Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | 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 \(\chi_{3549}(1265,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dc
\(\chi_{7098}(101,\cdot)\) \(\chi_{7098}(173,\cdot)\) \(\chi_{7098}(647,\cdot)\) \(\chi_{7098}(719,\cdot)\) \(\chi_{7098}(1193,\cdot)\) \(\chi_{7098}(1265,\cdot)\) \(\chi_{7098}(1739,\cdot)\) \(\chi_{7098}(1811,\cdot)\) \(\chi_{7098}(2285,\cdot)\) \(\chi_{7098}(2357,\cdot)\) \(\chi_{7098}(2831,\cdot)\) \(\chi_{7098}(2903,\cdot)\) \(\chi_{7098}(3377,\cdot)\) \(\chi_{7098}(3449,\cdot)\) \(\chi_{7098}(3923,\cdot)\) \(\chi_{7098}(3995,\cdot)\) \(\chi_{7098}(4469,\cdot)\) \(\chi_{7098}(5015,\cdot)\) \(\chi_{7098}(5087,\cdot)\) \(\chi_{7098}(5561,\cdot)\) \(\chi_{7098}(5633,\cdot)\) \(\chi_{7098}(6179,\cdot)\) \(\chi_{7098}(6653,\cdot)\) \(\chi_{7098}(6725,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{43}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(1265, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) |