Basic properties
Modulus: | \(4014\) | |
Conductor: | \(669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{669}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.bj
\(\chi_{4014}(35,\cdot)\) \(\chi_{4014}(71,\cdot)\) \(\chi_{4014}(107,\cdot)\) \(\chi_{4014}(161,\cdot)\) \(\chi_{4014}(233,\cdot)\) \(\chi_{4014}(269,\cdot)\) \(\chi_{4014}(377,\cdot)\) \(\chi_{4014}(449,\cdot)\) \(\chi_{4014}(467,\cdot)\) \(\chi_{4014}(503,\cdot)\) \(\chi_{4014}(521,\cdot)\) \(\chi_{4014}(539,\cdot)\) \(\chi_{4014}(575,\cdot)\) \(\chi_{4014}(593,\cdot)\) \(\chi_{4014}(611,\cdot)\) \(\chi_{4014}(791,\cdot)\) \(\chi_{4014}(809,\cdot)\) \(\chi_{4014}(827,\cdot)\) \(\chi_{4014}(845,\cdot)\) \(\chi_{4014}(863,\cdot)\) \(\chi_{4014}(953,\cdot)\) \(\chi_{4014}(971,\cdot)\) \(\chi_{4014}(989,\cdot)\) \(\chi_{4014}(1043,\cdot)\) \(\chi_{4014}(1079,\cdot)\) \(\chi_{4014}(1097,\cdot)\) \(\chi_{4014}(1205,\cdot)\) \(\chi_{4014}(1295,\cdot)\) \(\chi_{4014}(1313,\cdot)\) \(\chi_{4014}(1349,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{111})$ |
Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,2233)\) → \((-1,e\left(\frac{157}{222}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4014 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{111}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{19}{111}\right)\) | \(e\left(\frac{71}{74}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{71}{111}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{98}{111}\right)\) | \(e\left(\frac{5}{222}\right)\) | \(e\left(\frac{110}{111}\right)\) |