LMFDB - Embedded newform 1895.1.d.i.1894.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1895,1,Mod(1894,1895)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1895, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1895.1894");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1895 = 5 \cdot 379 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1895.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$0.945728198940$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{48})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 1 $ x^8 - 8x^6 + 20x^4 - 16*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{24}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{24} - \cdots)$

Embedding invariants

Embedding label			1894.7
Root			$-1.58671$ of defining polynomial
Character	$\chi$	$=$	1895.1894

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.58671 q^{2} +1.98289 q^{3} +1.51764 q^{4} -1.00000 q^{5} +3.14626 q^{6} -1.21752 q^{7} +0.821340 q^{8} +2.93185 q^{9} +O(q^{10})$	\(q+1.58671 q^{2} +1.98289 q^{3} +1.51764 q^{4} -1.00000 q^{5} +3.14626 q^{6} -1.21752 q^{7} +0.821340 q^{8} +2.93185 q^{9} -1.58671 q^{10} +3.00931 q^{12} -0.261052 q^{13} -1.93185 q^{14} -1.98289 q^{15} -0.214413 q^{16} -1.84776 q^{17} +4.65199 q^{18} +1.00000 q^{19} -1.51764 q^{20} -2.41421 q^{21} +1.62863 q^{24} +1.00000 q^{25} -0.414214 q^{26} +3.83065 q^{27} -1.84776 q^{28} -3.14626 q^{30} -1.16155 q^{32} -2.93185 q^{34} +1.21752 q^{35} +4.44949 q^{36} +1.58671 q^{38} -0.517638 q^{39} -0.821340 q^{40} -1.73205 q^{41} -3.83065 q^{42} +0.261052 q^{43} -2.93185 q^{45} +0.765367 q^{47} -0.425157 q^{48} +0.482362 q^{49} +1.58671 q^{50} -3.66390 q^{51} -0.396183 q^{52} -1.58671 q^{53} +6.07812 q^{54} -1.00000 q^{56} +1.98289 q^{57} -3.00931 q^{60} -3.56960 q^{63} -1.62863 q^{64} +0.261052 q^{65} -2.80423 q^{68} +1.93185 q^{70} +2.40805 q^{72} -0.765367 q^{73} +1.98289 q^{75} +1.51764 q^{76} -0.821340 q^{78} +1.41421 q^{79} +0.214413 q^{80} +4.66390 q^{81} -2.74826 q^{82} -3.66390 q^{84} +1.84776 q^{85} +0.414214 q^{86} -4.65199 q^{90} +0.317837 q^{91} +1.21441 q^{94} -1.00000 q^{95} -2.30323 q^{96} +0.765367 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{5} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^5 + 8 * q^9	$ 8 q + 8 q^{4} - 8 q^{5} + 8 q^{9} + 8 q^{16} + 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{24} + 8 q^{25} + 8 q^{26} - 8 q^{34} + 16 q^{36} - 8 q^{45} + 8 q^{49} + 8 q^{54} - 8 q^{56} + 8 q^{64} + 8 q^{76} - 8 q^{80} + 8 q^{81} - 8 q^{86} - 8 q^{95} - 24 q^{96}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^5 + 8 * q^9 + 8 * q^16 + 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^24 + 8 * q^25 + 8 * q^26 - 8 * q^34 + 16 * q^36 - 8 * q^45 + 8 * q^49 + 8 * q^54 - 8 * q^56 + 8 * q^64 + 8 * q^76 - 8 * q^80 + 8 * q^81 - 8 * q^86 - 8 * q^95 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1895\mathbb{Z}\right)^\times$.

