Basic properties
Modulus: | \(4008\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{167}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.q
\(\chi_{4008}(25,\cdot)\) \(\chi_{4008}(49,\cdot)\) \(\chi_{4008}(97,\cdot)\) \(\chi_{4008}(121,\cdot)\) \(\chi_{4008}(169,\cdot)\) \(\chi_{4008}(217,\cdot)\) \(\chi_{4008}(265,\cdot)\) \(\chi_{4008}(289,\cdot)\) \(\chi_{4008}(337,\cdot)\) \(\chi_{4008}(361,\cdot)\) \(\chi_{4008}(409,\cdot)\) \(\chi_{4008}(433,\cdot)\) \(\chi_{4008}(481,\cdot)\) \(\chi_{4008}(505,\cdot)\) \(\chi_{4008}(529,\cdot)\) \(\chi_{4008}(577,\cdot)\) \(\chi_{4008}(601,\cdot)\) \(\chi_{4008}(625,\cdot)\) \(\chi_{4008}(697,\cdot)\) \(\chi_{4008}(745,\cdot)\) \(\chi_{4008}(841,\cdot)\) \(\chi_{4008}(889,\cdot)\) \(\chi_{4008}(961,\cdot)\) \(\chi_{4008}(985,\cdot)\) \(\chi_{4008}(1009,\cdot)\) \(\chi_{4008}(1033,\cdot)\) \(\chi_{4008}(1129,\cdot)\) \(\chi_{4008}(1177,\cdot)\) \(\chi_{4008}(1201,\cdot)\) \(\chi_{4008}(1225,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((3007,2005,1337,673)\) → \((1,1,1,e\left(\frac{69}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(577, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{55}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) |