Basic properties
Modulus: | \(9075\) | |
Conductor: | \(9075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.fz
\(\chi_{9075}(53,\cdot)\) \(\chi_{9075}(377,\cdot)\) \(\chi_{9075}(467,\cdot)\) \(\chi_{9075}(488,\cdot)\) \(\chi_{9075}(533,\cdot)\) \(\chi_{9075}(587,\cdot)\) \(\chi_{9075}(647,\cdot)\) \(\chi_{9075}(773,\cdot)\) \(\chi_{9075}(878,\cdot)\) \(\chi_{9075}(1202,\cdot)\) \(\chi_{9075}(1292,\cdot)\) \(\chi_{9075}(1313,\cdot)\) \(\chi_{9075}(1472,\cdot)\) \(\chi_{9075}(1598,\cdot)\) \(\chi_{9075}(2027,\cdot)\) \(\chi_{9075}(2117,\cdot)\) \(\chi_{9075}(2183,\cdot)\) \(\chi_{9075}(2237,\cdot)\) \(\chi_{9075}(2297,\cdot)\) \(\chi_{9075}(2528,\cdot)\) \(\chi_{9075}(2852,\cdot)\) \(\chi_{9075}(2942,\cdot)\) \(\chi_{9075}(2963,\cdot)\) \(\chi_{9075}(3008,\cdot)\) \(\chi_{9075}(3062,\cdot)\) \(\chi_{9075}(3122,\cdot)\) \(\chi_{9075}(3248,\cdot)\) \(\chi_{9075}(3353,\cdot)\) \(\chi_{9075}(3677,\cdot)\) \(\chi_{9075}(3767,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{53}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 9075 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{59}{220}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) |