$n$	$381$	$1517$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$2$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$3$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$3$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$4$	1.51764	1.51764
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	3.14626	3.14626
$7$	−1.21752	−1.21752	−0.608761	−	0.793353i	$-0.708333\pi$
$7$	−1.21752	−1.21752	−0.608761	+	0.793353i	$0.708333\pi$
$8$	0.821340	0.821340
$9$	2.93185	2.93185
$10$	−1.58671	−1.58671
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	3.00931	3.00931
$13$	−0.261052	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$13$	−0.261052	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$14$	−1.93185	−1.93185
$15$	−1.98289	−1.98289
$16$	−0.214413	−0.214413
$17$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$17$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$18$	4.65199	4.65199
$19$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$19$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$20$	−1.51764	−1.51764
$21$	−2.41421	−2.41421
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	1.62863	1.62863
$25$	1.00000	1.00000
$26$	−0.414214	−0.414214
$27$	3.83065	3.83065
$28$	−1.84776	−1.84776
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	−3.14626	−3.14626
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−1.16155	−1.16155
$33$	0	0
$34$	−2.93185	−2.93185
$35$	1.21752	1.21752
$36$	4.44949	4.44949
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	1.58671	1.58671
$39$	−0.517638	−0.517638
$40$	−0.821340	−0.821340
$41$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$41$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$42$	−3.83065	−3.83065
$43$	0.261052	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$43$	0.261052	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$44$	0	0
$45$	−2.93185	−2.93185
$46$	0	0
$47$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$47$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$48$	−0.425157	−0.425157
$49$	0.482362	0.482362
$50$	1.58671	1.58671
$51$	−3.66390	−3.66390
$52$	−0.396183	−0.396183
$53$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$53$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$54$	6.07812	6.07812
$55$	0	0
$56$	−1.00000	−1.00000
$57$	1.98289	1.98289
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−3.00931	−3.00931
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	−3.56960	−3.56960
$64$	−1.62863	−1.62863
$65$	0.261052	0.261052
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−2.80423	−2.80423
$69$	0	0
$70$	1.93185	1.93185
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	2.40805	2.40805
$73$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$73$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$74$	0	0
$75$	1.98289	1.98289
$76$	1.51764	1.51764
$77$	0	0
$78$	−0.821340	−0.821340
$79$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$79$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$80$	0.214413	0.214413
$81$	4.66390	4.66390
$82$	−2.74826	−2.74826
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−3.66390	−3.66390
$85$	1.84776	1.84776
$86$	0.414214	0.414214
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	−4.65199	−4.65199
$91$	0.317837	0.317837
$92$	0	0
$93$	0	0
$94$	1.21441	1.21441
$95$	−1.00000	−1.00000
$96$	−2.30323	−2.30323
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0.765367	0.765367
$99$	0	0
$100$	1.51764	1.51764
$101$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$101$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$102$	−5.81354	−5.81354
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−0.214413	−0.214413
$105$	2.41421	2.41421
$106$	−2.51764	−2.51764
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	5.81354	5.81354
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0.261052	0.261052
$113$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$113$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$114$	3.14626	3.14626
$115$	0	0
$116$	0	0
$117$	−0.765367	−0.765367
$118$	0	0
$119$	2.24969	2.24969
$120$	−1.62863	−1.62863
$121$	1.00000	1.00000
$122$	0	0
$123$	−3.43447	−3.43447
$124$	0	0
$125$	−1.00000	−1.00000
$126$	−5.66390	−5.66390
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.42260	−1.42260
$129$	0.517638	0.517638
$130$	0.414214	0.414214
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	−1.21752	−1.21752
$134$	0	0
$135$	−3.83065	−3.83065
$136$	−1.51764	−1.51764
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$140$	1.84776	1.84776
$141$	1.51764	1.51764
