Basic properties
| Modulus: | \(2450\) | |
| 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 \(\chi_{1225}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bp
\(\chi_{2450}(13,\cdot)\) \(\chi_{2450}(27,\cdot)\) \(\chi_{2450}(83,\cdot)\) \(\chi_{2450}(153,\cdot)\) \(\chi_{2450}(167,\cdot)\) \(\chi_{2450}(223,\cdot)\) \(\chi_{2450}(237,\cdot)\) \(\chi_{2450}(363,\cdot)\) \(\chi_{2450}(377,\cdot)\) \(\chi_{2450}(433,\cdot)\) \(\chi_{2450}(447,\cdot)\) \(\chi_{2450}(503,\cdot)\) \(\chi_{2450}(517,\cdot)\) \(\chi_{2450}(573,\cdot)\) \(\chi_{2450}(713,\cdot)\) \(\chi_{2450}(727,\cdot)\) \(\chi_{2450}(797,\cdot)\) \(\chi_{2450}(853,\cdot)\) \(\chi_{2450}(867,\cdot)\) \(\chi_{2450}(923,\cdot)\) \(\chi_{2450}(937,\cdot)\) \(\chi_{2450}(1063,\cdot)\) \(\chi_{2450}(1133,\cdot)\) \(\chi_{2450}(1147,\cdot)\) \(\chi_{2450}(1203,\cdot)\) \(\chi_{2450}(1217,\cdot)\) \(\chi_{2450}(1287,\cdot)\) \(\chi_{2450}(1413,\cdot)\) \(\chi_{2450}(1427,\cdot)\) \(\chi_{2450}(1483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 2450 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) |