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 \(\chi_{4563}(979,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9126.di
\(\chi_{9126}(43,\cdot)\) \(\chi_{9126}(49,\cdot)\) \(\chi_{9126}(277,\cdot)\) \(\chi_{9126}(283,\cdot)\) \(\chi_{9126}(511,\cdot)\) \(\chi_{9126}(517,\cdot)\) \(\chi_{9126}(745,\cdot)\) \(\chi_{9126}(751,\cdot)\) \(\chi_{9126}(979,\cdot)\) \(\chi_{9126}(985,\cdot)\) \(\chi_{9126}(1213,\cdot)\) \(\chi_{9126}(1219,\cdot)\) \(\chi_{9126}(1447,\cdot)\) \(\chi_{9126}(1453,\cdot)\) \(\chi_{9126}(1681,\cdot)\) \(\chi_{9126}(1687,\cdot)\) \(\chi_{9126}(1915,\cdot)\) \(\chi_{9126}(1921,\cdot)\) \(\chi_{9126}(2149,\cdot)\) \(\chi_{9126}(2155,\cdot)\) \(\chi_{9126}(2383,\cdot)\) \(\chi_{9126}(2617,\cdot)\) \(\chi_{9126}(2623,\cdot)\) \(\chi_{9126}(2857,\cdot)\) \(\chi_{9126}(3085,\cdot)\) \(\chi_{9126}(3091,\cdot)\) \(\chi_{9126}(3319,\cdot)\) \(\chi_{9126}(3325,\cdot)\) \(\chi_{9126}(3553,\cdot)\) \(\chi_{9126}(3559,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((677,3889)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{19}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 9126 }(979, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(-1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{12}{13}\right)\) |