LMFDB - Embedded newform 8009.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8009,2,Mod(1,8009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8009, 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("8009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8009 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8009.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:	$63.9521869788$
Analytic rank:	$1$
Dimension:	$306$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66884 q^{2} +3.40767 q^{3} +5.12268 q^{4} +0.00216831 q^{5} -9.09450 q^{6} -2.11405 q^{7} -8.33393 q^{8} +8.61218 q^{9} +O(q^{10})$	\(q-2.66884 q^{2} +3.40767 q^{3} +5.12268 q^{4} +0.00216831 q^{5} -9.09450 q^{6} -2.11405 q^{7} -8.33393 q^{8} +8.61218 q^{9} -0.00578687 q^{10} +2.83690 q^{11} +17.4564 q^{12} -3.19304 q^{13} +5.64205 q^{14} +0.00738889 q^{15} +11.9965 q^{16} -3.86570 q^{17} -22.9845 q^{18} +1.39163 q^{19} +0.0111076 q^{20} -7.20398 q^{21} -7.57123 q^{22} -5.24437 q^{23} -28.3992 q^{24} -5.00000 q^{25} +8.52169 q^{26} +19.1244 q^{27} -10.8296 q^{28} -6.29857 q^{29} -0.0197197 q^{30} -8.35282 q^{31} -15.3489 q^{32} +9.66722 q^{33} +10.3169 q^{34} -0.00458392 q^{35} +44.1175 q^{36} -0.706319 q^{37} -3.71403 q^{38} -10.8808 q^{39} -0.0180706 q^{40} -1.84865 q^{41} +19.2262 q^{42} +12.8966 q^{43} +14.5326 q^{44} +0.0186739 q^{45} +13.9964 q^{46} +9.00519 q^{47} +40.8801 q^{48} -2.53079 q^{49} +13.3442 q^{50} -13.1730 q^{51} -16.3569 q^{52} +7.04062 q^{53} -51.0400 q^{54} +0.00615130 q^{55} +17.6183 q^{56} +4.74220 q^{57} +16.8098 q^{58} -7.71425 q^{59} +0.0378509 q^{60} -7.49774 q^{61} +22.2923 q^{62} -18.2066 q^{63} +16.9706 q^{64} -0.00692350 q^{65} -25.8002 q^{66} +1.32225 q^{67} -19.8028 q^{68} -17.8710 q^{69} +0.0122337 q^{70} +14.1025 q^{71} -71.7733 q^{72} -0.651775 q^{73} +1.88505 q^{74} -17.0383 q^{75} +7.12887 q^{76} -5.99736 q^{77} +29.0391 q^{78} -16.5080 q^{79} +0.0260122 q^{80} +39.3331 q^{81} +4.93374 q^{82} -1.92554 q^{83} -36.9037 q^{84} -0.00838205 q^{85} -34.4188 q^{86} -21.4634 q^{87} -23.6426 q^{88} +5.54234 q^{89} -0.0498376 q^{90} +6.75024 q^{91} -26.8652 q^{92} -28.4636 q^{93} -24.0334 q^{94} +0.00301748 q^{95} -52.3039 q^{96} +0.833321 q^{97} +6.75426 q^{98} +24.4319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9}+O(q^{10}) $ 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9} - 61 q^{10} - 43 q^{11} - 50 q^{12} - 89 q^{13} - 40 q^{14} - 61 q^{15} + 151 q^{16} - 52 q^{17} - 57 q^{18} - 185 q^{19} - 66 q^{20} - 63 q^{21} - 55 q^{22} - 62 q^{23} - 131 q^{24} + 209 q^{25} - 57 q^{26} - 88 q^{27} - 182 q^{28} - 67 q^{29} - 68 q^{30} - 240 q^{31} - 64 q^{32} - 52 q^{33} - 128 q^{34} - 99 q^{35} + 106 q^{36} - 49 q^{37} - 45 q^{38} - 190 q^{39} - 158 q^{40} - 72 q^{41} - 36 q^{42} - 141 q^{43} - 80 q^{44} - 100 q^{45} - 91 q^{46} - 105 q^{47} - 85 q^{48} + 116 q^{49} - 51 q^{50} - 145 q^{51} - 237 q^{52} - 48 q^{53} - 156 q^{54} - 420 q^{55} - 116 q^{56} - 35 q^{57} - 43 q^{58} - 139 q^{59} - 73 q^{60} - 233 q^{61} - 58 q^{62} - 252 q^{63} - 3 q^{64} - 45 q^{65} - 127 q^{66} - 108 q^{67} - 85 q^{68} - 164 q^{69} - 56 q^{70} - 131 q^{71} - 117 q^{72} - 118 q^{73} - 47 q^{74} - 112 q^{75} - 389 q^{76} - 36 q^{77} + 9 q^{78} - 382 q^{79} - 119 q^{80} + 102 q^{81} - 131 q^{82} - 59 q^{83} - 144 q^{84} - 140 q^{85} - 38 q^{86} - 301 q^{87} - 131 q^{88} - 98 q^{89} - 138 q^{90} - 176 q^{91} - 97 q^{92} - 60 q^{93} - 342 q^{94} - 154 q^{95} - 243 q^{96} - 109 q^{97} - 21 q^{98} - 173 q^{99}+O(q^{100}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9 - 61 * q^10 - 43 * q^11 - 50 * q^12 - 89 * q^13 - 40 * q^14 - 61 * q^15 + 151 * q^16 - 52 * q^17 - 57 * q^18 - 185 * q^19 - 66 * q^20 - 63 * q^21 - 55 * q^22 - 62 * q^23 - 131 * q^24 + 209 * q^25 - 57 * q^26 - 88 * q^27 - 182 * q^28 - 67 * q^29 - 68 * q^30 - 240 * q^31 - 64 * q^32 - 52 * q^33 - 128 * q^34 - 99 * q^35 + 106 * q^36 - 49 * q^37 - 45 * q^38 - 190 * q^39 - 158 * q^40 - 72 * q^41 - 36 * q^42 - 141 * q^43 - 80 * q^44 - 100 * q^45 - 91 * q^46 - 105 * q^47 - 85 * q^48 + 116 * q^49 - 51 * q^50 - 145 * q^51 - 237 * q^52 - 48 * q^53 - 156 * q^54 - 420 * q^55 - 116 * q^56 - 35 * q^57 - 43 * q^58 - 139 * q^59 - 73 * q^60 - 233 * q^61 - 58 * q^62 - 252 * q^63 - 3 * q^64 - 45 * q^65 - 127 * q^66 - 108 * q^67 - 85 * q^68 - 164 * q^69 - 56 * q^70 - 131 * q^71 - 117 * q^72 - 118 * q^73 - 47 * q^74 - 112 * q^75 - 389 * q^76 - 36 * q^77 + 9 * q^78 - 382 * q^79 - 119 * q^80 + 102 * q^81 - 131 * q^82 - 59 * q^83 - 144 * q^84 - 140 * q^85 - 38 * q^86 - 301 * q^87 - 131 * q^88 - 98 * q^89 - 138 * q^90 - 176 * q^91 - 97 * q^92 - 60 * q^93 - 342 * q^94 - 154 * q^95 - 243 * q^96 - 109 * q^97 - 21 * q^98 - 173 * 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 $

$2$	−2.66884	−1.88715	−0.943576	−	0.331156i	$-0.892561\pi$
$2$	−2.66884	−1.88715	−0.943576	+	0.331156i	$0.892561\pi$
$3$	3.40767	1.96742	0.983708	−	0.179773i	$-0.0575362\pi$
$3$	3.40767	1.96742	0.983708	+	0.179773i	$0.0575362\pi$
$4$	5.12268	2.56134
$5$	0.00216831	0.000969699 0	0.000484850	−	1.00000i	$-0.499846\pi$
$5$	0.00216831	0.000969699 0	0.000484850		1.00000i	$0.499846\pi$
$6$	−9.09450	−3.71281
$7$	−2.11405	−0.799036	−0.399518	−	0.916725i	$-0.630822\pi$
$7$	−2.11405	−0.799036	−0.399518	+	0.916725i	$0.630822\pi$
$8$	−8.33393	−2.94649
$9$	8.61218	2.87073
$10$	−0.00578687	−0.00182997
$11$	2.83690	0.855359	0.427680	−	0.903930i	$-0.359331\pi$
$11$	2.83690	0.855359	0.427680	+	0.903930i	$0.359331\pi$
$12$	17.4564	5.03923
$13$	−3.19304	−0.885589	−0.442794	−	0.896623i	$-0.646013\pi$
$13$	−3.19304	−0.885589	−0.442794	+	0.896623i	$0.646013\pi$
$14$	5.64205	1.50790
$15$	0.00738889	0.00190780
$16$	11.9965	2.99913
$17$	−3.86570	−0.937570	−0.468785	−	0.883312i	$-0.655308\pi$
$17$	−3.86570	−0.937570	−0.468785	+	0.883312i	$0.655308\pi$
$18$	−22.9845	−5.41750
$19$	1.39163	0.319261	0.159631	−	0.987177i	$-0.448970\pi$
$19$	1.39163	0.319261	0.159631	+	0.987177i	$0.448970\pi$
$20$	0.0111076	0.00248373
$21$	−7.20398	−1.57204
$22$	−7.57123	−1.61419
$23$	−5.24437	−1.09353	−0.546763	−	0.837287i	$-0.684140\pi$
$23$	−5.24437	−1.09353	−0.546763	+	0.837287i	$0.684140\pi$
$24$	−28.3992	−5.79697
$25$	−5.00000	−0.999999
$26$	8.52169	1.67124
$27$	19.1244	3.68050
$28$	−10.8296	−2.04660
