Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(553,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bs
\(\chi_{1815}(37,\cdot)\) \(\chi_{1815}(58,\cdot)\) \(\chi_{1815}(82,\cdot)\) \(\chi_{1815}(97,\cdot)\) \(\chi_{1815}(103,\cdot)\) \(\chi_{1815}(157,\cdot)\) \(\chi_{1815}(163,\cdot)\) \(\chi_{1815}(223,\cdot)\) \(\chi_{1815}(247,\cdot)\) \(\chi_{1815}(262,\cdot)\) \(\chi_{1815}(268,\cdot)\) \(\chi_{1815}(313,\cdot)\) \(\chi_{1815}(322,\cdot)\) \(\chi_{1815}(328,\cdot)\) \(\chi_{1815}(367,\cdot)\) \(\chi_{1815}(388,\cdot)\) \(\chi_{1815}(412,\cdot)\) \(\chi_{1815}(427,\cdot)\) \(\chi_{1815}(433,\cdot)\) \(\chi_{1815}(478,\cdot)\) \(\chi_{1815}(532,\cdot)\) \(\chi_{1815}(553,\cdot)\) \(\chi_{1815}(577,\cdot)\) \(\chi_{1815}(592,\cdot)\) \(\chi_{1815}(598,\cdot)\) \(\chi_{1815}(643,\cdot)\) \(\chi_{1815}(652,\cdot)\) \(\chi_{1815}(658,\cdot)\) \(\chi_{1815}(697,\cdot)\) \(\chi_{1815}(718,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((1,-i,e\left(\frac{24}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(553, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{35}{44}\right)\) |