Properties

Label 32.2.g.b.5.1
Level $32$
Weight $2$
Character 32.5
Analytic conductor $0.256$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,2,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.255521286468\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.1
Root \(0.500000 + 2.10607i\) of defining polynomial
Character \(\chi\) \(=\) 32.5
Dual form 32.2.g.b.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26330 - 0.635665i) q^{2} +(-1.07947 - 2.60607i) q^{3} +(1.19186 + 1.60607i) q^{4} +(0.707107 + 0.292893i) q^{5} +(-0.292893 + 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(-0.484753 - 2.78658i) q^{8} +(-3.50504 + 3.50504i) q^{9} +O(q^{10})\) \(q+(-1.26330 - 0.635665i) q^{2} +(-1.07947 - 2.60607i) q^{3} +(1.19186 + 1.60607i) q^{4} +(0.707107 + 0.292893i) q^{5} +(-0.292893 + 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(-0.484753 - 2.78658i) q^{8} +(-3.50504 + 3.50504i) q^{9} +(-0.707107 - 0.819496i) q^{10} +(-0.334743 + 0.808140i) q^{11} +(2.89897 - 4.83978i) q^{12} +(1.09083 - 0.451835i) q^{13} +(-1.05791 - 3.20079i) q^{14} -2.15894i q^{15} +(-1.15894 + 3.82843i) q^{16} -0.224777i q^{17} +(6.65595 - 2.19989i) q^{18} +(-2.87740 + 1.19186i) q^{19} +(0.372364 + 1.48475i) q^{20} +(2.57316 - 6.21215i) q^{21} +(0.936588 - 0.808140i) q^{22} +(-3.68554 + 3.68554i) q^{23} +(-6.73875 + 4.27133i) q^{24} +(-3.12132 - 3.12132i) q^{25} +(-1.66526 - 0.122597i) q^{26} +(5.09976 + 2.11239i) q^{27} +(-0.698175 + 4.71604i) q^{28} +(2.34610 + 5.66398i) q^{29} +(-1.37236 + 2.72739i) q^{30} +6.82843 q^{31} +(3.89769 - 4.09976i) q^{32} +2.46742 q^{33} +(-0.142883 + 0.283962i) q^{34} +(0.698175 + 1.68554i) q^{35} +(-9.80686 - 1.45183i) q^{36} +(-9.87613 - 4.09083i) q^{37} +(4.39265 + 0.323388i) q^{38} +(-2.35503 - 2.35503i) q^{39} +(0.473398 - 2.11239i) q^{40} +(6.37109 - 6.37109i) q^{41} +(-7.19951 + 6.21215i) q^{42} +(1.90790 - 4.60607i) q^{43} +(-1.69690 + 0.425569i) q^{44} +(-3.50504 + 1.45183i) q^{45} +(6.99872 - 2.31318i) q^{46} -0.542661i q^{47} +(11.2282 - 1.11239i) q^{48} -1.31788i q^{49} +(1.95905 + 5.92728i) q^{50} +(-0.585786 + 0.242641i) q^{51} +(2.02579 + 1.21342i) q^{52} +(-3.91925 + 9.46191i) q^{53} +(-5.09976 - 5.91032i) q^{54} +(-0.473398 + 0.473398i) q^{55} +(3.87983 - 5.51397i) q^{56} +(6.21215 + 6.21215i) q^{57} +(0.636568 - 8.64665i) q^{58} +(-3.36524 - 1.39393i) q^{59} +(3.46742 - 2.57316i) q^{60} +(0.398630 + 0.962379i) q^{61} +(-8.62636 - 4.34059i) q^{62} -11.8158 q^{63} +(-7.53003 + 2.70160i) q^{64} +0.903670 q^{65} +(-3.11709 - 1.56845i) q^{66} +(1.48105 + 3.57558i) q^{67} +(0.361009 - 0.267903i) q^{68} +(13.5832 + 5.62636i) q^{69} +(0.189436 - 2.57316i) q^{70} +(-5.39978 - 5.39978i) q^{71} +(11.4661 + 8.06799i) q^{72} +(-5.15894 + 5.15894i) q^{73} +(9.87613 + 11.4459i) q^{74} +(-4.76501 + 11.5038i) q^{75} +(-5.34367 - 3.20079i) q^{76} +(-1.92638 + 0.797933i) q^{77} +(1.47810 + 4.47212i) q^{78} -8.39218i q^{79} +(-1.94082 + 2.36766i) q^{80} -0.699980i q^{81} +(-12.0985 + 3.99872i) q^{82} +(11.2180 - 4.64665i) q^{83} +(13.0440 - 3.27133i) q^{84} +(0.0658358 - 0.158942i) q^{85} +(-5.33817 + 4.60607i) q^{86} +(12.2282 - 12.2282i) q^{87} +(2.41421 + 0.541038i) q^{88} +(-5.92638 - 5.92638i) q^{89} +(5.35080 + 0.393927i) q^{90} +(2.60022 + 1.07705i) q^{91} +(-10.3119 - 1.52660i) q^{92} +(-7.37109 - 17.7954i) q^{93} +(-0.344951 + 0.685544i) q^{94} -2.38372 q^{95} +(-14.8917 - 5.73210i) q^{96} -4.19951 q^{97} +(-0.837733 + 1.66488i) q^{98} +(-1.65928 - 4.00585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 4 q^{11} + 12 q^{12} - 8 q^{13} + 12 q^{14} + 20 q^{18} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} - 20 q^{26} + 8 q^{27} - 16 q^{28} - 12 q^{30} + 32 q^{31} - 24 q^{32} - 16 q^{33} + 16 q^{35} - 40 q^{36} - 8 q^{37} + 8 q^{38} + 16 q^{39} + 16 q^{40} + 8 q^{41} + 8 q^{42} - 12 q^{43} + 20 q^{44} + 12 q^{46} + 48 q^{48} + 16 q^{50} - 16 q^{51} + 12 q^{52} + 8 q^{53} - 8 q^{54} - 16 q^{55} + 8 q^{56} + 16 q^{57} - 12 q^{58} - 20 q^{59} - 8 q^{60} + 24 q^{61} - 24 q^{62} - 40 q^{63} - 8 q^{64} - 28 q^{66} - 36 q^{67} + 16 q^{68} + 32 q^{69} - 8 q^{70} - 24 q^{71} + 12 q^{72} - 32 q^{73} + 8 q^{74} - 12 q^{75} - 20 q^{76} + 16 q^{77} + 28 q^{78} + 8 q^{80} - 20 q^{82} + 20 q^{83} + 8 q^{84} + 8 q^{85} + 4 q^{86} + 56 q^{87} + 8 q^{88} - 16 q^{89} + 28 q^{90} + 40 q^{91} - 16 q^{92} - 16 q^{93} - 24 q^{94} - 8 q^{95} - 16 q^{96} + 32 q^{97} - 24 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26330 0.635665i −0.893289 0.449483i
\(3\) −1.07947 2.60607i −0.623233 1.50462i −0.847886 0.530178i \(-0.822125\pi\)
0.224653 0.974439i \(-0.427875\pi\)
\(4\) 1.19186 + 1.60607i 0.595930 + 0.803037i
\(5\) 0.707107 + 0.292893i 0.316228 + 0.130986i 0.535151 0.844756i \(-0.320255\pi\)
−0.218924 + 0.975742i \(0.570255\pi\)
\(6\) −0.292893 + 3.97844i −0.119573 + 1.62419i
\(7\) 1.68554 + 1.68554i 0.637076 + 0.637076i 0.949833 0.312757i \(-0.101253\pi\)
−0.312757 + 0.949833i \(0.601253\pi\)
\(8\) −0.484753 2.78658i −0.171386 0.985204i
\(9\) −3.50504 + 3.50504i −1.16835 + 1.16835i
\(10\) −0.707107 0.819496i −0.223607 0.259147i
\(11\) −0.334743 + 0.808140i −0.100929 + 0.243664i −0.966276 0.257510i \(-0.917098\pi\)
0.865347 + 0.501173i \(0.167098\pi\)
\(12\) 2.89897 4.83978i 0.836859 1.39712i
\(13\) 1.09083 0.451835i 0.302541 0.125316i −0.226249 0.974070i \(-0.572646\pi\)
0.528789 + 0.848753i \(0.322646\pi\)
\(14\) −1.05791 3.20079i −0.282738 0.855447i
\(15\) 2.15894i 0.557436i
\(16\) −1.15894 + 3.82843i −0.289735 + 0.957107i
\(17\) 0.224777i 0.0545165i −0.999628 0.0272583i \(-0.991322\pi\)
0.999628 0.0272583i \(-0.00867765\pi\)
\(18\) 6.65595 2.19989i 1.56882 0.518519i
\(19\) −2.87740 + 1.19186i −0.660122 + 0.273431i −0.687490 0.726194i \(-0.741287\pi\)
0.0273681 + 0.999625i \(0.491287\pi\)
\(20\) 0.372364 + 1.48475i 0.0832631 + 0.332001i
\(21\) 2.57316 6.21215i 0.561509 1.35560i
\(22\) 0.936588 0.808140i 0.199681 0.172296i
\(23\) −3.68554 + 3.68554i −0.768489 + 0.768489i −0.977840 0.209351i \(-0.932865\pi\)
0.209351 + 0.977840i \(0.432865\pi\)
\(24\) −6.73875 + 4.27133i −1.37554 + 0.871882i
\(25\) −3.12132 3.12132i −0.624264 0.624264i
\(26\) −1.66526 0.122597i −0.326584 0.0240432i
\(27\) 5.09976 + 2.11239i 0.981449 + 0.406529i
\(28\) −0.698175 + 4.71604i −0.131943 + 0.891247i
\(29\) 2.34610 + 5.66398i 0.435659 + 1.05177i 0.977432 + 0.211250i \(0.0677534\pi\)
−0.541773 + 0.840525i \(0.682247\pi\)
\(30\) −1.37236 + 2.72739i −0.250558 + 0.497952i
\(31\) 6.82843 1.22642 0.613211 0.789919i \(-0.289878\pi\)
0.613211 + 0.789919i \(0.289878\pi\)
\(32\) 3.89769 4.09976i 0.689021 0.724742i
\(33\) 2.46742 0.429522
\(34\) −0.142883 + 0.283962i −0.0245043 + 0.0486990i
\(35\) 0.698175 + 1.68554i 0.118013 + 0.284909i
\(36\) −9.80686 1.45183i −1.63448 0.241972i
\(37\) −9.87613 4.09083i −1.62363 0.672528i −0.629129 0.777301i \(-0.716588\pi\)
−0.994496 + 0.104773i \(0.966588\pi\)
\(38\) 4.39265 + 0.323388i 0.712582 + 0.0524604i
\(39\) −2.35503 2.35503i −0.377107 0.377107i
\(40\) 0.473398 2.11239i 0.0748508 0.333998i
\(41\) 6.37109 6.37109i 0.994997 0.994997i −0.00499079 0.999988i \(-0.501589\pi\)
0.999988 + 0.00499079i \(0.00158862\pi\)
\(42\) −7.19951 + 6.21215i −1.11091 + 0.958555i
\(43\) 1.90790 4.60607i 0.290952 0.702420i −0.709045 0.705164i \(-0.750873\pi\)
0.999996 + 0.00274415i \(0.000873491\pi\)
\(44\) −1.69690 + 0.425569i −0.255817 + 0.0641569i
\(45\) −3.50504 + 1.45183i −0.522500 + 0.216427i
\(46\) 6.99872 2.31318i 1.03191 0.341060i
\(47\) 0.542661i 0.0791552i −0.999216 0.0395776i \(-0.987399\pi\)
0.999216 0.0395776i \(-0.0126012\pi\)
\(48\) 11.2282 1.11239i 1.62065 0.160559i
\(49\) 1.31788i 0.188269i
\(50\) 1.95905 + 5.92728i 0.277052 + 0.838244i
\(51\) −0.585786 + 0.242641i −0.0820265 + 0.0339765i
\(52\) 2.02579 + 1.21342i 0.280927 + 0.168271i
\(53\) −3.91925 + 9.46191i −0.538351 + 1.29969i 0.387523 + 0.921860i \(0.373331\pi\)
−0.925873 + 0.377834i \(0.876669\pi\)
\(54\) −5.09976 5.91032i −0.693989 0.804293i
\(55\) −0.473398 + 0.473398i −0.0638329 + 0.0638329i
