Properties

Label 672.2.cf.a.187.14
Level $672$
Weight $2$
Character 672.187
Analytic conductor $5.366$
Analytic rank $0$
Dimension $512$
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] = [672,2,Mod(19,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 21, 0, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.cf (of order \(24\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(512\)
Relative dimension: \(64\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 187.14
Character \(\chi\) \(=\) 672.187
Dual form 672.2.cf.a.115.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11481 - 0.870166i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.485621 + 1.94015i) q^{4} +(1.92826 + 2.51295i) q^{5} +(1.36901 - 0.354718i) q^{6} +(0.478372 - 2.60215i) q^{7} +(1.14687 - 2.58548i) q^{8} +(-0.258819 - 0.965926i) q^{9} +O(q^{10})\) \(q+(-1.11481 - 0.870166i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(0.485621 + 1.94015i) q^{4} +(1.92826 + 2.51295i) q^{5} +(1.36901 - 0.354718i) q^{6} +(0.478372 - 2.60215i) q^{7} +(1.14687 - 2.58548i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.0370391 - 4.47938i) q^{10} +(-0.484210 - 3.67794i) q^{11} +(-1.83485 - 0.795818i) q^{12} +(-1.16612 - 2.81526i) q^{13} +(-2.79759 + 2.48465i) q^{14} -3.16751 q^{15} +(-3.52834 + 1.88435i) q^{16} +(-0.233216 - 0.403943i) q^{17} +(-0.551981 + 1.30204i) q^{18} +(0.566269 - 4.30124i) q^{19} +(-3.93910 + 4.96145i) q^{20} +(1.77321 + 1.96360i) q^{21} +(-2.66062 + 4.52157i) q^{22} +(7.22999 - 1.93727i) q^{23} +(1.35302 + 2.48381i) q^{24} +(-1.30266 + 4.86161i) q^{25} +(-1.14974 + 4.15321i) q^{26} +(0.923880 + 0.382683i) q^{27} +(5.28085 - 0.335545i) q^{28} +(-0.610755 - 1.47449i) q^{29} +(3.53118 + 2.75626i) q^{30} +(-0.413043 - 0.715411i) q^{31} +(5.57315 + 0.969541i) q^{32} +(3.21268 + 1.85484i) q^{33} +(-0.0915044 + 0.653258i) q^{34} +(7.46149 - 3.81548i) q^{35} +(1.74835 - 0.971221i) q^{36} +(3.11223 - 2.38810i) q^{37} +(-4.37408 + 4.30234i) q^{38} +(2.94338 + 0.788678i) q^{39} +(8.70864 - 2.10342i) q^{40} +(8.29724 + 8.29724i) q^{41} +(-0.268134 - 3.73204i) q^{42} +(-10.4223 - 4.31705i) q^{43} +(6.90061 - 2.72553i) q^{44} +(1.92826 - 2.51295i) q^{45} +(-9.74584 - 4.13160i) q^{46} +(8.66642 + 5.00356i) q^{47} +(0.652961 - 3.94635i) q^{48} +(-6.54232 - 2.48959i) q^{49} +(5.68263 - 4.28625i) q^{50} +(0.462443 + 0.0608817i) q^{51} +(4.89573 - 3.62959i) q^{52} +(-7.50339 + 0.987840i) q^{53} +(-0.696956 - 1.23055i) q^{54} +(8.30881 - 8.30881i) q^{55} +(-6.17915 - 4.22115i) q^{56} +(3.06768 + 3.06768i) q^{57} +(-0.602175 + 2.17524i) q^{58} +(-0.295095 - 2.24147i) q^{59} +(-1.53821 - 6.14543i) q^{60} +(-0.101037 + 0.767455i) q^{61} +(-0.162061 + 1.15697i) q^{62} +(-2.63729 + 0.211413i) q^{63} +(-5.36936 - 5.93042i) q^{64} +(4.82604 - 8.35895i) q^{65} +(-1.96752 - 4.86336i) q^{66} +(3.95660 + 3.03601i) q^{67} +(0.670454 - 0.648638i) q^{68} +(-2.86440 + 6.91527i) q^{69} +(-11.6383 - 2.23919i) q^{70} +(-8.58760 + 8.58760i) q^{71} +(-2.79421 - 0.438624i) q^{72} +(0.885238 - 3.30375i) q^{73} +(-5.54760 - 0.0458720i) q^{74} +(-3.06396 - 3.99303i) q^{75} +(8.62003 - 0.990129i) q^{76} +(-9.80217 - 0.499439i) q^{77} +(-2.59505 - 3.44046i) q^{78} +(2.49152 - 4.31544i) q^{79} +(-11.5388 - 5.23304i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-2.02990 - 16.4699i) q^{82} +(14.3259 - 5.93396i) q^{83} +(-2.94857 + 4.39385i) q^{84} +(0.565388 - 1.36497i) q^{85} +(7.86235 + 13.8818i) q^{86} +(1.54160 + 0.413070i) q^{87} +(-10.0646 - 2.96622i) q^{88} +(-0.647173 - 2.41528i) q^{89} +(-4.33633 + 1.12357i) q^{90} +(-7.88356 + 1.68767i) q^{91} +(7.26963 + 13.0865i) q^{92} +(0.819019 + 0.107826i) q^{93} +(-5.30752 - 13.1193i) q^{94} +(11.9007 - 6.87089i) q^{95} +(-4.16191 + 3.83126i) q^{96} +4.60116i q^{97} +(5.12712 + 8.46833i) q^{98} +(-3.42730 + 1.41963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 512 q+O(q^{10}) \) Copy content Toggle raw display \( 512 q + 64 q^{14} + 8 q^{16} - 8 q^{18} - 16 q^{22} - 16 q^{23} - 40 q^{28} + 48 q^{35} + 32 q^{43} + 8 q^{44} + 48 q^{50} - 72 q^{52} + 32 q^{53} + 32 q^{58} - 192 q^{59} - 48 q^{60} + 144 q^{64} - 144 q^{66} - 16 q^{67} - 72 q^{70} + 128 q^{71} + 32 q^{74} + 48 q^{78} - 72 q^{80} - 120 q^{82} + 88 q^{88} - 48 q^{91} + 128 q^{92} - 72 q^{94} - 120 q^{96} - 136 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11481 0.870166i −0.788293 0.615300i
\(3\) −0.608761 + 0.793353i −0.351469 + 0.458043i
\(4\) 0.485621 + 1.94015i 0.242811 + 0.970074i
\(5\) 1.92826 + 2.51295i 0.862343 + 1.12383i 0.991227 + 0.132167i \(0.0421936\pi\)
−0.128885 + 0.991660i \(0.541140\pi\)
\(6\) 1.36901 0.354718i 0.558894 0.144813i
\(7\) 0.478372 2.60215i 0.180808 0.983518i
\(8\) 1.14687 2.58548i 0.405481 0.914103i
\(9\) −0.258819 0.965926i −0.0862730 0.321975i
\(10\) 0.0370391 4.47938i 0.0117128 1.41650i
\(11\) −0.484210 3.67794i −0.145995 1.10894i −0.894901 0.446265i \(-0.852754\pi\)
0.748906 0.662676i \(-0.230579\pi\)
\(12\) −1.83485 0.795818i −0.529676 0.229733i
\(13\) −1.16612 2.81526i −0.323423 0.780813i −0.999050 0.0435693i \(-0.986127\pi\)
0.675627 0.737243i \(-0.263873\pi\)
\(14\) −2.79759 + 2.48465i −0.747689 + 0.664049i
\(15\) −3.16751 −0.817847
\(16\) −3.52834 + 1.88435i −0.882086 + 0.471088i
\(17\) −0.233216 0.403943i −0.0565633 0.0979705i 0.836357 0.548185i \(-0.184681\pi\)
−0.892921 + 0.450214i \(0.851348\pi\)
\(18\) −0.551981 + 1.30204i −0.130103 + 0.306895i
\(19\) 0.566269 4.30124i 0.129911 0.986772i −0.795005 0.606602i \(-0.792532\pi\)
0.924917 0.380170i \(-0.124135\pi\)
\(20\) −3.93910 + 4.96145i −0.880809 + 1.10941i
\(21\) 1.77321 + 1.96360i 0.386945 + 0.428493i
\(22\) −2.66062 + 4.52157i −0.567245 + 0.964001i
\(23\) 7.22999 1.93727i 1.50756 0.403949i 0.591934 0.805986i \(-0.298365\pi\)
0.915623 + 0.402038i \(0.131698\pi\)
\(24\) 1.35302 + 2.48381i 0.276185 + 0.507006i
\(25\) −1.30266 + 4.86161i −0.260533 + 0.972321i
\(26\) −1.14974 + 4.15321i −0.225482 + 0.814511i
\(27\) 0.923880 + 0.382683i 0.177801 + 0.0736475i
\(28\) 5.28085 0.335545i 0.997987 0.0634121i
\(29\) −0.610755 1.47449i −0.113414 0.273806i 0.856973 0.515362i \(-0.172342\pi\)
−0.970387 + 0.241555i \(0.922342\pi\)
\(30\) 3.53118 + 2.75626i 0.644703 + 0.503222i
\(31\) −0.413043 0.715411i −0.0741847 0.128492i 0.826547 0.562868i \(-0.190302\pi\)
−0.900731 + 0.434376i \(0.856969\pi\)
\(32\) 5.57315 + 0.969541i 0.985203 + 0.171392i
\(33\) 3.21268 + 1.85484i 0.559255 + 0.322886i
\(34\) −0.0915044 + 0.653258i −0.0156929 + 0.112033i
\(35\) 7.46149 3.81548i 1.26122 0.644933i
\(36\) 1.74835 0.971221i 0.291392 0.161870i
\(37\) 3.11223 2.38810i 0.511648 0.392601i −0.320420 0.947276i \(-0.603824\pi\)
0.832067 + 0.554675i \(0.187157\pi\)
\(38\) −4.37408 + 4.30234i −0.709569 + 0.697931i
\(39\) 2.94338 + 0.788678i 0.471319 + 0.126289i
\(40\) 8.70864 2.10342i 1.37696 0.332580i
\(41\) 8.29724 + 8.29724i 1.29581 + 1.29581i 0.931134 + 0.364678i \(0.118821\pi\)
0.364678 + 0.931134i \(0.381179\pi\)
\(42\) −0.268134 3.73204i −0.0413739 0.575866i
\(43\) −10.4223 4.31705i −1.58938 0.658344i −0.599518 0.800361i \(-0.704641\pi\)
−0.989864 + 0.142018i \(0.954641\pi\)
\(44\) 6.90061 2.72553i 1.04031 0.410889i
\(45\) 1.92826 2.51295i 0.287448 0.374609i
\(46\) −9.74584 4.13160i −1.43695 0.609171i
\(47\) 8.66642 + 5.00356i 1.26413 + 0.729844i 0.973870 0.227105i \(-0.0729260\pi\)
0.290257 + 0.956949i \(0.406259\pi\)
\(48\) 0.652961 3.94635i 0.0942468 0.569606i
\(49\) −6.54232 2.48959i −0.934617 0.355655i
\(50\) 5.68263 4.28625i 0.803646 0.606168i
\(51\) 0.462443 + 0.0608817i 0.0647549 + 0.00852515i
\(52\) 4.89573 3.62959i 0.678915 0.503334i
\(53\) −7.50339 + 0.987840i −1.03067 + 0.135690i −0.626844 0.779145i \(-0.715653\pi\)
−0.403827 + 0.914835i \(0.632320\pi\)
\(54\) −0.696956 1.23055i −0.0948437 0.167457i
\(55\) 8.30881 8.30881i 1.12036 1.12036i
\(56\) −6.17915 4.22115i −0.825724 0.564075i
\(57\) 3.06768 + 3.06768i 0.406324 + 0.406324i
\(58\) −0.602175 + 2.17524i −0.0790695 + 0.285623i
\(59\) −0.295095 2.24147i −0.0384180 0.291814i −0.999859 0.0168020i \(-0.994652\pi\)
