LMFDB - Embedded newform 1895.1.d.i.1894.1

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			1894.1
Root			$1.98289$ 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)

$f(q)$	$=$	$q-1.98289 q^{2} +1.58671 q^{3} +2.93185 q^{4} -1.00000 q^{5} -3.14626 q^{6} +0.261052 q^{7} -3.83065 q^{8} +1.51764 q^{9} +O(q^{10})$	\(q-1.98289 q^{2} +1.58671 q^{3} +2.93185 q^{4} -1.00000 q^{5} -3.14626 q^{6} +0.261052 q^{7} -3.83065 q^{8} +1.51764 q^{9} +1.98289 q^{10} +4.65199 q^{12} -1.21752 q^{13} -0.517638 q^{14} -1.58671 q^{15} +4.66390 q^{16} +0.765367 q^{17} -3.00931 q^{18} +1.00000 q^{19} -2.93185 q^{20} +0.414214 q^{21} -6.07812 q^{24} +1.00000 q^{25} +2.41421 q^{26} +0.821340 q^{27} +0.765367 q^{28} +3.14626 q^{30} -5.41736 q^{32} -1.51764 q^{34} -0.261052 q^{35} +4.44949 q^{36} -1.98289 q^{38} -1.93185 q^{39} +3.83065 q^{40} +1.73205 q^{41} -0.821340 q^{42} +1.21752 q^{43} -1.51764 q^{45} +1.84776 q^{47} +7.40025 q^{48} -0.931852 q^{49} -1.98289 q^{50} +1.21441 q^{51} -3.56960 q^{52} +1.98289 q^{53} -1.62863 q^{54} -1.00000 q^{56} +1.58671 q^{57} -4.65199 q^{60} +0.396183 q^{63} +6.07812 q^{64} +1.21752 q^{65} +2.24394 q^{68} +0.517638 q^{70} -5.81354 q^{72} -1.84776 q^{73} +1.58671 q^{75} +2.93185 q^{76} +3.83065 q^{78} -1.41421 q^{79} -4.66390 q^{80} -0.214413 q^{81} -3.43447 q^{82} +1.21441 q^{84} -0.765367 q^{85} -2.41421 q^{86} +3.00931 q^{90} -0.317837 q^{91} -3.66390 q^{94} -1.00000 q^{95} -8.59575 q^{96} +1.84776 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$2$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$3$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$3$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$4$	2.93185	2.93185
$5$	−1.00000	−1.00000
$5$	−1.00000	−1.00000
$6$	−3.14626	−3.14626
$7$	0.261052	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$7$	0.261052	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$8$	−3.83065	−3.83065
$9$	1.51764	1.51764
$10$	1.98289	1.98289
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	4.65199	4.65199
$13$	−1.21752	−1.21752	−0.608761	−	0.793353i	$-0.708333\pi$
$13$	−1.21752	−1.21752	−0.608761	+	0.793353i	$0.708333\pi$
$14$	−0.517638	−0.517638
$15$	−1.58671	−1.58671
$16$	4.66390	4.66390
$17$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$17$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$18$	−3.00931	−3.00931
$19$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$19$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$20$	−2.93185	−2.93185
$21$	0.414214	0.414214
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−6.07812	−6.07812
$25$	1.00000	1.00000
$26$	2.41421	2.41421
$27$	0.821340	0.821340
$28$	0.765367	0.765367
$29$	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			$\pi$
$32$	−5.41736	−5.41736
$33$	0	0
$34$	−1.51764	−1.51764
$35$	−0.261052	−0.261052
$36$	4.44949	4.44949
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	−1.98289	−1.98289
$39$	−1.93185	−1.93185
$40$	3.83065	3.83065
$41$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$41$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$42$	−0.821340	−0.821340
$43$	1.21752	1.21752	0.608761	−	0.793353i	$-0.291667\pi$
$43$	1.21752	1.21752	0.608761	+	0.793353i	$0.291667\pi$
$44$	0	0
$45$	−1.51764	−1.51764
$46$	0	0
$47$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$47$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$48$	7.40025	7.40025
$49$	−0.931852	−0.931852
$50$	−1.98289	−1.98289
$51$	1.21441	1.21441
$52$	−3.56960	−3.56960
$53$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$53$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$54$	−1.62863	−1.62863
$55$	0	0
$56$	−1.00000	−1.00000
$57$	1.58671	1.58671
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−4.65199	−4.65199
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0.396183	0.396183
$64$	6.07812	6.07812
$65$	1.21752	1.21752
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	2.24394	2.24394
$69$	0	0
$70$	0.517638	0.517638
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−5.81354	−5.81354