\(56\) 3.87983 5.51397i 0.518464 0.736835i
\(57\) 6.21215 + 6.21215i 0.822819 + 0.822819i
\(58\) 0.636568 8.64665i 0.0835854 1.13536i
\(59\) −3.36524 1.39393i −0.438117 0.181474i 0.152712 0.988271i \(-0.451199\pi\)
−0.590829 + 0.806797i \(0.701199\pi\)
\(60\) 3.46742 2.57316i 0.447642 0.332193i
\(61\) 0.398630 + 0.962379i 0.0510394 + 0.123220i 0.947343 0.320222i \(-0.103757\pi\)
−0.896303 + 0.443442i \(0.853757\pi\)
\(62\) −8.62636 4.34059i −1.09555 0.551256i
\(63\) −11.8158 −1.48865
\(64\) −7.53003 + 2.70160i −0.941254 + 0.337700i
\(65\) 0.903670 0.112086
\(66\) −3.11709 1.56845i −0.383688 0.193063i
\(67\) 1.48105 + 3.57558i 0.180939 + 0.436826i 0.988161 0.153423i \(-0.0490296\pi\)
−0.807221 + 0.590249i \(0.799030\pi\)
\(68\) 0.361009 0.267903i 0.0437788 0.0324880i
\(69\) 13.5832 + 5.62636i 1.63523 + 0.677334i
\(70\) 0.189436 2.57316i 0.0226419 0.307551i
\(71\) −5.39978 5.39978i −0.640836 0.640836i 0.309925 0.950761i \(-0.399696\pi\)
−0.950761 + 0.309925i \(0.899696\pi\)
\(72\) 11.4661 + 8.06799i 1.35130 + 0.950821i
\(73\) −5.15894 + 5.15894i −0.603808 + 0.603808i −0.941321 0.337513i \(-0.890414\pi\)
0.337513 + 0.941321i \(0.390414\pi\)
\(74\) 9.87613 + 11.4459i 1.14808 + 1.33055i
\(75\) −4.76501 + 11.5038i −0.550217 + 1.32834i
\(76\) −5.34367 3.20079i −0.612961 0.367156i
\(77\) −1.92638 + 0.797933i −0.219531 + 0.0909329i
\(78\) 1.47810 + 4.47212i 0.167362 + 0.506368i
\(79\) 8.39218i 0.944194i −0.881547 0.472097i \(-0.843497\pi\)
0.881547 0.472097i \(-0.156503\pi\)
\(80\) −1.94082 + 2.36766i −0.216990 + 0.264713i
\(81\) 0.699980i 0.0777755i
\(82\) −12.0985 + 3.99872i −1.33605 + 0.441585i
\(83\) 11.2180 4.64665i 1.23134 0.510036i 0.330339 0.943862i \(-0.392837\pi\)
0.900996 + 0.433827i \(0.142837\pi\)
\(84\) 13.0440 3.27133i 1.42322 0.356931i
\(85\) 0.0658358 0.158942i 0.00714089 0.0172396i
\(86\) −5.33817 + 4.60607i −0.575630 + 0.496686i
\(87\) 12.2282 12.2282i 1.31100 1.31100i
\(88\) 2.41421 + 0.541038i 0.257356 + 0.0576749i
\(89\) −5.92638 5.92638i −0.628195 0.628195i 0.319419 0.947614i \(-0.396512\pi\)
−0.947614 + 0.319419i \(0.896512\pi\)
\(90\) 5.35080 + 0.393927i 0.564024 + 0.0415235i
\(91\) 2.60022 + 1.07705i 0.272577 + 0.112905i
\(92\) −10.3119 1.52660i −1.07509 0.159159i
\(93\) −7.37109 17.7954i −0.764346 1.84529i
\(94\) −0.344951 + 0.685544i −0.0355789 + 0.0707085i
\(95\) −2.38372 −0.244564
\(96\) −14.8917 5.73210i −1.51988 0.585030i
\(97\) −4.19951 −0.426396 −0.213198 0.977009i \(-0.568388\pi\)
−0.213198 + 0.977009i \(0.568388\pi\)
\(98\) −0.837733 + 1.66488i −0.0846238 + 0.168179i
\(99\) −1.65928 4.00585i −0.166764 0.402603i
\(100\) 1.29289 8.73324i 0.129289 0.873324i
\(101\) 4.46191 + 1.84819i 0.443977 + 0.183901i 0.593461 0.804863i \(-0.297761\pi\)
−0.149484 + 0.988764i \(0.547761\pi\)
\(102\) 0.894263 + 0.0658358i 0.0885452 + 0.00651871i
\(103\) 10.9635 + 10.9635i 1.08027 + 1.08027i 0.996484 + 0.0837844i \(0.0267007\pi\)
0.0837844 + 0.996484i \(0.473299\pi\)
\(104\) −1.78785 2.82064i −0.175313 0.276587i
\(105\) 3.63899 3.63899i 0.355129 0.355129i
\(106\) 10.9658 9.46191i 1.06509 0.919022i
\(107\) 3.34737 8.08128i 0.323603 0.781246i −0.675436 0.737418i \(-0.736045\pi\)
0.999039 0.0438280i \(-0.0139554\pi\)
\(108\) 2.68554 + 10.7083i 0.258417 + 1.03040i
\(109\) 8.62086 3.57088i 0.825728 0.342028i 0.0705180 0.997511i \(-0.477535\pi\)
0.755210 + 0.655483i \(0.227535\pi\)
\(110\) 0.898966 0.297121i 0.0857131 0.0283294i
\(111\) 30.1538i 2.86208i
\(112\) −8.40643 + 4.49954i −0.794333 + 0.425166i
\(113\) 2.42429i 0.228058i 0.993477 + 0.114029i \(0.0363757\pi\)
−0.993477 + 0.114029i \(0.963624\pi\)
\(114\) −3.89897 11.7967i −0.365172 1.10486i
\(115\) −3.68554 + 1.52660i −0.343679 + 0.142356i
\(116\) −6.30055 + 10.5187i −0.584991 + 0.976634i
\(117\) −2.23969 + 5.40709i −0.207059 + 0.499885i
\(118\) 3.36524 + 3.90011i 0.309795 + 0.359035i
\(119\) 0.378872 0.378872i 0.0347312 0.0347312i
\(120\) −6.01606 + 1.04655i −0.549188 + 0.0955368i
\(121\) 7.23714 + 7.23714i 0.657921 + 0.657921i
\(122\) 0.108161 1.46917i 0.00979239 0.133012i
\(123\) −23.4809 9.72612i −2.11720 0.876974i
\(124\) 8.13853 + 10.9670i 0.730861 + 0.984861i
\(125\) −2.75736 6.65685i −0.246626 0.595407i
\(126\) 14.9269 + 7.51089i 1.32979 + 0.669123i
\(127\) −2.19266 −0.194567 −0.0972836 0.995257i \(-0.531015\pi\)
−0.0972836 + 0.995257i \(0.531015\pi\)
\(128\) 11.2300 + 1.37364i 0.992602 + 0.121414i
\(129\) −14.0633 −1.23820
\(130\) −1.14161 0.574431i −0.100126 0.0503810i
\(131\) 3.16317 + 7.63657i 0.276367 + 0.667210i 0.999729 0.0232589i \(-0.00740422\pi\)
−0.723362 + 0.690469i \(0.757404\pi\)
\(132\) 2.94082 + 3.96285i 0.255965 + 0.344922i
\(133\) −6.85892 2.84106i −0.594744 0.246351i
\(134\) 0.401855 5.45849i 0.0347150 0.471541i
\(135\) 2.98737 + 2.98737i 0.257112 + 0.257112i
\(136\) −0.626360 + 0.108961i −0.0537099 + 0.00934337i
\(137\) 7.76744 7.76744i 0.663617 0.663617i −0.292614 0.956231i \(-0.594525\pi\)
0.956231 + 0.292614i \(0.0945250\pi\)
\(138\) −13.5832 15.7422i −1.15628 1.34006i
\(139\) 0.357453 0.862967i 0.0303188 0.0731959i −0.907995 0.418981i \(-0.862387\pi\)
0.938314 + 0.345785i \(0.112387\pi\)
\(140\) −1.87498 + 3.13025i −0.158465 + 0.264555i
\(141\) −1.41421 + 0.585786i −0.119098 + 0.0493321i
\(142\) 3.38909 + 10.2540i 0.284406 + 0.860496i
\(143\) 1.03279i 0.0863662i
\(144\) −9.35665 17.4809i −0.779721 1.45674i
\(145\) 4.69220i 0.389666i
\(146\) 9.79666 3.23794i 0.810777 0.267974i
\(147\) −3.43450 + 1.42262i −0.283273 + 0.117335i
\(148\) −5.20079 20.7375i −0.427502 1.70461i
\(149\) 2.34610 5.66398i 0.192200 0.464011i −0.798175 0.602426i \(-0.794201\pi\)
0.990374 + 0.138415i \(0.0442007\pi\)
\(150\) 13.3322 11.5038i 1.08857 0.939278i
\(151\) −8.17083 + 8.17083i −0.664932 + 0.664932i −0.956538 0.291606i \(-0.905810\pi\)
0.291606 + 0.956538i \(0.405810\pi\)
\(152\) 4.71604 + 7.44035i 0.382521 + 0.603492i
\(153\) 0.787854 + 0.787854i 0.0636942 + 0.0636942i
\(154\) 2.94082 + 0.216503i 0.236978 + 0.0174463i
\(155\) 4.82843 + 2.00000i 0.387829 + 0.160644i
\(156\) 0.975485 6.58921i 0.0781013 0.527559i
\(157\) 4.88391 + 11.7908i 0.389779 + 0.941009i 0.989986 + 0.141164i \(0.0450846\pi\)
−0.600208 + 0.799844i \(0.704915\pi\)
\(158\) −5.33461 + 10.6018i −0.424399 + 0.843437i
\(159\) 28.8892 2.29106
\(160\) 3.95687 1.75736i 0.312818 0.138931i
\(161\) −12.4243 −0.979171
\(162\) −0.444953 + 0.884285i −0.0349588 + 0.0694760i
\(163\) 0.753131 + 1.81822i 0.0589898 + 0.142414i 0.950626 0.310338i \(-0.100442\pi\)
−0.891636 + 0.452752i \(0.850442\pi\)
\(164\) 17.8259 + 2.63899i 1.39197 + 0.206071i
\(165\) 1.74473 + 0.722690i 0.135827 + 0.0562613i
\(166\) −17.1254 1.26078i −1.32919 0.0978552i
\(167\) −15.1630 15.1630i −1.17335 1.17335i −0.981406 0.191946i \(-0.938520\pi\)
−0.191946 0.981406i \(-0.561480\pi\)
\(168\) −18.5580 4.15894i −1.43178 0.320869i
\(169\) −8.20664 + 8.20664i −0.631280 + 0.631280i
\(170\) −0.184204 + 0.158942i −0.0141278 + 0.0121903i
\(171\) 5.90790 14.2629i 0.451788 1.09071i
\(172\) 9.67164 2.42557i 0.737455 0.184948i
\(173\) 4.54817 1.88391i 0.345791 0.143231i −0.203027 0.979173i \(-0.565078\pi\)
0.548818 + 0.835942i \(0.315078\pi\)
\(174\) −23.2209 + 7.67486i −1.76038 + 0.581830i
\(175\) 10.5222i 0.795407i
\(176\) −2.70596 2.21813i −0.203969 0.167198i
\(177\) 10.2748i 0.772298i
\(178\) 3.71961 + 11.2540i 0.278796 + 0.843523i
\(179\) 7.27899 3.01505i 0.544057 0.225356i −0.0936904 0.995601i \(-0.529866\pi\)
0.637747 + 0.770246i \(0.279866\pi\)
\(180\) −6.50927 3.89897i −0.485172 0.290612i
\(181\) 6.12132 14.7782i 0.454994 1.09845i −0.515405 0.856947i \(-0.672359\pi\)
0.970399 0.241506i \(-0.0776415\pi\)
\(182\) −2.60022 3.01351i −0.192741 0.223376i
\(183\) 2.07772 2.07772i 0.153589 0.153589i
\(184\) 12.0566 + 8.48348i 0.888827 + 0.625410i
\(185\) −5.78530 5.78530i −0.425344 0.425344i
\(186\) −2.00000 + 27.1665i −0.146647 + 1.99194i
\(187\) 0.181652 + 0.0752426i 0.0132837 + 0.00550228i
\(188\) 0.871553 0.646775i 0.0635645 0.0471709i
\(189\) 5.03534 + 12.1564i 0.366267 + 0.884247i
