + 0.152719i
\(757\) 46.4748 1.68916 0.844578 0.535433i \(-0.179851\pi\)
0.844578 + 0.535433i \(0.179851\pi\)
\(758\) −10.2879 + 19.0746i −0.373673 + 0.692822i
\(759\) −19.2408 4.16620i −0.698397 0.151224i
\(760\) 12.1474 + 1.06715i 0.440632 + 0.0387095i
\(761\) 34.3388 40.9234i 1.24478 1.48347i 0.430942 0.902380i \(-0.358181\pi\)
0.813838 0.581092i \(-0.197374\pi\)
\(762\) −12.1121 34.3136i −0.438776 1.24305i
\(763\) −6.69273 + 18.3881i −0.242293 + 0.665694i
\(764\) −12.2162 + 11.5199i −0.441967 + 0.416774i
\(765\) 10.5749 15.4239i 0.382336 0.557651i
\(766\) −19.2121 48.3765i −0.694160 1.74791i
\(767\) −19.9357 + 16.7280i −0.719837 + 0.604015i
\(768\) −13.4097 + 24.2524i −0.483879 + 0.875135i
\(769\) 4.11818 23.3554i 0.148506 0.842217i −0.815980 0.578080i \(-0.803802\pi\)
0.964485 0.264136i \(-0.0850869\pi\)
\(770\) 1.67391 + 1.88141i 0.0603236 + 0.0678014i
\(771\) 4.18728 + 30.6380i 0.150801 + 1.10340i
\(772\) −1.98196 1.47625i −0.0713323 0.0531315i
\(773\) 24.4917 + 14.1403i 0.880907 + 0.508592i 0.870957 0.491359i \(-0.163500\pi\)
0.00994940 + 0.999951i \(0.496833\pi\)
\(774\) −17.0461 15.7713i −0.612711 0.566888i
\(775\) 17.3593 10.0224i 0.623565 0.360015i
\(776\) 8.74456 + 8.75083i 0.313911 + 0.314136i
\(777\) −10.0449 + 15.9401i −0.360357 + 0.571848i
\(778\) −2.56919 12.4501i −0.0921101 0.446359i
\(779\) 19.3527 7.04382i 0.693384 0.252371i
\(780\) 6.34982 0.122146i 0.227360 0.00437354i
\(781\) 4.17803 + 23.6948i 0.149502 + 0.847866i
\(782\) 45.0242 + 35.6093i 1.61006 + 1.27338i
\(783\) 17.1743 + 8.62010i 0.613761 + 0.308057i
\(784\) −21.3069 + 10.6880i −0.760959 + 0.381713i
\(785\) −14.8548 + 2.61931i −0.530192 + 0.0934872i
\(786\) 1.26142 + 7.58496i 0.0449934 + 0.270546i
\(787\) 2.69409 + 7.40195i 0.0960339 + 0.263851i 0.978403 0.206707i \(-0.0662748\pi\)
−0.882369 + 0.470558i \(0.844053\pi\)
\(788\) 5.22394 + 2.62513i 0.186095 + 0.0935163i
\(789\) 0.493577 12.7460i 0.0175718 0.453769i
\(790\) −14.8120 + 9.13373i −0.526987 + 0.324963i
\(791\) 2.53715 + 4.39448i 0.0902108 + 0.156250i
\(792\) 17.1825 + 2.86174i 0.610555 + 0.101688i
\(793\) 0.576796 0.999040i 0.0204826 0.0354769i
\(794\) −0.193128 6.66479i −0.00685387 0.236525i
\(795\) −3.09612 + 7.58013i −0.109808 + 0.268840i
\(796\) −1.67177 28.8218i −0.0592542 1.02156i
\(797\) 1.80271 + 0.317867i 0.0638553 + 0.0112594i 0.205485 0.978660i \(-0.434123\pi\)
−0.141629 + 0.989920i \(0.545234\pi\)
\(798\) −12.6694 0.123347i −0.448492 0.00436643i
\(799\) 20.5821 + 24.5288i 0.728141 + 0.867765i
\(800\) −18.0642 16.0952i −0.638667 0.569050i
\(801\) 4.88885 10.7598i 0.172739 0.380179i
\(802\) −3.52496 + 24.0447i −0.124471 + 0.849048i
