Properties

Label 920.2.bb.a.11.3
Level $920$
Weight $2$
Character 920.11
Analytic conductor $7.346$
Analytic rank $0$
Dimension $480$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(11,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bb (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(48\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 11.3
Character \(\chi\) \(=\) 920.11
Dual form 920.2.bb.a.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41066 + 0.100200i) q^{2} +(0.472161 - 3.28395i) q^{3} +(1.97992 - 0.282697i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.337006 + 4.67985i) q^{6} +(-2.50066 - 2.88591i) q^{7} +(-2.76467 + 0.597177i) q^{8} +(-7.68293 - 2.25591i) q^{9} +(1.32529 - 0.493570i) q^{10} +(3.41038 - 5.30666i) q^{11} +(0.00647816 - 6.63544i) q^{12} +(-2.21330 - 1.91783i) q^{13} +(3.81675 + 3.82047i) q^{14} +(0.472161 + 3.28395i) q^{15} +(3.84017 - 1.11943i) q^{16} +(2.31222 - 1.05596i) q^{17} +(11.0640 + 2.41249i) q^{18} +(4.58611 + 2.09441i) q^{19} +(-1.82007 + 0.829053i) q^{20} +(-10.6579 + 6.84943i) q^{21} +(-4.27916 + 7.82761i) q^{22} +(-4.07093 - 2.53526i) q^{23} +(0.655734 + 9.36100i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.31438 + 2.48364i) q^{26} +(-6.90119 + 15.1115i) q^{27} +(-5.76694 - 5.00695i) q^{28} +(-2.30440 + 1.05238i) q^{29} +(-0.995111 - 4.58523i) q^{30} +(7.20895 - 1.03649i) q^{31} +(-5.30500 + 1.96393i) q^{32} +(-15.8166 - 13.7051i) q^{33} +(-3.15595 + 1.72128i) q^{34} +(3.21242 + 2.06450i) q^{35} +(-15.8493 - 2.29458i) q^{36} +(4.44531 + 1.30526i) q^{37} +(-6.67930 - 2.49497i) q^{38} +(-7.34310 + 6.36284i) q^{39} +(2.48443 - 1.35188i) q^{40} +(-1.04437 + 0.306656i) q^{41} +(14.3484 - 10.7301i) q^{42} +(2.20221 + 0.316629i) q^{43} +(5.25211 - 11.4709i) q^{44} +8.00728 q^{45} +(5.99672 + 3.16849i) q^{46} +3.74592i q^{47} +(-1.86299 - 13.1395i) q^{48} +(-1.07900 + 7.50461i) q^{49} +(-1.13255 + 0.846954i) q^{50} +(-2.37597 - 8.09181i) q^{51} +(-4.92432 - 3.17146i) q^{52} +(2.63107 + 3.03642i) q^{53} +(8.22106 - 22.0087i) q^{54} +(-1.77718 + 6.05252i) q^{55} +(8.63689 + 6.48525i) q^{56} +(9.04332 - 14.0717i) q^{57} +(3.14527 - 1.71545i) q^{58} +(-6.58513 + 7.59965i) q^{59} +(1.86320 + 6.36848i) q^{60} +(0.283392 + 1.97104i) q^{61} +(-10.0655 + 2.18447i) q^{62} +(12.7020 + 27.8135i) q^{63} +(7.28676 - 3.30199i) q^{64} +(2.66396 + 1.21659i) q^{65} +(23.6851 + 17.7485i) q^{66} +(-4.44821 - 6.92155i) q^{67} +(4.27950 - 2.74437i) q^{68} +(-10.2478 + 12.1717i) q^{69} +(-4.73849 - 2.59042i) q^{70} +(-0.130034 - 0.202337i) q^{71} +(22.5879 + 1.64877i) q^{72} +(1.49297 - 3.26915i) q^{73} +(-6.40161 - 1.39586i) q^{74} +(-1.37823 - 3.01791i) q^{75} +(9.67222 + 2.85028i) q^{76} +(-23.8428 + 3.42807i) q^{77} +(9.72106 - 9.71157i) q^{78} +(6.19095 - 7.14474i) q^{79} +(-3.36923 + 2.15599i) q^{80} +(26.1585 + 16.8111i) q^{81} +(1.44253 - 0.537233i) q^{82} +(0.562599 - 1.91603i) q^{83} +(-19.1655 + 16.5743i) q^{84} +(-1.92106 + 1.66461i) q^{85} +(-3.13829 - 0.225995i) q^{86} +(2.36793 + 8.06442i) q^{87} +(-6.25956 + 16.7078i) q^{88} +(-6.65719 - 0.957159i) q^{89} +(-11.2955 + 0.802332i) q^{90} +11.1832i q^{91} +(-8.77682 - 3.86878i) q^{92} -24.1633i q^{93} +(-0.375342 - 5.28421i) q^{94} +(-4.99041 - 0.717512i) q^{95} +(3.94463 + 18.3486i) q^{96} +(-2.22710 - 7.58480i) q^{97} +(0.770138 - 10.6946i) q^{98} +(-38.1731 + 33.0772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41066 + 0.100200i −0.997487 + 0.0708523i
\(3\) 0.472161 3.28395i 0.272602 1.89599i −0.148394 0.988928i \(-0.547410\pi\)
0.420996 0.907063i \(-0.361681\pi\)
\(4\) 1.97992 0.282697i 0.989960 0.141348i
\(5\) −0.959493 + 0.281733i −0.429098 + 0.125995i
\(6\) −0.337006 + 4.67985i −0.137582 + 1.91054i
\(7\) −2.50066 2.88591i −0.945160 1.09077i −0.995754 0.0920532i \(-0.970657\pi\)
0.0505944 0.998719i \(-0.483888\pi\)
\(8\) −2.76467 + 0.597177i −0.977457 + 0.211134i
\(9\) −7.68293 2.25591i −2.56098 0.751971i
\(10\) 1.32529 0.493570i 0.419093 0.156081i
\(11\) 3.41038 5.30666i 1.02827 1.60002i 0.253957 0.967215i \(-0.418268\pi\)
0.774313 0.632803i \(-0.218096\pi\)
\(12\) 0.00647816 6.63544i 0.00187008 1.91549i
\(13\) −2.21330 1.91783i −0.613858 0.531911i 0.291494 0.956573i \(-0.405848\pi\)
−0.905352 + 0.424662i \(0.860393\pi\)
\(14\) 3.81675 + 3.82047i 1.02007 + 1.02106i
\(15\) 0.472161 + 3.28395i 0.121911 + 0.847913i
\(16\) 3.84017 1.11943i 0.960041 0.279859i
\(17\) 2.31222 1.05596i 0.560796 0.256107i −0.114788 0.993390i \(-0.536619\pi\)
0.675584 + 0.737283i \(0.263892\pi\)
\(18\) 11.0640 + 2.41249i 2.60782 + 0.568630i
\(19\) 4.58611 + 2.09441i 1.05213 + 0.480490i 0.864961 0.501838i \(-0.167343\pi\)
0.187165 + 0.982328i \(0.440070\pi\)
\(20\) −1.82007 + 0.829053i −0.406981 + 0.185382i
\(21\) −10.6579 + 6.84943i −2.32575 + 1.49467i
\(22\) −4.27916 + 7.82761i −0.912320 + 1.66885i
\(23\) −4.07093 2.53526i −0.848847 0.528639i
\(24\) 0.655734 + 9.36100i 0.133851 + 1.91081i
\(25\) 0.841254 0.540641i 0.168251 0.108128i
\(26\) 3.31438 + 2.48364i 0.650002 + 0.487081i
\(27\) −6.90119 + 15.1115i −1.32814 + 2.90821i
\(28\) −5.76694 5.00695i −1.08985 0.946224i
\(29\) −2.30440 + 1.05238i −0.427916 + 0.195423i −0.617718 0.786400i \(-0.711943\pi\)
0.189802 + 0.981822i \(0.439215\pi\)
\(30\) −0.995111 4.58523i −0.181682 0.837144i
\(31\) 7.20895 1.03649i 1.29477 0.186159i 0.539728 0.841840i \(-0.318527\pi\)
0.755039 + 0.655680i \(0.227618\pi\)
\(32\) −5.30500 + 1.96393i −0.937800 + 0.347176i
\(33\) −15.8166 13.7051i −2.75331 2.38576i
\(34\) −3.15595 + 1.72128i −0.541241 + 0.295197i
\(35\) 3.21242 + 2.06450i 0.542998 + 0.348964i
\(36\) −15.8493 2.29458i −2.64155 0.382431i
\(37\) 4.44531 + 1.30526i 0.730804 + 0.214584i 0.625905 0.779899i \(-0.284730\pi\)
0.104899 + 0.994483i \(0.466548\pi\)
\(38\) −6.67930 2.49497i −1.08353 0.404737i
\(39\) −7.34310 + 6.36284i −1.17584 + 1.01887i
\(40\) 2.48443 1.35188i 0.392823 0.213752i
\(41\) −1.04437 + 0.306656i −0.163104 + 0.0478916i −0.362265 0.932075i \(-0.617996\pi\)
0.199161 + 0.979967i \(0.436178\pi\)
\(42\) 14.3484 10.7301i 2.21400 1.65570i
\(43\) 2.20221 + 0.316629i 0.335833 + 0.0482855i 0.308169 0.951332i \(-0.400284\pi\)
0.0276646 + 0.999617i \(0.491193\pi\)
\(44\) 5.25211 11.4709i 0.791786 1.72930i
\(45\) 8.00728 1.19365
\(46\) 5.99672 + 3.16849i 0.884169 + 0.467168i
\(47\) 3.74592i 0.546398i 0.961958 + 0.273199i \(0.0880818\pi\)
−0.961958 + 0.273199i \(0.911918\pi\)
\(48\) −1.86299 13.1395i −0.268900 1.89652i
\(49\) −1.07900 + 7.50461i −0.154143 + 1.07209i
\(50\) −1.13255 + 0.846954i −0.160167 + 0.119777i
\(51\) −2.37597 8.09181i −0.332702 1.13308i
\(52\) −4.92432 3.17146i −0.682880 0.439803i
\(53\) 2.63107 + 3.03642i 0.361406 + 0.417084i 0.907110 0.420893i \(-0.138283\pi\)
−0.545704 + 0.837978i \(0.683738\pi\)
\(54\) 8.22106 22.0087i 1.11874 2.99500i
\(55\) −1.77718 + 6.05252i −0.239635 + 0.816122i
\(56\) 8.63689 + 6.48525i 1.15415 + 0.866628i
\(57\) 9.04332 14.0717i 1.19782 1.86384i
\(58\) 3.14527 1.71545i 0.412994 0.225250i
\(59\) −6.58513 + 7.59965i −0.857311 + 0.989390i −1.00000 0.000377513i \(-0.999880\pi\)
0.142688 + 0.989768i \(0.454425\pi\)
\(60\) 1.86320 + 6.36848i 0.240539 + 0.822168i
\(61\) 0.283392 + 1.97104i 0.0362847 + 0.252365i 0.999888 0.0149710i \(-0.00476560\pi\)
−0.963603 + 0.267336i \(0.913857\pi\)
\(62\) −10.0655 + 2.18447i −1.27832 + 0.277429i
\(63\) 12.7020 + 27.8135i 1.60030 + 3.50418i
\(64\) 7.28676 3.30199i 0.910845 0.412749i
\(65\) 2.66396 + 1.21659i 0.330423 + 0.150899i
\(66\) 23.6851 + 17.7485i 2.91543 + 2.18468i
\(67\) −4.44821 6.92155i −0.543435 0.845602i 0.455570 0.890200i \(-0.349436\pi\)
−0.999005 + 0.0445982i \(0.985799\pi\)
\(68\) 4.27950 2.74437i 0.518966 0.332803i
\(69\) −10.2478 + 12.1717i −1.23369 + 1.46530i
\(70\) −4.73849 2.59042i −0.566358 0.309614i
\(71\) −0.130034 0.202337i −0.0154322 0.0240130i 0.833452 0.552592i \(-0.186361\pi\)
