LMFDB - Embedded newform 6011.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51760 q^{2} +1.78803 q^{3} +4.33833 q^{4} +0.754203 q^{5} -4.50154 q^{6} +4.46405 q^{7} -5.88698 q^{8} +0.197034 q^{9} +O(q^{10})$	\(q-2.51760 q^{2} +1.78803 q^{3} +4.33833 q^{4} +0.754203 q^{5} -4.50154 q^{6} +4.46405 q^{7} -5.88698 q^{8} +0.197034 q^{9} -1.89878 q^{10} -3.50791 q^{11} +7.75704 q^{12} -2.42586 q^{13} -11.2387 q^{14} +1.34853 q^{15} +6.14442 q^{16} +3.51144 q^{17} -0.496053 q^{18} -5.14688 q^{19} +3.27198 q^{20} +7.98184 q^{21} +8.83153 q^{22} +6.81327 q^{23} -10.5261 q^{24} -4.43118 q^{25} +6.10736 q^{26} -5.01177 q^{27} +19.3665 q^{28} -5.40005 q^{29} -3.39507 q^{30} -6.74761 q^{31} -3.69525 q^{32} -6.27224 q^{33} -8.84042 q^{34} +3.36680 q^{35} +0.854797 q^{36} -7.77879 q^{37} +12.9578 q^{38} -4.33750 q^{39} -4.43997 q^{40} +4.68577 q^{41} -20.0951 q^{42} -5.28334 q^{43} -15.2185 q^{44} +0.148603 q^{45} -17.1531 q^{46} -1.29913 q^{47} +10.9864 q^{48} +12.9278 q^{49} +11.1559 q^{50} +6.27855 q^{51} -10.5242 q^{52} -10.2582 q^{53} +12.6177 q^{54} -2.64568 q^{55} -26.2798 q^{56} -9.20274 q^{57} +13.5952 q^{58} +10.8248 q^{59} +5.85038 q^{60} +6.38073 q^{61} +16.9878 q^{62} +0.879569 q^{63} -2.98565 q^{64} -1.82959 q^{65} +15.7910 q^{66} -4.20565 q^{67} +15.2338 q^{68} +12.1823 q^{69} -8.47627 q^{70} +0.361122 q^{71} -1.15993 q^{72} +16.2937 q^{73} +19.5839 q^{74} -7.92306 q^{75} -22.3288 q^{76} -15.6595 q^{77} +10.9201 q^{78} +2.61294 q^{79} +4.63414 q^{80} -9.55228 q^{81} -11.7969 q^{82} +3.14050 q^{83} +34.6278 q^{84} +2.64834 q^{85} +13.3014 q^{86} -9.65543 q^{87} +20.6510 q^{88} +1.19545 q^{89} -0.374125 q^{90} -10.8292 q^{91} +29.5582 q^{92} -12.0649 q^{93} +3.27069 q^{94} -3.88179 q^{95} -6.60721 q^{96} -3.57769 q^{97} -32.5469 q^{98} -0.691178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.51760	−1.78021	−0.890107	−	0.455751i	$-0.849371\pi$
$2$	−2.51760	−1.78021	−0.890107	+	0.455751i	$0.849371\pi$
$3$	1.78803	1.03232	0.516158	−	0.856493i	$-0.327362\pi$
$3$	1.78803	1.03232	0.516158	+	0.856493i	$0.327362\pi$
$4$	4.33833	2.16916
$5$	0.754203	0.337290	0.168645	−	0.985677i	$-0.446061\pi$
$5$	0.754203	0.337290	0.168645	+	0.985677i	$0.446061\pi$
$6$	−4.50154	−1.83775
$7$	4.46405	1.68725	0.843626	−	0.536931i	$-0.180416\pi$
$7$	4.46405	1.68725	0.843626	+	0.536931i	$0.180416\pi$
$8$	−5.88698	−2.08136
$9$	0.197034	0.0656779
$10$	−1.89878	−0.600448
$11$	−3.50791	−1.05768	−0.528838	−	0.848723i	$-0.677372\pi$
$11$	−3.50791	−1.05768	−0.528838	+	0.848723i	$0.677372\pi$
$12$	7.75704	2.23926
$13$	−2.42586	−0.672813	−0.336407	−	0.941717i	$-0.609212\pi$
$13$	−2.42586	−0.672813	−0.336407	+	0.941717i	$0.609212\pi$
$14$	−11.2387	−3.00367
$15$	1.34853	0.348190
$16$	6.14442	1.53610
$17$	3.51144	0.851650	0.425825	−	0.904806i	$-0.359984\pi$
$17$	3.51144	0.851650	0.425825	+	0.904806i	$0.359984\pi$
$18$	−0.496053	−0.116921
$19$	−5.14688	−1.18077	−0.590387	−	0.807120i	$-0.701025\pi$
$19$	−5.14688	−1.18077	−0.590387	+	0.807120i	$0.701025\pi$
$20$	3.27198	0.731636
$21$	7.98184	1.74178
$22$	8.83153	1.88289
$23$	6.81327	1.42066	0.710332	−	0.703867i	$-0.248545\pi$
$23$	6.81327	1.42066	0.710332	+	0.703867i	$0.248545\pi$
$24$	−10.5261	−2.14862
$25$	−4.43118	−0.886236
$26$	6.10736	1.19775
$27$	−5.01177	−0.964516
$28$	19.3665	3.65993
$29$	−5.40005	−1.00276	−0.501382	−	0.865226i	$-0.667175\pi$
$29$	−5.40005	−1.00276	−0.501382	+	0.865226i	$0.667175\pi$
$30$	−3.39507	−0.619853
$31$	−6.74761	−1.21191	−0.605954	−	0.795500i	$-0.707208\pi$
$31$	−6.74761	−1.21191	−0.605954	+	0.795500i	$0.707208\pi$
$32$	−3.69525	−0.653235
$33$	−6.27224	−1.09186
$34$	−8.84042	−1.51612
$35$	3.36680	0.569093
$36$	0.854797	0.142466
$37$	−7.77879	−1.27883	−0.639413	−	0.768864i	$-0.720822\pi$
$37$	−7.77879	−1.27883	−0.639413	+	0.768864i	$0.720822\pi$
$38$	12.9578	2.10203
$39$	−4.33750	−0.694556
$40$	−4.43997	−0.702022
$41$	4.68577	0.731795	0.365897	−	0.930655i	$-0.380762\pi$
$41$	4.68577	0.731795	0.365897	+	0.930655i	$0.380762\pi$
$42$	−20.0951	−3.10074
$43$	−5.28334	−0.805702	−0.402851	−	0.915266i	$-0.631981\pi$
$43$	−5.28334	−0.805702	−0.402851	+	0.915266i	$0.631981\pi$
$44$	−15.2185	−2.29427
$45$	0.148603	0.0221525
$46$	−17.1531	−2.52909
$47$	−1.29913	−0.189497	−0.0947487	−	0.995501i	$-0.530205\pi$
$47$	−1.29913	−0.189497	−0.0947487	+	0.995501i	$0.530205\pi$
$48$	10.9864	1.58575
$49$	12.9278	1.84682
$50$	11.1559	1.57769
$51$	6.27855	0.879173
$52$	−10.5242	−1.45944
$53$	−10.2582	−1.40907	−0.704534	−	0.709670i	$-0.748844\pi$
$53$	−10.2582	−1.40907	−0.704534	+	0.709670i	$0.748844\pi$
$54$	12.6177	1.71705
$55$	−2.64568	−0.356743
$56$	−26.2798	−3.51178
$57$	−9.20274	−1.21893
$58$	13.5952	1.78514
$59$	10.8248	1.40927	0.704637	−	0.709568i	$-0.251110\pi$
$59$	10.8248	1.40927	0.704637	+	0.709568i	$0.251110\pi$
$60$	5.85038	0.755281
$61$	6.38073	0.816968	0.408484	−	0.912765i	$-0.366058\pi$
$61$	6.38073	0.816968	0.408484	+	0.912765i	$0.366058\pi$
$62$	16.9878	2.15745
$63$	0.879569	0.110815
$64$	−2.98565	−0.373207
$65$	−1.82959	−0.226933
$66$	15.7910	1.94374
$67$	−4.20565	−0.513802	−0.256901	−	0.966438i	$-0.582702\pi$
$67$	−4.20565	−0.513802	−0.256901	+	0.966438i	$0.582702\pi$
$68$	15.2338	1.84737
$69$	12.1823	1.46658
$70$	−8.47627	−1.01311
$71$	0.361122	0.0428573	0.0214286	−	0.999770i	$-0.493179\pi$
$71$	0.361122	0.0428573	0.0214286	+	0.999770i	$0.493179\pi$
$72$	−1.15993	−0.136699
$73$	16.2937	1.90704	0.953519	−	0.301332i	$-0.0974313\pi$
$73$	16.2937	1.90704	0.953519	+	0.301332i	$0.0974313\pi$
