Basic properties
| Modulus: | \(4900\) | |
| 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 \(\chi_{1225}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4900.df
\(\chi_{4900}(13,\cdot)\) \(\chi_{4900}(153,\cdot)\) \(\chi_{4900}(237,\cdot)\) \(\chi_{4900}(377,\cdot)\) \(\chi_{4900}(433,\cdot)\) \(\chi_{4900}(517,\cdot)\) \(\chi_{4900}(573,\cdot)\) \(\chi_{4900}(713,\cdot)\) \(\chi_{4900}(797,\cdot)\) \(\chi_{4900}(853,\cdot)\) \(\chi_{4900}(937,\cdot)\) \(\chi_{4900}(1133,\cdot)\) \(\chi_{4900}(1217,\cdot)\) \(\chi_{4900}(1413,\cdot)\) \(\chi_{4900}(1497,\cdot)\) \(\chi_{4900}(1553,\cdot)\) \(\chi_{4900}(1637,\cdot)\) \(\chi_{4900}(1777,\cdot)\) \(\chi_{4900}(1833,\cdot)\) \(\chi_{4900}(1917,\cdot)\) \(\chi_{4900}(1973,\cdot)\) \(\chi_{4900}(2113,\cdot)\) \(\chi_{4900}(2197,\cdot)\) \(\chi_{4900}(2337,\cdot)\) \(\chi_{4900}(2477,\cdot)\) \(\chi_{4900}(2533,\cdot)\) \(\chi_{4900}(2617,\cdot)\) \(\chi_{4900}(2673,\cdot)\) \(\chi_{4900}(2813,\cdot)\) \(\chi_{4900}(2897,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((1,e\left(\frac{19}{20}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 4900 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) |