Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | 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 \(\chi_{4725}(2041,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.fk
\(\chi_{9450}(121,\cdot)\) \(\chi_{9450}(781,\cdot)\) \(\chi_{9450}(1381,\cdot)\) \(\chi_{9450}(1411,\cdot)\) \(\chi_{9450}(2011,\cdot)\) \(\chi_{9450}(2041,\cdot)\) \(\chi_{9450}(2641,\cdot)\) \(\chi_{9450}(2671,\cdot)\) \(\chi_{9450}(3271,\cdot)\) \(\chi_{9450}(3931,\cdot)\) \(\chi_{9450}(4531,\cdot)\) \(\chi_{9450}(4561,\cdot)\) \(\chi_{9450}(5161,\cdot)\) \(\chi_{9450}(5191,\cdot)\) \(\chi_{9450}(5791,\cdot)\) \(\chi_{9450}(5821,\cdot)\) \(\chi_{9450}(6421,\cdot)\) \(\chi_{9450}(7081,\cdot)\) \(\chi_{9450}(7681,\cdot)\) \(\chi_{9450}(7711,\cdot)\) \(\chi_{9450}(8311,\cdot)\) \(\chi_{9450}(8341,\cdot)\) \(\chi_{9450}(8941,\cdot)\) \(\chi_{9450}(8971,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{1}{5}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(2041, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) |