LMFDB - Embedded newform 1849.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.847401$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.847401 q^{2} +0.0176385 q^{3} -1.28191 q^{4} +3.43657 q^{5} -0.0149469 q^{6} +0.269043 q^{7} +2.78110 q^{8} -2.99969 q^{9} +O(q^{10})$	\(q-0.847401 q^{2} +0.0176385 q^{3} -1.28191 q^{4} +3.43657 q^{5} -0.0149469 q^{6} +0.269043 q^{7} +2.78110 q^{8} -2.99969 q^{9} -2.91216 q^{10} +3.29404 q^{11} -0.0226110 q^{12} -2.01588 q^{13} -0.227987 q^{14} +0.0606161 q^{15} +0.207117 q^{16} -6.44598 q^{17} +2.54194 q^{18} -6.01187 q^{19} -4.40538 q^{20} +0.00474553 q^{21} -2.79137 q^{22} -2.22146 q^{23} +0.0490545 q^{24} +6.81002 q^{25} +1.70826 q^{26} -0.105826 q^{27} -0.344889 q^{28} -2.40077 q^{29} -0.0513662 q^{30} -5.16963 q^{31} -5.73770 q^{32} +0.0581020 q^{33} +5.46233 q^{34} +0.924585 q^{35} +3.84533 q^{36} -5.27515 q^{37} +5.09447 q^{38} -0.0355573 q^{39} +9.55743 q^{40} +2.89135 q^{41} -0.00402137 q^{42} -4.22266 q^{44} -10.3086 q^{45} +1.88247 q^{46} +5.90293 q^{47} +0.00365325 q^{48} -6.92762 q^{49} -5.77082 q^{50} -0.113698 q^{51} +2.58418 q^{52} +6.41738 q^{53} +0.0896769 q^{54} +11.3202 q^{55} +0.748234 q^{56} -0.106041 q^{57} +2.03441 q^{58} +13.4123 q^{59} -0.0777045 q^{60} -9.94333 q^{61} +4.38076 q^{62} -0.807045 q^{63} +4.44790 q^{64} -6.92773 q^{65} -0.0492357 q^{66} -12.7138 q^{67} +8.26317 q^{68} -0.0391834 q^{69} -0.783495 q^{70} -6.03609 q^{71} -8.34242 q^{72} +1.66898 q^{73} +4.47017 q^{74} +0.120119 q^{75} +7.70668 q^{76} +0.886237 q^{77} +0.0301313 q^{78} -13.9434 q^{79} +0.711773 q^{80} +8.99720 q^{81} -2.45014 q^{82} +7.64454 q^{83} -0.00608334 q^{84} -22.1521 q^{85} -0.0423461 q^{87} +9.16103 q^{88} +1.80962 q^{89} +8.73556 q^{90} -0.542359 q^{91} +2.84772 q^{92} -0.0911848 q^{93} -5.00215 q^{94} -20.6602 q^{95} -0.101205 q^{96} -2.62504 q^{97} +5.87047 q^{98} -9.88109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.847401	−0.599203	−0.299602	−	0.954064i	$-0.596854\pi$
$2$	−0.847401	−0.599203	−0.299602	+	0.954064i	$0.596854\pi$
$3$	0.0176385	0.0101836	0.00509181	−	0.999987i	$-0.498379\pi$
$3$	0.0176385	0.0101836	0.00509181	+	0.999987i	$0.498379\pi$
$4$	−1.28191	−0.640955
$5$	3.43657	1.53688	0.768441	−	0.639921i	$-0.221033\pi$
$5$	3.43657	1.53688	0.768441	+	0.639921i	$0.221033\pi$
$6$	−0.0149469	−0.00610206
$7$	0.269043	0.101689	0.0508443	−	0.998707i	$-0.483809\pi$
$7$	0.269043	0.101689	0.0508443	+	0.998707i	$0.483809\pi$
$8$	2.78110	0.983266
$9$	−2.99969	−0.999896
$10$	−2.91216	−0.920904
$11$	3.29404	0.993189	0.496595	−	0.867983i	$-0.334584\pi$
$11$	3.29404	0.993189	0.496595	+	0.867983i	$0.334584\pi$
$12$	−0.0226110	−0.00652725
$13$	−2.01588	−0.559105	−0.279553	−	0.960130i	$-0.590186\pi$
$13$	−2.01588	−0.559105	−0.279553	+	0.960130i	$0.590186\pi$
$14$	−0.227987	−0.0609322
$15$	0.0606161	0.0156510
$16$	0.207117	0.0517793
$17$	−6.44598	−1.56338	−0.781689	−	0.623668i	$-0.785642\pi$
$17$	−6.44598	−1.56338	−0.781689	+	0.623668i	$0.785642\pi$
$18$	2.54194	0.599141
$19$	−6.01187	−1.37922	−0.689609	−	0.724182i	$-0.742217\pi$
$19$	−6.01187	−1.37922	−0.689609	+	0.724182i	$0.742217\pi$
$20$	−4.40538	−0.985072
$21$	0.00474553	0.00103556
$22$	−2.79137	−0.595122
$23$	−2.22146	−0.463207	−0.231603	−	0.972810i	$-0.574397\pi$
$23$	−2.22146	−0.463207	−0.231603	+	0.972810i	$0.574397\pi$
$24$	0.0490545	0.0100132
$25$	6.81002	1.36200
$26$	1.70826	0.335018
$27$	−0.105826	−0.0203662
$28$	−0.344889	−0.0651779
$29$	−2.40077	−0.445812	−0.222906	−	0.974840i	$-0.571554\pi$
$29$	−2.40077	−0.445812	−0.222906	+	0.974840i	$0.571554\pi$
$30$	−0.0513662	−0.00937814
$31$	−5.16963	−0.928494	−0.464247	−	0.885706i	$-0.653675\pi$
$31$	−5.16963	−0.928494	−0.464247	+	0.885706i	$0.653675\pi$
$32$	−5.73770	−1.01429
$33$	0.0581020	0.0101143
$34$	5.46233	0.936782
$35$	0.924585	0.156283
$36$	3.84533	0.640889
$37$	−5.27515	−0.867229	−0.433615	−	0.901098i	$-0.642762\pi$
$37$	−5.27515	−0.867229	−0.433615	+	0.901098i	$0.642762\pi$
$38$	5.09447	0.826431
$39$	−0.0355573	−0.00569372
$40$	9.55743	1.51116
$41$	2.89135	0.451553	0.225777	−	0.974179i	$-0.427508\pi$
$41$	2.89135	0.451553	0.225777	+	0.974179i	$0.427508\pi$
$42$	−0.00402137	−0.000620510 0
$43$	0	0
$43$	0	0
$44$	−4.22266	−0.636590
$45$	−10.3086	−1.53672
$46$	1.88247	0.277555
$47$	5.90293	0.861030	0.430515	−	0.902583i	$-0.358332\pi$
$47$	5.90293	0.861030	0.430515	+	0.902583i	$0.358332\pi$
$48$	0.00365325	0.000527301 0
$49$	−6.92762	−0.989659
$50$	−5.77082	−0.816117
$51$	−0.113698	−0.0159209
$52$	2.58418	0.358362
$53$	6.41738	0.881495	0.440748	−	0.897631i	$-0.354713\pi$
$53$	6.41738	0.881495	0.440748	+	0.897631i	$0.354713\pi$
$54$	0.0896769	0.0122035
$55$	11.3202	1.52641
$56$	0.748234	0.0999870
$57$	−0.106041	−0.0140454
$58$	2.03441	0.267132
$59$	13.4123	1.74613	0.873067	−	0.487600i	$-0.162127\pi$
$59$	13.4123	1.74613	0.873067	+	0.487600i	$0.162127\pi$
$60$	−0.0777045	−0.0100316
$61$	−9.94333	−1.27311	−0.636557	−	0.771230i	$-0.719642\pi$
$61$	−9.94333	−1.27311	−0.636557	+	0.771230i	$0.719642\pi$
$62$	4.38076	0.556356
$63$	−0.807045	−0.101678
$64$	4.44790	0.555988
$65$	−6.92773	−0.859279
$66$	−0.0492357	−0.00606050
$67$	−12.7138	−1.55324	−0.776621	−	0.629968i	$-0.783068\pi$
$67$	−12.7138	−1.55324	−0.776621	+	0.629968i	$0.783068\pi$
$68$	8.26317	1.00206
$69$	−0.0391834	−0.00471712
$70$	−0.783495	−0.0936455
$71$	−6.03609	−0.716352	−0.358176	−	0.933654i	$-0.616601\pi$
$71$	−6.03609	−0.716352	−0.358176	+	0.933654i	$0.616601\pi$
$72$	−8.34242	−0.983164
$73$	1.66898	0.195339	0.0976696	−	0.995219i	$-0.468861\pi$
$73$	1.66898	0.195339	0.0976696	+	0.995219i	$0.468861\pi$
$74$	4.47017	0.519646
$75$	0.120119	0.0138701
$76$	7.70668	0.884017
