Properties

Label 164.2.o.b.111.4
Level $164$
Weight $2$
Character 164.111
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
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] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), 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: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 111.4
Character \(\chi\) \(=\) 164.111
Dual form 164.2.o.b.99.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.09937 - 0.889595i) q^{2} +(-0.323235 - 0.133889i) q^{3} +(0.417242 + 1.95599i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.236250 + 0.434742i) q^{6} +(-2.28906 - 3.73541i) q^{7} +(1.28134 - 2.52154i) q^{8} +(-2.03477 - 2.03477i) q^{9} +O(q^{10})\) \(q+(-1.09937 - 0.889595i) q^{2} +(-0.323235 - 0.133889i) q^{3} +(0.417242 + 1.95599i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.236250 + 0.434742i) q^{6} +(-2.28906 - 3.73541i) q^{7} +(1.28134 - 2.52154i) q^{8} +(-2.03477 - 2.03477i) q^{9} +(1.09616 + 0.232580i) q^{10} +(2.94031 + 0.231408i) q^{11} +(0.127018 - 0.688110i) q^{12} +(-1.05491 - 4.39401i) q^{13} +(-0.806469 + 6.14295i) q^{14} +(0.276365 - 0.0217504i) q^{15} +(-3.65182 + 1.63224i) q^{16} +(-2.76691 + 2.36316i) q^{17} +(0.426849 + 4.04708i) q^{18} +(-4.50401 - 1.08132i) q^{19} +(-0.998183 - 1.23083i) q^{20} +(0.239778 + 1.51390i) q^{21} +(-3.02664 - 2.87009i) q^{22} +(6.50021 - 4.72268i) q^{23} +(-0.751779 + 0.643495i) q^{24} +(-2.56990 + 3.53716i) q^{25} +(-2.74915 + 5.76910i) q^{26} +(0.786942 + 1.89985i) q^{27} +(6.35134 - 6.03596i) q^{28} +(5.31907 + 4.54292i) q^{29} +(-0.323177 - 0.221941i) q^{30} +(-0.131241 - 0.403918i) q^{31} +(5.46675 + 1.45419i) q^{32} +(-0.919431 - 0.468474i) q^{33} +(5.14413 - 0.136570i) q^{34} +(2.95977 + 1.81375i) q^{35} +(3.13100 - 4.82898i) q^{36} +(2.21897 - 6.82927i) q^{37} +(3.98965 + 5.19551i) q^{38} +(-0.247324 + 1.56154i) q^{39} +(0.00243738 + 2.24112i) q^{40} +(1.56856 - 6.20803i) q^{41} +(1.08315 - 1.87764i) q^{42} +(3.65616 + 0.579078i) q^{43} +(0.774190 + 5.84779i) q^{44} +(2.16848 + 0.704582i) q^{45} +(-11.3474 - 0.590569i) q^{46} +(-4.08444 + 6.66520i) q^{47} +(1.39894 - 0.0386625i) q^{48} +(-5.53555 + 10.8641i) q^{49} +(5.97192 - 1.60249i) q^{50} +(1.21076 - 0.393401i) q^{51} +(8.15450 - 3.89676i) q^{52} +(-1.61175 + 1.88712i) q^{53} +(0.824951 - 2.78870i) q^{54} +(-2.15908 + 0.894322i) q^{55} +(-12.3521 + 0.985646i) q^{56} +(1.31108 + 0.952555i) q^{57} +(-1.80629 - 9.72618i) q^{58} +(-2.29771 - 3.16253i) q^{59} +(0.157854 + 0.531492i) q^{60} +(12.3904 - 1.96244i) q^{61} +(-0.215041 + 0.560807i) q^{62} +(-2.94298 + 12.2584i) q^{63} +(-4.71635 - 6.46189i) q^{64} +(2.32538 + 2.72267i) q^{65} +(0.594046 + 1.33295i) q^{66} +(-0.516254 - 6.55963i) q^{67} +(-5.77680 - 4.42605i) q^{68} +(-2.73341 + 0.656234i) q^{69} +(-1.64039 - 4.62698i) q^{70} +(-0.111273 + 1.41386i) q^{71} +(-7.73797 + 2.52353i) q^{72} +(2.08819 - 2.08819i) q^{73} +(-8.51476 + 5.53394i) q^{74} +(1.30427 - 0.799256i) q^{75} +(0.235788 - 9.26098i) q^{76} +(-5.86616 - 11.5130i) q^{77} +(1.66104 - 1.49670i) q^{78} +(-3.24666 + 7.83812i) q^{79} +(1.99101 - 2.46599i) q^{80} +7.91332i q^{81} +(-7.24707 + 5.42955i) q^{82} -5.01948i q^{83} +(-2.86112 + 1.10066i) q^{84} +(1.10334 - 2.66370i) q^{85} +(-3.50433 - 3.88912i) q^{86} +(-1.11107 - 2.18059i) q^{87} +(4.35104 - 7.11762i) q^{88} +(-5.31834 + 3.25908i) q^{89} +(-1.75718 - 2.70367i) q^{90} +(-13.9987 + 13.9987i) q^{91} +(11.9497 + 10.7439i) q^{92} +(-0.0116583 + 0.148132i) q^{93} +(10.4196 - 3.69404i) q^{94} +(3.56877 - 0.856786i) q^{95} +(-1.57235 - 1.20198i) q^{96} +(0.157358 + 1.99942i) q^{97} +(15.7503 - 7.01933i) q^{98} +(-5.51199 - 6.45371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{40}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09937 0.889595i −0.777374 0.629039i
\(3\) −0.323235 0.133889i −0.186620 0.0773006i 0.287417 0.957806i \(-0.407204\pi\)
−0.474037 + 0.880505i \(0.657204\pi\)
\(4\) 0.417242 + 1.95599i 0.208621 + 0.977997i
\(5\) −0.705993 + 0.359722i −0.315730 + 0.160872i −0.604673 0.796474i \(-0.706696\pi\)
0.288943 + 0.957346i \(0.406696\pi\)
\(6\) 0.236250 + 0.434742i 0.0964486 + 0.177483i
\(7\) −2.28906 3.73541i −0.865184 1.41185i −0.910780 0.412892i \(-0.864519\pi\)
0.0455958 0.998960i \(-0.485481\pi\)
\(8\) 1.28134 2.52154i 0.453021 0.891500i
\(9\) −2.03477 2.03477i −0.678255 0.678255i
\(10\) 1.09616 + 0.232580i 0.346635 + 0.0735482i
\(11\) 2.94031 + 0.231408i 0.886538 + 0.0697721i 0.513546 0.858062i \(-0.328332\pi\)
0.372993 + 0.927834i \(0.378332\pi\)
\(12\) 0.127018 0.688110i 0.0366669 0.198640i
\(13\) −1.05491 4.39401i −0.292579 1.21868i −0.904055 0.427416i \(-0.859424\pi\)
0.611476 0.791263i \(-0.290576\pi\)
\(14\) −0.806469 + 6.14295i −0.215538 + 1.64177i
\(15\) 0.276365 0.0217504i 0.0713570 0.00561592i
\(16\) −3.65182 + 1.63224i −0.912955 + 0.408061i
\(17\) −2.76691 + 2.36316i −0.671074 + 0.573152i −0.918338 0.395797i \(-0.870469\pi\)
0.247264 + 0.968948i \(0.420469\pi\)
\(18\) 0.426849 + 4.04708i 0.100609 + 0.953907i
\(19\) −4.50401 1.08132i −1.03329 0.248071i −0.318878 0.947796i \(-0.603306\pi\)
−0.714413 + 0.699725i \(0.753306\pi\)
\(20\) −0.998183 1.23083i −0.223200 0.275221i
\(21\) 0.239778 + 1.51390i 0.0523238 + 0.330359i
\(22\) −3.02664 2.87009i −0.645282 0.611906i
\(23\) 6.50021 4.72268i 1.35539 0.984747i 0.356665 0.934232i \(-0.383914\pi\)
0.998723 0.0505147i \(-0.0160862\pi\)
\(24\) −0.751779 + 0.643495i −0.153456 + 0.131353i
\(25\) −2.56990 + 3.53716i −0.513980 + 0.707433i
\(26\) −2.74915 + 5.76910i −0.539153 + 1.13141i
\(27\) 0.786942 + 1.89985i 0.151447 + 0.365626i
\(28\) 6.35134 6.03596i 1.20029 1.14069i
\(29\) 5.31907 + 4.54292i 0.987727 + 0.843598i 0.987694 0.156402i \(-0.0499894\pi\)
3.32856e−5 1.00000i \(0.499989\pi\)
\(30\) −0.323177 0.221941i −0.0590037 0.0405207i
\(31\) −0.131241 0.403918i −0.0235715 0.0725458i 0.938579 0.345065i \(-0.112143\pi\)
−0.962150 + 0.272519i \(0.912143\pi\)
\(32\) 5.46675 + 1.45419i 0.966393 + 0.257068i
\(33\) −0.919431 0.468474i −0.160052 0.0815508i
\(34\) 5.14413 0.136570i 0.882210 0.0234215i
\(35\) 2.95977 + 1.81375i 0.500292 + 0.306580i
\(36\) 3.13100 4.82898i 0.521833 0.804829i
\(37\) 2.21897 6.82927i 0.364796 1.12273i −0.585313 0.810807i \(-0.699028\pi\)
0.950109 0.311918i \(-0.100972\pi\)
\(38\) 3.98965 + 5.19551i 0.647207 + 0.842824i
\(39\) −0.247324 + 1.56154i −0.0396035 + 0.250046i
\(40\) 0.00243738 + 2.24112i 0.000385384 + 0.354352i
\(41\) 1.56856 6.20803i 0.244968 0.969531i
\(42\) 1.08315 1.87764i 0.167134 0.289726i
\(43\) 3.65616 + 0.579078i 0.557559 + 0.0883086i 0.428853 0.903374i \(-0.358918\pi\)
0.128705 + 0.991683i \(0.458918\pi\)
\(44\) 0.774190 + 5.84779i 0.116713 + 0.881587i
\(45\) 2.16848 + 0.704582i 0.323258 + 0.105033i
\(46\) −11.3474 0.590569i −1.67309 0.0870746i
\(47\) −4.08444 + 6.66520i −0.595777 + 0.972219i 0.402606 + 0.915373i \(0.368104\pi\)
−0.998383 + 0.0568459i \(0.981896\pi\)
\(48\) 1.39894 0.0386625i 0.201919 0.00558045i
\(49\) −5.53555 + 10.8641i −0.790792 + 1.55202i
\(50\) 5.97192 1.60249i 0.844557 0.226627i
\(51\) 1.21076 0.393401i 0.169541 0.0550872i
\(52\) 8.15450 3.89676i 1.13083 0.540383i
\(53\) −1.61175 + 1.88712i −0.221391 + 0.259216i −0.859975 0.510337i \(-0.829521\pi\)
0.638583 + 0.769553i \(0.279521\pi\)
\(54\) 0.824951 2.78870i 0.112262 0.379494i
\(55\) −2.15908 + 0.894322i −0.291131 + 0.120590i
\(56\) −12.3521 + 0.985646i −1.65061 + 0.131712i
\(57\) 1.31108 + 0.952555i 0.173657 + 0.126169i
\(58\) −1.80629 9.72618i −0.237177 1.27711i
\(59\) −2.29771 3.16253i −0.299136 0.411726i 0.632819 0.774300i \(-0.281898\pi\)
−0.931955 + 0.362574i \(0.881898\pi\)
\(60\) 0.157854 + 0.531492i 0.0203789 + 0.0686153i
\(61\) 12.3904 1.96244i 1.58643 0.251265i 0.700002 0.714141i \(-0.253182\pi\)
0.886423 + 0.462875i \(0.153182\pi\)
\(62\) −0.215041 + 0.560807i −0.0273102 + 0.0712226i
\(63\) −2.94298 + 12.2584i −0.370780 + 1.54441i
\(64\) −4.71635 6.46189i −0.589544 0.807737i
\(65\) 2.32538 + 2.72267i 0.288428 + 0.337705i
