Basic properties
Modulus: | \(7220\) | |
Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1805}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7220.bz
\(\chi_{7220}(49,\cdot)\) \(\chi_{7220}(349,\cdot)\) \(\chi_{7220}(729,\cdot)\) \(\chi_{7220}(809,\cdot)\) \(\chi_{7220}(1109,\cdot)\) \(\chi_{7220}(1189,\cdot)\) \(\chi_{7220}(1489,\cdot)\) \(\chi_{7220}(1569,\cdot)\) \(\chi_{7220}(1869,\cdot)\) \(\chi_{7220}(1949,\cdot)\) \(\chi_{7220}(2249,\cdot)\) \(\chi_{7220}(2329,\cdot)\) \(\chi_{7220}(2629,\cdot)\) \(\chi_{7220}(2709,\cdot)\) \(\chi_{7220}(3009,\cdot)\) \(\chi_{7220}(3089,\cdot)\) \(\chi_{7220}(3389,\cdot)\) \(\chi_{7220}(3469,\cdot)\) \(\chi_{7220}(3769,\cdot)\) \(\chi_{7220}(3849,\cdot)\) \(\chi_{7220}(4149,\cdot)\) \(\chi_{7220}(4229,\cdot)\) \(\chi_{7220}(4529,\cdot)\) \(\chi_{7220}(4609,\cdot)\) \(\chi_{7220}(4909,\cdot)\) \(\chi_{7220}(4989,\cdot)\) \(\chi_{7220}(5289,\cdot)\) \(\chi_{7220}(5369,\cdot)\) \(\chi_{7220}(5669,\cdot)\) \(\chi_{7220}(5749,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,5777,6861)\) → \((1,-1,e\left(\frac{50}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 7220 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{52}{57}\right)\) |