LMFDB - Embedded newform 946.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, 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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 11x^{5} + 31x^{4} + 39x^{3} - 91x^{2} - 48x + 64 $ x^7 - 3x^6 - 11x^5 + 31x^4 + 39x^3 - 91x^2 - 48x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.35403$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.35403 q^{3} +1.00000 q^{4} -2.03689 q^{5} -2.35403 q^{6} -2.66006 q^{7} +1.00000 q^{8} +2.54146 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.35403 q^{3} +1.00000 q^{4} -2.03689 q^{5} -2.35403 q^{6} -2.66006 q^{7} +1.00000 q^{8} +2.54146 q^{9} -2.03689 q^{10} +1.00000 q^{11} -2.35403 q^{12} -2.32063 q^{13} -2.66006 q^{14} +4.79489 q^{15} +1.00000 q^{16} +5.61174 q^{17} +2.54146 q^{18} +5.93467 q^{19} -2.03689 q^{20} +6.26187 q^{21} +1.00000 q^{22} -7.13563 q^{23} -2.35403 q^{24} -0.851089 q^{25} -2.32063 q^{26} +1.07943 q^{27} -2.66006 q^{28} +4.68595 q^{29} +4.79489 q^{30} +4.51115 q^{31} +1.00000 q^{32} -2.35403 q^{33} +5.61174 q^{34} +5.41825 q^{35} +2.54146 q^{36} +6.98951 q^{37} +5.93467 q^{38} +5.46283 q^{39} -2.03689 q^{40} +12.4546 q^{41} +6.26187 q^{42} +1.00000 q^{43} +1.00000 q^{44} -5.17666 q^{45} -7.13563 q^{46} -0.808975 q^{47} -2.35403 q^{48} +0.0759371 q^{49} -0.851089 q^{50} -13.2102 q^{51} -2.32063 q^{52} -6.57672 q^{53} +1.07943 q^{54} -2.03689 q^{55} -2.66006 q^{56} -13.9704 q^{57} +4.68595 q^{58} -1.67752 q^{59} +4.79489 q^{60} +9.80426 q^{61} +4.51115 q^{62} -6.76044 q^{63} +1.00000 q^{64} +4.72686 q^{65} -2.35403 q^{66} -4.04800 q^{67} +5.61174 q^{68} +16.7975 q^{69} +5.41825 q^{70} +0.814867 q^{71} +2.54146 q^{72} +7.75514 q^{73} +6.98951 q^{74} +2.00349 q^{75} +5.93467 q^{76} -2.66006 q^{77} +5.46283 q^{78} -7.57362 q^{79} -2.03689 q^{80} -10.1654 q^{81} +12.4546 q^{82} -1.26230 q^{83} +6.26187 q^{84} -11.4305 q^{85} +1.00000 q^{86} -11.0309 q^{87} +1.00000 q^{88} +9.26165 q^{89} -5.17666 q^{90} +6.17302 q^{91} -7.13563 q^{92} -10.6194 q^{93} -0.808975 q^{94} -12.0883 q^{95} -2.35403 q^{96} +6.34616 q^{97} +0.0759371 q^{98} +2.54146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.35403	−1.35910	−0.679550	−	0.733629i	$-0.737825\pi$
$3$	−2.35403	−1.35910	−0.679550	+	0.733629i	$0.737825\pi$
$4$	1.00000	0.500000
$5$	−2.03689	−0.910924	−0.455462	−	0.890255i	$-0.650526\pi$
$5$	−2.03689	−0.910924	−0.455462	+	0.890255i	$0.650526\pi$
$6$	−2.35403	−0.961029
$7$	−2.66006	−1.00541	−0.502705	−	0.864458i	$-0.667662\pi$
$7$	−2.66006	−1.00541	−0.502705	+	0.864458i	$0.667662\pi$
$8$	1.00000	0.353553
$9$	2.54146	0.847152
$10$	−2.03689	−0.644120
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.35403	−0.679550
$13$	−2.32063	−0.643627	−0.321813	−	0.946803i	$-0.604292\pi$
$13$	−2.32063	−0.643627	−0.321813	+	0.946803i	$0.604292\pi$
$14$	−2.66006	−0.710932
$15$	4.79489	1.23804
$16$	1.00000	0.250000
$17$	5.61174	1.36105	0.680524	−	0.732726i	$-0.261752\pi$
$17$	5.61174	1.36105	0.680524	+	0.732726i	$0.261752\pi$
$18$	2.54146	0.599027
$19$	5.93467	1.36151	0.680753	−	0.732513i	$-0.261653\pi$
$19$	5.93467	1.36151	0.680753	+	0.732513i	$0.261653\pi$
$20$	−2.03689	−0.455462
$21$	6.26187	1.36645
$22$	1.00000	0.213201
$23$	−7.13563	−1.48788	−0.743941	−	0.668245i	$-0.767046\pi$
$23$	−7.13563	−1.48788	−0.743941	+	0.668245i	$0.767046\pi$
$24$	−2.35403	−0.480514
$25$	−0.851089	−0.170218
$26$	−2.32063	−0.455113
$27$	1.07943	0.207735
$28$	−2.66006	−0.502705
$29$	4.68595	0.870160	0.435080	−	0.900392i	$-0.356720\pi$
$29$	4.68595	0.870160	0.435080	+	0.900392i	$0.356720\pi$
$30$	4.79489	0.875424
$31$	4.51115	0.810227	0.405113	−	0.914266i	$-0.367232\pi$
$31$	4.51115	0.810227	0.405113	+	0.914266i	$0.367232\pi$
$32$	1.00000	0.176777
$33$	−2.35403	−0.409784
$34$	5.61174	0.962406
$35$	5.41825	0.915851
$36$	2.54146	0.423576
$37$	6.98951	1.14907	0.574534	−	0.818481i	$-0.305183\pi$
$37$	6.98951	1.14907	0.574534	+	0.818481i	$0.305183\pi$
$38$	5.93467	0.962730
$39$	5.46283	0.874753
$40$	−2.03689	−0.322060
$41$	12.4546	1.94509	0.972544	−	0.232721i	$-0.0747629\pi$
$41$	12.4546	1.94509	0.972544	+	0.232721i	$0.0747629\pi$
$42$	6.26187	0.966227
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−5.17666	−0.771691
$46$	−7.13563	−1.05209
$47$	−0.808975	−0.118001	−0.0590005	−	0.998258i	$-0.518791\pi$
$47$	−0.808975	−0.118001	−0.0590005	+	0.998258i	$0.518791\pi$
$48$	−2.35403	−0.339775
$49$	0.0759371	0.0108482
$50$	−0.851089	−0.120362
$51$	−13.2102	−1.84980
$52$	−2.32063	−0.321813
$53$	−6.57672	−0.903382	−0.451691	−	0.892175i	$-0.649179\pi$
$53$	−6.57672	−0.903382	−0.451691	+	0.892175i	$0.649179\pi$
$54$	1.07943	0.146891
$55$	−2.03689	−0.274654
$56$	−2.66006	−0.355466
$57$	−13.9704	−1.85042
$58$	4.68595	0.615296
$59$	−1.67752	−0.218395	−0.109197	−	0.994020i	$-0.534828\pi$
$59$	−1.67752	−0.218395	−0.109197	+	0.994020i	$0.534828\pi$
$60$	4.79489	0.619018
$61$	9.80426	1.25531	0.627654	−	0.778493i	$-0.284015\pi$
$61$	9.80426	1.25531	0.627654	+	0.778493i	$0.284015\pi$
$62$	4.51115	0.572917
$63$	−6.76044	−0.851735
$64$	1.00000	0.125000
$65$	4.72686	0.586295
$66$	−2.35403	−0.289761
$67$	−4.04800	−0.494541	−0.247271	−	0.968946i	$-0.579534\pi$
$67$	−4.04800	−0.494541	−0.247271	+	0.968946i	$0.579534\pi$
$68$	5.61174	0.680524
$69$	16.7975	2.02218
$70$	5.41825	0.647605
$71$	0.814867	0.0967070	0.0483535	−	0.998830i	$-0.484603\pi$
$71$	0.814867	0.0967070	0.0483535	+	0.998830i	$0.484603\pi$
$72$	2.54146	0.299514
$73$	7.75514	0.907671	0.453835	−	0.891085i	$-0.350055\pi$
$73$	7.75514	0.907671	0.453835	+	0.891085i	$0.350055\pi$
$74$	6.98951	0.812514