−0.848884 + 0.528579i \(0.822725\pi\)
\(72\) 22.5879 + 1.64877i 2.66201 + 0.194310i
\(73\) 1.49297 3.26915i 0.174739 0.382626i −0.801916 0.597436i \(-0.796186\pi\)
0.976656 + 0.214811i \(0.0689134\pi\)
\(74\) −6.40161 1.39586i −0.744172 0.162265i
\(75\) −1.37823 3.01791i −0.159144 0.348478i
\(76\) 9.67222 + 2.85028i 1.10948 + 0.326950i
\(77\) −23.8428 + 3.42807i −2.71714 + 0.390665i
\(78\) 9.72106 9.71157i 1.10069 1.09962i
\(79\) 6.19095 7.14474i 0.696537 0.803846i −0.291744 0.956497i \(-0.594235\pi\)
0.988280 + 0.152650i \(0.0487808\pi\)
\(80\) −3.36923 + 2.15599i −0.376691 + 0.241047i
\(81\) 26.1585 + 16.8111i 2.90650 + 1.86790i
\(82\) 1.44253 0.537233i 0.159301 0.0593275i
\(83\) 0.562599 1.91603i 0.0617532 0.210312i −0.922837 0.385192i \(-0.874135\pi\)
0.984590 + 0.174879i \(0.0559536\pi\)
\(84\) −19.1655 + 16.5743i −2.09113 + 1.80840i
\(85\) −1.92106 + 1.66461i −0.208369 + 0.180552i
\(86\) −3.13829 0.225995i −0.338410 0.0243696i
\(87\) 2.36793 + 8.06442i 0.253869 + 0.864597i
\(88\) −6.25956 + 16.7078i −0.667271 + 1.78105i
\(89\) −6.65719 0.957159i −0.705661 0.101459i −0.219864 0.975531i \(-0.570561\pi\)
−0.485797 + 0.874072i \(0.661470\pi\)
\(90\) −11.2955 + 0.802332i −1.19066 + 0.0845732i
\(91\) 11.1832i 1.17232i
\(92\) −8.77682 3.86878i −0.915046 0.403349i
\(93\) 24.1633i 2.50561i
\(94\) −0.375342 5.28421i −0.0387136 0.545025i
\(95\) −4.99041 0.717512i −0.512005 0.0736152i
\(96\) 3.94463 + 18.3486i 0.402597 + 1.87270i
\(97\) −2.22710 7.58480i −0.226127 0.770119i −0.991901 0.127010i \(-0.959462\pi\)
0.765774 0.643110i \(-0.222356\pi\)
\(98\) 0.770138 10.6946i 0.0777957 1.08031i
\(99\) −38.1731 + 33.0772i −3.83654 + 3.32438i
\(100\) 1.51278 1.30825i 0.151278 0.130825i
\(101\) 2.31322 7.87811i 0.230174 0.783901i −0.760699 0.649105i \(-0.775144\pi\)
0.990873 0.134797i \(-0.0430381\pi\)
\(102\) 4.16249 + 11.1767i 0.412148 + 1.10666i
\(103\) 10.3382 + 6.64398i 1.01866 + 0.654651i 0.939619 0.342221i \(-0.111179\pi\)
0.0790369 + 0.996872i \(0.474816\pi\)
\(104\) 7.26431 + 3.98044i 0.712324 + 0.390314i
\(105\) 8.29649 9.57466i 0.809654 0.934391i
\(106\) −4.01580 4.01972i −0.390049 0.390430i
\(107\) −0.276759 + 0.0397919i −0.0267553 + 0.00384683i −0.155679 0.987808i \(-0.549757\pi\)
0.128924 + 0.991654i \(0.458848\pi\)
\(108\) −9.39183 + 31.8705i −0.903730 + 3.06674i
\(109\) 3.94901 + 8.64712i 0.378246 + 0.828244i 0.999020 + 0.0442543i \(0.0140912\pi\)
−0.620774 + 0.783990i \(0.713182\pi\)
\(110\) 1.90053 8.71612i 0.181209 0.831049i
\(111\) 6.38532 13.9819i 0.606067 1.32710i
\(112\) −12.8335 8.28306i −1.21265 0.782676i
\(113\) 8.24399 + 12.8279i 0.775530 + 1.20675i 0.973979 + 0.226637i \(0.0727730\pi\)
−0.198450 + 0.980111i \(0.563591\pi\)
\(114\) −11.3471 + 20.7565i −1.06275 + 1.94402i
\(115\) 4.62029 + 1.28566i 0.430844 + 0.119888i
\(116\) −4.26502 + 2.73508i −0.395997 + 0.253946i
\(117\) 12.6781 + 19.7276i 1.17209 + 1.82381i
\(118\) 8.52789 11.3803i 0.785056 1.04765i
\(119\) −8.82948 4.03229i −0.809397 0.369639i
\(120\) −3.26647 8.79707i −0.298187 0.803059i
\(121\) −11.9604 26.1896i −1.08731 2.38087i
\(122\) −0.597268 2.75207i −0.0540741 0.249160i
\(123\) 0.513930 + 3.57446i 0.0463395 + 0.322298i
\(124\) 13.9801 4.09012i 1.25545 0.367303i
\(125\) −0.654861 + 0.755750i −0.0585725 + 0.0675963i
\(126\) −20.7051 37.9627i −1.84456 3.38198i
\(127\) 9.94328 15.4720i 0.882324 1.37292i −0.0451288 0.998981i \(-0.514370\pi\)
0.927452 0.373941i \(-0.121994\pi\)
\(128\) −9.94827 + 5.38812i −0.879311 + 0.476247i
\(129\) 2.07959 7.08244i 0.183098 0.623574i
\(130\) −3.87984 1.44926i −0.340285 0.127109i
\(131\) 2.51164 + 2.89858i 0.219443 + 0.253250i 0.854787 0.518978i \(-0.173687\pi\)
−0.635345 + 0.772229i \(0.719142\pi\)
\(132\) −35.1900 22.6638i −3.06289 1.97263i
\(133\) −5.42402 18.4725i −0.470322 1.60177i
\(134\) 6.96845 + 9.31824i 0.601982 + 0.804973i
\(135\) 2.36424 16.4437i 0.203482 1.41525i
\(136\) −5.76193 + 4.30018i −0.494082 + 0.368737i
\(137\) 7.96683i 0.680652i 0.940307 + 0.340326i \(0.110538\pi\)
−0.940307 + 0.340326i \(0.889462\pi\)
\(138\) 13.2366 18.1969i 1.12677 1.54902i
\(139\) 1.92759 0.163496 0.0817480 0.996653i \(-0.473950\pi\)
0.0817480 + 0.996653i \(0.473950\pi\)
\(140\) 6.94396 + 3.17940i 0.586872 + 0.268708i
\(141\) 12.3014 + 1.76868i 1.03597 + 0.148949i
\(142\) 0.203708 + 0.272399i 0.0170948 + 0.0228592i
\(143\) −17.7255 + 5.20467i −1.48228 + 0.435236i
\(144\) −32.0291 0.0625398i −2.66909 0.00521165i
\(145\) 1.91456 1.65898i 0.158996 0.137771i
\(146\) −1.77851 + 4.76126i −0.147190 + 0.394045i
\(147\) 24.1353 + 7.08677i 1.99065 + 0.584507i
\(148\) 9.17035 + 1.32764i 0.753798 + 0.109131i
\(149\) −18.4088 11.8306i −1.50811 0.969201i −0.993751 0.111623i \(-0.964395\pi\)
−0.514355 0.857577i \(-0.671969\pi\)
\(150\) 2.24661 + 4.11914i 0.183435 + 0.336326i
\(151\) −1.27629 1.10592i −0.103863 0.0899981i 0.601381 0.798962i \(-0.294617\pi\)
−0.705245 + 0.708964i \(0.749163\pi\)
\(152\) −13.9298 3.05162i −1.12986 0.247519i
\(153\) −20.1468 + 2.89667i −1.62877 + 0.234182i
\(154\) 33.2905 7.22489i 2.68263 0.582199i
\(155\) −6.62493 + 3.02550i −0.532127 + 0.243014i
\(156\) −12.7400 + 14.6738i −1.02002 + 1.17484i
\(157\) −7.78932 + 17.0562i −0.621655 + 1.36123i 0.292654 + 0.956218i \(0.405462\pi\)
−0.914309 + 0.405017i \(0.867266\pi\)
\(158\) −8.01742 + 10.6991i −0.637832 + 0.851177i
\(159\) 11.2138 7.20664i 0.889308 0.571524i
\(160\) 4.53681 3.37896i 0.358666 0.267131i
\(161\) 2.86344 + 18.0882i 0.225670 + 1.42555i
\(162\) −38.5853 21.0936i −3.03154 1.65727i
\(163\) −8.17565 + 5.25417i −0.640366 + 0.411538i −0.820135 0.572171i \(-0.806102\pi\)
0.179768 + 0.983709i \(0.442465\pi\)
\(164\) −1.98108 + 0.902394i −0.154697 + 0.0704652i
\(165\) 19.0371 + 8.69394i 1.48203 + 0.676822i
\(166\) −0.601648 + 2.75924i −0.0466969 + 0.214159i
\(167\) −5.15435 + 2.35391i −0.398855 + 0.182151i −0.604736 0.796426i \(-0.706721\pi\)
0.205881 + 0.978577i \(0.433994\pi\)
\(168\) 25.3753 25.3010i 1.95774 1.95202i
\(169\) −0.629492 4.37821i −0.0484225 0.336786i
\(170\) 2.54317 2.54069i 0.195052 0.194862i
\(171\) −30.5100 26.4371i −2.33316 2.02169i
\(172\) 4.44970 + 0.00434423i 0.339287 + 0.000331244i
\(173\) 1.58177 2.46128i 0.120260 0.187128i −0.775904 0.630851i \(-0.782706\pi\)
0.896164 + 0.443723i \(0.146342\pi\)
\(174\) −4.14840 11.1389i −0.314489 0.844437i
\(175\) −3.66393 1.07583i −0.276967 0.0813249i
\(176\) 7.15598 24.1962i 0.539402 1.82385i
\(177\) 21.8476 + 25.2135i 1.64217 + 1.89516i
\(178\) 9.48694 + 0.683174i 0.711076 + 0.0512061i
\(179\) −6.07908 + 1.78498i −0.454372 + 0.133416i −0.500907 0.865501i \(-0.667000\pi\)
0.0465353 + 0.998917i \(0.485182\pi\)
\(180\) 15.8538 2.26363i 1.18167 0.168721i
\(181\) 0.694522 4.83050i 0.0516234 0.359049i −0.947593 0.319479i \(-0.896492\pi\)
0.999217 0.0395698i \(-0.0125987\pi\)
\(182\) −1.12056 15.7757i −0.0830616 1.16937i
\(183\) 6.60660 0.488374
\(184\) 12.7688 + 4.57810i 0.941325 + 0.337502i
\(185\) −4.63298 −0.340623
\(186\) 2.42116 + 34.0861i 0.177528 + 2.49932i
\(187\) 2.28196 15.8714i 0.166874 1.16063i
\(188\) 1.05896 + 7.41662i 0.0772325 + 0.540912i
\(189\) 60.8680 17.8725i 4.42750 1.30003i
\(190\) 7.11166 + 0.512125i 0.515934 + 0.0371535i
\(191\) −9.58928 11.0666i −0.693856 0.800753i 0.294053 0.955789i \(-0.404996\pi\)
−0.987909 + 0.155037i \(0.950450\pi\)
\(192\) −7.40306 25.4884i −0.534270 1.83947i
\(193\) 25.8414 + 7.58771i 1.86010 + 0.546175i 0.999307 + 0.0372227i \(0.0118511\pi\)
0.860795 + 0.508952i \(0.169967\pi\)
\(194\) 3.90167 + 10.4764i 0.280124 + 0.752162i
\(195\) 5.25304 8.17389i 0.376178 0.585344i
\(196\) −0.0148041 + 15.1636i −0.00105744 + 1.08311i
\(197\) 4.08293 + 3.53788i 0.290897 + 0.252064i 0.788067 0.615590i \(-0.211082\pi\)
−0.497170 + 0.867653i \(0.665627\pi\)
\(198\) 50.5349 50.4856i 3.59136 3.58786i
