Basic properties
Modulus: | \(4017\) | |
Conductor: | \(103\) | 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 \(\chi_{103}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.dr
\(\chi_{4017}(40,\cdot)\) \(\chi_{4017}(157,\cdot)\) \(\chi_{4017}(352,\cdot)\) \(\chi_{4017}(508,\cdot)\) \(\chi_{4017}(586,\cdot)\) \(\chi_{4017}(703,\cdot)\) \(\chi_{4017}(742,\cdot)\) \(\chi_{4017}(820,\cdot)\) \(\chi_{4017}(859,\cdot)\) \(\chi_{4017}(898,\cdot)\) \(\chi_{4017}(1015,\cdot)\) \(\chi_{4017}(1210,\cdot)\) \(\chi_{4017}(1756,\cdot)\) \(\chi_{4017}(1795,\cdot)\) \(\chi_{4017}(2146,\cdot)\) \(\chi_{4017}(2341,\cdot)\) \(\chi_{4017}(2380,\cdot)\) \(\chi_{4017}(2653,\cdot)\) \(\chi_{4017}(2731,\cdot)\) \(\chi_{4017}(2848,\cdot)\) \(\chi_{4017}(3160,\cdot)\) \(\chi_{4017}(3199,\cdot)\) \(\chi_{4017}(3238,\cdot)\) \(\chi_{4017}(3277,\cdot)\) \(\chi_{4017}(3316,\cdot)\) \(\chi_{4017}(3550,\cdot)\) \(\chi_{4017}(3589,\cdot)\) \(\chi_{4017}(3667,\cdot)\) \(\chi_{4017}(3706,\cdot)\) \(\chi_{4017}(3823,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,1,e\left(\frac{1}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 4017 }(1756, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) |