0.961441 0.275012i \(-0.0886818\pi\)
\(60\) −1.53821 6.14543i −0.198582 0.793372i
\(61\) −0.101037 + 0.767455i −0.0129365 + 0.0982625i −0.996695 0.0812346i \(-0.974114\pi\)
0.983759 + 0.179497i \(0.0574470\pi\)
\(62\) −0.162061 + 1.15697i −0.0205817 + 0.146935i
\(63\) −2.63729 + 0.211413i −0.332267 + 0.0266355i
\(64\) −5.36936 5.93042i −0.671170 0.741303i
\(65\) 4.82604 8.35895i 0.598597 1.03680i
\(66\) −1.96752 4.86336i −0.242185 0.598639i
\(67\) 3.95660 + 3.03601i 0.483376 + 0.370908i 0.821513 0.570189i \(-0.193130\pi\)
−0.338137 + 0.941097i \(0.609797\pi\)
\(68\) 0.670454 0.648638i 0.0813044 0.0786589i
\(69\) −2.86440 + 6.91527i −0.344833 + 0.832501i
\(70\) −11.6383 2.23919i −1.39104 0.267634i
\(71\) −8.58760 + 8.58760i −1.01916 + 1.01916i −0.0193483 + 0.999813i \(0.506159\pi\)
−0.999813 + 0.0193483i \(0.993841\pi\)
\(72\) −2.79421 0.438624i −0.329301 0.0516924i
\(73\) 0.885238 3.30375i 0.103609 0.386675i −0.894574 0.446919i \(-0.852521\pi\)
0.998184 + 0.0602440i \(0.0191879\pi\)
\(74\) −5.54760 0.0458720i −0.644896 0.00533251i
\(75\) −3.06396 3.99303i −0.353796 0.461076i
\(76\) 8.62003 0.990129i 0.988786 0.113576i
\(77\) −9.80217 0.499439i −1.11706 0.0569163i
\(78\) −2.59505 3.44046i −0.293831 0.389556i
\(79\) 2.49152 4.31544i 0.280318 0.485525i −0.691145 0.722716i \(-0.742893\pi\)
0.971463 + 0.237191i \(0.0762268\pi\)
\(80\) −11.5388 5.23304i −1.29008 0.585072i
\(81\) −0.866025 + 0.500000i −0.0962250 + 0.0555556i
\(82\) −2.02990 16.4699i −0.224165 1.81879i
\(83\) 14.3259 5.93396i 1.57247 0.651337i 0.585269 0.810839i \(-0.300989\pi\)
0.987198 + 0.159502i \(0.0509888\pi\)
\(84\) −2.94857 + 4.39385i −0.321716 + 0.479408i
\(85\) 0.565388 1.36497i 0.0613249 0.148051i
\(86\) 7.86235 + 13.8818i 0.847819 + 1.49692i
\(87\) 1.54160 + 0.413070i 0.165277 + 0.0442857i
\(88\) −10.0646 2.96622i −1.07289 0.316200i
\(89\) −0.647173 2.41528i −0.0686002 0.256020i 0.923106 0.384546i \(-0.125642\pi\)
−0.991706 + 0.128526i \(0.958975\pi\)
\(90\) −4.33633 + 1.12357i −0.457090 + 0.118435i
\(91\) −7.88356 + 1.68767i −0.826421 + 0.176916i
\(92\) 7.26963 + 13.0865i 0.757911 + 1.36436i
\(93\) 0.819019 + 0.107826i 0.0849283 + 0.0111810i
\(94\) −5.30752 13.1193i −0.547429 1.35315i
\(95\) 11.9007 6.87089i 1.22099 0.704938i
\(96\) −4.16191 + 3.83126i −0.424773 + 0.391026i
\(97\) 4.60116i 0.467177i 0.972336 + 0.233589i \(0.0750469\pi\)
−0.972336 + 0.233589i \(0.924953\pi\)
\(98\) 5.12712 + 8.46833i 0.517917 + 0.855431i
\(99\) −3.42730 + 1.41963i −0.344456 + 0.142678i
\(100\) −10.0648 0.166459i −1.00648 0.0166459i
\(101\) −0.729800 + 0.0960800i −0.0726178 + 0.00956032i −0.166748 0.986000i \(-0.553326\pi\)
0.0941297 + 0.995560i \(0.469993\pi\)
\(102\) −0.462560 0.470274i −0.0458003 0.0465640i
\(103\) 8.95422 2.39927i 0.882285 0.236408i 0.210892 0.977509i \(-0.432363\pi\)
0.671393 + 0.741102i \(0.265696\pi\)
\(104\) −8.61618 0.213775i −0.844886 0.0209624i
\(105\) −1.51525 + 8.24232i −0.147873 + 0.804368i
\(106\) 9.22447 + 5.42794i 0.895960 + 0.527208i
\(107\) 13.3083 10.2118i 1.28656 0.987213i 0.286989 0.957934i \(-0.407346\pi\)
0.999571 0.0292790i \(-0.00932114\pi\)
\(108\) −0.293807 + 1.97830i −0.0282716 + 0.190362i
\(109\) −6.04475 4.63830i −0.578982 0.444269i 0.277295 0.960785i \(-0.410562\pi\)
−0.856277 + 0.516516i \(0.827229\pi\)
\(110\) −16.4928 + 2.03273i −1.57253 + 0.193814i
\(111\) 3.92288i 0.372343i
\(112\) 3.21550 + 10.0827i 0.303836 + 0.952724i
\(113\) 16.6088i 1.56242i 0.624267 + 0.781211i \(0.285398\pi\)
−0.624267 + 0.781211i \(0.714602\pi\)
\(114\) −0.750502 6.08929i −0.0702909 0.570314i
\(115\) 18.8095 + 14.4331i 1.75400 + 1.34589i
\(116\) 2.56414 1.90100i 0.238074 0.176503i
\(117\) −2.41752 + 1.85503i −0.223500 + 0.171497i
\(118\) −1.62147 + 2.75560i −0.149269 + 0.253673i
\(119\) −1.16268 + 0.413628i −0.106583 + 0.0379172i
\(120\) −3.63273 + 8.18951i −0.331621 + 0.747597i
\(121\) −2.66762 + 0.714786i −0.242511 + 0.0649805i
\(122\) 0.780451 0.767650i 0.0706587 0.0694998i
\(123\) −11.6337 + 1.53160i −1.04897 + 0.138100i
\(124\) 1.18742 1.14878i 0.106634 0.103164i
\(125\) −0.0968809 + 0.0401294i −0.00866529 + 0.00358928i
\(126\) 3.12405 + 2.05920i 0.278313 + 0.183448i
\(127\) 5.37991i 0.477390i −0.971095 0.238695i \(-0.923280\pi\)
0.971095 0.238695i \(-0.0767196\pi\)
\(128\) 0.825387 + 11.2836i 0.0729546 + 0.997335i
\(129\) 9.76962 5.64050i 0.860167 0.496618i
\(130\) −12.6538 + 5.11922i −1.10981 + 0.448985i
\(131\) −17.3557 2.28492i −1.51637 0.199634i −0.674082 0.738656i \(-0.735461\pi\)
−0.842292 + 0.539022i \(0.818794\pi\)
\(132\) −2.03852 + 7.13382i −0.177430 + 0.620919i
\(133\) −10.9216 3.53111i −0.947020 0.306186i
\(134\) −1.76905 6.82749i −0.152822 0.589805i
\(135\) 0.819811 + 3.05958i 0.0705581 + 0.263327i
\(136\) −1.31185 + 0.139704i −0.112491 + 0.0119795i
\(137\) 0.632074 + 0.169364i 0.0540018 + 0.0144697i 0.285719 0.958314i \(-0.407768\pi\)
−0.231717 + 0.972783i \(0.574434\pi\)
\(138\) 9.21071 5.21674i 0.784068 0.444078i
\(139\) −6.38437 + 15.4132i −0.541516 + 1.30733i 0.382138 + 0.924105i \(0.375188\pi\)
−0.923653 + 0.383229i \(0.874812\pi\)
\(140\) 11.0260 + 12.6235i 0.931871 + 1.06688i
\(141\) −9.24537 + 3.82956i −0.778601 + 0.322507i
\(142\) 17.0462 2.10094i 1.43049 0.176307i
\(143\) −9.78972 + 5.65210i −0.818657 + 0.472652i
\(144\) 2.73335 + 2.92041i 0.227779 + 0.243368i
\(145\) 2.52764 4.37800i 0.209909 0.363573i
\(146\) −3.86169 + 2.91277i −0.319596 + 0.241062i
\(147\) 5.95783 3.67481i 0.491394 0.303093i
\(148\) 6.14463 + 4.87848i 0.505086 + 0.401008i
\(149\) 0.978107 + 1.27469i 0.0801296 + 0.104427i 0.831698 0.555228i \(-0.187369\pi\)
−0.751568 + 0.659655i \(0.770702\pi\)
\(150\) −0.0588543 + 7.11764i −0.00480544 + 0.581153i
\(151\) −0.311320 + 1.16186i −0.0253349 + 0.0945510i −0.977436 0.211233i \(-0.932252\pi\)
0.952101 + 0.305784i \(0.0989187\pi\)
\(152\) −10.4713 6.39705i −0.849336 0.518870i
\(153\) −0.329818 + 0.329818i −0.0266642 + 0.0266642i
\(154\) 10.4930 + 9.08630i 0.845551 + 0.732195i
\(155\) 1.00134 2.41745i 0.0804297 0.194175i
\(156\) −0.100780 + 6.09360i −0.00806888 + 0.487878i
\(157\) 7.28958 + 5.59349i 0.581772 + 0.446409i 0.857252 0.514898i \(-0.172170\pi\)
−0.275480 + 0.961307i \(0.588837\pi\)
\(158\) −6.53273 + 2.64288i −0.519716 + 0.210256i
\(159\) 3.78407 6.55420i 0.300096 0.519782i
\(160\) 8.31005 + 15.8746i 0.656967 + 1.25500i
\(161\) −1.58243 19.7402i −0.124713 1.55575i
\(162\) 1.40054 + 0.196179i 0.110037 + 0.0154133i
\(163\) −1.75516 + 13.3317i −0.137475 + 1.04422i 0.774093 + 0.633072i \(0.218206\pi\)
−0.911567 + 0.411151i \(0.865127\pi\)
\(164\) −12.0686 + 20.1272i −0.942396 + 1.57167i
\(165\) 1.53374 + 11.6499i 0.119401 + 0.906944i
\(166\) −21.1342 5.85061i −1.64033 0.454095i
\(167\) −10.2535 10.2535i −0.793441 0.793441i 0.188611 0.982052i \(-0.439602\pi\)
−0.982052 + 0.188611i \(0.939602\pi\)
\(168\) 7.11049 2.33258i 0.548586 0.179962i
\(169\) 2.62653 2.62653i 0.202041 0.202041i
\(170\) −1.81805 + 1.02970i −0.139438 + 0.0789746i
\(171\) −4.30124 + 0.566269i −0.328924 + 0.0433037i
\(172\) 3.31443 22.3172i 0.252723 1.70167i
\(173\) 17.3989 + 2.29061i 1.32282 + 0.174152i 0.758645 0.651505i \(-0.225862\pi\)
0.564173 + 0.825657i \(0.309195\pi\)
\(174\) −1.35916 1.80194i −0.103037 0.136605i
\(175\) 12.0275 + 5.71538i 0.909190 + 0.432042i
\(176\) 8.63901 + 12.0646i 0.651190 + 0.909405i
\(177\) 1.95792 + 1.13040i 0.147166 + 0.0849663i
\(178\) −1.38022 + 3.25574i −0.103452 + 0.244028i
\(179\) −7.40223 + 9.64677i −0.553269 + 0.721034i −0.983343 0.181760i \(-0.941821\pi\)
0.430074 + 0.902793i \(0.358487\pi\)
\(180\) 5.81190 + 2.52076i 0.433194 + 0.187886i
\(181\) −4.53606 1.87890i −0.337163 0.139657i 0.207677 0.978197i \(-0.433410\pi\)
−0.544840 + 0.838540i \(0.683410\pi\)
\(182\) 10.2573 + 4.97857i 0.760318 + 0.369036i
\(183\) −0.547355 0.547355i −0.0404616 0.0404616i
\(184\) 3.28312 20.9148i 0.242035 1.54186i
\(185\) 12.0024 + 3.21602i 0.882431 + 0.236447i
\(186\) −0.819227 0.832888i −0.0600686 0.0610703i
\(187\) −1.37275 + 1.05335i −0.100386 + 0.0770286i
\(188\) −5.49904 + 19.2440i −0.401059 + 1.40351i