\(199\) −1.30163 9.05300i −0.0922698 0.641750i −0.982503 0.186246i \(-0.940368\pi\)
0.890233 0.455505i \(-0.150541\pi\)
\(200\) −2.00293 + 1.99707i −0.141628 + 0.141214i
\(201\) −24.8303 + 11.3396i −1.75140 + 0.799836i
\(202\) −2.47378 + 11.3451i −0.174055 + 0.798239i
\(203\) 8.79959 + 4.01864i 0.617610 + 0.282053i
\(204\) −6.99176 15.3495i −0.489521 1.07468i
\(205\) 0.915674 0.588468i 0.0639534 0.0411004i
\(206\) −15.2495 8.33650i −1.06248 0.580831i
\(207\) 25.5573 + 28.6619i 1.77636 + 1.99214i
\(208\) −10.6463 4.88715i −0.738189 0.338863i
\(209\) 26.7547 17.1942i 1.85066 1.18935i
\(210\) −10.7441 + 14.3379i −0.741416 + 0.989408i
\(211\) −2.83880 + 6.21610i −0.195431 + 0.427934i −0.981824 0.189792i \(-0.939219\pi\)
0.786393 + 0.617726i \(0.211946\pi\)
\(212\) 6.06770 + 5.26807i 0.416731 + 0.361813i
\(213\) −0.725862 + 0.331490i −0.0497352 + 0.0227133i
\(214\) 0.386425 0.0838641i 0.0264155 0.00573283i
\(215\) −2.20221 + 0.316629i −0.150189 + 0.0215939i
\(216\) 10.0552 45.8995i 0.684173 3.12307i
\(217\) −21.0183 18.2125i −1.42682 1.23635i
\(218\) −6.43715 11.8024i −0.435979 0.799363i
\(219\) −10.0308 6.44642i −0.677820 0.435609i
\(220\) −1.80765 + 12.4859i −0.121872 + 0.841800i
\(221\) −7.14278 2.09731i −0.480476 0.141080i
\(222\) −7.60652 + 20.3635i −0.510516 + 1.36671i
\(223\) 11.5546 10.0121i 0.773750 0.670458i −0.175676 0.984448i \(-0.556211\pi\)
0.949426 + 0.313990i \(0.101666\pi\)
\(224\) 18.9337 + 10.3987i 1.26506 + 0.694789i
\(225\) −7.68293 + 2.25591i −0.512195 + 0.150394i
\(226\) −12.9148 17.2698i −0.859081 1.14877i
\(227\) 4.93879 + 0.710090i 0.327799 + 0.0471304i 0.304250 0.952592i \(-0.401594\pi\)
0.0235492 + 0.999723i \(0.492503\pi\)
\(228\) 13.9270 30.4173i 0.922340 2.01444i
\(229\) −5.90998 −0.390543 −0.195271 0.980749i \(-0.562559\pi\)
−0.195271 + 0.980749i \(0.562559\pi\)
\(230\) −6.64648 1.35067i −0.438256 0.0890605i
\(231\) 79.9171i 5.25816i
\(232\) 5.74243 4.28562i 0.377009 0.281365i
\(233\) 2.56986 17.8737i 0.168357 1.17095i −0.713923 0.700224i \(-0.753084\pi\)
0.882280 0.470724i \(-0.156007\pi\)
\(234\) −19.8612 26.5585i −1.29837 1.73619i
\(235\) −1.05535 3.59418i −0.0688432 0.234459i
\(236\) −10.8896 + 16.9083i −0.708855 + 1.10064i
\(237\) −20.5399 23.7043i −1.33421 1.53976i
\(238\) 12.8594 + 4.80347i 0.833552 + 0.311363i
\(239\) −2.70416 + 9.20954i −0.174918 + 0.595715i 0.824631 + 0.565671i \(0.191383\pi\)
−0.999549 + 0.0300441i \(0.990435\pi\)
\(240\) 5.48935 + 12.0824i 0.354336 + 0.779913i
\(241\) −10.6466 + 16.5665i −0.685810 + 1.06714i 0.307487 + 0.951552i \(0.400512\pi\)
−0.993297 + 0.115589i \(0.963124\pi\)
\(242\) 19.4962 + 35.7461i 1.25326 + 2.29785i
\(243\) 34.9206 40.3006i 2.24016 2.58528i
\(244\) 1.11830 + 3.82238i 0.0715918 + 0.244703i
\(245\) −1.07900 7.50461i −0.0689348 0.479452i
\(246\) −1.08314 4.99085i −0.0690586 0.318205i
\(247\) −6.13371 13.4309i −0.390278 0.854591i
\(248\) −19.3114 + 7.17058i −1.22627 + 0.455332i
\(249\) −6.02653 2.75222i −0.381916 0.174415i
\(250\) 0.848059 1.13172i 0.0536360 0.0715764i
\(251\) 1.14395 + 1.78002i 0.0722054 + 0.112354i 0.875478 0.483257i \(-0.160546\pi\)
−0.803273 + 0.595611i \(0.796910\pi\)
\(252\) 33.0118 + 51.4777i 2.07955 + 3.24279i
\(253\) −27.3372 + 12.9568i −1.71868 + 0.814587i
\(254\) −12.4763 + 22.8221i −0.782831 + 1.43199i
\(255\) 4.55945 + 7.09465i 0.285524 + 0.444284i
\(256\) 13.4937 8.59762i 0.843358 0.537351i
\(257\) 4.81085 10.5343i 0.300092 0.657111i −0.698176 0.715926i \(-0.746005\pi\)
0.998269 + 0.0588149i \(0.0187322\pi\)
\(258\) −2.22393 + 10.1993i −0.138456 + 0.634980i
\(259\) −7.34933 16.0928i −0.456665 0.999957i
\(260\) 5.61835 + 1.65566i 0.348435 + 0.102679i
\(261\) 20.0786 2.88687i 1.24283 0.178693i
\(262\) −3.83350 3.83725i −0.236834 0.237066i
\(263\) 1.52686 1.76209i 0.0941501 0.108655i −0.706719 0.707494i \(-0.749826\pi\)
0.800869 + 0.598839i \(0.204371\pi\)
\(264\) 51.9120 + 28.4448i 3.19496 + 1.75066i
\(265\) −3.37996 2.17217i −0.207629 0.133435i
\(266\) 9.50240 + 25.5149i 0.582629 + 1.56442i
\(267\) −6.28653 + 21.4100i −0.384730 + 1.31027i
\(268\) −10.7638 12.4466i −0.657504 0.760298i
\(269\) 22.1402 19.1846i 1.34991 1.16970i 0.380352 0.924842i \(-0.375803\pi\)
0.969558 0.244861i \(-0.0787425\pi\)
\(270\) −1.68748 + 23.4333i −0.102697 + 1.42611i
\(271\) −4.20792 14.3309i −0.255613 0.870539i −0.982890 0.184194i \(-0.941032\pi\)
0.727277 0.686344i \(-0.240786\pi\)
\(272\) 7.69724 6.64343i 0.466714 0.402817i
\(273\) 36.7252 + 5.28028i 2.22271 + 0.319577i
\(274\) −0.798279 11.2385i −0.0482258 0.678942i
\(275\) 6.30804i 0.380389i
\(276\) −16.8490 + 26.9960i −1.01419 + 1.62497i
\(277\) 25.9316i 1.55808i −0.626977 0.779038i \(-0.715708\pi\)
0.626977 0.779038i \(-0.284292\pi\)
\(278\) −2.71917 + 0.193145i −0.163085 + 0.0115841i
\(279\) −57.7241 8.29948i −3.45585 0.496877i
\(280\) −10.1141 3.78926i −0.604435 0.226452i
\(281\) −6.52226 22.2128i −0.389085 1.32510i −0.888554 0.458771i \(-0.848290\pi\)
0.499469 0.866332i \(-0.333528\pi\)
\(282\) −17.5303 1.26240i −1.04392 0.0751745i
\(283\) 9.87372 8.55563i 0.586932 0.508579i −0.310007 0.950734i \(-0.600331\pi\)
0.896939 + 0.442155i \(0.145786\pi\)
\(284\) −0.314657 0.363851i −0.0186715 0.0215906i
\(285\) −4.71255 + 16.0495i −0.279147 + 0.950689i
\(286\) 24.4831 9.11812i 1.44772 0.539165i
\(287\) 3.49660 + 2.24713i 0.206398 + 0.132644i
\(288\) 45.1884 3.12110i 2.66275 0.183912i
\(289\) −6.90130 + 7.96453i −0.405959 + 0.468502i
\(290\) −2.53456 + 2.53209i −0.148835 + 0.148690i
\(291\) −25.9597 + 3.73244i −1.52178 + 0.218799i
\(292\) 2.03179 6.89472i 0.118901 0.403483i
\(293\) −2.06410 4.51974i −0.120586 0.264046i 0.839707 0.543039i \(-0.182727\pi\)
−0.960293 + 0.278993i \(0.909999\pi\)
\(294\) −34.7568 7.57865i −2.02706 0.441996i
\(295\) 4.17732 9.14706i 0.243213 0.532562i
\(296\) −13.0693 0.953972i −0.759636 0.0554485i
\(297\) 56.6559 + 88.1583i 3.28751 + 5.11547i
\(298\) 27.1539 + 14.8444i 1.57299 + 0.859912i
\(299\) 4.14795 + 13.4186i 0.239882 + 0.776020i
\(300\) −3.58194 5.58559i −0.206803 0.322484i
\(301\) −4.59320 7.14716i −0.264748 0.411955i
\(302\) 1.91123 + 1.43219i 0.109979 + 0.0824130i
\(303\) −24.7791 11.3162i −1.42352 0.650101i
\(304\) 19.9560 + 2.90902i 1.14455 + 0.166844i
\(305\) −0.827218 1.81135i −0.0473664 0.103718i
\(306\) 28.1300 6.10493i 1.60809 0.348996i
\(307\) 0.845010 + 5.87717i 0.0482273 + 0.335428i 0.999623 + 0.0274569i \(0.00874090\pi\)
−0.951396 + 0.307971i \(0.900350\pi\)
\(308\) −46.2377 + 13.5276i −2.63464 + 0.770806i
\(309\) 26.6998 30.8132i 1.51890 1.75290i
\(310\) 9.04236 4.93177i 0.513572 0.280106i
\(311\) 4.93134 7.67331i 0.279630 0.435113i −0.672820 0.739806i \(-0.734917\pi\)
0.952451 + 0.304692i \(0.0985537\pi\)
\(312\) 16.5015 21.9763i 0.934213 1.24416i
\(313\) −1.67260 + 5.69636i −0.0945411 + 0.321977i −0.993161 0.116750i \(-0.962752\pi\)
0.898620 + 0.438727i \(0.144571\pi\)
\(314\) 9.27904 24.8410i 0.523646 1.40186i
\(315\) −20.0235 23.1083i −1.12819 1.30201i
\(316\) 10.2378 15.8962i 0.575921 0.894230i
\(317\) 3.28144 + 11.1755i 0.184304 + 0.627681i 0.998866 + 0.0476051i \(0.0151589\pi\)
−0.814562 + 0.580076i \(0.803023\pi\)
\(318\) −15.0967 + 11.2897i −0.846580 + 0.633097i
\(319\) −2.27424 + 15.8177i −0.127333 + 0.885620i
\(320\) −6.06131 + 5.22116i −0.338838 + 0.291871i
\(321\) 0.927651i 0.0517764i
\(322\) −5.85177 25.2293i −0.326107 1.40598i
\(323\) 12.8157 0.713086
\(324\) 56.5442 + 25.8896i 3.14135 + 1.43831i
\(325\) −2.89880 0.416785i −0.160797 0.0231191i
\(326\) 11.0066 8.23105i 0.609599 0.455876i
\(327\) 30.2613 8.88552i 1.67345 0.491370i
\(328\) 2.70421 1.47148i 0.149315 0.0812487i
\(329\) 10.8104 9.36726i 0.595996 0.516434i
\(330\) −27.7260 10.3567i −1.52626 0.570116i
\(331\) 6.35492 + 1.86597i 0.349298 + 0.102563i 0.451675 0.892183i \(-0.350827\pi\)
−0.102377 + 0.994746i \(0.532645\pi\)
\(332\) 0.572243 3.95264i 0.0314059 0.216929i
