Basic properties
Modulus: | \(3525\) | |
Conductor: | \(3525\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bl
\(\chi_{3525}(56,\cdot)\) \(\chi_{3525}(71,\cdot)\) \(\chi_{3525}(131,\cdot)\) \(\chi_{3525}(191,\cdot)\) \(\chi_{3525}(206,\cdot)\) \(\chi_{3525}(296,\cdot)\) \(\chi_{3525}(341,\cdot)\) \(\chi_{3525}(356,\cdot)\) \(\chi_{3525}(371,\cdot)\) \(\chi_{3525}(431,\cdot)\) \(\chi_{3525}(491,\cdot)\) \(\chi_{3525}(506,\cdot)\) \(\chi_{3525}(521,\cdot)\) \(\chi_{3525}(566,\cdot)\) \(\chi_{3525}(581,\cdot)\) \(\chi_{3525}(596,\cdot)\) \(\chi_{3525}(686,\cdot)\) \(\chi_{3525}(761,\cdot)\) \(\chi_{3525}(806,\cdot)\) \(\chi_{3525}(836,\cdot)\) \(\chi_{3525}(896,\cdot)\) \(\chi_{3525}(911,\cdot)\) \(\chi_{3525}(956,\cdot)\) \(\chi_{3525}(1046,\cdot)\) \(\chi_{3525}(1061,\cdot)\) \(\chi_{3525}(1106,\cdot)\) \(\chi_{3525}(1136,\cdot)\) \(\chi_{3525}(1181,\cdot)\) \(\chi_{3525}(1196,\cdot)\) \(\chi_{3525}(1211,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{20}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(56, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{230}\right)\) | \(e\left(\frac{12}{115}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{227}{230}\right)\) | \(e\left(\frac{19}{115}\right)\) | \(e\left(\frac{87}{230}\right)\) | \(e\left(\frac{24}{115}\right)\) | \(e\left(\frac{141}{230}\right)\) | \(e\left(\frac{38}{115}\right)\) |