$74$	19.5839	2.27658
$75$	−7.92306	−0.914876
$76$	−22.3288	−2.56129
$77$	−15.6595	−1.78457
$78$	10.9201	1.23646
$79$	2.61294	0.293978	0.146989	−	0.989138i	$-0.453042\pi$
$79$	2.61294	0.293978	0.146989	+	0.989138i	$0.453042\pi$
$80$	4.63414	0.518112
$81$	−9.55228	−1.06136
$82$	−11.7969	−1.30275
$83$	3.14050	0.344715	0.172357	−	0.985034i	$-0.444862\pi$
$83$	3.14050	0.344715	0.172357	+	0.985034i	$0.444862\pi$
$84$	34.6278	3.77820
$85$	2.64834	0.287253
$86$	13.3014	1.43432
$87$	−9.65543	−1.03517
$88$	20.6510	2.20140
$89$	1.19545	0.126717	0.0633587	−	0.997991i	$-0.479819\pi$
$89$	1.19545	0.126717	0.0633587	+	0.997991i	$0.479819\pi$
$90$	−0.374125	−0.0394362
$91$	−10.8292	−1.13521
$92$	29.5582	3.08165
$93$	−12.0649	−1.25107
$94$	3.27069	0.337346
$95$	−3.88179	−0.398263
$96$	−6.60721	−0.674345
$97$	−3.57769	−0.363259	−0.181630	−	0.983367i	$-0.558137\pi$
$97$	−3.57769	−0.363259	−0.181630	+	0.983367i	$0.558137\pi$
$98$	−32.5469	−3.28774
$99$	−0.691178	−0.0694660
$100$	−19.2239	−1.92239
$101$	−14.1552	−1.40850	−0.704249	−	0.709953i	$-0.748716\pi$
$101$	−14.1552	−1.40850	−0.704249	+	0.709953i	$0.748716\pi$
$102$	−15.8069	−1.56512
$103$	−16.9921	−1.67429	−0.837143	−	0.546984i	$-0.815776\pi$
$103$	−16.9921	−1.67429	−0.837143	+	0.546984i	$0.815776\pi$
$104$	14.2810	1.40037
$105$	6.01992	0.587484
$106$	25.8260	2.50844
$107$	−4.87647	−0.471426	−0.235713	−	0.971823i	$-0.575743\pi$
$107$	−4.87647	−0.471426	−0.235713	+	0.971823i	$0.575743\pi$
$108$	−21.7427	−2.09219
$109$	−14.4439	−1.38347	−0.691736	−	0.722151i	$-0.743154\pi$
$109$	−14.4439	−1.38347	−0.691736	+	0.722151i	$0.743154\pi$
$110$	6.66077	0.635079
$111$	−13.9087	−1.32015
$112$	27.4290	2.59180
$113$	5.47403	0.514954	0.257477	−	0.966284i	$-0.417109\pi$
$113$	5.47403	0.514954	0.257477	+	0.966284i	$0.417109\pi$
$114$	23.1689	2.16996
$115$	5.13858	0.479175
$116$	−23.4272	−2.17516
$117$	−0.477977	−0.0441890
$118$	−27.2526	−2.50881
$119$	15.6753	1.43695
$120$	−7.93879	−0.724709
$121$	1.30545	0.118678
$122$	−16.0641	−1.45438
$123$	8.37828	0.755444
$124$	−29.2733	−2.62882
$125$	−7.11302	−0.636208
$126$	−2.21441	−0.197275
$127$	−16.2968	−1.44610	−0.723052	−	0.690794i	$-0.757261\pi$
$127$	−16.2968	−1.44610	−0.723052	+	0.690794i	$0.757261\pi$
$128$	14.9072	1.31762
$129$	−9.44674	−0.831739
$130$	4.60619	0.403989
$131$	−9.33124	−0.815274	−0.407637	−	0.913144i	$-0.633647\pi$
$131$	−9.33124	−0.815274	−0.407637	+	0.913144i	$0.633647\pi$
$132$	−27.2110	−2.36841
$133$	−22.9759	−1.99226
$134$	10.5882	0.914678
$135$	−3.77989	−0.325322
$136$	−20.6718	−1.77259
$137$	1.57391	0.134468	0.0672342	−	0.997737i	$-0.478583\pi$
$137$	1.57391	0.134468	0.0672342	+	0.997737i	$0.478583\pi$
$138$	−30.6702	−2.61082
$139$	14.8839	1.26244	0.631220	−	0.775604i	$-0.282555\pi$
$139$	14.8839	1.26244	0.631220	+	0.775604i	$0.282555\pi$
$140$	14.6063	1.23446
$141$	−2.32288	−0.195621
$142$	−0.909161	−0.0762951
$143$	8.50972	0.711618
$144$	1.21066	0.100888
$145$	−4.07274	−0.338222
$146$	−41.0212	−3.39494
$147$	23.1151	1.90650
$148$	−33.7469	−2.77398
$149$	−14.7569	−1.20893	−0.604465	−	0.796632i	$-0.706613\pi$
$149$	−14.7569	−1.20893	−0.604465	+	0.796632i	$0.706613\pi$
$150$	19.9471	1.62868
$151$	17.3955	1.41563	0.707815	−	0.706398i	$-0.249681\pi$
$151$	17.3955	1.41563	0.707815	+	0.706398i	$0.249681\pi$
$152$	30.2995	2.45762
$153$	0.691873	0.0559346
$154$	39.4244	3.17691
$155$	−5.08907	−0.408764
$156$	−18.8175	−1.50661
$157$	−6.15161	−0.490952	−0.245476	−	0.969403i	$-0.578944\pi$
$157$	−6.15161	−0.490952	−0.245476	+	0.969403i	$0.578944\pi$
$158$	−6.57834	−0.523345
$159$	−18.3419	−1.45460
$160$	−2.78697	−0.220329
$161$	30.4148	2.39702
$162$	24.0488	1.88946
$163$	−22.3741	−1.75248	−0.876238	−	0.481878i	$-0.839955\pi$
$163$	−22.3741	−1.75248	−0.876238	+	0.481878i	$0.839955\pi$
$164$	20.3284	1.58738
$165$	−4.73054	−0.368272
$166$	−7.90654	−0.613667
$167$	−3.56415	−0.275802	−0.137901	−	0.990446i	$-0.544036\pi$
$167$	−3.56415	−0.275802	−0.137901	+	0.990446i	$0.544036\pi$
$168$	−46.9889	−3.62527
$169$	−7.11519	−0.547322
$170$	−6.66747	−0.511372
$171$	−1.01411	−0.0775508
$172$	−22.9208	−1.74770
$173$	−4.45421	−0.338647	−0.169324	−	0.985561i	$-0.554158\pi$
$173$	−4.45421	−0.338647	−0.169324	+	0.985561i	$0.554158\pi$
$174$	24.3085	1.84283
$175$	−19.7810	−1.49530
$176$	−21.5541	−1.62470
$177$	19.3551	1.45482
$178$	−3.00967	−0.225584
$179$	1.95734	0.146299	0.0731493	−	0.997321i	$-0.476695\pi$
$179$	1.95734	0.146299	0.0731493	+	0.997321i	$0.476695\pi$
$180$	0.644690	0.0480524
$181$	12.5425	0.932275	0.466137	−	0.884712i	$-0.345645\pi$
$181$	12.5425	0.932275	0.466137	+	0.884712i	$0.345645\pi$
$182$	27.2636	2.02091
$183$	11.4089	0.843370
$184$	−40.1095	−2.95691
$185$	−5.86679	−0.431335
$186$	30.3746	2.22718
$187$	−12.3178	−0.900769
$188$	−5.63605	−0.411051
$189$	−22.3728	−1.62738
$190$	9.77280	0.708994
$191$	16.0149	1.15880	0.579398	−	0.815045i	$-0.303288\pi$
$191$	16.0149	1.15880	0.579398	+	0.815045i	$0.303288\pi$
$192$	−5.33842	−0.385267
$193$	−21.8409	−1.57215	−0.786073	−	0.618134i	$-0.787889\pi$
$193$	−21.8409	−1.57215	−0.786073	+	0.618134i	$0.787889\pi$
$194$	9.00720	0.646679
$195$	−3.27136	−0.234267
$196$	56.0848	4.00606
$197$	11.4604	0.816518	0.408259	−	0.912866i	$-0.366136\pi$
$197$	11.4604	0.816518	0.408259	+	0.912866i	$0.366136\pi$
$198$	1.74011	0.123664
$199$	24.3331	1.72493	0.862466	−	0.506116i	$-0.168919\pi$
$199$	24.3331	1.72493	0.862466	+	0.506116i	$0.168919\pi$
$200$	26.0862	1.84458
$201$	−7.51982	−0.530407
$202$	35.6373	2.50743
$203$	−24.1061	−1.69192
