Basic properties
Modulus: | \(8100\) | |
Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2700}(2471,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.cs
\(\chi_{8100}(71,\cdot)\) \(\chi_{8100}(611,\cdot)\) \(\chi_{8100}(791,\cdot)\) \(\chi_{8100}(1331,\cdot)\) \(\chi_{8100}(1691,\cdot)\) \(\chi_{8100}(1871,\cdot)\) \(\chi_{8100}(2231,\cdot)\) \(\chi_{8100}(2411,\cdot)\) \(\chi_{8100}(2771,\cdot)\) \(\chi_{8100}(3311,\cdot)\) \(\chi_{8100}(3491,\cdot)\) \(\chi_{8100}(4031,\cdot)\) \(\chi_{8100}(4391,\cdot)\) \(\chi_{8100}(4571,\cdot)\) \(\chi_{8100}(4931,\cdot)\) \(\chi_{8100}(5111,\cdot)\) \(\chi_{8100}(5471,\cdot)\) \(\chi_{8100}(6011,\cdot)\) \(\chi_{8100}(6191,\cdot)\) \(\chi_{8100}(6731,\cdot)\) \(\chi_{8100}(7091,\cdot)\) \(\chi_{8100}(7271,\cdot)\) \(\chi_{8100}(7631,\cdot)\) \(\chi_{8100}(7811,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4051,6401,7777)\) → \((-1,e\left(\frac{17}{18}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8100 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{41}{90}\right)\) |