Properties

Label 65.2.o.a.32.5
Level $65$
Weight $2$
Character 65.32
Analytic conductor $0.519$
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] = [65,2,Mod(2,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.o (of order \(12\), 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: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + 1263 x^{4} + 78 x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.5
Root \(-2.25081i\) of defining polynomial
Character \(\chi\) \(=\) 65.32
Dual form 65.2.o.a.63.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12540 - 1.94926i) q^{2} +(0.514229 + 1.91913i) q^{3} +(-1.53307 - 2.65535i) q^{4} +(-2.22228 - 0.247944i) q^{5} +(4.31958 + 1.15743i) q^{6} +(-1.10607 + 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 + 0.473740i) q^{9} +O(q^{10})\) \(q+(1.12540 - 1.94926i) q^{2} +(0.514229 + 1.91913i) q^{3} +(-1.53307 - 2.65535i) q^{4} +(-2.22228 - 0.247944i) q^{5} +(4.31958 + 1.15743i) q^{6} +(-1.10607 + 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 + 0.473740i) q^{9} +(-2.98427 + 4.05275i) q^{10} +(-5.27612 + 1.41373i) q^{11} +(4.30760 - 4.30760i) q^{12} +(3.50617 - 0.840691i) q^{13} +2.87469i q^{14} +(-0.666923 - 4.39234i) q^{15} +(0.365551 - 0.633152i) q^{16} +(3.11179 + 0.833802i) q^{17} +2.13259i q^{18} +(0.315395 - 1.17707i) q^{19} +(2.74852 + 6.28104i) q^{20} +(-1.79431 - 1.79431i) q^{21} +(-3.18204 + 11.8755i) q^{22} +(0.160006 - 0.0428736i) q^{23} +(-1.23397 - 4.60524i) q^{24} +(4.87705 + 1.10200i) q^{25} +(2.30714 - 7.78054i) q^{26} +(2.88358 + 2.88358i) q^{27} +(3.39137 + 1.95801i) q^{28} +(-8.41068 - 4.85591i) q^{29} +(-9.31234 - 3.64315i) q^{30} +(0.233305 - 0.233305i) q^{31} +(-3.22244 - 5.58143i) q^{32} +(-5.42627 - 9.39857i) q^{33} +(5.12732 - 5.12732i) q^{34} +(2.61634 - 1.14488i) q^{35} +(2.51589 + 1.45255i) q^{36} +(-1.14457 - 0.660816i) q^{37} +(-1.93947 - 1.93947i) q^{38} +(3.41637 + 6.29648i) q^{39} +(5.33270 + 0.594981i) q^{40} +(0.129579 + 0.483595i) q^{41} +(-5.51690 + 1.47825i) q^{42} +(-1.72444 + 6.43569i) q^{43} +(11.8426 + 11.8426i) q^{44} +(1.94093 - 0.849334i) q^{45} +(0.0965002 - 0.360144i) q^{46} +3.20027i q^{47} +(1.40308 + 0.375953i) q^{48} +(-2.68440 + 4.64952i) q^{49} +(7.63673 - 8.26642i) q^{50} +6.40069i q^{51} +(-7.60752 - 8.02127i) q^{52} +(4.49845 - 4.49845i) q^{53} +(8.86603 - 2.37565i) q^{54} +(12.0755 - 1.83353i) q^{55} +(2.65420 - 1.53240i) q^{56} +2.42113 q^{57} +(-18.9308 + 10.9297i) q^{58} +(-0.00222123 - 0.000595178i) q^{59} +(-10.6407 + 8.50465i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(-0.192209 - 0.717332i) q^{62} +(0.605053 - 1.04798i) q^{63} -13.0440 q^{64} +(-8.00014 + 0.998915i) q^{65} -24.4270 q^{66} +(-3.03718 + 5.26055i) q^{67} +(-2.55655 - 9.54117i) q^{68} +(0.164560 + 0.285026i) q^{69} +(0.712764 - 6.38837i) q^{70} +(11.7428 + 3.14648i) q^{71} +(1.96902 - 1.13681i) q^{72} +7.34614 q^{73} +(-2.57620 + 1.48737i) q^{74} +(0.393034 + 9.92635i) q^{75} +(-3.60906 + 0.967044i) q^{76} +(4.93298 - 4.93298i) q^{77} +(16.1182 + 0.426708i) q^{78} -11.1774i q^{79} +(-0.969342 + 1.31640i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(1.08848 + 0.291657i) q^{82} -2.65539i q^{83} +(-2.01373 + 7.51533i) q^{84} +(-6.70854 - 2.62449i) q^{85} +(10.6041 + 10.6041i) q^{86} +(4.99409 - 18.6382i) q^{87} +(12.6609 - 3.39247i) q^{88} +(1.86638 + 6.96542i) q^{89} +(0.528764 - 4.73922i) q^{90} +(-3.34123 + 3.16888i) q^{91} +(-0.359145 - 0.359145i) q^{92} +(0.567713 + 0.327769i) q^{93} +(6.23815 + 3.60160i) q^{94} +(-0.992745 + 2.53758i) q^{95} +(9.05440 - 9.05440i) q^{96} +(-2.09035 - 3.62059i) q^{97} +(6.04207 + 10.4652i) q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.12540 1.94926i 0.795780 1.37833i −0.126562 0.991959i \(-0.540394\pi\)
0.922342 0.386373i \(-0.126272\pi\)
\(3\) 0.514229 + 1.91913i 0.296890 + 1.10801i 0.939705 + 0.341987i \(0.111100\pi\)
−0.642815 + 0.766022i \(0.722233\pi\)
\(4\) −1.53307 2.65535i −0.766533 1.32767i
\(5\) −2.22228 0.247944i −0.993833 0.110884i
\(6\) 4.31958 + 1.15743i 1.76346 + 0.472518i
\(7\) −1.10607 + 0.638592i −0.418057 + 0.241365i −0.694245 0.719738i \(-0.744262\pi\)
0.276189 + 0.961103i \(0.410928\pi\)
\(8\) −2.39966 −0.848406
\(9\) −0.820542 + 0.473740i −0.273514 + 0.157913i
\(10\) −2.98427 + 4.05275i −0.943708 + 1.28159i
\(11\) −5.27612 + 1.41373i −1.59081 + 0.426257i −0.942251 0.334907i \(-0.891295\pi\)
−0.648560 + 0.761163i \(0.724629\pi\)
\(12\) 4.30760 4.30760i 1.24350 1.24350i
\(13\) 3.50617 0.840691i 0.972437 0.233166i
\(14\) 2.87469i 0.768294i
\(15\) −0.666923 4.39234i −0.172199 1.13410i
\(16\) 0.365551 0.633152i 0.0913876 0.158288i
\(17\) 3.11179 + 0.833802i 0.754721 + 0.202227i 0.615611 0.788050i \(-0.288909\pi\)
0.139110 + 0.990277i \(0.455576\pi\)
\(18\) 2.13259i 0.502657i
\(19\) 0.315395 1.17707i 0.0723567 0.270039i −0.920264 0.391297i \(-0.872026\pi\)
0.992621 + 0.121259i \(0.0386931\pi\)
\(20\) 2.74852 + 6.28104i 0.614588 + 1.40448i
\(21\) −1.79431 1.79431i −0.391551 0.391551i
\(22\) −3.18204 + 11.8755i −0.678413 + 2.53187i
\(23\) 0.160006 0.0428736i 0.0333637 0.00893976i −0.242099 0.970252i \(-0.577836\pi\)
0.275462 + 0.961312i \(0.411169\pi\)
\(24\) −1.23397 4.60524i −0.251883 0.940042i
\(25\) 4.87705 + 1.10200i 0.975409 + 0.220401i
\(26\) 2.30714 7.78054i 0.452466 1.52589i
\(27\) 2.88358 + 2.88358i 0.554946 + 0.554946i
\(28\) 3.39137 + 1.95801i 0.640908 + 0.370029i
\(29\) −8.41068 4.85591i −1.56182 0.901719i −0.997073 0.0764575i \(-0.975639\pi\)
−0.564751 0.825262i \(-0.691028\pi\)
\(30\) −9.31234 3.64315i −1.70019 0.665145i
\(31\) 0.233305 0.233305i 0.0419027 0.0419027i −0.685845 0.727748i \(-0.740567\pi\)
0.727748 + 0.685845i \(0.240567\pi\)
\(32\) −3.22244 5.58143i −0.569652 0.986667i
\(33\) −5.42627 9.39857i −0.944592 1.63608i
\(34\) 5.12732 5.12732i 0.879328 0.879328i
\(35\) 2.61634 1.14488i 0.442242 0.193521i
\(36\) 2.51589 + 1.45255i 0.419315 + 0.242091i
\(37\) −1.14457 0.660816i −0.188166 0.108638i 0.402958 0.915219i \(-0.367982\pi\)
−0.591124 + 0.806581i \(0.701315\pi\)
\(38\) −1.93947 1.93947i −0.314623 0.314623i
\(39\) 3.41637 + 6.29648i 0.547057 + 1.00824i
\(40\) 5.33270 + 0.594981i 0.843175 + 0.0940747i
\(41\) 0.129579 + 0.483595i 0.0202368 + 0.0755249i 0.975306 0.220859i \(-0.0708860\pi\)
−0.955069 + 0.296384i \(0.904219\pi\)
\(42\) −5.51690 + 1.47825i −0.851277 + 0.228099i
\(43\) −1.72444 + 6.43569i −0.262974 + 0.981434i 0.700504 + 0.713648i \(0.252959\pi\)
−0.963479 + 0.267786i \(0.913708\pi\)
\(44\) 11.8426 + 11.8426i 1.78534 + 1.78534i
\(45\) 1.94093 0.849334i 0.289337 0.126611i
\(46\) 0.0965002 0.360144i 0.0142282 0.0531003i
\(47\) 3.20027i 0.466808i 0.972380 + 0.233404i \(0.0749864\pi\)
−0.972380 + 0.233404i \(0.925014\pi\)
\(48\) 1.40308 + 0.375953i 0.202517 + 0.0542642i
\(49\) −2.68440 + 4.64952i −0.383486 + 0.664217i
\(50\) 7.63673 8.26642i 1.08000 1.16905i
\(51\) 6.40069i 0.896276i
\(52\) −7.60752 8.02127i −1.05497 1.11235i
\(53\) 4.49845 4.49845i 0.617909 0.617909i −0.327086 0.944995i \(-0.606067\pi\)
0.944995 + 0.327086i \(0.106067\pi\)
\(54\) 8.86603 2.37565i 1.20651 0.323285i
\(55\) 12.0755 1.83353i 1.62827 0.247232i
\(56\) 2.65420 1.53240i 0.354682 0.204776i
\(57\) 2.42113 0.320687
\(58\) −18.9308 + 10.9297i −2.48574 + 1.43514i
\(59\) −0.00222123 0.000595178i −0.000289180 7.74855e-5i 0.258674 0.965965i \(-0.416714\pi\)
−0.258964 + 0.965887i \(0.583381\pi\)
\(60\) −10.6407 + 8.50465i −1.37371 + 1.09795i
\(61\) −0.695993 1.20550i −0.0891128 0.154348i 0.818024 0.575185i \(-0.195070\pi\)
−0.907136 + 0.420837i \(0.861736\pi\)
\(62\) −0.192209 0.717332i −0.0244105 0.0911013i
\(63\) 0.605053 1.04798i 0.0762295 0.132033i
\(64\) −13.0440 −1.63050
\(65\) −8.00014 + 0.998915i −0.992295 + 0.123900i
\(66\) −24.4270 −3.00675
\(67\) −3.03718 + 5.26055i −0.371050 + 0.642678i −0.989727 0.142967i \(-0.954336\pi\)
0.618677 + 0.785645i \(0.287669\pi\)
\(68\) −2.55655 9.54117i −0.310027 1.15704i
\(69\) 0.164560 + 0.285026i 0.0198107 + 0.0343131i
