Basic properties
Modulus: | \(3004\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(375\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{751}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.bc
\(\chi_{3004}(5,\cdot)\) \(\chi_{3004}(9,\cdot)\) \(\chi_{3004}(13,\cdot)\) \(\chi_{3004}(21,\cdot)\) \(\chi_{3004}(25,\cdot)\) \(\chi_{3004}(33,\cdot)\) \(\chi_{3004}(37,\cdot)\) \(\chi_{3004}(65,\cdot)\) \(\chi_{3004}(77,\cdot)\) \(\chi_{3004}(81,\cdot)\) \(\chi_{3004}(89,\cdot)\) \(\chi_{3004}(97,\cdot)\) \(\chi_{3004}(105,\cdot)\) \(\chi_{3004}(109,\cdot)\) \(\chi_{3004}(149,\cdot)\) \(\chi_{3004}(169,\cdot)\) \(\chi_{3004}(181,\cdot)\) \(\chi_{3004}(201,\cdot)\) \(\chi_{3004}(217,\cdot)\) \(\chi_{3004}(225,\cdot)\) \(\chi_{3004}(233,\cdot)\) \(\chi_{3004}(245,\cdot)\) \(\chi_{3004}(265,\cdot)\) \(\chi_{3004}(269,\cdot)\) \(\chi_{3004}(289,\cdot)\) \(\chi_{3004}(297,\cdot)\) \(\chi_{3004}(309,\cdot)\) \(\chi_{3004}(333,\cdot)\) \(\chi_{3004}(361,\cdot)\) \(\chi_{3004}(385,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((1,e\left(\frac{368}{375}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3004 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{368}{375}\right)\) | \(e\left(\frac{98}{375}\right)\) | \(e\left(\frac{106}{125}\right)\) | \(e\left(\frac{361}{375}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{194}{375}\right)\) | \(e\left(\frac{91}{375}\right)\) | \(e\left(\frac{322}{375}\right)\) | \(e\left(\frac{374}{375}\right)\) | \(e\left(\frac{311}{375}\right)\) |