$29$	−6.29857	−1.16962	−0.584808	−	0.811172i	$-0.698830\pi$
$29$	−6.29857	−1.16962	−0.584808	+	0.811172i	$0.698830\pi$
$30$	−0.0197197	−0.00360031
$31$	−8.35282	−1.50021	−0.750105	−	0.661319i	$-0.769997\pi$
$31$	−8.35282	−1.50021	−0.750105	+	0.661319i	$0.769997\pi$
$32$	−15.3489	−2.71332
$33$	9.66722	1.68285
$34$	10.3169	1.76934
$35$	−0.00458392	−0.000774825 0
$36$	44.1175	7.35291
$37$	−0.706319	−0.116118	−0.0580591	−	0.998313i	$-0.518491\pi$
$37$	−0.706319	−0.116118	−0.0580591	+	0.998313i	$0.518491\pi$
$38$	−3.71403	−0.602494
$39$	−10.8808	−1.74232
$40$	−0.0180706	−0.00285721
$41$	−1.84865	−0.288711	−0.144355	−	0.989526i	$-0.546111\pi$
$41$	−1.84865	−0.288711	−0.144355	+	0.989526i	$0.546111\pi$
$42$	19.2262	2.96667
$43$	12.8966	1.96671	0.983355	−	0.181696i	$-0.0581586\pi$
$43$	12.8966	1.96671	0.983355	+	0.181696i	$0.0581586\pi$
$44$	14.5326	2.19087
$45$	0.0186739	0.00278374
$46$	13.9964	2.06365
$47$	9.00519	1.31354	0.656771	−	0.754090i	$-0.271922\pi$
$47$	9.00519	1.31354	0.656771	+	0.754090i	$0.271922\pi$
$48$	40.8801	5.90054
$49$	−2.53079	−0.361541
$50$	13.3442	1.88715
$51$	−13.1730	−1.84459
$52$	−16.3569	−2.26830
$53$	7.04062	0.967104	0.483552	−	0.875316i	$-0.339346\pi$
$53$	7.04062	0.967104	0.483552	+	0.875316i	$0.339346\pi$
$54$	−51.0400	−6.94566
$55$	0.00615130	0.000829441 0
$56$	17.6183	2.35435
$57$	4.74220	0.628120
$58$	16.8098	2.20724
$59$	−7.71425	−1.00431	−0.502155	−	0.864778i	$-0.667459\pi$
$59$	−7.71425	−1.00431	−0.502155	+	0.864778i	$0.667459\pi$
$60$	0.0378509	0.00488653
$61$	−7.49774	−0.959987	−0.479993	−	0.877272i	$-0.659361\pi$
$61$	−7.49774	−0.959987	−0.479993	+	0.877272i	$0.659361\pi$
$62$	22.2923	2.83112
$63$	−18.2066	−2.29381
$64$	16.9706	2.12133
$65$	−0.00692350	−0.000858755 0
$66$	−25.8002	−3.17579
$67$	1.32225	0.161539	0.0807695	−	0.996733i	$-0.474262\pi$
$67$	1.32225	0.161539	0.0807695	+	0.996733i	$0.474262\pi$
$68$	−19.8028	−2.40144
$69$	−17.8710	−2.15142
$70$	0.0122337	0.00146221
$71$	14.1025	1.67366	0.836832	−	0.547459i	$-0.184405\pi$
$71$	14.1025	1.67366	0.836832	+	0.547459i	$0.184405\pi$
$72$	−71.7733	−8.45857
$73$	−0.651775	−0.0762845	−0.0381422	−	0.999272i	$-0.512144\pi$
$73$	−0.651775	−0.0762845	−0.0381422	+	0.999272i	$0.512144\pi$
$74$	1.88505	0.219133
$75$	−17.0383	−1.96741
$76$	7.12887	0.817737
$77$	−5.99736	−0.683463
$78$	29.0391	3.28803
$79$	−16.5080	−1.85730	−0.928648	−	0.370961i	$-0.879028\pi$
$79$	−16.5080	−1.85730	−0.928648	+	0.370961i	$0.879028\pi$
$80$	0.0260122	0.00290825
$81$	39.3331	4.37035
$82$	4.93374	0.544841
$83$	−1.92554	−0.211356	−0.105678	−	0.994400i	$-0.533701\pi$
$83$	−1.92554	−0.211356	−0.105678	+	0.994400i	$0.533701\pi$
$84$	−36.9037	−4.02652
$85$	−0.00838205	−0.000909161 0
$86$	−34.4188	−3.71148
$87$	−21.4634	−2.30112
$88$	−23.6426	−2.52031
$89$	5.54234	0.587487	0.293743	−	0.955884i	$-0.405099\pi$
$89$	5.54234	0.587487	0.293743	+	0.955884i	$0.405099\pi$
$90$	−0.0498376	−0.00525334
$91$	6.75024	0.707617
$92$	−26.8652	−2.80089
$93$	−28.4636	−2.95154
$94$	−24.0334	−2.47885
$95$	0.00301748	0.000309587 0
$96$	−52.3039	−5.33824
$97$	0.833321	0.0846109	0.0423055	−	0.999105i	$-0.486530\pi$
$97$	0.833321	0.0846109	0.0423055	+	0.999105i	$0.486530\pi$
$98$	6.75426	0.682284
$99$	24.4319	2.45550
$100$	−25.6134	−2.56134
$101$	−17.2969	−1.72111	−0.860554	−	0.509360i	$-0.829882\pi$
$101$	−17.2969	−1.72111	−0.860554	+	0.509360i	$0.829882\pi$
$102$	35.1566	3.48102
$103$	4.13036	0.406976	0.203488	−	0.979077i	$-0.434772\pi$
$103$	4.13036	0.406976	0.203488	+	0.979077i	$0.434772\pi$
$104$	26.6105	2.60938
$105$	−0.0156205	−0.00152440
$106$	−18.7903	−1.82507
$107$	−11.8828	−1.14876	−0.574378	−	0.818591i	$-0.694756\pi$
$107$	−11.8828	−1.14876	−0.574378	+	0.818591i	$0.694756\pi$
$108$	97.9684	9.42702
$109$	−3.20741	−0.307214	−0.153607	−	0.988132i	$-0.549089\pi$
$109$	−3.20741	−0.307214	−0.153607	+	0.988132i	$0.549089\pi$
$110$	−0.0164168	−0.00156528
$111$	−2.40690	−0.228453
$112$	−25.3613	−2.39641
$113$	−13.4064	−1.26117	−0.630585	−	0.776120i	$-0.717185\pi$
$113$	−13.4064	−1.26117	−0.630585	+	0.776120i	$0.717185\pi$
$114$	−12.6562	−1.18536
$115$	−0.0113714	−0.00106039
$116$	−32.2656	−2.99578
$117$	−27.4990	−2.54228
$118$	20.5881	1.89529
$119$	8.17228	0.749152
$120$	−0.0615785	−0.00562132
$121$	−2.95197	−0.268361
$122$	20.0102	1.81164
$123$	−6.29958	−0.568014
$124$	−42.7888	−3.84255
$125$	−0.0216831	−0.00193940
$126$	48.5904	4.32878
$127$	−1.42297	−0.126269	−0.0631343	−	0.998005i	$-0.520110\pi$
$127$	−1.42297	−0.126269	−0.0631343	+	0.998005i	$0.520110\pi$
$128$	−14.5940	−1.28994
$129$	43.9472	3.86934
$130$	0.0184777	0.00162060
$131$	−3.97016	−0.346875	−0.173437	−	0.984845i	$-0.555487\pi$
$131$	−3.97016	−0.346875	−0.173437	+	0.984845i	$0.555487\pi$
$132$	49.5221	4.31035
$133$	−2.94197	−0.255101
$134$	−3.52888	−0.304849
$135$	0.0414678	0.00356898
$136$	32.2165	2.76254
$137$	1.03166	0.0881403	0.0440702	−	0.999028i	$-0.485967\pi$
$137$	1.03166	0.0881403	0.0440702	+	0.999028i	$0.485967\pi$
$138$	47.6949	4.06006
$139$	−5.46290	−0.463357	−0.231678	−	0.972792i	$-0.574422\pi$
$139$	−5.46290	−0.463357	−0.231678	+	0.972792i	$0.574422\pi$
$140$	−0.0234820	−0.00198459
$141$	30.6867	2.58428
$142$	−37.6374	−3.15846
$143$	−9.05834	−0.757496
$144$	103.316	8.60968
$145$	−0.0136573	−0.00113417
$146$	1.73948	0.143960
$147$	−8.62409	−0.711303
$148$	−3.61825	−0.297418
$149$	12.5042	1.02439	0.512193	−	0.858870i	$-0.328833\pi$
$149$	12.5042	1.02439	0.512193	+	0.858870i	$0.328833\pi$
$150$	45.4724	3.71281
$151$	−6.69915	−0.545169	−0.272585	−	0.962132i	$-0.587878\pi$
$151$	−6.69915	−0.545169	−0.272585	+	0.962132i	$0.587878\pi$
$152$	−11.5977	−0.940700
$153$	−33.2921	−2.69151
$154$	16.0060	1.28980
$155$	−0.0181115	−0.00145475
$156$	−55.7389	−4.46268
$157$	−22.3330	−1.78237	−0.891183	−	0.453643i	$-0.850124\pi$
$157$	−22.3330	−1.78237	−0.891183	+	0.453643i	$0.850124\pi$
$158$	44.0572	3.50500
$159$	23.9921	1.90270
$160$	−0.0332812	−0.00263111
$161$	11.0869	0.873767
$162$	−104.974	−8.24751
$163$	14.7106	1.15222	0.576112	−	0.817371i	$-0.304569\pi$
$163$	14.7106	1.15222	0.576112	+	0.817371i	$0.304569\pi$
$164$	−9.47005	−0.739486
$165$	0.0209616	0.00163186
$166$	5.13896	0.398861
$167$	14.2683	1.10412	0.552059	−	0.833805i	$-0.313842\pi$
$167$	14.2683	1.10412	0.552059	+	0.833805i	$0.313842\pi$
