Basic properties
Modulus: | \(4008\) | |
Conductor: | \(1336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1336}(907,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.bd
\(\chi_{4008}(19,\cdot)\) \(\chi_{4008}(115,\cdot)\) \(\chi_{4008}(211,\cdot)\) \(\chi_{4008}(283,\cdot)\) \(\chi_{4008}(355,\cdot)\) \(\chi_{4008}(427,\cdot)\) \(\chi_{4008}(475,\cdot)\) \(\chi_{4008}(523,\cdot)\) \(\chi_{4008}(595,\cdot)\) \(\chi_{4008}(715,\cdot)\) \(\chi_{4008}(859,\cdot)\) \(\chi_{4008}(883,\cdot)\) \(\chi_{4008}(907,\cdot)\) \(\chi_{4008}(931,\cdot)\) \(\chi_{4008}(979,\cdot)\) \(\chi_{4008}(1027,\cdot)\) \(\chi_{4008}(1051,\cdot)\) \(\chi_{4008}(1099,\cdot)\) \(\chi_{4008}(1123,\cdot)\) \(\chi_{4008}(1171,\cdot)\) \(\chi_{4008}(1219,\cdot)\) \(\chi_{4008}(1267,\cdot)\) \(\chi_{4008}(1291,\cdot)\) \(\chi_{4008}(1339,\cdot)\) \(\chi_{4008}(1363,\cdot)\) \(\chi_{4008}(1411,\cdot)\) \(\chi_{4008}(1435,\cdot)\) \(\chi_{4008}(1483,\cdot)\) \(\chi_{4008}(1507,\cdot)\) \(\chi_{4008}(1531,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((-1,-1,1,e\left(\frac{71}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(907, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{73}{166}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{81}{166}\right)\) |