\(333\) −31.2085 20.0565i −1.71021 1.09909i
\(334\) 7.03516 3.83703i 0.384947 0.209953i
\(335\) 6.21805 + 5.38797i 0.339729 + 0.294376i
\(336\) −33.2607 + 38.2338i −1.81452 + 2.08582i
\(337\) −7.52130 + 1.08140i −0.409711 + 0.0589076i −0.344089 0.938937i \(-0.611812\pi\)
−0.0656221 + 0.997845i \(0.520903\pi\)
\(338\) 1.32670 + 6.11309i 0.0721628 + 0.332508i
\(339\) 46.0187 21.0160i 2.49939 1.14144i
\(340\) −3.33297 + 3.83888i −0.180756 + 0.208192i
\(341\) 19.0850 41.7903i 1.03351 2.26307i
\(342\) 45.6882 + 34.2366i 2.47054 + 1.85130i
\(343\) 1.86892 1.20108i 0.100912 0.0648524i
\(344\) −6.27745 + 0.439733i −0.338457 + 0.0237088i
\(345\) 6.40356 14.5658i 0.344756 0.784195i
\(346\) −1.98472 + 3.63052i −0.106699 + 0.195178i
\(347\) −12.3076 + 7.90962i −0.660707 + 0.424611i −0.827565 0.561370i \(-0.810274\pi\)
0.166858 + 0.985981i \(0.446638\pi\)
\(348\) 6.96810 + 15.2975i 0.373529 + 0.820032i
\(349\) 22.1363 + 10.1093i 1.18493 + 0.541139i 0.907682 0.419659i \(-0.137850\pi\)
0.277248 + 0.960798i \(0.410578\pi\)
\(350\) 5.27635 + 1.15050i 0.282033 + 0.0614967i
\(351\) 44.2557 20.2109i 2.36220 1.07878i
\(352\) −7.67019 + 34.8496i −0.408823 + 1.85749i
\(353\) −1.62579 11.3076i −0.0865320 0.601844i −0.986236 0.165343i \(-0.947127\pi\)
0.899704 0.436500i \(-0.143782\pi\)
\(354\) −33.3460 33.3786i −1.77232 1.77405i
\(355\) 0.181772 + 0.157506i 0.00964744 + 0.00835955i
\(356\) −13.4513 0.0131324i −0.712917 0.000696018i
\(357\) −17.4108 + 27.0917i −0.921476 + 1.43384i
\(358\) 8.39666 3.12712i 0.443777 0.165274i
\(359\) −16.1990 4.75645i −0.854949 0.251036i −0.175247 0.984524i \(-0.556073\pi\)
−0.679702 + 0.733489i \(0.737891\pi\)
\(360\) −22.1375 + 4.78177i −1.16675 + 0.252021i
\(361\) 4.20354 + 4.85114i 0.221239 + 0.255323i
\(362\) −0.495716 + 6.88379i −0.0260542 + 0.361804i
\(363\) −91.6525 + 26.9116i −4.81051 + 1.41249i
\(364\) 3.16146 + 22.1419i 0.165706 + 1.16055i
\(365\) −0.511470 + 3.55735i −0.0267716 + 0.186200i
\(366\) −9.31966 + 0.661983i −0.487146 + 0.0346024i
\(367\) −36.9007 −1.92620 −0.963102 0.269138i \(-0.913261\pi\)
−0.963102 + 0.269138i \(0.913261\pi\)
\(368\) −18.4711 5.17870i −0.962872 0.269959i
\(369\) 8.71563 0.453718
\(370\) 6.53555 0.464226i 0.339767 0.0241339i
\(371\) 2.18343 15.1861i 0.113358 0.788423i
\(372\) −6.83088 47.8413i −0.354164 2.48046i
\(373\) −10.9357 + 3.21101i −0.566228 + 0.166260i −0.552303 0.833643i \(-0.686251\pi\)
−0.0139252 + 0.999903i \(0.504433\pi\)
\(374\) −1.62875 + 22.6178i −0.0842209 + 1.16954i
\(375\) 2.17265 + 2.50737i 0.112195 + 0.129480i
\(376\) −2.23698 10.3562i −0.115363 0.534081i
\(377\) 7.11861 + 2.09021i 0.366627 + 0.107651i
\(378\) −84.0732 + 31.3109i −4.32426 + 1.61046i
\(379\) −8.70294 + 13.5420i −0.447040 + 0.695608i −0.989510 0.144468i \(-0.953853\pi\)
0.542470 + 0.840075i \(0.317489\pi\)
\(380\) −10.0834 0.00984443i −0.517270 0.000505009i
\(381\) −46.1146 39.9586i −2.36252 2.04714i
\(382\) 14.6361 + 14.6504i 0.748847 + 0.749579i
\(383\) 2.88632 + 20.0748i 0.147484 + 1.02577i 0.920320 + 0.391167i \(0.127928\pi\)
−0.772836 + 0.634606i \(0.781162\pi\)
\(384\) 12.9971 + 35.2137i 0.663258 + 1.79699i
\(385\) 21.9112 10.0065i 1.11670 0.509978i
\(386\) −37.2136 8.11436i −1.89412 0.413010i
\(387\) −16.2051 7.40062i −0.823752 0.376195i
\(388\) −6.55367 14.3877i −0.332712 0.730425i
\(389\) −22.0958 + 14.2001i −1.12030 + 0.719974i −0.963514 0.267658i \(-0.913750\pi\)
−0.156788 + 0.987632i \(0.550114\pi\)
\(390\) −6.59122 + 12.0569i −0.333760 + 0.610526i
\(391\) −12.0900 1.56338i −0.611418 0.0790634i
\(392\) −1.49851 21.3921i −0.0756861 1.08046i
\(393\) 10.7047 6.87949i 0.539981 0.347025i
\(394\) −6.11412 4.58163i −0.308025 0.230819i
\(395\) −3.92727 + 8.59952i −0.197602 + 0.432689i
\(396\) −66.2289 + 76.2816i −3.32813 + 3.83329i
\(397\) −26.0458 + 11.8947i −1.30720 + 0.596980i −0.942519 0.334152i \(-0.891550\pi\)
−0.364684 + 0.931131i \(0.618823\pi\)
\(398\) 2.74326 + 12.6403i 0.137507 + 0.633600i
\(399\) −63.2239 + 9.09022i −3.16515 + 0.455080i
\(400\) 2.62534 3.01788i 0.131267 0.150894i
\(401\) −4.84985 4.20242i −0.242190 0.209859i 0.525305 0.850914i \(-0.323951\pi\)
−0.767495 + 0.641056i \(0.778497\pi\)
\(402\) 33.8909 18.4844i 1.69032 0.921916i
\(403\) −17.9434 11.5315i −0.893823 0.574425i
\(404\) 2.35288 16.2520i 0.117060 0.808566i
\(405\) −29.8352 8.76039i −1.48252 0.435307i
\(406\) −12.8159 4.78721i −0.636042 0.237585i
\(407\) 22.0868 19.1383i 1.09480 0.948651i
\(408\) 11.4010 + 20.9523i 0.564434 + 1.03729i
\(409\) 13.0567 3.83380i 0.645613 0.189569i 0.0574969 0.998346i \(-0.481688\pi\)
0.588116 + 0.808777i \(0.299870\pi\)
\(410\) −1.23274 + 0.921878i −0.0608806 + 0.0455283i
\(411\) 26.1627 + 3.76163i 1.29051 + 0.185547i
\(412\) 22.3471 + 10.2320i 1.10096 + 0.504092i
\(413\) 38.3991 1.88950
\(414\) −38.9246 37.8713i −1.91304 1.86128i
\(415\) 1.99692i 0.0980252i
\(416\) 15.5080 + 5.82735i 0.760343 + 0.285709i
\(417\) 0.910133 6.33011i 0.0445694 0.309987i
\(418\) −36.0189 + 26.9360i −1.76174 + 1.31748i
\(419\) 4.05425 + 13.8075i 0.198063 + 0.674541i 0.997294 + 0.0735171i \(0.0234224\pi\)
−0.799231 + 0.601024i \(0.794759\pi\)
\(420\) 13.7197 21.3024i 0.669451 1.03945i
\(421\) 21.8898 + 25.2622i 1.06685 + 1.23121i 0.971818 + 0.235731i \(0.0757485\pi\)
0.0950277 + 0.995475i \(0.469706\pi\)
\(422\) 3.38172 9.05325i 0.164620 0.440705i
\(423\) 8.45046 28.7796i 0.410875 1.39931i
\(424\) −9.08732 6.82347i −0.441319 0.331377i
\(425\) 1.37427 2.13841i 0.0666620 0.103728i
\(426\) 0.990729 0.540351i 0.0480010 0.0261801i
\(427\) 4.97957 5.74673i 0.240978 0.278104i
\(428\) −0.536711 + 0.157024i −0.0259429 + 0.00759002i
\(429\) 8.72261 + 60.6671i 0.421132 + 2.92903i
\(430\) 3.07484 0.667318i 0.148282 0.0321809i
\(431\) −0.396216 0.867592i −0.0190851 0.0417905i 0.899849 0.436201i \(-0.143676\pi\)
−0.918935 + 0.394410i \(0.870949\pi\)
\(432\) −9.58539 + 65.7561i −0.461177 + 3.16369i
\(433\) −35.3548 16.1460i −1.69905 0.775928i −0.998027 0.0627850i \(-0.980002\pi\)
−0.701018 0.713143i \(-0.747271\pi\)
\(434\) 31.4746 + 23.5856i 1.51083 + 1.13214i
\(435\) −4.54402 7.07064i −0.217869 0.339011i
\(436\) 10.2632 + 16.0042i 0.491520 + 0.766464i
\(437\) −13.3598 20.1532i −0.639088 0.964058i
\(438\) 14.7960 + 8.08861i 0.706981 + 0.386489i
\(439\) −7.86280 12.2347i −0.375271 0.583933i 0.601328 0.799002i \(-0.294639\pi\)
−0.976599 + 0.215070i \(0.931002\pi\)
\(440\) 1.29888 17.7945i 0.0619218 0.848319i
\(441\) 25.2196 55.2233i 1.20093 2.62968i
\(442\) 10.2862 + 2.24288i 0.489264 + 0.106683i
\(443\) −9.37626 20.5311i −0.445480 0.975464i −0.990560 0.137080i \(-0.956228\pi\)
0.545080 0.838384i \(-0.316499\pi\)
\(444\) 8.68978 29.4881i 0.412399 1.39945i
\(445\) 6.65719 0.957159i 0.315581 0.0453737i
\(446\) −15.2963 + 15.2814i −0.724302 + 0.723595i
\(447\) −47.5430 + 54.8676i −2.24871 + 2.59515i
\(448\) −27.7509 12.7718i −1.31111 0.603411i
\(449\) −17.1643 11.0308i −0.810032 0.520576i 0.0688433 0.997627i \(-0.478069\pi\)
−0.878875 + 0.477052i \(0.841705\pi\)
\(450\) 10.6120 3.95215i 0.500252 0.186306i
\(451\) −1.93440 + 6.58795i −0.0910871 + 0.310214i
\(452\) 19.9489 + 23.0677i 0.938315 + 1.08501i
\(453\) −4.23439 + 3.66912i −0.198949 + 0.172390i
\(454\) −7.03810 0.506828i −0.330314 0.0237866i
\(455\) −3.15068 10.7302i −0.147706 0.503041i
\(456\) −16.5985 + 44.3040i −0.777295 + 2.07472i
\(457\) −14.8702 2.13801i −0.695597 0.100012i −0.214558 0.976711i \(-0.568831\pi\)
−0.481038 + 0.876700i \(0.659740\pi\)
\(458\) 8.33697 0.592182i 0.389561 0.0276708i
\(459\) 42.2285i 1.97106i
\(460\) 9.51126 + 1.23936i 0.443465 + 0.0577853i
\(461\) 7.52873i 0.350648i 0.984511 + 0.175324i \(0.0560973\pi\)
−0.984511 + 0.175324i \(0.943903\pi\)
\(462\) −8.00772 112.736i −0.372553 5.24495i
\(463\) 35.3314 + 5.07989i 1.64199 + 0.236083i 0.900492 0.434872i \(-0.143206\pi\)