\(70\) 0.712764 6.38837i 0.0851916 0.763557i
\(71\) 11.7428 + 3.14648i 1.39361 + 0.373418i 0.876048 0.482225i \(-0.160171\pi\)
0.517567 + 0.855643i \(0.326838\pi\)
\(72\) 1.96902 1.13681i 0.232051 0.133975i
\(73\) 7.34614 0.859801 0.429901 0.902876i \(-0.358549\pi\)
0.429901 + 0.902876i \(0.358549\pi\)
\(74\) −2.57620 + 1.48737i −0.299477 + 0.172903i
\(75\) 0.393034 + 9.92635i 0.0453837 + 1.14620i
\(76\) −3.60906 + 0.967044i −0.413987 + 0.110928i
\(77\) 4.93298 4.93298i 0.562166 0.562166i
\(78\) 16.1182 + 0.426708i 1.82503 + 0.0483152i
\(79\) 11.1774i 1.25756i −0.777584 0.628779i \(-0.783555\pi\)
0.777584 0.628779i \(-0.216445\pi\)
\(80\) −0.969342 + 1.31640i −0.108376 + 0.147178i
\(81\) −5.47236 + 9.47841i −0.608040 + 1.05316i
\(82\) 1.08848 + 0.291657i 0.120202 + 0.0322081i
\(83\) 2.65539i 0.291467i −0.989324 0.145733i \(-0.953446\pi\)
0.989324 0.145733i \(-0.0465542\pi\)
\(84\) −2.01373 + 7.51533i −0.219716 + 0.819990i
\(85\) −6.70854 2.62449i −0.727643 0.284666i
\(86\) 10.6041 + 10.6041i 1.14347 + 1.14347i
\(87\) 4.99409 18.6382i 0.535423 1.99823i
\(88\) 12.6609 3.39247i 1.34965 0.361639i
\(89\) 1.86638 + 6.96542i 0.197836 + 0.738333i 0.991515 + 0.129996i \(0.0414964\pi\)
−0.793679 + 0.608337i \(0.791837\pi\)
\(90\) 0.528764 4.73922i 0.0557367 0.499558i
\(91\) −3.34123 + 3.16888i −0.350256 + 0.332189i
\(92\) −0.359145 0.359145i −0.0374434 0.0374434i
\(93\) 0.567713 + 0.327769i 0.0588691 + 0.0339881i
\(94\) 6.23815 + 3.60160i 0.643416 + 0.371477i
\(95\) −0.992745 + 2.53758i −0.101853 + 0.260350i
\(96\) 9.05440 9.05440i 0.924111 0.924111i
\(97\) −2.09035 3.62059i −0.212243 0.367616i 0.740173 0.672416i \(-0.234743\pi\)
−0.952416 + 0.304801i \(0.901410\pi\)
\(98\) 6.04207 + 10.4652i 0.610341 + 1.05714i
\(99\) 3.65954 3.65954i 0.367797 0.367797i
\(100\) −4.55063 14.6397i −0.455063 1.46397i
\(101\) −7.47319 4.31465i −0.743610 0.429323i 0.0797704 0.996813i \(-0.474581\pi\)
−0.823380 + 0.567490i \(0.807915\pi\)
\(102\) 12.4766 + 7.20336i 1.23537 + 0.713239i
\(103\) −1.07603 1.07603i −0.106025 0.106025i 0.652104 0.758129i \(-0.273886\pi\)
−0.758129 + 0.652104i \(0.773886\pi\)
\(104\) −8.41360 + 2.01737i −0.825022 + 0.197819i
\(105\) 3.54258 + 4.43236i 0.345720 + 0.432554i
\(106\) −3.70606 13.8312i −0.359964 1.34340i
\(107\) −14.0309 + 3.75956i −1.35642 + 0.363451i −0.862499 0.506058i \(-0.831102\pi\)
−0.493917 + 0.869509i \(0.664435\pi\)
\(108\) 3.23619 12.0776i 0.311403 1.16217i
\(109\) 4.72405 + 4.72405i 0.452481 + 0.452481i 0.896177 0.443696i \(-0.146333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(110\) 10.0159 25.6018i 0.954974 2.44103i
\(111\) 0.679621 2.53638i 0.0645068 0.240743i
\(112\) 0.933751i 0.0882311i
\(113\) −11.0065 2.94919i −1.03541 0.277437i −0.299199 0.954191i \(-0.596719\pi\)
−0.736209 + 0.676754i \(0.763386\pi\)
\(114\) 2.72475 4.71941i 0.255197 0.442013i
\(115\) −0.366209 + 0.0556044i −0.0341492 + 0.00518514i
\(116\) 29.7777i 2.76479i
\(117\) −2.47869 + 2.35084i −0.229155 + 0.217335i
\(118\) −0.00365994 + 0.00365994i −0.000336925 + 0.000336925i
\(119\) −3.97433 + 1.06492i −0.364326 + 0.0976210i
\(120\) 1.60039 + 10.5401i 0.146094 + 0.962175i
\(121\) 16.3126 9.41807i 1.48296 0.856188i
\(122\) −3.13309 −0.283657
\(123\) −0.861447 + 0.497357i −0.0776741 + 0.0448452i
\(124\) −0.977176 0.261833i −0.0877530 0.0235133i
\(125\) −10.5649 3.65819i −0.944956 0.327199i
\(126\) −1.36186 2.35881i −0.121324 0.210139i
\(127\) −0.135757 0.506651i −0.0120465 0.0449580i 0.959641 0.281228i \(-0.0907417\pi\)
−0.971687 + 0.236270i \(0.924075\pi\)
\(128\) −8.23486 + 14.2632i −0.727865 + 1.26070i
\(129\) −13.2377 −1.16551
\(130\) −7.05624 + 16.7185i −0.618873 + 1.46631i
\(131\) 5.09883 0.445486 0.222743 0.974877i \(-0.428499\pi\)
0.222743 + 0.974877i \(0.428499\pi\)
\(132\) −16.6377 + 28.8173i −1.44812 + 2.50822i
\(133\) 0.402818 + 1.50334i 0.0349287 + 0.130356i
\(134\) 6.83610 + 11.8405i 0.590549 + 1.02286i
\(135\) −5.69316 7.12309i −0.489989 0.613058i
\(136\) −7.46723 2.00084i −0.640310 0.171571i
\(137\) 3.29390 1.90173i 0.281417 0.162476i −0.352648 0.935756i \(-0.614719\pi\)
0.634065 + 0.773280i \(0.281385\pi\)
\(138\) 0.740785 0.0630598
\(139\) 1.28017 0.739106i 0.108583 0.0626902i −0.444725 0.895667i \(-0.646699\pi\)
0.553308 + 0.832977i \(0.313365\pi\)
\(140\) −7.05109 5.19211i −0.595926 0.438813i
\(141\) −6.14173 + 1.64567i −0.517227 + 0.138591i
\(142\) 19.3487 19.3487i 1.62371 1.62371i
\(143\) −17.3105 + 9.39238i −1.44758 + 0.785431i
\(144\) 0.692704i 0.0577253i
\(145\) 17.4869 + 12.8766i 1.45221 + 1.06934i
\(146\) 8.26737 14.3195i 0.684213 1.18509i
\(147\) −10.3034 2.76079i −0.849811 0.227706i
\(148\) 4.05230i 0.333097i
\(149\) 4.45586 16.6295i 0.365038 1.36234i −0.502331 0.864675i \(-0.667524\pi\)
0.867369 0.497665i \(-0.165809\pi\)
\(150\) 19.7913 + 10.4050i 1.61596 + 0.849567i
\(151\) −10.0539 10.0539i −0.818178 0.818178i 0.167666 0.985844i \(-0.446377\pi\)
−0.985844 + 0.167666i \(0.946377\pi\)
\(152\) −0.756840 + 2.82457i −0.0613879 + 0.229103i
\(153\) −2.94836 + 0.790011i −0.238361 + 0.0638686i
\(154\) −4.06405 15.1672i −0.327491 1.22221i
\(155\) −0.576314 + 0.460621i −0.0462907 + 0.0369980i
\(156\) 11.4818 18.7246i 0.919282 1.49916i
\(157\) 3.07230 + 3.07230i 0.245196 + 0.245196i 0.818996 0.573799i \(-0.194531\pi\)
−0.573799 + 0.818996i \(0.694531\pi\)
\(158\) −21.7876 12.5791i −1.73333 1.00074i
\(159\) 10.9463 + 6.31986i 0.868100 + 0.501198i
\(160\) 5.77728 + 13.2025i 0.456734 + 1.04375i
\(161\) −0.149600 + 0.149600i −0.0117902 + 0.0117902i
\(162\) 12.3172 + 21.3341i 0.967733 + 1.67616i
\(163\) −4.60251 7.97177i −0.360496 0.624398i 0.627546 0.778579i \(-0.284059\pi\)
−0.988043 + 0.154182i \(0.950726\pi\)
\(164\) 1.08546 1.08546i 0.0847602 0.0847602i
\(165\) 9.72836 + 22.2317i 0.757352 + 1.73073i
\(166\) −5.17603 2.98838i −0.401738 0.231944i
\(167\) 10.9455 + 6.31936i 0.846985 + 0.489007i 0.859632 0.510913i \(-0.170693\pi\)
−0.0126474 + 0.999920i \(0.504026\pi\)
\(168\) 4.30574 + 4.30574i 0.332195 + 0.332195i
\(169\) 11.5865 5.89521i 0.891267 0.453478i
\(170\) −12.6656 + 10.1230i −0.971409 + 0.776402i
\(171\) 0.298831 + 1.11525i 0.0228522 + 0.0852854i
\(172\) 19.7327 5.28736i 1.50460 0.403157i
\(173\) −3.54983 + 13.2481i −0.269888 + 1.00724i 0.689302 + 0.724474i \(0.257917\pi\)
−0.959190 + 0.282762i \(0.908749\pi\)
\(174\) −30.7103 30.7103i −2.32814 2.32814i
\(175\) −6.09810 + 1.89555i −0.460973 + 0.143290i
\(176\) −1.03358 + 3.85738i −0.0779092 + 0.290761i
\(177\) 0.00456889i 0.000343419i
\(178\) 15.6778 + 4.20086i 1.17510 + 0.314867i
\(179\) 6.32126 10.9487i 0.472473 0.818347i −0.527031 0.849846i \(-0.676695\pi\)
0.999504 + 0.0314989i \(0.0100281\pi\)
\(180\) −5.23085 3.85177i −0.389885 0.287094i
\(181\) 8.16619i 0.606988i 0.952833 + 0.303494i \(0.0981533\pi\)
−0.952833 + 0.303494i \(0.901847\pi\)
\(182\) 2.41673 + 10.0792i 0.179140 + 0.747118i
\(183\) 1.95560 1.95560i 0.144562 0.144562i
\(184\) −0.383960 + 0.102882i −0.0283059 + 0.00758455i
\(185\) 2.37970 + 1.75231i 0.174959 + 0.128832i
\(186\) 1.27781 0.737745i 0.0936937 0.0540941i
\(187\) −17.5970 −1.28682
\(188\) 8.49784 4.90623i 0.619769 0.357824i
\(189\) −5.03089 1.34802i −0.365943 0.0980542i
\(190\) 3.82916 + 4.79091i 0.277796 + 0.347569i
\(191\) 7.37692 + 12.7772i 0.533775 + 0.924526i 0.999222 + 0.0394498i \(0.0125605\pi\)
−0.465446 + 0.885076i \(0.654106\pi\)
\(192\) −6.70758 25.0330i −0.484078 1.80660i
\(193\) 7.54845 13.0743i 0.543349 0.941109i −0.455359 0.890308i \(-0.650489\pi\)
0.998709 0.0508011i \(-0.0161775\pi\)
\(194\) −9.40995 −0.675595
\(195\) −6.03094 14.8396i −0.431885 1.06269i
\(196\) 16.4614 1.17582
\(197\) 7.68576 13.3121i 0.547588 0.948450i −0.450851 0.892599i \(-0.648879\pi\)
0.998439 0.0558510i \(-0.0177872\pi\)
\(198\) −3.01492 11.2518i −0.214261 0.799633i
\(199\) −5.72810 9.92136i −0.406054 0.703307i 0.588389 0.808578i \(-0.299762\pi\)
−0.994444 + 0.105271i \(0.966429\pi\)