$77$	0.886237	0.100996
$78$	0.0301313	0.00341169
$79$	−13.9434	−1.56876	−0.784380	−	0.620281i	$-0.787019\pi$
$79$	−13.9434	−1.56876	−0.784380	+	0.620281i	$0.787019\pi$
$80$	0.711773	0.0795787
$81$	8.99720	0.999689
$82$	−2.45014	−0.270572
$83$	7.64454	0.839097	0.419548	−	0.907733i	$-0.362188\pi$
$83$	7.64454	0.839097	0.419548	+	0.907733i	$0.362188\pi$
$84$	−0.00608334	−0.000663747 0
$85$	−22.1521	−2.40273
$86$	0	0
$87$	−0.0423461	−0.00453998
$88$	9.16103	0.976569
$89$	1.80962	0.191819	0.0959096	−	0.995390i	$-0.469424\pi$
$89$	1.80962	0.191819	0.0959096	+	0.995390i	$0.469424\pi$
$90$	8.73556	0.920809
$91$	−0.542359	−0.0568547
$92$	2.84772	0.296895
$93$	−0.0911848	−0.00945543
$94$	−5.00215	−0.515932
$95$	−20.6602	−2.11969
$96$	−0.101205	−0.0103292
$97$	−2.62504	−0.266533	−0.133266	−	0.991080i	$-0.542547\pi$
$97$	−2.62504	−0.266533	−0.133266	+	0.991080i	$0.542547\pi$
$98$	5.87047	0.593007
$99$	−9.88109	−0.993086
$100$	−8.72984	−0.872984
$101$	8.86124	0.881727	0.440863	−	0.897574i	$-0.354672\pi$
$101$	8.86124	0.881727	0.440863	+	0.897574i	$0.354672\pi$
$102$	0.0963476	0.00953983
$103$	0.757110	0.0746003	0.0373001	−	0.999304i	$-0.488124\pi$
$103$	0.757110	0.0746003	0.0373001	+	0.999304i	$0.488124\pi$
$104$	−5.60637	−0.549749
$105$	0.0163083	0.00159153
$106$	−5.43810	−0.528195
$107$	−3.31471	−0.320445	−0.160223	−	0.987081i	$-0.551221\pi$
$107$	−3.31471	−0.320445	−0.160223	+	0.987081i	$0.551221\pi$
$108$	0.135659	0.0130538
$109$	10.0940	0.966831	0.483416	−	0.875391i	$-0.339396\pi$
$109$	10.0940	0.966831	0.483416	+	0.875391i	$0.339396\pi$
$110$	−9.59275	−0.914632
$111$	−0.0930459	−0.00883153
$112$	0.0557235	0.00526537
$113$	−5.60601	−0.527369	−0.263684	−	0.964609i	$-0.584938\pi$
$113$	−5.60601	−0.527369	−0.263684	+	0.964609i	$0.584938\pi$
$114$	0.0898590	0.00841606
$115$	−7.63421	−0.711894
$116$	3.07757	0.285745
$117$	6.04702	0.559048
$118$	−11.3656	−1.04629
$119$	−1.73424	−0.158978
$120$	0.168579	0.0153891
$121$	−0.149322	−0.0135747
$122$	8.42599	0.762854
$123$	0.0509992	0.00459845
$124$	6.62701	0.595123
$125$	6.22027	0.556358
$126$	0.683891	0.0609259
$127$	−9.29036	−0.824386	−0.412193	−	0.911096i	$-0.635237\pi$
$127$	−9.29036	−0.824386	−0.412193	+	0.911096i	$0.635237\pi$
$128$	7.70625	0.681142
$129$	0	0
$130$	5.87057	0.514883
$131$	−5.42427	−0.473921	−0.236960	−	0.971519i	$-0.576151\pi$
$131$	−5.42427	−0.473921	−0.236960	+	0.971519i	$0.576151\pi$
$132$	−0.0744816	−0.00648279
$133$	−1.61745	−0.140251
$134$	10.7737	0.930708
$135$	−0.363678	−0.0313004
$136$	−17.9269	−1.53722
$137$	11.0453	0.943666	0.471833	−	0.881688i	$-0.343592\pi$
$137$	11.0453	0.943666	0.471833	+	0.881688i	$0.343592\pi$
$138$	0.0332040	0.00282651
$139$	−7.68806	−0.652092	−0.326046	−	0.945354i	$-0.605717\pi$
$139$	−7.68806	−0.652092	−0.326046	+	0.945354i	$0.605717\pi$
$140$	−1.18524	−0.100171
$141$	0.104119	0.00876840
$142$	5.11499	0.429240
$143$	−6.64039	−0.555298
$144$	−0.621288	−0.0517740
$145$	−8.25041	−0.685159
$146$	−1.41429	−0.117048
$147$	−0.122193	−0.0100783
$148$	6.76227	0.555855
$149$	−0.940191	−0.0770234	−0.0385117	−	0.999258i	$-0.512262\pi$
$149$	−0.940191	−0.0770234	−0.0385117	+	0.999258i	$0.512262\pi$
$150$	−0.101789	−0.00831103
$151$	−10.9982	−0.895019	−0.447510	−	0.894279i	$-0.647689\pi$
$151$	−10.9982	−0.895019	−0.447510	+	0.894279i	$0.647689\pi$
$152$	−16.7196	−1.35614
$153$	19.3359	1.56322
$154$	−0.750999	−0.0605172
$155$	−17.7658	−1.42698
$156$	0.0455812	0.00364942
$157$	−19.2338	−1.53502	−0.767511	−	0.641036i	$-0.778505\pi$
$157$	−19.2338	−1.53502	−0.767511	+	0.641036i	$0.778505\pi$
$158$	11.8157	0.940006
$159$	0.113193	0.00897681
$160$	−19.7180	−1.55885
$161$	−0.597669	−0.0471029
$162$	−7.62424	−0.599017
$163$	19.1896	1.50305	0.751523	−	0.659706i	$-0.229319\pi$
$163$	19.1896	1.50305	0.751523	+	0.659706i	$0.229319\pi$
$164$	−3.70646	−0.289426
$165$	0.199672	0.0155444
$166$	−6.47799	−0.502790
$167$	−6.07181	−0.469850	−0.234925	−	0.972013i	$-0.575485\pi$
$167$	−6.07181	−0.469850	−0.234925	+	0.972013i	$0.575485\pi$
$168$	0.0131978	0.00101823
$169$	−8.93621	−0.687401
$170$	18.7717	1.43972
$171$	18.0337	1.37907
$172$	0	0
$173$	−11.0260	−0.838294	−0.419147	−	0.907918i	$-0.637671\pi$
$173$	−11.0260	−0.838294	−0.419147	+	0.907918i	$0.637671\pi$
$174$	0.0358841	0.00272037
$175$	1.83219	0.138500
$176$	0.682252	0.0514267
$177$	0.236574	0.0177820
$178$	−1.53347	−0.114939
$179$	8.13358	0.607932	0.303966	−	0.952683i	$-0.401689\pi$
$179$	8.13358	0.607932	0.303966	+	0.952683i	$0.401689\pi$
$180$	13.2148	0.984970
$181$	6.04612	0.449405	0.224702	−	0.974427i	$-0.427859\pi$
$181$	6.04612	0.449405	0.224702	+	0.974427i	$0.427859\pi$
$182$	0.459596	0.0340675
$183$	−0.175386	−0.0129649
$184$	−6.17810	−0.455455
$185$	−18.1284	−1.33283
$186$	0.0772702	0.00566572
$187$	−21.2333	−1.55273
$188$	−7.56702	−0.551882
$189$	−0.0284717	−0.00207101
$190$	17.5075	1.27013
$191$	−15.4293	−1.11643	−0.558214	−	0.829697i	$-0.688513\pi$
$191$	−15.4293	−1.11643	−0.558214	+	0.829697i	$0.688513\pi$
$192$	0.0784545	0.00566197
$193$	−2.43694	−0.175415	−0.0877074	−	0.996146i	$-0.527954\pi$
$193$	−2.43694	−0.175415	−0.0877074	+	0.996146i	$0.527954\pi$
$194$	2.22446	0.159707
$195$	−0.122195	−0.00875057
$196$	8.88059	0.634328
$197$	−2.49146	−0.177509	−0.0887547	−	0.996054i	$-0.528289\pi$
$197$	−2.49146	−0.177509	−0.0887547	+	0.996054i	$0.528289\pi$
$198$	8.37325	0.595061
$199$	8.26117	0.585619	0.292809	−	0.956171i	$-0.405410\pi$
$199$	8.26117	0.585619	0.292809	+	0.956171i	$0.405410\pi$
$200$	18.9393	1.33921
$201$	−0.224254	−0.0158176
$202$	−7.50903	−0.528333
$203$	−0.645910	−0.0453340
$204$	0.145750	0.0102046
$205$	9.93634	0.693984
$206$	−0.641576	−0.0447007
