Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(7581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.eg
\(\chi_{7581}(17,\cdot)\) \(\chi_{7581}(47,\cdot)\) \(\chi_{7581}(194,\cdot)\) \(\chi_{7581}(206,\cdot)\) \(\chi_{7581}(215,\cdot)\) \(\chi_{7581}(290,\cdot)\) \(\chi_{7581}(416,\cdot)\) \(\chi_{7581}(446,\cdot)\) \(\chi_{7581}(593,\cdot)\) \(\chi_{7581}(605,\cdot)\) \(\chi_{7581}(614,\cdot)\) \(\chi_{7581}(689,\cdot)\) \(\chi_{7581}(815,\cdot)\) \(\chi_{7581}(845,\cdot)\) \(\chi_{7581}(992,\cdot)\) \(\chi_{7581}(1004,\cdot)\) \(\chi_{7581}(1013,\cdot)\) \(\chi_{7581}(1088,\cdot)\) \(\chi_{7581}(1214,\cdot)\) \(\chi_{7581}(1244,\cdot)\) \(\chi_{7581}(1391,\cdot)\) \(\chi_{7581}(1403,\cdot)\) \(\chi_{7581}(1412,\cdot)\) \(\chi_{7581}(1487,\cdot)\) \(\chi_{7581}(1613,\cdot)\) \(\chi_{7581}(1643,\cdot)\) \(\chi_{7581}(1790,\cdot)\) \(\chi_{7581}(1802,\cdot)\) \(\chi_{7581}(1811,\cdot)\) \(\chi_{7581}(1886,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{113}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{342}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{47}{342}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{311}{342}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{12}{19}\right)\) |