LMFDB - Embedded newform 1151.1.b.a.1150.4

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			1150.4
Root			$1.08714$ 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)

$f(q)$	$=$	$q-1.71914 q^{2} -1.94739 q^{3} +1.95544 q^{4} -0.818137 q^{5} +3.34784 q^{6} +1.97656 q^{7} -1.64253 q^{8} +2.79233 q^{9} +O(q^{10})$	\(q-1.71914 q^{2} -1.94739 q^{3} +1.95544 q^{4} -0.818137 q^{5} +3.34784 q^{6} +1.97656 q^{7} -1.64253 q^{8} +2.79233 q^{9} +1.40649 q^{10} +0.676034 q^{11} -3.80801 q^{12} -3.39798 q^{14} +1.59323 q^{15} +0.868305 q^{16} -4.80041 q^{18} -1.59982 q^{20} -3.84914 q^{21} -1.16220 q^{22} +3.19866 q^{24} -0.330651 q^{25} -3.49037 q^{27} +3.86505 q^{28} +1.63586 q^{29} -2.73899 q^{30} +0.149797 q^{32} -1.31650 q^{33} -1.61710 q^{35} +5.46023 q^{36} -0.529963 q^{37} +1.34382 q^{40} +6.61720 q^{42} +0.0766055 q^{43} +1.32194 q^{44} -2.28451 q^{45} -0.229367 q^{47} -1.69093 q^{48} +2.90679 q^{49} +0.568436 q^{50} +1.44104 q^{53} +6.00043 q^{54} -0.553088 q^{55} -3.24657 q^{56} -2.81227 q^{58} -1.33065 q^{59} +3.11547 q^{60} +5.51921 q^{63} -1.12583 q^{64} +2.26325 q^{66} -1.85500 q^{67} +2.78002 q^{70} -4.58650 q^{72} +0.911080 q^{74} +0.643908 q^{75} +1.33622 q^{77} -0.710392 q^{80} +4.00478 q^{81} +1.90679 q^{83} -7.52675 q^{84} -0.131695 q^{86} -3.18566 q^{87} -1.11041 q^{88} +3.92739 q^{90} +0.394314 q^{94} -0.291714 q^{96} -4.99718 q^{98} +1.88771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$2$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$3$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$3$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$4$	1.95544	1.95544
$5$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$5$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$6$	3.34784	3.34784
$7$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$7$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$8$	−1.64253	−1.64253
$9$	2.79233	2.79233
$10$	1.40649	1.40649
$11$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$11$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$12$	−3.80801	−3.80801
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−3.39798	−3.39798
$15$	1.59323	1.59323
$16$	0.868305	0.868305
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−4.80041	−4.80041
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−1.59982	−1.59982
$21$	−3.84914	−3.84914
$22$	−1.16220	−1.16220
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	3.19866	3.19866
$25$	−0.330651	−0.330651
$26$	0	0
$27$	−3.49037	−3.49037
$28$	3.86505	3.86505
$29$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$29$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$30$	−2.73899	−2.73899
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0.149797	0.149797
$33$	−1.31650	−1.31650
$34$	0	0
$35$	−1.61710	−1.61710
$36$	5.46023	5.46023
$37$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$37$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$38$	0	0
$39$	0	0
$40$	1.34382	1.34382
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	6.61720	6.61720
$43$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$43$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$44$	1.32194	1.32194
$45$	−2.28451	−2.28451
$46$	0	0
$47$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$47$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$48$	−1.69093	−1.69093
$49$	2.90679	2.90679
$50$	0.568436	0.568436
$51$	0	0
$52$	0	0
$53$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$53$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$54$	6.00043	6.00043
$55$	−0.553088	−0.553088
$56$	−3.24657	−3.24657
$57$	0	0
$58$	−2.81227	−2.81227
$59$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$59$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$60$	3.11547	3.11547
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	5.51921	5.51921
$64$	−1.12583	−1.12583
$65$	0	0
$66$	2.26325	2.26325
$67$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$67$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$68$	0	0
$69$	0	0
$70$	2.78002	2.78002
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−4.58650	−4.58650
