Basic properties
Modulus: | \(2888\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{361}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bo
\(\chi_{2888}(9,\cdot)\) \(\chi_{2888}(17,\cdot)\) \(\chi_{2888}(25,\cdot)\) \(\chi_{2888}(73,\cdot)\) \(\chi_{2888}(81,\cdot)\) \(\chi_{2888}(137,\cdot)\) \(\chi_{2888}(161,\cdot)\) \(\chi_{2888}(169,\cdot)\) \(\chi_{2888}(177,\cdot)\) \(\chi_{2888}(225,\cdot)\) \(\chi_{2888}(233,\cdot)\) \(\chi_{2888}(289,\cdot)\) \(\chi_{2888}(313,\cdot)\) \(\chi_{2888}(321,\cdot)\) \(\chi_{2888}(329,\cdot)\) \(\chi_{2888}(377,\cdot)\) \(\chi_{2888}(385,\cdot)\) \(\chi_{2888}(441,\cdot)\) \(\chi_{2888}(465,\cdot)\) \(\chi_{2888}(473,\cdot)\) \(\chi_{2888}(481,\cdot)\) \(\chi_{2888}(529,\cdot)\) \(\chi_{2888}(537,\cdot)\) \(\chi_{2888}(593,\cdot)\) \(\chi_{2888}(617,\cdot)\) \(\chi_{2888}(625,\cdot)\) \(\chi_{2888}(633,\cdot)\) \(\chi_{2888}(681,\cdot)\) \(\chi_{2888}(689,\cdot)\) \(\chi_{2888}(745,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,1,e\left(\frac{61}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{100}{171}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{29}{171}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{16}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) |