$204$	27.2384	1.90707
$205$	3.53402	0.246827
$206$	42.7795	2.98059
$207$	1.34244	0.0933063
$208$	−14.9055	−1.03351
$209$	18.0548	1.24888
$210$	−15.1558	−1.04585
$211$	−23.8321	−1.64067	−0.820335	−	0.571883i	$-0.806213\pi$
$211$	−23.8321	−1.64067	−0.820335	+	0.571883i	$0.806213\pi$
$212$	−44.5033	−3.05650
$213$	0.645695	0.0442423
$214$	12.2770	0.839239
$215$	−3.98471	−0.271755
$216$	29.5042	2.00751
$217$	−30.1217	−2.04479
$218$	36.3639	2.46288
$219$	29.1336	1.96867
$220$	−11.4778	−0.773834
$221$	−8.51828	−0.573001
$222$	35.0165	2.35015
$223$	−12.1699	−0.814956	−0.407478	−	0.913215i	$-0.633592\pi$
$223$	−12.1699	−0.814956	−0.407478	+	0.913215i	$0.633592\pi$
$224$	−16.4958	−1.10217
$225$	−0.873092	−0.0582061
$226$	−13.7814	−0.916728
$227$	−7.48406	−0.496734	−0.248367	−	0.968666i	$-0.579894\pi$
$227$	−7.48406	−0.496734	−0.248367	+	0.968666i	$0.579894\pi$
$228$	−39.9245	−2.64406
$229$	1.81943	0.120232	0.0601158	−	0.998191i	$-0.480853\pi$
$229$	1.81943	0.120232	0.0601158	+	0.998191i	$0.480853\pi$
$230$	−12.9369	−0.853035
$231$	−27.9996	−1.84224
$232$	31.7900	2.08712
$233$	14.9044	0.976418	0.488209	−	0.872727i	$-0.337650\pi$
$233$	14.9044	0.976418	0.488209	+	0.872727i	$0.337650\pi$
$234$	1.20336	0.0786659
$235$	−0.979807	−0.0639156
$236$	46.9617	3.05694
$237$	4.67200	0.303479
$238$	−39.4641	−2.55808
$239$	−11.4486	−0.740548	−0.370274	−	0.928923i	$-0.620736\pi$
$239$	−11.4486	−0.740548	−0.370274	+	0.928923i	$0.620736\pi$
$240$	8.28595	0.534856
$241$	−22.9959	−1.48130	−0.740648	−	0.671893i	$-0.765481\pi$
$241$	−22.9959	−1.48130	−0.740648	+	0.671893i	$0.765481\pi$
$242$	−3.28662	−0.211272
$243$	−2.04439	−0.131148
$244$	27.6817	1.77214
$245$	9.75015	0.622914
$246$	−21.0932	−1.34485
$247$	12.4856	0.794441
$248$	39.7230	2.52242
$249$	5.61530	0.355855
$250$	17.9078	1.13259
$251$	9.00817	0.568590	0.284295	−	0.958737i	$-0.408240\pi$
$251$	9.00817	0.568590	0.284295	+	0.958737i	$0.408240\pi$
$252$	3.81586	0.240376
$253$	−23.9003	−1.50260
$254$	41.0288	2.57437
$255$	4.73530	0.296536
$256$	−31.5591	−1.97244
$257$	0.132978	0.00829496	0.00414748	−	0.999991i	$-0.498680\pi$
$257$	0.132978	0.00829496	0.00414748	+	0.999991i	$0.498680\pi$
$258$	23.7831	1.48067
$259$	−34.7249	−2.15770
$260$	−7.93737	−0.492255
$261$	−1.06399	−0.0658595
$262$	23.4923	1.45136
$263$	−7.14891	−0.440820	−0.220410	−	0.975407i	$-0.570740\pi$
$263$	−7.14891	−0.440820	−0.220410	+	0.975407i	$0.570740\pi$
$264$	36.9245	2.27255
$265$	−7.73674	−0.475264
$266$	57.8442	3.54666
$267$	2.13749	0.130812
$268$	−18.2455	−1.11452
$269$	4.39919	0.268224	0.134112	−	0.990966i	$-0.457182\pi$
$269$	4.39919	0.268224	0.134112	+	0.990966i	$0.457182\pi$
$270$	9.51627	0.579142
$271$	−14.9021	−0.905239	−0.452619	−	0.891704i	$-0.649510\pi$
$271$	−14.9021	−0.905239	−0.452619	+	0.891704i	$0.649510\pi$
$272$	21.5758	1.30822
$273$	−19.3628	−1.17189
$274$	−3.96249	−0.239383
$275$	15.5442	0.937350
$276$	52.8507	3.18124
$277$	17.1458	1.03019	0.515094	−	0.857134i	$-0.327757\pi$
$277$	17.1458	1.03019	0.515094	+	0.857134i	$0.327757\pi$
$278$	−37.4719	−2.24741
$279$	−1.32951	−0.0795956
$280$	−19.8203	−1.18449
$281$	18.3574	1.09511	0.547556	−	0.836769i	$-0.315558\pi$
$281$	18.3574	1.09511	0.547556	+	0.836769i	$0.315558\pi$
$282$	5.84808	0.348248
$283$	11.9824	0.712280	0.356140	−	0.934433i	$-0.384093\pi$
$283$	11.9824	0.712280	0.356140	+	0.934433i	$0.384093\pi$
$284$	1.56666	0.0929644
$285$	−6.94074	−0.411134
$286$	−21.4241	−1.26683
$287$	20.9175	1.23472
$288$	−0.728090	−0.0429031
$289$	−4.66977	−0.274692
$290$	10.2535	0.602108
$291$	−6.39699	−0.374998
$292$	70.6876	4.13668
$293$	8.18126	0.477954	0.238977	−	0.971025i	$-0.423188\pi$
$293$	8.18126	0.477954	0.238977	+	0.971025i	$0.423188\pi$
$294$	−58.1948	−3.39399
$295$	8.16412	0.475334
$296$	45.7935	2.66170
$297$	17.5809	1.02015
$298$	37.1520	2.15216
$299$	−16.5280	−0.955842
$300$	−34.3728	−1.98451
$301$	−23.5851	−1.35942
$302$	−43.7951	−2.52012
$303$	−25.3099	−1.45402
$304$	−31.6246	−1.81379
$305$	4.81236	0.275555
$306$	−1.74186	−0.0995756
$307$	−20.3026	−1.15873	−0.579365	−	0.815068i	$-0.696699\pi$
$307$	−20.3026	−1.15873	−0.579365	+	0.815068i	$0.696699\pi$
$308$	−67.9360	−3.87101
$309$	−30.3824	−1.72839
$310$	12.8123	0.727687
$311$	−14.5250	−0.823638	−0.411819	−	0.911266i	$-0.635106\pi$
$311$	−14.5250	−0.823638	−0.411819	+	0.911266i	$0.635106\pi$
$312$	25.5348	1.44562
$313$	0.313920	0.0177438	0.00887191	−	0.999961i	$-0.497176\pi$
$313$	0.313920	0.0177438	0.00887191	+	0.999961i	$0.497176\pi$
$314$	15.4873	0.874000
$315$	0.663373	0.0373769
$316$	11.3358	0.637687
$317$	−24.0221	−1.34922	−0.674608	−	0.738176i	$-0.735688\pi$
$317$	−24.0221	−1.34922	−0.674608	+	0.738176i	$0.735688\pi$
$318$	46.1775	2.58951
$319$	18.9429	1.06060
$320$	−2.25179	−0.125879
$321$	−8.71925	−0.486661
$322$	−76.5723	−4.26721
$323$	−18.0730	−1.00561
$324$	−41.4409	−2.30227
$325$	10.7494	0.596271
$326$	56.3292	3.11978
$327$	−25.8260	−1.42818
$328$	−27.5850	−1.52313
$329$	−5.79938	−0.319730
$330$	11.9096	0.655603
$331$	30.4748	1.67505	0.837524	−	0.546401i	$-0.184003\pi$
$331$	30.4748	1.67505	0.837524	+	0.546401i	$0.184003\pi$
$332$	13.6245	0.747743
$333$	−1.53268	−0.0839906
$334$	8.97312	0.490987
$335$	−3.17192	−0.173300
$336$	49.0437	2.67555
$337$	8.52513	0.464394	0.232197	−	0.972669i	$-0.425409\pi$
$337$	8.52513	0.464394	0.232197	+	0.972669i	$0.425409\pi$
$338$	17.9132	0.974351
$339$	9.78771	0.531595
$340$	11.4894	0.623098
$341$	23.6700	1.28180
$342$	2.55312	0.138057
$343$	26.4618	1.42880