\(200\) −11.7032 2.64443i −0.827544 0.186989i
\(201\) −11.6575 3.12361i −0.822254 0.220322i
\(202\) −16.8207 + 9.71144i −1.18350 + 0.683294i
\(203\) 12.4038 0.870574
\(204\) 16.9961 9.81268i 1.18996 0.687025i
\(205\) −0.168056 1.10681i −0.0117375 0.0773031i
\(206\) −3.30843 + 0.886492i −0.230509 + 0.0617648i
\(207\) −0.110981 + 0.110981i −0.00771372 + 0.00771372i
\(208\) 0.749397 2.52726i 0.0519614 0.175234i
\(209\) 6.65626i 0.460423i
\(210\) 12.6266 1.91720i 0.871320 0.132299i
\(211\) −1.59195 + 2.75735i −0.109595 + 0.189823i −0.915606 0.402076i \(-0.868289\pi\)
0.806011 + 0.591900i \(0.201622\pi\)
\(212\) −18.8414 5.04852i −1.29403 0.346734i
\(213\) 24.1539i 1.65500i
\(214\) −8.46205 + 31.5808i −0.578454 + 2.15882i
\(215\) 5.42788 13.8743i 0.370178 0.946222i
\(216\) −6.91961 6.91961i −0.470820 0.470820i
\(217\) −0.109066 + 0.407038i −0.00740386 + 0.0276316i
\(218\) 14.5248 3.89192i 0.983746 0.263594i
\(219\) 3.77760 + 14.0982i 0.255266 + 0.952667i
\(220\) −23.3813 29.2539i −1.57636 1.97230i
\(221\) 11.6115 + 0.307397i 0.781071 + 0.0206778i
\(222\) −4.17921 4.17921i −0.280490 0.280490i
\(223\) −10.2862 5.93874i −0.688815 0.397688i 0.114353 0.993440i \(-0.463521\pi\)
−0.803168 + 0.595753i \(0.796854\pi\)
\(224\) 7.12851 + 4.11565i 0.476294 + 0.274988i
\(225\) −4.52388 + 1.40621i −0.301592 + 0.0937475i
\(226\) −18.1355 + 18.1355i −1.20636 + 1.20636i
\(227\) 13.8333 + 23.9600i 0.918149 + 1.59028i 0.802225 + 0.597022i \(0.203650\pi\)
0.115924 + 0.993258i \(0.463017\pi\)
\(228\) −3.71176 6.42896i −0.245817 0.425768i
\(229\) −12.9000 + 12.9000i −0.852455 + 0.852455i −0.990435 0.137980i \(-0.955939\pi\)
0.137980 + 0.990435i \(0.455939\pi\)
\(230\) −0.303746 + 0.776413i −0.0200284 + 0.0511952i
\(231\) 12.0037 + 6.93034i 0.789786 + 0.455983i
\(232\) 20.1827 + 11.6525i 1.32506 + 0.765024i
\(233\) 16.3545 + 16.3545i 1.07142 + 1.07142i 0.997246 + 0.0741712i \(0.0236311\pi\)
0.0741712 + 0.997246i \(0.476369\pi\)
\(234\) 1.79285 + 7.47724i 0.117202 + 0.488803i
\(235\) 0.793489 7.11190i 0.0517615 0.463929i
\(236\) 0.00182489 + 0.00681059i 0.000118790 + 0.000443332i
\(237\) 21.4509 5.74774i 1.39338 0.373356i
\(238\) −2.39693 + 8.94546i −0.155370 + 0.579848i
\(239\) 2.61794 + 2.61794i 0.169341 + 0.169341i 0.786690 0.617349i \(-0.211793\pi\)
−0.617349 + 0.786690i \(0.711793\pi\)
\(240\) −3.02481 1.18336i −0.195251 0.0763854i
\(241\) 5.38613 20.1013i 0.346951 1.29484i −0.543365 0.839496i \(-0.682850\pi\)
0.890316 0.455343i \(-0.150483\pi\)
\(242\) 42.3965i 2.72535i
\(243\) −9.18717 2.46169i −0.589357 0.157918i
\(244\) −2.13401 + 3.69621i −0.136616 + 0.236625i
\(245\) 7.11831 9.66694i 0.454772 0.617598i
\(246\) 2.23891i 0.142748i
\(247\) 0.116277 4.39216i 0.00739850 0.279467i
\(248\) −0.559851 + 0.559851i −0.0355505 + 0.0355505i
\(249\) 5.09603 1.36548i 0.322948 0.0865336i
\(250\) −19.0206 + 16.4768i −1.20297 + 1.04208i
\(251\) −2.05050 + 1.18386i −0.129427 + 0.0747245i −0.563315 0.826242i \(-0.690474\pi\)
0.433889 + 0.900966i \(0.357141\pi\)
\(252\) −3.71034 −0.233730
\(253\) −0.783602 + 0.452413i −0.0492647 + 0.0284430i
\(254\) −1.14037 0.305562i −0.0715533 0.0191727i
\(255\) 1.58701 14.2241i 0.0993827 0.890749i
\(256\) 5.49109 + 9.51085i 0.343193 + 0.594428i
\(257\) 0.225182 + 0.840391i 0.0140465 + 0.0524221i 0.972593 0.232513i \(-0.0746947\pi\)
−0.958547 + 0.284935i \(0.908028\pi\)
\(258\) −14.8977 + 25.8036i −0.927492 + 1.60646i
\(259\) 1.68797 0.104885
\(260\) 14.9172 + 19.7117i 0.925126 + 1.22247i
\(261\) 9.20175 0.569574
\(262\) 5.73824 9.93892i 0.354509 0.614028i
\(263\) −3.93099 14.6707i −0.242395 0.904632i −0.974675 0.223627i \(-0.928210\pi\)
0.732279 0.681004i \(-0.238457\pi\)
\(264\) 13.0212 + 22.5533i 0.801398 + 1.38806i
\(265\) −11.1122 + 8.88144i −0.682615 + 0.545582i
\(266\) 3.38372 + 0.906665i 0.207469 + 0.0555912i
\(267\) −12.4078 + 7.16363i −0.759343 + 0.438407i
\(268\) 18.6248 1.13769
\(269\) −21.1150 + 12.1908i −1.28741 + 0.743285i −0.978191 0.207707i \(-0.933400\pi\)
−0.309216 + 0.950992i \(0.600067\pi\)
\(270\) −20.2918 + 3.08107i −1.23492 + 0.187508i
\(271\) −12.6697 + 3.39484i −0.769630 + 0.206222i −0.622208 0.782852i \(-0.713764\pi\)
−0.147422 + 0.989074i \(0.547097\pi\)
\(272\) 1.66544 1.66544i 0.100982 0.100982i
\(273\) −7.79964 4.78271i −0.472055 0.289463i
\(274\) 8.56086i 0.517181i
\(275\) −27.2898 + 1.08054i −1.64564 + 0.0651591i
\(276\) 0.504562 0.873927i 0.0303711 0.0526042i
\(277\) 11.8109 + 3.16472i 0.709647 + 0.190149i 0.595548 0.803320i \(-0.296935\pi\)
0.114099 + 0.993469i \(0.463602\pi\)
\(278\) 3.32717i 0.199550i
\(279\) −0.0809104 + 0.301962i −0.00484398 + 0.0180780i
\(280\) −6.27831 + 2.74733i −0.375201 + 0.164184i
\(281\) −6.43529 6.43529i −0.383897 0.383897i 0.488607 0.872504i \(-0.337505\pi\)
−0.872504 + 0.488607i \(0.837505\pi\)
\(282\) −3.70409 + 13.8239i −0.220575 + 0.823198i
\(283\) 26.4212 7.07953i 1.57057 0.420834i 0.634583 0.772855i \(-0.281172\pi\)
0.935992 + 0.352021i \(0.114505\pi\)
\(284\) −9.64751 36.0050i −0.572474 2.13650i
\(285\) −5.38044 0.600307i −0.318710 0.0355591i
\(286\) −1.17312 + 44.3128i −0.0693681 + 2.62027i
\(287\) −0.452144 0.452144i −0.0266892 0.0266892i
\(288\) 5.28829 + 3.05320i 0.311616 + 0.179911i
\(289\) −5.73440 3.31076i −0.337318 0.194750i
\(290\) 44.7795 19.5951i 2.62954 1.15066i
\(291\) 5.87346 5.87346i 0.344308 0.344308i
\(292\) −11.2621 19.5066i −0.659066 1.14154i
\(293\) 13.0620 + 22.6241i 0.763092 + 1.32171i 0.941249 + 0.337713i \(0.109653\pi\)
−0.178157 + 0.984002i \(0.557013\pi\)
\(294\) −16.9770 + 16.9770i −0.990118 + 0.990118i
\(295\) 0.00478863 + 0.00187339i 0.000278805 + 0.000109073i
\(296\) 2.74657 + 1.58573i 0.159641 + 0.0921688i
\(297\) −19.2908 11.1375i −1.11936 0.646265i
\(298\) −27.4005 27.4005i −1.58727 1.58727i
\(299\) 0.524967 0.284838i 0.0303596 0.0164726i
\(300\) 25.7554 16.2614i 1.48699 0.938852i
\(301\) −2.20243 8.21957i −0.126946 0.473768i
\(302\) −30.9124 + 8.28296i −1.77881 + 0.476631i
\(303\) 4.43743 16.5607i 0.254924 0.951388i
\(304\) −0.629972 0.629972i −0.0361314 0.0361314i
\(305\) 1.24780 + 2.85151i 0.0714485 + 0.163277i
\(306\) −1.77816 + 6.63619i −0.101651 + 0.379366i
\(307\) 14.7038i 0.839189i 0.907712 + 0.419595i \(0.137828\pi\)
−0.907712 + 0.419595i \(0.862172\pi\)
\(308\) −20.6614 5.53620i −1.17729 0.315454i
\(309\) 1.51172 2.61837i 0.0859985 0.148954i
\(310\) 0.249283 + 1.64177i 0.0141583 + 0.0932462i
\(311\) 31.8525i 1.80619i −0.429440 0.903095i \(-0.641289\pi\)
0.429440 0.903095i \(-0.358711\pi\)
\(312\) −8.19810 15.1094i −0.464126 0.855401i
\(313\) −11.9865 + 11.9865i −0.677519 + 0.677519i −0.959438 0.281919i \(-0.909029\pi\)
0.281919 + 0.959438i \(0.409029\pi\)
\(314\) 9.44628 2.53112i 0.533084 0.142840i
\(315\) −1.60444 + 2.17889i −0.0903998 + 0.122767i
\(316\) −29.6799 + 17.1357i −1.66963 + 0.963959i
\(317\) 15.5627 0.874088 0.437044 0.899440i \(-0.356025\pi\)
0.437044 + 0.899440i \(0.356025\pi\)
\(318\) 24.6380 14.2248i 1.38163 0.797686i
\(319\) 51.2407 + 13.7299i 2.86893 + 0.768728i
\(320\) 28.9874 + 3.23418i 1.62044 + 0.180796i
\(321\) −14.4302 24.9938i −0.805413 1.39502i
\(322\) 0.123249 + 0.459970i 0.00686837 + 0.0256331i
\(323\) 1.96289 3.39983i 0.109218 0.189171i
\(324\) 33.5580 1.86433
\(325\) 18.0262 0.236281i 0.999914 0.0131065i
\(326\) −20.7187 −1.14750
\(327\) −6.63680 + 11.4953i −0.367016 + 0.635691i
\(328\) −0.310945 1.16046i −0.0171691 0.0640758i
\(329\) −2.04367 3.53974i −0.112671 0.195152i
\(330\) 54.2835 + 6.05653i 2.98821 + 0.333401i
\(331\) −16.4820 4.41633i −0.905930 0.242743i −0.224369 0.974504i \(-0.572032\pi\)
−0.681561 + 0.731761i \(0.738699\pi\)
\(332\) −7.05098 + 4.07089i −0.386973 + 0.223419i
\(333\) 1.25222 0.0686212
\(334\) 24.6361 14.2237i 1.34803 0.778284i
\(335\) 8.05378 10.9374i 0.440025 0.597571i
\(336\) −1.79199 + 0.480161i −0.0977609 + 0.0261949i
\(337\) −25.0560 + 25.0560i −1.36489 + 1.36489i −0.497319 + 0.867568i \(0.665682\pi\)
−0.867568 + 0.497319i \(0.834318\pi\)
