LMFDB - Embedded newform 841.2.a.f.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(1,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$6.71541880999$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.80194 q^{2} -0.445042 q^{3} +1.24698 q^{4} +0.356896 q^{5} -0.801938 q^{6} -4.04892 q^{7} -1.35690 q^{8} -2.80194 q^{9} +0.643104 q^{10} -2.91185 q^{11} -0.554958 q^{12} +5.18598 q^{13} -7.29590 q^{14} -0.158834 q^{15} -4.93900 q^{16} -1.10992 q^{17} -5.04892 q^{18} -2.04892 q^{19} +0.445042 q^{20} +1.80194 q^{21} -5.24698 q^{22} -4.13706 q^{23} +0.603875 q^{24} -4.87263 q^{25} +9.34481 q^{26} +2.58211 q^{27} -5.04892 q^{28} -0.286208 q^{30} +6.35690 q^{31} -6.18598 q^{32} +1.29590 q^{33} -2.00000 q^{34} -1.44504 q^{35} -3.49396 q^{36} +2.91185 q^{37} -3.69202 q^{38} -2.30798 q^{39} -0.484271 q^{40} -0.396125 q^{41} +3.24698 q^{42} -5.74094 q^{43} -3.63102 q^{44} -1.00000 q^{45} -7.45473 q^{46} +7.80194 q^{47} +2.19806 q^{48} +9.39373 q^{49} -8.78017 q^{50} +0.493959 q^{51} +6.46681 q^{52} -4.35690 q^{53} +4.65279 q^{54} -1.03923 q^{55} +5.49396 q^{56} +0.911854 q^{57} -9.10992 q^{59} -0.198062 q^{60} +6.04892 q^{61} +11.4547 q^{62} +11.3448 q^{63} -1.26875 q^{64} +1.85086 q^{65} +2.33513 q^{66} +0.374354 q^{67} -1.38404 q^{68} +1.84117 q^{69} -2.60388 q^{70} -11.4058 q^{71} +3.80194 q^{72} +8.94869 q^{73} +5.24698 q^{74} +2.16852 q^{75} -2.55496 q^{76} +11.7899 q^{77} -4.15883 q^{78} +0.594187 q^{79} -1.76271 q^{80} +7.25667 q^{81} -0.713792 q^{82} -9.43296 q^{83} +2.24698 q^{84} -0.396125 q^{85} -10.3448 q^{86} +3.95108 q^{88} -1.42327 q^{89} -1.80194 q^{90} -20.9976 q^{91} -5.15883 q^{92} -2.82908 q^{93} +14.0586 q^{94} -0.731250 q^{95} +2.75302 q^{96} -15.7506 q^{97} +16.9269 q^{98} +8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 4 q^{9} + 6 q^{10} - 5 q^{11} - 2 q^{12} + q^{13} - 8 q^{14} + 8 q^{15} - 5 q^{16} - 4 q^{17} - 6 q^{18} + 3 q^{19} + q^{20} + q^{21} - 11 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) $ 3 * q + q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 4 * q^9 + 6 * q^10 - 5 * q^11 - 2 * q^12 + q^13 - 8 * q^14 + 8 * q^15 - 5 * q^16 - 4 * q^17 - 6 * q^18 + 3 * q^19 + q^20 + q^21 - 11 * q^22 - 7 * q^23 - 7 * q^24 + 2 * q^25 + 5 * q^26 + 2 * q^27 - 6 * q^28 - 9 * q^30 + 15 * q^31 - 4 * q^32 - 10 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 5 * q^37 - 6 * q^38 - 12 * q^39 - 14 * q^40 - 10 * q^41 + 5 * q^42 - 3 * q^43 + 4 * q^44 - 3 * q^45 + 19 * q^47 + 11 * q^48 - 4 * q^49 - 25 * q^50 - 8 * q^51 + 16 * q^52 - 9 * q^53 - 4 * q^54 - 16 * q^55 + 7 * q^56 - q^57 - 28 * q^59 - 5 * q^60 + 9 * q^61 + 12 * q^62 + 11 * q^63 + 4 * q^64 - 8 * q^65 + 6 * q^66 + 13 * q^67 + 6 * q^68 + 14 * q^69 + q^70 - 21 * q^71 + 7 * q^72 - 5 * q^73 + 11 * q^74 - 24 * q^75 - 8 * q^76 + 12 * q^77 - 4 * q^78 + 15 * q^79 + 12 * q^80 - 5 * q^81 + 6 * q^82 - 9 * q^83 + 2 * q^84 - 10 * q^85 - 8 * q^86 + 21 * q^88 - 7 * q^89 - q^90 - 22 * q^91 - 7 * q^92 + 2 * q^93 + 11 * q^94 - 10 * q^95 + 13 * q^96 - 11 * q^97 + 22 * q^98 + 16 * q^99

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 $

$2$	1.80194	1.27416	0.637081	−	0.770797i	$-0.280142\pi$
$2$	1.80194	1.27416	0.637081	+	0.770797i	$0.280142\pi$
$3$	−0.445042	−0.256945	−0.128473	−	0.991713i	$-0.541007\pi$
$3$	−0.445042	−0.256945	−0.128473	+	0.991713i	$0.541007\pi$
$4$	1.24698	0.623490
$5$	0.356896	0.159609	0.0798043	−	0.996811i	$-0.474570\pi$
$5$	0.356896	0.159609	0.0798043	+	0.996811i	$0.474570\pi$
$6$	−0.801938	−0.327390
$7$	−4.04892	−1.53035	−0.765173	−	0.643824i	$-0.777347\pi$
$7$	−4.04892	−1.53035	−0.765173	+	0.643824i	$0.777347\pi$
$8$	−1.35690	−0.479735
$9$	−2.80194	−0.933979
$10$	0.643104	0.203367
$11$	−2.91185	−0.877957	−0.438979	−	0.898498i	$-0.644660\pi$
$11$	−2.91185	−0.877957	−0.438979	+	0.898498i	$0.644660\pi$
$12$	−0.554958	−0.160203
$13$	5.18598	1.43833	0.719166	−	0.694838i	$-0.244524\pi$
$13$	5.18598	1.43833	0.719166	+	0.694838i	$0.244524\pi$
$14$	−7.29590	−1.94991
$15$	−0.158834	−0.0410107
$16$	−4.93900	−1.23475
$17$	−1.10992	−0.269194	−0.134597	−	0.990900i	$-0.542974\pi$
$17$	−1.10992	−0.269194	−0.134597	+	0.990900i	$0.542974\pi$
$18$	−5.04892	−1.19004
$19$	−2.04892	−0.470054	−0.235027	−	0.971989i	$-0.575518\pi$
$19$	−2.04892	−0.470054	−0.235027	+	0.971989i	$0.575518\pi$
$20$	0.445042	0.0995144
$21$	1.80194	0.393215
$22$	−5.24698	−1.11866
$23$	−4.13706	−0.862637	−0.431319	−	0.902200i	$-0.641952\pi$
$23$	−4.13706	−0.862637	−0.431319	+	0.902200i	$0.641952\pi$
$24$	0.603875	0.123266
$25$	−4.87263	−0.974525
$26$	9.34481	1.83267
$27$	2.58211	0.496926
$28$	−5.04892	−0.954156
$29$	0	0
$29$	0	0
$30$	−0.286208	−0.0522542
$31$	6.35690	1.14173	0.570866	−	0.821043i	$-0.306608\pi$
$31$	6.35690	1.14173	0.570866	+	0.821043i	$0.306608\pi$
$32$	−6.18598	−1.09354
$33$	1.29590	0.225587
$34$	−2.00000	−0.342997
$35$	−1.44504	−0.244257
$36$	−3.49396	−0.582327
$37$	2.91185	0.478706	0.239353	−	0.970933i	$-0.423065\pi$
$37$	2.91185	0.478706	0.239353	+	0.970933i	$0.423065\pi$
$38$	−3.69202	−0.598925
$39$	−2.30798	−0.369572
$40$	−0.484271	−0.0765699
$41$	−0.396125	−0.0618643	−0.0309321	−	0.999521i	$-0.509848\pi$
$41$	−0.396125	−0.0618643	−0.0309321	+	0.999521i	$0.509848\pi$
$42$	3.24698	0.501020
$43$	−5.74094	−0.875485	−0.437742	−	0.899100i	$-0.644222\pi$
$43$	−5.74094	−0.875485	−0.437742	+	0.899100i	$0.644222\pi$
$44$	−3.63102	−0.547397
$45$	−1.00000	−0.149071
$46$	−7.45473	−1.09914
$47$	7.80194	1.13803	0.569015	−	0.822327i	$-0.307325\pi$
$47$	7.80194	1.13803	0.569015	+	0.822327i	$0.307325\pi$
$48$	2.19806	0.317263
$49$	9.39373	1.34196
$50$	−8.78017	−1.24170
$51$	0.493959	0.0691681
$52$	6.46681	0.896785
$53$	−4.35690	−0.598466	−0.299233	−	0.954180i	$-0.596731\pi$
$53$	−4.35690	−0.598466	−0.299233	+	0.954180i	$0.596731\pi$
$54$	4.65279	0.633165
$55$	−1.03923	−0.140130
$56$	5.49396	0.734161
$57$	0.911854	0.120778
$58$	0	0
$59$	−9.10992	−1.18601	−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992	−1.18601	−0.593005	+	0.805199i	$0.702059\pi$
$60$	−0.198062	−0.0255697
$61$	6.04892	0.774485	0.387242	−	0.921978i	$-0.373428\pi$