\(66\) 0.594046 + 1.33295i 0.0731220 + 0.164075i
\(67\) −0.516254 6.55963i −0.0630705 0.801386i −0.944382 0.328851i \(-0.893339\pi\)
0.881311 0.472536i \(-0.156661\pi\)
\(68\) −5.77680 4.42605i −0.700540 0.536737i
\(69\) −2.73341 + 0.656234i −0.329064 + 0.0790013i
\(70\) −1.64039 4.62698i −0.196064 0.553030i
\(71\) −0.111273 + 1.41386i −0.0132057 + 0.167794i 0.986778 + 0.162078i \(0.0518196\pi\)
−0.999984 + 0.00571647i \(0.998180\pi\)
\(72\) −7.73797 + 2.52353i −0.911928 + 0.297400i
\(73\) 2.08819 2.08819i 0.244404 0.244404i −0.574265 0.818669i \(-0.694712\pi\)
0.818669 + 0.574265i \(0.194712\pi\)
\(74\) −8.51476 + 5.53394i −0.989821 + 0.643307i
\(75\) 1.30427 0.799256i 0.150604 0.0922902i
\(76\) 0.235788 9.26098i 0.0270468 1.06231i
\(77\) −5.86616 11.5130i −0.668511 1.31203i
\(78\) 1.66104 1.49670i 0.188076 0.169468i
\(79\) −3.24666 + 7.83812i −0.365277 + 0.881858i 0.629233 + 0.777217i \(0.283369\pi\)
−0.994510 + 0.104641i \(0.966631\pi\)
\(80\) 1.99101 2.46599i 0.222601 0.275706i
\(81\) 7.91332i 0.879258i
\(82\) −7.24707 + 5.42955i −0.800305 + 0.599594i
\(83\) 5.01948i 0.550959i −0.961307 0.275480i \(-0.911163\pi\)
0.961307 0.275480i \(-0.0888366\pi\)
\(84\) −2.86112 + 1.10066i −0.312174 + 0.120092i
\(85\) 1.10334 2.66370i 0.119674 0.288918i
\(86\) −3.50433 3.88912i −0.377882 0.419375i
\(87\) −1.11107 2.18059i −0.119119 0.233784i
\(88\) 4.35104 7.11762i 0.463822 0.758740i
\(89\) −5.31834 + 3.25908i −0.563743 + 0.345462i −0.774993 0.631970i \(-0.782247\pi\)
0.211250 + 0.977432i \(0.432247\pi\)
\(90\) −1.75718 2.70367i −0.185223 0.284991i
\(91\) −13.9987 + 13.9987i −1.46746 + 1.46746i
\(92\) 11.9497 + 10.7439i 1.24584 + 1.12013i
\(93\) −0.0116583 + 0.148132i −0.00120890 + 0.0153606i
\(94\) 10.4196 3.69404i 1.07470 0.381011i
\(95\) 3.56877 0.856786i 0.366148 0.0879044i
\(96\) −1.57235 1.20198i −0.160477 0.122677i
\(97\) 0.157358 + 1.99942i 0.0159772 + 0.203010i 0.999725 + 0.0234538i \(0.00746625\pi\)
−0.983748 + 0.179556i \(0.942534\pi\)
\(98\) 15.7503 7.01933i 1.59102 0.709059i
\(99\) −5.51199 6.45371i −0.553976 0.648622i
\(100\) −7.99094 3.55085i −0.799094 0.355085i
\(101\) 3.78349 15.7593i 0.376471 1.56811i −0.386880 0.922130i \(-0.626447\pi\)
0.763351 0.645984i \(-0.223553\pi\)
\(102\) −1.68105 0.644595i −0.166449 0.0638244i
\(103\) −1.52470 + 0.241489i −0.150233 + 0.0237946i −0.231098 0.972930i \(-0.574232\pi\)
0.0808647 + 0.996725i \(0.474232\pi\)
\(104\) −12.4314 2.97021i −1.21900 0.291253i
\(105\) −0.713862 0.982547i −0.0696658 0.0958868i
\(106\) 3.45069 0.640842i 0.335161 0.0622441i
\(107\) −0.703145 0.510864i −0.0679755 0.0493871i 0.553279 0.832996i \(-0.313377\pi\)
−0.621254 + 0.783609i \(0.713377\pi\)
\(108\) −3.38774 + 2.33195i −0.325986 + 0.224392i
\(109\) 10.4947 4.34703i 1.00521 0.416370i 0.181502 0.983391i \(-0.441904\pi\)
0.823704 + 0.567021i \(0.191904\pi\)
\(110\) 3.16922 + 0.937517i 0.302174 + 0.0893888i
\(111\) −1.63161 + 1.91037i −0.154866 + 0.181324i
\(112\) 14.4563 + 9.90473i 1.36600 + 0.935909i
\(113\) 1.51165 0.491163i 0.142204 0.0462048i −0.237050 0.971497i \(-0.576181\pi\)
0.379254 + 0.925293i \(0.376181\pi\)
\(114\) −0.593977 2.21354i −0.0556311 0.207317i
\(115\) −2.89026 + 5.67245i −0.269518 + 0.528958i
\(116\) −6.66658 + 12.2996i −0.618976 + 1.14199i
\(117\) −6.79429 + 11.0873i −0.628132 + 1.02502i
\(118\) −0.287327 + 5.52083i −0.0264506 + 0.508233i
\(119\) 15.1610 + 4.92611i 1.38981 + 0.451576i
\(120\) 0.299272 0.724735i 0.0273197 0.0661589i
\(121\) −2.27267 0.359956i −0.206607 0.0327233i
\(122\) −15.3674 8.86496i −1.39130 0.802596i
\(123\) −1.33820 + 1.79664i −0.120661 + 0.161998i
\(124\) 0.735301 0.425237i 0.0660320 0.0381875i
\(125\) 1.16170 7.33466i 0.103905 0.656032i
\(126\) 14.1404 10.8585i 1.25973 0.967350i
\(127\) 5.39088 16.5914i 0.478364 1.47225i −0.363004 0.931788i \(-0.618249\pi\)
0.841367 0.540464i \(-0.181751\pi\)
\(128\) −0.563441 + 11.2997i −0.0498016 + 0.998759i
\(129\) −1.10427 0.676696i −0.0972253 0.0595797i
\(130\) −0.134386 5.06187i −0.0117864 0.443955i
\(131\) 7.43509 + 3.78837i 0.649607 + 0.330991i 0.747555 0.664200i \(-0.231228\pi\)
−0.0979479 + 0.995192i \(0.531228\pi\)
\(132\) 0.532706 1.99387i 0.0463661 0.173544i
\(133\) 6.27079 + 19.2995i 0.543747 + 1.67348i
\(134\) −5.26786 + 7.67074i −0.455074 + 0.662651i
\(135\) −1.23899 1.05820i −0.106635 0.0910752i
\(136\) 2.41347 + 10.0049i 0.206954 + 0.857912i
\(137\) 4.55146 + 10.9882i 0.388858 + 0.938785i 0.990183 + 0.139781i \(0.0446397\pi\)
−0.601325 + 0.799005i \(0.705360\pi\)
\(138\) 3.58882 + 1.71018i 0.305501 + 0.145580i
\(139\) 6.04258 8.31690i 0.512525 0.705430i −0.471818 0.881696i \(-0.656402\pi\)
0.984343 + 0.176266i \(0.0564020\pi\)
\(140\) −2.31274 + 6.54606i −0.195462 + 0.553243i
\(141\) 2.21263 1.60757i 0.186337 0.135382i
\(142\) 1.38009 1.45537i 0.115815 0.122132i
\(143\) −2.08495 13.1639i −0.174353 1.10082i
\(144\) 10.7518 + 4.10936i 0.895986 + 0.342447i
\(145\) −5.38941 1.29388i −0.447566 0.107451i
\(146\) −4.15334 + 0.438056i −0.343733 + 0.0362538i
\(147\) 3.24387 2.77052i 0.267550 0.228509i
\(148\) 14.2839 + 1.49082i 1.17413 + 0.122545i
\(149\) −7.30837 + 0.575181i −0.598725 + 0.0471207i −0.374201 0.927348i \(-0.622083\pi\)
−0.224524 + 0.974468i \(0.572083\pi\)
\(150\) −2.14489 0.281589i −0.175130 0.0229917i
\(151\) −3.19774 13.3195i −0.260228 1.08393i −0.937442 0.348142i \(-0.886813\pi\)
0.677213 0.735787i \(-0.263187\pi\)
\(152\) −8.49774 + 9.97152i −0.689258 + 0.808797i
\(153\) 10.4385 + 0.821528i 0.843903 + 0.0664166i
\(154\) −3.79280 + 17.8756i −0.305632 + 1.44045i
\(155\) 0.237953 + 0.237953i 0.0191128 + 0.0191128i
\(156\) −3.15755 + 0.167776i −0.252807 + 0.0134328i
\(157\) −3.07843 5.02354i −0.245686 0.400922i 0.705898 0.708314i \(-0.250544\pi\)
−0.951583 + 0.307391i \(0.900544\pi\)
\(158\) 10.5420 5.72881i 0.838680 0.455760i
\(159\) 0.773640 0.394189i 0.0613536 0.0312612i
\(160\) −4.38259 + 0.939855i −0.346474 + 0.0743020i
\(161\) −32.5205 13.4704i −2.56298 1.06162i
\(162\) 7.03965 8.69969i 0.553087 0.683512i
\(163\) 13.4559 1.05395 0.526973 0.849882i \(-0.323327\pi\)
0.526973 + 0.849882i \(0.323327\pi\)
\(164\) 12.7973 + 0.477851i 0.999304 + 0.0373139i
\(165\) 0.817632 0.0636526
\(166\) −4.46530 + 5.51828i −0.346574 + 0.428301i
\(167\) 0.0425390 + 0.0176203i 0.00329177 + 0.00136350i 0.384329 0.923196i \(-0.374433\pi\)
−0.381037 + 0.924560i \(0.624433\pi\)
\(168\) 4.12459 + 1.33520i 0.318219 + 0.103013i
\(169\) −6.61140 + 3.36868i −0.508569 + 0.259129i
\(170\) −3.58259 + 1.94687i −0.274772 + 0.149318i
\(171\) 6.96437 + 11.3648i 0.532579 + 0.869090i
\(172\) 0.392828 + 7.39303i 0.0299528 + 0.563713i
\(173\) 1.82188 + 1.82188i 0.138515 + 0.138515i 0.772964 0.634450i \(-0.218773\pi\)
−0.634450 + 0.772964i \(0.718773\pi\)
\(174\) −0.718367 + 3.38569i −0.0544593 + 0.256668i
\(175\) 19.0954 + 1.50284i 1.44348 + 0.113604i
\(176\) −11.1152 + 3.95425i −0.837840 + 0.298063i
\(177\) 0.319275 + 1.32988i 0.0239982 + 0.0999597i
\(178\) 8.74610 + 1.14822i 0.655548 + 0.0860627i
\(179\) 4.95719 0.390139i 0.370518 0.0291604i 0.108166 0.994133i \(-0.465502\pi\)
0.262351 + 0.964972i \(0.415502\pi\)
\(180\) −0.473377 + 4.53551i −0.0352834 + 0.338057i
\(181\) −1.52780 + 1.30487i −0.113561 + 0.0969899i −0.704415 0.709788i \(-0.748791\pi\)
0.590855 + 0.806778i \(0.298791\pi\)
\(182\) 27.8429 2.93661i 2.06385 0.217676i
\(183\) −4.26776 1.02460i −0.315482 0.0757405i
\(184\) −3.57947 22.4419i −0.263882 1.65444i
\(185\) 0.890062 + 5.61963i 0.0654387 + 0.413164i
\(186\) 0.144594 0.152481i 0.0106022 0.0111805i
\(187\) −8.68244 + 6.30816i −0.634923 + 0.461299i
\(188\) −14.7413 5.20814i −1.07512 0.379842i
\(189\) 5.29535 7.28842i 0.385180 0.530154i
\(190\) −4.68560 2.23283i −0.339930 0.161987i
\(191\) 3.03196 + 7.31979i 0.219385 + 0.529642i 0.994804 0.101805i \(-0.0324617\pi\)
−0.775420 + 0.631446i \(0.782462\pi\)
\(192\) 0.659318 + 2.72018i 0.0475822 + 0.196312i
\(193\) −6.27221 5.35697i −0.451484 0.385603i 0.394428 0.918927i \(-0.370943\pi\)
−0.845911 + 0.533324i \(0.820943\pi\)