$142$	0	0
$143$	0	0
$144$	−0.628626	−0.628626
$145$	0	0
$146$	−1.21441	−1.21441
$147$	0.956470	0.956470
$148$	0	0
$149$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$149$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$150$	3.14626	3.14626
$151$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$151$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$152$	0.821340	0.821340
$153$	−5.41736	−5.41736
$154$	0	0
$155$	0	0
$156$	−0.785587	−0.785587
$157$	1.21752	1.21752	0.608761	−	0.793353i	$-0.291667\pi$
$157$	1.21752	1.21752	0.608761	+	0.793353i	$0.291667\pi$
$158$	2.24394	2.24394
$159$	−3.14626	−3.14626
$160$	1.16155	1.16155
$161$	0	0
$162$	7.40025	7.40025
$163$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$163$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$164$	−2.62863	−2.62863
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	−1.98289	−1.98289
$169$	−0.931852	−0.931852
$170$	2.93185	2.93185
$171$	2.93185	2.93185
$172$	0.396183	0.396183
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−1.21752	−1.21752
$176$	0	0
$177$	0	0
$178$	0	0
$179$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$179$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$180$	−4.44949	−4.44949
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0.504314	0.504314
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	1.16155	1.16155
$189$	−4.66390	−4.66390
$190$	−1.58671	−1.58671
$191$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$191$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$192$	−3.22939	−3.22939
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0.517638	0.517638
$196$	0.732051	0.732051
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0.821340	0.821340
$201$	0	0
$202$	2.24394	2.24394
$203$	0	0
$204$	−5.56048	−5.56048
$205$	1.73205	1.73205
$206$	0	0
$207$	0	0
$208$	0.0559730	0.0559730
$209$	0	0
$210$	3.83065	3.83065
$211$	1.93185	1.93185	0.965926	−	0.258819i	$-0.0833333\pi$
$211$	1.93185	1.93185	0.965926	+	0.258819i	$0.0833333\pi$
$212$	−2.40805	−2.40805
$213$	0	0
$214$	0	0
$215$	−0.261052	−0.261052
$216$	3.14626	3.14626
$217$	0	0
$218$	0	0
$219$	−1.51764	−1.51764
$220$	0	0
$221$	0.482362	0.482362
$222$	0	0
$223$	1.21752	1.21752	0.608761	−	0.793353i	$-0.291667\pi$
$223$	1.21752	1.21752	0.608761	+	0.793353i	$0.291667\pi$
$224$	1.41421	1.41421
$225$	2.93185	2.93185
$226$	2.93185	2.93185
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	3.00931	3.00931
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$233$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$234$	−1.21441	−1.21441
$235$	−0.765367	−0.765367
$236$	0	0
$237$	2.80423	2.80423
$238$	3.56960	3.56960
$239$	1.93185	1.93185	0.965926	−	0.258819i	$-0.0833333\pi$
$239$	1.93185	1.93185	0.965926	+	0.258819i	$0.0833333\pi$
$240$	0.425157	0.425157
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	1.58671	1.58671
$243$	5.41736	5.41736
$244$	0	0
$245$	−0.482362	−0.482362
$246$	−5.44949	−5.44949
$247$	−0.261052	−0.261052
$248$	0	0
$249$	0	0
$250$	−1.58671	−1.58671
$251$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$251$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$252$	−5.41736	−5.41736
$253$	0	0
$254$	0	0
$255$	3.66390	3.66390
$256$	−0.628626	−0.628626
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0.821340	0.821340
$259$	0	0
$260$	0.396183	0.396183
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	1.58671	1.58671
$266$	−1.93185	−1.93185
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−6.07812	−6.07812
$271$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$272$	0.396183	0.396183
$273$	0.630236	0.630236
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	−1.58671	−1.58671
$279$	0	0
$280$	1.00000	1.00000
$281$	0.517638	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$281$	0.517638	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$282$	2.40805	2.40805
$283$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$283$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$284$	0	0
$285$	−1.98289	−1.98289
$286$	0	0
$287$	2.10881	2.10881
$288$	−3.40549	−3.40549
$289$	2.41421	2.41421
$290$	0	0
$291$	0	0
$292$	−1.16155	−1.16155
$293$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$293$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$294$	1.51764	1.51764
$295$	0	0
$296$	0	0
$297$	0	0
$298$	2.74826	2.74826
$299$	0	0
$300$	3.00931	3.00931
$301$	−0.317837	−0.317837
$302$	−3.06528	−3.06528
$303$	2.80423	2.80423
$304$	−0.214413	−0.214413
$305$	0	0
$306$	−8.59575	−8.59575
