LMFDB - Embedded newform 841.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(1,841)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			1.1
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	$-0.719858\pi$
$2$	−1.80194	−1.27416	−0.637081	+	0.770797i	$0.719858\pi$
$3$	0.445042	0.256945	0.128473	−	0.991713i	$-0.458993\pi$
$3$	0.445042	0.256945	0.128473	+	0.991713i	$0.458993\pi$
$4$	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	$-0.355340\pi$
$11$	2.91185	0.877957	0.438979	+	0.898498i	$0.355340\pi$
$12$	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	$-0.457026\pi$
$17$	1.10992	0.269194	0.134597	+	0.990900i	$0.457026\pi$
$18$	5.04892	1.19004
$19$	2.04892	0.470054	0.235027	−	0.971989i	$-0.424482\pi$
$19$	2.04892	0.470054	0.235027	+	0.971989i	$0.424482\pi$
$20$	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	$-0.693392\pi$
$31$	−6.35690	−1.14173	−0.570866	+	0.821043i	$0.693392\pi$
$32$	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	$-0.576935\pi$
$37$	−2.91185	−0.478706	−0.239353	+	0.970933i	$0.576935\pi$
$38$	−3.69202	−0.598925
$39$	2.30798	0.369572
$40$	0.484271	0.0765699
$41$	0.396125	0.0618643	0.0309321	−	0.999521i	$-0.490152\pi$
$41$	0.396125	0.0618643	0.0309321	+	0.999521i	$0.490152\pi$
$42$	3.24698	0.501020
$43$	5.74094	0.875485	0.437742	−	0.899100i	$-0.355778\pi$
$43$	5.74094	0.875485	0.437742	+	0.899100i	$0.355778\pi$
$44$	3.63102	0.547397
$45$	−1.00000	−0.149071
$46$	7.45473	1.09914
$47$	−7.80194	−1.13803	−0.569015	−	0.822327i	$-0.692675\pi$
$47$	−7.80194	−1.13803	−0.569015	+	0.822327i	$0.692675\pi$
$48$	−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	$-0.626572\pi$
$61$	−6.04892	−0.774485	−0.387242	+	0.921978i	$0.626572\pi$
$62$	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	$-0.675442\pi$
$73$	−8.94869	−1.04736	−0.523682	+	0.851914i	$0.675442\pi$
$74$	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	$-0.510642\pi$
$79$	−0.594187	−0.0668512	−0.0334256	+	0.999441i	$0.510642\pi$
$80$	−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	$-0.475966\pi$
$89$	1.42327	0.150866	0.0754332	+	0.997151i	$0.475966\pi$
$90$	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	$-0.205036\pi$
$97$	15.7506	1.59923	0.799617	+	0.600510i	$0.205036\pi$
$98$	−16.9269	−1.70988
$99$	−8.15883	−0.819994
$100$	−6.07606	−0.607606
$101$	−17.4426	−1.73561	−0.867804	−	0.496906i	$-0.834469\pi$
$101$	−17.4426	−1.73561	−0.867804	+	0.496906i	$0.834469\pi$
$102$	−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	$-0.366775\pi$
$113$	8.64071	0.812850	0.406425	+	0.913684i	$0.366775\pi$
$114$	−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	$-0.346188\pi$
$127$	10.4722	0.929257	0.464628	+	0.885506i	$0.346188\pi$
$128$	−10.0858	−0.891463
$129$	2.55496	0.224952
$130$	−3.33513	−0.292510
$131$	−0.454731	−0.0397300	−0.0198650	−	0.999803i	$-0.506324\pi$
$131$	−0.454731	−0.0397300	−0.0198650	+	0.999803i	$0.506324\pi$
$132$	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	$-0.691354\pi$
$137$	−13.2403	−1.13119	−0.565597	+	0.824682i	$0.691354\pi$
$138$	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	$-0.250762\pi$