\(194\) 1.60568 2.33809i 0.115281 0.167865i
\(195\) −0.387111 1.19140i −0.0277216 0.0853182i
\(196\) −23.5598 6.29453i −1.68284 0.449609i
\(197\) −5.64488 2.87621i −0.402181 0.204922i 0.241187 0.970479i \(-0.422463\pi\)
−0.643368 + 0.765557i \(0.722463\pi\)
\(198\) 0.318544 + 11.9985i 0.0226379 + 0.852694i
\(199\) −14.7707 9.05148i −1.04706 0.641642i −0.111126 0.993806i \(-0.535446\pi\)
−0.935938 + 0.352164i \(0.885446\pi\)
\(200\) 5.62620 + 11.0124i 0.397832 + 0.778695i
\(201\) −0.711387 + 2.18943i −0.0501774 + 0.154430i
\(202\) −18.1789 + 13.9596i −1.27906 + 0.982196i
\(203\) 4.79397 30.2679i 0.336471 2.12439i
\(204\) 1.27467 + 2.20410i 0.0892448 + 0.154318i
\(205\) 1.12577 + 4.94707i 0.0786269 + 0.345518i
\(206\) 1.89104 + 1.09088i 0.131755 + 0.0760053i
\(207\) −22.8360 3.61686i −1.58721 0.251389i
\(208\) 11.0244 + 14.3243i 0.764407 + 0.993209i
\(209\) −12.9930 4.22167i −0.898743 0.292019i
\(210\) −0.0892681 + 1.71523i −0.00616008 + 0.118362i
\(211\) −11.6615 + 19.0298i −0.802807 + 1.31006i 0.144425 + 0.989516i \(0.453867\pi\)
−0.947233 + 0.320547i \(0.896133\pi\)
\(212\) −4.36369 2.36519i −0.299699 0.162442i
\(213\) 0.225267 0.442112i 0.0154351 0.0302930i
\(214\) 0.318556 + 1.18714i 0.0217760 + 0.0811515i
\(215\) −2.78953 + 0.906373i −0.190244 + 0.0618141i
\(216\) 5.79888 + 0.450037i 0.394564 + 0.0306211i
\(217\) −1.20838 + 1.41483i −0.0820302 + 0.0960450i
\(218\) −15.4046 4.55699i −1.04333 0.308638i
\(219\) −0.954561 + 0.395392i −0.0645033 + 0.0267181i
\(220\) −2.65015 3.85001i −0.178673 0.259567i
\(221\) 13.3026 + 9.66491i 0.894830 + 0.650132i
\(222\) 3.49320 0.648737i 0.234448 0.0435404i
\(223\) −7.80365 10.7408i −0.522571 0.719257i 0.463405 0.886147i \(-0.346628\pi\)
−0.985976 + 0.166890i \(0.946628\pi\)
\(224\) −7.08171 23.7493i −0.473167 1.58682i
\(225\) 12.4264 1.96815i 0.828429 0.131210i
\(226\) −2.09880 0.804781i −0.139610 0.0535332i
\(227\) 0.891771 3.71449i 0.0591889 0.246540i −0.934930 0.354832i \(-0.884538\pi\)
0.994119 + 0.108292i \(0.0345382\pi\)
\(228\) −1.31615 + 2.96191i −0.0871644 + 0.196157i
\(229\) −5.77472 6.76133i −0.381604 0.446801i 0.536047 0.844188i \(-0.319917\pi\)
−0.917651 + 0.397387i \(0.869917\pi\)
\(230\) 8.22365 3.66498i 0.542251 0.241661i
\(231\) 0.354694 + 4.50682i 0.0233372 + 0.296527i
\(232\) 18.2707 7.59125i 1.19953 0.498390i
\(233\) 14.3261 3.43938i 0.938531 0.225321i 0.264805 0.964302i \(-0.414693\pi\)
0.673727 + 0.738981i \(0.264693\pi\)
\(234\) 17.3326 6.14488i 1.13307 0.401703i
\(235\) 0.485971 6.17485i 0.0317012 0.402803i
\(236\) 5.22718 5.81384i 0.340260 0.378449i
\(237\) 2.09887 2.09887i 0.136336 0.136336i
\(238\) −12.2854 18.9028i −0.796342 1.22529i
\(239\) 24.5473 15.0426i 1.58784 0.973027i 0.603367 0.797464i \(-0.293825\pi\)
0.984468 0.175563i \(-0.0561747\pi\)
\(240\) −0.973732 + 0.530523i −0.0628541 + 0.0342451i
\(241\) 7.01085 + 13.7596i 0.451608 + 0.886331i 0.998783 + 0.0493130i \(0.0157032\pi\)
−0.547175 + 0.837018i \(0.684297\pi\)
\(242\) 2.17830 + 2.41748i 0.140026 + 0.155402i
\(243\) 3.42033 8.25740i 0.219414 0.529713i
\(244\) 9.00831 + 23.4167i 0.576698 + 1.49910i
\(245\) 9.66125i 0.617235i
\(246\) 3.06946 0.784725i 0.195702 0.0500322i
\(247\) 20.9313i 1.33183i
\(248\) −1.18666 0.186626i −0.0753529 0.0118507i
\(249\) −0.672050 + 1.62247i −0.0425894 + 0.102820i
\(250\) −7.80201 + 7.03009i −0.493443 + 0.444622i
\(251\) 11.8937 + 23.3427i 0.750724 + 1.47338i 0.876542 + 0.481325i \(0.159844\pi\)
−0.125818 + 0.992053i \(0.540156\pi\)
\(252\) −25.2053 0.641736i −1.58778 0.0404255i
\(253\) 20.2055 12.3820i 1.27031 0.778448i
\(254\) −20.6862 + 13.4445i −1.29797 + 0.843581i
\(255\) −0.713276 + 0.713276i −0.0446671 + 0.0446671i
\(256\) 10.6716 11.9213i 0.666973 0.745082i
\(257\) −0.256622 + 3.26070i −0.0160077 + 0.203397i 0.983713 + 0.179748i \(0.0575283\pi\)
−0.999720 + 0.0236486i \(0.992472\pi\)
\(258\) 0.612016 + 1.72629i 0.0381025 + 0.107474i
\(259\) −30.5895 + 7.34389i −1.90074 + 0.456327i
\(260\) −4.35527 + 5.68443i −0.270103 + 0.352534i
\(261\) −1.57929 20.0668i −0.0977558 1.24211i
\(262\) −4.80382 10.7790i −0.296781 0.665932i
\(263\) −0.939777 1.10034i −0.0579491 0.0678497i 0.730674 0.682726i \(-0.239206\pi\)
−0.788623 + 0.614877i \(0.789206\pi\)
\(264\) −2.35938 + 1.71811i −0.145210 + 0.105742i
\(265\) 0.459049 1.91208i 0.0281992 0.117458i
\(266\) 10.2748 26.7958i 0.629989 1.64296i
\(267\) 2.15543 0.341386i 0.131910 0.0208925i
\(268\) 12.6152 3.74674i 0.770595 0.228869i
\(269\) 5.24896 + 7.22457i 0.320035 + 0.440490i 0.938478 0.345340i \(-0.112236\pi\)
−0.618443 + 0.785830i \(0.712236\pi\)
\(270\) 0.420745 + 2.26556i 0.0256058 + 0.137877i
\(271\) 8.83318 + 6.41768i 0.536577 + 0.389846i 0.822812 0.568313i \(-0.192404\pi\)
−0.286235 + 0.958159i \(0.592404\pi\)
\(272\) 6.24699 13.1461i 0.378780 0.797101i
\(273\) 6.39913 2.65061i 0.387293 0.160422i
\(274\) 4.77129 16.1291i 0.288244 0.974394i
\(275\) −8.37484 + 9.80568i −0.505022 + 0.591305i
\(276\) −2.42408 5.07273i −0.145913 0.305342i
\(277\) −30.2769 + 9.83757i −1.81916 + 0.591082i −0.819321 + 0.573335i \(0.805650\pi\)
−0.999843 + 0.0177475i \(0.994350\pi\)
\(278\) −14.0417 + 3.76792i −0.842166 + 0.225985i
\(279\) −0.554833 + 1.08892i −0.0332170 + 0.0651921i
\(280\) 8.36591 5.13916i 0.499959 0.307123i
\(281\) 4.01399 6.55023i 0.239454 0.390754i −0.710226 0.703973i \(-0.751407\pi\)
0.949681 + 0.313219i \(0.101407\pi\)
\(282\) −3.86259 0.201026i −0.230014 0.0119709i
\(283\) 6.99558 + 2.27300i 0.415844 + 0.135116i 0.509464 0.860492i \(-0.329844\pi\)
−0.0936196 + 0.995608i \(0.529844\pi\)
\(284\) −2.81193 + 0.372272i −0.166857 + 0.0220903i
\(285\) −1.26827 0.200874i −0.0751257 0.0118987i
\(286\) −9.41838 + 16.3268i −0.556921 + 0.965423i
\(287\) −26.7801 + 8.35133i −1.58078 + 0.492964i
\(288\) −8.16460 14.0825i −0.481104 0.829819i
\(289\) −0.588140 + 3.71337i −0.0345965 + 0.218434i
\(290\) 4.77394 + 6.21686i 0.280336 + 0.365066i
\(291\) 0.216836 0.667351i 0.0127111 0.0391208i
\(292\) 4.95576 + 3.21320i 0.290014 + 0.188038i
\(293\) 17.4618 + 10.7006i 1.02013 + 0.625136i 0.928760 0.370682i \(-0.120876\pi\)
0.0913686 + 0.995817i \(0.470876\pi\)
\(294\) −6.03086 + 0.160112i −0.351727 + 0.00933790i
\(295\) 2.75980 + 1.40619i 0.160682 + 0.0818713i
\(296\) −14.3771 14.3458i −0.835650 0.833834i
\(297\) 1.87422 + 5.76825i 0.108753 + 0.334708i
\(298\) 8.54630 + 5.86915i 0.495074 + 0.339991i
\(299\) −27.6086 23.5800i −1.59665 1.36367i
\(300\) 2.10754 + 2.21766i 0.121679 + 0.128036i
\(301\) −6.20607 14.9828i −0.357712 0.863593i
\(302\) −8.33349 + 17.4878i −0.479539 + 1.00631i
\(303\) −3.33295 + 4.58742i −0.191473 + 0.263540i
\(304\) 18.2128 3.40287i 1.04458 0.195168i
\(305\) −8.04159 + 5.84256i −0.460460 + 0.334544i
\(306\) −10.7450 10.1892i −0.614249 0.582478i
\(307\) 4.80089 + 30.3116i 0.274001 + 1.72998i 0.613786 + 0.789472i \(0.289646\pi\)
−0.339785 + 0.940503i \(0.610354\pi\)
\(308\) 20.0717 16.2779i 1.14369 0.927517i
\(309\) 0.525171 + 0.126082i 0.0298759 + 0.00717257i
\(310\) −0.0499173 0.473281i −0.00283511 0.0268806i
\(311\) −6.63079 + 5.66323i −0.375998 + 0.321132i −0.817285 0.576233i \(-0.804522\pi\)
0.441287 + 0.897366i \(0.354522\pi\)
\(312\) 3.62058 + 2.62450i 0.204975 + 0.148583i
\(313\) −27.2026 + 2.14089i −1.53758 + 0.121010i −0.818741 0.574163i \(-0.805327\pi\)
−0.718842 + 0.695174i \(0.755327\pi\)
\(314\) −1.08457 + 8.26131i −0.0612061 + 0.466212i
\(315\) −2.33188 9.71299i −0.131387 0.547265i
\(316\) −16.6860 3.08005i −0.938658 0.173266i
\(317\) −5.74002 0.451749i −0.322392 0.0253728i −0.0837692 0.996485i \(-0.526696\pi\)
−0.238623 + 0.971112i \(0.576696\pi\)
\(318\) −1.20119 0.254865i −0.0673593 0.0142921i
\(319\) 14.5885 + 14.5885i 0.816798 + 0.816798i
\(320\) 5.65419 + 2.86548i 0.316079 + 0.160185i
\(321\) 0.158882 + 0.259272i 0.00886795 + 0.0144712i
\(322\) 23.7690 + 43.7392i 1.32459 + 2.43749i
\(323\) 15.0175 7.65181i 0.835597 0.425758i
\(324\) −15.4784 + 3.30177i −0.859911 + 0.183431i
\(325\) 18.2533 + 7.56078i 1.01251 + 0.419397i
\(326\) −14.7930 11.9703i −0.819311 0.662973i