$207$	6.66369	0.463159
$208$	−0.417524	−0.0289501
$209$	−19.8033	−1.36982
$210$	−0.0138197	−0.000953651 0
$211$	−14.3174	−0.985651	−0.492826	−	0.870128i	$-0.664036\pi$
$211$	−14.3174	−0.985651	−0.492826	+	0.870128i	$0.664036\pi$
$212$	−8.22651	−0.564999
$213$	−0.106468	−0.00729505
$214$	2.80889	0.192012
$215$	0	0
$216$	−0.294312	−0.0200254
$217$	−1.39085	−0.0944173
$218$	−8.55368	−0.579328
$219$	0.0294384	0.00198926
$220$	−14.5115	−0.978364
$221$	12.9943	0.874094
$222$	0.0788473	0.00529188
$223$	−6.82554	−0.457072	−0.228536	−	0.973535i	$-0.573394\pi$
$223$	−6.82554	−0.457072	−0.228536	+	0.973535i	$0.573394\pi$
$224$	−1.54369	−0.103142
$225$	−20.4279	−1.36186
$226$	4.75054	0.316001
$227$	−23.5383	−1.56229	−0.781146	−	0.624349i	$-0.785364\pi$
$227$	−23.5383	−1.56229	−0.781146	+	0.624349i	$0.785364\pi$
$228$	0.135935	0.00900249
$229$	15.7832	1.04299	0.521493	−	0.853256i	$-0.325375\pi$
$229$	15.7832	1.04299	0.521493	+	0.853256i	$0.325375\pi$
$230$	6.46924	0.426569
$231$	0.0156319	0.00102851
$232$	−6.67677	−0.438351
$233$	−2.79797	−0.183301	−0.0916506	−	0.995791i	$-0.529214\pi$
$233$	−2.79797	−0.183301	−0.0916506	+	0.995791i	$0.529214\pi$
$234$	−5.12426	−0.334983
$235$	20.2858	1.32330
$236$	−17.1934	−1.11919
$237$	−0.245942	−0.0159757
$238$	1.46960	0.0952601
$239$	5.11794	0.331052	0.165526	−	0.986205i	$-0.447068\pi$
$239$	5.11794	0.331052	0.165526	+	0.986205i	$0.447068\pi$
$240$	0.0125546	0.000810399 0
$241$	−5.84154	−0.376287	−0.188143	−	0.982142i	$-0.560247\pi$
$241$	−5.84154	−0.376287	−0.188143	+	0.982142i	$0.560247\pi$
$242$	0.126535	0.00813400
$243$	0.476175	0.0305466
$244$	12.7465	0.816009
$245$	−23.8072	−1.52099
$246$	−0.0432168	−0.00275540
$247$	12.1192	0.771128
$248$	−14.3772	−0.912956
$249$	0.134839	0.00854504
$250$	−5.27106	−0.333371
$251$	−8.79216	−0.554956	−0.277478	−	0.960732i	$-0.589499\pi$
$251$	−8.79216	−0.554956	−0.277478	+	0.960732i	$0.589499\pi$
$252$	1.03456	0.0651712
$253$	−7.31758	−0.460052
$254$	7.87267	0.493975
$255$	−0.390730	−0.0244685
$256$	−15.4261	−0.964131
$257$	−6.02274	−0.375688	−0.187844	−	0.982199i	$-0.560150\pi$
$257$	−6.02274	−0.375688	−0.187844	+	0.982199i	$0.560150\pi$
$258$	0	0
$259$	−1.41924	−0.0881874
$260$	8.88073	0.550759
$261$	7.20156	0.445765
$262$	4.59654	0.283975
$263$	24.1654	1.49010	0.745052	−	0.667006i	$-0.232425\pi$
$263$	24.1654	1.49010	0.745052	+	0.667006i	$0.232425\pi$
$264$	0.161587	0.00994501
$265$	22.0538	1.35475
$266$	1.37063	0.0840387
$267$	0.0319191	0.00195341
$268$	16.2980	0.995559
$269$	−4.38341	−0.267261	−0.133631	−	0.991031i	$-0.542664\pi$
$269$	−4.38341	−0.267261	−0.133631	+	0.991031i	$0.542664\pi$
$270$	0.308181	0.0187553
$271$	28.2720	1.71740	0.858701	−	0.512477i	$-0.171272\pi$
$271$	28.2720	1.71740	0.858701	+	0.512477i	$0.171272\pi$
$272$	−1.33507	−0.0809507
$273$	−0.00956643	−0.000578987 0
$274$	−9.35983	−0.565448
$275$	22.4325	1.35273
$276$	0.0502296	0.00302346
$277$	23.0478	1.38481	0.692405	−	0.721509i	$-0.256551\pi$
$277$	23.0478	1.38481	0.692405	+	0.721509i	$0.256551\pi$
$278$	6.51487	0.390736
$279$	15.5073	0.928397
$280$	2.57136	0.153668
$281$	17.8656	1.06577	0.532886	−	0.846187i	$-0.321108\pi$
$281$	17.8656	1.06577	0.532886	+	0.846187i	$0.321108\pi$
$282$	−0.0882306	−0.00525406
$283$	−14.1069	−0.838570	−0.419285	−	0.907855i	$-0.637719\pi$
$283$	−14.1069	−0.838570	−0.419285	+	0.907855i	$0.637719\pi$
$284$	7.73772	0.459149
$285$	−0.364416	−0.0215861
$286$	5.62708	0.332736
$287$	0.777898	0.0459179
$288$	17.2113	1.01419
$289$	24.5506	1.44415
$290$	6.99141	0.410550
$291$	−0.0463019	−0.00271427
$292$	−2.13948	−0.125204
$293$	6.23884	0.364477	0.182238	−	0.983254i	$-0.441666\pi$
$293$	6.23884	0.364477	0.182238	+	0.983254i	$0.441666\pi$
$294$	0.103547	0.00603896
$295$	46.0924	2.68360
$296$	−14.6707	−0.852717
$297$	−0.348594	−0.0202275
$298$	0.796719	0.0461527
$299$	4.47821	0.258981
$300$	−0.153982	−0.00889014
$301$	0	0
$302$	9.31987	0.536298
$303$	0.156299	0.00897917
$304$	−1.24516	−0.0714149
$305$	−34.1710	−1.95662
$306$	−16.3853	−0.936685
$307$	4.99872	0.285292	0.142646	−	0.989774i	$-0.454439\pi$
$307$	4.99872	0.285292	0.142646	+	0.989774i	$0.454439\pi$
$308$	−1.13608	−0.0647340
$309$	0.0133543	0.000759701 0
$310$	15.0548	0.855054
$311$	4.93459	0.279815	0.139908	−	0.990165i	$-0.455319\pi$
$311$	4.93459	0.279815	0.139908	+	0.990165i	$0.455319\pi$
$312$	−0.0988881	−0.00559844
$313$	8.38219	0.473790	0.236895	−	0.971535i	$-0.423870\pi$
$313$	8.38219	0.473790	0.236895	+	0.971535i	$0.423870\pi$
$314$	16.2987	0.919790
$315$	−2.77347	−0.156267
$316$	17.8743	1.00551
$317$	18.0644	1.01460	0.507300	−	0.861769i	$-0.330644\pi$
$317$	18.0644	1.01460	0.507300	+	0.861769i	$0.330644\pi$
$318$	−0.0959201	−0.00537893
$319$	−7.90822	−0.442775
$320$	15.2855	0.854487
$321$	−0.0584667	−0.00326329
$322$	0.506465	0.0282242
$323$	38.7524	2.15624
$324$	−11.5336	−0.640756
$325$	−13.7282	−0.761504
$326$	−16.2613	−0.900631
$327$	0.178044	0.00984584
$328$	8.04113	0.443997
$329$	1.58814	0.0875570
$330$	−0.169202	−0.00931427
$331$	1.89353	0.104078	0.0520390	−	0.998645i	$-0.483428\pi$
$331$	1.89353	0.104078	0.0520390	+	0.998645i	$0.483428\pi$
$332$	−9.79961	−0.537824
$333$	15.8238	0.867139
$334$	5.14526	0.281536
$335$	−43.6920	−2.38715
$336$	0.000982881 0	5.36205e−5 0
$337$	0.317635	0.0173027	0.00865135	−	0.999963i	$-0.497246\pi$
$337$	0.317635	0.0173027	0.00865135	+	0.999963i	$0.497246\pi$
$338$	7.57256	0.411893
$339$	−0.0988818	−0.00537052
$340$	28.3970	1.54004
$341$	−17.0290	−0.922170
$342$	−15.2818	−0.826346
$343$	−3.74713	−0.202326
$344$	0	0
$345$	−0.134656	−0.00724966
$346$	9.34347	0.502308
$347$	−27.7129	−1.48771	−0.743853	−	0.668343i	$-0.767004\pi$
