Basic properties
Modulus: | \(3004\) | |
Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 3004.y
\(\chi_{3004}(11,\cdot)\) \(\chi_{3004}(83,\cdot)\) \(\chi_{3004}(223,\cdot)\) \(\chi_{3004}(243,\cdot)\) \(\chi_{3004}(251,\cdot)\) \(\chi_{3004}(379,\cdot)\) \(\chi_{3004}(455,\cdot)\) \(\chi_{3004}(467,\cdot)\) \(\chi_{3004}(551,\cdot)\) \(\chi_{3004}(567,\cdot)\) \(\chi_{3004}(571,\cdot)\) \(\chi_{3004}(699,\cdot)\) \(\chi_{3004}(719,\cdot)\) \(\chi_{3004}(859,\cdot)\) \(\chi_{3004}(863,\cdot)\) \(\chi_{3004}(871,\cdot)\) \(\chi_{3004}(1031,\cdot)\) \(\chi_{3004}(1051,\cdot)\) \(\chi_{3004}(1103,\cdot)\) \(\chi_{3004}(1195,\cdot)\) \(\chi_{3004}(1203,\cdot)\) \(\chi_{3004}(1339,\cdot)\) \(\chi_{3004}(1371,\cdot)\) \(\chi_{3004}(1383,\cdot)\) \(\chi_{3004}(1395,\cdot)\) \(\chi_{3004}(1631,\cdot)\) \(\chi_{3004}(1875,\cdot)\) \(\chi_{3004}(1879,\cdot)\) \(\chi_{3004}(2059,\cdot)\) \(\chi_{3004}(2063,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((-1,e\left(\frac{67}{150}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3004 }(1879, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{68}{75}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{143}{150}\right)\) | \(e\left(\frac{31}{150}\right)\) | \(e\left(\frac{17}{75}\right)\) |