LMFDB - Embedded newform 349.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, 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("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - x^{9} + 35x^{8} - 24x^{7} - 80x^{6} + 66x^{5} + 77x^{4} - 56x^{3} - 31x^{2} + 15x + 4 $ x^11 - 5x^10 - x^9 + 35x^8 - 24x^7 - 80x^6 + 66x^5 + 77x^4 - 56x^3 - 31x^2 + 15*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.767986$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.767986 q^{2} +0.193628 q^{3} -1.41020 q^{4} -0.953573 q^{5} +0.148703 q^{6} -2.43623 q^{7} -2.61898 q^{8} -2.96251 q^{9} +O(q^{10})$	\(q+0.767986 q^{2} +0.193628 q^{3} -1.41020 q^{4} -0.953573 q^{5} +0.148703 q^{6} -2.43623 q^{7} -2.61898 q^{8} -2.96251 q^{9} -0.732330 q^{10} -1.86888 q^{11} -0.273053 q^{12} -0.753820 q^{13} -1.87099 q^{14} -0.184638 q^{15} +0.809055 q^{16} -2.32183 q^{17} -2.27516 q^{18} +8.15083 q^{19} +1.34473 q^{20} -0.471721 q^{21} -1.43527 q^{22} +2.32353 q^{23} -0.507107 q^{24} -4.09070 q^{25} -0.578923 q^{26} -1.15451 q^{27} +3.43556 q^{28} -1.04598 q^{29} -0.141799 q^{30} -9.69453 q^{31} +5.85931 q^{32} -0.361867 q^{33} -1.78313 q^{34} +2.32312 q^{35} +4.17772 q^{36} +6.87034 q^{37} +6.25972 q^{38} -0.145960 q^{39} +2.49739 q^{40} -4.63000 q^{41} -0.362275 q^{42} -4.27609 q^{43} +2.63549 q^{44} +2.82497 q^{45} +1.78443 q^{46} -9.35254 q^{47} +0.156655 q^{48} -1.06480 q^{49} -3.14160 q^{50} -0.449570 q^{51} +1.06304 q^{52} +13.0459 q^{53} -0.886644 q^{54} +1.78211 q^{55} +6.38043 q^{56} +1.57822 q^{57} -0.803300 q^{58} +5.63108 q^{59} +0.260376 q^{60} +1.18980 q^{61} -7.44526 q^{62} +7.21734 q^{63} +2.88176 q^{64} +0.718822 q^{65} -0.277909 q^{66} -8.45151 q^{67} +3.27424 q^{68} +0.449899 q^{69} +1.78412 q^{70} -7.10914 q^{71} +7.75876 q^{72} +4.70076 q^{73} +5.27632 q^{74} -0.792072 q^{75} -11.4943 q^{76} +4.55302 q^{77} -0.112095 q^{78} +5.13811 q^{79} -0.771492 q^{80} +8.66398 q^{81} -3.55578 q^{82} -15.3036 q^{83} +0.665219 q^{84} +2.21403 q^{85} -3.28397 q^{86} -0.202531 q^{87} +4.89457 q^{88} -7.74670 q^{89} +2.16953 q^{90} +1.83648 q^{91} -3.27663 q^{92} -1.87713 q^{93} -7.18262 q^{94} -7.77240 q^{95} +1.13452 q^{96} -1.00058 q^{97} -0.817754 q^{98} +5.53658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.767986	0.543048	0.271524	−	0.962432i	$-0.412472\pi$
$2$	0.767986	0.543048	0.271524	+	0.962432i	$0.412472\pi$
$3$	0.193628	0.111791	0.0558955	−	0.998437i	$-0.482199\pi$
$3$	0.193628	0.111791	0.0558955	+	0.998437i	$0.482199\pi$
$4$	−1.41020	−0.705099
$5$	−0.953573	−0.426451	−0.213225	−	0.977003i	$-0.568397\pi$
$5$	−0.953573	−0.426451	−0.213225	+	0.977003i	$0.568397\pi$
$6$	0.148703	0.0607078
$7$	−2.43623	−0.920807	−0.460403	−	0.887710i	$-0.652295\pi$
$7$	−2.43623	−0.920807	−0.460403	+	0.887710i	$0.652295\pi$
$8$	−2.61898	−0.925950
$9$	−2.96251	−0.987503
$10$	−0.732330	−0.231583
$11$	−1.86888	−0.563489	−0.281744	−	0.959489i	$-0.590913\pi$
$11$	−1.86888	−0.563489	−0.281744	+	0.959489i	$0.590913\pi$
$12$	−0.273053	−0.0788237
$13$	−0.753820	−0.209072	−0.104536	−	0.994521i	$-0.533336\pi$
$13$	−0.753820	−0.209072	−0.104536	+	0.994521i	$0.533336\pi$
$14$	−1.87099	−0.500042
$15$	−0.184638	−0.0476733
$16$	0.809055	0.202264
$17$	−2.32183	−0.563126	−0.281563	−	0.959543i	$-0.590853\pi$
$17$	−2.32183	−0.563126	−0.281563	+	0.959543i	$0.590853\pi$
$18$	−2.27516	−0.536261
$19$	8.15083	1.86993	0.934964	−	0.354743i	$-0.115432\pi$
$19$	8.15083	1.86993	0.934964	+	0.354743i	$0.115432\pi$
$20$	1.34473	0.300690
$21$	−0.471721	−0.102938
$22$	−1.43527	−0.306001
$23$	2.32353	0.484489	0.242244	−	0.970215i	$-0.422116\pi$
$23$	2.32353	0.484489	0.242244	+	0.970215i	$0.422116\pi$
$24$	−0.507107	−0.103513
$25$	−4.09070	−0.818140
$26$	−0.578923	−0.113536
$27$	−1.15451	−0.222185
$28$	3.43556	0.649260
$29$	−1.04598	−0.194234	−0.0971171	−	0.995273i	$-0.530962\pi$
$29$	−1.04598	−0.194234	−0.0971171	+	0.995273i	$0.530962\pi$
$30$	−0.141799	−0.0258889
$31$	−9.69453	−1.74119	−0.870594	−	0.492002i	$-0.836265\pi$
$31$	−9.69453	−1.74119	−0.870594	+	0.492002i	$0.836265\pi$
$32$	5.85931	1.03579
$33$	−0.361867	−0.0629930
$34$	−1.78313	−0.305805
$35$	2.32312	0.392679
$36$	4.17772	0.696287
$37$	6.87034	1.12948	0.564738	−	0.825270i	$-0.308977\pi$
$37$	6.87034	1.12948	0.564738	+	0.825270i	$0.308977\pi$
$38$	6.25972	1.01546
$39$	−0.145960	−0.0233724
$40$	2.49739	0.394872
$41$	−4.63000	−0.723085	−0.361543	−	0.932356i	$-0.617750\pi$
$41$	−4.63000	−0.723085	−0.361543	+	0.932356i	$0.617750\pi$
$42$	−0.362275	−0.0559002
$43$	−4.27609	−0.652097	−0.326048	−	0.945353i	$-0.605717\pi$
$43$	−4.27609	−0.652097	−0.326048	+	0.945353i	$0.605717\pi$
$44$	2.63549	0.397315
$45$	2.82497	0.421121
$46$	1.78443	0.263101
$47$	−9.35254	−1.36421	−0.682104	−	0.731255i	$-0.738935\pi$
$47$	−9.35254	−1.36421	−0.682104	+	0.731255i	$0.738935\pi$
$48$	0.156655	0.0226112
$49$	−1.06480	−0.152115
$50$	−3.14160	−0.444289
$51$	−0.449570	−0.0629524
$52$	1.06304	0.147416
$53$	13.0459	1.79199	0.895993	−	0.444068i	$-0.146465\pi$
$53$	13.0459	1.79199	0.895993	+	0.444068i	$0.146465\pi$
$54$	−0.886644	−0.120657
$55$	1.78211	0.240300
$56$	6.38043	0.852621
$57$	1.57822	0.209041
$58$	−0.803300	−0.105479
$59$	5.63108	0.733105	0.366552	−	0.930397i	$-0.380538\pi$
$59$	5.63108	0.733105	0.366552	+	0.930397i	$0.380538\pi$
$60$	0.260376	0.0336144
$61$	1.18980	0.152338	0.0761692	−	0.997095i	$-0.475731\pi$
$61$	1.18980	0.152338	0.0761692	+	0.997095i	$0.475731\pi$
$62$	−7.44526	−0.945549
$63$	7.21734	0.909299
$64$	2.88176	0.360219
$65$	0.718822	0.0891589
$66$	−0.277909	−0.0342082
$67$	−8.45151	−1.03252	−0.516258	−	0.856433i	$-0.672676\pi$
$67$	−8.45151	−1.03252	−0.516258	+	0.856433i	$0.672676\pi$