\(338\) 1.54818 29.2195i 0.0842098 1.58933i
\(339\) 22.6395i 1.22961i
\(340\) 3.31569 + 21.8370i 0.179818 + 1.18428i
\(341\) −0.901114 + 1.56077i −0.0487980 + 0.0845207i
\(342\) 2.51022 + 0.672610i 0.135737 + 0.0363706i
\(343\) 15.7972i 0.852971i
\(344\) 4.13806 15.4435i 0.223109 0.832655i
\(345\) −0.295027 0.674209i −0.0158837 0.0362982i
\(346\) 21.8290 + 21.8290i 1.17354 + 1.17354i
\(347\) 3.33874 12.4604i 0.179233 0.668907i −0.816559 0.577262i \(-0.804121\pi\)
0.995792 0.0916446i \(-0.0292124\pi\)
\(348\) −57.1472 + 15.3125i −3.06341 + 0.820838i
\(349\) 6.94957 + 25.9362i 0.372002 + 1.38833i 0.857676 + 0.514191i \(0.171908\pi\)
−0.485674 + 0.874140i \(0.661426\pi\)
\(350\) −3.16792 + 14.0200i −0.169332 + 0.749402i
\(351\) 12.5345 + 7.68613i 0.669044 + 0.410255i
\(352\) 24.8926 + 24.8926i 1.32678 + 1.32678i
\(353\) 20.1885 + 11.6558i 1.07453 + 0.620378i 0.929414 0.369038i \(-0.120313\pi\)
0.145111 + 0.989415i \(0.453646\pi\)
\(354\) −0.00890593 0.00514184i −0.000473345 0.000273286i
\(355\) −25.3156 9.90391i −1.34361 0.525645i
\(356\) 15.6343 15.6343i 0.828617 0.828617i
\(357\) −4.08743 7.07964i −0.216330 0.374694i
\(358\) −14.2279 24.6435i −0.751970 1.30245i
\(359\) −9.17222 + 9.17222i −0.484091 + 0.484091i −0.906435 0.422344i \(-0.861207\pi\)
0.422344 + 0.906435i \(0.361207\pi\)
\(360\) −4.65757 + 2.03811i −0.245476 + 0.107418i
\(361\) 15.1685 + 8.75751i 0.798340 + 0.460922i
\(362\) 15.9180 + 9.19026i 0.836631 + 0.483029i
\(363\) 26.4629 + 26.4629i 1.38894 + 1.38894i
\(364\) 13.5368 + 4.01402i 0.709521 + 0.210392i
\(365\) −16.3252 1.82143i −0.854499 0.0953382i
\(366\) −1.61113 6.01280i −0.0842149 0.314294i
\(367\) −14.3602 + 3.84780i −0.749595 + 0.200853i −0.613338 0.789820i \(-0.710174\pi\)
−0.136256 + 0.990674i \(0.543507\pi\)
\(368\) 0.0313449 0.116981i 0.00163397 0.00609805i
\(369\) −0.335423 0.335423i −0.0174614 0.0174614i
\(370\) 6.09382 2.66660i 0.316803 0.138630i
\(371\) −2.10294 + 7.84829i −0.109179 + 0.407463i
\(372\) 2.00997i 0.104212i
\(373\) −5.97055 1.59980i −0.309144 0.0828348i 0.100912 0.994895i \(-0.467824\pi\)
−0.410055 + 0.912061i \(0.634491\pi\)
\(374\) −19.8037 + 34.3010i −1.02403 + 1.77366i
\(375\) 1.58775 22.1566i 0.0819911 1.14416i
\(376\) 7.67955i 0.396043i
\(377\) −33.5716 9.95486i −1.72902 0.512701i
\(378\) −8.28942 + 8.28942i −0.426362 + 0.426362i
\(379\) −17.6464 + 4.72834i −0.906435 + 0.242878i −0.681778 0.731559i \(-0.738793\pi\)
−0.224657 + 0.974438i \(0.572126\pi\)
\(380\) 8.26010 1.25420i 0.423734 0.0643389i
\(381\) 0.902517 0.521068i 0.0462373 0.0266951i
\(382\) 33.2081 1.69907
\(383\) −8.87106 + 5.12171i −0.453290 + 0.261707i −0.709219 0.704989i \(-0.750952\pi\)
0.255929 + 0.966696i \(0.417619\pi\)
\(384\) −31.6075 8.46920i −1.61296 0.432192i
\(385\) −12.1856 + 9.73936i −0.621034 + 0.496364i
\(386\) −16.9901 29.4277i −0.864774 1.49783i
\(387\) −1.63387 6.09769i −0.0830543 0.309963i
\(388\) −6.40929 + 11.1012i −0.325382 + 0.563579i
\(389\) 3.41200 0.172995 0.0864977 0.996252i \(-0.472432\pi\)
0.0864977 + 0.996252i \(0.472432\pi\)
\(390\) −35.7134 4.94469i −1.80842 0.250384i
\(391\) 0.533655 0.0269881
\(392\) 6.44164 11.1572i 0.325352 0.563526i
\(393\) 2.62196 + 9.78529i 0.132260 + 0.493603i
\(394\) −17.2992 29.9630i −0.871519 1.50952i
\(395\) −2.77138 + 24.8393i −0.139443 + 1.24980i
\(396\) −15.3277 4.10703i −0.770244 0.206386i
\(397\) −10.3335 + 5.96603i −0.518622 + 0.299426i −0.736371 0.676578i \(-0.763462\pi\)
0.217749 + 0.976005i \(0.430129\pi\)
\(398\) −25.7857 −1.29252
\(399\) −2.67795 + 1.54612i −0.134065 + 0.0774027i
\(400\) 2.48054 2.68508i 0.124027 0.134254i
\(401\) 3.93721 1.05497i 0.196615 0.0526828i −0.159168 0.987252i \(-0.550881\pi\)
0.355783 + 0.934569i \(0.384214\pi\)
\(402\) −19.2081 + 19.2081i −0.958011 + 0.958011i
\(403\) 0.621869 1.01414i 0.0309775 0.0505181i
\(404\) 26.4586i 1.31636i
\(405\) 14.5112 19.7068i 0.721069 0.979240i
\(406\) 13.9592 24.1781i 0.692786 1.19994i
\(407\) 6.97310 + 1.86844i 0.345644 + 0.0926149i
\(408\) 15.3595i 0.760406i
\(409\) 1.79597 6.70266i 0.0888051 0.331425i −0.907202 0.420694i \(-0.861786\pi\)
0.996008 + 0.0892692i \(0.0284531\pi\)
\(410\) −2.34659 0.918026i −0.115890 0.0453381i
\(411\) 5.34348 + 5.34348i 0.263574 + 0.263574i
\(412\) −1.20761 + 4.50687i −0.0594948 + 0.222037i
\(413\) 0.00283692 0.000760151i 0.000139596 3.74046e-5i
\(414\) 0.0914320 + 0.341229i 0.00449364 + 0.0167705i
\(415\) −0.658389 + 5.90102i −0.0323190 + 0.289670i
\(416\) −15.9907 16.8604i −0.784008 0.826648i
\(417\) 2.07674 + 2.07674i 0.101698 + 0.101698i
\(418\) 12.9748 + 7.49098i 0.634616 + 0.366396i
\(419\) 18.3846 + 10.6144i 0.898147 + 0.518546i 0.876599 0.481222i \(-0.159807\pi\)
0.0215487 + 0.999768i \(0.493140\pi\)
\(420\) 6.33844 16.2019i 0.309284 0.790570i
\(421\) −3.15727 + 3.15727i −0.153876 + 0.153876i −0.779847 0.625971i \(-0.784703\pi\)
0.625971 + 0.779847i \(0.284703\pi\)
\(422\) 3.58318 + 6.20625i 0.174427 + 0.302116i
\(423\) −1.51610 2.62596i −0.0737152 0.127678i
\(424\) −10.7947 + 10.7947i −0.524238 + 0.524238i
\(425\) 14.2575 + 7.49570i 0.691591 + 0.363595i
\(426\) 47.0822 + 27.1829i 2.28114 + 1.31702i
\(427\) 1.53964 + 0.888911i 0.0745084 + 0.0430174i
\(428\) 31.4932 + 31.4932i 1.52228 + 1.52228i
\(429\) −26.9267 28.3912i −1.30003 1.37074i
\(430\) −20.9361 26.1946i −1.00963 1.26321i
\(431\) 9.27711 + 34.6226i 0.446863 + 1.66771i 0.710971 + 0.703221i \(0.248256\pi\)
−0.264109 + 0.964493i \(0.585078\pi\)
\(432\) 2.87984 0.771651i 0.138556 0.0371261i
\(433\) 2.09465 7.81733i 0.100662 0.375677i −0.897155 0.441716i \(-0.854370\pi\)
0.997817 + 0.0660397i \(0.0210364\pi\)
\(434\) 0.670679 + 0.670679i 0.0321936 + 0.0321936i
\(435\) −15.7195 + 40.1810i −0.753692 + 1.92653i
\(436\) 5.30171 19.7863i 0.253906 0.947590i
\(437\) 0.201861i 0.00965633i
\(438\) 31.7323 + 8.50264i 1.51623 + 0.406272i
\(439\) −14.3336 + 24.8265i −0.684104 + 1.18490i 0.289613 + 0.957144i \(0.406473\pi\)
−0.973717 + 0.227759i \(0.926860\pi\)
\(440\) −28.9772 + 4.39983i −1.38143 + 0.209754i
\(441\) 5.08683i 0.242230i
\(442\) 13.6668 22.2877i 0.650062 1.06012i
\(443\) −17.1586 + 17.1586i −0.815229 + 0.815229i −0.985412 0.170184i \(-0.945564\pi\)
0.170184 + 0.985412i \(0.445564\pi\)
\(444\) −7.77688 + 2.08381i −0.369074 + 0.0988931i
\(445\) −2.42058 15.9419i −0.114746 0.755716i
\(446\) −23.1523 + 13.3670i −1.09629 + 0.632944i
\(447\) 34.2054 1.61786
\(448\) 14.4276 8.32978i 0.681640 0.393545i
\(449\) −8.85389 2.37239i −0.417841 0.111960i 0.0437720 0.999042i \(-0.486062\pi\)
−0.461613 + 0.887081i \(0.652729\pi\)
\(450\) −2.35012 + 10.4008i −0.110786 + 0.490297i
\(451\) −1.36735 2.36832i −0.0643860 0.111520i
\(452\) 9.04261 + 33.7475i 0.425329 + 1.58735i
\(453\) 14.1248 24.4648i 0.663639 1.14946i
\(454\) 62.2722 2.92258
\(455\) 8.21084 6.21370i 0.384930 0.291303i
\(456\) −5.80989 −0.272073
\(457\) 10.7399 18.6021i 0.502391 0.870167i −0.497605 0.867404i \(-0.665787\pi\)
0.999996 0.00276341i \(-0.000879623\pi\)
\(458\) 10.6277 + 39.6631i 0.496599 + 1.85333i
\(459\) 6.56877 + 11.3775i 0.306604 + 0.531054i
\(460\) 0.709072 + 0.887168i 0.0330607 + 0.0413644i
\(461\) −4.90591 1.31453i −0.228491 0.0612240i 0.142757 0.989758i \(-0.454403\pi\)
−0.371248 + 0.928534i \(0.621070\pi\)
\(462\) 27.0180 15.5989i 1.25699 0.725725i
\(463\) −20.0793 −0.933163 −0.466581 0.884478i \(-0.654515\pi\)
−0.466581 + 0.884478i \(0.654515\pi\)
\(464\) −6.14905 + 3.55016i −0.285463 + 0.164812i
\(465\) −1.18035 0.869156i −0.0547373 0.0403061i
\(466\) 50.2844 13.4737i 2.32938 0.624156i
\(467\) 21.4507 21.4507i 0.992618 0.992618i −0.00735447 0.999973i \(-0.502341\pi\)
0.999973 + 0.00735447i \(0.00234102\pi\)
\(468\) 10.0423 + 2.97780i 0.464205 + 0.137649i
\(469\) 7.75807i 0.358234i
\(470\) −12.9699 9.55047i −0.598258 0.440530i
\(471\) −4.31627 + 7.47600i −0.198883 + 0.344476i
\(472\) 0.00533020 + 0.00142822i 0.000245342 + 6.57392e-5i
\(473\) 36.3934i 1.67337i
\(474\) 12.9371 48.2818i 0.594219 2.21766i