$61$	6.04892	0.774485	0.387242	+	0.921978i	$0.373428\pi$
$62$	11.4547	1.45475
$63$	11.3448	1.42931
$64$	−1.26875	−0.158594
$65$	1.85086	0.229570
$66$	2.33513	0.287434
$67$	0.374354	0.0457347	0.0228673	−	0.999739i	$-0.492720\pi$
$67$	0.374354	0.0457347	0.0228673	+	0.999739i	$0.492720\pi$
$68$	−1.38404	−0.167840
$69$	1.84117	0.221650
$70$	−2.60388	−0.311223
$71$	−11.4058	−1.35362	−0.676810	−	0.736157i	$-0.736638\pi$
$71$	−11.4058	−1.35362	−0.676810	+	0.736157i	$0.736638\pi$
$72$	3.80194	0.448063
$73$	8.94869	1.04736	0.523682	−	0.851914i	$-0.324558\pi$
$73$	8.94869	1.04736	0.523682	+	0.851914i	$0.324558\pi$
$74$	5.24698	0.609949
$75$	2.16852	0.250399
$76$	−2.55496	−0.293074
$77$	11.7899	1.34358
$78$	−4.15883	−0.470895
$79$	0.594187	0.0668512	0.0334256	−	0.999441i	$-0.489358\pi$
$79$	0.594187	0.0668512	0.0334256	+	0.999441i	$0.489358\pi$
$80$	−1.76271	−0.197077
$81$	7.25667	0.806296
$82$	−0.713792	−0.0788251
$83$	−9.43296	−1.03540	−0.517701	−	0.855562i	$-0.673212\pi$
$83$	−9.43296	−1.03540	−0.517701	+	0.855562i	$0.673212\pi$
$84$	2.24698	0.245166
$85$	−0.396125	−0.0429657
$86$	−10.3448	−1.11551
$87$	0	0
$88$	3.95108	0.421187
$89$	−1.42327	−0.150866	−0.0754332	−	0.997151i	$-0.524034\pi$
$89$	−1.42327	−0.150866	−0.0754332	+	0.997151i	$0.524034\pi$
$90$	−1.80194	−0.189941
$91$	−20.9976	−2.20115
$92$	−5.15883	−0.537846
$93$	−2.82908	−0.293362
$94$	14.0586	1.45003
$95$	−0.731250	−0.0750247
$96$	2.75302	0.280979
$97$	−15.7506	−1.59923	−0.799617	−	0.600510i	$-0.794964\pi$
$97$	−15.7506	−1.59923	−0.799617	+	0.600510i	$0.794964\pi$
$98$	16.9269	1.70988
$99$	8.15883	0.819994
$100$	−6.07606	−0.607606
$101$	17.4426	1.73561	0.867804	−	0.496906i	$-0.165531\pi$
$101$	17.4426	1.73561	0.867804	+	0.496906i	$0.165531\pi$
$102$	0.890084	0.0881314
$103$	−2.81402	−0.277274	−0.138637	−	0.990343i	$-0.544272\pi$
$103$	−2.81402	−0.277274	−0.138637	+	0.990343i	$0.544272\pi$
$104$	−7.03684	−0.690019
$105$	0.643104	0.0627605
$106$	−7.85086	−0.762542
$107$	−7.46011	−0.721196	−0.360598	−	0.932721i	$-0.617427\pi$
$107$	−7.46011	−0.721196	−0.360598	+	0.932721i	$0.617427\pi$
$108$	3.21983	0.309829
$109$	−1.65279	−0.158309	−0.0791544	−	0.996862i	$-0.525222\pi$
$109$	−1.65279	−0.158309	−0.0791544	+	0.996862i	$0.525222\pi$
$110$	−1.87263	−0.178548
$111$	−1.29590	−0.123001
$112$	19.9976	1.88960
$113$	−8.64071	−0.812850	−0.406425	−	0.913684i	$-0.633225\pi$
$113$	−8.64071	−0.812850	−0.406425	+	0.913684i	$0.633225\pi$
$114$	1.64310	0.153891
$115$	−1.47650	−0.137684
$116$	0	0
$117$	−14.5308	−1.34337
$118$	−16.4155	−1.51117
$119$	4.49396	0.411961
$120$	0.215521	0.0196743
$121$	−2.52111	−0.229191
$122$	10.8998	0.986819
$123$	0.176292	0.0158957
$124$	7.92692	0.711858
$125$	−3.52350	−0.315151
$126$	20.4426	1.82118
$127$	−10.4722	−0.929257	−0.464628	−	0.885506i	$-0.653812\pi$
$127$	−10.4722	−0.929257	−0.464628	+	0.885506i	$0.653812\pi$
$128$	10.0858	0.891463
$129$	2.55496	0.224952
$130$	3.33513	0.292510
$131$	0.454731	0.0397300	0.0198650	−	0.999803i	$-0.493676\pi$
$131$	0.454731	0.0397300	0.0198650	+	0.999803i	$0.493676\pi$
$132$	1.61596	0.140651
$133$	8.29590	0.719345
$134$	0.674563	0.0582734
$135$	0.921543	0.0793138
$136$	1.50604	0.129142
$137$	13.2403	1.13119	0.565597	−	0.824682i	$-0.308646\pi$
$137$	13.2403	1.13119	0.565597	+	0.824682i	$0.308646\pi$
$138$	3.31767	0.282419
$139$	−2.79656	−0.237201	−0.118601	−	0.992942i	$-0.537841\pi$
$139$	−2.79656	−0.237201	−0.118601	+	0.992942i	$0.537841\pi$
$140$	−1.80194	−0.152292
$141$	−3.47219	−0.292411
$142$	−20.5526	−1.72473
$143$	−15.1008	−1.26279
$144$	13.8388	1.15323
$145$	0	0
$146$	16.1250	1.33451
$147$	−4.18060	−0.344810
$148$	3.63102	0.298468
$149$	2.70841	0.221882	0.110941	−	0.993827i	$-0.464614\pi$
$149$	2.70841	0.221882	0.110941	+	0.993827i	$0.464614\pi$
$150$	3.90754	0.319049
$151$	−2.43535	−0.198186	−0.0990931	−	0.995078i	$-0.531594\pi$
$151$	−2.43535	−0.198186	−0.0990931	+	0.995078i	$0.531594\pi$
$152$	2.78017	0.225501
$153$	3.10992	0.251422
$154$	21.2446	1.71194
$155$	2.26875	0.182230
$156$	−2.87800	−0.230425
$157$	−17.6775	−1.41082	−0.705411	−	0.708799i	$-0.749238\pi$
$157$	−17.6775	−1.41082	−0.705411	+	0.708799i	$0.749238\pi$
$158$	1.07069	0.0851793
$159$	1.93900	0.153773
$160$	−2.20775	−0.174538
$161$	16.7506	1.32013
$162$	13.0761	1.02735
$163$	4.96615	0.388979	0.194489	−	0.980905i	$-0.437695\pi$
$163$	4.96615	0.388979	0.194489	+	0.980905i	$0.437695\pi$
$164$	−0.493959	−0.0385717
$165$	0.462500	0.0360056
$166$	−16.9976	−1.31927
$167$	14.4644	1.11929	0.559645	−	0.828732i	$-0.310937\pi$
$167$	14.4644	1.11929	0.559645	+	0.828732i	$0.310937\pi$
$168$	−2.44504	−0.188639
$169$	13.8944	1.06880
$170$	−0.713792	−0.0547453
$171$	5.74094	0.439021
$172$	−7.15883	−0.545856
$173$	10.5133	0.799314	0.399657	−	0.916665i	$-0.369129\pi$
$173$	10.5133	0.799314	0.399657	+	0.916665i	$0.369129\pi$
$174$	0	0
$175$	19.7289	1.49136
$176$	14.3817	1.08406
$177$	4.05429	0.304739
$178$	−2.56465	−0.192228
$179$	−5.74094	−0.429098	−0.214549	−	0.976713i	$-0.568828\pi$
$179$	−5.74094	−0.429098	−0.214549	+	0.976713i	$0.568828\pi$
$180$	−1.24698	−0.0929444
$181$	−6.64071	−0.493600	−0.246800	−	0.969066i	$-0.579379\pi$
$181$	−6.64071	−0.493600	−0.246800	+	0.969066i	$0.579379\pi$
$182$	−37.8364	−2.80462
$183$	−2.69202	−0.199000
$184$	5.61356	0.413837
$185$	1.03923	0.0764056
$186$	−5.09783	−0.373791
$187$	3.23191	0.236341
$188$	9.72886	0.709550
$189$	−10.4547	−0.760470
$190$	−1.31767	−0.0955936
$191$	18.8116	1.36116	0.680581	−	0.732673i	$-0.261728\pi$
$191$	18.8116	1.36116	0.680581	+	0.732673i	$0.261728\pi$
$192$	0.564647	0.0407499
$193$	−10.8847	−0.783498	−0.391749	−	0.920072i	$-0.628130\pi$
$193$	−10.8847	−0.783498	−0.391749	+	0.920072i	$0.628130\pi$
$194$	−28.3817	−2.03768
$195$	−0.823708	−0.0589870
$196$	11.7138	0.836699
$197$	−8.40044	−0.598506	−0.299253	−	0.954174i	$-0.596738\pi$
$197$	−8.40044	−0.598506	−0.299253	+	0.954174i	$0.596738\pi$
$198$	14.7017	1.04481
$199$	−6.62133	−0.469374	−0.234687	−	0.972071i	$-0.575407\pi$
$199$	−6.62133	−0.469374	−0.234687	+	0.972071i	$0.575407\pi$
$200$	6.61165	0.467514
$201$	−0.166603	−0.0117513