0.741499 + 0.670954i \(0.234115\pi\)
\(464\) −7.67119 + 6.62094i −0.356126 + 0.307370i
\(465\) 6.80758 + 23.1845i 0.315694 + 1.07515i
\(466\) −1.83424 + 25.4713i −0.0849695 + 1.17993i
\(467\) −14.2578 + 12.3545i −0.659773 + 0.571696i −0.919067 0.394102i \(-0.871056\pi\)
0.259294 + 0.965798i \(0.416510\pi\)
\(468\) 30.6786 + 35.4749i 1.41812 + 1.63983i
\(469\) −8.85154 + 30.1456i −0.408726 + 1.39199i
\(470\) 1.84887 + 4.96442i 0.0852821 + 0.228992i
\(471\) 52.3340 + 33.6330i 2.41142 + 1.54973i
\(472\) 13.6674 24.9430i 0.629091 1.14809i
\(473\) 9.19061 10.6065i 0.422585 0.487689i
\(474\) 31.3499 + 31.3806i 1.43995 + 1.44136i
\(475\) 4.99041 0.717512i 0.228976 0.0329217i
\(476\) −18.6216 5.48754i −0.853518 0.251521i
\(477\) −13.3645 29.2641i −0.611916 1.33991i
\(478\) 2.89186 13.2625i 0.132270 0.606612i
\(479\) 12.3817 27.1122i 0.565735 1.23879i −0.383302 0.923623i \(-0.625213\pi\)
0.949037 0.315164i \(-0.102060\pi\)
\(480\) −8.95425 16.4941i −0.408704 0.752848i
\(481\) −7.33552 11.4143i −0.334471 0.520447i
\(482\) 13.3588 24.4365i 0.608477 1.11305i
\(483\) 60.7527 0.862862i 2.76434 0.0392616i
\(484\) −31.0843 48.4721i −1.41292 2.20328i
\(485\) 4.27377 + 6.65011i 0.194062 + 0.301966i
\(486\) −45.2230 + 60.3494i −2.05136 + 2.73751i
\(487\) 15.9971 + 7.30562i 0.724897 + 0.331049i 0.743462 0.668778i \(-0.233182\pi\)
−0.0185650 + 0.999828i \(0.505910\pi\)
\(488\) −1.96054 5.28002i −0.0887496 0.239015i
\(489\) 13.3942 + 29.3293i 0.605708 + 1.32632i
\(490\) 2.27406 + 10.4783i 0.102732 + 0.473363i
\(491\) 1.75601 + 12.2133i 0.0792477 + 0.551180i 0.990306 + 0.138902i \(0.0443574\pi\)
−0.911058 + 0.412277i \(0.864733\pi\)
\(492\) 2.02803 + 6.93186i 0.0914306 + 0.312512i
\(493\) −4.21701 + 4.86669i −0.189925 + 0.219185i
\(494\) 9.99835 + 18.3319i 0.449847 + 0.824791i
\(495\) 27.3079 42.4919i 1.22740 1.90987i
\(496\) 26.5233 12.0502i 1.19093 0.541072i
\(497\) −0.258756 + 0.881242i −0.0116068 + 0.0395291i
\(498\) 8.77716 + 3.27859i 0.393314 + 0.146917i
\(499\) 26.3208 + 30.3759i 1.17828 + 1.35981i 0.919121 + 0.393976i \(0.128901\pi\)
0.259161 + 0.965834i \(0.416554\pi\)
\(500\) −1.08292 + 1.68145i −0.0484298 + 0.0751968i
\(501\) 5.29645 + 18.0381i 0.236628 + 0.805881i
\(502\) −1.79208 2.39638i −0.0799844 0.106955i
\(503\) −2.01754 + 14.0323i −0.0899575 + 0.625668i 0.894107 + 0.447854i \(0.147812\pi\)
−0.984064 + 0.177814i \(0.943097\pi\)
\(504\) −51.7264 69.3098i −2.30408 3.08730i
\(505\) 8.21070i 0.365371i
\(506\) 37.2652 21.0168i 1.65664 0.934312i
\(507\) −14.6751 −0.651743
\(508\) 15.3130 33.4444i 0.679405 1.48385i
\(509\) −12.4446 1.78926i −0.551597 0.0793076i −0.139120 0.990276i \(-0.544427\pi\)
−0.412477 + 0.910968i \(0.635336\pi\)
\(510\) −7.14272 9.55127i −0.316285 0.422938i
\(511\) −13.1679 + 3.86645i −0.582514 + 0.171042i
\(512\) −18.1736 + 13.4804i −0.803166 + 0.595755i
\(513\) −63.2993 + 54.8492i −2.79473 + 2.42165i
\(514\) −5.73093 + 15.3423i −0.252780 + 0.676722i
\(515\) −11.7913 3.46223i −0.519586 0.152564i
\(516\) 2.11524 14.6106i 0.0931183 0.643194i
\(517\) 19.8783 + 12.7750i 0.874247 + 0.561845i
\(518\) 11.9799 + 21.9650i 0.526367 + 0.965088i
\(519\) −7.33588 6.35658i −0.322010 0.279023i
\(520\) −8.09148 1.77261i −0.354835 0.0777340i
\(521\) −26.4935 + 3.80918i −1.16070 + 0.166883i −0.695636 0.718394i \(-0.744878\pi\)
−0.465063 + 0.885277i \(0.653968\pi\)
\(522\) −28.0348 + 6.08427i −1.22705 + 0.266301i
\(523\) 8.09353 3.69619i 0.353905 0.161623i −0.230526 0.973066i \(-0.574045\pi\)
0.584432 + 0.811443i \(0.301318\pi\)
\(524\) 5.79226 + 5.02893i 0.253036 + 0.219690i
\(525\) −5.26293 + 11.5242i −0.229693 + 0.502958i
\(526\) −1.97731 + 2.63870i −0.0862150 + 0.115053i
\(527\) 15.5742 10.0089i 0.678424 0.435996i
\(528\) −76.0803 34.9244i −3.31097 1.51989i
\(529\) 10.1449 + 20.6417i 0.441081 + 0.897467i
\(530\) 4.98562 + 2.72551i 0.216561 + 0.118389i
\(531\) 67.7373 43.5321i 2.93955 1.88913i
\(532\) −15.9613 35.0408i −0.692008 1.51921i
\(533\) 2.89962 + 1.32421i 0.125597 + 0.0573580i
\(534\) 6.72287 30.8321i 0.290927 1.33423i
\(535\) 0.254337 0.116152i 0.0109960 0.00502169i
\(536\) 16.4312 + 16.4794i 0.709720 + 0.711802i
\(537\) 2.99148 + 20.8062i 0.129092 + 0.897854i
\(538\) −29.3099 + 29.2813i −1.26364 + 1.26241i
\(539\) 36.1446 + 31.3195i 1.55686 + 1.34903i
\(540\) 0.0324380 33.2255i 0.00139591 1.42980i
\(541\) −6.05141 + 9.41619i −0.260171 + 0.404833i −0.946624 0.322341i \(-0.895530\pi\)
0.686453 + 0.727174i \(0.259167\pi\)
\(542\) 7.37191 + 19.7943i 0.316650 + 0.850240i
\(543\) −15.5352 4.56155i −0.666680 0.195755i
\(544\) −10.1925 + 10.1429i −0.437001 + 0.434872i
\(545\) −6.22522 7.18429i −0.266659 0.307741i
\(546\) −52.3358 3.76881i −2.23977 0.161290i
\(547\) 28.7980 8.45586i 1.23131 0.361547i 0.399569 0.916703i \(-0.369160\pi\)
0.831746 + 0.555157i \(0.187342\pi\)
\(548\) 2.25220 + 15.7737i 0.0962091 + 0.673819i
\(549\) 2.26920 15.7826i 0.0968472 0.673587i
\(550\) 0.632067 + 8.89850i 0.0269514 + 0.379433i
\(551\) −12.7723 −0.544120
\(552\) 21.0632 39.7704i 0.896508 1.69274i
\(553\) −36.1006 −1.53515
\(554\) 2.59835 + 36.5806i 0.110393 + 1.55416i
\(555\) −2.18751 + 15.2145i −0.0928547 + 0.645819i
\(556\) 3.81647 0.544924i 0.161855 0.0231099i
\(557\) −9.15771 + 2.68894i −0.388024 + 0.113934i −0.469925 0.882706i \(-0.655719\pi\)
0.0819008 + 0.996640i \(0.473901\pi\)
\(558\) 82.2607 + 5.92376i 3.48237 + 0.250773i
\(559\) −4.26689 4.92426i −0.180470 0.208274i
\(560\) 14.6473 + 4.33192i 0.618961 + 0.183057i
\(561\) −51.0435 14.9877i −2.15506 0.632782i
\(562\) 11.4264 + 30.6811i 0.481994 + 1.29421i
\(563\) 8.73447 13.5911i 0.368114 0.572797i −0.606944 0.794744i \(-0.707605\pi\)
0.975059 + 0.221947i \(0.0712413\pi\)
\(564\) 24.8558 + 0.0242666i 1.04662 + 0.00102181i
\(565\) −11.5241 9.98568i −0.484822 0.420101i
\(566\) −13.0712 + 13.0584i −0.549423 + 0.548887i
\(567\) −16.8983 117.530i −0.709660 4.93579i
\(568\) 0.480332 + 0.481741i 0.0201543 + 0.0202134i
\(569\) 0.719580 0.328621i 0.0301664 0.0137765i −0.400275 0.916395i \(-0.631085\pi\)
0.430441 + 0.902619i \(0.358358\pi\)
\(570\) 5.03964 23.1125i 0.211087 0.968078i
\(571\) 13.9637 + 6.37702i 0.584364 + 0.266870i 0.685584 0.727994i \(-0.259547\pi\)
−0.101219 + 0.994864i \(0.532274\pi\)
\(572\) −33.6237 + 15.3158i −1.40588 + 0.640384i
\(573\) −40.8699 + 26.2655i −1.70737 + 1.09726i
\(574\) −5.15767 2.81957i −0.215277 0.117687i
\(575\) −4.79535 + 0.0681077i −0.199980 + 0.00284029i
\(576\) −63.4327 + 8.93069i −2.64303 + 0.372112i
\(577\) −34.9950 + 22.4899i −1.45686 + 0.936269i −0.457982 + 0.888962i \(0.651428\pi\)
−0.998880 + 0.0473070i \(0.984936\pi\)
\(578\) 8.93734 11.9267i 0.371744 0.496087i
\(579\) 37.1190 81.2792i 1.54261 3.37785i
\(580\) 3.32169 3.82588i 0.137926 0.158861i
\(581\) −6.93638 + 3.16774i −0.287769 + 0.131420i
\(582\) 36.2463 7.86636i 1.50246 0.326071i
\(583\) 25.0862 3.60686i 1.03897 0.149381i
\(584\) −2.17531 + 9.92969i −0.0900148 + 0.410894i
\(585\) −17.7225 15.3566i −0.732735 0.634918i
\(586\) 3.36461 + 6.16899i 0.138991 + 0.254839i
\(587\) 26.2152 + 16.8475i 1.08202 + 0.695370i 0.955022 0.296534i \(-0.0958307\pi\)
0.126994 + 0.991903i \(0.459467\pi\)
\(588\) 49.7894 + 7.20826i 2.05328 + 0.297263i
\(589\) 35.2319 + 10.3450i 1.45171 + 0.426259i
\(590\) −4.97624 + 13.3220i −0.204869 + 0.548456i
\(591\) 13.5460 11.7377i 0.557209 0.482825i
\(592\) 18.5319 + 0.0361852i 0.761655 + 0.00148720i
\(593\) 32.9447 9.67343i 1.35288 0.397240i 0.476630 0.879104i \(-0.341858\pi\)
0.876246 + 0.481864i \(0.160040\pi\)
\(594\) −88.7557 118.684i −3.64169 4.86968i
\(595\) 9.60785 + 1.38140i 0.393883 + 0.0566319i
\(596\) −39.7924 18.2195i −1.62996 0.746301i
\(597\) −30.3442 −1.24191
\(598\) −7.19590 18.5135i −0.294262 0.757074i
\(599\) 31.0476i 1.26857i 0.773100 + 0.634284i \(0.218705\pi\)
−0.773100 + 0.634284i \(0.781295\pi\)
\(600\) 5.61258 + 7.52045i 0.229132 + 0.307021i
