Properties

Label 170.2.n.b.59.4
Level $170$
Weight $2$
Character 170.59
Analytic conductor $1.357$
Analytic rank $0$
Dimension $20$
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] = [170,2,Mod(9,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.n (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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} - 14520 x^{8} + 27936 x^{7} + 27880 x^{6} - 121104 x^{5} + 187460 x^{4} + \cdots + 2048 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 59.4
Root \(-0.826884 + 1.99627i\) of defining polynomial
Character \(\chi\) \(=\) 170.59
Dual form 170.2.n.b.49.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.99627 + 0.826884i) q^{3} +1.00000i q^{4} +(0.399242 - 2.20014i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(-1.32795 - 3.20595i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.99627 + 0.826884i) q^{3} +1.00000i q^{4} +(0.399242 - 2.20014i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(-1.32795 - 3.20595i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +(-1.83804 + 1.27343i) q^{10} +(1.63382 + 3.94439i) q^{11} +(-0.826884 + 1.99627i) q^{12} +5.21229 q^{13} +(-1.32795 + 3.20595i) q^{14} +(2.61625 - 4.06195i) q^{15} -1.00000 q^{16} +(-2.46922 + 3.30196i) q^{17} -1.66885i q^{18} +(-0.305686 + 0.305686i) q^{19} +(2.20014 + 0.399242i) q^{20} -7.49802i q^{21} +(1.63382 - 3.94439i) q^{22} +(-6.86651 + 2.84420i) q^{23} +(1.99627 - 0.826884i) q^{24} +(-4.68121 - 1.75677i) q^{25} +(-3.68564 - 3.68564i) q^{26} +(-1.10071 - 2.65734i) q^{27} +(3.20595 - 1.32795i) q^{28} +(3.46752 + 1.43630i) q^{29} +(-4.72221 + 1.02226i) q^{30} +(-0.648377 + 1.56532i) q^{31} +(0.707107 + 0.707107i) q^{32} +9.22506i q^{33} +(4.08084 - 0.588835i) q^{34} +(-7.58371 + 1.64172i) q^{35} +(-1.18005 + 1.18005i) q^{36} +(4.56523 + 1.89098i) q^{37} +0.432305 q^{38} +(10.4052 + 4.30996i) q^{39} +(-1.27343 - 1.83804i) q^{40} +(-4.20525 + 1.74187i) q^{41} +(-5.30190 + 5.30190i) q^{42} +(-2.38395 + 2.38395i) q^{43} +(-3.94439 + 1.63382i) q^{44} +(3.06741 - 2.12515i) q^{45} +(6.86651 + 2.84420i) q^{46} -3.47098 q^{47} +(-1.99627 - 0.826884i) q^{48} +(-3.56493 + 3.56493i) q^{49} +(2.06789 + 4.55234i) q^{50} +(-7.65958 + 4.54986i) q^{51} +5.21229i q^{52} +(-9.73490 - 9.73490i) q^{53} +(-1.10071 + 2.65734i) q^{54} +(9.33048 - 2.01986i) q^{55} +(-3.20595 - 1.32795i) q^{56} +(-0.863000 + 0.357466i) q^{57} +(-1.43630 - 3.46752i) q^{58} +(6.37226 + 6.37226i) q^{59} +(4.06195 + 2.61625i) q^{60} +(5.75032 - 2.38186i) q^{61} +(1.56532 - 0.648377i) q^{62} +(2.21615 - 5.35025i) q^{63} -1.00000i q^{64} +(2.08096 - 11.4678i) q^{65} +(6.52310 - 6.52310i) q^{66} +0.409276i q^{67} +(-3.30196 - 2.46922i) q^{68} -16.0593 q^{69} +(6.52336 + 4.20162i) q^{70} +(-3.84587 + 9.28474i) q^{71} +1.66885 q^{72} +(-0.401916 + 0.970312i) q^{73} +(-1.89098 - 4.56523i) q^{74} +(-7.89234 - 7.37782i) q^{75} +(-0.305686 - 0.305686i) q^{76} +(10.4759 - 10.4759i) q^{77} +(-4.30996 - 10.4052i) q^{78} +(0.218700 + 0.527989i) q^{79} +(-0.399242 + 2.20014i) q^{80} -11.2215i q^{81} +(4.20525 + 1.74187i) q^{82} +(10.6949 + 10.6949i) q^{83} +7.49802 q^{84} +(6.27895 + 6.75091i) q^{85} +3.37141 q^{86} +(5.73448 + 5.73448i) q^{87} +(3.94439 + 1.63382i) q^{88} -14.5683i q^{89} +(-3.67170 - 0.666274i) q^{90} +(-6.92165 - 16.7103i) q^{91} +(-2.84420 - 6.86651i) q^{92} +(-2.58868 + 2.58868i) q^{93} +(2.45435 + 2.45435i) q^{94} +(0.550509 + 0.794594i) q^{95} +(0.826884 + 1.99627i) q^{96} +(3.70749 - 8.95068i) q^{97} +5.04157 q^{98} +(-2.72660 + 6.58259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 1.99627 + 0.826884i 1.15255 + 0.477402i 0.875388 0.483422i \(-0.160606\pi\)
0.277162 + 0.960823i \(0.410606\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0.399242 2.20014i 0.178546 0.983932i
\(6\) −0.826884 1.99627i −0.337574 0.814976i
\(7\) −1.32795 3.20595i −0.501917 1.21174i −0.948438 0.316962i \(-0.897337\pi\)
0.446521 0.894773i \(-0.352663\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.18005 + 1.18005i 0.393351 + 0.393351i
\(10\) −1.83804 + 1.27343i −0.581239 + 0.402693i
\(11\) 1.63382 + 3.94439i 0.492615 + 1.18928i 0.953385 + 0.301758i \(0.0975734\pi\)
−0.460770 + 0.887520i \(0.652427\pi\)
\(12\) −0.826884 + 1.99627i −0.238701 + 0.576275i
\(13\) 5.21229 1.44563 0.722814 0.691042i \(-0.242848\pi\)
0.722814 + 0.691042i \(0.242848\pi\)
\(14\) −1.32795 + 3.20595i −0.354909 + 0.856827i
\(15\) 2.61625 4.06195i 0.675514 1.04879i
\(16\) −1.00000 −0.250000
\(17\) −2.46922 + 3.30196i −0.598874 + 0.800843i
\(18\) 1.66885i 0.393351i
\(19\) −0.305686 + 0.305686i −0.0701292 + 0.0701292i −0.741301 0.671172i \(-0.765791\pi\)
0.671172 + 0.741301i \(0.265791\pi\)
\(20\) 2.20014 + 0.399242i 0.491966 + 0.0892732i
\(21\) 7.49802i 1.63620i
\(22\) 1.63382 3.94439i 0.348331 0.840946i
\(23\) −6.86651 + 2.84420i −1.43177 + 0.593057i −0.957787 0.287479i \(-0.907183\pi\)
−0.473980 + 0.880536i \(0.657183\pi\)
\(24\) 1.99627 0.826884i 0.407488 0.168787i
\(25\) −4.68121 1.75677i −0.936242 0.351355i
\(26\) −3.68564 3.68564i −0.722814 0.722814i
\(27\) −1.10071 2.65734i −0.211831 0.511406i
\(28\) 3.20595 1.32795i 0.605868 0.250959i
\(29\) 3.46752 + 1.43630i 0.643903 + 0.266713i 0.680647 0.732611i \(-0.261699\pi\)
−0.0367441 + 0.999325i \(0.511699\pi\)
\(30\) −4.72221 + 1.02226i −0.862153 + 0.186639i
\(31\) −0.648377 + 1.56532i −0.116452 + 0.281140i −0.971349 0.237658i \(-0.923620\pi\)
0.854897 + 0.518798i \(0.173620\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 9.22506i 1.60588i
\(34\) 4.08084 0.588835i 0.699859 0.100984i
\(35\) −7.58371 + 1.64172i −1.28188 + 0.277501i
\(36\) −1.18005 + 1.18005i −0.196676 + 0.196676i
\(37\) 4.56523 + 1.89098i 0.750519 + 0.310875i 0.724953 0.688798i \(-0.241861\pi\)
0.0255657 + 0.999673i \(0.491861\pi\)
\(38\) 0.432305 0.0701292
\(39\) 10.4052 + 4.30996i 1.66616 + 0.690146i
\(40\) −1.27343 1.83804i −0.201346 0.290619i
\(41\) −4.20525 + 1.74187i −0.656750 + 0.272035i −0.686070 0.727535i \(-0.740666\pi\)
0.0293201 + 0.999570i \(0.490666\pi\)
\(42\) −5.30190 + 5.30190i −0.818101 + 0.818101i
\(43\) −2.38395 + 2.38395i −0.363549 + 0.363549i −0.865118 0.501569i \(-0.832756\pi\)
0.501569 + 0.865118i \(0.332756\pi\)
\(44\) −3.94439 + 1.63382i −0.594639 + 0.246307i
\(45\) 3.06741 2.12515i 0.457262 0.316799i
\(46\) 6.86651 + 2.84420i 1.01241 + 0.419355i
\(47\) −3.47098 −0.506294 −0.253147 0.967428i \(-0.581466\pi\)
−0.253147 + 0.967428i \(0.581466\pi\)
\(48\) −1.99627 0.826884i −0.288137 0.119350i
\(49\) −3.56493 + 3.56493i −0.509276 + 0.509276i
\(50\) 2.06789 + 4.55234i 0.292444 + 0.643799i
\(51\) −7.65958 + 4.54986i −1.07256 + 0.637108i
\(52\) 5.21229i 0.722814i
\(53\) −9.73490 9.73490i −1.33719 1.33719i −0.898769 0.438422i \(-0.855537\pi\)
−0.438422 0.898769i \(-0.644463\pi\)
\(54\) −1.10071 + 2.65734i −0.149787 + 0.361619i
\(55\) 9.33048 2.01986i 1.25812 0.272358i
\(56\) −3.20595 1.32795i −0.428413 0.177455i
\(57\) −0.863000 + 0.357466i −0.114307 + 0.0473476i
\(58\) −1.43630 3.46752i −0.188595 0.455308i
\(59\) 6.37226 + 6.37226i 0.829598 + 0.829598i 0.987461 0.157863i \(-0.0504605\pi\)
−0.157863 + 0.987461i \(0.550461\pi\)
\(60\) 4.06195 + 2.61625i 0.524396 + 0.337757i
\(61\) 5.75032 2.38186i 0.736253 0.304966i 0.0171342 0.999853i \(-0.494546\pi\)
0.719119 + 0.694887i \(0.244546\pi\)
\(62\) 1.56532 0.648377i 0.198796 0.0823439i
\(63\) 2.21615 5.35025i 0.279208 0.674068i
\(64\) 1.00000i 0.125000i
\(65\) 2.08096 11.4678i 0.258112 1.42240i
\(66\) 6.52310 6.52310i 0.802938 0.802938i
