Basic properties
Modulus: | \(1504\) | |
Conductor: | \(1504\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(184\) | 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 1504.be
\(\chi_{1504}(21,\cdot)\) \(\chi_{1504}(37,\cdot)\) \(\chi_{1504}(53,\cdot)\) \(\chi_{1504}(61,\cdot)\) \(\chi_{1504}(101,\cdot)\) \(\chi_{1504}(149,\cdot)\) \(\chi_{1504}(157,\cdot)\) \(\chi_{1504}(165,\cdot)\) \(\chi_{1504}(173,\cdot)\) \(\chi_{1504}(197,\cdot)\) \(\chi_{1504}(205,\cdot)\) \(\chi_{1504}(213,\cdot)\) \(\chi_{1504}(237,\cdot)\) \(\chi_{1504}(253,\cdot)\) \(\chi_{1504}(269,\cdot)\) \(\chi_{1504}(277,\cdot)\) \(\chi_{1504}(285,\cdot)\) \(\chi_{1504}(309,\cdot)\) \(\chi_{1504}(333,\cdot)\) \(\chi_{1504}(341,\cdot)\) \(\chi_{1504}(357,\cdot)\) \(\chi_{1504}(365,\cdot)\) \(\chi_{1504}(397,\cdot)\) \(\chi_{1504}(413,\cdot)\) \(\chi_{1504}(429,\cdot)\) \(\chi_{1504}(437,\cdot)\) \(\chi_{1504}(477,\cdot)\) \(\chi_{1504}(525,\cdot)\) \(\chi_{1504}(533,\cdot)\) \(\chi_{1504}(541,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{184})$ |
Fixed field: | Number field defined by a degree 184 polynomial (not computed) |
Values on generators
\((95,1317,193)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1504 }(1365, a) \) | \(1\) | \(1\) | \(e\left(\frac{129}{184}\right)\) | \(e\left(\frac{3}{184}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{159}{184}\right)\) | \(e\left(\frac{125}{184}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{181}{184}\right)\) | \(e\left(\frac{87}{184}\right)\) |