Basic properties
Modulus: | \(4008\) | |
Conductor: | \(167\) | 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 \(\chi_{167}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4008.z
\(\chi_{4008}(73,\cdot)\) \(\chi_{4008}(145,\cdot)\) \(\chi_{4008}(193,\cdot)\) \(\chi_{4008}(241,\cdot)\) \(\chi_{4008}(313,\cdot)\) \(\chi_{4008}(385,\cdot)\) \(\chi_{4008}(457,\cdot)\) \(\chi_{4008}(553,\cdot)\) \(\chi_{4008}(649,\cdot)\) \(\chi_{4008}(673,\cdot)\) \(\chi_{4008}(721,\cdot)\) \(\chi_{4008}(769,\cdot)\) \(\chi_{4008}(793,\cdot)\) \(\chi_{4008}(817,\cdot)\) \(\chi_{4008}(865,\cdot)\) \(\chi_{4008}(913,\cdot)\) \(\chi_{4008}(937,\cdot)\) \(\chi_{4008}(1057,\cdot)\) \(\chi_{4008}(1081,\cdot)\) \(\chi_{4008}(1105,\cdot)\) \(\chi_{4008}(1153,\cdot)\) \(\chi_{4008}(1249,\cdot)\) \(\chi_{4008}(1273,\cdot)\) \(\chi_{4008}(1441,\cdot)\) \(\chi_{4008}(1465,\cdot)\) \(\chi_{4008}(1489,\cdot)\) \(\chi_{4008}(1513,\cdot)\) \(\chi_{4008}(1537,\cdot)\) \(\chi_{4008}(1585,\cdot)\) \(\chi_{4008}(1609,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,2005,1337,673)\) → \((1,1,1,e\left(\frac{93}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4008 }(1537, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{117}{166}\right)\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{41}{83}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{10}{83}\right)\) | \(e\left(\frac{3}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) |