$68$	3.27424	0.397060
$69$	0.449899	0.0541615
$70$	1.78412	0.213243
$71$	−7.10914	−0.843700	−0.421850	−	0.906666i	$-0.638619\pi$
$71$	−7.10914	−0.843700	−0.421850	+	0.906666i	$0.638619\pi$
$72$	7.75876	0.914379
$73$	4.70076	0.550183	0.275091	−	0.961418i	$-0.411292\pi$
$73$	4.70076	0.550183	0.275091	+	0.961418i	$0.411292\pi$
$74$	5.27632	0.613360
$75$	−0.792072	−0.0914606
$76$	−11.4943	−1.31848
$77$	4.55302	0.518864
$78$	−0.112095	−0.0126923
$79$	5.13811	0.578083	0.289041	−	0.957317i	$-0.406663\pi$
$79$	5.13811	0.578083	0.289041	+	0.957317i	$0.406663\pi$
$80$	−0.771492	−0.0862555
$81$	8.66398	0.962665
$82$	−3.55578	−0.392670
$83$	−15.3036	−1.67979	−0.839893	−	0.542751i	$-0.817383\pi$
$83$	−15.3036	−1.67979	−0.839893	+	0.542751i	$0.817383\pi$
$84$	0.665219	0.0725814
$85$	2.21403	0.240146
$86$	−3.28397	−0.354120
$87$	−0.202531	−0.0217136
$88$	4.89457	0.521763
$89$	−7.74670	−0.821148	−0.410574	−	0.911827i	$-0.634672\pi$
$89$	−7.74670	−0.821148	−0.410574	+	0.911827i	$0.634672\pi$
$90$	2.16953	0.228689
$91$	1.83648	0.192515
$92$	−3.27663	−0.341613
$93$	−1.87713	−0.194649
$94$	−7.18262	−0.740831
$95$	−7.77240	−0.797432
$96$	1.13452	0.115792
$97$	−1.00058	−0.101594	−0.0507968	−	0.998709i	$-0.516176\pi$
$97$	−1.00058	−0.101594	−0.0507968	+	0.998709i	$0.516176\pi$
$98$	−0.817754	−0.0826057
$99$	5.53658	0.556447
$100$	5.76870	0.576870
$101$	−12.3366	−1.22754	−0.613769	−	0.789486i	$-0.710347\pi$
$101$	−12.3366	−1.22754	−0.613769	+	0.789486i	$0.710347\pi$
$102$	−0.345264	−0.0341862
$103$	18.7589	1.84837	0.924184	−	0.381948i	$-0.124747\pi$
$103$	18.7589	1.84837	0.924184	+	0.381948i	$0.124747\pi$
$104$	1.97424	0.193590
$105$	0.449820	0.0438979
$106$	10.0190	0.973134
$107$	−15.0644	−1.45633	−0.728164	−	0.685402i	$-0.759626\pi$
$107$	−15.0644	−1.45633	−0.728164	+	0.685402i	$0.759626\pi$
$108$	1.62808	0.156662
$109$	1.94532	0.186328	0.0931638	−	0.995651i	$-0.470302\pi$
$109$	1.94532	0.186328	0.0931638	+	0.995651i	$0.470302\pi$
$110$	1.36864	0.130494
$111$	1.33029	0.126265
$112$	−1.97104	−0.186246
$113$	9.37410	0.881842	0.440921	−	0.897546i	$-0.354652\pi$
$113$	9.37410	0.881842	0.440921	+	0.897546i	$0.354652\pi$
$114$	1.21205	0.113519
$115$	−2.21565	−0.206611
$116$	1.47504	0.136954
$117$	2.23320	0.206459
$118$	4.32459	0.398111
$119$	5.65650	0.518531
$120$	0.483564	0.0441431
$121$	−7.50728	−0.682480
$122$	0.913750	0.0827270
$123$	−0.896497	−0.0808344
$124$	13.6712	1.22771
$125$	8.66864	0.775347
$126$	5.54281	0.493793
$127$	−15.1250	−1.34212	−0.671061	−	0.741402i	$-0.734161\pi$
$127$	−15.1250	−1.34212	−0.671061	+	0.741402i	$0.734161\pi$
$128$	−9.50547	−0.840173
$129$	−0.827968	−0.0728985
$130$	0.552045	0.0484175
$131$	−6.00166	−0.524367	−0.262184	−	0.965018i	$-0.584443\pi$
$131$	−6.00166	−0.524367	−0.262184	+	0.965018i	$0.584443\pi$
$132$	0.510304	0.0444163
$133$	−19.8573	−1.72184
$134$	−6.49064	−0.560706
$135$	1.10091	0.0947509
$136$	6.08083	0.521427
$137$	5.50700	0.470495	0.235247	−	0.971936i	$-0.424410\pi$
$137$	5.50700	0.470495	0.235247	+	0.971936i	$0.424410\pi$
$138$	0.345516	0.0294123
$139$	21.0869	1.78856	0.894282	−	0.447504i	$-0.147687\pi$
$139$	21.0869	1.78856	0.894282	+	0.447504i	$0.147687\pi$
$140$	−3.27606	−0.276877
$141$	−1.81091	−0.152506
$142$	−5.45972	−0.458169
$143$	1.40880	0.117810
$144$	−2.39683	−0.199736
$145$	0.997421	0.0828313
$146$	3.61012	0.298776
$147$	−0.206175	−0.0170051
$148$	−9.68854	−0.796393
$149$	2.28726	0.187380	0.0936900	−	0.995601i	$-0.470134\pi$
$149$	2.28726	0.187380	0.0936900	+	0.995601i	$0.470134\pi$
$150$	−0.608300	−0.0496675
$151$	8.21563	0.668579	0.334289	−	0.942470i	$-0.391504\pi$
$151$	8.21563	0.668579	0.334289	+	0.942470i	$0.391504\pi$
$152$	−21.3469	−1.73146
$153$	6.87844	0.556089
$154$	3.49665	0.281768
$155$	9.24443	0.742531
$156$	0.205833	0.0164798
$157$	3.71606	0.296574	0.148287	−	0.988944i	$-0.452624\pi$
$157$	3.71606	0.296574	0.148287	+	0.988944i	$0.452624\pi$
$158$	3.94600	0.313927
$159$	2.52604	0.200328
$160$	−5.58728	−0.441713
$161$	−5.66063	−0.446121
$162$	6.65381	0.522773
$163$	−14.7130	−1.15241	−0.576206	−	0.817305i	$-0.695467\pi$
$163$	−14.7130	−1.15241	−0.576206	+	0.817305i	$0.695467\pi$
$164$	6.52922	0.509847
$165$	0.345066	0.0268634
$166$	−11.7529	−0.912205
$167$	5.83555	0.451568	0.225784	−	0.974177i	$-0.427506\pi$
$167$	5.83555	0.451568	0.225784	+	0.974177i	$0.427506\pi$
$168$	1.23543	0.0953154
$169$	−12.4318	−0.956289
$170$	1.70035	0.130411
$171$	−24.1469	−1.84656
$172$	6.03013	0.459793
$173$	−25.0690	−1.90596	−0.952980	−	0.303032i	$-0.902001\pi$
$173$	−25.0690	−1.90596	−0.952980	+	0.303032i	$0.902001\pi$
$174$	−0.155541	−0.0117915
$175$	9.96587	0.753349
$176$	−1.51203	−0.113973
$177$	1.09033	0.0819545
$178$	−5.94935	−0.445923
$179$	−15.3488	−1.14723	−0.573613	−	0.819127i	$-0.694459\pi$
$179$	−15.3488	−1.14723	−0.573613	+	0.819127i	$0.694459\pi$
$180$	−3.98376	−0.296932
$181$	5.77045	0.428914	0.214457	−	0.976733i	$-0.431202\pi$
$181$	5.77045	0.428914	0.214457	+	0.976733i	$0.431202\pi$
$182$	1.41039	0.104545
$183$	0.230378	0.0170300
$184$	−6.08528	−0.448613
$185$	−6.55137	−0.481666
$186$	−1.44161	−0.105704
$187$	4.33922	0.317315
$188$	13.1889	0.961902
$189$	2.81264	0.204589
$190$	−5.96909	−0.433044
$191$	−15.4057	−1.11472	−0.557360	−	0.830271i	$-0.688186\pi$
$191$	−15.4057	−1.11472	−0.557360	+	0.830271i	$0.688186\pi$
$192$	0.557987	0.0402693
$193$	19.2752	1.38746	0.693730	−	0.720236i	$-0.255966\pi$
$193$	19.2752	1.38746	0.693730	+	0.720236i	$0.255966\pi$
$194$	−0.768431	−0.0551701
$195$	0.139184	0.00996716
$196$	1.50158	0.107256
$197$	0.829466	0.0590970	0.0295485	−	0.999563i	$-0.490593\pi$