$344$	31.1029	1.67696
$345$	9.18792	0.494661
$346$	11.2139	0.602865
$347$	16.6360	0.893065	0.446533	−	0.894767i	$-0.352659\pi$
$347$	16.6360	0.893065	0.446533	+	0.894767i	$0.352659\pi$
$348$	−41.8884	−2.24545
$349$	4.05860	0.217252	0.108626	−	0.994083i	$-0.465355\pi$
$349$	4.05860	0.217252	0.108626	+	0.994083i	$0.465355\pi$
$350$	49.8007	2.66196
$351$	12.1579	0.648939
$352$	12.9626	0.690910
$353$	23.9147	1.27285	0.636425	−	0.771339i	$-0.280412\pi$
$353$	23.9147	1.27285	0.636425	+	0.771339i	$0.280412\pi$
$354$	−48.7284	−2.58989
$355$	0.272359	0.0144553
$356$	5.18625	0.274871
$357$	28.0278	1.48339
$358$	−4.92781	−0.260443
$359$	13.1666	0.694909	0.347454	−	0.937697i	$-0.387046\pi$
$359$	13.1666	0.694909	0.347454	+	0.937697i	$0.387046\pi$
$360$	−0.874825	−0.0461073
$361$	7.49033	0.394228
$362$	−31.5770	−1.65965
$363$	2.33418	0.122513
$364$	−46.9805	−2.46245
$365$	12.2888	0.643225
$366$	−28.7231	−1.50138
$367$	26.3156	1.37367	0.686833	−	0.726816i	$-0.259001\pi$
$367$	26.3156	1.37367	0.686833	+	0.726816i	$0.259001\pi$
$368$	41.8636	2.18229
$369$	0.923256	0.0480628
$370$	14.7702	0.767868
$371$	−45.7930	−2.37745
$372$	−52.3415	−2.71378
$373$	−16.3740	−0.847814	−0.423907	−	0.905706i	$-0.639342\pi$
$373$	−16.3740	−0.847814	−0.423907	+	0.905706i	$0.639342\pi$
$374$	31.0114	1.60356
$375$	−12.7183	−0.656768
$376$	7.64794	0.394413
$377$	13.0998	0.674674
$378$	56.3259	2.89709
$379$	−8.33864	−0.428327	−0.214164	−	0.976798i	$-0.568703\pi$
$379$	−8.33864	−0.428327	−0.214164	+	0.976798i	$0.568703\pi$
$380$	−16.8405	−0.863898
$381$	−29.1390	−1.49284
$382$	−40.3191	−2.06290
$383$	−3.52606	−0.180173	−0.0900866	−	0.995934i	$-0.528714\pi$
$383$	−3.52606	−0.180173	−0.0900866	+	0.995934i	$0.528714\pi$
$384$	26.6544	1.36020
$385$	−11.8104	−0.601916
$386$	54.9868	2.79876
$387$	−1.04100	−0.0529168
$388$	−15.5212	−0.787968
$389$	5.70290	0.289149	0.144574	−	0.989494i	$-0.453819\pi$
$389$	5.70290	0.289149	0.144574	+	0.989494i	$0.453819\pi$
$390$	8.23598	0.417045
$391$	23.9244	1.20991
$392$	−76.1054	−3.84390
$393$	−16.6845	−0.841621
$394$	−28.8527	−1.45358
$395$	1.97068	0.0991559
$396$	−2.99855	−0.150683
$397$	16.7566	0.840991	0.420496	−	0.907295i	$-0.361856\pi$
$397$	16.7566	0.840991	0.420496	+	0.907295i	$0.361856\pi$
$398$	−61.2612	−3.07075
$399$	−41.0815	−2.05665
$400$	−27.2270	−1.36135
$401$	2.13428	0.106581	0.0532905	−	0.998579i	$-0.483029\pi$
$401$	2.13428	0.106581	0.0532905	+	0.998579i	$0.483029\pi$
$402$	18.9319	0.944238
$403$	16.3688	0.815387
$404$	−61.4100	−3.05526
$405$	−7.20436	−0.357987
$406$	60.6896	3.01198
$407$	27.2873	1.35258
$408$	−36.9617	−1.82987
$409$	−24.5085	−1.21187	−0.605935	−	0.795514i	$-0.707201\pi$
$409$	−24.5085	−1.21187	−0.605935	+	0.795514i	$0.707201\pi$
$410$	−8.89727	−0.439405
$411$	2.81420	0.138814
$412$	−73.7174	−3.63180
$413$	48.3226	2.37780
$414$	−3.37974	−0.166105
$415$	2.36858	0.116269
$416$	8.96418	0.439505
$417$	26.6129	1.30324
$418$	−45.4548	−2.22327
$419$	17.6951	0.864464	0.432232	−	0.901762i	$-0.357726\pi$
$419$	17.6951	0.864464	0.432232	+	0.901762i	$0.357726\pi$
$420$	26.1164	1.27435
$421$	13.8600	0.675497	0.337748	−	0.941236i	$-0.390335\pi$
$421$	13.8600	0.675497	0.337748	+	0.941236i	$0.390335\pi$
$422$	59.9998	2.92074
$423$	−0.255972	−0.0124458
$424$	60.3896	2.93278
$425$	−15.5598	−0.754762
$426$	−1.62560	−0.0787607
$427$	28.4839	1.37843
$428$	−21.1557	−1.02260
$429$	15.2156	0.734615
$430$	10.0319	0.483782
$431$	−0.00625153	−0.000301125 0	−0.000150563	−	1.00000i	$-0.500048\pi$
$431$	−0.00625153	−0.000301125 0	−0.000150563		1.00000i	$0.500048\pi$
$432$	−30.7944	−1.48160
$433$	0.283340	0.0136165	0.00680824	−	0.999977i	$-0.497833\pi$
$433$	0.283340	0.0136165	0.00680824	+	0.999977i	$0.497833\pi$
$434$	75.8345	3.64017
$435$	−7.28216	−0.349153
$436$	−62.6622	−3.00097
$437$	−35.0670	−1.67748
$438$	−73.3469	−3.50465
$439$	−2.87934	−0.137424	−0.0687118	−	0.997637i	$-0.521889\pi$
$439$	−2.87934	−0.137424	−0.0687118	+	0.997637i	$0.521889\pi$
$440$	15.5750	0.742511
$441$	2.54720	0.121295
$442$	21.4456	1.02007
$443$	−7.61704	−0.361896	−0.180948	−	0.983493i	$-0.557917\pi$
$443$	−7.61704	−0.361896	−0.180948	+	0.983493i	$0.557917\pi$
$444$	−60.3403	−2.86363
$445$	0.901611	0.0427405
$446$	30.6390	1.45080
$447$	−26.3857	−1.24800
$448$	−13.3281	−0.629694
$449$	24.8669	1.17354	0.586770	−	0.809754i	$-0.300399\pi$
$449$	24.8669	1.17354	0.586770	+	0.809754i	$0.300399\pi$
$450$	2.19810	0.103619
$451$	−16.4373	−0.774001
$452$	23.7481	1.11702
$453$	31.1037	1.46138
$454$	18.8419	0.884294
$455$	−8.16740	−0.382893
$456$	54.1763	2.53704
$457$	10.0411	0.469704	0.234852	−	0.972031i	$-0.424540\pi$
$457$	10.0411	0.469704	0.234852	+	0.972031i	$0.424540\pi$
$458$	−4.58061	−0.214038
$459$	−17.5986	−0.821430
$460$	22.2929	1.03941
$461$	37.0013	1.72332	0.861660	−	0.507485i	$-0.169425\pi$
$461$	37.0013	1.72332	0.861660	+	0.507485i	$0.169425\pi$
$462$	70.4918	3.27958
$463$	−8.01490	−0.372484	−0.186242	−	0.982504i	$-0.559631\pi$
$463$	−8.01490	−0.372484	−0.186242	+	0.982504i	$0.559631\pi$
$464$	−33.1802	−1.54035
$465$	−9.09938	−0.421974
$466$	−37.5233	−1.73823
$467$	−17.0224	−0.787704	−0.393852	−	0.919174i	$-0.628858\pi$
$467$	−17.0224	−0.787704	−0.393852	+	0.919174i	$0.628858\pi$
$468$	−2.07362	−0.0958531
$469$	−18.7743	−0.866915
$470$	2.46677	0.113783
$471$	−10.9992	−0.506818
$472$	−63.7256	−2.93321
$473$	18.5335	0.852171
$474$	−11.7622	−0.540257
$475$	22.8067	1.04644
$476$	68.0044	3.11698
$477$	−2.02121	−0.0925447
$478$	28.8230	1.31833
