LMFDB - Embedded newform 1151.1.b.a.1150.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1151,1,Mod(1150,1151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1151, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1151.1150");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1151 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1151.b (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:	$0.574423829541$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{82})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 19 x^{18} + 18 x^{17} + 153 x^{16} - 136 x^{15} - 680 x^{14} + 560 x^{13} + 1820 x^{12} + \cdots + 1 $ x^20 - x^19 - 19x^18 + 18x^17 + 153x^16 - 136x^15 - 680x^14 + 560x^13 + 1820x^12 - 1365x^11 - 3003x^10 + 2002x^9 + 3003x^8 - 1716x^7 - 1716x^6 + 792x^5 + 495x^4 - 165x^3 - 55x^2 + 10x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{41}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{41} - \cdots)$

Embedding invariants

Embedding label			1150.18
Root			$0.529963$ of defining polynomial
Character	$\chi$	$=$	1151.1150

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.79233 q^{2} -0.818137 q^{3} +2.21245 q^{4} -1.71914 q^{5} -1.46637 q^{6} +1.44104 q^{7} +2.17311 q^{8} -0.330651 q^{9} +O(q^{10})$	\(q+1.79233 q^{2} -0.818137 q^{3} +2.21245 q^{4} -1.71914 q^{5} -1.46637 q^{6} +1.44104 q^{7} +2.17311 q^{8} -0.330651 q^{9} -3.08127 q^{10} +1.97656 q^{11} -1.81009 q^{12} +2.58283 q^{14} +1.40649 q^{15} +1.68249 q^{16} -0.592637 q^{18} -3.80351 q^{20} -1.17897 q^{21} +3.54265 q^{22} -1.77791 q^{24} +1.95544 q^{25} +1.08866 q^{27} +3.18824 q^{28} -1.99413 q^{29} +2.52090 q^{30} +0.842462 q^{32} -1.61710 q^{33} -2.47735 q^{35} -0.731550 q^{36} -1.94739 q^{37} -3.73588 q^{40} -2.11311 q^{42} +0.380782 q^{43} +4.37304 q^{44} +0.568436 q^{45} -1.08714 q^{47} -1.37651 q^{48} +1.07661 q^{49} +3.50480 q^{50} -1.54298 q^{53} +1.95123 q^{54} -3.39798 q^{55} +3.13155 q^{56} -3.57414 q^{58} +0.955440 q^{59} +3.11179 q^{60} -0.476483 q^{63} -0.172517 q^{64} -2.89838 q^{66} +0.676034 q^{67} -4.44024 q^{70} -0.718543 q^{72} -3.49037 q^{74} -1.59982 q^{75} +2.84831 q^{77} -2.89243 q^{80} -0.560018 q^{81} +0.0766055 q^{83} -2.60842 q^{84} +0.682488 q^{86} +1.63147 q^{87} +4.29529 q^{88} +1.01883 q^{90} -1.94851 q^{94} -0.689250 q^{96} +1.92963 q^{98} -0.653553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} - q^{3} + 19 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 19 q^{9}+O(q^{10}) $ 20 * q - q^2 - q^3 + 19 * q^4 - q^5 - 2 * q^6 - q^7 - 2 * q^8 + 19 * q^9	$ 20 q - q^{2} - q^{3} + 19 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 19 q^{9} - 2 q^{10} - q^{11} - 3 q^{12} - 2 q^{14} - 2 q^{15} + 18 q^{16} - 3 q^{18} - 3 q^{20} - 2 q^{21} - 2 q^{22} - 4 q^{24} + 19 q^{25} - 2 q^{27} - 3 q^{28} - q^{29} - 4 q^{30} - 3 q^{32} - 2 q^{33} - 2 q^{35} + 16 q^{36} - q^{37} - 4 q^{40} - 4 q^{42} - q^{43} - 3 q^{44} - 3 q^{45} - q^{47} - 5 q^{48} + 19 q^{49} - 3 q^{50} - q^{53} - 4 q^{54} - 2 q^{55} - 4 q^{56} - 2 q^{58} - q^{59} - 6 q^{60} - 3 q^{63} + 17 q^{64} - 4 q^{66} - q^{67} - 4 q^{70} - 6 q^{72} - 2 q^{74} - 3 q^{75} - 2 q^{77} - 5 q^{80} + 18 q^{81} - q^{83} - 6 q^{84} - 2 q^{86} - 2 q^{87} - 4 q^{88} - 6 q^{90} - 2 q^{94} - 6 q^{96} - 3 q^{98} - 3 q^{99}+O(q^{100}) $ 20 * q - q^2 - q^3 + 19 * q^4 - q^5 - 2 * q^6 - q^7 - 2 * q^8 + 19 * q^9 - 2 * q^10 - q^11 - 3 * q^12 - 2 * q^14 - 2 * q^15 + 18 * q^16 - 3 * q^18 - 3 * q^20 - 2 * q^21 - 2 * q^22 - 4 * q^24 + 19 * q^25 - 2 * q^27 - 3 * q^28 - q^29 - 4 * q^30 - 3 * q^32 - 2 * q^33 - 2 * q^35 + 16 * q^36 - q^37 - 4 * q^40 - 4 * q^42 - q^43 - 3 * q^44 - 3 * q^45 - q^47 - 5 * q^48 + 19 * q^49 - 3 * q^50 - q^53 - 4 * q^54 - 2 * q^55 - 4 * q^56 - 2 * q^58 - q^59 - 6 * q^60 - 3 * q^63 + 17 * q^64 - 4 * q^66 - q^67 - 4 * q^70 - 6 * q^72 - 2 * q^74 - 3 * q^75 - 2 * q^77 - 5 * q^80 + 18 * q^81 - q^83 - 6 * q^84 - 2 * q^86 - 2 * q^87 - 4 * q^88 - 6 * q^90 - 2 * q^94 - 6 * q^96 - 3 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1151\mathbb{Z}\right)^\times$.