$197$	0.829466	0.0590970	0.0295485	+	0.999563i	$0.490593\pi$
$198$	4.25201	0.302177
$199$	−12.4256	−0.880829	−0.440414	−	0.897795i	$-0.645168\pi$
$199$	−12.4256	−0.880829	−0.440414	+	0.897795i	$0.645168\pi$
$200$	10.7135	0.757557
$201$	−1.63645	−0.115426
$202$	−9.47434	−0.666612
$203$	2.54825	0.178852
$204$	0.633983	0.0443877
$205$	4.41505	0.308360
$206$	14.4066	1.00375
$207$	−6.88347	−0.478434
$208$	−0.609881	−0.0422877
$209$	−15.2329	−1.05368
$210$	0.345455	0.0238387
$211$	−6.92315	−0.476609	−0.238305	−	0.971190i	$-0.576592\pi$
$211$	−6.92315	−0.476609	−0.238305	+	0.971190i	$0.576592\pi$
$212$	−18.3972	−1.26353
$213$	−1.37653	−0.0943180
$214$	−11.5692	−0.790856
$215$	4.07756	0.278087
$216$	3.02363	0.205732
$217$	23.6181	1.60330
$218$	1.49398	0.101185
$219$	0.910198	0.0615055
$220$	−2.51313	−0.169435
$221$	1.75024	0.117734
$222$	1.02164	0.0685681
$223$	−2.70185	−0.180929	−0.0904647	−	0.995900i	$-0.528835\pi$
$223$	−2.70185	−0.180929	−0.0904647	+	0.995900i	$0.528835\pi$
$224$	−14.2746	−0.953762
$225$	12.1187	0.807915
$226$	7.19918	0.478882
$227$	−3.55838	−0.236178	−0.118089	−	0.993003i	$-0.537677\pi$
$227$	−3.55838	−0.236178	−0.118089	+	0.993003i	$0.537677\pi$
$228$	−2.22561	−0.147395
$229$	24.1664	1.59696	0.798481	−	0.602021i	$-0.205637\pi$
$229$	24.1664	1.59696	0.798481	+	0.602021i	$0.205637\pi$
$230$	−1.70159	−0.112199
$231$	0.881590	0.0580043
$232$	2.73941	0.179851
$233$	−8.69866	−0.569868	−0.284934	−	0.958547i	$-0.591972\pi$
$233$	−8.69866	−0.569868	−0.284934	+	0.958547i	$0.591972\pi$
$234$	1.71506	0.112117
$235$	8.91833	0.581768
$236$	−7.94094	−0.516911
$237$	0.994880	0.0646244
$238$	4.34411	0.281587
$239$	−24.0326	−1.55454	−0.777269	−	0.629168i	$-0.783396\pi$
$239$	−24.0326	−1.55454	−0.777269	+	0.629168i	$0.783396\pi$
$240$	−0.149382	−0.00964258
$241$	16.6594	1.07313	0.536563	−	0.843860i	$-0.319722\pi$
$241$	16.6594	1.07313	0.536563	+	0.843860i	$0.319722\pi$
$242$	−5.76549	−0.370619
$243$	5.14110	0.329802
$244$	−1.67785	−0.107414
$245$	1.01537	0.0648695
$246$	−0.688497	−0.0438969
$247$	−6.14425	−0.390950
$248$	25.3898	1.61225
$249$	−2.96320	−0.187785
$250$	6.65739	0.421050
$251$	−6.67234	−0.421154	−0.210577	−	0.977577i	$-0.567534\pi$
$251$	−6.67234	−0.421154	−0.210577	+	0.977577i	$0.567534\pi$
$252$	−10.1779	−0.641146
$253$	−4.34239	−0.273004
$254$	−11.6157	−0.728837
$255$	0.428698	0.0268461
$256$	−13.0636	−0.816474
$257$	16.3562	1.02027	0.510136	−	0.860094i	$-0.329595\pi$
$257$	16.3562	1.02027	0.510136	+	0.860094i	$0.329595\pi$
$258$	−0.635868	−0.0395874
$259$	−16.7377	−1.04003
$260$	−1.01368	−0.0628658
$261$	3.09874	0.191807
$262$	−4.60919	−0.284757
$263$	7.63340	0.470695	0.235348	−	0.971911i	$-0.424377\pi$
$263$	7.63340	0.470695	0.235348	+	0.971911i	$0.424377\pi$
$264$	0.947723	0.0583283
$265$	−12.4402	−0.764193
$266$	−15.2501	−0.935043
$267$	−1.49997	−0.0917970
$268$	11.9183	0.728027
$269$	18.6702	1.13834	0.569170	−	0.822220i	$-0.307265\pi$
$269$	18.6702	1.13834	0.569170	+	0.822220i	$0.307265\pi$
$270$	0.845480	0.0514542
$271$	8.89135	0.540111	0.270056	−	0.962845i	$-0.412958\pi$
$271$	8.89135	0.540111	0.270056	+	0.962845i	$0.412958\pi$
$272$	−1.87849	−0.113900
$273$	0.355592	0.0215214
$274$	4.22930	0.255501
$275$	7.64503	0.461013
$276$	−0.634446	−0.0381892
$277$	9.19773	0.552638	0.276319	−	0.961066i	$-0.410885\pi$
$277$	9.19773	0.552638	0.276319	+	0.961066i	$0.410885\pi$
$278$	16.1944	0.971276
$279$	28.7201	1.71943
$280$	−6.08421	−0.363601
$281$	−21.9262	−1.30801	−0.654003	−	0.756492i	$-0.726912\pi$
$281$	−21.9262	−1.30801	−0.654003	+	0.756492i	$0.726912\pi$
$282$	−1.39075	−0.0828182
$283$	3.74644	0.222703	0.111351	−	0.993781i	$-0.464482\pi$
$283$	3.74644	0.222703	0.111351	+	0.993781i	$0.464482\pi$
$284$	10.0253	0.594892
$285$	−1.50495	−0.0891457
$286$	1.08194	0.0639763
$287$	11.2797	0.665822
$288$	−17.3583	−1.02284
$289$	−11.6091	−0.682889
$290$	0.766005	0.0449814
$291$	−0.193740	−0.0113572
$292$	−6.62901	−0.387933
$293$	13.1931	0.770750	0.385375	−	0.922760i	$-0.374072\pi$
$293$	13.1931	0.770750	0.385375	+	0.922760i	$0.374072\pi$
$294$	−0.158340	−0.00923457
$295$	−5.36965	−0.312633
$296$	−17.9933	−1.04584
$297$	2.15763	0.125199
$298$	1.75659	0.101756
$299$	−1.75152	−0.101293
$300$	1.11698	0.0644888
$301$	10.4175	0.600455
$302$	6.30949	0.363070
$303$	−2.38871	−0.137228
$304$	6.59446	0.378218
$305$	−1.13456	−0.0649648
$306$	5.28254	0.301983
$307$	1.82781	0.104319	0.0521594	−	0.998639i	$-0.483390\pi$
$307$	1.82781	0.104319	0.0521594	+	0.998639i	$0.483390\pi$
$308$	−6.42065	−0.365851
$309$	3.63224	0.206631
$310$	7.09959	0.403230
$311$	−22.4041	−1.27042	−0.635211	−	0.772338i	$-0.719087\pi$
$311$	−22.4041	−1.27042	−0.635211	+	0.772338i	$0.719087\pi$
$312$	0.382268	0.0216416
$313$	30.1261	1.70283	0.851414	−	0.524494i	$-0.175745\pi$
$313$	30.1261	1.70283	0.851414	+	0.524494i	$0.175745\pi$
$314$	2.85388	0.161054
$315$	−6.88226	−0.387771
$316$	−7.24576	−0.407606
$317$	24.1587	1.35689	0.678445	−	0.734651i	$-0.262654\pi$
$317$	24.1587	1.35689	0.678445	+	0.734651i	$0.262654\pi$
$318$	1.93996	0.108788
$319$	1.95482	0.109449
$320$	−2.74796	−0.153616
$321$	−2.91688	−0.162804
$322$	−4.34729	−0.242265
$323$	−18.9248	−1.05301
$324$	−12.2179	−0.678774
$325$	3.08365	0.171050
$326$	−11.2994	−0.625815
$327$	0.376667	0.0208297
$328$	12.1259	0.669541
$329$	22.7849	1.25617
$330$	0.265006	0.0145881
$331$	−5.78944	−0.318217	−0.159108	−	0.987261i	$-0.550862\pi$
$331$	−5.78944	−0.318217	−0.159108	+	0.987261i	$0.550862\pi$
$332$	21.5811	1.18442
$333$	−20.3534	−1.11536
$334$	4.48162	0.245223
$335$	8.05913	0.440317
$336$	−0.381648	−0.0208206
$337$	0.678825	0.0369780	0.0184890	−	0.999829i	$-0.494114\pi$