$479$	−42.1632	−1.92648	−0.963242	−	0.268635i	$-0.913427\pi$
$479$	−42.1632	−1.92648	−0.963242	+	0.268635i	$0.913427\pi$
$480$	−4.98317	−0.227450
$481$	18.8703	0.860411
$482$	57.8946	2.63703
$483$	54.3824	2.47448
$484$	5.66348	0.257431
$485$	−2.69830	−0.122524
$486$	5.14697	0.233471
$487$	41.6052	1.88531	0.942656	−	0.333767i	$-0.108320\pi$
$487$	41.6052	1.88531	0.942656	+	0.333767i	$0.108320\pi$
$488$	−37.5632	−1.70041
$489$	−40.0055	−1.80911
$490$	−24.5470	−1.10892
$491$	4.90720	0.221459	0.110729	−	0.993851i	$-0.464681\pi$
$491$	4.90720	0.221459	0.110729	+	0.993851i	$0.464681\pi$
$492$	36.3477	1.63868
$493$	−18.9620	−0.854005
$494$	−31.4338	−1.41427
$495$	−0.521288	−0.0234302
$496$	−41.4602	−1.86162
$497$	1.61207	0.0723111
$498$	−14.1371	−0.633498
$499$	−26.6648	−1.19368	−0.596841	−	0.802359i	$-0.703578\pi$
$499$	−26.6648	−1.19368	−0.596841	+	0.802359i	$0.703578\pi$
$500$	−30.8586	−1.38004
$501$	−6.37279	−0.284715
$502$	−22.6790	−1.01221
$503$	−36.6422	−1.63379	−0.816897	−	0.576784i	$-0.804307\pi$
$503$	−36.6422	−1.63379	−0.816897	+	0.576784i	$0.804307\pi$
$504$	−5.17800	−0.230647
$505$	−10.6759	−0.475072
$506$	60.1716	2.67495
$507$	−12.7221	−0.565010
$508$	−70.7007	−3.13683
$509$	−32.9120	−1.45880	−0.729399	−	0.684088i	$-0.760200\pi$
$509$	−32.9120	−1.45880	−0.729399	+	0.684088i	$0.760200\pi$
$510$	−11.9216	−0.527897
$511$	72.7361	3.21766
$512$	49.6389	2.19375
$513$	25.7950	1.13888
$514$	−0.334787	−0.0147668
$515$	−12.8155	−0.564719
$516$	−40.9830	−1.80418
$517$	4.55723	0.200427
$518$	87.4235	3.84117
$519$	−7.96424	−0.349591
$520$	10.7708	0.472329
$521$	−19.3600	−0.848178	−0.424089	−	0.905620i	$-0.639406\pi$
$521$	−19.3600	−0.848178	−0.424089	+	0.905620i	$0.639406\pi$
$522$	2.67871	0.117244
$523$	34.3017	1.49991	0.749955	−	0.661489i	$-0.230075\pi$
$523$	34.3017	1.49991	0.749955	+	0.661489i	$0.230075\pi$
$524$	−40.4819	−1.76846
$525$	−35.3689	−1.54363
$526$	17.9981	0.784755
$527$	−23.6939	−1.03212
$528$	−38.5392	−1.67721
$529$	23.4206	1.01829
$530$	19.4780	0.846072
$531$	2.13286	0.0925582
$532$	−99.6770	−4.32155
$533$	−11.3670	−0.492361
$534$	−5.38136	−0.232874
$535$	−3.67785	−0.159007
$536$	24.7586	1.06941
$537$	3.49978	0.151026
$538$	−11.0754	−0.477495
$539$	−45.3494	−1.95334
$540$	−16.3984	−0.705675
$541$	22.8722	0.983353	0.491676	−	0.870778i	$-0.336384\pi$
$541$	22.8722	0.983353	0.491676	+	0.870778i	$0.336384\pi$
$542$	37.5176	1.61152
$543$	22.4263	0.962403
$544$	−12.9757	−0.556327
$545$	−10.8936	−0.466631
$546$	48.7479	2.08622
$547$	−39.7192	−1.69827	−0.849135	−	0.528176i	$-0.822876\pi$
$547$	−39.7192	−1.69827	−0.849135	+	0.528176i	$0.822876\pi$
$548$	6.82815	0.291684
$549$	1.25722	0.0536568
$550$	−39.1341	−1.66868
$551$	27.7934	1.18404
$552$	−71.7168	−3.05247
$553$	11.6643	0.496016
$554$	−43.1662	−1.83396
$555$	−10.4900	−0.445274
$556$	64.5714	2.73844
$557$	−12.5566	−0.532039	−0.266019	−	0.963968i	$-0.585708\pi$
$557$	−12.5566	−0.532039	−0.266019	+	0.963968i	$0.585708\pi$
$558$	3.34717	0.141697
$559$	12.8167	0.542087
$560$	20.6870	0.874186
$561$	−22.0246	−0.929879
$562$	−46.2167	−1.94953
$563$	19.5083	0.822176	0.411088	−	0.911596i	$-0.365149\pi$
$563$	19.5083	0.822176	0.411088	+	0.911596i	$0.365149\pi$
$564$	−10.0774	−0.424335
$565$	4.12853	0.173689
$566$	−30.1669	−1.26801
$567$	−42.6419	−1.79079
$568$	−2.12592	−0.0892014
$569$	−12.6424	−0.529998	−0.264999	−	0.964249i	$-0.585372\pi$
$569$	−12.6424	−0.529998	−0.264999	+	0.964249i	$0.585372\pi$
$570$	17.4740	0.731906
$571$	18.6936	0.782304	0.391152	−	0.920326i	$-0.372077\pi$
$571$	18.6936	0.782304	0.391152	+	0.920326i	$0.372077\pi$
$572$	36.9179	1.54362
$573$	28.6350	1.19624
$574$	−52.6620	−2.19807
$575$	−30.1908	−1.25904
$576$	−0.588275	−0.0245114
$577$	−35.9511	−1.49666	−0.748332	−	0.663324i	$-0.769145\pi$
$577$	−35.9511	−1.49666	−0.748332	+	0.663324i	$0.769145\pi$
$578$	11.7566	0.489011
$579$	−39.0522	−1.62295
$580$	−17.6689	−0.733659
$581$	14.0194	0.581621
$582$	16.1051	0.667577
$583$	35.9848	1.49034
$584$	−95.9209	−3.96923
$585$	−0.360492	−0.0149045
$586$	−20.5972	−0.850861
$587$	11.4040	0.470694	0.235347	−	0.971911i	$-0.424377\pi$
$587$	11.4040	0.470694	0.235347	+	0.971911i	$0.424377\pi$
$588$	100.281	4.13552
$589$	34.7291	1.43099
$590$	−20.5540	−0.846196
$591$	20.4914	0.842906
$592$	−47.7961	−1.96441
$593$	−46.9862	−1.92949	−0.964746	−	0.263183i	$-0.915228\pi$
$593$	−46.9862	−1.92949	−0.964746	+	0.263183i	$0.915228\pi$
$594$	−44.2616	−1.81608
$595$	11.8223	0.484668
$596$	−64.0201	−2.62237
$597$	43.5083	1.78068
$598$	41.6111	1.70160
$599$	34.4222	1.40645	0.703227	−	0.710966i	$-0.251742\pi$
$599$	34.4222	1.40645	0.703227	+	0.710966i	$0.251742\pi$
$600$	46.6428	1.90419
$601$	−1.14402	−0.0466656	−0.0233328	−	0.999728i	$-0.507428\pi$
$601$	−1.14402	−0.0466656	−0.0233328	+	0.999728i	$0.507428\pi$
$602$	59.3779	2.42006
$603$	−0.828656	−0.0337455
$604$	75.4675	3.07073
$605$	0.984577	0.0400288
$606$	63.7203	2.58846
$607$	−16.2059	−0.657777	−0.328888	−	0.944369i	$-0.606674\pi$
$607$	−16.2059	−0.657777	−0.328888	+	0.944369i	$0.606674\pi$
$608$	19.0190	0.771323
$609$	−43.1023	−1.74660
$610$	−12.1156	−0.490547
$611$	3.15151	0.127496
$612$	3.00157	0.121331
$613$	3.71233	0.149940	0.0749699	−	0.997186i	$-0.476114\pi$
$613$	3.71233	0.149940	0.0749699	+	0.997186i	$0.476114\pi$
$614$	51.1138	2.06279
$615$	6.31892	0.254804
$616$	92.1871	3.71432
$617$	45.2398	1.82129	0.910643	−	0.413193i	$-0.135587\pi$
$617$	45.2398	1.82129	0.910643	+	0.413193i	$0.135587\pi$
$618$	76.4908	3.07691
$619$	−12.2751	−0.493379	−0.246690	−	0.969095i	$-0.579343\pi$
