LMFDB - Embedded newform 2667.2.a.p.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 $ x^18 - 6x^17 - 11x^16 + 123x^15 - 35x^14 - 982x^13 + 988x^12 + 3872x^11 - 5421x^10 - 7882x^9 + 13376x^8 + 7948x^7 - 15795x^6 - 3858x^5 + 8199x^4 + 1453x^3 - 1610x^2 - 380*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.60620$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.60620 q^{2} -1.00000 q^{3} +0.579871 q^{4} -3.54808 q^{5} +1.60620 q^{6} +1.00000 q^{7} +2.28101 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.60620 q^{2} -1.00000 q^{3} +0.579871 q^{4} -3.54808 q^{5} +1.60620 q^{6} +1.00000 q^{7} +2.28101 q^{8} +1.00000 q^{9} +5.69892 q^{10} -2.78529 q^{11} -0.579871 q^{12} +2.43579 q^{13} -1.60620 q^{14} +3.54808 q^{15} -4.82349 q^{16} -6.06028 q^{17} -1.60620 q^{18} -1.93658 q^{19} -2.05743 q^{20} -1.00000 q^{21} +4.47373 q^{22} +3.19860 q^{23} -2.28101 q^{24} +7.58887 q^{25} -3.91236 q^{26} -1.00000 q^{27} +0.579871 q^{28} +2.42395 q^{29} -5.69892 q^{30} +3.23823 q^{31} +3.18546 q^{32} +2.78529 q^{33} +9.73400 q^{34} -3.54808 q^{35} +0.579871 q^{36} -1.06507 q^{37} +3.11054 q^{38} -2.43579 q^{39} -8.09320 q^{40} -3.51151 q^{41} +1.60620 q^{42} +5.82642 q^{43} -1.61511 q^{44} -3.54808 q^{45} -5.13759 q^{46} -2.39519 q^{47} +4.82349 q^{48} +1.00000 q^{49} -12.1892 q^{50} +6.06028 q^{51} +1.41244 q^{52} +11.1491 q^{53} +1.60620 q^{54} +9.88243 q^{55} +2.28101 q^{56} +1.93658 q^{57} -3.89334 q^{58} -2.80705 q^{59} +2.05743 q^{60} +8.16721 q^{61} -5.20123 q^{62} +1.00000 q^{63} +4.53050 q^{64} -8.64238 q^{65} -4.47373 q^{66} +5.97952 q^{67} -3.51418 q^{68} -3.19860 q^{69} +5.69892 q^{70} +12.1587 q^{71} +2.28101 q^{72} +2.47476 q^{73} +1.71072 q^{74} -7.58887 q^{75} -1.12297 q^{76} -2.78529 q^{77} +3.91236 q^{78} -3.02097 q^{79} +17.1141 q^{80} +1.00000 q^{81} +5.64018 q^{82} -10.1939 q^{83} -0.579871 q^{84} +21.5023 q^{85} -9.35838 q^{86} -2.42395 q^{87} -6.35327 q^{88} -2.30092 q^{89} +5.69892 q^{90} +2.43579 q^{91} +1.85478 q^{92} -3.23823 q^{93} +3.84715 q^{94} +6.87116 q^{95} -3.18546 q^{96} -0.707978 q^{97} -1.60620 q^{98} -2.78529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19} - 21 q^{20} - 18 q^{21} + 5 q^{22} - 14 q^{23} + 21 q^{24} + 28 q^{25} - 8 q^{26} - 18 q^{27} + 22 q^{28} - 17 q^{29} + 4 q^{30} + 5 q^{31} - 53 q^{32} + 9 q^{33} - 19 q^{34} - 10 q^{35} + 22 q^{36} - 15 q^{37} - 22 q^{38} + 25 q^{39} - q^{40} - 17 q^{41} + 6 q^{42} + q^{43} - 33 q^{44} - 10 q^{45} + 10 q^{46} - 31 q^{47} - 34 q^{48} + 18 q^{49} - 35 q^{50} + 17 q^{51} - 70 q^{52} - 35 q^{53} + 6 q^{54} + 4 q^{55} - 21 q^{56} + 