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0.911080	0.911080
$75$	0.643908	0.643908
$76$	0	0
$77$	1.33622	1.33622
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−0.710392	−0.710392
$81$	4.00478	4.00478
$82$	0	0
$83$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$83$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$84$	−7.52675	−7.52675
$85$	0	0
$86$	−0.131695	−0.131695
$87$	−3.18566	−3.18566
$88$	−1.11041	−1.11041
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	3.92739	3.92739
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0.394314	0.394314
$95$	0	0
$96$	−0.291714	−0.291714
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−4.99718	−4.99718
$99$	1.88771	1.88771
$100$	−0.646569	−0.646569
$101$	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
$105$	3.14912	3.14912
$106$	−2.47735	−2.47735
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−6.82521	−6.82521
$109$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$109$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$110$	0.950836	0.950836
$111$	1.03205	1.03205
$112$	1.71626	1.71626
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	3.19882	3.19882
$117$	0	0
$118$	2.28758	2.28758
$119$	0	0
$120$	−2.61694	−2.61694
$121$	−0.542978	−0.542978
$122$	0	0
$123$	0	0
$124$	0	0
$125$	1.08866	1.08866
$126$	−9.48829	−9.48829
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	1.78566	1.78566
$129$	−0.149181	−0.149181
$130$	0	0
$131$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$131$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$132$	−2.57434	−2.57434
$133$	0	0
$134$	3.18901	3.18901
$135$	2.85560	2.85560
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$139$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$140$	−3.16214	−3.16214
$141$	0.446667	0.446667
$142$	0	0
$143$	0	0
$144$	2.42459	2.42459
$145$	−1.33836	−1.33836
$146$	0	0
$147$	−5.66066	−5.66066
$148$	−1.03631	−1.03631
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−1.10697	−1.10697
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	−2.29715	−2.29715
$155$	0	0
$156$	0	0
$157$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$157$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$158$	0	0
$159$	−2.80627	−2.80627
$160$	−0.122555	−0.122555
$161$	0	0
$162$	−6.88478	−6.88478
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	1.07708	1.07708
$166$	−3.27804	−3.27804
$167$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$167$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$168$	6.32234	6.32234
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	0.149797	0.149797
$173$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$173$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$174$	5.47659	5.47659
$175$	−0.653553	−0.653553
$176$	0.587003	0.587003
$177$	2.59130	2.59130
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	−4.46722	−4.46722
$181$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$181$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0.433582	0.433582
$186$	0	0
$187$	0	0
$188$	−0.448513	−0.448513
$189$	−6.89893	−6.89893
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	2.19243	2.19243
$193$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$193$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$194$	0	0
$195$	0	0
$196$	5.68406	5.68406
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−3.24524	−3.24524
$199$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$199$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$200$	0.543106	0.543106
$201$	3.61242	3.61242
$202$	0	0
$203$	3.23337	3.23337
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	−5.41378	−5.41378
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	2.81787	2.81787
$213$	0	0
$214$	0	0
$215$	−0.0626738	−0.0626738
$216$	5.73305	5.73305
$217$	0	0
$218$	−2.08437	−2.08437
$219$	0	0
$220$	−1.08153	−1.08153
$221$	0	0
$222$	−1.77423	−1.77423
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0.296084	0.296084
$225$	−0.923288	−0.923288
$226$	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
$231$	−2.60215	−2.60215
