Basic properties
| Modulus: | \(10008\) | |
| Conductor: | \(3336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3336}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10008.ff
\(\chi_{10008}(35,\cdot)\) \(\chi_{10008}(107,\cdot)\) \(\chi_{10008}(395,\cdot)\) \(\chi_{10008}(539,\cdot)\) \(\chi_{10008}(683,\cdot)\) \(\chi_{10008}(971,\cdot)\) \(\chi_{10008}(1403,\cdot)\) \(\chi_{10008}(1835,\cdot)\) \(\chi_{10008}(2123,\cdot)\) \(\chi_{10008}(2483,\cdot)\) \(\chi_{10008}(3275,\cdot)\) \(\chi_{10008}(3347,\cdot)\) \(\chi_{10008}(3419,\cdot)\) \(\chi_{10008}(3491,\cdot)\) \(\chi_{10008}(3923,\cdot)\) \(\chi_{10008}(4211,\cdot)\) \(\chi_{10008}(4283,\cdot)\) \(\chi_{10008}(4355,\cdot)\) \(\chi_{10008}(4427,\cdot)\) \(\chi_{10008}(4499,\cdot)\) \(\chi_{10008}(4931,\cdot)\) \(\chi_{10008}(5075,\cdot)\) \(\chi_{10008}(5147,\cdot)\) \(\chi_{10008}(5291,\cdot)\) \(\chi_{10008}(5363,\cdot)\) \(\chi_{10008}(5507,\cdot)\) \(\chi_{10008}(5723,\cdot)\) \(\chi_{10008}(5867,\cdot)\) \(\chi_{10008}(6443,\cdot)\) \(\chi_{10008}(6515,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((2503,5005,2225,4033)\) → \((-1,-1,-1,e\left(\frac{68}{69}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 10008 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{107}{138}\right)\) | \(e\left(\frac{55}{138}\right)\) | \(e\left(\frac{79}{138}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{95}{138}\right)\) |