\(189\) 1.43776 2.22100i 0.104581 0.161554i
\(190\) −19.2459 2.69585i −1.39625 0.195577i
\(191\) −15.5113 8.95544i −1.12236 0.647993i −0.180355 0.983602i \(-0.557725\pi\)
−0.942001 + 0.335609i \(0.891058\pi\)
\(192\) 7.97358 0.649589i 0.575444 0.0468800i
\(193\) 11.8114 + 20.4580i 0.850207 + 1.47260i 0.881022 + 0.473076i \(0.156856\pi\)
−0.0308151 + 0.999525i \(0.509810\pi\)
\(194\) 4.00377 5.12944i 0.287454 0.368272i
\(195\) 3.69369 + 8.91736i 0.264511 + 0.638585i
\(196\) 1.65307 13.9021i 0.118077 0.993004i
\(197\) −15.2069 6.29890i −1.08345 0.448778i −0.231730 0.972780i \(-0.574438\pi\)
−0.851717 + 0.524002i \(0.824438\pi\)
\(198\) 5.05612 + 1.39969i 0.359322 + 0.0994717i
\(199\) 6.95702 25.9640i 0.493170 1.84054i −0.0468766 0.998901i \(-0.514927\pi\)
0.540047 0.841635i \(-0.318407\pi\)
\(200\) 11.0756 + 8.94365i 0.783161 + 0.632412i
\(201\) −4.81726 + 1.29078i −0.339783 + 0.0910446i
\(202\) 0.897197 + 0.527936i 0.0631266 + 0.0371455i
\(203\) −4.12901 + 0.883917i −0.289800 + 0.0620388i
\(204\) 0.106452 + 0.926772i 0.00745316 + 0.0648870i
\(205\) −4.85137 + 36.8498i −0.338834 + 2.57370i
\(206\) −12.0701 5.11691i −0.840961 0.356512i
\(207\) −3.74252 6.48223i −0.260123 0.450546i
\(208\) 9.41942 + 7.73583i 0.653119 + 0.536383i
\(209\) −16.0939 −1.11324
\(210\) 8.86140 7.87013i 0.611495 0.543091i
\(211\) 3.48448 + 8.41228i 0.239881 + 0.579125i 0.997270 0.0738392i \(-0.0235252\pi\)
−0.757389 + 0.652964i \(0.773525\pi\)
\(212\) −5.56036 14.0780i −0.381887 0.966879i
\(213\) −1.58520 12.0408i −0.108616 0.825022i
\(214\) −23.7222 0.196154i −1.62162 0.0134088i
\(215\) −9.24828 34.5151i −0.630728 2.35391i
\(216\) 2.04899 1.94978i 0.139416 0.132666i
\(217\) −2.05919 + 0.732565i −0.139787 + 0.0497297i
\(218\) 2.70268 + 10.4308i 0.183049 + 0.706462i
\(219\) 2.08214 + 2.71350i 0.140698 + 0.183362i
\(220\) 20.1553 + 12.0854i 1.35887 + 0.814797i
\(221\) −0.865246 + 1.12761i −0.0582027 + 0.0758513i
\(222\) 3.41356 4.37328i 0.229103 0.293516i
\(223\) −27.0292 −1.81001 −0.905003 0.425405i \(-0.860132\pi\)
−0.905003 + 0.425405i \(0.860132\pi\)
\(224\) 5.18893 14.0383i 0.346700 0.937976i
\(225\) 5.03311 0.335540
\(226\) 14.4524 18.5157i 0.961359 1.23165i
\(227\) −0.481980 + 0.628129i −0.0319902 + 0.0416904i −0.809075 0.587706i \(-0.800031\pi\)
0.777084 + 0.629396i \(0.216698\pi\)
\(228\) −4.46202 + 7.44149i −0.295505 + 0.492824i
\(229\) −0.371317 0.483910i −0.0245373 0.0319777i 0.780924 0.624627i \(-0.214749\pi\)
−0.805461 + 0.592649i \(0.798082\pi\)
\(230\) −8.40998 32.4576i −0.554537 2.14019i
\(231\) 6.36342 7.47255i 0.418682 0.491658i
\(232\) −4.51272 0.111965i −0.296275 0.00735084i
\(233\) 4.15120 + 15.4925i 0.271954 + 1.01495i 0.957855 + 0.287251i \(0.0927414\pi\)
−0.685901 + 0.727694i \(0.740592\pi\)
\(234\) 4.30927 + 0.0356324i 0.281706 + 0.00232937i
\(235\) 4.13737 + 31.4264i 0.269892 + 2.05004i
\(236\) 4.20547 1.66103i 0.273753 0.108124i
\(237\) 1.90693 + 4.60373i 0.123868 + 0.299044i
\(238\) 1.65610 + 0.550608i 0.107349 + 0.0356906i
\(239\) −27.8702 −1.80277 −0.901385 0.433018i \(-0.857449\pi\)
−0.901385 + 0.433018i \(0.857449\pi\)
\(240\) 11.1761 5.96871i 0.721411 0.385278i
\(241\) −3.07474 5.32560i −0.198061 0.343052i 0.749839 0.661621i \(-0.230131\pi\)
−0.947900 + 0.318569i \(0.896798\pi\)
\(242\) 3.59588 + 1.52442i 0.231152 + 0.0979932i
\(243\) 0.130526 0.991445i 0.00837326 0.0636012i
\(244\) −1.53804 + 0.176665i −0.0984630 + 0.0113098i
\(245\) −6.35906 21.2411i −0.406265 1.35704i
\(246\) 14.3021 + 8.41579i 0.911872 + 0.536571i
\(247\) −12.7695 + 3.42156i −0.812501 + 0.217709i
\(248\) −2.32339 + 0.247426i −0.147535 + 0.0157116i
\(249\) −4.01330 + 14.9778i −0.254332 + 0.949182i
\(250\) 0.142923 + 0.0395657i 0.00903927 + 0.00250235i
\(251\) −11.3493 4.70103i −0.716361 0.296726i −0.00542708 0.999985i \(-0.501728\pi\)
−0.710934 + 0.703259i \(0.751728\pi\)
\(252\) −1.69090 5.01407i −0.106517 0.315857i
\(253\) −10.6260 25.6534i −0.668051 1.61282i
\(254\) −4.68142 + 5.99760i −0.293738 + 0.376323i
\(255\) 0.738715 + 1.27949i 0.0462601 + 0.0801249i
\(256\) 8.89842 13.2973i 0.556151 0.831081i
\(257\) 12.2182 + 7.05417i 0.762149 + 0.440027i 0.830067 0.557664i \(-0.188302\pi\)
−0.0679175 + 0.997691i \(0.521635\pi\)
\(258\) −15.7995 2.21309i −0.983633 0.137781i
\(259\) −4.72538 9.24088i −0.293621 0.574200i
\(260\) 18.5612 + 5.30395i 1.15112 + 0.328937i
\(261\) −1.26618 + 0.971570i −0.0783743 + 0.0601387i
\(262\) 17.3601 + 17.6496i 1.07251 + 1.09040i
\(263\) 5.37894 + 1.44128i 0.331680 + 0.0888733i 0.420816 0.907146i \(-0.361744\pi\)
−0.0891360 + 0.996019i \(0.528411\pi\)
\(264\) 8.48017 6.17903i 0.521919 0.380293i
\(265\) −16.9509 16.9509i −1.04128 1.04128i
\(266\) 9.10287 + 13.4401i 0.558133 + 0.824066i
\(267\) 2.31015 + 0.956895i 0.141379 + 0.0585610i
\(268\) −3.96889 + 9.15075i −0.242439 + 0.558971i
\(269\) −13.0556 + 17.0143i −0.796012 + 1.03738i 0.202301 + 0.979323i \(0.435158\pi\)
−0.998313 + 0.0580596i \(0.981509\pi\)
\(270\) 1.74840 4.12423i 0.106404 0.250993i
\(271\) 7.12641 + 4.11443i 0.432898 + 0.249934i 0.700581 0.713573i \(-0.252924\pi\)
−0.267682 + 0.963507i \(0.586258\pi\)
\(272\) 1.58404 + 0.985787i 0.0960465 + 0.0597721i
\(273\) 3.46029 7.28183i 0.209426 0.440717i
\(274\) −0.557271 0.738819i −0.0336660 0.0446337i
\(275\) 18.5115 + 2.43708i 1.11628 + 0.146962i
\(276\) −14.8077 2.19915i −0.891317 0.132374i
\(277\) −6.18375 + 0.814106i −0.371545 + 0.0489149i −0.313987 0.949427i \(-0.601665\pi\)
−0.0575583 + 0.998342i \(0.518332\pi\)
\(278\) 20.5295 11.6274i 1.23128 0.697367i
\(279\) −0.584131 + 0.584131i −0.0349710 + 0.0349710i
\(280\) −1.30744 23.6674i −0.0781343 1.41440i
\(281\) 18.2947 + 18.2947i 1.09137 + 1.09137i 0.995382 + 0.0959891i \(0.0306014\pi\)
0.0959891 + 0.995382i \(0.469399\pi\)
\(282\) 13.6392 + 3.77576i 0.812204 + 0.224844i
\(283\) 2.11145 + 16.0380i 0.125513 + 0.953363i 0.932088 + 0.362232i \(0.117985\pi\)
−0.806575 + 0.591131i \(0.798682\pi\)
\(284\) −20.8315 12.4909i −1.23612 0.741198i
\(285\) −1.79366 + 13.6242i −0.106247 + 0.807029i
\(286\) 15.8320 + 2.21765i 0.936165 + 0.131132i
\(287\) 25.5598 17.6215i 1.50875 1.04016i
\(288\) −0.505932 5.63418i −0.0298123 0.331997i
\(289\) 8.39122 14.5340i 0.493601 0.854942i
\(290\) −6.62743 + 2.68119i −0.389176 + 0.157445i
\(291\) −3.65035 2.80101i −0.213987 0.164198i
\(292\) 6.83966 + 0.113119i 0.400261 + 0.00661980i
\(293\) 1.28076 3.09203i 0.0748228 0.180638i −0.882043 0.471169i \(-0.843832\pi\)
0.956866 + 0.290531i \(0.0938320\pi\)
\(294\) −9.83957 1.08758i −0.573855 0.0634289i
\(295\) 5.06368 5.06368i 0.294819 0.294819i
\(296\) −2.60504 10.7854i −0.151415 0.626891i
\(297\) 0.960136 3.58328i 0.0557127 0.207923i
\(298\) 0.0187880 2.27216i 0.00108836 0.131623i
\(299\) −13.8850 18.0952i −0.802987 1.04647i
\(300\) 6.25914 7.88364i 0.361372 0.455162i
\(301\) −16.2193 + 25.0551i −0.934866 + 1.44415i
\(302\) 1.35808 1.02436i 0.0781486 0.0589453i
\(303\) 0.368049 0.637479i 0.0211438 0.0366222i
\(304\) 6.10707 + 16.2433i 0.350264 + 0.931618i
\(305\) −2.12340 + 1.22595i −0.121586 + 0.0701975i
\(306\) 0.654682 0.0806893i 0.0374257 0.00461270i
\(307\) 15.3303 6.35000i 0.874945 0.362414i 0.100411 0.994946i \(-0.467984\pi\)
0.774534 + 0.632532i \(0.217984\pi\)
\(308\) −3.79116 19.2602i −0.216021 1.09745i
\(309\) −3.54751 + 8.56444i −0.201811 + 0.487214i
\(310\) −3.21990 + 1.82368i −0.182878 + 0.103578i
\(311\) 7.29109 + 1.95364i 0.413440 + 0.110781i 0.459542 0.888156i \(-0.348013\pi\)
−0.0461025 + 0.998937i \(0.514680\pi\)
\(312\) 5.41480 6.70553i 0.306552 0.379626i
\(313\) −3.33497 12.4463i −0.188504 0.703506i −0.993853 0.110706i \(-0.964689\pi\)
0.805349 0.592801i \(-0.201978\pi\)
\(314\) −3.25926 12.5789i −0.183931 0.709866i
\(315\) −5.61664 6.21973i −0.316462 0.350442i
\(316\) 9.58253 + 2.73825i 0.539059 + 0.154038i
\(317\) −15.0316 1.97895i −0.844259 0.111149i −0.304026 0.952664i \(-0.598331\pi\)
−0.540234 + 0.841515i \(0.681664\pi\)
\(318\) −9.92178 + 4.01395i −0.556386 + 0.225091i
\(319\) −5.12736 + 2.96029i −0.287077 + 0.165744i