$202$	31.4306	2.21145
$203$	0	0
$204$	0.615957	0.0431256
$205$	−0.141375	−0.00987407
$206$	−5.07069	−0.353292
$207$	11.5918	0.805685
$208$	−25.6136	−1.77598
$209$	5.96615	0.412687
$210$	1.15883	0.0799671
$211$	8.10023	0.557643	0.278821	−	0.960343i	$-0.410056\pi$
$211$	8.10023	0.557643	0.278821	+	0.960343i	$0.410056\pi$
$212$	−5.43296	−0.373137
$213$	5.07606	0.347806
$214$	−13.4426	−0.918921
$215$	−2.04892	−0.139735
$216$	−3.50365	−0.238393
$217$	−25.7385	−1.74725
$218$	−2.97823	−0.201711
$219$	−3.98254	−0.269115
$220$	−1.29590	−0.0873694
$221$	−5.75600	−0.387191
$222$	−2.33513	−0.156723
$223$	21.9191	1.46781	0.733907	−	0.679250i	$-0.237695\pi$
$223$	21.9191	1.46781	0.733907	+	0.679250i	$0.237695\pi$
$224$	25.0465	1.67349
$225$	13.6528	0.910186
$226$	−15.5700	−1.03570
$227$	−18.2784	−1.21318	−0.606591	−	0.795014i	$-0.707464\pi$
$227$	−18.2784	−1.21318	−0.606591	+	0.795014i	$0.707464\pi$
$228$	1.13706	0.0753039
$229$	−16.0248	−1.05895	−0.529473	−	0.848327i	$-0.677610\pi$
$229$	−16.0248	−1.05895	−0.529473	+	0.848327i	$0.677610\pi$
$230$	−2.66056	−0.175432
$231$	−5.24698	−0.345226
$232$	0	0
$233$	1.95646	0.128172	0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646	0.128172	0.0640860	+	0.997944i	$0.479587\pi$
$234$	−26.1836	−1.71167
$235$	2.78448	0.181639
$236$	−11.3599	−0.739465
$237$	−0.264438	−0.0171771
$238$	8.09783	0.524905
$239$	−8.96316	−0.579779	−0.289889	−	0.957060i	$-0.593619\pi$
$239$	−8.96316	−0.579779	−0.289889	+	0.957060i	$0.593619\pi$
$240$	0.784479	0.0506379
$241$	19.8998	1.28186	0.640929	−	0.767601i	$-0.278549\pi$
$241$	19.8998	1.28186	0.640929	+	0.767601i	$0.278549\pi$
$242$	−4.54288	−0.292027
$243$	−10.9758	−0.704100
$244$	7.54288	0.482883
$245$	3.35258	0.214189
$246$	0.317667	0.0202537
$247$	−10.6256	−0.676094
$248$	−8.62565	−0.547729
$249$	4.19806	0.266041
$250$	−6.34913	−0.401554
$251$	−25.8049	−1.62879	−0.814396	−	0.580309i	$-0.802932\pi$
$251$	−25.8049	−1.62879	−0.814396	+	0.580309i	$0.802932\pi$
$252$	14.1468	0.891162
$253$	12.0465	0.757359
$254$	−18.8702	−1.18402
$255$	0.176292	0.0110398
$256$	20.7114	1.29446
$257$	11.9511	0.745488	0.372744	−	0.927934i	$-0.378417\pi$
$257$	11.9511	0.745488	0.372744	+	0.927934i	$0.378417\pi$
$258$	4.60388	0.286625
$259$	−11.7899	−0.732586
$260$	2.30798	0.143135
$261$	0	0
$262$	0.819396	0.0506225
$263$	0.332733	0.0205172	0.0102586	−	0.999947i	$-0.496735\pi$
$263$	0.332733	0.0205172	0.0102586	+	0.999947i	$0.496735\pi$
$264$	−1.75840	−0.108222
$265$	−1.55496	−0.0955203
$266$	14.9487	0.916563
$267$	0.633415	0.0387644
$268$	0.466812	0.0285151
$269$	1.06398	0.0648722	0.0324361	−	0.999474i	$-0.489673\pi$
$269$	1.06398	0.0648722	0.0324361	+	0.999474i	$0.489673\pi$
$270$	1.66056	0.101059
$271$	16.4644	1.00014	0.500071	−	0.865984i	$-0.333307\pi$
$271$	16.4644	1.00014	0.500071	+	0.865984i	$0.333307\pi$
$272$	5.48188	0.332388
$273$	9.34481	0.565574
$274$	23.8582	1.44132
$275$	14.1884	0.855591
$276$	2.29590	0.138197
$277$	6.59419	0.396206	0.198103	−	0.980181i	$-0.436522\pi$
$277$	6.59419	0.396206	0.198103	+	0.980181i	$0.436522\pi$
$278$	−5.03923	−0.302233
$279$	−17.8116	−1.06635
$280$	1.96077	0.117179
$281$	−30.5351	−1.82157	−0.910786	−	0.412879i	$-0.864523\pi$
$281$	−30.5351	−1.82157	−0.910786	+	0.412879i	$0.864523\pi$
$282$	−6.25667	−0.372579
$283$	−3.55496	−0.211320	−0.105660	−	0.994402i	$-0.533696\pi$
$283$	−3.55496	−0.211320	−0.105660	+	0.994402i	$0.533696\pi$
$284$	−14.2228	−0.843969
$285$	0.325437	0.0192772
$286$	−27.2107	−1.60900
$287$	1.60388	0.0946738
$288$	17.3327	1.02134
$289$	−15.7681	−0.927534
$290$	0	0
$291$	7.00969	0.410915
$292$	11.1588	0.653021
$293$	−32.8799	−1.92087	−0.960433	−	0.278512i	$-0.910159\pi$
$293$	−32.8799	−1.92087	−0.960433	+	0.278512i	$0.910159\pi$
$294$	−7.53319	−0.439344
$295$	−3.25129	−0.189298
$296$	−3.95108	−0.229652
$297$	−7.51871	−0.436280
$298$	4.88040	0.282714
$299$	−21.4547	−1.24076
$300$	2.70410	0.156121
$301$	23.2446	1.33980
$302$	−4.38835	−0.252521
$303$	−7.76271	−0.445956
$304$	10.1196	0.580399
$305$	2.15883	0.123614
$306$	5.60388	0.320352
$307$	−14.6703	−0.837275	−0.418638	−	0.908153i	$-0.637492\pi$
$307$	−14.6703	−0.837275	−0.418638	+	0.908153i	$0.637492\pi$
$308$	14.7017	0.837708
$309$	1.25236	0.0712441
$310$	4.08815	0.232191
$311$	−18.5265	−1.05054	−0.525270	−	0.850935i	$-0.676036\pi$
$311$	−18.5265	−1.05054	−0.525270	+	0.850935i	$0.676036\pi$
$312$	3.13169	0.177297
$313$	22.9922	1.29960	0.649799	−	0.760106i	$-0.274853\pi$
$313$	22.9922	1.29960	0.649799	+	0.760106i	$0.274853\pi$
$314$	−31.8538	−1.79762
$315$	4.04892	0.228131
$316$	0.740939	0.0416811
$317$	−14.0586	−0.789610	−0.394805	−	0.918765i	$-0.629188\pi$
$317$	−14.0586	−0.789610	−0.394805	+	0.918765i	$0.629188\pi$
$318$	3.49396	0.195932
$319$	0	0
$320$	−0.452812	−0.0253129
$321$	3.32006	0.185308
$322$	30.1836	1.68207
$323$	2.27413	0.126536
$324$	9.04892	0.502718
$325$	−25.2693	−1.40169
$326$	8.94869	0.495622
$327$	0.735562	0.0406767
$328$	0.537500	0.0296785
$329$	−31.5894	−1.74158
$330$	0.833397	0.0458770
$331$	−13.9565	−0.767116	−0.383558	−	0.923517i	$-0.625301\pi$
$331$	−13.9565	−0.767116	−0.383558	+	0.923517i	$0.625301\pi$
$332$	−11.7627	−0.645563
$333$	−8.15883	−0.447101
$334$	26.0640	1.42616
$335$	0.133605	0.00729965
$336$	−8.89977	−0.485522
$337$	13.9976	0.762498	0.381249	−	0.924472i	$-0.375494\pi$
$337$	13.9976	0.762498	0.381249	+	0.924472i	$0.375494\pi$
$338$	25.0368	1.36182
$339$	3.84548	0.208858
$340$	−0.493959	−0.0267887
$341$	−18.5104	−1.00239
$342$	10.3448	0.559383
$343$	−9.69202	−0.523320
$344$	7.78986	0.420001
$345$	0.657105	0.0353773
$346$	18.9444	1.01846
$347$	−19.8538	−1.06581	−0.532905	−	0.846175i	$-0.678900\pi$
$347$	−19.8538	−1.06581	−0.532905	+	0.846175i	$0.678900\pi$
$348$	0	0
$349$	−26.9202	−1.44101	−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202	−1.44101	−0.720503	+	0.693452i	$0.756089\pi$
$350$	35.5502	1.90024
$351$	13.3907	0.714745
$352$	18.0127	0.960079
$353$	−4.01507	−0.213700	−0.106850	−	0.994275i	$-0.534077\pi$
$353$	−4.01507	−0.213700	−0.106850	+	0.994275i	$0.534077\pi$
$354$	7.30559	0.388287
