Basic properties
Modulus: | \(953\) | |
Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 953.k
\(\chi_{953}(2,\cdot)\) \(\chi_{953}(8,\cdot)\) \(\chi_{953}(32,\cdot)\) \(\chi_{953}(67,\cdot)\) \(\chi_{953}(119,\cdot)\) \(\chi_{953}(128,\cdot)\) \(\chi_{953}(138,\cdot)\) \(\chi_{953}(142,\cdot)\) \(\chi_{953}(255,\cdot)\) \(\chi_{953}(268,\cdot)\) \(\chi_{953}(302,\cdot)\) \(\chi_{953}(366,\cdot)\) \(\chi_{953}(385,\cdot)\) \(\chi_{953}(401,\cdot)\) \(\chi_{953}(441,\cdot)\) \(\chi_{953}(476,\cdot)\) \(\chi_{953}(477,\cdot)\) \(\chi_{953}(512,\cdot)\) \(\chi_{953}(552,\cdot)\) \(\chi_{953}(568,\cdot)\) \(\chi_{953}(587,\cdot)\) \(\chi_{953}(651,\cdot)\) \(\chi_{953}(685,\cdot)\) \(\chi_{953}(698,\cdot)\) \(\chi_{953}(811,\cdot)\) \(\chi_{953}(815,\cdot)\) \(\chi_{953}(825,\cdot)\) \(\chi_{953}(834,\cdot)\) \(\chi_{953}(886,\cdot)\) \(\chi_{953}(921,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\(3\) → \(e\left(\frac{9}{68}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 953 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{11}{68}\right)\) |