$n$	$17$
$\chi(n)$	$-1$

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 $

$2$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$2$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$3$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$3$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$4$	2.21245	2.21245
$5$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$5$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$6$	−1.46637	−1.46637
$7$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$7$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$8$	2.17311	2.17311
$9$	−0.330651	−0.330651
$10$	−3.08127	−3.08127
$11$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$11$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$12$	−1.81009	−1.81009
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	2.58283	2.58283
$15$	1.40649	1.40649
$16$	1.68249	1.68249
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−0.592637	−0.592637
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−3.80351	−3.80351
$21$	−1.17897	−1.17897
$22$	3.54265	3.54265
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−1.77791	−1.77791
$25$	1.95544	1.95544
$26$	0	0
$27$	1.08866	1.08866
$28$	3.18824	3.18824
$29$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$29$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$30$	2.52090	2.52090
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0.842462	0.842462
$33$	−1.61710	−1.61710
$34$	0	0
$35$	−2.47735	−2.47735
$36$	−0.731550	−0.731550
$37$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$37$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$38$	0	0
$39$	0	0
$40$	−3.73588	−3.73588
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	−2.11311	−2.11311
$43$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$43$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$44$	4.37304	4.37304
$45$	0.568436	0.568436
$46$	0	0
$47$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$47$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$48$	−1.37651	−1.37651
$49$	1.07661	1.07661
$50$	3.50480	3.50480
$51$	0	0
$52$	0	0
$53$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$53$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$54$	1.95123	1.95123
$55$	−3.39798	−3.39798
$56$	3.13155	3.13155
$57$	0	0
$58$	−3.57414	−3.57414
$59$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$59$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$60$	3.11179	3.11179
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−0.476483	−0.476483
$64$	−0.172517	−0.172517
$65$	0	0
$66$	−2.89838	−2.89838
$67$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$67$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$68$	0	0
$69$	0	0
$70$	−4.44024	−4.44024
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−0.718543	−0.718543
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−3.49037	−3.49037
$75$	−1.59982	−1.59982
$76$	0	0
$77$	2.84831	2.84831
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−2.89243	−2.89243
$81$	−0.560018	−0.560018
$82$	0	0
$83$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$83$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$84$	−2.60842	−2.60842
$85$	0	0
$86$	0.682488	0.682488
$87$	1.63147	1.63147
$88$	4.29529	4.29529
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	1.01883	1.01883
$91$	0	0
$92$	0	0
$93$	0	0
$94$	−1.94851	−1.94851
$95$	0	0
$96$	−0.689250	−0.689250
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	1.92963	1.92963
$99$	−0.653553	−0.653553
$100$	4.32631	4.32631
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	2.02682	2.02682
$106$	−2.76553	−2.76553
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	2.40860	2.40860
$109$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$109$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$110$	−6.09031	−6.09031
$111$	1.59323	1.59323
$112$	2.42454	2.42454
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	−4.41192	−4.41192
$117$	0	0
$118$	1.71246	1.71246
$119$	0	0
$120$	3.05647	3.05647
$121$	2.90679	2.90679