\(67\) 0.409276i 0.0500010i 0.999687 + 0.0250005i \(0.00795873\pi\)
−0.999687 + 0.0250005i \(0.992041\pi\)
\(68\) −3.30196 2.46922i −0.400422 0.299437i
\(69\) −16.0593 −1.93331
\(70\) 6.52336 + 4.20162i 0.779691 + 0.502190i
\(71\) −3.84587 + 9.28474i −0.456420 + 1.10190i 0.513416 + 0.858140i \(0.328380\pi\)
−0.969836 + 0.243757i \(0.921620\pi\)
\(72\) 1.66885 0.196676
\(73\) −0.401916 + 0.970312i −0.0470407 + 0.113566i −0.945653 0.325177i \(-0.894576\pi\)
0.898613 + 0.438743i \(0.144576\pi\)
\(74\) −1.89098 4.56523i −0.219822 0.530697i
\(75\) −7.89234 7.37782i −0.911328 0.851917i
\(76\) −0.305686 0.305686i −0.0350646 0.0350646i
\(77\) 10.4759 10.4759i 1.19384 1.19384i
\(78\) −4.30996 10.4052i −0.488007 1.17815i
\(79\) 0.218700 + 0.527989i 0.0246057 + 0.0594034i 0.935705 0.352784i \(-0.114765\pi\)
−0.911099 + 0.412187i \(0.864765\pi\)
\(80\) −0.399242 + 2.20014i −0.0446366 + 0.245983i
\(81\) 11.2215i 1.24683i
\(82\) 4.20525 + 1.74187i 0.464393 + 0.192358i
\(83\) 10.6949 + 10.6949i 1.17391 + 1.17391i 0.981269 + 0.192644i \(0.0617062\pi\)
0.192644 + 0.981269i \(0.438294\pi\)
\(84\) 7.49802 0.818101
\(85\) 6.27895 + 6.75091i 0.681048 + 0.732239i
\(86\) 3.37141 0.363549
\(87\) 5.73448 + 5.73448i 0.614801 + 0.614801i
\(88\) 3.94439 + 1.63382i 0.420473 + 0.174166i
\(89\) 14.5683i 1.54424i −0.635478 0.772119i \(-0.719197\pi\)
0.635478 0.772119i \(-0.280803\pi\)
\(90\) −3.67170 0.666274i −0.387031 0.0702315i
\(91\) −6.92165 16.7103i −0.725586 1.75172i
\(92\) −2.84420 6.86651i −0.296529 0.715883i
\(93\) −2.58868 + 2.58868i −0.268433 + 0.268433i
\(94\) 2.45435 + 2.45435i 0.253147 + 0.253147i
\(95\) 0.550509 + 0.794594i 0.0564810 + 0.0815236i
\(96\) 0.826884 + 1.99627i 0.0843935 + 0.203744i
\(97\) 3.70749 8.95068i 0.376439 0.908804i −0.616188 0.787599i \(-0.711324\pi\)
0.992627 0.121205i \(-0.0386760\pi\)
\(98\) 5.04157 0.509276
\(99\) −2.72660 + 6.58259i −0.274033 + 0.661575i
\(100\) 1.75677 4.68121i 0.175677 0.468121i
\(101\) 11.0547 1.09999 0.549993 0.835170i \(-0.314631\pi\)
0.549993 + 0.835170i \(0.314631\pi\)
\(102\) 8.63338 + 2.19891i 0.854832 + 0.217724i
\(103\) 6.34442i 0.625135i −0.949896 0.312567i \(-0.898811\pi\)
0.949896 0.312567i \(-0.101189\pi\)
\(104\) 3.68564 3.68564i 0.361407 0.361407i
\(105\) −16.4967 2.99352i −1.60991 0.292138i
\(106\) 13.7672i 1.33719i
\(107\) −0.619790 + 1.49630i −0.0599173 + 0.144653i −0.951003 0.309182i \(-0.899945\pi\)
0.891085 + 0.453836i \(0.149945\pi\)
\(108\) 2.65734 1.10071i 0.255703 0.105916i
\(109\) −7.65614 + 3.17128i −0.733325 + 0.303753i −0.717918 0.696128i \(-0.754905\pi\)
−0.0154075 + 0.999881i \(0.504905\pi\)
\(110\) −8.02591 5.16939i −0.765240 0.492882i
\(111\) 7.54983 + 7.54983i 0.716598 + 0.716598i
\(112\) 1.32795 + 3.20595i 0.125479 + 0.302934i
\(113\) −6.24358 + 2.58618i −0.587347 + 0.243287i −0.656509 0.754318i \(-0.727967\pi\)
0.0691619 + 0.997605i \(0.477967\pi\)
\(114\) 0.863000 + 0.357466i 0.0808274 + 0.0334798i
\(115\) 3.51624 + 16.2428i 0.327891 + 1.51465i
\(116\) −1.43630 + 3.46752i −0.133357 + 0.321952i
\(117\) 6.15078 + 6.15078i 0.568640 + 0.568640i
\(118\) 9.01174i 0.829598i
\(119\) 13.8649 + 3.53137i 1.27100 + 0.323720i
\(120\) −1.02226 4.72221i −0.0933194 0.431076i
\(121\) −5.11065 + 5.11065i −0.464605 + 0.464605i
\(122\) −5.75032 2.38186i −0.520609 0.215643i
\(123\) −9.83517 −0.886807
\(124\) −1.56532 0.648377i −0.140570 0.0582260i
\(125\) −5.73408 + 9.59793i −0.512872 + 0.858465i
\(126\) −5.35025 + 2.21615i −0.476638 + 0.197430i
\(127\) −1.28241 + 1.28241i −0.113796 + 0.113796i −0.761712 0.647916i \(-0.775641\pi\)
0.647916 + 0.761712i \(0.275641\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −6.73026 + 2.78777i −0.592567 + 0.245449i
\(130\) −9.58039 + 6.63746i −0.840256 + 0.582144i
\(131\) −3.98341 1.64998i −0.348032 0.144160i 0.201818 0.979423i \(-0.435315\pi\)
−0.549850 + 0.835263i \(0.685315\pi\)
\(132\) −9.22506 −0.802938
\(133\) 1.38595 + 0.574079i 0.120177 + 0.0497790i
\(134\) 0.289402 0.289402i 0.0250005 0.0250005i
\(135\) −6.28597 + 1.36079i −0.541010 + 0.117118i
\(136\) 0.588835 + 4.08084i 0.0504922 + 0.349929i
\(137\) 4.41897i 0.377538i −0.982022 0.188769i \(-0.939550\pi\)
0.982022 0.188769i \(-0.0604497\pi\)
\(138\) 11.3556 + 11.3556i 0.966654 + 0.966654i
\(139\) 2.07037 4.99833i 0.175607 0.423952i −0.811429 0.584451i \(-0.801310\pi\)
0.987036 + 0.160498i \(0.0513101\pi\)
\(140\) −1.64172 7.58371i −0.138751 0.640940i
\(141\) −6.92902 2.87009i −0.583529 0.241706i
\(142\) 9.28474 3.84587i 0.779158 0.322738i
\(143\) 8.51593 + 20.5593i 0.712138 + 1.71925i
\(144\) −1.18005 1.18005i −0.0983379 0.0983379i
\(145\) 4.54443 7.05560i 0.377394 0.585936i
\(146\) 0.970312 0.401916i 0.0803036 0.0332628i
\(147\) −10.0644 + 4.16879i −0.830094 + 0.343836i
\(148\) −1.89098 + 4.56523i −0.155438 + 0.375260i
\(149\) 10.4546i 0.856472i −0.903667 0.428236i \(-0.859135\pi\)
0.903667 0.428236i \(-0.140865\pi\)
\(150\) 0.363817 + 10.7976i 0.0297055 + 0.881623i
\(151\) 12.2681 12.2681i 0.998364 0.998364i −0.00163493 0.999999i \(-0.500520\pi\)
0.999999 + 0.00163493i \(0.000520415\pi\)
\(152\) 0.432305i 0.0350646i
\(153\) −6.81031 + 0.982677i −0.550581 + 0.0794447i
\(154\) −14.8151 −1.19384
\(155\) 3.18506 + 2.05146i 0.255830 + 0.164777i
\(156\) −4.30996 + 10.4052i −0.345073 + 0.833079i
\(157\) 2.90181 0.231589 0.115795 0.993273i \(-0.463059\pi\)
0.115795 + 0.993273i \(0.463059\pi\)
\(158\) 0.218700 0.527989i 0.0173989 0.0420046i
\(159\) −11.3839 27.4832i −0.902802 2.17956i
\(160\) 1.83804 1.27343i 0.145310 0.100673i
\(161\) 18.2367 + 18.2367i 1.43726 + 1.43726i
\(162\) −7.93479 + 7.93479i −0.623416 + 0.623416i
\(163\) 1.43563 + 3.46591i 0.112447 + 0.271471i 0.970078 0.242795i \(-0.0780643\pi\)
−0.857631 + 0.514266i \(0.828064\pi\)
\(164\) −1.74187 4.20525i −0.136017 0.328375i
\(165\) 20.2964 + 3.68303i 1.58007 + 0.286723i
\(166\) 15.1248i 1.17391i
\(167\) −21.8009 9.03022i −1.68700 0.698779i −0.687381 0.726297i \(-0.741240\pi\)
−0.999621 + 0.0275182i \(0.991240\pi\)
\(168\) −5.30190 5.30190i −0.409050 0.409050i
\(169\) 14.1680 1.08984
\(170\) 0.333724 9.21350i 0.0255955 0.706643i
\(171\) −0.721452 −0.0551708
\(172\) −2.38395 2.38395i −0.181774 0.181774i
\(173\) 13.9467 + 5.77690i 1.06035 + 0.439209i 0.843574 0.537013i \(-0.180447\pi\)
0.216771 + 0.976222i \(0.430447\pi\)
\(174\) 8.10978i 0.614801i
\(175\) 0.584277 + 17.3406i 0.0441672 + 1.31083i
\(176\) −1.63382 3.94439i −0.123154 0.297319i
\(177\) 7.45166 + 17.9899i 0.560101 + 1.35220i
\(178\) −10.3013 + 10.3013i −0.772119 + 0.772119i
\(179\) −8.99629 8.99629i −0.672415 0.672415i 0.285858 0.958272i \(-0.407722\pi\)
−0.958272 + 0.285858i \(0.907722\pi\)
\(180\) 2.12515 + 3.06741i 0.158400 + 0.228631i
\(181\) −5.92939 14.3148i −0.440728 1.06401i −0.975694 0.219138i \(-0.929676\pi\)
0.534966 0.844873i \(-0.320324\pi\)
\(182\) −6.92165 + 16.7103i −0.513067 + 1.23865i
\(183\) 13.4487 0.994159
\(184\) −2.84420 + 6.86651i −0.209677 + 0.506206i
\(185\) 5.98305 9.28917i 0.439882 0.682954i
\(186\) 3.66094 0.268433
\(187\) −17.0585 4.34476i −1.24744 0.317721i
\(188\) 3.47098i 0.253147i
\(189\) −7.05763 + 7.05763i −0.513367 + 0.513367i
\(190\) 0.172594 0.951131i 0.0125213 0.0690023i
\(191\) 8.44496i 0.611056i 0.952183 + 0.305528i \(0.0988329\pi\)
−0.952183 + 0.305528i \(0.901167\pi\)
\(192\) 0.826884 1.99627i 0.0596752 0.144069i
\(193\) 19.7167 8.16694i 1.41924 0.587870i 0.464572 0.885535i \(-0.346208\pi\)
0.954670 + 0.297666i \(0.0962080\pi\)
\(194\) −8.95068 + 3.70749i −0.642622 + 0.266183i
\(195\) 13.6367 21.1721i 0.976543 1.51616i
