LMFDB - Embedded newform 667.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.65670$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65670 q^{2} -1.05120 q^{3} +0.744648 q^{4} +1.18716 q^{5} -1.74152 q^{6} -3.31827 q^{7} -2.07974 q^{8} -1.89498 q^{9} +O(q^{10})$	\(q+1.65670 q^{2} -1.05120 q^{3} +0.744648 q^{4} +1.18716 q^{5} -1.74152 q^{6} -3.31827 q^{7} -2.07974 q^{8} -1.89498 q^{9} +1.96676 q^{10} -2.10133 q^{11} -0.782771 q^{12} -0.667034 q^{13} -5.49737 q^{14} -1.24793 q^{15} -4.93480 q^{16} -5.75873 q^{17} -3.13942 q^{18} +7.40791 q^{19} +0.884013 q^{20} +3.48815 q^{21} -3.48128 q^{22} -1.00000 q^{23} +2.18622 q^{24} -3.59066 q^{25} -1.10507 q^{26} +5.14559 q^{27} -2.47094 q^{28} -1.00000 q^{29} -2.06745 q^{30} +5.06209 q^{31} -4.01599 q^{32} +2.20892 q^{33} -9.54047 q^{34} -3.93930 q^{35} -1.41110 q^{36} +2.21157 q^{37} +12.2727 q^{38} +0.701184 q^{39} -2.46897 q^{40} +0.348972 q^{41} +5.77881 q^{42} -6.47690 q^{43} -1.56475 q^{44} -2.24964 q^{45} -1.65670 q^{46} -10.5854 q^{47} +5.18744 q^{48} +4.01089 q^{49} -5.94864 q^{50} +6.05356 q^{51} -0.496706 q^{52} -3.16242 q^{53} +8.52469 q^{54} -2.49461 q^{55} +6.90113 q^{56} -7.78718 q^{57} -1.65670 q^{58} +7.62843 q^{59} -0.929271 q^{60} +1.50105 q^{61} +8.38636 q^{62} +6.28807 q^{63} +3.21632 q^{64} -0.791873 q^{65} +3.65951 q^{66} +8.31597 q^{67} -4.28822 q^{68} +1.05120 q^{69} -6.52623 q^{70} +2.83894 q^{71} +3.94107 q^{72} -10.4481 q^{73} +3.66391 q^{74} +3.77449 q^{75} +5.51629 q^{76} +6.97279 q^{77} +1.16165 q^{78} -14.0868 q^{79} -5.85837 q^{80} +0.275923 q^{81} +0.578142 q^{82} +4.20358 q^{83} +2.59744 q^{84} -6.83651 q^{85} -10.7303 q^{86} +1.05120 q^{87} +4.37023 q^{88} -8.05501 q^{89} -3.72698 q^{90} +2.21340 q^{91} -0.744648 q^{92} -5.32125 q^{93} -17.5368 q^{94} +8.79435 q^{95} +4.22159 q^{96} -8.26493 q^{97} +6.64484 q^{98} +3.98200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * 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 $

$2$	1.65670	1.17146	0.585731	−	0.810505i	$-0.300807\pi$
$2$	1.65670	1.17146	0.585731	+	0.810505i	$0.300807\pi$
$3$	−1.05120	−0.606909	−0.303454	−	0.952846i	$-0.598140\pi$
$3$	−1.05120	−0.606909	−0.303454	+	0.952846i	$0.598140\pi$
$4$	0.744648	0.372324
$5$	1.18716	0.530912	0.265456	−	0.964123i	$-0.414477\pi$
$5$	1.18716	0.530912	0.265456	+	0.964123i	$0.414477\pi$
$6$	−1.74152	−0.710971
$7$	−3.31827	−1.25419	−0.627093	−	0.778944i	$-0.715756\pi$
$7$	−3.31827	−1.25419	−0.627093	+	0.778944i	$0.715756\pi$
$8$	−2.07974	−0.735299
$9$	−1.89498	−0.631662
$10$	1.96676	0.621943
$11$	−2.10133	−0.633576	−0.316788	−	0.948496i	$-0.602604\pi$
$11$	−2.10133	−0.633576	−0.316788	+	0.948496i	$0.602604\pi$
$12$	−0.782771	−0.225967
$13$	−0.667034	−0.185002	−0.0925010	−	0.995713i	$-0.529486\pi$
$13$	−0.667034	−0.185002	−0.0925010	+	0.995713i	$0.529486\pi$
$14$	−5.49737	−1.46923
$15$	−1.24793	−0.322215
$16$	−4.93480	−1.23370
$17$	−5.75873	−1.39670	−0.698348	−	0.715758i	$-0.746081\pi$
$17$	−5.75873	−1.39670	−0.698348	+	0.715758i	$0.746081\pi$
$18$	−3.13942	−0.739968
$19$	7.40791	1.69949	0.849746	−	0.527192i	$-0.176755\pi$
$19$	7.40791	1.69949	0.849746	+	0.527192i	$0.176755\pi$
$20$	0.884013	0.197671
$21$	3.48815	0.761177
$22$	−3.48128	−0.742211
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.18622	0.446259
$25$	−3.59066	−0.718132
$26$	−1.10507	−0.216723
$27$	5.14559	0.990270
$28$	−2.47094	−0.466964
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−2.06745	−0.377463
$31$	5.06209	0.909178	0.454589	−	0.890701i	$-0.349786\pi$
$31$	5.06209	0.909178	0.454589	+	0.890701i	$0.349786\pi$
$32$	−4.01599	−0.709933
$33$	2.20892	0.384523
$34$	−9.54047	−1.63618
$35$	−3.93930	−0.665863
$36$	−1.41110	−0.235183
$37$	2.21157	0.363580	0.181790	−	0.983337i	$-0.441811\pi$
$37$	2.21157	0.363580	0.181790	+	0.983337i	$0.441811\pi$
$38$	12.2727	1.99089
$39$	0.701184	0.112279
$40$	−2.46897	−0.390379
$41$	0.348972	0.0545003	0.0272502	−	0.999629i	$-0.491325\pi$
$41$	0.348972	0.0545003	0.0272502	+	0.999629i	$0.491325\pi$
$42$	5.77881	0.891690
$43$	−6.47690	−0.987718	−0.493859	−	0.869542i	$-0.664414\pi$
$43$	−6.47690	−0.987718	−0.493859	+	0.869542i	$0.664414\pi$
$44$	−1.56475	−0.235896
$45$	−2.24964	−0.335357
$46$	−1.65670	−0.244267
$47$	−10.5854	−1.54404	−0.772020	−	0.635598i	$-0.780754\pi$
$47$	−10.5854	−1.54404	−0.772020	+	0.635598i	$0.780754\pi$
$48$	5.18744	0.748743
$49$	4.01089	0.572985
$50$	−5.94864	−0.841265
$51$	6.05356	0.847668
$52$	−0.496706	−0.0688807
$53$	−3.16242	−0.434391	−0.217196	−	0.976128i	$-0.569691\pi$
$53$	−3.16242	−0.434391	−0.217196	+	0.976128i	$0.569691\pi$
$54$	8.52469	1.16006
$55$	−2.49461	−0.336373
$56$	6.90113	0.922202
$57$	−7.78718	−1.03144
$58$	−1.65670	−0.217535
$59$	7.62843	0.993137	0.496568	−	0.867998i	$-0.334593\pi$
$59$	7.62843	0.993137	0.496568	+	0.867998i	$0.334593\pi$
$60$	−0.929271	−0.119968
$61$	1.50105	0.192189	0.0960947	−	0.995372i	$-0.469365\pi$
$61$	1.50105	0.192189	0.0960947	+	0.995372i	$0.469365\pi$
$62$	8.38636	1.06507
$63$	6.28807	0.792222
$64$	3.21632	0.402039
$65$	−0.791873	−0.0982198
$66$	3.65951	0.450454
$67$	8.31597	1.01596	0.507979	−	0.861370i	$-0.330393\pi$
$67$	8.31597	1.01596	0.507979	+	0.861370i	$0.330393\pi$
$68$	−4.28822	−0.520023
$69$	1.05120	0.126549
$70$	−6.52623	−0.780033
$71$	2.83894	0.336920	0.168460	−	0.985708i	$-0.446121\pi$
$71$	2.83894	0.336920	0.168460	+	0.985708i	$0.446121\pi$
$72$	3.94107	0.464460
$73$	−10.4481	−1.22286	−0.611432	−	0.791297i	$-0.709406\pi$
$73$	−10.4481	−1.22286	−0.611432	+	0.791297i	$0.709406\pi$
$74$	3.66391	0.425921
$75$	3.77449	0.435841
$76$	5.51629	0.632761
$77$	6.97279	0.794623
$78$	1.16165	0.131531
$79$	−14.0868	−1.58489	−0.792444	−	0.609944i	$-0.791192\pi$
$79$	−14.0868	−1.58489	−0.792444	+	0.609944i	$0.791192\pi$
$80$	−5.85837	−0.654986
$81$	0.275923	0.0306581
$82$	0.578142	0.0638451
$83$	4.20358	0.461403	0.230701	−	0.973025i	$-0.425898\pi$
$83$	4.20358	0.461403	0.230701	+	0.973025i	$0.425898\pi$
$84$	2.59744	0.283404
$85$	−6.83651	−0.741523
$86$	−10.7303	−1.15707
$87$	1.05120	0.112700
$88$	4.37023	0.465868
$89$	−8.05501	−0.853829	−0.426915	−	0.904292i	$-0.640400\pi$
$89$	−8.05501	−0.853829	−0.426915	+	0.904292i	$0.640400\pi$
$90$	−3.72698	−0.392858
$91$	2.21340	0.232027
$92$	−0.744648	−0.0776349
$93$	−5.32125	−0.551788
$94$	−17.5368	−1.80878
$95$	8.79435	0.902281
$96$	4.22159	0.430864
$97$	−8.26493	−0.839177	−0.419588	−	0.907715i	$-0.637826\pi$
$97$	−8.26493	−0.839177	−0.419588	+	0.907715i	$0.637826\pi$
$98$	6.64484	0.671230
$99$	3.98200	0.400206
$100$	−2.67378	−0.267378
$101$	3.73673	0.371819	0.185909	−	0.982567i	$-0.440477\pi$
$101$	3.73673	0.371819	0.185909	+	0.982567i	$0.440477\pi$
$102$	10.0289	0.993011
$103$	7.73267	0.761922	0.380961	−	0.924591i	$-0.375593\pi$
$103$	7.73267	0.761922	0.380961	+	0.924591i	$0.375593\pi$
$104$	1.38726	0.136032
$105$	4.14098	0.404118
$106$	−5.23917	−0.508873
$107$	4.44422	0.429639	0.214819	−	0.976654i	$-0.431084\pi$
$107$	4.44422	0.429639	0.214819	+	0.976654i	$0.431084\pi$
$108$	3.83165	0.368701
$109$	6.92130	0.662941	0.331470	−	0.943466i	$-0.392455\pi$
$109$	6.92130	0.662941	0.331470	+	0.943466i	$0.392455\pi$
$110$	−4.13282	−0.394049
$111$	−2.32480	−0.220660
$112$	16.3750	1.54729
$113$	−13.5198	−1.27183	−0.635917	−	0.771758i	$-0.719378\pi$
$113$	−13.5198	−1.27183	−0.635917	+	0.771758i	$0.719378\pi$
$114$	−12.9010	−1.20829
$115$	−1.18716	−0.110703
$116$	−0.744648	−0.0691388
$117$	1.26402	0.116859
$118$	12.6380	1.16342
$119$	19.1090	1.75172
$120$	2.59538	0.236925
$121$	−6.58439	−0.598581
$122$	2.48678	0.225143
$123$	−0.366839	−0.0330767
$124$	3.76947	0.338509
$125$	−10.1985	−0.912177
$126$	10.4174	0.928058
$127$	5.12844	0.455075	0.227538	−	0.973769i	$-0.426932\pi$
$127$	5.12844	0.455075	0.227538	+	0.973769i	$0.426932\pi$
$128$	13.3604	1.18091
$129$	6.80850	0.599455
$130$	−1.31189	−0.115061
$131$	21.1939	1.85172	0.925859	−	0.377870i	$-0.123343\pi$
$131$	21.1939	1.85172	0.925859	+	0.377870i	$0.123343\pi$
$132$	1.64486	0.143167
$133$	−24.5814	−2.13148
$134$	13.7771	1.19016
$135$	6.10862	0.525746
$136$	11.9767	1.02699
$137$	2.13071	0.182039	0.0910196	−	0.995849i	$-0.470987\pi$
$137$	2.13071	0.182039	0.0910196	+	0.995849i	$0.470987\pi$
$138$	1.74152	0.148248
$139$	−5.84259	−0.495562	−0.247781	−	0.968816i	$-0.579701\pi$
$139$	−5.84259	−0.495562	−0.247781	+	0.968816i	$0.579701\pi$
$140$	−2.93339	−0.247917
$141$	11.1273	0.937092
$142$	4.70327	0.394689
$143$	1.40166	0.117213
$144$	9.35136	0.779280
$145$	−1.18716	−0.0985879
$146$	−17.3094	−1.43254
$147$	−4.21624	−0.347750
$148$	1.64684	0.135370
$149$	−1.75828	−0.144044	−0.0720219	−	0.997403i	$-0.522945\pi$
$149$	−1.75828	−0.144044	−0.0720219	+	0.997403i	$0.522945\pi$
$150$	6.25319	0.510571
$151$	11.1797	0.909788	0.454894	−	0.890546i	$-0.349677\pi$
$151$	11.1797	0.909788	0.454894	+	0.890546i	$0.349677\pi$
$152$	−15.4065	−1.24963
$153$	10.9127	0.882240
$154$	11.5518	0.930871
$155$	6.00949	0.482694
$156$	0.522135	0.0418043
$157$	8.12000	0.648047	0.324023	−	0.946049i	$-0.394964\pi$
$157$	8.12000	0.648047	0.324023	+	0.946049i	$0.394964\pi$
$158$	−23.3376	−1.85664
$159$	3.32432	0.263636
$160$	−4.76760	−0.376912
$161$	3.31827	0.261516
$162$	0.457121	0.0359148
$163$	−4.71191	−0.369065	−0.184533	−	0.982826i	$-0.559077\pi$
$163$	−4.71191	−0.369065	−0.184533	+	0.982826i	$0.559077\pi$
$164$	0.259861	0.0202918
$165$	2.62233	0.204148
$166$	6.96406	0.540516
$167$	−10.8653	−0.840786	−0.420393	−	0.907342i	$-0.638108\pi$
$167$	−10.8653	−0.840786	−0.420393	+	0.907342i	$0.638108\pi$
$168$	−7.25445	−0.559693
$169$	−12.5551	−0.965774
$170$	−11.3260	−0.868666
$171$	−14.0379	−1.07350
$172$	−4.82301	−0.367751
$173$	−11.2783	−0.857476	−0.428738	−	0.903429i	$-0.641042\pi$
$173$	−11.2783	−0.857476	−0.428738	+	0.903429i	$0.641042\pi$
$174$	1.74152	0.132024
$175$	11.9148	0.900672
$176$	10.3697	0.781642
$177$	−8.01898	−0.602743
$178$	−13.3447	−1.00023
$179$	−14.6880	−1.09784	−0.548918	−	0.835876i	$-0.684960\pi$
$179$	−14.6880	−1.09784	−0.548918	+	0.835876i	$0.684960\pi$
$180$	−1.67519	−0.124861
$181$	−17.4127	−1.29427	−0.647137	−	0.762374i	$-0.724034\pi$
$181$	−17.4127	−1.29427	−0.647137	+	0.762374i	$0.724034\pi$
$182$	3.66693	0.271811
$183$	−1.57790	−0.116641
$184$	2.07974	0.153320
$185$	2.62548	0.193029
$186$	−8.81571	−0.646399
$187$	12.1010	0.884914
$188$	−7.88240	−0.574883
$189$	−17.0745	−1.24198
$190$	14.5696	1.05699
$191$	−10.5270	−0.761709	−0.380855	−	0.924635i	$-0.624370\pi$
$191$	−10.5270	−0.761709	−0.380855	+	0.924635i	$0.624370\pi$
$192$	−3.38098	−0.244001
$193$	7.87465	0.566830	0.283415	−	0.958997i	$-0.408533\pi$
$193$	7.87465	0.566830	0.283415	+	0.958997i	$0.408533\pi$
$194$	−13.6925	−0.983064
$195$	0.832415	0.0596105
$196$	2.98670	0.213336
$197$	10.7074	0.762870	0.381435	−	0.924396i	$-0.375430\pi$
$197$	10.7074	0.762870	0.381435	+	0.924396i	$0.375430\pi$
$198$	6.59697	0.468826
$199$	2.52248	0.178814	0.0894070	−	0.995995i	$-0.471503\pi$
$199$	2.52248	0.178814	0.0894070	+	0.995995i	$0.471503\pi$
$200$	7.46764	0.528042
$201$	−8.74173	−0.616594
$202$	6.19064	0.435572
$203$	3.31827	0.232897
$204$	4.50777	0.315607
$205$	0.414284	0.0289349
$206$	12.8107	0.892563
$207$	1.89498	0.131711
$208$	3.29168	0.228237
$209$	−15.5665	−1.07676
$210$	6.86035	0.473409
$211$	16.9843	1.16925	0.584624	−	0.811304i	$-0.301242\pi$
$211$	16.9843	1.16925	0.584624	+	0.811304i	$0.301242\pi$
$212$	−2.35489	−0.161734
$213$	−2.98429	−0.204480
$214$	7.36273	0.503306
$215$	−7.68909	−0.524391
$216$	−10.7015	−0.728144
$217$	−16.7974	−1.14028
$218$	11.4665	0.776610
$219$	10.9831	0.742166
$220$	−1.85761	−0.125240
$221$	3.84127	0.258392
$222$	−3.85149	−0.258495
$223$	−19.1638	−1.28331	−0.641653	−	0.766995i	$-0.721751\pi$
$223$	−19.1638	−1.28331	−0.641653	+	0.766995i	$0.721751\pi$
$224$	13.3261	0.890388
$225$	6.80425	0.453617
$226$	−22.3982	−1.48991
$227$	−22.9978	−1.52642	−0.763210	−	0.646151i	$-0.776378\pi$
$227$	−22.9978	−1.52642	−0.763210	+	0.646151i	$0.776378\pi$
$228$	−5.79870	−0.384029
$229$	5.34322	0.353090	0.176545	−	0.984293i	$-0.443508\pi$
$229$	5.34322	0.353090	0.176545	+	0.984293i	$0.443508\pi$
$230$	−1.96676	−0.129684
$231$	−7.32977	−0.482264
$232$	2.07974	0.136542
$233$	−4.86205	−0.318523	−0.159262	−	0.987236i	$-0.550911\pi$
$233$	−4.86205	−0.318523	−0.159262	+	0.987236i	$0.550911\pi$
$234$	2.09410	0.136896
$235$	−12.5665	−0.819750
$236$	5.68049	0.369769
$237$	14.8080	0.961883
$238$	31.6578	2.05207
$239$	−28.1206	−1.81897	−0.909484	−	0.415738i	$-0.863523\pi$
$239$	−28.1206	−1.81897	−0.909484	+	0.415738i	$0.863523\pi$
$240$	6.15830	0.397517
$241$	−26.5821	−1.71230	−0.856152	−	0.516724i	$-0.827151\pi$
$241$	−26.5821	−1.71230	−0.856152	+	0.516724i	$0.827151\pi$
$242$	−10.9083	−0.701215
$243$	−15.7268	−1.00888
$244$	1.11775	0.0715567
$245$	4.76155	0.304205
$246$	−0.607741	−0.0387481
$247$	−4.94133	−0.314409
$248$	−10.5278	−0.668518
$249$	−4.41879	−0.280029
$250$	−16.8958	−1.06858
$251$	−13.0717	−0.825079	−0.412539	−	0.910940i	$-0.635358\pi$
$251$	−13.0717	−0.825079	−0.412539	+	0.910940i	$0.635358\pi$
$252$	4.68239	0.294963
$253$	2.10133	0.132110
$254$	8.49628	0.533104
$255$	7.18651	0.450037
$256$	15.7016	0.981348
$257$	13.3772	0.834445	0.417222	−	0.908804i	$-0.363004\pi$
$257$	13.3772	0.834445	0.417222	+	0.908804i	$0.363004\pi$
$258$	11.2796	0.702238
$259$	−7.33859	−0.455998
$260$	−0.589667	−0.0365696
$261$	1.89498	0.117297
$262$	35.1118	2.16922
$263$	3.27219	0.201772	0.100886	−	0.994898i	$-0.467832\pi$
$263$	3.27219	0.201772	0.100886	+	0.994898i	$0.467832\pi$
$264$	−4.59397	−0.282739
$265$	−3.75428	−0.230623
$266$	−40.7240	−2.49695
$267$	8.46740	0.518197
$268$	6.19247	0.378265
$269$	23.0186	1.40347	0.701736	−	0.712438i	$-0.252409\pi$
$269$	23.0186	1.40347	0.701736	+	0.712438i	$0.252409\pi$
$270$	10.1201	0.615892
$271$	−15.2567	−0.926777	−0.463388	−	0.886155i	$-0.653367\pi$
$271$	−15.2567	−0.926777	−0.463388	+	0.886155i	$0.653367\pi$
$272$	28.4181	1.72310
$273$	−2.32672	−0.140819
$274$	3.52995	0.213252
$275$	7.54518	0.454992
$276$	0.782771	0.0471173
$277$	22.0758	1.32641	0.663203	−	0.748440i	$-0.269197\pi$
$277$	22.0758	1.32641	0.663203	+	0.748440i	$0.269197\pi$
$278$	−9.67940	−0.580532
$279$	−9.59259	−0.574293
$280$	8.19271	0.489608
$281$	−2.43791	−0.145434	−0.0727169	−	0.997353i	$-0.523167\pi$
$281$	−2.43791	−0.145434	−0.0727169	+	0.997353i	$0.523167\pi$
$282$	18.4347	1.09777
$283$	−7.55424	−0.449053	−0.224526	−	0.974468i	$-0.572084\pi$
$283$	−7.55424	−0.449053	−0.224526	+	0.974468i	$0.572084\pi$
$284$	2.11401	0.125443
$285$	−9.24459	−0.547602
$286$	2.32213	0.137310
$287$	−1.15798	−0.0683536
$288$	7.61023	0.448437
$289$	16.1629	0.950762
$290$	−1.96676	−0.115492
$291$	8.68807	0.509304
$292$	−7.78019	−0.455301
$293$	−31.2724	−1.82695	−0.913477	−	0.406890i	$-0.866613\pi$
$293$	−31.2724	−1.82695	−0.913477	+	0.406890i	$0.866613\pi$
$294$	−6.98503	−0.407375
$295$	9.05613	0.527268
$296$	−4.59949	−0.267340
$297$	−10.8126	−0.627411
$298$	−2.91294	−0.168742
$299$	0.667034	0.0385756
$300$	2.81067	0.162274
$301$	21.4921	1.23878
$302$	18.5213	1.06578
$303$	−3.92804	−0.225660
$304$	−36.5565	−2.09666
$305$	1.78198	0.102036
$306$	18.0791	1.03351
$307$	16.9870	0.969501	0.484750	−	0.874653i	$-0.338910\pi$
$307$	16.9870	0.969501	0.484750	+	0.874653i	$0.338910\pi$
$308$	5.19227	0.295857
$309$	−8.12856	−0.462417
$310$	9.95591	0.565458
$311$	18.3265	1.03920	0.519601	−	0.854409i	$-0.326081\pi$
$311$	18.3265	1.03920	0.519601	+	0.854409i	$0.326081\pi$
$312$	−1.45828	−0.0825589
$313$	12.5371	0.708638	0.354319	−	0.935125i	$-0.384713\pi$
$313$	12.5371	0.708638	0.354319	+	0.935125i	$0.384713\pi$
$314$	13.4524	0.759162
$315$	7.46491	0.420600
$316$	−10.4897	−0.590092
$317$	−8.36668	−0.469920	−0.234960	−	0.972005i	$-0.575496\pi$
$317$	−8.36668	−0.469920	−0.234960	+	0.972005i	$0.575496\pi$
$318$	5.50740	0.308839
$319$	2.10133	0.117652
$320$	3.81827	0.213448
$321$	−4.67175	−0.260752
$322$	5.49737	0.306356
$323$	−42.6602	−2.37367
$324$	0.205465	0.0114147
$325$	2.39509	0.132856
$326$	−7.80621	−0.432346
$327$	−7.27565	−0.402345
$328$	−0.725771	−0.0400740
$329$	35.1252	1.93652
$330$	4.34440	0.239152
$331$	35.1468	1.93184	0.965921	−	0.258835i	$-0.0833387\pi$
$331$	35.1468	1.93184	0.965921	+	0.258835i	$0.0833387\pi$
$332$	3.13018	0.171791
$333$	−4.19090	−0.229660
$334$	−18.0006	−0.984949
$335$	9.87235	0.539384
$336$	−17.2133	−0.939063
$337$	−26.2484	−1.42984	−0.714920	−	0.699206i	$-0.753537\pi$
$337$	−26.2484	−1.42984	−0.714920	+	0.699206i	$0.753537\pi$
$338$	−20.7999	−1.13137
$339$	14.2119	0.771887
$340$	−5.09079	−0.276087
$341$	−10.6371	−0.576034
$342$	−23.2565	−1.25757
$343$	9.91865	0.535557
$344$	13.4703	0.726268
$345$	1.24793	0.0671865
$346$	−18.6848	−1.00450
$347$	35.2992	1.89496	0.947480	−	0.319815i	$-0.103621\pi$
$347$	35.2992	1.89496	0.947480	+	0.319815i	$0.103621\pi$
$348$	0.782771	0.0419610
$349$	−3.64912	−0.195333	−0.0976665	−	0.995219i	$-0.531138\pi$
$349$	−3.64912	−0.195333	−0.0976665	+	0.995219i	$0.531138\pi$
$350$	19.7392	1.05510
$351$	−3.43229	−0.183202
$352$	8.43893	0.449797
$353$	−28.6053	−1.52251	−0.761254	−	0.648454i	$-0.775416\pi$
$353$	−28.6053	−1.52251	−0.761254	+	0.648454i	$0.775416\pi$
$354$	−13.2850	−0.706091
$355$	3.37026	0.178875
$356$	−5.99815	−0.317901
$357$	−20.0873	−1.06313
$358$	−24.3336	−1.28607
$359$	−7.54381	−0.398147	−0.199073	−	0.979985i	$-0.563793\pi$
$359$	−7.54381	−0.398147	−0.199073	+	0.979985i	$0.563793\pi$
$360$	4.67867	0.246587
$361$	35.8772	1.88827
$362$	−28.8475	−1.51619
$363$	6.92149	0.363284
$364$	1.64820	0.0863892
$365$	−12.4036	−0.649233
$366$	−2.61410	−0.136641
$367$	−6.99198	−0.364979	−0.182489	−	0.983208i	$-0.558415\pi$
$367$	−6.99198	−0.364979	−0.182489	+	0.983208i	$0.558415\pi$
$368$	4.93480	0.257244
$369$	−0.661297	−0.0344258
$370$	4.34963	0.226126
$371$	10.4937	0.544808
$372$	−3.96246	−0.205444
$373$	18.0966	0.937008	0.468504	−	0.883461i	$-0.344793\pi$
$373$	18.0966	0.937008	0.468504	+	0.883461i	$0.344793\pi$
$374$	20.0477	1.03664
$375$	10.7206	0.553608
$376$	22.0149	1.13533
$377$	0.667034	0.0343540
$378$	−28.2872	−1.45494
$379$	−31.5333	−1.61976	−0.809878	−	0.586598i	$-0.800467\pi$
$379$	−31.5333	−1.61976	−0.809878	+	0.586598i	$0.800467\pi$
$380$	6.54869	0.335941
$381$	−5.39100	−0.276189
$382$	−17.4401	−0.892314
$383$	−37.2254	−1.90213	−0.951066	−	0.308989i	$-0.900009\pi$
$383$	−37.2254	−1.90213	−0.951066	+	0.308989i	$0.900009\pi$
$384$	−14.0444	−0.716703
$385$	8.27778	0.421875
$386$	13.0459	0.664020
$387$	12.2736	0.623903
$388$	−6.15446	−0.312445
$389$	−15.4113	−0.781386	−0.390693	−	0.920521i	$-0.627765\pi$
$389$	−15.4113	−0.781386	−0.390693	+	0.920521i	$0.627765\pi$
$390$	1.37906	0.0698314
$391$	5.75873	0.291231
$392$	−8.34161	−0.421315
$393$	−22.2789	−1.12382
$394$	17.7389	0.893673
$395$	−16.7232	−0.841436
$396$	2.96519	0.149006
$397$	2.31242	0.116057	0.0580285	−	0.998315i	$-0.481519\pi$
$397$	2.31242	0.116057	0.0580285	+	0.998315i	$0.481519\pi$
$398$	4.17899	0.209474
$399$	25.8399	1.29361
$400$	17.7192	0.885959
$401$	10.2282	0.510774	0.255387	−	0.966839i	$-0.417797\pi$
$401$	10.2282	0.510774	0.255387	+	0.966839i	$0.417797\pi$
$402$	−14.4824	−0.722316
$403$	−3.37659	−0.168200
$404$	2.78255	0.138437
$405$	0.327563	0.0162768
$406$	5.49737	0.272830
$407$	−4.64725	−0.230356
$408$	−12.5898	−0.623289
$409$	2.55718	0.126445	0.0632223	−	0.997999i	$-0.479862\pi$
$409$	2.55718	0.126445	0.0632223	+	0.997999i	$0.479862\pi$
$410$	0.686344	0.0338961
$411$	−2.23980	−0.110481
$412$	5.75811	0.283682
$413$	−25.3132	−1.24558
$414$	3.13942	0.154294
$415$	4.99030	0.244964
$416$	2.67880	0.131339
$417$	6.14171	0.300761
$418$	−25.7890	−1.26138
$419$	−11.7562	−0.574328	−0.287164	−	0.957881i	$-0.592712\pi$
$419$	−11.7562	−0.574328	−0.287164	+	0.957881i	$0.592712\pi$
$420$	3.08357	0.150463
$421$	−7.26763	−0.354203	−0.177101	−	0.984193i	$-0.556672\pi$
$421$	−7.26763	−0.354203	−0.177101	+	0.984193i	$0.556672\pi$
$422$	28.1379	1.36973
$423$	20.0592	0.975311
$424$	6.57700	0.319407
$425$	20.6776	1.00301
$426$	−4.94406	−0.239540
$427$	−4.98087	−0.241041
$428$	3.30938	0.159965
$429$	−1.47342	−0.0711375
$430$	−12.7385	−0.614305
$431$	23.9034	1.15138	0.575692	−	0.817666i	$-0.304733\pi$
$431$	23.9034	1.15138	0.575692	+	0.817666i	$0.304733\pi$
$432$	−25.3924	−1.22169
$433$	19.0216	0.914118	0.457059	−	0.889436i	$-0.348903\pi$
$433$	19.0216	0.914118	0.457059	+	0.889436i	$0.348903\pi$
$434$	−27.8282	−1.33579
$435$	1.24793	0.0598339
$436$	5.15393	0.246829
$437$	−7.40791	−0.354369
$438$	18.1956	0.869420
$439$	18.5778	0.886672	0.443336	−	0.896355i	$-0.353795\pi$
$439$	18.5778	0.886672	0.443336	+	0.896355i	$0.353795\pi$
$440$	5.18814	0.247335
$441$	−7.60058	−0.361933
$442$	6.36382	0.302696
$443$	0.555962	0.0264145	0.0132073	−	0.999913i	$-0.495796\pi$
$443$	0.555962	0.0264145	0.0132073	+	0.999913i	$0.495796\pi$
$444$	−1.73116	−0.0821570
$445$	−9.56255	−0.453308
$446$	−31.7487	−1.50334
$447$	1.84830	0.0874215
$448$	−10.6726	−0.504233
$449$	6.47081	0.305376	0.152688	−	0.988274i	$-0.451207\pi$
$449$	6.47081	0.305376	0.152688	+	0.988274i	$0.451207\pi$
$450$	11.2726	0.531395
$451$	−0.733308	−0.0345301
$452$	−10.0675	−0.473534
$453$	−11.7520	−0.552158
$454$	−38.1005	−1.78814
$455$	2.62765	0.123186
$456$	16.1953	0.758414
$457$	15.3345	0.717318	0.358659	−	0.933469i	$-0.383234\pi$
$457$	15.3345	0.717318	0.358659	+	0.933469i	$0.383234\pi$
$458$	8.85210	0.413632
$459$	−29.6321	−1.38311
$460$	−0.884013	−0.0412173
$461$	1.13745	0.0529763	0.0264882	−	0.999649i	$-0.491568\pi$
$461$	1.13745	0.0529763	0.0264882	+	0.999649i	$0.491568\pi$
$462$	−12.1432	−0.564954
$463$	−31.4203	−1.46022	−0.730112	−	0.683327i	$-0.760532\pi$
$463$	−31.4203	−1.46022	−0.730112	+	0.683327i	$0.760532\pi$
$464$	4.93480	0.229092
$465$	−6.31716	−0.292951
$466$	−8.05494	−0.373138
$467$	18.8179	0.870786	0.435393	−	0.900240i	$-0.356609\pi$
$467$	18.8179	0.870786	0.435393	+	0.900240i	$0.356609\pi$
$468$	0.941250	0.0435093
$469$	−27.5946	−1.27420
$470$	−20.8189	−0.960306
$471$	−8.53572	−0.393305
$472$	−15.8651	−0.730252
$473$	13.6101	0.625795
$474$	24.5324	1.12681
$475$	−26.5993	−1.22046
$476$	14.2295	0.652207
$477$	5.99273	0.274388
$478$	−46.5873	−2.13085
$479$	28.5635	1.30510	0.652550	−	0.757745i	$-0.273699\pi$
$479$	28.5635	1.30510	0.652550	+	0.757745i	$0.273699\pi$
$480$	5.01169	0.228751
$481$	−1.47519	−0.0672631
$482$	−44.0385	−2.00590
$483$	−3.48815	−0.158716
$484$	−4.90305	−0.222866
$485$	−9.81176	−0.445529
$486$	−26.0546	−1.18186
$487$	30.3730	1.37633	0.688167	−	0.725552i	$-0.258416\pi$
$487$	30.3730	1.37633	0.688167	+	0.725552i	$0.258416\pi$
$488$	−3.12179	−0.141317
$489$	4.95315	0.223989
$490$	7.88846	0.356364
$491$	43.1194	1.94595	0.972976	−	0.230907i	$-0.0741692\pi$
$491$	43.1194	1.94595	0.972976	+	0.230907i	$0.0741692\pi$
$492$	−0.273166	−0.0123153
$493$	5.75873	0.259360
$494$	−8.18630	−0.368319
$495$	4.72725	0.212474
$496$	−24.9804	−1.12165
$497$	−9.42036	−0.422561
$498$	−7.32060	−0.328044
$499$	−31.7206	−1.42001	−0.710005	−	0.704196i	$-0.751308\pi$
$499$	−31.7206	−1.42001	−0.710005	+	0.704196i	$0.751308\pi$
$500$	−7.59425	−0.339625
$501$	11.4216	0.510280
$502$	−21.6559	−0.966549
$503$	−0.00213666	−9.52688e−5 0	−4.76344e−5	−	1.00000i	$-0.500015\pi$
$503$	−0.00213666	−9.52688e−5 0	−4.76344e−5		1.00000i	$0.500015\pi$
$504$	−13.0775	−0.582520
$505$	4.43608	0.197403
$506$	3.48128	0.154762
$507$	13.1978	0.586137
$508$	3.81888	0.169435
$509$	6.11584	0.271080	0.135540	−	0.990772i	$-0.456723\pi$
$509$	6.11584	0.271080	0.135540	+	0.990772i	$0.456723\pi$
$510$	11.9059	0.527201
$511$	34.6697	1.53370
$512$	−0.708108	−0.0312943
$513$	38.1181	1.68296
$514$	22.1619	0.977521
$515$	9.17988	0.404514
$516$	5.06993	0.223191
$517$	22.2435	0.978267
$518$	−12.1578	−0.534184
$519$	11.8558	0.520410
$520$	1.64689	0.0722209
$521$	−41.7107	−1.82738	−0.913690	−	0.406413i	$-0.866780\pi$
$521$	−41.7107	−1.82738	−0.913690	+	0.406413i	$0.866780\pi$
$522$	3.13942	0.137409
$523$	14.6642	0.641223	0.320611	−	0.947211i	$-0.396112\pi$
$523$	14.6642	0.641223	0.320611	+	0.947211i	$0.396112\pi$
$524$	15.7820	0.689438
$525$	−12.5248	−0.546626
$526$	5.42103	0.236368
$527$	−29.1512	−1.26985
$528$	−10.9006	−0.474386
$529$	1.00000	0.0434783
$530$	−6.21971	−0.270167
$531$	−14.4558	−0.627326
$532$	−18.3045	−0.793601
$533$	−0.232776	−0.0100827
$534$	14.0279	0.607048
$535$	5.27598	0.228100
$536$	−17.2951	−0.747033
$537$	15.4400	0.666286
$538$	38.1349	1.64411
$539$	−8.42823	−0.363030
$540$	4.54877	0.195748
$541$	27.3856	1.17740	0.588700	−	0.808352i	$-0.299640\pi$
$541$	27.3856	1.17740	0.588700	+	0.808352i	$0.299640\pi$
$542$	−25.2757	−1.08568
$543$	18.3042	0.785506
$544$	23.1270	0.991561
$545$	8.21666	0.351963
$546$	−3.85467	−0.164965
$547$	−17.9335	−0.766781	−0.383390	−	0.923586i	$-0.625244\pi$
$547$	−17.9335	−0.766781	−0.383390	+	0.923586i	$0.625244\pi$
$548$	1.58663	0.0677775
$549$	−2.84446	−0.121399
$550$	12.5001	0.533006
$551$	−7.40791	−0.315588
$552$	−2.18622	−0.0930515
$553$	46.7437	1.98775
$554$	36.5729	1.55383
$555$	−2.75990	−0.117151
$556$	−4.35067	−0.184509
$557$	−2.76543	−0.117175	−0.0585875	−	0.998282i	$-0.518660\pi$
$557$	−2.76543	−0.117175	−0.0585875	+	0.998282i	$0.518660\pi$
$558$	−15.8920	−0.672763
$559$	4.32031	0.182730
$560$	19.4396	0.821474
$561$	−12.7205	−0.537062
$562$	−4.03889	−0.170370
$563$	−31.0577	−1.30892	−0.654462	−	0.756095i	$-0.727105\pi$
$563$	−31.0577	−1.30892	−0.654462	+	0.756095i	$0.727105\pi$
$564$	8.28595	0.348902
$565$	−16.0501	−0.675232
$566$	−12.5151	−0.526049
$567$	−0.915586	−0.0384510
$568$	−5.90426	−0.247737
$569$	−2.73413	−0.114621	−0.0573103	−	0.998356i	$-0.518252\pi$
$569$	−2.73413	−0.114621	−0.0573103	+	0.998356i	$0.518252\pi$
$570$	−15.3155	−0.641495
$571$	21.2992	0.891343	0.445671	−	0.895197i	$-0.352965\pi$
$571$	21.2992	0.891343	0.445671	+	0.895197i	$0.352965\pi$
$572$	1.04374	0.0436412
$573$	11.0660	0.462288
$574$	−1.91843	−0.0800736
$575$	3.59066	0.149741
$576$	−6.09487	−0.253953
$577$	23.1589	0.964120	0.482060	−	0.876138i	$-0.339889\pi$
$577$	23.1589	0.964120	0.482060	+	0.876138i	$0.339889\pi$
$578$	26.7771	1.11378
$579$	−8.27781	−0.344014
$580$	−0.884013	−0.0367066
$581$	−13.9486	−0.578685
$582$	14.3935	0.596630
$583$	6.64529	0.275220
$584$	21.7294	0.899170
$585$	1.50059	0.0620417
$586$	−51.8090	−2.14021
$587$	−2.92107	−0.120566	−0.0602828	−	0.998181i	$-0.519200\pi$
$587$	−2.92107	−0.120566	−0.0602828	+	0.998181i	$0.519200\pi$
$588$	−3.13961	−0.129475
$589$	37.4995	1.54514
$590$	15.0033	0.617675
$591$	−11.2556	−0.462992
$592$	−10.9137	−0.448549
$593$	−44.1659	−1.81368	−0.906838	−	0.421480i	$-0.861511\pi$
$593$	−44.1659	−1.81368	−0.906838	+	0.421480i	$0.861511\pi$
$594$	−17.9132	−0.734989
$595$	22.6853	0.930009
$596$	−1.30930	−0.0536310
$597$	−2.65162	−0.108524
$598$	1.10507	0.0451898
$599$	−19.2414	−0.786184	−0.393092	−	0.919499i	$-0.628595\pi$
$599$	−19.2414	−0.786184	−0.393092	+	0.919499i	$0.628595\pi$
$600$	−7.84996	−0.320473
$601$	20.8981	0.852453	0.426226	−	0.904617i	$-0.359843\pi$
$601$	20.8981	0.852453	0.426226	+	0.904617i	$0.359843\pi$
$602$	35.6059	1.45119
$603$	−15.7586	−0.641742
$604$	8.32491	0.338736
$605$	−7.81670	−0.317794
$606$	−6.50758	−0.264352
$607$	2.64492	0.107354	0.0536771	−	0.998558i	$-0.482906\pi$
$607$	2.64492	0.107354	0.0536771	+	0.998558i	$0.482906\pi$
$608$	−29.7501	−1.20652
$609$	−3.48815	−0.141347
$610$	2.95220	0.119531
$611$	7.06083	0.285651
$612$	8.12612	0.328479
$613$	−21.2877	−0.859800	−0.429900	−	0.902876i	$-0.641451\pi$
$613$	−21.2877	−0.859800	−0.429900	+	0.902876i	$0.641451\pi$
$614$	28.1424	1.13573
$615$	−0.435494	−0.0175608
$616$	−14.5016	−0.584285
$617$	43.7793	1.76249	0.881245	−	0.472660i	$-0.156706\pi$
$617$	43.7793	1.76249	0.881245	+	0.472660i	$0.156706\pi$
$618$	−13.4666	−0.541705
$619$	27.8802	1.12060	0.560300	−	0.828290i	$-0.310686\pi$
$619$	27.8802	1.12060	0.560300	+	0.828290i	$0.310686\pi$
$620$	4.47495	0.179718
$621$	−5.14559	−0.206486
$622$	30.3615	1.21738
$623$	26.7287	1.07086
$624$	−3.46020	−0.138519
$625$	5.84616	0.233846
$626$	20.7702	0.830142
$627$	16.3635	0.653494
$628$	6.04654	0.241283
$629$	−12.7358	−0.507811
$630$	12.3671	0.492717
$631$	1.31889	0.0525042	0.0262521	−	0.999655i	$-0.491643\pi$
$631$	1.31889	0.0525042	0.0262521	+	0.999655i	$0.491643\pi$
$632$	29.2969	1.16537
$633$	−17.8539	−0.709627
$634$	−13.8611	−0.550493
$635$	6.08826	0.241605
$636$	2.47545	0.0981579
$637$	−2.67540	−0.106003
$638$	3.48128	0.137825
$639$	−5.37975	−0.212820
$640$	15.8609	0.626958
$641$	−6.30601	−0.249072	−0.124536	−	0.992215i	$-0.539744\pi$
$641$	−6.30601	−0.249072	−0.124536	+	0.992215i	$0.539744\pi$
$642$	−7.73968	−0.305461
$643$	16.5697	0.653446	0.326723	−	0.945120i	$-0.394056\pi$
$643$	16.5697	0.653446	0.326723	+	0.945120i	$0.394056\pi$
$644$	2.47094	0.0973687
$645$	8.08274	0.318258
$646$	−70.6750	−2.78067
$647$	49.9257	1.96278	0.981392	−	0.192017i	$-0.0615030\pi$
$647$	49.9257	1.96278	0.981392	+	0.192017i	$0.0615030\pi$
$648$	−0.573848	−0.0225429
$649$	−16.0299	−0.629228
$650$	3.96795	0.155636
$651$	17.6573	0.692046
$652$	−3.50871	−0.137412
$653$	3.74979	0.146741	0.0733703	−	0.997305i	$-0.476624\pi$
$653$	3.74979	0.146741	0.0733703	+	0.997305i	$0.476624\pi$
$654$	−12.0536	−0.471332
$655$	25.1604	0.983099
$656$	−1.72211	−0.0672370
$657$	19.7991	0.772436
$658$	58.1918	2.26855
$659$	−33.9686	−1.32323	−0.661614	−	0.749845i	$-0.730128\pi$
$659$	−33.9686	−1.32323	−0.661614	+	0.749845i	$0.730128\pi$
$660$	1.95271	0.0760091
$661$	−24.6703	−0.959563	−0.479781	−	0.877388i	$-0.659284\pi$
$661$	−24.6703	−0.959563	−0.479781	+	0.877388i	$0.659284\pi$
$662$	58.2276	2.26308
$663$	−4.03793	−0.156820
$664$	−8.74235	−0.339269
$665$	−29.1820	−1.13163
$666$	−6.94305	−0.269038
$667$	1.00000	0.0387202
$668$	−8.09085	−0.313045
$669$	20.1450	0.778849
$670$	16.3555	0.631868
$671$	−3.15420	−0.121767
$672$	−14.0084	−0.540385
$673$	49.6387	1.91343	0.956716	−	0.291023i	$-0.0939955\pi$
$673$	49.6387	1.91343	0.956716	+	0.291023i	$0.0939955\pi$
$674$	−43.4856	−1.67500
$675$	−18.4761	−0.711145
$676$	−9.34910	−0.359581
$677$	18.0058	0.692020	0.346010	−	0.938231i	$-0.387536\pi$
$677$	18.0058	0.692020	0.346010	+	0.938231i	$0.387536\pi$
$678$	23.5449	0.904237
$679$	27.4252	1.05248
$680$	14.2181	0.545241
$681$	24.1753	0.926398
$682$	−17.6225	−0.674802
$683$	−11.9342	−0.456650	−0.228325	−	0.973585i	$-0.573325\pi$
$683$	−11.9342	−0.456650	−0.228325	+	0.973585i	$0.573325\pi$
$684$	−10.4533	−0.399691
$685$	2.52949	0.0966468
$686$	16.4322	0.627385
$687$	−5.61678	−0.214293
$688$	31.9622	1.21855
$689$	2.10944	0.0803632
$690$	2.06745	0.0787065
$691$	−2.21755	−0.0843596	−0.0421798	−	0.999110i	$-0.513430\pi$
$691$	−2.21755	−0.0843596	−0.0421798	+	0.999110i	$0.513430\pi$
$692$	−8.39839	−0.319259
$693$	−13.2133	−0.501933
$694$	58.4801	2.21987
$695$	−6.93606	−0.263100
$696$	−2.18622	−0.0828683
$697$	−2.00964	−0.0761204
$698$	−6.04549	−0.228825
$699$	5.11097	0.193315
$700$	8.87231	0.335342
$701$	−39.3798	−1.48735	−0.743677	−	0.668540i	$-0.766920\pi$
$701$	−39.3798	−1.48735	−0.743677	+	0.668540i	$0.766920\pi$
$702$	−5.68626	−0.214614
$703$	16.3831	0.617902
$704$	−6.75856	−0.254723
$705$	13.2099	0.497513
$706$	−47.3904	−1.78356
$707$	−12.3995	−0.466330
$708$	−5.97132	−0.224416
$709$	−23.4737	−0.881575	−0.440787	−	0.897612i	$-0.645301\pi$
$709$	−23.4737	−0.881575	−0.440787	+	0.897612i	$0.645301\pi$
$710$	5.58351	0.209545
$711$	26.6943	1.00111
$712$	16.7523	0.627820
$713$	−5.06209	−0.189577
$714$	−33.2786	−1.24542
$715$	1.66399	0.0622297
$716$	−10.9374	−0.408750
$717$	29.5603	1.10395
$718$	−12.4978	−0.466414
$719$	22.0001	0.820464	0.410232	−	0.911981i	$-0.365448\pi$
$719$	22.0001	0.820464	0.410232	+	0.911981i	$0.365448\pi$
$720$	11.1015	0.413729
$721$	−25.6591	−0.955593
$722$	59.4377	2.21204
$723$	27.9430	1.03921
$724$	−12.9663	−0.481889
$725$	3.59066	0.133354
$726$	11.4668	0.425574
$727$	41.1560	1.52639	0.763195	−	0.646168i	$-0.223629\pi$
$727$	41.1560	1.52639	0.763195	+	0.646168i	$0.223629\pi$
$728$	−4.60329	−0.170609
$729$	15.7042	0.581638
$730$	−20.5490	−0.760552
$731$	37.2987	1.37954
$732$	−1.17498	−0.0434284
$733$	−39.7030	−1.46646	−0.733232	−	0.679979i	$-0.761989\pi$
$733$	−39.7030	−1.46646	−0.733232	+	0.679979i	$0.761989\pi$
$734$	−11.5836	−0.427559
$735$	−5.00533	−0.184624
$736$	4.01599	0.148031
$737$	−17.4746	−0.643687
$738$	−1.09557	−0.0403285
$739$	42.5860	1.56655	0.783275	−	0.621675i	$-0.213547\pi$
$739$	42.5860	1.56655	0.783275	+	0.621675i	$0.213547\pi$
$740$	1.95506	0.0718694
$741$	5.19431	0.190818
$742$	17.3850	0.638222
$743$	−43.7417	−1.60473	−0.802364	−	0.596836i	$-0.796424\pi$
$743$	−43.7417	−1.60473	−0.802364	+	0.596836i	$0.796424\pi$
$744$	11.0668	0.405729
$745$	−2.08735	−0.0764746
$746$	29.9807	1.09767
$747$	−7.96572	−0.291450
$748$	9.01099	0.329475
$749$	−14.7471	−0.538847
$750$	17.7608	0.648531
$751$	40.2598	1.46910	0.734550	−	0.678555i	$-0.237393\pi$
$751$	40.2598	1.46910	0.734550	+	0.678555i	$0.237393\pi$
$752$	52.2368	1.90488
$753$	13.7409	0.500748
$754$	1.10507	0.0402444
$755$	13.2720	0.483017
$756$	−12.7145	−0.462420
$757$	−10.0182	−0.364118	−0.182059	−	0.983288i	$-0.558276\pi$
$757$	−10.0182	−0.364118	−0.182059	+	0.983288i	$0.558276\pi$
$758$	−52.2411	−1.89748
$759$	−2.20892	−0.0801786
$760$	−18.2899	−0.663446
$761$	−36.8749	−1.33672	−0.668358	−	0.743840i	$-0.733002\pi$
$761$	−36.8749	−1.33672	−0.668358	+	0.743840i	$0.733002\pi$
$762$	−8.93126	−0.323545
$763$	−22.9667	−0.831452
$764$	−7.83893	−0.283603
$765$	12.9551	0.468392
$766$	−61.6713	−2.22828
$767$	−5.08842	−0.183732
$768$	−16.5054	−0.595589
$769$	48.8484	1.76152	0.880759	−	0.473564i	$-0.157033\pi$
$769$	48.8484	1.76152	0.880759	+	0.473564i	$0.157033\pi$
$770$	13.7138	0.494211
$771$	−14.0620	−0.506432
$772$	5.86384	0.211044
$773$	30.1679	1.08506	0.542531	−	0.840036i	$-0.317466\pi$
$773$	30.1679	1.08506	0.542531	+	0.840036i	$0.317466\pi$
$774$	20.3337	0.730879
$775$	−18.1763	−0.652910
$776$	17.1889	0.617046
$777$	7.71430	0.276749
$778$	−25.5319	−0.915364
$779$	2.58516	0.0926228
$780$	0.619856	0.0221944
$781$	−5.96556	−0.213465
$782$	9.54047	0.341167
$783$	−5.14559	−0.183889
$784$	−19.7929	−0.706891
$785$	9.63971	0.344056
$786$	−36.9095	−1.31652
$787$	−48.6965	−1.73584	−0.867922	−	0.496701i	$-0.834545\pi$
$787$	−48.6965	−1.73584	−0.867922	+	0.496701i	$0.834545\pi$
$788$	7.97323	0.284035
$789$	−3.43972	−0.122457
$790$	−27.7053	−0.985711
$791$	44.8622	1.59512
$792$	−8.28152	−0.294271
$793$	−1.00125	−0.0355554
$794$	3.83098	0.135956
$795$	3.94649	0.139967
$796$	1.87836	0.0665767
$797$	−27.1436	−0.961477	−0.480739	−	0.876864i	$-0.659631\pi$
$797$	−27.1436	−0.961477	−0.480739	+	0.876864i	$0.659631\pi$
$798$	42.8090	1.51542
$799$	60.9585	2.15656
$800$	14.4200	0.509826
$801$	15.2641	0.539331
$802$	16.9451	0.598353
$803$	21.9551	0.774777
$804$	−6.50951	−0.229573
$805$	3.93930	0.138842
$806$	−5.59399	−0.197040
$807$	−24.1971	−0.851779
$808$	−7.77143	−0.273398
$809$	6.48979	0.228169	0.114084	−	0.993471i	$-0.463607\pi$
$809$	6.48979	0.228169	0.114084	+	0.993471i	$0.463607\pi$
$810$	0.542674	0.0190676
$811$	−7.89795	−0.277335	−0.138667	−	0.990339i	$-0.544282\pi$
$811$	−7.89795	−0.277335	−0.138667	+	0.990339i	$0.544282\pi$
$812$	2.47094	0.0867130
$813$	16.0378	0.562469
$814$	−7.69910	−0.269853
$815$	−5.59377	−0.195941
$816$	−29.8731	−1.04577
$817$	−47.9803	−1.67862
$818$	4.23648	0.148125
$819$	−4.19436	−0.146563
$820$	0.308496	0.0107731
$821$	−24.0416	−0.839059	−0.419530	−	0.907742i	$-0.637805\pi$
$821$	−24.0416	−0.839059	−0.419530	+	0.907742i	$0.637805\pi$
$822$	−3.71067	−0.129424
$823$	−10.9659	−0.382248	−0.191124	−	0.981566i	$-0.561213\pi$
$823$	−10.9659	−0.382248	−0.191124	+	0.981566i	$0.561213\pi$
$824$	−16.0819	−0.560241
$825$	−7.93147	−0.276138
$826$	−41.9363	−1.45915
$827$	1.54551	0.0537428	0.0268714	−	0.999639i	$-0.491446\pi$
$827$	1.54551	0.0537428	0.0268714	+	0.999639i	$0.491446\pi$
$828$	1.41110	0.0490390
$829$	39.8166	1.38289	0.691445	−	0.722430i	$-0.256975\pi$
$829$	39.8166	1.38289	0.691445	+	0.722430i	$0.256975\pi$
$830$	8.26742	0.286966
$831$	−23.2060	−0.805007
$832$	−2.14539	−0.0743781
$833$	−23.0976	−0.800286
$834$	10.1750	0.352330
$835$	−12.8989	−0.446383
$836$	−11.5916	−0.400903
$837$	26.0475	0.900332
$838$	−19.4765	−0.672803
$839$	−26.7520	−0.923580	−0.461790	−	0.886989i	$-0.652793\pi$
$839$	−26.7520	−0.923580	−0.461790	+	0.886989i	$0.652793\pi$
$840$	−8.61216	−0.297148
$841$	1.00000	0.0344828
$842$	−12.0403	−0.414935
$843$	2.56273	0.0882651
$844$	12.6473	0.435339
$845$	−14.9048	−0.512741
$846$	33.2320	1.14254
$847$	21.8488	0.750733
$848$	15.6059	0.535908
$849$	7.94099	0.272534
$850$	34.2566	1.17499
$851$	−2.21157	−0.0758117
$852$	−2.22224	−0.0761327
$853$	40.2749	1.37899	0.689493	−	0.724292i	$-0.257833\pi$
$853$	40.2749	1.37899	0.689493	+	0.724292i	$0.257833\pi$
$854$	−8.25180	−0.282371
$855$	−16.6652	−0.569936
$856$	−9.24281	−0.315913
$857$	48.9554	1.67229	0.836143	−	0.548512i	$-0.184806\pi$
$857$	48.9554	1.67229	0.836143	+	0.548512i	$0.184806\pi$
$858$	−2.44102	−0.0833349
$859$	−33.6240	−1.14724	−0.573618	−	0.819123i	$-0.694461\pi$
$859$	−33.6240	−1.14724	−0.573618	+	0.819123i	$0.694461\pi$
$860$	−5.72566	−0.195243
$861$	1.21727	0.0414844
$862$	39.6006	1.34880
$863$	−14.2421	−0.484807	−0.242403	−	0.970176i	$-0.577936\pi$
$863$	−14.2421	−0.484807	−0.242403	+	0.970176i	$0.577936\pi$
$864$	−20.6646	−0.703025
$865$	−13.3891	−0.455245
$866$	31.5130	1.07085
$867$	−16.9904	−0.577026
$868$	−12.5081	−0.424553
$869$	29.6011	1.00415
$870$	2.06745	0.0700931
$871$	−5.54704	−0.187954
$872$	−14.3945	−0.487460
$873$	15.6619	0.530076
$874$	−12.2727	−0.415129
$875$	33.8412	1.14404
$876$	8.17851	0.276326
$877$	52.9812	1.78905	0.894524	−	0.447020i	$-0.147515\pi$
$877$	52.9812	1.78905	0.894524	+	0.447020i	$0.147515\pi$
$878$	30.7779	1.03870
$879$	32.8735	1.10879
$880$	12.3104	0.414983
$881$	12.4189	0.418403	0.209202	−	0.977873i	$-0.432914\pi$
$881$	12.4189	0.418403	0.209202	+	0.977873i	$0.432914\pi$
$882$	−12.5919	−0.423990
$883$	11.5052	0.387180	0.193590	−	0.981083i	$-0.437987\pi$
$883$	11.5052	0.387180	0.193590	+	0.981083i	$0.437987\pi$
$884$	2.86039	0.0962054
$885$	−9.51978	−0.320004
$886$	0.921061	0.0309436
$887$	−50.7787	−1.70498	−0.852491	−	0.522742i	$-0.824909\pi$
$887$	−50.7787	−1.70498	−0.852491	+	0.522742i	$0.824909\pi$
$888$	4.83497	0.162251
$889$	−17.0175	−0.570750
$890$	−15.8423	−0.531034
$891$	−0.579806	−0.0194242
$892$	−14.2703	−0.477805
$893$	−78.4158	−2.62408
$894$	3.06207	0.102411
$895$	−17.4370	−0.582854
$896$	−44.3335	−1.48108
$897$	−0.701184	−0.0234119
$898$	10.7202	0.357737
$899$	−5.06209	−0.168830
$900$	5.06677	0.168892
$901$	18.2115	0.606713
$902$	−1.21487	−0.0404507
$903$	−22.5924	−0.751828
$904$	28.1176	0.935178
$905$	−20.6716	−0.687146
$906$	−19.4695	−0.646832
$907$	5.12992	0.170336	0.0851681	−	0.996367i	$-0.472857\pi$
$907$	5.12992	0.170336	0.0851681	+	0.996367i	$0.472857\pi$
$908$	−17.1253	−0.568323
$909$	−7.08105	−0.234864