5 q^{57} + 3 q^{58} - 46 q^{59} + 21 q^{60} - 5 q^{61} - 10 q^{62} + 18 q^{63} + 63 q^{64} - 12 q^{65} - 5 q^{66} + 6 q^{67} - 56 q^{68} + 14 q^{69} - 4 q^{70} - 22 q^{71} - 21 q^{72} - 16 q^{73} + 18 q^{74} - 28 q^{75} + 32 q^{76} - 9 q^{77} + 8 q^{78} + 46 q^{79} - 30 q^{80} + 18 q^{81} - 12 q^{82} - 46 q^{83} - 22 q^{84} + 4 q^{85} + 18 q^{86} + 17 q^{87} + 30 q^{88} - 42 q^{89} - 4 q^{90} - 25 q^{91} - 48 q^{92} - 5 q^{93} + 3 q^{94} - 2 q^{95} + 53 q^{96} - 35 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * 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 $

$2$	−1.60620	−1.13575	−0.567877	−	0.823114i	$-0.692235\pi$
$2$	−1.60620	−1.13575	−0.567877	+	0.823114i	$0.692235\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.579871	0.289935
$5$	−3.54808	−1.58675	−0.793375	−	0.608733i	$-0.791678\pi$
$5$	−3.54808	−1.58675	−0.793375	+	0.608733i	$0.791678\pi$
$6$	1.60620	0.655727
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.28101	0.806458
$9$	1.00000	0.333333
$10$	5.69892	1.80216
$11$	−2.78529	−0.839796	−0.419898	−	0.907571i	$-0.637934\pi$
$11$	−2.78529	−0.839796	−0.419898	+	0.907571i	$0.637934\pi$
$12$	−0.579871	−0.167394
$13$	2.43579	0.675567	0.337784	−	0.941224i	$-0.390323\pi$
$13$	2.43579	0.675567	0.337784	+	0.941224i	$0.390323\pi$
$14$	−1.60620	−0.429274
$15$	3.54808	0.916110
$16$	−4.82349	−1.20587
$17$	−6.06028	−1.46983	−0.734917	−	0.678158i	$-0.762779\pi$
$17$	−6.06028	−1.46983	−0.734917	+	0.678158i	$0.762779\pi$
$18$	−1.60620	−0.378584
$19$	−1.93658	−0.444283	−0.222141	−	0.975014i	$-0.571305\pi$
$19$	−1.93658	−0.444283	−0.222141	+	0.975014i	$0.571305\pi$
$20$	−2.05743	−0.460055
$21$	−1.00000	−0.218218
$22$	4.47373	0.953802
$23$	3.19860	0.666955	0.333477	−	0.942758i	$-0.391778\pi$
$23$	3.19860	0.666955	0.333477	+	0.942758i	$0.391778\pi$
$24$	−2.28101	−0.465609
$25$	7.58887	1.51777
$26$	−3.91236	−0.767277
$27$	−1.00000	−0.192450
$28$	0.579871	0.109585
$29$	2.42395	0.450116	0.225058	−	0.974345i	$-0.427743\pi$
$29$	2.42395	0.450116	0.225058	+	0.974345i	$0.427743\pi$
$30$	−5.69892	−1.04048
$31$	3.23823	0.581603	0.290801	−	0.956783i	$-0.406078\pi$
$31$	3.23823	0.581603	0.290801	+	0.956783i	$0.406078\pi$
$32$	3.18546	0.563116
$33$	2.78529	0.484857
$34$	9.73400	1.66937
$35$	−3.54808	−0.599735
$36$	0.579871	0.0966451
$37$	−1.06507	−0.175097	−0.0875484	−	0.996160i	$-0.527903\pi$
$37$	−1.06507	−0.175097	−0.0875484	+	0.996160i	$0.527903\pi$
$38$	3.11054	0.504596
$39$	−2.43579	−0.390039
$40$	−8.09320	−1.27965
$41$	−3.51151	−0.548406	−0.274203	−	0.961672i	$-0.588414\pi$
$41$	−3.51151	−0.548406	−0.274203	+	0.961672i	$0.588414\pi$
