Basic properties
Modulus: | \(5390\) | |
Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2695}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5390.cr
\(\chi_{5390}(169,\cdot)\) \(\chi_{5390}(379,\cdot)\) \(\chi_{5390}(449,\cdot)\) \(\chi_{5390}(729,\cdot)\) \(\chi_{5390}(939,\cdot)\) \(\chi_{5390}(1149,\cdot)\) \(\chi_{5390}(1219,\cdot)\) \(\chi_{5390}(1499,\cdot)\) \(\chi_{5390}(1709,\cdot)\) \(\chi_{5390}(1919,\cdot)\) \(\chi_{5390}(1989,\cdot)\) \(\chi_{5390}(2269,\cdot)\) \(\chi_{5390}(2479,\cdot)\) \(\chi_{5390}(2689,\cdot)\) \(\chi_{5390}(2759,\cdot)\) \(\chi_{5390}(3249,\cdot)\) \(\chi_{5390}(3459,\cdot)\) \(\chi_{5390}(3809,\cdot)\) \(\chi_{5390}(4229,\cdot)\) \(\chi_{5390}(4299,\cdot)\) \(\chi_{5390}(4579,\cdot)\) \(\chi_{5390}(4789,\cdot)\) \(\chi_{5390}(5069,\cdot)\) \(\chi_{5390}(5349,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,4511,981)\) → \((-1,e\left(\frac{4}{7}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5390 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{70}\right)\) |