Basic properties
Modulus: | \(3525\) | |
Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1175}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bn
\(\chi_{3525}(19,\cdot)\) \(\chi_{3525}(109,\cdot)\) \(\chi_{3525}(139,\cdot)\) \(\chi_{3525}(154,\cdot)\) \(\chi_{3525}(184,\cdot)\) \(\chi_{3525}(214,\cdot)\) \(\chi_{3525}(229,\cdot)\) \(\chi_{3525}(304,\cdot)\) \(\chi_{3525}(334,\cdot)\) \(\chi_{3525}(364,\cdot)\) \(\chi_{3525}(409,\cdot)\) \(\chi_{3525}(454,\cdot)\) \(\chi_{3525}(514,\cdot)\) \(\chi_{3525}(604,\cdot)\) \(\chi_{3525}(634,\cdot)\) \(\chi_{3525}(814,\cdot)\) \(\chi_{3525}(829,\cdot)\) \(\chi_{3525}(844,\cdot)\) \(\chi_{3525}(859,\cdot)\) \(\chi_{3525}(889,\cdot)\) \(\chi_{3525}(904,\cdot)\) \(\chi_{3525}(919,\cdot)\) \(\chi_{3525}(934,\cdot)\) \(\chi_{3525}(979,\cdot)\) \(\chi_{3525}(1009,\cdot)\) \(\chi_{3525}(1039,\cdot)\) \(\chi_{3525}(1054,\cdot)\) \(\chi_{3525}(1069,\cdot)\) \(\chi_{3525}(1114,\cdot)\) \(\chi_{3525}(1159,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{45}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{121}{230}\right)\) | \(e\left(\frac{57}{230}\right)\) | \(e\left(\frac{99}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{51}{230}\right)\) |