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$311$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$312$	−0.425157	−0.425157
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	1.93185	1.93185
$315$	3.56960	3.56960
$316$	2.14626	2.14626
$317$	−1.21752	−1.21752	−0.608761	−	0.793353i	$-0.708333\pi$
$317$	−1.21752	−1.21752	−0.608761	+	0.793353i	$0.708333\pi$
$318$	−4.99220	−4.99220
$319$	0	0
$320$	1.62863	1.62863
$321$	0	0
$322$	0	0
$323$	−1.84776	−1.84776
$324$	7.07812	7.07812
$325$	−0.261052	−0.261052
$326$	1.21441	1.21441
$327$	0	0
$328$	−1.42260	−1.42260
$329$	−0.931852	−0.931852
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0.517638	0.517638
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−1.47858	−1.47858
$339$	3.66390	3.66390
$340$	2.80423	2.80423
$341$	0	0
$342$	4.65199	4.65199
$343$	0.630236	0.630236
$344$	0.214413	0.214413
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−1.93185	−1.93185
$351$	−1.00000	−1.00000
$352$	0	0
$353$	−1.21752	−1.21752	−0.608761	−	0.793353i	$-0.708333\pi$
$353$	−1.21752	−1.21752	−0.608761	+	0.793353i	$0.708333\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	4.46088	4.46088
$358$	2.24394	2.24394
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−2.40805	−2.40805
$361$	0	0
$362$	0	0
$363$	1.98289	1.98289
$364$	0.482362	0.482362
$365$	0.765367	0.765367
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	−5.07812	−5.07812
$370$	0	0
$371$	1.93185	1.93185
$372$	0	0
$373$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$373$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$374$	0	0
$375$	−1.98289	−1.98289
$376$	0.628626	0.628626
$377$	0	0
$378$	−7.40025	−7.40025
$379$	−1.00000	−1.00000
$379$	−1.00000	−1.00000
$380$	−1.51764	−1.51764
$381$	0	0
$382$	−2.24394	−2.24394
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−2.82086	−2.82086
$385$	0	0
$386$	0	0
$387$	0.765367	0.765367
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0.821340	0.821340
$391$	0	0
$392$	0.396183	0.396183
$393$	0	0
$394$	0	0
$395$	−1.41421	−1.41421
$396$	0	0
$397$	0.261052	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$397$	0.261052	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$398$	0	0
$399$	−2.41421	−2.41421
$400$	−0.214413	−0.214413
$401$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$401$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$402$	0	0
$403$	0	0
$404$	2.14626	2.14626
$405$	−4.66390	−4.66390
$406$	0	0
$407$	0	0
$408$	−3.00931	−3.00931
$409$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$409$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$410$	2.74826	2.74826
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0.303225	0.303225
$417$	−1.98289	−1.98289
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	3.66390	3.66390
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	3.06528	3.06528
$423$	2.24394	2.24394
$424$	−1.30323	−1.30323
$425$	−1.84776	−1.84776
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	−0.414214	−0.414214
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−0.821340	−0.821340
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	−2.40805	−2.40805
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	1.41421	1.41421
$442$	0.765367	0.765367
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	1.93185	1.93185
$447$	3.43447	3.43447
$448$	1.98289	1.98289
$449$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$450$	4.65199	4.65199
$451$	0	0
$452$	2.80423	2.80423
$453$	−3.83065	−3.83065
$454$	0	0
$455$	−0.317837	−0.317837
$456$	1.62863	1.62863
$457$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$457$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$458$	0	0
$459$	−7.07812	−7.07812
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	−3.14626	−3.14626
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	−1.16155	−1.16155
$469$	0	0
$470$	−1.21441	−1.21441
$471$	2.41421	2.41421
$472$	0	0
$473$	0	0
$474$	4.44949	4.44949
$475$	1.00000	1.00000
$476$	3.41421	3.41421
$477$	−4.65199	−4.65199
$478$	3.06528	3.06528
$479$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$479$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$480$	2.30323	2.30323
$481$	0	0
$482$	0	0
$483$	0	0
$484$	1.51764	1.51764
$485$	0	0
$486$	8.59575	8.59575
$487$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$487$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$488$	0	0
$489$	1.51764	1.51764
$490$	−0.765367	−0.765367
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	−5.21228	−5.21228
$493$	0	0
$494$	−0.414214	−0.414214
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$499$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$500$	−1.51764	−1.51764
