Basic properties
Modulus: | \(4008\) | |
Conductor: | \(1336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1336}(229,\cdot)\) | 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 4008.bb
\(\chi_{4008}(61,\cdot)\) \(\chi_{4008}(85,\cdot)\) \(\chi_{4008}(133,\cdot)\) \(\chi_{4008}(157,\cdot)\) \(\chi_{4008}(181,\cdot)\) \(\chi_{4008}(205,\cdot)\) \(\chi_{4008}(229,\cdot)\) \(\chi_{4008}(397,\cdot)\) \(\chi_{4008}(421,\cdot)\) \(\chi_{4008}(517,\cdot)\) \(\chi_{4008}(565,\cdot)\) \(\chi_{4008}(589,\cdot)\) \(\chi_{4008}(613,\cdot)\) \(\chi_{4008}(733,\cdot)\) \(\chi_{4008}(757,\cdot)\) \(\chi_{4008}(805,\cdot)\) \(\chi_{4008}(853,\cdot)\) \(\chi_{4008}(877,\cdot)\) \(\chi_{4008}(901,\cdot)\) \(\chi_{4008}(949,\cdot)\) \(\chi_{4008}(997,\cdot)\) \(\chi_{4008}(1021,\cdot)\) \(\chi_{4008}(1117,\cdot)\) \(\chi_{4008}(1213,\cdot)\) \(\chi_{4008}(1285,\cdot)\) \(\chi_{4008}(1357,\cdot)\) \(\chi_{4008}(1429,\cdot)\) \(\chi_{4008}(1477,\cdot)\) \(\chi_{4008}(1525,\cdot)\) \(\chi_{4008}(1597,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,-1,1,e\left(\frac{65}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{42}{83}\right)\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{44}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{40}{83}\right)\) |