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.64253	−1.64253
$126$	−0.854015	−0.854015
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−1.15167	−1.15167
$129$	−0.311532	−0.311532
$130$	0	0
$131$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$131$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$132$	−3.57775	−3.57775
$133$	0	0
$134$	1.21168	1.21168
$135$	−1.87155	−1.87155
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$139$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$140$	−5.48102	−5.48102
$141$	0.889426	0.889426
$142$	0	0
$143$	0	0
$144$	−0.556317	−0.556317
$145$	3.42819	3.42819
$146$	0	0
$147$	−0.880811	−0.880811
$148$	−4.30851	−4.30851
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−2.86740	−2.86740
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	5.10511	5.10511
$155$	0	0
$156$	0	0
$157$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$157$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$158$	0	0
$159$	1.26237	1.26237
$160$	−1.44831	−1.44831
$161$	0	0
$162$	−1.00374	−1.00374
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	2.78002	2.78002
$166$	0.137302	0.137302
$167$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$167$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$168$	−2.56204	−2.56204
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	0.842462	0.842462
$173$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$173$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$174$	2.92414	2.92414
$175$	2.81787	2.81787
$176$	3.32554	3.32554
$177$	−0.781681	−0.781681
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	1.25764	1.25764
$181$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$181$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	3.34784	3.34784
$186$	0	0
$187$	0	0
$188$	−2.40523	−2.40523
$189$	1.56880	1.56880
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0.141143	0.141143
$193$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$193$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$194$	0	0
$195$	0	0
$196$	2.38194	2.38194
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−1.17138	−1.17138
$199$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$199$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$200$	4.24939	4.24939
$201$	−0.553088	−0.553088
$202$	0	0
$203$	−2.87363	−2.87363
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	3.63272	3.63272
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	−3.41376	−3.41376
$213$	0	0
$214$	0	0
$215$	−0.654618	−0.654618
$216$	2.36577	2.36577
$217$	0	0
$218$	−0.411101	−0.411101
$219$	0	0
$220$	−7.51787	−7.51787
$221$	0	0
$222$	2.85560	2.85560
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	1.21402	1.21402
$225$	−0.646569	−0.646569
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−2.33031	−2.33031
$232$	−4.33347	−4.33347
$233$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$233$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$234$	0	0
$235$	1.86894	1.86894
$236$	2.11386	2.11386
$237$	0	0
$238$	0	0
$239$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$239$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$240$	2.36641	2.36641
$241$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$241$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$242$	5.20994	5.20994
$243$	−0.630484	−0.630484
$244$	0	0
$245$	−1.85083	−1.85083
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−0.0626738	−0.0626738
$250$	−2.94396	−2.94396
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−1.05420	−1.05420
$253$	0	0
$254$	0	0
$255$	0	0
$256$	−1.89166	−1.89166
$257$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$257$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$258$	−0.558369	−0.558369
$259$	−2.80627	−2.80627
$260$	0	0
$261$	0.659362	0.659362
$262$	−3.32478	−3.32478
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	−3.51414	−3.51414
$265$	2.65259	2.65259
$266$	0	0
$267$	0	0
$268$	1.49569	1.49569
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−3.35444	−3.35444
