Basic properties
Modulus: | \(4002\) | |
Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2001}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bv
\(\chi_{4002}(77,\cdot)\) \(\chi_{4002}(95,\cdot)\) \(\chi_{4002}(101,\cdot)\) \(\chi_{4002}(119,\cdot)\) \(\chi_{4002}(131,\cdot)\) \(\chi_{4002}(269,\cdot)\) \(\chi_{4002}(305,\cdot)\) \(\chi_{4002}(311,\cdot)\) \(\chi_{4002}(317,\cdot)\) \(\chi_{4002}(395,\cdot)\) \(\chi_{4002}(443,\cdot)\) \(\chi_{4002}(449,\cdot)\) \(\chi_{4002}(485,\cdot)\) \(\chi_{4002}(491,\cdot)\) \(\chi_{4002}(533,\cdot)\) \(\chi_{4002}(611,\cdot)\) \(\chi_{4002}(623,\cdot)\) \(\chi_{4002}(653,\cdot)\) \(\chi_{4002}(785,\cdot)\) \(\chi_{4002}(791,\cdot)\) \(\chi_{4002}(809,\cdot)\) \(\chi_{4002}(947,\cdot)\) \(\chi_{4002}(959,\cdot)\) \(\chi_{4002}(1001,\cdot)\) \(\chi_{4002}(1007,\cdot)\) \(\chi_{4002}(1025,\cdot)\) \(\chi_{4002}(1133,\cdot)\) \(\chi_{4002}(1139,\cdot)\) \(\chi_{4002}(1145,\cdot)\) \(\chi_{4002}(1163,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((-1,e\left(\frac{3}{11}\right),e\left(\frac{9}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 4002 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{305}{308}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{303}{308}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{295}{308}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{213}{308}\right)\) |