$73$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$73$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$74$	0	0
$75$	1.58671	1.58671
$76$	2.93185	2.93185
$77$	0	0
$78$	3.83065	3.83065
$79$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$79$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$80$	−4.66390	−4.66390
$81$	−0.214413	−0.214413
$82$	−3.43447	−3.43447
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	1.21441	1.21441
$85$	−0.765367	−0.765367
$86$	−2.41421	−2.41421
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	3.00931	3.00931
$91$	−0.317837	−0.317837
$92$	0	0
$93$	0	0
$94$	−3.66390	−3.66390
$95$	−1.00000	−1.00000
$96$	−8.59575	−8.59575
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	1.84776	1.84776
$99$	0	0
$100$	2.93185	2.93185
$101$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$101$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$102$	−2.40805	−2.40805
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	4.66390	4.66390
$105$	−0.414214	−0.414214
$106$	−3.93185	−3.93185
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	2.40805	2.40805
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	1.21752	1.21752
$113$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$113$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$114$	−3.14626	−3.14626
$115$	0	0
$116$	0	0
$117$	−1.84776	−1.84776
$118$	0	0
$119$	0.199801	0.199801
$120$	6.07812	6.07812
$121$	1.00000	1.00000
$122$	0	0
$123$	2.74826	2.74826
$124$	0	0
$125$	−1.00000	−1.00000
$126$	−0.785587	−0.785587
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−6.63488	−6.63488
$129$	1.93185	1.93185
$130$	−2.41421	−2.41421
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0.261052	0.261052
$134$	0	0
$135$	−0.821340	−0.821340
$136$	−2.93185	−2.93185
$137$	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	$0.666667\pi$
$140$	−0.765367	−0.765367
$141$	2.93185	2.93185
$142$	0	0
$143$	0	0
$144$	7.07812	7.07812
$145$	0	0
$146$	3.66390	3.66390
$147$	−1.47858	−1.47858
$148$	0	0
$149$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$149$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$150$	−3.14626	−3.14626
$151$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$151$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$152$	−3.83065	−3.83065
$153$	1.16155	1.16155
$154$	0	0
$155$	0	0
$156$	−5.66390	−5.66390
$157$	−0.261052	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$157$	−0.261052	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$158$	2.80423	2.80423
$159$	3.14626	3.14626
$160$	5.41736	5.41736
$161$	0	0
$162$	0.425157	0.425157
$163$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$163$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$164$	5.07812	5.07812
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	−1.58671	−1.58671
$169$	0.482362	0.482362
$170$	1.51764	1.51764
$171$	1.51764	1.51764
$172$	3.56960	3.56960
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0.261052	0.261052
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$179$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$180$	−4.44949	−4.44949
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0.630236	0.630236
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	5.41736	5.41736
$189$	0.214413	0.214413
$190$	1.98289	1.98289
$191$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$191$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$192$	9.64419	9.64419
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	1.93185	1.93185
$196$	−2.73205	−2.73205
$197$	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			$\pi$
$200$	−3.83065	−3.83065
$201$	0	0
$202$	2.80423	2.80423
$203$	0	0
$204$	3.56048	3.56048
$205$	−1.73205	−1.73205
$206$	0	0
$207$	0	0
$208$	−5.67841	−5.67841
$209$	0	0
$210$	0.821340	0.821340
$211$	0.517638	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$211$	0.517638	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$212$	5.81354	5.81354
$213$	0	0
$214$	0	0
$215$	−1.21752	−1.21752
