Basic properties
Modulus: | \(1502\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{751}(197,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1502.k
\(\chi_{1502}(61,\cdot)\) \(\chi_{1502}(107,\cdot)\) \(\chi_{1502}(119,\cdot)\) \(\chi_{1502}(121,\cdot)\) \(\chi_{1502}(131,\cdot)\) \(\chi_{1502}(163,\cdot)\) \(\chi_{1502}(197,\cdot)\) \(\chi_{1502}(229,\cdot)\) \(\chi_{1502}(273,\cdot)\) \(\chi_{1502}(299,\cdot)\) \(\chi_{1502}(307,\cdot)\) \(\chi_{1502}(399,\cdot)\) \(\chi_{1502}(405,\cdot)\) \(\chi_{1502}(451,\cdot)\) \(\chi_{1502}(471,\cdot)\) \(\chi_{1502}(631,\cdot)\) \(\chi_{1502}(637,\cdot)\) \(\chi_{1502}(639,\cdot)\) \(\chi_{1502}(643,\cdot)\) \(\chi_{1502}(717,\cdot)\) \(\chi_{1502}(783,\cdot)\) \(\chi_{1502}(803,\cdot)\) \(\chi_{1502}(837,\cdot)\) \(\chi_{1502}(881,\cdot)\) \(\chi_{1502}(931,\cdot)\) \(\chi_{1502}(935,\cdot)\) \(\chi_{1502}(941,\cdot)\) \(\chi_{1502}(945,\cdot)\) \(\chi_{1502}(951,\cdot)\) \(\chi_{1502}(1035,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\(3\) → \(e\left(\frac{19}{75}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1502 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{75}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{38}{75}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{53}{75}\right)\) | \(e\left(\frac{26}{75}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{13}{75}\right)\) |