$347$	−27.7129	−1.48771	−0.743853	+	0.668343i	$0.767004\pi$
$348$	0.0542839	0.00290992
$349$	−27.1671	−1.45422	−0.727110	−	0.686521i	$-0.759137\pi$
$349$	−27.1671	−1.45422	−0.727110	+	0.686521i	$0.759137\pi$
$350$	−1.55260	−0.0829899
$351$	0.213332	0.0113868
$352$	−18.9002	−1.00738
$353$	19.6647	1.04665	0.523323	−	0.852134i	$-0.324692\pi$
$353$	19.6647	1.04665	0.523323	+	0.852134i	$0.324692\pi$
$354$	−0.200473	−0.0106550
$355$	−20.7434	−1.10095
$356$	−2.31977	−0.122948
$357$	−0.0305896	−0.00161897
$358$	−6.89241	−0.364275
$359$	−7.90163	−0.417032	−0.208516	−	0.978019i	$-0.566863\pi$
$359$	−7.90163	−0.417032	−0.208516	+	0.978019i	$0.566863\pi$
$360$	−28.6693	−1.51101
$361$	17.1426	0.902240
$362$	−5.12349	−0.269285
$363$	−0.00263382	−0.000138240 0
$364$	0.695256	0.0364413
$365$	5.73556	0.300213
$366$	0.148622	0.00776861
$367$	20.1655	1.05263	0.526315	−	0.850290i	$-0.323573\pi$
$367$	20.1655	1.05263	0.526315	+	0.850290i	$0.323573\pi$
$368$	−0.460103	−0.0239845
$369$	−8.67316	−0.451506
$370$	15.3620	0.798635
$371$	1.72655	0.0896381
$372$	0.116891	0.00606051
$373$	−7.90525	−0.409318	−0.204659	−	0.978833i	$-0.565609\pi$
$373$	−7.90525	−0.409318	−0.204659	+	0.978833i	$0.565609\pi$
$374$	17.9931	0.930402
$375$	0.109717	0.00566574
$376$	16.4166	0.846622
$377$	4.83967	0.249256
$378$	0.0241269	0.00124096
$379$	−24.4878	−1.25785	−0.628926	−	0.777465i	$-0.716505\pi$
$379$	−24.4878	−1.25785	−0.628926	+	0.777465i	$0.716505\pi$
$380$	26.4846	1.35863
$381$	−0.163869	−0.00839524
$382$	13.0748	0.668967
$383$	−27.6184	−1.41123	−0.705616	−	0.708594i	$-0.749330\pi$
$383$	−27.6184	−1.41123	−0.705616	+	0.708594i	$0.749330\pi$
$384$	0.135927	0.00693650
$385$	3.04562	0.155219
$386$	2.06507	0.105109
$387$	0	0
$388$	3.36507	0.170836
$389$	27.6699	1.40292	0.701459	−	0.712710i	$-0.252532\pi$
$389$	27.6699	1.40292	0.701459	+	0.712710i	$0.252532\pi$
$390$	0.103548	0.00524337
$391$	14.3195	0.724168
$392$	−19.2664	−0.973098
$393$	−0.0956763	−0.00482623
$394$	2.11127	0.106364
$395$	−47.9176	−2.41100
$396$	12.6667	0.636524
$397$	10.0979	0.506798	0.253399	−	0.967362i	$-0.418451\pi$
$397$	10.0979	0.506798	0.253399	+	0.967362i	$0.418451\pi$
$398$	−7.00053	−0.350905
$399$	−0.0285295	−0.00142826
$400$	1.41047	0.0705237
$401$	33.4526	1.67054	0.835272	−	0.549837i	$-0.185310\pi$
$401$	33.4526	1.67054	0.835272	+	0.549837i	$0.185310\pi$
$402$	0.190033	0.00947798
$403$	10.4214	0.519126
$404$	−11.3593	−0.565147
$405$	30.9195	1.53640
$406$	0.547345	0.0271643
$407$	−17.3765	−0.861323
$408$	−0.316204	−0.0156544
$409$	23.3947	1.15679	0.578397	−	0.815756i	$-0.303679\pi$
$409$	23.3947	1.15679	0.578397	+	0.815756i	$0.303679\pi$
$410$	−8.42006	−0.415837
$411$	0.194824	0.00960994
$412$	−0.970548	−0.0478155
$413$	3.60849	0.177562
$414$	−5.64682	−0.277526
$415$	26.2710	1.28959
$416$	11.5665	0.567096
$417$	−0.135606	−0.00664066
$418$	16.7814	0.820803
$419$	−18.1737	−0.887845	−0.443922	−	0.896065i	$-0.646413\pi$
$419$	−18.1737	−0.887845	−0.443922	+	0.896065i	$0.646413\pi$
$420$	−0.0209058	−0.00102010
$421$	−29.2978	−1.42789	−0.713944	−	0.700203i	$-0.753093\pi$
$421$	−29.2978	−1.42789	−0.713944	+	0.700203i	$0.753093\pi$
$422$	12.1326	0.590606
$423$	−17.7069	−0.860941
$424$	17.8474	0.866744
$425$	−43.8972	−2.12933
$426$	0.0902210	0.00437122
$427$	−2.67518	−0.129461
$428$	4.24916	0.205391
$429$	−0.117127	−0.00565494
$430$	0	0
$431$	2.95198	0.142192	0.0710959	−	0.997469i	$-0.477350\pi$
$431$	2.95198	0.142192	0.0710959	+	0.997469i	$0.477350\pi$
$432$	−0.0219184	−0.00105455
$433$	33.6108	1.61523	0.807616	−	0.589709i	$-0.200758\pi$
$433$	33.6108	1.61523	0.807616	+	0.589709i	$0.200758\pi$
$434$	1.17861	0.0565752
$435$	−0.145525	−0.00697740
$436$	−12.9396	−0.619696
$437$	13.3551	0.638863
$438$	−0.0249461	−0.00119197
$439$	21.5906	1.03046	0.515231	−	0.857051i	$-0.327706\pi$
$439$	21.5906	1.03046	0.515231	+	0.857051i	$0.327706\pi$
$440$	31.4825	1.50087
$441$	20.7807	0.989557
$442$	−11.0114	−0.523760
$443$	3.54384	0.168373	0.0841864	−	0.996450i	$-0.473171\pi$
$443$	3.54384	0.168373	0.0841864	+	0.996450i	$0.473171\pi$
$444$	0.119277	0.00566062
$445$	6.21888	0.294803
$446$	5.78397	0.273879
$447$	−0.0165836	−0.000784377 0
$448$	1.19668	0.0565377
$449$	−23.0312	−1.08691	−0.543455	−	0.839438i	$-0.682884\pi$
$449$	−23.0312	−1.08691	−0.543455	+	0.839438i	$0.682884\pi$
$450$	17.3107	0.816033
$451$	9.52422	0.448478
$452$	7.18640	0.338020
$453$	−0.193992	−0.00911454
$454$	19.9464	0.936130
$455$	−1.86386	−0.0873789
$456$	−0.294909	−0.0138104
$457$	−8.08585	−0.378240	−0.189120	−	0.981954i	$-0.560564\pi$
$457$	−8.08585	−0.378240	−0.189120	+	0.981954i	$0.560564\pi$
$458$	−13.3747	−0.624960
$459$	0.682151	0.0318401
$460$	9.78638	0.456292
$461$	9.83400	0.458015	0.229007	−	0.973425i	$-0.426452\pi$
$461$	9.83400	0.458015	0.229007	+	0.973425i	$0.426452\pi$
$462$	−0.0132465	−0.000616284 0
$463$	−30.1484	−1.40112	−0.700558	−	0.713596i	$-0.747065\pi$
$463$	−30.1484	−1.40112	−0.700558	+	0.713596i	$0.747065\pi$
$464$	−0.497241	−0.0230838
$465$	−0.313363	−0.0145319
$466$	2.37101	0.109835
$467$	−24.2643	−1.12282	−0.561409	−	0.827538i	$-0.689741\pi$
$467$	−24.2643	−1.12282	−0.561409	+	0.827538i	$0.689741\pi$
$468$	−7.75175	−0.358325
$469$	−3.42057	−0.157947
$470$	−17.1902	−0.792926
$471$	−0.339256	−0.0156321
$472$	37.3009	1.71691
$473$	0	0
$474$	0.208412	0.00957266
$475$	−40.9409	−1.87850
$476$	2.22315	0.101898
$477$	−19.2501	−0.881404
$478$	−4.33695	−0.198368
$479$	−0.0611425	−0.00279367	−0.00139683	−	0.999999i	$-0.500445\pi$
$479$	−0.0611425	−0.00279367	−0.00139683	+	0.999999i	$0.500445\pi$
$480$	−0.347797	−0.0158747
$481$	10.6341	0.484872
$482$	4.95013	0.225472
$483$	−0.0105420	−0.000479678 0
