Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(17424\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{17424}(13147,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.lh
\(\chi_{69696}(79,\cdot)\) \(\chi_{69696}(655,\cdot)\) \(\chi_{69696}(943,\cdot)\) \(\chi_{69696}(1327,\cdot)\) \(\chi_{69696}(2191,\cdot)\) \(\chi_{69696}(2383,\cdot)\) \(\chi_{69696}(2767,\cdot)\) \(\chi_{69696}(3055,\cdot)\) \(\chi_{69696}(3247,\cdot)\) \(\chi_{69696}(3823,\cdot)\) \(\chi_{69696}(4495,\cdot)\) \(\chi_{69696}(5359,\cdot)\) \(\chi_{69696}(5551,\cdot)\) \(\chi_{69696}(5935,\cdot)\) \(\chi_{69696}(6223,\cdot)\) \(\chi_{69696}(6415,\cdot)\) \(\chi_{69696}(7279,\cdot)\) \(\chi_{69696}(8527,\cdot)\) \(\chi_{69696}(8719,\cdot)\) \(\chi_{69696}(9103,\cdot)\) \(\chi_{69696}(9391,\cdot)\) \(\chi_{69696}(9583,\cdot)\) \(\chi_{69696}(10159,\cdot)\) \(\chi_{69696}(10447,\cdot)\) \(\chi_{69696}(10831,\cdot)\) \(\chi_{69696}(11695,\cdot)\) \(\chi_{69696}(11887,\cdot)\) \(\chi_{69696}(12271,\cdot)\) \(\chi_{69696}(12559,\cdot)\) \(\chi_{69696}(12751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{41}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{660}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{481}{660}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{497}{660}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{97}{220}\right)\) |