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	3.86505	3.86505
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	−2.38497	−2.38497
$279$	0	0
$280$	−5.38357	−5.38357
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	1.59415	1.59415
$283$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$283$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−0.278561	−0.278561
$289$	1.00000	1.00000
$290$	6.14445	6.14445
$291$	0	0
$292$	0	0
$293$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$293$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$294$	−1.57871	−1.57871
$295$	−1.64253	−1.64253
$296$	−4.23190	−4.23190
$297$	2.15179	2.15179
$298$	0	0
$299$	0	0
$300$	−3.53952	−3.53952
$301$	0.548724	0.548724
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$307$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$308$	6.30174	6.30174
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	3.54265	3.54265
$315$	0.819141	0.819141
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	2.26258	2.26258
$319$	−3.94152	−3.94152
$320$	0.296581	0.296581
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−1.23901	−1.23901
$325$	0	0
$326$	0	0
$327$	0.187654	0.187654
$328$	0	0
$329$	−1.56661	−1.56661
$330$	4.98271	4.98271
$331$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$331$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$332$	0.169486	0.169486
$333$	0.643908	0.643908
$334$	2.17311	2.17311
$335$	−1.16220	−1.16220
$336$	−1.98360	−1.98360
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	1.79233	1.79233
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0.110392	0.110392
$344$	0.827483	0.827483
$345$	0	0
$346$	−0.411101	−0.411101
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	3.60955	3.60955
$349$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$349$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$350$	5.05056	5.05056
$351$	0	0
$352$	1.66518	1.66518
$353$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$353$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$354$	−1.40103	−1.40103
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	1.23528	1.23528
$361$	1.00000	1.00000
$362$	−0.949869	−0.949869
$363$	−2.37816	−2.37816
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	6.00043	6.00043
$371$	−2.22350	−2.22350
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	1.34382	1.34382
$376$	−2.36247	−2.36247
$377$	0	0
$378$	2.81181	2.81181
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0.942224	0.942224
$385$	−4.89664	−4.89664
$386$	−2.76553	−2.76553
$387$	−0.125906	−0.125906
$388$	0	0
$389$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$389$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$390$	0	0
$391$	0	0
$392$	2.33959	2.33959
$393$	1.51765	1.51765
$394$	0	0
$395$	0	0
$396$	−1.44595	−1.44595
$397$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$397$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$398$	3.21245	3.21245
$399$	0	0
$400$	3.29000	3.29000
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	−0.991318	−0.991318
$403$	0	0
$404$	0	0
$405$	0.962749	0.962749
$406$	−5.15050	−5.15050
$407$	−3.84914	−3.84914
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	1.37683	1.37683
$414$	0	0
$415$	−0.131695	−0.131695
$416$	0	0
$417$	1.08866	1.08866
$418$	0	0
$419$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$419$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$420$	4.48423	4.48423
$421$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$421$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$422$	0	0
$423$	0.359463	0.359463
$424$	−3.35307	−3.35307
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	−1.17329	−1.17329
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	1.83165	1.83165
$433$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$433$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$434$	0	0
$435$	−2.80473	−2.80473
$436$	−0.507463	−0.507463
$437$	0	0
$438$	0	0
$439$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$439$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$440$	−7.38420	−7.38420