\(320\) 4.54937 24.9283i 0.254317 1.39354i
\(321\) 16.7747i 0.936274i
\(322\) −15.4132 + 23.3837i −0.858942 + 1.30312i
\(323\) −1.86952 + 0.774380i −0.104023 + 0.0430877i
\(324\) −1.39063 1.43741i −0.0772575 0.0798559i
\(325\) 15.2058 2.00188i 0.843463 0.111044i
\(326\) 13.5575 13.3351i 0.750881 0.738565i
\(327\) 7.35962 1.97201i 0.406988 0.109052i
\(328\) 30.9682 11.9364i 1.70993 0.659079i
\(329\) 17.1658 20.1577i 0.946379 1.11133i
\(330\) 8.42753 14.3221i 0.463920 0.788405i
\(331\) −18.7057 + 14.3534i −1.02816 + 0.788934i −0.977745 0.209795i \(-0.932720\pi\)
−0.0504128 + 0.998728i \(0.516054\pi\)
\(332\) 18.4697 + 24.9126i 1.01366 + 1.36726i
\(333\) −3.11223 2.38810i −0.170549 0.130867i
\(334\) 2.50850 + 20.3530i 0.137259 + 1.11367i
\(335\) 15.7970i 0.863080i
\(336\) −9.95661 3.58692i −0.543177 0.195683i
\(337\) 7.18298i 0.391282i 0.980676 + 0.195641i \(0.0626787\pi\)
−0.980676 + 0.195641i \(0.937321\pi\)
\(338\) −5.21361 + 0.642575i −0.283583 + 0.0349515i
\(339\) −13.1766 10.1108i −0.715656 0.549142i
\(340\) 2.92280 + 0.434079i 0.158511 + 0.0235412i
\(341\) −2.43124 + 1.86556i −0.131659 + 0.101026i
\(342\) 5.28783 + 3.11151i 0.285933 + 0.168251i
\(343\) −9.60793 + 15.8331i −0.518779 + 0.854908i
\(344\) −23.1147 + 21.9954i −1.24626 + 1.18591i
\(345\) −22.9011 + 6.13632i −1.23295 + 0.330368i
\(346\) −17.4034 17.6936i −0.935611 0.951213i
\(347\) 20.5427 2.70450i 1.10279 0.145185i 0.442918 0.896562i \(-0.353943\pi\)
0.659873 + 0.751377i \(0.270610\pi\)
\(348\) −0.0527837 + 3.19152i −0.00282950 + 0.171084i
\(349\) 33.2745 13.7827i 1.78114 0.737773i 0.788740 0.614727i \(-0.210734\pi\)
0.992401 0.123045i \(-0.0392661\pi\)
\(350\) −8.43504 16.8375i −0.450872 0.900000i
\(351\) 3.04722i 0.162648i
\(352\) 0.867341 20.9672i 0.0462294 1.11755i
\(353\) 17.2070 9.93447i 0.915837 0.528759i 0.0335324 0.999438i \(-0.489324\pi\)
0.882305 + 0.470679i \(0.155991\pi\)
\(354\) −1.19907 2.96390i −0.0637301 0.157530i
\(355\) −38.1394 5.02114i −2.02423 0.266494i
\(356\) 4.37173 2.42853i 0.231701 0.128712i
\(357\) 0.379643 1.17422i 0.0200928 0.0621462i
\(358\) 16.6464 4.31319i 0.879790 0.227959i
\(359\) −4.09937 15.2991i −0.216356 0.807453i −0.985685 0.168600i \(-0.946076\pi\)
0.769328 0.638854i \(-0.220591\pi\)
\(360\) −4.28571 7.86750i −0.225877 0.414654i
\(361\) 0.172575 + 0.0462412i 0.00908287 + 0.00243375i
\(362\) 3.42191 + 6.04175i 0.179852 + 0.317547i
\(363\) 1.05686 2.55150i 0.0554710 0.133919i
\(364\) −7.10275 14.4757i −0.372285 0.758732i
\(365\) 10.0091 4.14592i 0.523902 0.217007i
\(366\) 0.133909 + 1.08649i 0.00699955 + 0.0567917i
\(367\) −1.15691 + 0.667943i −0.0603902 + 0.0348663i −0.529891 0.848066i \(-0.677767\pi\)
0.469501 + 0.882932i \(0.344434\pi\)
\(368\) −21.8594 + 20.4592i −1.13950 + 1.06651i
\(369\) 5.86704 10.1620i 0.305426 0.529013i
\(370\) −10.5819 14.0293i −0.550128 0.729350i
\(371\) −1.01891 + 19.9975i −0.0528991 + 1.03822i
\(372\) 0.188535 + 1.64138i 0.00977508 + 0.0851015i
\(373\) −13.7943 17.9770i −0.714240 0.930816i 0.285379 0.958415i \(-0.407881\pi\)
−0.999619 + 0.0275989i \(0.991214\pi\)
\(374\) 2.44695 + 0.0202334i 0.126529 + 0.00104624i
\(375\) 0.0271406 0.101290i 0.00140153 0.00523059i
\(376\) 22.8759 16.6684i 1.17973 0.859605i
\(377\) −3.43887 + 3.43887i −0.177111 + 0.177111i
\(378\) −3.53547 + 1.22492i −0.181845 + 0.0630031i
\(379\) 3.44760 8.32324i 0.177091 0.427536i −0.810263 0.586067i \(-0.800676\pi\)
0.987354 + 0.158531i \(0.0506757\pi\)
\(380\) 19.1098 + 19.7525i 0.980311 + 1.01328i
\(381\) 4.26817 + 3.27508i 0.218665 + 0.167788i
\(382\) 9.49947 + 23.4810i 0.486035 + 1.20139i
\(383\) 5.87653 10.1784i 0.300277 0.520094i −0.675922 0.736973i \(-0.736254\pi\)
0.976198 + 0.216879i \(0.0695877\pi\)
\(384\) −9.45431 6.21417i −0.482463 0.317116i
\(385\) −17.6460 25.5954i −0.899325 1.30446i
\(386\) 4.63432 33.0848i 0.235880 1.68397i
\(387\) −1.47246 + 11.1845i −0.0748496 + 0.568539i
\(388\) −8.92693 + 2.23442i −0.453196 + 0.113436i
\(389\) −2.01293 15.2897i −0.102060 0.775220i −0.963566 0.267472i \(-0.913812\pi\)
0.861506 0.507747i \(-0.169522\pi\)
\(390\) 3.64181 13.1553i 0.184410 0.666146i
\(391\) −2.46870 2.46870i −0.124847 0.124847i
\(392\) −13.9400 + 14.0598i −0.704075 + 0.710125i
\(393\) 12.3782 12.3782i 0.624399 0.624399i
\(394\) 11.4718 + 20.2546i 0.577940 + 1.02041i
\(395\) 15.6488 2.06020i 0.787376 0.103660i
\(396\) −4.41867 5.96006i −0.222046 0.299504i
\(397\) 3.38342 + 0.445436i 0.169809 + 0.0223558i 0.214951 0.976625i \(-0.431041\pi\)
−0.0451421 + 0.998981i \(0.514374\pi\)
\(398\) −30.3487 + 22.8912i −1.52124 + 1.14743i
\(399\) 9.45005 6.51506i 0.473094 0.326161i
\(400\) −4.56474 19.6081i −0.228237 0.980405i
\(401\) 31.4665 + 18.1672i 1.57136 + 0.907227i 0.996002 + 0.0893276i \(0.0284718\pi\)
0.575361 + 0.817899i \(0.304862\pi\)
\(402\) 6.49354 + 2.75283i 0.323868 + 0.137299i
\(403\) −1.53241 + 1.99708i −0.0763349 + 0.0994815i
\(404\) −0.540816 1.36926i −0.0269066 0.0681233i
\(405\) −2.92640 1.21215i −0.145414 0.0602324i
\(406\) 5.37223 + 2.60752i 0.266620 + 0.129409i
\(407\) −10.2903 10.2903i −0.510070 0.510070i
\(408\) 0.687771 1.12581i 0.0340497 0.0557359i
\(409\) −25.2604 6.76849i −1.24904 0.334680i −0.427077 0.904215i \(-0.640457\pi\)
−0.821967 + 0.569535i \(0.807123\pi\)
\(410\) 37.4738 36.8592i 1.85070 1.82034i
\(411\) −0.519148 + 0.398356i −0.0256077 + 0.0196495i
\(412\) 9.00331 + 16.2074i 0.443561 + 0.798479i
\(413\) −5.97378 0.304375i −0.293951 0.0149773i
\(414\) −1.46841 + 10.4831i −0.0721683 + 0.515216i
\(415\) 42.5357 + 24.5580i 2.08800 + 1.20550i
\(416\) −3.76944 16.8205i −0.184812 0.824691i
\(417\) −8.34159 14.4481i −0.408489 0.707524i
\(418\) 17.9417 + 14.0044i 0.877558 + 0.684977i
\(419\) 0.755181 + 1.82317i 0.0368930 + 0.0890676i 0.941252 0.337705i \(-0.109651\pi\)
−0.904359 + 0.426772i \(0.859651\pi\)
\(420\) −16.7271 + 1.06284i −0.816201 + 0.0518614i
\(421\) −14.4168 5.97164i −0.702632 0.291040i 0.00261985 0.999997i \(-0.499166\pi\)
−0.705252 + 0.708957i \(0.749166\pi\)
\(422\) 3.43553 12.4102i 0.167239 0.604119i
\(423\) 2.59003 9.66613i 0.125932 0.469984i
\(424\) −6.05140 + 20.5328i −0.293882 + 0.997159i
\(425\) 2.26761 0.607605i 0.109995 0.0294732i
\(426\) −8.71030 + 14.8027i −0.422015 + 0.717191i
\(427\) 1.94869 + 0.630043i 0.0943040 + 0.0304899i
\(428\) 26.2752 + 20.8610i 1.27006 + 1.00835i
\(429\) 1.47549 11.2075i 0.0712375 0.541102i
\(430\) −19.7237 + 46.5254i −0.951163 + 2.24366i
\(431\) 15.5843 + 26.9928i 0.750670 + 1.30020i 0.947499 + 0.319760i \(0.103602\pi\)
−0.196829 + 0.980438i \(0.563064\pi\)
\(432\) −3.98088 + 0.390677i −0.191530 + 0.0187965i
\(433\) −3.42120 −0.164413 −0.0822063 0.996615i \(-0.526197\pi\)
−0.0822063 + 0.996615i \(0.526197\pi\)
\(434\) 2.93307 + 0.975166i 0.140792 + 0.0468095i
\(435\) 1.93457 + 4.67047i 0.0927556 + 0.223932i
\(436\) 6.06353 13.9802i 0.290390 0.669529i
\(437\) −4.23855 32.1950i −0.202757 1.54009i
\(438\) 0.0399950 4.83686i 0.00191104 0.231114i
\(439\) 4.00381 + 14.9424i 0.191091 + 0.713162i 0.993244 + 0.116043i \(0.0370212\pi\)
−0.802153 + 0.597119i \(0.796312\pi\)
\(440\) −11.9531 31.0114i −0.569841 1.47841i
\(441\) −0.711479 + 6.96375i −0.0338799 + 0.331607i
\(442\) 1.94580 0.504168i 0.0925521 0.0239808i
\(443\) −25.1790 32.8140i −1.19629 1.55904i −0.745656 0.666331i \(-0.767864\pi\)
−0.450636 0.892708i \(-0.648803\pi\)
\(444\) −7.61097 + 1.90504i −0.361201 + 0.0904090i
\(445\) 4.82158 6.28360i 0.228565 0.297871i
\(446\) 30.1325 + 23.5199i 1.42681 + 1.11370i
\(447\) −1.60672 −0.0759951
\(448\) −18.0004 + 11.1349i −0.850438 + 0.526075i
\(449\) −5.00521 −0.236211 −0.118105 0.993001i \(-0.537682\pi\)
−0.118105 + 0.993001i \(0.537682\pi\)
\(450\) −5.61098 4.37964i −0.264504 0.206458i
\(451\) 26.4992 34.5344i 1.24780 1.62616i
\(452\) −32.2235 + 8.06557i −1.51566 + 0.379373i
\(453\) −0.732248 0.954284i −0.0344040 0.0448362i
\(454\) 1.08390 0.280844i 0.0508697 0.0131807i
\(455\) −19.4426 16.5567i −0.911481 0.776192i
\(456\) 11.4497 4.41317i 0.536179 0.206666i
\(457\) 8.32557 + 31.0715i 0.389454 + 1.45346i 0.831025 + 0.556235i \(0.187755\pi\)