$157$	17.6775	1.41082	0.705411	+	0.708799i	$0.250762\pi$
$158$	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	$-0.562305\pi$
$163$	−4.96615	−0.388979	−0.194489	+	0.980905i	$0.562305\pi$
$164$	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	$-0.738272\pi$
$191$	−18.8116	−1.36116	−0.680581	+	0.732673i	$0.738272\pi$
$192$	−0.564647	−0.0407499
$193$	10.8847	0.783498	0.391749	−	0.920072i	$-0.371870\pi$
$193$	10.8847	0.783498	0.391749	+	0.920072i	$0.371870\pi$
$194$	−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	$-0.589944\pi$
$211$	−8.10023	−0.557643	−0.278821	+	0.960343i	$0.589944\pi$
$212$	−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	$-0.322390\pi$
$229$	16.0248	1.05895	0.529473	+	0.848327i	$0.322390\pi$
$230$	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	$-0.197068\pi$
$251$	25.8049	1.62879	0.814396	+	0.580309i	$0.197068\pi$
$252$	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	$-0.503265\pi$
$263$	−0.332733	−0.0205172	−0.0102586	+	0.999947i	$0.503265\pi$
$264$	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	$-0.510327\pi$
$269$	−1.06398	−0.0648722	−0.0324361	+	0.999474i	$0.510327\pi$
$270$	1.66056	0.101059
$271$	−16.4644	−1.00014	−0.500071	−	0.865984i	$-0.666693\pi$
$271$	−16.4644	−1.00014	−0.500071	+	0.865984i	$0.666693\pi$
$272$	−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	$-0.0898412\pi$
$293$	32.8799	1.92087	0.960433	+	0.278512i	$0.0898412\pi$
$294$	−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	$-0.362508\pi$
$307$	14.6703	0.837275	0.418638	+	0.908153i	$0.362508\pi$
$308$	−14.7017	−0.837708
$309$	−1.25236	−0.0712441
$310$	4.08815	0.232191
$311$	18.5265	1.05054	0.525270	−	0.850935i	$-0.323964\pi$
$311$	18.5265	1.05054	0.525270	+	0.850935i	$0.323964\pi$
$312$	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	$-0.370812\pi$
$317$	14.0586	0.789610	0.394805	+	0.918765i	$0.370812\pi$
$318$	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	$-0.374699\pi$
$331$	13.9565	0.767116	0.383558	+	0.923517i	$0.374699\pi$
$332$	−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	$-0.624506\pi$
$337$	−13.9976	−0.762498	−0.381249	+	0.924472i	$0.624506\pi$
$338$	−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	$-0.506269\pi$
$359$	−0.746316	−0.0393890	−0.0196945	+	0.999806i	$0.506269\pi$
$360$	−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	$-0.848370\pi$
$367$	−34.0489	−1.77734	−0.888670	+	0.458548i	$0.848370\pi$
$368$	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	$-0.300050\pi$
$379$	22.8810	1.17532	0.587659	+	0.809109i	$0.300050\pi$
$380$	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	$-0.584854\pi$
$389$	−10.3913	−0.526862	−0.263431	+	0.964678i	$0.584854\pi$
$390$	−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	$-0.345277\pi$
$409$	18.8955	0.934320	0.467160	+	0.884173i	$0.345277\pi$
$410$	−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	$-0.661695\pi$
$421$	−19.9608	−0.972828	−0.486414	+	0.873728i	$0.661695\pi$
$422$	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	$-0.661241\pi$
$433$	−20.1914	−0.970335	−0.485167	+	0.874421i	$0.661241\pi$