$75$	2.00349	0.231343
$76$	5.93467	0.680753
$77$	−2.66006	−0.303142
$78$	5.46283	0.618544
$79$	−7.57362	−0.852099	−0.426049	−	0.904700i	$-0.640095\pi$
$79$	−7.57362	−0.852099	−0.426049	+	0.904700i	$0.640095\pi$
$80$	−2.03689	−0.227731
$81$	−10.1654	−1.12949
$82$	12.4546	1.37538
$83$	−1.26230	−0.138556	−0.0692778	−	0.997597i	$-0.522069\pi$
$83$	−1.26230	−0.138556	−0.0692778	+	0.997597i	$0.522069\pi$
$84$	6.26187	0.683226
$85$	−11.4305	−1.23981
$86$	1.00000	0.107833
$87$	−11.0309	−1.18263
$88$	1.00000	0.106600
$89$	9.26165	0.981733	0.490866	−	0.871235i	$-0.336680\pi$
$89$	9.26165	0.981733	0.490866	+	0.871235i	$0.336680\pi$
$90$	−5.17666	−0.545668
$91$	6.17302	0.647109
$92$	−7.13563	−0.743941
$93$	−10.6194	−1.10118
$94$	−0.808975	−0.0834394
$95$	−12.0883	−1.24023
$96$	−2.35403	−0.240257
$97$	6.34616	0.644354	0.322177	−	0.946679i	$-0.395585\pi$
$97$	6.34616	0.644354	0.322177	+	0.946679i	$0.395585\pi$
$98$	0.0759371	0.00767081
$99$	2.54146	0.255426
$100$	−0.851089	−0.0851089
$101$	−6.08507	−0.605487	−0.302743	−	0.953072i	$-0.597903\pi$
$101$	−6.08507	−0.605487	−0.302743	+	0.953072i	$0.597903\pi$
$102$	−13.2102	−1.30801
$103$	1.31919	0.129983	0.0649917	−	0.997886i	$-0.479298\pi$
$103$	1.31919	0.129983	0.0649917	+	0.997886i	$0.479298\pi$
$104$	−2.32063	−0.227557
$105$	−12.7547	−1.24473
$106$	−6.57672	−0.638787
$107$	9.19139	0.888565	0.444283	−	0.895887i	$-0.353459\pi$
$107$	9.19139	0.888565	0.444283	+	0.895887i	$0.353459\pi$
$108$	1.07943	0.103868
$109$	4.93611	0.472794	0.236397	−	0.971657i	$-0.424033\pi$
$109$	4.93611	0.472794	0.236397	+	0.971657i	$0.424033\pi$
$110$	−2.03689	−0.194210
$111$	−16.4535	−1.56170
$112$	−2.66006	−0.251352
$113$	−0.352795	−0.0331882	−0.0165941	−	0.999862i	$-0.505282\pi$
$113$	−0.352795	−0.0331882	−0.0165941	+	0.999862i	$0.505282\pi$
$114$	−13.9704	−1.30845
$115$	14.5345	1.35535
$116$	4.68595	0.435080
$117$	−5.89778	−0.545250
$118$	−1.67752	−0.154428
$119$	−14.9276	−1.36841
$120$	4.79489	0.437712
$121$	1.00000	0.0909091
$122$	9.80426	0.887636
$123$	−29.3186	−2.64357
$124$	4.51115	0.405113
$125$	11.9180	1.06598
$126$	−6.76044	−0.602267
$127$	−9.28106	−0.823561	−0.411781	−	0.911283i	$-0.635093\pi$
$127$	−9.28106	−0.823561	−0.411781	+	0.911283i	$0.635093\pi$
$128$	1.00000	0.0883883
$129$	−2.35403	−0.207261
$130$	4.72686	0.414573
$131$	18.5635	1.62190	0.810949	−	0.585117i	$-0.198951\pi$
$131$	18.5635	1.62190	0.810949	+	0.585117i	$0.198951\pi$
$132$	−2.35403	−0.204892
$133$	−15.7866	−1.36887
$134$	−4.04800	−0.349694
$135$	−2.19867	−0.189231
$136$	5.61174	0.481203
$137$	9.43458	0.806051	0.403025	−	0.915189i	$-0.367959\pi$
$137$	9.43458	0.806051	0.403025	+	0.915189i	$0.367959\pi$
$138$	16.7975	1.42990
$139$	−19.3819	−1.64395	−0.821975	−	0.569523i	$-0.807128\pi$
$139$	−19.3819	−1.64395	−0.821975	+	0.569523i	$0.807128\pi$
$140$	5.41825	0.457926
$141$	1.90435	0.160375
$142$	0.814867	0.0683822
$143$	−2.32063	−0.194061
$144$	2.54146	0.211788
$145$	−9.54476	−0.792649
$146$	7.75514	0.641820
$147$	−0.178758	−0.0147437
$148$	6.98951	0.574534
$149$	−7.10502	−0.582066	−0.291033	−	0.956713i	$-0.593999\pi$
$149$	−7.10502	−0.582066	−0.291033	+	0.956713i	$0.593999\pi$
$150$	2.00349	0.163584
$151$	4.30721	0.350515	0.175258	−	0.984523i	$-0.443924\pi$
$151$	4.30721	0.350515	0.175258	+	0.984523i	$0.443924\pi$
$152$	5.93467	0.481365
$153$	14.2620	1.15301
$154$	−2.66006	−0.214354
$155$	−9.18871	−0.738055
$156$	5.46283	0.437377
$157$	12.0336	0.960388	0.480194	−	0.877162i	$-0.340566\pi$
$157$	12.0336	0.960388	0.480194	+	0.877162i	$0.340566\pi$
$158$	−7.57362	−0.602525
$159$	15.4818	1.22779
$160$	−2.03689	−0.161030
$161$	18.9812	1.49593
$162$	−10.1654	−0.798667
$163$	−20.8033	−1.62944	−0.814719	−	0.579856i	$-0.803109\pi$
$163$	−20.8033	−1.62944	−0.814719	+	0.579856i	$0.803109\pi$
$164$	12.4546	0.972544
$165$	4.79489	0.373282
$166$	−1.26230	−0.0979737
$167$	−13.3473	−1.03285	−0.516423	−	0.856333i	$-0.672737\pi$
$167$	−13.3473	−1.03285	−0.516423	+	0.856333i	$0.672737\pi$
$168$	6.26187	0.483114
$169$	−7.61468	−0.585744
$170$	−11.4305	−0.876679
$171$	15.0827	1.15340
$172$	1.00000	0.0762493
$173$	9.54678	0.725828	0.362914	−	0.931823i	$-0.381782\pi$
$173$	9.54678	0.725828	0.362914	+	0.931823i	$0.381782\pi$
$174$	−11.0309	−0.836248
$175$	2.26395	0.171139
$176$	1.00000	0.0753778
$177$	3.94894	0.296820
$178$	9.26165	0.694190
$179$	25.1235	1.87781	0.938907	−	0.344170i	$-0.111840\pi$
$179$	25.1235	1.87781	0.938907	+	0.344170i	$0.111840\pi$
$180$	−5.17666	−0.385846
$181$	−1.94436	−0.144523	−0.0722616	−	0.997386i	$-0.523022\pi$
$181$	−1.94436	−0.144523	−0.0722616	+	0.997386i	$0.523022\pi$
$182$	6.17302	0.457575
$183$	−23.0795	−1.70609
$184$	−7.13563	−0.526046
$185$	−14.2368	−1.04671
$186$	−10.6194	−0.778651
$187$	5.61174	0.410371
$188$	−0.808975	−0.0590005
$189$	−2.87134	−0.208859
$190$	−12.0883	−0.876974
$191$	−25.1230	−1.81783	−0.908917	−	0.416978i	$-0.863089\pi$
$191$	−25.1230	−1.81783	−0.908917	+	0.416978i	$0.863089\pi$
$192$	−2.35403	−0.169887
$193$	−0.961485	−0.0692092	−0.0346046	−	0.999401i	$-0.511017\pi$
$193$	−0.961485	−0.0692092	−0.0346046	+	0.999401i	$0.511017\pi$
$194$	6.34616	0.455627
$195$	−11.1272	−0.796834
$196$	0.0759371	0.00542408
$197$	19.9356	1.42035	0.710176	−	0.704024i	$-0.248615\pi$
$197$	19.9356	1.42035	0.710176	+	0.704024i	$0.248615\pi$
$198$	2.54146	0.180613
$199$	−25.8978	−1.83585	−0.917923	−	0.396758i	$-0.870135\pi$
$199$	−25.8978	−1.83585	−0.917923	+	0.396758i	$0.870135\pi$
$200$	−0.851089	−0.0601811
$201$	9.52910	0.672131
$202$	−6.08507	−0.428144
$203$	−12.4649	−0.874867
$204$	−13.2102	−0.924900