−0.441571 + 0.897226i \(0.645579\pi\)
\(458\) −0.00713247 + 0.862577i −0.000333279 + 0.0403056i
\(459\) −0.0608817 0.462443i −0.00284172 0.0215850i
\(460\) −18.8680 + 43.5023i −0.879724 + 2.02831i
\(461\) −3.57812 8.63835i −0.166650 0.402328i 0.818388 0.574666i \(-0.194868\pi\)
−0.985038 + 0.172338i \(0.944868\pi\)
\(462\) −13.5964 + 2.79327i −0.632561 + 0.129955i
\(463\) −10.0089 −0.465155 −0.232578 0.972578i \(-0.574716\pi\)
−0.232578 + 0.972578i \(0.574716\pi\)
\(464\) 4.93342 + 4.05164i 0.229028 + 0.188093i
\(465\) 1.30832 + 2.26607i 0.0606717 + 0.105087i
\(466\) 8.85322 20.8835i 0.410117 0.967408i
\(467\) −4.40675 + 33.4726i −0.203920 + 1.54893i 0.517047 + 0.855957i \(0.327031\pi\)
−0.720967 + 0.692969i \(0.756302\pi\)
\(468\) −4.77303 3.78950i −0.220633 0.175170i
\(469\) 9.79287 8.84332i 0.452192 0.408346i
\(470\) 22.7338 38.6349i 1.04863 1.78209i
\(471\) −8.87523 + 2.37811i −0.408949 + 0.109578i
\(472\) −6.13369 1.80772i −0.282326 0.0832069i
\(473\) −10.8313 + 40.4229i −0.498023 + 1.85865i
\(474\) 1.88014 6.79165i 0.0863577 0.311951i
\(475\) 20.1733 + 8.35605i 0.925614 + 0.383402i
\(476\) −1.36712 2.05491i −0.0626620 0.0941865i
\(477\) 2.89620 + 6.99205i 0.132608 + 0.320144i
\(478\) 31.0700 + 24.2517i 1.42111 + 1.10925i
\(479\) 9.11622 + 15.7897i 0.416531 + 0.721452i 0.995588 0.0938348i \(-0.0299126\pi\)
−0.579057 + 0.815287i \(0.696579\pi\)
\(480\) −17.6530 3.07103i −0.805745 0.140173i
\(481\) −10.3524 5.97693i −0.472027 0.272525i
\(482\) −1.20640 + 8.61259i −0.0549499 + 0.392293i
\(483\) 16.6243 + 10.7617i 0.756432 + 0.489672i
\(484\) −2.68224 4.82846i −0.121920 0.219475i
\(485\) −11.5625 + 8.87222i −0.525026 + 0.402867i
\(486\) −1.00823 + 0.991697i −0.0457344 + 0.0449843i
\(487\) −1.72314 0.461715i −0.0780831 0.0209223i 0.219566 0.975598i \(-0.429536\pi\)
−0.297649 + 0.954675i \(0.596203\pi\)
\(488\) 1.86836 + 1.14140i 0.0845766 + 0.0516689i
\(489\) −9.50831 9.50831i −0.429981 0.429981i
\(490\) −11.3941 + 29.2133i −0.514734 + 1.31972i
\(491\) −10.4516 4.32920i −0.471675 0.195374i 0.134168 0.990959i \(-0.457164\pi\)
−0.605843 + 0.795585i \(0.707164\pi\)
\(492\) −8.62110 21.8273i −0.388669 0.984050i
\(493\) −0.453172 + 0.590586i −0.0204099 + 0.0265987i
\(494\) 17.2129 + 7.29714i 0.774445 + 0.328314i
\(495\) −10.1762 5.87522i −0.457385 0.264071i
\(496\) 2.80545 + 1.74590i 0.125968 + 0.0783931i
\(497\) 18.2381 + 26.4543i 0.818092 + 1.18664i
\(498\) 17.5073 13.2053i 0.784520 0.591742i
\(499\) 15.2937 + 2.01345i 0.684639 + 0.0901344i 0.464819 0.885406i \(-0.346120\pi\)
0.219820 + 0.975540i \(0.429453\pi\)
\(500\) −0.124904 0.168476i −0.00558589 0.00753446i
\(501\) 14.3766 1.89272i 0.642300 0.0845604i
\(502\) 8.56167 + 15.1165i 0.382126 + 0.674685i
\(503\) −18.9185 + 18.9185i −0.843535 + 0.843535i −0.989317 0.145782i \(-0.953430\pi\)
0.145782 + 0.989317i \(0.453430\pi\)
\(504\) −2.47804 + 7.06111i −0.110380 + 0.314527i
\(505\) −1.64869 1.64869i −0.0733656 0.0733656i
\(506\) −10.4767 + 37.8452i −0.465748 + 1.68243i
\(507\) 0.484836 + 3.68270i 0.0215323 + 0.163554i
\(508\) 10.4378 2.61260i 0.463104 0.115915i
\(509\) −0.592397 + 4.49970i −0.0262575 + 0.199446i −0.999546 0.0301414i \(-0.990404\pi\)
0.973288 + 0.229587i \(0.0737376\pi\)
\(510\) 0.289841 2.06920i 0.0128344 0.0916257i
\(511\) −8.17337 3.88394i −0.361569 0.171815i
\(512\) −21.4909 + 7.08091i −0.949775 + 0.312935i
\(513\) 2.16918 3.75713i 0.0957716 0.165881i
\(514\) −7.48270 18.4959i −0.330048 0.815821i
\(515\) 23.2953 + 17.8751i 1.02651 + 0.787671i
\(516\) 15.6877 + 16.2154i 0.690614 + 0.713842i
\(517\) 14.2064 34.2974i 0.624798 1.50840i
\(518\) −2.77318 + 14.4137i −0.121847 + 0.633303i
\(519\) −12.4091 + 12.4091i −0.544698 + 0.544698i
\(520\) −16.0770 22.0643i −0.705023 0.967582i
\(521\) −8.02383 + 29.9453i −0.351530 + 1.31193i 0.533264 + 0.845949i \(0.320965\pi\)
−0.884795 + 0.465981i \(0.845702\pi\)
\(522\) 2.25698 + 0.0186625i 0.0987852 + 0.000816835i
\(523\) 22.8670 + 29.8008i 0.999903 + 1.30310i 0.952602 + 0.304219i \(0.0983954\pi\)
0.0473014 + 0.998881i \(0.484938\pi\)
\(524\) −3.99521 34.7822i −0.174532 1.51947i
\(525\) −11.8562 + 6.06272i −0.517445 + 0.264599i
\(526\) −4.74236 6.28734i −0.206777 0.274141i
\(527\) −0.192657 + 0.333691i −0.00839226 + 0.0145358i
\(528\) −14.8306 0.490693i −0.645419 0.0213547i
\(529\) 28.6012 16.5129i 1.24353 0.717952i
\(530\) 4.14699 + 33.6471i 0.180134 + 1.46154i
\(531\) −2.08871 + 0.865173i −0.0906424 + 0.0375453i
\(532\) 1.54712 22.9042i 0.0670763 0.993024i
\(533\) 13.6833 33.0345i 0.592691 1.43088i
\(534\) −1.74273 3.07697i −0.0754152 0.133154i
\(535\) 51.3236 + 13.7521i 2.21891 + 0.594556i
\(536\) 12.3872 6.74778i 0.535048 0.291460i
\(537\) −3.14711 11.7452i −0.135808 0.506841i
\(538\) 29.3598 7.60732i 1.26579 0.327975i
\(539\) −5.98870 + 25.2678i −0.257951 + 1.08836i
\(540\) −5.53791 + 3.07635i −0.238314 + 0.132385i
\(541\) −0.271734 0.0357744i −0.0116827 0.00153806i 0.124683 0.992197i \(-0.460209\pi\)
−0.136365 + 0.990659i \(0.543542\pi\)
\(542\) −4.36438 10.7880i −0.187466 0.463384i
\(543\) 4.25201 2.45490i 0.182471 0.105350i
\(544\) −0.908111 2.47735i −0.0389349 0.106215i
\(545\) 24.1340i 1.03379i
\(546\) −10.1940 + 5.10687i −0.436262 + 0.218554i
\(547\) 11.9152 4.93545i 0.509458 0.211025i −0.113121 0.993581i \(-0.536085\pi\)
0.622579 + 0.782557i \(0.286085\pi\)
\(548\) −0.0216420 + 1.30856i −0.000924500 + 0.0558991i
\(549\) 0.767455 0.101037i 0.0327542 0.00431217i
\(550\) −18.5162 18.8250i −0.789533 0.802699i
\(551\) −6.68800 + 1.79204i −0.284918 + 0.0763436i
\(552\) 14.5942 + 15.3368i 0.621169 + 0.652777i
\(553\) −10.0375 8.54768i −0.426839 0.363484i
\(554\) 7.60214 + 4.47331i 0.322984 + 0.190053i
\(555\) −9.85802 + 7.56432i −0.418450 + 0.321088i
\(556\) −33.0044 4.90163i −1.39970 0.207875i
\(557\) 27.1364 + 20.8225i 1.14981 + 0.882278i 0.994411 0.105574i \(-0.0336679\pi\)
0.155396 + 0.987852i \(0.450335\pi\)
\(558\) 1.15949 0.142906i 0.0490851 0.00604971i
\(559\) 34.3756i 1.45393i
\(560\) −19.1370 + 27.5224i −0.808686 + 1.16303i
\(561\) 1.73032i 0.0730540i
\(562\) −4.47577 36.3147i −0.188799 1.53184i
\(563\) −11.5927 8.89540i −0.488574 0.374896i 0.334896 0.942255i \(-0.391299\pi\)
−0.823471 + 0.567359i \(0.807965\pi\)
\(564\) −11.9197 16.0777i −0.501908 0.676992i
\(565\) −41.7371 + 32.0260i −1.75589 + 1.34734i
\(566\) 11.6019 19.7168i 0.487664 0.828757i
\(567\) 0.886790 + 2.49271i 0.0372417 + 0.104684i
\(568\) 12.3541 + 32.0519i 0.518368 + 1.34487i
\(569\) −28.2934 + 7.58118i −1.18612 + 0.317820i −0.797351 0.603516i \(-0.793766\pi\)
−0.388768 + 0.921336i \(0.627099\pi\)
\(570\) 13.8549 13.6277i 0.580319 0.570801i
\(571\) −41.5886 + 5.47524i −1.74043 + 0.229132i −0.932758 0.360502i \(-0.882605\pi\)
−0.807671 + 0.589634i \(0.799272\pi\)
\(572\) −15.7200 16.2487i −0.657286 0.679393i
\(573\) 16.5475 6.85419i 0.691281 0.286338i
\(574\) −43.8280 2.59662i −1.82935 0.108381i
\(575\) 37.6730i 1.57107i
\(576\) −4.33866 + 6.72131i −0.180777 + 0.280055i
\(577\) −24.6708 + 14.2437i −1.02706 + 0.592973i −0.916141 0.400856i \(-0.868713\pi\)
−0.110919 + 0.993829i \(0.535379\pi\)
\(578\) −22.0017 + 8.90097i −0.915149 + 0.370232i
\(579\) −23.4208 3.08341i −0.973335 0.128142i
\(580\) 9.72144 + 2.77794i 0.403661 + 0.115348i
\(581\) −8.58795 40.1166i −0.356288 1.66432i
\(582\) 1.63211 + 6.29901i 0.0676533 + 0.261102i
\(583\) 7.26644 + 27.1187i 0.300945 + 1.12314i
\(584\) −7.52651 6.07775i −0.311449 0.251499i
\(585\) −9.32319 2.49814i −0.385467 0.103285i
\(586\) −4.11839 + 2.33256i −0.170129 + 0.0963573i
\(587\) −13.5181 + 32.6357i −0.557953 + 1.34702i 0.353430 + 0.935461i \(0.385015\pi\)
−0.911384 + 0.411558i \(0.864985\pi\)
\(588\) 10.0229 + 9.77451i 0.413338 + 0.403094i
\(589\) −3.31105 + 1.37148i −0.136429 + 0.0565109i
\(590\) −10.0513 + 1.23882i −0.413806 + 0.0510014i
\(591\) 14.2546 8.22991i 0.586357 0.338533i
\(592\) −6.48100 + 14.2906i −0.266367 + 0.587339i
\(593\) 18.1975 31.5190i 0.747281 1.29433i −0.201840 0.979419i \(-0.564692\pi\)
0.949121 0.314911i \(-0.101975\pi\)
\(594\) −4.18842 + 3.15921i −0.171853 + 0.129624i