\(190\) 3.01136 + 1.51525i 0.218467 + 0.109928i
\(191\) −15.4642 −1.11895 −0.559475 0.828847i \(-0.688997\pi\)
−0.559475 + 0.828847i \(0.688997\pi\)
\(192\) 15.1690 + 16.7075i 1.09473 + 1.20576i
\(193\) 13.2206 0.951640 0.475820 0.879543i \(-0.342151\pi\)
0.475820 + 0.879543i \(0.342151\pi\)
\(194\) 5.30525 + 2.66949i 0.380895 + 0.191658i
\(195\) −0.975485 2.35503i −0.0698559 0.168647i
\(196\) 2.11662 1.57073i 0.151187 0.112195i
\(197\) −0.602992 0.249768i −0.0429614 0.0177952i 0.361099 0.932527i \(-0.382402\pi\)
−0.404061 + 0.914732i \(0.632402\pi\)
\(198\) −0.450212 + 6.11534i −0.0319952 + 0.434598i
\(199\) −1.86490 1.86490i −0.132199 0.132199i 0.637911 0.770110i \(-0.279799\pi\)
−0.770110 + 0.637911i \(0.779799\pi\)
\(200\) −7.18473 + 10.2109i −0.508037 + 0.722018i
\(201\) 7.71947 7.71947i 0.544489 0.544489i
\(202\) −4.46191 5.17110i −0.313939 0.363837i
\(203\) −5.59244 + 13.5013i −0.392512 + 0.947608i
\(204\) −1.08787 0.651622i −0.0761664 0.0456227i
\(205\) 6.37109 2.63899i 0.444976 0.184315i
\(206\) −6.88110 20.8194i −0.479429 1.45055i
\(207\) 25.8360i 1.79572i
\(208\) 0.465613 + 4.69980i 0.0322845 + 0.325872i
\(209\) 2.72431i 0.188445i
\(210\) −6.91032 + 2.28396i −0.476857 + 0.157608i
\(211\) −19.0338 + 7.88406i −1.31034 + 0.542761i −0.924984 0.380007i \(-0.875922\pi\)
−0.385357 + 0.922768i \(0.625922\pi\)
\(212\) −19.8677 + 4.98267i −1.36452 + 0.342211i
\(213\) −8.24331 + 19.9011i −0.564822 + 1.36360i
\(214\) −9.36573 + 8.08128i −0.640228 + 0.552425i
\(215\) 2.69818 2.69818i 0.184014 0.184014i
\(216\) 3.41421 15.2349i 0.232308 1.03660i
\(217\) 11.5096 + 11.5096i 0.781324 + 0.781324i
\(218\) −13.1606 0.968887i −0.891349 0.0656213i
\(219\) 19.0135 + 7.87565i 1.28481 + 0.532187i
\(220\) −1.32453 0.196088i −0.0893001 0.0132202i
\(221\) −0.101562 0.245193i −0.00683182 0.0164935i
\(222\) 19.1677 38.0934i 1.28645 2.55666i
\(223\) −17.2119 −1.15259 −0.576297 0.817241i \(-0.695503\pi\)
−0.576297 + 0.817241i \(0.695503\pi\)
\(224\) 13.4800 0.340593i 0.900674 0.0227569i
\(225\) 21.8807 1.45871
\(226\) 1.54104 3.06261i 0.102508 0.203722i
\(227\) −0.629916 1.52075i −0.0418090 0.100936i 0.901596 0.432580i \(-0.142397\pi\)
−0.943405 + 0.331644i \(0.892397\pi\)
\(228\) −2.57316 + 17.3812i −0.170411 + 1.15110i
\(229\) 2.45021 + 1.01491i 0.161915 + 0.0670672i 0.462169 0.886792i \(-0.347071\pi\)
−0.300254 + 0.953859i \(0.597071\pi\)
\(230\) 5.62636 + 0.414214i 0.370991 + 0.0273124i
\(231\) 4.15894 + 4.15894i 0.273638 + 0.273638i
\(232\) 14.6458 9.28321i 0.961547 0.609473i
\(233\) −10.9475 + 10.9475i −0.717192 + 0.717192i −0.968029 0.250837i \(-0.919294\pi\)
0.250837 + 0.968029i \(0.419294\pi\)
\(234\) 6.26650 5.40709i 0.409654 0.353472i
\(235\) 0.158942 0.383719i 0.0103682 0.0250311i
\(236\) −1.77214 7.06618i −0.115357 0.459969i
\(237\) −21.8706 + 9.05911i −1.42065 + 0.588452i
\(238\) −0.719466 + 0.237794i −0.0466360 + 0.0154139i
\(239\) 18.2858i 1.18281i 0.806375 + 0.591404i \(0.201426\pi\)
−0.806375 + 0.591404i \(0.798574\pi\)
\(240\) 8.26535 + 2.50209i 0.533526 + 0.161509i
\(241\) 27.8155i 1.79176i −0.444300 0.895878i \(-0.646548\pi\)
0.444300 0.895878i \(-0.353452\pi\)
\(242\) −4.54229 13.7431i −0.291989 0.883439i
\(243\) 13.4751 5.58156i 0.864426 0.358057i
\(244\) −1.07054 + 1.78725i −0.0685342 + 0.114417i
\(245\) 0.385999 0.931884i 0.0246606 0.0595359i
\(246\) 23.4809 + 27.2130i 1.49709 + 1.73504i
\(247\) −2.60022 + 2.60022i −0.165448 + 0.165448i
\(248\) −3.31010 19.0279i −0.210191 1.20828i
\(249\) −24.2190 24.2190i −1.53482 1.53482i
\(250\) −0.748155 + 10.1624i −0.0473175 + 0.642725i
\(251\) 9.37694 + 3.88406i 0.591867 + 0.245159i 0.658454 0.752621i \(-0.271211\pi\)
−0.0665866 + 0.997781i \(0.521211\pi\)
\(252\) −14.0828 18.9770i −0.887131 1.19544i
\(253\) −1.74473 4.21215i −0.109690 0.264815i
\(254\) 2.76999 + 1.39380i 0.173805 + 0.0874547i
\(255\) −0.485281 −0.0303895
\(256\) −13.3137 8.87385i −0.832107 0.554615i
\(257\) 20.0656 1.25166 0.625828 0.779961i \(-0.284761\pi\)
0.625828 + 0.779961i \(0.284761\pi\)
\(258\) 17.7662 + 8.93954i 1.10607 + 0.556551i
\(259\) −9.75138 23.5419i −0.605921 1.46282i
\(260\) 1.07705 + 1.45136i 0.0667956 + 0.0900095i
\(261\) −28.0756 11.6293i −1.73784 0.719836i
\(262\) 0.858264 11.6580i 0.0530237 0.720234i
\(263\) 17.9782 + 17.9782i 1.10858 + 1.10858i 0.993337 + 0.115244i \(0.0367650\pi\)
0.115244 + 0.993337i \(0.463235\pi\)
\(264\) −1.19609 6.87565i −0.0736141 0.423167i
\(265\) −5.54266 + 5.54266i −0.340483 + 0.340483i
\(266\) 6.85892 + 7.94909i 0.420547 + 0.487390i
\(267\) −9.04722 + 21.8419i −0.553681 + 1.33670i
\(268\) −3.97743 + 6.64027i −0.242960 + 0.405619i
\(269\) −25.6598 + 10.6286i −1.56451 + 0.648040i −0.985865 0.167543i \(-0.946417\pi\)
−0.578641 + 0.815582i \(0.696417\pi\)
\(270\) −1.87498 5.67291i −0.114108 0.345242i
\(271\) 16.4921i 1.00183i −0.865498 0.500913i \(-0.832998\pi\)
0.865498 0.500913i \(-0.167002\pi\)
\(272\) 0.860544 + 0.260504i 0.0521781 + 0.0157954i
\(273\) 7.93901i 0.480491i
\(274\) −14.7501 + 4.87512i −0.891086 + 0.294517i
\(275\) 3.56730 1.47763i 0.215117 0.0891042i
\(276\) 7.15296 + 28.5215i 0.430558 + 1.71679i
\(277\) −2.31978 + 5.60044i −0.139382 + 0.336498i −0.978121 0.208035i \(-0.933293\pi\)
0.838739 + 0.544533i \(0.183293\pi\)
\(278\) −1.00013 + 0.862967i −0.0599837 + 0.0517573i
\(279\) −23.9339 + 23.9339i −1.43289 + 1.43289i
\(280\) 4.35846 2.76259i 0.260468 0.165096i
\(281\) 9.80801 + 9.80801i 0.585097 + 0.585097i 0.936299 0.351203i \(-0.114227\pi\)
−0.351203 + 0.936299i \(0.614227\pi\)
\(282\) 2.15894 + 0.158942i 0.128563 + 0.00946484i
\(283\) 21.3627 + 8.84871i 1.26988 + 0.526001i 0.912928 0.408121i \(-0.133816\pi\)
0.356952 + 0.934123i \(0.383816\pi\)
\(284\) 2.23666 15.1082i 0.132721 0.896508i
\(285\) 2.57316 + 6.21215i 0.152421 + 0.367976i
\(286\) 0.656508 1.30472i 0.0388201 0.0771499i
\(287\) 21.4775 1.26778
\(288\) 0.708254 + 28.0314i 0.0417343 + 1.65176i
\(289\) 16.9495 0.997028
\(290\) 2.98267 5.92766i 0.175148 0.348084i
\(291\) 4.53325 + 10.9442i 0.265744 + 0.641563i
\(292\) −14.4344 2.13690i −0.844708 0.125053i
\(293\) 20.4415 + 8.46715i 1.19421 + 0.494656i 0.889122 0.457670i \(-0.151316\pi\)
0.305083 + 0.952326i \(0.401316\pi\)
\(294\) 5.24312 + 0.385999i 0.305785 + 0.0225119i
\(295\) −1.97131 1.97131i −0.114774 0.114774i
\(296\) −6.61192 + 29.5036i −0.384310 + 1.71486i
\(297\) −3.41421 + 3.41421i −0.198113 + 0.198113i
\(298\) −6.56422 + 5.66398i −0.380255 + 0.328106i
\(299\) −2.35503 + 5.68554i −0.136195 + 0.328803i
\(300\) −24.1551 + 6.05791i −1.39460 + 0.349753i
\(301\) 10.9796 4.54789i 0.632853 0.262136i
\(302\) 15.5161 5.12830i 0.892852 0.295101i
\(303\) 13.6231i 0.782629i
\(304\) −1.22820 12.3972i −0.0704424 0.711030i
\(305\) 0.797261i 0.0456510i
\(306\) −0.494485 1.49611i −0.0282678 0.0855268i
\(307\) −15.6196 + 6.46984i −0.891456 + 0.369253i −0.780929 0.624620i \(-0.785254\pi\)
−0.110527 + 0.993873i \(0.535254\pi\)
\(308\) −3.57751 2.14288i −0.203848 0.122102i
\(309\) 16.7369 40.4066i 0.952131 2.29865i
\(310\) −4.82843 5.59587i −0.274236 0.317824i
\(311\) 7.24929 7.24929i 0.411070 0.411070i −0.471041 0.882111i \(-0.656122\pi\)
0.882111 + 0.471041i \(0.156122\pi\)
\(312\) −5.42087 + 7.70408i −0.306896 + 0.436158i
\(313\) −10.1596 10.1596i −0.574255 0.574255i 0.359059 0.933315i \(-0.383098\pi\)
−0.933315 + 0.359059i \(0.883098\pi\)
\(314\) 1.32515 17.9999i 0.0747827 1.01579i
\(315\) −8.35503 3.46077i −0.470753 0.194992i
\(316\) 13.4784 10.0023i 0.758222 0.562673i
\(317\) −1.34287 3.24198i −0.0754233 0.182088i 0.881671 0.471865i \(-0.156419\pi\)
−0.957094 + 0.289777i \(0.906419\pi\)
\(318\) −36.4957 18.3638i −2.04658 1.02979i
\(319\) −5.36263 −0.300250
\(320\) −6.11582 0.295173i −0.341885 0.0165007i
\(321\) −24.6738 −1.37716
\(322\) 15.6956 + 7.89769i 0.874683 + 0.440121i
\(323\) 0.267903 + 0.646775i 0.0149065 + 0.0359875i
\(324\) 1.12422 0.834278i 0.0624566 0.0463488i
\(325\) −4.81514 1.99450i −0.267096 0.110635i
\(326\) 0.204347 2.77570i 0.0113178 0.153732i
\(327\) −18.6119 18.6119i −1.02924 1.02924i