$355$	−4.07069	−0.216050
$356$	−1.77479	−0.0940637
$357$	−2.00000	−0.105851
$358$	−10.3448	−0.546740
$359$	0.746316	0.0393890	0.0196945	−	0.999806i	$-0.493731\pi$
$359$	0.746316	0.0393890	0.0196945	+	0.999806i	$0.493731\pi$
$360$	1.35690	0.0715147
$361$	−14.8019	−0.779049
$362$	−11.9661	−0.628927
$363$	1.12200	0.0588896
$364$	−26.1836	−1.37239
$365$	3.19375	0.167169
$366$	−4.85086	−0.253558
$367$	34.0489	1.77734	0.888670	−	0.458548i	$-0.151630\pi$
$367$	34.0489	1.77734	0.888670	+	0.458548i	$0.151630\pi$
$368$	20.4330	1.06514
$369$	1.10992	0.0577799
$370$	1.87263	0.0973532
$371$	17.6407	0.915860
$372$	−3.52781	−0.182908
$373$	28.0006	1.44982	0.724908	−	0.688846i	$-0.241882\pi$
$373$	28.0006	1.44982	0.724908	+	0.688846i	$0.241882\pi$
$374$	5.82371	0.301137
$375$	1.56810	0.0809766
$376$	−10.5864	−0.545953
$377$	0	0
$378$	−18.8388	−0.968962
$379$	−22.8810	−1.17532	−0.587659	−	0.809109i	$-0.699950\pi$
$379$	−22.8810	−1.17532	−0.587659	+	0.809109i	$0.699950\pi$
$380$	−0.911854	−0.0467771
$381$	4.66056	0.238768
$382$	33.8974	1.73434
$383$	11.8582	0.605923	0.302962	−	0.953003i	$-0.402025\pi$
$383$	11.8582	0.605923	0.302962	+	0.953003i	$0.402025\pi$
$384$	−4.48858	−0.229057
$385$	4.20775	0.214447
$386$	−19.6136	−0.998304
$387$	16.0858	0.817685
$388$	−19.6407	−0.997106
$389$	10.3913	0.526862	0.263431	−	0.964678i	$-0.415146\pi$
$389$	10.3913	0.526862	0.263431	+	0.964678i	$0.415146\pi$
$390$	−1.48427	−0.0751590
$391$	4.59179	0.232217
$392$	−12.7463	−0.643786
$393$	−0.202374	−0.0102084
$394$	−15.1371	−0.762594
$395$	0.212063	0.0106700
$396$	10.1739	0.511258
$397$	8.21744	0.412421	0.206211	−	0.978508i	$-0.433887\pi$
$397$	8.21744	0.412421	0.206211	+	0.978508i	$0.433887\pi$
$398$	−11.9312	−0.598059
$399$	−3.69202	−0.184832
$400$	24.0659	1.20330
$401$	24.8810	1.24250	0.621249	−	0.783614i	$-0.286626\pi$
$401$	24.8810	1.24250	0.621249	+	0.783614i	$0.286626\pi$
$402$	−0.300209	−0.0149731
$403$	32.9667	1.64219
$404$	21.7506	1.08213
$405$	2.58987	0.128692
$406$	0	0
$407$	−8.47889	−0.420283
$408$	−0.670251	−0.0331824
$409$	−18.8955	−0.934320	−0.467160	−	0.884173i	$-0.654723\pi$
$409$	−18.8955	−0.934320	−0.467160	+	0.884173i	$0.654723\pi$
$410$	−0.254749	−0.0125812
$411$	−5.89248	−0.290654
$412$	−3.50902	−0.172877
$413$	36.8853	1.81501
$414$	20.8877	1.02657
$415$	−3.36658	−0.165259
$416$	−32.0804	−1.57287
$417$	1.24459	0.0609477
$418$	10.7506	0.525830
$419$	−10.8925	−0.532132	−0.266066	−	0.963955i	$-0.585724\pi$
$419$	−10.8925	−0.532132	−0.266066	+	0.963955i	$0.585724\pi$
$420$	0.801938	0.0391306
$421$	19.9608	0.972828	0.486414	−	0.873728i	$-0.338305\pi$
$421$	19.9608	0.972828	0.486414	+	0.873728i	$0.338305\pi$
$422$	14.5961	0.710527
$423$	−21.8605	−1.06290
$424$	5.91185	0.287105
$425$	5.40821	0.262337
$426$	9.14675	0.443162
$427$	−24.4916	−1.18523
$428$	−9.30260	−0.449658
$429$	6.72050	0.324469
$430$	−3.69202	−0.178045
$431$	−30.1903	−1.45422	−0.727108	−	0.686524i	$-0.759136\pi$
$431$	−30.1903	−1.45422	−0.727108	+	0.686524i	$0.759136\pi$
$432$	−12.7530	−0.613580
$433$	20.1914	0.970335	0.485167	−	0.874421i	$-0.338759\pi$
$433$	20.1914	0.970335	0.485167	+	0.874421i	$0.338759\pi$
$434$	−46.3793	−2.22628
$435$	0	0
$436$	−2.06100	−0.0987039
$437$	8.47650	0.405486
$438$	−7.17629	−0.342896
$439$	−10.6649	−0.509007	−0.254503	−	0.967072i	$-0.581912\pi$
$439$	−10.6649	−0.509007	−0.254503	+	0.967072i	$0.581912\pi$
$440$	1.41013	0.0672251
$441$	−26.3207	−1.25336
$442$	−10.3720	−0.493344
$443$	20.3502	0.966867	0.483433	−	0.875381i	$-0.339390\pi$
$443$	20.3502	0.966867	0.483433	+	0.875381i	$0.339390\pi$
$444$	−1.61596	−0.0766899
$445$	−0.507960	−0.0240796
$446$	39.4969	1.87023
$447$	−1.20536	−0.0570115
$448$	5.13706	0.242703
$449$	−19.4233	−0.916641	−0.458320	−	0.888787i	$-0.651549\pi$
$449$	−19.4233	−0.916641	−0.458320	+	0.888787i	$0.651549\pi$
$450$	24.6015	1.15973
$451$	1.15346	0.0543142
$452$	−10.7748	−0.506804
$453$	1.08383	0.0509230
$454$	−32.9366	−1.54579
$455$	−7.49396	−0.351322
$456$	−1.23729	−0.0579415
$457$	−12.4209	−0.581024	−0.290512	−	0.956871i	$-0.593826\pi$
$457$	−12.4209	−0.581024	−0.290512	+	0.956871i	$0.593826\pi$
$458$	−28.8756	−1.34927
$459$	−2.86592	−0.133770
$460$	−1.84117	−0.0858448
$461$	21.9463	1.02214	0.511070	−	0.859539i	$-0.329249\pi$
$461$	21.9463	1.02214	0.511070	+	0.859539i	$0.329249\pi$
$462$	−9.45473	−0.439874
$463$	−33.0073	−1.53398	−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073	−1.53398	−0.766990	+	0.641660i	$0.778246\pi$
$464$	0	0
$465$	−1.00969	−0.0468232
$466$	3.52542	0.163312
$467$	26.1032	1.20791	0.603956	−	0.797017i	$-0.293590\pi$
$467$	26.1032	1.20791	0.603956	+	0.797017i	$0.293590\pi$
$468$	−18.1196	−0.837579
$469$	−1.51573	−0.0699899
$470$	5.01746	0.231438
$471$	7.86725	0.362504
$472$	12.3612	0.568971
$473$	16.7168	0.768638
$474$	−0.476501	−0.0218864
$475$	9.98361	0.458079
$476$	5.60388	0.256853
$477$	12.2078	0.558955
$478$	−16.1511	−0.738732
$479$	−33.0659	−1.51082	−0.755410	−	0.655253i	$-0.772562\pi$
$479$	−33.0659	−1.51082	−0.755410	+	0.655253i	$0.772562\pi$
$480$	0.982542	0.0448467
$481$	15.1008	0.688538
$482$	35.8582	1.63329
$483$	−7.45473	−0.339202
$484$	−3.14377	−0.142899
$485$	−5.62133	−0.255252
$486$	−19.7778	−0.897138
$487$	−10.1564	−0.460232	−0.230116	−	0.973163i	$-0.573911\pi$
$487$	−10.1564	−0.460232	−0.230116	+	0.973163i	$0.573911\pi$
$488$	−8.20775	−0.371547
$489$	−2.21014	−0.0999462
$490$	6.04115	0.272911
$491$	19.6819	0.888230	0.444115	−	0.895970i	$-0.353518\pi$
$491$	19.6819	0.888230	0.444115	+	0.895970i	$0.353518\pi$
$492$	0.219833	0.00991082
$493$	0	0
$494$	−19.1468	−0.861453
$495$	2.91185	0.130878
$496$	−31.3967	−1.40975
$497$	46.1812	2.07151
$498$	7.56465	0.338980
$499$	27.8495	1.24672	0.623358	−	0.781937i	$-0.285768\pi$
$499$	27.8495	1.24672	0.623358	+	0.781937i	$0.285768\pi$
$500$	−4.39373	−0.196494
$501$	−6.43727	−0.287596
$502$	−46.4989	−2.07535
$503$	0.225209	0.0100416	0.00502079	−	0.999987i	$-0.498402\pi$
$503$	0.225209	0.0100416	0.00502079	+	0.999987i	$0.498402\pi$
$504$	−15.3937	−0.685691
$505$	6.22521	0.277018
$506$	21.7071	0.964998
$507$	−6.18359	−0.274623
