Basic properties
Modulus: | \(2695\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.cf
\(\chi_{2695}(36,\cdot)\) \(\chi_{2695}(71,\cdot)\) \(\chi_{2695}(141,\cdot)\) \(\chi_{2695}(421,\cdot)\) \(\chi_{2695}(456,\cdot)\) \(\chi_{2695}(526,\cdot)\) \(\chi_{2695}(631,\cdot)\) \(\chi_{2695}(806,\cdot)\) \(\chi_{2695}(841,\cdot)\) \(\chi_{2695}(911,\cdot)\) \(\chi_{2695}(1016,\cdot)\) \(\chi_{2695}(1191,\cdot)\) \(\chi_{2695}(1296,\cdot)\) \(\chi_{2695}(1401,\cdot)\) \(\chi_{2695}(1576,\cdot)\) \(\chi_{2695}(1611,\cdot)\) \(\chi_{2695}(1681,\cdot)\) \(\chi_{2695}(1786,\cdot)\) \(\chi_{2695}(1996,\cdot)\) \(\chi_{2695}(2066,\cdot)\) \(\chi_{2695}(2171,\cdot)\) \(\chi_{2695}(2346,\cdot)\) \(\chi_{2695}(2381,\cdot)\) \(\chi_{2695}(2556,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((2157,1816,981)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 2695 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) |