\(803\) 2.96918 + 1.08069i 0.104780 + 0.0381368i
\(804\) −16.9698 + 14.8048i −0.598479 + 0.522124i
\(805\) 3.67900 + 3.08704i 0.129668 + 0.108804i
\(806\) 13.5651 + 4.49677i 0.477809 + 0.158392i
\(807\) −1.49577 + 0.479731i −0.0526536 + 0.0168873i
\(808\) −16.5112 4.43050i −0.580861 0.155864i
\(809\) 0.784403i 0.0275781i −0.999905 0.0137891i \(-0.995611\pi\)
0.999905 0.0137891i \(-0.00438933\pi\)
\(810\) −0.526659 10.8096i −0.0185049 0.379809i
\(811\) 41.4637i 1.45599i 0.685584 + 0.727994i \(0.259547\pi\)
−0.685584 + 0.727994i \(0.740453\pi\)
\(812\) 6.92893 2.98688i 0.243158 0.104819i
\(813\) −11.0759 + 3.55232i −0.388448 + 0.124585i
\(814\) −9.74095 + 29.3848i −0.341420 + 1.02994i
\(815\) 11.7502 + 9.85955i 0.411590 + 0.345365i
\(816\) −41.3103 29.5517i −1.44615 1.03452i
\(817\) 26.0800 + 9.49236i 0.912425 + 0.332096i
\(818\) 27.0280 + 3.96233i 0.945014 + 0.138539i
\(819\) −6.56773 + 0.639894i −0.229495 + 0.0223597i
\(820\) 6.61669 + 1.98263i 0.231065 + 0.0692364i
\(821\) −1.49518 1.78189i −0.0521823 0.0621884i 0.739322 0.673352i \(-0.235146\pi\)
−0.791504 + 0.611164i \(0.790702\pi\)
\(822\) −0.286474 + 29.4248i −0.00999194 + 1.02631i
\(823\) −44.3729 7.82414i −1.54674 0.272732i −0.665863 0.746074i \(-0.731937\pi\)
−0.880879 + 0.473341i \(0.843048\pi\)
\(824\) 0.396549 + 0.277879i 0.0138144 + 0.00968036i
\(825\) −5.75042 + 14.0786i −0.200204 + 0.490154i
\(826\) 17.4054 0.504364i 0.605612 0.0175491i
\(827\) −20.6443 + 35.7571i −0.717874 + 1.24339i 0.243966 + 0.969784i \(0.421551\pi\)
−0.961840 + 0.273611i \(0.911782\pi\)
\(828\) 33.2138 + 0.646787i 1.15426 + 0.0224774i
\(829\) −2.75417 4.77037i −0.0956564 0.165682i 0.814226 0.580548i \(-0.197162\pi\)
−0.909882 + 0.414866i \(0.863828\pi\)
\(830\) −3.33008 5.40033i −0.115589 0.187448i
\(831\) 0.120046 3.10003i 0.00416434 0.107539i
\(832\) 0.0123714 17.2495i 0.000428900 0.598018i
\(833\) −14.9425 41.0542i −0.517728 1.42245i
\(834\) −6.94560 + 1.15509i −0.240507 + 0.0399976i
\(835\) 13.4592 2.37321i 0.465774 0.0821285i
\(836\) −20.2578 + 4.79606i −0.700629 + 0.165875i
\(837\) 6.97875 23.3311i 0.241221 0.806441i
\(838\) −13.4612 + 17.0203i −0.465011 + 0.587957i
\(839\) 4.43317 + 25.1418i 0.153050 + 0.867990i 0.960547 + 0.278118i \(0.0897107\pi\)
−0.807497 + 0.589872i \(0.799178\pi\)
\(840\) −3.38309 2.57146i −0.116728 0.0887238i
\(841\) −14.3994 + 5.24096i −0.496532 + 0.180723i
\(842\) −32.2215 + 6.64918i −1.11043 + 0.229146i
\(843\) −5.31017 + 8.42665i −0.182892 + 0.290229i
\(844\) 11.0802 + 1.29777i 0.381395 + 0.0446711i
\(845\) 6.14933 3.55032i 0.211543 0.122135i
\(846\) 18.0715 + 4.09760i 0.621312 + 0.140878i