$42$	1.60620	0.247842
$43$	5.82642	0.888521	0.444260	−	0.895898i	$-0.353466\pi$
$43$	5.82642	0.888521	0.444260	+	0.895898i	$0.353466\pi$
$44$	−1.61511	−0.243487
$45$	−3.54808	−0.528917
$46$	−5.13759	−0.757496
$47$	−2.39519	−0.349375	−0.174687	−	0.984624i	$-0.555891\pi$
$47$	−2.39519	−0.349375	−0.174687	+	0.984624i	$0.555891\pi$
$48$	4.82349	0.696211
$49$	1.00000	0.142857
$50$	−12.1892	−1.72382
$51$	6.06028	0.848609
$52$	1.41244	0.195871
$53$	11.1491	1.53145	0.765723	−	0.643171i	$-0.222381\pi$
$53$	11.1491	1.53145	0.765723	+	0.643171i	$0.222381\pi$
$54$	1.60620	0.218576
$55$	9.88243	1.33255
$56$	2.28101	0.304813
$57$	1.93658	0.256507
$58$	−3.89334	−0.511221
$59$	−2.80705	−0.365447	−0.182723	−	0.983164i	$-0.558491\pi$
$59$	−2.80705	−0.365447	−0.182723	+	0.983164i	$0.558491\pi$
$60$	2.05743	0.265613
$61$	8.16721	1.04570	0.522852	−	0.852423i	$-0.324868\pi$
$61$	8.16721	1.04570	0.522852	+	0.852423i	$0.324868\pi$
$62$	−5.20123	−0.660557
$63$	1.00000	0.125988
$64$	4.53050	0.566312
$65$	−8.64238	−1.07196
$66$	−4.47373	−0.550678
$67$	5.97952	0.730515	0.365257	−	0.930907i	$-0.380981\pi$
$67$	5.97952	0.730515	0.365257	+	0.930907i	$0.380981\pi$
$68$	−3.51418	−0.426157
$69$	−3.19860	−0.385066
$70$	5.69892	0.681151
$71$	12.1587	1.44297	0.721484	−	0.692431i	$-0.243460\pi$
$71$	12.1587	1.44297	0.721484	+	0.692431i	$0.243460\pi$
$72$	2.28101	0.268819
$73$	2.47476	0.289649	0.144824	−	0.989457i	$-0.453738\pi$
$73$	2.47476	0.289649	0.144824	+	0.989457i	$0.453738\pi$
$74$	1.71072	0.198867
$75$	−7.58887	−0.876287
$76$	−1.12297	−0.128813
$77$	−2.78529	−0.317413
$78$	3.91236	0.442988
$79$	−3.02097	−0.339885	−0.169943	−	0.985454i	$-0.554358\pi$
$79$	−3.02097	−0.339885	−0.169943	+	0.985454i	$0.554358\pi$
$80$	17.1141	1.91342
$81$	1.00000	0.111111
$82$	5.64018	0.622854
$83$	−10.1939	−1.11893	−0.559465	−	0.828854i	$-0.688993\pi$
$83$	−10.1939	−1.11893	−0.559465	+	0.828854i	$0.688993\pi$
$84$	−0.579871	−0.0632691
$85$	21.5023	2.33226
$86$	−9.35838	−1.00914
$87$	−2.42395	−0.259875
$88$	−6.35327	−0.677261
$89$	−2.30092	−0.243897	−0.121949	−	0.992536i	$-0.538914\pi$
$89$	−2.30092	−0.243897	−0.121949	+	0.992536i	$0.538914\pi$
$90$	5.69892	0.600719
$91$	2.43579	0.255340
$92$	1.85478	0.193374
$93$	−3.23823	−0.335789
$94$	3.84715	0.396804
$95$	6.87116	0.704966
$96$	−3.18546	−0.325115
$97$	−0.707978	−0.0718843	−0.0359422	−	0.999354i	$-0.511443\pi$
$97$	−0.707978	−0.0718843	−0.0359422	+	0.999354i	$0.511443\pi$
$98$	−1.60620	−0.162250
$99$	−2.78529	−0.279932
$100$	4.40057	0.440057
$101$	11.1926	1.11371	0.556853	−	0.830611i	$-0.312009\pi$