$216$	−3.14626	−3.14626
$217$	0	0
$218$	0	0
$219$	−2.93185	−2.93185
$220$	0	0
$221$	−0.931852	−0.931852
$222$	0	0
$223$	−0.261052	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$223$	−0.261052	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$224$	−1.41421	−1.41421
$225$	1.51764	1.51764
$226$	1.51764	1.51764
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	4.65199	4.65199
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$233$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$234$	3.66390	3.66390
$235$	−1.84776	−1.84776
$236$	0	0
$237$	−2.24394	−2.24394
$238$	−0.396183	−0.396183
$239$	0.517638	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$239$	0.517638	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$240$	−7.40025	−7.40025
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−1.98289	−1.98289
$243$	−1.16155	−1.16155
$244$	0	0
$245$	0.931852	0.931852
$246$	−5.44949	−5.44949
$247$	−1.21752	−1.21752
$248$	0	0
$249$	0	0
$250$	1.98289	1.98289
$251$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$251$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$252$	1.16155	1.16155
$253$	0	0
$254$	0	0
$255$	−1.21441	−1.21441
$256$	7.07812	7.07812
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	−3.83065	−3.83065
$259$	0	0
$260$	3.56960	3.56960
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	−1.98289	−1.98289
$266$	−0.517638	−0.517638
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	1.62863	1.62863
$271$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$271$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$272$	3.56960	3.56960
$273$	−0.504314	−0.504314
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	1.98289	1.98289
$279$	0	0
$280$	1.00000	1.00000
$281$	1.93185	1.93185	0.965926	−	0.258819i	$-0.0833333\pi$
$281$	1.93185	1.93185	0.965926	+	0.258819i	$0.0833333\pi$
$282$	−5.81354	−5.81354
$283$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$283$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$284$	0	0
$285$	−1.58671	−1.58671
$286$	0	0
$287$	0.452156	0.452156
$288$	−8.22159	−8.22159
$289$	−0.414214	−0.414214
$290$	0	0
$291$	0	0
$292$	−5.41736	−5.41736
$293$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$293$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$294$	2.93185	2.93185
$295$	0	0
$296$	0	0
$297$	0	0
$298$	3.43447	3.43447
$299$	0	0
$300$	4.65199	4.65199
$301$	0.317837	0.317837
$302$	1.02642	1.02642
$303$	−2.24394	−2.24394
$304$	4.66390	4.66390
$305$	0	0
$306$	−2.30323	−2.30323
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$311$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$312$	7.40025	7.40025
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0.517638	0.517638
$315$	−0.396183	−0.396183
$316$	−4.14626	−4.14626
$317$	0.261052	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$317$	0.261052	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$318$	−6.23870	−6.23870
$319$	0	0
$320$	−6.07812	−6.07812
$321$	0	0
$322$	0	0
$323$	0.765367	0.765367
$324$	−0.628626	−0.628626
$325$	−1.21752	−1.21752
$326$	−3.66390	−3.66390
$327$	0	0
$328$	−6.63488	−6.63488
$329$	0.482362	0.482362
$330$	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
$336$	1.93185	1.93185
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−0.956470	−0.956470
$339$	−1.21441	−1.21441
$340$	−2.24394	−2.24394
$341$	0	0
$342$	−3.00931	−3.00931
$343$	−0.504314	−0.504314
$344$	−4.66390	−4.66390
$345$	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			$\pi$
$350$	−0.517638	−0.517638
$351$	−1.00000	−1.00000
$352$	0	0
$353$	0.261052	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$353$	0.261052	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0.317025	0.317025
$358$	2.80423	2.80423
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	5.81354	5.81354
$361$	0	0
$362$	0	0
$363$	1.58671	1.58671
$364$	−0.931852	−0.931852
$365$	1.84776	1.84776
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	2.62863	2.62863
$370$	0	0
$371$	0.517638	0.517638
$372$	0	0