\(847\) 5.99495 + 3.46119i 0.205989 + 0.118928i
\(848\) 20.4160 + 8.81817i 0.701088 + 0.302817i
\(849\) 2.42796 + 17.7652i 0.0833275 + 0.609700i
\(850\) 33.1293 29.4755i 1.13633 1.01100i
\(851\) −10.2519 + 58.1415i −0.351431 + 1.99306i
\(852\) −14.6173 37.8777i −0.500781 1.29767i
\(853\) 35.0320 29.3953i 1.19947 1.00648i 0.199827 0.979831i \(-0.435962\pi\)
0.999645 0.0266448i \(-0.00848230\pi\)
\(854\) −0.717365 + 0.284891i −0.0245477 + 0.00974878i
\(855\) 5.58136 + 11.6676i 0.190879 + 0.399024i
\(856\) 2.00641 + 23.0285i 0.0685776 + 0.787096i
\(857\) −14.1429 + 38.8574i −0.483113 + 1.32734i 0.423697 + 0.905804i \(0.360732\pi\)
−0.906810 + 0.421539i \(0.861490\pi\)
\(858\) −10.2241 + 3.60894i −0.349045 + 0.123207i
\(859\) 36.1399 43.0699i 1.23308 1.46953i 0.399866 0.916574i \(-0.369057\pi\)
0.833213 0.552952i \(-0.186499\pi\)
\(860\) 5.11321 + 7.77831i 0.174359 + 0.265238i
\(861\) −7.01433 1.51881i −0.239048 0.0517609i
\(862\) 21.0023 + 11.3276i 0.715341 + 0.385819i
\(863\) −12.4602 −0.424150 −0.212075 0.977253i \(-0.568022\pi\)
−0.212075 + 0.977253i \(0.568022\pi\)
\(864\) −29.3817 + 0.844432i −0.999587 + 0.0287282i
\(865\) 4.64525 0.157943
\(866\) −3.47835 1.87604i −0.118199 0.0637506i
\(867\) 42.7676 47.1370i 1.45246 1.60086i
\(868\) −5.25252 7.99024i −0.178282 0.271206i
\(869\) 19.0960 22.7577i 0.647786 0.772002i
\(870\) −5.85193 5.00824i −0.198399 0.169795i
\(871\) 4.79421 13.1720i 0.162446 0.446316i
\(872\) −4.70922 54.0498i −0.159474 1.83036i
\(873\) −3.27101 + 12.7073i −0.110707 + 0.430077i
\(874\) −36.8982 + 14.6536i −1.24810 + 0.495666i
\(875\) 6.16435 5.17251i 0.208393 0.174863i
\(876\) −5.26769 0.824709i −0.177979 0.0278643i
\(877\) −3.26229 + 18.5014i −0.110160 + 0.624747i 0.878873 + 0.477055i \(0.158296\pi\)
−0.989033 + 0.147693i \(0.952815\pi\)
\(878\) −5.95221 + 5.29574i −0.200877 + 0.178723i
\(879\) −17.1657 + 13.3066i −0.578984 + 0.448821i
\(880\) −6.40978 2.76855i −0.216074 0.0933277i
\(881\) −13.9892 8.07667i −0.471308 0.272110i 0.245479 0.969402i \(-0.421055\pi\)
−0.716787 + 0.697292i \(0.754388\pi\)
\(882\) −21.2581 13.6870i −0.715798 0.460866i
\(883\) 1.99218 1.15019i 0.0670423 0.0387069i −0.466104 0.884730i \(-0.654343\pi\)
0.533146 + 0.846023i \(0.321009\pi\)
\(884\) 31.4003 + 3.67777i 1.05610 + 0.123697i
\(885\) −8.28535 15.7263i −0.278509 0.528633i
\(886\) −7.58073 + 1.56435i −0.254679 + 0.0525553i
\(887\) −9.36820 + 3.40975i −0.314553 + 0.114488i −0.494472 0.869193i \(-0.664639\pi\)
0.179919 + 0.983681i \(0.442416\pi\)
\(888\) 6.58174 51.8222i 0.220869 1.73904i
\(889\) −2.63159 14.9245i −0.0882608 0.500552i