$484$	0.191417	0.00870077
$485$	−9.02114	−0.409629
$486$	−0.403511	−0.0183036
$487$	23.2133	1.05189	0.525947	−	0.850517i	$-0.323711\pi$
$487$	23.2133	1.05189	0.525947	+	0.850517i	$0.323711\pi$
$488$	−27.6534	−1.25181
$489$	0.338477	0.0153065
$490$	20.1743	0.911382
$491$	−10.3707	−0.468022	−0.234011	−	0.972234i	$-0.575185\pi$
$491$	−10.3707	−0.468022	−0.234011	+	0.972234i	$0.575185\pi$
$492$	−0.0653765	−0.00294740
$493$	15.4753	0.696972
$494$	−10.2698	−0.462062
$495$	−33.9571	−1.52626
$496$	−1.07072	−0.0480768
$497$	−1.62397	−0.0728449
$498$	−0.114262	−0.00512022
$499$	12.0910	0.541270	0.270635	−	0.962682i	$-0.412766\pi$
$499$	12.0910	0.541270	0.270635	+	0.962682i	$0.412766\pi$
$500$	−7.97383	−0.356601
$501$	−0.107098	−0.00478478
$502$	7.45049	0.332531
$503$	−16.6877	−0.744066	−0.372033	−	0.928219i	$-0.621339\pi$
$503$	−16.6877	−0.744066	−0.372033	+	0.928219i	$0.621339\pi$
$504$	−2.24447	−0.0999766
$505$	30.4523	1.35511
$506$	6.20092	0.275665
$507$	−0.157622	−0.00700023
$508$	11.9094	0.528395
$509$	32.3196	1.43254	0.716271	−	0.697823i	$-0.245848\pi$
$509$	32.3196	1.43254	0.716271	+	0.697823i	$0.245848\pi$
$510$	0.331105	0.0146616
$511$	0.449027	0.0198638
$512$	−2.34040	−0.103432
$513$	0.636211	0.0280894
$514$	5.10368	0.225114
$515$	2.60186	0.114652
$516$	0	0
$517$	19.4445	0.855166
$518$	1.20267	0.0528422
$519$	−0.194483	−0.00853686
$520$	−19.2667	−0.844900
$521$	36.4517	1.59698	0.798489	−	0.602010i	$-0.205633\pi$
$521$	36.4517	1.59698	0.798489	+	0.602010i	$0.205633\pi$
$522$	−6.10261	−0.267104
$523$	26.5323	1.16018	0.580088	−	0.814554i	$-0.303018\pi$
$523$	26.5323	1.16018	0.580088	+	0.814554i	$0.303018\pi$
$524$	6.95343	0.303762
$525$	0.0323171	0.00141044
$526$	−20.4778	−0.892875
$527$	33.3233	1.45159
$528$	0.0120339	0.000523710 0
$529$	−18.0651	−0.785440
$530$	−18.6884	−0.811773
$531$	−40.2328	−1.74595
$532$	2.07343	0.0898945
$533$	−5.82863	−0.252466
$534$	−0.0270482	−0.00117049
$535$	−11.3912	−0.492486
$536$	−35.3584	−1.52725
$537$	0.143465	0.00619095
$538$	3.71451	0.160144
$539$	−22.8198	−0.982919
$540$	0.466203	0.0200622
$541$	−16.3247	−0.701855	−0.350927	−	0.936403i	$-0.614134\pi$
$541$	−16.3247	−0.701855	−0.350927	+	0.936403i	$0.614134\pi$
$542$	−23.9577	−1.02907
$543$	0.106645	0.00457657
$544$	36.9851	1.58572
$545$	34.6888	1.48590
$546$	0.00810661	0.000346931 0
$547$	26.8078	1.14622	0.573110	−	0.819479i	$-0.305737\pi$
$547$	26.8078	1.14622	0.573110	+	0.819479i	$0.305737\pi$
$548$	−14.1591	−0.604848
$549$	29.8269	1.27298
$550$	−19.0093	−0.810559
$551$	14.4331	0.614871
$552$	−0.108973	−0.00463818
$553$	−3.75139	−0.159525
$554$	−19.5308	−0.829783
$555$	−0.319759	−0.0135730
$556$	9.85540	0.417962
$557$	2.00197	0.0848263	0.0424132	−	0.999100i	$-0.486495\pi$
$557$	2.00197	0.0848263	0.0424132	+	0.999100i	$0.486495\pi$
$558$	−13.1409	−0.556299
$559$	0	0
$560$	0.191498	0.00809225
$561$	−0.374524	−0.0158124
$562$	−15.1393	−0.638614
$563$	−31.0633	−1.30916	−0.654582	−	0.755991i	$-0.727155\pi$
$563$	−31.0633	−1.30916	−0.654582	+	0.755991i	$0.727155\pi$
$564$	−0.133471	−0.00562016
$565$	−19.2654	−0.810503
$566$	11.9542	0.502474
$567$	2.42063	0.101657
$568$	−16.7869	−0.704364
$569$	1.90303	0.0797792	0.0398896	−	0.999204i	$-0.487299\pi$
$569$	1.90303	0.0797792	0.0398896	+	0.999204i	$0.487299\pi$
$570$	0.308807	0.0129345
$571$	−1.90771	−0.0798350	−0.0399175	−	0.999203i	$-0.512710\pi$
$571$	−1.90771	−0.0798350	−0.0399175	+	0.999203i	$0.512710\pi$
$572$	8.51239	0.355921
$573$	−0.272151	−0.0113693
$574$	−0.659192	−0.0275141
$575$	−15.1282	−0.630890
$576$	−13.3423	−0.555930
$577$	11.9561	0.497739	0.248869	−	0.968537i	$-0.419941\pi$
$577$	11.9561	0.497739	0.248869	+	0.968537i	$0.419941\pi$
$578$	−20.8042	−0.865341
$579$	−0.0429841	−0.00178636
$580$	10.5763	0.439157
$581$	2.05671	0.0853266
$582$	0.0392363	0.00162640
$583$	21.1391	0.875492
$584$	4.64159	0.192070
$585$	20.7810	0.859190
$586$	−5.28680	−0.218396
$587$	12.7418	0.525909	0.262954	−	0.964808i	$-0.415303\pi$
$587$	12.7418	0.525909	0.262954	+	0.964808i	$0.415303\pi$
$588$	0.156641	0.00645975
$589$	31.0792	1.28059
$590$	−39.0587	−1.60802
$591$	−0.0439458	−0.00180769
$592$	−1.09257	−0.0449045
$593$	22.6597	0.930522	0.465261	−	0.885174i	$-0.345961\pi$
$593$	22.6597	0.930522	0.465261	+	0.885174i	$0.345961\pi$
$594$	0.295399	0.0121204
$595$	−5.95985	−0.244330
$596$	1.20524	0.0493686
$597$	0.145715	0.00596372
$598$	−3.79484	−0.155183
$599$	−26.5835	−1.08617	−0.543086	−	0.839677i	$-0.682744\pi$
$599$	−26.5835	−1.08617	−0.543086	+	0.839677i	$0.682744\pi$
$600$	0.334062	0.0136380
$601$	5.51022	0.224766	0.112383	−	0.993665i	$-0.464152\pi$
$601$	5.51022	0.224766	0.112383	+	0.993665i	$0.464152\pi$
$602$	0	0
$603$	38.1376	1.55308
$604$	14.0987	0.573667
$605$	−0.513154	−0.0208627
$606$	−0.132448	−0.00538035
$607$	−2.81687	−0.114333	−0.0571667	−	0.998365i	$-0.518207\pi$
$607$	−2.81687	−0.114333	−0.0571667	+	0.998365i	$0.518207\pi$
$608$	34.4943	1.39893
$609$	−0.0113929	−0.000461664 0
$610$	28.9565	1.17242
$611$	−11.8996	−0.481407
$612$	−24.7869	−1.00195
$613$	−3.84496	−0.155296	−0.0776481	−	0.996981i	$-0.524741\pi$
$613$	−3.84496	−0.155296	−0.0776481	+	0.996981i	$0.524741\pi$
$614$	−4.23593	−0.170948
$615$	0.175263	0.00706727
$616$	2.46471	0.0993060
$617$	40.7413	1.64018	0.820091	−	0.572233i	$-0.193923\pi$
$617$	40.7413	1.64018	0.820091	+	0.572233i	$0.193923\pi$
$618$	−0.0113165	−0.000455215 0
$619$	−33.3575	−1.34075	−0.670376	−	0.742021i	$-0.733867\pi$
$619$	−33.3575	−1.34075	−0.670376	+	0.742021i	$0.733867\pi$
$620$	22.7742	0.914634
$621$	0.235088	0.00943375
$622$	−4.18158	−0.167666
$623$	0.486865	0.0195058
$624$	−0.00736452	−0.000294817 0
$625$	−12.6737	−0.506948