$101$	11.1926	1.11371	0.556853	+	0.830611i	$0.312009\pi$
$102$	−9.73400	−0.963810
$103$	9.42373	0.928548	0.464274	−	0.885692i	$-0.346315\pi$
$103$	9.42373	0.928548	0.464274	+	0.885692i	$0.346315\pi$
$104$	5.55606	0.544817
$105$	3.54808	0.346257
$106$	−17.9076	−1.73934
$107$	−6.56198	−0.634371	−0.317185	−	0.948364i	$-0.602738\pi$
$107$	−6.56198	−0.634371	−0.317185	+	0.948364i	$0.602738\pi$
$108$	−0.579871	−0.0557981
$109$	−15.5034	−1.48495	−0.742476	−	0.669872i	$-0.766349\pi$
$109$	−15.5034	−1.48495	−0.742476	+	0.669872i	$0.766349\pi$
$110$	−15.8731	−1.51344
$111$	1.06507	0.101092
$112$	−4.82349	−0.455777
$113$	14.8683	1.39869	0.699344	−	0.714786i	$-0.253476\pi$
$113$	14.8683	1.39869	0.699344	+	0.714786i	$0.253476\pi$
$114$	−3.11054	−0.291328
$115$	−11.3489	−1.05829
$116$	1.40558	0.130505
$117$	2.43579	0.225189
$118$	4.50868	0.415057
$119$	−6.06028	−0.555545
$120$	8.09320	0.738805
$121$	−3.24216	−0.294742
$122$	−13.1182	−1.18766
$123$	3.51151	0.316622
$124$	1.87775	0.168627
$125$	−9.18552	−0.821578
$126$	−1.60620	−0.143091
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−13.6478	−1.20631
$129$	−5.82642	−0.512988
$130$	13.8814	1.21748
$131$	−16.9371	−1.47981	−0.739903	−	0.672714i	$-0.765129\pi$
$131$	−16.9371	−1.47981	−0.739903	+	0.672714i	$0.765129\pi$
$132$	1.61511	0.140577
$133$	−1.93658	−0.167923
$134$	−9.60429	−0.829684
$135$	3.54808	0.305370
$136$	−13.8235	−1.18536
$137$	−8.14622	−0.695979	−0.347989	−	0.937498i	$-0.613135\pi$
$137$	−8.14622	−0.695979	−0.347989	+	0.937498i	$0.613135\pi$
$138$	5.13759	0.437340
$139$	−10.0461	−0.852099	−0.426050	−	0.904700i	$-0.640095\pi$
$139$	−10.0461	−0.852099	−0.426050	+	0.904700i	$0.640095\pi$
$140$	−2.05743	−0.173884
$141$	2.39519	0.201712
$142$	−19.5292	−1.63886
$143$	−6.78439	−0.567339
$144$	−4.82349	−0.401958
$145$	−8.60037	−0.714222
$146$	−3.97495	−0.328969
$147$	−1.00000	−0.0824786
$148$	−0.617604	−0.0507667
$149$	−4.50378	−0.368964	−0.184482	−	0.982836i	$-0.559061\pi$
$149$	−4.50378	−0.368964	−0.184482	+	0.982836i	$0.559061\pi$
$150$	12.1892	0.995246
$151$	−13.3733	−1.08831	−0.544154	−	0.838986i	$-0.683149\pi$
$151$	−13.3733	−1.08831	−0.544154	+	0.838986i	$0.683149\pi$
$152$	−4.41736	−0.358296
$153$	−6.06028	−0.489944
$154$	4.47373	0.360503
$155$	−11.4895	−0.922858
$156$	−1.41244	−0.113086
$157$	−7.76796	−0.619951	−0.309975	−	0.950745i	$-0.600321\pi$
$157$	−7.76796	−0.619951	−0.309975	+	0.950745i	$0.600321\pi$
$158$	4.85227	0.386026
$159$	−11.1491	−0.884181
$160$	−11.3023	−0.893524
$161$	3.19860	0.252085
$162$	−1.60620	−0.126195
$163$	11.3737	0.890858	0.445429	−	0.895317i	$-0.353051\pi$