\(890\) −2.93860 + 3.71555i −0.0985020 + 0.124545i
\(891\) 6.66013 + 17.2337i 0.223123 + 0.577351i
\(892\) −26.4467 + 6.26131i −0.885502 + 0.209644i
\(893\) −21.8091 + 3.84554i −0.729815 + 0.128686i
\(894\) 9.54105 25.4404i 0.319100 0.850855i
\(895\) 3.91918 + 10.7679i 0.131004 + 0.359930i
\(896\) −7.16606 + 9.04740i −0.239401 + 0.302252i
\(897\) −18.2938 + 9.63804i −0.610813 + 0.321805i
\(898\) −18.2961 29.6704i −0.610547 0.990113i
\(899\) −8.66598 15.0099i −0.289027 0.500609i
\(900\) 4.94737 25.1807i 0.164912 0.839355i
\(901\) −20.3798 + 35.2989i −0.678951 + 1.17598i
\(902\) −11.7872 + 0.341562i −0.392471 + 0.0113728i
\(903\) −5.92549 7.64394i −0.197188 0.254375i
\(904\) −11.5217 8.07375i −0.383206 0.268529i
\(905\) 12.0071 + 2.11718i 0.399131 + 0.0703775i
\(906\) 12.5607 7.08976i 0.417300 0.235542i
\(907\) 17.6103 + 20.9872i 0.584741 + 0.696868i 0.974586 0.224013i \(-0.0719158\pi\)
−0.389845 + 0.920881i \(0.627471\pi\)
\(908\) 34.4495 + 10.3225i 1.14325 + 0.342564i
\(909\) −4.86538 17.4673i −0.161375 0.579354i
\(910\) 2.61703 + 0.383658i 0.0867537 + 0.0127181i
\(911\) −43.0029 15.6518i −1.42475 0.518566i −0.489327 0.872100i \(-0.662758\pi\)
−0.935422 + 0.353534i \(0.884980\pi\)
\(912\) 31.9856 14.5239i 1.05915 0.480935i
\(913\) 8.29727 + 6.96224i 0.274600 + 0.230416i
\(914\) 5.07415 15.3068i 0.167838 0.506304i
\(915\) 0.583546 + 0.529454i 0.0192914 + 0.0175032i
\(916\) 25.5102 10.9968i 0.842881 0.363344i
\(917\) 3.20230i 0.105749i
\(918\) 4.68884 53.6688i 0.154755 1.77133i
\(919\) 35.8178i 1.18152i −0.806847 0.590760i \(-0.798828\pi\)
0.806847 0.590760i \(-0.201172\pi\)
\(920\) −12.8606 3.45094i −0.424003 0.113774i
\(921\) −9.74255 + 44.9941i −0.321028 + 1.48261i
\(922\) 25.1012 + 8.32096i 0.826664 + 0.274036i
\(923\) 19.3588 + 16.2440i 0.637203 + 0.534676i
\(924\) 6.86355 + 2.34965i 0.225794 + 0.0772977i
\(925\) 42.8560 + 15.5983i 1.40910 + 0.512869i
\(926\) −7.26686 + 49.5691i −0.238804 + 1.62894i
\(927\) −0.0397172 + 0.512053i −0.00130448 + 0.0168180i
\(928\) −13.9169 + 15.6194i −0.456844 + 0.512734i
\(929\) −9.73496 11.6017i −0.319394 0.380639i 0.582329 0.812953i \(-0.302141\pi\)
−0.901723 + 0.432314i \(0.857697\pi\)
\(930\) −4.96266 + 8.40552i −0.162732 + 0.275628i
\(931\) 29.7570 + 5.24696i 0.975246 + 0.171962i
\(932\) 0.283514 + 4.88789i 0.00928682 + 0.160108i
\(933\) −37.9584 + 5.18776i −1.24270 + 0.169840i
\(934\) −0.133155 4.59514i −0.00435697 0.150357i
\(935\) 6.39844 11.0824i 0.209251 0.362434i
\(936\) 15.7570 9.29800i 0.515035 0.303915i
\(937\) −20.1768 34.9472i −0.659147 1.14168i −0.980837 0.194831i \(-0.937584\pi\)
0.321690 0.946845i \(-0.395749\pi\)