$508$	−13.0586	−0.579382
$509$	−25.3032	−1.12154	−0.560772	−	0.827970i	$-0.689496\pi$
$509$	−25.3032	−1.12154	−0.560772	+	0.827970i	$0.689496\pi$
$510$	0.317667	0.0140665
$511$	−36.2325	−1.60283
$512$	17.1491	0.757892
$513$	−5.29052	−0.233582
$514$	21.5351	0.949873
$515$	−1.00431	−0.0442553
$516$	3.18598	0.140255
$517$	−22.7181	−0.999141
$518$	−21.2446	−0.933434
$519$	−4.67887	−0.205380
$520$	−2.51142	−0.110133
$521$	23.5797	1.03305	0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797	1.03305	0.516523	+	0.856273i	$0.327226\pi$
$522$	0	0
$523$	3.96508	0.173381	0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508	0.173381	0.0866905	+	0.996235i	$0.472371\pi$
$524$	0.567040	0.0247712
$525$	−8.78017	−0.383198
$526$	0.599564	0.0261422
$527$	−7.05562	−0.307348
$528$	−6.40044	−0.278543
$529$	−5.88471	−0.255857
$530$	−2.80194	−0.121708
$531$	25.5254	1.10771
$532$	10.3448	0.448505
$533$	−2.05429	−0.0889814
$534$	1.14138	0.0493921
$535$	−2.66248	−0.115109
$536$	−0.507960	−0.0219405
$537$	2.55496	0.110255
$538$	1.91723	0.0826577
$539$	−27.3532	−1.17818
$540$	1.14914	0.0494513
$541$	24.6601	1.06022	0.530110	−	0.847929i	$-0.322151\pi$
$541$	24.6601	1.06022	0.530110	+	0.847929i	$0.322151\pi$
$542$	29.6679	1.27434
$543$	2.95539	0.126828
$544$	6.86592	0.294374
$545$	−0.589875	−0.0252675
$546$	16.8388	0.720633
$547$	24.8412	1.06213	0.531066	−	0.847331i	$-0.321792\pi$
$547$	24.8412	1.06213	0.531066	+	0.847331i	$0.321792\pi$
$548$	16.5104	0.705287
$549$	−16.9487	−0.723352
$550$	25.5666	1.09016
$551$	0	0
$552$	−2.49827	−0.106333
$553$	−2.40581	−0.102306
$554$	11.8823	0.504831
$555$	−0.462500	−0.0196320
$556$	−3.48725	−0.147893
$557$	7.76510	0.329018	0.164509	−	0.986376i	$-0.447396\pi$
$557$	7.76510	0.329018	0.164509	+	0.986376i	$0.447396\pi$
$558$	−32.0954	−1.35871
$559$	−29.7724	−1.25924
$560$	7.13706	0.301596
$561$	−1.43834	−0.0607266
$562$	−55.0224	−2.32098
$563$	−20.8009	−0.876652	−0.438326	−	0.898816i	$-0.644429\pi$
$563$	−20.8009	−0.876652	−0.438326	+	0.898816i	$0.644429\pi$
$564$	−4.32975	−0.182315
$565$	−3.08383	−0.129738
$566$	−6.40581	−0.269256
$567$	−29.3817	−1.23391
$568$	15.4765	0.649380
$569$	−2.80923	−0.117769	−0.0588846	−	0.998265i	$-0.518754\pi$
$569$	−2.80923	−0.117769	−0.0588846	+	0.998265i	$0.518754\pi$
$570$	0.586417	0.0245623
$571$	2.89248	0.121046	0.0605232	−	0.998167i	$-0.480723\pi$
$571$	2.89248	0.121046	0.0605232	+	0.998167i	$0.480723\pi$
$572$	−18.8304	−0.787339
$573$	−8.37196	−0.349744
$574$	2.89008	0.120630
$575$	20.1584	0.840662
$576$	3.55496	0.148123
$577$	−7.18896	−0.299281	−0.149640	−	0.988741i	$-0.547812\pi$
$577$	−7.18896	−0.299281	−0.149640	+	0.988741i	$0.547812\pi$
$578$	−28.4131	−1.18183
$579$	4.84415	0.201316
$580$	0	0
$581$	38.1933	1.58452
$582$	12.6310	0.523573
$583$	12.6866	0.525427
$584$	−12.1424	−0.502458
$585$	−5.18598	−0.214414
$586$	−59.2476	−2.44749
$587$	−31.0368	−1.28103	−0.640514	−	0.767947i	$-0.721279\pi$
$587$	−31.0368	−1.28103	−0.640514	+	0.767947i	$0.721279\pi$
$588$	−5.21313	−0.214986
$589$	−13.0248	−0.536676
$590$	−5.85862	−0.241196
$591$	3.73855	0.153783
$592$	−14.3817	−0.591082
$593$	36.4674	1.49754	0.748768	−	0.662832i	$-0.230646\pi$
$593$	36.4674	1.49754	0.748768	+	0.662832i	$0.230646\pi$
$594$	−13.5483	−0.555892
$595$	1.60388	0.0657525
$596$	3.37734	0.138341
$597$	2.94677	0.120603
$598$	−38.6601	−1.58093
$599$	−30.0683	−1.22856	−0.614279	−	0.789089i	$-0.710553\pi$
$599$	−30.0683	−1.22856	−0.614279	+	0.789089i	$0.710553\pi$
$600$	−2.94246	−0.120125
$601$	33.1860	1.35368	0.676842	−	0.736128i	$-0.263348\pi$
$601$	33.1860	1.35368	0.676842	+	0.736128i	$0.263348\pi$
$602$	41.8853	1.70712
$603$	−1.04892	−0.0427152
$604$	−3.03684	−0.123567
$605$	−0.899772	−0.0365810
$606$	−13.9879	−0.568220
$607$	15.1202	0.613710	0.306855	−	0.951756i	$-0.400723\pi$
$607$	15.1202	0.613710	0.306855	+	0.951756i	$0.400723\pi$
$608$	12.6746	0.514021
$609$	0	0
$610$	3.89008	0.157505
$611$	40.4607	1.63686
$612$	3.87800	0.156759
$613$	3.75541	0.151680	0.0758399	−	0.997120i	$-0.475836\pi$
$613$	3.75541	0.151680	0.0758399	+	0.997120i	$0.475836\pi$
$614$	−26.4349	−1.06682
$615$	0.0629179	0.00253709
$616$	−15.9976	−0.644562
$617$	−29.8562	−1.20197	−0.600983	−	0.799262i	$-0.705224\pi$
$617$	−29.8562	−1.20197	−0.600983	+	0.799262i	$0.705224\pi$
$618$	2.25667	0.0907765
$619$	46.1178	1.85363	0.926816	−	0.375517i	$-0.122535\pi$
$619$	46.1178	1.85363	0.926816	+	0.375517i	$0.122535\pi$
$620$	2.82908	0.113619
$621$	−10.6823	−0.428667
$622$	−33.3836	−1.33856
$623$	5.76271	0.230878
$624$	11.3991	0.456330
$625$	23.1056	0.924224
$626$	41.4306	1.65590
$627$	−2.65519	−0.106038
$628$	−22.0435	−0.879633
$629$	−3.23191	−0.128865
$630$	7.29590	0.290675
$631$	12.6300	0.502791	0.251395	−	0.967884i	$-0.419111\pi$
$631$	12.6300	0.502791	0.251395	+	0.967884i	$0.419111\pi$
$632$	−0.806250	−0.0320709
$633$	−3.60494	−0.143284
$634$	−25.3327	−1.00609
$635$	−3.73748	−0.148317
$636$	2.41789	0.0958758
$637$	48.7157	1.93019
$638$	0	0
$639$	31.9584	1.26425
$640$	3.59956	0.142285
$641$	−39.0019	−1.54048	−0.770242	−	0.637752i	$-0.779864\pi$
$641$	−39.0019	−1.54048	−0.770242	+	0.637752i	$0.779864\pi$
$642$	5.98254	0.236112
$643$	41.2965	1.62857	0.814287	−	0.580462i	$-0.197128\pi$
$643$	41.2965	1.62857	0.814287	+	0.580462i	$0.197128\pi$
$644$	20.8877	0.823090
$645$	0.911854	0.0359042
$646$	4.09783	0.161227
$647$	−17.9105	−0.704135	−0.352068	−	0.935975i	$-0.614521\pi$
$647$	−17.9105	−0.704135	−0.352068	+	0.935975i	$0.614521\pi$
$648$	−9.84654	−0.386809
$649$	26.5267	1.04127
$650$	−45.5338	−1.78598
$651$	11.4547	0.448946
$652$	6.19269	0.242524
$653$	13.3207	0.521277	0.260639	−	0.965436i	$-0.416067\pi$
$653$	13.3207	0.521277	0.260639	+	0.965436i	$0.416067\pi$
$654$	1.32544	0.0518287
$655$	0.162291	0.00634125
$656$	1.95646	0.0763869
$657$	−25.0737	−0.978217
$658$	−56.9221	−2.21906
$659$	−18.7657	−0.731008	−0.365504	−	0.930810i	$-0.619103\pi$
$659$	−18.7657	−0.731008	−0.365504	+	0.930810i	$0.619103\pi$
$660$	0.576728	0.0224491
$661$	−24.7289	−0.961841	−0.480921	−	0.876764i	$-0.659697\pi$
$661$	−24.7289	−0.961841	−0.480921	+	0.876764i	$0.659697\pi$
