Basic properties
Modulus: | \(8100\) | |
Conductor: | \(2025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(540\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2025}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.dr
\(\chi_{8100}(77,\cdot)\) \(\chi_{8100}(113,\cdot)\) \(\chi_{8100}(137,\cdot)\) \(\chi_{8100}(173,\cdot)\) \(\chi_{8100}(317,\cdot)\) \(\chi_{8100}(353,\cdot)\) \(\chi_{8100}(437,\cdot)\) \(\chi_{8100}(473,\cdot)\) \(\chi_{8100}(497,\cdot)\) \(\chi_{8100}(533,\cdot)\) \(\chi_{8100}(617,\cdot)\) \(\chi_{8100}(653,\cdot)\) \(\chi_{8100}(677,\cdot)\) \(\chi_{8100}(713,\cdot)\) \(\chi_{8100}(797,\cdot)\) \(\chi_{8100}(833,\cdot)\) \(\chi_{8100}(977,\cdot)\) \(\chi_{8100}(1013,\cdot)\) \(\chi_{8100}(1037,\cdot)\) \(\chi_{8100}(1073,\cdot)\) \(\chi_{8100}(1217,\cdot)\) \(\chi_{8100}(1253,\cdot)\) \(\chi_{8100}(1337,\cdot)\) \(\chi_{8100}(1373,\cdot)\) \(\chi_{8100}(1397,\cdot)\) \(\chi_{8100}(1433,\cdot)\) \(\chi_{8100}(1517,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{540})$ |
Fixed field: | Number field defined by a degree 540 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((1,e\left(\frac{29}{54}\right),e\left(\frac{1}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8100 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{211}{270}\right)\) | \(e\left(\frac{133}{540}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{247}{540}\right)\) | \(e\left(\frac{131}{135}\right)\) | \(e\left(\frac{19}{135}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{179}{270}\right)\) |