$168$	60.0374	4.63199
$169$	−2.80453	−0.215733
$170$	0.0223703	0.00171572
$171$	11.9849	0.916512
$172$	66.0651	5.03742
$173$	9.73219	0.739925	0.369962	−	0.929047i	$-0.379371\pi$
$173$	9.73219	0.739925	0.369962	+	0.929047i	$0.379371\pi$
$174$	57.2823	4.34256
$175$	10.5702	0.799035
$176$	34.0330	2.56533
$177$	−26.2876	−1.97590
$178$	−14.7916	−1.10868
$179$	−8.05957	−0.602400	−0.301200	−	0.953561i	$-0.597387\pi$
$179$	−8.05957	−0.602400	−0.301200	+	0.953561i	$0.597387\pi$
$180$	0.0956605	0.00713011
$181$	−4.86170	−0.361368	−0.180684	−	0.983541i	$-0.557831\pi$
$181$	−4.86170	−0.361368	−0.180684	+	0.983541i	$0.557831\pi$
$182$	−18.0153	−1.33538
$183$	−25.5498	−1.88869
$184$	43.7062	3.22206
$185$	−0.00153152	−0.000112600 0
$186$	75.9647	5.57000
$187$	−10.9666	−0.801959
$188$	46.1307	3.36443
$189$	−40.4300	−2.94085
$190$	−0.00805317	−0.000584238 0
$191$	−23.5065	−1.70087	−0.850437	−	0.526077i	$-0.823662\pi$
$191$	−23.5065	−1.70087	−0.850437	+	0.526077i	$0.823662\pi$
$192$	57.8301	4.17353
$193$	−2.43521	−0.175290	−0.0876452	−	0.996152i	$-0.527934\pi$
$193$	−2.43521	−0.175290	−0.0876452	+	0.996152i	$0.527934\pi$
$194$	−2.22400	−0.159674
$195$	−0.0235930	−0.00168953
$196$	−12.9644	−0.926031
$197$	−17.0869	−1.21739	−0.608697	−	0.793403i	$-0.708307\pi$
$197$	−17.0869	−1.21739	−0.608697	+	0.793403i	$0.708307\pi$
$198$	−65.2048	−4.63391
$199$	−9.15215	−0.648779	−0.324390	−	0.945924i	$-0.605159\pi$
$199$	−9.15215	−0.648779	−0.324390	+	0.945924i	$0.605159\pi$
$200$	41.6696	2.94649
$201$	4.50580	0.317815
$202$	46.1626	3.24799
$203$	13.3155	0.934565
$204$	−67.4812	−4.72463
$205$	−0.00400845	−0.000279962 0
$206$	−11.0232	−0.768026
$207$	−45.1654	−3.13922
$208$	−38.3053	−2.65600
$209$	3.94791	0.273083
$210$	0.0416885	0.00287678
$211$	−0.511628	−0.0352219	−0.0176110	−	0.999845i	$-0.505606\pi$
$211$	−0.511628	−0.0352219	−0.0176110	+	0.999845i	$0.505606\pi$
$212$	36.0669	2.47708
$213$	48.0568	3.29280
$214$	31.7133	2.16788
$215$	0.0279638	0.00190712
$216$	−159.382	−10.8446
$217$	17.6583	1.19872
$218$	8.56005	0.579759
$219$	−2.22103	−0.150083
$220$	0.0315112	0.00212448
$221$	12.3433	0.830301
$222$	6.42362	0.431125
$223$	−6.93601	−0.464470	−0.232235	−	0.972660i	$-0.574604\pi$
$223$	−6.93601	−0.464470	−0.232235	+	0.972660i	$0.574604\pi$
$224$	32.4483	2.16804
$225$	−43.0609	−2.87072
$226$	35.7795	2.38002
$227$	12.5395	0.832274	0.416137	−	0.909302i	$-0.363384\pi$
$227$	12.5395	0.832274	0.416137	+	0.909302i	$0.363384\pi$
$228$	24.2928	1.60883
$229$	−24.2139	−1.60010	−0.800048	−	0.599936i	$-0.795193\pi$
$229$	−24.2139	−1.60010	−0.800048	+	0.599936i	$0.795193\pi$
$230$	0.0303485	0.00200112
$231$	−20.4370	−1.34466
$232$	52.4918	3.44626
$233$	−13.3498	−0.874572	−0.437286	−	0.899322i	$-0.644060\pi$
$233$	−13.3498	−0.874572	−0.437286	+	0.899322i	$0.644060\pi$
$234$	73.3903	4.79767
$235$	0.0195261	0.00127374
$236$	−39.5177	−2.57238
$237$	−56.2538	−3.65408
$238$	−21.8105	−1.41376
$239$	−5.66065	−0.366157	−0.183078	−	0.983098i	$-0.558606\pi$
$239$	−5.66065	−0.366157	−0.183078	+	0.983098i	$0.558606\pi$
$240$	0.0886409	0.00572175
$241$	−4.27688	−0.275498	−0.137749	−	0.990467i	$-0.543987\pi$
$241$	−4.27688	−0.275498	−0.137749	+	0.990467i	$0.543987\pi$
$242$	7.87832	0.506438
$243$	76.6608	4.91779
$244$	−38.4085	−2.45885
$245$	−0.00548755	−0.000350586 0
$246$	16.8125	1.07193
$247$	−4.44352	−0.282734
$248$	69.6118	4.42035
$249$	−6.56161	−0.415825
$250$	0.0578687	0.00365994
$251$	6.18888	0.390638	0.195319	−	0.980740i	$-0.437426\pi$
$251$	6.18888	0.390638	0.195319	+	0.980740i	$0.437426\pi$
$252$	−93.2666	−5.87524
$253$	−14.8778	−0.935357
$254$	3.79768	0.238288
$255$	−0.0285632	−0.00178870
$256$	5.00775	0.312984
$257$	18.6879	1.16572	0.582859	−	0.812573i	$-0.301934\pi$
$257$	18.6879	1.16572	0.582859	+	0.812573i	$0.301934\pi$
$258$	−117.288	−7.30203
$259$	1.49319	0.0927826
$260$	−0.0354669	−0.00219956
$261$	−54.2444	−3.35765
$262$	10.5957	0.654605
$263$	−0.0946907	−0.00583888	−0.00291944	−	0.999996i	$-0.500929\pi$
$263$	−0.0946907	−0.00583888	−0.00291944	+	0.999996i	$0.500929\pi$
$264$	−80.5659	−4.95849
$265$	0.0152663	0.000937800 0
$266$	7.85164	0.481415
$267$	18.8864	1.15583
$268$	6.77349	0.413757
$269$	26.6387	1.62419	0.812095	−	0.583525i	$-0.198327\pi$
$269$	26.6387	1.62419	0.812095	+	0.583525i	$0.198327\pi$
$270$	−0.110671	−0.00673520
$271$	12.4097	0.753836	0.376918	−	0.926247i	$-0.376984\pi$
$271$	12.4097	0.753836	0.376918	+	0.926247i	$0.376984\pi$
$272$	−46.3749	−2.81189
$273$	23.0026	1.39218
$274$	−2.75332	−0.166334
$275$	−14.1845	−0.855358
$276$	−91.5477	−5.51052
$277$	−31.5105	−1.89328	−0.946642	−	0.322288i	$-0.895548\pi$
$277$	−31.5105	−1.89328	−0.946642	+	0.322288i	$0.895548\pi$
$278$	14.5796	0.874425
$279$	−71.9360	−4.30669
$280$	0.0382021	0.00228301
$281$	−11.6172	−0.693025	−0.346512	−	0.938045i	$-0.612634\pi$
$281$	−11.6172	−0.693025	−0.346512	+	0.938045i	$0.612634\pi$
$282$	−81.8976	−4.87693
$283$	24.4844	1.45544	0.727722	−	0.685872i	$-0.240579\pi$
$283$	24.4844	1.45544	0.727722	+	0.685872i	$0.240579\pi$
$284$	72.2429	4.28683
$285$	0.0102826	0.000609087 0
$286$	24.1752	1.42951
$287$	3.90814	0.230690
$288$	−132.187	−7.78922
$289$	−2.05637	−0.120963
$290$	0.0364490	0.00214036
$291$	2.83968	0.166465
$292$	−3.33884	−0.195391
$293$	11.0898	0.647874	0.323937	−	0.946079i	$-0.394993\pi$
$293$	11.0898	0.647874	0.323937	+	0.946079i	$0.394993\pi$
$294$	23.0163	1.34234
$295$	−0.0167269	−0.000973879 0
$296$	5.88641	0.342141
$297$	54.2542	3.14815
$298$	−33.3717	−1.93317
$299$	16.7454	0.968414
$300$	−87.2819	−5.03922
$301$	−27.2640	−1.57147
$302$	17.8789	1.02882
$303$	−58.9421	−3.38613
$304$	16.6947	0.957506
$305$	−0.0162574	−0.000930899 0
$306$	88.8512	5.07928
$307$	−24.4901	−1.39772	−0.698861	−	0.715257i	$-0.746310\pi$
$307$	−24.4901	−1.39772	−0.698861	+	0.715257i	$0.746310\pi$
$308$	−30.7226	−1.75058
$309$	14.0749	0.800692
$310$	0.0483367	0.00274534
$311$	−33.3393	−1.89050	−0.945248	−	0.326352i	$-0.894180\pi$
$311$	−33.3393	−1.89050	−0.945248	+	0.326352i	$0.894180\pi$
$312$	90.6798	5.13373
$313$	−14.1893	−0.802028	−0.401014	−	0.916072i	$-0.631342\pi$
$313$	−14.1893	−0.802028	−0.401014	+	0.916072i	$0.631342\pi$
$314$	59.6031	3.36360
$315$	−0.0394776	−0.00222431
$316$	−84.5653	−4.75717
$317$	5.18463	0.291198	0.145599	−	0.989344i	$-0.453489\pi$
