Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.em
\(\chi_{7581}(13,\cdot)\) \(\chi_{7581}(34,\cdot)\) \(\chi_{7581}(97,\cdot)\) \(\chi_{7581}(181,\cdot)\) \(\chi_{7581}(223,\cdot)\) \(\chi_{7581}(412,\cdot)\) \(\chi_{7581}(433,\cdot)\) \(\chi_{7581}(496,\cdot)\) \(\chi_{7581}(580,\cdot)\) \(\chi_{7581}(622,\cdot)\) \(\chi_{7581}(706,\cdot)\) \(\chi_{7581}(811,\cdot)\) \(\chi_{7581}(832,\cdot)\) \(\chi_{7581}(895,\cdot)\) \(\chi_{7581}(979,\cdot)\) \(\chi_{7581}(1105,\cdot)\) \(\chi_{7581}(1231,\cdot)\) \(\chi_{7581}(1294,\cdot)\) \(\chi_{7581}(1378,\cdot)\) \(\chi_{7581}(1420,\cdot)\) \(\chi_{7581}(1504,\cdot)\) \(\chi_{7581}(1609,\cdot)\) \(\chi_{7581}(1630,\cdot)\) \(\chi_{7581}(1693,\cdot)\) \(\chi_{7581}(1819,\cdot)\) \(\chi_{7581}(1903,\cdot)\) \(\chi_{7581}(2008,\cdot)\) \(\chi_{7581}(2029,\cdot)\) \(\chi_{7581}(2092,\cdot)\) \(\chi_{7581}(2176,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,-1,e\left(\frac{329}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{329}{342}\right)\) | \(e\left(\frac{158}{171}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{170}{171}\right)\) | \(e\left(\frac{145}{171}\right)\) | \(e\left(\frac{311}{342}\right)\) | \(e\left(\frac{23}{38}\right)\) |