\(595\) −3.28138 2.12418i −0.134523 0.0870830i
\(596\) −1.99810 + 2.51669i −0.0818455 + 0.103088i
\(597\) 16.3634 + 21.3252i 0.669710 + 0.872783i
\(598\) −0.266710 + 32.2550i −0.0109066 + 1.31901i
\(599\) −2.57485 + 9.60947i −0.105206 + 0.392632i −0.998368 0.0571010i \(-0.981814\pi\)
0.893163 + 0.449733i \(0.148481\pi\)
\(600\) −13.8379 + 3.34229i −0.564928 + 0.136449i
\(601\) 27.1957 27.1957i 1.10934 1.10934i 0.116098 0.993238i \(-0.462961\pi\)
0.993238 0.116098i \(-0.0370386\pi\)
\(602\) 39.8836 13.8183i 1.62554 0.563192i
\(603\) 1.90852 4.60756i 0.0777207 0.187634i
\(604\) −2.40537 0.0397817i −0.0978730 0.00161869i
\(605\) −6.94007 5.32531i −0.282154 0.216504i
\(606\) −0.965019 + 0.390407i −0.0392012 + 0.0158592i
\(607\) −4.52040 + 7.82957i −0.183477 + 0.317792i −0.943062 0.332616i \(-0.892069\pi\)
0.759585 + 0.650408i \(0.225402\pi\)
\(608\) 7.32613 23.4224i 0.297114 0.949905i
\(609\) 1.81232 3.81386i 0.0734391 0.154545i
\(610\) 3.43398 + 0.481010i 0.139038 + 0.0194755i
\(611\) 3.98025 30.2330i 0.161024 1.22310i
\(612\) −0.800062 0.479729i −0.0323406 0.0193919i
\(613\) 1.18201 + 8.97827i 0.0477410 + 0.362629i 0.998595 + 0.0529895i \(0.0168750\pi\)
−0.950854 + 0.309639i \(0.899792\pi\)
\(614\) −22.6160 6.26081i −0.912706 0.252666i
\(615\) −26.2816 26.2816i −1.05978 1.05978i
\(616\) −12.5331 + 24.7705i −0.504975 + 0.998031i
\(617\) −9.02914 + 9.02914i −0.363500 + 0.363500i −0.865100 0.501600i \(-0.832745\pi\)
0.501600 + 0.865100i \(0.332745\pi\)
\(618\) 11.4073 6.46084i 0.458869 0.259893i
\(619\) 12.6268 1.66235i 0.507514 0.0668155i 0.127579 0.991828i \(-0.459279\pi\)
0.379936 + 0.925013i \(0.375946\pi\)
\(620\) 5.17649 + 0.768784i 0.207893 + 0.0308751i
\(621\) 7.42100 + 0.976993i 0.297795 + 0.0392054i
\(622\) −6.42822 8.52241i −0.257748 0.341718i
\(623\) −6.59451 + 0.528635i −0.264203 + 0.0211793i
\(624\) −11.8714 + 2.76365i −0.475237 + 0.110635i
\(625\) 21.5063 + 12.4167i 0.860253 + 0.496667i
\(626\) −7.11247 + 16.7773i −0.284271 + 0.670555i
\(627\) 9.79735 12.7682i 0.391269 0.509911i
\(628\) −7.31222 + 16.8592i −0.291790 + 0.672755i
\(629\) −1.69048 0.700219i −0.0674038 0.0279196i
\(630\) 0.849316 + 11.8213i 0.0338376 + 0.470970i
\(631\) 6.64665 + 6.64665i 0.264599 + 0.264599i 0.826919 0.562321i \(-0.190091\pi\)
−0.562321 + 0.826919i \(0.690091\pi\)
\(632\) −8.30000 11.3910i −0.330156 0.453111i
\(633\) −8.79513 2.35665i −0.349575 0.0936683i
\(634\) 15.0354 + 15.2862i 0.597134 + 0.607091i
\(635\) 13.5195 10.3739i 0.536504 0.411674i
\(636\) 14.5537 + 4.15879i 0.577093 + 0.164907i
\(637\) 0.620290 + 21.3215i 0.0245768 + 0.844788i
\(638\) 8.29200 + 1.16149i 0.328283 + 0.0459839i
\(639\) 10.5176 + 6.07235i 0.416071 + 0.240219i
\(640\) −26.7635 + 23.8318i −1.05792 + 0.942033i
\(641\) 6.67028 + 11.5533i 0.263460 + 0.456326i 0.967159 0.254172i \(-0.0818029\pi\)
−0.703699 + 0.710498i \(0.748470\pi\)
\(642\) 14.5968 18.7007i 0.576090 0.738058i
\(643\) 15.4271 + 37.2444i 0.608387 + 1.46878i 0.864754 + 0.502196i \(0.167475\pi\)
−0.256367 + 0.966580i \(0.582525\pi\)
\(644\) 37.5305 12.6564i 1.47891 0.498733i
\(645\) 33.0126 + 13.6743i 1.29987 + 0.538424i
\(646\) 2.75801 + 0.763502i 0.108512 + 0.0300396i
\(647\) 3.89071 14.5203i 0.152959 0.570853i −0.846312 0.532688i \(-0.821182\pi\)
0.999271 0.0381650i \(-0.0121512\pi\)
\(648\) 0.299516 + 2.81252i 0.0117661 + 0.110486i
\(649\) −8.10109 + 2.17068i −0.317996 + 0.0852067i
\(650\) −18.6936 10.9998i −0.733221 0.431448i
\(651\) 0.672374 2.07962i 0.0263524 0.0815069i
\(652\) −26.7179 + 3.06892i −1.04635 + 0.120188i
\(653\) −1.15252 + 8.75425i −0.0451015 + 0.342580i 0.953985 + 0.299853i \(0.0969378\pi\)
−0.999087 + 0.0427266i \(0.986396\pi\)
\(654\) −9.92058 4.20568i −0.387926 0.164455i
\(655\) −27.7243 48.0199i −1.08328 1.87629i
\(656\) −44.9105 13.6406i −1.75346 0.532575i
\(657\) −3.42030 −0.133438
\(658\) −36.6772 + 7.53505i −1.42983 + 0.293747i
\(659\) −3.22414 7.78377i −0.125595 0.303213i 0.848558 0.529102i \(-0.177471\pi\)
−0.974153 + 0.225890i \(0.927471\pi\)
\(660\) −21.8577 + 8.63313i −0.850811 + 0.336044i
\(661\) −0.584778 4.44183i −0.0227452 0.172767i 0.976302 0.216413i \(-0.0694359\pi\)
−0.999047 + 0.0436463i \(0.986103\pi\)
\(662\) 33.3432 + 0.275708i 1.29592 + 0.0107157i
\(663\) −0.367865 1.37289i −0.0142867 0.0533187i
\(664\) 1.08783 43.8446i 0.0422158 1.70150i
\(665\) −12.1861 34.2543i −0.472556 1.32832i
\(666\) 1.39152 + 5.37045i 0.0539202 + 0.208101i
\(667\) −7.27224 9.47737i −0.281582 0.366965i
\(668\) 14.9140 24.8727i 0.577041 0.962353i
\(669\) 16.4543 21.4437i 0.636160 0.829060i
\(670\) 13.7460 17.6107i 0.531054 0.680360i
\(671\) 2.87158 0.110856
\(672\) 7.97855 + 12.6627i 0.307779 + 0.488472i
\(673\) 26.2098 1.01031 0.505156 0.863028i \(-0.331435\pi\)
0.505156 + 0.863028i \(0.331435\pi\)
\(674\) 6.25038 8.00768i 0.240756 0.308444i
\(675\) −3.06396 + 3.99303i −0.117932 + 0.153692i
\(676\) 6.37135 + 3.82036i 0.245052 + 0.146937i
\(677\) 11.7733 + 15.3432i 0.452483 + 0.589688i 0.962772 0.270316i \(-0.0871280\pi\)
−0.510288 + 0.860003i \(0.670461\pi\)
\(678\) 5.89143 + 22.7375i 0.226259 + 0.873228i
\(679\) 11.9729 + 2.20107i 0.459477 + 0.0844692i
\(680\) −2.88066 3.02724i −0.110468 0.116089i
\(681\) −0.204917 0.764762i −0.00785245 0.0293057i
\(682\) 4.33373 + 0.0358347i 0.165947 + 0.00137218i
\(683\) −0.683678 5.19305i −0.0261602 0.198707i 0.973374 0.229222i \(-0.0736183\pi\)
−0.999534 + 0.0305158i \(0.990285\pi\)
\(684\) −3.18742 8.07005i −0.121874 0.308566i
\(685\) 0.793198 + 1.91495i 0.0303066 + 0.0731665i
\(686\) 24.4885 9.29049i 0.934975 0.354713i
\(687\) 0.609955 0.0232712
\(688\) 44.9082 4.40723i 1.71211 0.168024i
\(689\) 11.5309 + 19.9721i 0.439291 + 0.760875i
\(690\) 30.8700 + 13.0869i 1.17520 + 0.498209i
\(691\) −0.503824 + 3.82692i −0.0191664 + 0.145583i −0.998352 0.0573824i \(-0.981725\pi\)
0.979186 + 0.202965i \(0.0650579\pi\)
\(692\) 4.00517 + 34.8689i 0.152254 + 1.32552i
\(693\) 2.05457 + 9.59744i 0.0780466 + 0.364576i
\(694\) −25.2547 14.8606i −0.958655 0.564099i
\(695\) −51.0435 + 13.6771i −1.93619 + 0.518800i
\(696\) 2.83600 3.51202i 0.107498 0.133123i
\(697\) 1.41656 5.28667i 0.0536559 0.200247i
\(698\) −49.0881 13.5891i −1.85801 0.514356i
\(699\) −14.8181 6.13785i −0.560472 0.232155i
\(700\) −5.24789 + 26.1105i −0.198351 + 0.986885i
\(701\) 14.6502 + 35.3687i 0.553330 + 1.33586i 0.914964 + 0.403536i \(0.132219\pi\)
−0.361634 + 0.932320i \(0.617781\pi\)
\(702\) −2.65158 + 3.39708i −0.100078 + 0.128215i
\(703\) −8.50943 14.7388i −0.320939 0.555883i
\(704\) −19.2119 + 22.6198i −0.724074 + 0.852515i
\(705\) −27.4509 15.8488i −1.03386 0.596901i
\(706\) −27.8273 3.89787i −1.04729 0.146698i
\(707\) −0.0991018 + 1.94501i −0.00372711 + 0.0731495i
\(708\) −1.24234 + 4.34759i −0.0466901 + 0.163393i
\(709\) −36.3802 + 27.9155i −1.36629 + 1.04839i −0.373610 + 0.927586i \(0.621880\pi\)
−0.992677 + 0.120803i \(0.961453\pi\)
\(710\) 38.1491 + 38.7852i 1.43171 + 1.45558i
\(711\) −4.81325 1.28971i −0.180511 0.0483678i
\(712\) −6.98688 1.09677i −0.261844 0.0411033i
\(713\) −4.37224 4.37224i −0.163742 0.163742i
\(714\) −1.44500 + 0.978683i −0.0540776 + 0.0366263i
\(715\) −33.0805 13.7024i −1.23714 0.512441i
\(716\) −22.3108 9.67674i −0.833795 0.361637i
\(717\) 16.9663 22.1109i 0.633617 0.825746i
\(718\) −8.74269 + 20.6227i −0.326274 + 0.769634i
\(719\) −3.40386 1.96522i −0.126943 0.0732904i 0.435184 0.900342i \(-0.356683\pi\)
−0.562127 + 0.827051i \(0.690017\pi\)
\(720\) −2.06826 + 12.5001i −0.0770795 + 0.465850i
\(721\) −1.95982 24.4479i −0.0729874 0.910488i
\(722\) −0.152151 0.201719i −0.00566248 0.00750720i
\(723\) 6.09686 + 0.802667i 0.226745 + 0.0298515i
\(724\) 1.44253 9.71306i 0.0536113 0.360983i
\(725\) 7.96401 1.04848i 0.295776 0.0389396i
\(726\) −3.39843 + 1.92480i −0.126128 + 0.0714359i
\(727\) 24.7945 24.7945i 0.919577 0.919577i −0.0774211 0.996998i \(-0.524669\pi\)
0.996998 + 0.0774211i \(0.0246686\pi\)
\(728\) −4.67801 + 22.3183i −0.173379 + 0.827170i
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) −14.7660 4.08768i −0.546513 0.151292i