$163$	11.3737	0.890858	0.445429	+	0.895317i	$0.353051\pi$
$164$	−2.03622	−0.159002
$165$	−9.88243	−0.769346
$166$	16.3735	1.27083
$167$	2.47601	0.191600	0.0957998	−	0.995401i	$-0.469459\pi$
$167$	2.47601	0.191600	0.0957998	+	0.995401i	$0.469459\pi$
$168$	−2.28101	−0.175984
$169$	−7.06692	−0.543609
$170$	−34.5370	−2.64887
$171$	−1.93658	−0.148094
$172$	3.37857	0.257614
$173$	−10.7831	−0.819820	−0.409910	−	0.912126i	$-0.634440\pi$
$173$	−10.7831	−0.819820	−0.409910	+	0.912126i	$0.634440\pi$
$174$	3.89334	0.295154
$175$	7.58887	0.573665
$176$	13.4348	1.01269
$177$	2.80705	0.210991
$178$	3.69573	0.277007
$179$	−12.0233	−0.898667	−0.449333	−	0.893364i	$-0.648338\pi$
$179$	−12.0233	−0.898667	−0.449333	+	0.893364i	$0.648338\pi$
$180$	−2.05743	−0.153352
$181$	17.0378	1.26641	0.633204	−	0.773985i	$-0.281739\pi$
$181$	17.0378	1.26641	0.633204	+	0.773985i	$0.281739\pi$
$182$	−3.91236	−0.290004
$183$	−8.16721	−0.603738
$184$	7.29604	0.537871
$185$	3.77896	0.277835
$186$	5.20123	0.381373
$187$	16.8796	1.23436
$188$	−1.38890	−0.101296
$189$	−1.00000	−0.0727393
$190$	−11.0364	−0.800667
$191$	13.9297	1.00792	0.503959	−	0.863727i	$-0.331876\pi$
$191$	13.9297	1.00792	0.503959	+	0.863727i	$0.331876\pi$
$192$	−4.53050	−0.326960
$193$	−23.5610	−1.69596	−0.847979	−	0.530030i	$-0.822181\pi$
$193$	−23.5610	−1.69596	−0.847979	+	0.530030i	$0.822181\pi$
$194$	1.13715	0.0816428
$195$	8.64238	0.618894
$196$	0.579871	0.0414193
$197$	−6.52931	−0.465194	−0.232597	−	0.972573i	$-0.574722\pi$
$197$	−6.52931	−0.465194	−0.232597	+	0.972573i	$0.574722\pi$
$198$	4.47373	0.317934
$199$	19.0272	1.34881	0.674403	−	0.738364i	$-0.264401\pi$
$199$	19.0272	1.34881	0.674403	+	0.738364i	$0.264401\pi$
$200$	17.3103	1.22402
$201$	−5.97952	−0.421763
$202$	−17.9776	−1.26490
$203$	2.42395	0.170128
$204$	3.51418	0.246042
$205$	12.4591	0.870182
$206$	−15.1364	−1.05460
$207$	3.19860	0.222318
$208$	−11.7490	−0.814648
$209$	5.39395	0.373107
$210$	−5.69892	−0.393263
$211$	−12.5670	−0.865151	−0.432575	−	0.901598i	$-0.642395\pi$
$211$	−12.5670	−0.865151	−0.432575	+	0.901598i	$0.642395\pi$
$212$	6.46503	0.444020
$213$	−12.1587	−0.833098
$214$	10.5398	0.720489
$215$	−20.6726	−1.40986
$216$	−2.28101	−0.155203
$217$	3.23823	0.219825
$218$	24.9015	1.68654
$219$	−2.47476	−0.167229
$220$	5.73053	0.386352
$221$	−14.7616	−0.992971
$222$	−1.71072	−0.114816
$223$	27.9633	1.87256	0.936280	−	0.351255i	$-0.114245\pi$
$223$	27.9633	1.87256	0.936280	+	0.351255i	$0.114245\pi$
$224$	3.18546	0.212838
$225$	7.58887	0.505925
$226$	−23.8814	−1.58856
$227$	−17.2281	−1.14347	−0.571733	−	0.820440i	$-0.693729\pi$