\(601\) 5.15493 35.8533i 0.210274 1.46249i −0.561968 0.827159i \(-0.689955\pi\)
0.772242 0.635329i \(-0.219135\pi\)
\(602\) 7.19559 + 9.62196i 0.293270 + 0.392162i
\(603\) 18.5609 + 63.2126i 0.755858 + 2.57421i
\(604\) −2.83960 1.82882i −0.115542 0.0744136i
\(605\) 18.8543 + 21.7591i 0.766538 + 0.884632i
\(606\) 36.0888 + 13.4805i 1.46601 + 0.547608i
\(607\) 9.33300 31.7853i 0.378815 1.29012i −0.520889 0.853624i \(-0.674400\pi\)
0.899704 0.436500i \(-0.143782\pi\)
\(608\) −28.4426 2.10404i −1.15350 0.0853302i
\(609\) 17.3518 27.0000i 0.703132 1.09410i
\(610\) 1.34842 + 2.47232i 0.0545960 + 0.100101i
\(611\) 7.18404 8.29083i 0.290635 0.335411i
\(612\) −39.0702 + 11.4306i −1.57932 + 0.462055i
\(613\) 1.36167 + 9.47063i 0.0549974 + 0.382515i 0.998667 + 0.0516247i \(0.0164400\pi\)
−0.943669 + 0.330890i \(0.892651\pi\)
\(614\) −1.78091 8.20602i −0.0718719 0.331168i
\(615\) −1.50015 3.28488i −0.0604921 0.132459i
\(616\) 63.8701 23.7158i 2.57340 0.955538i
\(617\) 5.71630 + 2.61055i 0.230130 + 0.105097i 0.527143 0.849777i \(-0.323263\pi\)
−0.297013 + 0.954873i \(0.595991\pi\)
\(618\) −34.5769 + 46.1423i −1.39089 + 1.85612i
\(619\) 14.2016 + 22.0982i 0.570812 + 0.888201i 0.999886 0.0150681i \(-0.00479651\pi\)
−0.429074 + 0.903269i \(0.641160\pi\)
\(620\) −12.2615 + 7.86310i −0.492435 + 0.315790i
\(621\) 66.4059 44.0215i 2.66478 1.76652i
\(622\) −6.18757 + 11.3185i −0.248099 + 0.453832i
\(623\) 13.8851 + 21.6056i 0.556294 + 0.865610i
\(624\) −21.0760 + 32.6545i −0.843713 + 1.30722i
\(625\) 0.415415 0.909632i 0.0166166 0.0363853i
\(626\) 1.78870 8.20322i 0.0714906 0.327867i
\(627\) −43.8325 95.9797i −1.75050 3.83306i
\(628\) −10.6005 + 35.9720i −0.423005 + 1.43544i
\(629\) 11.6568 1.67600i 0.464789 0.0668266i
\(630\) 30.5618 + 30.5916i 1.21761 + 1.21880i
\(631\) 13.0996 15.1178i 0.521489 0.601830i −0.432514 0.901627i \(-0.642374\pi\)
0.954003 + 0.299797i \(0.0969190\pi\)
\(632\) −12.8492 + 23.4499i −0.511115 + 0.932788i
\(633\) 19.0730 + 12.2575i 0.758084 + 0.487191i
\(634\) −5.74878 15.4361i −0.228313 0.613045i
\(635\) −5.18153 + 17.6467i −0.205623 + 0.700287i
\(636\) 20.1650 17.4387i 0.799596 0.691488i
\(637\) 16.7807 14.5406i 0.664877 0.576119i
\(638\) 1.62324 22.5412i 0.0642648 0.892416i
\(639\) 0.542588 + 1.84789i 0.0214645 + 0.0731012i
\(640\) 8.02729 7.97262i 0.317306 0.315145i
\(641\) 21.7337 + 3.12484i 0.858430 + 0.123424i 0.557454 0.830208i \(-0.311778\pi\)
0.300976 + 0.953632i \(0.402687\pi\)
\(642\) −0.0929508 1.30860i −0.00366848 0.0516463i
\(643\) 8.65195i 0.341200i −0.985340 0.170600i \(-0.945429\pi\)
0.985340 0.170600i \(-0.0545705\pi\)
\(644\) 10.7828 + 35.0036i 0.424903 + 1.37934i
\(645\) 7.38144i 0.290644i
\(646\) −18.0786 + 1.28414i −0.711294 + 0.0505238i
\(647\) 11.5671 + 1.66310i 0.454750 + 0.0653832i 0.365884 0.930660i \(-0.380767\pi\)
0.0888658 + 0.996044i \(0.471676\pi\)
\(648\) −82.3588 30.8557i −3.23536 1.21213i
\(649\) 17.8709 + 60.8628i 0.701495 + 2.38907i
\(650\) 4.13098 + 0.297481i 0.162031 + 0.0116682i
\(651\) −69.7330 + 60.4240i −2.73305 + 2.36820i
\(652\) −14.7018 + 12.7141i −0.575767 + 0.497921i
\(653\) −5.18740 + 17.6667i −0.202999 + 0.691350i 0.793562 + 0.608489i \(0.208224\pi\)
−0.996561 + 0.0828613i \(0.973594\pi\)
\(654\) −41.7981 + 15.5666i −1.63443 + 0.608703i
\(655\) −3.22652 2.07356i −0.126071 0.0810207i
\(656\) −3.66728 + 2.34671i −0.143183 + 0.0916238i
\(657\) −18.8453 + 21.7487i −0.735226 + 0.848497i
\(658\) −14.3112 + 14.2972i −0.557908 + 0.557363i
\(659\) 33.5260 4.82031i 1.30599 0.187773i 0.546041 0.837758i \(-0.316134\pi\)
0.759947 + 0.649986i \(0.225225\pi\)
\(660\) 40.1496 + 11.8316i 1.56282 + 0.460544i
\(661\) 16.6281 + 36.4105i 0.646758 + 1.41620i 0.894363 + 0.447342i \(0.147629\pi\)
−0.247605 + 0.968861i \(0.579643\pi\)
\(662\) −9.15160 1.99549i −0.355687 0.0775568i
\(663\) −10.2600 + 22.4663i −0.398466 + 0.872519i
\(664\) −0.411185 + 5.63317i −0.0159571 + 0.218609i
\(665\) 10.4086 + 16.1961i 0.403629 + 0.628059i
\(666\) 46.0342 + 25.1657i 1.78379 + 0.975152i
\(667\) 12.0491 + 1.55809i 0.466543 + 0.0603293i
\(668\) −9.53975 + 6.11767i −0.369104 + 0.236700i
\(669\) −27.4236 42.6719i −1.06026 1.64979i
\(670\) −9.31143 6.97755i −0.359732 0.269566i
\(671\) 11.4261 + 5.21813i 0.441100 + 0.201444i
\(672\) 43.0884 57.2675i 1.66217 2.20914i
\(673\) 11.3035 + 24.7513i 0.435720 + 0.954093i 0.992364 + 0.123342i \(0.0393612\pi\)
−0.556645 + 0.830751i \(0.687911\pi\)
\(674\) 10.5016 2.27912i 0.404508 0.0877885i
\(675\) 2.36424 + 16.4437i 0.0909998 + 0.632917i
\(676\) −2.48405 8.49056i −0.0955404 0.326560i
\(677\) 8.72040 10.0639i 0.335152 0.386786i −0.563010 0.826450i \(-0.690357\pi\)
0.898163 + 0.439664i \(0.144902\pi\)
\(678\) −62.8109 + 34.2576i −2.41224 + 1.31565i
\(679\) −16.3199 + 25.3942i −0.626299 + 0.974540i
\(680\) 4.31703 5.74931i 0.165551 0.220476i
\(681\) 4.66381 15.8835i 0.178717 0.608656i
\(682\) −22.7350 + 60.8642i −0.870569 + 2.33061i
\(683\) 5.83371 + 6.73246i 0.223221 + 0.257610i 0.856303 0.516474i \(-0.172756\pi\)
−0.633082 + 0.774085i \(0.718210\pi\)
\(684\) −67.8810 43.7182i −2.59550 1.67161i
\(685\) −2.24452 7.64412i −0.0857586 0.292067i
\(686\) −2.51607 + 1.88159i −0.0960638 + 0.0718393i
\(687\) −2.79046 + 19.4081i −0.106463 + 0.740465i
\(688\) 8.81128 1.24932i 0.335927 0.0476297i
\(689\) 11.7665i 0.448266i
\(690\) −7.57374 + 21.1890i −0.288328 + 0.806651i
\(691\) −1.20960 −0.0460155 −0.0230078 0.999735i \(-0.507324\pi\)
−0.0230078 + 0.999735i \(0.507324\pi\)
\(692\) 2.43598 5.32030i 0.0926021 0.202248i
\(693\) 190.916 + 27.4495i 7.25229 + 1.04272i
\(694\) 16.5693 12.3910i 0.628962 0.470356i
\(695\) −1.84951 + 0.543065i −0.0701559 + 0.0205996i
\(696\) −11.3624 20.8814i −0.430692 0.791506i
\(697\) −2.09101 + 1.81187i −0.0792026 + 0.0686294i
\(698\) −32.2398 12.0427i −1.22029 0.455824i
\(699\) −57.4832 16.8786i −2.17421 0.638406i
\(700\) −7.55842 1.09427i −0.285681 0.0413595i
\(701\) 2.11593 + 1.35983i 0.0799177 + 0.0513600i 0.579989 0.814624i \(-0.303057\pi\)
−0.500072 + 0.865984i \(0.666693\pi\)
\(702\) −60.4046 + 32.9451i −2.27983 + 1.24343i
\(703\) 17.6529 + 15.2964i 0.665794 + 0.576913i
\(704\) 7.32809 49.9294i 0.276188 1.88179i
\(705\) −12.3014 + 1.76868i −0.463298 + 0.0666122i
\(706\) 3.42646 + 15.7883i 0.128957 + 0.594200i
\(707\) −28.5201 + 13.0247i −1.07261 + 0.489844i
\(708\) 50.3844 + 43.7445i 1.89356 + 1.64402i
\(709\) 7.15096 15.6584i 0.268560 0.588064i −0.726519 0.687146i \(-0.758863\pi\)
0.995079 + 0.0990818i \(0.0315905\pi\)
\(710\) −0.272200 0.203974i −0.0102155 0.00765500i
\(711\) −63.6826 + 40.9263i −2.38828 + 1.53486i
\(712\) 18.9765 1.32930i 0.711175 0.0498175i
\(713\) −31.9749 14.0571i −1.19747 0.526444i
\(714\) 21.8461 39.9617i 0.817569 1.49553i
\(715\) 15.5412 9.98769i 0.581206 0.373518i
\(716\) −11.5315 + 5.25265i −0.430952 + 0.196301i
\(717\) 28.9669 + 13.2287i 1.08179 + 0.494036i
\(718\) 23.3278 + 5.08659i 0.870587 + 0.189830i
\(719\) 48.1029 21.9679i 1.79394 0.819264i 0.827893 0.560886i \(-0.189539\pi\)
0.966044 0.258378i \(-0.0831879\pi\)
\(720\) 30.7493 8.96362i 1.14596 0.334055i
\(721\) −6.67844 46.4496i −0.248718 1.72987i
\(722\) −6.41585 6.42212i −0.238773 0.239006i
\(723\) 49.3767 + 42.7851i 1.83634 + 1.59120i
\(724\) 0.00952900 9.76035i 0.000354142 0.362741i
\(725\) −1.36962 + 2.13117i −0.0508664 + 0.0791497i
\(726\) 126.594 47.1467i 4.69834 1.74978i
\(727\) 37.5962 + 11.0392i 1.39437 + 0.409423i 0.890746 0.454502i \(-0.150183\pi\)
0.503621 + 0.863925i \(0.332001\pi\)
\(728\) −6.67837 30.9179i −0.247517 1.14589i
\(729\) −54.7689 63.2067i −2.02848 2.34099i
\(730\) 0.365062 5.06946i 0.0135116 0.187629i
\(731\) 5.42634 1.59332i 0.200700 0.0589309i
\(732\) 13.0805 1.86766i 0.483470 0.0690309i
\(733\) 5.08741 35.3837i 0.187908 1.30693i −0.649506 0.760357i \(-0.725024\pi\)
0.837413 0.546570i \(-0.184067\pi\)