$232$	−2.68695	−2.68695
$233$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$233$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$234$	0	0
$235$	0.187654	0.187654
$236$	−2.60201	−2.60201
$237$	0	0
$238$	0	0
$239$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$239$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$240$	1.38341	1.38341
$241$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$241$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$242$	0.933455	0.933455
$243$	−4.30851	−4.30851
$244$	0	0
$245$	−2.37816	−2.37816
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−3.71327	−3.71327
$250$	−1.87155	−1.87155
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	10.7925	10.7925
$253$	0	0
$254$	0	0
$255$	0	0
$256$	−1.94396	−1.94396
$257$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$257$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$258$	0.256463	0.256463
$259$	−1.04750	−1.04750
$260$	0	0
$261$	4.56786	4.56786
$262$	3.42819	3.42819
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	2.16240	2.16240
$265$	−1.17897	−1.17897
$266$	0	0
$267$	0	0
$268$	−3.62735	−3.62735
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−4.90918	−4.90918
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−0.223532	−0.223532
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	−3.08127	−3.08127
$279$	0	0
$280$	2.65614	2.65614
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	−0.767883	−0.767883
$283$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$283$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0.418284	0.418284
$289$	1.00000	1.00000
$290$	2.30082	2.30082
$291$	0	0
$292$	0	0
$293$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$293$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$294$	9.73147	9.73147
$295$	1.08866	1.08866
$296$	0.870482	0.870482
$297$	−2.35961	−2.35961
$298$	0	0
$299$	0	0
$300$	1.25912	1.25912
$301$	0.151415	0.151415
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$307$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$308$	2.61290	2.61290
$309$	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			$\pi$
$314$	−1.16220	−1.16220
$315$	−4.51547	−4.51547
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	4.82438	4.82438
$319$	1.10590	1.10590
$320$	0.921081	0.921081
$321$	0	0
$322$	0	0
$323$	0	0
$324$	7.83111	7.83111
$325$	0	0
$326$	0	0
$327$	−2.36112	−2.36112
$328$	0	0
$329$	−0.453358	−0.453358
$330$	−1.85165	−1.85165
$331$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$331$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$332$	3.72862	3.72862
$333$	−1.47983	−1.47983
$334$	−1.64253	−1.64253
$335$	1.51765	1.51765
$336$	−3.34222	−3.34222
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−1.71914	−1.71914
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	3.76889	3.76889
$344$	−0.125827	−0.125827
$345$	0	0
$346$	−2.08437	−2.08437
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−6.22936	−6.22936
$349$	1.44104	1.44104	0.720522	−	0.693433i	$-0.243902\pi$
$349$	1.44104	1.44104	0.720522	+	0.693433i	$0.243902\pi$
$350$	1.12355	1.12355
$351$	0	0
$352$	0.101268	0.101268
$353$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$353$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$354$	−4.45480	−4.45480
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	3.75239	3.75239
$361$	1.00000	1.00000
$362$	1.86894	1.86894
$363$	1.05739	1.05739
$364$	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
$370$	−0.745389	−0.745389
$371$	2.84831	2.84831
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	−2.12004	−2.12004
$376$	0.376743	0.376743
$377$	0	0
$378$	11.8602	11.8602
$379$	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			$\pi$
$384$	−3.47737	−3.47737
$385$	−1.09321	−1.09321
$386$	−2.47735	−2.47735
$387$	0.213908	0.213908
$388$	0	0
$389$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$389$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$390$	0	0
$391$	0	0
$392$	−4.77451	−4.77451
$393$	3.88335	3.88335
$394$	0	0
$395$	0	0
$396$	3.69130	3.69130
