Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 1225.bd
\(\chi_{1225}(36,\cdot)\) \(\chi_{1225}(71,\cdot)\) \(\chi_{1225}(106,\cdot)\) \(\chi_{1225}(141,\cdot)\) \(\chi_{1225}(211,\cdot)\) \(\chi_{1225}(281,\cdot)\) \(\chi_{1225}(316,\cdot)\) \(\chi_{1225}(386,\cdot)\) \(\chi_{1225}(421,\cdot)\) \(\chi_{1225}(456,\cdot)\) \(\chi_{1225}(561,\cdot)\) \(\chi_{1225}(596,\cdot)\) \(\chi_{1225}(631,\cdot)\) \(\chi_{1225}(666,\cdot)\) \(\chi_{1225}(771,\cdot)\) \(\chi_{1225}(806,\cdot)\) \(\chi_{1225}(841,\cdot)\) \(\chi_{1225}(911,\cdot)\) \(\chi_{1225}(946,\cdot)\) \(\chi_{1225}(1016,\cdot)\) \(\chi_{1225}(1086,\cdot)\) \(\chi_{1225}(1121,\cdot)\) \(\chi_{1225}(1156,\cdot)\) \(\chi_{1225}(1191,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(386, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) |