$441$	−0.355981	−0.355981
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	3.52495	3.52495
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−0.248605	−0.248605
$449$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$449$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$450$	−1.15887	−1.15887
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$457$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$461$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$462$	−4.17668	−4.17668
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	−3.35510	−3.35510
$465$	0	0
$466$	−3.32478	−3.32478
$467$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$467$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$468$	0	0
$469$	0.974194	0.974194
$470$	3.34975	3.34975
$471$	−1.61710	−1.61710
$472$	2.07628	2.07628
$473$	0.752639	0.752639
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0.510188	0.510188
$478$	3.41760	3.41760
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	1.18492	1.18492
$481$	0	0
$482$	0.682488	0.682488
$483$	0	0
$484$	6.43114	6.43114
$485$	0	0
$486$	−1.13004	−1.13004
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	−3.31731	−3.31731
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	1.12355	1.12355
$496$	0	0
$497$	0	0
$498$	−0.112332	−0.112332
$499$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$499$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$500$	−3.63403	−3.63403
$501$	−0.991951	−0.991951
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	−1.03545	−1.03545
$505$	0	0
$506$	0	0
$507$	−0.818137	−0.818137
$508$	0	0
$509$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$509$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$510$	0	0
$511$	0	0
$512$	−2.23880	−2.23880
$513$	0	0
$514$	−0.411101	−0.411101
$515$	0	0
$516$	−0.689250	−0.689250
$517$	−2.14879	−2.14879
$518$	−5.02977	−5.02977
$519$	0.187654	0.187654
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	1.18180	1.18180
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	−4.10411	−4.10411
$525$	−2.30541	−2.30541
$526$	0	0
$527$	0	0
$528$	−2.72075	−2.72075
$529$	1.00000	1.00000
$530$	4.75433	4.75433
$531$	−0.315917	−0.315917
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	1.46910	1.46910
$537$	0	0
$538$	0	0
$539$	2.12798	2.12798
$540$	−4.14071	−4.14071
$541$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$541$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$542$	0	0
$543$	0.433582	0.433582
$544$	0	0
$545$	0.394314	0.394314
$546$	0	0
$547$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$547$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$548$	0	0
$549$	0	0
$550$	6.92744	6.92744
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−2.73899	−2.73899
$556$	−2.94400	−2.94400
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−4.16812	−4.16812
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	1.96781	1.96781
$565$	0	0
$566$	−3.57414	−3.57414
$567$	−0.807010	−0.807010
$568$	0	0
$569$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$569$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0.0570430	0.0570430
$577$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$577$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$578$	1.79233	1.79233
$579$	1.26237	1.26237
$580$	7.58470	7.58470
$581$	0.110392	0.110392
$582$	0	0
$583$	−3.04979	−3.04979
$584$	0	0
$585$	0	0
$586$	2.58283	2.58283
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−1.94875	−1.94875
$589$	0	0
$590$	−2.94396	−2.94396
$591$	0	0
$592$	−3.27646	−3.27646
$593$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$593$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$594$	3.85673	3.85673
$595$	0	0
$596$	0	0
$597$	−1.46637	−1.46637
$598$	0	0
$599$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$599$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$600$	−3.47659	−3.47659
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0.983494	0.983494
$603$	−0.223532	−0.223532
$604$	0	0