$397$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$397$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$398$	2.95544	2.95544
$399$	0	0
$400$	−0.287106	−0.287106
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	−6.21025	−6.21025
$403$	0	0
$404$	0	0
$405$	−3.27646	−3.27646
$406$	−5.55862	−5.55862
$407$	−0.358273	−0.358273
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−2.63011	−2.63011
$414$	0	0
$415$	−1.56002	−1.56002
$416$	0	0
$417$	−3.49037	−3.49037
$418$	0	0
$419$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$419$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$420$	6.15792	6.15792
$421$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$421$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$422$	0	0
$423$	−0.640468	−0.640468
$424$	−2.36696	−2.36696
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0.107745	0.107745
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−3.03070	−3.03070
$433$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$433$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$434$	0	0
$435$	2.60630	2.60630
$436$	2.37087	2.37087
$437$	0	0
$438$	0	0
$439$	0.676034	0.676034	0.338017	−	0.941140i	$-0.390244\pi$
$439$	0.676034	0.676034	0.338017	+	0.941140i	$0.390244\pi$
$440$	0.908466	0.908466
$441$	8.11673	8.11673
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	2.01810	2.01810
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−2.22527	−2.22527
$449$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$449$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$450$	1.58726	1.58726
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$457$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$461$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$462$	4.47345	4.47345
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	1.42042	1.42042
$465$	0	0
$466$	3.42819	3.42819
$467$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$467$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$468$	0	0
$469$	−3.66653	−3.66653
$470$	−0.322603	−0.322603
$471$	−1.31650	−1.31650
$472$	2.18564	2.18564
$473$	0.0517879	0.0517879
$474$	0	0
$475$	0	0
$476$	0	0
$477$	4.02387	4.02387
$478$	2.65259	2.65259
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0.238662	0.238662
$481$	0	0
$482$	−0.131695	−0.131695
$483$	0	0
$484$	−1.06176	−1.06176
$485$	0	0
$486$	7.40692	7.40692
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	4.08838	4.08838
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−1.54441	−1.54441
$496$	0	0
$497$	0	0
$498$	6.38363	6.38363
$499$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$499$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$500$	2.12880	2.12880
$501$	−1.86061	−1.86061
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	−9.06549	−9.06549
$505$	0	0
$506$	0	0
$507$	−1.94739	−1.94739
$508$	0	0
$509$	0.0766055	0.0766055	0.0383027	−	0.999266i	$-0.487805\pi$
$509$	0.0766055	0.0766055	0.0383027	+	0.999266i	$0.487805\pi$
$510$	0	0
$511$	0	0
$512$	1.55629	1.55629
$513$	0	0
$514$	−2.08437	−2.08437
$515$	0	0
$516$	−0.291714	−0.291714
$517$	−0.155060	−0.155060
$518$	1.80081	1.80081
$519$	−2.36112	−2.36112
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	−7.85279	−7.85279
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	−3.89940	−3.89940
$525$	1.27272	1.27272
$526$	0	0
$527$	0	0
$528$	−1.14312	−1.14312
$529$	1.00000	1.00000
$530$	2.02682	2.02682
$531$	−3.71562	−3.71562
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	3.04691	3.04691
$537$	0	0
$538$	0	0
$539$	1.96509	1.96509
$540$	5.58396	5.58396
$541$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$541$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$542$	0	0
$543$	2.11708	2.11708
$544$	0	0
$545$	−0.991951	−0.991951
$546$	0	0
$547$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$547$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$548$	0	0
$549$	0	0
$550$	0.384282	0.384282
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−0.844355	−0.844355
$556$	3.50480	3.50480
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−1.40413	−1.40413
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0.873430	0.873430