\(196\) −3.56493 3.56493i −0.254638 0.254638i
\(197\) −0.345500 0.834111i −0.0246159 0.0594280i 0.911094 0.412199i \(-0.135239\pi\)
−0.935710 + 0.352771i \(0.885239\pi\)
\(198\) 6.58259 2.72660i 0.467804 0.193771i
\(199\) −0.329021 0.136285i −0.0233237 0.00966099i 0.370991 0.928636i \(-0.379018\pi\)
−0.394315 + 0.918975i \(0.629018\pi\)
\(200\) −4.55234 + 2.06789i −0.321899 + 0.146222i
\(201\) −0.338423 + 0.817026i −0.0238705 + 0.0576286i
\(202\) −7.81686 7.81686i −0.549993 0.549993i
\(203\) 13.0240i 0.914109i
\(204\) −4.54986 7.65958i −0.318554 0.536278i
\(205\) 2.15345 + 9.94757i 0.150403 + 0.694768i
\(206\) −4.48618 + 4.48618i −0.312567 + 0.312567i
\(207\) −11.4592 4.74654i −0.796467 0.329908i
\(208\) −5.21229 −0.361407
\(209\) −1.70518 0.706309i −0.117950 0.0488564i
\(210\) 9.54817 + 13.7816i 0.658886 + 0.951024i
\(211\) −10.4640 + 4.33435i −0.720374 + 0.298389i −0.712590 0.701581i \(-0.752478\pi\)
−0.00778455 + 0.999970i \(0.502478\pi\)
\(212\) 9.73490 9.73490i 0.668596 0.668596i
\(213\) −15.3548 + 15.3548i −1.05209 + 1.05209i
\(214\) 1.49630 0.619790i 0.102285 0.0423680i
\(215\) 4.29324 + 6.19679i 0.292797 + 0.422617i
\(216\) −2.65734 1.10071i −0.180809 0.0748937i
\(217\) 5.87935 0.399116
\(218\) 7.65614 + 3.17128i 0.518539 + 0.214786i
\(219\) −1.60467 + 1.60467i −0.108434 + 0.108434i
\(220\) 2.01986 + 9.33048i 0.136179 + 0.629061i
\(221\) −12.8703 + 17.2108i −0.865750 + 1.15772i
\(222\) 10.6771i 0.716598i
\(223\) −12.2971 12.2971i −0.823478 0.823478i 0.163127 0.986605i \(-0.447842\pi\)
−0.986605 + 0.163127i \(0.947842\pi\)
\(224\) 1.32795 3.20595i 0.0887273 0.214207i
\(225\) −3.45100 7.59717i −0.230066 0.506478i
\(226\) 6.24358 + 2.58618i 0.415317 + 0.172030i
\(227\) 11.0487 4.57652i 0.733328 0.303755i 0.0154095 0.999881i \(-0.495095\pi\)
0.717919 + 0.696127i \(0.245095\pi\)
\(228\) −0.357466 0.863000i −0.0236738 0.0571536i
\(229\) −8.31862 8.31862i −0.549710 0.549710i 0.376647 0.926357i \(-0.377077\pi\)
−0.926357 + 0.376647i \(0.877077\pi\)
\(230\) 8.99904 13.9717i 0.593379 0.921270i
\(231\) 29.5751 12.2504i 1.94590 0.806017i
\(232\) 3.46752 1.43630i 0.227654 0.0942974i
\(233\) −8.94925 + 21.6054i −0.586285 + 1.41542i 0.300744 + 0.953705i \(0.402765\pi\)
−0.887030 + 0.461713i \(0.847235\pi\)
\(234\) 8.69852i 0.568640i
\(235\) −1.38576 + 7.63663i −0.0903969 + 0.498159i
\(236\) −6.37226 + 6.37226i −0.414799 + 0.414799i
\(237\) 1.23485i 0.0802122i
\(238\) −7.30692 12.3010i −0.473638 0.797358i
\(239\) 13.2057 0.854206 0.427103 0.904203i \(-0.359534\pi\)
0.427103 + 0.904203i \(0.359534\pi\)
\(240\) −2.61625 + 4.06195i −0.168879 + 0.262198i
\(241\) −8.66402 + 20.9168i −0.558098 + 1.34737i 0.353171 + 0.935559i \(0.385103\pi\)
−0.911270 + 0.411810i \(0.864897\pi\)
\(242\) 7.22756 0.464605
\(243\) 5.97675 14.4291i 0.383409 0.925630i
\(244\) 2.38186 + 5.75032i 0.152483 + 0.368126i
\(245\) 6.42007 + 9.26660i 0.410163 + 0.592022i
\(246\) 6.95451 + 6.95451i 0.443404 + 0.443404i
\(247\) −1.59332 + 1.59332i −0.101381 + 0.101381i
\(248\) 0.648377 + 1.56532i 0.0411720 + 0.0993979i
\(249\) 12.5065 + 30.1933i 0.792565 + 1.91342i
\(250\) 10.8414 2.73216i 0.685668 0.172797i
\(251\) 3.13046i 0.197593i 0.995108 + 0.0987965i \(0.0314993\pi\)
−0.995108 + 0.0987965i \(0.968501\pi\)
\(252\) 5.35025 + 2.21615i 0.337034 + 0.139604i
\(253\) −22.4373 22.4373i −1.41062 1.41062i
\(254\) 1.81360 0.113796
\(255\) 6.95229 + 18.6686i 0.435369 + 1.16908i
\(256\) 1.00000 0.0625000
\(257\) 5.80608 + 5.80608i 0.362173 + 0.362173i 0.864613 0.502439i \(-0.167564\pi\)
−0.502439 + 0.864613i \(0.667564\pi\)
\(258\) 6.73026 + 2.78777i 0.419008 + 0.173559i
\(259\) 17.1470i 1.06546i
\(260\) 11.4678 + 2.08096i 0.711200 + 0.129056i
\(261\) 2.39696 + 5.78677i 0.148368 + 0.358192i
\(262\) 1.64998 + 3.98341i 0.101936 + 0.246096i
\(263\) 17.8286 17.8286i 1.09936 1.09936i 0.104871 0.994486i \(-0.466557\pi\)
0.994486 0.104871i \(-0.0334431\pi\)
\(264\) 6.52310 + 6.52310i 0.401469 + 0.401469i
\(265\) −25.3047 + 17.5315i −1.55446 + 1.07695i
\(266\) −0.574079 1.38595i −0.0351991 0.0849780i
\(267\) 12.0463 29.0823i 0.737222 1.77981i
\(268\) −0.409276 −0.0250005
\(269\) 5.72583 13.8234i 0.349110 0.842827i −0.647615 0.761968i \(-0.724234\pi\)
0.996726 0.0808593i \(-0.0257664\pi\)
\(270\) 5.40707 + 3.48263i 0.329064 + 0.211946i
\(271\) −1.77027 −0.107536 −0.0537681 0.998553i \(-0.517123\pi\)
−0.0537681 + 0.998553i \(0.517123\pi\)
\(272\) 2.46922 3.30196i 0.149719 0.200211i
\(273\) 39.0818i 2.36534i
\(274\) −3.12468 + 3.12468i −0.188769 + 0.188769i
\(275\) −0.718856 21.3348i −0.0433486 1.28653i
\(276\) 16.0593i 0.966654i
\(277\) −6.08957 + 14.7015i −0.365887 + 0.883329i 0.628528 + 0.777787i \(0.283658\pi\)
−0.994415 + 0.105542i \(0.966342\pi\)
\(278\) −4.99833 + 2.07037i −0.299780 + 0.124173i
\(279\) −2.61228 + 1.08204i −0.156393 + 0.0647802i
\(280\) −4.20162 + 6.52336i −0.251095 + 0.389845i
\(281\) −1.76322 1.76322i −0.105185 0.105185i 0.652556 0.757741i \(-0.273697\pi\)
−0.757741 + 0.652556i \(0.773697\pi\)
\(282\) 2.87009 + 6.92902i 0.170912 + 0.412617i
\(283\) −16.6129 + 6.88128i −0.987534 + 0.409050i −0.817211 0.576339i \(-0.804481\pi\)
−0.170323 + 0.985388i \(0.554481\pi\)
\(284\) −9.28474 3.84587i −0.550948 0.228210i
\(285\) 0.441930 + 2.04143i 0.0261776 + 0.120924i
\(286\) 8.51593 20.5593i 0.503558 1.21570i
\(287\) 11.1687 + 11.1687i 0.659269 + 0.659269i
\(288\) 1.66885i 0.0983379i
\(289\) −4.80589 16.3065i −0.282699 0.959209i
\(290\) −8.20246 + 1.77567i −0.481665 + 0.104271i
\(291\) 14.8024 14.8024i 0.867729 0.867729i
\(292\) −0.970312 0.401916i −0.0567832 0.0235204i
\(293\) −6.71505 −0.392297 −0.196149 0.980574i \(-0.562843\pi\)
−0.196149 + 0.980574i \(0.562843\pi\)
\(294\) 10.0644 + 4.16879i 0.586965 + 0.243129i
\(295\) 16.5639 11.4758i 0.964389 0.668146i
\(296\) 4.56523 1.89098i 0.265349 0.109911i
\(297\) 8.68323 8.68323i 0.503852 0.503852i
\(298\) −7.39250 + 7.39250i −0.428236 + 0.428236i
\(299\) −35.7902 + 14.8248i −2.06980 + 0.857341i
\(300\) 7.37782 7.89234i 0.425959 0.455664i
\(301\) 10.8086 + 4.47706i 0.622996 + 0.258054i
\(302\) −17.3497 −0.998364
\(303\) 22.0682 + 9.14097i 1.26779 + 0.525135i
\(304\) 0.305686 0.305686i 0.0175323 0.0175323i
\(305\) −2.94465 13.6024i −0.168610 0.778873i
\(306\) 5.51047 + 4.12076i 0.315013 + 0.235568i
\(307\) 33.9861i 1.93969i 0.243726 + 0.969844i \(0.421630\pi\)
−0.243726 + 0.969844i \(0.578370\pi\)
\(308\) 10.4759 + 10.4759i 0.596919 + 0.596919i
\(309\) 5.24610 12.6652i 0.298440 0.720499i
\(310\) −0.801577 3.70278i −0.0455265 0.210304i
\(311\) −24.0661 9.96849i −1.36466 0.565261i −0.424325 0.905510i \(-0.639489\pi\)
−0.940335 + 0.340249i \(0.889489\pi\)
\(312\) 10.4052 4.30996i 0.589076 0.244003i
\(313\) −0.809278 1.95377i −0.0457431 0.110434i 0.899356 0.437216i \(-0.144036\pi\)
−0.945100 + 0.326783i \(0.894036\pi\)
\(314\) −2.05189 2.05189i −0.115795 0.115795i
\(315\) −10.8865 7.01187i −0.613385 0.395074i
\(316\) −0.527989 + 0.218700i −0.0297017 + 0.0123029i
\(317\) 7.50100 3.10702i 0.421298 0.174507i −0.161954 0.986798i \(-0.551780\pi\)
0.583253 + 0.812291i \(0.301780\pi\)
\(318\) −11.3839 + 27.4832i −0.638377 + 1.54118i
\(319\) 16.0239i 0.897167i
\(320\) −2.20014 0.399242i −0.122991 0.0223183i
\(321\) −2.47454 + 2.47454i −0.138115 + 0.138115i
\(322\) 25.7907i 1.43726i
\(323\) −0.254557 1.76417i −0.0141639 0.0981610i
\(324\) 11.2215 0.623416
\(325\) −24.3998 9.15681i −1.35346 0.507929i
\(326\) 1.43563 3.46591i 0.0795120 0.191959i
\(327\) −17.9060 −0.990206
\(328\) −1.74187 + 4.20525i −0.0961789 + 0.232196i
\(329\) 4.60928 + 11.1278i 0.254118 + 0.613494i
