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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9555, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,7,4,14]))
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pari:[g,chi] = znchar(Mod(6707,9555))
| Modulus: | \(9555\) | |
| Conductor: | \(9555\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(28\) |
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sage:chi.multiplicative_order()
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pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
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sage:chi.is_primitive()
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pari:#znconreyconductor(g,chi)==1
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| Minimal: | yes |
| Parity: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{9555}(428,\cdot)\)
\(\chi_{9555}(1247,\cdot)\)
\(\chi_{9555}(1793,\cdot)\)
\(\chi_{9555}(2612,\cdot)\)
\(\chi_{9555}(3158,\cdot)\)
\(\chi_{9555}(3977,\cdot)\)
\(\chi_{9555}(4523,\cdot)\)
\(\chi_{9555}(5888,\cdot)\)
\(\chi_{9555}(6707,\cdot)\)
\(\chi_{9555}(8072,\cdot)\)
\(\chi_{9555}(8618,\cdot)\)
\(\chi_{9555}(9437,\cdot)\)
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sage:chi.galois_orbit()
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pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((6371,1912,9166,1471)\) → \((-1,i,e\left(\frac{1}{7}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) | \(29\) |
| \( \chi_{ 9555 }(6707, a) \) |
\(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) |
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sage:chi.jacobi_sum(n)
