Basic properties
Modulus: | \(3004\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(750\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{751}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.bf
\(\chi_{3004}(17,\cdot)\) \(\chi_{3004}(29,\cdot)\) \(\chi_{3004}(57,\cdot)\) \(\chi_{3004}(69,\cdot)\) \(\chi_{3004}(101,\cdot)\) \(\chi_{3004}(113,\cdot)\) \(\chi_{3004}(133,\cdot)\) \(\chi_{3004}(141,\cdot)\) \(\chi_{3004}(145,\cdot)\) \(\chi_{3004}(153,\cdot)\) \(\chi_{3004}(161,\cdot)\) \(\chi_{3004}(177,\cdot)\) \(\chi_{3004}(205,\cdot)\) \(\chi_{3004}(209,\cdot)\) \(\chi_{3004}(213,\cdot)\) \(\chi_{3004}(253,\cdot)\) \(\chi_{3004}(257,\cdot)\) \(\chi_{3004}(277,\cdot)\) \(\chi_{3004}(281,\cdot)\) \(\chi_{3004}(293,\cdot)\) \(\chi_{3004}(313,\cdot)\) \(\chi_{3004}(317,\cdot)\) \(\chi_{3004}(329,\cdot)\) \(\chi_{3004}(349,\cdot)\) \(\chi_{3004}(353,\cdot)\) \(\chi_{3004}(365,\cdot)\) \(\chi_{3004}(369,\cdot)\) \(\chi_{3004}(381,\cdot)\) \(\chi_{3004}(389,\cdot)\) \(\chi_{3004}(393,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\((1503,1505)\) → \((1,e\left(\frac{577}{750}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3004 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{577}{750}\right)\) | \(e\left(\frac{86}{375}\right)\) | \(e\left(\frac{209}{250}\right)\) | \(e\left(\frac{202}{375}\right)\) | \(e\left(\frac{11}{150}\right)\) | \(e\left(\frac{308}{375}\right)\) | \(e\left(\frac{749}{750}\right)\) | \(e\left(\frac{83}{750}\right)\) | \(e\left(\frac{68}{375}\right)\) | \(e\left(\frac{227}{375}\right)\) |