$662$	−25.1487	−0.977431
$663$	2.56166	0.0994867
$664$	12.7995	0.496719
$665$	2.96077	0.114814
$666$	−14.7017	−0.569680
$667$	0	0
$668$	18.0368	0.697866
$669$	−9.75494	−0.377148
$670$	0.240749	0.00930094
$671$	−17.6136	−0.679964
$672$	−11.1468	−0.429995
$673$	25.4426	0.980742	0.490371	−	0.871514i	$-0.336861\pi$
$673$	25.4426	0.980742	0.490371	+	0.871514i	$0.336861\pi$
$674$	25.2228	0.971547
$675$	−12.5816	−0.484267
$676$	17.3260	0.666386
$677$	−0.616548	−0.0236959	−0.0118479	−	0.999930i	$-0.503771\pi$
$677$	−0.616548	−0.0236959	−0.0118479	+	0.999930i	$0.503771\pi$
$678$	6.92931	0.266119
$679$	63.7730	2.44738
$680$	0.537500	0.0206122
$681$	8.13467	0.311721
$682$	−33.3545	−1.27721
$683$	18.0218	0.689584	0.344792	−	0.938679i	$-0.387949\pi$
$683$	18.0218	0.689584	0.344792	+	0.938679i	$0.387949\pi$
$684$	7.15883	0.273725
$685$	4.72540	0.180548
$686$	−17.4644	−0.666795
$687$	7.13169	0.272091
$688$	28.3545	1.08101
$689$	−22.5948	−0.860792
$690$	1.18406	0.0450765
$691$	12.3461	0.469669	0.234835	−	0.972035i	$-0.424545\pi$
$691$	12.3461	0.469669	0.234835	+	0.972035i	$0.424545\pi$
$692$	13.1099	0.498364
$693$	−33.0344	−1.25487
$694$	−35.7754	−1.35801
$695$	−0.998081	−0.0378594
$696$	0	0
$697$	0.439665	0.0166535
$698$	−48.5086	−1.83608
$699$	−0.870706	−0.0329331
$700$	24.6015	0.929849
$701$	−34.0974	−1.28784	−0.643920	−	0.765093i	$-0.722693\pi$
$701$	−34.0974	−1.28784	−0.643920	+	0.765093i	$0.722693\pi$
$702$	24.1293	0.910702
$703$	−5.96615	−0.225018
$704$	3.69441	0.139238
$705$	−1.23921	−0.0466713
$706$	−7.23490	−0.272289
$707$	−70.6238	−2.65608
$708$	5.05562	0.190002
$709$	42.0954	1.58093	0.790464	−	0.612509i	$-0.209840\pi$
$709$	42.0954	1.58093	0.790464	+	0.612509i	$0.209840\pi$
$710$	−7.33513	−0.275282
$711$	−1.66487	−0.0624377
$712$	1.93123	0.0723760
$713$	−26.2989	−0.984901
$714$	−3.60388	−0.134872
$715$	−5.38942	−0.201553
$716$	−7.15883	−0.267538
$717$	3.98898	0.148971
$718$	1.34481	0.0501880
$719$	−52.2543	−1.94876	−0.974378	−	0.224917i	$-0.927789\pi$
$719$	−52.2543	−1.94876	−0.974378	+	0.224917i	$0.927789\pi$
$720$	4.93900	0.184066
$721$	11.3937	0.424325
$722$	−26.6722	−0.992635
$723$	−8.85623	−0.329367
$724$	−8.28083	−0.307755
$725$	0	0
$726$	2.02177	0.0750349
$727$	−29.9849	−1.11208	−0.556040	−	0.831156i	$-0.687680\pi$
$727$	−29.9849	−1.11208	−0.556040	+	0.831156i	$0.687680\pi$
$728$	28.4916	1.05597
$729$	−16.8853	−0.625381
$730$	5.75494	0.213000
$731$	6.37196	0.235676
$732$	−3.35690	−0.124074
$733$	−3.01447	−0.111342	−0.0556711	−	0.998449i	$-0.517730\pi$
$733$	−3.01447	−0.111342	−0.0556711	+	0.998449i	$0.517730\pi$
$734$	61.3540	2.26462
$735$	−1.49204	−0.0550347
$736$	25.5918	0.943326
$737$	−1.09006	−0.0401531
$738$	2.00000	0.0736210
$739$	20.8374	0.766518	0.383259	−	0.923641i	$-0.374802\pi$
$739$	20.8374	0.766518	0.383259	+	0.923641i	$0.374802\pi$
$740$	1.29590	0.0476381
$741$	4.72886	0.173719
$742$	31.7875	1.16695
$743$	30.7657	1.12868	0.564342	−	0.825541i	$-0.309130\pi$
$743$	30.7657	1.12868	0.564342	+	0.825541i	$0.309130\pi$
$744$	3.83877	0.140736
$745$	0.966622	0.0354143
$746$	50.4553	1.84730
$747$	26.4306	0.967044
$748$	4.03013	0.147356
$749$	30.2054	1.10368
$750$	2.82563	0.103177
$751$	4.46921	0.163084	0.0815418	−	0.996670i	$-0.474016\pi$
$751$	4.46921	0.163084	0.0815418	+	0.996670i	$0.474016\pi$
$752$	−38.5338	−1.40518
$753$	11.4843	0.418510
$754$	0	0
$755$	−0.869167	−0.0316322
$756$	−13.0368	−0.474145
$757$	8.45580	0.307331	0.153666	−	0.988123i	$-0.450892\pi$
$757$	8.45580	0.307331	0.153666	+	0.988123i	$0.450892\pi$
$758$	−41.2301	−1.49755
$759$	−5.36121	−0.194600
$760$	0.992230	0.0359920
$761$	24.6950	0.895193	0.447597	−	0.894236i	$-0.352280\pi$
$761$	24.6950	0.895193	0.447597	+	0.894236i	$0.352280\pi$
$762$	8.39804	0.304229
$763$	6.69202	0.242267
$764$	23.4577	0.848670
$765$	1.10992	0.0401291
$766$	21.3676	0.772045
$767$	−47.2438	−1.70588
$768$	−9.21744	−0.332606
$769$	−30.1430	−1.08699	−0.543493	−	0.839414i	$-0.682898\pi$
$769$	−30.1430	−1.08699	−0.543493	+	0.839414i	$0.682898\pi$
$770$	7.58211	0.273240
$771$	−5.31873	−0.191549
$772$	−13.5730	−0.488503
$773$	−5.67696	−0.204186	−0.102093	−	0.994775i	$-0.532554\pi$
$773$	−5.67696	−0.204186	−0.102093	+	0.994775i	$0.532554\pi$
$774$	28.9855	1.04186
$775$	−30.9748	−1.11265
$776$	21.3720	0.767209
$777$	5.24698	0.188234
$778$	18.7245	0.671307
$779$	0.811626	0.0290795
$780$	−1.02715	−0.0367778
$781$	33.2121	1.18842
$782$	8.27413	0.295882
$783$	0	0
$784$	−46.3957	−1.65699
$785$	−6.30904	−0.225179
$786$	−0.364666	−0.0130072
$787$	−3.60925	−0.128656	−0.0643280	−	0.997929i	$-0.520490\pi$
$787$	−3.60925	−0.128656	−0.0643280	+	0.997929i	$0.520490\pi$
$788$	−10.4752	−0.373163
$789$	−0.148080	−0.00527179
$790$	0.382124	0.0135954
$791$	34.9855	1.24394
$792$	−11.0707	−0.393380
$793$	31.3696	1.11397
$794$	14.8073	0.525492
$795$	0.692021	0.0245435
$796$	−8.25667	−0.292650
$797$	30.7832	1.09040	0.545198	−	0.838308i	$-0.316455\pi$
$797$	30.7832	1.09040	0.545198	+	0.838308i	$0.316455\pi$
$798$	−6.65279	−0.235506
$799$	−8.65950	−0.306351
$800$	30.1420	1.06568
$801$	3.98792	0.140906
$802$	44.8340	1.58314
$803$	−26.0573	−0.919541
$804$	−0.207751	−0.00732681
$805$	5.97823	0.210705
$806$	59.4040	2.09242
$807$	−0.473517	−0.0166686
$808$	−23.6679	−0.832632
$809$	−5.23729	−0.184133	−0.0920667	−	0.995753i	$-0.529347\pi$
$809$	−5.23729	−0.184133	−0.0920667	+	0.995753i	$0.529347\pi$
$810$	4.66679	0.163974
$811$	41.8646	1.47006	0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646	1.47006	0.735032	+	0.678032i	$0.237167\pi$
$812$	0	0
$813$	−7.32736	−0.256982
$814$	−15.2784	−0.535509
$815$	1.77240	0.0620844
$816$	−2.43967	−0.0854054
$817$	11.7627	0.411525
$818$	−34.0484	−1.19048
$819$	58.8340	2.05583
$820$	−0.176292	−0.00615638
$821$	15.4058	0.537667	0.268833	−	0.963187i	$-0.413362\pi$
$821$	15.4058	0.537667	0.268833	+	0.963187i	$0.413362\pi$
$822$	−10.6179	−0.370341
$823$	35.6558	1.24288	0.621441	−	0.783461i	$-0.286548\pi$
$823$	35.6558	1.24288	0.621441	+	0.783461i	$0.286548\pi$
$824$	3.81833	0.133018
$825$	−6.31442	−0.219840
$826$	66.4650	2.31261