$337$	0.678825	0.0369780	0.0184890	+	0.999829i	$0.494114\pi$
$338$	−9.54741	−0.519311
$339$	1.81509	0.0985819
$340$	−3.12222	−0.169326
$341$	18.1179	0.981140
$342$	−18.5445	−1.00277
$343$	19.6477	1.06088
$344$	11.1990	0.603809
$345$	−0.429011	−0.0230972
$346$	−19.2526	−1.03503
$347$	8.17849	0.439045	0.219522	−	0.975607i	$-0.429550\pi$
$347$	8.17849	0.439045	0.219522	+	0.975607i	$0.429550\pi$
$348$	0.285609	0.0153103
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	7.65364	0.409104
$351$	0.870290	0.0464526
$352$	−10.9504	−0.583656
$353$	−7.23394	−0.385024	−0.192512	−	0.981295i	$-0.561663\pi$
$353$	−7.23394	−0.385024	−0.192512	+	0.981295i	$0.561663\pi$
$354$	0.837360	0.0445052
$355$	6.77908	0.359796
$356$	10.9244	0.578991
$357$	1.09525	0.0579670
$358$	−11.7877	−0.622998
$359$	25.5218	1.34699	0.673496	−	0.739191i	$-0.264792\pi$
$359$	25.5218	1.34699	0.673496	+	0.739191i	$0.264792\pi$
$360$	−7.39854	−0.389937
$361$	47.4360	2.49663
$362$	4.43163	0.232921
$363$	−1.45362	−0.0762951
$364$	−2.58979	−0.135742
$365$	−4.48252	−0.234626
$366$	0.176927	0.00924813
$367$	6.41250	0.334730	0.167365	−	0.985895i	$-0.446474\pi$
$367$	6.41250	0.334730	0.167365	+	0.985895i	$0.446474\pi$
$368$	1.87986	0.0979945
$369$	13.7164	0.714049
$370$	−5.03135	−0.261568
$371$	−31.7826	−1.65007
$372$	2.64712	0.137247
$373$	3.04806	0.157823	0.0789113	−	0.996882i	$-0.474856\pi$
$373$	3.04806	0.157823	0.0789113	+	0.996882i	$0.474856\pi$
$374$	3.33246	0.172317
$375$	1.67849	0.0866768
$376$	24.4942	1.26319
$377$	0.788483	0.0406090
$378$	2.16007	0.111102
$379$	23.9854	1.23205	0.616023	−	0.787728i	$-0.288743\pi$
$379$	23.9854	1.23205	0.616023	+	0.787728i	$0.288743\pi$
$380$	10.9606	0.562268
$381$	−2.92861	−0.150037
$382$	−11.8314	−0.605347
$383$	−12.9256	−0.660468	−0.330234	−	0.943899i	$-0.607128\pi$
$383$	−12.9256	−0.660468	−0.330234	+	0.943899i	$0.607128\pi$
$384$	−1.84052	−0.0939237
$385$	−4.34163	−0.221270
$386$	14.8031	0.753457
$387$	12.6679	0.643948
$388$	1.41102	0.0716335
$389$	16.6632	0.844855	0.422428	−	0.906397i	$-0.361178\pi$
$389$	16.6632	0.844855	0.422428	+	0.906397i	$0.361178\pi$
$390$	0.106891	0.00541264
$391$	−5.39483	−0.272828
$392$	2.78870	0.140851
$393$	−1.16209	−0.0586195
$394$	0.637018	0.0320925
$395$	−4.89956	−0.246524
$396$	−7.80767	−0.392350
$397$	−18.7666	−0.941871	−0.470935	−	0.882168i	$-0.656083\pi$
$397$	−18.7666	−0.941871	−0.470935	+	0.882168i	$0.656083\pi$
$398$	−9.54270	−0.478332
$399$	−3.84491	−0.192486
$400$	−3.30960	−0.165480
$401$	−11.5272	−0.575640	−0.287820	−	0.957685i	$-0.592930\pi$
$401$	−11.5272	−0.575640	−0.287820	+	0.957685i	$0.592930\pi$
$402$	−1.25677	−0.0626819
$403$	7.30793	0.364034
$404$	17.3971	0.865536
$405$	−8.26173	−0.410529
$406$	1.95702	0.0971253
$407$	−12.8398	−0.636447
$408$	1.17742	0.0582908
$409$	−23.1072	−1.14258	−0.571290	−	0.820748i	$-0.693557\pi$
$409$	−23.1072	−1.14258	−0.571290	+	0.820748i	$0.693557\pi$
$410$	3.39069	0.167454
$411$	1.06631	0.0525971
$412$	−26.4537	−1.30328
$413$	−13.7186	−0.675048
$414$	−5.28640	−0.259813
$415$	14.5931	0.716346
$416$	−4.41686	−0.216555
$417$	4.08300	0.199945
$418$	−11.6987	−0.572200
$419$	−19.7721	−0.965933	−0.482966	−	0.875639i	$-0.660441\pi$
$419$	−19.7721	−0.965933	−0.482966	+	0.875639i	$0.660441\pi$
$420$	−0.634335	−0.0309524
$421$	−5.91766	−0.288409	−0.144205	−	0.989548i	$-0.546062\pi$
$421$	−5.91766	−0.288409	−0.144205	+	0.989548i	$0.546062\pi$
$422$	−5.31688	−0.258822
$423$	27.7070	1.34716
$424$	−34.1669	−1.65929
$425$	9.49791	0.460716
$426$	−1.05715	−0.0512192
$427$	−2.89862	−0.140274
$428$	21.2438	1.02686
$429$	0.272783	0.0131701
$430$	3.13151	0.151015
$431$	31.7797	1.53078	0.765388	−	0.643569i	$-0.222547\pi$
$431$	31.7797	1.53078	0.765388	+	0.643569i	$0.222547\pi$
$432$	−0.934059	−0.0449399
$433$	6.19186	0.297562	0.148781	−	0.988870i	$-0.452465\pi$
$433$	6.19186	0.297562	0.148781	+	0.988870i	$0.452465\pi$
$434$	18.1383	0.870667
$435$	0.193128	0.00925979
$436$	−2.74328	−0.131379
$437$	18.9387	0.905959
$438$	0.699019	0.0334004
$439$	23.0402	1.09965	0.549825	−	0.835280i	$-0.314695\pi$
$439$	23.0402	1.09965	0.549825	+	0.835280i	$0.314695\pi$
$440$	−4.66733	−0.222506
$441$	3.15449	0.150214
$442$	1.34416	0.0639352
$443$	12.3743	0.587921	0.293961	−	0.955818i	$-0.405027\pi$
$443$	12.3743	0.587921	0.293961	+	0.955818i	$0.405027\pi$
$444$	−1.87597	−0.0890295
$445$	7.38704	0.350179
$446$	−2.07498	−0.0982533
$447$	0.442877	0.0209474
$448$	−7.02061	−0.331693
$449$	−27.8700	−1.31527	−0.657634	−	0.753337i	$-0.728443\pi$
$449$	−27.8700	−1.31527	−0.657634	+	0.753337i	$0.728443\pi$
$450$	9.30701	0.438737
$451$	8.65293	0.407450
$452$	−13.2193	−0.621786
$453$	1.59077	0.0747411
$454$	−2.73279	−0.128256
$455$	−1.75121	−0.0820981
$456$	−4.13334	−0.193562
$457$	−27.7120	−1.29631	−0.648155	−	0.761508i	$-0.724459\pi$
$457$	−27.7120	−1.29631	−0.648155	+	0.761508i	$0.724459\pi$
$458$	18.5595	0.867226
$459$	2.68057	0.125118
$460$	3.12451	0.145681
$461$	−9.15186	−0.426245	−0.213122	−	0.977026i	$-0.568363\pi$
$461$	−9.15186	−0.426245	−0.213122	+	0.977026i	$0.568363\pi$
$462$	0.677048	0.0314991
$463$	14.3855	0.668549	0.334274	−	0.942476i	$-0.391509\pi$
$463$	14.3855	0.668549	0.334274	+	0.942476i	$0.391509\pi$
$464$	−0.846258	−0.0392865
$465$	1.78998	0.0830082
$466$	−6.68045	−0.309466
$467$	−15.8196	−0.732045	−0.366023	−	0.930606i	$-0.619281\pi$
$467$	−15.8196	−0.732045	−0.366023	+	0.930606i	$0.619281\pi$
$468$	−3.14925	−0.145574
$469$	20.5898	0.950749
$470$	6.84915	0.315928
$471$	0.719532	0.0331543
$472$	−14.7477	−0.678819
$473$	7.99150	0.367449
$474$	0.764054	0.0350942
$475$	−33.3426	−1.52986
$476$	−7.97679	−0.365615