\(330\) −11.7474 16.9560i −0.646675 0.933398i
\(331\) 0.185865 + 0.185865i 0.0102161 + 0.0102161i 0.712196 0.701980i \(-0.247701\pi\)
−0.701980 + 0.712196i \(0.747701\pi\)
\(332\) −10.6949 + 10.6949i −0.586956 + 0.586956i
\(333\) 3.15576 + 7.61868i 0.172935 + 0.417501i
\(334\) 9.03022 + 21.8009i 0.494111 + 1.19289i
\(335\) 0.900463 + 0.163400i 0.0491975 + 0.00892749i
\(336\) 7.49802i 0.409050i
\(337\) −19.4419 8.05310i −1.05907 0.438680i −0.215947 0.976405i \(-0.569284\pi\)
−0.843120 + 0.537725i \(0.819284\pi\)
\(338\) −10.0183 10.0183i −0.544921 0.544921i
\(339\) −14.6024 −0.793092
\(340\) −6.75091 + 6.27895i −0.366119 + 0.340524i
\(341\) −7.23356 −0.391719
\(342\) 0.510144 + 0.510144i 0.0275854 + 0.0275854i
\(343\) −6.27863 2.60069i −0.339014 0.140424i
\(344\) 3.37141i 0.181774i
\(345\) −6.41153 + 35.3326i −0.345185 + 1.90224i
\(346\) −5.77690 13.9467i −0.310568 0.749777i
\(347\) −13.4154 32.3876i −0.720176 1.73866i −0.672850 0.739779i \(-0.734930\pi\)
−0.0473262 0.998879i \(-0.515070\pi\)
\(348\) −5.73448 + 5.73448i −0.307400 + 0.307400i
\(349\) 24.8197 + 24.8197i 1.32857 + 1.32857i 0.906619 + 0.421950i \(0.138654\pi\)
0.421950 + 0.906619i \(0.361346\pi\)
\(350\) 11.8485 12.6748i 0.633331 0.677498i
\(351\) −5.73721 13.8508i −0.306229 0.739303i
\(352\) −1.63382 + 3.94439i −0.0870828 + 0.210237i
\(353\) 16.7906 0.893676 0.446838 0.894615i \(-0.352550\pi\)
0.446838 + 0.894615i \(0.352550\pi\)
\(354\) 7.45166 17.9899i 0.396051 0.956152i
\(355\) 18.8923 + 12.1683i 1.00270 + 0.645826i
\(356\) 14.5683 0.772119
\(357\) 24.7582 + 18.5143i 1.31034 + 0.979879i
\(358\) 12.7227i 0.672415i
\(359\) 17.1981 17.1981i 0.907681 0.907681i −0.0884041 0.996085i \(-0.528177\pi\)
0.996085 + 0.0884041i \(0.0281767\pi\)
\(360\) 0.666274 3.67170i 0.0351157 0.193515i
\(361\) 18.8131i 0.990164i
\(362\) −5.92939 + 14.3148i −0.311642 + 0.752369i
\(363\) −14.4282 + 5.97635i −0.757283 + 0.313677i
\(364\) 16.7103 6.92165i 0.875860 0.362793i
\(365\) 1.97436 + 1.27166i 0.103343 + 0.0665617i
\(366\) −9.50969 9.50969i −0.497080 0.497080i
\(367\) 7.31730 + 17.6655i 0.381960 + 0.922133i 0.991587 + 0.129444i \(0.0413193\pi\)
−0.609627 + 0.792689i \(0.708681\pi\)
\(368\) 6.86651 2.84420i 0.357942 0.148264i
\(369\) −7.01793 2.90692i −0.365339 0.151328i
\(370\) −10.7991 + 2.33779i −0.561418 + 0.121536i
\(371\) −18.2822 + 44.1371i −0.949163 + 2.29148i
\(372\) −2.58868 2.58868i −0.134217 0.134217i
\(373\) 6.43835i 0.333365i 0.986011 + 0.166683i \(0.0533055\pi\)
−0.986011 + 0.166683i \(0.946694\pi\)
\(374\) 8.98995 + 15.1344i 0.464859 + 0.782580i
\(375\) −19.3832 + 14.4187i −1.00094 + 0.744578i
\(376\) −2.45435 + 2.45435i −0.126573 + 0.126573i
\(377\) 18.0737 + 7.48639i 0.930845 + 0.385569i
\(378\) 9.98100 0.513367
\(379\) −15.4328 6.39249i −0.792732 0.328360i −0.0506903 0.998714i \(-0.516142\pi\)
−0.742041 + 0.670354i \(0.766142\pi\)
\(380\) −0.794594 + 0.550509i −0.0407618 + 0.0282405i
\(381\) −3.62045 + 1.49964i −0.185481 + 0.0768289i
\(382\) 5.97149 5.97149i 0.305528 0.305528i
\(383\) 0.704366 0.704366i 0.0359914 0.0359914i −0.688882 0.724873i \(-0.741898\pi\)
0.724873 + 0.688882i \(0.241898\pi\)
\(384\) −1.99627 + 0.826884i −0.101872 + 0.0421967i
\(385\) −18.8660 27.2308i −0.961499 1.38781i
\(386\) −19.7167 8.16694i −1.00356 0.415687i
\(387\) −5.62638 −0.286005
\(388\) 8.95068 + 3.70749i 0.454402 + 0.188220i
\(389\) −7.00072 + 7.00072i −0.354950 + 0.354950i −0.861948 0.506997i \(-0.830755\pi\)
0.506997 + 0.861948i \(0.330755\pi\)
\(390\) −24.6135 + 5.32833i −1.24635 + 0.269810i
\(391\) 7.56350 29.6959i 0.382503 1.50179i
\(392\) 5.04157i 0.254638i
\(393\) −6.58764 6.58764i −0.332302 0.332302i
\(394\) −0.345500 + 0.834111i −0.0174060 + 0.0420219i
\(395\) 1.24896 0.270375i 0.0628422 0.0136041i
\(396\) −6.58259 2.72660i −0.330787 0.137017i
\(397\) −34.3102 + 14.2118i −1.72198 + 0.713268i −0.722214 + 0.691670i \(0.756875\pi\)
−0.999767 + 0.0215980i \(0.993125\pi\)
\(398\) 0.136285 + 0.329021i 0.00683135 + 0.0164923i
\(399\) 2.29204 + 2.29204i 0.114745 + 0.114745i
\(400\) 4.68121 + 1.75677i 0.234061 + 0.0878387i
\(401\) 11.9320 4.94241i 0.595858 0.246812i −0.0643108 0.997930i \(-0.520485\pi\)
0.660168 + 0.751118i \(0.270485\pi\)
\(402\) 0.817026 0.338423i 0.0407496 0.0168790i
\(403\) −3.37953 + 8.15890i −0.168346 + 0.406424i
\(404\) 11.0547i 0.549993i
\(405\) −24.6888 4.48009i −1.22680 0.222617i
\(406\) −9.20939 + 9.20939i −0.457054 + 0.457054i
\(407\) 21.0966i 1.04572i
\(408\) −2.19891 + 8.63338i −0.108862 + 0.427416i
\(409\) 10.7462 0.531366 0.265683 0.964060i \(-0.414403\pi\)
0.265683 + 0.964060i \(0.414403\pi\)
\(410\) 5.51127 8.55671i 0.272182 0.422586i
\(411\) 3.65397 8.82147i 0.180237 0.435131i
\(412\) 6.34442 0.312567
\(413\) 11.9671 28.8912i 0.588864 1.42164i
\(414\) 4.74654 + 11.4592i 0.233280 + 0.563188i
\(415\) 27.8000 19.2603i 1.36465 0.945452i
\(416\) 3.68564 + 3.68564i 0.180704 + 0.180704i
\(417\) 8.26607 8.26607i 0.404791 0.404791i
\(418\) 0.706309 + 1.70518i 0.0345467 + 0.0834031i
\(419\) 0.821783 + 1.98396i 0.0401467 + 0.0969228i 0.942681 0.333695i \(-0.108296\pi\)
−0.902534 + 0.430618i \(0.858296\pi\)
\(420\) 2.99352 16.4967i 0.146069 0.804955i
\(421\) 27.9741i 1.36337i −0.731644 0.681687i \(-0.761246\pi\)
0.731644 0.681687i \(-0.238754\pi\)
\(422\) 10.4640 + 4.33435i 0.509382 + 0.210993i
\(423\) −4.09594 4.09594i −0.199151 0.199151i
\(424\) −13.7672 −0.668596
\(425\) 17.3597 11.1193i 0.842072 0.539366i
\(426\) 21.7150 1.05209
\(427\) −15.2723 15.2723i −0.739076 0.739076i
\(428\) −1.49630 0.619790i −0.0723266 0.0299587i
\(429\) 48.0837i 2.32150i
\(430\) 1.34601 7.41757i 0.0649103 0.357707i
\(431\) 6.62107 + 15.9847i 0.318926 + 0.769955i 0.999312 + 0.0371008i \(0.0118123\pi\)
−0.680386 + 0.732854i \(0.738188\pi\)
\(432\) 1.10071 + 2.65734i 0.0529578 + 0.127851i
\(433\) −3.89798 + 3.89798i −0.187325 + 0.187325i −0.794539 0.607214i \(-0.792287\pi\)
0.607214 + 0.794539i \(0.292287\pi\)
\(434\) −4.15733 4.15733i −0.199558 0.199558i
\(435\) 14.9061 10.3272i 0.714692 0.495152i
\(436\) −3.17128 7.65614i −0.151877 0.366663i
\(437\) 1.22956 2.96843i 0.0588180 0.141999i
\(438\) 2.26935 0.108434
\(439\) 2.10538 5.08283i 0.100484 0.242590i −0.865640 0.500666i \(-0.833088\pi\)
0.966125 + 0.258076i \(0.0830884\pi\)
\(440\) 5.16939 8.02591i 0.246441 0.382620i
\(441\) −8.41362 −0.400649
\(442\) 21.2705 3.06918i 1.01174 0.145986i
\(443\) 15.0462i 0.714865i 0.933939 + 0.357433i \(0.116348\pi\)
−0.933939 + 0.357433i \(0.883652\pi\)
\(444\) −7.54983 + 7.54983i −0.358299 + 0.358299i
\(445\) −32.0523 5.81628i −1.51942 0.275718i
\(446\) 17.3908i 0.823478i
\(447\) 8.64472 20.8702i 0.408881 0.987127i
\(448\) −3.20595 + 1.32795i −0.151467 + 0.0627397i
\(449\) 10.3001 4.26643i 0.486091 0.201345i −0.126159 0.992010i \(-0.540265\pi\)
0.612249 + 0.790665i \(0.290265\pi\)
\(450\) −2.93179 + 7.81223i −0.138206 + 0.368272i
\(451\) −13.7412 13.7412i −0.647050 0.647050i
\(452\) −2.58618 6.24358i −0.121644 0.293673i
\(453\) 34.6348 14.3462i 1.62728 0.674043i
\(454\) −11.0487 4.57652i −0.518542 0.214787i
\(455\) −39.5285 + 8.55712i −1.85312 + 0.401164i
\(456\) −0.357466 + 0.863000i −0.0167399 + 0.0404137i
\(457\) 15.4608 + 15.4608i 0.723225 + 0.723225i 0.969261 0.246036i \(-0.0791280\pi\)
−0.246036 + 0.969261i \(0.579128\pi\)
\(458\) 11.7643i 0.549710i
\(459\) 11.4923 + 2.92708i 0.536416 + 0.136624i
\(460\) −16.2428 + 3.51624i −0.757324 + 0.163945i
\(461\) 6.63452 6.63452i 0.309000 0.309000i −0.535521 0.844522i \(-0.679885\pi\)
0.844522 + 0.535521i \(0.179885\pi\)