$227$	−17.2281	−1.14347	−0.571733	+	0.820440i	$0.693729\pi$
$228$	1.12297	0.0743704
$229$	−17.7667	−1.17406	−0.587030	−	0.809565i	$-0.699703\pi$
$229$	−17.7667	−1.17406	−0.587030	+	0.809565i	$0.699703\pi$
$230$	18.2286	1.20196
$231$	2.78529	0.183259
$232$	5.52905	0.363000
$233$	14.0286	0.919043	0.459521	−	0.888167i	$-0.348021\pi$
$233$	14.0286	0.919043	0.459521	+	0.888167i	$0.348021\pi$
$234$	−3.91236	−0.255759
$235$	8.49834	0.554370
$236$	−1.62773	−0.105956
$237$	3.02097	0.196233
$238$	9.73400	0.630962
$239$	−21.4428	−1.38702	−0.693510	−	0.720447i	$-0.743937\pi$
$239$	−21.4428	−1.38702	−0.693510	+	0.720447i	$0.743937\pi$
$240$	−17.1141	−1.10471
$241$	−4.57437	−0.294661	−0.147331	−	0.989087i	$-0.547068\pi$
$241$	−4.57437	−0.294661	−0.147331	+	0.989087i	$0.547068\pi$
$242$	5.20755	0.334754
$243$	−1.00000	−0.0641500
$244$	4.73593	0.303187
$245$	−3.54808	−0.226679
$246$	−5.64018	−0.359605
$247$	−4.71712	−0.300143
$248$	7.38642	0.469038
$249$	10.1939	0.646015
$250$	14.7538	0.933110
$251$	11.2949	0.712925	0.356462	−	0.934310i	$-0.383983\pi$
$251$	11.2949	0.712925	0.356462	+	0.934310i	$0.383983\pi$
$252$	0.579871	0.0365284
$253$	−8.90903	−0.560106
$254$	−1.60620	−0.100782
$255$	−21.5023	−1.34653
$256$	12.8601	0.803755
$257$	−27.1572	−1.69402	−0.847010	−	0.531576i	$-0.821600\pi$
$257$	−27.1572	−1.69402	−0.847010	+	0.531576i	$0.821600\pi$
$258$	9.35838	0.582628
$259$	−1.06507	−0.0661803
$260$	−5.01147	−0.310798
$261$	2.42395	0.150039
$262$	27.2044	1.68069
$263$	1.15314	0.0711058	0.0355529	−	0.999368i	$-0.488681\pi$
$263$	1.15314	0.0711058	0.0355529	+	0.999368i	$0.488681\pi$
$264$	6.35327	0.391017
$265$	−39.5579	−2.43002
$266$	3.11054	0.190719
$267$	2.30092	0.140814
$268$	3.46735	0.211802
$269$	15.9024	0.969584	0.484792	−	0.874629i	$-0.338895\pi$
$269$	15.9024	0.969584	0.484792	+	0.874629i	$0.338895\pi$
$270$	−5.69892	−0.346825
$271$	3.54720	0.215477	0.107739	−	0.994179i	$-0.465639\pi$
$271$	3.54720	0.215477	0.107739	+	0.994179i	$0.465639\pi$
$272$	29.2317	1.77243
$273$	−2.43579	−0.147421
$274$	13.0844	0.790460
$275$	−21.1372	−1.27462
$276$	−1.85478	−0.111644
$277$	0.879357	0.0528355	0.0264177	−	0.999651i	$-0.491590\pi$
$277$	0.879357	0.0528355	0.0264177	+	0.999651i	$0.491590\pi$
$278$	16.1360	0.967774
$279$	3.23823	0.193868
$280$	−8.09320	−0.483661
$281$	15.5204	0.925868	0.462934	−	0.886393i	$-0.346797\pi$
$281$	15.5204	0.925868	0.462934	+	0.886393i	$0.346797\pi$
$282$	−3.84715	−0.229095
$283$	−27.1358	−1.61306	−0.806528	−	0.591196i	$-0.798656\pi$
$283$	−27.1358	−1.61306	−0.806528	+	0.591196i	$0.798656\pi$
