Basic properties
Modulus: | \(4024\) | |
Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(251\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{503}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.i
\(\chi_{4024}(9,\cdot)\) \(\chi_{4024}(25,\cdot)\) \(\chi_{4024}(33,\cdot)\) \(\chi_{4024}(49,\cdot)\) \(\chi_{4024}(73,\cdot)\) \(\chi_{4024}(81,\cdot)\) \(\chi_{4024}(97,\cdot)\) \(\chi_{4024}(113,\cdot)\) \(\chi_{4024}(121,\cdot)\) \(\chi_{4024}(129,\cdot)\) \(\chi_{4024}(145,\cdot)\) \(\chi_{4024}(161,\cdot)\) \(\chi_{4024}(169,\cdot)\) \(\chi_{4024}(177,\cdot)\) \(\chi_{4024}(185,\cdot)\) \(\chi_{4024}(201,\cdot)\) \(\chi_{4024}(225,\cdot)\) \(\chi_{4024}(233,\cdot)\) \(\chi_{4024}(249,\cdot)\) \(\chi_{4024}(257,\cdot)\) \(\chi_{4024}(265,\cdot)\) \(\chi_{4024}(273,\cdot)\) \(\chi_{4024}(281,\cdot)\) \(\chi_{4024}(289,\cdot)\) \(\chi_{4024}(297,\cdot)\) \(\chi_{4024}(329,\cdot)\) \(\chi_{4024}(361,\cdot)\) \(\chi_{4024}(393,\cdot)\) \(\chi_{4024}(401,\cdot)\) \(\chi_{4024}(433,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{251})$ |
Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((1,1,e\left(\frac{113}{251}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4024 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{58}{251}\right)\) | \(e\left(\frac{113}{251}\right)\) | \(e\left(\frac{180}{251}\right)\) | \(e\left(\frac{116}{251}\right)\) | \(e\left(\frac{228}{251}\right)\) | \(e\left(\frac{207}{251}\right)\) | \(e\left(\frac{171}{251}\right)\) | \(e\left(\frac{24}{251}\right)\) | \(e\left(\frac{175}{251}\right)\) | \(e\left(\frac{238}{251}\right)\) |