\(462\) −29.5751 12.2504i −1.37596 0.569940i
\(463\) 19.1390 0.889464 0.444732 0.895664i \(-0.353299\pi\)
0.444732 + 0.895664i \(0.353299\pi\)
\(464\) −3.46752 1.43630i −0.160976 0.0666784i
\(465\) 4.66194 + 6.72895i 0.216192 + 0.312048i
\(466\) 21.6054 8.94925i 1.00085 0.414566i
\(467\) −14.0361 + 14.0361i −0.649512 + 0.649512i −0.952875 0.303363i \(-0.901891\pi\)
0.303363 + 0.952875i \(0.401891\pi\)
\(468\) −6.15078 + 6.15078i −0.284320 + 0.284320i
\(469\) 1.31212 0.543497i 0.0605880 0.0250964i
\(470\) 6.37979 4.42003i 0.294278 0.203881i
\(471\) 5.79280 + 2.39946i 0.266918 + 0.110561i
\(472\) 9.01174 0.414799
\(473\) −13.2982 5.50828i −0.611450 0.253271i
\(474\) 0.873172 0.873172i 0.0401061 0.0401061i
\(475\) 1.96800 0.893960i 0.0902981 0.0410177i
\(476\) −3.53137 + 13.8649i −0.161860 + 0.635498i
\(477\) 22.9754i 1.05197i
\(478\) −9.33784 9.33784i −0.427103 0.427103i
\(479\) −3.80402 + 9.18371i −0.173810 + 0.419614i −0.986646 0.162878i \(-0.947922\pi\)
0.812836 + 0.582492i \(0.197922\pi\)
\(480\) 4.72221 1.02226i 0.215538 0.0466597i
\(481\) 23.7953 + 9.85633i 1.08497 + 0.449410i
\(482\) 20.9168 8.66402i 0.952733 0.394635i
\(483\) 21.3259 + 51.4852i 0.970361 + 2.34266i
\(484\) −5.11065 5.11065i −0.232302 0.232302i
\(485\) −18.2125 11.7305i −0.826989 0.532654i
\(486\) −14.4291 + 5.97675i −0.654519 + 0.271111i
\(487\) 8.06967 3.34257i 0.365672 0.151466i −0.192279 0.981340i \(-0.561588\pi\)
0.557951 + 0.829874i \(0.311588\pi\)
\(488\) 2.38186 5.75032i 0.107822 0.260305i
\(489\) 8.10601i 0.366566i
\(490\) 2.01281 11.0921i 0.0909293 0.501092i
\(491\) −1.63435 + 1.63435i −0.0737571 + 0.0737571i −0.743023 0.669266i \(-0.766609\pi\)
0.669266 + 0.743023i \(0.266609\pi\)
\(492\) 9.83517i 0.443404i
\(493\) −13.3047 + 7.90310i −0.599213 + 0.355938i
\(494\) 2.25330 0.101381
\(495\) 13.3940 + 8.62693i 0.602017 + 0.387752i
\(496\) 0.648377 1.56532i 0.0291130 0.0702849i
\(497\) 34.8736 1.56429
\(498\) 12.5065 30.1933i 0.560428 1.35299i
\(499\) 11.1408 + 26.8962i 0.498730 + 1.20404i 0.950168 + 0.311738i \(0.100911\pi\)
−0.451438 + 0.892303i \(0.649089\pi\)
\(500\) −9.59793 5.73408i −0.429233 0.256436i
\(501\) −36.0536 36.0536i −1.61076 1.61076i
\(502\) 2.21357 2.21357i 0.0987965 0.0987965i
\(503\) −11.5670 27.9252i −0.515747 1.24512i −0.940494 0.339811i \(-0.889637\pi\)
0.424747 0.905312i \(-0.360363\pi\)
\(504\) −2.21615 5.35025i −0.0987150 0.238319i
\(505\) 4.41350 24.3219i 0.196398 1.08231i
\(506\) 31.7311i 1.41062i
\(507\) 28.2831 + 11.7153i 1.25610 + 0.520293i
\(508\) −1.28241 1.28241i −0.0568978 0.0568978i
\(509\) 37.2373 1.65052 0.825258 0.564756i \(-0.191030\pi\)
0.825258 + 0.564756i \(0.191030\pi\)
\(510\) 8.28470 18.1167i 0.366853 0.802222i
\(511\) 3.64450 0.161223
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 1.14878 + 0.475842i 0.0507200 + 0.0210089i
\(514\) 8.21104i 0.362173i
\(515\) −13.9586 2.53296i −0.615090 0.111615i
\(516\) −2.78777 6.73026i −0.122725 0.296283i
\(517\) −5.67095 13.6909i −0.249408 0.602124i
\(518\) −12.1248 + 12.1248i −0.532732 + 0.532732i
\(519\) 23.0645 + 23.0645i 1.01242 + 1.01242i
\(520\) −6.63746 9.58039i −0.291072 0.420128i
\(521\) 3.27311 + 7.90198i 0.143398 + 0.346192i 0.979218 0.202811i \(-0.0650076\pi\)
−0.835820 + 0.549003i \(0.815008\pi\)
\(522\) 2.39696 5.78677i 0.104912 0.253280i
\(523\) 39.2933 1.71818 0.859088 0.511828i \(-0.171031\pi\)
0.859088 + 0.511828i \(0.171031\pi\)
\(524\) 1.64998 3.98341i 0.0720798 0.174016i
\(525\) −13.1723 + 35.0998i −0.574887 + 1.53188i
\(526\) −25.2134 −1.09936
\(527\) −3.56764 6.00604i −0.155409 0.261627i
\(528\) 9.22506i 0.401469i
\(529\) 22.7960 22.7960i 0.991133 0.991133i
\(530\) 30.2898 + 5.49645i 1.31570 + 0.238751i
\(531\) 15.0392i 0.652647i
\(532\) −0.574079 + 1.38595i −0.0248895 + 0.0600886i
\(533\) −21.9190 + 9.07915i −0.949417 + 0.393261i
\(534\) −29.0823 + 12.0463i −1.25852 + 0.521294i
\(535\) 3.04463 + 1.96101i 0.131631 + 0.0847819i
\(536\) 0.289402 + 0.289402i 0.0125002 + 0.0125002i
\(537\) −10.5202 25.3980i −0.453979 1.09600i
\(538\) −13.8234 + 5.72583i −0.595969 + 0.246858i
\(539\) −19.8859 8.23701i −0.856547 0.354793i
\(540\) −1.36079 6.28597i −0.0585589 0.270505i
\(541\) 11.7894 28.4621i 0.506866 1.22368i −0.438813 0.898579i \(-0.644601\pi\)
0.945678 0.325104i \(-0.105399\pi\)
\(542\) 1.25177 + 1.25177i 0.0537681 + 0.0537681i
\(543\) 33.4792i 1.43673i
\(544\) −4.08084 + 0.588835i −0.174965 + 0.0252461i
\(545\) 3.92059 + 18.1107i 0.167940 + 0.775776i
\(546\) −27.6350 + 27.6350i −1.18267 + 1.18267i
\(547\) −5.07321 2.10139i −0.216915 0.0898491i 0.271580 0.962416i \(-0.412454\pi\)
−0.488495 + 0.872567i \(0.662454\pi\)
\(548\) 4.41897 0.188769
\(549\) 9.59641 + 3.97496i 0.409565 + 0.169647i
\(550\) −14.5776 + 15.5943i −0.621593 + 0.664942i
\(551\) −1.49903 + 0.620918i −0.0638608 + 0.0264520i
\(552\) −11.3556 + 11.3556i −0.483327 + 0.483327i
\(553\) 1.40228 1.40228i 0.0596312 0.0596312i
\(554\) 14.7015 6.08957i 0.624608 0.258721i
\(555\) 19.6249 13.5965i 0.833029 0.577137i
\(556\) 4.99833 + 2.07037i 0.211976 + 0.0878034i
\(557\) 9.65747 0.409200 0.204600 0.978846i \(-0.434411\pi\)
0.204600 + 0.978846i \(0.434411\pi\)
\(558\) 2.61228 + 1.08204i 0.110587 + 0.0458065i
\(559\) −12.4258 + 12.4258i −0.525556 + 0.525556i
\(560\) 7.58371 1.64172i 0.320470 0.0693753i
\(561\) −30.4608 22.7787i −1.28606 0.961718i
\(562\) 2.49357i 0.105185i
\(563\) −13.5365 13.5365i −0.570496 0.570496i 0.361771 0.932267i \(-0.382172\pi\)
−0.932267 + 0.361771i \(0.882172\pi\)
\(564\) 2.87009 6.92902i 0.120853 0.291764i
\(565\) 3.19725 + 14.7693i 0.134509 + 0.621347i
\(566\) 16.6129 + 6.88128i 0.698292 + 0.289242i
\(567\) −35.9756 + 14.9016i −1.51083 + 0.625807i
\(568\) 3.84587 + 9.28474i 0.161369 + 0.389579i
\(569\) −16.9921 16.9921i −0.712348 0.712348i 0.254678 0.967026i \(-0.418030\pi\)
−0.967026 + 0.254678i \(0.918030\pi\)
\(570\) 1.13102 1.75600i 0.0473733 0.0735509i
\(571\) 12.8892 5.33889i 0.539397 0.223426i −0.0963163 0.995351i \(-0.530706\pi\)
0.635713 + 0.771925i \(0.280706\pi\)
\(572\) −20.5593 + 8.51593i −0.859627 + 0.356069i
\(573\) −6.98300 + 16.8585i −0.291719 + 0.704272i
\(574\) 15.7950i 0.659269i
\(575\) 37.1402 1.25141i 1.54885 0.0521873i
\(576\) 1.18005 1.18005i 0.0491689 0.0491689i
\(577\) 14.4087i 0.599842i 0.953964 + 0.299921i \(0.0969603\pi\)
−0.953964 + 0.299921i \(0.903040\pi\)
\(578\) −8.13219 + 14.9287i −0.338255 + 0.620954i
\(579\) 46.1132 1.91640
\(580\) 7.05560 + 4.54443i 0.292968 + 0.188697i
\(581\) 20.0850 48.4894i 0.833265 2.01168i
\(582\) −20.9337 −0.867729
\(583\) 22.4932 54.3033i 0.931571 2.24901i
\(584\) 0.401916 + 0.970312i 0.0166314 + 0.0401518i
\(585\) 15.9882 11.0769i 0.661032 0.457974i
\(586\) 4.74825 + 4.74825i 0.196149 + 0.196149i
\(587\) 9.34651 9.34651i 0.385772 0.385772i −0.487405 0.873176i \(-0.662056\pi\)
0.873176 + 0.487405i \(0.162056\pi\)
\(588\) −4.16879 10.0644i −0.171918 0.415047i
\(589\) −0.280297 0.676696i −0.0115494 0.0278828i
\(590\) −19.8271 3.59786i −0.816267 0.148122i
\(591\) 1.95080i 0.0802453i
\(592\) −4.56523 1.89098i −0.187630 0.0777188i
\(593\) −23.3715 23.3715i −0.959754 0.959754i 0.0394671 0.999221i \(-0.487434\pi\)
−0.999221 + 0.0394671i \(0.987434\pi\)
\(594\) −12.2799 −0.503852
\(595\) 13.3050 29.0949i 0.545450 1.19277i
\(596\) 10.4546 0.428236
\(597\) −0.544125 0.544125i −0.0222695 0.0222695i
\(598\) 35.7902 + 14.8248i 1.46357 + 0.606231i
\(599\) 14.3939i 0.588118i 0.955787 + 0.294059i \(0.0950062\pi\)
−0.955787 + 0.294059i \(0.904994\pi\)
\(600\) −10.7976 + 0.363817i −0.440811 + 0.0148527i