\(327\) −3.97426 −0.219777
\(328\) −13.6439 11.9098i −0.753361 0.657607i
\(329\) 34.2468 1.88809
\(330\) −0.898883 0.727361i −0.0494819 0.0400399i
\(331\) 20.2682 + 8.39535i 1.11404 + 0.461450i 0.862327 0.506352i \(-0.169006\pi\)
0.251712 + 0.967802i \(0.419006\pi\)
\(332\) 9.81806 2.09433i 0.538836 0.114942i
\(333\) −18.4110 + 9.38090i −1.00892 + 0.514070i
\(334\) −0.0310914 0.0572138i −0.00170125 0.00313060i
\(335\) 2.72411 + 4.44535i 0.148834 + 0.242875i
\(336\) −3.34667 5.13710i −0.182576 0.280252i
\(337\) 13.5042 + 13.5042i 0.735622 + 0.735622i 0.971727 0.236106i \(-0.0758711\pi\)
−0.236106 + 0.971727i \(0.575871\pi\)
\(338\) 10.2651 + 2.17804i 0.558351 + 0.118470i
\(339\) −0.554379 0.0436305i −0.0301097 0.00236969i
\(340\) 5.67053 + 1.04672i 0.307528 + 0.0567663i
\(341\) −0.292420 1.21802i −0.0158354 0.0659592i
\(342\) 2.45365 18.6897i 0.132678 1.01062i
\(343\) 22.6808 1.78501i 1.22465 0.0963817i
\(344\) 6.14494 8.47716i 0.331313 0.457058i
\(345\) 1.69371 1.44656i 0.0911862 0.0778804i
\(346\) −0.382190 3.62366i −0.0205466 0.194809i
\(347\) −11.3378 2.72196i −0.608643 0.146122i −0.0826037 0.996582i \(-0.526324\pi\)
−0.526039 + 0.850460i \(0.676324\pi\)
\(348\) 3.80164 3.08308i 0.203789 0.165270i
\(349\) 1.55129 + 9.79445i 0.0830386 + 0.524285i 0.993785 + 0.111318i \(0.0355074\pi\)
−0.910746 + 0.412967i \(0.864493\pi\)
\(350\) −19.6561 18.6394i −1.05066 0.996316i
\(351\) 7.51779 5.46199i 0.401270 0.291540i
\(352\) 15.7374 + 5.54084i 0.838808 + 0.295328i
\(353\) −11.3727 + 15.6532i −0.605309 + 0.833136i −0.996181 0.0873089i \(-0.972173\pi\)
0.390873 + 0.920445i \(0.372173\pi\)
\(354\) 0.832050 1.74606i 0.0442229 0.0928019i
\(355\) −0.430038 1.03820i −0.0228241 0.0551021i
\(356\) −8.59377 9.04281i −0.455469 0.479268i
\(357\) −4.24103 3.62218i −0.224459 0.191706i
\(358\) −5.79687 3.98098i −0.306374 0.210401i
\(359\) 9.08716 + 27.9674i 0.479602 + 1.47606i 0.839650 + 0.543128i \(0.182760\pi\)
−0.360048 + 0.932934i \(0.617240\pi\)
\(360\) 4.55519 4.56511i 0.240079 0.240602i
\(361\) 2.18772 + 1.11470i 0.115143 + 0.0586684i
\(362\) 2.84043 0.0754096i 0.149289 0.00396344i
\(363\) 0.686414 + 0.420635i 0.0360274 + 0.0220776i
\(364\) −33.2221 21.5405i −1.74131 1.12903i
\(365\) −0.723081 + 2.22541i −0.0378478 + 0.116483i
\(366\) 3.78038 + 4.92299i 0.197604 + 0.257329i
\(367\) 3.53600 22.3254i 0.184578 1.16538i −0.705209 0.709000i \(-0.749147\pi\)
0.889786 0.456377i \(-0.150853\pi\)
\(368\) −16.0290 + 27.8563i −0.835571 + 1.45211i
\(369\) −15.8235 + 9.44022i −0.823740 + 0.491438i
\(370\) 4.02069 6.96987i 0.209025 0.362346i
\(371\) 10.7386 + 1.70082i 0.557519 + 0.0883024i
\(372\) −0.294610 + 0.0390034i −0.0152748 + 0.00202223i
\(373\) 16.5106 + 5.36463i 0.854888 + 0.277770i 0.703492 0.710703i \(-0.251623\pi\)
0.151396 + 0.988473i \(0.451623\pi\)
\(374\) 15.1570 + 0.788832i 0.783747 + 0.0407896i
\(375\) −1.35753 + 2.21528i −0.0701024 + 0.114397i
\(376\) 11.5730 + 18.8395i 0.596834 + 0.971571i
\(377\) 14.3505 28.1644i 0.739087 1.45054i
\(378\) −12.3053 + 3.30198i −0.632916 + 0.169835i
\(379\) 26.3680 8.56749i 1.35443 0.440082i 0.460253 0.887788i \(-0.347759\pi\)
0.894181 + 0.447705i \(0.147759\pi\)
\(380\) 3.16491 + 6.62301i 0.162356 + 0.339753i
\(381\) −3.96393 + 4.64116i −0.203078 + 0.237774i
\(382\) 3.17840 10.7444i 0.162621 0.549731i
\(383\) −24.0206 + 9.94967i −1.22740 + 0.508405i −0.899754 0.436397i \(-0.856254\pi\)
−0.327643 + 0.944802i \(0.606254\pi\)
\(384\) 1.69502 3.57702i 0.0864986 0.182539i
\(385\) 8.28294 + 6.01791i 0.422138 + 0.306701i
\(386\) 2.12996 + 11.4690i 0.108412 + 0.583759i
\(387\) −6.26113 8.61771i −0.318271 0.438063i
\(388\) −3.84519 + 1.14203i −0.195210 + 0.0579779i
\(389\) −6.51857 + 1.03244i −0.330504 + 0.0523468i −0.319482 0.947592i \(-0.603509\pi\)
−0.0110228 + 0.999939i \(0.503509\pi\)
\(390\) −0.634288 + 1.65417i −0.0321184 + 0.0837621i
\(391\) −6.82503 + 28.4283i −0.345157 + 1.43768i
\(392\) 20.3014 + 27.8787i 1.02538 + 1.40809i
\(393\) −1.89607 2.22001i −0.0956439 0.111985i
\(394\) 3.64717 + 8.18369i 0.183742 + 0.412288i
\(395\) −0.527424 6.70156i −0.0265376 0.337192i
\(396\) 10.3236 13.4742i 0.518780 0.677103i
\(397\) 11.8694 2.84959i 0.595709 0.143017i 0.0756310 0.997136i \(-0.475903\pi\)
0.520078 + 0.854119i \(0.325903\pi\)
\(398\) 8.18632 + 23.0909i 0.410343 + 1.15744i
\(399\) 0.557041 7.07788i 0.0278869 0.354337i
\(400\) 3.61129 17.1118i 0.180565 0.855589i
\(401\) 9.57283 9.57283i 0.478044 0.478044i −0.426461 0.904506i \(-0.640240\pi\)
0.904506 + 0.426461i \(0.140240\pi\)
\(402\) 2.72978 1.77415i 0.136149 0.0884865i
\(403\) −1.63637 + 1.00277i −0.0815134 + 0.0499515i
\(404\) 32.4038 + 0.825014i 1.61215 + 0.0410460i
\(405\) −2.84659 5.58675i −0.141448 0.277608i
\(406\) −32.1966 + 29.0111i −1.59789 + 1.43979i
\(407\) 8.10480 19.5667i 0.401740 0.969887i
\(408\) 0.559420 3.55707i 0.0276954 0.176101i
\(409\) 39.9052i 1.97318i −0.163208 0.986592i \(-0.552184\pi\)
0.163208 0.986592i \(-0.447816\pi\)
\(410\) 3.16325 6.44015i 0.156222 0.318056i
\(411\) 4.16116i 0.205255i
\(412\) −1.10852 2.88155i −0.0546129 0.141964i
\(413\) −6.55373 + 15.8221i −0.322488 + 0.778555i
\(414\) 21.8877 + 24.2910i 1.07572 + 1.19384i
\(415\) 1.80561 + 3.54372i 0.0886341 + 0.173954i
\(416\) 0.622829 25.5550i 0.0305367 1.25294i
\(417\) −3.06671 + 1.87928i −0.150178 + 0.0920289i
\(418\) 10.5285 + 16.1997i 0.514968 + 0.792352i
\(419\) −12.8287 + 12.8287i −0.626725 + 0.626725i −0.947243 0.320518i \(-0.896143\pi\)
0.320518 + 0.947243i \(0.396143\pi\)
\(420\) 1.62400 1.80627i 0.0792432 0.0881369i
\(421\) −1.61823 + 20.5616i −0.0788677 + 1.00211i 0.822418 + 0.568884i \(0.192625\pi\)
−0.901286 + 0.433226i \(0.857375\pi\)
\(422\) 29.7491 10.5468i 1.44816 0.513412i
\(423\) 21.8730 5.25124i 1.06350 0.255324i
\(424\) 2.69326 + 6.48215i 0.130796 + 0.314801i
\(425\) −1.24822 15.8601i −0.0605474 0.769328i
\(426\) −0.640953 + 0.285649i −0.0310543 + 0.0138398i
\(427\) −35.6929 41.7910i −1.72730 2.02241i
\(428\) 0.705866 1.58850i 0.0341193 0.0767830i
\(429\) −1.08856 + 4.53418i −0.0525562 + 0.218913i
\(430\) 3.87304 + 1.48511i 0.186774 + 0.0716183i
\(431\) −5.90755 + 0.935665i −0.284557 + 0.0450694i −0.297081 0.954852i \(-0.596013\pi\)
0.0125245 + 0.999922i \(0.496013\pi\)
\(432\) −5.97478 5.65341i −0.287462 0.272000i
\(433\) −23.4383 32.2600i −1.12637 1.55032i −0.794782 0.606895i \(-0.792415\pi\)
−0.331591 0.943423i \(-0.607585\pi\)
\(434\) 2.58709 0.480458i 0.124184 0.0230627i
\(435\) 1.56881 + 1.13981i 0.0752188 + 0.0546497i
\(436\) 12.8816 + 18.7137i 0.616915 + 0.896224i
\(437\) −34.3837 + 14.2422i −1.64480 + 0.681297i
\(438\) 1.40116 + 0.414489i 0.0669499 + 0.0198051i
\(439\) −11.2823 + 13.2099i −0.538475 + 0.630473i −0.961222 0.275774i \(-0.911066\pi\)
0.422747 + 0.906248i \(0.361066\pi\)
\(440\) −0.511445 + 6.59015i −0.0243822 + 0.314173i
\(441\) 33.3695 10.8424i 1.58902 0.516305i
\(442\) −6.02667 22.4593i −0.286659 1.06828i
\(443\) −15.8069 + 31.0228i −0.751009 + 1.47394i 0.125265 + 0.992123i \(0.460022\pi\)
−0.876274 + 0.481814i \(0.839978\pi\)
\(444\) −4.41745 2.39433i −0.209643 0.113630i
\(445\) 2.58235 4.21401i 0.122415 0.199763i
\(446\) −0.975842 + 18.7502i −0.0462075 + 0.887849i
\(447\) 2.43933 + 0.792588i 0.115377 + 0.0374881i
\(448\) −13.3418 + 32.4092i −0.630341 + 1.53119i
\(449\) 16.4974 + 2.61294i 0.778562 + 0.123312i 0.533053 0.846082i \(-0.321045\pi\)
0.245510 + 0.969394i \(0.421045\pi\)
\(450\) −15.4122 8.89076i −0.726536 0.419114i
\(451\) 6.04866 17.8906i 0.284820 0.842434i
\(452\) 1.59143 + 2.75183i 0.0748548 + 0.129435i
\(453\) −0.749711 + 4.73349i −0.0352245 + 0.222399i
\(454\) −4.28478 + 3.29030i −0.201095 + 0.154421i
\(455\) 4.84734 14.9186i 0.227247 0.699394i
\(456\) 4.08184 2.08540i 0.191150 0.0976577i
\(457\) −7.93267 4.86114i −0.371074 0.227395i 0.324441 0.945906i \(-0.394824\pi\)
−0.695515 + 0.718511i \(0.744824\pi\)
\(458\) 0.333727 + 12.5704i 0.0155940 + 0.587375i
\(459\) −6.66705 3.39703i −0.311191 0.158560i
\(460\) −12.3012 3.28654i −0.573547 0.153236i
