Basic properties
Modulus: | \(4008\) | |
Conductor: | \(501\) | 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 \(\chi_{501}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.t
\(\chi_{4008}(17,\cdot)\) \(\chi_{4008}(41,\cdot)\) \(\chi_{4008}(113,\cdot)\) \(\chi_{4008}(161,\cdot)\) \(\chi_{4008}(257,\cdot)\) \(\chi_{4008}(305,\cdot)\) \(\chi_{4008}(377,\cdot)\) \(\chi_{4008}(401,\cdot)\) \(\chi_{4008}(425,\cdot)\) \(\chi_{4008}(473,\cdot)\) \(\chi_{4008}(497,\cdot)\) \(\chi_{4008}(521,\cdot)\) \(\chi_{4008}(569,\cdot)\) \(\chi_{4008}(593,\cdot)\) \(\chi_{4008}(641,\cdot)\) \(\chi_{4008}(665,\cdot)\) \(\chi_{4008}(713,\cdot)\) \(\chi_{4008}(737,\cdot)\) \(\chi_{4008}(785,\cdot)\) \(\chi_{4008}(833,\cdot)\) \(\chi_{4008}(881,\cdot)\) \(\chi_{4008}(905,\cdot)\) \(\chi_{4008}(953,\cdot)\) \(\chi_{4008}(977,\cdot)\) \(\chi_{4008}(1025,\cdot)\) \(\chi_{4008}(1073,\cdot)\) \(\chi_{4008}(1097,\cdot)\) \(\chi_{4008}(1121,\cdot)\) \(\chi_{4008}(1145,\cdot)\) \(\chi_{4008}(1289,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,1,-1,e\left(\frac{59}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(1097, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{75}{166}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) |