$205$	−25.3687	−1.77183
$206$	1.31919	0.0919121
$207$	−18.1349	−1.26046
$208$	−2.32063	−0.160907
$209$	5.93467	0.410510
$210$	−12.7547	−0.880160
$211$	22.6786	1.56126	0.780628	−	0.624995i	$-0.214899\pi$
$211$	22.6786	1.56126	0.780628	+	0.624995i	$0.214899\pi$
$212$	−6.57672	−0.451691
$213$	−1.91822	−0.131434
$214$	9.19139	0.628311
$215$	−2.03689	−0.138915
$216$	1.07943	0.0734456
$217$	−12.0000	−0.814610
$218$	4.93611	0.334316
$219$	−18.2558	−1.23362
$220$	−2.03689	−0.137327
$221$	−13.0228	−0.876007
$222$	−16.4535	−1.10429
$223$	2.27091	0.152071	0.0760355	−	0.997105i	$-0.475774\pi$
$223$	2.27091	0.152071	0.0760355	+	0.997105i	$0.475774\pi$
$224$	−2.66006	−0.177733
$225$	−2.16300	−0.144200
$226$	−0.352795	−0.0234676
$227$	18.9570	1.25822	0.629109	−	0.777317i	$-0.283420\pi$
$227$	18.9570	1.25822	0.629109	+	0.777317i	$0.283420\pi$
$228$	−13.9704	−0.925211
$229$	−7.35354	−0.485935	−0.242968	−	0.970034i	$-0.578121\pi$
$229$	−7.35354	−0.485935	−0.242968	+	0.970034i	$0.578121\pi$
$230$	14.5345	0.958375
$231$	6.26187	0.412001
$232$	4.68595	0.307648
$233$	15.5266	1.01718	0.508589	−	0.861009i	$-0.330167\pi$
$233$	15.5266	1.01718	0.508589	+	0.861009i	$0.330167\pi$
$234$	−5.89778	−0.385550
$235$	1.64779	0.107490
$236$	−1.67752	−0.109197
$237$	17.8285	1.15809
$238$	−14.9276	−0.967612
$239$	26.8272	1.73531	0.867654	−	0.497169i	$-0.165627\pi$
$239$	26.8272	1.73531	0.867654	+	0.497169i	$0.165627\pi$
$240$	4.79489	0.309509
$241$	−26.2967	−1.69392	−0.846958	−	0.531659i	$-0.821569\pi$
$241$	−26.2967	−1.69392	−0.846958	+	0.531659i	$0.821569\pi$
$242$	1.00000	0.0642824
$243$	20.6913	1.32735
$244$	9.80426	0.627654
$245$	−0.154675	−0.00988185
$246$	−29.3186	−1.86928
$247$	−13.7722	−0.876302
$248$	4.51115	0.286458
$249$	2.97150	0.188311
$250$	11.9180	0.753761
$251$	21.1280	1.33359	0.666793	−	0.745243i	$-0.267667\pi$
$251$	21.1280	1.33359	0.666793	+	0.745243i	$0.267667\pi$
$252$	−6.76044	−0.425867
$253$	−7.13563	−0.448613
$254$	−9.28106	−0.582346
$255$	26.9077	1.68503
$256$	1.00000	0.0625000
$257$	−30.2794	−1.88877	−0.944387	−	0.328836i	$-0.893344\pi$
$257$	−30.2794	−1.88877	−0.944387	+	0.328836i	$0.893344\pi$
$258$	−2.35403	−0.146555
$259$	−18.5925	−1.15528
$260$	4.72686	0.293148
$261$	11.9091	0.737158
$262$	18.5635	1.14685
$263$	2.29895	0.141759	0.0708796	−	0.997485i	$-0.477419\pi$
$263$	2.29895	0.141759	0.0708796	+	0.997485i	$0.477419\pi$
$264$	−2.35403	−0.144881
$265$	13.3960	0.822912
$266$	−15.7866	−0.967938
$267$	−21.8022	−1.33427
$268$	−4.04800	−0.247271
$269$	22.9282	1.39796	0.698978	−	0.715143i	$-0.253638\pi$
$269$	22.9282	1.39796	0.698978	+	0.715143i	$0.253638\pi$
$270$	−2.19867	−0.133807
$271$	−2.37817	−0.144463	−0.0722317	−	0.997388i	$-0.523012\pi$
$271$	−2.37817	−0.144463	−0.0722317	+	0.997388i	$0.523012\pi$
$272$	5.61174	0.340262
$273$	−14.5315	−0.879485
$274$	9.43458	0.569964
$275$	−0.851089	−0.0513226
$276$	16.7975	1.01109
$277$	25.5166	1.53314	0.766571	−	0.642160i	$-0.221961\pi$
$277$	25.5166	1.53314	0.766571	+	0.642160i	$0.221961\pi$
$278$	−19.3819	−1.16245
$279$	11.4649	0.686385
$280$	5.41825	0.323802
$281$	9.99467	0.596232	0.298116	−	0.954530i	$-0.403642\pi$
$281$	9.99467	0.596232	0.298116	+	0.954530i	$0.403642\pi$
$282$	1.90435	0.113402
$283$	−2.90492	−0.172680	−0.0863398	−	0.996266i	$-0.527517\pi$
$283$	−2.90492	−0.172680	−0.0863398	+	0.996266i	$0.527517\pi$
$284$	0.814867	0.0483535
$285$	28.4561	1.68559
$286$	−2.32063	−0.137222
$287$	−33.1301	−1.95561
$288$	2.54146	0.149757
$289$	14.4917	0.852451
$290$	−9.54476	−0.560488
$291$	−14.9390	−0.875742
$292$	7.75514	0.453835
$293$	−7.07327	−0.413225	−0.206612	−	0.978423i	$-0.566244\pi$
$293$	−7.07327	−0.413225	−0.206612	+	0.978423i	$0.566244\pi$
$294$	−0.178758	−0.0104254
$295$	3.41692	0.198941
$296$	6.98951	0.406257
$297$	1.07943	0.0626346
$298$	−7.10502	−0.411583
$299$	16.5592	0.957641
$300$	2.00349	0.115671
$301$	−2.66006	−0.153324
$302$	4.30721	0.247852
$303$	14.3244	0.822917
$304$	5.93467	0.340377
$305$	−19.9702	−1.14349
$306$	14.2620	0.815304
$307$	16.2614	0.928089	0.464045	−	0.885812i	$-0.346398\pi$
$307$	16.2614	0.928089	0.464045	+	0.885812i	$0.346398\pi$
$308$	−2.66006	−0.151571
$309$	−3.10541	−0.176660
$310$	−9.18871	−0.521884
$311$	−10.8301	−0.614121	−0.307060	−	0.951690i	$-0.599345\pi$
$311$	−10.8301	−0.614121	−0.307060	+	0.951690i	$0.599345\pi$
$312$	5.46283	0.309272
$313$	−11.8755	−0.671242	−0.335621	−	0.941997i	$-0.608946\pi$
$313$	−11.8755	−0.671242	−0.335621	+	0.941997i	$0.608946\pi$
$314$	12.0336	0.679097
$315$	13.7702	0.775866
$316$	−7.57362	−0.426049
$317$	29.6972	1.66796	0.833981	−	0.551793i	$-0.186056\pi$
$317$	29.6972	1.66796	0.833981	+	0.551793i	$0.186056\pi$
$318$	15.4818	0.868176
$319$	4.68595	0.262363
$320$	−2.03689	−0.113865
$321$	−21.6368	−1.20765
$322$	18.9812	1.05778
$323$	33.3038	1.85308
$324$	−10.1654	−0.564743
$325$	1.97506	0.109557
$326$	−20.8033	−1.15219
$327$	−11.6198	−0.642574
$328$	12.4546	0.687692
$329$	2.15192	0.118639
$330$	4.79489	0.263950
$331$	10.8591	0.596869	0.298435	−	0.954430i	$-0.403535\pi$
$331$	10.8591	0.596869	0.298435	+	0.954430i	$0.403535\pi$
$332$	−1.26230	−0.0692778
$333$	17.7635	0.973435
$334$	−13.3473	−0.730333
$335$	8.24531	0.450490
$336$	6.26187	0.341613
$337$	12.2347	0.666468	0.333234	−	0.942844i	$-0.391860\pi$
$337$	12.2347	0.666468	0.333234	+	0.942844i	$0.391860\pi$
$338$	−7.61468	−0.414184
$339$	0.830490	0.0451060
$340$	−11.4305	−0.619905
$341$	4.51115	0.244293
$342$	15.0827	0.815579
$343$	18.4184	0.994503
$344$	1.00000	0.0539164
$345$	−34.2146	−1.84205
$346$	9.54678	0.513238