$434$	−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	$-0.660610\pi$
$443$	−20.3502	−0.966867	−0.483433	+	0.875381i	$0.660610\pi$
$444$	−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	$-0.348451\pi$
$449$	19.4233	0.916641	0.458320	+	0.888787i	$0.348451\pi$
$450$	−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	$-0.670751\pi$
$461$	−21.9463	−1.02214	−0.511070	+	0.859539i	$0.670751\pi$
$462$	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	$-0.706410\pi$
$467$	−26.1032	−1.20791	−0.603956	+	0.797017i	$0.706410\pi$
$468$	−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	$-0.227438\pi$
$479$	33.0659	1.51082	0.755410	+	0.655253i	$0.227438\pi$
$480$	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	$-0.646482\pi$
$491$	−19.6819	−0.888230	−0.444115	+	0.895970i	$0.646482\pi$
$492$	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	$-0.501598\pi$
$503$	−0.225209	−0.0100416	−0.00502079	+	0.999987i	$0.501598\pi$
$504$	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	$-0.677849\pi$
$541$	−24.6601	−1.06022	−0.530110	+	0.847929i	$0.677849\pi$
$542$	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	$-0.355571\pi$
$563$	20.8009	0.876652	0.438326	+	0.898816i	$0.355571\pi$
$564$	−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	$-0.481246\pi$
$569$	2.80923	0.117769	0.0588846	+	0.998265i	$0.481246\pi$
$570$	−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	$-0.452188\pi$
$577$	7.18896	0.299281	0.149640	+	0.988741i	$0.452188\pi$
$578$	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	$-0.289447\pi$
$599$	30.0683	1.22856	0.614279	+	0.789089i	$0.289447\pi$
$600$	−2.94246	−0.120125
$601$	−33.1860	−1.35368	−0.676842	−	0.736128i	$-0.736652\pi$
$601$	−33.1860	−1.35368	−0.676842	+	0.736128i	$0.736652\pi$
$602$	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	$-0.599277\pi$
$607$	−15.1202	−0.613710	−0.306855	+	0.951756i	$0.599277\pi$
$608$	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	$-0.294776\pi$
$617$	29.8562	1.20197	0.600983	+	0.799262i	$0.294776\pi$
$618$	2.25667	0.0907765
$619$	−46.1178	−1.85363	−0.926816	−	0.375517i	$-0.877465\pi$
$619$	−46.1178	−1.85363	−0.926816	+	0.375517i	$0.877465\pi$
$620$	−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	$-0.220136\pi$
$641$	39.0019	1.54048	0.770242	+	0.637752i	$0.220136\pi$
$642$	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	$-0.583933\pi$
$653$	−13.3207	−0.521277	−0.260639	+	0.965436i	$0.583933\pi$
$654$	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	$-0.380897\pi$
$659$	18.7657	0.731008	0.365504	+	0.930810i	$0.380897\pi$
$660$	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	$-0.496229\pi$
$677$	0.616548	0.0236959	0.0118479	+	0.999930i	$0.496229\pi$
$678$	−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	$-0.312320\pi$
$727$	29.9849	1.11208	0.556040	+	0.831156i	$0.312320\pi$
$728$	−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	$-0.482270\pi$
$733$	3.01447	0.111342	0.0556711	+	0.998449i	$0.482270\pi$
$734$	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	$-0.625198\pi$