\(328\) −20.8419 14.6651i −1.15080 0.809746i
\(329\) 0.914679 0.914679i 0.0504279 0.0504279i
\(330\) −1.74473 2.02204i −0.0960441 0.111310i
\(331\) 6.43270 15.5299i 0.353573 0.853601i −0.642600 0.766201i \(-0.722144\pi\)
0.996173 0.0873991i \(-0.0278555\pi\)
\(332\) 20.8331 + 12.4788i 1.14337 + 0.684862i
\(333\) 48.9547 20.2777i 2.68270 1.11121i
\(334\) 9.51687 + 28.7941i 0.520740 + 1.57554i
\(335\) 2.96211i 0.161837i
\(336\) 20.8006 + 17.0507i 1.13477 + 0.930189i
\(337\) 2.10641i 0.114743i 0.998353 + 0.0573717i \(0.0182720\pi\)
−0.998353 + 0.0573717i \(0.981728\pi\)
\(338\) 15.5841 5.15078i 0.847665 0.280166i
\(339\) 6.31788 2.61695i 0.343140 0.142133i
\(340\) 0.333739 0.0836990i 0.0180995 0.00453922i
\(341\) −2.28577 + 5.51833i −0.123781 + 0.298834i
\(342\) −16.5299 + 14.2629i −0.893835 + 0.771251i
\(343\) 14.0202 14.0202i 0.757017 0.757017i
\(344\) −13.7600 3.08370i −0.741892 0.166262i
\(345\) 7.95687 + 7.95687i 0.428384 + 0.428384i
\(346\) −6.94324 0.511162i −0.373271 0.0274803i
\(347\) −12.3896 5.13193i −0.665107 0.275496i 0.0244788 0.999700i \(-0.492207\pi\)
−0.689586 + 0.724204i \(0.742207\pi\)
\(348\) 34.2137 + 5.06509i 1.83405 + 0.271517i
\(349\) 7.52453 + 18.1658i 0.402779 + 0.972394i 0.986988 + 0.160791i \(0.0514045\pi\)
−0.584210 + 0.811603i \(0.698596\pi\)
\(350\) −6.68862 + 13.2928i −0.357522 + 0.710528i
\(351\) 6.51740 0.347873
\(352\) 2.00846 + 4.52225i 0.107051 + 0.241036i
\(353\) −28.7013 −1.52762 −0.763809 0.645442i \(-0.776673\pi\)
−0.763809 + 0.645442i \(0.776673\pi\)
\(354\) 6.53131 12.9801i 0.347135 0.689885i
\(355\) −2.23666 5.39978i −0.118710 0.286590i
\(356\) 2.45479 16.5816i 0.130103 0.878824i
\(357\) −1.39635 0.578387i −0.0739027 0.0306115i
\(358\) −11.1121 0.818076i −0.587294 0.0432367i
\(359\) 6.39199 + 6.39199i 0.337356 + 0.337356i 0.855372 0.518015i \(-0.173329\pi\)
−0.518015 + 0.855372i \(0.673329\pi\)
\(360\) 5.74473 + 9.06328i 0.302774 + 0.477677i
\(361\) −6.57611 + 6.57611i −0.346111 + 0.346111i
\(362\) −17.1270 + 14.7782i −0.900177 + 0.776724i
\(363\) 11.0482 26.6728i 0.579882 1.39996i
\(364\) 1.36928 + 5.45984i 0.0717699 + 0.286173i
\(365\) −5.15894 + 2.13690i −0.270031 + 0.111851i
\(366\) −3.94552 + 1.30405i −0.206236 + 0.0681639i
\(367\) 14.5985i 0.762038i 0.924567 + 0.381019i \(0.124427\pi\)
−0.924567 + 0.381019i \(0.875573\pi\)
\(368\) −9.83851 18.3812i −0.512868 0.958185i
\(369\) 44.6618i 2.32500i
\(370\) 3.63106 + 10.9861i 0.188770 + 0.571140i
\(371\) −22.5545 + 9.34240i −1.17097 + 0.485033i
\(372\) 19.7954 33.0481i 1.02634 1.71346i
\(373\) −6.03762 + 14.5761i −0.312616 + 0.754722i 0.686990 + 0.726667i \(0.258932\pi\)
−0.999606 + 0.0280555i \(0.991068\pi\)
\(374\) −0.181652 0.210524i −0.00939299 0.0108859i
\(375\) −14.3718 + 14.3718i −0.742154 + 0.742154i
\(376\) −1.51217 + 0.263056i −0.0779840 + 0.0135661i
\(377\) 5.11837 + 5.11837i 0.263609 + 0.263609i
\(378\) 1.36624 18.5580i 0.0702719 0.954519i
\(379\) −5.68312 2.35403i −0.291922 0.120918i 0.231916 0.972736i \(-0.425500\pi\)
−0.523839 + 0.851818i \(0.675500\pi\)
\(380\) −2.84106 3.82843i −0.145743 0.196394i
\(381\) 2.36691 + 5.71423i 0.121261 + 0.292749i
\(382\) 19.5359 + 9.83005i 0.999545 + 0.502949i
\(383\) 12.4633 0.636843 0.318422 0.947949i \(-0.396847\pi\)
0.318422 + 0.947949i \(0.396847\pi\)
\(384\) −8.54266 30.7490i −0.435941 1.56915i
\(385\) −1.59587 −0.0813328
\(386\) −16.7016 8.40388i −0.850089 0.427746i
\(387\) 9.45721 + 22.8317i 0.480737 + 1.16060i
\(388\) −5.00523 6.74473i −0.254102 0.342412i
\(389\) −14.1298 5.85275i −0.716408 0.296746i −0.00545476 0.999985i \(-0.501736\pi\)
−0.710953 + 0.703239i \(0.751736\pi\)
\(390\) −0.264679 + 3.59519i −0.0134025 + 0.182050i
\(391\) 0.828427 + 0.828427i 0.0418954 + 0.0418954i
\(392\) −3.67238 + 0.638848i −0.185483 + 0.0322667i
\(393\) 16.4869 16.4869i 0.831654 0.831654i
\(394\) 0.602992 + 0.698833i 0.0303783 + 0.0352067i
\(395\) 2.45801 5.93416i 0.123676 0.298580i
\(396\) 4.45606 7.43933i 0.223926 0.373841i
\(397\) −25.5736 + 10.5929i −1.28350 + 0.531643i −0.917042 0.398791i \(-0.869430\pi\)
−0.366458 + 0.930434i \(0.619430\pi\)
\(398\) 1.17048 + 3.54138i 0.0586708 + 0.177514i
\(399\) 20.9417i 1.04840i
\(400\) 15.5672 8.33232i 0.778359 0.416616i
\(401\) 16.5018i 0.824062i 0.911170 + 0.412031i \(0.135180\pi\)
−0.911170 + 0.412031i \(0.864820\pi\)
\(402\) −14.6590 + 4.84501i −0.731125 + 0.241647i
\(403\) 7.44862 3.08532i 0.371042 0.153691i
\(404\) 2.34965 + 9.36894i 0.116900 + 0.466122i
\(405\) 0.205019 0.494961i 0.0101875 0.0245948i
\(406\) 15.6473 13.5013i 0.776561 0.670060i
\(407\) 6.61192 6.61192i 0.327741 0.327741i
\(408\) 0.960099 + 1.51472i 0.0475320 + 0.0749897i
\(409\) 1.28577 + 1.28577i 0.0635771 + 0.0635771i 0.738180 0.674603i \(-0.235685\pi\)
−0.674603 + 0.738180i \(0.735685\pi\)
\(410\) −9.72612 0.716038i −0.480339 0.0353626i
\(411\) −28.6272 11.8578i −1.41208 0.584902i
\(412\) −4.54124 + 30.6752i −0.223731 + 1.51126i
\(413\) −3.32273 8.02178i −0.163501 0.394726i
\(414\) −16.4230 + 32.6386i −0.807147 + 1.60410i
\(415\) 9.29329 0.456190
\(416\) 2.39929 6.23323i 0.117635 0.305609i
\(417\) −2.63482 −0.129028
\(418\) −1.73175 + 3.44163i −0.0847027 + 0.168335i
\(419\) −14.9887 36.1858i −0.732244 1.76779i −0.634972 0.772535i \(-0.718988\pi\)
−0.0972723 0.995258i \(-0.531012\pi\)
\(420\) 10.1817 + 1.50732i 0.496814 + 0.0735497i
\(421\) 13.6131 + 5.63872i 0.663460 + 0.274814i 0.688894 0.724862i \(-0.258097\pi\)
−0.0254334 + 0.999677i \(0.508097\pi\)
\(422\) 29.0570 + 2.13918i 1.41447 + 0.104134i
\(423\) 1.90205 + 1.90205i 0.0924807 + 0.0924807i
\(424\) 28.2662 + 6.33461i 1.37273 + 0.307636i
\(425\) −0.701602 + 0.701602i −0.0340327 + 0.0340327i
\(426\) 23.0642 19.9011i 1.11747 0.964212i
\(427\) −0.950223 + 2.29404i −0.0459845 + 0.111016i
\(428\) 16.9687 4.25562i 0.820214 0.205703i
\(429\) 2.69152 1.11487i 0.129948 0.0538262i
\(430\) −5.12374 + 1.69347i −0.247089 + 0.0816665i
\(431\) 2.85730i 0.137631i −0.997629 0.0688156i \(-0.978078\pi\)
0.997629 0.0688156i \(-0.0219220\pi\)
\(432\) −13.9974 + 17.0759i −0.673453 + 0.821565i
\(433\) 22.5174i 1.08212i −0.840985 0.541059i \(-0.818024\pi\)
0.840985 0.541059i \(-0.181976\pi\)
\(434\) −7.22385 21.8564i −0.346756 1.04914i
\(435\) 12.2282 5.06509i 0.586298 0.242852i
\(436\) 16.0099 + 9.58974i 0.766737 + 0.459265i
\(437\) 6.21215 14.9974i 0.297167 0.717425i
\(438\) −19.0135 22.0355i −0.908500 1.05290i
\(439\) −8.87727 + 8.87727i −0.423689 + 0.423689i −0.886472 0.462783i \(-0.846851\pi\)
0.462783 + 0.886472i \(0.346851\pi\)
\(440\) 1.54864 + 1.08968i 0.0738285 + 0.0519484i
\(441\) 4.61923 + 4.61923i 0.219963 + 0.219963i
\(442\) −0.0275569 + 0.374312i −0.00131075 + 0.0178042i
\(443\) −23.7377 9.83247i −1.12781 0.467155i −0.260775 0.965400i \(-0.583978\pi\)
−0.867036 + 0.498245i \(0.833978\pi\)
\(444\) −48.4293 + 35.9391i −2.29835 + 1.70560i
\(445\) −2.45479 5.92638i −0.116368 0.280937i
\(446\) 21.7438 + 10.9410i 1.02960 + 0.518071i
\(447\) −17.2933 −0.817945
\(448\) −17.2459 8.13853i −0.814791 0.384509i
\(449\) 8.83528 0.416963 0.208481 0.978026i \(-0.433148\pi\)
0.208481 + 0.978026i \(0.433148\pi\)
\(450\) −27.6419 13.9088i −1.30305 0.655667i
\(451\) 3.01606 + 7.28141i 0.142021 + 0.342868i
\(452\) −3.89359 + 2.88942i −0.183139 + 0.135907i
\(453\) 30.1139 + 12.4736i 1.41488 + 0.586061i
\(454\) −0.170915 + 2.32158i −0.00802145 + 0.108957i
\(455\) 1.52318 + 1.52318i 0.0714075 + 0.0714075i
\(456\) 14.2993 20.3220i 0.669625 0.951664i
\(457\) 7.58808 7.58808i 0.354955 0.354955i −0.506994 0.861950i \(-0.669243\pi\)
0.861950 + 0.506994i \(0.169243\pi\)
\(458\) −2.45021 2.83965i −0.114491 0.132688i
\(459\) 0.474817 1.14631i 0.0221626 0.0535052i
\(460\) −6.84449 4.09976i −0.319126 0.191152i
\(461\) 15.2534 6.31816i 0.710421 0.294266i 0.00194197 0.999998i \(-0.499382\pi\)
0.708479 + 0.705732i \(0.249382\pi\)
\(462\) −2.61030 7.89769i −0.121442 0.367434i
\(463\) 18.7996i 0.873689i 0.899537 + 0.436845i \(0.143904\pi\)
−0.899537 + 0.436845i \(0.856096\pi\)
