Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.di
\(\chi_{8034}(157,\cdot)\) \(\chi_{8034}(703,\cdot)\) \(\chi_{8034}(859,\cdot)\) \(\chi_{8034}(1015,\cdot)\) \(\chi_{8034}(1795,\cdot)\) \(\chi_{8034}(2341,\cdot)\) \(\chi_{8034}(2653,\cdot)\) \(\chi_{8034}(2731,\cdot)\) \(\chi_{8034}(3199,\cdot)\) \(\chi_{8034}(3277,\cdot)\) \(\chi_{8034}(3589,\cdot)\) \(\chi_{8034}(3667,\cdot)\) \(\chi_{8034}(3823,\cdot)\) \(\chi_{8034}(3979,\cdot)\) \(\chi_{8034}(4057,\cdot)\) \(\chi_{8034}(4369,\cdot)\) \(\chi_{8034}(4525,\cdot)\) \(\chi_{8034}(4603,\cdot)\) \(\chi_{8034}(4759,\cdot)\) \(\chi_{8034}(4837,\cdot)\) \(\chi_{8034}(4915,\cdot)\) \(\chi_{8034}(5227,\cdot)\) \(\chi_{8034}(5773,\cdot)\) \(\chi_{8034}(6163,\cdot)\) \(\chi_{8034}(6397,\cdot)\) \(\chi_{8034}(6865,\cdot)\) \(\chi_{8034}(7177,\cdot)\) \(\chi_{8034}(7255,\cdot)\) \(\chi_{8034}(7333,\cdot)\) \(\chi_{8034}(7567,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,1,e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(5773, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{5}{102}\right)\) |