Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(441,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.cv
\(\chi_{8018}(441,\cdot)\) \(\chi_{8018}(1403,\cdot)\) \(\chi_{8018}(1467,\cdot)\) \(\chi_{8018}(1771,\cdot)\) \(\chi_{8018}(2049,\cdot)\) \(\chi_{8018}(2247,\cdot)\) \(\chi_{8018}(2455,\cdot)\) \(\chi_{8018}(2893,\cdot)\) \(\chi_{8018}(2973,\cdot)\) \(\chi_{8018}(3265,\cdot)\) \(\chi_{8018}(3513,\cdot)\) \(\chi_{8018}(3999,\cdot)\) \(\chi_{8018}(4109,\cdot)\) \(\chi_{8018}(4159,\cdot)\) \(\chi_{8018}(4303,\cdot)\) \(\chi_{8018}(4661,\cdot)\) \(\chi_{8018}(4987,\cdot)\) \(\chi_{8018}(5375,\cdot)\) \(\chi_{8018}(5507,\cdot)\) \(\chi_{8018}(5687,\cdot)\) \(\chi_{8018}(5991,\cdot)\) \(\chi_{8018}(6351,\cdot)\) \(\chi_{8018}(6675,\cdot)\) \(\chi_{8018}(7617,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{11}{15}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(441, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) |