$565$	0	0
$566$	−2.81227	−2.81227
$567$	7.91570	7.91570
$568$	0	0
$569$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$569$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$570$	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
$576$	−3.14368	−3.14368
$577$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$577$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$578$	−1.71914	−1.71914
$579$	−2.80627	−2.80627
$580$	−2.61708	−2.61708
$581$	3.76889	3.76889
$582$	0	0
$583$	0.974194	0.974194
$584$	0	0
$585$	0	0
$586$	−3.39798	−3.39798
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	−11.0691	−11.0691
$589$	0	0
$590$	−1.87155	−1.87155
$591$	0	0
$592$	−0.460169	−0.460169
$593$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$593$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$594$	4.05649	4.05649
$595$	0	0
$596$	0	0
$597$	3.34784	3.34784
$598$	0	0
$599$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$599$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$600$	−1.05764	−1.05764
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−0.260304	−0.260304
$603$	−5.17979	−5.17979
$604$	0	0
$605$	0.444231	0.444231
$606$	0	0
$607$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$607$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$608$	0	0
$609$	−6.29664	−6.29664
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$613$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$614$	−2.08437	−2.08437
$615$	0	0
$616$	−2.19479	−2.19479
$617$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$617$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$618$	0	0
$619$	−0.529963	−0.529963	−0.264982	−	0.964253i	$-0.585366\pi$
$619$	−0.529963	−0.529963	−0.264982	+	0.964253i	$0.585366\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−0.560018	−0.560018
$626$	0	0
$627$	0	0
$628$	1.32194	1.32194
$629$	0	0
$630$	7.76273	7.76273
$631$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$631$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	−5.48750	−5.48750
$637$	0	0
$638$	−1.90119	−1.90119
$639$	0	0
$640$	−1.46091	−1.46091
$641$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$641$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$642$	0	0
$643$	0.380782	0.380782	0.190391	−	0.981708i	$-0.439024\pi$
$643$	0.380782	0.380782	0.190391	+	0.981708i	$0.439024\pi$
$644$	0	0
$645$	0.122050	0.122050
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−6.57799	−6.57799
$649$	−0.899565	−0.899565
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	4.05909	4.05909
$655$	1.63147	1.63147
$656$	0	0
$657$	0	0
$658$	0.779385	0.779385
$659$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$659$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$660$	2.10616	2.10616
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−0.654618	−0.654618
$663$	0	0
$664$	−3.13197	−3.13197
$665$	0	0
$666$	2.54404	2.54404
$667$	0	0
$668$	1.86830	1.86830
$669$	0	0
$670$	−2.60905	−2.60905
$671$	0	0
$672$	−0.576591	−0.576591
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.15410	1.15410
$676$	1.95544	1.95544
$677$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$677$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$683$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$684$	0	0
$685$	0	0
$686$	−6.47925	−6.47925
$687$	0	0
$688$	0.0665169	0.0665169
$689$	0	0
$690$	0	0
$691$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$691$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$692$	2.37087	2.37087
$693$	3.73117	3.73117
$694$	0	0
$695$	−1.46637	−1.46637
$696$	5.23255	5.23255
$697$	0	0
$698$	−2.47735	−2.47735
$699$	3.88335	3.88335
$700$	−1.27798	−1.27798
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−0.761097	−0.761097
$705$	−0.365435	−0.365435
$706$	3.18901	3.18901
$707$	0	0
$708$	5.06713	5.06713
$709$	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
$717$	3.00478	3.00478
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−1.98365	−1.98365
$721$	0	0
$722$	−1.71914	−1.71914
$723$	−0.149181	−0.149181
$724$	−2.12583	−2.12583
$725$	−0.540899	−0.540899