\(475\) 2.83533 5.39307i 0.130094 0.247451i
\(476\) 8.92064 + 8.92064i 0.408877 + 0.408877i
\(477\) −1.56007 + 5.82226i −0.0714306 + 0.266583i
\(478\) 8.04928 2.15680i 0.368166 0.0986497i
\(479\) −8.05179 30.0497i −0.367896 1.37300i −0.863453 0.504430i \(-0.831703\pi\)
0.495557 0.868575i \(-0.334964\pi\)
\(480\) −22.3664 + 17.8764i −1.02088 + 0.815943i
\(481\) −4.56859 1.35471i −0.208310 0.0617693i
\(482\) −33.1210 33.1210i −1.50862 1.50862i
\(483\) −0.364031 0.210173i −0.0165640 0.00956321i
\(484\) −50.0165 28.8770i −2.27348 1.31259i
\(485\) 3.74764 + 8.56426i 0.170171 + 0.388883i
\(486\) −15.1377 + 15.1377i −0.686662 + 0.686662i
\(487\) −9.71579 16.8282i −0.440264 0.762560i 0.557445 0.830214i \(-0.311782\pi\)
−0.997709 + 0.0676540i \(0.978449\pi\)
\(488\) 1.67014 + 2.89277i 0.0756039 + 0.130950i
\(489\) 12.9321 12.9321i 0.584810 0.584810i
\(490\) −10.8324 24.7546i −0.489357 1.11830i
\(491\) −30.5824 17.6568i −1.38017 0.796839i −0.387987 0.921665i \(-0.626830\pi\)
−0.992179 + 0.124825i \(0.960163\pi\)
\(492\) 2.64131 + 1.52496i 0.119079 + 0.0687506i
\(493\) −22.1234 22.1234i −0.996389 0.996389i
\(494\) −8.43059 5.16961i −0.379310 0.232592i
\(495\) −9.03988 + 7.22515i −0.406312 + 0.324746i
\(496\) −0.0624327 0.233002i −0.00280331 0.0104621i
\(497\) −14.9977 + 4.01863i −0.672740 + 0.180260i
\(498\) 3.07343 11.4702i 0.137723 0.513991i
\(499\) 9.44430 + 9.44430i 0.422785 + 0.422785i 0.886161 0.463377i \(-0.153362\pi\)
−0.463377 + 0.886161i \(0.653362\pi\)
\(500\) 6.48295 + 33.6618i 0.289926 + 1.50540i
\(501\) −6.49919 + 24.2553i −0.290363 + 1.08365i
\(502\) 5.32928i 0.237857i
\(503\) 23.3052 + 6.24460i 1.03913 + 0.278433i 0.737751 0.675073i \(-0.235888\pi\)
0.301375 + 0.953506i \(0.402554\pi\)
\(504\) −1.45192 + 2.51480i −0.0646736 + 0.112018i
\(505\) 15.5377 + 11.4413i 0.691419 + 0.509130i
\(506\) 2.03659i 0.0905374i
\(507\) 17.2718 + 19.2044i 0.767066 + 0.852899i
\(508\) −1.13721 + 1.13721i −0.0504555 + 0.0504555i
\(509\) −3.59537 + 0.963376i −0.159362 + 0.0427009i −0.337618 0.941283i \(-0.609621\pi\)
0.178256 + 0.983984i \(0.442954\pi\)
\(510\) −25.9404 19.1014i −1.14866 0.845823i
\(511\) −8.12538 + 4.69119i −0.359446 + 0.207526i
\(512\) −8.22064 −0.363304
\(513\) 4.30365 2.48471i 0.190011 0.109703i
\(514\) 1.89156 + 0.506841i 0.0834330 + 0.0223558i
\(515\) 2.12445 + 2.65804i 0.0936144 + 0.117127i
\(516\) 20.2942 + 35.1506i 0.893403 + 1.54742i
\(517\) −4.52433 16.8850i −0.198980 0.742603i
\(518\) 1.89964 3.29028i 0.0834656 0.144567i
\(519\) −27.2503 −1.19615
\(520\) 19.1976 2.39705i 0.841869 0.105118i
\(521\) 45.2323 1.98166 0.990832 0.135103i \(-0.0431364\pi\)
0.990832 + 0.135103i \(0.0431364\pi\)
\(522\) 10.3557 17.9366i 0.453256 0.785062i
\(523\) 0.295439 + 1.10259i 0.0129187 + 0.0482131i 0.972084 0.234632i \(-0.0753885\pi\)
−0.959166 + 0.282845i \(0.908722\pi\)
\(524\) −7.81683 13.5392i −0.341480 0.591461i
\(525\) −6.77362 10.7283i −0.295625 0.468221i
\(526\) −33.0208 8.84790i −1.43978 0.385787i
\(527\) 0.920525 0.531466i 0.0400987 0.0231510i
\(528\) −7.93430 −0.345296
\(529\) −19.8948 + 11.4863i −0.864992 + 0.499403i
\(530\) 4.80653 + 31.6557i 0.208782 + 1.37503i
\(531\) 0.00210457 0.000563919i 9.13307e−5 2.44720e-5i
\(532\) 3.37434 3.37434i 0.146296 0.146296i
\(533\) 0.860880 + 1.58663i 0.0372889 + 0.0687246i
\(534\) 32.2479i 1.39550i
\(535\) 32.1127 4.87592i 1.38835 0.210804i
\(536\) 7.28818 12.6235i 0.314801 0.545252i
\(537\) 24.2626 + 6.50114i 1.04701 + 0.280545i
\(538\) 54.8782i 2.36597i
\(539\) 7.59005 28.3265i 0.326927 1.22011i
\(540\) −10.1863 + 26.0375i −0.438349 + 1.12047i
\(541\) 22.3573 + 22.3573i 0.961218 + 0.961218i 0.999276 0.0380580i \(-0.0121172\pi\)
−0.0380580 + 0.999276i \(0.512117\pi\)
\(542\) −7.64112 + 28.5171i −0.328214 + 1.22491i
\(543\) −15.6720 + 4.19929i −0.672548 + 0.180209i
\(544\) −5.37376 20.0551i −0.230398 0.859857i
\(545\) −9.32685 11.6694i −0.399518 0.499864i
\(546\) −18.1005 + 9.82101i −0.774628 + 0.420300i
\(547\) −5.20384 5.20384i −0.222500 0.222500i 0.587050 0.809550i \(-0.300289\pi\)
−0.809550 + 0.587050i \(0.800289\pi\)
\(548\) −10.0995 5.83096i −0.431430 0.249086i
\(549\) 1.14218 + 0.659440i 0.0487472 + 0.0281442i
\(550\) −28.6058 + 54.4109i −1.21976 + 2.32009i
\(551\) −8.36844 + 8.36844i −0.356507 + 0.356507i
\(552\) −0.394887 0.683964i −0.0168075 0.0291114i
\(553\) 7.13781 + 12.3630i 0.303530 + 0.525730i
\(554\) 19.4608 19.4608i 0.826812 0.826812i
\(555\) −2.13919 + 5.46804i −0.0908035 + 0.232105i
\(556\) −3.92517 2.26620i −0.166464 0.0961081i
\(557\) −5.70401 3.29321i −0.241687 0.139538i 0.374265 0.927322i \(-0.377895\pi\)
−0.615952 + 0.787784i \(0.711228\pi\)
\(558\) 0.497544 + 0.497544i 0.0210627 + 0.0210627i
\(559\) −0.635748 + 24.0144i −0.0268893 + 1.01570i
\(560\) 0.231518 2.07505i 0.00978343 0.0876871i
\(561\) −9.04887 33.7709i −0.382044 1.42581i
\(562\) −19.7863 + 5.30173i −0.834636 + 0.223640i
\(563\) 7.59751 28.3543i 0.320197 1.19499i −0.598856 0.800856i \(-0.704378\pi\)
0.919053 0.394134i \(-0.128955\pi\)
\(564\) 13.7855 + 13.7855i 0.580475 + 0.580475i
\(565\) 23.7284 + 9.28293i 0.998259 + 0.390536i
\(566\) 15.9347 59.4689i 0.669783 2.49967i
\(567\) 13.9784i 0.587039i
\(568\) −28.1787 7.55046i −1.18235 0.316810i
\(569\) 16.9543 29.3658i 0.710763 1.23108i −0.253808 0.967255i \(-0.581683\pi\)
0.964571 0.263823i \(-0.0849835\pi\)
\(570\) −7.22531 + 9.81226i −0.302635 + 0.410990i
\(571\) 33.5525i 1.40413i −0.712113 0.702065i \(-0.752262\pi\)
0.712113 0.702065i \(-0.247738\pi\)
\(572\) 51.4782 + 31.5662i 2.15241 + 1.31985i
\(573\) −20.7277 + 20.7277i −0.865910 + 0.865910i
\(574\) −1.39019 + 0.372500i −0.0580253 + 0.0155478i
\(575\) 0.827606 0.0327691i 0.0345136 0.00136656i
\(576\) 10.7031 6.17945i 0.445964 0.257477i
\(577\) 11.0413 0.459654 0.229827 0.973232i \(-0.426184\pi\)
0.229827 + 0.973232i \(0.426184\pi\)
\(578\) −12.9070 + 7.45188i −0.536862 + 0.309957i
\(579\) 28.9729 + 7.76326i 1.20407 + 0.322630i
\(580\) 7.38321 66.1743i 0.306571 2.74774i
\(581\) 1.69571 + 2.93706i 0.0703499 + 0.121850i
\(582\) −4.83886 18.0589i −0.200577 0.748565i
\(583\) −17.3748 + 30.0940i −0.719589 + 1.24636i
\(584\) −17.6282 −0.729461
\(585\) 6.09122 4.60964i 0.251841 0.190585i
\(586\) 58.8002 2.42902
\(587\) −11.7529 + 20.3567i −0.485095 + 0.840209i −0.999853 0.0171260i \(-0.994548\pi\)
0.514758 + 0.857335i \(0.327882\pi\)
\(588\) 8.46495 + 31.5916i 0.349089 + 1.30282i
\(589\) −0.201033 0.348199i −0.00828342 0.0143473i
\(590\) 0.00904086 0.00722594i 0.000372206 0.000297487i
\(591\) 29.4999 + 7.90448i 1.21346 + 0.325147i
\(592\) −0.836794 + 0.483123i −0.0343920 + 0.0198563i
\(593\) −30.6582 −1.25898 −0.629491 0.777007i \(-0.716737\pi\)
−0.629491 + 0.777007i \(0.716737\pi\)
\(594\) −43.4198 + 25.0684i −1.78153 + 1.02857i
\(595\) 9.09612 1.38113i 0.372904 0.0566210i
\(596\) −50.9882 + 13.6622i −2.08856 + 0.559627i
\(597\) 16.0948 16.0948i 0.658717 0.658717i
\(598\) 0.0355767 1.34385i 0.00145484 0.0549542i
\(599\) 7.49378i 0.306188i 0.988212 + 0.153094i \(0.0489237\pi\)
−0.988212 + 0.153094i \(0.951076\pi\)
\(600\) −0.943146 23.8198i −0.0385038 0.972441i
\(601\) 7.04653 12.2049i 0.287434 0.497850i −0.685763 0.727825i \(-0.740531\pi\)
0.973196 + 0.229975i \(0.0738645\pi\)
\(602\) −18.5007 4.95724i −0.754030 0.202042i
\(603\) 5.75533i 0.234375i
\(604\) −11.2834 + 42.1101i −0.459113 + 1.71343i
\(605\) −38.5862 + 16.8850i −1.56875 + 0.686471i
\(606\) −27.2872 27.2872i −1.10847 1.10847i
\(607\) 3.90296 14.5660i 0.158416 0.591218i −0.840372 0.542010i \(-0.817664\pi\)
0.998789 0.0492080i \(-0.0156697\pi\)
\(608\) −7.58608 + 2.03268i −0.307656 + 0.0824363i
\(609\) 6.37837 + 23.8044i 0.258465 + 0.964604i
\(610\) 6.96260 + 0.776832i 0.281908 + 0.0314530i
\(611\) 2.69044 + 11.2207i 0.108844 + 0.453941i
\(612\) 6.61779 + 6.61779i 0.267508 + 0.267508i
\(613\) 10.3197 + 5.95807i 0.416808 + 0.240644i 0.693711 0.720254i \(-0.255975\pi\)
−0.276903 + 0.960898i \(0.589308\pi\)