\(464\) −24.4031 + 2.41764i −1.13289 + 0.112236i
\(465\) 14.7422i 0.683652i
\(466\) 20.7889 6.87102i 0.963026 0.318294i
\(467\) 9.28999 3.84804i 0.429890 0.178066i −0.157238 0.987561i \(-0.550259\pi\)
0.587127 + 0.809495i \(0.300259\pi\)
\(468\) −11.3536 + 2.84738i −0.524819 + 0.131620i
\(469\) −3.53041 + 8.52318i −0.163019 + 0.393564i
\(470\) −0.444708 + 0.383719i −0.0205129 + 0.0176996i
\(471\) 25.4557 25.4557i 1.17293 1.17293i
\(472\) −2.25298 + 10.0532i −0.103702 + 0.462736i
\(473\) 3.08370 + 3.08370i 0.141789 + 0.141789i
\(474\) 33.3877 + 2.45801i 1.53355 + 0.112900i
\(475\) 12.7015 + 5.26112i 0.582784 + 0.241397i
\(476\) 1.06006 + 0.156934i 0.0485877 + 0.00719306i
\(477\) −19.4272 46.9015i −0.889512 2.14747i
\(478\) 11.6236 23.1004i 0.531652 1.05659i
\(479\) −14.7779 −0.675220 −0.337610 0.941286i \(-0.609618\pi\)
−0.337610 + 0.941286i \(0.609618\pi\)
\(480\) −8.85114 8.41489i −0.403997 0.384085i
\(481\) −12.6215 −0.575491
\(482\) −17.6814 + 35.1394i −0.805364 + 1.60056i
\(483\) 13.4117 + 32.3786i 0.610252 + 1.47328i
\(484\) −2.99772 + 20.2490i −0.136260 + 0.920410i
\(485\) −2.96951 1.23001i −0.134838 0.0558519i
\(486\) −20.5711 1.51445i −0.933123 0.0686967i
\(487\) 13.0855 + 13.0855i 0.592961 + 0.592961i 0.938430 0.345469i \(-0.112280\pi\)
−0.345469 + 0.938430i \(0.612280\pi\)
\(488\) 2.48851 1.57733i 0.112649 0.0714024i
\(489\) 3.92543 3.92543i 0.177514 0.177514i
\(490\) −1.08000 + 0.931884i −0.0487894 + 0.0420982i
\(491\) −11.7944 + 28.4741i −0.532273 + 1.28502i 0.397742 + 0.917497i \(0.369794\pi\)
−0.930015 + 0.367523i \(0.880206\pi\)
\(492\) −12.3651 49.3042i −0.557462 2.22281i
\(493\) 1.27314 0.527350i 0.0573391 0.0237506i
\(494\) 4.93773 1.63199i 0.222159 0.0734268i
\(495\) 3.31856i 0.149158i
\(496\) −7.91375 + 26.1421i −0.355338 + 1.17382i
\(497\) 18.2031i 0.816522i
\(498\) 15.2007 + 45.9911i 0.681160 + 2.06091i
\(499\) 22.4253 9.28886i 1.00389 0.415827i 0.180670 0.983544i \(-0.442173\pi\)
0.823224 + 0.567717i \(0.192173\pi\)
\(500\) 7.40501 12.3626i 0.331162 0.552870i
\(501\) −23.1479 + 55.8841i −1.03417 + 2.49672i
\(502\) −9.37694 10.8673i −0.418513 0.485032i
\(503\) 23.5062 23.5062i 1.04809 1.04809i 0.0493053 0.998784i \(-0.484299\pi\)
0.998784 0.0493053i \(-0.0157007\pi\)
\(504\) 5.72774 + 32.9256i 0.255134 + 1.46662i
\(505\) 2.61373 + 2.61373i 0.116309 + 0.116309i
\(506\) −0.473398 + 6.43027i −0.0210451 + 0.285860i
\(507\) 30.2459 + 12.5283i 1.34327 + 0.556400i
\(508\) −2.61334 3.52157i −0.115948 0.156245i
\(509\) −13.1651 31.7834i −0.583534 1.40877i −0.889589 0.456761i \(-0.849009\pi\)
0.306056 0.952014i \(-0.400991\pi\)
\(510\) 0.613057 + 0.308476i 0.0271466 + 0.0136596i
\(511\) −17.3912 −0.769343
\(512\) 11.1784 + 19.6734i 0.494021 + 0.869450i
\(513\) −17.1917 −0.759033
\(514\) −25.3489 12.7550i −1.11809 0.562598i
\(515\) 4.54124 + 10.9635i 0.200111 + 0.483111i
\(516\) −16.7615 22.5867i −0.737882 0.994322i
\(517\) 0.438546 + 0.181652i 0.0192872 + 0.00798903i
\(518\) −2.64585 + 35.9391i −0.116252 + 1.57908i
\(519\) −9.81922 9.81922i −0.431016 0.431016i
\(520\) −0.438056 2.51815i −0.0192100 0.110428i
\(521\) −10.8936 + 10.8936i −0.477257 + 0.477257i −0.904253 0.426996i \(-0.859572\pi\)
0.426996 + 0.904253i \(0.359572\pi\)
\(522\) 28.0756 + 32.5380i 1.22884 + 1.42415i
\(523\) −6.48657 + 15.6600i −0.283638 + 0.684763i −0.999915 0.0130536i \(-0.995845\pi\)
0.716277 + 0.697816i \(0.245845\pi\)
\(524\) −8.49483 + 14.1820i −0.371098 + 0.619543i
\(525\) −27.4217 + 11.3585i −1.19678 + 0.495724i
\(526\) −11.2837 34.1399i −0.491995 1.48857i
\(527\) 1.53488i 0.0668603i
\(528\) −2.85959 + 9.44633i −0.124448 + 0.411099i
\(529\) 4.16647i 0.181151i
\(530\) 10.5253 3.47877i 0.457191 0.151108i
\(531\) 16.6811 6.90952i 0.723896 0.299848i
\(532\) −3.61192 14.4021i −0.156597 0.624409i
\(533\) 4.07107 9.82843i 0.176338 0.425716i
\(534\) 25.3135 21.8419i 1.09542 0.945193i
\(535\) 4.73390 4.73390i 0.204664 0.204664i
\(536\) 9.24568 5.86034i 0.399353 0.253128i
\(537\) −15.7149 15.7149i −0.678148 0.678148i
\(538\) 39.1723 + 2.88387i 1.68884 + 0.124333i
\(539\) 1.06503 + 0.441152i 0.0458743 + 0.0190018i
\(540\) −1.23741 + 8.35846i −0.0532496 + 0.359691i
\(541\) 1.10183 + 2.66006i 0.0473716 + 0.114365i 0.945794 0.324767i \(-0.105286\pi\)
−0.898422 + 0.439132i \(0.855286\pi\)
\(542\) −10.4835 + 20.8345i −0.450304 + 0.894920i
\(543\) −45.1208 −1.93632
\(544\) −0.921533 0.876113i −0.0395104 0.0375630i
\(545\) 7.14175 0.305919
\(546\) −5.04655 + 10.0294i −0.215973 + 0.429217i
\(547\) 10.4159 + 25.1462i 0.445351 + 1.07517i 0.974044 + 0.226360i \(0.0726825\pi\)
−0.528693 + 0.848813i \(0.677318\pi\)
\(548\) 21.7328 + 3.21738i 0.928378 + 0.137440i
\(549\) −4.77039 1.97596i −0.203595 0.0843319i
\(550\) −5.44586 0.400925i −0.232212 0.0170955i
\(551\) −13.5013 13.5013i −0.575176 0.575176i
\(552\) 9.09378 40.5781i 0.387057 1.72712i
\(553\) 14.1454 14.1454i 0.601523 0.601523i
\(554\) 6.49058 5.60044i 0.275758 0.237940i
\(555\) −8.83185 + 21.3220i −0.374891 + 0.905068i
\(556\) 1.81202 0.454441i 0.0768469 0.0192726i
\(557\) 26.4367 10.9504i 1.12016 0.463984i 0.255733 0.966748i \(-0.417683\pi\)
0.864424 + 0.502763i \(0.167683\pi\)
\(558\) 45.4497 15.0218i 1.92404 0.635923i
\(559\) 5.88648i 0.248972i
\(560\) −7.26213 + 0.719466i −0.306881 + 0.0304030i
\(561\) 0.554620i 0.0234161i
\(562\) −6.15586 18.6251i −0.259669 0.785652i
\(563\) −22.9131 + 9.49093i −0.965673 + 0.399995i −0.809100 0.587671i \(-0.800045\pi\)
−0.156574 + 0.987666i \(0.550045\pi\)
\(564\) −2.62636 1.57316i −0.110590 0.0662418i
\(565\) −0.710059 + 1.71423i −0.0298724 + 0.0721184i
\(566\) −21.3627 24.7581i −0.897941 1.04066i
\(567\) 1.17985 1.17985i 0.0495489 0.0495489i
\(568\) −12.4293 + 17.6645i −0.521524 + 0.741184i
\(569\) 12.2981 + 12.2981i 0.515565 + 0.515565i 0.916226 0.400661i \(-0.131220\pi\)
−0.400661 + 0.916226i \(0.631220\pi\)
\(570\) 0.698175 9.48348i 0.0292433 0.397219i
\(571\) 4.93839 + 2.04555i 0.206665 + 0.0856036i 0.483615 0.875281i \(-0.339324\pi\)
−0.276950 + 0.960884i \(0.589324\pi\)
\(572\) −1.65873 + 1.23094i −0.0693552 + 0.0514682i
\(573\) 16.6931 + 40.3008i 0.697366 + 1.68359i
\(574\) −27.1325 13.6525i −1.13249 0.569844i
\(575\) 23.0075 0.959480
\(576\) 16.9238 35.8623i 0.705159 1.49426i
\(577\) 2.06423 0.0859352 0.0429676 0.999076i \(-0.486319\pi\)
0.0429676 + 0.999076i \(0.486319\pi\)
\(578\) −21.4123 10.7742i −0.890634 0.448147i
\(579\) −14.2713 34.4539i −0.593093 1.43185i
\(580\) −7.53601 + 5.59244i −0.312916 + 0.232213i
\(581\) 26.7406 + 11.0763i 1.10939 + 0.459522i
\(582\) 1.23001 16.7075i 0.0509855 0.692548i
\(583\) −6.33461 6.33461i −0.262353 0.262353i
\(584\) 16.8766 + 11.8750i 0.698359 + 0.491390i
\(585\) −3.16740 + 3.16740i −0.130956 + 0.130956i
\(586\) −20.4415 23.6905i −0.844431 0.978646i
\(587\) 8.74223 21.1056i 0.360830 0.871122i −0.634349 0.773047i \(-0.718732\pi\)
0.995179 0.0980746i \(-0.0312684\pi\)
\(588\) −6.37827 3.82050i −0.263035 0.157555i
\(589\) −19.6481 + 8.13853i −0.809588 + 0.335342i
\(590\) 1.23727 + 3.74345i 0.0509374 + 0.154115i
\(591\) 1.84106i 0.0757310i
\(592\) 27.1073 33.0690i 1.11410 1.35913i
\(593\) 24.2771i 0.996939i 0.866907 + 0.498470i \(0.166104\pi\)
−0.866907 + 0.498470i \(0.833896\pi\)
\(594\) 6.48348 2.14288i 0.266020 0.0879236i
\(595\) 0.378872 0.156934i 0.0155322 0.00643367i
\(596\) 11.8930 2.98267i 0.487156 0.122175i
\(597\) −2.84696 + 6.87318i −0.116518 + 0.281300i
\(598\) 6.58921 5.68554i 0.269453 0.232499i
\(599\) −33.3626 + 33.3626i −1.36316 + 1.36316i −0.493295 + 0.869862i \(0.664208\pi\)
−0.869862 + 0.493295i \(0.835792\pi\)
\(600\) 34.3660 + 7.70160i 1.40299 + 0.314417i
\(601\) −21.0676 21.0676i −0.859365 0.859365i 0.131898 0.991263i \(-0.457893\pi\)
−0.991263 + 0.131898i \(0.957893\pi\)
\(602\) −16.7615 1.23398i −0.683146 0.0502933i
\(603\) −17.7237 7.34139i −0.721765 0.298965i
\(604\) −22.8614 3.38447i −0.930218 0.137712i
\(605\) 2.99772 + 7.23714i 0.121875 + 0.294231i
\(606\) −8.65975 + 17.2101i −0.351778 + 0.699113i
\(607\) 3.82750 0.155353 0.0776767 0.996979i \(-0.475250\pi\)