$501$	0	0
$502$	−0.821340	−0.821340
$503$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$503$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$504$	−2.93185	−2.93185
$505$	−1.41421	−1.41421
$506$	0	0
$507$	−1.84776	−1.84776
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	5.81354	5.81354
$511$	0.931852	0.931852
$512$	0.425157	0.425157
$513$	3.83065	3.83065
$514$	0	0
$515$	0	0
$516$	0.785587	0.785587
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0.214413	0.214413
$521$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$521$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−2.41421	−2.41421
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	1.00000
$530$	2.51764	2.51764
$531$	0	0
$532$	−1.84776	−1.84776
$533$	0.452156	0.452156
$534$	0	0
$535$	0	0
$536$	0	0
$537$	2.80423	2.80423
$538$	0	0
$539$	0	0
$540$	−5.81354	−5.81354
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	−2.74826	−2.74826
$543$	0	0
$544$	2.14626	2.14626
$545$	0	0
$546$	1.00000	1.00000
$547$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$547$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−1.72184	−1.72184
$554$	0	0
$555$	0	0
$556$	−1.51764	−1.51764
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−0.0681483	−0.0681483
$560$	−0.261052	−0.261052
$561$	0	0
$562$	0.821340	0.821340
$563$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$563$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$564$	2.30323	2.30323
$565$	−1.84776	−1.84776
$566$	−2.93185	−2.93185
$567$	−5.67841	−5.67841
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	−3.14626	−3.14626
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	−2.80423	−2.80423
$574$	3.34607	3.34607
$575$	0	0
$576$	−4.77489	−4.77489
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	3.83065	3.83065
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	−0.628626	−0.628626
$585$	0.765367	0.765367
$586$	−3.14626	−3.14626
$587$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$587$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$588$	1.45158	1.45158
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$593$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$594$	0	0
$595$	−2.24969	−2.24969
$596$	2.62863	2.62863
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	1.62863	1.62863
$601$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$601$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$602$	−0.504314	−0.504314
$603$	0	0
$604$	−2.93185	−2.93185
$605$	−1.00000	−1.00000
$606$	4.44949	4.44949
$607$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$607$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$608$	−1.16155	−1.16155
$609$	0	0
$610$	0	0
$611$	−0.199801	−0.199801
$612$	−8.22159	−8.22159
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	3.43447	3.43447
$616$	0	0
$617$	−0.261052	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$617$	−0.261052	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	−3.06528	−3.06528
$623$	0	0
$624$	0.110988	0.110988
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	1.84776	1.84776
$629$	0	0
$630$	5.66390	5.66390
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	1.16155	1.16155
$633$	3.83065	3.83065
$634$	−1.93185	−1.93185
$635$	0	0
$636$	−4.77489	−4.77489
$637$	−0.125922	−0.125922
$638$	0	0
$639$	0	0
$640$	1.42260	1.42260
$641$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$641$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$642$	0	0
$643$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$643$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$644$	0	0
$645$	−0.517638	−0.517638
$646$	−2.93185	−2.93185
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	3.83065	3.83065
$649$	0	0
$650$	−0.414214	−0.414214
$651$	0	0
$652$	1.16155	1.16155
$653$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$653$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$654$	0	0
$655$	0	0
$656$	0.371374	0.371374
$657$	−2.24394	−2.24394
$658$	−1.47858	−1.47858
$659$	0.517638	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$659$	0.517638	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0.956470	0.956470
$664$	0	0
$665$	1.21752	1.21752
$666$	0	0
$667$	0	0
$668$	0	0
$669$	2.41421	2.41421
$670$	0	0
$671$	0	0
$672$	2.80423	2.80423
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	3.83065	3.83065
$676$	−1.41421	−1.41421
$677$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$677$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$678$	5.81354	5.81354