$626$	−7.10308	−0.283896
$627$	−0.349302	−0.0139498
$628$	24.6560	0.983880
$629$	34.0035	1.35581
$630$	2.35024	0.0936358
$631$	−26.8330	−1.06820	−0.534102	−	0.845420i	$-0.679350\pi$
$631$	−26.8330	−1.06820	−0.534102	+	0.845420i	$0.679350\pi$
$632$	−38.7780	−1.54251
$633$	−0.252538	−0.0100375
$634$	−15.3078	−0.607952
$635$	−31.9270	−1.26698
$636$	−0.145104	−0.00575374
$637$	13.9653	0.553324
$638$	6.70144	0.265312
$639$	18.1064	0.716277
$640$	26.4831	1.04684
$641$	39.6165	1.56476	0.782379	−	0.622802i	$-0.214006\pi$
$641$	39.6165	1.56476	0.782379	+	0.622802i	$0.214006\pi$
$642$	0.0495447	0.00195537
$643$	−9.53873	−0.376171	−0.188085	−	0.982153i	$-0.560228\pi$
$643$	−9.53873	−0.376171	−0.188085	+	0.982153i	$0.560228\pi$
$644$	0.766158	0.0301908
$645$	0	0
$646$	−32.8388	−1.29203
$647$	23.6364	0.929244	0.464622	−	0.885509i	$-0.346190\pi$
$647$	23.6364	0.929244	0.464622	+	0.885509i	$0.346190\pi$
$648$	25.0221	0.982960
$649$	44.1807	1.73424
$650$	11.6333	0.456296
$651$	−0.0245326	−0.000961510 0
$652$	−24.5994	−0.963386
$653$	1.35482	0.0530181	0.0265090	−	0.999649i	$-0.491561\pi$
$653$	1.35482	0.0530181	0.0265090	+	0.999649i	$0.491561\pi$
$654$	−0.150875	−0.00589966
$655$	−18.6409	−0.728360
$656$	0.598849	0.0233811
$657$	−5.00642	−0.195319
$658$	−1.34579	−0.0524645
$659$	−15.4161	−0.600525	−0.300262	−	0.953857i	$-0.597074\pi$
$659$	−15.4161	−0.600525	−0.300262	+	0.953857i	$0.597074\pi$
$660$	−0.255961	−0.00996328
$661$	−15.3691	−0.597790	−0.298895	−	0.954286i	$-0.596618\pi$
$661$	−15.3691	−0.597790	−0.298895	+	0.954286i	$0.596618\pi$
$662$	−1.60458	−0.0623638
$663$	0.229201	0.00890144
$664$	21.2602	0.825055
$665$	−5.55848	−0.215549
$666$	−13.4091	−0.519593
$667$	5.33321	0.206503
$668$	7.78351	0.301153
$669$	−0.120393	−0.00465465
$670$	37.0247	1.43039
$671$	−32.7537	−1.26444
$672$	−0.0272284	−0.00105036
$673$	−45.2670	−1.74492	−0.872458	−	0.488690i	$-0.837475\pi$
$673$	−45.2670	−1.74492	−0.872458	+	0.488690i	$0.837475\pi$
$674$	−0.269165	−0.0103678
$675$	−0.720676	−0.0277388
$676$	11.4554	0.440593
$677$	6.02395	0.231519	0.115760	−	0.993277i	$-0.463070\pi$
$677$	6.02395	0.231519	0.115760	+	0.993277i	$0.463070\pi$
$678$	0.0837926	0.00321803
$679$	−0.706249	−0.0271034
$680$	−61.6070	−2.36252
$681$	−0.415181	−0.0159098
$682$	14.4304	0.552567
$683$	2.83752	0.108575	0.0542873	−	0.998525i	$-0.482711\pi$
$683$	2.83752	0.108575	0.0542873	+	0.998525i	$0.482711\pi$
$684$	−23.1176	−0.883925
$685$	37.9581	1.45030
$686$	3.17532	0.121234
$687$	0.278393	0.0106214
$688$	0	0
$689$	−12.9367	−0.492849
$690$	0.114108	0.00434402
$691$	−24.9600	−0.949521	−0.474761	−	0.880115i	$-0.657465\pi$
$691$	−24.9600	−0.949521	−0.474761	+	0.880115i	$0.657465\pi$
$692$	14.1344	0.537309
$693$	−2.65844	−0.100986
$694$	23.4839	0.891438
$695$	−26.4206	−1.00219
$696$	−0.117768	−0.00446400
$697$	−18.6376	−0.705949
$698$	23.0214	0.871373
$699$	−0.0493522	−0.00186667
$700$	−2.34870	−0.0887726
$701$	10.9069	0.411947	0.205974	−	0.978558i	$-0.433964\pi$
$701$	10.9069	0.411947	0.205974	+	0.978558i	$0.433964\pi$
$702$	−0.180778	−0.00682303
$703$	31.7135	1.19610
$704$	14.6516	0.552201
$705$	0.357812	0.0134760
$706$	−16.6639	−0.627154
$707$	2.38406	0.0896616
$708$	−0.303266	−0.0113975
$709$	−4.63734	−0.174159	−0.0870796	−	0.996201i	$-0.527753\pi$
$709$	−4.63734	−0.174159	−0.0870796	+	0.996201i	$0.527753\pi$
$710$	17.5780	0.659691
$711$	41.8260	1.56860
$712$	5.03272	0.188609
$713$	11.4841	0.430085
$714$	0.0259216	0.000970093 0
$715$	−22.8202	−0.853427
$716$	−10.4265	−0.389658
$717$	0.0902731	0.00337131
$718$	6.69585	0.249887
$719$	−42.3159	−1.57812	−0.789059	−	0.614318i	$-0.789431\pi$
$719$	−42.3159	−1.57812	−0.789059	+	0.614318i	$0.789431\pi$
$720$	−2.13510	−0.0795704
$721$	0.203695	0.00758600
$722$	−14.5266	−0.540625
$723$	−0.103036	−0.00383196
$724$	−7.75059	−0.288048
$725$	−16.3493	−0.607197
$726$	0.00223190	8.28336e−5 0
$727$	−2.77806	−0.103033	−0.0515164	−	0.998672i	$-0.516405\pi$
$727$	−2.77806	−0.103033	−0.0515164	+	0.998672i	$0.516405\pi$
$728$	−1.50835	−0.0559033
$729$	−26.9832	−0.999378
$730$	−4.86032	−0.179889
$731$	0	0
$732$	0.224829	0.00830993
$733$	−43.6136	−1.61091	−0.805453	−	0.592660i	$-0.798078\pi$
$733$	−43.6136	−1.61091	−0.805453	+	0.592660i	$0.798078\pi$
$734$	−17.0882	−0.630739
$735$	−0.419925	−0.0154892
$736$	12.7461	0.469827
$737$	−41.8798	−1.54266
$738$	7.34964	0.270544
$739$	−2.73322	−0.100543	−0.0502715	−	0.998736i	$-0.516009\pi$
$739$	−2.73322	−0.100543	−0.0502715	+	0.998736i	$0.516009\pi$
$740$	23.2390	0.854283
$741$	0.213766	0.00785287
$742$	−1.46308	−0.0537114
$743$	39.8709	1.46272	0.731361	−	0.681990i	$-0.238885\pi$
$743$	39.8709	1.46272	0.731361	+	0.681990i	$0.238885\pi$
$744$	−0.253594	−0.00929720
$745$	−3.23103	−0.118376
$746$	6.69892	0.245265
$747$	−22.9312	−0.839010
$748$	27.2192	0.995232
$749$	−0.891799	−0.0325856
$750$	−0.0929739	−0.00339493
$751$	44.9390	1.63985	0.819924	−	0.572473i	$-0.194016\pi$
$751$	44.9390	1.63985	0.819924	+	0.572473i	$0.194016\pi$
$752$	1.22260	0.0445836
$753$	−0.155081	−0.00565146
$754$	−4.10114	−0.149355
$755$	−37.7960	−1.37554
$756$	0.0364982	0.00132743
$757$	12.8706	0.467791	0.233896	−	0.972262i	$-0.424853\pi$
$757$	12.8706	0.467791	0.233896	+	0.972262i	$0.424853\pi$
$758$	20.7510	0.753709
$759$	−0.129071	−0.00468500
$760$	−57.4580	−2.08422
$761$	−8.43959	−0.305935	−0.152967	−	0.988231i	$-0.548883\pi$
$761$	−8.43959	−0.305935	−0.152967	+	0.988231i	$0.548883\pi$
$762$	0.138862	0.00503045
$763$	2.71572	0.0983158
$764$	19.7790	0.715580
$765$	66.4493	2.40248
$766$	23.4038	0.845615
$767$	−27.0377	−0.976273
$768$	−0.272094	−0.00981834
$769$	29.4761	1.06294	0.531468	−	0.847078i	$-0.321640\pi$