$317$	5.18463	0.291198	0.145599	+	0.989344i	$0.453489\pi$
$318$	−64.0309	−3.59068
$319$	−17.8684	−1.00044
$320$	0.0367976	0.00205705
$321$	−40.4927	−2.26008
$322$	−29.5890	−1.64893
$323$	−5.37961	−0.299330
$324$	201.491	11.1940
$325$	15.9652	0.885588
$326$	−39.2602	−2.17442
$327$	−10.9298	−0.604418
$328$	15.4065	0.850683
$329$	−19.0374	−1.04957
$330$	−0.0559430	−0.00307956
$331$	34.0493	1.87152	0.935758	−	0.352642i	$-0.114717\pi$
$331$	34.0493	1.87152	0.935758	+	0.352642i	$0.114717\pi$
$332$	−9.86395	−0.541355
$333$	−6.08295	−0.333344
$334$	−38.0799	−2.08364
$335$	0.00286706	0.000156644 0
$336$	−86.4227	−4.71474
$337$	−15.4219	−0.840087	−0.420043	−	0.907504i	$-0.637985\pi$
$337$	−15.4219	−0.840087	−0.420043	+	0.907504i	$0.637985\pi$
$338$	7.48482	0.407120
$339$	−45.6846	−2.48125
$340$	−0.0429386	−0.00232867
$341$	−23.6961	−1.28322
$342$	−31.9859	−1.72960
$343$	20.1486	1.08792
$344$	−107.479	−5.79489
$345$	−0.0387500	−0.00208623
$346$	−25.9736	−1.39635
$347$	32.5767	1.74881	0.874404	−	0.485199i	$-0.161253\pi$
$347$	32.5767	1.74881	0.874404	+	0.485199i	$0.161253\pi$
$348$	−109.950	−5.89395
$349$	10.4213	0.557838	0.278919	−	0.960315i	$-0.410024\pi$
$349$	10.4213	0.557838	0.278919	+	0.960315i	$0.410024\pi$
$350$	−28.2102	−1.50790
$351$	−61.0650	−3.25941
$352$	−43.5433	−2.32087
$353$	−0.258979	−0.0137840	−0.00689202	−	0.999976i	$-0.502194\pi$
$353$	−0.258979	−0.0137840	−0.00689202	+	0.999976i	$0.502194\pi$
$354$	70.1573	3.72882
$355$	0.0305787	0.00162295
$356$	28.3917	1.50475
$357$	27.8484	1.47389
$358$	21.5097	1.13682
$359$	13.9038	0.733813	0.366906	−	0.930258i	$-0.380417\pi$
$359$	13.9038	0.733813	0.366906	+	0.930258i	$0.380417\pi$
$360$	−0.155627	−0.00820226
$361$	−17.0634	−0.898072
$362$	12.9751	0.681956
$363$	−10.0593	−0.527978
$364$	34.5793	1.81245
$365$	−0.00141325	−7.39730e−5 0
$366$	68.1882	3.56425
$367$	18.4139	0.961196	0.480598	−	0.876941i	$-0.340420\pi$
$367$	18.4139	0.961196	0.480598	+	0.876941i	$0.340420\pi$
$368$	−62.9142	−3.27963
$369$	−15.9209	−0.828809
$370$	0.00408738	0.000212493 0
$371$	−14.8842	−0.772751
$372$	−145.810	−7.55990
$373$	−27.8928	−1.44423	−0.722116	−	0.691772i	$-0.756831\pi$
$373$	−27.8928	−1.44423	−0.722116	+	0.691772i	$0.756831\pi$
$374$	29.2681	1.51342
$375$	−0.0738888	−0.00381560
$376$	−75.0486	−3.87034
$377$	20.1116	1.03580
$378$	107.901	5.54983
$379$	−2.98561	−0.153360	−0.0766801	−	0.997056i	$-0.524432\pi$
$379$	−2.98561	−0.153360	−0.0766801	+	0.997056i	$0.524432\pi$
$380$	0.0154576	0.000792959 0
$381$	−4.84902	−0.248423
$382$	62.7351	3.20981
$383$	7.61548	0.389133	0.194566	−	0.980889i	$-0.437670\pi$
$383$	7.61548	0.389133	0.194566	+	0.980889i	$0.437670\pi$
$384$	−49.7314	−2.53785
$385$	−0.0130042	−0.000662753 0
$386$	6.49918	0.330799
$387$	111.068	5.64589
$388$	4.26884	0.216717
$389$	16.0694	0.814752	0.407376	−	0.913261i	$-0.366444\pi$
$389$	16.0694	0.814752	0.407376	+	0.913261i	$0.366444\pi$
$390$	0.0629658	0.00318840
$391$	20.2731	1.02526
$392$	21.0914	1.06528
$393$	−13.5290	−0.682447
$394$	45.6022	2.29741
$395$	−0.0357945	−0.00180102
$396$	125.157	6.28938
$397$	18.0702	0.906916	0.453458	−	0.891278i	$-0.350190\pi$
$397$	18.0702	0.906916	0.453458	+	0.891278i	$0.350190\pi$
$398$	24.4256	1.22434
$399$	−10.0253	−0.501890
$400$	−59.9825	−2.99913
$401$	−25.9841	−1.29758	−0.648792	−	0.760966i	$-0.724725\pi$
$401$	−25.9841	−1.29758	−0.648792	+	0.760966i	$0.724725\pi$
$402$	−12.0252	−0.599764
$403$	26.6708	1.32857
$404$	−88.6066	−4.40834
$405$	0.0852865	0.00423792
$406$	−35.5369	−1.76367
$407$	−2.00376	−0.0993227
$408$	109.783	5.43507
$409$	3.48188	0.172168	0.0860839	−	0.996288i	$-0.472565\pi$
$409$	3.48188	0.172168	0.0860839	+	0.996288i	$0.472565\pi$
$410$	0.0106979	0.000528332 0
$411$	3.51554	0.173409
$412$	21.1585	1.04241
$413$	16.3083	0.802480
$414$	120.539	5.92418
$415$	−0.00417518	−0.000204952 0
$416$	49.0095	2.40289
$417$	−18.6157	−0.911616
$418$	−10.5363	−0.515349
$419$	16.7056	0.816120	0.408060	−	0.912955i	$-0.366205\pi$
$419$	16.7056	0.816120	0.408060	+	0.912955i	$0.366205\pi$
$420$	−0.0800188	−0.00390452
$421$	−10.4007	−0.506899	−0.253450	−	0.967349i	$-0.581565\pi$
$421$	−10.4007	−0.506899	−0.253450	+	0.967349i	$0.581565\pi$
$422$	1.36545	0.0664691
$423$	77.5543	3.77082
$424$	−58.6761	−2.84956
$425$	19.3285	0.937569
$426$	−128.256	−6.21400
$427$	15.8506	0.767064
$428$	−60.8719	−2.94235
$429$	−30.8678	−1.49031
$430$	−0.0746308	−0.00359902
$431$	−24.0143	−1.15673	−0.578363	−	0.815779i	$-0.696308\pi$
$431$	−24.0143	−1.15673	−0.578363	+	0.815779i	$0.696308\pi$
$432$	229.427	11.0383
$433$	−22.5272	−1.08259	−0.541294	−	0.840833i	$-0.682065\pi$
$433$	−22.5272	−1.08259	−0.541294	+	0.840833i	$0.682065\pi$
$434$	−47.1270	−2.26217
$435$	−0.0465394	−0.00223139
$436$	−16.4305	−0.786880
$437$	−7.29821	−0.349121
$438$	5.92757	0.283230
$439$	−17.2961	−0.825495	−0.412748	−	0.910845i	$-0.635431\pi$
$439$	−17.2961	−0.825495	−0.412748	+	0.910845i	$0.635431\pi$
$440$	−0.0512645	−0.00244394
$441$	−21.7956	−1.03789
$442$	−32.9423	−1.56690
$443$	29.0188	1.37873	0.689363	−	0.724416i	$-0.257890\pi$
$443$	29.0188	1.37873	0.689363	+	0.724416i	$0.257890\pi$
$444$	−12.3298	−0.585146
$445$	0.0120175	0.000569686 0
$446$	18.5111	0.876525
$447$	42.6102	2.01540
$448$	−35.8767	−1.69502
$449$	8.62142	0.406870	0.203435	−	0.979088i	$-0.434789\pi$
$449$	8.62142	0.406870	0.203435	+	0.979088i	$0.434789\pi$
$450$	114.922	5.41749
$451$	−5.24444	−0.246951
$452$	−68.6768	−3.23029
$453$	−22.8285	−1.07257
$454$	−33.4658	−1.57063
$455$	0.0146366	0.000686176 0
$456$	−39.5212	−1.85075
$457$	−3.32094	−0.155347	−0.0776735	−	0.996979i	$-0.524749\pi$
$457$	−3.32094	−0.155347	−0.0776735	+	0.996979i	$0.524749\pi$
$458$	64.6228	3.01962
$459$	−73.9293	−3.45073
$460$	−0.0582522	−0.00271602
$461$	−32.8343	−1.52924	−0.764622	−	0.644479i	$-0.777074\pi$
$461$	−32.8343	−1.52924	−0.764622	+	0.644479i	$0.777074\pi$
$462$	54.5430	2.53757
$463$	18.9701	0.881614	0.440807	−	0.897602i	$-0.354692\pi$
$463$	18.9701	0.881614	0.440807	+	0.897602i	$0.354692\pi$
$464$	−75.5609	−3.50783
$465$	−0.0617180	−0.00286210
$466$	35.6283	1.65045
$467$	−8.43863	−0.390493	−0.195247	−	0.980754i	$-0.562551\pi$
$467$	−8.43863	−0.390493	−0.195247	+	0.980754i	$0.562551\pi$
$468$	−140.869	−6.51166
$469$	−2.79531	−0.129076
