Basic properties
Modulus: | \(6004\) | |
Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1501}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.du
\(\chi_{6004}(69,\cdot)\) \(\chi_{6004}(373,\cdot)\) \(\chi_{6004}(673,\cdot)\) \(\chi_{6004}(981,\cdot)\) \(\chi_{6004}(1133,\cdot)\) \(\chi_{6004}(1281,\cdot)\) \(\chi_{6004}(1357,\cdot)\) \(\chi_{6004}(1437,\cdot)\) \(\chi_{6004}(1513,\cdot)\) \(\chi_{6004}(1965,\cdot)\) \(\chi_{6004}(2269,\cdot)\) \(\chi_{6004}(2273,\cdot)\) \(\chi_{6004}(2349,\cdot)\) \(\chi_{6004}(2877,\cdot)\) \(\chi_{6004}(3029,\cdot)\) \(\chi_{6004}(3333,\cdot)\) \(\chi_{6004}(3409,\cdot)\) \(\chi_{6004}(4021,\cdot)\) \(\chi_{6004}(4169,\cdot)\) \(\chi_{6004}(4245,\cdot)\) \(\chi_{6004}(4781,\cdot)\) \(\chi_{6004}(5389,\cdot)\) \(\chi_{6004}(5465,\cdot)\) \(\chi_{6004}(5917,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{9}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) |