$373$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$373$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$374$	0	0
$375$	−1.58671	−1.58671
$376$	−7.07812	−7.07812
$377$	0	0
$378$	−0.425157	−0.425157
$379$	−1.00000	−1.00000
$379$	−1.00000	−1.00000
$380$	−2.93185	−2.93185
$381$	0	0
$382$	−2.80423	−2.80423
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−10.5276	−10.5276
$385$	0	0
$386$	0	0
$387$	1.84776	1.84776
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	−3.83065	−3.83065
$391$	0	0
$392$	3.56960	3.56960
$393$	0	0
$394$	0	0
$395$	1.41421	1.41421
$396$	0	0
$397$	1.21752	1.21752	0.608761	−	0.793353i	$-0.291667\pi$
$397$	1.21752	1.21752	0.608761	+	0.793353i	$0.291667\pi$
$398$	0	0
$399$	0.414214	0.414214
$400$	4.66390	4.66390
$401$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$401$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$402$	0	0
$403$	0	0
$404$	−4.14626	−4.14626
$405$	0.214413	0.214413
$406$	0	0
$407$	0	0
$408$	−4.65199	−4.65199
$409$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$409$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$410$	3.43447	3.43447
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	6.59575	6.59575
$417$	−1.58671	−1.58671
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	−1.21441	−1.21441
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	−1.02642	−1.02642
$423$	2.80423	2.80423
$424$	−7.59575	−7.59575
$425$	0.765367	0.765367
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	2.41421	2.41421
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	3.83065	3.83065
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	5.81354	5.81354
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−1.41421	−1.41421
$442$	1.84776	1.84776
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0.517638	0.517638
$447$	−2.74826	−2.74826
$448$	1.58671	1.58671
$449$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$450$	−3.00931	−3.00931
$451$	0	0
$452$	−2.24394	−2.24394
$453$	−0.821340	−0.821340
$454$	0	0
$455$	0.317837	0.317837
$456$	−6.07812	−6.07812
$457$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$457$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$458$	0	0
$459$	0.628626	0.628626
$460$	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			$\pi$
$468$	−5.41736	−5.41736
$469$	0	0
$470$	3.66390	3.66390
$471$	−0.414214	−0.414214
$472$	0	0
$473$	0	0
$474$	4.44949	4.44949
$475$	1.00000	1.00000
$476$	0.585786	0.585786
$477$	3.00931	3.00931
$478$	−1.02642	−1.02642
$479$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$479$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$480$	8.59575	8.59575
$481$	0	0
$482$	0	0
$483$	0	0
$484$	2.93185	2.93185
$485$	0	0
$486$	2.30323	2.30323
$487$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$487$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$488$	0	0
$489$	2.93185	2.93185
$490$	−1.84776	−1.84776
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	8.05748	8.05748
$493$	0	0
$494$	2.41421	2.41421
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$499$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$500$	−2.93185	−2.93185
$501$	0	0
$502$	3.83065	3.83065
$503$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$503$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$504$	−1.51764	−1.51764
$505$	1.41421	1.41421
$506$	0	0
$507$	0.765367	0.765367
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	2.40805	2.40805
$511$	−0.482362	−0.482362
$512$	−7.40025	−7.40025
$513$	0.821340	0.821340
$514$	0	0
$515$	0	0
$516$	5.66390	5.66390
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−4.66390	−4.66390
$521$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$521$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0.414214	0.414214
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	1.00000
$530$	3.93185	3.93185
$531$	0	0
$532$	0.765367	0.765367
$533$	−2.10881	−2.10881
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−2.24394	−2.24394
$538$	0	0
$539$	0	0
$540$	−2.40805	−2.40805