\(461\) 3.33116 + 10.2523i 0.155148 + 0.477495i 0.998176 0.0603741i \(-0.0192294\pi\)
−0.843028 + 0.537869i \(0.819229\pi\)
\(462\) 3.61930 5.27021i 0.168385 0.245192i
\(463\) −4.09007 3.49325i −0.190082 0.162345i 0.549315 0.835616i \(-0.314889\pi\)
−0.739396 + 0.673271i \(0.764889\pi\)
\(464\) −26.8394 7.90789i −1.24599 0.367114i
\(465\) −0.0450557 0.108774i −0.00208941 0.00504428i
\(466\) −18.8093 8.96323i −0.871326 0.415213i
\(467\) 9.33868 12.8536i 0.432142 0.594793i −0.536301 0.844027i \(-0.680179\pi\)
0.968443 + 0.249234i \(0.0801788\pi\)
\(468\) −24.5215 8.66351i −1.13351 0.400471i
\(469\) −23.3212 + 16.9438i −1.07687 + 0.782393i
\(470\) −6.02738 + 6.35614i −0.278022 + 0.293187i
\(471\) 0.322463 + 2.03595i 0.0148583 + 0.0938118i
\(472\) −10.9186 + 1.74151i −0.502569 + 0.0801594i
\(473\) 10.6162 + 2.54873i 0.488135 + 0.117191i
\(474\) −4.17458 + 0.440297i −0.191745 + 0.0202235i
\(475\) 15.3996 13.1525i 0.706584 0.603480i
\(476\) −3.30964 + 31.7102i −0.151697 + 1.45344i
\(477\) 7.11939 0.560308i 0.325975 0.0256548i
\(478\) −40.3685 5.29973i −1.84641 0.242404i
\(479\) −9.27763 38.6441i −0.423906 1.76569i −0.619487 0.785007i \(-0.712659\pi\)
0.195581 0.980687i \(-0.437341\pi\)
\(480\) 1.54244 + 0.282984i 0.0704026 + 0.0129164i
\(481\) −32.3487 2.54590i −1.47497 0.116083i
\(482\) 4.53290 21.3637i 0.206468 0.973090i
\(483\) 8.70825 + 8.70825i 0.396239 + 0.396239i
\(484\) −0.244182 4.59552i −0.0110992 0.208887i
\(485\) −0.830327 1.35497i −0.0377032 0.0615261i
\(486\) −11.1060 + 6.03526i −0.503777 + 0.273765i
\(487\) 17.8399 9.08986i 0.808401 0.411901i −0.000388037 1.00000i \(-0.500124\pi\)
0.808789 + 0.588099i \(0.200124\pi\)
\(488\) 10.9279 33.7574i 0.494682 1.52813i
\(489\) −4.34942 1.80159i −0.196688 0.0814707i
\(490\) −8.59460 + 10.6213i −0.388265 + 0.479822i
\(491\) 21.4025 0.965880 0.482940 0.875653i \(-0.339569\pi\)
0.482940 + 0.875653i \(0.339569\pi\)
\(492\) −4.07257 1.86787i −0.183606 0.0842103i
\(493\) −25.4531 −1.14635
\(494\) 18.6204 23.0114i 0.837772 1.03533i
\(495\) 6.21297 + 2.57349i 0.279252 + 0.115670i
\(496\) 1.13856 + 1.26082i 0.0511228 + 0.0566124i
\(497\) 5.53606 2.82076i 0.248326 0.126529i
\(498\) 2.18218 1.18585i 0.0977857 0.0531392i
\(499\) −5.03879 8.22256i −0.225567 0.368092i 0.719756 0.694227i \(-0.244254\pi\)
−0.945323 + 0.326135i \(0.894254\pi\)
\(500\) 14.8313 0.788056i 0.663274 0.0352429i
\(501\) −0.0113910 0.0113910i −0.000508911 0.000508911i
\(502\) 7.68994 36.2429i 0.343219 1.61760i
\(503\) −43.5925 3.43081i −1.94370 0.152972i −0.954363 0.298649i \(-0.903464\pi\)
−0.989332 + 0.145676i \(0.953464\pi\)
\(504\) 27.1391 + 23.1280i 1.20887 + 1.03020i
\(505\) 2.99786 + 12.4870i 0.133403 + 0.555664i
\(506\) −33.2284 4.36234i −1.47718 0.193930i
\(507\) 2.58807 0.203685i 0.114940 0.00904598i
\(508\) 34.7020 + 3.62189i 1.53965 + 0.160696i
\(509\) 23.4359 20.0161i 1.03878 0.887199i 0.0450444 0.998985i \(-0.485657\pi\)
0.993732 + 0.111786i \(0.0356571\pi\)
\(510\) 1.41868 0.149630i 0.0628204 0.00662571i
\(511\) −12.5802 3.02025i −0.556517 0.133608i
\(512\) −22.3372 + 3.61261i −0.987173 + 0.159656i
\(513\) −1.49006 9.40786i −0.0657877 0.415367i
\(514\) 3.18282 3.35643i 0.140388 0.148046i
\(515\) 0.989561 0.718958i 0.0436053 0.0316811i
\(516\) 0.862866 2.44228i 0.0379856 0.107516i
\(517\) −13.5519 + 18.6526i −0.596013 + 0.820341i
\(518\) 40.1623 + 19.1386i 1.76463 + 0.840901i
\(519\) −0.344967 0.832824i −0.0151424 0.0365569i
\(520\) 9.84491 2.37488i 0.431728 0.104145i
\(521\) 12.3344 + 10.5346i 0.540381 + 0.461529i 0.877258 0.480020i \(-0.159371\pi\)
−0.336877 + 0.941549i \(0.609371\pi\)
\(522\) −16.1151 + 23.4659i −0.705340 + 1.02707i
\(523\) 4.94887 + 15.2311i 0.216399 + 0.666008i 0.999051 + 0.0435487i \(0.0138664\pi\)
−0.782652 + 0.622459i \(0.786134\pi\)
\(524\) −4.30779 + 16.1236i −0.188187 + 0.704365i
\(525\) −5.97110 3.04243i −0.260600 0.132782i
\(526\) 0.0543107 + 2.04570i 0.00236806 + 0.0891969i
\(527\) 1.31766 + 0.807460i 0.0573980 + 0.0351735i
\(528\) 4.12226 + 0.210045i 0.179398 + 0.00914102i
\(529\) 12.8417 39.5226i 0.558333 1.71837i
\(530\) −2.20564 + 1.69372i −0.0958069 + 0.0735704i
\(531\) −1.75970 + 11.1103i −0.0763644 + 0.482146i
\(532\) −35.1333 + 20.3182i −1.52322 + 0.880905i
\(533\) −28.9328 0.343382i −1.25322 0.0148735i
\(534\) −2.67332 1.54215i −0.115686 0.0667353i
\(535\) 0.680184 + 0.107731i 0.0294069 + 0.00465760i
\(536\) −17.2019 7.10334i −0.743008 0.306818i
\(537\) −1.65457 0.537604i −0.0714002 0.0231993i
\(538\) 0.656380 12.6119i 0.0282985 0.543740i
\(539\) −18.7903 + 30.6630i −0.809355 + 1.32075i
\(540\) 1.55287 2.86498i 0.0668249 0.123289i
\(541\) 6.52465 12.8054i 0.280517 0.550545i −0.707160 0.707054i \(-0.750024\pi\)
0.987677 + 0.156509i \(0.0500239\pi\)
\(542\) −4.00182 14.9134i −0.171893 0.640584i
\(543\) 0.668546 0.217224i 0.0286901 0.00932197i
\(544\) −18.5625 + 8.89520i −0.795861 + 0.381378i
\(545\) −5.84544 + 6.84413i −0.250391 + 0.293170i
\(546\) −9.39299 2.77863i −0.401983 0.118914i
\(547\) 14.4186 5.97236i 0.616493 0.255360i −0.0525089 0.998620i \(-0.516722\pi\)
0.669002 + 0.743261i \(0.266722\pi\)
\(548\) −19.5938 + 13.4874i −0.837005 + 0.576152i
\(549\) −29.2046 21.2184i −1.24642 0.905579i
\(550\) 17.9302 3.32988i 0.764544 0.141987i
\(551\) −19.0448 26.2129i −0.811336 1.11671i
\(552\) −1.84770 + 7.73327i −0.0786434 + 0.329150i
\(553\) 36.7104 5.81436i 1.56109 0.247252i
\(554\) 42.0371 + 16.1190i 1.78598 + 0.684832i
\(555\) 0.464704 1.93563i 0.0197256 0.0821631i
\(556\) 18.7890 + 8.34909i 0.796831 + 0.354080i
\(557\) −6.66607 7.80497i −0.282451 0.330707i 0.600985 0.799261i \(-0.294775\pi\)
−0.883435 + 0.468554i \(0.844775\pi\)
\(558\) 1.57867 0.703554i 0.0668304 0.0297838i
\(559\) −1.31243 16.6761i −0.0555100 0.705322i
\(560\) −13.7690 1.79242i −0.581847 0.0757435i
\(561\) 3.65106 0.876543i 0.154148 0.0370077i
\(562\) −10.2399 + 3.63032i −0.431945 + 0.153136i
\(563\) 1.29198 16.4162i 0.0544506 0.691861i −0.907749 0.419515i \(-0.862200\pi\)
0.962199 0.272346i \(-0.0877997\pi\)
\(564\) 4.06760 + 3.65714i 0.171277 + 0.153993i
\(565\) −0.890530 + 0.890530i −0.0374649 + 0.0374649i
\(566\) −5.66870 8.72211i −0.238273 0.366618i
\(567\) 29.5595 18.1141i 1.24138 0.760720i
\(568\) 3.42253 + 2.09221i 0.143606 + 0.0877873i
\(569\) 10.9819 + 21.5532i 0.460385 + 0.903556i 0.998170 + 0.0604738i \(0.0192611\pi\)
−0.537785 + 0.843082i \(0.680739\pi\)
\(570\) 1.21560 + 1.34908i 0.0509160 + 0.0565067i
\(571\) 5.91140 14.2714i 0.247384 0.597239i −0.750596 0.660761i \(-0.770233\pi\)
0.997980 + 0.0635226i \(0.0202335\pi\)
\(572\) 24.8785 9.57068i 1.04022 0.400170i
\(573\) 2.77196i 0.115800i
\(574\) 36.8706 + 14.6422i 1.53895 + 0.611153i
\(575\) 35.1291i 1.46499i
\(576\) −3.55177 + 22.7451i −0.147990 + 0.947712i
\(577\) −12.8937 + 31.1282i −0.536773 + 1.29588i 0.390191 + 0.920734i \(0.372409\pi\)
−0.926964 + 0.375151i \(0.877591\pi\)
\(578\) 3.94998 3.55917i 0.164298 0.148042i
\(579\) 1.31016 + 2.57134i 0.0544485 + 0.106861i
\(580\) 0.282140 11.0815i 0.0117152 0.460135i
\(581\) −18.7498 + 11.4899i −0.777873 + 0.476681i
\(582\) −0.832056 + 0.540772i −0.0344898 + 0.0224157i
\(583\) −5.17576 + 5.17576i −0.214358 + 0.214358i
\(584\) −2.58978 7.94113i −0.107166 0.328606i
\(585\) 0.808391 10.2716i 0.0334229 0.424678i
\(586\) −9.67782 27.2979i −0.399787 1.12766i
\(587\) 2.73564 0.656768i 0.112912 0.0271077i −0.176596 0.984283i \(-0.556508\pi\)
0.289507 + 0.957176i \(0.406508\pi\)
\(588\) 6.77260 + 5.18900i 0.279297 + 0.213991i
\(589\) 0.154347 + 1.96116i 0.00635975 + 0.0808083i
\(590\) −1.78311 4.00102i −0.0734094 0.164720i
\(591\) 1.43953 + 1.68548i 0.0592145 + 0.0693313i
\(592\) 3.04378 + 28.5612i 0.125099 + 1.17386i
\(593\) −9.04729 + 37.6847i −0.371528 + 1.54752i 0.403129 + 0.915143i \(0.367923\pi\)
−0.774657 + 0.632382i \(0.782077\pi\)
\(594\) 3.07094 8.00875i 0.126002 0.328603i
\(595\) −12.4756 + 1.97594i −0.511450 + 0.0810057i
\(596\) −4.17441 14.0551i −0.170990 0.575721i
\(597\) 3.56251 + 4.90338i 0.145804 + 0.200682i
\(598\) 9.37553 + 50.4837i 0.383394 + 2.06443i