$347$	−15.1749	−0.814629	−0.407314	−	0.913288i	$-0.633535\pi$
$347$	−15.1749	−0.814629	−0.407314	+	0.913288i	$0.633535\pi$
$348$	−11.0309	−0.591317
$349$	29.5819	1.58348	0.791742	−	0.610855i	$-0.209174\pi$
$349$	29.5819	1.58348	0.791742	+	0.610855i	$0.209174\pi$
$350$	2.26395	0.121013
$351$	−2.50495	−0.133704
$352$	1.00000	0.0533002
$353$	−11.2175	−0.597047	−0.298524	−	0.954402i	$-0.596494\pi$
$353$	−11.2175	−0.597047	−0.298524	+	0.954402i	$0.596494\pi$
$354$	3.94894	0.209884
$355$	−1.65979	−0.0880927
$356$	9.26165	0.490866
$357$	35.1400	1.85981
$358$	25.1235	1.32782
$359$	−11.2542	−0.593976	−0.296988	−	0.954881i	$-0.595982\pi$
$359$	−11.2542	−0.593976	−0.296988	+	0.954881i	$0.595982\pi$
$360$	−5.17666	−0.272834
$361$	16.2203	0.853699
$362$	−1.94436	−0.102193
$363$	−2.35403	−0.123555
$364$	6.17302	0.323554
$365$	−15.7964	−0.826819
$366$	−23.0795	−1.20639
$367$	19.7059	1.02864	0.514320	−	0.857598i	$-0.328044\pi$
$367$	19.7059	1.02864	0.514320	+	0.857598i	$0.328044\pi$
$368$	−7.13563	−0.371971
$369$	31.6529	1.64778
$370$	−14.2368	−0.740138
$371$	17.4945	0.908268
$372$	−10.6194	−0.550590
$373$	−16.2855	−0.843230	−0.421615	−	0.906775i	$-0.638537\pi$
$373$	−16.2855	−0.843230	−0.421615	+	0.906775i	$0.638537\pi$
$374$	5.61174	0.290176
$375$	−28.0554	−1.44877
$376$	−0.808975	−0.0417197
$377$	−10.8744	−0.560058
$378$	−2.87134	−0.147686
$379$	0.0678062	0.00348297	0.00174149	−	0.999998i	$-0.499446\pi$
$379$	0.0678062	0.00348297	0.00174149	+	0.999998i	$0.499446\pi$
$380$	−12.0883	−0.620114
$381$	21.8479	1.11930
$382$	−25.1230	−1.28540
$383$	3.48118	0.177880	0.0889399	−	0.996037i	$-0.471652\pi$
$383$	3.48118	0.177880	0.0889399	+	0.996037i	$0.471652\pi$
$384$	−2.35403	−0.120129
$385$	5.41825	0.276140
$386$	−0.961485	−0.0489383
$387$	2.54146	0.129189
$388$	6.34616	0.322177
$389$	−0.159121	−0.00806776	−0.00403388	−	0.999992i	$-0.501284\pi$
$389$	−0.159121	−0.00806776	−0.00403388	+	0.999992i	$0.501284\pi$
$390$	−11.1272	−0.563446
$391$	−40.0433	−2.02508
$392$	0.0759371	0.00383540
$393$	−43.6990	−2.20432
$394$	19.9356	1.00434
$395$	15.4266	0.776197
$396$	2.54146	0.127713
$397$	−23.4879	−1.17882	−0.589411	−	0.807833i	$-0.700640\pi$
$397$	−23.4879	−1.17882	−0.589411	+	0.807833i	$0.700640\pi$
$398$	−25.8978	−1.29814
$399$	37.1621	1.86043
$400$	−0.851089	−0.0425544
$401$	11.7643	0.587480	0.293740	−	0.955885i	$-0.405100\pi$
$401$	11.7643	0.587480	0.293740	+	0.955885i	$0.405100\pi$
$402$	9.52910	0.475269
$403$	−10.4687	−0.521484
$404$	−6.08507	−0.302743
$405$	20.7057	1.02888
$406$	−12.4649	−0.618624
$407$	6.98951	0.346457
$408$	−13.2102	−0.654003
$409$	13.0710	0.646321	0.323160	−	0.946344i	$-0.395255\pi$
$409$	13.0710	0.646321	0.323160	+	0.946344i	$0.395255\pi$
$410$	−25.3687	−1.25287
$411$	−22.2093	−1.09550
$412$	1.31919	0.0649917
$413$	4.46232	0.219576
$414$	−18.1349	−0.891282
$415$	2.57117	0.126214
$416$	−2.32063	−0.113778
$417$	45.6256	2.23429
$418$	5.93467	0.290274
$419$	29.4609	1.43926	0.719628	−	0.694359i	$-0.244312\pi$
$419$	29.4609	1.43926	0.719628	+	0.694359i	$0.244312\pi$
$420$	−12.7547	−0.622367
$421$	11.3771	0.554487	0.277244	−	0.960800i	$-0.410579\pi$
$421$	11.3771	0.554487	0.277244	+	0.960800i	$0.410579\pi$
$422$	22.6786	1.10398
$423$	−2.05597	−0.0999649
$424$	−6.57672	−0.319394
$425$	−4.77609	−0.231674
$426$	−1.91822	−0.0929382
$427$	−26.0800	−1.26210
$428$	9.19139	0.444283
$429$	5.46283	0.263748
$430$	−2.03689	−0.0982274
$431$	16.7498	0.806808	0.403404	−	0.915022i	$-0.367827\pi$
$431$	16.7498	0.806808	0.403404	+	0.915022i	$0.367827\pi$
$432$	1.07943	0.0519339
$433$	9.01908	0.433429	0.216715	−	0.976235i	$-0.430466\pi$
$433$	9.01908	0.433429	0.216715	+	0.976235i	$0.430466\pi$
$434$	−12.0000	−0.576016
$435$	22.4686	1.07729
$436$	4.93611	0.236397
$437$	−42.3476	−2.02576
$438$	−18.2558	−0.872298
$439$	−19.1011	−0.911646	−0.455823	−	0.890070i	$-0.650655\pi$
$439$	−19.1011	−0.911646	−0.455823	+	0.890070i	$0.650655\pi$
$440$	−2.03689	−0.0971048
$441$	0.192991	0.00919004
$442$	−13.0228	−0.619431
$443$	31.4958	1.49641	0.748205	−	0.663467i	$-0.230916\pi$
$443$	31.4958	1.49641	0.748205	+	0.663467i	$0.230916\pi$
$444$	−16.4535	−0.780849
$445$	−18.8649	−0.894284
$446$	2.27091	0.107531
$447$	16.7254	0.791086
$448$	−2.66006	−0.125676
$449$	25.9452	1.22443	0.612215	−	0.790691i	$-0.290279\pi$
$449$	25.9452	1.22443	0.612215	+	0.790691i	$0.290279\pi$
$450$	−2.16300	−0.101965
$451$	12.4546	0.586466
$452$	−0.352795	−0.0165941
$453$	−10.1393	−0.476385
$454$	18.9570	0.889695
$455$	−12.5738	−0.589467
$456$	−13.9704	−0.654223
$457$	−14.8093	−0.692752	−0.346376	−	0.938096i	$-0.612588\pi$
$457$	−14.8093	−0.692752	−0.346376	+	0.938096i	$0.612588\pi$
$458$	−7.35354	−0.343608
$459$	6.05746	0.282738
$460$	14.5345	0.677674
$461$	−13.2391	−0.616605	−0.308302	−	0.951288i	$-0.599761\pi$
$461$	−13.2391	−0.616605	−0.308302	+	0.951288i	$0.599761\pi$
$462$	6.26187	0.291328
$463$	−21.9421	−1.01974	−0.509868	−	0.860253i	$-0.670306\pi$
$463$	−21.9421	−1.01974	−0.509868	+	0.860253i	$0.670306\pi$
$464$	4.68595	0.217540
$465$	21.6305	1.00309
$466$	15.5266	0.719254
$467$	−16.8943	−0.781776	−0.390888	−	0.920438i	$-0.627832\pi$
$467$	−16.8943	−0.781776	−0.390888	+	0.920438i	$0.627832\pi$
$468$	−5.89778	−0.272625
$469$	10.7679	0.497217
$470$	1.64779	0.0760069
$471$	−28.3275	−1.30526
$472$	−1.67752	−0.0772142
$473$	1.00000	0.0459800
$474$	17.8285	0.818892
$475$	−5.05093	−0.231752
$476$	−14.9276	−0.684205
$477$	−16.7144	−0.765302
$478$	26.8272	1.22705
$479$	−11.2888	−0.515800	−0.257900	−	0.966172i	$-0.583031\pi$
$479$	−11.2888	−0.515800	−0.257900	+	0.966172i	$0.583031\pi$