$739$	−20.8374	−0.766518	−0.383259	+	0.923641i	$0.625198\pi$
$740$	−1.29590	−0.0476381
$741$	4.72886	0.173719
$742$	−31.7875	−1.16695
$743$	−30.7657	−1.12868	−0.564342	−	0.825541i	$-0.690870\pi$
$743$	−30.7657	−1.12868	−0.564342	+	0.825541i	$0.690870\pi$
$744$	−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	$-0.525984\pi$
$751$	−4.46921	−0.163084	−0.0815418	+	0.996670i	$0.525984\pi$
$752$	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	$-0.549108\pi$
$757$	−8.45580	−0.307331	−0.153666	+	0.988123i	$0.549108\pi$
$758$	−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	$-0.317102\pi$
$769$	30.1430	1.08699	0.543493	+	0.839414i	$0.317102\pi$
$770$	7.58211	0.273240
$771$	5.31873	0.191549
$772$	13.5730	0.488503
$773$	5.67696	0.204186	0.102093	−	0.994775i	$-0.467446\pi$
$773$	5.67696	0.204186	0.102093	+	0.994775i	$0.467446\pi$
$774$	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	$-0.683545\pi$
$797$	−30.7832	−1.09040	−0.545198	+	0.838308i	$0.683545\pi$
$798$	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	$-0.470653\pi$
$809$	5.23729	0.184133	0.0920667	+	0.995753i	$0.470653\pi$
$810$	−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	$-0.713452\pi$
$823$	−35.6558	−1.24288	−0.621441	+	0.783461i	$0.713452\pi$
$824$	−3.81833	−0.133018
$825$	−6.31442	−0.219840
$826$	−66.4650	−2.31261
$827$	−52.0538	−1.81009	−0.905044	−	0.425317i	$-0.860163\pi$
$827$	−52.0538	−1.81009	−0.905044	+	0.425317i	$0.860163\pi$
$828$	14.4547	0.502337
$829$	−13.4168	−0.465986	−0.232993	−	0.972478i	$-0.574852\pi$
$829$	−13.4168	−0.465986	−0.232993	+	0.972478i	$0.574852\pi$
$830$	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	$-0.680067\pi$
$839$	−31.0513	−1.07201	−0.536005	+	0.844215i	$0.680067\pi$
$840$	−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	$-0.380980\pi$
$853$	21.3357	0.730521	0.365261	+	0.930905i	$0.380980\pi$
$854$	−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	$-0.844765\pi$
$859$	−51.7837	−1.76684	−0.883419	+	0.468583i	$0.844765\pi$
$860$	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	$-0.601656\pi$
$881$	−18.6377	−0.627921	−0.313960	+	0.949436i	$0.601656\pi$
$882$	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	$-0.532993\pi$
$887$	−6.16288	−0.206929	−0.103465	+	0.994633i	$0.532993\pi$
$888$	−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	$-0.239410\pi$
$907$	43.9842	1.46047	0.730236	+	0.683195i	$0.239410\pi$
$908$	−22.7928	−0.756407
$909$	48.8732	1.62102
$910$	13.5036	0.447642
$911$	−25.6233	−0.848936	−0.424468	−	0.905443i	$-0.639539\pi$
$911$	−25.6233	−0.848936	−0.424468	+	0.905443i	$0.639539\pi$
$912$	−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	$-0.799209\pi$
$947$	−49.7023	−1.61511	−0.807554	+	0.589794i	$0.799209\pi$
$948$	−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	$-0.566471\pi$
$967$	−12.8933	−0.414622	−0.207311	+	0.978275i	$0.566471\pi$
$968$	−3.42088	−0.109951
$969$	1.01208	0.0325127
$970$	−10.1293	−0.325232
$971$	4.83745	0.155241	0.0776205	−	0.996983i	$-0.475268\pi$
$971$	4.83745	0.155241	0.0776205	+	0.996983i	$0.475268\pi$
$972$	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	$-0.361118\pi$