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	−3.43447	−3.43447
$543$	0	0
$544$	−4.14626	−4.14626
$545$	0	0
$546$	1.00000	1.00000
$547$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$547$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−0.369184	−0.369184
$554$	0	0
$555$	0	0
$556$	−2.93185	−2.93185
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−1.48236	−1.48236
$560$	−1.21752	−1.21752
$561$	0	0
$562$	−3.83065	−3.83065
$563$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$563$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$564$	8.59575	8.59575
$565$	0.765367	0.765367
$566$	−1.51764	−1.51764
$567$	−0.0559730	−0.0559730
$568$	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
$573$	2.24394	2.24394
$574$	−0.896575	−0.896575
$575$	0	0
$576$	9.22438	9.22438
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0.821340	0.821340
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	7.07812	7.07812
$585$	1.84776	1.84776
$586$	3.14626	3.14626
$587$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$587$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$588$	−4.33496	−4.33496
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$593$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$594$	0	0
$595$	−0.199801	−0.199801
$596$	−5.07812	−5.07812
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	−6.07812	−6.07812
$601$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$601$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$602$	−0.630236	−0.630236
$603$	0	0
$604$	−1.51764	−1.51764
$605$	−1.00000	−1.00000
$606$	4.44949	4.44949
$607$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$607$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$608$	−5.41736	−5.41736
$609$	0	0
$610$	0	0
$611$	−2.24969	−2.24969
$612$	3.40549	3.40549
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	−2.74826	−2.74826
$616$	0	0
$617$	−1.21752	−1.21752	−0.608761	−	0.793353i	$-0.708333\pi$
$617$	−1.21752	−1.21752	−0.608761	+	0.793353i	$0.708333\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	1.02642	1.02642
$623$	0	0
$624$	−9.00997	−9.00997
$625$	1.00000	1.00000
$626$	0	0
$627$	0	0
$628$	−0.765367	−0.765367
$629$	0	0
$630$	0.785587	0.785587
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	5.41736	5.41736
$633$	0.821340	0.821340
$634$	−0.517638	−0.517638
$635$	0	0
$636$	9.22438	9.22438
$637$	1.13455	1.13455
$638$	0	0
$639$	0	0
$640$	6.63488	6.63488
$641$	−1.93185	−1.93185	−0.965926	−	0.258819i	$-0.916667\pi$
$641$	−1.93185	−1.93185	−0.965926	+	0.258819i	$0.916667\pi$
$642$	0	0
$643$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$643$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$644$	0	0
$645$	−1.93185	−1.93185
$646$	−1.51764	−1.51764
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0.821340	0.821340
$649$	0	0
$650$	2.41421	2.41421
$651$	0	0
$652$	5.41736	5.41736
$653$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$653$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$654$	0	0
$655$	0	0
$656$	8.07812	8.07812
$657$	−2.80423	−2.80423
$658$	−0.956470	−0.956470
$659$	1.93185	1.93185	0.965926	−	0.258819i	$-0.0833333\pi$
$659$	1.93185	1.93185	0.965926	+	0.258819i	$0.0833333\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	−1.47858	−1.47858
$664$	0	0
$665$	−0.261052	−0.261052
$666$	0	0
$667$	0	0
$668$	0	0
$669$	−0.414214	−0.414214
$670$	0	0
$671$	0	0
$672$	−2.24394	−2.24394
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0.821340	0.821340
$676$	1.41421	1.41421
$677$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$677$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$678$	2.40805	2.40805
$679$	0	0
$680$	2.93185	2.93185
$681$	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
$688$	5.67841	5.67841
$689$	−2.41421	−2.41421
$690$	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
$697$	1.32565	1.32565
$698$	0	0
$699$	−2.51764	−2.51764
$700$	0.765367	0.765367
$701$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$701$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$702$	1.98289	1.98289