$605$	−4.99718	−4.99718
$606$	0	0
$607$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$607$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$608$	0	0
$609$	2.35102	2.35102
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$613$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$614$	−0.411101	−0.411101
$615$	0	0
$616$	6.18970	6.18970
$617$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$617$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$618$	0	0
$619$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$619$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0.868305	0.868305
$626$	0	0
$627$	0	0
$628$	4.37304	4.37304
$629$	0	0
$630$	1.46817	1.46817
$631$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$631$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	2.79293	2.79293
$637$	0	0
$638$	−7.06451	−7.06451
$639$	0	0
$640$	1.97988	1.97988
$641$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$641$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$642$	0	0
$643$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$643$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$644$	0	0
$645$	0.535567	0.535567
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−1.21698	−1.21698
$649$	1.88848	1.88848
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0.336337	0.336337
$655$	3.18901	3.18901
$656$	0	0
$657$	0	0
$658$	−2.80788	−2.80788
$659$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$659$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$660$	6.15065	6.15065
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	2.93200	2.93200
$663$	0	0
$664$	0.166472	0.166472
$665$	0	0
$666$	1.15410	1.15410
$667$	0	0
$668$	2.68249	2.68249
$669$	0	0
$670$	−2.08304	−2.08304
$671$	0	0
$672$	−0.993238	−0.993238
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	2.12880	2.12880
$676$	2.21245	2.21245
$677$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$677$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$683$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$684$	0	0
$685$	0	0
$686$	0.197859	0.197859
$687$	0	0
$688$	0.640661	0.640661
$689$	0	0
$690$	0	0
$691$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$691$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$692$	−0.507463	−0.507463
$693$	−0.941798	−0.941798
$694$	0	0
$695$	2.28758	2.28758
$696$	3.54538	3.54538
$697$	0	0
$698$	−2.76553	−2.76553
$699$	1.51765	1.51765
$700$	6.23441	6.23441
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−0.340991	−0.340991
$705$	−1.52905	−1.52905
$706$	1.21168	1.21168
$707$	0	0
$708$	−1.72943	−1.72943
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−1.56002	−1.56002
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0.956386	0.956386
$721$	0	0
$722$	1.79233	1.79233
$723$	−0.311532	−0.311532
$724$	−1.17252	−1.17252
$725$	−3.89940	−3.89940
$726$	−4.26244	−4.26244
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	1.07584	1.07584
$730$	0	0
$731$	0	0
$732$	0	0
$733$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$733$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$734$	0	0
$735$	1.51424	1.51424
$736$	0	0
$737$	1.33622	1.33622
$738$	0	0
$739$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$739$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$740$	7.40692	7.40692
$741$	0	0
$742$	−3.98525	−3.98525
$743$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$743$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−0.0253297	−0.0253297
$748$	0	0
$749$	0	0
$750$	2.40857	2.40857
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−1.82909	−1.82909
$753$	0	0
$754$	0	0
$755$	0	0
$756$	3.47089	3.47089
$757$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$757$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$761$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$762$	0	0
$763$	−0.330528	−0.330528
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	1.54763	1.54763
$769$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$769$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$770$	−8.77640	−8.77640