\(601\) 14.6516 + 35.3721i 0.597652 + 1.44286i 0.875968 + 0.482370i \(0.160224\pi\)
−0.278316 + 0.960490i \(0.589776\pi\)
\(602\) −4.47706 10.8086i −0.182471 0.440525i
\(603\) −0.482967 + 0.482967i −0.0196680 + 0.0196680i
\(604\) 12.2681 + 12.2681i 0.499182 + 0.499182i
\(605\) 9.20376 + 13.2845i 0.374186 + 0.540093i
\(606\) −9.14097 22.0682i −0.371326 0.896461i
\(607\) −6.37537 + 15.3915i −0.258768 + 0.624722i −0.998858 0.0477868i \(-0.984783\pi\)
0.740089 + 0.672509i \(0.234783\pi\)
\(608\) −0.432305 −0.0175323
\(609\) 10.7694 25.9996i 0.436397 1.05356i
\(610\) −7.53619 + 11.7006i −0.305131 + 0.473742i
\(611\) −18.0917 −0.731913
\(612\) −0.982677 6.81031i −0.0397224 0.275290i
\(613\) 0.270516i 0.0109261i 0.999985 + 0.00546303i \(0.00173894\pi\)
−0.999985 + 0.00546303i \(0.998261\pi\)
\(614\) 24.0318 24.0318i 0.969844 0.969844i
\(615\) −3.92661 + 21.6387i −0.158336 + 0.872558i
\(616\) 14.8151i 0.596919i
\(617\) −13.8689 + 33.4825i −0.558340 + 1.34795i 0.352739 + 0.935722i \(0.385250\pi\)
−0.911079 + 0.412231i \(0.864750\pi\)
\(618\) −12.6652 + 5.24610i −0.509469 + 0.211029i
\(619\) −2.78040 + 1.15168i −0.111754 + 0.0462899i −0.437860 0.899043i \(-0.644263\pi\)
0.326106 + 0.945333i \(0.394263\pi\)
\(620\) −2.05146 + 3.18506i −0.0823886 + 0.127915i
\(621\) 15.1160 + 15.1160i 0.606586 + 0.606586i
\(622\) 9.96849 + 24.0661i 0.399700 + 0.964961i
\(623\) −46.7053 + 19.3460i −1.87121 + 0.775080i
\(624\) −10.4052 4.30996i −0.416540 0.172536i
\(625\) 18.8275 + 16.4477i 0.753100 + 0.657906i
\(626\) −0.809278 + 1.95377i −0.0323453 + 0.0780884i
\(627\) −2.81997 2.81997i −0.112619 0.112619i
\(628\) 2.90181i 0.115795i
\(629\) −17.5165 + 10.4050i −0.698429 + 0.414873i
\(630\) 2.73978 + 12.6561i 0.109156 + 0.504229i
\(631\) −14.7927 + 14.7927i −0.588890 + 0.588890i −0.937331 0.348441i \(-0.886711\pi\)
0.348441 + 0.937331i \(0.386711\pi\)
\(632\) 0.527989 + 0.218700i 0.0210023 + 0.00869943i
\(633\) −24.4731 −0.972719
\(634\) −7.50100 3.10702i −0.297903 0.123395i
\(635\) 2.30949 + 3.33348i 0.0916493 + 0.132285i
\(636\) 27.4832 11.3839i 1.08978 0.451401i
\(637\) −18.5814 + 18.5814i −0.736223 + 0.736223i
\(638\) 11.3306 11.3306i 0.448583 0.448583i
\(639\) −15.4948 + 6.41817i −0.612966 + 0.253899i
\(640\) 1.27343 + 1.83804i 0.0503366 + 0.0726549i
\(641\) −22.3306 9.24965i −0.882007 0.365339i −0.104732 0.994500i \(-0.533399\pi\)
−0.777275 + 0.629161i \(0.783399\pi\)
\(642\) 3.49953 0.138115
\(643\) −11.6947 4.84409i −0.461193 0.191032i 0.139975 0.990155i \(-0.455298\pi\)
−0.601168 + 0.799123i \(0.705298\pi\)
\(644\) −18.2367 + 18.2367i −0.718629 + 0.718629i
\(645\) 3.44647 + 15.9205i 0.135705 + 0.626869i
\(646\) −1.06746 + 1.42746i −0.0419986 + 0.0561625i
\(647\) 11.1531i 0.438472i 0.975672 + 0.219236i \(0.0703565\pi\)
−0.975672 + 0.219236i \(0.929643\pi\)
\(648\) −7.93479 7.93479i −0.311708 0.311708i
\(649\) −14.7235 + 35.5458i −0.577950 + 1.39529i
\(650\) 10.7784 + 23.7281i 0.422765 + 0.930694i
\(651\) 11.7368 + 4.86154i 0.460001 + 0.190539i
\(652\) −3.46591 + 1.43563i −0.135736 + 0.0562235i
\(653\) 11.3392 + 27.3752i 0.443736 + 1.07127i 0.974627 + 0.223834i \(0.0718572\pi\)
−0.530891 + 0.847440i \(0.678143\pi\)
\(654\) 12.6615 + 12.6615i 0.495103 + 0.495103i
\(655\) −5.22053 + 8.10531i −0.203983 + 0.316701i
\(656\) 4.20525 1.74187i 0.164188 0.0680087i
\(657\) −1.61930 + 0.670737i −0.0631750 + 0.0261680i
\(658\) 4.60928 11.1278i 0.179688 0.433806i
\(659\) 30.0437i 1.17034i −0.810912 0.585169i \(-0.801028\pi\)
0.810912 0.585169i \(-0.198972\pi\)
\(660\) −3.68303 + 20.2964i −0.143362 + 0.790036i
\(661\) −20.9920 + 20.9920i −0.816494 + 0.816494i −0.985598 0.169104i \(-0.945913\pi\)
0.169104 + 0.985598i \(0.445913\pi\)
\(662\) 0.262853i 0.0102161i
\(663\) −39.9240 + 23.7152i −1.55052 + 0.921021i
\(664\) 15.1248 0.586956
\(665\) 1.81638 2.82008i 0.0704363 0.109358i
\(666\) 3.15576 7.61868i 0.122283 0.295218i
\(667\) −27.8949 −1.08010
\(668\) 9.03022 21.8009i 0.349390 0.843501i
\(669\) −14.3802 34.7168i −0.555969 1.34223i
\(670\) −0.521182 0.752264i −0.0201350 0.0290625i
\(671\) 18.7900 + 18.7900i 0.725378 + 0.725378i
\(672\) 5.30190 5.30190i 0.204525 0.204525i
\(673\) 14.4888 + 34.9790i 0.558502 + 1.34834i 0.910952 + 0.412513i \(0.135349\pi\)
−0.352450 + 0.935831i \(0.614651\pi\)
\(674\) 8.05310 + 19.4419i 0.310194 + 0.748874i
\(675\) 0.484295 + 14.3733i 0.0186405 + 0.553228i
\(676\) 14.1680i 0.544921i
\(677\) 0.664177 + 0.275111i 0.0255264 + 0.0105734i 0.395410 0.918505i \(-0.370602\pi\)
−0.369884 + 0.929078i \(0.620602\pi\)
\(678\) 10.3254 + 10.3254i 0.396546 + 0.396546i
\(679\) −33.6188 −1.29017
\(680\) 9.21350 + 0.333724i 0.353322 + 0.0127977i
\(681\) 25.8405 0.990210
\(682\) 5.11490 + 5.11490i 0.195860 + 0.195860i
\(683\) 34.0830 + 14.1176i 1.30415 + 0.540197i 0.923172 0.384387i \(-0.125587\pi\)
0.380979 + 0.924584i \(0.375587\pi\)
\(684\) 0.721452i 0.0275854i
\(685\) −9.72234 1.76424i −0.371471 0.0674080i
\(686\) 2.60069 + 6.27863i 0.0992949 + 0.239719i
\(687\) −9.72771 23.4848i −0.371135 0.896000i
\(688\) 2.38395 2.38395i 0.0908872 0.0908872i
\(689\) −50.7411 50.7411i −1.93308 1.93308i
\(690\) 29.5176 20.4503i 1.12371 0.778529i
\(691\) 14.8476 + 35.8452i 0.564828 + 1.36362i 0.905866 + 0.423565i \(0.139222\pi\)
−0.341038 + 0.940050i \(0.610778\pi\)
\(692\) −5.77690 + 13.9467i −0.219605 + 0.530173i
\(693\) 24.7242 0.939196
\(694\) −13.4154 + 32.3876i −0.509241 + 1.22942i
\(695\) −10.1704 6.55065i −0.385786 0.248480i
\(696\) 8.10978 0.307400
\(697\) 4.63211 18.1867i 0.175454 0.688869i
\(698\) 35.1004i 1.32857i
\(699\) −35.7303 + 35.7303i −1.35145 + 1.35145i
\(700\) −17.3406 + 0.584277i −0.655415 + 0.0220836i
\(701\) 20.7195i 0.782566i −0.920270 0.391283i \(-0.872031\pi\)
0.920270 0.391283i \(-0.127969\pi\)
\(702\) −5.73721 + 13.8508i −0.216537 + 0.522766i
\(703\) −1.97357 + 0.817481i −0.0744347 + 0.0308319i
\(704\) 3.94439 1.63382i 0.148660 0.0615769i
\(705\) −9.08096 + 14.0989i −0.342009 + 0.530997i
\(706\) −11.8728 11.8728i −0.446838 0.446838i
\(707\) −14.6801 35.4409i −0.552102 1.33289i
\(708\) −17.9899 + 7.45166i −0.676102 + 0.280051i
\(709\) −11.7625 4.87221i −0.441752 0.182980i 0.150710 0.988578i \(-0.451844\pi\)
−0.592462 + 0.805598i \(0.701844\pi\)
\(710\) −4.75458 21.9631i −0.178436 0.824262i
\(711\) −0.364978 + 0.881134i −0.0136877 + 0.0330451i
\(712\) −10.3013 10.3013i −0.386059 0.386059i
\(713\) 12.5924i 0.471589i
\(714\) −4.41510 30.5982i −0.165231 1.14511i
\(715\) 48.6332 10.5281i 1.81878 0.393729i
\(716\) 8.99629 8.99629i 0.336207 0.336207i
\(717\) 26.3622 + 10.9196i 0.984515 + 0.407799i
\(718\) −24.3218 −0.907681
\(719\) −20.3836 8.44316i −0.760179 0.314877i −0.0312920 0.999510i \(-0.509962\pi\)
−0.728887 + 0.684634i \(0.759962\pi\)
\(720\) −3.06741 + 2.12515i −0.114316 + 0.0791998i
\(721\) −20.3399 + 8.42507i −0.757498 + 0.313766i
\(722\) 13.3029 13.3029i 0.495082 0.495082i
\(723\) −34.5915 + 34.5915i −1.28647 + 1.28647i
\(724\) 14.3148 5.92939i 0.532006 0.220364i
\(725\) −13.7090 12.8153i −0.509138 0.475947i
\(726\) 14.4282 + 5.97635i 0.535480 + 0.221803i
\(727\) −23.3953 −0.867682 −0.433841 0.900989i \(-0.642842\pi\)
−0.433841 + 0.900989i \(0.642842\pi\)
\(728\) −16.7103 6.92165i −0.619327 0.256533i
\(729\) 0.0580801 0.0580801i 0.00215111 0.00215111i
\(730\) −0.496882 2.29528i −0.0183904 0.0849522i
\(731\) −1.98521 13.7582i −0.0734255 0.508865i
\(732\) 13.4487i 0.497080i
\(733\) 21.9647 + 21.9647i 0.811283 + 0.811283i 0.984826 0.173543i \(-0.0555217\pi\)
−0.173543 + 0.984826i \(0.555522\pi\)
\(734\) 7.31730 17.6655i 0.270086 0.652046i