$470$	−0.0521119	−0.00240374
$471$	−76.1034	−3.50666
$472$	64.2900	2.95919
$473$	36.5864	1.68224
$474$	150.132	6.89580
$475$	−6.95813	−0.319261
$476$	41.8640	1.91883
$477$	60.6351	2.77629
$478$	15.1073	0.690993
$479$	23.5285	1.07505	0.537523	−	0.843249i	$-0.319360\pi$
$479$	23.5285	1.07505	0.537523	+	0.843249i	$0.319360\pi$
$480$	−0.113411	−0.00517649
$481$	2.25530	0.102833
$482$	11.4143	0.519906
$483$	37.7803	1.71906
$484$	−15.1220	−0.687364
$485$	0.00180690	8.20471e−5 0
$486$	−204.595	−9.28062
$487$	−5.39103	−0.244291	−0.122145	−	0.992512i	$-0.538977\pi$
$487$	−5.39103	−0.244291	−0.122145	+	0.992512i	$0.538977\pi$
$488$	62.4856	2.82859
$489$	50.1288	2.26690
$490$	0.0146454	0.000661610 0
$491$	23.5614	1.06331	0.531656	−	0.846960i	$-0.321570\pi$
$491$	23.5614	1.06331	0.531656	+	0.846960i	$0.321570\pi$
$492$	−32.2708	−1.45488
$493$	24.3484	1.09660
$494$	11.8590	0.533562
$495$	0.0529761	0.00238110
$496$	−100.205	−4.49932
$497$	−29.8135	−1.33732
$498$	17.5119	0.784725
$499$	−13.7467	−0.615387	−0.307694	−	0.951485i	$-0.599557\pi$
$499$	−13.7467	−0.615387	−0.307694	+	0.951485i	$0.599557\pi$
$500$	−0.111076	−0.00496746
$501$	48.6217	2.17226
$502$	−16.5171	−0.737194
$503$	41.0608	1.83081	0.915405	−	0.402533i	$-0.131870\pi$
$503$	41.0608	1.83081	0.915405	+	0.402533i	$0.131870\pi$
$504$	151.732	6.75870
$505$	−0.0375051	−0.00166896
$506$	39.7063	1.76516
$507$	−9.55689	−0.424436
$508$	−7.28945	−0.323417
$509$	−4.84880	−0.214919	−0.107460	−	0.994209i	$-0.534272\pi$
$509$	−4.84880	−0.214919	−0.107460	+	0.994209i	$0.534272\pi$
$510$	0.0762305	0.00337554
$511$	1.37789	0.0609540
$512$	15.8231	0.699290
$513$	26.6141	1.17504
$514$	−49.8749	−2.19989
$515$	0.00895591	0.000394645 0
$516$	225.128	9.91069
$517$	25.5469	1.12355
$518$	−3.98509	−0.175095
$519$	33.1641	1.45574
$520$	0.0577000	0.00253031
$521$	−0.777543	−0.0340648	−0.0170324	−	0.999855i	$-0.505422\pi$
$521$	−0.777543	−0.0340648	−0.0170324	+	0.999855i	$0.505422\pi$
$522$	144.769	6.33639
$523$	5.67212	0.248024	0.124012	−	0.992281i	$-0.460424\pi$
$523$	5.67212	0.248024	0.124012	+	0.992281i	$0.460424\pi$
$524$	−20.3379	−0.888465
$525$	36.0198	1.57204
$526$	0.252714	0.0110189
$527$	32.2895	1.40655
$528$	115.973	5.04708
$529$	4.50338	0.195799
$530$	−0.0407432	−0.00176977
$531$	−66.4366	−2.88310
$532$	−15.0708	−0.653401
$533$	5.90280	0.255679
$534$	−50.4048	−2.18123
$535$	−0.0257657	−0.00111395
$536$	−11.0196	−0.475973
$537$	−27.4643	−1.18517
$538$	−71.0943	−3.06509
$539$	−7.17961	−0.309248
$540$	0.212426	0.00914137
$541$	13.1885	0.567017	0.283508	−	0.958970i	$-0.408502\pi$
$541$	13.1885	0.567017	0.283508	+	0.958970i	$0.408502\pi$
$542$	−33.1194	−1.42260
$543$	−16.5671	−0.710961
$544$	59.3342	2.54393
$545$	−0.00695467	−0.000297905 0
$546$	−61.3900	−2.62725
$547$	−33.5541	−1.43467	−0.717336	−	0.696728i	$-0.754639\pi$
$547$	−33.5541	−1.43467	−0.717336	+	0.696728i	$0.754639\pi$
$548$	5.28485	0.225757
$549$	−64.5719	−2.75586
$550$	37.8561	1.61419
$551$	−8.76526	−0.373413
$552$	148.936	6.33914
$553$	34.8988	1.48405
$554$	84.0964	3.57291
$555$	−0.00521891	−0.000221530 0
$556$	−27.9847	−1.18682
$557$	32.4058	1.37308	0.686538	−	0.727094i	$-0.259130\pi$
$557$	32.4058	1.37308	0.686538	+	0.727094i	$0.259130\pi$
$558$	191.985	8.12738
$559$	−41.1792	−1.74170
$560$	−0.0549911	−0.00232380
$561$	−37.3706	−1.57779
$562$	31.0044	1.30784
$563$	−12.4751	−0.525762	−0.262881	−	0.964828i	$-0.584673\pi$
$563$	−12.4751	−0.525762	−0.262881	+	0.964828i	$0.584673\pi$
$564$	157.198	6.61923
$565$	−0.0290693	−0.00122295
$566$	−65.3447	−2.74664
$567$	−83.1522	−3.49207
$568$	−117.530	−4.93143
$569$	−38.6774	−1.62144	−0.810720	−	0.585434i	$-0.800924\pi$
$569$	−38.6774	−1.62144	−0.810720	+	0.585434i	$0.800924\pi$
$570$	−0.0274425	−0.00114944
$571$	19.6940	0.824166	0.412083	−	0.911146i	$-0.364801\pi$
$571$	19.6940	0.824166	0.412083	+	0.911146i	$0.364801\pi$
$572$	−46.4030	−1.94021
$573$	−80.1024	−3.34633
$574$	−10.4302	−0.435347
$575$	26.2218	1.09353
$576$	146.154	6.08975
$577$	5.70094	0.237333	0.118667	−	0.992934i	$-0.462138\pi$
$577$	5.70094	0.237333	0.118667	+	0.992934i	$0.462138\pi$
$578$	5.48810	0.228275
$579$	−8.29838	−0.344869
$580$	−0.0699619	−0.00290501
$581$	4.07070	0.168881
$582$	−7.57863	−0.314144
$583$	19.9736	0.827221
$584$	5.43185	0.224771
$585$	−0.0596264	−0.00246525
$586$	−29.5969	−1.22264
$587$	0.610675	0.0252053	0.0126026	−	0.999921i	$-0.495988\pi$
$587$	0.610675	0.0252053	0.0126026	+	0.999921i	$0.495988\pi$
$588$	−44.1785	−1.82189
$589$	−11.6240	−0.478959
$590$	0.0446414	0.00183786
$591$	−58.2265	−2.39512
$592$	−8.47337	−0.348253
$593$	−5.32262	−0.218574	−0.109287	−	0.994010i	$-0.534857\pi$
$593$	−5.32262	−0.218574	−0.109287	+	0.994010i	$0.534857\pi$
$594$	−144.796	−5.94103
$595$	0.0177201	0.000726452 0
$596$	64.0552	2.62380
$597$	−31.1875	−1.27642
$598$	−44.6908	−1.82754
$599$	27.9551	1.14221	0.571107	−	0.820876i	$-0.306514\pi$
$599$	27.9551	1.14221	0.571107	+	0.820876i	$0.306514\pi$
$600$	141.996	5.79697
$601$	2.60744	0.106360	0.0531798	−	0.998585i	$-0.483064\pi$
$601$	2.60744	0.106360	0.0531798	+	0.998585i	$0.483064\pi$
$602$	72.7632	2.96561
$603$	11.3875	0.463735
$604$	−34.3176	−1.39636
$605$	−0.00640080	−0.000260229 0
$606$	157.307	6.39015
$607$	28.4774	1.15586	0.577930	−	0.816086i	$-0.303861\pi$
$607$	28.4774	1.15586	0.577930	+	0.816086i	$0.303861\pi$
$608$	−21.3599	−0.866259
$609$	45.3748	1.83868
$610$	0.0433884	0.00175675
$611$	−28.7539	−1.16326
$612$	−170.545	−6.89387
$613$	3.10121	0.125257	0.0626283	−	0.998037i	$-0.480052\pi$
$613$	3.10121	0.125257	0.0626283	+	0.998037i	$0.480052\pi$
$614$	65.3600	2.63771
$615$	−0.0136595	−0.000550803 0
$616$	49.9816	2.01382
$617$	−43.0611	−1.73357	−0.866787	−	0.498679i	$-0.833819\pi$
$617$	−43.0611	−1.73357	−0.866787	+	0.498679i	$0.833819\pi$
$618$	−37.5635	−1.51103
$619$	−0.862411	−0.0346632	−0.0173316	−	0.999850i	$-0.505517\pi$
$619$	−0.862411	−0.0346632	−0.0173316	+	0.999850i	$0.505517\pi$
$620$	−0.0927796	−0.00372612
$621$	−100.296	−4.02472
$622$	88.9770	3.56765
$623$	−11.7168	−0.469423
$624$	−130.532	−5.22545
$625$	24.9999	0.999997
$626$	37.8690	1.51355
$627$	13.4532	0.537268
$628$	−114.405	−4.56525
$629$	2.73042	0.108869
$630$	0.105359	0.00419761
$631$	−9.15032	−0.364269	−0.182134	−	0.983274i	$-0.558301\pi$
