Basic properties
| Modulus: | \(9126\) | |
| Conductor: | \(4563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4563}(2911,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9126.dj
\(\chi_{9126}(25,\cdot)\) \(\chi_{9126}(103,\cdot)\) \(\chi_{9126}(259,\cdot)\) \(\chi_{9126}(493,\cdot)\) \(\chi_{9126}(571,\cdot)\) \(\chi_{9126}(727,\cdot)\) \(\chi_{9126}(805,\cdot)\) \(\chi_{9126}(961,\cdot)\) \(\chi_{9126}(1039,\cdot)\) \(\chi_{9126}(1195,\cdot)\) \(\chi_{9126}(1273,\cdot)\) \(\chi_{9126}(1429,\cdot)\) \(\chi_{9126}(1507,\cdot)\) \(\chi_{9126}(1663,\cdot)\) \(\chi_{9126}(1741,\cdot)\) \(\chi_{9126}(1897,\cdot)\) \(\chi_{9126}(1975,\cdot)\) \(\chi_{9126}(2131,\cdot)\) \(\chi_{9126}(2209,\cdot)\) \(\chi_{9126}(2443,\cdot)\) \(\chi_{9126}(2599,\cdot)\) \(\chi_{9126}(2677,\cdot)\) \(\chi_{9126}(2833,\cdot)\) \(\chi_{9126}(2911,\cdot)\) \(\chi_{9126}(3067,\cdot)\) \(\chi_{9126}(3145,\cdot)\) \(\chi_{9126}(3301,\cdot)\) \(\chi_{9126}(3535,\cdot)\) \(\chi_{9126}(3613,\cdot)\) \(\chi_{9126}(3769,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((677,3889)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{11}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 9126 }(2911, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{103}{234}\right)\) | \(e\left(\frac{16}{39}\right)\) |