\(735\) 5.15381 + 23.8073i 0.190101 + 0.878147i
\(736\) −6.86651 2.84420i −0.253103 0.104839i
\(737\) −1.61434 + 0.668682i −0.0594650 + 0.0246312i
\(738\) 2.90692 + 7.01793i 0.107005 + 0.258334i
\(739\) 5.46858 + 5.46858i 0.201165 + 0.201165i 0.800499 0.599334i \(-0.204568\pi\)
−0.599334 + 0.800499i \(0.704568\pi\)
\(740\) 9.28917 + 5.98305i 0.341477 + 0.219941i
\(741\) −4.49821 + 1.86322i −0.165246 + 0.0684470i
\(742\) 44.1371 18.2822i 1.62032 0.671160i
\(743\) 12.6211 30.4700i 0.463023 1.11784i −0.504127 0.863629i \(-0.668186\pi\)
0.967150 0.254206i \(-0.0818143\pi\)
\(744\) 3.66094i 0.134217i
\(745\) −23.0015 4.17390i −0.842710 0.152920i
\(746\) 4.55260 4.55260i 0.166683 0.166683i
\(747\) 25.2410i 0.923520i
\(748\) 4.34476 17.0585i 0.158860 0.623720i
\(749\) 5.62013 0.205355
\(750\) 23.9015 + 3.51042i 0.872760 + 0.128182i
\(751\) 13.6564 32.9695i 0.498329 1.20307i −0.452054 0.891991i \(-0.649308\pi\)
0.950383 0.311083i \(-0.100692\pi\)
\(752\) 3.47098 0.126573
\(753\) −2.58853 + 6.24926i −0.0943312 + 0.227736i
\(754\) −7.48639 18.0737i −0.272638 0.658207i
\(755\) −22.0936 31.8894i −0.804067 1.16058i
\(756\) −7.05763 7.05763i −0.256684 0.256684i
\(757\) 36.8619 36.8619i 1.33977 1.33977i 0.443491 0.896279i \(-0.353740\pi\)
0.896279 0.443491i \(-0.146260\pi\)
\(758\) 6.39249 + 15.4328i 0.232186 + 0.560546i
\(759\) −26.2379 63.3440i −0.952377 2.29924i
\(760\) 0.951131 + 0.172594i 0.0345012 + 0.00626066i
\(761\) 30.3827i 1.10137i 0.834713 + 0.550686i \(0.185634\pi\)
−0.834713 + 0.550686i \(0.814366\pi\)
\(762\) 3.62045 + 1.49964i 0.131155 + 0.0543262i
\(763\) 20.3339 + 20.3339i 0.736137 + 0.736137i
\(764\) −8.44496 −0.305528
\(765\) −0.556935 + 15.3759i −0.0201360 + 0.555918i
\(766\) −0.996123 −0.0359914
\(767\) 33.2141 + 33.2141i 1.19929 + 1.19929i
\(768\) 1.99627 + 0.826884i 0.0720343 + 0.0298376i
\(769\) 16.6957i 0.602063i −0.953614 0.301031i \(-0.902669\pi\)
0.953614 0.301031i \(-0.0973309\pi\)
\(770\) −5.91482 + 32.5954i −0.213155 + 1.17465i
\(771\) 6.78958 + 16.3915i 0.244521 + 0.590325i
\(772\) 8.16694 + 19.7167i 0.293935 + 0.709621i
\(773\) −16.1621 + 16.1621i −0.581312 + 0.581312i −0.935264 0.353952i \(-0.884838\pi\)
0.353952 + 0.935264i \(0.384838\pi\)
\(774\) 3.97845 + 3.97845i 0.143002 + 0.143002i
\(775\) 5.78510 6.18854i 0.207807 0.222299i
\(776\) −3.70749 8.95068i −0.133091 0.321311i
\(777\) 14.1786 34.2302i 0.508654 1.22800i
\(778\) 9.90051 0.354950
\(779\) 0.753021 1.81795i 0.0269798 0.0651350i
\(780\) 21.1721 + 13.6367i 0.758082 + 0.488271i
\(781\) −42.9061 −1.53530
\(782\) −26.3464 + 15.6500i −0.942145 + 0.559642i
\(783\) 10.7953i 0.385794i
\(784\) 3.56493 3.56493i 0.127319 0.127319i
\(785\) 1.15852 6.38437i 0.0413494 0.227868i
\(786\) 9.31633i 0.332302i
\(787\) 0.207485 0.500913i 0.00739604 0.0178556i −0.920138 0.391593i \(-0.871924\pi\)
0.927534 + 0.373738i \(0.121924\pi\)
\(788\) 0.834111 0.345500i 0.0297140 0.0123079i
\(789\) 50.3329 20.8486i 1.79190 0.742229i
\(790\) −1.07433 0.691966i −0.0382231 0.0246190i
\(791\) 16.5823 + 16.5823i 0.589599 + 0.589599i
\(792\) 2.72660 + 6.58259i 0.0968854 + 0.233902i
\(793\) 29.9723 12.4149i 1.06435 0.440867i
\(794\) 34.3102 + 14.2118i 1.21762 + 0.504356i
\(795\) −65.0117 + 14.0737i −2.30573 + 0.499143i
\(796\) 0.136285 0.329021i 0.00483049 0.0116618i
\(797\) −30.3202 30.3202i −1.07400 1.07400i −0.997034 0.0769632i \(-0.975478\pi\)
−0.0769632 0.997034i \(-0.524522\pi\)
\(798\) 3.24143i 0.114745i
\(799\) 8.57061 11.4610i 0.303206 0.405462i
\(800\) −2.06789 4.55234i −0.0731110 0.160950i
\(801\) 17.1914 17.1914i 0.607428 0.607428i
\(802\) −11.9320 4.94241i −0.421335 0.174523i
\(803\) −4.48394 −0.158235
\(804\) −0.817026 0.338423i −0.0288143 0.0119353i
\(805\) 47.4042 32.8425i 1.67078 1.15755i
\(806\) 8.15890 3.37953i 0.287385 0.119039i
\(807\) 22.8607 22.8607i 0.804734 0.804734i
\(808\) 7.81686 7.81686i 0.274996 0.274996i
\(809\) 20.9224 8.66632i 0.735591 0.304692i 0.0167436 0.999860i \(-0.494670\pi\)
0.718847 + 0.695168i \(0.244670\pi\)
\(810\) 14.2897 + 20.6255i 0.502090 + 0.724707i
\(811\) 17.2005 + 7.12470i 0.603993 + 0.250182i 0.663658 0.748036i \(-0.269003\pi\)
−0.0596648 + 0.998218i \(0.519003\pi\)
\(812\) 13.0240 0.457054
\(813\) −3.53394 1.46381i −0.123941 0.0513380i
\(814\) 14.9175 14.9175i 0.522859 0.522859i
\(815\) 8.19864 1.77484i 0.287186 0.0621700i
\(816\) 7.65958 4.54986i 0.268139 0.159277i
\(817\) 1.45748i 0.0509907i
\(818\) −7.59872 7.59872i −0.265683 0.265683i
\(819\) 11.5512 27.8870i 0.403631 0.974452i
\(820\) −9.94757 + 2.15345i −0.347384 + 0.0752017i
\(821\) −8.29260 3.43491i −0.289414 0.119879i 0.233253 0.972416i \(-0.425063\pi\)
−0.522667 + 0.852537i \(0.675063\pi\)
\(822\) −8.82147 + 3.65397i −0.307684 + 0.127447i
\(823\) −4.41319 10.6544i −0.153834 0.371389i 0.828108 0.560568i \(-0.189417\pi\)
−0.981943 + 0.189179i \(0.939417\pi\)
\(824\) −4.48618 4.48618i −0.156284 0.156284i
\(825\) 16.2063 43.1845i 0.564232 1.50349i
\(826\) −28.8912 + 11.9671i −1.00525 + 0.416389i
\(827\) −7.64533 + 3.16680i −0.265854 + 0.110120i −0.511629 0.859207i \(-0.670958\pi\)
0.245775 + 0.969327i \(0.420958\pi\)
\(828\) 4.74654 11.4592i 0.164954 0.398234i
\(829\) 11.0240i 0.382880i 0.981504 + 0.191440i \(0.0613157\pi\)
−0.981504 + 0.191440i \(0.938684\pi\)
\(830\) −33.2767 6.03845i −1.15505 0.209598i
\(831\) −24.3129 + 24.3129i −0.843406 + 0.843406i
\(832\) 5.21229i 0.180704i
\(833\) −2.96865 20.5739i −0.102858 0.712842i
\(834\) −11.6900 −0.404791
\(835\) −28.5715 + 44.3597i −0.988759 + 1.53513i
\(836\) 0.706309 1.70518i 0.0244282 0.0589749i
\(837\) 4.87327 0.168445
\(838\) 0.821783 1.98396i 0.0283880 0.0685348i
\(839\) 14.9538 + 36.1016i 0.516262 + 1.24637i 0.940184 + 0.340667i \(0.110653\pi\)
−0.423922 + 0.905699i \(0.639347\pi\)
\(840\) −13.7816 + 9.54817i −0.475512 + 0.329443i
\(841\) −10.5453 10.5453i −0.363632 0.363632i
\(842\) −19.7807 + 19.7807i −0.681687 + 0.681687i
\(843\) −2.06189 4.97785i −0.0710153 0.171446i
\(844\) −4.33435 10.4640i −0.149194 0.360187i
\(845\) 5.65644 31.1714i 0.194587 1.07233i
\(846\) 5.79253i 0.199151i
\(847\) 23.1712 + 9.59782i 0.796172 + 0.329785i
\(848\) 9.73490 + 9.73490i 0.334298 + 0.334298i
\(849\) −38.8539 −1.33346
\(850\) −20.1377 4.41265i −0.690719 0.151353i
\(851\) −36.7255 −1.25894
\(852\) −15.3548 15.3548i −0.526047 0.526047i
\(853\) 34.8497 + 14.4352i 1.19323 + 0.494252i 0.888806 0.458284i \(-0.151536\pi\)
0.304424 + 0.952536i \(0.401536\pi\)
\(854\) 21.5982i 0.739076i
\(855\) −0.288034 + 1.58729i −0.00985055 + 0.0542843i
\(856\) 0.619790 + 1.49630i 0.0211840 + 0.0511426i
\(857\) 12.4506 + 30.0585i 0.425305 + 1.02678i 0.980758 + 0.195230i \(0.0625452\pi\)
−0.555452 + 0.831548i \(0.687455\pi\)
\(858\) 34.0003 34.0003i 1.16075 1.16075i
\(859\) 2.67780 + 2.67780i 0.0913655 + 0.0913655i 0.751312 0.659947i \(-0.229421\pi\)
−0.659947 + 0.751312i \(0.729421\pi\)
\(860\) −6.19679 + 4.29324i −0.211309 + 0.146398i
\(861\) 13.0606 + 31.5311i 0.445104 + 1.07458i
\(862\) 6.62107 15.9847i 0.225515 0.544440i
\(863\) 27.0902 0.922163 0.461081 0.887358i \(-0.347462\pi\)
0.461081 + 0.887358i \(0.347462\pi\)
\(864\) 1.10071 2.65734i 0.0374468 0.0904047i
\(865\) 18.2781 28.3782i 0.621473 0.964888i
\(866\) 5.51258 0.187325
\(867\) 3.88975 36.5263i 0.132103 1.24050i
\(868\) 5.87935i 0.199558i
\(869\) −1.72528 + 1.72528i −0.0585260 + 0.0585260i
\(870\) −17.8426 3.23776i −0.604922 0.109770i
\(871\) 2.13326i 0.0722828i
\(872\) −3.17128 + 7.65614i −0.107393 + 0.259270i
\(873\) 14.9373 6.18725i 0.505552 0.209407i
\(874\) −2.96843 + 1.22956i −0.100409 + 0.0415906i