$827$	52.0538	1.81009	0.905044	−	0.425317i	$-0.139837\pi$
$827$	52.0538	1.81009	0.905044	+	0.425317i	$0.139837\pi$
$828$	14.4547	0.502337
$829$	13.4168	0.465986	0.232993	−	0.972478i	$-0.425148\pi$
$829$	13.4168	0.465986	0.232993	+	0.972478i	$0.425148\pi$
$830$	−6.06638	−0.210567
$831$	−2.93469	−0.101803
$832$	−6.57971	−0.228110
$833$	−10.4263	−0.361248
$834$	2.24267	0.0776572
$835$	5.16229	0.178648
$836$	7.43967	0.257306
$837$	16.4142	0.567357
$838$	−19.6276	−0.678023
$839$	31.0513	1.07201	0.536005	−	0.844215i	$-0.319933\pi$
$839$	31.0513	1.07201	0.536005	+	0.844215i	$0.319933\pi$
$840$	−0.872625	−0.0301084
$841$	0	0
$842$	35.9681	1.23954
$843$	13.5894	0.468044
$844$	10.1008	0.347685
$845$	4.95885	0.170590
$846$	−39.3913	−1.35430
$847$	10.2078	0.350742
$848$	21.5187	0.738956
$849$	1.58211	0.0542977
$850$	9.74525	0.334259
$851$	−12.0465	−0.412950
$852$	6.32975	0.216854
$853$	−21.3357	−0.730521	−0.365261	−	0.930905i	$-0.619020\pi$
$853$	−21.3357	−0.730521	−0.365261	+	0.930905i	$0.619020\pi$
$854$	−44.1323	−1.51018
$855$	2.04892	0.0700715
$856$	10.1226	0.345983
$857$	−9.83207	−0.335857	−0.167929	−	0.985799i	$-0.553708\pi$
$857$	−9.83207	−0.335857	−0.167929	+	0.985799i	$0.553708\pi$
$858$	12.1099	0.413426
$859$	51.7837	1.76684	0.883419	−	0.468583i	$-0.155235\pi$
$859$	51.7837	1.76684	0.883419	+	0.468583i	$0.155235\pi$
$860$	−2.55496	−0.0871233
$861$	−0.713792	−0.0243260
$862$	−54.4010	−1.85291
$863$	−16.2747	−0.553998	−0.276999	−	0.960870i	$-0.589340\pi$
$863$	−16.2747	−0.553998	−0.276999	+	0.960870i	$0.589340\pi$
$864$	−15.9729	−0.543407
$865$	3.75217	0.127577
$866$	36.3836	1.23636
$867$	7.01746	0.238325
$868$	−32.0954	−1.08939
$869$	−1.73019	−0.0586925
$870$	0	0
$871$	1.94139	0.0657816
$872$	2.24267	0.0759463
$873$	44.1323	1.49365
$874$	15.2741	0.516655
$875$	14.2664	0.482291
$876$	−4.96615	−0.167791
$877$	14.8062	0.499972	0.249986	−	0.968250i	$-0.419574\pi$
$877$	14.8062	0.499972	0.249986	+	0.968250i	$0.419574\pi$
$878$	−19.2174	−0.648557
$879$	14.6329	0.493557
$880$	5.13275	0.173025
$881$	18.6377	0.627921	0.313960	−	0.949436i	$-0.398344\pi$
$881$	18.6377	0.627921	0.313960	+	0.949436i	$0.398344\pi$
$882$	−47.4282	−1.59699
$883$	−32.3937	−1.09014	−0.545068	−	0.838392i	$-0.683496\pi$
$883$	−32.3937	−1.09014	−0.545068	+	0.838392i	$0.683496\pi$
$884$	−7.17762	−0.241409
$885$	1.44696	0.0486391
$886$	36.6698	1.23195
$887$	6.16288	0.206929	0.103465	−	0.994633i	$-0.467007\pi$
$887$	6.16288	0.206929	0.103465	+	0.994633i	$0.467007\pi$
$888$	1.75840	0.0590079
$889$	42.4010	1.42208
$890$	−0.915312	−0.0306813
$891$	−21.1304	−0.707894
$892$	27.3327	0.915168
$893$	−15.9855	−0.534935
$894$	−2.17198	−0.0726419
$895$	−2.04892	−0.0684878
$896$	−40.8364	−1.36425
$897$	9.54825	0.318807
$898$	−34.9995	−1.16795
$899$	0	0
$900$	17.0248	0.567492
$901$	4.83579	0.161104
$902$	2.07846	0.0692051
$903$	−10.3448	−0.344254
$904$	11.7245	0.389953
$905$	−2.37004	−0.0787829
$906$	1.95300	0.0648841
$907$	−43.9842	−1.46047	−0.730236	−	0.683195i	$-0.760590\pi$
$907$	−43.9842	−1.46047	−0.730236	+	0.683195i	$0.760590\pi$
$908$	−22.7928	−0.756407
$909$	−48.8732	−1.62102
$910$	−13.5036	−0.447642
$911$	25.6233	0.848936	0.424468	−	0.905443i	$-0.360461\pi$
$911$	25.6233	0.848936	0.424468	+	0.905443i	$0.360461\pi$
$912$	−4.50365	−0.149131
$913$	27.4674	0.909038
$914$	−22.3817	−0.740319
$915$	−0.960771	−0.0317621
$916$	−19.9825	−0.660242
$917$	−1.84117	−0.0608007
$918$	−5.16421	−0.170444
$919$	−6.24160	−0.205891	−0.102946	−	0.994687i	$-0.532827\pi$
$919$	−6.24160	−0.205891	−0.102946	+	0.994687i	$0.532827\pi$
$920$	2.00346	0.0660520
$921$	6.52888	0.215134
$922$	39.5459	1.30237
$923$	−59.1503	−1.94696
$924$	−6.54288	−0.215245
$925$	−14.1884	−0.466511
$926$	−59.4771	−1.95454
$927$	7.88471	0.258968
$928$	0	0
$929$	−24.5133	−0.804256	−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133	−0.804256	−0.402128	+	0.915583i	$0.631729\pi$
$930$	−1.81940	−0.0596603
$931$	−19.2470	−0.630794
$932$	2.43967	0.0799139
$933$	8.24506	0.269931
$934$	47.0364	1.53908
$935$	1.15346	0.0377221
$936$	19.7168	0.644463
$937$	−4.08947	−0.133597	−0.0667986	−	0.997766i	$-0.521279\pi$
$937$	−4.08947	−0.133597	−0.0667986	+	0.997766i	$0.521279\pi$
$938$	−2.73125	−0.0891785
$939$	−10.2325	−0.333925
$940$	3.47219	0.113250
$941$	6.16315	0.200913	0.100456	−	0.994941i	$-0.467970\pi$
$941$	6.16315	0.200913	0.100456	+	0.994941i	$0.467970\pi$
$942$	14.1763	0.461889
$943$	1.63879	0.0533664
$944$	44.9939	1.46443
$945$	−3.73125	−0.121378
$946$	30.1226	0.979370
$947$	49.7023	1.61511	0.807554	−	0.589794i	$-0.200791\pi$
$947$	49.7023	1.61511	0.807554	+	0.589794i	$0.200791\pi$
$948$	−0.329749	−0.0107097
$949$	46.4077	1.50646
$950$	17.9898	0.583667
$951$	6.25667	0.202886
$952$	−6.09783	−0.197632
$953$	17.6856	0.572892	0.286446	−	0.958096i	$-0.407526\pi$
$953$	17.6856	0.572892	0.286446	+	0.958096i	$0.407526\pi$
$954$	21.9976	0.712199
$955$	6.71379	0.217253
$956$	−11.1769	−0.361486
$957$	0	0
$958$	−59.5827	−1.92503
$959$	−53.6088	−1.73112
$960$	0.201520	0.00650403
$961$	9.41013	0.303552
$962$	27.2107	0.877309
$963$	20.9028	0.673582
$964$	24.8146	0.799225
$965$	−3.88471	−0.125053
$966$	−13.4330	−0.432198
$967$	12.8933	0.414622	0.207311	−	0.978275i	$-0.433529\pi$
$967$	12.8933	0.414622	0.207311	+	0.978275i	$0.433529\pi$
$968$	3.42088	0.109951
$969$	−1.01208	−0.0325127
$970$	−10.1293	−0.325232
$971$	−4.83745	−0.155241	−0.0776205	−	0.996983i	$-0.524732\pi$
$971$	−4.83745	−0.155241	−0.0776205	+	0.996983i	$0.524732\pi$
$972$	−13.6866	−0.438999
$973$	11.3230	0.363000
$974$	−18.3013	−0.586411
$975$	11.2459	0.360158
$976$	−29.8756	−0.956295
$977$	16.4421	0.526028	0.263014	−	0.964792i	$-0.415283\pi$
$977$	16.4421	0.526028	0.263014	+	0.964792i	$0.415283\pi$
$978$	−3.98254	−0.127348
$979$	4.14436	0.132454
$980$	4.18060	0.133544
$981$	4.63102	0.147857
$982$	35.4655	1.13175
$983$	−26.4993	−0.845198	−0.422599	−	0.906317i	$-0.638882\pi$
$983$	−26.4993	−0.845198	−0.422599	+	0.906317i	$0.638882\pi$
$984$	−0.239210	−0.00762573
$985$	−2.99808	−0.0955268
$986$	0	0
$987$	14.0586	0.447490
$988$	−13.2500	−0.421537
