Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(346,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cx
\(\chi_{8034}(31,\cdot)\) \(\chi_{8034}(73,\cdot)\) \(\chi_{8034}(655,\cdot)\) \(\chi_{8034}(811,\cdot)\) \(\chi_{8034}(1555,\cdot)\) \(\chi_{8034}(1981,\cdot)\) \(\chi_{8034}(2257,\cdot)\) \(\chi_{8034}(2293,\cdot)\) \(\chi_{8034}(2335,\cdot)\) \(\chi_{8034}(2449,\cdot)\) \(\chi_{8034}(2803,\cdot)\) \(\chi_{8034}(3385,\cdot)\) \(\chi_{8034}(3505,\cdot)\) \(\chi_{8034}(3541,\cdot)\) \(\chi_{8034}(3739,\cdot)\) \(\chi_{8034}(3853,\cdot)\) \(\chi_{8034}(4009,\cdot)\) \(\chi_{8034}(4363,\cdot)\) \(\chi_{8034}(4399,\cdot)\) \(\chi_{8034}(4519,\cdot)\) \(\chi_{8034}(5689,\cdot)\) \(\chi_{8034}(5881,\cdot)\) \(\chi_{8034}(6001,\cdot)\) \(\chi_{8034}(6157,\cdot)\) \(\chi_{8034}(6583,\cdot)\) \(\chi_{8034}(6661,\cdot)\) \(\chi_{8034}(7093,\cdot)\) \(\chi_{8034}(7129,\cdot)\) \(\chi_{8034}(7249,\cdot)\) \(\chi_{8034}(7561,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,i,e\left(\frac{31}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(4363, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{19}{34}\right)\) |