Basic properties
Modulus: | \(8034\) | |
Conductor: | \(309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{309}(86,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dt
\(\chi_{8034}(53,\cdot)\) \(\chi_{8034}(521,\cdot)\) \(\chi_{8034}(599,\cdot)\) \(\chi_{8034}(911,\cdot)\) \(\chi_{8034}(989,\cdot)\) \(\chi_{8034}(1145,\cdot)\) \(\chi_{8034}(1301,\cdot)\) \(\chi_{8034}(1379,\cdot)\) \(\chi_{8034}(1691,\cdot)\) \(\chi_{8034}(1847,\cdot)\) \(\chi_{8034}(1925,\cdot)\) \(\chi_{8034}(2081,\cdot)\) \(\chi_{8034}(2159,\cdot)\) \(\chi_{8034}(2237,\cdot)\) \(\chi_{8034}(2549,\cdot)\) \(\chi_{8034}(3095,\cdot)\) \(\chi_{8034}(3485,\cdot)\) \(\chi_{8034}(3719,\cdot)\) \(\chi_{8034}(4187,\cdot)\) \(\chi_{8034}(4499,\cdot)\) \(\chi_{8034}(4577,\cdot)\) \(\chi_{8034}(4655,\cdot)\) \(\chi_{8034}(4889,\cdot)\) \(\chi_{8034}(5045,\cdot)\) \(\chi_{8034}(5201,\cdot)\) \(\chi_{8034}(5513,\cdot)\) \(\chi_{8034}(6059,\cdot)\) \(\chi_{8034}(6215,\cdot)\) \(\chi_{8034}(6371,\cdot)\) \(\chi_{8034}(7151,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,1,e\left(\frac{19}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3485, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{22}{51}\right)\) |