0.0776767 + 0.996979i \(0.475250\pi\)
\(608\) −6.32889 + 16.4422i −0.256670 + 0.666817i
\(609\) 41.2224 1.67041
\(610\) 0.506791 1.00718i 0.0205194 0.0407795i
\(611\) −0.245193 0.591948i −0.00991945 0.0239477i
\(612\) −0.326340 + 2.20436i −0.0131915 + 0.0891060i
\(613\) −29.0883 12.0488i −1.17486 0.486645i −0.292067 0.956398i \(-0.594343\pi\)
−0.882798 + 0.469753i \(0.844343\pi\)
\(614\) 23.8449 + 1.75546i 0.962301 + 0.0708448i
\(615\) −13.7548 13.7548i −0.554647 0.554647i
\(616\) 3.15732 + 4.98121i 0.127212 + 0.200699i
\(617\) 22.2479 22.2479i 0.895666 0.895666i −0.0993836 0.995049i \(-0.531687\pi\)
0.995049 + 0.0993836i \(0.0316871\pi\)
\(618\) −46.8288 + 40.4066i −1.88373 + 1.62539i
\(619\) 2.70650 6.53408i 0.108784 0.262627i −0.860108 0.510112i \(-0.829604\pi\)
0.968892 + 0.247485i \(0.0796041\pi\)
\(620\) 2.54266 + 10.1385i 0.102116 + 0.407173i
\(621\) −26.5807 + 11.0101i −1.06665 + 0.441819i
\(622\) −13.7662 + 4.54992i −0.551973 + 0.182435i
\(623\) 19.9783i 0.800416i
\(624\) 11.7454 6.28672i 0.470192 0.251670i
\(625\) 16.5563i 0.662254i
\(626\) 6.37654 + 19.2928i 0.254858 + 0.771094i
\(627\) −7.09976 + 2.94082i −0.283537 + 0.117445i
\(628\) −13.1160 + 21.8969i −0.523384 + 0.873782i
\(629\) −0.919525 + 2.21993i −0.0366639 + 0.0885144i
\(630\) 8.35503 + 9.68299i 0.332872 + 0.385780i
\(631\) 1.24929 1.24929i 0.0497335 0.0497335i −0.681803 0.731536i \(-0.738804\pi\)
0.731536 + 0.681803i \(0.238804\pi\)
\(632\) −23.3854 + 4.06813i −0.930223 + 0.161822i
\(633\) 41.0928 + 41.0928i 1.63329 + 1.63329i
\(634\) −0.364362 + 4.94922i −0.0144707 + 0.196559i
\(635\) −1.55045 0.642215i −0.0615275 0.0254855i
\(636\) 34.4318 + 46.3981i 1.36531 + 1.83980i
\(637\) −0.595466 1.43758i −0.0235932 0.0569590i
\(638\) 6.77462 + 3.40884i 0.268210 + 0.134957i
\(639\) 37.8529 1.49744
\(640\) 7.53849 + 4.26050i 0.297985 + 0.168411i
\(641\) 11.2362 0.443802 0.221901 0.975069i \(-0.428774\pi\)
0.221901 + 0.975069i \(0.428774\pi\)
\(642\) 31.1704 + 15.6843i 1.23020 + 0.619009i
\(643\) 5.74440 + 13.8682i 0.226537 + 0.546908i 0.995751 0.0920822i \(-0.0293523\pi\)
−0.769215 + 0.638991i \(0.779352\pi\)
\(644\) −14.8080 19.9543i −0.583517 0.786310i
\(645\) −9.94424 4.11904i −0.391554 0.162187i
\(646\) 0.0726903 0.987369i 0.00285996 0.0388475i
\(647\) 13.9424 + 13.9424i 0.548134 + 0.548134i 0.925901 0.377767i \(-0.123308\pi\)
−0.377767 + 0.925901i \(0.623308\pi\)
\(648\) −1.95055 + 0.339317i −0.0766248 + 0.0133296i
\(649\) 2.25298 2.25298i 0.0884371 0.0884371i
\(650\) 4.81514 + 5.58046i 0.188865 + 0.218884i
\(651\) 17.5706 42.4192i 0.688646 1.66254i
\(652\) −2.02257 + 3.37665i −0.0792098 + 0.132240i
\(653\) −0.361667 + 0.149807i −0.0141531 + 0.00586241i −0.389749 0.920921i \(-0.627438\pi\)
0.375596 + 0.926784i \(0.377438\pi\)
\(654\) 11.6815 + 35.3434i 0.456783 + 1.38204i
\(655\) 6.32634i 0.247191i
\(656\) 17.0075 + 31.7750i 0.664032 + 1.24060i
\(657\) 36.1646i 1.41091i
\(658\) −1.73694 + 0.574085i −0.0677131 + 0.0223802i
\(659\) −18.5077 + 7.66613i −0.720957 + 0.298630i −0.712830 0.701337i \(-0.752587\pi\)
−0.00812687 + 0.999967i \(0.502587\pi\)
\(660\) 0.918778 + 3.66351i 0.0357634 + 0.142602i
\(661\) 12.4139 29.9699i 0.482846 1.16569i −0.475405 0.879767i \(-0.657698\pi\)
0.958251 0.285927i \(-0.0923015\pi\)
\(662\) −17.9982 + 15.5299i −0.699522 + 0.603587i
\(663\) −0.529357 + 0.529357i −0.0205585 + 0.0205585i
\(664\) −18.3862 29.0073i −0.713523 1.12570i
\(665\) −4.01786 4.01786i −0.155806 0.155806i
\(666\) −74.7344 5.50196i −2.89590 0.213197i
\(667\) −29.5215 12.2282i −1.14308 0.473478i
\(668\) 6.28074 42.4252i 0.243009 1.64148i
\(669\) 18.5797 + 44.8554i 0.718334 + 1.73421i
\(670\) 1.88291 3.74203i 0.0727431 0.144567i
\(671\) −0.911176 −0.0351755
\(672\) −15.4389 34.7623i −0.595570 1.34099i
\(673\) −47.5269 −1.83203 −0.916014 0.401146i \(-0.868612\pi\)
−0.916014 + 0.401146i \(0.868612\pi\)
\(674\) 1.33897 2.66103i 0.0515752 0.102499i
\(675\) −9.32453 22.5114i −0.358902 0.866465i
\(676\) −22.9616 3.39930i −0.883140 0.130742i
\(677\) −41.7848 17.3078i −1.60592 0.665194i −0.613682 0.789553i \(-0.710312\pi\)
−0.992237 + 0.124360i \(0.960312\pi\)
\(678\) −9.64490 0.710059i −0.370410 0.0272696i
\(679\) −7.07847 7.07847i −0.271647 0.271647i
\(680\) −0.474817 0.106409i −0.0182084 0.00408060i
\(681\) −3.28321 + 3.28321i −0.125813 + 0.125813i
\(682\) 6.39542 5.51833i 0.244893 0.211308i
\(683\) 13.2754 32.0496i 0.507968 1.22634i −0.437083 0.899421i \(-0.643988\pi\)
0.945051 0.326922i \(-0.106012\pi\)
\(684\) 29.9487 7.51089i 1.14512 0.287186i
\(685\) 7.76744 3.21738i 0.296779 0.122930i
\(686\) −26.6238 + 8.79956i −1.01650 + 0.335969i
\(687\) 7.48100i 0.285418i
\(688\) 15.4229 + 12.6424i 0.587992 + 0.481988i
\(689\) 12.0922i 0.460674i
\(690\) −4.99402 15.1098i −0.190119 0.575222i
\(691\) 46.1276 19.1067i 1.75478 0.726852i 0.757520 0.652812i \(-0.226411\pi\)
0.997255 0.0740401i \(-0.0235893\pi\)
\(692\) 8.44647 + 5.05933i 0.321087 + 0.192327i
\(693\) 3.95525 9.54882i 0.150248 0.362730i
\(694\) 12.3896 + 14.3588i 0.470302 + 0.545052i
\(695\) 0.505515 0.505515i 0.0191753 0.0191753i
\(696\) −40.0025 28.1472i −1.51629 1.06692i
\(697\) −1.43208 1.43208i −0.0542438 0.0542438i
\(698\) 2.04163 27.7320i 0.0772769 1.04967i
\(699\) 40.3474 + 16.7124i 1.52608 + 0.632122i
\(700\) 16.8995 12.5410i 0.638741 0.474007i
\(701\) 5.34543 + 12.9050i 0.201894 + 0.487415i 0.992104 0.125422i \(-0.0400283\pi\)
−0.790210 + 0.612837i \(0.790028\pi\)
\(702\) −8.23344 4.14288i −0.310751 0.156363i
\(703\) 33.2933 1.25568
\(704\) 0.337349 6.98966i 0.0127143 0.263433i
\(705\) −1.17157 −0.0441240
\(706\) 36.2584 + 18.2444i 1.36460 + 0.686639i
\(707\) 4.40555 + 10.6359i 0.165688 + 0.400006i
\(708\) −16.5020 + 12.2461i −0.620184 + 0.460235i
\(709\) 31.1013 + 12.8826i 1.16803 + 0.483815i 0.880542 0.473968i \(-0.157179\pi\)
0.287491 + 0.957783i \(0.407179\pi\)
\(710\) −0.606874 + 8.24331i −0.0227756 + 0.309366i
\(711\) 29.4149 + 29.4149i 1.10315 + 1.10315i
\(712\) −13.6415 + 19.3871i −0.511236 + 0.726564i
\(713\) −25.1665 + 25.1665i −0.942492 + 0.942492i
\(714\) 1.39635 + 1.61829i 0.0522571 + 0.0605629i
\(715\) −0.302497 + 0.730292i −0.0113127 + 0.0273114i
\(716\) 13.5179 + 8.09706i 0.505189 + 0.302601i
\(717\) 47.6540 19.7390i 1.77967 0.737165i
\(718\) −4.01184 12.1382i −0.149721 0.452993i
\(719\) 0.571168i 0.0213010i −0.999943 0.0106505i \(-0.996610\pi\)
0.999943 0.0106505i \(-0.00339022\pi\)
\(720\) −1.49611 15.1014i −0.0557566 0.562795i
\(721\) 36.9590i 1.37643i
\(722\) 12.4878 4.12740i 0.464748 0.153606i
\(723\) −72.4893 + 30.0261i −2.69591 + 1.11668i
\(724\) 31.0306 7.78222i 1.15324 0.289224i
\(725\) 10.3562 25.0020i 0.384619 0.928552i
\(726\) −30.9122 + 26.6728i −1.14726 + 0.989920i
\(727\) −23.0479 + 23.0479i −0.854800 + 0.854800i −0.990720 0.135920i \(-0.956601\pi\)
0.135920 + 0.990720i \(0.456601\pi\)
\(728\) 1.74081 7.76782i 0.0645188 0.287895i
\(729\) −30.5768 30.5768i −1.13247 1.13247i
\(730\) 7.87565 + 0.579807i 0.291491 + 0.0214596i
\(731\) −1.03534 0.428852i −0.0382935 0.0158617i
\(732\) 5.81332 + 0.860620i 0.214866 + 0.0318094i
\(733\) −11.8891 28.7029i −0.439136 1.06017i −0.976248 0.216656i \(-0.930485\pi\)
0.537112 0.843511i \(-0.319515\pi\)
\(734\) 9.27979 18.4424i 0.342523 0.680720i
\(735\) −2.84523 −0.104948
\(736\) 0.744728 + 29.4749i 0.0274510 + 1.08646i
\(737\) −3.38534 −0.124701
\(738\) 28.3900 56.4213i 1.04505 2.07690i
\(739\) 2.87645 + 6.94437i 0.105812 + 0.255453i 0.967914 0.251282i \(-0.0808522\pi\)
−0.862102 + 0.506735i \(0.830852\pi\)
\(740\) 2.39635 16.1869i 0.0880916 0.595042i
\(741\) 9.58323 + 3.96951i 0.352049 + 0.145823i
\(742\) 34.4318 + 2.53488i 1.26403 + 0.0930582i
\(743\) −16.6576 16.6576i −0.611108 0.611108i 0.332127 0.943235i \(-0.392234\pi\)
−0.943235 + 0.332127i \(0.892234\pi\)
\(744\) −46.0151 + 29.1665i −1.68699 + 1.06929i
\(745\) 3.31788 3.31788i 0.121558 0.121558i
\(746\) 16.8929 14.5761i 0.618491 0.533669i
\(747\) −23.0328 + 55.6062i −0.842728 + 2.03452i
\(748\) 0.0956582 + 0.381425i 0.00349761 + 0.0139463i
