Basic properties
Modulus: | \(4332\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4332.bo
\(\chi_{4332}(25,\cdot)\) \(\chi_{4332}(61,\cdot)\) \(\chi_{4332}(73,\cdot)\) \(\chi_{4332}(85,\cdot)\) \(\chi_{4332}(157,\cdot)\) \(\chi_{4332}(169,\cdot)\) \(\chi_{4332}(253,\cdot)\) \(\chi_{4332}(289,\cdot)\) \(\chi_{4332}(301,\cdot)\) \(\chi_{4332}(313,\cdot)\) \(\chi_{4332}(385,\cdot)\) \(\chi_{4332}(397,\cdot)\) \(\chi_{4332}(481,\cdot)\) \(\chi_{4332}(517,\cdot)\) \(\chi_{4332}(529,\cdot)\) \(\chi_{4332}(541,\cdot)\) \(\chi_{4332}(613,\cdot)\) \(\chi_{4332}(625,\cdot)\) \(\chi_{4332}(709,\cdot)\) \(\chi_{4332}(745,\cdot)\) \(\chi_{4332}(757,\cdot)\) \(\chi_{4332}(769,\cdot)\) \(\chi_{4332}(841,\cdot)\) \(\chi_{4332}(853,\cdot)\) \(\chi_{4332}(937,\cdot)\) \(\chi_{4332}(973,\cdot)\) \(\chi_{4332}(985,\cdot)\) \(\chi_{4332}(997,\cdot)\) \(\chi_{4332}(1069,\cdot)\) \(\chi_{4332}(1081,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((2167,1445,3973)\) → \((1,1,e\left(\frac{61}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4332 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{46}{171}\right)\) |