\(938\) −7.98318 + 4.92278i −0.260660 + 0.160735i
\(939\) 8.04455 + 5.06938i 0.262524 + 0.165433i
\(940\) −6.63664 3.33503i −0.216463 0.108777i
\(941\) −12.8302 35.2506i −0.418252 1.14914i −0.952694 0.303932i \(-0.901701\pi\)
0.534442 0.845205i \(-0.320522\pi\)
\(942\) −33.5578 + 27.6061i −1.09337 + 0.899456i
\(943\) −22.1471 + 3.90513i −0.721208 + 0.127168i
\(944\) −43.1534 + 21.6466i −1.40452 + 0.704538i
\(945\) 0.522176 4.47686i 0.0169864 0.145632i
\(946\) −12.4642 9.85782i −0.405245 0.320505i
\(947\) −1.96803 11.1613i −0.0639525 0.362693i −0.999943 0.0106676i \(-0.996604\pi\)
0.935991 0.352025i \(-0.114507\pi\)
\(948\) −24.2257 + 43.8884i −0.786813 + 1.42543i
\(949\) 3.11860 1.13508i 0.101234 0.0368462i
\(950\) 6.19818 + 30.0360i 0.201096 + 0.974495i
\(951\) −34.7110 1.34415i −1.12558 0.0435871i
\(952\) −14.9524 14.9631i −0.484609 0.484957i
\(953\) 34.5149 19.9272i 1.11805 0.645505i 0.177145 0.984185i \(-0.443314\pi\)
0.940902 + 0.338680i \(0.109980\pi\)
\(954\) 2.96640 + 23.4007i 0.0960407 + 0.757627i
\(955\) 6.18226 + 3.56933i 0.200053 + 0.115501i
\(956\) −24.7104 18.4054i −0.799191 0.595273i
\(957\) 12.1732 + 4.97217i 0.393504 + 0.160727i
\(958\) 36.5597 + 41.0917i 1.18119 + 1.32761i
\(959\) −2.12809 + 12.0690i −0.0687195 + 0.389728i
\(960\) 11.5133 + 2.50161i 0.371590 + 0.0807392i
\(961\) 6.92155 5.80787i 0.223276 0.187351i
\(962\) 12.0012 + 30.2193i 0.386934 + 0.974310i
\(963\) −19.9443 + 14.2602i −0.642696 + 0.459527i
\(964\) −17.0081 + 16.0386i −0.547792 + 0.516568i
\(965\) −0.359351 + 0.987308i −0.0115679 + 0.0317826i
\(966\) 13.6010 + 2.53499i 0.437604 + 0.0815619i
\(967\) 12.8413 15.3037i 0.412948 0.492132i −0.518974 0.854790i \(-0.673686\pi\)
0.931923 + 0.362657i \(0.118130\pi\)
\(968\) −19.1192 1.67963i −0.614516 0.0539852i
\(969\) 19.6630 + 61.3080i 0.631668 + 1.96950i
\(970\) 2.49671 4.62912i 0.0801646 0.148632i
\(971\) −7.27802 −0.233563 −0.116781 0.993158i \(-0.537258\pi\)
−0.116781 + 0.993158i \(0.537258\pi\)
\(972\) −16.6280 26.3725i −0.533342 0.845900i
\(973\) −2.93237 −0.0940074
\(974\) −9.72455 + 18.0301i −0.311595 + 0.577723i
\(975\) 4.87820 + 15.2099i 0.156227 + 0.487106i
\(976\) 1.46934 1.55592i 0.0470325 0.0498038i
\(977\) −11.3127 + 13.4819i −0.361925 + 0.431325i −0.916023 0.401126i \(-0.868619\pi\)
0.554098 + 0.832451i \(0.313063\pi\)
\(978\) 43.4394 + 8.09636i 1.38904 + 0.258893i
\(979\) 2.76599 7.59951i 0.0884015 0.242881i
\(980\) 6.95279 + 7.37305i 0.222099 + 0.235524i
\(981\) 46.8110 33.4699i 1.49456 1.06861i
\(982\) 3.80640 + 9.58463i 0.121467 + 0.305858i
\(983\) −30.8633 + 25.8973i −0.984385 + 0.825997i −0.984745 0.174003i \(-0.944330\pi\)