$619$	−12.2751	−0.493379	−0.246690	+	0.969095i	$0.579343\pi$
$620$	−22.0780	−0.886675
$621$	−34.1465	−1.37025
$622$	36.5682	1.46625
$623$	5.33655	0.213804
$624$	−26.6514	−1.06691
$625$	16.7912	0.671649
$626$	−0.790326	−0.0315878
$627$	32.2824	1.28924
$628$	−26.6877	−1.06495
$629$	−27.3148	−1.08911
$630$	−1.67011	−0.0665388
$631$	−21.5913	−0.859537	−0.429768	−	0.902939i	$-0.641405\pi$
$631$	−21.5913	−0.859537	−0.429768	+	0.902939i	$0.641405\pi$
$632$	−15.3823	−0.611875
$633$	−42.6124	−1.69369
$634$	60.4782	2.40190
$635$	−12.2911	−0.487756
$636$	−79.5730	−3.15527
$637$	−31.3610	−1.24257
$638$	−47.6908	−1.88810
$639$	0.0711532	0.00281478
$640$	11.2431	0.444421
$641$	28.4425	1.12341	0.561705	−	0.827338i	$-0.310146\pi$
$641$	28.4425	1.12341	0.561705	+	0.827338i	$0.310146\pi$
$642$	21.9516	0.866361
$643$	−14.8711	−0.586458	−0.293229	−	0.956042i	$-0.594730\pi$
$643$	−14.8711	−0.586458	−0.293229	+	0.956042i	$0.594730\pi$
$644$	131.949	5.19953
$645$	−7.12476	−0.280537
$646$	45.5005	1.79019
$647$	20.4454	0.803791	0.401895	−	0.915686i	$-0.368352\pi$
$647$	20.4454	0.803791	0.401895	+	0.915686i	$0.368352\pi$
$648$	56.2340	2.20908
$649$	−37.9726	−1.49055
$650$	−27.0628	−1.06149
$651$	−53.8583	−2.11087
$652$	−97.0662	−3.80141
$653$	17.9563	0.702685	0.351343	−	0.936247i	$-0.385725\pi$
$653$	17.9563	0.702685	0.351343	+	0.936247i	$0.385725\pi$
$654$	65.0196	2.54247
$655$	−7.03764	−0.274984
$656$	28.7913	1.12411
$657$	3.21042	0.125250
$658$	14.6005	0.569188
$659$	8.64445	0.336740	0.168370	−	0.985724i	$-0.446150\pi$
$659$	8.64445	0.336740	0.168370	+	0.985724i	$0.446150\pi$
$660$	−20.5226	−0.798842
$661$	−2.87657	−0.111886	−0.0559428	−	0.998434i	$-0.517816\pi$
$661$	−2.87657	−0.111886	−0.0559428	+	0.998434i	$0.517816\pi$
$662$	−76.7235	−2.98194
$663$	−15.2309	−0.591519
$664$	−18.4881	−0.717476
$665$	−17.3285	−0.671971
$666$	3.85869	0.149521
$667$	−36.7920	−1.42459
$668$	−15.4624	−0.598260
$669$	−21.7601	−0.841293
$670$	7.98563	0.308512
$671$	−22.3830	−0.864087
$672$	−29.4949	−1.13779
$673$	43.6617	1.68303	0.841517	−	0.540231i	$-0.181663\pi$
$673$	43.6617	1.68303	0.841517	+	0.540231i	$0.181663\pi$
$674$	−21.4629	−0.826720
$675$	22.2081	0.854789
$676$	−30.8680	−1.18723
$677$	21.8916	0.841361	0.420680	−	0.907209i	$-0.361791\pi$
$677$	21.8916	0.841361	0.420680	+	0.907209i	$0.361791\pi$
$678$	−24.6416	−0.946353
$679$	−15.9710	−0.612910
$680$	−15.5907	−0.597877
$681$	−13.3817	−0.512787
$682$	−59.5918	−2.28189
$683$	3.56351	0.136354	0.0681769	−	0.997673i	$-0.478282\pi$
$683$	3.56351	0.136354	0.0681769	+	0.997673i	$0.478282\pi$
$684$	−4.39953	−0.168220
$685$	1.18705	0.0453548
$686$	−66.6203	−2.54357
$687$	3.25319	0.124117
$688$	−32.4630	−1.23764
$689$	24.8849	0.948040
$690$	−23.1315	−0.880602
$691$	24.4024	0.928313	0.464156	−	0.885753i	$-0.346358\pi$
$691$	24.4024	0.928313	0.464156	+	0.885753i	$0.346358\pi$
$692$	−19.3238	−0.734581
$693$	−3.08545	−0.117207
$694$	−41.8827	−1.58985
$695$	11.2255	0.425808
$696$	56.8413	2.15456
$697$	16.4538	0.623233
$698$	−10.2180	−0.386755
$699$	26.6494	1.00797
$700$	−85.8164	−3.24356
$701$	−15.3368	−0.579264	−0.289632	−	0.957138i	$-0.593533\pi$
$701$	−15.3368	−0.579264	−0.289632	+	0.957138i	$0.593533\pi$
$702$	−30.6087	−1.15525
$703$	40.0365	1.51000
$704$	10.4734	0.394731
$705$	−1.75192	−0.0659811
$706$	−60.2077	−2.26595
$707$	−63.1897	−2.37649
$708$	83.9686	3.15574
$709$	2.62854	0.0987168	0.0493584	−	0.998781i	$-0.484282\pi$
$709$	2.62854	0.0987168	0.0493584	+	0.998781i	$0.484282\pi$
$710$	−0.685692	−0.0257336
$711$	0.514837	0.0193079
$712$	−7.03758	−0.263745
$713$	−45.9733	−1.72171
$714$	−70.5628	−2.64075
$715$	6.41805	0.240022
$716$	8.49159	0.317345
$717$	−20.4704	−0.764480
$718$	−33.1484	−1.23709
$719$	13.1448	0.490217	0.245108	−	0.969496i	$-0.421176\pi$
$719$	13.1448	0.490217	0.245108	+	0.969496i	$0.421176\pi$
$720$	0.913082	0.0340286
$721$	−75.8538	−2.82494
$722$	−18.8577	−0.701810
$723$	−41.1173	−1.52917
$724$	54.4133	2.02226
$725$	23.9286	0.888686
$726$	−5.87655	−0.218099
$727$	5.41084	0.200677	0.100338	−	0.994953i	$-0.468007\pi$
$727$	5.41084	0.200677	0.100338	+	0.994953i	$0.468007\pi$
$728$	63.7511	2.36277
$729$	25.0014	0.925978
$730$	−30.9383	−1.14508
$731$	−18.5521	−0.686176
$732$	49.4955	1.82941
$733$	−20.1289	−0.743476	−0.371738	−	0.928338i	$-0.621238\pi$
$733$	−20.1289	−0.743476	−0.371738	+	0.928338i	$0.621238\pi$
$734$	−66.2523	−2.44542
$735$	17.4335	0.643045
$736$	−25.1767	−0.928027
$737$	14.7531	0.543436
$738$	−2.32439	−0.0855620
$739$	5.04474	0.185574	0.0927868	−	0.995686i	$-0.470422\pi$
$739$	5.04474	0.185574	0.0927868	+	0.995686i	$0.470422\pi$
$740$	−25.4520	−0.935635
$741$	22.3246	0.820114
$742$	115.289	4.23238
$743$	−9.40851	−0.345165	−0.172582	−	0.984995i	$-0.555211\pi$
$743$	−9.40851	−0.345165	−0.172582	+	0.984995i	$0.555211\pi$
$744$	71.0258	2.60393
$745$	−11.1297	−0.407760
$746$	41.2232	1.50929
$747$	0.618785	0.0226402
$748$	−53.4388	−1.95392
$749$	−21.7688	−0.795415
$750$	32.0195	1.16919
$751$	12.2537	0.447146	0.223573	−	0.974687i	$-0.428228\pi$
$751$	12.2537	0.447146	0.223573	+	0.974687i	$0.428228\pi$
$752$	−7.98239	−0.291088
$753$	16.1068	0.586965
$754$	−32.9801	−1.20106
$755$	13.1198	0.477477
$756$	−97.0606	−3.53006
$757$	−26.9899	−0.980964	−0.490482	−	0.871451i	$-0.663179\pi$
$757$	−26.9899	−0.980964	−0.490482	+	0.871451i	$0.663179\pi$
$758$	20.9934	0.762515
$759$	−42.7344	−1.55116
$760$	22.8520	0.828929
$761$	−24.4913	−0.887810	−0.443905	−	0.896074i	$-0.646407\pi$
