Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(577,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dq
\(\chi_{8007}(577,\cdot)\) \(\chi_{8007}(832,\cdot)\) \(\chi_{8007}(1291,\cdot)\) \(\chi_{8007}(1903,\cdot)\) \(\chi_{8007}(2005,\cdot)\) \(\chi_{8007}(2209,\cdot)\) \(\chi_{8007}(2311,\cdot)\) \(\chi_{8007}(2464,\cdot)\) \(\chi_{8007}(3229,\cdot)\) \(\chi_{8007}(3484,\cdot)\) \(\chi_{8007}(3535,\cdot)\) \(\chi_{8007}(3586,\cdot)\) \(\chi_{8007}(3892,\cdot)\) \(\chi_{8007}(4810,\cdot)\) \(\chi_{8007}(5014,\cdot)\) \(\chi_{8007}(5218,\cdot)\) \(\chi_{8007}(5983,\cdot)\) \(\chi_{8007}(6238,\cdot)\) \(\chi_{8007}(6289,\cdot)\) \(\chi_{8007}(6646,\cdot)\) \(\chi_{8007}(6748,\cdot)\) \(\chi_{8007}(7105,\cdot)\) \(\chi_{8007}(7819,\cdot)\) \(\chi_{8007}(7921,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5339,1414,7855)\) → \((1,-1,e\left(\frac{11}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(577, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) |