Basic properties
Modulus: | \(3004\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{751}(493,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.v
\(\chi_{3004}(45,\cdot)\) \(\chi_{3004}(49,\cdot)\) \(\chi_{3004}(93,\cdot)\) \(\chi_{3004}(125,\cdot)\) \(\chi_{3004}(165,\cdot)\) \(\chi_{3004}(185,\cdot)\) \(\chi_{3004}(189,\cdot)\) \(\chi_{3004}(237,\cdot)\) \(\chi_{3004}(249,\cdot)\) \(\chi_{3004}(305,\cdot)\) \(\chi_{3004}(341,\cdot)\) \(\chi_{3004}(429,\cdot)\) \(\chi_{3004}(433,\cdot)\) \(\chi_{3004}(445,\cdot)\) \(\chi_{3004}(457,\cdot)\) \(\chi_{3004}(493,\cdot)\) \(\chi_{3004}(525,\cdot)\) \(\chi_{3004}(545,\cdot)\) \(\chi_{3004}(605,\cdot)\) \(\chi_{3004}(617,\cdot)\) \(\chi_{3004}(681,\cdot)\) \(\chi_{3004}(693,\cdot)\) \(\chi_{3004}(729,\cdot)\) \(\chi_{3004}(745,\cdot)\) \(\chi_{3004}(761,\cdot)\) \(\chi_{3004}(777,\cdot)\) \(\chi_{3004}(789,\cdot)\) \(\chi_{3004}(793,\cdot)\) \(\chi_{3004}(797,\cdot)\) \(\chi_{3004}(845,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((1,e\left(\frac{26}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3004 }(493, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{125}\right)\) | \(e\left(\frac{11}{125}\right)\) | \(e\left(\frac{51}{125}\right)\) | \(e\left(\frac{52}{125}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{83}{125}\right)\) | \(e\left(\frac{37}{125}\right)\) | \(e\left(\frac{54}{125}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{77}{125}\right)\) |