$703$	0	0
$704$	0	0
$705$	−2.93185	−2.93185
$706$	−0.517638	−0.517638
$707$	−0.369184	−0.369184
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	−2.14626	−2.14626
$712$	0	0
$713$	0	0
$714$	−0.628626	−0.628626
$715$	0	0
$716$	−4.14626	−4.14626
$717$	0.821340	0.821340
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−7.07812	−7.07812
$721$	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			$\pi$
$728$	1.21752	1.21752
$729$	−1.62863	−1.62863
$730$	−3.66390	−3.66390
$731$	0.931852	0.931852
$732$	0	0
$733$	−1.98289	−1.98289	−0.991445	−	0.130526i	$-0.958333\pi$
$733$	−1.98289	−1.98289	−0.991445	+	0.130526i	$0.958333\pi$
$734$	0	0
$735$	1.47858	1.47858
$736$	0	0
$737$	0	0
$738$	−5.21228	−5.21228
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	−1.93185	−1.93185
$742$	−1.02642	−1.02642
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	1.73205	1.73205
$746$	3.93185	3.93185
$747$	0	0
$748$	0	0
$749$	0	0
$750$	3.14626	3.14626
$751$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$751$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$752$	8.61777	8.61777
$753$	−3.06528	−3.06528
$754$	0	0
$755$	0.517638	0.517638
$756$	0.628626	0.628626
$757$	1.98289	1.98289	0.991445	−	0.130526i	$-0.0416667\pi$
$757$	1.98289	1.98289	0.991445	+	0.130526i	$0.0416667\pi$
$758$	1.98289	1.98289
$759$	0	0
$760$	3.83065	3.83065
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	4.14626	4.14626
$765$	−1.16155	−1.16155
$766$	0	0
$767$	0	0
$768$	11.2309	11.2309
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−0.261052	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$773$	−0.261052	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$774$	−3.66390	−3.66390
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	1.73205	1.73205
$780$	5.66390	5.66390
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−4.34607	−4.34607
$785$	0.261052	0.261052
$786$	0	0
$787$	−1.58671	−1.58671	−0.793353	−	0.608761i	$-0.791667\pi$
$787$	−1.58671	−1.58671	−0.793353	+	0.608761i	$0.791667\pi$
$788$	0	0
$789$	0	0
$790$	−2.80423	−2.80423
$791$	−0.199801	−0.199801
$792$	0	0
$793$	0	0
$794$	−2.41421	−2.41421
$795$	−3.14626	−3.14626
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	−0.821340	−0.821340
$799$	1.41421	1.41421
$800$	−5.41736	−5.41736
$801$	0	0
$802$	−2.80423	−2.80423
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	5.41736	5.41736
$809$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$809$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$810$	−0.425157	−0.425157
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	2.74826	2.74826
$814$	0	0
$815$	−1.84776	−1.84776
$816$	5.66390	5.66390
$817$	1.21752	1.21752
$818$	3.43447	3.43447
$819$	−0.482362	−0.482362
$820$	−5.07812	−5.07812
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$823$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$827$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	−7.40025	−7.40025
$833$	−0.713208	−0.713208
$834$	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	$0.5\pi$
$840$	1.58671	1.58671
$841$	1.00000	1.00000
$842$	0	0
$843$	3.06528	3.06528
$844$	1.51764	1.51764
$845$	−0.482362	−0.482362
$846$	−5.56048	−5.56048
$847$	0.261052	0.261052
$848$	9.24800	9.24800
$849$	1.21441	1.21441
$850$	−1.51764	−1.51764
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	−1.51764	−1.51764
$856$	0	0
$857$	1.58671	1.58671	0.793353	−	0.608761i	$-0.208333\pi$
$857$	1.58671	1.58671	0.793353	+	0.608761i	$0.208333\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	−3.56960	−3.56960
$861$	0.717439	0.717439
$862$	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
$867$	−0.657235	−0.657235
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−0.261052	−0.261052
$876$	−8.59575	−8.59575
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	−2.51764	−2.51764
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	2.80423	2.80423
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	−2.73205	−2.73205
$885$	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