$726$	−1.81780	−1.81780
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	4.38556	4.38556
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$733$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$734$	0	0
$735$	4.63120	4.63120
$736$	0	0
$737$	−1.25405	−1.25405
$738$	0	0
$739$	−1.71914	−1.71914	−0.859570	−	0.511019i	$-0.829268\pi$
$739$	−1.71914	−1.71914	−0.859570	+	0.511019i	$0.829268\pi$
$740$	0.847844	0.847844
$741$	0	0
$742$	−4.89664	−4.89664
$743$	−1.33065	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$743$	−1.33065	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	5.32440	5.32440
$748$	0	0
$749$	0	0
$750$	3.64464	3.64464
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−0.199160	−0.199160
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−13.4904	−13.4904
$757$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$757$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$761$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$762$	0	0
$763$	2.39648	2.39648
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	3.78566	3.78566
$769$	−1.94739	−1.94739	−0.973695	−	0.227854i	$-0.926829\pi$
$769$	−1.94739	−1.94739	−0.973695	+	0.227854i	$0.926829\pi$
$770$	1.87939	1.87939
$771$	−2.36112	−2.36112
$772$	2.81787	2.81787
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−0.367737	−0.367737
$775$	0	0
$776$	0	0
$777$	2.03990	2.03990
$778$	3.34784	3.34784
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−5.70975	−5.70975
$784$	2.52398	2.52398
$785$	−0.553088	−0.553088
$786$	−6.67603	−6.67603
$787$	−1.99413	−1.99413	−0.997066	−	0.0765493i	$-0.975610\pi$
$787$	−1.99413	−1.99413	−0.997066	+	0.0765493i	$0.975610\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	−3.10063	−3.10063
$793$	0	0
$794$	2.95544	2.95544
$795$	2.29592	2.29592
$796$	−3.36167	−3.36167
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−0.0495307	−0.0495307
$801$	0	0
$802$	0	0
$803$	0	0
$804$	7.06387	7.06387
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$809$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$810$	5.63269	5.63269
$811$	−1.54298	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$811$	−1.54298	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$812$	6.32267	6.32267
$813$	0	0
$814$	0.615921	0.615921
$815$	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
$823$	0.955440	0.955440	0.477720	−	0.878512i	$-0.341463\pi$
$823$	0.955440	0.955440	0.477720	+	0.878512i	$0.341463\pi$
$824$	0	0
$825$	0.435303	0.435303
$826$	4.52153	4.52153
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	1.63586	1.63586	0.817929	−	0.575319i	$-0.195122\pi$
$829$	1.63586	1.63586	0.817929	+	0.575319i	$0.195122\pi$
$830$	2.68189	2.68189
$831$	0	0
$832$	0	0
$833$	0	0
$834$	6.00043	6.00043
$835$	−0.781681	−0.781681
$836$	0	0
$837$	0	0
$838$	−0.654618	−0.654618
$839$	1.79233	1.79233	0.896166	−	0.443720i	$-0.146341\pi$
$839$	1.79233	1.79233	0.896166	+	0.443720i	$0.146341\pi$
$840$	−5.17254	−5.17254
$841$	1.67603	1.67603
$842$	−0.131695	−0.131695
$843$	0	0
$844$	0	0
$845$	−0.818137	−0.818137
$846$	1.10105	1.10105
$847$	−1.07323	−1.07323
$848$	1.25126	1.25126
$849$	−3.18566	−3.18566
$850$	0	0
$851$	0	0
$852$	0	0
$853$	1.90679	1.90679	0.953396	−	0.301721i	$-0.0975610\pi$
$853$	1.90679	1.90679	0.953396	+	0.301721i	$0.0975610\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	1.21245	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$859$	1.21245	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$860$	−0.122555	−0.122555
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	−0.522848	−0.522848
$865$	−0.991951	−0.991951
$866$	3.42819	3.42819
$867$	−1.94739	−1.94739
$868$	0	0
$869$	0	0
$870$	−4.48060	−4.48060
$871$	0	0
$872$	−1.99149	−1.99149
$873$	0	0
$874$	0	0
$875$	2.15179	2.15179
$876$	0	0
$877$	−1.85500	−1.85500	−0.927502	−	0.373817i	$-0.878049\pi$
$877$	−1.85500	−1.85500	−0.927502	+	0.373817i	$0.878049\pi$
$878$	−1.16220	−1.16220
$879$	−3.84914	−3.84914
$880$	−0.480249	−0.480249
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−13.9538	−13.9538
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	−2.12004	−2.12004