$631$	−9.15032	−0.364269	−0.182134	+	0.983274i	$0.558301\pi$
$632$	137.577	5.47250
$633$	−1.74346	−0.0692962
$634$	−13.8369	−0.549535
$635$	−0.00308545	−0.000122443 0
$636$	122.904	4.87345
$637$	8.08090	0.320177
$638$	47.6879	1.88798
$639$	121.454	4.80463
$640$	−0.0316443	−0.00125085
$641$	−3.14868	−0.124365	−0.0621827	−	0.998065i	$-0.519806\pi$
$641$	−3.14868	−0.124365	−0.0621827	+	0.998065i	$0.519806\pi$
$642$	108.068	4.26511
$643$	21.2704	0.838824	0.419412	−	0.907796i	$-0.362236\pi$
$643$	21.2704	0.838824	0.419412	+	0.907796i	$0.362236\pi$
$644$	56.7945	2.23802
$645$	0.0952913	0.00375209
$646$	14.3573	0.564881
$647$	6.36118	0.250084	0.125042	−	0.992151i	$-0.460093\pi$
$647$	6.36118	0.250084	0.125042	+	0.992151i	$0.460093\pi$
$648$	−327.800	−12.8772
$649$	−21.8846	−0.859046
$650$	−42.6084	−1.67124
$651$	60.1735	2.35838
$652$	75.3578	2.95124
$653$	20.9380	0.819366	0.409683	−	0.912228i	$-0.365639\pi$
$653$	20.9380	0.819366	0.409683	+	0.912228i	$0.365639\pi$
$654$	29.1698	1.14063
$655$	−0.00860856	−0.000336364 0
$656$	−22.1774	−0.865881
$657$	−5.61320	−0.218992
$658$	50.8077	1.98069
$659$	28.8666	1.12448	0.562242	−	0.826973i	$-0.309939\pi$
$659$	28.8666	1.12448	0.562242	+	0.826973i	$0.309939\pi$
$660$	0.107379	0.00417974
$661$	24.5925	0.956539	0.478270	−	0.878213i	$-0.341264\pi$
$661$	24.5925	0.956539	0.478270	+	0.878213i	$0.341264\pi$
$662$	−90.8719	−3.53184
$663$	42.0619	1.63355
$664$	16.0474	0.622758
$665$	−0.00637911	−0.000247371 0
$666$	16.2344	0.629070
$667$	33.0320	1.27900
$668$	73.0922	2.82802
$669$	−23.6356	−0.913806
$670$	−0.00765172	−0.000295612 0
$671$	−21.2704	−0.821133
$672$	110.573	4.26545
$673$	48.6393	1.87491	0.937454	−	0.348109i	$-0.113176\pi$
$673$	48.6393	1.87491	0.937454	+	0.348109i	$0.113176\pi$
$674$	41.1586	1.58537
$675$	−95.6221	−3.68050
$676$	−14.3667	−0.552565
$677$	−3.04752	−0.117126	−0.0585628	−	0.998284i	$-0.518652\pi$
$677$	−3.04752	−0.117126	−0.0585628	+	0.998284i	$0.518652\pi$
$678$	121.925	4.68249
$679$	−1.76168	−0.0676072
$680$	0.0698554	0.00267883
$681$	42.7303	1.63743
$682$	63.2411	2.42163
$683$	−44.2366	−1.69267	−0.846334	−	0.532653i	$-0.821195\pi$
$683$	−44.2366	−1.69267	−0.846334	+	0.532653i	$0.821195\pi$
$684$	61.3951	2.34750
$685$	0.00223695	8.54696e−5 0
$686$	−53.7732	−2.05307
$687$	−82.5127	−3.14806
$688$	154.714	5.89842
$689$	−22.4810	−0.856456
$690$	0.103417	0.00393704
$691$	−17.5920	−0.669232	−0.334616	−	0.942355i	$-0.608607\pi$
$691$	−17.5920	−0.669232	−0.334616	+	0.942355i	$0.608607\pi$
$692$	49.8549	1.89520
$693$	−51.6504	−1.96203
$694$	−86.9418	−3.30026
$695$	−0.0118453	−0.000449317 0
$696$	178.875	6.78022
$697$	7.14632	0.270686
$698$	−27.8127	−1.05272
$699$	−45.4915	−1.72065
$700$	54.1480	2.04660
$701$	49.0384	1.85215	0.926077	−	0.377334i	$-0.123159\pi$
$701$	49.0384	1.85215	0.926077	+	0.377334i	$0.123159\pi$
$702$	162.972	6.15100
$703$	−0.982933	−0.0370720
$704$	48.1440	1.81449
$705$	0.0665383	0.00250598
$706$	0.691171	0.0260126
$707$	36.5665	1.37523
$708$	−134.663	−5.06095
$709$	−16.1023	−0.604736	−0.302368	−	0.953191i	$-0.597777\pi$
$709$	−16.1023	−0.604736	−0.302368	+	0.953191i	$0.597777\pi$
$710$	−0.0816096	−0.00306276
$711$	−142.170	−5.33179
$712$	−46.1895	−1.73102
$713$	43.8052	1.64052
$714$	−74.3228	−2.78146
$715$	−0.0196413	−0.000734543 0
$716$	−41.2866	−1.54295
$717$	−19.2896	−0.720383
$718$	−37.1069	−1.38482
$719$	34.3536	1.28117	0.640586	−	0.767886i	$-0.278691\pi$
$719$	34.3536	1.28117	0.640586	+	0.767886i	$0.278691\pi$
$720$	0.224022	0.00834880
$721$	−8.73178	−0.325189
$722$	45.5393	1.69480
$723$	−14.5742	−0.542019
$724$	−24.9050	−0.925586
$725$	31.4928	1.16961
$726$	26.8467	0.996374
$727$	−19.3175	−0.716445	−0.358223	−	0.933636i	$-0.616617\pi$
$727$	−19.3175	−0.716445	−0.358223	+	0.933636i	$0.616617\pi$
$728$	−56.2560	−2.08499
$729$	143.235	5.30500
$730$	0.00377174	0.000139598 0
$731$	−49.8543	−1.84393
$732$	−130.883	−4.83759
$733$	−46.2606	−1.70867	−0.854337	−	0.519719i	$-0.826037\pi$
$733$	−46.2606	−1.70867	−0.854337	+	0.519719i	$0.826037\pi$
$734$	−49.1436	−1.81392
$735$	−0.0186997	−0.000689750 0
$736$	80.4952	2.96709
$737$	3.75111	0.138174
$738$	42.4903	1.56409
$739$	33.7912	1.24303	0.621515	−	0.783402i	$-0.286518\pi$
$739$	33.7912	1.24303	0.621515	+	0.783402i	$0.286518\pi$
$740$	−0.00784550	−0.000288406 0
$741$	−15.1420	−0.556256
$742$	39.7236	1.45830
$743$	48.2788	1.77118	0.885588	−	0.464471i	$-0.153756\pi$
$743$	48.2788	1.77118	0.885588	+	0.464471i	$0.153756\pi$
$744$	237.214	8.69667
$745$	0.0271131	0.000993347 0
$746$	74.4412	2.72549
$747$	−16.5831	−0.606745
$748$	−56.1785	−2.05409
$749$	25.1209	0.917897
$750$	0.197197	0.00720062
$751$	−1.99297	−0.0727245	−0.0363622	−	0.999339i	$-0.511577\pi$
$751$	−1.99297	−0.0727245	−0.0363622	+	0.999339i	$0.511577\pi$
$752$	108.031	3.93948
$753$	21.0896	0.768548
$754$	−53.6744	−1.95471
$755$	−0.0145259	−0.000528650 0
$756$	−207.110	−7.53253
$757$	−23.7421	−0.862922	−0.431461	−	0.902132i	$-0.642002\pi$
$757$	−23.7421	−0.862922	−0.431461	+	0.902132i	$0.642002\pi$
$758$	7.96809	0.289414
$759$	−50.6985	−1.84024
$760$	−0.0251475	−0.000912196 0
$761$	−29.4561	−1.06778	−0.533892	−	0.845553i	$-0.679271\pi$
$761$	−29.4561	−1.06778	−0.533892	+	0.845553i	$0.679271\pi$
$762$	12.9412	0.468812
$763$	6.78062	0.245475
$764$	−120.417	−4.35652
$765$	−0.0721877	−0.00260995
$766$	−20.3245	−0.734353
$767$	24.6319	0.889406
$768$	17.0647	0.615770
$769$	−33.7743	−1.21793	−0.608966	−	0.793196i	$-0.708416\pi$
$769$	−33.7743	−1.21793	−0.608966	+	0.793196i	$0.708416\pi$
$770$	0.0347060	0.00125072
$771$	63.6820	2.29345
$772$	−12.4748	−0.448978
$773$	−24.6048	−0.884974	−0.442487	−	0.896775i	$-0.645904\pi$
$773$	−24.6048	−0.884974	−0.442487	+	0.896775i	$0.645904\pi$
$774$	−296.421	−10.6546
$775$	41.7640	1.50021
$776$	−6.94484	−0.249305
$777$	5.08831	0.182542
$778$	−42.8866	−1.53756
$779$	−2.57263	−0.0921741
$780$	−0.120859	−0.00432746
$781$	40.0076	1.43158
$782$	−54.1057	−1.93482
$783$	−120.457	−4.30477
$784$	−30.3607	−1.08431
$785$	−0.0484249	−0.00172836
$786$	36.1066	1.28788
$787$	−40.4249	−1.44099	−0.720496	−	0.693459i	$-0.756086\pi$
$787$	−40.4249	−1.44099	−0.720496	+	0.693459i	$0.756086\pi$
$788$	−87.5309	−3.11816
$789$	−0.322674	−0.0114875
$790$	0.0955298	0.00339880
$791$	28.3418	1.00772