$480$	4.79489	0.218856
$481$	−16.2201	−0.739571
$482$	−26.2967	−1.19778
$483$	−44.6824	−2.03312
$484$	1.00000	0.0454545
$485$	−12.9264	−0.586958
$486$	20.6913	0.938577
$487$	−19.9149	−0.902428	−0.451214	−	0.892416i	$-0.649009\pi$
$487$	−19.9149	−0.902428	−0.451214	+	0.892416i	$0.649009\pi$
$488$	9.80426	0.443818
$489$	48.9715	2.21457
$490$	−0.154675	−0.00698752
$491$	−38.8434	−1.75298	−0.876490	−	0.481420i	$-0.840121\pi$
$491$	−38.8434	−1.75298	−0.876490	+	0.481420i	$0.840121\pi$
$492$	−29.3186	−1.32178
$493$	26.2964	1.18433
$494$	−13.7722	−0.619639
$495$	−5.17666	−0.232674
$496$	4.51115	0.202557
$497$	−2.16760	−0.0972301
$498$	2.97150	0.133156
$499$	−4.91389	−0.219976	−0.109988	−	0.993933i	$-0.535081\pi$
$499$	−4.91389	−0.219976	−0.109988	+	0.993933i	$0.535081\pi$
$500$	11.9180	0.532990
$501$	31.4200	1.40374
$502$	21.1280	0.942987
$503$	25.2645	1.12649	0.563244	−	0.826290i	$-0.309553\pi$
$503$	25.2645	1.12649	0.563244	+	0.826290i	$0.309553\pi$
$504$	−6.76044	−0.301134
$505$	12.3946	0.551553
$506$	−7.13563	−0.317218
$507$	17.9252	0.796085
$508$	−9.28106	−0.411781
$509$	30.0988	1.33410	0.667052	−	0.745011i	$-0.267556\pi$
$509$	30.0988	1.33410	0.667052	+	0.745011i	$0.267556\pi$
$510$	26.9077	1.19149
$511$	−20.6292	−0.912581
$512$	1.00000	0.0441942
$513$	6.40603	0.282833
$514$	−30.2794	−1.33556
$515$	−2.68704	−0.118405
$516$	−2.35403	−0.103630
$517$	−0.808975	−0.0355787
$518$	−18.5925	−0.816909
$519$	−22.4734	−0.986473
$520$	4.72686	0.207287
$521$	5.01173	0.219568	0.109784	−	0.993955i	$-0.464984\pi$
$521$	5.01173	0.219568	0.109784	+	0.993955i	$0.464984\pi$
$522$	11.9091	0.521249
$523$	−14.6122	−0.638946	−0.319473	−	0.947595i	$-0.603506\pi$
$523$	−14.6122	−0.638946	−0.319473	+	0.947595i	$0.603506\pi$
$524$	18.5635	0.810949
$525$	−5.32940	−0.232594
$526$	2.29895	0.100239
$527$	25.3154	1.10276
$528$	−2.35403	−0.102446
$529$	27.9172	1.21379
$530$	13.3960	0.581886
$531$	−4.26335	−0.185014
$532$	−15.7866	−0.684436
$533$	−28.9026	−1.25191
$534$	−21.8022	−0.943473
$535$	−18.7218	−0.809415
$536$	−4.04800	−0.174847
$537$	−59.1414	−2.55214
$538$	22.9282	0.988505
$539$	0.0759371	0.00327084
$540$	−2.19867	−0.0946156
$541$	−27.5145	−1.18294	−0.591471	−	0.806327i	$-0.701452\pi$
$541$	−27.5145	−1.18294	−0.591471	+	0.806327i	$0.701452\pi$
$542$	−2.37817	−0.102151
$543$	4.57709	0.196422
$544$	5.61174	0.240602
$545$	−10.0543	−0.430679
$546$	−14.5315	−0.621890
$547$	−4.26673	−0.182432	−0.0912162	−	0.995831i	$-0.529075\pi$
$547$	−4.26673	−0.182432	−0.0912162	+	0.995831i	$0.529075\pi$
$548$	9.43458	0.403025
$549$	24.9171	1.06344
$550$	−0.851089	−0.0362905
$551$	27.8096	1.18473
$552$	16.7975	0.714949
$553$	20.1463	0.856708
$554$	25.5166	1.08409
$555$	33.5140	1.42259
$556$	−19.3819	−0.821975
$557$	−32.8259	−1.39088	−0.695439	−	0.718585i	$-0.744790\pi$
$557$	−32.8259	−1.39088	−0.695439	+	0.718585i	$0.744790\pi$
$558$	11.4649	0.485348
$559$	−2.32063	−0.0981522
$560$	5.41825	0.228963
$561$	−13.2102	−0.557736
$562$	9.99467	0.421600
$563$	−22.2112	−0.936092	−0.468046	−	0.883704i	$-0.655042\pi$
$563$	−22.2112	−0.936092	−0.468046	+	0.883704i	$0.655042\pi$
$564$	1.90435	0.0801876
$565$	0.718604	0.0302319
$566$	−2.90492	−0.122103
$567$	27.0405	1.13560
$568$	0.814867	0.0341911
$569$	−22.0415	−0.924027	−0.462013	−	0.886873i	$-0.652873\pi$
$569$	−22.0415	−0.924027	−0.462013	+	0.886873i	$0.652873\pi$
$570$	28.4561	1.19190
$571$	−38.8473	−1.62571	−0.812855	−	0.582466i	$-0.802088\pi$
$571$	−38.8473	−1.62571	−0.812855	+	0.582466i	$0.802088\pi$
$572$	−2.32063	−0.0970304
$573$	59.1402	2.47062
$574$	−33.1301	−1.38282
$575$	6.07306	0.253264
$576$	2.54146	0.105894
$577$	−14.1409	−0.588695	−0.294347	−	0.955699i	$-0.595102\pi$
$577$	−14.1409	−0.588695	−0.294347	+	0.955699i	$0.595102\pi$
$578$	14.4917	0.602774
$579$	2.26336	0.0940622
$580$	−9.54476	−0.396325
$581$	3.35780	0.139305
$582$	−14.9390	−0.619243
$583$	−6.57672	−0.272380
$584$	7.75514	0.320910
$585$	12.0131	0.496681
$586$	−7.07327	−0.292194
$587$	−0.853592	−0.0352315	−0.0176157	−	0.999845i	$-0.505608\pi$
$587$	−0.853592	−0.0352315	−0.0176157	+	0.999845i	$0.505608\pi$
$588$	−0.178758	−0.00737187
$589$	26.7722	1.10313
$590$	3.41692	0.140673
$591$	−46.9290	−1.93040
$592$	6.98951	0.287267
$593$	6.87759	0.282429	0.141214	−	0.989979i	$-0.454899\pi$
$593$	6.87759	0.282429	0.141214	+	0.989979i	$0.454899\pi$
$594$	1.07943	0.0442893
$595$	30.4058	1.24652
$596$	−7.10502	−0.291033
$597$	60.9642	2.49510
$598$	16.5592	0.677155
$599$	−3.63243	−0.148417	−0.0742086	−	0.997243i	$-0.523643\pi$
$599$	−3.63243	−0.148417	−0.0742086	+	0.997243i	$0.523643\pi$
$600$	2.00349	0.0817921
$601$	−2.02701	−0.0826833	−0.0413417	−	0.999145i	$-0.513163\pi$
$601$	−2.02701	−0.0826833	−0.0413417	+	0.999145i	$0.513163\pi$
$602$	−2.66006	−0.108416
$603$	−10.2878	−0.418952
$604$	4.30721	0.175258
$605$	−2.03689	−0.0828113
$606$	14.3244	0.581890
$607$	31.8787	1.29391	0.646957	−	0.762526i	$-0.276041\pi$
$607$	31.8787	1.29391	0.646957	+	0.762526i	$0.276041\pi$
$608$	5.93467	0.240683
$609$	29.3428	1.18903
$610$	−19.9702	−0.808569
$611$	1.87733	0.0759487
$612$	14.2620	0.576507
$613$	−1.87676	−0.0758016	−0.0379008	−	0.999282i	$-0.512067\pi$
$613$	−1.87676	−0.0758016	−0.0379008	+	0.999282i	$0.512067\pi$
$614$	16.2614	0.656258
$615$	59.7187	2.40809
$616$	−2.66006	−0.107177
$617$	−8.32874	−0.335302	−0.167651	−	0.985846i	$-0.553618\pi$
$617$	−8.32874	−0.335302	−0.167651	+	0.985846i	$0.553618\pi$
$618$	−3.10541	−0.124918
$619$	7.25907	0.291767	0.145883	−	0.989302i	$-0.453398\pi$
$619$	7.25907	0.291767	0.145883	+	0.989302i	$0.453398\pi$
$620$	−9.18871	−0.369027
$621$	−7.70238	−0.309086
$622$	−10.8301	−0.434249
$623$	−24.6366	−0.987043
$624$	5.46283	0.218688
$625$	−20.0202	−0.800808
$626$	−11.8755	−0.474640
$627$	−13.9704	−0.557923
$628$	12.0336	0.480194
$629$	39.2233	1.56394
$630$	13.7702	0.548620
$631$	39.9772	1.59147	0.795734	−	0.605647i	$-0.207086\pi$
$631$	39.9772	1.59147	0.795734	+	0.605647i	$0.207086\pi$
$632$	−7.57362	−0.301262
$633$	−53.3860	−2.12190
$634$	29.6972	1.17943
$635$	18.9045	0.750202
$636$	15.4818	0.613893
$637$	−0.176222	−0.00698217
$638$	4.68595	0.185519
$639$	2.07095	0.0819255
$640$	−2.03689	−0.0805151
$641$	−46.4676	−1.83536	−0.917681	−	0.397319i	$-0.869941\pi$
$641$	−46.4676	−1.83536	−0.917681	+	0.397319i	$0.869941\pi$
$642$	−21.6368	−0.853937
$643$	−18.8032	−0.741524	−0.370762	−	0.928728i	$-0.620904\pi$
$643$	−18.8032	−0.741524	−0.370762	+	0.928728i	$0.620904\pi$
$644$	18.9812	0.747965
$645$	4.79489	0.188799
$646$	33.3038	1.31032
$647$	−1.65946	−0.0652403	−0.0326201	−	0.999468i	$-0.510385\pi$
$647$	−1.65946	−0.0652403	−0.0326201	+	0.999468i	$0.510385\pi$
$648$	−10.1654	−0.399333
$649$	−1.67752	−0.0658485
$650$	1.97506	0.0774683
$651$	28.2482	1.10714
$652$	−20.8033	−0.814719
$653$	−46.4694	−1.81849	−0.909243	−	0.416265i	$-0.863339\pi$
$653$	−46.4694	−1.81849	−0.909243	+	0.416265i	$0.863339\pi$
$654$	−11.6198	−0.454368
$655$	−37.8117	−1.47743
$656$	12.4546	0.486272
$657$	19.7094	0.768935
$658$	2.15192	0.0838907
$659$	39.3776	1.53393	0.766967	−	0.641687i	$-0.221765\pi$
$659$	39.3776	1.53393	0.766967	+	0.641687i	$0.221765\pi$
$660$	4.79489	0.186641
$661$	28.5003	1.10853	0.554267	−	0.832339i	$-0.312999\pi$
$661$	28.5003	1.10853	0.554267	+	0.832339i	$0.312999\pi$
$662$	10.8591	0.422050
$663$	30.6560	1.19058
$664$	−1.26230	−0.0489868
$665$	32.1555	1.24694
$666$	17.7635	0.688323
$667$	−33.4372	−1.29469
$668$	−13.3473	−0.516423
$669$	−5.34578	−0.206680
$670$	8.24531	0.318544
$671$	9.80426	0.378489
$672$	6.26187	0.241557
$673$	1.09112	0.0420598	0.0210299	−	0.999779i	$-0.493305\pi$
$673$	1.09112	0.0420598	0.0210299	+	0.999779i	$0.493305\pi$
$674$	12.2347	0.471264
$675$	−0.918686	−0.0353603
$676$	−7.61468	−0.292872
$677$	−31.8964	−1.22588	−0.612939	−	0.790130i	$-0.710013\pi$
$677$	−31.8964	−1.22588	−0.612939	+	0.790130i	$0.710013\pi$
$678$	0.830490	0.0318948
$679$	−16.8812	−0.647840
$680$	−11.4305	−0.438339
$681$	−44.6253	−1.71004
$682$	4.51115	0.172741
$683$	12.6926	0.485668	0.242834	−	0.970068i	$-0.421923\pi$
$683$	12.6926	0.485668	0.242834	+	0.970068i	$0.421923\pi$
$684$	15.0827	0.576701
$685$	−19.2172	−0.734251
$686$	18.4184	0.703220
$687$	17.3104	0.660435
$688$	1.00000	0.0381246
$689$	15.2621	0.581441
$690$	−34.2146	−1.30253
$691$	−36.9358	−1.40511	−0.702553	−	0.711632i	$-0.747957\pi$
$691$	−36.9358	−1.40511	−0.702553	+	0.711632i	$0.747957\pi$
$692$	9.54678	0.362914
$693$	−6.76044	−0.256808
$694$	−15.1749	−0.576030
$695$	39.4787	1.49751
$696$	−11.0309	−0.418124
$697$	69.8922	2.64736
$698$	29.5819	1.11969
$699$	−36.5500	−1.38245
$700$	2.26395	0.0855693
$701$	−12.2402	−0.462306	−0.231153	−	0.972917i	$-0.574250\pi$
$701$	−12.2402	−0.462306	−0.231153	+	0.972917i	$0.574250\pi$
$702$	−2.50495	−0.0945431
$703$	41.4804	1.56446
$704$	1.00000	0.0376889
$705$	−3.87895	−0.146090
$706$	−11.2175	−0.422176
$707$	16.1867	0.608762
$708$	3.94894	0.148410
$709$	−37.9318	−1.42456	−0.712278	−	0.701897i	$-0.752337\pi$
$709$	−37.9318	−1.42456	−0.712278	+	0.701897i	$0.752337\pi$
$710$	−1.65979	−0.0622909
$711$	−19.2480	−0.721857
$712$	9.26165	0.347095
$713$	−32.1899	−1.20552
$714$	35.1400	1.31508
$715$	4.72686	0.176775
$716$	25.1235	0.938907
$717$	−63.1520	−2.35846
$718$	−11.2542	−0.420004
$719$	15.4982	0.577986	0.288993	−	0.957331i	$-0.406680\pi$
$719$	15.4982	0.577986	0.288993	+	0.957331i	$0.406680\pi$
$720$	−5.17666	−0.192923
$721$	−3.50912	−0.130686
$722$	16.2203	0.603657
$723$	61.9031	2.30220
$724$	−1.94436	−0.0722616
$725$	−3.98816	−0.148117
$726$	−2.35403	−0.0873662
$727$	21.2612	0.788534	0.394267	−	0.918996i	$-0.370999\pi$
$727$	21.2612	0.788534	0.394267	+	0.918996i	$0.370999\pi$
$728$	6.17302	0.228787
$729$	−18.2118	−0.674513
$730$	−15.7964	−0.584649
$731$	5.61174	0.207558
$732$	−23.0795	−0.853044
$733$	42.3386	1.56381	0.781905	−	0.623397i	$-0.214248\pi$
$733$	42.3386	1.56381	0.781905	+	0.623397i	$0.214248\pi$
$734$	19.7059	0.727358
$735$	0.364111	0.0134304
$736$	−7.13563	−0.263023
$737$	−4.04800	−0.149110
$738$	31.6529	1.16516
$739$	−22.6345	−0.832622	−0.416311	−	0.909222i	$-0.636677\pi$
$739$	−22.6345	−0.832622	−0.416311	+	0.909222i	$0.636677\pi$
$740$	−14.2368	−0.523357
$741$	32.4201	1.19098
$742$	17.4945	0.642243
$743$	38.6748	1.41884	0.709420	−	0.704786i	$-0.248957\pi$
$743$	38.6748	1.41884	0.709420	+	0.704786i	$0.248957\pi$
$744$	−10.6194	−0.389326
$745$	14.4721	0.530218
$746$	−16.2855	−0.596254
$747$	−3.20809	−0.117378
$748$	5.61174	0.205186
$749$	−24.4497	−0.893372
$750$	−28.0554	−1.02444
$751$	−24.8339	−0.906201	−0.453101	−	0.891459i	$-0.649682\pi$
$751$	−24.8339	−0.906201	−0.453101	+	0.891459i	$0.649682\pi$
$752$	−0.808975	−0.0295003
$753$	−49.7359	−1.81248
$754$	−10.8744	−0.396021
$755$	−8.77329	−0.319293
$756$	−2.87134	−0.104430
$757$	−32.0770	−1.16586	−0.582930	−	0.812522i	$-0.698094\pi$
$757$	−32.0770	−1.16586	−0.582930	+	0.812522i	$0.698094\pi$
$758$	0.0678062	0.00246283
$759$	16.7975	0.609710
$760$	−12.0883	−0.438487
$761$	−13.5245	−0.490264	−0.245132	−	0.969490i	$-0.578831\pi$
$761$	−13.5245	−0.490264	−0.245132	+	0.969490i	$0.578831\pi$
$762$	21.8479	0.791466
$763$	−13.1304	−0.475351
$764$	−25.1230	−0.908917
$765$	−29.0501	−1.05031
$766$	3.48118	0.125780
$767$	3.89291	0.140565
$768$	−2.35403	−0.0849437
$769$	−10.5895	−0.381866	−0.190933	−	0.981603i	$-0.561151\pi$
$769$	−10.5895	−0.381866	−0.190933	+	0.981603i	$0.561151\pi$
$770$	5.41825	0.195260
$771$	71.2785	2.56703
$772$	−0.961485	−0.0346046
$773$	15.7322	0.565848	0.282924	−	0.959142i	$-0.408696\pi$
$773$	15.7322	0.565848	0.282924	+	0.959142i	$0.408696\pi$
$774$	2.54146	0.0913508
$775$	−3.83939	−0.137915
$776$	6.34616	0.227814
$777$	43.7674	1.57015
$778$	−0.159121	−0.00570477
$779$	73.9141	2.64825
$780$	−11.1272	−0.398417
$781$	0.814867	0.0291583
$782$	−40.0433	−1.43195
$783$	5.05814	0.180763
$784$	0.0759371	0.00271204
$785$	−24.5112	−0.874841
$786$	−43.6990	−1.55869
$787$	−4.23399	−0.150925	−0.0754627	−	0.997149i	$-0.524043\pi$
$787$	−4.23399	−0.150925	−0.0754627	+	0.997149i	$0.524043\pi$
$788$	19.9356	0.710176
$789$	−5.41179	−0.192665
$790$	15.4266	0.548854
$791$	0.938457	0.0333677
$792$	2.54146	0.0903067
$793$	−22.7521	−0.807950
$794$	−23.4879	−0.833554
$795$	−31.5347	−1.11842
$796$	−25.8978	−0.917923
$797$	17.8141	0.631008	0.315504	−	0.948924i	$-0.397826\pi$
$797$	17.8141	0.631008	0.315504	+	0.948924i	$0.397826\pi$
$798$	37.1621	1.31552
$799$	−4.53976	−0.160605
$800$	−0.851089	−0.0300905
$801$	23.5381	0.831677
$802$	11.7643	0.415411
$803$	7.75514	0.273673
$804$	9.52910	0.336066
$805$	−38.6626	−1.36268
$806$	−10.4687	−0.368745
$807$	−53.9737	−1.89996
$808$	−6.08507	−0.214072
$809$	26.7617	0.940892	0.470446	−	0.882429i	$-0.344093\pi$
$809$	26.7617	0.940892	0.470446	+	0.882429i	$0.344093\pi$
$810$	20.7057	0.727525
$811$	−37.9038	−1.33098	−0.665491	−	0.746406i	$-0.731778\pi$
$811$	−37.9038	−1.33098	−0.665491	+	0.746406i	$0.731778\pi$
$812$	−12.4649	−0.437433
$813$	5.59828	0.196340
$814$	6.98951	0.244982
$815$	42.3739	1.48429
$816$	−13.2102	−0.462450
$817$	5.93467	0.207628
$818$	13.0710	0.457018
$819$	15.6885	0.548199
$820$	−25.3687	−0.885913
$821$	−4.51514	−0.157579	−0.0787897	−	0.996891i	$-0.525106\pi$
$821$	−4.51514	−0.157579	−0.0787897	+	0.996891i	$0.525106\pi$
$822$	−22.2093	−0.774638
$823$	23.5130	0.819612	0.409806	−	0.912173i	$-0.365596\pi$
$823$	23.5130	0.819612	0.409806	+	0.912173i	$0.365596\pi$
$824$	1.31919	0.0459561
$825$	2.00349	0.0697525
$826$	4.46232	0.155264
$827$	−10.1903	−0.354352	−0.177176	−	0.984179i	$-0.556696\pi$
$827$	−10.1903	−0.354352	−0.177176	+	0.984179i	$0.556696\pi$
$828$	−18.1349	−0.630231
$829$	18.2358	0.633356	0.316678	−	0.948533i	$-0.397433\pi$
$829$	18.2358	0.633356	0.316678	+	0.948533i	$0.397433\pi$
$830$	2.57117	0.0892465
$831$	−60.0668	−2.08369
$832$	−2.32063	−0.0804534
$833$	0.426140	0.0147649
$834$	45.6256	1.57988
$835$	27.1870	0.940845
$836$	5.93467	0.205255
$837$	4.86945	0.168313
$838$	29.4609	1.01771
$839$	49.7209	1.71656	0.858278	−	0.513185i	$-0.171535\pi$
$839$	49.7209	1.71656	0.858278	+	0.513185i	$0.171535\pi$
$840$	−12.7547	−0.440080
$841$	−7.04184	−0.242822
$842$	11.3771	0.392082
$843$	−23.5277	−0.810339
$844$	22.6786	0.780628
$845$	15.5102	0.533568
$846$	−2.05597	−0.0706858
$847$	−2.66006	−0.0914009
$848$	−6.57672	−0.225845
$849$	6.83827	0.234689
$850$	−4.77609	−0.163819
$851$	−49.8746	−1.70968
$852$	−1.91822	−0.0657172
$853$	−35.2416	−1.20665	−0.603324	−	0.797496i	$-0.706158\pi$
$853$	−35.2416	−1.20665	−0.603324	+	0.797496i	$0.706158\pi$
$854$	−26.0800	−0.892438
$855$	−30.7218	−1.05066
$856$	9.19139	0.314155
$857$	−50.6265	−1.72937	−0.864685	−	0.502315i	$-0.832482\pi$
$857$	−50.6265	−1.72937	−0.864685	+	0.502315i	$0.832482\pi$
$858$	5.46283	0.186498
$859$	−33.9779	−1.15931	−0.579655	−	0.814862i	$-0.696813\pi$
$859$	−33.9779	−1.15931	−0.579655	+	0.814862i	$0.696813\pi$
$860$	−2.03689	−0.0694573
$861$	77.9893	2.65787
$862$	16.7498	0.570499
$863$	−4.04714	−0.137766	−0.0688831	−	0.997625i	$-0.521944\pi$
$863$	−4.04714	−0.137766	−0.0688831	+	0.997625i	$0.521944\pi$
$864$	1.07943	0.0367228
$865$	−19.4457	−0.661174
$866$	9.01908	0.306481
$867$	−34.1138	−1.15857
$868$	−12.0000	−0.407305
$869$	−7.57362	−0.256918
$870$	22.4686	0.761759
$871$	9.39390	0.318300
$872$	4.93611	0.167158
$873$	16.1285	0.545866
$874$	−42.3476	−1.43243
$875$	−31.7027	−1.07175
$876$	−18.2558	−0.616808
$877$	18.3301	0.618962	0.309481	−	0.950906i	$-0.399845\pi$
$877$	18.3301	0.618962	0.309481	+	0.950906i	$0.399845\pi$
$878$	−19.1011	−0.644631
$879$	16.6507	0.561614
$880$	−2.03689	−0.0686635
$881$	16.9898	0.572403	0.286201	−	0.958170i	$-0.407607\pi$
$881$	16.9898	0.572403	0.286201	+	0.958170i	$0.407607\pi$
$882$	0.192991	0.00649834
$883$	9.97730	0.335763	0.167881	−	0.985807i	$-0.446307\pi$
$883$	9.97730	0.335763	0.167881	+	0.985807i	$0.446307\pi$
$884$	−13.0228	−0.438004
$885$	−8.04354	−0.270381
$886$	31.4958	1.05812
$887$	−21.4844	−0.721374	−0.360687	−	0.932687i	$-0.617458\pi$
$887$	−21.4844	−0.721374	−0.360687	+	0.932687i	$0.617458\pi$
$888$	−16.4535	−0.552144
$889$	24.6882	0.828016
$890$	−18.8649	−0.632354
$891$	−10.1654	−0.340553
$892$	2.27091	0.0760355
$893$	−4.80100	−0.160659
$894$	16.7254	0.559382
$895$	−51.1736	−1.71055
$896$	−2.66006	−0.0888665
$897$	−38.9808	−1.30153
$898$	25.9452	0.865803
$899$	21.1390	0.705027
$900$	−2.16300	−0.0721002
$901$	−36.9068	−1.22955
$902$	12.4546	0.414694
$903$	6.26187	0.208382
$904$	−0.352795	−0.0117338
$905$	3.96045	0.131650
$906$	−10.1393	−0.336855
$907$	0.498323	0.0165466	0.00827328	−	0.999966i	$-0.497367\pi$
$907$	0.498323	0.0165466	0.00827328	+	0.999966i	$0.497367\pi$
$908$	18.9570	0.629109
$909$	−15.4649	−0.512940
$910$	−12.5738	−0.416816
$911$	−14.4464	−0.478629	−0.239315	−	0.970942i	$-0.576923\pi$
$911$	−14.4464	−0.478629	−0.239315	+	0.970942i	$0.576923\pi$
$912$	−13.9704	−0.462606
$913$	−1.26230	−0.0417761
$914$	−14.8093	−0.489850
$915$	47.0104	1.55412
$916$	−7.35354	−0.242968
$917$	−49.3800	−1.63067
$918$	6.05746	0.199926
$919$	−14.3259	−0.472569	−0.236285	−	0.971684i	$-0.575930\pi$
$919$	−14.3259	−0.472569	−0.236285	+	0.971684i	$0.575930\pi$
$920$	14.5345	0.479188
$921$	−38.2799	−1.26137
$922$	−13.2391	−0.436005
$923$	−1.89101	−0.0622432
$924$	6.26187	0.206000
$925$	−5.94869	−0.195592
$926$	−21.9421	−0.721062
$927$	3.35266	0.110116
$928$	4.68595	0.153824
$929$	−10.3630	−0.339999	−0.169999	−	0.985444i	$-0.554377\pi$
$929$	−10.3630	−0.339999	−0.169999	+	0.985444i	$0.554377\pi$
$930$	21.6305	0.709292
$931$	0.450662	0.0147698
$932$	15.5266	0.508589
$933$	25.4945	0.834651
$934$	−16.8943	−0.552799
$935$	−11.4305	−0.373817
$936$	−5.89778	−0.192775
$937$	−49.3744	−1.61299	−0.806496	−	0.591239i	$-0.798639\pi$
$937$	−49.3744	−1.61299	−0.806496	+	0.591239i	$0.798639\pi$
$938$	10.7679	0.351585
$939$	27.9552	0.912284
$940$	1.64779	0.0537450
$941$	−31.0335	−1.01166	−0.505832	−	0.862632i	$-0.668814\pi$
$941$	−31.0335	−1.01166	−0.505832	+	0.862632i	$0.668814\pi$
$942$	−28.3275	−0.922961
$943$	−88.8717	−2.89406
$944$	−1.67752	−0.0545987
$945$	5.84860	0.190255
$946$	1.00000	0.0325128
$947$	14.1458	0.459675	0.229838	−	0.973229i	$-0.426180\pi$
$947$	14.1458	0.459675	0.229838	+	0.973229i	$0.426180\pi$
$948$	17.8285	0.579044
$949$	−17.9968	−0.584202
$950$	−5.05093	−0.163874
$951$	−69.9081	−2.26693
$952$	−14.9276	−0.483806
$953$	−58.2439	−1.88670	−0.943352	−	0.331794i	$-0.892346\pi$
$953$	−58.2439	−1.88670	−0.943352	+	0.331794i	$0.892346\pi$
$954$	−16.7144	−0.541150
$955$	51.1726	1.65591
$956$	26.8272	0.867654
$957$	−11.0309	−0.356577
$958$	−11.2888	−0.364726
$959$	−25.0966	−0.810411
$960$	4.79489	0.154755
$961$	−10.6495	−0.343533
$962$	−16.2201	−0.522956
$963$	23.3595	0.752750
$964$	−26.2967	−0.846958
$965$	1.95844	0.0630443
$966$	−44.6824	−1.43763
$967$	50.3223	1.61825	0.809127	−	0.587633i	$-0.199940\pi$
$967$	50.3223	1.61825	0.809127	+	0.587633i	$0.199940\pi$
$968$	1.00000	0.0321412
$969$	−78.3982	−2.51851
$970$	−12.9264	−0.415042
$971$	−29.9649	−0.961620	−0.480810	−	0.876825i	$-0.659657\pi$
$971$	−29.9649	−0.961620	−0.480810	+	0.876825i	$0.659657\pi$
$972$	20.6913	0.663674
$973$	51.5571	1.65284
$974$	−19.9149	−0.638113
$975$	−4.64935	−0.148899
$976$	9.80426	0.313827
$977$	−32.0631	−1.02579	−0.512895	−	0.858451i	$-0.671427\pi$
$977$	−32.0631	−1.02579	−0.512895	+	0.858451i	$0.671427\pi$
$978$	48.9715	1.56594
$979$	9.26165	0.296004
$980$	−0.154675	−0.00494093
$981$	12.5449	0.400528
$982$	−38.8434	−1.23954
$983$	−32.0146	−1.02111	−0.510553	−	0.859846i	$-0.670559\pi$
$983$	−32.0146	−1.02111	−0.510553	+	0.859846i	$0.670559\pi$
$984$	−29.3186	−0.934642
$985$	−40.6066	−1.29383
$986$	26.2964	0.837447
$987$	−5.06569	−0.161243
$988$	−13.7722	−0.438151
$989$	−7.13563	−0.226900
$990$	−5.17666	−0.164525
$991$	−16.8135	−0.534097	−0.267048	−	0.963683i	$-0.586048\pi$
$991$	−16.8135	−0.534097	−0.267048	+	0.963683i	$0.586048\pi$
$992$	4.51115	0.143229
$993$	−25.5626	−0.811205
$994$	−2.16760	−0.0687521
$995$	52.7509	1.67232
$996$	2.97150	0.0941555
$997$	−23.7897	−0.753428	−0.376714	−	0.926330i	$-0.622946\pi$
$997$	−23.7897	−0.753428	−0.376714	+	0.926330i	$0.622946\pi$
$998$	−4.91389	−0.155547
$999$	7.54465	0.238702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.k.1.1	✓	7
3.2	odd	2		8514.2.a.bl.1.6		7
4.3	odd	2		7568.2.a.bg.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.k.1.1	✓	7	1.1	even	1	trivial
7568.2.a.bg.1.7		7	4.3	odd	2
8514.2.a.bl.1.6		7	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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.35403 q^{3} +1.00000 q^{4} -2.03689 q^{5} -2.35403 q^{6} -2.66006 q^{7} +1.00000 q^{8} +2.54146 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.35403 q^{3} +1.00000 q^{4} -2.03689 q^{5} -2.35403 q^{6} -2.66006 q^{7} +1.00000 q^{8} +2.54146 q^{9} -2.03689 q^{10} +1.00000 q^{11} -2.35403 q^{12} -2.32063 q^{13} -2.66006 q^{14} +4.79489 q^{15} +1.00000 q^{16} +5.61174 q^{17} +2.54146 q^{18} +5.93467 q^{19} -2.03689 q^{20} +6.26187 q^{21} +1.00000 q^{22} -7.13563 q^{23} -2.35403 q^{24} -0.851089 q^{25} -2.32063 q^{26} +1.07943 q^{27} -2.66006 q^{28} +4.68595 q^{29} +4.79489 q^{30} +4.51115 q^{31} +1.00000 q^{32} -2.35403 q^{33} +5.61174 q^{34} +5.41825 q^{35} +2.54146 q^{36} +6.98951 q^{37} +5.93467 q^{38} +5.46283 q^{39} -2.03689 q^{40} +12.4546 q^{41} +6.26187 q^{42} +1.00000 q^{43} +1.00000 q^{44} -5.17666 q^{45} -7.13563 q^{46} -0.808975 q^{47} -2.35403 q^{48} +0.0759371 q^{49} -0.851089 q^{50} -13.2102 q^{51} -2.32063 q^{52} -6.57672 q^{53} +1.07943 q^{54} -2.03689 q^{55} -2.66006 q^{56} -13.9704 q^{57} +4.68595 q^{58} -1.67752 q^{59} +4.79489 q^{60} +9.80426 q^{61} +4.51115 q^{62} -6.76044 q^{63} +1.00000 q^{64} +4.72686 q^{65} -2.35403 q^{66} -4.04800 q^{67} +5.61174 q^{68} +16.7975 q^{69} +5.41825 q^{70} +0.814867 q^{71} +2.54146 q^{72} +7.75514 q^{73} +6.98951 q^{74} +2.00349 q^{75} +5.93467 q^{76} -2.66006 q^{77} +5.46283 q^{78} -7.57362 q^{79} -2.03689 q^{80} -10.1654 q^{81} +12.4546 q^{82} -1.26230 q^{83} +6.26187 q^{84} -11.4305 q^{85} +1.00000 q^{86} -11.0309 q^{87} +1.00000 q^{88} +9.26165 q^{89} -5.17666 q^{90} +6.17302 q^{91} -7.13563 q^{92} -10.6194 q^{93} -0.808975 q^{94} -12.0883 q^{95} -2.35403 q^{96} +6.34616 q^{97} +0.0759371 q^{98} +2.54146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * q^99

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