\(749\) 19.2635 7.97920i 0.703873 0.291554i
\(750\) 27.2915 9.02023i 0.996544 0.329372i
\(751\) 31.1077i 1.13514i −0.823326 0.567569i \(-0.807884\pi\)
0.823326 0.567569i \(-0.192116\pi\)
\(752\) 2.07754 + 0.628912i 0.0757600 + 0.0229341i
\(753\) 28.6297i 1.04332i
\(754\) −3.21247 9.71961i −0.116991 0.353967i
\(755\) −8.17083 + 3.38447i −0.297367 + 0.123173i
\(756\) −13.5226 + 22.5758i −0.491813 + 0.821075i
\(757\) −2.35711 + 5.69056i −0.0856705 + 0.206827i −0.960909 0.276865i \(-0.910704\pi\)
0.875238 + 0.483692i \(0.160704\pi\)
\(758\) 5.68312 + 6.58641i 0.206420 + 0.239229i
\(759\) −9.09378 + 9.09378i −0.330083 + 0.330083i
\(760\) 1.15551 + 6.64242i 0.0419149 + 0.240946i
\(761\) −14.2913 14.2913i −0.518059 0.518059i 0.398925 0.916984i \(-0.369383\pi\)
−0.916984 + 0.398925i \(0.869383\pi\)
\(762\) 0.642215 8.72336i 0.0232650 0.316014i
\(763\) 20.5497 + 8.51196i 0.743949 + 0.308154i
\(764\) −18.4311 24.8366i −0.666815 0.898558i
\(765\) 0.326340 + 0.787854i 0.0117988 + 0.0284849i
\(766\) −15.7449 7.92246i −0.568885 0.286250i
\(767\) −4.30071 −0.155290
\(768\) −8.75413 + 44.2756i −0.315888 + 1.59766i
\(769\) 8.95004 0.322747 0.161373 0.986893i \(-0.448408\pi\)
0.161373 + 0.986893i \(0.448408\pi\)
\(770\) 2.01606 + 1.01444i 0.0726537 + 0.0365577i
\(771\) −21.6602 52.2924i −0.780073 1.88326i
\(772\) 15.7571 + 21.2333i 0.567110 + 0.764202i
\(773\) −26.6270 11.0293i −0.957707 0.396695i −0.151585 0.988444i \(-0.548438\pi\)
−0.806122 + 0.591749i \(0.798438\pi\)
\(774\) 2.56603 34.8550i 0.0922340 1.25284i
\(775\) −21.3137 21.3137i −0.765611 0.765611i
\(776\) 2.03573 + 11.7023i 0.0730783 + 0.420087i
\(777\) −50.8256 + 50.8256i −1.82336 + 1.82336i
\(778\) 14.1298 + 16.3756i 0.506577 + 0.587093i
\(779\) −10.7387 + 25.9256i −0.384756 + 0.928882i
\(780\) 2.61971 4.37356i 0.0938006 0.156599i
\(781\) 6.17132 2.55624i 0.220827 0.0914695i
\(782\) −0.519951 1.57316i −0.0185934 0.0562559i
\(783\) 33.8408i 1.20937i
\(784\) 5.04542 + 1.52735i 0.180194 + 0.0545482i
\(785\) 9.76782i 0.348629i
\(786\) −31.3081 + 10.3478i −1.11672 + 0.369093i
\(787\) 4.45056 1.84348i 0.158645 0.0657130i −0.301948 0.953324i \(-0.597637\pi\)
0.460593 + 0.887611i \(0.347637\pi\)
\(788\) −0.317537 1.26614i −0.0113118 0.0451043i
\(789\) 27.4455 66.2593i 0.977086 2.35889i
\(790\) −6.87735 + 5.93416i −0.244685 + 0.211128i
\(791\) −4.08625 + 4.08625i −0.145290 + 0.145290i
\(792\) −10.3583 + 6.56555i −0.368065 + 0.233297i
\(793\) 0.869673 + 0.869673i 0.0308830 + 0.0308830i
\(794\) 39.0406 + 2.87418i 1.38550 + 0.102001i
\(795\) 20.4277 + 8.46144i 0.724497 + 0.300096i
\(796\) 0.772467 5.21787i 0.0273794 0.184942i
\(797\) 14.9972 + 36.2064i 0.531227 + 1.28250i 0.930711 + 0.365756i \(0.119189\pi\)
−0.399484 + 0.916740i \(0.630811\pi\)
\(798\) 13.3119 26.4557i 0.471236 0.936520i
\(799\) −0.121978 −0.00431527
\(800\) −24.9626 + 0.630717i −0.882561 + 0.0222992i
\(801\) 41.5444 1.46790
\(802\) 10.4896 20.8468i 0.370402 0.736125i
\(803\) −2.44223 5.89607i −0.0861845 0.208068i
\(804\) 21.5985 + 3.19751i 0.761722 + 0.112767i
\(805\) −8.78530 3.63899i −0.309641 0.128258i
\(806\) −11.3711 0.837141i −0.400529 0.0294870i
\(807\) 55.3980 + 55.3980i 1.95010 + 1.95010i
\(808\) 2.98719 13.3294i 0.105089 0.468926i
\(809\) −18.3458 + 18.3458i −0.645005 + 0.645005i −0.951782 0.306777i \(-0.900750\pi\)
0.306777 + 0.951782i \(0.400750\pi\)
\(810\) −0.573630 + 0.494961i −0.0201553 + 0.0173911i
\(811\) −14.5476 + 35.1209i −0.510834 + 1.23326i 0.432565 + 0.901603i \(0.357609\pi\)
−0.943399 + 0.331660i \(0.892391\pi\)
\(812\) −28.3495 + 7.10984i −0.994874 + 0.249506i
\(813\) −42.9797 + 17.8028i −1.50736 + 0.624371i
\(814\) −12.5558 + 4.14988i −0.440081 + 0.145453i
\(815\) 1.50626i 0.0527621i
\(816\) −0.250040 2.52385i −0.00875315 0.0883523i
\(817\) 15.5275i 0.543238i
\(818\) −0.806993 2.44163i −0.0282159 0.0853695i
\(819\) −12.8890 + 5.33879i −0.450377 + 0.186552i
\(820\) 11.8319 + 7.08713i 0.413186 + 0.247493i
\(821\) −10.1999 + 24.6248i −0.355979 + 0.859410i 0.639877 + 0.768477i \(0.278985\pi\)
−0.995857 + 0.0909335i \(0.971015\pi\)
\(822\) 28.6272 + 33.1773i 0.998489 + 1.15719i
\(823\) −1.53506 + 1.53506i −0.0535088 + 0.0535088i −0.733355 0.679846i \(-0.762047\pi\)
0.679846 + 0.733355i \(0.262047\pi\)
\(824\) 25.2361 35.8653i 0.879142 1.24943i
\(825\) −7.70160 7.70160i −0.268135 0.268135i
\(826\) −0.901558 + 12.2461i −0.0313692 + 0.426095i
\(827\) 18.6205 + 7.71287i 0.647499 + 0.268203i 0.682167 0.731196i \(-0.261038\pi\)
−0.0346687 + 0.999399i \(0.511038\pi\)
\(828\) 41.4944 30.7928i 1.44203 1.07012i
\(829\) −9.98710 24.1110i −0.346866 0.837409i −0.996986 0.0775776i \(-0.975281\pi\)
0.650120 0.759831i \(-0.274719\pi\)
\(830\) −11.7402 5.90742i −0.407509 0.205050i
\(831\) 17.0993 0.593168
\(832\) −6.99327 + 6.34931i −0.242448 + 0.220123i
\(833\) −0.296230 −0.0102638
\(834\) 3.32857 + 1.67486i 0.115259 + 0.0579957i
\(835\) −6.28074 15.1630i −0.217354 0.524739i
\(836\) 4.37545 3.24700i 0.151328 0.112300i
\(837\) 34.8233 + 14.4243i 1.20367 + 0.498576i
\(838\) −4.06688 + 55.2414i −0.140488 + 1.90828i
\(839\) 31.2561 + 31.2561i 1.07908 + 1.07908i 0.996592 + 0.0824901i \(0.0262873\pi\)
0.0824901 + 0.996592i \(0.473713\pi\)
\(840\) −11.9043 8.37632i −0.410739 0.289010i
\(841\) −6.07041 + 6.07041i −0.209324 + 0.209324i
\(842\) −13.6131 15.7768i −0.469137 0.543703i
\(843\) 14.9729 36.1479i 0.515695 1.24500i
\(844\) −35.3480 21.1730i −1.21673 0.728804i
\(845\) −8.20664 + 3.39930i −0.282317 + 0.116940i
\(846\) −1.19379 3.61192i −0.0410435 0.124180i
\(847\) 24.3970i 0.838292i
\(848\) −31.6821 25.9704i −1.08797 0.891827i
\(849\) 65.2246i 2.23850i
\(850\) 1.33232 0.440351i 0.0456982 0.0151039i
\(851\) 51.4758 21.3220i 1.76457 0.730908i
\(852\) −41.7875 + 10.4800i −1.43162 + 0.359038i
\(853\) −7.73304 + 18.6692i −0.264774 + 0.639222i −0.999222 0.0394438i \(-0.987441\pi\)
0.734447 + 0.678666i \(0.237441\pi\)
\(854\) 2.65866 2.29404i 0.0909774 0.0785004i
\(855\) 8.35503 8.35503i 0.285736 0.285736i
\(856\) −24.1418 5.41030i −0.825148 0.184920i
\(857\) 4.21699 + 4.21699i 0.144050 + 0.144050i 0.775454 0.631404i \(-0.217521\pi\)
−0.631404 + 0.775454i \(0.717521\pi\)
\(858\) −4.10889 0.302497i −0.140275 0.0103271i
\(859\) −32.3968 13.4192i −1.10536 0.457857i −0.246025 0.969263i \(-0.579125\pi\)
−0.859339 + 0.511407i \(0.829125\pi\)
\(860\) 7.54931 + 1.11762i 0.257429 + 0.0381106i
\(861\) −23.1843 55.9719i −0.790120 1.90752i
\(862\) −1.81629 + 3.60963i −0.0618629 + 0.122944i
\(863\) −18.7779 −0.639207 −0.319604 0.947551i \(-0.603550\pi\)
−0.319604 + 0.947551i \(0.603550\pi\)
\(864\) 28.5376 12.6743i 0.970867 0.431190i
\(865\) 3.76782 0.128110
\(866\) −14.3135 + 28.4463i −0.486393 + 0.966643i
\(867\) −18.2965 44.1716i −0.621380 1.50015i
\(868\) −4.76744 + 32.2031i −0.161817 + 1.09305i
\(869\) 6.78206 + 2.80922i 0.230066 + 0.0952963i
\(870\) −18.6676 1.37431i −0.632891 0.0465935i
\(871\) 3.23114 + 3.23114i 0.109483 + 0.109483i
\(872\) −14.1295 22.2917i −0.478485 0.754892i
\(873\) 14.7195 14.7195i 0.498178 0.498178i
\(874\) −17.3812 + 14.9974i −0.587927 + 0.507296i
\(875\) 6.57277 15.8681i 0.222200 0.536439i
\(876\) 10.0126 + 39.9238i 0.338293 + 1.34890i
\(877\) 5.59652 2.31816i 0.188981 0.0782786i −0.286186 0.958174i \(-0.592388\pi\)
0.475167 + 0.879895i \(0.342388\pi\)
\(878\) 16.8576 5.57170i 0.568918 0.188036i
\(879\) 62.4121i 2.10511i
\(880\) −1.26373 2.36101i −0.0426003 0.0795896i
\(881\) 16.3413i 0.550552i −0.961365 0.275276i \(-0.911231\pi\)
0.961365 0.275276i \(-0.0887692\pi\)
\(882\) −2.89920 8.77177i −0.0976210 0.295361i
\(883\) −0.366860 + 0.151958i −0.0123458 + 0.00511380i −0.388848 0.921302i \(-0.627127\pi\)
0.376502 + 0.926416i \(0.377127\pi\)
\(884\) 0.272750 0.455352i 0.00917357 0.0153151i
\(885\) −3.00941 + 7.26535i −0.101160 + 0.244222i
\(886\) 23.7377 + 27.5106i 0.797483 + 0.924237i
\(887\) −6.38554 + 6.38554i −0.214406 + 0.214406i −0.806136 0.591730i \(-0.798445\pi\)
0.591730 + 0.806136i \(0.298445\pi\)
\(888\) 84.0260 14.6172i 2.81973 0.490520i