\(599\) −0.135318 0.0983142i −0.00552894 0.00401701i 0.585017 0.811021i \(-0.301088\pi\)
−0.590546 + 0.807004i \(0.701088\pi\)
\(600\) −0.344151 4.31288i −0.0140499 0.176073i
\(601\) 21.1471 8.75944i 0.862610 0.357305i 0.0928824 0.995677i \(-0.470392\pi\)
0.769728 + 0.638372i \(0.220392\pi\)
\(602\) −6.50582 + 21.9926i −0.265157 + 0.896350i
\(603\) −12.2969 + 14.3978i −0.500766 + 0.586322i
\(604\) 24.7187 11.8122i 1.00579 0.480633i
\(605\) 1.73398 0.563403i 0.0704961 0.0229056i
\(606\) 7.74510 2.07830i 0.314623 0.0844253i
\(607\) 4.16571 8.17566i 0.169081 0.331840i −0.790881 0.611969i \(-0.790378\pi\)
0.959962 + 0.280130i \(0.0903775\pi\)
\(608\) −23.0498 12.4610i −0.934794 0.505360i
\(609\) −5.60211 + 9.14181i −0.227009 + 0.370445i
\(610\) 14.0382 + 0.730609i 0.568391 + 0.0295815i
\(611\) 33.5957 + 10.9159i 1.35913 + 0.441610i
\(612\) 2.74847 + 20.7604i 0.111100 + 0.839190i
\(613\) −2.70083 0.427770i −0.109086 0.0172774i 0.101653 0.994820i \(-0.467587\pi\)
−0.210739 + 0.977542i \(0.567587\pi\)
\(614\) 21.6871 37.5946i 0.875220 1.51720i
\(615\) 0.298469 1.74980i 0.0120354 0.0705586i
\(616\) −36.5470 + 0.0397476i −1.47252 + 0.00160148i
\(617\) 3.72748 23.5344i 0.150063 0.947459i −0.791634 0.610996i \(-0.790769\pi\)
0.941697 0.336463i \(-0.109231\pi\)
\(618\) −0.465196 0.605801i −0.0187129 0.0243689i
\(619\) −1.33096 + 4.09627i −0.0534957 + 0.164643i −0.974235 0.225536i \(-0.927587\pi\)
0.920739 + 0.390179i \(0.127587\pi\)
\(620\) −0.366151 + 0.564718i −0.0147050 + 0.0226796i
\(621\) 14.0877 + 8.63293i 0.565318 + 0.346428i
\(622\) 12.3277 0.327284i 0.494296 0.0131229i
\(623\) 24.3480 + 12.4059i 0.975482 + 0.497033i
\(624\) −1.64563 6.10615i −0.0658780 0.244442i
\(625\) −4.93709 15.1948i −0.197484 0.607793i
\(626\) 31.8103 + 21.8457i 1.27140 + 0.873129i
\(627\) 3.63456 + 3.10420i 0.145150 + 0.123970i
\(628\) 8.54157 8.11742i 0.340846 0.323920i
\(629\) 9.99902 + 24.1398i 0.398687 + 0.962516i
\(630\) −6.07702 + 12.7526i −0.242114 + 0.508077i
\(631\) −14.0857 + 19.3873i −0.560743 + 0.771796i −0.991421 0.130710i \(-0.958274\pi\)
0.430678 + 0.902506i \(0.358274\pi\)
\(632\) 15.6041 + 18.2299i 0.620698 + 0.725145i
\(633\) 6.31726 4.58976i 0.251089 0.182427i
\(634\) 5.90855 + 5.60294i 0.234659 + 0.222521i
\(635\) 2.16237 + 13.6527i 0.0858110 + 0.541789i
\(636\) 1.09383 + 1.34876i 0.0433730 + 0.0534819i
\(637\) 53.5765 + 12.8626i 2.12278 + 0.509634i
\(638\) −3.06034 29.0160i −0.121160 1.14875i
\(639\) 3.10329 2.65046i 0.122764 0.104851i
\(640\) −3.66695 8.18017i −0.144949 0.323350i
\(641\) 24.8579 1.95636i 0.981829 0.0772716i 0.422628 0.906303i \(-0.361108\pi\)
0.559201 + 0.829032i \(0.311108\pi\)
\(642\) 0.0559765 0.426378i 0.00220922 0.0168278i
\(643\) 3.22559 + 13.4356i 0.127205 + 0.529846i 0.999187 + 0.0403092i \(0.0128343\pi\)
−0.871982 + 0.489537i \(0.837166\pi\)
\(644\) 12.7792 69.2304i 0.503570 2.72806i
\(645\) 1.02303 + 0.0805140i 0.0402817 + 0.00317024i
\(646\) −23.3169 4.94732i −0.917390 0.194650i
\(647\) −12.1590 12.1590i −0.478021 0.478021i 0.426478 0.904498i \(-0.359754\pi\)
−0.904498 + 0.426478i \(0.859754\pi\)
\(648\) 19.9538 + 10.1396i 0.783858 + 0.398322i
\(649\) −6.02416 9.83053i −0.236469 0.385882i
\(650\) −13.3412 24.5502i −0.523285 0.962938i
\(651\) 0.580021 0.295535i 0.0227328 0.0115829i
\(652\) 5.61436 + 26.3196i 0.219875 + 1.03076i
\(653\) −0.343848 0.142426i −0.0134558 0.00557357i 0.375945 0.926642i \(-0.377318\pi\)
−0.389401 + 0.921068i \(0.627318\pi\)
\(654\) 4.36920 + 3.53548i 0.170849 + 0.138248i
\(655\) −6.61188 −0.258348
\(656\) 4.40491 + 25.2309i 0.171983 + 0.985100i
\(657\) −8.49795 −0.331536
\(658\) −37.6500 30.4658i −1.46775 1.18768i
\(659\) −6.27264 2.59821i −0.244347 0.101212i 0.257149 0.966372i \(-0.417217\pi\)
−0.501496 + 0.865160i \(0.667217\pi\)
\(660\) 0.341150 + 1.59928i 0.0132793 + 0.0622520i
\(661\) 29.8801 15.2247i 1.16220 0.592171i 0.236949 0.971522i \(-0.423853\pi\)
0.925253 + 0.379351i \(0.123853\pi\)
\(662\) −14.8138 27.2601i −0.575755 1.05949i
\(663\) −3.00585 4.90511i −0.116738 0.190499i
\(664\) −12.6568 6.43164i −0.491180 0.249596i
\(665\) −11.3696 11.3696i −0.440894 0.440894i
\(666\) 28.5858 + 6.06527i 1.10768 + 0.235024i
\(667\) 56.0298 + 4.40964i 2.16948 + 0.170742i
\(668\) −0.0167160 + 0.0905580i −0.000646762 + 0.00350379i
\(669\) 1.08435 + 4.51663i 0.0419232 + 0.174623i
\(670\) 0.959743 7.31045i 0.0370781 0.282427i
\(671\) 36.8857 2.90297i 1.42396 0.112068i
\(672\) −0.890697 + 8.62477i −0.0343594 + 0.332708i
\(673\) −14.6744 + 12.5331i −0.565655 + 0.483115i −0.885681 0.464294i \(-0.846308\pi\)
0.320026 + 0.947409i \(0.396308\pi\)
\(674\) −2.83289 26.8595i −0.109119 1.03459i
\(675\) −8.74243 2.09887i −0.336496 0.0807856i
\(676\) −9.34766 11.5263i −0.359525 0.443319i
\(677\) 0.883366 + 5.57736i 0.0339505 + 0.214355i 0.998831 0.0483331i \(-0.0153909\pi\)
−0.964881 + 0.262688i \(0.915391\pi\)
\(678\) 0.570655 + 0.541139i 0.0219159 + 0.0207823i
\(679\) 7.10845 5.16459i 0.272797 0.198199i
\(680\) −5.30287 6.19521i −0.203356 0.237575i
\(681\) −0.785580 + 1.08126i −0.0301035 + 0.0414339i
\(682\) −0.762062 + 1.59919i −0.0291809 + 0.0612361i
\(683\) 11.3178 + 27.3236i 0.433064 + 1.04551i 0.978294 + 0.207222i \(0.0664424\pi\)
−0.545230 + 0.838287i \(0.683558\pi\)
\(684\) −19.3237 + 18.3641i −0.738860 + 0.702171i
\(685\) −7.16599 6.12034i −0.273798 0.233846i
\(686\) −26.5225 18.2143i −1.01264 0.695425i
\(687\) 0.961330 + 2.95867i 0.0366770 + 0.112880i
\(688\) −14.2968 + 3.85305i −0.545061 + 0.146896i
\(689\) 9.99228 + 5.09132i 0.380676 + 0.193964i
\(690\) −3.14887 + 0.0835985i −0.119876 + 0.00318254i
\(691\) −38.4016 23.5325i −1.46087 0.895220i −0.999970 0.00776607i \(-0.997528\pi\)
−0.460896 0.887454i \(-0.652472\pi\)
\(692\) −2.80342 + 4.32374i −0.106570 + 0.164364i
\(693\) −11.4900 + 35.3625i −0.436468 + 1.34331i
\(694\) 10.0430 + 13.0785i 0.381227 + 0.496452i
\(695\) −1.27425 + 8.04532i −0.0483352 + 0.305176i
\(696\) −6.92211 + 0.00752832i −0.262382 + 0.000285360i
\(697\) 10.3305 + 20.8838i 0.391296 + 0.791031i
\(698\) 7.00765 12.1478i 0.265243 0.459800i
\(699\) −5.09118 0.806364i −0.192566 0.0304995i
\(700\) 5.02785 + 37.9775i 0.190035 + 1.43542i
\(701\) −26.6916 8.67264i −1.00813 0.327561i −0.242020 0.970271i \(-0.577810\pi\)
−0.766109 + 0.642710i \(0.777810\pi\)
\(702\) −13.1238 0.683019i −0.495327 0.0257789i
\(703\) −17.3788 + 28.3597i −0.655456 + 1.06961i
\(704\) −12.3722 20.0914i −0.466295 0.757223i
\(705\) −0.983824 + 1.93086i −0.0370530 + 0.0727205i
\(706\) 26.4279 7.09159i 0.994626 0.266896i
\(707\) −67.5283 + 21.9413i −2.53966 + 0.825186i
\(708\) −2.46802 + 1.17938i −0.0927537 + 0.0443238i
\(709\) −2.43790 + 2.85441i −0.0915571 + 0.107200i −0.804293 0.594233i \(-0.797456\pi\)
0.712736 + 0.701432i \(0.247456\pi\)
\(710\) −0.450809 + 1.52393i −0.0169185 + 0.0571922i
\(711\) 22.5549 9.34256i 0.845876 0.350373i
\(712\) 1.40333 + 17.5864i 0.0525919 + 0.659078i
\(713\) −2.76067 2.00574i −0.103388 0.0751157i
\(714\) 1.44020 + 7.75492i 0.0538981 + 0.290221i
\(715\) 6.20730 + 8.54361i 0.232140 + 0.319513i
\(716\) 2.83146 + 9.53345i 0.105816 + 0.356282i
\(717\) −9.94861 + 1.57570i −0.371537 + 0.0588458i
\(718\) 14.8895 38.8305i 0.555670 1.44914i
\(719\) −11.6256 + 48.4243i −0.433563 + 1.80592i 0.144003 + 0.989577i \(0.454003\pi\)
−0.577566 + 0.816344i \(0.695997\pi\)
\(720\) −9.06894 + 0.966483i −0.337980 + 0.0360187i
\(721\) 4.39220 + 5.14261i 0.163574 + 0.191521i
\(722\) −1.41349 3.17166i −0.0526047 0.118037i
\(723\) −0.423907 5.38625i −0.0157653 0.200317i
\(724\) −3.18977 2.44393i −0.118547 0.0908278i
\(725\) −29.7385 + 7.13959i −1.10446 + 0.265158i
\(726\) −0.380430 1.07307i −0.0141191 0.0398252i
\(727\) −0.626741 + 7.96350i −0.0232445 + 0.295350i 0.974297 + 0.225268i \(0.0723259\pi\)
−0.997541 + 0.0700815i \(0.977674\pi\)
\(728\) 17.3612 + 53.2353i 0.643450 + 1.97303i
\(729\) 14.5755 14.5755i 0.539835 0.539835i
\(730\) 2.77465 1.80331i 0.102694 0.0667435i
\(731\) −11.4847 + 7.03784i −0.424777 + 0.260304i
\(732\) 0.223420 8.77521i 0.00825785 0.324341i
