Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9800.gj
\(\chi_{9800}(153,\cdot)\) \(\chi_{9800}(377,\cdot)\) \(\chi_{9800}(433,\cdot)\) \(\chi_{9800}(713,\cdot)\) \(\chi_{9800}(937,\cdot)\) \(\chi_{9800}(1217,\cdot)\) \(\chi_{9800}(1497,\cdot)\) \(\chi_{9800}(1553,\cdot)\) \(\chi_{9800}(1777,\cdot)\) \(\chi_{9800}(1833,\cdot)\) \(\chi_{9800}(2113,\cdot)\) \(\chi_{9800}(2337,\cdot)\) \(\chi_{9800}(2617,\cdot)\) \(\chi_{9800}(2673,\cdot)\) \(\chi_{9800}(2897,\cdot)\) \(\chi_{9800}(2953,\cdot)\) \(\chi_{9800}(3177,\cdot)\) \(\chi_{9800}(3513,\cdot)\) \(\chi_{9800}(3737,\cdot)\) \(\chi_{9800}(4073,\cdot)\) \(\chi_{9800}(4297,\cdot)\) \(\chi_{9800}(4353,\cdot)\) \(\chi_{9800}(4577,\cdot)\) \(\chi_{9800}(4633,\cdot)\) \(\chi_{9800}(4913,\cdot)\) \(\chi_{9800}(5137,\cdot)\) \(\chi_{9800}(5417,\cdot)\) \(\chi_{9800}(5473,\cdot)\) \(\chi_{9800}(5697,\cdot)\) \(\chi_{9800}(5753,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((7351,4901,1177,5001)\) → \((1,1,e\left(\frac{7}{20}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) |