Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(12,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.gb
\(\chi_{9800}(257,\cdot)\) \(\chi_{9800}(593,\cdot)\) \(\chi_{9800}(857,\cdot)\) \(\chi_{9800}(1193,\cdot)\) \(\chi_{9800}(1657,\cdot)\) \(\chi_{9800}(1993,\cdot)\) \(\chi_{9800}(2257,\cdot)\) \(\chi_{9800}(2593,\cdot)\) \(\chi_{9800}(3393,\cdot)\) \(\chi_{9800}(3993,\cdot)\) \(\chi_{9800}(4457,\cdot)\) \(\chi_{9800}(4793,\cdot)\) \(\chi_{9800}(5057,\cdot)\) \(\chi_{9800}(5393,\cdot)\) \(\chi_{9800}(5857,\cdot)\) \(\chi_{9800}(6457,\cdot)\) \(\chi_{9800}(7257,\cdot)\) \(\chi_{9800}(7593,\cdot)\) \(\chi_{9800}(7857,\cdot)\) \(\chi_{9800}(8193,\cdot)\) \(\chi_{9800}(8657,\cdot)\) \(\chi_{9800}(8993,\cdot)\) \(\chi_{9800}(9257,\cdot)\) \(\chi_{9800}(9593,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((7351,4901,1177,5001)\) → \((1,1,i,e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(257, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |