Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4017}(3299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dw
\(\chi_{8034}(95,\cdot)\) \(\chi_{8034}(485,\cdot)\) \(\chi_{8034}(1349,\cdot)\) \(\chi_{8034}(1967,\cdot)\) \(\chi_{8034}(2051,\cdot)\) \(\chi_{8034}(2129,\cdot)\) \(\chi_{8034}(2597,\cdot)\) \(\chi_{8034}(2669,\cdot)\) \(\chi_{8034}(2747,\cdot)\) \(\chi_{8034}(3215,\cdot)\) \(\chi_{8034}(3299,\cdot)\) \(\chi_{8034}(3533,\cdot)\) \(\chi_{8034}(3917,\cdot)\) \(\chi_{8034}(4151,\cdot)\) \(\chi_{8034}(4157,\cdot)\) \(\chi_{8034}(4313,\cdot)\) \(\chi_{8034}(4775,\cdot)\) \(\chi_{8034}(4931,\cdot)\) \(\chi_{8034}(5483,\cdot)\) \(\chi_{8034}(5795,\cdot)\) \(\chi_{8034}(5951,\cdot)\) \(\chi_{8034}(6101,\cdot)\) \(\chi_{8034}(6413,\cdot)\) \(\chi_{8034}(6569,\cdot)\) \(\chi_{8034}(6887,\cdot)\) \(\chi_{8034}(7043,\cdot)\) \(\chi_{8034}(7355,\cdot)\) \(\chi_{8034}(7505,\cdot)\) \(\chi_{8034}(7511,\cdot)\) \(\chi_{8034}(7661,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{13}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3299, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{73}{102}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{4}{51}\right)\) |