$477$	−38.6485	−1.76959
$478$	−18.4567	−0.844189
$479$	4.93286	0.225388	0.112694	−	0.993630i	$-0.464052\pi$
$479$	4.93286	0.225388	0.112694	+	0.993630i	$0.464052\pi$
$480$	−1.08185	−0.0493795
$481$	−5.17900	−0.236142
$482$	12.7942	0.582759
$483$	−1.09606	−0.0498722
$484$	10.5868	0.481216
$485$	0.954126	0.0433246
$486$	3.94829	0.179098
$487$	−14.3013	−0.648056	−0.324028	−	0.946047i	$-0.605037\pi$
$487$	−14.3013	−0.648056	−0.324028	+	0.946047i	$0.605037\pi$
$488$	−3.11607	−0.141058
$489$	−2.84884	−0.128829
$490$	0.779788	0.0352272
$491$	−41.3235	−1.86490	−0.932452	−	0.361295i	$-0.882335\pi$
$491$	−41.3235	−1.86490	−0.932452	+	0.361295i	$0.882335\pi$
$492$	1.26424	0.0569962
$493$	2.42860	0.109378
$494$	−4.71870	−0.212304
$495$	−5.27953	−0.237297
$496$	−7.84340	−0.352179
$497$	17.3195	0.776884
$498$	−2.27569	−0.101976
$499$	−42.3819	−1.89727	−0.948637	−	0.316366i	$-0.897537\pi$
$499$	−42.3819	−1.89727	−0.948637	+	0.316366i	$0.897537\pi$
$500$	−12.2245	−0.546696
$501$	1.12992	0.0504812
$502$	−5.12426	−0.228707
$503$	−36.2126	−1.61464	−0.807319	−	0.590115i	$-0.799083\pi$
$503$	−36.2126	−1.61464	−0.807319	+	0.590115i	$0.799083\pi$
$504$	−18.9021	−0.841966
$505$	11.7638	0.523484
$506$	−3.33490	−0.148254
$507$	−2.40713	−0.106904
$508$	21.3292	0.946330
$509$	14.6775	0.650569	0.325284	−	0.945616i	$-0.394540\pi$
$509$	14.6775	0.650569	0.325284	+	0.945616i	$0.394540\pi$
$510$	0.329234	0.0145787
$511$	−11.4521	−0.506612
$512$	8.97830	0.396789
$513$	−9.41018	−0.415470
$514$	12.5613	0.554056
$515$	−17.8880	−0.788238
$516$	1.16760	0.0514007
$517$	17.4788	0.768716
$518$	−12.8543	−0.564786
$519$	−4.85405	−0.213069
$520$	−1.88258	−0.0825567
$521$	−30.2001	−1.32309	−0.661545	−	0.749906i	$-0.730099\pi$
$521$	−30.2001	−1.32309	−0.661545	+	0.749906i	$0.730099\pi$
$522$	2.37978	0.104160
$523$	32.6027	1.42562	0.712808	−	0.701359i	$-0.247423\pi$
$523$	32.6027	1.42562	0.712808	+	0.701359i	$0.247423\pi$
$524$	8.46353	0.369731
$525$	1.92967	0.0842176
$526$	5.86234	0.255610
$527$	22.5090	0.980509
$528$	−0.292770	−0.0127412
$529$	−17.6012	−0.765271
$530$	−9.55387	−0.414994
$531$	−16.6821	−0.723943
$532$	28.0027	1.21407
$533$	3.49019	0.151177
$534$	−1.15196	−0.0498501
$535$	14.3650	0.621052
$536$	22.1344	0.956059
$537$	−2.97196	−0.128249
$538$	14.3384	0.618173
$539$	1.98999	0.0857150
$540$	−1.55249	−0.0668087
$541$	−9.62727	−0.413909	−0.206954	−	0.978351i	$-0.566355\pi$
$541$	−9.62727	−0.413909	−0.206954	+	0.978351i	$0.566355\pi$
$542$	6.82843	0.293306
$543$	1.11732	0.0479488
$544$	−13.6043	−0.583280
$545$	−1.85500	−0.0794595
$546$	0.273090	0.0116872
$547$	−22.9140	−0.979733	−0.489866	−	0.871798i	$-0.662954\pi$
$547$	−22.9140	−0.979733	−0.489866	+	0.871798i	$0.662954\pi$
$548$	−7.76596	−0.331745
$549$	−3.52479	−0.150435
$550$	5.87127	0.250352
$551$	−8.52563	−0.363204
$552$	−1.17828	−0.0501508
$553$	−12.5176	−0.532303
$554$	7.06373	0.300109
$555$	−1.26853	−0.0538459
$556$	−29.7366	−1.26111
$557$	10.6983	0.453303	0.226651	−	0.973976i	$-0.427222\pi$
$557$	10.6983	0.453303	0.226651	+	0.973976i	$0.427222\pi$
$558$	22.0566	0.933732
$559$	3.22340	0.136335
$560$	1.87953	0.0794246
$561$	0.840193	0.0354730
$562$	−16.8390	−0.710310
$563$	−7.54904	−0.318154	−0.159077	−	0.987266i	$-0.550852\pi$
$563$	−7.54904	−0.318154	−0.159077	+	0.987266i	$0.550852\pi$
$564$	2.55374	0.107532
$565$	−8.93889	−0.376062
$566$	2.87722	0.120938
$567$	−21.1074	−0.886428
$568$	18.6187	0.781224
$569$	−14.8334	−0.621850	−0.310925	−	0.950434i	$-0.600639\pi$
$569$	−14.8334	−0.621850	−0.310925	+	0.950434i	$0.600639\pi$
$570$	−1.15578	−0.0484104
$571$	−12.5588	−0.525568	−0.262784	−	0.964855i	$-0.584641\pi$
$571$	−12.5588	−0.525568	−0.262784	+	0.964855i	$0.584641\pi$
$572$	−1.98669	−0.0830675
$573$	−2.98298	−0.124616
$574$	8.66268	0.361573
$575$	−9.50485	−0.396380
$576$	−8.53723	−0.355718
$577$	38.0891	1.58567	0.792835	−	0.609437i	$-0.208604\pi$
$577$	38.0891	1.58567	0.792835	+	0.609437i	$0.208604\pi$
$578$	−8.91563	−0.370841
$579$	3.73221	0.155105
$580$	−1.40656	−0.0584043
$581$	37.2830	1.54676
$582$	−0.148789	−0.00616752
$583$	−24.3811	−1.00976
$584$	−12.3112	−0.509442
$585$	−2.12952	−0.0880447
$586$	10.1321	0.418554
$587$	1.45753	0.0601586	0.0300793	−	0.999548i	$-0.490424\pi$
$587$	1.45753	0.0601586	0.0300793	+	0.999548i	$0.490424\pi$
$588$	0.290748	0.0119903
$589$	−79.0184	−3.25590
$590$	−4.12381	−0.169775
$591$	0.160608	0.00660651
$592$	5.55848	0.228452
$593$	−2.30785	−0.0947721	−0.0473861	−	0.998877i	$-0.515089\pi$
$593$	−2.30785	−0.0947721	−0.0473861	+	0.998877i	$0.515089\pi$
$594$	1.65703	0.0679889
$595$	−5.39388	−0.221128
$596$	−3.22549	−0.132121
$597$	−2.40594	−0.0984687
$598$	−1.34514	−0.0550070
$599$	−33.9711	−1.38802	−0.694011	−	0.719965i	$-0.744158\pi$
$599$	−33.9711	−1.38802	−0.694011	+	0.719965i	$0.744158\pi$
$600$	2.07442	0.0846880
$601$	11.5746	0.472137	0.236068	−	0.971736i	$-0.424141\pi$
$601$	11.5746	0.472137	0.236068	+	0.971736i	$0.424141\pi$
$602$	8.00050	0.326076
$603$	25.0377	1.01961
$604$	−11.5857	−0.471414
$605$	7.15874	0.291044
$606$	−1.83449	−0.0745212
$607$	10.2092	0.414378	0.207189	−	0.978301i	$-0.433569\pi$
$607$	10.2092	0.414378	0.207189	+	0.978301i	$0.433569\pi$
$608$	47.7582	1.93685
$609$	0.493412	0.0199941
$610$	−0.871326	−0.0352790
$611$	7.05013	0.285218
$612$	−9.69996	−0.392098
$613$	−18.6379	−0.752779	−0.376390	−	0.926462i	$-0.622835\pi$
$613$	−18.6379	−0.752779	−0.376390	+	0.926462i	$0.622835\pi$
$614$	1.40374	0.0566501
$615$	0.854875	0.0344719
$616$	−11.9243	−0.480443
$617$	11.5722	0.465880	0.232940	−	0.972491i	$-0.425166\pi$
$617$	11.5722	0.465880	0.232940	+	0.972491i	$0.425166\pi$
$618$	2.78951	0.112210