\(614\) 28.6614 + 16.5477i 1.15668 + 0.667810i
\(615\) 2.03769 0.891675i 0.0821677 0.0359558i
\(616\) −11.8375 + 11.8375i −0.476945 + 0.476945i
\(617\) 19.4158 + 33.6292i 0.781652 + 1.35386i 0.930979 + 0.365074i \(0.118956\pi\)
−0.149326 + 0.988788i \(0.547710\pi\)
\(618\) −3.40258 5.89344i −0.136872 0.237069i
\(619\) 14.9567 14.9567i 0.601159 0.601159i −0.339461 0.940620i \(-0.610245\pi\)
0.940620 + 0.339461i \(0.110245\pi\)
\(620\) 2.10664 + 0.824152i 0.0846046 + 0.0330987i
\(621\) 0.585021 + 0.337762i 0.0234761 + 0.0135539i
\(622\) −62.0887 35.8469i −2.48953 1.43733i
\(623\) −6.51241 6.51241i −0.260914 0.260914i
\(624\) 5.23549 + 0.138602i 0.209587 + 0.00554853i
\(625\) 22.5712 + 10.7490i 0.902847 + 0.429961i
\(626\) 9.87514 + 36.8545i 0.394690 + 1.47300i
\(627\) −12.7742 + 3.42284i −0.510153 + 0.136695i
\(628\) 3.44799 12.8681i 0.137590 0.513492i
\(629\) −3.01067 3.01067i −0.120043 0.120043i
\(630\) 2.44157 + 5.57959i 0.0972747 + 0.222296i
\(631\) −10.1085 + 37.7256i −0.402415 + 1.50183i 0.406360 + 0.913713i \(0.366798\pi\)
−0.808775 + 0.588119i \(0.799869\pi\)
\(632\) 26.8219i 1.06692i
\(633\) −6.11032 1.63726i −0.242864 0.0650751i
\(634\) 17.5143 30.3357i 0.695582 1.20478i
\(635\) 0.176068 + 1.15958i 0.00698704 + 0.0460165i
\(636\) 38.7550i 1.53674i
\(637\) −5.50316 + 18.5588i −0.218043 + 0.735325i
\(638\) 84.4296 84.4296i 3.34260 3.34260i
\(639\) −11.1261 + 2.98122i −0.440141 + 0.117935i
\(640\) 21.8366 29.6550i 0.863168 1.17222i
\(641\) −7.55607 + 4.36250i −0.298447 + 0.172308i −0.641745 0.766918i \(-0.721789\pi\)
0.343298 + 0.939226i \(0.388456\pi\)
\(642\) −64.9590 −2.56373
\(643\) −12.8146 + 7.39852i −0.505359 + 0.291769i −0.730924 0.682459i \(-0.760911\pi\)
0.225565 + 0.974228i \(0.427577\pi\)
\(644\) 0.626588 + 0.167894i 0.0246910 + 0.00661594i
\(645\) 29.4178 + 3.28220i 1.15832 + 0.129237i
\(646\) −4.41809 7.65235i −0.173827 0.301078i
\(647\) 8.76765 + 32.7213i 0.344692 + 1.28641i 0.892972 + 0.450113i \(0.148616\pi\)
−0.548280 + 0.836295i \(0.684717\pi\)
\(648\) 13.1318 22.7449i 0.515865 0.893505i
\(649\) 0.0125609 0.000493060
\(650\) 19.8262 35.4036i 0.777647 1.38864i
\(651\) −0.837243 −0.0328141
\(652\) −14.1119 + 24.4425i −0.552664 + 0.957242i
\(653\) −5.24059 19.5581i −0.205080 0.765369i −0.989425 0.145044i \(-0.953667\pi\)
0.784345 0.620325i \(-0.212999\pi\)
\(654\) 14.9382 + 25.8737i 0.584128 + 1.01174i
\(655\) −11.3310 1.26422i −0.442739 0.0493973i
\(656\) 0.353557 + 0.0947353i 0.0138041 + 0.00369879i
\(657\) −6.02782 + 3.48016i −0.235168 + 0.135774i
\(658\) −9.19981 −0.358646
\(659\) 26.2317 15.1449i 1.02184 0.589961i 0.107205 0.994237i \(-0.465810\pi\)
0.914637 + 0.404276i \(0.132477\pi\)
\(660\) 44.1186 59.9148i 1.71731 2.33218i
\(661\) −21.1339 + 5.66280i −0.822012 + 0.220257i −0.645226 0.763992i \(-0.723237\pi\)
−0.176786 + 0.984249i \(0.556570\pi\)
\(662\) −27.1574 + 27.1574i −1.05550 + 1.05550i
\(663\) 5.38101 + 22.4419i 0.208981 + 0.871572i
\(664\) 6.37202i 0.247282i
\(665\) −0.522430 3.44071i −0.0202590 0.133425i
\(666\) 1.40925 2.44090i 0.0546074 0.0945829i
\(667\) −1.55395 0.416380i −0.0601693 0.0161223i
\(668\) 38.7520i 1.49936i
\(669\) 6.10774 22.7944i 0.236139 0.881282i
\(670\) −12.2559 28.0078i −0.473488 1.08204i
\(671\) 5.37640 + 5.37640i 0.207553 + 0.207553i
\(672\) −4.23277 + 15.7969i −0.163283 + 0.609379i
\(673\) 0.554664 0.148622i 0.0213807 0.00572895i −0.248113 0.968731i \(-0.579810\pi\)
0.269494 + 0.963002i \(0.413144\pi\)
\(674\) 20.6424 + 77.0386i 0.795117 + 2.96742i
\(675\) 10.8857 + 17.2411i 0.418989 + 0.663610i
\(676\) −33.4167 21.7284i −1.28526 0.835707i
\(677\) −11.5229 11.5229i −0.442862 0.442862i 0.450111 0.892973i \(-0.351385\pi\)
−0.892973 + 0.450111i \(0.851385\pi\)
\(678\) −44.1302 25.4786i −1.69481 0.978498i
\(679\) 4.62416 + 2.66976i 0.177459 + 0.102456i
\(680\) 16.0982 + 6.29788i 0.617337 + 0.241513i
\(681\) −38.8688 + 38.8688i −1.48946 + 1.48946i
\(682\) 2.02823 + 3.51300i 0.0776650 + 0.134520i
\(683\) −10.0529 17.4121i −0.384663 0.666256i 0.607059 0.794657i \(-0.292349\pi\)
−0.991722 + 0.128400i \(0.959016\pi\)
\(684\) 2.50325 2.50325i 0.0957143 0.0957143i
\(685\) −7.79148 + 3.40948i −0.297697 + 0.130269i
\(686\) −30.7929 17.7783i −1.17568 0.678777i
\(687\) −31.3902 18.1232i −1.19761 0.691442i
\(688\) 3.44440 + 3.44440i 0.131317 + 0.131317i
\(689\) 11.9905 19.5541i 0.456802 0.744953i
\(690\) −1.64623 0.183673i −0.0626709 0.00699232i
\(691\) −11.2156 41.8571i −0.426661 1.59232i −0.760269 0.649608i \(-0.774933\pi\)
0.333608 0.942712i \(-0.391734\pi\)
\(692\) 40.6205 10.8842i 1.54416 0.413756i
\(693\) −1.71077 + 6.38467i −0.0649867 + 0.242534i
\(694\) −20.5310 20.5310i −0.779346 0.779346i
\(695\) −3.02815 + 1.32509i −0.114864 + 0.0502635i
\(696\) −11.9841 + 44.7253i −0.454256 + 1.69531i
\(697\) 1.61289i 0.0610926i
\(698\) 58.3773 + 15.6421i 2.20961 + 0.592064i
\(699\) −22.9764 + 39.7962i −0.869046 + 1.50523i
\(700\) 14.3821 + 13.2866i 0.543593 + 0.502186i
\(701\) 8.03468i 0.303466i −0.988422 0.151733i \(-0.951515\pi\)
0.988422 0.151733i \(-0.0484853\pi\)
\(702\) 29.0886 15.7830i 1.09788 0.595692i
\(703\) −1.13882 + 1.13882i −0.0429514 + 0.0429514i
\(704\) 68.8216 18.4407i 2.59381 0.695010i
\(705\) 14.0567 2.13434i 0.529405 0.0803837i
\(706\) 45.4404 26.2350i 1.71017 0.987369i
\(707\) 11.0212 0.414495
\(708\) −0.0121320 + 0.00700440i −0.000455948 + 0.000263242i
\(709\) −21.9526 5.88217i −0.824446 0.220910i −0.178157 0.984002i \(-0.557013\pi\)
−0.646289 + 0.763092i \(0.723680\pi\)
\(710\) −47.7956 + 38.2008i −1.79374 + 1.43365i
\(711\) 5.29519 + 9.17153i 0.198585 + 0.343959i
\(712\) −4.47866 16.7146i −0.167845 0.626406i
\(713\) 0.0273276 0.0473328i 0.00102343 0.00177263i
\(714\) −18.4000 −0.688604
\(715\) 40.7975 16.5805i 1.52574 0.620074i
\(716\) −38.7636 −1.44866
\(717\) −3.67794 + 6.37039i −0.137355 + 0.237906i
\(718\) 7.55655 + 28.2014i 0.282008 + 1.05247i
\(719\) −21.4786 37.2021i −0.801018 1.38740i −0.918946 0.394382i \(-0.870959\pi\)
0.117928 0.993022i \(-0.462375\pi\)
\(720\) 0.171752 1.53938i 0.00640081 0.0573693i
\(721\) 1.87732 + 0.503026i 0.0699149 + 0.0187336i
\(722\) 34.1413 19.7115i 1.27061 0.733585i
\(723\) 41.3467 1.53770
\(724\) 21.6841 12.5193i 0.805882 0.465276i
\(725\) −35.6680 32.9511i −1.32468 1.22377i
\(726\) 81.3643 21.8015i 3.01971 0.809129i
\(727\) 1.42786 1.42786i 0.0529563 0.0529563i −0.680133 0.733089i \(-0.738078\pi\)
0.733089 + 0.680133i \(0.238078\pi\)
\(728\) 8.01779 7.60422i 0.297159 0.281831i
\(729\) 13.9369i 0.516183i
\(730\) −21.9229 + 29.7721i −0.811401 + 1.10191i
\(731\) −10.7322 + 18.5887i −0.396945 + 0.687528i
\(732\) −8.19086 2.19473i −0.302743 0.0811197i
\(733\) 32.1064i 1.18588i −0.805247 0.592939i \(-0.797967\pi\)
0.805247 0.592939i \(-0.202033\pi\)
\(734\) −8.66065 + 32.3220i −0.319670 + 1.19303i
\(735\) 22.2125 + 8.68992i 0.819322 + 0.320532i
\(736\) −0.754907 0.754907i −0.0278262 0.0278262i
\(737\) 8.58752 32.0491i 0.316325 1.18054i
\(738\) −1.03131 + 0.276339i −0.0379631 + 0.0101722i
\(739\) −5.31771 19.8460i −0.195615 0.730046i −0.992107 0.125396i \(-0.959980\pi\)
0.796492 0.604650i \(-0.206687\pi\)
\(740\) 1.00474 9.00534i 0.0369351 0.331043i
\(741\) 8.48891 2.03543i 0.311848 0.0747733i
\(742\) 12.9317 + 12.9317i 0.474736 + 0.474736i
\(743\) 19.4891 + 11.2520i 0.714985 + 0.412797i 0.812904 0.582398i \(-0.197885\pi\)
−0.0979193 + 0.995194i \(0.531219\pi\)
\(744\) −1.36232 0.786533i −0.0499449 0.0288357i
\(745\) −14.0253 + 35.8505i −0.513849 + 1.31346i
\(746\) −9.83771 + 9.83771i −0.360184 + 0.360184i
\(747\) 1.25796 + 2.17886i 0.0460265 + 0.0797202i
\(748\) 26.9773 + 46.7261i 0.986389 + 1.70848i
\(749\) 13.1184 13.1184i 0.479334 0.479334i
\(750\) −41.4020 28.0300i −1.51179 1.02351i
\(751\) 1.44204 + 0.832560i 0.0526207 + 0.0303806i 0.526080 0.850435i \(-0.323661\pi\)
−0.473459 + 0.880816i \(0.656995\pi\)
\(752\) 2.02626 + 1.16986i 0.0738901 + 0.0426605i
\(753\) −3.32640 3.32640i −0.121221 0.121221i