\(733\) −13.6264 26.7432i −0.503301 0.987784i −0.993246 0.116031i \(-0.962983\pi\)
0.489944 0.871754i \(-0.337017\pi\)
\(734\) −23.7480 + 21.3984i −0.876553 + 0.789828i
\(735\) −1.29353 + 3.12286i −0.0477126 + 0.115188i
\(736\) 42.4027 16.3651i 1.56298 0.603227i
\(737\) 19.4068i 0.714860i
\(738\) 25.7939 + 3.69822i 0.949488 + 0.136133i
\(739\) 36.2334i 1.33287i −0.745564 0.666434i \(-0.767820\pi\)
0.745564 0.666434i \(-0.232180\pi\)
\(740\) −10.6206 + 4.08570i −0.390421 + 0.150193i
\(741\) 2.80247 6.76575i 0.102951 0.248546i
\(742\) −10.2927 11.4228i −0.377855 0.419345i
\(743\) −3.72148 7.30381i −0.136528 0.267951i 0.812612 0.582804i \(-0.198045\pi\)
−0.949140 + 0.314853i \(0.898045\pi\)
\(744\) 0.358583 + 0.219204i 0.0131463 + 0.00803641i
\(745\) 4.95275 3.03505i 0.181455 0.111196i
\(746\) −13.3790 20.5855i −0.489840 0.753689i
\(747\) −10.2135 + 10.2135i −0.373691 + 0.373691i
\(748\) −15.9614 14.3508i −0.583607 0.524716i
\(749\) −0.298746 + 3.79593i −0.0109160 + 0.138700i
\(750\) 3.46314 1.22777i 0.126456 0.0448320i
\(751\) 17.4094 4.17963i 0.635278 0.152517i 0.0970005 0.995284i \(-0.469075\pi\)
0.538278 + 0.842768i \(0.319075\pi\)
\(752\) 4.03640 31.0069i 0.147192 1.13071i
\(753\) −0.719146 9.13762i −0.0262072 0.332993i
\(754\) −40.8314 + 18.1971i −1.48699 + 0.662698i
\(755\) 7.04891 + 8.25321i 0.256536 + 0.300365i
\(756\) 16.4655 + 7.31663i 0.598846 + 0.266103i
\(757\) 5.31897 22.1551i 0.193321 0.805240i −0.788438 0.615114i \(-0.789110\pi\)
0.981760 0.190127i \(-0.0608899\pi\)
\(758\) −36.6099 14.0380i −1.32973 0.509883i
\(759\) −8.18895 + 1.29700i −0.297240 + 0.0470782i
\(760\) 2.41238 10.0966i 0.0875062 0.366244i
\(761\) 17.9378 + 24.6893i 0.650246 + 0.894986i 0.999110 0.0421869i \(-0.0134325\pi\)
−0.348864 + 0.937173i \(0.613433\pi\)
\(762\) 8.48659 1.57608i 0.307437 0.0570953i
\(763\) −40.2609 29.2512i −1.45754 1.05897i
\(764\) −13.0524 + 8.98461i −0.472219 + 0.325052i
\(765\) −7.66503 + 3.17496i −0.277130 + 0.114791i
\(766\) 35.2588 + 10.4302i 1.27395 + 0.376860i
\(767\) −11.4723 + 13.4323i −0.414241 + 0.485013i
\(768\) −5.04555 + 2.42459i −0.182066 + 0.0874900i
\(769\) −1.57203 + 0.510784i −0.0566889 + 0.0184194i −0.337224 0.941424i \(-0.609488\pi\)
0.280535 + 0.959844i \(0.409488\pi\)
\(770\) −3.75254 13.9844i −0.135232 0.503962i
\(771\) 0.519519 1.01961i 0.0187100 0.0367205i
\(772\) 7.86118 14.5036i 0.282930 0.521994i
\(773\) −23.9501 + 39.0830i −0.861426 + 1.40572i 0.0519713 + 0.998649i \(0.483450\pi\)
−0.913397 + 0.407070i \(0.866550\pi\)
\(774\) −0.782951 + 15.0439i −0.0281426 + 0.540743i
\(775\) 1.76600 + 0.573808i 0.0634365 + 0.0206118i
\(776\) 5.24325 + 2.16515i 0.188222 + 0.0777242i
\(777\) 10.8709 + 1.72178i 0.389990 + 0.0617684i
\(778\) 8.08479 + 4.66385i 0.289854 + 0.167207i
\(779\) −13.7777 + 26.2649i −0.493636 + 0.941038i
\(780\) 2.16886 1.25429i 0.0776576 0.0449108i
\(781\) −0.654357 + 4.13145i −0.0234147 + 0.147835i
\(782\) 32.7929 25.1818i 1.17267 0.900499i
\(783\) −4.44504 + 13.6804i −0.158853 + 0.488899i
\(784\) 2.48192 48.7092i 0.0886399 1.73961i
\(785\) 3.98043 + 2.43921i 0.142068 + 0.0870591i
\(786\) 0.109576 + 4.12735i 0.00390843 + 0.147218i
\(787\) 11.2127 + 5.71314i 0.399688 + 0.203651i 0.642268 0.766480i \(-0.277994\pi\)
−0.242580 + 0.970131i \(0.577994\pi\)
\(788\) 3.27057 12.2414i 0.116509 0.436083i
\(789\) 0.156447 + 0.481493i 0.00556965 + 0.0171416i
\(790\) −5.38183 + 7.83670i −0.191477 + 0.278817i
\(791\) −5.29495 4.52231i −0.188267 0.160795i
\(792\) −23.3360 + 5.62933i −0.829209 + 0.200030i
\(793\) −21.6937 52.3732i −0.770366 1.85983i
\(794\) −15.5839 7.42620i −0.553052 0.263546i
\(795\) −0.404386 + 0.556590i −0.0143421 + 0.0197402i
\(796\) 11.5417 32.6680i 0.409084 1.15789i
\(797\) 21.1237 15.3473i 0.748241 0.543629i −0.147040 0.989131i \(-0.546975\pi\)
0.895281 + 0.445502i \(0.146975\pi\)
\(798\) −6.90884 + 7.28568i −0.244570 + 0.257910i
\(799\) −4.44969 28.0942i −0.157419 0.993902i
\(800\) −19.1927 + 15.5996i −0.678565 + 0.551531i
\(801\) 17.4530 + 4.19010i 0.616673 + 0.148050i
\(802\) −19.0401 + 2.00817i −0.672328 + 0.0709109i
\(803\) 6.62315 5.65671i 0.233726 0.199621i
\(804\) −4.57932 0.477949i −0.161500 0.0168560i
\(805\) 27.8049 2.18829i 0.979994 0.0771272i
\(806\) 2.69104 + 0.353290i 0.0947879 + 0.0124441i
\(807\) −0.729362 3.03801i −0.0256748 0.106943i
\(808\) −34.8899 29.7333i −1.22742 1.04601i
\(809\) 32.6829 + 2.57220i 1.14907 + 0.0904337i 0.638654 0.769494i \(-0.279492\pi\)
0.510415 + 0.859928i \(0.329492\pi\)
\(810\) −1.84048 + 8.67423i −0.0646678 + 0.304782i
\(811\) 29.7404 + 29.7404i 1.04433 + 1.04433i 0.998971 + 0.0453568i \(0.0144425\pi\)
0.0453568 + 0.998971i \(0.485558\pi\)
\(812\) 61.2041 3.25207i 2.14784 0.114125i
\(813\) −1.99594 3.25708i −0.0700008 0.114231i
\(814\) −26.3167 + 14.3011i −0.922399 + 0.501255i
\(815\) −9.49977 + 4.84037i −0.332762 + 0.169551i
\(816\) −3.77936 + 3.41289i −0.132304 + 0.119475i
\(817\) −15.8412 6.56164i −0.554213 0.229563i
\(818\) −35.4994 + 43.8707i −1.24121 + 1.53390i
\(819\) 56.9680 1.99062
\(820\) −9.20672 + 4.26612i −0.321513 + 0.148979i
\(821\) 3.69779 0.129054 0.0645269 0.997916i \(-0.479446\pi\)
0.0645269 + 0.997916i \(0.479446\pi\)
\(822\) −3.70175 + 4.57467i −0.129113 + 0.159560i
\(823\) −26.4320 10.9485i −0.921361 0.381640i −0.128966 0.991649i \(-0.541166\pi\)
−0.792395 + 0.610009i \(0.791166\pi\)
\(824\) −1.34473 + 4.15403i −0.0468460 + 0.144713i
\(825\) 4.01991 2.04825i 0.139955 0.0713108i
\(826\) 21.2803 11.5642i 0.740435 0.402371i
\(827\) −22.2130 36.2484i −0.772423 1.26048i −0.960487 0.278324i \(-0.910221\pi\)
0.188064 0.982157i \(-0.439779\pi\)
\(828\) −2.45356 46.1761i −0.0852671 1.60473i
\(829\) 11.3356 + 11.3356i 0.393703 + 0.393703i 0.876005 0.482302i \(-0.160199\pi\)
−0.482302 + 0.876005i \(0.660199\pi\)
\(830\) 1.16743 5.50213i 0.0405221 0.190982i
\(831\) 11.1037 + 0.873881i 0.385183 + 0.0303146i
\(832\) −23.4183 + 27.5404i −0.811883 + 0.954791i
\(833\) −10.3573 43.1415i −0.358861 1.49476i
\(834\) 5.04326 + 0.662098i 0.174634 + 0.0229266i
\(835\) −0.0363707 + 0.00286243i −0.00125866 + 9.90586e-5i
\(836\) 2.83635 27.1756i 0.0980974 0.939889i
\(837\) 0.664103 0.567197i 0.0229547 0.0196052i
\(838\) 25.5160 2.69119i 0.881434 0.0929655i
\(839\) 45.2802 + 10.8708i 1.56325 + 0.375302i 0.920489 0.390768i \(-0.127791\pi\)
0.642757 + 0.766070i \(0.277791\pi\)
\(840\) −3.39223 + 0.541059i −0.117043 + 0.0186683i
\(841\) 3.11784 + 19.6852i 0.107512 + 0.678801i
\(842\) 20.0705 21.1653i 0.691675 0.729403i
\(843\) −2.17446 + 1.57984i −0.0748925 + 0.0544126i
\(844\) −42.0877 14.8697i −1.44872 0.511837i
\(845\) 3.45582 4.75652i 0.118884 0.163629i
\(846\) −28.7181 13.6850i −0.987347 0.470501i
\(847\) 3.85770 + 9.31332i 0.132552 + 0.320010i
\(848\) 2.80559 9.52220i 0.0963444 0.326994i
\(849\) −1.95689 1.67134i −0.0671603 0.0573603i
\(850\) −12.7368 + 18.5466i −0.436869 + 0.636143i
\(851\) −17.8287 54.8712i −0.611161 1.88096i
\(852\) 0.958759 + 0.256154i 0.0328465 + 0.00877568i
\(853\) 40.6461 + 20.7102i 1.39170 + 0.709104i 0.979397 0.201945i \(-0.0647261\pi\)
0.412298 + 0.911049i \(0.364726\pi\)
\(854\) 2.06273 + 77.6961i 0.0705852 + 2.65871i
\(855\) −9.00497 5.51826i −0.307964 0.188720i
\(856\) −2.18913 + 1.11842i −0.0748230 + 0.0382268i
\(857\) −2.45010 + 7.54062i −0.0836937 + 0.257583i −0.984143 0.177379i \(-0.943238\pi\)
0.900449 + 0.434962i \(0.143238\pi\)
\(858\) 5.23032 4.01638i 0.178560 0.137117i
\(859\) 5.08378 32.0977i 0.173456 1.09516i −0.735272 0.677773i \(-0.762945\pi\)
0.908728 0.417389i \(-0.137055\pi\)
\(860\) −2.93677 5.07812i −0.100143 0.173163i
\(861\) 9.77441 + 0.886096i 0.333111 + 0.0301981i
\(862\) 7.32697 + 4.22669i 0.249557 + 0.143961i
\(863\) 3.62073 + 0.573467i 0.123251 + 0.0195210i 0.217755 0.976003i \(-0.430127\pi\)
−0.0945042 + 0.995524i \(0.530127\pi\)
\(864\) 1.53927 + 11.5303i 0.0523669 + 0.392270i
\(865\) −1.94160 0.630865i −0.0660164 0.0214500i
\(866\) −2.93095 + 56.3164i −0.0995976 + 1.91371i
\(867\) 0.687286 1.12155i 0.0233414 0.0380898i