$619$	−39.8973	−1.60361	−0.801805	−	0.597586i	$-0.796127\pi$
$619$	−39.8973	−1.60361	−0.801805	+	0.597586i	$0.796127\pi$
$620$	−13.0365	−0.523558
$621$	−2.68253	−0.107646
$622$	−17.2061	−0.689900
$623$	18.8727	0.756119
$624$	−0.118090	−0.00472738
$625$	12.1873	0.487493
$626$	23.1364	0.924717
$627$	−2.94951	−0.117792
$628$	−5.24038	−0.209114
$629$	−15.9518	−0.636038
$630$	−5.28547	−0.210578
$631$	17.7060	0.704864	0.352432	−	0.935837i	$-0.385355\pi$
$631$	17.7060	0.704864	0.352432	+	0.935837i	$0.385355\pi$
$632$	−13.4566	−0.535276
$633$	−1.34051	−0.0532806
$634$	18.5536	0.736856
$635$	14.4227	0.572349
$636$	−3.56221	−0.141251
$637$	0.802671	0.0318030
$638$	1.50127	0.0594360
$639$	21.0609	0.833156
$640$	9.06416	0.358292
$641$	14.7387	0.582144	0.291072	−	0.956701i	$-0.405988\pi$
$641$	14.7387	0.582144	0.291072	+	0.956701i	$0.405988\pi$
$642$	−2.24012	−0.0884106
$643$	18.4242	0.726578	0.363289	−	0.931677i	$-0.381654\pi$
$643$	18.4242	0.726578	0.363289	+	0.931677i	$0.381654\pi$
$644$	7.98262	0.314559
$645$	0.789528	0.0310876
$646$	−14.5340	−0.571832
$647$	29.3815	1.15511	0.577553	−	0.816353i	$-0.304008\pi$
$647$	29.3815	1.15511	0.577553	+	0.816353i	$0.304008\pi$
$648$	−22.6908	−0.891380
$649$	−10.5238	−0.413096
$650$	2.36820	0.0928884
$651$	4.57311	0.179234
$652$	20.7483	0.812564
$653$	31.9544	1.25047	0.625237	−	0.780435i	$-0.285002\pi$
$653$	31.9544	1.25047	0.625237	+	0.780435i	$0.285002\pi$
$654$	0.289275	0.0113115
$655$	5.72302	0.223617
$656$	−3.74593	−0.146254
$657$	−13.9261	−0.543307
$658$	17.4985	0.682162
$659$	−11.8303	−0.460842	−0.230421	−	0.973091i	$-0.574010\pi$
$659$	−11.8303	−0.460842	−0.230421	+	0.973091i	$0.574010\pi$
$660$	−0.486612	−0.0189413
$661$	−35.8050	−1.39265	−0.696327	−	0.717724i	$-0.745184\pi$
$661$	−35.8050	−1.39265	−0.696327	+	0.717724i	$0.745184\pi$
$662$	−4.44621	−0.172807
$663$	0.338895	0.0131616
$664$	40.0798	1.55540
$665$	18.9353	0.734281
$666$	−15.6311	−0.605695
$667$	−2.43037	−0.0941043
$668$	−8.22928	−0.318400
$669$	−0.523153	−0.0202263
$670$	6.18930	0.239113
$671$	−2.22360	−0.0858409
$672$	−2.76396	−0.106622
$673$	40.1674	1.54834	0.774169	−	0.632979i	$-0.218168\pi$
$673$	40.1674	1.54834	0.774169	+	0.632979i	$0.218168\pi$
$674$	0.521328	0.0200808
$675$	4.72274	0.181778
$676$	17.5312	0.674278
$677$	37.6836	1.44830	0.724149	−	0.689644i	$-0.242233\pi$
$677$	37.6836	1.44830	0.724149	+	0.689644i	$0.242233\pi$
$678$	1.39396	0.0535347
$679$	2.43764	0.0935480
$680$	−5.79851	−0.222363
$681$	−0.689001	−0.0264026
$682$	13.9143	0.532806
$683$	4.72999	0.180988	0.0904940	−	0.995897i	$-0.471155\pi$
$683$	4.72999	0.180988	0.0904940	+	0.995897i	$0.471155\pi$
$684$	34.0519	1.30201
$685$	−5.25132	−0.200643
$686$	15.0891	0.576106
$687$	4.67928	0.178526
$688$	−3.45959	−0.131896
$689$	−9.83422	−0.374654
$690$	−0.329474	−0.0125429
$691$	−35.2225	−1.33993	−0.669963	−	0.742395i	$-0.733690\pi$
$691$	−35.2225	−1.33993	−0.669963	+	0.742395i	$0.733690\pi$
$692$	35.3523	1.34389
$693$	−13.4883	−0.512380
$694$	6.28097	0.238422
$695$	−20.1078	−0.762734
$696$	0.530426	0.0201057
$697$	10.7501	0.407188
$698$	−0.767986	−0.0290687
$699$	−1.68430	−0.0637061
$700$	−14.0538	−0.531185
$701$	5.42565	0.204924	0.102462	−	0.994737i	$-0.467328\pi$
$701$	5.42565	0.204924	0.102462	+	0.994737i	$0.467328\pi$
$702$	0.668370	0.0252260
$703$	55.9989	2.11204
$704$	−5.38566	−0.202980
$705$	1.72683	0.0650364
$706$	−5.55556	−0.209086
$707$	30.0548	1.13033
$708$	−1.53759	−0.0577860
$709$	−38.3232	−1.43926	−0.719630	−	0.694358i	$-0.755688\pi$
$709$	−38.3232	−1.43926	−0.719630	+	0.694358i	$0.755688\pi$
$710$	5.20624	0.195387
$711$	−15.2217	−0.570858
$712$	20.2885	0.760343
$713$	−22.5255	−0.843586
$714$	0.841140	0.0314789
$715$	−1.34339	−0.0502400
$716$	21.6449	0.808907
$717$	−4.65337	−0.173783
$718$	19.6004	0.731481
$719$	42.7482	1.59424	0.797120	−	0.603821i	$-0.206356\pi$
$719$	42.7482	1.59424	0.797120	+	0.603821i	$0.206356\pi$
$720$	2.28555	0.0851775
$721$	−45.7009	−1.70199
$722$	36.4301	1.35579
$723$	3.22572	0.119966
$724$	−8.13748	−0.302427
$725$	4.27880	0.158911
$726$	−1.11636	−0.0414319
$727$	−35.5904	−1.31997	−0.659987	−	0.751277i	$-0.729438\pi$
$727$	−35.5904	−1.31997	−0.659987	+	0.751277i	$0.729438\pi$
$728$	−4.80970	−0.178259
$729$	−24.9965	−0.925796
$730$	−3.44251	−0.127413
$731$	9.92834	0.367213
$732$	−0.324879	−0.0120079
$733$	−15.9714	−0.589916	−0.294958	−	0.955510i	$-0.595306\pi$
$733$	−15.9714	−0.589916	−0.294958	+	0.955510i	$0.595306\pi$
$734$	4.92470	0.181774
$735$	0.196603	0.00725182
$736$	13.6143	0.501828
$737$	15.7949	0.581812
$738$	10.5340	0.387763
$739$	10.7507	0.395473	0.197736	−	0.980255i	$-0.436641\pi$
$739$	10.7507	0.395473	0.197736	+	0.980255i	$0.436641\pi$
$740$	9.23872	0.339622
$741$	−1.18970	−0.0437046
$742$	−24.4086	−0.896068
$743$	−16.2142	−0.594841	−0.297421	−	0.954747i	$-0.596126\pi$
$743$	−16.2142	−0.594841	−0.297421	+	0.954747i	$0.596126\pi$
$744$	4.91617	0.180235
$745$	−2.18107	−0.0799083
$746$	2.34087	0.0857052
$747$	45.3370	1.65879
$748$	−6.11916	−0.223739
$749$	36.7002	1.34100
$750$	1.28905	0.0470696
$751$	5.85090	0.213502	0.106751	−	0.994286i	$-0.465955\pi$
$751$	5.85090	0.213502	0.106751	+	0.994286i	$0.465955\pi$
$752$	−7.56672	−0.275930
$753$	−1.29195	−0.0470812
$754$	0.605544	0.0220526
$755$	−7.83420	−0.285116
$756$	−3.96638	−0.144256
$757$	−47.7970	−1.73721	−0.868606	−	0.495503i	$-0.834984\pi$
$757$	−47.7970	−1.73721	−0.868606	+	0.495503i	$0.834984\pi$
$758$	18.4204	0.669060
$759$	−0.840807	−0.0305194
$760$	20.3558	0.738382
$761$	−2.86564	−0.103879	−0.0519397	−	0.998650i	$-0.516540\pi$
$761$	−2.86564	−0.103879	−0.0519397	+	0.998650i	$0.516540\pi$