\(734\) 52.0544 3.69746i 1.92136 0.136476i
\(735\) −25.1542 −0.927828
\(736\) 26.5753 + 5.45458i 0.979579 + 0.201058i
\(737\) −51.9004 −1.91178
\(738\) −12.2948 + 0.873308i −0.452577 + 0.0321469i
\(739\) −5.17621 + 36.0013i −0.190410 + 1.32433i 0.640515 + 0.767945i \(0.278721\pi\)
−0.830925 + 0.556384i \(0.812188\pi\)
\(740\) −9.17293 + 1.30973i −0.337203 + 0.0481466i
\(741\) −47.0027 + 13.8012i −1.72669 + 0.507001i
\(742\) −1.55843 + 21.6412i −0.0572117 + 0.794473i
\(743\) −25.3646 29.2724i −0.930539 1.07390i −0.997099 0.0761165i \(-0.975748\pi\)
0.0665602 0.997782i \(-0.478798\pi\)
\(744\) 14.4297 + 66.8033i 0.529020 + 2.44913i
\(745\) 20.9962 + 6.16503i 0.769240 + 0.225869i
\(746\) 15.1048 5.62539i 0.553025 0.205960i
\(747\) −8.64481 + 13.4516i −0.316297 + 0.492168i
\(748\) 0.0313091 32.0692i 0.00114477 1.17257i
\(749\) 0.806915 + 0.699196i 0.0294840 + 0.0255481i
\(750\) −3.31610 3.31934i −0.121087 0.121205i
\(751\) −4.13765 28.7780i −0.150985 1.05012i −0.914573 0.404421i \(-0.867473\pi\)
0.763588 0.645704i \(-0.223436\pi\)
\(752\) 4.19331 + 14.3849i 0.152914 + 0.524565i
\(753\) 6.38562 2.91622i 0.232705 0.106273i
\(754\) −10.2514 2.23529i −0.373333 0.0814045i
\(755\) 1.53617 + 0.701545i 0.0559069 + 0.0255318i
\(756\) 115.461 52.5932i 4.19929 1.91280i
\(757\) −18.1974 + 11.6948i −0.661395 + 0.425053i −0.827814 0.561002i \(-0.810416\pi\)
0.166419 + 0.986055i \(0.446780\pi\)
\(758\) 10.9200 19.9752i 0.396631 0.725533i
\(759\) 29.6419 + 95.8918i 1.07593 + 3.48065i
\(760\) 14.2253 0.996476i 0.516006 0.0361460i
\(761\) −34.5120 + 22.1795i −1.25106 + 0.804007i −0.987034 0.160508i \(-0.948687\pi\)
−0.264025 + 0.964516i \(0.585050\pi\)
\(762\) 69.0559 + 51.7472i 2.50163 + 1.87460i
\(763\) 15.0797 33.0200i 0.545922 1.19540i
\(764\) −22.1145 19.2002i −0.800075 0.694637i
\(765\) 18.5146 8.45534i 0.669397 0.305704i
\(766\) −6.08311 28.0295i −0.219792 1.01275i
\(767\) 29.1497 4.19110i 1.05254 0.151332i
\(768\) −21.8630 48.3722i −0.788912 1.74548i
\(769\) −29.3137 25.4005i −1.05708 0.915965i −0.0604641 0.998170i \(-0.519258\pi\)
−0.996615 + 0.0822058i \(0.973804\pi\)
\(770\) −29.9065 + 16.3113i −1.07776 + 0.587817i
\(771\) −32.3226 20.7725i −1.16407 0.748103i
\(772\) 53.3088 + 7.71778i 1.91863 + 0.277769i
\(773\) −20.6966 6.07708i −0.744406 0.218577i −0.112532 0.993648i \(-0.535896\pi\)
−0.631874 + 0.775071i \(0.717714\pi\)
\(774\) 23.6014 + 8.81600i 0.848336 + 0.316885i
\(775\) 5.50419 4.76941i 0.197716 0.171322i
\(776\) 10.6867 + 19.6395i 0.383628 + 0.705016i
\(777\) −56.3180 + 16.5365i −2.02040 + 0.593242i
\(778\) 29.7468 22.2455i 1.06647 0.797541i
\(779\) −5.43187 0.780986i −0.194617 0.0279817i
\(780\) 8.08986 17.6687i 0.289664 0.632639i
\(781\) −1.51720 −0.0542897
\(782\) 17.2115 + 0.993969i 0.615484 + 0.0355443i
\(783\) 42.0856i 1.50402i
\(784\) 4.25738 + 30.0268i 0.152049 + 1.07239i
\(785\) 2.66850 18.5598i 0.0952429 0.662429i
\(786\) −14.4114 + 10.7772i −0.514036 + 0.384411i
\(787\) 12.5387 + 42.7029i 0.446957 + 1.52220i 0.807736 + 0.589544i \(0.200693\pi\)
−0.360779 + 0.932651i \(0.617489\pi\)
\(788\) 9.08403 + 5.85049i 0.323605 + 0.208415i
\(789\) −5.06569 5.84612i −0.180343 0.208127i
\(790\) 4.67837 12.5245i 0.166449 0.445602i
\(791\) 16.4048 55.8696i 0.583288 1.98650i
\(792\) 85.7830 114.243i 3.04816 4.05947i
\(793\) 3.15289 4.90599i 0.111962 0.174217i
\(794\) 35.5500 19.3892i 1.26162 0.688098i
\(795\) −8.72917 + 10.0740i −0.309592 + 0.357288i
\(796\) −5.13637 17.5563i −0.182054 0.622265i
\(797\) −2.72490 18.9521i −0.0965208 0.671317i −0.979432 0.201776i \(-0.935329\pi\)
0.882911 0.469541i \(-0.155580\pi\)
\(798\) 88.2765 19.1583i 3.12496 0.678195i
\(799\) 3.95553 + 8.66140i 0.139936 + 0.306418i
\(800\) −3.40107 + 4.52026i −0.120246 + 0.159815i
\(801\) 48.9875 + 22.3718i 1.73089 + 0.790470i
\(802\) 7.26257 + 5.44222i 0.256450 + 0.192172i
\(803\) −12.2567 19.0718i −0.432529 0.673028i
\(804\) −45.9564 + 29.4710i −1.62076 + 1.03936i
\(805\) −7.84347 16.5487i −0.276446 0.583267i
\(806\) 26.4674 + 14.4691i 0.932276 + 0.509652i
\(807\) −52.5475 81.7655i −1.84976 2.87828i
\(808\) −1.69066 + 23.1617i −0.0594771 + 0.814827i
\(809\) 17.5032 38.3266i 0.615378 1.34749i −0.303455 0.952846i \(-0.598140\pi\)
0.918834 0.394645i \(-0.129132\pi\)
\(810\) 42.9650 + 9.36844i 1.50964 + 0.329173i
\(811\) −0.397935 0.871357i −0.0139734 0.0305975i 0.902517 0.430655i \(-0.141717\pi\)
−0.916490 + 0.400058i \(0.868990\pi\)
\(812\) 18.5585 + 5.46897i 0.651277 + 0.191923i
\(813\) −49.0487 + 7.05214i −1.72021 + 0.247329i
\(814\) −29.2393 + 29.2107i −1.02484 + 1.02384i
\(815\) 6.36421 7.34469i 0.222928 0.257273i
\(816\) −18.1824 28.4142i −0.636510 0.994694i
\(817\) 9.43642 + 6.06442i 0.330138 + 0.212167i
\(818\) −18.0344 + 6.71647i −0.630559 + 0.234836i
\(819\) 25.2284 85.9199i 0.881550 3.00229i
\(820\) 1.64660 1.42398i 0.0575019 0.0497274i
\(821\) −39.8420 + 34.5233i −1.39050 + 1.20487i −0.438512 + 0.898725i \(0.644494\pi\)
−0.951984 + 0.306147i \(0.900960\pi\)
\(822\) −37.2836 2.68487i −1.30041 0.0936455i
\(823\) 11.9771 + 40.7901i 0.417494 + 1.42185i 0.853114 + 0.521724i \(0.174711\pi\)
−0.435620 + 0.900131i \(0.643471\pi\)
\(824\) −32.5494 12.1946i −1.13391 0.424820i
\(825\) −20.7153 2.97841i −0.721214 0.103695i
\(826\) −54.1680 + 3.84760i −1.88475 + 0.133875i
\(827\) 11.3451i 0.394508i 0.980352 + 0.197254i \(0.0632024\pi\)
−0.980352 + 0.197254i \(0.936798\pi\)
\(828\) 58.7040 + 49.5233i 2.04011 + 1.72105i
\(829\) 30.6448i 1.06434i −0.846638 0.532169i \(-0.821377\pi\)
0.846638 0.532169i \(-0.178623\pi\)
\(830\) −0.200092 2.81698i −0.00694530 0.0977788i
\(831\) −85.1580 12.2439i −2.95410 0.424735i
\(832\) −22.4604 6.66649i −0.778675 0.231119i
\(833\) 5.42965 + 18.4917i 0.188126 + 0.640700i
\(834\) −0.649609 + 9.02083i −0.0224941 + 0.312366i
\(835\) 4.28239 3.71071i 0.148198 0.128414i
\(836\) 48.1115 41.6067i 1.66397 1.43900i
\(837\) −34.0874 + 116.091i −1.17823 + 4.01270i
\(838\) −7.10269 19.0715i −0.245358 0.658813i
\(839\) 28.4595 + 18.2898i 0.982532 + 0.631435i 0.930145 0.367192i \(-0.119681\pi\)
0.0523867 + 0.998627i \(0.483317\pi\)
\(840\) −17.2193 + 31.4252i −0.594121 + 1.08427i
\(841\) −14.7882 + 17.0665i −0.509939 + 0.588501i
\(842\) −33.4104 33.4430i −1.15140 1.15252i
\(843\) −76.0253 + 10.9308i −2.61845 + 0.376476i
\(844\) −3.86332 + 13.1099i −0.132981 + 0.451261i
\(845\) 1.83748 + 4.02352i 0.0632112 + 0.138413i
\(846\) −9.03699 + 41.4450i −0.310698 + 1.42491i
\(847\) −45.6720 + 100.008i −1.56931 + 3.43631i
\(848\) 13.5028 + 8.71504i 0.463689 + 0.299276i
\(849\) −23.4343 36.4645i −0.804263 1.25146i
\(850\) −1.72436 + 3.15427i −0.0591451 + 0.108191i
\(851\) −14.7873 16.5837i −0.506904 0.568480i
\(852\) −1.34344 + 0.861523i −0.0460254 + 0.0295153i
\(853\) 11.6781 + 18.1715i 0.399851 + 0.622180i 0.981546 0.191227i \(-0.0612467\pi\)
−0.581695 + 0.813407i \(0.697610\pi\)
\(854\) −6.44866 + 8.60564i −0.220668 + 0.294479i
\(855\) 36.7223 + 16.7705i 1.25588 + 0.573539i
\(856\) 0.741383 0.275285i 0.0253399 0.00940906i
\(857\) −11.4363 25.0421i −0.390658 0.855421i −0.998133 0.0610825i \(-0.980545\pi\)
0.607475 0.794339i \(-0.292183\pi\)
\(858\) −18.3835 84.7066i −0.627602 2.89184i
\(859\) −3.69794 25.7198i −0.126172 0.877547i −0.950343 0.311205i \(-0.899267\pi\)
0.824170 0.566342i \(-0.191642\pi\)
\(860\) −4.27068 + 1.24946i −0.145629 + 0.0426061i
\(861\) 9.03042 10.4217i 0.307756 0.355169i
\(862\) 0.645859 + 1.18418i 0.0219980 + 0.0403332i
\(863\) −4.13293 + 6.43097i −0.140687 + 0.218913i −0.904446 0.426589i \(-0.859715\pi\)
0.763759 + 0.645501i \(0.223352\pi\)
\(864\) 6.93294 93.7199i 0.235863 3.18842i
\(865\) −0.824274 + 2.80722i −0.0280262 + 0.0954483i
\(866\) 51.4915 + 19.2340i 1.74975 + 0.653597i
\(867\) 22.8966 + 26.4241i 0.777609 + 0.897409i
\(868\) −46.7633 30.1175i −1.58725 1.02225i