\(868\) −3.27159 1.77326i −0.111045 0.0601882i
\(869\) −11.3600 + 22.2952i −0.385361 + 0.756314i
\(870\) −0.710742 2.64868i −0.0240964 0.0897988i
\(871\) −28.2785 + 9.18823i −0.958179 + 0.311331i
\(872\) 2.48598 32.0327i 0.0841859 1.08477i
\(873\) 3.74816 4.38853i 0.126856 0.148529i
\(874\) 50.4703 + 14.9301i 1.70718 + 0.505018i
\(875\) −30.0572 + 12.4501i −1.01612 + 0.420890i
\(876\) −1.17167 1.70214i −0.0395870 0.0575100i
\(877\) 24.1992 + 17.5818i 0.817149 + 0.593694i 0.915894 0.401419i \(-0.131483\pi\)
−0.0987454 + 0.995113i \(0.531483\pi\)
\(878\) 24.1549 4.48590i 0.815188 0.151392i
\(879\) −4.21158 5.79675i −0.142053 0.195519i
\(880\) 6.42483 6.79005i 0.216581 0.228893i
\(881\) −39.6855 + 6.28556i −1.33704 + 0.211766i −0.783673 0.621173i \(-0.786656\pi\)
−0.553364 + 0.832939i \(0.686656\pi\)
\(882\) −46.3308 17.7655i −1.56004 0.598195i
\(883\) −2.80040 + 11.6645i −0.0942408 + 0.392541i −0.999476 0.0323697i \(-0.989695\pi\)
0.905235 + 0.424911i \(0.139695\pi\)
\(884\) −13.3541 + 30.0524i −0.449147 + 1.01077i
\(885\) −0.703792 0.824034i −0.0236577 0.0276996i
\(886\) 44.9754 20.0439i 1.51098 0.673387i
\(887\) −0.739603 9.39754i −0.0248334 0.315539i −0.996771 0.0802990i \(-0.974412\pi\)
0.971937 0.235240i \(-0.0755875\pi\)
\(888\) 2.72643 + 6.56200i 0.0914932 + 0.220206i
\(889\) −74.3159 + 17.8417i −2.49247 + 0.598390i
\(890\) −6.58773 + 2.33552i −0.220821 + 0.0782870i
\(891\) −1.83120 + 23.2676i −0.0613476 + 0.779495i
\(892\) 17.7529 19.7454i 0.594412 0.661125i
\(893\) 25.6035 25.6035i 0.856790 0.856790i
\(894\) −1.97666 3.04137i −0.0661093 0.101719i
\(895\) −3.35940 + 2.05864i −0.112292 + 0.0688129i
\(896\) 43.4986 23.7610i 1.45319 0.793798i
\(897\) 5.76700 + 11.3184i 0.192554 + 0.377909i
\(898\) −15.8124 17.5486i −0.527666 0.585605i
\(899\) 1.13689 2.74468i 0.0379172 0.0915403i
\(900\) 9.03453 + 23.4848i 0.301151 + 0.782828i
\(901\) 9.03034i 0.300844i
\(902\) −22.5651 + 14.2876i −0.751335 + 0.475724i
\(903\) 5.67389i 0.188815i
\(904\) 0.698439 4.44102i 0.0232297 0.147706i
\(905\) 0.609229 1.47081i 0.0202515 0.0488914i
\(906\) 5.03510 4.53693i 0.167280 0.150729i
\(907\) −6.54641 12.8480i −0.217370 0.426612i 0.756412 0.654095i \(-0.226950\pi\)
−0.973782 + 0.227483i \(0.926950\pi\)
\(908\) 7.63761 + 0.194456i 0.253463 + 0.00645326i
\(909\) −39.7651 + 24.3681i −1.31892 + 0.808238i
\(910\) −18.6005 + 12.0889i −0.616602 + 0.400744i
\(911\) −18.4932 + 18.4932i −0.612708 + 0.612708i −0.943651 0.330943i \(-0.892633\pi\)
0.330943 + 0.943651i \(0.392633\pi\)
\(912\) −6.34263 1.33856i −0.210025 0.0443240i
\(913\) 1.16155 14.7588i 0.0384415 0.488446i
\(914\) 4.39651 + 12.4011i 0.145424 + 0.410191i
\(915\) 3.38158 0.811845i 0.111792 0.0268388i
\(916\) 10.8157 14.1164i 0.357359 0.466419i
\(917\) −2.86828 36.4449i −0.0947188 1.20352i
\(918\) 4.30759 + 9.66558i 0.142172 + 0.319012i
\(919\) 15.0766 + 17.6524i 0.497330 + 0.582299i 0.951125 0.308808i \(-0.0999299\pi\)
−0.453794 + 0.891106i \(0.649930\pi\)
\(920\) 10.5999 + 14.5562i 0.349469 + 0.479904i
\(921\) 2.50656 10.4406i 0.0825940 0.344029i
\(922\) 5.45817 14.2344i 0.179755 0.468786i
\(923\) 6.32990 1.00256i 0.208351 0.0329996i
\(924\) −8.66731 + 2.57421i −0.285134 + 0.0846853i
\(925\) 18.4537 + 25.3994i 0.606755 + 0.835127i
\(926\) 1.38893 + 7.47888i 0.0456432 + 0.245771i
\(927\) 3.59379 + 2.61104i 0.118035 + 0.0857578i
\(928\) 22.4717 + 32.5699i 0.737671 + 1.06916i
\(929\) 20.7739 8.60482i 0.681568 0.282315i −0.0149140 0.999889i \(-0.504747\pi\)
0.696482 + 0.717574i \(0.254747\pi\)
\(930\) −0.0472318 + 0.159665i −0.00154879 + 0.00523561i
\(931\) 36.6797 42.9464i 1.20213 1.40751i
\(932\) 12.7048 + 26.5866i 0.416161 + 0.870874i
\(933\) 2.90155 0.942770i 0.0949924 0.0308649i
\(934\) −21.7012 + 5.82325i −0.710084 + 0.190542i
\(935\) 3.86056 7.57678i 0.126254 0.247787i
\(936\) 19.2512 + 31.3386i 0.629246 + 1.02433i
\(937\) −9.18474 + 14.9881i −0.300052 + 0.489641i −0.966762 0.255676i \(-0.917702\pi\)
0.666710 + 0.745317i \(0.267702\pi\)
\(938\) 40.7118 + 2.11882i 1.32929 + 0.0691818i
\(939\) 9.07949 + 2.95011i 0.296298 + 0.0962731i
\(940\) 12.2807 1.62585i 0.400553 0.0530293i
\(941\) −52.3912 8.29795i −1.70790 0.270505i −0.775349 0.631533i \(-0.782426\pi\)
−0.932555 + 0.361028i \(0.882426\pi\)
\(942\) 1.45667 2.52513i 0.0474608 0.0822733i
\(943\) −19.1225 47.7613i −0.622716 1.55532i
\(944\) 13.5528 + 7.79855i 0.441107 + 0.253821i
\(945\) −1.11668 + 7.05042i −0.0363255 + 0.229350i
\(946\) −9.40387 12.2462i −0.305746 0.398157i
\(947\) 7.94924 24.4652i 0.258316 0.795014i −0.734843 0.678238i \(-0.762744\pi\)
0.993158 0.116776i \(-0.0372560\pi\)
\(948\) 4.98111 + 3.22964i 0.161779 + 0.104894i
\(949\) −11.3784 6.97267i −0.369357 0.226343i
\(950\) −28.6304 + 0.760099i −0.928892 + 0.0246609i
\(951\) 1.79489 + 0.914544i 0.0582034 + 0.0296561i
\(952\) 31.8478 31.9171i 1.03219 1.03444i
\(953\) −9.60517 29.5617i −0.311142 0.957596i −0.977314 0.211798i \(-0.932068\pi\)
0.666172 0.745798i \(-0.267932\pi\)
\(954\) −8.32531 5.71739i −0.269542 0.185107i
\(955\) −4.77363 4.07706i −0.154471 0.131931i
\(956\) 39.6655 + 41.7380i 1.28287 + 1.34990i
\(957\) −2.76228 6.66874i −0.0892919 0.215570i
\(958\) −24.1780 + 50.7376i −0.781157 + 1.63926i
\(959\) 30.6268 42.1542i 0.988992 1.36123i
\(960\) −1.44398 1.68326i −0.0466043 0.0543269i
\(961\) 24.9336 18.1153i 0.804310 0.584365i
\(962\) 33.2985 + 31.5761i 1.07359 + 1.01806i
\(963\) 0.391245 + 2.47022i 0.0126077 + 0.0796018i
\(964\) −23.9884 + 19.4542i −0.772614 + 0.626578i
\(965\) 6.35516 + 1.52574i 0.204580 + 0.0491153i
\(966\) −1.82680 17.3204i −0.0587763 0.557276i
\(967\) −11.0312 + 9.42156i −0.354741 + 0.302977i −0.808903 0.587942i \(-0.799938\pi\)
0.454163 + 0.890919i \(0.349938\pi\)
\(968\) −3.81970 + 5.26941i −0.122770 + 0.169365i
\(969\) −5.87868 + 0.462662i −0.188851 + 0.0148629i
\(970\) −0.292536 + 2.22827i −0.00939277 + 0.0715456i
\(971\) 5.94357 + 24.7568i 0.190738 + 0.794482i 0.982895 + 0.184165i \(0.0589581\pi\)
−0.792157 + 0.610317i \(0.791042\pi\)
\(972\) 17.5785 + 3.24481i 0.563832 + 0.104077i
\(973\) −44.8989 3.53362i −1.43939 0.113283i
\(974\) −27.6989 5.87710i −0.887531 0.188314i
\(975\) −4.88782 4.88782i −0.156536 0.156536i
\(976\) −42.0442 + 27.3906i −1.34580 + 0.876752i
\(977\) 11.5290 + 18.8137i 0.368847 + 0.601903i 0.982185 0.187917i \(-0.0601737\pi\)
−0.613338 + 0.789820i \(0.710174\pi\)
\(978\) 3.17895 + 5.84984i 0.101652 + 0.187057i
\(979\) −16.3918 + 8.35202i −0.523883 + 0.266932i
\(980\) 18.8973 4.03108i 0.603654 0.128768i
\(981\) −30.1993 12.5090i −0.964191 0.399381i
\(982\) −23.5293 19.0395i −0.750850 0.607576i
\(983\) 9.12057 0.290901 0.145450 0.989366i \(-0.453537\pi\)
0.145450 + 0.989366i \(0.453537\pi\)
\(984\) 2.81562 + 5.67643i 0.0897588 + 0.180958i
\(985\) 5.01988 0.159947
\(986\) 27.9824 + 22.6429i 0.891141 + 0.721097i
\(987\) −11.0698 4.58525i −0.352355 0.145950i
\(988\) −40.9416 + 8.73343i −1.30252 + 0.277847i
\(989\) 26.5006 13.5027i 0.842670 0.429362i
\(990\) −4.54100 8.35625i −0.144322 0.265579i
\(991\) 28.7489 + 46.9139i 0.913238 + 1.49027i 0.871070 + 0.491159i \(0.163427\pi\)
0.0421686 + 0.999111i \(0.486573\pi\)
\(992\) −0.130085 2.39897i −0.00413021 0.0761672i
\(993\) −5.42735 5.42735i −0.172232 0.172232i
\(994\) −8.59554 1.82378i −0.272634 0.0578468i
\(995\) 13.6840 + 1.07695i 0.433812 + 0.0341417i
\(996\) −3.45395 0.637562i −0.109443 0.0202019i
\(997\) −2.19554 9.14509i −0.0695335 0.289628i 0.926759 0.375656i \(-0.122583\pi\)
−0.996293 + 0.0860280i \(0.972583\pi\)
\(998\) −1.77524 + 13.5221i −0.0561942 + 0.428036i
\(999\) 14.7208 1.15855i 0.465745 0.0366549i
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 164.2.o.b.111.4 yes 288
4.3 odd 2 inner 164.2.o.b.111.16 yes 288
41.17 odd 40 inner 164.2.o.b.99.16 yes 288
164.99 even 40 inner 164.2.o.b.99.4 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.99.4 288 164.99 even 40 inner
164.2.o.b.99.16 yes 288 41.17 odd 40 inner
164.2.o.b.111.4 yes 288 1.1 even 1 trivial
164.2.o.b.111.16 yes 288 4.3 odd 2 inner