Basic properties
Modulus: | \(9126\) | |
Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1521}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9126.cj
\(\chi_{9126}(127,\cdot)\) \(\chi_{9126}(199,\cdot)\) \(\chi_{9126}(829,\cdot)\) \(\chi_{9126}(901,\cdot)\) \(\chi_{9126}(1531,\cdot)\) \(\chi_{9126}(1603,\cdot)\) \(\chi_{9126}(2233,\cdot)\) \(\chi_{9126}(2305,\cdot)\) \(\chi_{9126}(2935,\cdot)\) \(\chi_{9126}(3007,\cdot)\) \(\chi_{9126}(3637,\cdot)\) \(\chi_{9126}(3709,\cdot)\) \(\chi_{9126}(4339,\cdot)\) \(\chi_{9126}(4411,\cdot)\) \(\chi_{9126}(5041,\cdot)\) \(\chi_{9126}(5113,\cdot)\) \(\chi_{9126}(5743,\cdot)\) \(\chi_{9126}(5815,\cdot)\) \(\chi_{9126}(6517,\cdot)\) \(\chi_{9126}(7147,\cdot)\) \(\chi_{9126}(7219,\cdot)\) \(\chi_{9126}(7849,\cdot)\) \(\chi_{9126}(8551,\cdot)\) \(\chi_{9126}(8623,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,3889)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 9126 }(8623, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) |