\(731\) 0.686806 + 5.21681i 0.0254024 + 0.192951i
\(732\) 0.796142 1.32776i 0.0294263 0.0490753i
\(733\) 3.93003 29.8515i 0.145159 1.10259i −0.751457 0.659782i \(-0.770648\pi\)
0.896616 0.442810i \(-0.146018\pi\)
\(734\) 1.87096 + 0.262073i 0.0690585 + 0.00967328i
\(735\) 20.7229 + 7.88579i 0.764374 + 0.290872i
\(736\) 42.1721 3.78692i 1.55448 0.139588i
\(737\) 9.25044 16.0222i 0.340744 0.590186i
\(738\) −15.3833 + 6.22345i −0.566267 + 0.229088i
\(739\) −26.9817 20.7038i −0.992540 0.761602i −0.0213163 0.999773i \(-0.506786\pi\)
−0.971223 + 0.238170i \(0.923452\pi\)
\(740\) −0.410956 + 24.8481i −0.0151070 + 0.913435i
\(741\) 5.05904 12.2136i 0.185848 0.448678i
\(742\) 18.5370 21.4068i 0.680515 0.785870i
\(743\) 1.23986 1.23986i 0.0454862 0.0454862i −0.683998 0.729484i \(-0.739760\pi\)
0.729484 + 0.683998i \(0.239760\pi\)
\(744\) 1.21809 1.99389i 0.0446574 0.0730995i
\(745\) −1.31720 + 4.91587i −0.0482586 + 0.180104i
\(746\) −0.264968 + 32.0444i −0.00970118 + 1.17323i
\(747\) −9.43957 12.3019i −0.345376 0.450103i
\(748\) −2.71029 2.15181i −0.0990981 0.0786781i
\(749\) −20.2063 39.5151i −0.738322 1.44385i
\(750\) −0.118396 + 0.0893027i −0.00432321 + 0.00326088i
\(751\) −10.2201 + 17.7018i −0.372938 + 0.645948i −0.990016 0.140954i \(-0.954983\pi\)
0.617078 + 0.786902i \(0.288316\pi\)
\(752\) −40.0066 1.32368i −1.45889 0.0482695i
\(753\) 10.6386 6.14219i 0.387692 0.223834i
\(754\) 6.82608 0.841312i 0.248591 0.0306388i
\(755\) −3.52001 + 1.45804i −0.128106 + 0.0530634i
\(756\) 5.00728 + 1.71089i 0.182113 + 0.0622245i
\(757\) 6.54327 15.7969i 0.237819 0.574147i −0.759237 0.650814i \(-0.774428\pi\)
0.997057 + 0.0766671i \(0.0244279\pi\)
\(758\) −11.0860 + 6.27888i −0.402663 + 0.228059i
\(759\) 26.8209 + 7.18665i 0.973539 + 0.260859i
\(760\) −4.11588 38.6491i −0.149299 1.40195i
\(761\) −4.44578 16.5919i −0.161159 0.601454i −0.998499 0.0547715i \(-0.982557\pi\)
0.837340 0.546683i \(-0.184110\pi\)
\(762\) −1.90835 7.36513i −0.0691323 0.266811i
\(763\) −14.9612 + 13.5105i −0.541631 + 0.489113i
\(764\) 9.84226 34.4431i 0.356081 1.24611i
\(765\) −1.46479 0.192843i −0.0529596 0.00697226i
\(766\) −15.4082 + 6.23352i −0.556720 + 0.225226i
\(767\) −5.96619 + 3.44458i −0.215427 + 0.124377i
\(768\) 5.13244 + 15.1545i 0.185201 + 0.546840i
\(769\) 35.2927i 1.27269i −0.771405 0.636344i \(-0.780446\pi\)
0.771405 0.636344i \(-0.219554\pi\)
\(770\) −2.60024 + 43.8892i −0.0937061 + 1.58166i
\(771\) −13.0344 + 5.39903i −0.469423 + 0.194441i
\(772\) −33.9557 + 32.8508i −1.22209 + 1.18233i
\(773\) 9.02181 1.18774i 0.324492 0.0427202i 0.0334795 0.999439i \(-0.489341\pi\)
0.291013 + 0.956719i \(0.406008\pi\)
\(774\) 11.3739 11.1873i 0.408826 0.402120i
\(775\) 4.01610 1.07611i 0.144263 0.0386551i
\(776\) 11.8962 + 5.27695i 0.427048 + 0.189431i
\(777\) 10.2079 + 1.87660i 0.366207 + 0.0673225i
\(778\) −11.0606 + 18.7968i −0.396540 + 0.673897i
\(779\) 40.3869 30.9900i 1.44701 1.11033i
\(780\) −15.5073 + 11.4968i −0.555249 + 0.411650i
\(781\) 35.7429 + 27.4265i 1.27898 + 0.981398i
\(782\) 0.603962 + 4.90032i 0.0215976 + 0.175235i
\(783\) 1.59598i 0.0570356i
\(784\) 27.7748 3.54393i 0.991958 0.126569i
\(785\) 29.1041i 1.03877i
\(786\) −24.5705 + 3.02831i −0.876402 + 0.108016i
\(787\) −6.15820 4.72535i −0.219516 0.168441i 0.493149 0.869945i \(-0.335846\pi\)
−0.712665 + 0.701504i \(0.752512\pi\)
\(788\) 4.83601 32.5625i 0.172276 1.15999i
\(789\) −4.41794 + 3.39000i −0.157283 + 0.120687i
\(790\) −19.2382 11.3203i −0.684465 0.402758i
\(791\) 43.2184 + 7.94517i 1.53667 + 0.282498i
\(792\) −0.260250 + 10.4893i −0.00924757 + 0.372722i
\(793\) 2.27841 0.610497i 0.0809086 0.0216794i
\(794\) −3.38428 3.44072i −0.120104 0.122107i
\(795\) 23.7671 3.12899i 0.842931 0.110974i
\(796\) 53.7524 + 0.888995i 1.90520 + 0.0315096i
\(797\) 30.1015 12.4684i 1.06625 0.441655i 0.220584 0.975368i \(-0.429204\pi\)
0.845666 + 0.533713i \(0.179204\pi\)
\(798\) −16.2042 0.960030i −0.573624 0.0339847i
\(799\) 4.66765i 0.165130i
\(800\) −11.9735 + 25.8315i −0.423326 + 0.913281i
\(801\) −2.16548 + 1.25024i −0.0765136 + 0.0441752i
\(802\) −19.2708 47.6342i −0.680477 1.68202i
\(803\) −12.5797 1.65614i −0.443926 0.0584440i
\(804\) −4.84367 8.71936i −0.170823 0.307508i
\(805\) 46.5549 42.0408i 1.64085 1.48174i
\(806\) 3.44614 0.892918i 0.121385 0.0314517i
\(807\) −5.55066 20.7154i −0.195393 0.729215i
\(808\) −0.588576 + 1.99707i −0.0207060 + 0.0702567i
\(809\) −23.8221 6.38313i −0.837542 0.224419i −0.185541 0.982637i \(-0.559404\pi\)
−0.652001 + 0.758218i \(0.726070\pi\)
\(810\) 2.20761 + 3.89778i 0.0775676 + 0.136954i
\(811\) −11.1997 + 27.0384i −0.393274 + 0.949448i 0.595948 + 0.803023i \(0.296777\pi\)
−0.989222 + 0.146425i \(0.953223\pi\)
\(812\) −3.72006 7.58164i −0.130549 0.266063i
\(813\) −7.60248 + 3.14905i −0.266631 + 0.110442i
\(814\) 2.51749 + 20.4260i 0.0882381 + 0.715930i
\(815\) −36.8864 + 21.2964i −1.29208 + 0.745980i
\(816\) −1.74638 + 0.656594i −0.0611355 + 0.0229854i
\(817\) −24.4705 + 42.3841i −0.856114 + 1.48283i
\(818\) 22.2709 + 29.5263i 0.778683 + 1.03236i
\(819\) 3.67058 + 7.17813i 0.128260 + 0.250824i
\(820\) −73.8500 + 8.48268i −2.57895 + 0.296228i
\(821\) 15.4289 + 20.1073i 0.538472 + 0.701751i 0.980781 0.195112i \(-0.0625070\pi\)
−0.442308 + 0.896863i \(0.645840\pi\)
\(822\) 0.925390 + 0.00765186i 0.0322767 + 0.000266889i
\(823\) 10.4431 38.9742i 0.364024 1.35856i −0.504715 0.863286i \(-0.668402\pi\)
0.868739 0.495270i \(-0.164931\pi\)
\(824\) 4.06609 25.9026i 0.141649 0.902359i
\(825\) −13.2025 + 13.2025i −0.459653 + 0.459653i
\(826\) 6.39480 + 5.53751i 0.222504 + 0.192675i
\(827\) −1.19155 + 2.87666i −0.0414342 + 0.100031i −0.943242 0.332107i \(-0.892241\pi\)
0.901808 + 0.432138i \(0.142241\pi\)
\(828\) 10.7590 10.4089i 0.373902 0.361736i
\(829\) 36.5604 + 28.0537i 1.26979 + 0.974347i 0.999934 + 0.0114472i \(0.00364383\pi\)
0.269859 + 0.962900i \(0.413023\pi\)
\(830\) −26.0499 64.3907i −0.904204 2.23503i
\(831\) 3.11855 5.40149i 0.108181 0.187376i
\(832\) −10.4344 + 22.0317i −0.361747 + 0.763813i
\(833\) 0.520126 + 3.22334i 0.0180213 + 0.111682i
\(834\) −3.27289 + 23.3655i −0.113331 + 0.809080i
\(835\) 5.99520 45.5380i 0.207472 1.57591i
\(836\) −7.81555 31.2246i −0.270306 1.07992i
\(837\) −0.107826 0.819019i −0.00372701 0.0283094i
\(838\) 0.744573 2.68963i 0.0257208 0.0929116i
\(839\) 18.6831 + 18.6831i 0.645014 + 0.645014i 0.951784 0.306770i \(-0.0992482\pi\)
−0.306770 + 0.951784i \(0.599248\pi\)
\(840\) 19.5725 + 13.3705i 0.675316 + 0.461327i
\(841\) 18.7050 18.7050i 0.645000 0.645000i
\(842\) 10.8757 + 19.2023i 0.374803 + 0.661754i
\(843\) −25.6513 + 3.37706i −0.883478 + 0.116312i
\(844\) −14.6289 + 10.8456i −0.503548 + 0.373320i
\(845\) 11.6650 + 1.53572i 0.401287 + 0.0528305i
\(846\) −11.2985 + 8.52218i −0.388452 + 0.292999i
\(847\) 0.583863 + 7.28346i 0.0200618 + 0.250263i
\(848\) 24.6131 17.6245i 0.845218 0.605227i
\(849\) −14.0092 8.08822i −0.480795 0.277587i
\(850\) −3.05669 1.29583i −0.104843 0.0444467i
\(851\) 17.8750 23.2952i 0.612748 0.798548i
\(852\) 22.5911 8.92280i 0.773959 0.305690i
\(853\) −30.9157 12.8057i −1.05853 0.438459i −0.215602 0.976481i \(-0.569171\pi\)
−0.842930 + 0.538023i \(0.819171\pi\)
\(854\) −1.62419 2.39807i −0.0555787 0.0820602i
\(855\) −9.71690 9.71690i −0.332311 0.332311i
\(856\) −11.1395 46.1199i −0.380739 1.57635i
\(857\) −15.6044 4.18120i −0.533037 0.142827i −0.0177469 0.999843i \(-0.505649\pi\)
−0.515291 + 0.857016i \(0.672316\pi\)
\(858\) −11.3973 + 11.2103i −0.389097 + 0.382715i
\(859\) 26.8625 20.6123i 0.916536 0.703283i −0.0386614 0.999252i \(-0.512309\pi\)
0.955197 + 0.295970i \(0.0956427\pi\)
\(860\) 62.4731 34.7043i 2.13032 1.18341i
\(861\) −1.57977 + 31.0052i −0.0538385 + 1.05666i
\(862\) 6.11463 43.6529i 0.208265 1.48682i
\(863\) 5.25281 + 3.03271i 0.178808 + 0.103235i 0.586732 0.809781i \(-0.300414\pi\)
−0.407925 + 0.913016i \(0.633747\pi\)
\(864\) 4.77789 + 3.02849i 0.162547 + 0.103031i
\(865\) 27.7934 + 48.1396i 0.945005 + 1.63680i
\(866\) 3.81401 + 2.97702i 0.129605 + 0.101163i
\(867\) 6.42236 + 15.5050i 0.218115 + 0.526576i