$761$	−24.4913	−0.887810	−0.443905	+	0.896074i	$0.646407\pi$
$762$	73.3605	2.65757
$763$	−64.4782	−2.33427
$764$	69.4777	2.51362
$765$	0.521813	0.0188662
$766$	8.87722	0.320747
$767$	−26.2596	−0.948178
$768$	−56.4285	−2.03619
$769$	−42.5979	−1.53612	−0.768059	−	0.640379i	$-0.778777\pi$
$769$	−42.5979	−1.53612	−0.768059	+	0.640379i	$0.778777\pi$
$770$	29.7340	1.07154
$771$	0.237769	0.00856303
$772$	−94.7531	−3.41024
$773$	−41.4307	−1.49016	−0.745080	−	0.666975i	$-0.767589\pi$
$773$	−41.4307	−1.49016	−0.745080	+	0.666975i	$0.767589\pi$
$774$	2.62082	0.0942033
$775$	29.8999	1.07404
$776$	21.0618	0.756073
$777$	−62.0890	−2.22743
$778$	−14.3576	−0.514747
$779$	−24.1171	−0.864084
$780$	−14.1922	−0.508163
$781$	−1.26678	−0.0453291
$782$	−60.2321	−2.15390
$783$	27.0639	0.967183
$784$	79.4335	2.83691
$785$	−4.63956	−0.165593
$786$	42.0049	1.49827
$787$	−0.543846	−0.0193860	−0.00969301	−	0.999953i	$-0.503085\pi$
$787$	−0.543846	−0.0193860	−0.00969301	+	0.999953i	$0.503085\pi$
$788$	49.7189	1.77116
$789$	−12.7824	−0.455066
$790$	−4.96140	−0.176519
$791$	24.4364	0.868857
$792$	4.06895	0.144584
$793$	−15.4788	−0.549667
$794$	−42.1866	−1.49714
$795$	−13.8335	−0.490623
$796$	105.565	3.74166
$797$	34.2645	1.21371	0.606855	−	0.794813i	$-0.292431\pi$
$797$	34.2645	1.21371	0.606855	+	0.794813i	$0.292431\pi$
$798$	103.427	3.66127
$799$	−4.56182	−0.161386
$800$	16.3743	0.578920
$801$	0.235544	0.00832254
$802$	−5.37327	−0.189737
$803$	−57.1570	−2.01703
$804$	−32.6234	−1.15054
$805$	22.9389	0.808490
$806$	−41.2101	−1.45156
$807$	7.86587	0.276892
$808$	83.3315	2.93159
$809$	10.9509	0.385014	0.192507	−	0.981296i	$-0.438338\pi$
$809$	10.9509	0.385014	0.192507	+	0.981296i	$0.438338\pi$
$810$	18.1377	0.637294
$811$	−33.3090	−1.16964	−0.584818	−	0.811164i	$-0.698834\pi$
$811$	−33.3090	−1.16964	−0.584818	+	0.811164i	$0.698834\pi$
$812$	−104.580	−3.67005
$813$	−26.6453	−0.934493
$814$	−68.6986	−2.40789
$815$	−16.8746	−0.591092
$816$	38.5780	1.35050
$817$	27.1927	0.951352
$818$	61.7028	2.15739
$819$	−2.13371	−0.0745580
$820$	15.3317	0.535408
$821$	7.81120	0.272613	0.136306	−	0.990667i	$-0.456477\pi$
$821$	7.81120	0.272613	0.136306	+	0.990667i	$0.456477\pi$
$822$	−7.08503	−0.247119
$823$	44.8676	1.56399	0.781994	−	0.623287i	$-0.214203\pi$
$823$	44.8676	1.56399	0.781994	+	0.623287i	$0.214203\pi$
$824$	100.032	3.48479
$825$	27.7934	0.967642
$826$	−121.657	−4.23300
$827$	−53.9633	−1.87649	−0.938244	−	0.345974i	$-0.887548\pi$
$827$	−53.9633	−1.87649	−0.938244	+	0.345974i	$0.887548\pi$
$828$	5.82396	0.202397
$829$	44.7108	1.55287	0.776435	−	0.630198i	$-0.217026\pi$
$829$	44.7108	1.55287	0.776435	+	0.630198i	$0.217026\pi$
$830$	−5.96314	−0.206983
$831$	30.6570	1.06348
$832$	7.24278	0.251098
$833$	45.3951	1.57285
$834$	−67.0006	−2.32004
$835$	−2.68809	−0.0930253
$836$	78.3276	2.70902
$837$	33.8175	1.16890
$838$	−44.5493	−1.53893
$839$	4.77341	0.164796	0.0823982	−	0.996599i	$-0.473742\pi$
$839$	4.77341	0.164796	0.0823982	+	0.996599i	$0.473742\pi$
$840$	−35.4391	−1.22277
$841$	0.160588	0.00553752
$842$	−34.8941	−1.20253
$843$	32.8235	1.13050
$844$	−103.391	−3.55888
$845$	−5.36630	−0.184606
$846$	0.644437	0.0221562
$847$	5.82761	0.200239
$848$	−63.0305	−2.16448
$849$	21.4248	0.735299
$850$	39.1735	1.34364
$851$	−52.9990	−1.81678
$852$	2.80123	0.0959687
$853$	−30.5728	−1.04679	−0.523397	−	0.852089i	$-0.675335\pi$
$853$	−30.5728	−1.04679	−0.523397	+	0.852089i	$0.675335\pi$
$854$	−71.7111	−2.45390
$855$	−0.764844	−0.0261571
$856$	28.7076	0.981207
$857$	−0.258641	−0.00883501	−0.00441751	−	0.999990i	$-0.501406\pi$
$857$	−0.258641	−0.00883501	−0.00441751	+	0.999990i	$0.501406\pi$
$858$	−38.3068	−1.30777
$859$	−28.1858	−0.961686	−0.480843	−	0.876807i	$-0.659669\pi$
$859$	−28.1858	−0.961686	−0.480843	+	0.876807i	$0.659669\pi$
$860$	−17.2870	−0.589481
$861$	37.4011	1.27462
$862$	0.0157389	0.000536068 0
$863$	−17.6191	−0.599762	−0.299881	−	0.953977i	$-0.596947\pi$
$863$	−17.6191	−0.599762	−0.299881	+	0.953977i	$0.596947\pi$
$864$	18.5198	0.630056
$865$	−3.35938	−0.114222
$866$	−0.713339	−0.0242402
$867$	−8.34967	−0.283570
$868$	−130.678	−4.43549
$869$	−9.16596	−0.310934
$870$	18.3336	0.621566
$871$	10.2023	0.345693
$872$	85.0307	2.87950
$873$	−0.704925	−0.0238581
$874$	88.2849	2.98628
$875$	−31.7529	−1.07344
$876$	126.391	4.27036
$877$	44.7816	1.51217	0.756084	−	0.654475i	$-0.227110\pi$
$877$	44.7816	1.51217	0.756084	+	0.654475i	$0.227110\pi$
$878$	7.24905	0.244644
$879$	14.6283	0.493400
$880$	−16.2562	−0.547995
$881$	−12.8260	−0.432120	−0.216060	−	0.976380i	$-0.569321\pi$
$881$	−12.8260	−0.432120	−0.216060	+	0.976380i	$0.569321\pi$
$882$	−6.41285	−0.215932
$883$	51.2213	1.72373	0.861867	−	0.507134i	$-0.169295\pi$
$883$	51.2213	1.72373	0.861867	+	0.507134i	$0.169295\pi$
$884$	−36.9551	−1.24293
$885$	14.5977	0.490695
$886$	19.1767	0.644253
$887$	−29.7528	−0.999000	−0.499500	−	0.866314i	$-0.666483\pi$
$887$	−29.7528	−0.999000	−0.499500	+	0.866314i	$0.666483\pi$
$888$	81.8800	2.74771
$889$	−72.7496	−2.43994
$890$	−2.26990	−0.0760872
$891$	33.5086	1.12258
$892$	−52.7970	−1.76777
$893$	6.68646	0.223754
$894$	66.4286	2.22171
$895$	1.47623	0.0493450
$896$	66.5465	2.22316
$897$	−29.5526	−0.986731
$898$	−62.6049	−2.08915
$899$	36.4375	1.21526
$900$	−3.78776	−0.126259
$901$	−36.0210	−1.20003
$902$	41.3825	1.37789
$903$	−42.1707	−1.40335
$904$	−32.2255	−1.07180
$905$	9.45957	0.314447
$906$	−78.3067	−2.60157
$907$	9.94384	0.330180	0.165090	−	0.986279i	$-0.447209\pi$
$907$	9.94384	0.330180	0.165090	+	0.986279i	$0.447209\pi$