\(754\) −57.1861 + 54.2364i −2.08260 + 1.97517i
\(755\) 19.8498 + 24.8355i 0.722410 + 0.903855i
\(756\) 4.13321 + 15.4254i 0.150324 + 0.561015i
\(757\) 37.6990 10.1014i 1.37019 0.367143i 0.502645 0.864493i \(-0.332360\pi\)
0.867550 + 0.497350i \(0.165694\pi\)
\(758\) −10.6426 + 39.7186i −0.386556 + 1.44265i
\(759\) −1.27119 1.27119i −0.0461412 0.0461412i
\(760\) 2.38225 6.08932i 0.0864131 0.220883i
\(761\) −4.20973 + 15.7109i −0.152603 + 0.569521i 0.846696 + 0.532077i \(0.178588\pi\)
−0.999299 + 0.0374441i \(0.988078\pi\)
\(762\) 2.34565i 0.0849739i
\(763\) −8.24188 2.20841i −0.298376 0.0799496i
\(764\) 22.6186 39.1766i 0.818313 1.41736i
\(765\) 6.74796 1.02460i 0.243973 0.0370443i
\(766\) 23.0560i 0.833045i
\(767\) −0.00828839 0.000219424i −0.000299276 7.92293e-6i
\(768\) −15.4289 + 15.4289i −0.556741 + 0.556741i
\(769\) −38.5504 + 10.3296i −1.39016 + 0.372493i −0.874803 0.484479i \(-0.839009\pi\)
−0.515362 + 0.856973i \(0.672342\pi\)
\(770\) 5.27082 + 34.7135i 0.189947 + 1.25099i
\(771\) −1.49702 + 0.864306i −0.0539139 + 0.0311272i
\(772\) −46.2891 −1.66598
\(773\) −17.8304 + 10.2944i −0.641313 + 0.370262i −0.785120 0.619343i \(-0.787399\pi\)
0.143807 + 0.989606i \(0.454066\pi\)
\(774\) −13.7247 3.67753i −0.493325 0.132186i
\(775\) 1.39494 0.880735i 0.0501077 0.0316369i
\(776\) 5.01612 + 8.68818i 0.180068 + 0.311887i
\(777\) 0.868001 + 3.23942i 0.0311394 + 0.116214i
\(778\) 3.83988 6.65087i 0.137666 0.238445i
\(779\) 0.610095 0.0218589
\(780\) −30.1585 + 38.7643i −1.07985 + 1.38799i
\(781\) −66.4048 −2.37615
\(782\) 0.600577 1.04023i 0.0214766 0.0371986i
\(783\) −10.2505 38.2553i −0.366322 1.36713i
\(784\) 1.96257 + 3.39927i 0.0700917 + 0.121402i
\(785\) −6.06575 7.58927i −0.216496 0.270873i
\(786\) 22.0248 + 5.90153i 0.785599 + 0.210501i
\(787\) 24.8106 14.3244i 0.884404 0.510611i 0.0122960 0.999924i \(-0.496086\pi\)
0.872108 + 0.489314i \(0.162753\pi\)
\(788\) −47.1311 −1.67898
\(789\) 26.1334 15.0881i 0.930375 0.537152i
\(790\) 45.2993 + 33.3564i 1.61168 + 1.18677i
\(791\) 14.0574 3.76666i 0.499822 0.133927i
\(792\) −8.78163 + 8.78163i −0.312042 + 0.312042i
\(793\) −3.45372 3.64156i −0.122645 0.129316i
\(794\) 26.8568i 0.953111i
\(795\) −22.7588 16.7586i −0.807171 0.594365i
\(796\) −17.5631 + 30.4202i −0.622508 + 1.07822i
\(797\) −8.48530 2.27363i −0.300565 0.0805361i 0.105385 0.994432i \(-0.466393\pi\)
−0.405950 + 0.913895i \(0.633059\pi\)
\(798\) 6.96002i 0.246382i
\(799\) −2.66840 + 9.95859i −0.0944011 + 0.352310i
\(800\) −9.56524 30.7720i −0.338182 1.08796i
\(801\) −4.83124 4.83124i −0.170703 0.170703i
\(802\) 2.37454 8.86190i 0.0838479 0.312924i
\(803\) −38.7592 + 10.3855i −1.36778 + 0.366496i
\(804\) 9.57739 + 35.7433i 0.337768 + 1.26057i
\(805\) 0.369546 0.295361i 0.0130248 0.0104101i
\(806\) −1.27697 2.35350i −0.0449794 0.0828985i
\(807\) −34.2536 34.2536i −1.20578 1.20578i
\(808\) 17.9331 + 10.3537i 0.630884 + 0.364241i
\(809\) 0.820571 + 0.473757i 0.0288497 + 0.0166564i 0.514356 0.857577i \(-0.328031\pi\)
−0.485506 + 0.874233i \(0.661365\pi\)
\(810\) −22.0827 50.4642i −0.775905 1.77313i
\(811\) 28.8041 28.8041i 1.01145 1.01145i 0.0115151 0.999934i \(-0.496335\pi\)
0.999934 0.0115151i \(-0.00366545\pi\)
\(812\) −19.0158 32.9363i −0.667324 1.15584i
\(813\) −13.0302 22.5690i −0.456991 0.791531i
\(814\) 11.4896 11.4896i 0.402711 0.402711i
\(815\) 8.25150 + 18.8567i 0.289037 + 0.660520i
\(816\) 4.05261 + 2.33978i 0.141870 + 0.0819086i
\(817\) 7.03139 + 4.05958i 0.245997 + 0.142027i
\(818\) −11.0440 11.0440i −0.386145 0.386145i
\(819\) 1.24039 4.18307i 0.0433427 0.146168i
\(820\) −2.68133 + 2.14306i −0.0936361 + 0.0748390i
\(821\) 0.348249 + 1.29968i 0.0121540 + 0.0453592i 0.971737 0.236068i \(-0.0758588\pi\)
−0.959583 + 0.281427i \(0.909192\pi\)
\(822\) 16.4294 4.40224i 0.573041 0.153546i
\(823\) −8.55907 + 31.9429i −0.298350 + 1.11346i 0.640169 + 0.768234i \(0.278864\pi\)
−0.938520 + 0.345225i \(0.887803\pi\)
\(824\) 2.58211 + 2.58211i 0.0899520 + 0.0899520i
\(825\) −16.1069 51.8170i −0.560771 1.80404i
\(826\) 0.00171095 0.00638537i 5.95317e−5 0.000222175i
\(827\) 26.4195i 0.918697i −0.888256 0.459349i \(-0.848083\pi\)
0.888256 0.459349i \(-0.151917\pi\)
\(828\) 0.464834 + 0.124552i 0.0161541 + 0.00432848i
\(829\) −1.23034 + 2.13101i −0.0427314 + 0.0740130i −0.886600 0.462537i \(-0.846939\pi\)
0.843869 + 0.536550i \(0.180273\pi\)
\(830\) 10.7616 + 7.92439i 0.373542 + 0.275060i
\(831\) 24.2940i 0.842748i
\(832\) −45.7344 + 10.9660i −1.58556 + 0.380176i
\(833\) −12.2301 + 12.2301i −0.423747 + 0.423747i
\(834\) 6.38526 1.71093i 0.221104 0.0592445i
\(835\) −22.7570 16.7573i −0.787539 0.579909i
\(836\) 17.6747 10.2045i 0.611292 0.352929i
\(837\) 1.34551 0.0465075
\(838\) 41.3802 23.8909i 1.42946 0.825297i
\(839\) −48.6308 13.0306i −1.67892 0.449866i −0.711428 0.702759i \(-0.751951\pi\)
−0.967494 + 0.252893i \(0.918618\pi\)
\(840\) −8.50096 10.6361i −0.293311 0.366981i
\(841\) 32.6597 + 56.5682i 1.12619 + 1.95063i
\(842\) 2.60113 + 9.70754i 0.0896408 + 0.334544i
\(843\) 9.04093 15.6594i 0.311386 0.539337i
\(844\) 9.76228 0.336032
\(845\) −27.2101 + 10.2280i −0.936055 + 0.351854i
\(846\) −6.82488 −0.234644
\(847\) −12.0286 + 20.8342i −0.413308 + 0.715870i
\(848\) −1.20379 4.49261i −0.0413384 0.154277i
\(849\) 27.1730 + 47.0651i 0.932576 + 1.61527i
\(850\) 30.6565 19.3559i 1.05151 0.663900i
\(851\) −0.211470 0.0566632i −0.00724909 0.00194239i
\(852\) 64.1371 37.0296i 2.19730 1.26861i
\(853\) 42.9612 1.47096 0.735481 0.677545i \(-0.236956\pi\)
0.735481 + 0.677545i \(0.236956\pi\)
\(854\) 3.46543 2.00077i 0.118585 0.0684649i
\(855\) −0.387565 2.55249i −0.0132544 0.0872934i
\(856\) 33.6693 9.02166i 1.15079 0.308354i
\(857\) −29.0789 + 29.0789i −0.993316 + 0.993316i −0.999978 0.00666151i \(-0.997880\pi\)
0.00666151 + 0.999978i \(0.497880\pi\)
\(858\) −85.6451 + 20.5355i −2.92388 + 0.701072i
\(859\) 42.1283i 1.43740i −0.695321 0.718700i \(-0.744738\pi\)
0.695321 0.718700i \(-0.255262\pi\)
\(860\) −45.1625 + 6.85738i −1.54003 + 0.233835i
\(861\) 0.635216 1.10023i 0.0216481 0.0374956i
\(862\) 77.9289 + 20.8810i 2.65427 + 0.711209i
\(863\) 6.80768i 0.231736i −0.993265 0.115868i \(-0.963035\pi\)
0.993265 0.115868i \(-0.0369650\pi\)
\(864\) 6.80234 25.3867i 0.231420 0.863672i
\(865\) 11.1735 28.5609i 0.379910 0.971099i
\(866\) −12.8806 12.8806i −0.437702 0.437702i
\(867\) 3.40497 12.7075i 0.115639 0.431570i
\(868\) 1.24803 0.334410i 0.0423610 0.0113506i
\(869\) 15.8019 + 58.9734i 0.536042 + 2.00054i
\(870\) 60.6323 + 75.8612i 2.05563 + 2.57194i
\(871\) −6.22637 + 20.9977i −0.210973 + 0.711480i
\(872\) −11.3361 11.3361i −0.383888 0.383888i
\(873\) 3.43044 + 1.98056i 0.116103 + 0.0670320i
\(874\) −0.393479 0.227175i −0.0133096 0.00768432i
\(875\) 14.0217 2.70044i 0.474019 0.0912917i
\(876\) 31.6443 31.6443i 1.06916 1.06916i
\(877\) −23.8407 41.2933i −0.805043 1.39437i −0.916262 0.400579i \(-0.868809\pi\)
0.111219 0.993796i \(-0.464524\pi\)
\(878\) 32.2621 + 55.8796i 1.08879 + 1.88585i
\(879\) −36.7017 + 36.7017i −1.23792 + 1.23792i
\(880\) 3.25332 8.31591i 0.109669 0.280329i
\(881\) 4.43737 + 2.56192i 0.149499 + 0.0863133i 0.572884 0.819637i \(-0.305825\pi\)
−0.423385 + 0.905950i \(0.639158\pi\)
\(882\) −9.91554 5.72474i −0.333873 0.192762i
\(883\) 14.8283 + 14.8283i 0.499014 + 0.499014i 0.911131 0.412117i \(-0.135211\pi\)
−0.412117 + 0.911131i \(0.635211\pi\)
\(884\) −16.9849 31.3037i −0.571263 1.05286i
\(885\) −0.00113283 + 0.0101533i −3.80796e−5 + 0.000341301i
\(886\) 14.1361 + 52.7568i 0.474913 + 1.77240i
\(887\) 10.1735 2.72597i 0.341592 0.0915293i −0.0839449 0.996470i \(-0.526752\pi\)
0.425537 + 0.904941i \(0.360085\pi\)
\(888\) −1.63086 + 6.08644i −0.0547280 + 0.204248i
\(889\) 0.473700 + 0.473700i 0.0158874 + 0.0158874i
\(890\) −33.7989 13.2227i −1.13294 0.443226i
\(891\) 15.4729 57.7457i 0.518362 1.93455i
\(892\) 36.4179i 1.21936i
\(893\) 3.76695 + 1.00935i 0.126056 + 0.0337767i
\(894\) 38.4949 66.6751i 1.28746 2.22995i
