Basic properties
| Modulus: | \(2007\) | |
| Conductor: | \(2007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | 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 2007.bh
\(\chi_{2007}(59,\cdot)\) \(\chi_{2007}(95,\cdot)\) \(\chi_{2007}(104,\cdot)\) \(\chi_{2007}(155,\cdot)\) \(\chi_{2007}(167,\cdot)\) \(\chi_{2007}(182,\cdot)\) \(\chi_{2007}(191,\cdot)\) \(\chi_{2007}(209,\cdot)\) \(\chi_{2007}(221,\cdot)\) \(\chi_{2007}(236,\cdot)\) \(\chi_{2007}(275,\cdot)\) \(\chi_{2007}(326,\cdot)\) \(\chi_{2007}(380,\cdot)\) \(\chi_{2007}(416,\cdot)\) \(\chi_{2007}(473,\cdot)\) \(\chi_{2007}(500,\cdot)\) \(\chi_{2007}(533,\cdot)\) \(\chi_{2007}(554,\cdot)\) \(\chi_{2007}(587,\cdot)\) \(\chi_{2007}(605,\cdot)\) \(\chi_{2007}(635,\cdot)\) \(\chi_{2007}(641,\cdot)\) \(\chi_{2007}(653,\cdot)\) \(\chi_{2007}(662,\cdot)\) \(\chi_{2007}(695,\cdot)\) \(\chi_{2007}(794,\cdot)\) \(\chi_{2007}(824,\cdot)\) \(\chi_{2007}(851,\cdot)\) \(\chi_{2007}(860,\cdot)\) \(\chi_{2007}(875,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((893,226)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{21}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2007 }(275, a) \) | \(1\) | \(1\) | \(e\left(\frac{203}{222}\right)\) | \(e\left(\frac{92}{111}\right)\) | \(e\left(\frac{47}{111}\right)\) | \(e\left(\frac{103}{111}\right)\) | \(e\left(\frac{55}{74}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{22}{111}\right)\) | \(e\left(\frac{85}{222}\right)\) | \(e\left(\frac{187}{222}\right)\) | \(e\left(\frac{73}{111}\right)\) |