Basic properties
Modulus: | \(6422\) | |
Conductor: | \(169\) | 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 \(\chi_{169}(153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cp
\(\chi_{6422}(153,\cdot)\) \(\chi_{6422}(381,\cdot)\) \(\chi_{6422}(647,\cdot)\) \(\chi_{6422}(875,\cdot)\) \(\chi_{6422}(1141,\cdot)\) \(\chi_{6422}(1369,\cdot)\) \(\chi_{6422}(1635,\cdot)\) \(\chi_{6422}(1863,\cdot)\) \(\chi_{6422}(2129,\cdot)\) \(\chi_{6422}(2357,\cdot)\) \(\chi_{6422}(2623,\cdot)\) \(\chi_{6422}(3117,\cdot)\) \(\chi_{6422}(3345,\cdot)\) \(\chi_{6422}(3611,\cdot)\) \(\chi_{6422}(3839,\cdot)\) \(\chi_{6422}(4105,\cdot)\) \(\chi_{6422}(4333,\cdot)\) \(\chi_{6422}(4599,\cdot)\) \(\chi_{6422}(4827,\cdot)\) \(\chi_{6422}(5321,\cdot)\) \(\chi_{6422}(5587,\cdot)\) \(\chi_{6422}(5815,\cdot)\) \(\chi_{6422}(6081,\cdot)\) \(\chi_{6422}(6309,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{41}{78}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 6422 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{6}{13}\right)\) |