Basic properties
Modulus: | \(3525\) | |
Conductor: | \(3525\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 3525.bm
\(\chi_{3525}(11,\cdot)\) \(\chi_{3525}(41,\cdot)\) \(\chi_{3525}(86,\cdot)\) \(\chi_{3525}(116,\cdot)\) \(\chi_{3525}(146,\cdot)\) \(\chi_{3525}(161,\cdot)\) \(\chi_{3525}(221,\cdot)\) \(\chi_{3525}(266,\cdot)\) \(\chi_{3525}(311,\cdot)\) \(\chi_{3525}(386,\cdot)\) \(\chi_{3525}(416,\cdot)\) \(\chi_{3525}(446,\cdot)\) \(\chi_{3525}(461,\cdot)\) \(\chi_{3525}(536,\cdot)\) \(\chi_{3525}(641,\cdot)\) \(\chi_{3525}(656,\cdot)\) \(\chi_{3525}(671,\cdot)\) \(\chi_{3525}(716,\cdot)\) \(\chi_{3525}(731,\cdot)\) \(\chi_{3525}(746,\cdot)\) \(\chi_{3525}(791,\cdot)\) \(\chi_{3525}(821,\cdot)\) \(\chi_{3525}(866,\cdot)\) \(\chi_{3525}(881,\cdot)\) \(\chi_{3525}(971,\cdot)\) \(\chi_{3525}(1016,\cdot)\) \(\chi_{3525}(1031,\cdot)\) \(\chi_{3525}(1091,\cdot)\) \(\chi_{3525}(1121,\cdot)\) \(\chi_{3525}(1166,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{7}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{230}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{27}{230}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{201}{230}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{57}{230}\right)\) |