$908$	−32.4683	−1.07750
$909$	−2.78906	−0.0925073
$910$	20.5623	0.681632
$911$	−30.9717	−1.02614	−0.513069	−	0.858347i	$-0.671492\pi$
$911$	−30.9717	−1.02614	−0.513069	+	0.858347i	$0.671492\pi$
$912$	−56.5455	−1.87241
$913$	−11.0166	−0.364597
$914$	−25.2795	−0.836173
$915$	8.60462	0.284460
$916$	7.89330	0.260802
$917$	−41.6551	−1.37557
$918$	44.3062	1.46232
$919$	−10.7510	−0.354644	−0.177322	−	0.984153i	$-0.556743\pi$
$919$	−10.7510	−0.354644	−0.177322	+	0.984153i	$0.556743\pi$
$920$	−30.2507	−0.997337
$921$	−36.3015	−1.19618
$922$	−93.1545	−3.06788
$923$	−0.876032	−0.0288349
$924$	−121.471	−3.99611
$925$	34.4692	1.13334
$926$	20.1783	0.663101
$927$	−3.34803	−0.109964
$928$	19.9546	0.655041
$929$	−16.7617	−0.549935	−0.274967	−	0.961454i	$-0.588667\pi$
$929$	−16.7617	−0.549935	−0.274967	+	0.961454i	$0.588667\pi$
$930$	22.9086	0.751204
$931$	−66.5375	−2.18068
$932$	64.6600	2.11801
$933$	−25.9711	−0.850255
$934$	42.8557	1.40228
$935$	−9.29015	−0.303820
$936$	2.81384	0.0919732
$937$	19.2402	0.628550	0.314275	−	0.949332i	$-0.398239\pi$
$937$	19.2402	0.628550	0.314275	+	0.949332i	$0.398239\pi$
$938$	47.2661	1.54329
$939$	0.561297	0.0183172
$940$	−4.25072	−0.138643
$941$	−32.9534	−1.07425	−0.537126	−	0.843502i	$-0.680490\pi$
$941$	−32.9534	−1.07425	−0.537126	+	0.843502i	$0.680490\pi$
$942$	27.6917	0.902244
$943$	31.9254	1.03963
$944$	66.5123	2.16479
$945$	−16.8736	−0.548900
$946$	−46.6600	−1.51705
$947$	−48.2607	−1.56826	−0.784132	−	0.620594i	$-0.786891\pi$
$947$	−48.2607	−1.56826	−0.784132	+	0.620594i	$0.786891\pi$
$948$	20.2686	0.658295
$949$	−39.5264	−1.28308
$950$	−57.4183	−1.86290
$951$	−42.9522	−1.39282
$952$	−92.2799	−2.99081
$953$	12.4165	0.402211	0.201105	−	0.979570i	$-0.435547\pi$
$953$	12.4165	0.402211	0.201105	+	0.979570i	$0.435547\pi$
$954$	5.08860	0.164749
$955$	12.0785	0.390850
$956$	−49.6677	−1.60637
$957$	33.8704	1.09488
$958$	106.150	3.42955
$959$	7.02603	0.226882
$960$	−4.02625	−0.129947
$961$	14.5303	0.468719
$962$	−47.5079	−1.53172
$963$	−0.960829	−0.0309623
$964$	−99.7637	−3.21317
$965$	−16.4725	−0.530269
$966$	−136.913	−4.40511
$967$	−20.3303	−0.653780	−0.326890	−	0.945062i	$-0.606001\pi$
$967$	−20.3303	−0.653780	−0.326890	+	0.945062i	$0.606001\pi$
$968$	−7.68518	−0.247011
$969$	−32.3149	−1.03810
$970$	6.79325	0.218118
$971$	−56.1228	−1.80107	−0.900533	−	0.434787i	$-0.856824\pi$
$971$	−56.1228	−1.80107	−0.900533	+	0.434787i	$0.856824\pi$
$972$	−8.86924	−0.284481
$973$	66.4427	2.13005
$974$	−104.745	−3.35626
$975$	19.2203	0.615541
$976$	39.2058	1.25495
$977$	33.8865	1.08412	0.542062	−	0.840338i	$-0.317644\pi$
$977$	33.8865	1.08412	0.542062	+	0.840338i	$0.317644\pi$
$978$	100.718	3.22061
$979$	−4.19353	−0.134026
$980$	42.2993	1.35120
$981$	−2.84593	−0.0908636
$982$	−12.3544	−0.394244
$983$	−42.3961	−1.35223	−0.676113	−	0.736798i	$-0.736337\pi$
$983$	−42.3961	−1.35223	−0.676113	+	0.736798i	$0.736337\pi$
$984$	−49.3227	−1.57235
$985$	8.64345	0.275403
$986$	47.7387	1.52031
$987$	−10.3694	−0.330063
$988$	54.1667	1.72327
$989$	−35.9968	−1.14463
$990$	1.31240	0.0417107
$991$	−51.4924	−1.63571	−0.817855	−	0.575425i	$-0.804837\pi$
$991$	−51.4924	−1.63571	−0.817855	+	0.575425i	$0.804837\pi$
$992$	24.9341	0.791660
$993$	54.4897	1.72918
$994$	−4.05854	−0.128729
$995$	18.3521	0.581802
$996$	24.3610	0.771908
$997$	−2.04355	−0.0647200	−0.0323600	−	0.999476i	$-0.510302\pi$
$997$	−2.04355	−0.0647200	−0.0323600	+	0.999476i	$0.510302\pi$
$998$	67.1315	2.12501
$999$	38.9855	1.23345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.16	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.16	✓	221	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51760 q^{2} +1.78803 q^{3} +4.33833 q^{4} +0.754203 q^{5} -4.50154 q^{6} +4.46405 q^{7} -5.88698 q^{8} +0.197034 q^{9} +O(q^{10})\)	\(q-2.51760 q^{2} +1.78803 q^{3} +4.33833 q^{4} +0.754203 q^{5} -4.50154 q^{6} +4.46405 q^{7} -5.88698 q^{8} +0.197034 q^{9} -1.89878 q^{10} -3.50791 q^{11} +7.75704 q^{12} -2.42586 q^{13} -11.2387 q^{14} +1.34853 q^{15} +6.14442 q^{16} +3.51144 q^{17} -0.496053 q^{18} -5.14688 q^{19} +3.27198 q^{20} +7.98184 q^{21} +8.83153 q^{22} +6.81327 q^{23} -10.5261 q^{24} -4.43118 q^{25} +6.10736 q^{26} -5.01177 q^{27} +19.3665 q^{28} -5.40005 q^{29} -3.39507 q^{30} -6.74761 q^{31} -3.69525 q^{32} -6.27224 q^{33} -8.84042 q^{34} +3.36680 q^{35} +0.854797 q^{36} -7.77879 q^{37} +12.9578 q^{38} -4.33750 q^{39} -4.43997 q^{40} +4.68577 q^{41} -20.0951 q^{42} -5.28334 q^{43} -15.2185 q^{44} +0.148603 q^{45} -17.1531 q^{46} -1.29913 q^{47} +10.9864 q^{48} +12.9278 q^{49} +11.1559 q^{50} +6.27855 q^{51} -10.5242 q^{52} -10.2582 q^{53} +12.6177 q^{54} -2.64568 q^{55} -26.2798 q^{56} -9.20274 q^{57} +13.5952 q^{58} +10.8248 q^{59} +5.85038 q^{60} +6.38073 q^{61} +16.9878 q^{62} +0.879569 q^{63} -2.98565 q^{64} -1.82959 q^{65} +15.7910 q^{66} -4.20565 q^{67} +15.2338 q^{68} +12.1823 q^{69} -8.47627 q^{70} +0.361122 q^{71} -1.15993 q^{72} +16.2937 q^{73} +19.5839 q^{74} -7.92306 q^{75} -22.3288 q^{76} -15.6595 q^{77} +10.9201 q^{78} +2.61294 q^{79} +4.63414 q^{80} -9.55228 q^{81} -11.7969 q^{82} +3.14050 q^{83} +34.6278 q^{84} +2.64834 q^{85} +13.3014 q^{86} -9.65543 q^{87} +20.6510 q^{88} +1.19545 q^{89} -0.374125 q^{90} -10.8292 q^{91} +29.5582 q^{92} -12.0649 q^{93} +3.27069 q^{94} -3.88179 q^{95} -6.60721 q^{96} -3.57769 q^{97} -32.5469 q^{98} -0.691178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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