$771$	0.187654	0.187654
$772$	−3.41376	−3.41376
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−0.225666	−0.225666
$775$	0	0
$776$	0	0
$777$	2.29592	2.29592
$778$	−1.46637	−1.46637
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−2.17092	−2.17092
$784$	1.81138	1.81138
$785$	−3.39798	−3.39798
$786$	2.72013	2.72013
$787$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$787$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	−1.42024	−1.42024
$793$	0	0
$794$	3.21245	3.21245
$795$	−2.17019	−2.17019
$796$	3.96544	3.96544
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	1.64738	1.64738
$801$	0	0
$802$	0	0
$803$	0	0
$804$	−1.22368	−1.22368
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$809$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$810$	1.72557	1.72557
$811$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$811$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$812$	−6.35776	−6.35776
$813$	0	0
$814$	−6.89893	−6.89893
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$823$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$824$	0	0
$825$	−3.16214	−3.16214
$826$	2.46773	2.46773
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$829$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$830$	−0.236042	−0.236042
$831$	0	0
$832$	0	0
$833$	0	0
$834$	1.95123	1.95123
$835$	−2.08437	−2.08437
$836$	0	0
$837$	0	0
$838$	2.93200	2.93200
$839$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$839$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$840$	4.40450	4.40450
$841$	2.97656	2.97656
$842$	0.682488	0.682488
$843$	0	0
$844$	0	0
$845$	−1.71914	−1.71914
$846$	0.644276	0.644276
$847$	4.18881	4.18881
$848$	−2.59604	−2.59604
$849$	1.63147	1.63147
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$853$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$859$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$860$	−1.44831	−1.44831
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0.917151	0.917151
$865$	0.394314	0.394314
$866$	−3.32478	−3.32478
$867$	−0.818137	−0.818137
$868$	0	0
$869$	0	0
$870$	−5.02700	−5.02700
$871$	0	0
$872$	−0.498440	−0.498440
$873$	0	0
$874$	0	0
$875$	−2.36696	−2.36696
$876$	0	0
$877$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$877$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$878$	3.54265	3.54265
$879$	−1.17897	−1.17897
$880$	−5.71707	−5.71707
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−0.638036	−0.638036
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	1.34382	1.34382
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	3.46228	3.46228
$889$	0	0
$890$	0	0
$891$	−1.10691	−1.10691
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−1.65961	−1.65961
$897$	0	0
$898$	−1.46637	−1.46637
$899$	0	0
$900$	−1.43050	−1.43050
$901$	0	0
$902$	0	0
$903$	−0.448931	−0.448931
$904$	0	0
$905$	0.911080	0.911080
$906$	0	0
$907$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$907$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0.151415	0.151415
$914$	−3.57414	−3.57414
$915$	0	0
$916$	0	0
$917$	−2.67314	−2.67314
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0.187654	0.187654
$922$	−0.949869	−0.949869
$923$	0	0
$924$	−5.15569	−5.15569
$925$	−3.80801	−3.80801
$926$	0	0
$927$	0	0
$928$	−1.67998	−1.67998
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	−4.10411	−4.10411
$933$	0	0
$934$	2.93200	2.93200
$935$	0	0
$936$	0	0
$937$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$937$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$938$	1.74608	1.74608
$939$	0	0
$940$	4.13493	4.13493
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	−2.89838	−2.89838
$943$	0	0
$944$	1.60752	1.60752
$945$	−2.69698	−2.69698
$946$	1.34898	1.34898
$947$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$947$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0.914426	0.914426
$955$	0	0
$956$	4.21869	4.21869
$957$	3.22471	3.22471
$958$	0	0
$959$	0	0
$960$	−0.242644	−0.242644
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0.842462	0.842462
