Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4725}(2833,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hg
\(\chi_{9450}(187,\cdot)\) \(\chi_{9450}(283,\cdot)\) \(\chi_{9450}(313,\cdot)\) \(\chi_{9450}(787,\cdot)\) \(\chi_{9450}(817,\cdot)\) \(\chi_{9450}(913,\cdot)\) \(\chi_{9450}(1417,\cdot)\) \(\chi_{9450}(1447,\cdot)\) \(\chi_{9450}(1573,\cdot)\) \(\chi_{9450}(2047,\cdot)\) \(\chi_{9450}(2077,\cdot)\) \(\chi_{9450}(2173,\cdot)\) \(\chi_{9450}(2203,\cdot)\) \(\chi_{9450}(2677,\cdot)\) \(\chi_{9450}(2803,\cdot)\) \(\chi_{9450}(2833,\cdot)\) \(\chi_{9450}(3337,\cdot)\) \(\chi_{9450}(3433,\cdot)\) \(\chi_{9450}(3463,\cdot)\) \(\chi_{9450}(3937,\cdot)\) \(\chi_{9450}(3967,\cdot)\) \(\chi_{9450}(4063,\cdot)\) \(\chi_{9450}(4567,\cdot)\) \(\chi_{9450}(4597,\cdot)\) \(\chi_{9450}(4723,\cdot)\) \(\chi_{9450}(5197,\cdot)\) \(\chi_{9450}(5227,\cdot)\) \(\chi_{9450}(5323,\cdot)\) \(\chi_{9450}(5353,\cdot)\) \(\chi_{9450}(5827,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{3}{20}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(2833, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{17}{36}\right)\) |