$679$	0	0
$680$	1.51764	1.51764
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	4.44949	4.44949
$685$	0	0
$686$	1.00000	1.00000
$687$	0	0
$688$	−0.0559730	−0.0559730
$689$	0.414214	0.414214
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	1.00000	1.00000
$696$	0	0
$697$	3.20041	3.20041
$698$	0	0
$699$	−3.93185	−3.93185
$700$	−1.84776	−1.84776
$701$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$701$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$702$	−1.58671	−1.58671
$703$	0	0
$704$	0	0
$705$	−1.51764	−1.51764
$706$	−1.93185	−1.93185
$707$	−1.72184	−1.72184
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	4.14626	4.14626
$712$	0	0
$713$	0	0
$714$	7.07812	7.07812
$715$	0	0
$716$	2.14626	2.14626
$717$	3.83065	3.83065
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0.628626	0.628626
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	3.14626	3.14626
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0.261052	0.261052
$729$	6.07812	6.07812
$730$	1.21441	1.21441
$731$	−0.482362	−0.482362
$732$	0	0
$733$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$733$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$734$	0	0
$735$	−0.956470	−0.956470
$736$	0	0
$737$	0	0
$738$	−8.05748	−8.05748
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	−0.517638	−0.517638
$742$	3.06528	3.06528
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	−1.73205	−1.73205
$746$	2.51764	2.51764
$747$	0	0
$748$	0	0
$749$	0	0
$750$	−3.14626	−3.14626
$751$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$751$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$752$	−0.164104	−0.164104
$753$	−1.02642	−1.02642
$754$	0	0
$755$	1.93185	1.93185
$756$	−7.07812	−7.07812
$757$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$757$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$758$	−1.58671	−1.58671
$759$	0	0
$760$	−0.821340	−0.821340
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	−2.14626	−2.14626
$765$	5.41736	5.41736
$766$	0	0
$767$	0	0
$768$	−1.24650	−1.24650
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	1.21752	1.21752	0.608761	−	0.793353i	$-0.291667\pi$
$773$	1.21752	1.21752	0.608761	+	0.793353i	$0.291667\pi$
$774$	1.21441	1.21441
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−1.73205	−1.73205
$780$	0.785587	0.785587
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−0.103425	−0.103425
$785$	−1.21752	−1.21752
$786$	0	0
$787$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$787$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$788$	0	0
$789$	0	0
$790$	−2.24394	−2.24394
$791$	−2.24969	−2.24969
$792$	0	0
$793$	0	0
$794$	0.414214	0.414214
$795$	3.14626	3.14626
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	−3.83065	−3.83065
$799$	−1.41421	−1.41421
$800$	−1.16155	−1.16155
$801$	0	0
$802$	−2.24394	−2.24394
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	1.16155	1.16155
$809$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$809$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$810$	−7.40025	−7.40025
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	−3.43447	−3.43447
$814$	0	0
$815$	−0.765367	−0.765367
$816$	0.785587	0.785587
$817$	0.261052	0.261052
$818$	2.74826	2.74826
$819$	0.931852	0.931852
$820$	2.62863	2.62863
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$823$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$827$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0.425157	0.425157
$833$	−0.891289	−0.891289
$834$	−3.14626	−3.14626
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	1.98289	1.98289
$841$	1.00000	1.00000
$842$	0	0
$843$	1.02642	1.02642
$844$	2.93185	2.93185
$845$	0.931852	0.931852
$846$	3.56048	3.56048
$847$	−1.21752	−1.21752
$848$	0.340210	0.340210
$849$	−3.66390	−3.66390
$850$	−2.93185	−2.93185
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	−2.93185	−2.93185
$856$	0	0
$857$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$857$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	−0.396183	−0.396183
$861$	4.18154	4.18154
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	−4.44949	−4.44949
$865$	0	0
$866$	0	0
$867$	4.78712	4.78712
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	1.21752	1.21752
$876$	−2.30323	−2.30323
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	−3.93185	−3.93185
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	2.24394	2.24394
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0.732051	0.732051
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	1.84776	1.84776
$893$	0.765367	0.765367
$894$	5.44949	5.44949