$965$	2.65259	2.65259
$966$	0	0
$967$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$967$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$968$	6.31679	6.31679
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−1.39491	−1.39491
$973$	−1.91753	−1.91753
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	−4.09488	−4.09488
$981$	0.0758405	0.0758405
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	1.28170	1.28170
$988$	0	0
$989$	0	0
$990$	2.01377	2.01377
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	−1.33836	−1.33836
$994$	0	0
$995$	−3.08127	−3.08127
$996$	−0.138663	−0.138663
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.71246	1.71246
$999$	−2.12004	−2.12004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1151.1.b.a.1150.18	✓	20
1151.1150	odd	2	CM	1151.1.b.a.1150.18	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1151.1.b.a.1150.18	✓	20	1.1	even	1	trivial
1151.1.b.a.1150.18	✓	20	1151.1150	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:	\( N \)	\(=\)	\( 1151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1151.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.79233 q^{2} -0.818137 q^{3} +2.21245 q^{4} -1.71914 q^{5} -1.46637 q^{6} +1.44104 q^{7} +2.17311 q^{8} -0.330651 q^{9} +O(q^{10})\)	\(q+1.79233 q^{2} -0.818137 q^{3} +2.21245 q^{4} -1.71914 q^{5} -1.46637 q^{6} +1.44104 q^{7} +2.17311 q^{8} -0.330651 q^{9} -3.08127 q^{10} +1.97656 q^{11} -1.81009 q^{12} +2.58283 q^{14} +1.40649 q^{15} +1.68249 q^{16} -0.592637 q^{18} -3.80351 q^{20} -1.17897 q^{21} +3.54265 q^{22} -1.77791 q^{24} +1.95544 q^{25} +1.08866 q^{27} +3.18824 q^{28} -1.99413 q^{29} +2.52090 q^{30} +0.842462 q^{32} -1.61710 q^{33} -2.47735 q^{35} -0.731550 q^{36} -1.94739 q^{37} -3.73588 q^{40} -2.11311 q^{42} +0.380782 q^{43} +4.37304 q^{44} +0.568436 q^{45} -1.08714 q^{47} -1.37651 q^{48} +1.07661 q^{49} +3.50480 q^{50} -1.54298 q^{53} +1.95123 q^{54} -3.39798 q^{55} +3.13155 q^{56} -3.57414 q^{58} +0.955440 q^{59} +3.11179 q^{60} -0.476483 q^{63} -0.172517 q^{64} -2.89838 q^{66} +0.676034 q^{67} -4.44024 q^{70} -0.718543 q^{72} -3.49037 q^{74} -1.59982 q^{75} +2.84831 q^{77} -2.89243 q^{80} -0.560018 q^{81} +0.0766055 q^{83} -2.60842 q^{84} +0.682488 q^{86} +1.63147 q^{87} +4.29529 q^{88} +1.01883 q^{90} -1.94851 q^{94} -0.689250 q^{96} +1.92963 q^{98} -0.653553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - q^{3} + 19 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 19 q^{9}+O(q^{10}) \) 20 * q - q^2 - q^3 + 19 * q^4 - q^5 - 2 * q^6 - q^7 - 2 * q^8 + 19 * q^9	\( 20 q - q^{2} - q^{3} + 19 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 19 q^{9} - 2 q^{10} - q^{11} - 3 q^{12} - 2 q^{14} - 2 q^{15} + 18 q^{16} - 3 q^{18} - 3 q^{20} - 2 q^{21} - 2 q^{22} - 4 q^{24} + 19 q^{25} - 2 q^{27} - 3 q^{28} - q^{29} - 4 q^{30} - 3 q^{32} - 2 q^{33} - 2 q^{35} + 16 q^{36} - q^{37} - 4 q^{40} - 4 q^{42} - q^{43} - 3 q^{44} - 3 q^{45} - q^{47} - 5 q^{48} + 19 q^{49} - 3 q^{50} - q^{53} - 4 q^{54} - 2 q^{55} - 4 q^{56} - 2 q^{58} - q^{59} - 6 q^{60} - 3 q^{63} + 17 q^{64} - 4 q^{66} - q^{67} - 4 q^{70} - 6 q^{72} - 2 q^{74} - 3 q^{75} - 2 q^{77} - 5 q^{80} + 18 q^{81} - q^{83} - 6 q^{84} - 2 q^{86} - 2 q^{87} - 4 q^{88} - 6 q^{90} - 2 q^{94} - 6 q^{96} - 3 q^{98} - 3 q^{99}+O(q^{100}) \) 20 * q - q^2 - q^3 + 19 * q^4 - q^5 - 2 * q^6 - q^7 - 2 * q^8 + 19 * q^9 - 2 * q^10 - q^11 - 3 * q^12 - 2 * q^14 - 2 * q^15 + 18 * q^16 - 3 * q^18 - 3 * q^20 - 2 * q^21 - 2 * q^22 - 4 * q^24 + 19 * q^25 - 2 * q^27 - 3 * q^28 - q^29 - 4 * q^30 - 3 * q^32 - 2 * q^33 - 2 * q^35 + 16 * q^36 - q^37 - 4 * q^40 - 4 * q^42 - q^43 - 3 * q^44 - 3 * q^45 - q^47 - 5 * q^48 + 19 * q^49 - 3 * q^50 - q^53 - 4 * q^54 - 2 * q^55 - 4 * q^56 - 2 * q^58 - q^59 - 6 * q^60 - 3 * q^63 + 17 * q^64 - 4 * q^66 - q^67 - 4 * q^70 - 6 * q^72 - 2 * q^74 - 3 * q^75 - 2 * q^77 - 5 * q^80 + 18 * q^81 - q^83 - 6 * q^84 - 2 * q^86 - 2 * q^87 - 4 * q^88 - 6 * q^90 - 2 * q^94 - 6 * q^96 - 3 * q^98 - 3 * q^99

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