\(889\) −3.69583 3.69583i −0.123954 0.123954i
\(890\) −0.666058 + 9.04722i −0.0223263 + 0.303264i
\(891\) 0.565682 + 0.234313i 0.0189511 + 0.00784979i
\(892\) −20.5142 27.6436i −0.686865 0.925575i
\(893\) 0.646775 + 1.56145i 0.0216435 + 0.0522521i
\(894\) 21.8466 + 10.9927i 0.730661 + 0.367652i
\(895\) 6.03011 0.201564
\(896\) 16.6133 + 21.2440i 0.555013 + 0.709712i
\(897\) 17.3591 0.579604
\(898\) −11.1616 5.61628i −0.372468 0.187418i
\(899\) 16.0202 + 38.6761i 0.534302 + 1.28992i
\(900\) 26.0787 + 35.1420i 0.869291 + 1.17140i
\(901\) 2.12682 + 0.880960i 0.0708548 + 0.0293490i
\(902\) 0.818348 11.1158i 0.0272480 0.370116i
\(903\) −23.7043 23.7043i −0.788829 0.788829i
\(904\) 6.75548 1.17518i 0.224684 0.0390860i
\(905\) 8.65685 8.65685i 0.287764 0.287764i
\(906\) −30.1139 34.9003i −1.00047 1.15948i
\(907\) 14.6313 35.3230i 0.485823 1.17288i −0.470980 0.882144i \(-0.656100\pi\)
0.956803 0.290737i \(-0.0939004\pi\)
\(908\) 1.69167 2.82421i 0.0561399 0.0937248i
\(909\) −22.1171 + 9.16122i −0.733579 + 0.303859i
\(910\) −0.955999 2.89246i −0.0316911 0.0958841i
\(911\) 30.2904i 1.00356i −0.864994 0.501782i \(-0.832678\pi\)
0.864994 0.501782i \(-0.167322\pi\)
\(912\) −30.9823 + 16.5832i −1.02593 + 0.549126i
\(913\) 10.6211i 0.351509i
\(914\) −14.4095 + 4.76255i −0.476624 + 0.157531i
\(915\) 2.07772 0.860620i 0.0686873 0.0284512i
\(916\) 1.29029 + 5.14485i 0.0426323 + 0.169991i
\(917\) −7.54011 + 18.2034i −0.248996 + 0.601130i
\(918\) −1.32851 + 1.14631i −0.0438473 + 0.0378339i
\(919\) 42.1116 42.1116i 1.38913 1.38913i 0.561987 0.827146i \(-0.310037\pi\)
0.827146 0.561987i \(-0.189963\pi\)
\(920\) 6.04057 + 9.53003i 0.199152 + 0.314196i
\(921\) 33.7218 + 33.7218i 1.11117 + 1.11117i
\(922\) −23.2858 1.71431i −0.766878 0.0564577i
\(923\) −8.33002 3.45041i −0.274186 0.113572i
\(924\) −1.72269 + 11.6364i −0.0566723 + 0.382811i
\(925\) 18.0578 + 43.5953i 0.593736 + 1.43341i
\(926\) 11.9502 23.7495i 0.392709 0.780457i
\(927\) −76.8552 −2.52426
\(928\) 32.3653 + 12.4580i 1.06244 + 0.408954i
\(929\) 25.2271 0.827674 0.413837 0.910351i \(-0.364188\pi\)
0.413837 + 0.910351i \(0.364188\pi\)
\(930\) −9.37109 + 18.6238i −0.307290 + 0.610699i
\(931\) 1.57073 + 3.79208i 0.0514787 + 0.124280i
\(932\) −30.6303 4.53459i −1.00333 0.148535i
\(933\) −26.7176 11.0668i −0.874694 0.362310i
\(934\) −14.1821 1.04409i −0.464053 0.0341637i
\(935\) 0.106409 + 0.106409i 0.00347995 + 0.00347995i
\(936\) 16.1530 + 3.61997i 0.527976 + 0.118322i
\(937\) 30.3001 30.3001i 0.989863 0.989863i −0.0100865 0.999949i \(-0.503211\pi\)
0.999949 + 0.0100865i \(0.00321068\pi\)
\(938\) 9.87786 8.52318i 0.322524 0.278292i
\(939\) −15.5097 + 37.4437i −0.506140 + 1.22193i
\(940\) 0.805717 0.202067i 0.0262796 0.00659071i
\(941\) −1.05940 + 0.438818i −0.0345355 + 0.0143051i −0.399884 0.916566i \(-0.630950\pi\)
0.365349 + 0.930871i \(0.380950\pi\)
\(942\) −48.3394 + 15.9769i −1.57498 + 0.520555i
\(943\) 46.9618i 1.52929i
\(944\) 9.23666 11.2681i 0.300628 0.366745i
\(945\) 10.0707i 0.327599i
\(946\) −1.93544 5.85584i −0.0629266 0.190390i
\(947\) −25.2985 + 10.4790i −0.822089 + 0.340520i −0.753766 0.657143i \(-0.771765\pi\)
−0.0683231 + 0.997663i \(0.521765\pi\)
\(948\) −40.6163 24.3286i −1.31916 0.790157i
\(949\) −3.29652 + 7.95850i −0.107009 + 0.258344i
\(950\) −12.7015 14.7203i −0.412090 0.477589i
\(951\) −6.99925 + 6.99925i −0.226966 + 0.226966i
\(952\) −1.23942 0.872098i −0.0401697 0.0282648i
\(953\) 8.84307 + 8.84307i 0.286455 + 0.286455i 0.835677 0.549222i \(-0.185076\pi\)
−0.549222 + 0.835677i \(0.685076\pi\)
\(954\) −5.27120 + 71.6000i −0.170661 + 2.31813i
\(955\) −10.9348 4.52936i −0.353843 0.146567i
\(956\) −29.3683 + 21.7941i −0.949838 + 0.704870i
\(957\) 5.78880 + 13.9754i 0.187125 + 0.451761i
\(958\) 18.6689 + 9.39380i 0.603166 + 0.303500i
\(959\) 26.1847 0.845549
\(960\) 5.83260 + 16.2569i 0.188246 + 0.524689i
\(961\) 15.6274 0.504110
\(962\) 15.9448 + 8.02306i 0.514080 + 0.258674i
\(963\) 16.5925 + 40.0579i 0.534686 + 1.29085i
\(964\) 44.6738 33.1522i 1.43885 1.06776i
\(965\) 9.34838 + 3.87222i 0.300935 + 0.124651i
\(966\) 3.63899 49.4293i 0.117083 1.59036i
\(967\) −33.2189 33.2189i −1.06825 1.06825i −0.997494 0.0707549i \(-0.977459\pi\)
−0.0707549 0.997494i \(-0.522541\pi\)
\(968\) 16.6586 23.6751i 0.535428 0.760945i
\(969\) 1.39635 1.39635i 0.0448572 0.0448572i
\(970\) 2.96951 + 3.44148i 0.0953451 + 0.110499i
\(971\) −1.16696 + 2.81729i −0.0374495 + 0.0904111i −0.941498 0.337019i \(-0.890581\pi\)
0.904048 + 0.427431i \(0.140581\pi\)
\(972\) 25.0248 + 14.9895i 0.802670 + 0.480789i
\(973\) 2.05707 0.852067i 0.0659467 0.0273160i
\(974\) −8.21293 24.8489i −0.263159 0.796211i
\(975\) 14.7016i 0.470828i
\(976\) −4.14639 + 0.410786i −0.132723 + 0.0131489i
\(977\) 13.5807i 0.434484i 0.976118 + 0.217242i \(0.0697061\pi\)
−0.976118 + 0.217242i \(0.930294\pi\)
\(978\) −7.45426 + 2.46374i −0.238361 + 0.0787817i
\(979\) 6.77316 2.80553i 0.216471 0.0896653i
\(980\) 1.95673 0.490732i 0.0625055 0.0156759i
\(981\) −17.7004 + 42.7325i −0.565130 + 1.36434i
\(982\) 32.9999 28.4741i 1.05307 0.908646i
\(983\) −29.0855 + 29.0855i −0.927684 + 0.927684i −0.997556 0.0698724i \(-0.977741\pi\)
0.0698724 + 0.997556i \(0.477741\pi\)
\(984\) −15.7201 + 70.1462i −0.501140 + 2.23618i
\(985\) −0.353225 0.353225i −0.0112547 0.0112547i
\(986\) −1.94357 0.143086i −0.0618959 0.00455679i
\(987\) −3.37109 1.39635i −0.107303 0.0444463i
\(988\) −7.27525 1.07705i −0.231456 0.0342654i
\(989\) 9.94424 + 24.0075i 0.316209 + 0.763395i
\(990\) −2.10949 + 4.19233i −0.0670440 + 0.133241i
\(991\) 6.64680 0.211143 0.105571 0.994412i \(-0.466333\pi\)
0.105571 + 0.994412i \(0.466333\pi\)
\(992\) 26.6151 27.9949i 0.845030 0.888839i
\(993\) −47.4160 −1.50470
\(994\) −11.5711 + 22.9960i −0.367013 + 0.729390i
\(995\) −0.772467 1.86490i −0.0244889 0.0591213i
\(996\) 10.0318 67.7631i 0.317871 2.14716i
\(997\) 44.0238 + 18.2353i 1.39425 + 0.577516i 0.948252 0.317519i \(-0.102850\pi\)
0.445996 + 0.895035i \(0.352850\pi\)
\(998\) −34.2345 2.52035i −1.08367 0.0797803i
\(999\) −41.7244 41.7244i −1.32010 1.32010i
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 32.2.g.b.5.1 8
3.2 odd 2 288.2.v.b.37.2 8
4.3 odd 2 128.2.g.b.113.2 8
5.2 odd 4 800.2.ba.c.549.2 8
5.3 odd 4 800.2.ba.d.549.1 8
5.4 even 2 800.2.y.b.101.2 8
8.3 odd 2 256.2.g.c.225.1 8
8.5 even 2 256.2.g.d.225.2 8
12.11 even 2 1152.2.v.b.1009.1 8
16.3 odd 4 512.2.g.f.193.1 8
16.5 even 4 512.2.g.e.193.1 8
16.11 odd 4 512.2.g.g.193.2 8
16.13 even 4 512.2.g.h.193.2 8
32.3 odd 8 256.2.g.c.33.1 8
32.5 even 8 512.2.g.h.321.2 8
32.11 odd 8 512.2.g.g.321.2 8
32.13 even 8 inner 32.2.g.b.13.1 yes 8
32.19 odd 8 128.2.g.b.17.2 8
32.21 even 8 512.2.g.e.321.1 8
32.27 odd 8 512.2.g.f.321.1 8
32.29 even 8 256.2.g.d.33.2 8
64.13 even 16 4096.2.a.k.1.1 8
64.19 odd 16 4096.2.a.q.1.1 8
64.45 even 16 4096.2.a.k.1.8 8
64.51 odd 16 4096.2.a.q.1.8 8
96.77 odd 8 288.2.v.b.109.2 8
96.83 even 8 1152.2.v.b.145.1 8
160.13 odd 8 800.2.ba.c.749.2 8
160.77 odd 8 800.2.ba.d.749.1 8
160.109 even 8 800.2.y.b.301.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.b.5.1 8 1.1 even 1 trivial
32.2.g.b.13.1 yes 8 32.13 even 8 inner
128.2.g.b.17.2 8 32.19 odd 8
128.2.g.b.113.2 8 4.3 odd 2
256.2.g.c.33.1 8 32.3 odd 8
256.2.g.c.225.1 8 8.3 odd 2
256.2.g.d.33.2 8 32.29 even 8
256.2.g.d.225.2 8 8.5 even 2
288.2.v.b.37.2 8 3.2 odd 2
288.2.v.b.109.2 8 96.77 odd 8
512.2.g.e.193.1 8 16.5 even 4
512.2.g.e.321.1 8 32.21 even 8
512.2.g.f.193.1 8 16.3 odd 4
512.2.g.f.321.1 8 32.27 odd 8
512.2.g.g.193.2 8 16.11 odd 4
512.2.g.g.321.2 8 32.11 odd 8
512.2.g.h.193.2 8 16.13 even 4
512.2.g.h.321.2 8 32.5 even 8
800.2.y.b.101.2 8 5.4 even 2
800.2.y.b.301.2 8 160.109 even 8
800.2.ba.c.549.2 8 5.2 odd 4
800.2.ba.c.749.2 8 160.13 odd 8
800.2.ba.d.549.1 8 5.3 odd 4
800.2.ba.d.749.1 8 160.77 odd 8
1152.2.v.b.145.1 8 96.83 even 8
1152.2.v.b.1009.1 8 12.11 even 2
4096.2.a.k.1.1 8 64.13 even 16
4096.2.a.k.1.8 8 64.45 even 16
4096.2.a.q.1.1 8 64.19 odd 16
4096.2.a.q.1.8 8 64.51 odd 16