Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.du
\(\chi_{8034}(43,\cdot)\) \(\chi_{8034}(589,\cdot)\) \(\chi_{8034}(829,\cdot)\) \(\chi_{8034}(901,\cdot)\) \(\chi_{8034}(1219,\cdot)\) \(\chi_{8034}(1453,\cdot)\) \(\chi_{8034}(1921,\cdot)\) \(\chi_{8034}(2233,\cdot)\) \(\chi_{8034}(2311,\cdot)\) \(\chi_{8034}(2935,\cdot)\) \(\chi_{8034}(3007,\cdot)\) \(\chi_{8034}(3241,\cdot)\) \(\chi_{8034}(3397,\cdot)\) \(\chi_{8034}(3865,\cdot)\) \(\chi_{8034}(4105,\cdot)\) \(\chi_{8034}(4411,\cdot)\) \(\chi_{8034}(4567,\cdot)\) \(\chi_{8034}(5503,\cdot)\) \(\chi_{8034}(5821,\cdot)\) \(\chi_{8034}(6049,\cdot)\) \(\chi_{8034}(6361,\cdot)\) \(\chi_{8034}(6907,\cdot)\) \(\chi_{8034}(6913,\cdot)\) \(\chi_{8034}(6985,\cdot)\) \(\chi_{8034}(7069,\cdot)\) \(\chi_{8034}(7147,\cdot)\) \(\chi_{8034}(7297,\cdot)\) \(\chi_{8034}(7375,\cdot)\) \(\chi_{8034}(7615,\cdot)\) \(\chi_{8034}(7693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{77}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{11}{102}\right)\) |