\(875\) 38.3851 + 5.63762i 1.29765 + 0.190586i
\(876\) −1.60467 1.60467i −0.0542168 0.0542168i
\(877\) −2.17663 5.25485i −0.0734995 0.177444i 0.882860 0.469637i \(-0.155615\pi\)
−0.956359 + 0.292193i \(0.905615\pi\)
\(878\) −5.08283 + 2.10538i −0.171537 + 0.0710531i
\(879\) −13.4051 5.55256i −0.452142 0.187283i
\(880\) −9.33048 + 2.01986i −0.314531 + 0.0680895i
\(881\) −5.52498 + 13.3385i −0.186141 + 0.449385i −0.989211 0.146501i \(-0.953199\pi\)
0.803069 + 0.595886i \(0.203199\pi\)
\(882\) 5.94933 + 5.94933i 0.200324 + 0.200324i
\(883\) 29.8519i 1.00460i 0.864694 + 0.502299i \(0.167512\pi\)
−0.864694 + 0.502299i \(0.832488\pi\)
\(884\) −17.2108 12.8703i −0.578861 0.432875i
\(885\) 42.5553 9.21236i 1.43048 0.309670i
\(886\) 10.6393 10.6393i 0.357433 0.357433i
\(887\) −12.6831 5.25350i −0.425856 0.176395i 0.159453 0.987206i \(-0.449027\pi\)
−0.585309 + 0.810810i \(0.699027\pi\)
\(888\) 10.6771 0.358299
\(889\) 5.81433 + 2.40837i 0.195006 + 0.0807743i
\(890\) 18.5517 + 26.7771i 0.621853 + 0.897571i
\(891\) 44.2619 18.3339i 1.48283 0.614208i
\(892\) 12.2971 12.2971i 0.411739 0.411739i
\(893\) 1.06103 1.06103i 0.0355060 0.0355060i
\(894\) −20.8702 + 8.64472i −0.698004 + 0.289123i
\(895\) −23.3848 + 16.2014i −0.781667 + 0.541553i
\(896\) 3.20595 + 1.32795i 0.107103 + 0.0443636i
\(897\) −83.7055 −2.79485
\(898\) −10.3001 4.26643i −0.343718 0.142373i
\(899\) −4.49653 + 4.49653i −0.149968 + 0.149968i
\(900\) 7.59717 3.45100i 0.253239 0.115033i
\(901\) 56.1819 8.10663i 1.87169 0.270071i
\(902\) 19.4331i 0.647050i
\(903\) 17.8749 + 17.8749i 0.594839 + 0.594839i
\(904\) −2.58618 + 6.24358i −0.0860149 + 0.207658i
\(905\) −33.8618 + 7.33040i −1.12560 + 0.243671i
\(906\) −34.6348 14.3462i −1.15066 0.476621i
\(907\) 49.3266 20.4318i 1.63786 0.678425i 0.641784 0.766886i \(-0.278195\pi\)
0.996080 + 0.0884604i \(0.0281947\pi\)
\(908\) 4.57652 + 11.0487i 0.151877 + 0.366664i
\(909\) 13.0452 + 13.0452i 0.432681 + 0.432681i
\(910\) 34.0016 + 21.9001i 1.12714 + 0.725980i
\(911\) −45.5839 + 18.8815i −1.51026 + 0.625571i −0.975612 0.219502i \(-0.929557\pi\)
−0.534650 + 0.845073i \(0.679557\pi\)
\(912\) 0.863000 0.357466i 0.0285768 0.0118369i
\(913\) −24.7112 + 59.6581i −0.817821 + 1.97439i
\(914\) 21.8649i 0.723225i
\(915\) 5.36930 29.5891i 0.177503 0.978185i
\(916\) 8.31862 8.31862i 0.274855 0.274855i
\(917\) 14.9617i 0.494079i
\(918\) −6.05655 10.1961i −0.199896 0.336520i
\(919\) −22.4050 −0.739074 −0.369537 0.929216i \(-0.620484\pi\)
−0.369537 + 0.929216i \(0.620484\pi\)
\(920\) 13.9717 + 8.99904i 0.460635 + 0.296689i
\(921\) −28.1025 + 67.8456i −0.926010 + 2.23559i
\(922\) −9.38263 −0.309000
\(923\) −20.0458 + 48.3948i −0.659815 + 1.59293i
\(924\) 12.2504 + 29.5751i 0.403009 + 0.972949i
\(925\) −18.0488 16.8722i −0.593440 0.554753i
\(926\) −13.5333 13.5333i −0.444732 0.444732i
\(927\) 7.48676 7.48676i 0.245898 0.245898i
\(928\) 1.43630 + 3.46752i 0.0471487 + 0.113827i
\(929\) 2.78146 + 6.71505i 0.0912569 + 0.220314i 0.962917 0.269797i \(-0.0869565\pi\)
−0.871660 + 0.490110i \(0.836956\pi\)
\(930\) 1.46160 8.05457i 0.0479278 0.264120i
\(931\) 2.17950i 0.0714302i
\(932\) −21.6054 8.94925i −0.707709 0.293143i
\(933\) −39.7997 39.7997i −1.30298 1.30298i
\(934\) 19.8500 0.649512
\(935\) −16.3695 + 35.7964i −0.535341 + 1.17067i
\(936\) 8.69852 0.284320
\(937\) 15.8604 + 15.8604i 0.518135 + 0.518135i 0.917007 0.398872i \(-0.130598\pi\)
−0.398872 + 0.917007i \(0.630598\pi\)
\(938\) −1.31212 0.543497i −0.0428422 0.0177458i
\(939\) 4.56944i 0.149118i
\(940\) −7.63663 1.38576i −0.249079 0.0451985i
\(941\) 18.5277 + 44.7297i 0.603984 + 1.45815i 0.869447 + 0.494026i \(0.164475\pi\)
−0.265463 + 0.964121i \(0.585525\pi\)
\(942\) −2.39946 5.79280i −0.0781786 0.188740i
\(943\) 23.9212 23.9212i 0.778981 0.778981i
\(944\) −6.37226 6.37226i −0.207399 0.207399i
\(945\) 12.7101 + 18.3455i 0.413458 + 0.596778i
\(946\) 5.50828 + 13.2982i 0.179089 + 0.432360i
\(947\) 11.0613 26.7043i 0.359444 0.867773i −0.635935 0.771743i \(-0.719385\pi\)
0.995378 0.0960307i \(-0.0306147\pi\)
\(948\) −1.23485 −0.0401061
\(949\) −2.09490 + 5.05754i −0.0680034 + 0.164175i
\(950\) −2.02371 0.759463i −0.0656579 0.0246402i
\(951\) 17.5432 0.568877
\(952\) 12.3010 7.30692i 0.398679 0.236819i
\(953\) 8.42766i 0.272999i −0.990640 0.136499i \(-0.956415\pi\)
0.990640 0.136499i \(-0.0435851\pi\)
\(954\) −16.2461 + 16.2461i −0.525986 + 0.525986i
\(955\) 18.5801 + 3.37158i 0.601237 + 0.109102i
\(956\) 13.2057i 0.427103i
\(957\) −13.2499 + 31.9881i −0.428309 + 1.03403i
\(958\) 9.18371 3.80402i 0.296712 0.122902i
\(959\) −14.1670 + 5.86816i −0.457476 + 0.189493i
\(960\) −4.06195 2.61625i −0.131099 0.0844393i
\(961\) 19.8905 + 19.8905i 0.641628 + 0.641628i
\(962\) −9.85633 23.7953i −0.317781 0.767191i
\(963\) −2.49711 + 1.03434i −0.0804681 + 0.0333310i
\(964\) −20.9168 8.66402i −0.673684 0.279049i
\(965\) −10.0967 46.6401i −0.325023 1.50140i
\(966\) 21.3259 51.4852i 0.686149 1.65651i
\(967\) 23.4943 + 23.4943i 0.755527 + 0.755527i 0.975505 0.219978i \(-0.0705985\pi\)
−0.219978 + 0.975505i \(0.570599\pi\)
\(968\) 7.22756i 0.232302i
\(969\) 0.950599 3.73226i 0.0305376 0.119897i
\(970\) 4.58351 + 21.1729i 0.147168 + 0.679822i
\(971\) 28.5627 28.5627i 0.916621 0.916621i −0.0801605 0.996782i \(-0.525543\pi\)
0.996782 + 0.0801605i \(0.0255433\pi\)
\(972\) 14.4291 + 5.97675i 0.462815 + 0.191704i
\(973\) −18.7737 −0.601858
\(974\) −8.06967 3.34257i −0.258569 0.107103i
\(975\) −41.1371 38.4553i −1.31744 1.23156i
\(976\) −5.75032 + 2.38186i −0.184063 + 0.0762415i
\(977\) 0.211408 0.211408i 0.00676354 0.00676354i −0.703717 0.710480i \(-0.748478\pi\)
0.710480 + 0.703717i \(0.248478\pi\)
\(978\) 5.73181 5.73181i 0.183283 0.183283i
\(979\) 57.4630 23.8020i 1.83653 0.760714i
\(980\) −9.26660 + 6.42007i −0.296011 + 0.205081i
\(981\) −12.7769 5.29238i −0.407936 0.168973i
\(982\) 2.31132 0.0737571
\(983\) 20.7949 + 8.61355i 0.663256 + 0.274730i 0.688808 0.724944i \(-0.258134\pi\)
−0.0255520 + 0.999673i \(0.508134\pi\)
\(984\) −6.95451 + 6.95451i −0.221702 + 0.221702i
\(985\) −1.97310 + 0.427136i −0.0628681 + 0.0136097i
\(986\) 14.9962 + 3.81950i 0.477575 + 0.121638i
\(987\) 26.0254i 0.828399i
\(988\) −1.59332 1.59332i −0.0506904 0.0506904i
\(989\) 9.58898 23.1498i 0.304912 0.736122i
\(990\) −3.37084 15.5712i −0.107132 0.494884i
\(991\) 8.04403 + 3.33195i 0.255527 + 0.105843i 0.506770 0.862081i \(-0.330839\pi\)
−0.251243 + 0.967924i \(0.580839\pi\)
\(992\) −1.56532 + 0.648377i −0.0496990 + 0.0205860i
\(993\) 0.217349 + 0.524726i 0.00689735 + 0.0166517i
\(994\) −24.6593 24.6593i −0.782146 0.782146i
\(995\) −0.431205 + 0.669481i −0.0136701 + 0.0212240i
\(996\) −30.1933 + 12.5065i −0.956710 + 0.396282i
\(997\) −2.88867 + 1.19653i −0.0914852 + 0.0378944i −0.427957 0.903799i \(-0.640766\pi\)
0.336471 + 0.941694i \(0.390766\pi\)
\(998\) 11.1408 26.8962i 0.352655 0.851385i
\(999\) 14.2128i 0.449673i
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 170.2.n.b.59.4 yes 20
5.2 odd 4 850.2.l.h.501.4 20
5.3 odd 4 850.2.l.i.501.2 20
5.4 even 2 170.2.n.a.59.2 yes 20
17.15 even 8 170.2.n.a.49.2 20
85.32 odd 8 850.2.l.h.151.4 20
85.49 even 8 inner 170.2.n.b.49.4 yes 20
85.83 odd 8 850.2.l.i.151.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.n.a.49.2 20 17.15 even 8
170.2.n.a.59.2 yes 20 5.4 even 2
170.2.n.b.49.4 yes 20 85.49 even 8 inner
170.2.n.b.59.4 yes 20 1.1 even 1 trivial
850.2.l.h.151.4 20 85.32 odd 8
850.2.l.h.501.4 20 5.2 odd 4
850.2.l.i.151.2 20 85.83 odd 8
850.2.l.i.501.2 20 5.3 odd 4