$892$	−0.765367	−0.765367
$893$	1.84776	1.84776
$894$	5.44949	5.44949
$895$	1.41421	1.41421
$896$	−1.73205	−1.73205
$897$	0	0
$898$	1.98289	1.98289
$899$	0	0
$900$	4.44949	4.44949
$901$	1.51764	1.51764
$902$	0	0
$903$	0.504314	0.504314
$904$	2.93185	2.93185
$905$	0	0
$906$	1.62863	1.62863
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	−2.14626	−2.14626
$910$	−0.630236	−0.630236
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	7.40025	7.40025
$913$	0	0
$914$	−3.93185	−3.93185
$915$	0	0
$916$	0	0
$917$	0	0
$918$	−1.24650	−1.24650
$919$	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
$929$	−0.517638	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$929$	−0.517638	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$930$	0	0
$931$	−0.931852	−0.931852
$932$	−4.65199	−4.65199
$933$	−0.821340	−0.821340
$934$	0	0
$935$	0	0
$936$	7.07812	7.07812
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	−5.41736	−5.41736
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0.821340	0.821340
$943$	0	0
$944$	0	0
$945$	−0.214413	−0.214413
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	−6.57891	−6.57891
$949$	2.24969	2.24969
$950$	−1.98289	−1.98289
$951$	0.414214	0.414214
$952$	−0.765367	−0.765367
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	−5.96713	−5.96713
$955$	−1.41421	−1.41421
$956$	1.51764	1.51764
$957$	0	0
$958$	−1.98289	−1.98289
$959$	0	0
$960$	−9.64419	−9.64419
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$967$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$968$	−3.83065	−3.83065
$969$	1.21441	1.21441
$970$	0	0
$971$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$972$	−3.40549	−3.40549
$973$	−0.261052	−0.261052
$974$	3.66390	3.66390
$975$	−1.93185	−1.93185
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−5.81354	−5.81354
$979$	0	0
$980$	2.73205	2.73205
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	−10.5276	−10.5276
$985$	0	0
$986$	0	0
$987$	0.765367	0.765367
$988$	−3.56960	−3.56960
$989$	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			$\pi$
$998$	3.83065	3.83065
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1895.1.d.i.1894.1	✓	8
5.4	even	2	inner	1895.1.d.i.1894.8	yes	8
379.378	odd	2	inner	1895.1.d.i.1894.8	yes	8
1895.1894	odd	2	CM	1895.1.d.i.1894.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1895.1.d.i.1894.1	✓	8	1.1	even	1	trivial
1895.1.d.i.1894.1	✓	8	1895.1894	odd	2	CM
1895.1.d.i.1894.8	yes	8	5.4	even	2	inner
1895.1.d.i.1894.8	yes	8	379.378	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-1.98289 q^{2} +1.58671 q^{3} +2.93185 q^{4} -1.00000 q^{5} -3.14626 q^{6} +0.261052 q^{7} -3.83065 q^{8} +1.51764 q^{9} +O(q^{10})\)	\(q-1.98289 q^{2} +1.58671 q^{3} +2.93185 q^{4} -1.00000 q^{5} -3.14626 q^{6} +0.261052 q^{7} -3.83065 q^{8} +1.51764 q^{9} +1.98289 q^{10} +4.65199 q^{12} -1.21752 q^{13} -0.517638 q^{14} -1.58671 q^{15} +4.66390 q^{16} +0.765367 q^{17} -3.00931 q^{18} +1.00000 q^{19} -2.93185 q^{20} +0.414214 q^{21} -6.07812 q^{24} +1.00000 q^{25} +2.41421 q^{26} +0.821340 q^{27} +0.765367 q^{28} +3.14626 q^{30} -5.41736 q^{32} -1.51764 q^{34} -0.261052 q^{35} +4.44949 q^{36} -1.98289 q^{38} -1.93185 q^{39} +3.83065 q^{40} +1.73205 q^{41} -0.821340 q^{42} +1.21752 q^{43} -1.51764 q^{45} +1.84776 q^{47} +7.40025 q^{48} -0.931852 q^{49} -1.98289 q^{50} +1.21441 q^{51} -3.56960 q^{52} +1.98289 q^{53} -1.62863 q^{54} -1.00000 q^{56} +1.58671 q^{57} -4.65199 q^{60} +0.396183 q^{63} +6.07812 q^{64} +1.21752 q^{65} +2.24394 q^{68} +0.517638 q^{70} -5.81354 q^{72} -1.84776 q^{73} +1.58671 q^{75} +2.93185 q^{76} +3.83065 q^{78} -1.41421 q^{79} -4.66390 q^{80} -0.214413 q^{81} -3.43447 q^{82} +1.21441 q^{84} -0.765367 q^{85} -2.41421 q^{86} +3.00931 q^{90} -0.317837 q^{91} -3.66390 q^{94} -1.00000 q^{95} -8.59575 q^{96} +1.84776 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{5} + 8 q^{9}+O(q^{10}) \) 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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