$792$	−203.614	−7.23511
$793$	23.9405	0.850154
$794$	−48.2263	−1.71149
$795$	0.0520224	0.00184504
$796$	−46.8836	−1.66174
$797$	9.99904	0.354184	0.177092	−	0.984194i	$-0.443331\pi$
$797$	9.99904	0.354184	0.177092	+	0.984194i	$0.443331\pi$
$798$	26.7557	0.947143
$799$	−34.8113	−1.23154
$800$	76.7443	2.71332
$801$	47.7316	1.68651
$802$	69.3473	2.44874
$803$	−1.84902	−0.0652506
$804$	23.0818	0.814032
$805$	0.0240398	0.000847291 0
$806$	−71.1801	−2.50721
$807$	90.7757	3.19546
$808$	144.151	5.07122
$809$	−49.2628	−1.73199	−0.865993	−	0.500056i	$-0.833313\pi$
$809$	−49.2628	−1.73199	−0.865993	+	0.500056i	$0.833313\pi$
$810$	−0.227616	−0.00799760
$811$	−24.0172	−0.843358	−0.421679	−	0.906745i	$-0.638559\pi$
$811$	−24.0172	−0.843358	−0.421679	+	0.906745i	$0.638559\pi$
$812$	68.2111	2.39374
$813$	42.2881	1.48311
$814$	5.34771	0.187437
$815$	0.0318972	0.00111731
$816$	−158.030	−5.53217
$817$	17.9472	0.627894
$818$	−9.29256	−0.324907
$819$	58.1343	2.03138
$820$	−0.0205340	−0.000717079 0
$821$	−49.5711	−1.73004	−0.865022	−	0.501735i	$-0.832695\pi$
$821$	−49.5711	−1.73004	−0.865022	+	0.501735i	$0.832695\pi$
$822$	−9.38239	−0.327248
$823$	−24.4774	−0.853230	−0.426615	−	0.904433i	$-0.640294\pi$
$823$	−24.4774	−0.853230	−0.426615	+	0.904433i	$0.640294\pi$
$824$	−34.4221	−1.19915
$825$	−48.3361	−1.68285
$826$	−43.5242	−1.51440
$827$	−4.89383	−0.170175	−0.0850875	−	0.996373i	$-0.527117\pi$
$827$	−4.89383	−0.170175	−0.0850875	+	0.996373i	$0.527117\pi$
$828$	−231.368	−8.04060
$829$	14.5438	0.505128	0.252564	−	0.967580i	$-0.418726\pi$
$829$	14.5438	0.505128	0.252564	+	0.967580i	$0.418726\pi$
$830$	0.0111429	0.000386775 0
$831$	−107.377	−3.72488
$832$	−54.1877	−1.87862
$833$	9.78328	0.338970
$834$	49.6823	1.72036
$835$	0.0309382	0.00107066
$836$	20.2239	0.699459
$837$	−159.743	−5.52152
$838$	−44.5844	−1.54014
$839$	2.18664	0.0754913	0.0377457	−	0.999287i	$-0.487982\pi$
$839$	2.18664	0.0754913	0.0377457	+	0.999287i	$0.487982\pi$
$840$	0.130180	0.00449164
$841$	10.6720	0.368000
$842$	27.7578	0.956596
$843$	−39.5876	−1.36347
$844$	−2.62091	−0.0902153
$845$	−0.00608109	−0.000209196 0
$846$	−206.980	−7.11611
$847$	6.24062	0.214430
$848$	84.4630	2.90047
$849$	83.4345	2.86347
$850$	−51.5845	−1.76934
$851$	3.70420	0.126978
$852$	246.180	8.43397
$853$	−31.3060	−1.07190	−0.535948	−	0.844251i	$-0.680046\pi$
$853$	−31.3060	−1.07190	−0.535948	+	0.844251i	$0.680046\pi$
$854$	−42.3026	−1.44757
$855$	0.0259871	0.000888741 0
$856$	99.0305	3.38479
$857$	50.2725	1.71728	0.858638	−	0.512582i	$-0.171311\pi$
$857$	50.2725	1.71728	0.858638	+	0.512582i	$0.171311\pi$
$858$	82.3810	2.81244
$859$	−31.1005	−1.06114	−0.530568	−	0.847642i	$-0.678021\pi$
$859$	−31.1005	−1.06114	−0.530568	+	0.847642i	$0.678021\pi$
$860$	0.143250	0.00488478
$861$	13.3176	0.453864
$862$	64.0901	2.18292
$863$	−30.7919	−1.04817	−0.524084	−	0.851667i	$-0.675592\pi$
$863$	−30.7919	−1.04817	−0.524084	+	0.851667i	$0.675592\pi$
$864$	−293.539	−9.98639
$865$	0.0211024	0.000717505 0
$866$	60.1214	2.04301
$867$	−7.00741	−0.237984
$868$	90.4577	3.07034
$869$	−46.8317	−1.58866
$870$	0.124206	0.00421098
$871$	−4.22200	−0.143057
$872$	26.7303	0.905203
$873$	7.17671	0.242895
$874$	19.4777	0.658843
$875$	0.0458392	0.00154965
$876$	−11.3776	−0.384415
$877$	27.2699	0.920839	0.460420	−	0.887701i	$-0.347699\pi$
$877$	27.2699	0.920839	0.460420	+	0.887701i	$0.347699\pi$
$878$	46.1603	1.55784
$879$	37.7904	1.27464
$880$	0.0737942	0.00248760
$881$	18.5491	0.624934	0.312467	−	0.949929i	$-0.398845\pi$
$881$	18.5491	0.624934	0.312467	+	0.949929i	$0.398845\pi$
$882$	58.1689	1.95865
$883$	4.95761	0.166837	0.0834185	−	0.996515i	$-0.473416\pi$
$883$	4.95761	0.166837	0.0834185	+	0.996515i	$0.473416\pi$
$884$	63.2309	2.12669
$885$	−0.0569997	−0.00191603
$886$	−77.4465	−2.60187
$887$	16.7740	0.563215	0.281607	−	0.959530i	$-0.409132\pi$
$887$	16.7740	0.563215	0.281607	+	0.959530i	$0.409132\pi$
$888$	20.0589	0.673134
$889$	3.00824	0.100893
$890$	−0.0320728	−0.00107508
$891$	111.584	3.73822
$892$	−35.5310	−1.18967
$893$	12.5319	0.419363
$894$	−113.720	−3.80336
$895$	−0.0174757	−0.000584147 0
$896$	30.8524	1.03071
$897$	57.0629	1.90527
$898$	−23.0091	−0.767825
$899$	52.6108	1.75467
$900$	−220.587	−7.35291
$901$	−27.2169	−0.906727
$902$	13.9966	0.466034
$903$	−92.9066	−3.09174
$904$	111.728	3.71602
$905$	−0.0105417	−0.000350418 0
$906$	60.9254	2.02411
$907$	4.76398	0.158185	0.0790927	−	0.996867i	$-0.474798\pi$
$907$	4.76398	0.158185	0.0790927	+	0.996867i	$0.474798\pi$
$908$	64.2358	2.13174
$909$	−148.964	−4.94083
$910$	−0.0390628	−0.00129492
$911$	35.4815	1.17555	0.587777	−	0.809023i	$-0.300003\pi$
$911$	35.4815	1.17555	0.587777	+	0.809023i	$0.300003\pi$
$912$	56.8899	1.88381
$913$	−5.46259	−0.180785
$914$	8.86305	0.293164
$915$	−0.0553999	−0.00183147
$916$	−124.040	−4.09839
$917$	8.39313	0.277165
$918$	197.305	6.51204
$919$	−18.1848	−0.599860	−0.299930	−	0.953961i	$-0.596963\pi$
$919$	−18.1848	−0.599860	−0.299930	+	0.953961i	$0.596963\pi$
$920$	0.0947687	0.00312443
$921$	−83.4540	−2.74990
$922$	87.6293	2.88592
$923$	−45.0299	−1.48218
$924$	−104.692	−3.44412
$925$	3.53159	0.116118
$926$	−50.6280	−1.66374
$927$	35.5714	1.16832
$928$	96.6760	3.17355
$929$	57.9174	1.90021	0.950105	−	0.311931i	$-0.100976\pi$
$929$	57.9174	1.90021	0.950105	+	0.311931i	$0.100976\pi$
$930$	0.164715	0.00540122
$931$	−3.52192	−0.115426
$932$	−68.3866	−2.24008
$933$	−113.609	−3.71939
$934$	22.5213	0.736920
$935$	−0.0237791	−0.000777659 0
$936$	229.175	7.49081
$937$	41.5888	1.35865	0.679323	−	0.733839i	$-0.262273\pi$
$937$	41.5888	1.35865	0.679323	+	0.733839i	$0.262273\pi$
$938$	7.46023	0.243585
$939$	−48.3525	−1.57792
$940$	0.100026	0.00326248
$941$	6.55113	0.213561	0.106780	−	0.994283i	$-0.465946\pi$
$941$	6.55113	0.213561	0.106780	+	0.994283i	$0.465946\pi$
$942$	203.107	6.61760
$943$	9.69500	0.315713
$944$	−92.5442	−3.01206
$945$	−0.0876650	−0.00285174
$946$	−97.6430	−3.17465
$947$	39.0401	1.26863	0.634316	−	0.773074i	$-0.281282\pi$
$947$	39.0401	1.26863	0.634316	+	0.773074i	$0.281282\pi$
$948$	−288.170	−9.35934
$949$	2.08114	0.0675567
$950$	18.5701	0.602494
$951$	17.6675	0.572908
$952$	−68.1072	−2.20737
$953$	−4.59882	−0.148970	−0.0744852	−	0.997222i	$-0.523731\pi$
$953$	−4.59882	−0.148970	−0.0744852	+	0.997222i	$0.523731\pi$