0.000360257 1.00000i \(0.499885\pi\)
\(984\) 19.4070 4.39556i 0.618672 0.140125i
\(985\) 0.431616 2.44782i 0.0137524 0.0779939i
\(986\) −25.4864 28.6457i −0.811651 0.912264i
\(987\) 7.14434 + 2.91811i 0.227407 + 0.0928846i
\(988\) −13.0613 + 17.5356i −0.415535 + 0.557882i
\(989\) −26.2459 15.1531i −0.834571 0.481840i
\(990\) −0.931328 7.34687i −0.0295995 0.233499i
\(991\) 34.6152 19.9851i 1.09959 0.634848i 0.163476 0.986547i \(-0.447729\pi\)
0.936113 + 0.351700i \(0.114396\pi\)
\(992\) 22.5562 + 13.9315i 0.716159 + 0.442324i
\(993\) −40.4458 1.56623i −1.28351 0.0497027i
\(994\) −3.41728 16.5599i −0.108390 0.525249i
\(995\) −11.5338 + 4.19796i −0.365646 + 0.133084i
\(996\) −16.0013 8.83248i −0.507022 0.279868i
\(997\) 4.92799 + 27.9480i 0.156071 + 0.885123i 0.957800 + 0.287435i \(0.0928026\pi\)
−0.801729 + 0.597688i \(0.796086\pi\)
\(998\) −15.9464 12.6119i −0.504775 0.399222i
\(999\) 50.8706 21.9580i 1.60947 0.694719i
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 108.2.l.a.95.14 yes 96
3.2 odd 2 324.2.l.a.71.3 96
4.3 odd 2 inner 108.2.l.a.95.13 yes 96
9.2 odd 6 972.2.l.b.863.9 96
9.4 even 3 972.2.l.d.539.3 96
9.5 odd 6 972.2.l.a.539.14 96
9.7 even 3 972.2.l.c.863.8 96
12.11 even 2 324.2.l.a.71.4 96
27.2 odd 18 inner 108.2.l.a.83.13 96
27.7 even 9 972.2.l.b.107.16 96
27.11 odd 18 972.2.l.d.431.10 96
27.16 even 9 972.2.l.a.431.7 96
27.20 odd 18 972.2.l.c.107.1 96
27.25 even 9 324.2.l.a.251.4 96
36.7 odd 6 972.2.l.c.863.1 96
36.11 even 6 972.2.l.b.863.16 96
36.23 even 6 972.2.l.a.539.7 96
36.31 odd 6 972.2.l.d.539.10 96
108.7 odd 18 972.2.l.b.107.9 96
108.11 even 18 972.2.l.d.431.3 96
108.43 odd 18 972.2.l.a.431.14 96
108.47 even 18 972.2.l.c.107.8 96
108.79 odd 18 324.2.l.a.251.3 96
108.83 even 18 inner 108.2.l.a.83.14 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.83.13 96 27.2 odd 18 inner
108.2.l.a.83.14 yes 96 108.83 even 18 inner
108.2.l.a.95.13 yes 96 4.3 odd 2 inner
108.2.l.a.95.14 yes 96 1.1 even 1 trivial
324.2.l.a.71.3 96 3.2 odd 2
324.2.l.a.71.4 96 12.11 even 2
324.2.l.a.251.3 96 108.79 odd 18
324.2.l.a.251.4 96 27.25 even 9
972.2.l.a.431.7 96 27.16 even 9
972.2.l.a.431.14 96 108.43 odd 18
972.2.l.a.539.7 96 36.23 even 6
972.2.l.a.539.14 96 9.5 odd 6
972.2.l.b.107.9 96 108.7 odd 18
972.2.l.b.107.16 96 27.7 even 9
972.2.l.b.863.9 96 9.2 odd 6
972.2.l.b.863.16 96 36.11 even 6
972.2.l.c.107.1 96 27.20 odd 18
972.2.l.c.107.8 96 108.47 even 18
972.2.l.c.863.1 96 36.7 odd 6
972.2.l.c.863.8 96 9.7 even 3
972.2.l.d.431.3 96 108.11 even 18
972.2.l.d.431.10 96 27.11 odd 18
972.2.l.d.539.3 96 9.4 even 3
972.2.l.d.539.10 96 36.31 odd 6