\(895\) −16.7623 + 22.7638i −0.560301 + 0.760911i
\(896\) 21.0349i 0.702725i
\(897\) 0.816594 + 0.861006i 0.0272653 + 0.0287481i
\(898\) −14.5886 + 14.5886i −0.486828 + 0.486828i
\(899\) −3.09515 + 0.829344i −0.103229 + 0.0276602i
\(900\) 10.6694 + 9.85667i 0.355646 + 0.328556i
\(901\) 17.7490 10.2474i 0.591307 0.341391i
\(902\) −6.15528 −0.204948
\(903\) 14.6418 8.45347i 0.487250 0.281314i
\(904\) 26.4119 + 7.07704i 0.878446 + 0.235379i
\(905\) 2.02476 18.1476i 0.0673053 0.603245i
\(906\) −31.7921 55.0656i −1.05622 1.82943i
\(907\) 5.57417 + 20.8031i 0.185087 + 0.690755i 0.994612 + 0.103669i \(0.0330582\pi\)
−0.809525 + 0.587086i \(0.800275\pi\)
\(908\) 42.4147 73.4645i 1.40758 2.43800i
\(909\) 8.17608 0.271184
\(910\) −2.87158 22.9979i −0.0951918 0.762374i
\(911\) −16.6400 −0.551309 −0.275654 0.961257i \(-0.588895\pi\)
−0.275654 + 0.961257i \(0.588895\pi\)
\(912\) 0.885047 1.53295i 0.0293068 0.0507609i
\(913\) 3.75401 + 14.0102i 0.124240 + 0.463669i
\(914\) −24.1734 41.8696i −0.799586 1.38492i
\(915\) −4.83077 + 3.86101i −0.159700 + 0.127641i
\(916\) 54.0305 + 14.4774i 1.78522 + 0.478347i
\(917\) −5.63968 + 3.25607i −0.186239 + 0.107525i
\(918\) 29.5701 0.975958
\(919\) −5.95358 + 3.43730i −0.196390 + 0.113386i −0.594971 0.803747i \(-0.702836\pi\)
0.398580 + 0.917133i \(0.369503\pi\)
\(920\) 0.878776 0.133431i 0.0289724 0.00439911i
\(921\) −28.2184 + 7.56111i −0.929829 + 0.249147i
\(922\) −8.08349 + 8.08349i −0.266216 + 0.266216i
\(923\) 43.8175 + 1.16001i 1.44227 + 0.0381821i
\(924\) 42.4987i 1.39810i
\(925\) −4.85389 4.48415i −0.159595 0.147438i
\(926\) −22.5973 + 39.1396i −0.742593 + 1.28621i
\(927\) 1.39269 + 0.373170i 0.0457419 + 0.0122565i
\(928\) 62.5915i 2.05467i
\(929\) −11.5057 + 42.9399i −0.377490 + 1.40881i 0.472182 + 0.881501i \(0.343467\pi\)
−0.849672 + 0.527312i \(0.823200\pi\)
\(930\) −3.02257 + 1.32265i −0.0991141 + 0.0433714i
\(931\) 4.62617 + 4.62617i 0.151617 + 0.151617i
\(932\) 18.3543 68.4993i 0.601216 2.24377i
\(933\) 61.1290 16.3795i 2.00127 0.536240i
\(934\) −17.6722 65.9535i −0.578252 2.15806i
\(935\) 39.1054 + 4.36307i 1.27888 + 0.142688i
\(936\) 5.94800 5.64120i 0.194417 0.184388i
\(937\) 13.1724 + 13.1724i 0.430323 + 0.430323i 0.888738 0.458415i \(-0.151583\pi\)
−0.458415 + 0.888738i \(0.651583\pi\)
\(938\) −15.1225 8.73096i −0.493766 0.285076i
\(939\) −29.1675 16.8399i −0.951846 0.549548i
\(940\) −20.1010 + 8.79602i −0.655624 + 0.286895i
\(941\) 40.0251 40.0251i 1.30478 1.30478i 0.379650 0.925130i \(-0.376045\pi\)
0.925130 0.379650i \(-0.123955\pi\)
\(942\) 9.71510 + 16.8270i 0.316535 + 0.548255i
\(943\) 0.0414669 + 0.0718228i 0.00135035 + 0.00233887i
\(944\) −0.00118881 + 0.00118881i −3.86925e−5 + 3.86925e-5i
\(945\) 10.8458 + 4.24306i 0.352814 + 0.138027i
\(946\) −70.9401 40.9573i −2.30646 1.33164i
\(947\) 51.0040 + 29.4472i 1.65741 + 0.956904i 0.973905 + 0.226955i \(0.0728770\pi\)
0.683501 + 0.729949i \(0.260456\pi\)
\(948\) −48.1479 48.1479i −1.56377 1.56377i
\(949\) 25.7568 6.17584i 0.836102 0.200476i
\(950\) −7.32157 11.5962i −0.237543 0.376229i
\(951\) 8.00278 + 29.8668i 0.259508 + 0.968497i
\(952\) 9.53703 2.55544i 0.309097 0.0828223i
\(953\) −4.62094 + 17.2456i −0.149687 + 0.558640i 0.849815 + 0.527081i \(0.176714\pi\)
−0.999502 + 0.0315583i \(0.989953\pi\)
\(954\) 9.59336 + 9.59336i 0.310596 + 0.310596i
\(955\) −13.2255 30.2236i −0.427969 0.978012i
\(956\) 2.93807 10.9650i 0.0950240 0.354634i
\(957\) 105.398i 3.40703i
\(958\) −67.6360 18.1230i −2.18522 0.585528i
\(959\) −2.42886 + 4.20691i −0.0784320 + 0.135848i
\(960\) 8.69932 + 57.2935i 0.280769 + 1.84914i
\(961\) 30.8911i 0.996488i
\(962\) −7.78218 + 7.38076i −0.250908 + 0.237965i
\(963\) 9.73187 9.73187i 0.313605 0.313605i
\(964\) −61.6333 + 16.5146i −1.98507 + 0.531899i
\(965\) −20.0165 + 27.1832i −0.644353 + 0.875057i
\(966\) −0.819363 + 0.473059i −0.0263626 + 0.0152204i
\(967\) −23.2093 −0.746360 −0.373180 0.927759i \(-0.621733\pi\)
−0.373180 + 0.927759i \(0.621733\pi\)
\(968\) −39.1446 + 22.6001i −1.25815 + 0.726395i
\(969\) 7.53407 + 2.01875i 0.242029 + 0.0648515i
\(970\) 20.9115 + 2.33314i 0.671429 + 0.0749127i
\(971\) −21.1932 36.7078i −0.680123 1.17801i −0.974943 0.222455i \(-0.928593\pi\)
0.294820 0.955553i \(-0.404740\pi\)
\(972\) 7.54788 + 28.1691i 0.242098 + 0.903523i
\(973\) −0.943975 + 1.63501i −0.0302624 + 0.0524161i
\(974\) −43.7367 −1.40141
\(975\) 9.72304 + 34.4731i 0.311387 + 1.10402i
\(976\) −1.01768 −0.0325752
\(977\) 12.2049 21.1395i 0.390469 0.676312i −0.602043 0.798464i \(-0.705646\pi\)
0.992511 + 0.122152i \(0.0389796\pi\)
\(978\) −10.6541 39.7618i −0.340682 1.27144i
\(979\) −19.6945 34.1118i −0.629438 1.09022i
\(980\) −36.5819 4.08152i −1.16857 0.130379i
\(981\) −6.11424 1.63831i −0.195213 0.0523071i
\(982\) −68.8352 + 39.7420i −2.19662 + 1.26822i
\(983\) −4.47004 −0.142572 −0.0712860 0.997456i \(-0.522710\pi\)
−0.0712860 + 0.997456i \(0.522710\pi\)
\(984\) 2.06718 1.19349i 0.0658992 0.0380469i
\(985\) −20.3806 + 27.6776i −0.649379 + 0.881883i
\(986\) −68.0220 + 18.2264i −2.16626 + 0.580448i
\(987\) 5.74230 5.74230i 0.182779 0.182779i
\(988\) −11.8410 + 6.42472i −0.376712 + 0.204398i
\(989\) 1.10369i 0.0350952i
\(990\) 3.91016 + 25.7522i 0.124273 + 0.818460i
\(991\) 24.7675 42.8986i 0.786766 1.36272i −0.141172 0.989985i \(-0.545087\pi\)
0.927938 0.372734i \(-0.121580\pi\)
\(992\) −2.05398 0.550363i −0.0652140 0.0174740i
\(993\) 33.9020i 1.07585i
\(994\) −9.04516 + 33.7570i −0.286895 + 1.07071i
\(995\) 10.2695 + 23.4683i 0.325565 + 0.743995i
\(996\) −11.4384 11.4384i −0.362439 0.362439i
\(997\) −9.06967 + 33.8485i −0.287239 + 1.07199i 0.659948 + 0.751311i \(0.270578\pi\)
−0.947187 + 0.320681i \(0.896088\pi\)
\(998\) 29.0380 7.78071i 0.919182 0.246294i
\(999\) −1.39494 5.20597i −0.0441338 0.164710i
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 65.2.o.a.32.5 20
3.2 odd 2 585.2.cf.a.487.1 20
5.2 odd 4 325.2.x.b.318.5 20
5.3 odd 4 65.2.t.a.58.1 yes 20
5.4 even 2 325.2.s.b.32.1 20
13.2 odd 12 845.2.t.g.427.5 20
13.3 even 3 845.2.o.e.587.5 20
13.4 even 6 845.2.k.d.577.10 20
13.5 odd 4 845.2.t.e.657.1 20
13.6 odd 12 845.2.f.d.437.10 20
13.7 odd 12 845.2.f.e.437.1 20
13.8 odd 4 845.2.t.f.657.5 20
13.9 even 3 845.2.k.e.577.1 20
13.10 even 6 845.2.o.f.587.1 20
13.11 odd 12 65.2.t.a.37.1 yes 20
13.12 even 2 845.2.o.g.357.1 20
15.8 even 4 585.2.dp.a.253.5 20
39.11 even 12 585.2.dp.a.37.5 20
65.3 odd 12 845.2.t.f.418.5 20
65.8 even 4 845.2.o.e.488.5 20
65.18 even 4 845.2.o.f.488.1 20
65.23 odd 12 845.2.t.e.418.1 20
65.24 odd 12 325.2.x.b.232.5 20
65.28 even 12 845.2.o.g.258.1 20
65.33 even 12 845.2.k.e.268.1 20
65.37 even 12 325.2.s.b.193.1 20
65.38 odd 4 845.2.t.g.188.5 20
65.43 odd 12 845.2.f.d.408.1 20
65.48 odd 12 845.2.f.e.408.10 20
65.58 even 12 845.2.k.d.268.10 20
65.63 even 12 inner 65.2.o.a.63.5 yes 20
195.128 odd 12 585.2.cf.a.388.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.32.5 20 1.1 even 1 trivial
65.2.o.a.63.5 yes 20 65.63 even 12 inner
65.2.t.a.37.1 yes 20 13.11 odd 12
65.2.t.a.58.1 yes 20 5.3 odd 4
325.2.s.b.32.1 20 5.4 even 2
325.2.s.b.193.1 20 65.37 even 12
325.2.x.b.232.5 20 65.24 odd 12
325.2.x.b.318.5 20 5.2 odd 4
585.2.cf.a.388.1 20 195.128 odd 12
585.2.cf.a.487.1 20 3.2 odd 2
585.2.dp.a.37.5 20 39.11 even 12
585.2.dp.a.253.5 20 15.8 even 4
845.2.f.d.408.1 20 65.43 odd 12
845.2.f.d.437.10 20 13.6 odd 12
845.2.f.e.408.10 20 65.48 odd 12
845.2.f.e.437.1 20 13.7 odd 12
845.2.k.d.268.10 20 65.58 even 12
845.2.k.d.577.10 20 13.4 even 6
845.2.k.e.268.1 20 65.33 even 12
845.2.k.e.577.1 20 13.9 even 3
845.2.o.e.488.5 20 65.8 even 4
845.2.o.e.587.5 20 13.3 even 3
845.2.o.f.488.1 20 65.18 even 4
845.2.o.f.587.1 20 13.10 even 6
845.2.o.g.258.1 20 65.28 even 12
845.2.o.g.357.1 20 13.12 even 2
845.2.t.e.418.1 20 65.23 odd 12
845.2.t.e.657.1 20 13.5 odd 4
845.2.t.f.418.5 20 65.3 odd 12
845.2.t.f.657.5 20 13.8 odd 4
845.2.t.g.188.5 20 65.38 odd 4
845.2.t.g.427.5 20 13.2 odd 12