Basic properties
Modulus: | \(4851\) | |
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 \(\chi_{539}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4851.do
\(\chi_{4851}(64,\cdot)\) \(\chi_{4851}(190,\cdot)\) \(\chi_{4851}(379,\cdot)\) \(\chi_{4851}(631,\cdot)\) \(\chi_{4851}(757,\cdot)\) \(\chi_{4851}(1072,\cdot)\) \(\chi_{4851}(1450,\cdot)\) \(\chi_{4851}(1576,\cdot)\) \(\chi_{4851}(2017,\cdot)\) \(\chi_{4851}(2143,\cdot)\) \(\chi_{4851}(2269,\cdot)\) \(\chi_{4851}(2458,\cdot)\) \(\chi_{4851}(2710,\cdot)\) \(\chi_{4851}(2836,\cdot)\) \(\chi_{4851}(2962,\cdot)\) \(\chi_{4851}(3151,\cdot)\) \(\chi_{4851}(3403,\cdot)\) \(\chi_{4851}(3655,\cdot)\) \(\chi_{4851}(3844,\cdot)\) \(\chi_{4851}(4096,\cdot)\) \(\chi_{4851}(4222,\cdot)\) \(\chi_{4851}(4348,\cdot)\) \(\chi_{4851}(4537,\cdot)\) \(\chi_{4851}(4789,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((4313,199,442)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 4851 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{35}\right)\) |