Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4017}(2789,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.em
\(\chi_{8034}(137,\cdot)\) \(\chi_{8034}(167,\cdot)\) \(\chi_{8034}(215,\cdot)\) \(\chi_{8034}(323,\cdot)\) \(\chi_{8034}(587,\cdot)\) \(\chi_{8034}(821,\cdot)\) \(\chi_{8034}(917,\cdot)\) \(\chi_{8034}(1163,\cdot)\) \(\chi_{8034}(1259,\cdot)\) \(\chi_{8034}(1415,\cdot)\) \(\chi_{8034}(1523,\cdot)\) \(\chi_{8034}(1553,\cdot)\) \(\chi_{8034}(1709,\cdot)\) \(\chi_{8034}(1727,\cdot)\) \(\chi_{8034}(1991,\cdot)\) \(\chi_{8034}(2021,\cdot)\) \(\chi_{8034}(2069,\cdot)\) \(\chi_{8034}(2177,\cdot)\) \(\chi_{8034}(2399,\cdot)\) \(\chi_{8034}(2771,\cdot)\) \(\chi_{8034}(2789,\cdot)\) \(\chi_{8034}(2897,\cdot)\) \(\chi_{8034}(2945,\cdot)\) \(\chi_{8034}(3053,\cdot)\) \(\chi_{8034}(3113,\cdot)\) \(\chi_{8034}(3257,\cdot)\) \(\chi_{8034}(3269,\cdot)\) \(\chi_{8034}(3413,\cdot)\) \(\chi_{8034}(3581,\cdot)\) \(\chi_{8034}(3677,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{5}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(2789, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{53}{204}\right)\) | \(e\left(\frac{175}{204}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{23}{204}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{31}{102}\right)\) |