Basic properties
| Modulus: | \(3174\) | |
| Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(253\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{529}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3174.m
\(\chi_{3174}(13,\cdot)\) \(\chi_{3174}(25,\cdot)\) \(\chi_{3174}(31,\cdot)\) \(\chi_{3174}(49,\cdot)\) \(\chi_{3174}(55,\cdot)\) \(\chi_{3174}(73,\cdot)\) \(\chi_{3174}(85,\cdot)\) \(\chi_{3174}(121,\cdot)\) \(\chi_{3174}(127,\cdot)\) \(\chi_{3174}(133,\cdot)\) \(\chi_{3174}(151,\cdot)\) \(\chi_{3174}(163,\cdot)\) \(\chi_{3174}(169,\cdot)\) \(\chi_{3174}(187,\cdot)\) \(\chi_{3174}(193,\cdot)\) \(\chi_{3174}(211,\cdot)\) \(\chi_{3174}(223,\cdot)\) \(\chi_{3174}(259,\cdot)\) \(\chi_{3174}(265,\cdot)\) \(\chi_{3174}(271,\cdot)\) \(\chi_{3174}(289,\cdot)\) \(\chi_{3174}(301,\cdot)\) \(\chi_{3174}(307,\cdot)\) \(\chi_{3174}(325,\cdot)\) \(\chi_{3174}(331,\cdot)\) \(\chi_{3174}(349,\cdot)\) \(\chi_{3174}(361,\cdot)\) \(\chi_{3174}(397,\cdot)\) \(\chi_{3174}(403,\cdot)\) \(\chi_{3174}(409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\((2117,1063)\) → \((1,e\left(\frac{212}{253}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3174 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{212}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{53}{253}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{34}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) | \(e\left(\frac{175}{253}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{236}{253}\right)\) |