Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(578,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.gc
\(\chi_{7605}(28,\cdot)\) \(\chi_{7605}(37,\cdot)\) \(\chi_{7605}(253,\cdot)\) \(\chi_{7605}(397,\cdot)\) \(\chi_{7605}(613,\cdot)\) \(\chi_{7605}(622,\cdot)\) \(\chi_{7605}(838,\cdot)\) \(\chi_{7605}(982,\cdot)\) \(\chi_{7605}(1198,\cdot)\) \(\chi_{7605}(1207,\cdot)\) \(\chi_{7605}(1423,\cdot)\) \(\chi_{7605}(1567,\cdot)\) \(\chi_{7605}(1783,\cdot)\) \(\chi_{7605}(1792,\cdot)\) \(\chi_{7605}(2008,\cdot)\) \(\chi_{7605}(2152,\cdot)\) \(\chi_{7605}(2368,\cdot)\) \(\chi_{7605}(2377,\cdot)\) \(\chi_{7605}(2593,\cdot)\) \(\chi_{7605}(2737,\cdot)\) \(\chi_{7605}(3178,\cdot)\) \(\chi_{7605}(3322,\cdot)\) \(\chi_{7605}(3538,\cdot)\) \(\chi_{7605}(3547,\cdot)\) \(\chi_{7605}(3763,\cdot)\) \(\chi_{7605}(3907,\cdot)\) \(\chi_{7605}(4123,\cdot)\) \(\chi_{7605}(4132,\cdot)\) \(\chi_{7605}(4348,\cdot)\) \(\chi_{7605}(4492,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((1,-i,e\left(\frac{137}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(1423, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |