LMFDB - Embedded newform 671.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.96003$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44983 q^{2} +2.04164 q^{3} +4.00166 q^{4} -0.489803 q^{5} -5.00166 q^{6} -2.06203 q^{7} -4.90374 q^{8} +1.16828 q^{9} +O(q^{10})$	\(q-2.44983 q^{2} +2.04164 q^{3} +4.00166 q^{4} -0.489803 q^{5} -5.00166 q^{6} -2.06203 q^{7} -4.90374 q^{8} +1.16828 q^{9} +1.19993 q^{10} +1.00000 q^{11} +8.16995 q^{12} -4.04164 q^{13} +5.05163 q^{14} -1.00000 q^{15} +4.00999 q^{16} -0.510197 q^{17} -2.86210 q^{18} -6.39354 q^{19} -1.96003 q^{20} -4.20992 q^{21} -2.44983 q^{22} +2.07835 q^{23} -10.0117 q^{24} -4.76009 q^{25} +9.90132 q^{26} -3.73970 q^{27} -8.25156 q^{28} -2.48263 q^{29} +2.44983 q^{30} -5.23749 q^{31} -0.0163168 q^{32} +2.04164 q^{33} +1.24990 q^{34} +1.00999 q^{35} +4.67508 q^{36} +4.45557 q^{37} +15.6631 q^{38} -8.25156 q^{39} +2.40186 q^{40} -0.256224 q^{41} +10.3136 q^{42} +5.76584 q^{43} +4.00166 q^{44} -0.572229 q^{45} -5.09160 q^{46} +5.45149 q^{47} +8.18695 q^{48} -2.74802 q^{49} +11.6614 q^{50} -1.04164 q^{51} -16.1733 q^{52} +5.63544 q^{53} +9.16162 q^{54} -0.489803 q^{55} +10.1117 q^{56} -13.0533 q^{57} +6.08201 q^{58} -6.29986 q^{59} -4.00166 q^{60} +1.00000 q^{61} +12.8310 q^{62} -2.40904 q^{63} -7.98000 q^{64} +1.97961 q^{65} -5.00166 q^{66} -9.16655 q^{67} -2.04164 q^{68} +4.24324 q^{69} -2.47430 q^{70} -1.68647 q^{71} -5.72896 q^{72} +2.67134 q^{73} -10.9154 q^{74} -9.71839 q^{75} -25.5848 q^{76} -2.06203 q^{77} +20.2149 q^{78} -1.76968 q^{79} -1.96410 q^{80} -11.1400 q^{81} +0.627704 q^{82} -9.03172 q^{83} -16.8467 q^{84} +0.249896 q^{85} -14.1253 q^{86} -5.06862 q^{87} -4.90374 q^{88} -4.40068 q^{89} +1.40186 q^{90} +8.33399 q^{91} +8.31685 q^{92} -10.6931 q^{93} -13.3552 q^{94} +3.13157 q^{95} -0.0333130 q^{96} -11.5238 q^{97} +6.73219 q^{98} +1.16828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * 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 $

$2$	−2.44983	−1.73229	−0.866146	−	0.499792i	$-0.833410\pi$
$2$	−2.44983	−1.73229	−0.866146	+	0.499792i	$0.833410\pi$
$3$	2.04164	1.17874	0.589370	−	0.807863i	$-0.299376\pi$
$3$	2.04164	1.17874	0.589370	+	0.807863i	$0.299376\pi$
$4$	4.00166	2.00083
$5$	−0.489803	−0.219046	−0.109523	−	0.993984i	$-0.534932\pi$
$5$	−0.489803	−0.219046	−0.109523	+	0.993984i	$0.534932\pi$
$6$	−5.00166	−2.04192
$7$	−2.06203	−0.779375	−0.389687	−	0.920947i	$-0.627417\pi$
$7$	−2.06203	−0.779375	−0.389687	+	0.920947i	$0.627417\pi$
$8$	−4.90374	−1.73373
$9$	1.16828	0.389428
$10$	1.19993	0.379452
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	8.16995	2.35846
$13$	−4.04164	−1.12095	−0.560474	−	0.828172i	$-0.689381\pi$
$13$	−4.04164	−1.12095	−0.560474	+	0.828172i	$0.689381\pi$
$14$	5.05163	1.35010
$15$	−1.00000	−0.258199
$16$	4.00999	1.00250
$17$	−0.510197	−0.123741	−0.0618705	−	0.998084i	$-0.519707\pi$
$17$	−0.510197	−0.123741	−0.0618705	+	0.998084i	$0.519707\pi$
$18$	−2.86210	−0.674603
$19$	−6.39354	−1.46678	−0.733389	−	0.679809i	$-0.762063\pi$
$19$	−6.39354	−1.46678	−0.733389	+	0.679809i	$0.762063\pi$
$20$	−1.96003	−0.438275
$21$	−4.20992	−0.918680
$22$	−2.44983	−0.522305
$23$	2.07835	0.433366	0.216683	−	0.976242i	$-0.430476\pi$
$23$	2.07835	0.433366	0.216683	+	0.976242i	$0.430476\pi$
$24$	−10.0117	−2.04362
$25$	−4.76009	−0.952019
$26$	9.90132	1.94181
$27$	−3.73970	−0.719705
$28$	−8.25156	−1.55940
$29$	−2.48263	−0.461012	−0.230506	−	0.973071i	$-0.574038\pi$
$29$	−2.48263	−0.461012	−0.230506	+	0.973071i	$0.574038\pi$
$30$	2.44983	0.447276
$31$	−5.23749	−0.940682	−0.470341	−	0.882485i	$-0.655869\pi$
$31$	−5.23749	−0.940682	−0.470341	+	0.882485i	$0.655869\pi$
$32$	−0.0163168	−0.00288443
$33$	2.04164	0.355404
$34$	1.24990	0.214355
$35$	1.00999	0.170719
$36$	4.67508	0.779181
$37$	4.45557	0.732491	0.366246	−	0.930518i	$-0.380643\pi$
$37$	4.45557	0.732491	0.366246	+	0.930518i	$0.380643\pi$
$38$	15.6631	2.54089
$39$	−8.25156	−1.32131
$40$	2.40186	0.379768
$41$	−0.256224	−0.0400154	−0.0200077	−	0.999800i	$-0.506369\pi$
$41$	−0.256224	−0.0400154	−0.0200077	+	0.999800i	$0.506369\pi$
$42$	10.3136	1.59142
$43$	5.76584	0.879282	0.439641	−	0.898174i	$-0.355106\pi$
$43$	5.76584	0.879282	0.439641	+	0.898174i	$0.355106\pi$
$44$	4.00166	0.603274
$45$	−0.572229	−0.0853029
$46$	−5.09160	−0.750716
$47$	5.45149	0.795182	0.397591	−	0.917563i	$-0.369846\pi$
$47$	5.45149	0.795182	0.397591	+	0.917563i	$0.369846\pi$
$48$	8.18695	1.18168
$49$	−2.74802	−0.392575
$50$	11.6614	1.64917
$51$	−1.04164	−0.145858
$52$	−16.1733	−2.24283
$53$	5.63544	0.774088	0.387044	−	0.922061i	$-0.373496\pi$
$53$	5.63544	0.774088	0.387044	+	0.922061i	$0.373496\pi$
$54$	9.16162	1.24674
$55$	−0.489803	−0.0660450
$56$	10.1117	1.35123
$57$	−13.0533	−1.72895
$58$	6.08201	0.798607
$59$	−6.29986	−0.820172	−0.410086	−	0.912047i	$-0.634501\pi$
$59$	−6.29986	−0.820172	−0.410086	+	0.912047i	$0.634501\pi$
$60$	−4.00166	−0.516613
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	12.8310	1.62953
$63$	−2.40904	−0.303511
$64$	−7.98000	−0.997501
$65$	1.97961	0.245540
$66$	−5.00166	−0.615662
$67$	−9.16655	−1.11987	−0.559936	−	0.828536i	$-0.689174\pi$
$67$	−9.16655	−1.11987	−0.559936	+	0.828536i	$0.689174\pi$
$68$	−2.04164	−0.247585
$69$	4.24324	0.510826
$70$	−2.47430	−0.295736
$71$	−1.68647	−0.200148	−0.100074	−	0.994980i	$-0.531908\pi$
$71$	−1.68647	−0.200148	−0.100074	+	0.994980i	$0.531908\pi$
$72$	−5.72896	−0.675165
$73$	2.67134	0.312657	0.156328	−	0.987705i	$-0.450034\pi$
$73$	2.67134	0.312657	0.156328	+	0.987705i	$0.450034\pi$
$74$	−10.9154	−1.26889
$75$	−9.71839	−1.12218
$76$	−25.5848	−2.93478
$77$	−2.06203	−0.234990
$78$	20.2149	2.28889
$79$	−1.76968	−0.199105	−0.0995524	−	0.995032i	$-0.531741\pi$
$79$	−1.76968	−0.199105	−0.0995524	+	0.995032i	$0.531741\pi$
$80$	−1.96410	−0.219594
$81$	−11.1400	−1.23777
$82$	0.627704	0.0693183
$83$	−9.03172	−0.991360	−0.495680	−	0.868505i	$-0.665081\pi$
$83$	−9.03172	−0.991360	−0.495680	+	0.868505i	$0.665081\pi$
$84$	−16.8467	−1.83813
$85$	0.249896	0.0271050
$86$	−14.1253	−1.52317
$87$	−5.06862	−0.543413
$88$	−4.90374	−0.522740
$89$	−4.40068	−0.466471	−0.233236	−	0.972420i	$-0.574931\pi$
$89$	−4.40068	−0.466471	−0.233236	+	0.972420i	$0.574931\pi$
$90$	1.40186	0.147769
$91$	8.33399	0.873639
$92$	8.31685	0.867092
$93$	−10.6931	−1.10882
$94$	−13.3552	−1.37749
$95$	3.13157	0.321293
$96$	−0.0333130	−0.00339999
$97$	−11.5238	−1.17007	−0.585035	−	0.811008i	$-0.698919\pi$
$97$	−11.5238	−1.17007	−0.585035	+	0.811008i	$0.698919\pi$
$98$	6.73219	0.680054
$99$	1.16828	0.117417
$100$	−19.0483	−1.90483
$101$	−0.257236	−0.0255959	−0.0127980	−	0.999918i	$-0.504074\pi$
$101$	−0.257236	−0.0255959	−0.0127980	+	0.999918i	$0.504074\pi$
$102$	2.55183	0.252669
$103$	18.0678	1.78028	0.890139	−	0.455690i	$-0.150607\pi$
$103$	18.0678	1.78028	0.890139	+	0.455690i	$0.150607\pi$
$104$	19.8191	1.94343
$105$	2.06203	0.201234
$106$	−13.8059	−1.34095
$107$	−1.10086	−0.106424	−0.0532120	−	0.998583i	$-0.516946\pi$
$107$	−1.10086	−0.106424	−0.0532120	+	0.998583i	$0.516946\pi$
$108$	−14.9650	−1.44001
$109$	−12.7582	−1.22201	−0.611005	−	0.791627i	$-0.709235\pi$
$109$	−12.7582	−1.22201	−0.611005	+	0.791627i	$0.709235\pi$
$110$	1.19993	0.114409
$111$	9.09666	0.863417
$112$	−8.26873	−0.781321
$113$	14.5769	1.37128	0.685639	−	0.727942i	$-0.259523\pi$
$113$	14.5769	1.37128	0.685639	+	0.727942i	$0.259523\pi$
$114$	31.9783	2.99505
$115$	−1.01798	−0.0949272
$116$	−9.93464	−0.922408
$117$	−4.72178	−0.436529
$118$	15.4336	1.42078
$119$	1.05204	0.0964406
$120$	4.90374	0.447648
$121$	1.00000	0.0909091
$122$	−2.44983	−0.221797
$123$	−0.523116	−0.0471678
$124$	−20.9587	−1.88215
$125$	4.78052	0.427583
$126$	5.90174	0.525769
$127$	−7.27412	−0.645474	−0.322737	−	0.946489i	$-0.604603\pi$
$127$	−7.27412	−0.645474	−0.322737	+	0.946489i	$0.604603\pi$
$128$	19.5823	1.73085
$129$	11.7717	1.03644
$130$	−4.84970	−0.425347
$131$	−10.8620	−0.949020	−0.474510	−	0.880250i	$-0.657375\pi$
$131$	−10.8620	−0.949020	−0.474510	+	0.880250i	$0.657375\pi$
$132$	8.16995	0.711103
$133$	13.1837	1.14317
$134$	22.4565	1.93995
$135$	1.83172	0.157649
$136$	2.50187	0.214534
$137$	−19.1149	−1.63310	−0.816548	−	0.577277i	$-0.804115\pi$
$137$	−19.1149	−1.63310	−0.816548	+	0.577277i	$0.804115\pi$
$138$	−10.3952	−0.884899
$139$	22.9296	1.94487	0.972433	−	0.233181i	$-0.0749135\pi$
$139$	22.9296	1.94487	0.972433	+	0.233181i	$0.0749135\pi$
$140$	4.04164	0.341581
$141$	11.1300	0.937313
$142$	4.13157	0.346714
$143$	−4.04164	−0.337979
$144$	4.68481	0.390401
$145$	1.21600	0.100983
$146$	−6.54433	−0.541612
$147$	−5.61047	−0.462744
$148$	17.8297	1.46559
$149$	12.2159	1.00077	0.500384	−	0.865804i	$-0.333192\pi$
$149$	12.2159	1.00077	0.500384	+	0.865804i	$0.333192\pi$
$150$	23.8084	1.94395
$151$	−2.64618	−0.215343	−0.107672	−	0.994187i	$-0.534339\pi$
$151$	−2.64618	−0.215343	−0.107672	+	0.994187i	$0.534339\pi$
$152$	31.3522	2.54300
$153$	−0.596056	−0.0481882
$154$	5.05163	0.407072
$155$	2.56534	0.206053
$156$	−33.0200	−2.64371
$157$	20.8502	1.66403	0.832013	−	0.554756i	$-0.187188\pi$
$157$	20.8502	1.66403	0.832013	+	0.554756i	$0.187188\pi$
$158$	4.33542	0.344908
$159$	11.5055	0.912448
$160$	0.00799202	0.000631824 0
$161$	−4.28562	−0.337754
$162$	27.2910	2.14418
$163$	−12.4014	−0.971356	−0.485678	−	0.874138i	$-0.661427\pi$
$163$	−12.4014	−0.971356	−0.485678	+	0.874138i	$0.661427\pi$
$164$	−1.02532	−0.0800641
$165$	−1.00000	−0.0778499
$166$	22.1262	1.71732
$167$	−0.931606	−0.0720899	−0.0360449	−	0.999350i	$-0.511476\pi$
$167$	−0.931606	−0.0720899	−0.0360449	+	0.999350i	$0.511476\pi$
$168$	20.6444	1.59275
$169$	3.33484	0.256526
$170$	−0.612203	−0.0469538
$171$	−7.46948	−0.571205
$172$	23.0729	1.75929
$173$	12.7206	0.967129	0.483565	−	0.875309i	$-0.339342\pi$
$173$	12.7206	0.967129	0.483565	+	0.875309i	$0.339342\pi$
$174$	12.4173	0.941350
$175$	9.81546	0.741979
$176$	4.00999	0.302264
$177$	−12.8620	−0.966769
$178$	10.7809	0.808064
$179$	1.54861	0.115748	0.0578741	−	0.998324i	$-0.481568\pi$
$179$	1.54861	0.115748	0.0578741	+	0.998324i	$0.481568\pi$
$180$	−2.28987	−0.170677
$181$	−13.4605	−1.00051	−0.500254	−	0.865878i	$-0.666760\pi$
$181$	−13.4605	−1.00051	−0.500254	+	0.865878i	$0.666760\pi$
$182$	−20.4168	−1.51340
$183$	2.04164	0.150922
$184$	−10.1917	−0.751340
$185$	−2.18235	−0.160450
$186$	26.1962	1.92080
$187$	−0.510197	−0.0373093
$188$	21.8150	1.59103
$189$	7.71138	0.560920
$190$	−7.67182	−0.556572
$191$	−15.4558	−1.11834	−0.559170	−	0.829053i	$-0.688880\pi$
$191$	−15.4558	−1.11834	−0.559170	+	0.829053i	$0.688880\pi$
$192$	−16.2923	−1.17579
$193$	−13.8228	−0.994985	−0.497493	−	0.867468i	$-0.665746\pi$
$193$	−13.8228	−0.994985	−0.497493	+	0.867468i	$0.665746\pi$
$194$	28.2315	2.02690
$195$	4.04164	0.289428
$196$	−10.9967	−0.785476
$197$	1.52094	0.108363	0.0541813	−	0.998531i	$-0.482745\pi$
$197$	1.52094	0.108363	0.0541813	+	0.998531i	$0.482745\pi$
$198$	−2.86210	−0.203400
$199$	12.3936	0.878557	0.439279	−	0.898351i	$-0.355234\pi$
$199$	12.3936	0.878557	0.439279	+	0.898351i	$0.355234\pi$
$200$	23.3422	1.65055
$201$	−18.7148	−1.32004
$202$	0.630184	0.0443396
$203$	5.11925	0.359301
$204$	−4.16828	−0.291838
$205$	0.125499	0.00876523
$206$	−44.2631	−3.08396
$207$	2.42810	0.168765
$208$	−16.2069	−1.12375
$209$	−6.39354	−0.442250
$210$	−5.05163	−0.348595
$211$	3.04582	0.209683	0.104841	−	0.994489i	$-0.466567\pi$
$211$	3.04582	0.209683	0.104841	+	0.994489i	$0.466567\pi$
$212$	22.5512	1.54882
$213$	−3.44317	−0.235922
$214$	2.69691	0.184357
$215$	−2.82412	−0.192604
$216$	18.3385	1.24778
$217$	10.7999	0.733144
$218$	31.2553	2.11688
$219$	5.45391	0.368541
$220$	−1.96003	−0.132145
$221$	2.06203	0.138707
$222$	−22.2853	−1.49569
$223$	3.75968	0.251767	0.125883	−	0.992045i	$-0.459824\pi$
$223$	3.75968	0.251767	0.125883	+	0.992045i	$0.459824\pi$
$224$	0.0336458	0.00224805
$225$	−5.56114	−0.370743
$226$	−35.7109	−2.37545
$227$	9.12916	0.605924	0.302962	−	0.953003i	$-0.402025\pi$
$227$	9.12916	0.605924	0.302962	+	0.953003i	$0.402025\pi$
$228$	−52.2349	−3.45934
$229$	12.5185	0.827243	0.413622	−	0.910449i	$-0.364264\pi$
$229$	12.5185	0.827243	0.413622	+	0.910449i	$0.364264\pi$
$230$	2.49388	0.164442
$231$	−4.20992	−0.276993
$232$	12.1741	0.799272
$233$	16.4991	1.08089	0.540446	−	0.841379i	$-0.318255\pi$
$233$	16.4991	1.08089	0.540446	+	0.841379i	$0.318255\pi$
$234$	11.5676	0.756195
$235$	−2.67016	−0.174182
$236$	−25.2099	−1.64103
$237$	−3.61305	−0.234693
$238$	−2.57733	−0.167063
$239$	5.23699	0.338753	0.169376	−	0.985551i	$-0.445825\pi$
$239$	5.23699	0.338753	0.169376	+	0.985551i	$0.445825\pi$
$240$	−4.00999	−0.258844
$241$	−13.9497	−0.898576	−0.449288	−	0.893387i	$-0.648322\pi$
$241$	−13.9497	−0.898576	−0.449288	+	0.893387i	$0.648322\pi$
$242$	−2.44983	−0.157481
$243$	−11.5247	−0.739308
$244$	4.00166	0.256180
$245$	1.34599	0.0859921
$246$	1.28154	0.0817083
$247$	25.8404	1.64418
$248$	25.6833	1.63089
$249$	−18.4395	−1.16856
$250$	−11.7115	−0.740698
$251$	28.6600	1.80900	0.904502	−	0.426469i	$-0.140243\pi$
$251$	28.6600	1.80900	0.904502	+	0.426469i	$0.140243\pi$
$252$	−9.64017	−0.607274
$253$	2.07835	0.130665
$254$	17.8204	1.11815
$255$	0.510197	0.0319498
$256$	−32.0132	−2.00083
$257$	−13.1767	−0.821941	−0.410971	−	0.911649i	$-0.634810\pi$
$257$	−13.1767	−0.821941	−0.410971	+	0.911649i	$0.634810\pi$
$258$	−28.8388	−1.79542
$259$	−9.18753	−0.570885
$260$	7.92172	0.491284
$261$	−2.90041	−0.179531
$262$	26.6101	1.64398
$263$	−30.9021	−1.90551	−0.952754	−	0.303744i	$-0.901763\pi$
$263$	−30.9021	−1.90551	−0.952754	+	0.303744i	$0.901763\pi$
$264$	−10.0117	−0.616175
$265$	−2.76026	−0.169561
$266$	−32.2978	−1.98030
$267$	−8.98460	−0.549849
$268$	−36.6815	−2.24068
$269$	−0.0936807	−0.00571181	−0.00285591	−	0.999996i	$-0.500909\pi$
$269$	−0.0936807	−0.00571181	−0.00285591	+	0.999996i	$0.500909\pi$
$270$	−4.48739	−0.273094
$271$	21.4908	1.30547	0.652736	−	0.757586i	$-0.273621\pi$
$271$	21.4908	1.30547	0.652736	+	0.757586i	$0.273621\pi$
$272$	−2.04589	−0.124050
$273$	17.0150	1.02979
$274$	46.8283	2.82900
$275$	−4.76009	−0.287044
$276$	16.9800	1.02208
$277$	−14.1252	−0.848702	−0.424351	−	0.905498i	$-0.639498\pi$
$277$	−14.1252	−0.848702	−0.424351	+	0.905498i	$0.639498\pi$
$278$	−56.1737	−3.36908
$279$	−6.11888	−0.366328
$280$	−4.95272	−0.295982
$281$	26.4128	1.57566	0.787828	−	0.615896i	$-0.211206\pi$
$281$	26.4128	1.57566	0.787828	+	0.615896i	$0.211206\pi$
$282$	−27.2665	−1.62370
$283$	0.123784	0.00735820	0.00367910	−	0.999993i	$-0.498829\pi$
$283$	0.123784	0.00735820	0.00367910	+	0.999993i	$0.498829\pi$
$284$	−6.74870	−0.400462
$285$	6.39354	0.378721
$286$	9.90132	0.585478
$287$	0.528341	0.0311870
$288$	−0.0190627	−0.00112328
$289$	−16.7397	−0.984688
$290$	−2.97899	−0.174932
$291$	−23.5275	−1.37921
$292$	10.6898	0.625573
$293$	16.5097	0.964506	0.482253	−	0.876032i	$-0.339819\pi$
$293$	16.5097	0.964506	0.482253	+	0.876032i	$0.339819\pi$
$294$	13.7447	0.801607
$295$	3.08569	0.179656
$296$	−21.8489	−1.26994
$297$	−3.73970	−0.216999
$298$	−29.9269	−1.73362
$299$	−8.39993	−0.485781
$300$	−38.8897	−2.24530
$301$	−11.8893	−0.685290
$302$	6.48269	0.373037
$303$	−0.525182	−0.0301709
$304$	−25.6380	−1.47044
$305$	−0.489803	−0.0280460
$306$	1.46023	0.0834761
$307$	6.03055	0.344182	0.172091	−	0.985081i	$-0.444948\pi$
$307$	6.03055	0.344182	0.172091	+	0.985081i	$0.444948\pi$
$308$	−8.25156	−0.470176
$309$	36.8880	2.09848
$310$	−6.28464	−0.356944
$311$	0.939768	0.0532894	0.0266447	−	0.999645i	$-0.491518\pi$
$311$	0.939768	0.0532894	0.0266447	+	0.999645i	$0.491518\pi$
$312$	40.4635	2.29079
$313$	26.0692	1.47352	0.736760	−	0.676155i	$-0.236355\pi$
$313$	26.0692	1.47352	0.736760	+	0.676155i	$0.236355\pi$
$314$	−51.0794	−2.88258
$315$	1.17996	0.0664829
$316$	−7.08168	−0.398375
$317$	9.55726	0.536789	0.268395	−	0.963309i	$-0.413507\pi$
$317$	9.55726	0.536789	0.268395	+	0.963309i	$0.413507\pi$
$318$	−28.1866	−1.58063
$319$	−2.48263	−0.139000
$320$	3.90863	0.218499
$321$	−2.24755	−0.125446
$322$	10.4990	0.585089
$323$	3.26197	0.181501
$324$	−44.5784	−2.47658
$325$	19.2386	1.06716
$326$	30.3814	1.68267
$327$	−26.0475	−1.44043
$328$	1.25645	0.0693760
$329$	−11.2412	−0.619745
$330$	2.44983	0.134859
$331$	−33.2311	−1.82655	−0.913274	−	0.407346i	$-0.866454\pi$
$331$	−33.2311	−1.82655	−0.913274	+	0.407346i	$0.866454\pi$
$332$	−36.1419	−1.98354
$333$	5.20538	0.285253
$334$	2.28228	0.124881
$335$	4.48980	0.245304
$336$	−16.8817	−0.920975
$337$	13.1267	0.715058	0.357529	−	0.933902i	$-0.383619\pi$
$337$	13.1267	0.715058	0.357529	+	0.933902i	$0.383619\pi$
$338$	−8.16978	−0.444377
$339$	29.7607	1.61638
$340$	1.00000	0.0542326
$341$	−5.23749	−0.283626
$342$	18.2989	0.989493
$343$	20.1007	1.08534
$344$	−28.2741	−1.52444
$345$	−2.07835	−0.111895
$346$	−31.1633	−1.67535
$347$	5.80734	0.311754	0.155877	−	0.987776i	$-0.450180\pi$
$347$	5.80734	0.311754	0.155877	+	0.987776i	$0.450180\pi$
$348$	−20.2829	−1.08728
$349$	−8.67147	−0.464173	−0.232087	−	0.972695i	$-0.574555\pi$
$349$	−8.67147	−0.464173	−0.232087	+	0.972695i	$0.574555\pi$
$350$	−24.0462	−1.28532
$351$	15.1145	0.806753
$352$	−0.0163168	−0.000869688 0
$353$	4.52578	0.240883	0.120442	−	0.992720i	$-0.461569\pi$
$353$	4.52578	0.240883	0.120442	+	0.992720i	$0.461569\pi$
$354$	31.5098	1.67473
$355$	0.826040	0.0438416
$356$	−17.6101	−0.933331
$357$	2.14789	0.113678
$358$	−3.79382	−0.200510
$359$	26.5979	1.40378	0.701891	−	0.712284i	$-0.252339\pi$
$359$	26.5979	1.40378	0.701891	+	0.712284i	$0.252339\pi$
$360$	2.80606	0.147892
$361$	21.8773	1.15144
$362$	32.9759	1.73317
$363$	2.04164	0.107158
$364$	33.3498	1.74801
$365$	−1.30843	−0.0684863
$366$	−5.00166	−0.261441
$367$	0.407928	0.0212937	0.0106468	−	0.999943i	$-0.496611\pi$
$367$	0.407928	0.0212937	0.0106468	+	0.999943i	$0.496611\pi$
$368$	8.33416	0.434448
$369$	−0.299342	−0.0155831
$370$	5.34639	0.277946
$371$	−11.6205	−0.603304
$372$	−42.7901	−2.21856
$373$	−4.59539	−0.237940	−0.118970	−	0.992898i	$-0.537959\pi$
$373$	−4.59539	−0.237940	−0.118970	+	0.992898i	$0.537959\pi$
$374$	1.24990	0.0646306
$375$	9.76009	0.504009
$376$	−26.7327	−1.37863
$377$	10.0339	0.516771
$378$	−18.8916	−0.971677
$379$	−0.699992	−0.0359562	−0.0179781	−	0.999838i	$-0.505723\pi$
$379$	−0.699992	−0.0359562	−0.0179781	+	0.999838i	$0.505723\pi$
$380$	12.5315	0.642853
$381$	−14.8511	−0.760846
$382$	37.8640	1.93729
$383$	−4.95933	−0.253410	−0.126705	−	0.991940i	$-0.540440\pi$
$383$	−4.95933	−0.253410	−0.126705	+	0.991940i	$0.540440\pi$
$384$	39.9799	2.04022
$385$	1.00999	0.0514738
$386$	33.8634	1.72360
$387$	6.73614	0.342417
$388$	−46.1146	−2.34111
$389$	−37.0164	−1.87681	−0.938403	−	0.345543i	$-0.887695\pi$
$389$	−37.0164	−1.87681	−0.938403	+	0.345543i	$0.887695\pi$
$390$	−9.90132	−0.501373
$391$	−1.06037	−0.0536251
$392$	13.4756	0.680620
$393$	−22.1763	−1.11865
$394$	−3.72605	−0.187716
$395$	0.866796	0.0436132
$396$	4.67508	0.234932
$397$	−20.4490	−1.02631	−0.513153	−	0.858297i	$-0.671523\pi$
$397$	−20.4490	−1.02631	−0.513153	+	0.858297i	$0.671523\pi$
$398$	−30.3621	−1.52192
$399$	26.9163	1.34750
$400$	−19.0879	−0.954396
$401$	1.46283	0.0730501	0.0365251	−	0.999333i	$-0.488371\pi$
$401$	1.46283	0.0730501	0.0365251	+	0.999333i	$0.488371\pi$
$402$	45.8480	2.28669
$403$	21.1681	1.05446
$404$	−1.02937	−0.0512131
$405$	5.45639	0.271130
$406$	−12.5413	−0.622414
$407$	4.45557	0.220854
$408$	5.10792	0.252880
$409$	2.89526	0.143161	0.0715807	−	0.997435i	$-0.477196\pi$
$409$	2.89526	0.143161	0.0715807	+	0.997435i	$0.477196\pi$
$410$	−0.307451	−0.0151839
$411$	−39.0257	−1.92500
$412$	72.3014	3.56204
$413$	12.9905	0.639221
$414$	−5.94844	−0.292350
$415$	4.42376	0.217154
$416$	0.0659466	0.00323330
$417$	46.8140	2.29249
$418$	15.6631	0.766106
$419$	−12.8236	−0.626476	−0.313238	−	0.949675i	$-0.601414\pi$
$419$	−12.8236	−0.626476	−0.313238	+	0.949675i	$0.601414\pi$
$420$	8.25156	0.402635
$421$	−40.4135	−1.96964	−0.984818	−	0.173590i	$-0.944463\pi$
$421$	−40.4135	−1.96964	−0.984818	+	0.173590i	$0.944463\pi$
$422$	−7.46173	−0.363231
$423$	6.36890	0.309666
$424$	−27.6347	−1.34206
$425$	2.42859	0.117804
$426$	8.43518	0.408686
$427$	−2.06203	−0.0997887
$428$	−4.40526	−0.212936
$429$	−8.25156	−0.398389
$430$	6.91862	0.333645
$431$	−29.8168	−1.43622	−0.718112	−	0.695927i	$-0.754994\pi$
$431$	−29.8168	−1.43622	−0.718112	+	0.695927i	$0.754994\pi$
$432$	−14.9962	−0.721503
$433$	−0.945877	−0.0454559	−0.0227280	−	0.999742i	$-0.507235\pi$
$433$	−0.945877	−0.0454559	−0.0227280	+	0.999742i	$0.507235\pi$
$434$	−26.4579	−1.27002
$435$	2.48263	0.119033
$436$	−51.0539	−2.44504
$437$	−13.2880	−0.635651
$438$	−13.3611	−0.638420
$439$	11.2091	0.534982	0.267491	−	0.963560i	$-0.413805\pi$
$439$	11.2091	0.534982	0.267491	+	0.963560i	$0.413805\pi$
$440$	2.40186	0.114504
$441$	−3.21047	−0.152880
$442$	−5.05163	−0.240281
$443$	1.69673	0.0806140	0.0403070	−	0.999187i	$-0.487166\pi$
$443$	1.69673	0.0806140	0.0403070	+	0.999187i	$0.487166\pi$
$444$	36.4018	1.72755
$445$	2.15547	0.102179
$446$	−9.21057	−0.436133
$447$	24.9405	1.17965
$448$	16.4550	0.777427
$449$	−36.3074	−1.71345	−0.856727	−	0.515770i	$-0.827506\pi$
$449$	−36.3074	−1.71345	−0.856727	+	0.515770i	$0.827506\pi$
$450$	13.6239	0.642235
$451$	−0.256224	−0.0120651
$452$	58.3318	2.74370
$453$	−5.40254	−0.253834
$454$	−22.3649	−1.04964
$455$	−4.08201	−0.191368
$456$	64.0099	2.99754
$457$	−31.3473	−1.46637	−0.733183	−	0.680031i	$-0.761966\pi$
$457$	−31.3473	−1.46637	−0.733183	+	0.680031i	$0.761966\pi$
$458$	−30.6681	−1.43303
$459$	1.90798	0.0890571
$460$	−4.07362	−0.189933
$461$	−29.8994	−1.39255	−0.696277	−	0.717773i	$-0.745162\pi$
$461$	−29.8994	−1.39255	−0.696277	+	0.717773i	$0.745162\pi$
$462$	10.3136	0.479832
$463$	6.04730	0.281042	0.140521	−	0.990078i	$-0.455122\pi$
$463$	6.04730	0.281042	0.140521	+	0.990078i	$0.455122\pi$
$464$	−9.95530	−0.462163
$465$	5.23749	0.242883
$466$	−40.4200	−1.87242
$467$	28.1925	1.30459	0.652297	−	0.757964i	$-0.273806\pi$
$467$	28.1925	1.30459	0.652297	+	0.757964i	$0.273806\pi$
$468$	−18.8950	−0.873421
$469$	18.9017	0.872800
$470$	6.54143	0.301734
$471$	42.5685	1.96146
$472$	30.8928	1.42196
$473$	5.76584	0.265113
$474$	8.85136	0.406556
$475$	30.4338	1.39640
$476$	4.20992	0.192961
$477$	6.58380	0.301452
$478$	−12.8297	−0.586818
$479$	43.2803	1.97753	0.988764	−	0.149488i	$-0.0477625\pi$
$479$	43.2803	1.97753	0.988764	+	0.149488i	$0.0477625\pi$
$480$	0.0163168	0.000744757 0
$481$	−18.0078	−0.821085
$482$	34.1743	1.55660
$483$	−8.74969	−0.398125
$484$	4.00166	0.181894
$485$	5.64441	0.256300
$486$	28.2335	1.28070
$487$	12.1151	0.548990	0.274495	−	0.961589i	$-0.411489\pi$
$487$	12.1151	0.548990	0.274495	+	0.961589i	$0.411489\pi$
$488$	−4.90374	−0.221982
$489$	−25.3193	−1.14498
$490$	−3.29745	−0.148963
$491$	−14.2208	−0.641774	−0.320887	−	0.947118i	$-0.603981\pi$
$491$	−14.2208	−0.641774	−0.320887	+	0.947118i	$0.603981\pi$
$492$	−2.09333	−0.0943748
$493$	1.26663	0.0570461
$494$	−63.3045	−2.84820
$495$	−0.572229	−0.0257198
$496$	−21.0023	−0.943031
$497$	3.47756	0.155990
$498$	45.1736	2.02428
$499$	−35.1774	−1.57476	−0.787378	−	0.616471i	$-0.788562\pi$
$499$	−35.1774	−1.57476	−0.787378	+	0.616471i	$0.788562\pi$
$500$	19.1300	0.855522
$501$	−1.90200	−0.0849752
$502$	−70.2122	−3.13372
$503$	3.03811	0.135463	0.0677313	−	0.997704i	$-0.478424\pi$
$503$	3.03811	0.135463	0.0677313	+	0.997704i	$0.478424\pi$
$504$	11.8133	0.526206
$505$	0.125995	0.00560670
$506$	−5.09160	−0.226349
$507$	6.80853	0.302377
$508$	−29.1086	−1.29149
$509$	41.8623	1.85551	0.927757	−	0.373184i	$-0.121734\pi$
$509$	41.8623	1.85551	0.927757	+	0.373184i	$0.121734\pi$
$510$	−1.24990	−0.0553463
$511$	−5.50839	−0.243677
$512$	39.2624	1.73517
$513$	23.9099	1.05565
$514$	32.2807	1.42384
$515$	−8.84968	−0.389963
$516$	47.1066	2.07375
$517$	5.45149	0.239756
$518$	22.5079	0.988940
$519$	25.9709	1.13999
$520$	−9.70746	−0.425700
$521$	−7.44360	−0.326110	−0.163055	−	0.986617i	$-0.552135\pi$
$521$	−7.44360	−0.326110	−0.163055	+	0.986617i	$0.552135\pi$
$522$	7.10552	0.311000
$523$	−18.2137	−0.796430	−0.398215	−	0.917292i	$-0.630370\pi$
$523$	−18.2137	−0.796430	−0.398215	+	0.917292i	$0.630370\pi$
$524$	−43.4662	−1.89883
$525$	20.0396	0.874601
$526$	75.7050	3.30089
$527$	2.67215	0.116401
$528$	8.18695	0.356291
$529$	−18.6805	−0.812194
$530$	6.76216	0.293729
$531$	−7.36003	−0.319398
$532$	52.7567	2.28729
$533$	1.03556	0.0448552
$534$	22.0107	0.952498
$535$	0.539203	0.0233118
$536$	44.9504	1.94156
$537$	3.16169	0.136437
$538$	0.229502	0.00989452
$539$	−2.74802	−0.118366
$540$	7.32991	0.315429
$541$	1.83604	0.0789376	0.0394688	−	0.999221i	$-0.487433\pi$
$541$	1.83604	0.0789376	0.0394688	+	0.999221i	$0.487433\pi$
$542$	−52.6487	−2.26146
$543$	−27.4814	−1.17934
$544$	0.00832479	0.000356922 0
$545$	6.24898	0.267677
$546$	−41.6838	−1.78390
$547$	3.64086	0.155672	0.0778359	−	0.996966i	$-0.475199\pi$
$547$	3.64086	0.155672	0.0778359	+	0.996966i	$0.475199\pi$
$548$	−76.4914	−3.26755
$549$	1.16828	0.0498612
$550$	11.6614	0.497244
$551$	15.8728	0.676203
$552$	−20.8077	−0.885635
$553$	3.64914	0.155177
$554$	34.6044	1.47020
$555$	−4.45557	−0.189128
$556$	91.7567	3.89135
$557$	−32.7837	−1.38909	−0.694546	−	0.719449i	$-0.744395\pi$
$557$	−32.7837	−1.38909	−0.694546	+	0.719449i	$0.744395\pi$
$558$	14.9902	0.634587
$559$	−23.3034	−0.985630
$560$	4.05005	0.171146
$561$	−1.04164	−0.0439780
$562$	−64.7069	−2.72949
$563$	25.6163	1.07960	0.539799	−	0.841794i	$-0.318500\pi$
$563$	25.6163	1.07960	0.539799	+	0.841794i	$0.318500\pi$
$564$	44.5384	1.87541
$565$	−7.13980	−0.300374
$566$	−0.303250	−0.0127465
$567$	22.9710	0.964690
$568$	8.27002	0.347003
$569$	−37.9239	−1.58985	−0.794926	−	0.606706i	$-0.792491\pi$
$569$	−37.9239	−1.58985	−0.794926	+	0.606706i	$0.792491\pi$
$570$	−15.6631	−0.656054
$571$	−0.333654	−0.0139630	−0.00698149	−	0.999976i	$-0.502222\pi$
$571$	−0.333654	−0.0139630	−0.00698149	+	0.999976i	$0.502222\pi$
$572$	−16.1733	−0.676239
$573$	−31.5551	−1.31823
$574$	−1.29435	−0.0540250
$575$	−9.89313	−0.412572
$576$	−9.32292	−0.388455
$577$	−12.7870	−0.532330	−0.266165	−	0.963928i	$-0.585757\pi$
$577$	−12.7870	−0.532330	−0.266165	+	0.963928i	$0.585757\pi$
$578$	41.0094	1.70577
$579$	−28.2211	−1.17283
$580$	4.86601	0.202050
$581$	18.6237	0.772641
$582$	57.6384	2.38919
$583$	5.63544	0.233396
$584$	−13.0995	−0.542063
$585$	2.31274	0.0956202
$586$	−40.4459	−1.67080
$587$	−13.4841	−0.556549	−0.278275	−	0.960502i	$-0.589763\pi$
$587$	−13.4841	−0.556549	−0.278275	+	0.960502i	$0.589763\pi$
$588$	−22.4512	−0.925872
$589$	33.4861	1.37977
$590$	−7.55941	−0.311216
$591$	3.10521	0.127731
$592$	17.8668	0.734321
$593$	−20.2818	−0.832875	−0.416438	−	0.909164i	$-0.636722\pi$
$593$	−20.2818	−0.832875	−0.416438	+	0.909164i	$0.636722\pi$
$594$	9.16162	0.375906
$595$	−0.515294	−0.0211250
$596$	48.8840	2.00237
$597$	25.3032	1.03559
$598$	20.5784	0.841514
$599$	6.08830	0.248761	0.124381	−	0.992235i	$-0.460306\pi$
$599$	6.08830	0.248761	0.124381	+	0.992235i	$0.460306\pi$
$600$	47.6564	1.94556
$601$	3.75116	0.153013	0.0765064	−	0.997069i	$-0.475623\pi$
$601$	3.75116	0.153013	0.0765064	+	0.997069i	$0.475623\pi$
$602$	29.1268	1.18712
$603$	−10.7091	−0.436110
$604$	−10.5891	−0.430866
$605$	−0.489803	−0.0199133
$606$	1.28661	0.0522648
$607$	16.1755	0.656544	0.328272	−	0.944583i	$-0.393534\pi$
$607$	16.1755	0.656544	0.328272	+	0.944583i	$0.393534\pi$
$608$	0.104322	0.00423082
$609$	10.4517	0.423523
$610$	1.19993	0.0485839
$611$	−22.0330	−0.891358
$612$	−2.38521	−0.0964166
$613$	26.1429	1.05590	0.527950	−	0.849275i	$-0.322961\pi$
$613$	26.1429	1.05590	0.527950	+	0.849275i	$0.322961\pi$
$614$	−14.7738	−0.596223
$615$	0.256224	0.0103319
$616$	10.1117	0.407410
$617$	−17.4905	−0.704141	−0.352070	−	0.935974i	$-0.614522\pi$
$617$	−17.4905	−0.704141	−0.352070	+	0.935974i	$0.614522\pi$
$618$	−90.3693	−3.63519
$619$	−11.8189	−0.475040	−0.237520	−	0.971383i	$-0.576334\pi$
$619$	−11.8189	−0.475040	−0.237520	+	0.971383i	$0.576334\pi$
$620$	10.2656	0.412278
$621$	−7.77240	−0.311896
$622$	−2.30227	−0.0923127
$623$	9.07435	0.363556
$624$	−33.0887	−1.32461
$625$	21.4590	0.858358
$626$	−63.8652	−2.55256
$627$	−13.0533	−0.521298
$628$	83.4355	3.32944
$629$	−2.27322	−0.0906392
$630$	−2.89069	−0.115168
$631$	40.9921	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$631$	40.9921	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$632$	8.67806	0.345195
$633$	6.21845	0.247161
$634$	−23.4137	−0.929876
$635$	3.56289	0.141389
$636$	46.0413	1.82566
$637$	11.1065	0.440056
$638$	6.08201	0.240789
$639$	−1.97028	−0.0779432
$640$	−9.59146	−0.379136
$641$	−13.8684	−0.547769	−0.273884	−	0.961763i	$-0.588309\pi$
$641$	−13.8684	−0.547769	−0.273884	+	0.961763i	$0.588309\pi$
$642$	5.50612	0.217309
$643$	2.04999	0.0808437	0.0404219	−	0.999183i	$-0.487130\pi$
$643$	2.04999	0.0808437	0.0404219	+	0.999183i	$0.487130\pi$
$644$	−17.1496	−0.675790
$645$	−5.76584	−0.227030
$646$	−7.99126	−0.314412
$647$	−4.75558	−0.186961	−0.0934806	−	0.995621i	$-0.529799\pi$
$647$	−4.75558	−0.186961	−0.0934806	+	0.995621i	$0.529799\pi$
$648$	54.6275	2.14597
$649$	−6.29986	−0.247291
$650$	−47.1312	−1.84864
$651$	22.0494	0.864186
$652$	−49.6264	−1.94352
$653$	10.7929	0.422358	0.211179	−	0.977447i	$-0.432270\pi$
$653$	10.7929	0.422358	0.211179	+	0.977447i	$0.432270\pi$
$654$	63.8120	2.49525
$655$	5.32025	0.207879
$656$	−1.02745	−0.0401153
$657$	3.12089	0.121757
$658$	27.5389	1.07358
$659$	9.19338	0.358123	0.179062	−	0.983838i	$-0.442694\pi$
$659$	9.19338	0.358123	0.179062	+	0.983838i	$0.442694\pi$
$660$	−4.00166	−0.155765
$661$	−25.2261	−0.981183	−0.490591	−	0.871390i	$-0.663219\pi$
$661$	−25.2261	−0.981183	−0.490591	+	0.871390i	$0.663219\pi$
$662$	81.4106	3.16411
$663$	4.20992	0.163500
$664$	44.2892	1.71875
$665$	−6.45741	−0.250407
$666$	−12.7523	−0.494141
$667$	−5.15976	−0.199787
$668$	−3.72798	−0.144240
$669$	7.67590	0.296767
$670$	−10.9993	−0.424938
$671$	1.00000	0.0386046
$672$	0.0686925	0.00264987
$673$	−30.8904	−1.19074	−0.595369	−	0.803452i	$-0.702994\pi$
$673$	−30.8904	−1.19074	−0.595369	+	0.803452i	$0.702994\pi$
$674$	−32.1582	−1.23869
$675$	17.8013	0.685173
$676$	13.3449	0.513265
$677$	−50.9203	−1.95702	−0.978512	−	0.206188i	$-0.933894\pi$
$677$	−50.9203	−1.95702	−0.978512	+	0.206188i	$0.933894\pi$
$678$	−72.9087	−2.80004
$679$	23.7625	0.911923
$680$	−1.22542	−0.0469929
$681$	18.6384	0.714227
$682$	12.8310	0.491323
$683$	−20.1065	−0.769354	−0.384677	−	0.923051i	$-0.625687\pi$
$683$	−20.1065	−0.769354	−0.384677	+	0.923051i	$0.625687\pi$
$684$	−29.8903	−1.14289
$685$	9.36254	0.357724
$686$	−49.2434	−1.88012
$687$	25.5582	0.975105
$688$	23.1209	0.881477
$689$	−22.7764	−0.867713
$690$	5.09160	0.193834
$691$	36.4630	1.38712	0.693560	−	0.720399i	$-0.256041\pi$
$691$	36.4630	1.38712	0.693560	+	0.720399i	$0.256041\pi$
$692$	50.9036	1.93506
$693$	−2.40904	−0.0915119
$694$	−14.2270	−0.540049
$695$	−11.2310	−0.426016
$696$	24.8552	0.942134
$697$	0.130725	0.00495155
$698$	21.2436	0.804083
$699$	33.6852	1.27409
$700$	39.2782	1.48458
$701$	−40.4248	−1.52682	−0.763412	−	0.645912i	$-0.776477\pi$
$701$	−40.4248	−1.52682	−0.763412	+	0.645912i	$0.776477\pi$
$702$	−37.0280	−1.39753
$703$	−28.4869	−1.07440
$704$	−7.98000	−0.300758
$705$	−5.45149	−0.205315
$706$	−11.0874	−0.417280
$707$	0.530428	0.0199488
$708$	−51.4695	−1.93434
$709$	−40.4028	−1.51736	−0.758679	−	0.651464i	$-0.774155\pi$
$709$	−40.4028	−1.51736	−0.758679	+	0.651464i	$0.774155\pi$
$710$	−2.02366	−0.0759465
$711$	−2.06749	−0.0775371
$712$	21.5798	0.808737
$713$	−10.8853	−0.407659
$714$	−5.26197	−0.196924
$715$	1.97961	0.0740331
$716$	6.19700	0.231593
$717$	10.6920	0.399302
$718$	−65.1603	−2.43176
$719$	−11.5683	−0.431425	−0.215713	−	0.976457i	$-0.569207\pi$
$719$	−11.5683	−0.431425	−0.215713	+	0.976457i	$0.569207\pi$
$720$	−2.29463	−0.0855159
$721$	−37.2565	−1.38750
$722$	−53.5958	−1.99463
$723$	−28.4801	−1.05919
$724$	−53.8643	−2.00185
$725$	11.8175	0.438892
$726$	−5.00166	−0.185629
$727$	−49.1816	−1.82404	−0.912022	−	0.410141i	$-0.865479\pi$
$727$	−49.1816	−1.82404	−0.912022	+	0.410141i	$0.865479\pi$
$728$	−40.8677	−1.51466
$729$	9.89068	0.366321
$730$	3.20543	0.118638
$731$	−2.94171	−0.108803
$732$	8.16995	0.301970
$733$	−11.8404	−0.437336	−0.218668	−	0.975799i	$-0.570171\pi$
$733$	−11.8404	−0.437336	−0.218668	+	0.975799i	$0.570171\pi$
$734$	−0.999355	−0.0368868
$735$	2.74802	0.101362
$736$	−0.0339120	−0.00125001
$737$	−9.16655	−0.337654
$738$	0.733337	0.0269945
$739$	−16.3209	−0.600376	−0.300188	−	0.953880i	$-0.597049\pi$
$739$	−16.3209	−0.600376	−0.300188	+	0.953880i	$0.597049\pi$
$740$	−8.73304	−0.321033
$741$	52.7567	1.93806
$742$	28.4682	1.04510
$743$	9.04989	0.332008	0.166004	−	0.986125i	$-0.446913\pi$
$743$	9.04989	0.332008	0.166004	+	0.986125i	$0.446913\pi$
$744$	52.4360	1.92240
$745$	−5.98340	−0.219215
$746$	11.2579	0.412182
$747$	−10.5516	−0.386063
$748$	−2.04164	−0.0746497
$749$	2.27000	0.0829441
$750$	−23.9106	−0.873090
$751$	11.9535	0.436190	0.218095	−	0.975928i	$-0.430016\pi$
$751$	11.9535	0.436190	0.218095	+	0.975928i	$0.430016\pi$
$752$	21.8604	0.797168
$753$	58.5134	2.13235
$754$	−24.5813	−0.895198
$755$	1.29611	0.0471702
$756$	30.8584	1.12231
$757$	−44.6352	−1.62229	−0.811147	−	0.584842i	$-0.801157\pi$
$757$	−44.6352	−1.62229	−0.811147	+	0.584842i	$0.801157\pi$
$758$	1.71486	0.0622866
$759$	4.24324	0.154020
$760$	−15.3564	−0.557036
$761$	24.4741	0.887185	0.443592	−	0.896229i	$-0.353704\pi$
$761$	24.4741	0.887185	0.443592	+	0.896229i	$0.353704\pi$
$762$	36.3827	1.31801
$763$	26.3077	0.952404
$764$	−61.8487	−2.23761
$765$	0.291950	0.0105555
$766$	12.1495	0.438980
$767$	25.4617	0.919370
$768$	−65.3595	−2.35846
$769$	−25.7836	−0.929781	−0.464890	−	0.885368i	$-0.653906\pi$
$769$	−25.7836	−0.929781	−0.464890	+	0.885368i	$0.653906\pi$
$770$	−2.47430	−0.0891676
$771$	−26.9021	−0.968855
$772$	−55.3141	−1.99080
$773$	43.4228	1.56181	0.780905	−	0.624650i	$-0.214758\pi$
$773$	43.4228	1.56181	0.780905	+	0.624650i	$0.214758\pi$
$774$	−16.5024	−0.593166
$775$	24.9310	0.895546
$776$	56.5099	2.02859
$777$	−18.7576	−0.672926
$778$	90.6839	3.25117
$779$	1.63818	0.0586937
$780$	16.1733	0.579096
$781$	−1.68647	−0.0603468
$782$	2.59772	0.0928943
$783$	9.28427	0.331793
$784$	−11.0195	−0.393555
$785$	−10.2125	−0.364499
$786$	54.3282	1.93782
$787$	28.9736	1.03280	0.516398	−	0.856349i	$-0.327272\pi$
$787$	28.9736	1.03280	0.516398	+	0.856349i	$0.327272\pi$
$788$	6.08630	0.216815
$789$	−63.0910	−2.24610
$790$	−2.12350	−0.0755508
$791$	−30.0580	−1.06874
$792$	−5.72896	−0.203570
$793$	−4.04164	−0.143523
$794$	50.0966	1.77786
$795$	−5.63544	−0.199869
$796$	49.5949	1.75785
$797$	−37.7777	−1.33815	−0.669077	−	0.743193i	$-0.733310\pi$
$797$	−37.7777	−1.33815	−0.669077	+	0.743193i	$0.733310\pi$
$798$	−65.9404	−2.33426
$799$	−2.78134	−0.0983966
$800$	0.0776695	0.00274603
$801$	−5.14125	−0.181657
$802$	−3.58368	−0.126544
$803$	2.67134	0.0942695
$804$	−74.8903	−2.64118
$805$	2.09911	0.0739839
$806$	−51.8581	−1.82662
$807$	−0.191262	−0.00673274
$808$	1.26142	0.0443765
$809$	−56.1497	−1.97412	−0.987058	−	0.160361i	$-0.948734\pi$
$809$	−56.1497	−1.97412	−0.987058	+	0.160361i	$0.948734\pi$
$810$	−13.3672	−0.469676
$811$	−5.38124	−0.188961	−0.0944804	−	0.995527i	$-0.530119\pi$
$811$	−5.38124	−0.188961	−0.0944804	+	0.995527i	$0.530119\pi$
$812$	20.4855	0.718901
$813$	43.8764	1.53881
$814$	−10.9154	−0.382584
$815$	6.07426	0.212772
$816$	−4.17696	−0.146223
$817$	−36.8641	−1.28971
$818$	−7.09289	−0.247997
$819$	9.73647	0.340220
$820$	0.502205	0.0175378
$821$	−5.82120	−0.203161	−0.101581	−	0.994827i	$-0.532390\pi$
$821$	−5.82120	−0.203161	−0.101581	+	0.994827i	$0.532390\pi$
$822$	95.6064	3.33465
$823$	−42.2790	−1.47375	−0.736876	−	0.676028i	$-0.763700\pi$
$823$	−42.2790	−1.47375	−0.736876	+	0.676028i	$0.763700\pi$
$824$	−88.5999	−3.08652
$825$	−9.71839	−0.338351
$826$	−31.8245	−1.10732
$827$	−26.6972	−0.928353	−0.464177	−	0.885743i	$-0.653650\pi$
$827$	−26.6972	−0.928353	−0.464177	+	0.885743i	$0.653650\pi$
$828$	9.71646	0.337670
$829$	−4.76184	−0.165386	−0.0826928	−	0.996575i	$-0.526352\pi$
$829$	−4.76184	−0.165386	−0.0826928	+	0.996575i	$0.526352\pi$
$830$	−10.8375	−0.376174
$831$	−28.8386	−1.00040
$832$	32.2523	1.11815
$833$	1.40203	0.0485776
$834$	−114.686	−3.97126
$835$	0.456303	0.0157910
$836$	−25.5848	−0.884869
$837$	19.5866	0.677014
$838$	31.4157	1.08524
$839$	13.8010	0.476465	0.238232	−	0.971208i	$-0.423432\pi$
$839$	13.8010	0.476465	0.238232	+	0.971208i	$0.423432\pi$
$840$	−10.1117	−0.348885
$841$	−22.8366	−0.787468
$842$	99.0063	3.41198
$843$	53.9254	1.85729
$844$	12.1883	0.419540
$845$	−1.63341	−0.0561911
$846$	−15.6027	−0.536432
$847$	−2.06203	−0.0708523
$848$	22.5981	0.776021
$849$	0.252722	0.00867341
$850$	−5.94962	−0.204070
$851$	9.26023	0.317437
$852$	−13.7784	−0.472040
$853$	−32.2395	−1.10386	−0.551930	−	0.833891i	$-0.686108\pi$
$853$	−32.2395	−1.10386	−0.551930	+	0.833891i	$0.686108\pi$
$854$	5.05163	0.172863
$855$	3.65857	0.125120
$856$	5.39831	0.184511
$857$	−3.50549	−0.119745	−0.0598727	−	0.998206i	$-0.519069\pi$
$857$	−3.50549	−0.119745	−0.0598727	+	0.998206i	$0.519069\pi$
$858$	20.2149	0.690126
$859$	54.3897	1.85575	0.927876	−	0.372888i	$-0.121632\pi$
$859$	54.3897	1.85575	0.927876	+	0.372888i	$0.121632\pi$
$860$	−11.3012	−0.385367
$861$	1.07868	0.0367614
$862$	73.0461	2.48796
$863$	43.1790	1.46983	0.734916	−	0.678158i	$-0.237222\pi$
$863$	43.1790	1.46983	0.734916	+	0.678158i	$0.237222\pi$
$864$	0.0610199	0.00207594
$865$	−6.23059	−0.211846
$866$	2.31724	0.0787429
$867$	−34.1764	−1.16069
$868$	43.2175	1.46690
$869$	−1.76968	−0.0600324
$870$	−6.08201	−0.206199
$871$	37.0479	1.25532
$872$	62.5627	2.11864
$873$	−13.4631	−0.455658
$874$	32.5533	1.10113
$875$	−9.85759	−0.333247
$876$	21.8247	0.737388
$877$	−15.5646	−0.525578	−0.262789	−	0.964853i	$-0.584642\pi$
$877$	−15.5646	−0.525578	−0.262789	+	0.964853i	$0.584642\pi$
$878$	−27.4604	−0.926745
$879$	33.7068	1.13690
$880$	−1.96410	−0.0662099
$881$	53.4143	1.79957	0.899786	−	0.436331i	$-0.143722\pi$
$881$	53.4143	1.79957	0.899786	+	0.436331i	$0.143722\pi$
$882$	7.86511	0.264832
$883$	20.2678	0.682067	0.341033	−	0.940051i	$-0.389223\pi$
$883$	20.2678	0.682067	0.341033	+	0.940051i	$0.389223\pi$
$884$	8.25156	0.277530
$885$	6.29986	0.211767
$886$	−4.15670	−0.139647
$887$	−3.58676	−0.120432	−0.0602158	−	0.998185i	$-0.519179\pi$
$887$	−3.58676	−0.120432	−0.0602158	+	0.998185i	$0.519179\pi$
$888$	−44.6076	−1.49693
$889$	14.9995	0.503066
$890$	−5.28053	−0.177004
$891$	−11.1400	−0.373203
$892$	15.0450	0.503743
$893$	−34.8543	−1.16636
$894$	−61.1000	−2.04349
$895$	−0.758512	−0.0253543
$896$	−40.3793	−1.34898
$897$	−17.1496	−0.572609
$898$	88.9470	2.96820
$899$	13.0027	0.433666
$900$	−22.2538	−0.741794
$901$	−2.87519	−0.0957864
$902$	0.627704	0.0209003
$903$	−24.2737	−0.807779
$904$	−71.4812	−2.37743
$905$	6.59298	0.219158
$906$	13.2353	0.439714
$907$	39.8515	1.32325	0.661623	−	0.749837i	$-0.269868\pi$
$907$	39.8515	1.32325	0.661623	+	0.749837i	$0.269868\pi$
$908$	36.5318	1.21235
$909$	−0.300525	−0.00996777
$910$	10.0002	0.331504
$911$	23.9939	0.794954	0.397477	−	0.917612i	$-0.369886\pi$
$911$	23.9939	0.794954	0.397477	+	0.917612i	$0.369886\pi$
$912$	−52.3436	−1.73327
$913$	−9.03172	−0.298906
$914$	76.7956	2.54017
$915$	−1.00000	−0.0330590
$916$	50.0947	1.65517
$917$	22.3979	0.739642
$918$	−4.67423	−0.154273
$919$	−33.8575	−1.11686	−0.558428	−	0.829553i	$-0.688595\pi$
$919$	−33.8575	−1.11686	−0.558428	+	0.829553i	$0.688595\pi$
$920$	4.99191	0.164578
$921$	12.3122	0.405701
$922$	73.2485	2.41231
$923$	6.81612	0.224355
$924$	−16.8467	−0.554216
$925$	−21.2089	−0.697345
$926$	−14.8148	−0.486846
$927$	21.1084	0.693290
$928$	0.0405085	0.00132976
$929$	31.0220	1.01780	0.508899	−	0.860826i	$-0.330053\pi$
$929$	31.0220	1.01780	0.508899	+	0.860826i	$0.330053\pi$
$930$	−12.8310	−0.420744
$931$	17.5696	0.575820
$932$	66.0239	2.16268
$933$	1.91867	0.0628143
$934$	−69.0668	−2.25994
$935$	0.249896	0.00817247
$936$	23.1544	0.756825
$937$	26.8352	0.876669	0.438334	−	0.898812i	$-0.355569\pi$
$937$	26.8352	0.876669	0.438334	+	0.898812i	$0.355569\pi$
$938$	−46.3060	−1.51194
$939$	53.2239	1.73690
$940$	−10.6851	−0.348509
$941$	21.0891	0.687486	0.343743	−	0.939064i	$-0.388305\pi$
$941$	21.0891	0.687486	0.343743	+	0.939064i	$0.388305\pi$
$942$	−104.286	−3.39781
$943$	−0.532522	−0.0173413
$944$	−25.2624	−0.822220
$945$	−3.77706	−0.122868
$946$	−14.1253	−0.459254
$947$	55.3700	1.79928	0.899641	−	0.436630i	$-0.143828\pi$
$947$	55.3700	1.79928	0.899641	+	0.436630i	$0.143828\pi$
$948$	−14.4582	−0.469581
$949$	−10.7966	−0.350472
$950$	−74.5577	−2.41897
$951$	19.5125	0.632735
$952$	−5.15894	−0.167202
$953$	12.5368	0.406106	0.203053	−	0.979168i	$-0.434914\pi$
$953$	12.5368	0.406106	0.203053	+	0.979168i	$0.434914\pi$
$954$	−16.1292	−0.522202
$955$	7.57027	0.244968
$956$	20.9567	0.677788
$957$	−5.06862	−0.163845
$958$	−106.029	−3.42565
$959$	39.4156	1.27279
$960$	7.98000	0.257554
$961$	−3.56866	−0.115118
$962$	44.1161	1.42236
$963$	−1.28612	−0.0414445
$964$	−55.8218	−1.79790
$965$	6.77044	0.217948
$966$	21.4352	0.689668
$967$	22.1513	0.712339	0.356170	−	0.934421i	$-0.384083\pi$
$967$	22.1513	0.712339	0.356170	+	0.934421i	$0.384083\pi$
$968$	−4.90374	−0.157612
$969$	6.65975	0.213942
$970$	−13.8279	−0.443986
$971$	−45.3194	−1.45437	−0.727184	−	0.686443i	$-0.759171\pi$
$971$	−45.3194	−1.45437	−0.727184	+	0.686443i	$0.759171\pi$
$972$	−46.1179	−1.47923
$973$	−47.2817	−1.51578
$974$	−29.6800	−0.951010
$975$	39.2782	1.25791
$976$	4.00999	0.128357
$977$	39.8111	1.27367	0.636835	−	0.771000i	$-0.280243\pi$
$977$	39.8111	1.27367	0.636835	+	0.771000i	$0.280243\pi$
$978$	62.0279	1.98343
$979$	−4.40068	−0.140646
$980$	5.38620	0.172056
$981$	−14.9052	−0.475885
$982$	34.8384	1.11174
$983$	3.99096	0.127292	0.0636460	−	0.997973i	$-0.479727\pi$
$983$	3.99096	0.127292	0.0636460	+	0.997973i	$0.479727\pi$
$984$	2.56522	0.0817763
$985$	−0.744962	−0.0237365
$986$	−3.10302	−0.0988204
$987$	−22.9504	−0.730518
$988$	103.404	3.28974
$989$	11.9834	0.381050
$990$	1.40186	0.0445542
$991$	−58.2969	−1.85186	−0.925932	−	0.377691i	$-0.876718\pi$
$991$	−58.2969	−1.85186	−0.925932	+	0.377691i	$0.876718\pi$
$992$	0.0854591	0.00271333
$993$	−67.8459	−2.15303
$994$	−8.51944	−0.270220
$995$	−6.07041	−0.192445
$996$	−73.7887	−2.33808
$997$	31.0534	0.983472	0.491736	−	0.870744i	$-0.336363\pi$
$997$	31.0534	0.983472	0.491736	+	0.870744i	$0.336363\pi$
$998$	86.1786	2.72793
$999$	−16.6625	−0.527178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.a.1.1	✓	5
3.2	odd	2		6039.2.a.a.1.5		5
11.10	odd	2		7381.2.a.g.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.a.1.1	✓	5	1.1	even	1	trivial
6039.2.a.a.1.5		5	3.2	odd	2
7381.2.a.g.1.5		5	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44983 q^{2} +2.04164 q^{3} +4.00166 q^{4} -0.489803 q^{5} -5.00166 q^{6} -2.06203 q^{7} -4.90374 q^{8} +1.16828 q^{9} +O(q^{10})\)	\(q-2.44983 q^{2} +2.04164 q^{3} +4.00166 q^{4} -0.489803 q^{5} -5.00166 q^{6} -2.06203 q^{7} -4.90374 q^{8} +1.16828 q^{9} +1.19993 q^{10} +1.00000 q^{11} +8.16995 q^{12} -4.04164 q^{13} +5.05163 q^{14} -1.00000 q^{15} +4.00999 q^{16} -0.510197 q^{17} -2.86210 q^{18} -6.39354 q^{19} -1.96003 q^{20} -4.20992 q^{21} -2.44983 q^{22} +2.07835 q^{23} -10.0117 q^{24} -4.76009 q^{25} +9.90132 q^{26} -3.73970 q^{27} -8.25156 q^{28} -2.48263 q^{29} +2.44983 q^{30} -5.23749 q^{31} -0.0163168 q^{32} +2.04164 q^{33} +1.24990 q^{34} +1.00999 q^{35} +4.67508 q^{36} +4.45557 q^{37} +15.6631 q^{38} -8.25156 q^{39} +2.40186 q^{40} -0.256224 q^{41} +10.3136 q^{42} +5.76584 q^{43} +4.00166 q^{44} -0.572229 q^{45} -5.09160 q^{46} +5.45149 q^{47} +8.18695 q^{48} -2.74802 q^{49} +11.6614 q^{50} -1.04164 q^{51} -16.1733 q^{52} +5.63544 q^{53} +9.16162 q^{54} -0.489803 q^{55} +10.1117 q^{56} -13.0533 q^{57} +6.08201 q^{58} -6.29986 q^{59} -4.00166 q^{60} +1.00000 q^{61} +12.8310 q^{62} -2.40904 q^{63} -7.98000 q^{64} +1.97961 q^{65} -5.00166 q^{66} -9.16655 q^{67} -2.04164 q^{68} +4.24324 q^{69} -2.47430 q^{70} -1.68647 q^{71} -5.72896 q^{72} +2.67134 q^{73} -10.9154 q^{74} -9.71839 q^{75} -25.5848 q^{76} -2.06203 q^{77} +20.2149 q^{78} -1.76968 q^{79} -1.96410 q^{80} -11.1400 q^{81} +0.627704 q^{82} -9.03172 q^{83} -16.8467 q^{84} +0.249896 q^{85} -14.1253 q^{86} -5.06862 q^{87} -4.90374 q^{88} -4.40068 q^{89} +1.40186 q^{90} +8.33399 q^{91} +8.31685 q^{92} -10.6931 q^{93} -13.3552 q^{94} +3.13157 q^{95} -0.0333130 q^{96} -11.5238 q^{97} +6.73219 q^{98} +1.16828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * q^99

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