$769$	29.4761	1.06294	0.531468	+	0.847078i	$0.321640\pi$
$770$	−2.58086	−0.0930078
$771$	−0.106232	−0.00382587
$772$	3.12394	0.112433
$773$	−32.7084	−1.17644	−0.588220	−	0.808701i	$-0.700171\pi$
$773$	−32.7084	−1.17644	−0.588220	+	0.808701i	$0.700171\pi$
$774$	0	0
$775$	−35.2053	−1.26461
$776$	−7.30049	−0.262072
$777$	−0.0250334	−0.000898067 0
$778$	−23.4475	−0.840633
$779$	−17.3824	−0.622790
$780$	0.156643	0.00560872
$781$	−19.8831	−0.711473
$782$	−12.1344	−0.433924
$783$	0.254063	0.00907948
$784$	−1.43483	−0.0512439
$785$	−66.0982	−2.35915
$786$	0.0810762	0.00289189
$787$	3.49791	0.124687	0.0623434	−	0.998055i	$-0.480143\pi$
$787$	3.49791	0.124687	0.0623434	+	0.998055i	$0.480143\pi$
$788$	3.19383	0.113776
$789$	0.426243	0.0151747
$790$	40.6055	1.44468
$791$	−1.50826	−0.0536274
$792$	−27.4802	−0.976468
$793$	20.0446	0.711805
$794$	−8.55696	−0.303675
$795$	0.388997	0.0137963
$796$	−10.5901	−0.375356
$797$	9.92349	0.351508	0.175754	−	0.984434i	$-0.443764\pi$
$797$	9.92349	0.351508	0.175754	+	0.984434i	$0.443764\pi$
$798$	0.0241759	0.000855818 0
$799$	−38.0501	−1.34612
$800$	−39.0739	−1.38147
$801$	−5.42829	−0.191799
$802$	−28.3478	−1.00100
$803$	5.49768	0.194009
$804$	0.287473	0.0101384
$805$	−2.05393	−0.0723915
$806$	−8.83109	−0.311062
$807$	−0.0773170	−0.00272169
$808$	24.6440	0.866972
$809$	−7.95427	−0.279657	−0.139829	−	0.990176i	$-0.544655\pi$
$809$	−7.95427	−0.279657	−0.139829	+	0.990176i	$0.544655\pi$
$810$	−26.2012	−0.920618
$811$	−47.1017	−1.65396	−0.826982	−	0.562228i	$-0.809944\pi$
$811$	−47.1017	−1.65396	−0.826982	+	0.562228i	$0.809944\pi$
$812$	0.827999	0.0290571
$813$	0.498677	0.0174894
$814$	14.7249	0.516107
$815$	65.9465	2.31000
$816$	−0.0235488	−0.000824371 0
$817$	0	0
$818$	−19.8247	−0.693154
$819$	1.62691	0.0568488
$820$	−12.7375	−0.444813
$821$	43.7624	1.52732	0.763659	−	0.645620i	$-0.223401\pi$
$821$	43.7624	1.52732	0.763659	+	0.645620i	$0.223401\pi$
$822$	−0.165094	−0.00575831
$823$	55.8038	1.94520	0.972599	−	0.232491i	$-0.0746876\pi$
$823$	55.8038	1.94520	0.972599	+	0.232491i	$0.0746876\pi$
$824$	2.10560	0.0733519
$825$	0.395676	0.0137757
$826$	−3.05784	−0.106396
$827$	−5.13702	−0.178632	−0.0893158	−	0.996003i	$-0.528468\pi$
$827$	−5.13702	−0.178632	−0.0893158	+	0.996003i	$0.528468\pi$
$828$	−8.54226	−0.296864
$829$	−3.57650	−0.124217	−0.0621085	−	0.998069i	$-0.519782\pi$
$829$	−3.57650	−0.124217	−0.0621085	+	0.998069i	$0.519782\pi$
$830$	−22.2621	−0.772728
$831$	0.406530	0.0141024
$832$	−8.96645	−0.310856
$833$	44.6552	1.54721
$834$	0.114913	0.00397911
$835$	−20.8662	−0.722104
$836$	25.3861	0.877996
$837$	0.547081	0.0189099
$838$	15.4004	0.532000
$839$	−41.1238	−1.41975	−0.709875	−	0.704327i	$-0.751249\pi$
$839$	−41.1238	−1.41975	−0.709875	+	0.704327i	$0.751249\pi$
$840$	0.0453551	0.00156490
$841$	−23.2363	−0.801252
$842$	24.8270	0.855595
$843$	0.315123	0.0108534
$844$	18.3536	0.631759
$845$	−30.7099	−1.05645
$846$	15.0049	0.515879
$847$	−0.0401739	−0.00138039
$848$	1.32915	0.0456432
$849$	−0.248826	−0.00853968
$850$	37.1986	1.27590
$851$	11.7185	0.401706
$852$	0.136482	0.00467580
$853$	−21.1046	−0.722609	−0.361304	−	0.932448i	$-0.617668\pi$
$853$	−21.1046	−0.722609	−0.361304	+	0.932448i	$0.617668\pi$
$854$	2.26695	0.0775736
$855$	61.9742	2.11947
$856$	−9.21852	−0.315083
$857$	31.7404	1.08423	0.542116	−	0.840303i	$-0.317623\pi$
$857$	31.7404	1.08423	0.542116	+	0.840303i	$0.317623\pi$
$858$	0.0992535	0.00338846
$859$	−29.8703	−1.01916	−0.509581	−	0.860423i	$-0.670200\pi$
$859$	−29.8703	−1.01916	−0.509581	+	0.860423i	$0.670200\pi$
$860$	0	0
$861$	0.0137210	0.000467610 0
$862$	−2.50151	−0.0852018
$863$	29.7728	1.01348	0.506740	−	0.862099i	$-0.330851\pi$
$863$	29.7728	1.01348	0.506740	+	0.862099i	$0.330851\pi$
$864$	0.607197	0.0206573
$865$	−37.8917	−1.28836
$866$	−28.4818	−0.967852
$867$	0.433037	0.0147067
$868$	1.78295	0.0605173
$869$	−45.9302	−1.55808
$870$	0.123318	0.00418088
$871$	25.6296	0.868426
$872$	28.0724	0.950652
$873$	7.87431	0.266505
$874$	−11.3172	−0.382809
$875$	1.67352	0.0565753
$876$	−0.0377373	−0.00127503
$877$	10.6475	0.359540	0.179770	−	0.983709i	$-0.442465\pi$
$877$	10.6475	0.359540	0.179770	+	0.983709i	$0.442465\pi$
$878$	−18.2959	−0.617457
$879$	0.110044	0.00371169
$880$	2.34461	0.0790367
$881$	−8.78141	−0.295853	−0.147927	−	0.988998i	$-0.547260\pi$
$881$	−8.78141	−0.295853	−0.147927	+	0.988998i	$0.547260\pi$
$882$	−17.6096	−0.592946
$883$	−45.2027	−1.52119	−0.760596	−	0.649225i	$-0.775093\pi$
$883$	−45.2027	−1.52119	−0.760596	+	0.649225i	$0.775093\pi$
$884$	−16.6576	−0.560255
$885$	0.813002	0.0273288
$886$	−3.00305	−0.100890
$887$	−30.4551	−1.02258	−0.511291	−	0.859408i	$-0.670832\pi$
$887$	−30.4551	−1.02258	−0.511291	+	0.859408i	$0.670832\pi$
$888$	−0.258770	−0.00868374
$889$	−2.49951	−0.0838308
$890$	−5.26989	−0.176647
$891$	29.6371	0.992880
$892$	8.74973	0.292963
$893$	−35.4876	−1.18755
$894$	0.0140530	0.000470001 0
$895$	27.9516	0.934320
$896$	2.07331	0.0692645
$897$	0.0789891	0.00263737
$898$	19.5167	0.651280
$899$	12.4111	0.413933
$900$	26.1868	0.872894
$901$	−41.3663	−1.37811
$902$	−8.07084	−0.268729
$903$	0	0
$904$	−15.5908	−0.518544
$905$	20.7779	0.690682
$906$	0.164389	0.00546146
$907$	36.9663	1.22745	0.613724	−	0.789521i	$-0.289671\pi$
$907$	36.9663	1.22745	0.613724	+	0.789521i	$0.289671\pi$
$908$	30.1740	1.00136
$909$	−26.5810	−0.881635
$910$	1.57943	0.0523577
$911$	3.69609	0.122457	0.0612285	−	0.998124i	$-0.480498\pi$
$911$	3.69609	0.122457	0.0612285	+	0.998124i	$0.480498\pi$
$912$	−0.0219628	−0.000727263 0
$913$	25.1814	0.833382
$914$	6.85196	0.226643
$915$	−0.602726	−0.0199255
$916$	−20.2327	−0.668507
$917$	−1.45936	−0.0481924
$918$	−0.578055	−0.0190787