$762$	−2.24913	−0.0814774
$763$	−4.73923	−0.171572
$764$	21.7251	0.785988
$765$	−6.55909	−0.237144
$766$	−9.92669	−0.358666
$767$	−4.24482	−0.153272
$768$	−2.52947	−0.0912744
$769$	−21.5417	−0.776813	−0.388407	−	0.921488i	$-0.626974\pi$
$769$	−21.5417	−0.776813	−0.388407	+	0.921488i	$0.626974\pi$
$770$	−3.33431	−0.120160
$771$	3.16701	0.114057
$772$	−27.1818	−0.978296
$773$	50.5851	1.81942	0.909710	−	0.415244i	$-0.136304\pi$
$773$	50.5851	1.81942	0.909710	+	0.415244i	$0.136304\pi$
$774$	9.72880	0.349694
$775$	39.6574	1.42454
$776$	2.62050	0.0940706
$777$	−3.24088	−0.116266
$778$	12.7971	0.458797
$779$	−37.7384	−1.35212
$780$	−0.196277	−0.00702783
$781$	13.2861	0.475415
$782$	−4.14315	−0.148159
$783$	1.20759	0.0431559
$784$	−0.861485	−0.0307673
$785$	−3.54353	−0.126474
$786$	−0.892466	−0.0318332
$787$	16.8265	0.599800	0.299900	−	0.953971i	$-0.403047\pi$
$787$	16.8265	0.599800	0.299900	+	0.953971i	$0.403047\pi$
$788$	−1.16971	−0.0416693
$789$	1.47804	0.0526195
$790$	−3.76279	−0.133874
$791$	−22.8374	−0.812006
$792$	−14.5002	−0.515242
$793$	−0.896895	−0.0318497
$794$	−14.4125	−0.511481
$795$	−2.40876	−0.0854299
$796$	17.5226	0.621071
$797$	5.53893	0.196199	0.0980995	−	0.995177i	$-0.468724\pi$
$797$	5.53893	0.196199	0.0980995	+	0.995177i	$0.468724\pi$
$798$	−2.95284	−0.104529
$799$	21.7150	0.768222
$800$	−23.9687	−0.847420
$801$	22.9497	0.810886
$802$	−8.85270	−0.312600
$803$	−8.78517	−0.310022
$804$	2.30771	0.0813868
$805$	5.39783	0.190248
$806$	5.61238	0.197688
$807$	3.61506	0.127256
$808$	32.3094	1.13664
$809$	−22.3493	−0.785761	−0.392880	−	0.919590i	$-0.628521\pi$
$809$	−22.3493	−0.785761	−0.392880	+	0.919590i	$0.628521\pi$
$810$	−6.34489	−0.222937
$811$	−3.20760	−0.112634	−0.0563171	−	0.998413i	$-0.517936\pi$
$811$	−3.20760	−0.112634	−0.0563171	+	0.998413i	$0.517936\pi$
$812$	−3.59354	−0.126109
$813$	1.72161	0.0603795
$814$	−9.86082	−0.345621
$815$	14.0299	0.491447
$816$	−0.363727	−0.0127330
$817$	−34.8536	−1.21937
$818$	−17.7460	−0.620476
$819$	−5.44057	−0.190109
$820$	−6.22609	−0.217424
$821$	−38.7136	−1.35111	−0.675556	−	0.737308i	$-0.736096\pi$
$821$	−38.7136	−1.35111	−0.675556	+	0.737308i	$0.736096\pi$
$822$	0.818909	0.0285627
$823$	−36.9207	−1.28698	−0.643488	−	0.765456i	$-0.722513\pi$
$823$	−36.9207	−1.28698	−0.643488	+	0.765456i	$0.722513\pi$
$824$	−49.1292	−1.71150
$825$	1.48029	0.0515370
$826$	−10.5357	−0.366583
$827$	−14.3541	−0.499140	−0.249570	−	0.968357i	$-0.580289\pi$
$827$	−14.3541	−0.499140	−0.249570	+	0.968357i	$0.580289\pi$
$828$	9.70705	0.337343
$829$	5.33090	0.185150	0.0925750	−	0.995706i	$-0.470490\pi$
$829$	5.33090	0.185150	0.0925750	+	0.995706i	$0.470490\pi$
$830$	11.2073	0.389010
$831$	1.78094	0.0617800
$832$	−2.17232	−0.0753118
$833$	2.47229	0.0856599
$834$	3.13568	0.108580
$835$	−5.56462	−0.192572
$836$	21.4814	0.742951
$837$	11.1924	0.386866
$838$	−15.1847	−0.524548
$839$	−30.5765	−1.05562	−0.527809	−	0.849363i	$-0.676986\pi$
$839$	−30.5765	−1.05562	−0.527809	+	0.849363i	$0.676986\pi$
$840$	−1.17807	−0.0406473
$841$	−27.9059	−0.962273
$842$	−4.54468	−0.156620
$843$	−4.24551	−0.146223
$844$	9.76301	0.336057
$845$	11.8546	0.407810
$846$	21.2786	0.731572
$847$	18.2894	0.628433
$848$	10.5548	0.362454
$849$	0.725415	0.0248962
$850$	7.29426	0.250191
$851$	15.9634	0.547219
$852$	1.94117	0.0665035
$853$	10.1647	0.348032	0.174016	−	0.984743i	$-0.444326\pi$
$853$	10.1647	0.348032	0.174016	+	0.984743i	$0.444326\pi$
$854$	−2.22610	−0.0761756
$855$	23.0258	0.787466
$856$	39.4534	1.34849
$857$	17.1807	0.586880	0.293440	−	0.955977i	$-0.405200\pi$
$857$	17.1807	0.586880	0.293440	+	0.955977i	$0.405200\pi$
$858$	0.209493	0.00715198
$859$	33.5437	1.14450	0.572248	−	0.820081i	$-0.306072\pi$
$859$	33.5437	1.14450	0.572248	+	0.820081i	$0.306072\pi$
$860$	−5.75016	−0.196079
$861$	2.18407	0.0744329
$862$	24.4064	0.831285
$863$	18.8359	0.641182	0.320591	−	0.947218i	$-0.396119\pi$
$863$	18.8359	0.641182	0.320591	+	0.947218i	$0.396119\pi$
$864$	−6.76461	−0.230137
$865$	23.9051	0.812798
$866$	4.75526	0.161590
$867$	−2.24784	−0.0763408
$868$	−33.3061	−1.13048
$869$	−9.60252	−0.325743
$870$	0.148320	0.00502851
$871$	6.37092	0.215870
$872$	−5.09475	−0.172530
$873$	2.96423	0.100324
$874$	14.5446	0.491979
$875$	−21.1188	−0.713945
$876$	−1.28356	−0.0433674
$877$	−34.9494	−1.18016	−0.590078	−	0.807346i	$-0.700903\pi$
$877$	−34.9494	−1.18016	−0.590078	+	0.807346i	$0.700903\pi$
$878$	17.6946	0.597162
$879$	2.55455	0.0861629
$880$	1.44183	0.0486040
$881$	−30.1811	−1.01683	−0.508414	−	0.861113i	$-0.669768\pi$
$881$	−30.1811	−1.01683	−0.508414	+	0.861113i	$0.669768\pi$
$882$	2.42260	0.0815733
$883$	−18.9575	−0.637970	−0.318985	−	0.947760i	$-0.603342\pi$
$883$	−18.9575	−0.637970	−0.318985	+	0.947760i	$0.603342\pi$
$884$	−2.46819	−0.0830141
$885$	−1.03971	−0.0349495
$886$	9.50329	0.319269
$887$	−11.5409	−0.387504	−0.193752	−	0.981051i	$-0.562066\pi$
$887$	−11.5409	−0.387504	−0.193752	+	0.981051i	$0.562066\pi$
$888$	−3.48400	−0.116915
$889$	36.8478	1.23584
$890$	5.67314	0.190164
$891$	−16.1919	−0.542451
$892$	3.81015	0.127573
$893$	−76.2310	−2.55097
$894$	0.340123	0.0113754
$895$	14.6362	0.489235
$896$	23.1575	0.773637
$897$	−0.339143	−0.0113236
$898$	−21.4038	−0.714254
$899$	10.1403	0.338198
$900$	−17.0898	−0.569660
$901$	−30.2902	−1.00911
$902$	6.64532	0.221265
$903$	2.01712	0.0671255
$904$	−24.5506	−0.816541
$905$	−5.50255	−0.182911
$906$	1.22169	0.0405880
$907$	33.0742	1.09821	0.549105	−	0.835753i	$-0.314969\pi$
$907$	33.0742	1.09821	0.549105	+	0.835753i	$0.314969\pi$
$908$	5.01802	0.166529
$909$	36.5473	1.21220
$910$	−1.34491	−0.0445832
$911$	50.3623	1.66858	0.834289	−	0.551328i	$-0.185879\pi$