$895$	−1.41421	−1.41421
$896$	1.73205	1.73205
$897$	0	0
$898$	−1.58671	−1.58671
$899$	0	0
$900$	4.44949	4.44949
$901$	2.93185	2.93185
$902$	0	0
$903$	−0.630236	−0.630236
$904$	1.51764	1.51764
$905$	0	0
$906$	−6.07812	−6.07812
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	4.14626	4.14626
$910$	−0.504314	−0.504314
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	−0.425157	−0.425157
$913$	0	0
$914$	−2.51764	−2.51764
$915$	0	0
$916$	0	0
$917$	0	0
$918$	−11.2309	−11.2309
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$929$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$930$	0	0
$931$	0.482362	0.482362
$932$	−3.00931	−3.00931
$933$	−3.83065	−3.83065
$934$	0	0
$935$	0	0
$936$	−0.628626	−0.628626
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	−1.16155	−1.16155
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	3.83065	3.83065
$943$	0	0
$944$	0	0
$945$	4.66390	4.66390
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	4.25581	4.25581
$949$	0.199801	0.199801
$950$	1.58671	1.58671
$951$	−2.41421	−2.41421
$952$	1.84776	1.84776
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	−7.38134	−7.38134
$955$	1.41421	1.41421
$956$	2.93185	2.93185
$957$	0	0
$958$	1.58671	1.58671
$959$	0	0
$960$	3.22939	3.22939
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$967$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$968$	0.821340	0.821340
$969$	−3.66390	−3.66390
$970$	0	0
$971$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$972$	8.22159	8.22159
$973$	1.21752	1.21752
$974$	−1.21441	−1.21441
$975$	−0.517638	−0.517638
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	2.40805	2.40805
$979$	0	0
$980$	−0.732051	−0.732051
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	−2.82086	−2.82086
$985$	0	0
$986$	0	0
$987$	−1.84776	−1.84776
$988$	−0.396183	−0.396183
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	−0.821340	−0.821340
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1895.1.d.i.1894.7	yes	8
5.4	even	2	inner	1895.1.d.i.1894.2	✓	8
379.378	odd	2	inner	1895.1.d.i.1894.2	✓	8
1895.1894	odd	2	CM	1895.1.d.i.1894.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1895.1.d.i.1894.2	✓	8	5.4	even	2	inner
1895.1.d.i.1894.2	✓	8	379.378	odd	2	inner
1895.1.d.i.1894.7	yes	8	1.1	even	1	trivial
1895.1.d.i.1894.7	yes	8	1895.1894	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1895 = 5 \cdot 379 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1895.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.58671 q^{2} +1.98289 q^{3} +1.51764 q^{4} -1.00000 q^{5} +3.14626 q^{6} -1.21752 q^{7} +0.821340 q^{8} +2.93185 q^{9} +O(q^{10})\)	\(q+1.58671 q^{2} +1.98289 q^{3} +1.51764 q^{4} -1.00000 q^{5} +3.14626 q^{6} -1.21752 q^{7} +0.821340 q^{8} +2.93185 q^{9} -1.58671 q^{10} +3.00931 q^{12} -0.261052 q^{13} -1.93185 q^{14} -1.98289 q^{15} -0.214413 q^{16} -1.84776 q^{17} +4.65199 q^{18} +1.00000 q^{19} -1.51764 q^{20} -2.41421 q^{21} +1.62863 q^{24} +1.00000 q^{25} -0.414214 q^{26} +3.83065 q^{27} -1.84776 q^{28} -3.14626 q^{30} -1.16155 q^{32} -2.93185 q^{34} +1.21752 q^{35} +4.44949 q^{36} +1.58671 q^{38} -0.517638 q^{39} -0.821340 q^{40} -1.73205 q^{41} -3.83065 q^{42} +0.261052 q^{43} -2.93185 q^{45} +0.765367 q^{47} -0.425157 q^{48} +0.482362 q^{49} +1.58671 q^{50} -3.66390 q^{51} -0.396183 q^{52} -1.58671 q^{53} +6.07812 q^{54} -1.00000 q^{56} +1.98289 q^{57} -3.00931 q^{60} -3.56960 q^{63} -1.62863 q^{64} +0.261052 q^{65} -2.80423 q^{68} +1.93185 q^{70} +2.40805 q^{72} -0.765367 q^{73} +1.98289 q^{75} +1.51764 q^{76} -0.821340 q^{78} +1.41421 q^{79} +0.214413 q^{80} +4.66390 q^{81} -2.74826 q^{82} -3.66390 q^{84} +1.84776 q^{85} +0.414214 q^{86} -4.65199 q^{90} +0.317837 q^{91} +1.21441 q^{94} -1.00000 q^{95} -2.30323 q^{96} +0.765367 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{5} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^5 + 8 * q^9	\( 8 q + 8 q^{4} - 8 q^{5} + 8 q^{9} + 8 q^{16} + 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{24} + 8 q^{25} + 8 q^{26} - 8 q^{34} + 16 q^{36} - 8 q^{45} + 8 q^{49} + 8 q^{54} - 8 q^{56} + 8 q^{64} + 8 q^{76} - 8 q^{80} + 8 q^{81} - 8 q^{86} - 8 q^{95} - 24 q^{96}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^5 + 8 * q^9 + 8 * q^16 + 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^24 + 8 * q^25 + 8 * q^26 - 8 * q^34 + 16 * q^36 - 8 * q^45 + 8 * q^49 + 8 * q^54 - 8 * q^56 + 8 * q^64 + 8 * q^76 - 8 * q^80 + 8 * q^81 - 8 * q^86 - 8 * q^95 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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