$910$	4.35322	0.144308
$911$	−48.0243	−1.59112	−0.795558	−	0.605877i	$-0.792822\pi$
$911$	−48.0243	−1.59112	−0.795558	+	0.605877i	$0.792822\pi$
$912$	38.4281	1.27248
$913$	−8.83312	−0.292334
$914$	25.4046	0.840311
$915$	−1.87321	−0.0619263
$916$	3.97882	0.131464
$917$	−70.3269	−2.32240
$918$	−49.0914	−1.62026
$919$	−43.2925	−1.42809	−0.714045	−	0.700100i	$-0.753139\pi$
$919$	−43.2925	−1.42809	−0.714045	+	0.700100i	$0.753139\pi$
$920$	2.46897	0.0813997
$921$	−17.8567	−0.588399
$922$	1.88441	0.0620598
$923$	−1.89367	−0.0623309
$924$	−5.45810	−0.179558
$925$	−7.94101	−0.261099
$926$	−52.0539	−1.71060
$927$	−14.6533	−0.481277
$928$	4.01599	0.131831
$929$	7.32792	0.240421	0.120211	−	0.992748i	$-0.461643\pi$
$929$	7.32792	0.240421	0.120211	+	0.992748i	$0.461643\pi$
$930$	−10.4656	−0.343181
$931$	29.7124	0.973783
$932$	−3.62051	−0.118594
$933$	−19.2648	−0.630700
$934$	31.1755	1.02009
$935$	14.3658	0.469811
$936$	−2.62883	−0.0859261
$937$	−43.6703	−1.42665	−0.713323	−	0.700835i	$-0.752811\pi$
$937$	−43.6703	−1.42665	−0.713323	+	0.700835i	$0.752811\pi$
$938$	−45.7159	−1.49268
$939$	−13.1789	−0.430079
$940$	−9.35763	−0.305212
$941$	−10.0551	−0.327788	−0.163894	−	0.986478i	$-0.552405\pi$
$941$	−10.0551	−0.327788	−0.163894	+	0.986478i	$0.552405\pi$
$942$	−14.1411	−0.460742
$943$	−0.348972	−0.0113641
$944$	−37.6447	−1.22523
$945$	−20.2700	−0.659384
$946$	22.5479	0.733095
$947$	−30.6421	−0.995736	−0.497868	−	0.867253i	$-0.665884\pi$
$947$	−30.6421	−0.995736	−0.497868	+	0.867253i	$0.665884\pi$
$948$	11.0267	0.358132
$949$	6.96927	0.226232
$950$	−44.0670	−1.42972
$951$	8.79503	0.285198
$952$	−39.7417	−1.28804
$953$	−36.7418	−1.19018	−0.595092	−	0.803657i	$-0.702884\pi$
$953$	−36.7418	−1.19018	−0.595092	+	0.803657i	$0.702884\pi$
$954$	9.92814	0.321435
$955$	−12.4972	−0.404401
$956$	−20.9399	−0.677245
$957$	−2.20892	−0.0714041
$958$	47.3211	1.52888
$959$	−7.07027	−0.228311
$960$	−4.01375	−0.129543
$961$	−5.37523	−0.173395
$962$	−2.44395	−0.0787962
$963$	−8.42173	−0.271386
$964$	−19.7943	−0.637532
$965$	9.34844	0.300937
$966$	−5.77881	−0.185930
$967$	−7.79255	−0.250592	−0.125296	−	0.992119i	$-0.539988\pi$
$967$	−7.79255	−0.250592	−0.125296	+	0.992119i	$0.539988\pi$
$968$	13.6938	0.440136
$969$	44.8442	1.44060
$970$	−16.2551	−0.521920
$971$	5.06967	0.162694	0.0813468	−	0.996686i	$-0.474078\pi$
$971$	5.06967	0.162694	0.0813468	+	0.996686i	$0.474078\pi$
$972$	−11.7109	−0.375629
$973$	19.3873	0.621527
$974$	50.3190	1.61232
$975$	−2.51772	−0.0806314
$976$	−7.40736	−0.237104
$977$	−9.61482	−0.307605	−0.153803	−	0.988102i	$-0.549152\pi$
$977$	−9.61482	−0.307605	−0.153803	+	0.988102i	$0.549152\pi$
$978$	8.20586	0.262395
$979$	16.9263	0.540966
$980$	3.54568	0.113263
$981$	−13.1158	−0.418754
$982$	71.4358	2.27961
$983$	10.2713	0.327605	0.163802	−	0.986493i	$-0.447624\pi$
$983$	10.2713	0.327605	0.163802	+	0.986493i	$0.447624\pi$
$984$	0.762929	0.0243213
$985$	12.7113	0.405017
$986$	9.54047	0.303831
$987$	−36.9235	−1.17529
$988$	−3.67955	−0.117062
$989$	6.47690	0.205953
$990$	7.83163	0.248905
$991$	−33.9525	−1.07854	−0.539268	−	0.842134i	$-0.681299\pi$
$991$	−33.9525	−1.07854	−0.539268	+	0.842134i	$0.681299\pi$
$992$	−20.3293	−0.645455
$993$	−36.9462	−1.17245
$994$	−15.6067	−0.495014
$995$	2.99458	0.0949345
$996$	−3.29044	−0.104262
$997$	−34.4565	−1.09125	−0.545623	−	0.838030i	$-0.683707\pi$
$997$	−34.4565	−1.09125	−0.545623	+	0.838030i	$0.683707\pi$
$998$	−52.5515	−1.66349
$999$	11.3799	0.360043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.10	✓	12
3.2	odd	2		6003.2.a.n.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.10	✓	12	1.1	even	1	trivial
6003.2.a.n.1.3		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.65670 q^{2} -1.05120 q^{3} +0.744648 q^{4} +1.18716 q^{5} -1.74152 q^{6} -3.31827 q^{7} -2.07974 q^{8} -1.89498 q^{9} +O(q^{10})\)	\(q+1.65670 q^{2} -1.05120 q^{3} +0.744648 q^{4} +1.18716 q^{5} -1.74152 q^{6} -3.31827 q^{7} -2.07974 q^{8} -1.89498 q^{9} +1.96676 q^{10} -2.10133 q^{11} -0.782771 q^{12} -0.667034 q^{13} -5.49737 q^{14} -1.24793 q^{15} -4.93480 q^{16} -5.75873 q^{17} -3.13942 q^{18} +7.40791 q^{19} +0.884013 q^{20} +3.48815 q^{21} -3.48128 q^{22} -1.00000 q^{23} +2.18622 q^{24} -3.59066 q^{25} -1.10507 q^{26} +5.14559 q^{27} -2.47094 q^{28} -1.00000 q^{29} -2.06745 q^{30} +5.06209 q^{31} -4.01599 q^{32} +2.20892 q^{33} -9.54047 q^{34} -3.93930 q^{35} -1.41110 q^{36} +2.21157 q^{37} +12.2727 q^{38} +0.701184 q^{39} -2.46897 q^{40} +0.348972 q^{41} +5.77881 q^{42} -6.47690 q^{43} -1.56475 q^{44} -2.24964 q^{45} -1.65670 q^{46} -10.5854 q^{47} +5.18744 q^{48} +4.01089 q^{49} -5.94864 q^{50} +6.05356 q^{51} -0.496706 q^{52} -3.16242 q^{53} +8.52469 q^{54} -2.49461 q^{55} +6.90113 q^{56} -7.78718 q^{57} -1.65670 q^{58} +7.62843 q^{59} -0.929271 q^{60} +1.50105 q^{61} +8.38636 q^{62} +6.28807 q^{63} +3.21632 q^{64} -0.791873 q^{65} +3.65951 q^{66} +8.31597 q^{67} -4.28822 q^{68} +1.05120 q^{69} -6.52623 q^{70} +2.83894 q^{71} +3.94107 q^{72} -10.4481 q^{73} +3.66391 q^{74} +3.77449 q^{75} +5.51629 q^{76} +6.97279 q^{77} +1.16165 q^{78} -14.0868 q^{79} -5.85837 q^{80} +0.275923 q^{81} +0.578142 q^{82} +4.20358 q^{83} +2.59744 q^{84} -6.83651 q^{85} -10.7303 q^{86} +1.05120 q^{87} +4.37023 q^{88} -8.05501 q^{89} -3.72698 q^{90} +2.21340 q^{91} -0.744648 q^{92} -5.32125 q^{93} -17.5368 q^{94} +8.79435 q^{95} +4.22159 q^{96} -8.26493 q^{97} +6.64484 q^{98} +3.98200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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