$911$	50.3623	1.66858	0.834289	+	0.551328i	$0.185879\pi$
$912$	1.27687	0.0422814
$913$	28.6006	0.946541
$914$	−21.2824	−0.703959
$915$	−0.219682	−0.00726247
$916$	−34.0794	−1.12602
$917$	14.6214	0.482841
$918$	2.05864	0.0679451
$919$	43.3629	1.43041	0.715206	−	0.698914i	$-0.246333\pi$
$919$	43.3629	1.43041	0.715206	+	0.698914i	$0.246333\pi$
$920$	5.80275	0.191311
$921$	0.353915	0.0116619
$922$	−7.02850	−0.231471
$923$	5.35901	0.176394
$924$	−1.24322	−0.0408988
$925$	−28.1045	−0.924070
$926$	11.0478	0.363054
$927$	−55.5734	−1.82527
$928$	−6.12874	−0.201186
$929$	−15.0359	−0.493311	−0.246656	−	0.969103i	$-0.579332\pi$
$929$	−15.0359	−0.493311	−0.246656	+	0.969103i	$0.579332\pi$
$930$	1.37468	0.0450774
$931$	−8.67903	−0.284444
$932$	12.2668	0.401814
$933$	−4.33806	−0.142022
$934$	−12.1493	−0.397536
$935$	−4.13776	−0.135319
$936$	−5.84871	−0.191171
$937$	1.93277	0.0631409	0.0315704	−	0.999502i	$-0.489949\pi$
$937$	1.93277	0.0631409	0.0315704	+	0.999502i	$0.489949\pi$
$938$	15.8127	0.516302
$939$	5.83325	0.190361
$940$	−12.5766	−0.410204
$941$	19.5262	0.636537	0.318269	−	0.948001i	$-0.396899\pi$
$941$	19.5262	0.636537	0.318269	+	0.948001i	$0.396899\pi$
$942$	0.552590	0.0180044
$943$	−10.7579	−0.350327
$944$	4.55586	0.148280
$945$	−2.68205	−0.0872472
$946$	6.13735	0.199543
$947$	−43.9205	−1.42722	−0.713612	−	0.700541i	$-0.752942\pi$
$947$	−43.9205	−1.42722	−0.713612	+	0.700541i	$0.752942\pi$
$948$	−1.40298	−0.0455666
$949$	−3.54353	−0.115028
$950$	−25.6066	−0.830788
$951$	4.67780	0.151688
$952$	−14.8143	−0.480134
$953$	6.61476	0.214273	0.107137	−	0.994244i	$-0.465832\pi$
$953$	6.61476	0.214273	0.107137	+	0.994244i	$0.465832\pi$
$954$	−29.6815	−0.960973
$955$	14.6905	0.475373
$956$	33.8907	1.09610
$957$	0.378507	0.0122354
$958$	3.78836	0.122396
$959$	−13.4163	−0.433235
$960$	−0.532082	−0.0171729
$961$	62.9838	2.03174
$962$	−3.97740	−0.128236
$963$	44.6284	1.43813
$964$	−23.4931	−0.756661
$965$	−18.3803	−0.591683
$966$	−0.841755	−0.0270830
$967$	7.40873	0.238249	0.119124	−	0.992879i	$-0.461991\pi$
$967$	7.40873	0.238249	0.119124	+	0.992879i	$0.461991\pi$
$968$	19.6614	0.631943
$969$	−3.66437	−0.117716
$970$	0.732755	0.0235273
$971$	−20.5940	−0.660893	−0.330446	−	0.943825i	$-0.607199\pi$
$971$	−20.5940	−0.660893	−0.330446	+	0.943825i	$0.607199\pi$
$972$	−7.24998	−0.232543
$973$	−51.3723	−1.64692
$974$	−10.9832	−0.351925
$975$	0.597080	0.0191219
$976$	0.962613	0.0308125
$977$	−6.11777	−0.195725	−0.0978624	−	0.995200i	$-0.531201\pi$
$977$	−6.11777	−0.195725	−0.0978624	+	0.995200i	$0.531201\pi$
$978$	−2.18787	−0.0699604
$979$	14.4777	0.462708
$980$	−1.43187	−0.0457394
$981$	−5.76302	−0.183999
$982$	−31.7358	−1.01273
$983$	30.5026	0.972882	0.486441	−	0.873713i	$-0.338295\pi$
$983$	30.5026	0.972882	0.486441	+	0.873713i	$0.338295\pi$
$984$	2.34791	0.0748486
$985$	−0.790956	−0.0252020
$986$	1.86513	0.0593977
$987$	4.41179	0.140429
$988$	8.66462	0.275658
$989$	−9.93560	−0.315934
$990$	−4.05460	−0.128864
$991$	−4.84755	−0.153988	−0.0769938	−	0.997032i	$-0.524532\pi$
$991$	−4.84755	−0.153988	−0.0769938	+	0.997032i	$0.524532\pi$
$992$	−56.8032	−1.80350
$993$	−1.12100	−0.0355737
$994$	13.3011	0.421885
$995$	11.8487	0.375630
$996$	4.17869	0.132407
$997$	−16.1437	−0.511277	−0.255639	−	0.966772i	$-0.582286\pi$
$997$	−16.1437	−0.511277	−0.255639	+	0.966772i	$0.582286\pi$
$998$	−32.5487	−1.03031
$999$	−7.93185	−0.250953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.a.1.8	✓	11
3.2	odd	2		3141.2.a.b.1.4		11
4.3	odd	2		5584.2.a.j.1.5		11
5.4	even	2		8725.2.a.l.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.a.1.8	✓	11	1.1	even	1	trivial
3141.2.a.b.1.4		11	3.2	odd	2
5584.2.a.j.1.5		11	4.3	odd	2
8725.2.a.l.1.4		11	5.4	even	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+0.767986 q^{2} +0.193628 q^{3} -1.41020 q^{4} -0.953573 q^{5} +0.148703 q^{6} -2.43623 q^{7} -2.61898 q^{8} -2.96251 q^{9} +O(q^{10})\)	\(q+0.767986 q^{2} +0.193628 q^{3} -1.41020 q^{4} -0.953573 q^{5} +0.148703 q^{6} -2.43623 q^{7} -2.61898 q^{8} -2.96251 q^{9} -0.732330 q^{10} -1.86888 q^{11} -0.273053 q^{12} -0.753820 q^{13} -1.87099 q^{14} -0.184638 q^{15} +0.809055 q^{16} -2.32183 q^{17} -2.27516 q^{18} +8.15083 q^{19} +1.34473 q^{20} -0.471721 q^{21} -1.43527 q^{22} +2.32353 q^{23} -0.507107 q^{24} -4.09070 q^{25} -0.578923 q^{26} -1.15451 q^{27} +3.43556 q^{28} -1.04598 q^{29} -0.141799 q^{30} -9.69453 q^{31} +5.85931 q^{32} -0.361867 q^{33} -1.78313 q^{34} +2.32312 q^{35} +4.17772 q^{36} +6.87034 q^{37} +6.25972 q^{38} -0.145960 q^{39} +2.49739 q^{40} -4.63000 q^{41} -0.362275 q^{42} -4.27609 q^{43} +2.63549 q^{44} +2.82497 q^{45} +1.78443 q^{46} -9.35254 q^{47} +0.156655 q^{48} -1.06480 q^{49} -3.14160 q^{50} -0.449570 q^{51} +1.06304 q^{52} +13.0459 q^{53} -0.886644 q^{54} +1.78211 q^{55} +6.38043 q^{56} +1.57822 q^{57} -0.803300 q^{58} +5.63108 q^{59} +0.260376 q^{60} +1.18980 q^{61} -7.44526 q^{62} +7.21734 q^{63} +2.88176 q^{64} +0.718822 q^{65} -0.277909 q^{66} -8.45151 q^{67} +3.27424 q^{68} +0.449899 q^{69} +1.78412 q^{70} -7.10914 q^{71} +7.75876 q^{72} +4.70076 q^{73} +5.27632 q^{74} -0.792072 q^{75} -11.4943 q^{76} +4.55302 q^{77} -0.112095 q^{78} +5.13811 q^{79} -0.771492 q^{80} +8.66398 q^{81} -3.55578 q^{82} -15.3036 q^{83} +0.665219 q^{84} +2.21403 q^{85} -3.28397 q^{86} -0.202531 q^{87} +4.89457 q^{88} -7.74670 q^{89} +2.16953 q^{90} +1.83648 q^{91} -3.27663 q^{92} -1.87713 q^{93} -7.18262 q^{94} -7.77240 q^{95} +1.13452 q^{96} -1.00058 q^{97} -0.817754 q^{98} +5.53658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

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