$983$	26.4993	0.845198	0.422599	+	0.906317i	$0.361118\pi$
$984$	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	$-0.621129\pi$
$997$	−23.4553	−0.742837	−0.371419	+	0.928465i	$0.621129\pi$
$998$	−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.e.1.1		3
3.2	odd	2		7569.2.a.r.1.3		3
29.2	odd	28		841.2.e.c.236.1		12
29.3	odd	28		841.2.e.b.270.1		12
29.4	even	14		841.2.d.a.190.1		6
29.5	even	14		841.2.d.c.605.1		6
29.6	even	14		841.2.d.c.645.1		6
29.7	even	7		841.2.d.e.571.1		6
29.8	odd	28		841.2.e.d.267.1		12
29.9	even	14		841.2.d.d.574.1		6
29.10	odd	28		841.2.e.b.651.1		12
29.11	odd	28		841.2.e.d.63.1		12
29.12	odd	4		841.2.b.c.840.1		6
29.13	even	14		841.2.d.d.778.1		6
29.14	odd	28		841.2.e.c.196.2		12
29.15	odd	28		841.2.e.c.196.1		12
29.16	even	7		29.2.d.a.24.1	yes	6
29.17	odd	4		841.2.b.c.840.6		6
29.18	odd	28		841.2.e.d.63.2		12
29.19	odd	28		841.2.e.b.651.2		12
29.20	even	7		29.2.d.a.23.1	✓	6
29.21	odd	28		841.2.e.d.267.2		12
29.22	even	14		841.2.d.a.571.1		6
29.23	even	7		841.2.d.b.645.1		6
29.24	even	7		841.2.d.b.605.1		6
29.25	even	7		841.2.d.e.190.1		6
29.26	odd	28		841.2.e.b.270.2		12
29.27	odd	28		841.2.e.c.236.2		12
29.28	even	2		841.2.a.f.1.3		3
87.20	odd	14		261.2.k.a.226.1		6
87.74	odd	14		261.2.k.a.82.1		6
87.86	odd	2		7569.2.a.p.1.1		3
116.103	odd	14		464.2.u.f.401.1		6
116.107	odd	14		464.2.u.f.81.1		6
145.49	even	14		725.2.l.b.226.1		6
145.74	even	14		725.2.l.b.401.1		6
145.78	odd	28		725.2.r.b.574.2		12
145.103	odd	28		725.2.r.b.24.1		12
145.107	odd	28		725.2.r.b.574.1		12
145.132	odd	28		725.2.r.b.24.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.20	even	7
29.2.d.a.24.1	yes	6	29.16	even	7
261.2.k.a.82.1		6	87.74	odd	14
261.2.k.a.226.1		6	87.20	odd	14
464.2.u.f.81.1		6	116.107	odd	14
464.2.u.f.401.1		6	116.103	odd	14
725.2.l.b.226.1		6	145.49	even	14
725.2.l.b.401.1		6	145.74	even	14
725.2.r.b.24.1		12	145.103	odd	28
725.2.r.b.24.2		12	145.132	odd	28
725.2.r.b.574.1		12	145.107	odd	28
725.2.r.b.574.2		12	145.78	odd	28
841.2.a.e.1.1		3	1.1	even	1	trivial
841.2.a.f.1.3		3	29.28	even	2
841.2.b.c.840.1		6	29.12	odd	4
841.2.b.c.840.6		6	29.17	odd	4
841.2.d.a.190.1		6	29.4	even	14
841.2.d.a.571.1		6	29.22	even	14
841.2.d.b.605.1		6	29.24	even	7
841.2.d.b.645.1		6	29.23	even	7
841.2.d.c.605.1		6	29.5	even	14
841.2.d.c.645.1		6	29.6	even	14
841.2.d.d.574.1		6	29.9	even	14
841.2.d.d.778.1		6	29.13	even	14
841.2.d.e.190.1		6	29.25	even	7
841.2.d.e.571.1		6	29.7	even	7
841.2.e.b.270.1		12	29.3	odd	28
841.2.e.b.270.2		12	29.26	odd	28
841.2.e.b.651.1		12	29.10	odd	28
841.2.e.b.651.2		12	29.19	odd	28
841.2.e.c.196.1		12	29.15	odd	28
841.2.e.c.196.2		12	29.14	odd	28
841.2.e.c.236.1		12	29.2	odd	28
841.2.e.c.236.2		12	29.27	odd	28
841.2.e.d.63.1		12	29.11	odd	28
841.2.e.d.63.2		12	29.18	odd	28
841.2.e.d.267.1		12	29.8	odd	28
841.2.e.d.267.2		12	29.21	odd	28
7569.2.a.p.1.1		3	87.86	odd	2
7569.2.a.r.1.3		3	3.2	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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
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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