Basic properties
| Modulus: | \(7350\) | |
| Conductor: | \(3675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3675}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.dm
\(\chi_{7350}(59,\cdot)\) \(\chi_{7350}(89,\cdot)\) \(\chi_{7350}(269,\cdot)\) \(\chi_{7350}(479,\cdot)\) \(\chi_{7350}(689,\cdot)\) \(\chi_{7350}(719,\cdot)\) \(\chi_{7350}(929,\cdot)\) \(\chi_{7350}(1139,\cdot)\) \(\chi_{7350}(1319,\cdot)\) \(\chi_{7350}(1529,\cdot)\) \(\chi_{7350}(1559,\cdot)\) \(\chi_{7350}(1739,\cdot)\) \(\chi_{7350}(1769,\cdot)\) \(\chi_{7350}(2159,\cdot)\) \(\chi_{7350}(2189,\cdot)\) \(\chi_{7350}(2369,\cdot)\) \(\chi_{7350}(2609,\cdot)\) \(\chi_{7350}(2789,\cdot)\) \(\chi_{7350}(2819,\cdot)\) \(\chi_{7350}(3029,\cdot)\) \(\chi_{7350}(3209,\cdot)\) \(\chi_{7350}(3239,\cdot)\) \(\chi_{7350}(3419,\cdot)\) \(\chi_{7350}(3629,\cdot)\) \(\chi_{7350}(3659,\cdot)\) \(\chi_{7350}(3839,\cdot)\) \(\chi_{7350}(3869,\cdot)\) \(\chi_{7350}(4079,\cdot)\) \(\chi_{7350}(4259,\cdot)\) \(\chi_{7350}(4289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4901,1177,2551)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{5}{14}\right)\) |