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	−1.69517	−1.69517
$889$	0	0
$890$	0	0
$891$	2.70737	2.70737
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	3.52946	3.52946
$897$	0	0
$898$	3.34784	3.34784
$899$	0	0
$900$	−1.80543	−1.80543
$901$	0	0
$902$	0	0
$903$	−0.294865	−0.294865
$904$	0	0
$905$	0.889426	0.889426
$906$	0	0
$907$	−0.229367	−0.229367	−0.114683	−	0.993402i	$-0.536585\pi$
$907$	−0.229367	−0.229367	−0.114683	+	0.993402i	$0.536585\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	1.28906	1.28906
$914$	−2.81227	−2.81227
$915$	0	0
$916$	0	0
$917$	−3.94152	−3.94152
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	−2.36112	−2.36112
$922$	1.86894	1.86894
$923$	0	0
$924$	−5.08834	−5.08834
$925$	0.175233	0.175233
$926$	0	0
$927$	0	0
$928$	0.245047	0.245047
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	−3.89940	−3.89940
$933$	0	0
$934$	−0.654618	−0.654618
$935$	0	0
$936$	0	0
$937$	−0.818137	−0.818137	−0.409069	−	0.912504i	$-0.634146\pi$
$937$	−0.818137	−0.818137	−0.409069	+	0.912504i	$0.634146\pi$
$938$	6.30328	6.30328
$939$	0	0
$940$	0.366945	0.366945
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	2.26325	2.26325
$943$	0	0
$944$	−1.15541	−1.15541
$945$	5.64427	5.64427
$946$	−0.0890306	−0.0890306
$947$	1.97656	1.97656	0.988280	−	0.152649i	$-0.0487805\pi$
$947$	1.97656	1.97656	0.988280	+	0.152649i	$0.0487805\pi$
$948$	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			$\pi$
$954$	−6.91759	−6.91759
$955$	0	0
$956$	−3.01720	−3.01720
$957$	−2.15361	−2.15361
$958$	0	0
$959$	0	0
$960$	−1.79370	−1.79370
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0.149797	0.149797
$965$	−1.17897	−1.17897
$966$	0	0
$967$	−1.08714	−1.08714	−0.543568	−	0.839365i	$-0.682927\pi$
$967$	−1.08714	−1.08714	−0.543568	+	0.839365i	$0.682927\pi$
$968$	0.891860	0.891860
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−8.42502	−8.42502
$973$	3.54265	3.54265
$974$	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
$980$	−4.65034	−4.65034
$981$	3.38556	3.38556
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0.882864	0.882864
$988$	0	0
$989$	0	0
$990$	2.65505	2.65505
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	−0.741532	−0.741532
$994$	0	0
$995$	1.40649	1.40649
$996$	−7.26108	−7.26108
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	2.28758	2.28758
$999$	1.84977	1.84977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1151.1.b.a.1150.4	✓	20
1151.1150	odd	2	CM	1151.1.b.a.1150.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1151.1.b.a.1150.4	✓	20	1.1	even	1	trivial
1151.1.b.a.1150.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.71914 q^{2} -1.94739 q^{3} +1.95544 q^{4} -0.818137 q^{5} +3.34784 q^{6} +1.97656 q^{7} -1.64253 q^{8} +2.79233 q^{9} +O(q^{10})\)	\(q-1.71914 q^{2} -1.94739 q^{3} +1.95544 q^{4} -0.818137 q^{5} +3.34784 q^{6} +1.97656 q^{7} -1.64253 q^{8} +2.79233 q^{9} +1.40649 q^{10} +0.676034 q^{11} -3.80801 q^{12} -3.39798 q^{14} +1.59323 q^{15} +0.868305 q^{16} -4.80041 q^{18} -1.59982 q^{20} -3.84914 q^{21} -1.16220 q^{22} +3.19866 q^{24} -0.330651 q^{25} -3.49037 q^{27} +3.86505 q^{28} +1.63586 q^{29} -2.73899 q^{30} +0.149797 q^{32} -1.31650 q^{33} -1.61710 q^{35} +5.46023 q^{36} -0.529963 q^{37} +1.34382 q^{40} +6.61720 q^{42} +0.0766055 q^{43} +1.32194 q^{44} -2.28451 q^{45} -0.229367 q^{47} -1.69093 q^{48} +2.90679 q^{49} +0.568436 q^{50} +1.44104 q^{53} +6.00043 q^{54} -0.553088 q^{55} -3.24657 q^{56} -2.81227 q^{58} -1.33065 q^{59} +3.11547 q^{60} +5.51921 q^{63} -1.12583 q^{64} +2.26325 q^{66} -1.85500 q^{67} +2.78002 q^{70} -4.58650 q^{72} +0.911080 q^{74} +0.643908 q^{75} +1.33622 q^{77} -0.710392 q^{80} +4.00478 q^{81} +1.90679 q^{83} -7.52675 q^{84} -0.131695 q^{86} -3.18566 q^{87} -1.11041 q^{88} +3.92739 q^{90} +0.394314 q^{94} -0.291714 q^{96} -4.99718 q^{98} +1.88771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - q^{3} + 19 q^{4} - q^{5} - 2 q^{6} - q^{7} - 2 q^{8} + 19 q^{9}+O(q^{10}) \) 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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