\(869\) −16.8012 57.2196i −0.569942 1.94104i
\(870\) 7.11855 + 9.51895i 0.241341 + 0.322723i
\(871\) −3.42917 + 23.8504i −0.116193 + 0.808139i
\(872\) −16.0816 21.5481i −0.544590 0.729712i
\(873\) 63.2976i 2.14230i
\(874\) 20.8655 + 27.0906i 0.705788 + 0.916354i
\(875\) 3.81861 0.129093
\(876\) −21.6826 9.92771i −0.732588 0.335426i
\(877\) −47.8267 6.87645i −1.61499 0.232201i −0.725192 0.688547i \(-0.758249\pi\)
−0.889803 + 0.456346i \(0.849158\pi\)
\(878\) 12.3177 + 16.4712i 0.415701 + 0.555876i
\(879\) −15.8172 + 4.64435i −0.533501 + 0.156650i
\(880\) −0.0492681 + 25.2321i −0.00166083 + 0.850574i
\(881\) 14.6371 12.6831i 0.493135 0.427304i −0.372460 0.928048i \(-0.621486\pi\)
0.865595 + 0.500744i \(0.166940\pi\)
\(882\) −30.0429 + 80.4282i −1.01160 + 2.70816i
\(883\) −9.90800 2.90925i −0.333431 0.0979041i 0.110732 0.993850i \(-0.464681\pi\)
−0.444163 + 0.895946i \(0.646499\pi\)
\(884\) −14.7350 2.13326i −0.495593 0.0717494i
\(885\) −28.0661 18.0370i −0.943433 0.606307i
\(886\) 15.2839 + 28.0230i 0.513474 + 0.941449i
\(887\) −1.81259 1.57061i −0.0608607 0.0527361i 0.623899 0.781505i \(-0.285548\pi\)
−0.684760 + 0.728769i \(0.740093\pi\)
\(888\) −9.30360 + 42.4684i −0.312208 + 1.42515i
\(889\) −69.5157 + 9.99485i −2.33148 + 0.335217i
\(890\) −9.29512 + 2.01728i −0.311573 + 0.0676193i
\(891\) 178.421 81.4823i 5.97734 2.72976i
\(892\) 20.0467 23.0895i 0.671213 0.773095i
\(893\) −7.84548 + 17.1792i −0.262539 + 0.574880i
\(894\) 61.5693 82.1633i 2.05919 2.74795i
\(895\) 5.32995 3.42535i 0.178160 0.114497i
\(896\) 40.4269 + 15.2360i 1.35057 + 0.508999i
\(897\) 46.0247 7.28591i 1.53672 0.243270i
\(898\) 25.3182 + 13.8408i 0.844880 + 0.461875i
\(899\) −15.5215 + 9.97507i −0.517671 + 0.332687i
\(900\) −14.5738 + 6.63846i −0.485795 + 0.221282i
\(901\) 9.28996 + 4.24258i 0.309493 + 0.141341i
\(902\) 2.06866 9.48718i 0.0688788 0.315888i
\(903\) −25.6397 + 11.7092i −0.853234 + 0.389659i
\(904\) −30.4524 30.5417i −1.01283 1.01580i
\(905\) 0.694522 + 4.83050i 0.0230867 + 0.160571i
\(906\) 5.60564 5.60017i 0.186235 0.186053i
\(907\) −38.8379 33.6533i −1.28959 1.11744i −0.986374 0.164517i \(-0.947393\pi\)
−0.303218 0.952921i \(-0.598061\pi\)
\(908\) 9.97914 + 0.00974260i 0.331170 + 0.000323320i
\(909\) −35.5446 + 55.3085i −1.17894 + 1.83447i
\(910\) 5.51970 + 14.8210i 0.182976 + 0.491311i
\(911\) 5.62508 + 1.65167i 0.186367 + 0.0547224i 0.373584 0.927596i \(-0.378129\pi\)
−0.187217 + 0.982319i \(0.559947\pi\)
\(912\) 18.9755 64.1610i 0.628342 2.12458i
\(913\) −8.24907 9.51994i −0.273004 0.315064i
\(914\) 21.1910 + 1.52600i 0.700934 + 0.0504757i
\(915\) −6.33898 + 1.86129i −0.209560 + 0.0615325i
\(916\) −11.7013 + 1.67073i −0.386622 + 0.0552026i
\(917\) 2.08431 14.4967i 0.0688301 0.478724i
\(918\) −4.23131 59.5701i −0.139654 1.96611i
\(919\) 47.7657 1.57564 0.787822 0.615903i \(-0.211209\pi\)
0.787822 + 0.615903i \(0.211209\pi\)
\(920\) −13.5413 0.795279i −0.446444 0.0262196i
\(921\) 19.6993 0.649115
\(922\) −0.754380 10.6205i −0.0248442 0.349767i
\(923\) −0.100244 + 0.697215i −0.00329959 + 0.0229491i
\(924\) 22.5923 + 158.229i 0.743233 + 5.20537i
\(925\) 4.44531 1.30526i 0.146161 0.0429167i
\(926\) −50.3496 3.62578i −1.65459 0.119151i
\(927\) −64.4397 74.3674i −2.11648 2.44254i
\(928\) 10.1580 10.1086i 0.333453 0.331829i
\(929\) 49.2129 + 14.4502i 1.61462 + 0.474096i 0.959566 0.281484i \(-0.0908268\pi\)
0.655056 + 0.755580i \(0.272645\pi\)
\(930\) −11.9263 32.0233i −0.391077 1.05008i
\(931\) −20.6661 + 32.1571i −0.677305 + 1.05391i
\(932\) 0.0352590 36.1151i 0.00115495 1.18299i
\(933\) −22.8704 19.8173i −0.748743 0.648790i
\(934\) 18.8750 18.8566i 0.617609 0.617006i
\(935\) 2.28196 + 15.8714i 0.0746282 + 0.519050i
\(936\) −46.8317 46.9691i −1.53074 1.53523i
\(937\) 41.8425 19.1088i 1.36694 0.624259i 0.409343 0.912381i \(-0.365758\pi\)
0.957594 + 0.288122i \(0.0930308\pi\)
\(938\) 9.46591 43.4121i 0.309073 1.41745i
\(939\) 17.9168 + 8.18235i 0.584694 + 0.267021i
\(940\) −3.10557 6.81785i −0.101292 0.222374i
\(941\) −35.2493 + 22.6533i −1.14909 + 0.738477i −0.969458 0.245256i \(-0.921128\pi\)
−0.179635 + 0.983733i \(0.557492\pi\)
\(942\) −77.1955 42.2009i −2.51517 1.37498i
\(943\) 5.02902 + 1.39939i 0.163767 + 0.0455704i
\(944\) −16.7807 + 36.5555i −0.546165 + 1.18978i
\(945\) −53.3672 + 34.2970i −1.73603 + 1.11568i
\(946\) −11.9020 + 15.8831i −0.386969 + 0.516404i
\(947\) 10.6834 23.3934i 0.347164 0.760183i −0.652832 0.757502i \(-0.726419\pi\)
0.999996 0.00268076i \(-0.000853313\pi\)
\(948\) −47.3684 41.1260i −1.53845 1.33571i
\(949\) −9.57408 + 4.37234i −0.310788 + 0.141932i
\(950\) −6.96787 + 1.51221i −0.226068 + 0.0490624i
\(951\) 38.2493 5.49942i 1.24032 0.178331i
\(952\) 26.8185 + 5.87516i 0.869194 + 0.190415i
\(953\) 11.6474 + 10.0925i 0.377295 + 0.326928i 0.822779 0.568362i \(-0.192423\pi\)
−0.445483 + 0.895290i \(0.646968\pi\)
\(954\) 21.7850 + 39.9425i 0.705314 + 1.29319i
\(955\) 12.3187 + 7.91673i 0.398623 + 0.256179i
\(956\) −2.75052 + 18.9986i −0.0889582 + 0.614459i
\(957\) 50.8707 + 14.9370i 1.64442 + 0.482844i
\(958\) −14.7497 + 39.4867i −0.476542 + 1.27576i
\(959\) 22.9916 19.9223i 0.742437 0.643325i
\(960\) 14.2841 + 22.3703i 0.461018 + 0.721998i
\(961\) 21.1504 6.21033i 0.682272 0.200333i
\(962\) 11.4916 + 15.3667i 0.370505 + 0.495441i
\(963\) 2.21609 + 0.318625i 0.0714123 + 0.0102675i
\(964\) −16.3962 + 35.8101i −0.528086 + 1.15337i
\(965\) −26.9323 −0.866982
\(966\) −85.6149 + 7.30464i −2.75461 + 0.235023i
\(967\) 23.1422i 0.744202i −0.928192 0.372101i \(-0.878638\pi\)
0.928192 0.372101i \(-0.121362\pi\)
\(968\) 48.7063 + 65.2629i 1.56548 + 2.09763i
\(969\) 6.05109 42.0862i 0.194389 1.35200i
\(970\) −6.69518 8.95281i −0.214969 0.287458i
\(971\) 4.41267 + 15.0282i 0.141609 + 0.482277i 0.999502 0.0315517i \(-0.0100449\pi\)
−0.857893 + 0.513829i \(0.828227\pi\)
\(972\) 57.7472 89.6639i 1.85224 2.87597i
\(973\) −4.82024 5.56286i −0.154530 0.178337i
\(974\) −23.2985 8.70283i −0.746531 0.278857i
\(975\) −2.73740 + 9.32274i −0.0876671 + 0.298567i
\(976\) 3.29472 + 7.25187i 0.105461 + 0.232127i
\(977\) −17.0572 + 26.5415i −0.545709 + 0.849139i −0.999111 0.0421670i \(-0.986574\pi\)
0.453402 + 0.891306i \(0.350210\pi\)
\(978\) −21.8335 40.0315i −0.698158 1.28007i
\(979\) −27.7829 + 32.0632i −0.887945 + 1.02474i
\(980\) −4.25786 14.5535i −0.136012 0.464894i
\(981\) −10.8328 75.3438i −0.345865 2.40554i
\(982\) −3.70091 17.0529i −0.118101 0.544180i
\(983\) 9.87806 + 21.6299i 0.315061 + 0.689888i 0.999222 0.0394436i \(-0.0125585\pi\)
−0.684161 + 0.729331i \(0.739831\pi\)
\(984\) −3.55543 9.57529i −0.113343 0.305249i
\(985\) −4.91428 2.24428i −0.156582 0.0715086i
\(986\) 5.46112 7.28778i 0.173917 0.232090i
\(987\) −25.6574 39.9237i −0.816683 1.27078i
\(988\) −15.9411 24.8582i −0.507155 0.790845i
\(989\) −8.16228 6.87215i −0.259545 0.218522i
\(990\) −34.2645 + 62.6779i −1.08900 + 1.99203i
\(991\) 4.30473 + 6.69830i 0.136744 + 0.212778i 0.902871 0.429911i \(-0.141455\pi\)
−0.766127 + 0.642689i \(0.777819\pi\)
\(992\) −36.2079 + 19.6564i −1.14960 + 0.624092i
\(993\) 9.12831 19.9882i 0.289678 0.634307i
\(994\) 0.276716 1.26906i 0.00877690 0.0402521i
\(995\) 3.79943 + 8.31958i 0.120450 + 0.263749i
\(996\) −12.7101 3.74550i −0.402735 0.118681i
\(997\) 54.6260 7.85403i 1.73002 0.248740i 0.795832 0.605517i \(-0.207034\pi\)
0.934189 + 0.356778i \(0.116125\pi\)
\(998\) −40.1734 40.2126i −1.27167 1.27291i
\(999\) −50.4024 + 58.1675i −1.59466 + 1.84034i
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 920.2.bb.a.11.3 480
8.3 odd 2 920.2.bb.b.11.17 yes 480
23.21 odd 22 920.2.bb.b.251.17 yes 480
184.67 even 22 inner 920.2.bb.a.251.3 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bb.a.11.3 480 1.1 even 1 trivial
920.2.bb.a.251.3 yes 480 184.67 even 22 inner
920.2.bb.b.11.17 yes 480 8.3 odd 2
920.2.bb.b.251.17 yes 480 23.21 odd 22