$954$	−161.825	−5.23928
$955$	−0.0509696	−0.00164934
$956$	−28.9977	−0.937852
$957$	−60.8897	−1.96828
$958$	−62.7938	−2.02878
$959$	−2.18097	−0.0704273
$960$	0.125394	0.00404707
$961$	38.7695	1.25063
$962$	−6.01903	−0.194061
$963$	−102.337	−3.29776
$964$	−21.9091	−0.705644
$965$	−0.00528030	−0.000169979 0
$966$	−100.829	−3.24413
$967$	−61.5377	−1.97892	−0.989460	−	0.144807i	$-0.953744\pi$
$967$	−61.5377	−1.97892	−0.989460	+	0.144807i	$0.953744\pi$
$968$	24.6015	0.790723
$969$	−18.3319	−0.588906
$970$	−0.00482232	−0.000154835 0
$971$	−4.43388	−0.142290	−0.0711450	−	0.997466i	$-0.522665\pi$
$971$	−4.43388	−0.142290	−0.0711450	+	0.997466i	$0.522665\pi$
$972$	392.709	12.5962
$973$	11.5488	0.370239
$974$	14.3878	0.461014
$975$	54.4039	1.74232
$976$	−89.9468	−2.87913
$977$	8.49654	0.271828	0.135914	−	0.990721i	$-0.456603\pi$
$977$	8.49654	0.271828	0.135914	+	0.990721i	$0.456603\pi$
$978$	−133.786	−4.27799
$979$	15.7231	0.502512
$980$	−0.0281110	−0.000897972 0
$981$	−27.6228	−0.881928
$982$	−62.8815	−2.00663
$983$	−59.0271	−1.88267	−0.941336	−	0.337472i	$-0.890428\pi$
$983$	−59.0271	−1.88267	−0.941336	+	0.337472i	$0.890428\pi$
$984$	52.5002	1.67365
$985$	−0.0370498	−0.00118051
$986$	−64.9818	−2.06944
$987$	−64.8731	−2.06494
$988$	−22.7627	−0.724179
$989$	−67.6344	−2.15065
$990$	−0.141385	−0.00449349
$991$	−38.4970	−1.22290	−0.611448	−	0.791284i	$-0.709413\pi$
$991$	−38.4970	−1.22290	−0.611448	+	0.791284i	$0.709413\pi$
$992$	128.206	4.07056
$993$	116.028	3.68205
$994$	79.5673	2.52372
$995$	−0.0198447	−0.000629121 0
$996$	−33.6131	−1.06507
$997$	25.6687	0.812936	0.406468	−	0.913665i	$-0.366760\pi$
$997$	25.6687	0.812936	0.406468	+	0.913665i	$0.366760\pi$
$998$	36.6877	1.16133
$999$	−13.5080	−0.427373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.a.1.6	✓	306

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.a.1.6	✓	306	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:	\( N \)	\(=\)	\( 8009 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66884 q^{2} +3.40767 q^{3} +5.12268 q^{4} +0.00216831 q^{5} -9.09450 q^{6} -2.11405 q^{7} -8.33393 q^{8} +8.61218 q^{9} +O(q^{10})\)	\(q-2.66884 q^{2} +3.40767 q^{3} +5.12268 q^{4} +0.00216831 q^{5} -9.09450 q^{6} -2.11405 q^{7} -8.33393 q^{8} +8.61218 q^{9} -0.00578687 q^{10} +2.83690 q^{11} +17.4564 q^{12} -3.19304 q^{13} +5.64205 q^{14} +0.00738889 q^{15} +11.9965 q^{16} -3.86570 q^{17} -22.9845 q^{18} +1.39163 q^{19} +0.0111076 q^{20} -7.20398 q^{21} -7.57123 q^{22} -5.24437 q^{23} -28.3992 q^{24} -5.00000 q^{25} +8.52169 q^{26} +19.1244 q^{27} -10.8296 q^{28} -6.29857 q^{29} -0.0197197 q^{30} -8.35282 q^{31} -15.3489 q^{32} +9.66722 q^{33} +10.3169 q^{34} -0.00458392 q^{35} +44.1175 q^{36} -0.706319 q^{37} -3.71403 q^{38} -10.8808 q^{39} -0.0180706 q^{40} -1.84865 q^{41} +19.2262 q^{42} +12.8966 q^{43} +14.5326 q^{44} +0.0186739 q^{45} +13.9964 q^{46} +9.00519 q^{47} +40.8801 q^{48} -2.53079 q^{49} +13.3442 q^{50} -13.1730 q^{51} -16.3569 q^{52} +7.04062 q^{53} -51.0400 q^{54} +0.00615130 q^{55} +17.6183 q^{56} +4.74220 q^{57} +16.8098 q^{58} -7.71425 q^{59} +0.0378509 q^{60} -7.49774 q^{61} +22.2923 q^{62} -18.2066 q^{63} +16.9706 q^{64} -0.00692350 q^{65} -25.8002 q^{66} +1.32225 q^{67} -19.8028 q^{68} -17.8710 q^{69} +0.0122337 q^{70} +14.1025 q^{71} -71.7733 q^{72} -0.651775 q^{73} +1.88505 q^{74} -17.0383 q^{75} +7.12887 q^{76} -5.99736 q^{77} +29.0391 q^{78} -16.5080 q^{79} +0.0260122 q^{80} +39.3331 q^{81} +4.93374 q^{82} -1.92554 q^{83} -36.9037 q^{84} -0.00838205 q^{85} -34.4188 q^{86} -21.4634 q^{87} -23.6426 q^{88} +5.54234 q^{89} -0.0498376 q^{90} +6.75024 q^{91} -26.8652 q^{92} -28.4636 q^{93} -24.0334 q^{94} +0.00301748 q^{95} -52.3039 q^{96} +0.833321 q^{97} +6.75426 q^{98} +24.4319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9}+O(q^{10}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9} - 61 q^{10} - 43 q^{11} - 50 q^{12} - 89 q^{13} - 40 q^{14} - 61 q^{15} + 151 q^{16} - 52 q^{17} - 57 q^{18} - 185 q^{19} - 66 q^{20} - 63 q^{21} - 55 q^{22} - 62 q^{23} - 131 q^{24} + 209 q^{25} - 57 q^{26} - 88 q^{27} - 182 q^{28} - 67 q^{29} - 68 q^{30} - 240 q^{31} - 64 q^{32} - 52 q^{33} - 128 q^{34} - 99 q^{35} + 106 q^{36} - 49 q^{37} - 45 q^{38} - 190 q^{39} - 158 q^{40} - 72 q^{41} - 36 q^{42} - 141 q^{43} - 80 q^{44} - 100 q^{45} - 91 q^{46} - 105 q^{47} - 85 q^{48} + 116 q^{49} - 51 q^{50} - 145 q^{51} - 237 q^{52} - 48 q^{53} - 156 q^{54} - 420 q^{55} - 116 q^{56} - 35 q^{57} - 43 q^{58} - 139 q^{59} - 73 q^{60} - 233 q^{61} - 58 q^{62} - 252 q^{63} - 3 q^{64} - 45 q^{65} - 127 q^{66} - 108 q^{67} - 85 q^{68} - 164 q^{69} - 56 q^{70} - 131 q^{71} - 117 q^{72} - 118 q^{73} - 47 q^{74} - 112 q^{75} - 389 q^{76} - 36 q^{77} + 9 q^{78} - 382 q^{79} - 119 q^{80} + 102 q^{81} - 131 q^{82} - 59 q^{83} - 144 q^{84} - 140 q^{85} - 38 q^{86} - 301 q^{87} - 131 q^{88} - 98 q^{89} - 138 q^{90} - 176 q^{91} - 97 q^{92} - 60 q^{93} - 342 q^{94} - 154 q^{95} - 243 q^{96} - 109 q^{97} - 21 q^{98} - 173 q^{99}+O(q^{100}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9 - 61 * q^10 - 43 * q^11 - 50 * q^12 - 89 * q^13 - 40 * q^14 - 61 * q^15 + 151 * q^16 - 52 * q^17 - 57 * q^18 - 185 * q^19 - 66 * q^20 - 63 * q^21 - 55 * q^22 - 62 * q^23 - 131 * q^24 + 209 * q^25 - 57 * q^26 - 88 * q^27 - 182 * q^28 - 67 * q^29 - 68 * q^30 - 240 * q^31 - 64 * q^32 - 52 * q^33 - 128 * q^34 - 99 * q^35 + 106 * q^36 - 49 * q^37 - 45 * q^38 - 190 * q^39 - 158 * q^40 - 72 * q^41 - 36 * q^42 - 141 * q^43 - 80 * q^44 - 100 * q^45 - 91 * q^46 - 105 * q^47 - 85 * q^48 + 116 * q^49 - 51 * q^50 - 145 * q^51 - 237 * q^52 - 48 * q^53 - 156 * q^54 - 420 * q^55 - 116 * q^56 - 35 * q^57 - 43 * q^58 - 139 * q^59 - 73 * q^60 - 233 * q^61 - 58 * q^62 - 252 * q^63 - 3 * q^64 - 45 * q^65 - 127 * q^66 - 108 * q^67 - 85 * q^68 - 164 * q^69 - 56 * q^70 - 131 * q^71 - 117 * q^72 - 118 * q^73 - 47 * q^74 - 112 * q^75 - 389 * q^76 - 36 * q^77 + 9 * q^78 - 382 * q^79 - 119 * q^80 + 102 * q^81 - 131 * q^82 - 59 * q^83 - 144 * q^84 - 140 * q^85 - 38 * q^86 - 301 * q^87 - 131 * q^88 - 98 * q^89 - 138 * q^90 - 176 * q^91 - 97 * q^92 - 60 * q^93 - 342 * q^94 - 154 * q^95 - 243 * q^96 - 109 * q^97 - 21 * q^98 - 173 * q^99

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