Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(620,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cr
\(\chi_{8034}(367,\cdot)\) \(\chi_{8034}(445,\cdot)\) \(\chi_{8034}(757,\cdot)\) \(\chi_{8034}(1225,\cdot)\) \(\chi_{8034}(1459,\cdot)\) \(\chi_{8034}(1777,\cdot)\) \(\chi_{8034}(1849,\cdot)\) \(\chi_{8034}(2089,\cdot)\) \(\chi_{8034}(2635,\cdot)\) \(\chi_{8034}(2785,\cdot)\) \(\chi_{8034}(2863,\cdot)\) \(\chi_{8034}(3019,\cdot)\) \(\chi_{8034}(3097,\cdot)\) \(\chi_{8034}(3337,\cdot)\) \(\chi_{8034}(3415,\cdot)\) \(\chi_{8034}(3565,\cdot)\) \(\chi_{8034}(3643,\cdot)\) \(\chi_{8034}(3727,\cdot)\) \(\chi_{8034}(3799,\cdot)\) \(\chi_{8034}(3805,\cdot)\) \(\chi_{8034}(4351,\cdot)\) \(\chi_{8034}(4663,\cdot)\) \(\chi_{8034}(4891,\cdot)\) \(\chi_{8034}(5209,\cdot)\) \(\chi_{8034}(6145,\cdot)\) \(\chi_{8034}(6301,\cdot)\) \(\chi_{8034}(6607,\cdot)\) \(\chi_{8034}(6847,\cdot)\) \(\chi_{8034}(7315,\cdot)\) \(\chi_{8034}(7471,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{22}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(7315, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{25}{51}\right)\) |