$919$	−15.7274	−0.518798	−0.259399	−	0.965770i	$-0.583524\pi$
$919$	−15.7274	−0.518798	−0.259399	+	0.965770i	$0.583524\pi$
$920$	−21.2315	−0.699981
$921$	0.0881702	0.00290531
$922$	−8.33334	−0.274444
$923$	12.1680	0.400516
$924$	−0.0200388	−0.000659227 0
$925$	−35.9239	−1.18117
$926$	25.5478	0.839553
$927$	−2.27109	−0.0745925
$928$	13.7749	0.452183
$929$	−18.8021	−0.616876	−0.308438	−	0.951244i	$-0.599806\pi$
$929$	−18.8021	−0.616876	−0.308438	+	0.951244i	$0.599806\pi$
$930$	0.265544	0.00870754
$931$	41.6479	1.36496
$932$	3.58675	0.117488
$933$	0.0870390	0.00284953
$934$	20.5616	0.672797
$935$	−72.9697	−2.38636
$936$	16.8174	0.549692
$937$	11.3914	0.372139	0.186070	−	0.982537i	$-0.440425\pi$
$937$	11.3914	0.372139	0.186070	+	0.982537i	$0.440425\pi$
$938$	2.89859	0.0946425
$939$	0.147850	0.00482489
$940$	−26.0046	−0.848177
$941$	−38.6721	−1.26068	−0.630338	−	0.776321i	$-0.717084\pi$
$941$	−38.6721	−1.26068	−0.630338	+	0.776321i	$0.717084\pi$
$942$	0.287486	0.00936679
$943$	−6.42303	−0.209162
$944$	2.77792	0.0904137
$945$	−0.0978450	−0.00318290
$946$	0	0
$947$	−13.9735	−0.454077	−0.227039	−	0.973886i	$-0.572904\pi$
$947$	−13.9735	−0.454077	−0.227039	+	0.973886i	$0.572904\pi$
$948$	0.315276	0.0102397
$949$	−3.36447	−0.109215
$950$	34.6934	1.12560
$951$	0.318631	0.0103323
$952$	−4.82310	−0.156318
$953$	−58.2018	−1.88534	−0.942670	−	0.333725i	$-0.891694\pi$
$953$	−58.2018	−1.88534	−0.942670	+	0.333725i	$0.891694\pi$
$954$	16.3126	0.528140
$955$	−53.0240	−1.71582
$956$	−6.56075	−0.212190
$957$	−0.139490	−0.00450906
$958$	0.0518122	0.00167398
$959$	2.97167	0.0959602
$960$	0.269615	0.00870178
$961$	−4.27488	−0.137899
$962$	−9.01134	−0.290537
$963$	9.94310	0.320412
$964$	7.48833	0.241183
$965$	−8.37472	−0.269592
$966$	0.00893331	0.000287425 0
$967$	−20.0666	−0.645300	−0.322650	−	0.946518i	$-0.604574\pi$
$967$	−20.0666	−0.645300	−0.322650	+	0.946518i	$0.604574\pi$
$968$	−0.415278	−0.0133475
$969$	0.683535	0.0219583
$970$	7.64453	0.245451
$971$	59.2379	1.90104	0.950518	−	0.310670i	$-0.100553\pi$
$971$	59.2379	1.90104	0.950518	+	0.310670i	$0.100553\pi$
$972$	−0.610414	−0.0195790
$973$	−2.06842	−0.0663104
$974$	−19.6710	−0.630299
$975$	−0.242146	−0.00775487
$976$	−2.05944	−0.0659210
$977$	−43.5456	−1.39315	−0.696573	−	0.717486i	$-0.745293\pi$
$977$	−43.5456	−1.39315	−0.696573	+	0.717486i	$0.745293\pi$
$978$	−0.286826	−0.00917168
$979$	5.96095	0.190513
$980$	30.5188	0.974886
$981$	−30.2789	−0.966731
$982$	8.78812	0.280440
$983$	3.16541	0.100961	0.0504804	−	0.998725i	$-0.483925\pi$
$983$	3.16541	0.100961	0.0504804	+	0.998725i	$0.483925\pi$
$984$	0.141834	0.00452150
$985$	−8.56209	−0.272811
$986$	−13.1138	−0.417628
$987$	0.0280125	0.000891647 0
$988$	−15.5358	−0.494259
$989$	0	0
$990$	28.7753	0.914538
$991$	3.35622	0.106614	0.0533069	−	0.998578i	$-0.483024\pi$
$991$	3.35622	0.106614	0.0533069	+	0.998578i	$0.483024\pi$
$992$	29.6618	0.941764
$993$	0.0333992	0.00105989
$994$	1.37615	0.0436489
$995$	28.3901	0.900027
$996$	−0.172851	−0.00547699
$997$	53.7400	1.70196	0.850981	−	0.525196i	$-0.176008\pi$
$997$	53.7400	1.70196	0.850981	+	0.525196i	$0.176008\pi$
$998$	−10.2460	−0.324331
$999$	0.558247	0.0176621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.9		18
43.15	even	21		43.2.g.a.10.2	✓	36
43.23	even	21		43.2.g.a.13.2	yes	36
43.42	odd	2		1849.2.a.o.1.10		18
129.23	odd	42		387.2.y.c.271.2		36
129.101	odd	42		387.2.y.c.10.2		36
172.15	odd	42		688.2.bg.c.225.1		36
172.23	odd	42		688.2.bg.c.529.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.2	✓	36	43.15	even	21
43.2.g.a.13.2	yes	36	43.23	even	21
387.2.y.c.10.2		36	129.101	odd	42
387.2.y.c.271.2		36	129.23	odd	42
688.2.bg.c.225.1		36	172.15	odd	42
688.2.bg.c.529.1		36	172.23	odd	42
1849.2.a.n.1.9		18	1.1	even	1	trivial
1849.2.a.o.1.10		18	43.42	odd	2

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-0.847401 q^{2} +0.0176385 q^{3} -1.28191 q^{4} +3.43657 q^{5} -0.0149469 q^{6} +0.269043 q^{7} +2.78110 q^{8} -2.99969 q^{9} +O(q^{10})\)	\(q-0.847401 q^{2} +0.0176385 q^{3} -1.28191 q^{4} +3.43657 q^{5} -0.0149469 q^{6} +0.269043 q^{7} +2.78110 q^{8} -2.99969 q^{9} -2.91216 q^{10} +3.29404 q^{11} -0.0226110 q^{12} -2.01588 q^{13} -0.227987 q^{14} +0.0606161 q^{15} +0.207117 q^{16} -6.44598 q^{17} +2.54194 q^{18} -6.01187 q^{19} -4.40538 q^{20} +0.00474553 q^{21} -2.79137 q^{22} -2.22146 q^{23} +0.0490545 q^{24} +6.81002 q^{25} +1.70826 q^{26} -0.105826 q^{27} -0.344889 q^{28} -2.40077 q^{29} -0.0513662 q^{30} -5.16963 q^{31} -5.73770 q^{32} +0.0581020 q^{33} +5.46233 q^{34} +0.924585 q^{35} +3.84533 q^{36} -5.27515 q^{37} +5.09447 q^{38} -0.0355573 q^{39} +9.55743 q^{40} +2.89135 q^{41} -0.00402137 q^{42} -4.22266 q^{44} -10.3086 q^{45} +1.88247 q^{46} +5.90293 q^{47} +0.00365325 q^{48} -6.92762 q^{49} -5.77082 q^{50} -0.113698 q^{51} +2.58418 q^{52} +6.41738 q^{53} +0.0896769 q^{54} +11.3202 q^{55} +0.748234 q^{56} -0.106041 q^{57} +2.03441 q^{58} +13.4123 q^{59} -0.0777045 q^{60} -9.94333 q^{61} +4.38076 q^{62} -0.807045 q^{63} +4.44790 q^{64} -6.92773 q^{65} -0.0492357 q^{66} -12.7138 q^{67} +8.26317 q^{68} -0.0391834 q^{69} -0.783495 q^{70} -6.03609 q^{71} -8.34242 q^{72} +1.66898 q^{73} +4.47017 q^{74} +0.120119 q^{75} +7.70668 q^{76} +0.886237 q^{77} +0.0301313 q^{78} -13.9434 q^{79} +0.711773 q^{80} +8.99720 q^{81} -2.45014 q^{82} +7.64454 q^{83} -0.00608334 q^{84} -22.1521 q^{85} -0.0423461 q^{87} +9.16103 q^{88} +1.80962 q^{89} +8.73556 q^{90} -0.542359 q^{91} +2.84772 q^{92} -0.0911848 q^{93} -5.00215 q^{94} -20.6602 q^{95} -0.101205 q^{96} -2.62504 q^{97} +5.87047 q^{98} -9.88109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more