$989$	23.7506	0.755226
$990$	5.24698	0.166760
$991$	40.4064	1.28355	0.641776	−	0.766892i	$-0.278198\pi$
$991$	40.4064	1.28355	0.641776	+	0.766892i	$0.278198\pi$
$992$	−39.3236	−1.24853
$993$	6.21121	0.197107
$994$	83.2156	2.63944
$995$	−2.36313	−0.0749162
$996$	5.23490	0.165874
$997$	23.4553	0.742837	0.371419	−	0.928465i	$-0.378871\pi$
$997$	23.4553	0.742837	0.371419	+	0.928465i	$0.378871\pi$
$998$	50.1831	1.58852
$999$	7.51871	0.237882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.a.f.1.3		3
3.2	odd	2		7569.2.a.p.1.1		3
29.2	odd	28		841.2.e.c.236.2		12
29.3	odd	28		841.2.e.b.270.2		12
29.4	even	14		841.2.d.e.190.1		6
29.5	even	14		841.2.d.b.605.1		6
29.6	even	14		841.2.d.b.645.1		6
29.7	even	7		841.2.d.a.571.1		6
29.8	odd	28		841.2.e.d.267.2		12
29.9	even	14		29.2.d.a.23.1	✓	6
29.10	odd	28		841.2.e.b.651.2		12
29.11	odd	28		841.2.e.d.63.2		12
29.12	odd	4		841.2.b.c.840.6		6
29.13	even	14		29.2.d.a.24.1	yes	6
29.14	odd	28		841.2.e.c.196.1		12
29.15	odd	28		841.2.e.c.196.2		12
29.16	even	7		841.2.d.d.778.1		6
29.17	odd	4		841.2.b.c.840.1		6
29.18	odd	28		841.2.e.d.63.1		12
29.19	odd	28		841.2.e.b.651.1		12
29.20	even	7		841.2.d.d.574.1		6
29.21	odd	28		841.2.e.d.267.1		12
29.22	even	14		841.2.d.e.571.1		6
29.23	even	7		841.2.d.c.645.1		6
29.24	even	7		841.2.d.c.605.1		6
29.25	even	7		841.2.d.a.190.1		6
29.26	odd	28		841.2.e.b.270.1		12
29.27	odd	28		841.2.e.c.236.1		12
29.28	even	2		841.2.a.e.1.1		3
87.38	odd	14		261.2.k.a.226.1		6
87.71	odd	14		261.2.k.a.82.1		6
87.86	odd	2		7569.2.a.r.1.3		3
116.67	odd	14		464.2.u.f.81.1		6
116.71	odd	14		464.2.u.f.401.1		6
145.9	even	14		725.2.l.b.226.1		6
145.13	odd	28		725.2.r.b.24.1		12
145.38	odd	28		725.2.r.b.574.2		12
145.42	odd	28		725.2.r.b.24.2		12
145.67	odd	28		725.2.r.b.574.1		12
145.129	even	14		725.2.l.b.401.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.9	even	14
29.2.d.a.24.1	yes	6	29.13	even	14
261.2.k.a.82.1		6	87.71	odd	14
261.2.k.a.226.1		6	87.38	odd	14
464.2.u.f.81.1		6	116.67	odd	14
464.2.u.f.401.1		6	116.71	odd	14
725.2.l.b.226.1		6	145.9	even	14
725.2.l.b.401.1		6	145.129	even	14
725.2.r.b.24.1		12	145.13	odd	28
725.2.r.b.24.2		12	145.42	odd	28
725.2.r.b.574.1		12	145.67	odd	28
725.2.r.b.574.2		12	145.38	odd	28
841.2.a.e.1.1		3	29.28	even	2
841.2.a.f.1.3		3	1.1	even	1	trivial
841.2.b.c.840.1		6	29.17	odd	4
841.2.b.c.840.6		6	29.12	odd	4
841.2.d.a.190.1		6	29.25	even	7
841.2.d.a.571.1		6	29.7	even	7
841.2.d.b.605.1		6	29.5	even	14
841.2.d.b.645.1		6	29.6	even	14
841.2.d.c.605.1		6	29.24	even	7
841.2.d.c.645.1		6	29.23	even	7
841.2.d.d.574.1		6	29.20	even	7
841.2.d.d.778.1		6	29.16	even	7
841.2.d.e.190.1		6	29.4	even	14
841.2.d.e.571.1		6	29.22	even	14
841.2.e.b.270.1		12	29.26	odd	28
841.2.e.b.270.2		12	29.3	odd	28
841.2.e.b.651.1		12	29.19	odd	28
841.2.e.b.651.2		12	29.10	odd	28
841.2.e.c.196.1		12	29.14	odd	28
841.2.e.c.196.2		12	29.15	odd	28
841.2.e.c.236.1		12	29.27	odd	28
841.2.e.c.236.2		12	29.2	odd	28
841.2.e.d.63.1		12	29.18	odd	28
841.2.e.d.63.2		12	29.11	odd	28
841.2.e.d.267.1		12	29.21	odd	28
841.2.e.d.267.2		12	29.8	odd	28
7569.2.a.p.1.1		3	3.2	odd	2
7569.2.a.r.1.3		3	87.86	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q+1.80194 q^{2} -0.445042 q^{3} +1.24698 q^{4} +0.356896 q^{5} -0.801938 q^{6} -4.04892 q^{7} -1.35690 q^{8} -2.80194 q^{9} +0.643104 q^{10} -2.91185 q^{11} -0.554958 q^{12} +5.18598 q^{13} -7.29590 q^{14} -0.158834 q^{15} -4.93900 q^{16} -1.10992 q^{17} -5.04892 q^{18} -2.04892 q^{19} +0.445042 q^{20} +1.80194 q^{21} -5.24698 q^{22} -4.13706 q^{23} +0.603875 q^{24} -4.87263 q^{25} +9.34481 q^{26} +2.58211 q^{27} -5.04892 q^{28} -0.286208 q^{30} +6.35690 q^{31} -6.18598 q^{32} +1.29590 q^{33} -2.00000 q^{34} -1.44504 q^{35} -3.49396 q^{36} +2.91185 q^{37} -3.69202 q^{38} -2.30798 q^{39} -0.484271 q^{40} -0.396125 q^{41} +3.24698 q^{42} -5.74094 q^{43} -3.63102 q^{44} -1.00000 q^{45} -7.45473 q^{46} +7.80194 q^{47} +2.19806 q^{48} +9.39373 q^{49} -8.78017 q^{50} +0.493959 q^{51} +6.46681 q^{52} -4.35690 q^{53} +4.65279 q^{54} -1.03923 q^{55} +5.49396 q^{56} +0.911854 q^{57} -9.10992 q^{59} -0.198062 q^{60} +6.04892 q^{61} +11.4547 q^{62} +11.3448 q^{63} -1.26875 q^{64} +1.85086 q^{65} +2.33513 q^{66} +0.374354 q^{67} -1.38404 q^{68} +1.84117 q^{69} -2.60388 q^{70} -11.4058 q^{71} +3.80194 q^{72} +8.94869 q^{73} +5.24698 q^{74} +2.16852 q^{75} -2.55496 q^{76} +11.7899 q^{77} -4.15883 q^{78} +0.594187 q^{79} -1.76271 q^{80} +7.25667 q^{81} -0.713792 q^{82} -9.43296 q^{83} +2.24698 q^{84} -0.396125 q^{85} -10.3448 q^{86} +3.95108 q^{88} -1.42327 q^{89} -1.80194 q^{90} -20.9976 q^{91} -5.15883 q^{92} -2.82908 q^{93} +14.0586 q^{94} -0.731250 q^{95} +2.75302 q^{96} -15.7506 q^{97} +16.9269 q^{98} +8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 4 q^{9} + 6 q^{10} - 5 q^{11} - 2 q^{12} + q^{13} - 8 q^{14} + 8 q^{15} - 5 q^{16} - 4 q^{17} - 6 q^{18} + 3 q^{19} + q^{20} + q^{21} - 11 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) 3 * q + q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 4 * q^9 + 6 * q^10 - 5 * q^11 - 2 * q^12 + q^13 - 8 * q^14 + 8 * q^15 - 5 * q^16 - 4 * q^17 - 6 * q^18 + 3 * q^19 + q^20 + q^21 - 11 * q^22 - 7 * q^23 - 7 * q^24 + 2 * q^25 + 5 * q^26 + 2 * q^27 - 6 * q^28 - 9 * q^30 + 15 * q^31 - 4 * q^32 - 10 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 5 * q^37 - 6 * q^38 - 12 * q^39 - 14 * q^40 - 10 * q^41 + 5 * q^42 - 3 * q^43 + 4 * q^44 - 3 * q^45 + 19 * q^47 + 11 * q^48 - 4 * q^49 - 25 * q^50 - 8 * q^51 + 16 * q^52 - 9 * q^53 - 4 * q^54 - 16 * q^55 + 7 * q^56 - q^57 - 28 * q^59 - 5 * q^60 + 9 * q^61 + 12 * q^62 + 11 * q^63 + 4 * q^64 - 8 * q^65 + 6 * q^66 + 13 * q^67 + 6 * q^68 + 14 * q^69 + q^70 - 21 * q^71 + 7 * q^72 - 5 * q^73 + 11 * q^74 - 24 * q^75 - 8 * q^76 + 12 * q^77 - 4 * q^78 + 15 * q^79 + 12 * q^80 - 5 * q^81 + 6 * q^82 - 9 * q^83 + 2 * q^84 - 10 * q^85 - 8 * q^86 + 21 * q^88 - 7 * q^89 - q^90 - 22 * q^91 - 7 * q^92 + 2 * q^93 + 11 * q^94 - 10 * q^95 + 13 * q^96 - 11 * q^97 + 22 * q^98 + 16 * q^99

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