Basic properties
Modulus: | \(9800\) | |
Conductor: | \(1960\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1960}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.gc
\(\chi_{9800}(107,\cdot)\) \(\chi_{9800}(443,\cdot)\) \(\chi_{9800}(907,\cdot)\) \(\chi_{9800}(1507,\cdot)\) \(\chi_{9800}(2307,\cdot)\) \(\chi_{9800}(2643,\cdot)\) \(\chi_{9800}(2907,\cdot)\) \(\chi_{9800}(3243,\cdot)\) \(\chi_{9800}(3707,\cdot)\) \(\chi_{9800}(4043,\cdot)\) \(\chi_{9800}(4307,\cdot)\) \(\chi_{9800}(4643,\cdot)\) \(\chi_{9800}(5107,\cdot)\) \(\chi_{9800}(5443,\cdot)\) \(\chi_{9800}(5707,\cdot)\) \(\chi_{9800}(6043,\cdot)\) \(\chi_{9800}(6507,\cdot)\) \(\chi_{9800}(6843,\cdot)\) \(\chi_{9800}(7107,\cdot)\) \(\chi_{9800}(7443,\cdot)\) \(\chi_{9800}(8243,\cdot)\) \(\chi_{9800}(8843,\cdot)\) \(\chi_{9800}(9307,\cdot)\) \(\chi_{9800}(9643,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,-1,i,e\left(\frac{1}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 9800 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) |