\(868\) −2.42127 3.63939i −0.0821833 0.123529i
\(869\) −17.0784 7.07409i −0.579344 0.239972i
\(870\) 1.90740 6.89010i 0.0646668 0.233596i
\(871\) 3.93328 14.6792i 0.133274 0.497386i
\(872\) −18.9248 + 10.3090i −0.640874 + 0.349107i
\(873\) 4.44438 1.19087i 0.150419 0.0403048i
\(874\) −23.2898 + 39.5796i −0.787788 + 1.33880i
\(875\) 0.0580774 + 0.271295i 0.00196337 + 0.00917145i
\(876\) −4.25346 + 5.35740i −0.143711 + 0.181010i
\(877\) 6.81787 51.7869i 0.230223 1.74872i −0.352283 0.935893i \(-0.614595\pi\)
0.582507 0.812826i \(-0.302072\pi\)
\(878\) 8.53888 20.1420i 0.288173 0.679759i
\(879\) 1.67339 + 2.89840i 0.0564422 + 0.0977607i
\(880\) −13.6596 + 44.9731i −0.460465 + 1.51604i
\(881\) 7.61373 0.256513 0.128256 0.991741i \(-0.459062\pi\)
0.128256 + 0.991741i \(0.459062\pi\)
\(882\) 6.85279 7.14418i 0.230745 0.240557i
\(883\) −9.87102 23.8308i −0.332186 0.801969i −0.998418 0.0562240i \(-0.982094\pi\)
0.666232 0.745745i \(-0.267906\pi\)
\(884\) −2.60791 1.13111i −0.0877136 0.0380434i
\(885\) 0.934714 + 7.09986i 0.0314201 + 0.238659i
\(886\) −0.483654 + 58.4914i −0.0162487 + 1.96506i
\(887\) 5.10271 + 19.0436i 0.171332 + 0.639420i 0.997147 + 0.0754795i \(0.0240487\pi\)
−0.825815 + 0.563941i \(0.809285\pi\)
\(888\) 10.1425 + 4.49905i 0.340360 + 0.150978i
\(889\) −13.9993 2.57360i −0.469522 0.0863158i
\(890\) −10.8429 + 2.80948i −0.363456 + 0.0941738i
\(891\) 2.25831 + 2.94309i 0.0756562 + 0.0985971i
\(892\) −13.1259 52.4405i −0.439489 1.75584i
\(893\) 26.4290 34.4430i 0.884414 1.15259i
\(894\) 1.79119 + 1.39811i 0.0599064 + 0.0467598i
\(895\) −38.5153 −1.28742
\(896\) 29.7563 + 3.24996i 0.994088 + 0.108574i
\(897\) 22.8085 0.761555
\(898\) 5.57988 + 4.35537i 0.186203 + 0.145340i
\(899\) −0.802601 + 1.04597i −0.0267682 + 0.0348850i
\(900\) 2.44418 + 9.76497i 0.0814728 + 0.325499i
\(901\) 2.14895 + 2.80056i 0.0715918 + 0.0933002i
\(902\) −59.5923 + 15.4407i −1.98421 + 0.514121i
\(903\) −10.0039 28.1202i −0.332908 0.935783i
\(904\) 42.9416 + 19.0482i 1.42822 + 0.633532i
\(905\) −4.02511 15.0219i −0.133799 0.499345i
\(906\) −0.0140654 + 1.70103i −0.000467293 + 0.0565128i
\(907\) 1.83501 + 13.9383i 0.0609305 + 0.462813i 0.994526 + 0.104486i \(0.0333196\pi\)
−0.933596 + 0.358328i \(0.883347\pi\)
\(908\) −1.45272 0.630080i −0.0482103 0.0209099i
\(909\) 0.281692 + 0.680065i 0.00934314 + 0.0225563i
\(910\) 7.26771 + 35.3759i 0.240922 + 1.17270i
\(911\) −3.93805 −0.130473 −0.0652367 0.997870i \(-0.520780\pi\)
−0.0652367 + 0.997870i \(0.520780\pi\)
\(912\) −16.6044 5.04324i −0.549828 0.166998i
\(913\) −28.7615 49.8164i −0.951867 1.64868i
\(914\) 17.7559 41.8835i 0.587312 1.38538i
\(915\) 0.320036 2.43092i 0.0105801 0.0803637i
\(916\) 0.758537 0.955407i 0.0250628 0.0315675i
\(917\) −14.2482 + 44.0690i −0.470516 + 1.45529i
\(918\) −0.334530 + 0.568515i −0.0110411 + 0.0187638i
\(919\) 29.0395 7.78110i 0.957923 0.256675i 0.254202 0.967151i \(-0.418187\pi\)
0.703721 + 0.710476i \(0.251520\pi\)
\(920\) 58.8885 32.0787i 1.94150 1.05760i
\(921\) −4.29468 + 16.0280i −0.141514 + 0.528139i
\(922\) −3.52786 + 12.7437i −0.116184 + 0.419692i
\(923\) 34.1905 + 14.1622i 1.12539 + 0.466154i
\(924\) 17.5881 + 8.71714i 0.578605 + 0.286773i
\(925\) 7.55581 + 18.2413i 0.248433 + 0.599771i
\(926\) 11.1581 + 8.70945i 0.366678 + 0.286210i
\(927\) −4.63504 8.02813i −0.152235 0.263678i
\(928\) −1.97425 8.80972i −0.0648078 0.289193i
\(929\) 14.7366 + 8.50816i 0.483491 + 0.279144i 0.721870 0.692029i \(-0.243283\pi\)
−0.238379 + 0.971172i \(0.576616\pi\)
\(930\) 0.513328 3.66470i 0.0168327 0.120170i
\(931\) −14.4130 + 26.7303i −0.472368 + 0.876051i
\(932\) −28.0418 + 15.5774i −0.918539 + 0.510255i
\(933\) −5.98846 + 4.59511i −0.196054 + 0.150437i
\(934\) 34.0394 33.4811i 1.11380 1.09554i
\(935\) −5.29404 1.41853i −0.173134 0.0463910i
\(936\) 2.02354 + 8.37792i 0.0661415 + 0.273841i
\(937\) 27.4838 + 27.4838i 0.897857 + 0.897857i 0.995246 0.0973891i \(-0.0310491\pi\)
−0.0973891 + 0.995246i \(0.531049\pi\)
\(938\) −18.6124 + 1.33723i −0.607716 + 0.0436622i
\(939\) 11.9045 + 4.93101i 0.388489 + 0.160917i
\(940\) −58.9627 + 23.2885i −1.92315 + 0.759586i
\(941\) −11.0217 + 14.3638i −0.359297 + 0.468245i −0.937670 0.347528i \(-0.887021\pi\)
0.578373 + 0.815773i \(0.303688\pi\)
\(942\) 11.9636 + 5.07178i 0.389795 + 0.165247i
\(943\) 76.0630 + 43.9150i 2.47695 + 1.43007i
\(944\) 5.26491 + 7.35260i 0.171358 + 0.239307i
\(945\) 8.35364 0.669652i 0.271744 0.0217838i
\(946\) 47.2495 35.6390i 1.53621 1.15872i
\(947\) 25.1378 + 3.30946i 0.816869 + 0.107543i 0.527370 0.849636i \(-0.323178\pi\)
0.289499 + 0.957178i \(0.406511\pi\)
\(948\) −8.00587 + 5.93539i −0.260019 + 0.192772i
\(949\) −10.3332 + 1.36039i −0.335430 + 0.0441603i
\(950\) −15.2183 26.8696i −0.493747 0.871763i
\(951\) 10.7207 10.7207i 0.347642 0.347642i
\(952\) −0.264023 + 3.48046i −0.00855705 + 0.112803i
\(953\) −2.58794 2.58794i −0.0838315 0.0838315i 0.663948 0.747779i \(-0.268880\pi\)
−0.747779 + 0.663948i \(0.768880\pi\)
\(954\) 2.85552 10.3150i 0.0924508 0.333961i
\(955\) −7.40512 56.2475i −0.239624 1.82013i
\(956\) −13.5343 54.0722i −0.437732 1.74882i
\(957\) 0.772789 5.86992i 0.0249807 0.189748i
\(958\) 3.57682 25.5353i 0.115562 0.825007i
\(959\) 0.743076 1.56373i 0.0239952 0.0504955i
\(960\) 17.0075 + 18.7847i 0.548915 + 0.606273i
\(961\) 15.1588 26.2558i 0.488993 0.846961i
\(962\) 6.34002 + 15.6714i 0.204411 + 0.505268i
\(963\) −13.3083 10.2118i −0.428854 0.329071i
\(964\) 8.83929 8.55167i 0.284694 0.275431i
\(965\) −28.6346 + 69.1299i −0.921779 + 2.22537i
\(966\) −9.16857 26.4632i −0.294994 0.851438i
\(967\) −28.7286 + 28.7286i −0.923848 + 0.923848i −0.997299 0.0734504i \(-0.976599\pi\)
0.0734504 + 0.997299i \(0.476599\pi\)
\(968\) −1.21136 + 7.71683i −0.0389345 + 0.248028i
\(969\) 0.523734 1.95460i 0.0168248 0.0627908i
\(970\) 20.6103 + 0.170423i 0.661758 + 0.00547194i
\(971\) 30.4280 + 39.6546i 0.976482 + 1.27258i 0.962105 + 0.272680i \(0.0879100\pi\)
0.0143774 + 0.999897i \(0.495423\pi\)
\(972\) 1.98694 0.228227i 0.0637310 0.00732038i
\(973\) 37.0534 + 23.9863i 1.18788 + 0.768967i
\(974\) 1.51922 + 2.01415i 0.0486788 + 0.0645375i
\(975\) −7.66848 + 13.2822i −0.245588 + 0.425371i
\(976\) −1.08966 2.89823i −0.0348792 0.0927702i
\(977\) 7.81003 4.50912i 0.249865 0.144260i −0.369837 0.929096i \(-0.620587\pi\)
0.619702 + 0.784837i \(0.287253\pi\)
\(978\) 2.32619 + 18.8738i 0.0743833 + 0.603518i
\(979\) −8.56991 + 3.54977i −0.273895 + 0.113451i
\(980\) 38.1228 22.6526i 1.21779 0.723612i
\(981\) −2.91576 + 7.03926i −0.0930930 + 0.224746i
\(982\) 7.88448 + 13.9209i 0.251604 + 0.444234i
\(983\) 26.0550 + 6.98143i 0.831027 + 0.222673i 0.649162 0.760650i \(-0.275120\pi\)
0.181865 + 0.983323i \(0.441787\pi\)
\(984\) −9.38244 + 31.8352i −0.299101 + 1.01487i
\(985\) −13.4940 50.3601i −0.429953 1.60461i
\(986\) 1.01911 0.264058i 0.0324551 0.00840932i
\(987\) 5.54234 + 25.8898i 0.176415 + 0.824080i
\(988\) −12.8395 23.1130i −0.408478 0.735324i
\(989\) −83.7163 11.0215i −2.66202 0.350462i
\(990\) 6.23213 + 15.4047i 0.198070 + 0.489595i
\(991\) −47.9598 + 27.6896i −1.52349 + 0.879590i −0.523881 + 0.851792i \(0.675516\pi\)
−0.999614 + 0.0277980i \(0.991150\pi\)
\(992\) −1.60833 4.38756i −0.0510645 0.139305i
\(993\) 23.5780i 0.748226i
\(994\) 2.68749 45.3618i 0.0852419 1.43879i
\(995\) 78.6611 32.5825i 2.49372 1.03293i
\(996\) −31.0081 0.512835i −0.982531 0.0162498i
\(997\) −38.8373 + 5.11302i −1.22999 + 0.161931i −0.717374 0.696688i \(-0.754656\pi\)
−0.512614 + 0.858619i \(0.671323\pi\)
\(998\) −15.2976 15.5527i −0.484236 0.492311i
\(999\) 3.78921 1.01532i 0.119885 0.0321232i
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 672.2.cf.a.187.14 yes 512
7.3 odd 6 inner 672.2.cf.a.283.57 yes 512
32.19 odd 8 inner 672.2.cf.a.19.57 512
224.115 even 24 inner 672.2.cf.a.115.14 yes 512
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.cf.a.19.57 512 32.19 odd 8 inner
672.2.cf.a.115.14 yes 512 224.115 even 24 inner
672.2.cf.a.187.14 yes 512 1.1 even 1 trivial
672.2.cf.a.283.57 yes 512 7.3 odd 6 inner