$284$	7.05046	0.418368
$285$	−6.87116	−0.407012
$286$	10.8971	0.644357
$287$	−3.51151	−0.207278
$288$	3.18546	0.187705
$289$	19.7270	1.16041
$290$	13.8139	0.811180
$291$	0.707978	0.0415024
$292$	1.43504	0.0839794
$293$	−13.8186	−0.807294	−0.403647	−	0.914915i	$-0.632258\pi$
$293$	−13.8186	−0.807294	−0.403647	+	0.914915i	$0.632258\pi$
$294$	1.60620	0.0936753
$295$	9.95964	0.579873
$296$	−2.42944	−0.141208
$297$	2.78529	0.161619
$298$	7.23396	0.419052
$299$	7.79113	0.450573
$300$	−4.40057	−0.254067
$301$	5.82642	0.335829
$302$	21.4802	1.23605
$303$	−11.1926	−0.642999
$304$	9.34110	0.535749
$305$	−28.9779	−1.65927
$306$	9.73400	0.556456
$307$	−24.8063	−1.41577	−0.707885	−	0.706328i	$-0.750350\pi$
$307$	−24.8063	−1.41577	−0.707885	+	0.706328i	$0.750350\pi$
$308$	−1.61511	−0.0920293
$309$	−9.42373	−0.536098
$310$	18.4544	1.04814
$311$	−14.3789	−0.815355	−0.407677	−	0.913126i	$-0.633661\pi$
$311$	−14.3789	−0.815355	−0.407677	+	0.913126i	$0.633661\pi$
$312$	−5.55606	−0.314550
$313$	5.43949	0.307458	0.153729	−	0.988113i	$-0.450872\pi$
$313$	5.43949	0.307458	0.153729	+	0.988113i	$0.450872\pi$
$314$	12.4769	0.704111
$315$	−3.54808	−0.199912
$316$	−1.75177	−0.0985448
$317$	−0.807453	−0.0453511	−0.0226755	−	0.999743i	$-0.507218\pi$
$317$	−0.807453	−0.0453511	−0.0226755	+	0.999743i	$0.507218\pi$
$318$	17.9076	1.00421
$319$	−6.75141	−0.378006
$320$	−16.0746	−0.898596
$321$	6.56198	0.366254
$322$	−5.13759	−0.286307
$323$	11.7362	0.653022
$324$	0.579871	0.0322150
$325$	18.4849	1.02536
$326$	−18.2684	−1.01180
$327$	15.5034	0.857338
$328$	−8.00978	−0.442266
$329$	−2.39519	−0.132051
$330$	15.8731	0.873787
$331$	−4.60565	−0.253150	−0.126575	−	0.991957i	$-0.540398\pi$
$331$	−4.60565	−0.253150	−0.126575	+	0.991957i	$0.540398\pi$
$332$	−5.91117	−0.324417
$333$	−1.06507	−0.0583656
$334$	−3.97697	−0.217610
$335$	−21.2158	−1.15914
$336$	4.82349	0.263143
$337$	3.71254	0.202235	0.101118	−	0.994874i	$-0.467758\pi$
$337$	3.71254	0.202235	0.101118	+	0.994874i	$0.467758\pi$
$338$	11.3509	0.617406
$339$	−14.8683	−0.807533
$340$	12.4686	0.676204
$341$	−9.01940	−0.488428
$342$	3.11054	0.168199
$343$	1.00000	0.0539949
$344$	13.2901	0.716555
$345$	11.3489	0.611004
$346$	17.3197	0.931113
$347$	−5.38943	−0.289320	−0.144660	−	0.989481i	$-0.546209\pi$
$347$	−5.38943	−0.289320	−0.144660	+	0.989481i	$0.546209\pi$
$348$	−1.40558	−0.0753469
$349$	16.3138	0.873257	0.436629	−	0.899642i	$-0.356172\pi$
$349$	16.3138	0.873257	0.436629	+	0.899642i	$0.356172\pi$
$350$	−12.1892	−0.651542
$351$	−2.43579	−0.130013
$352$	−8.87244	−0.472903
$353$	3.10479	0.165251	0.0826256	−	0.996581i	$-0.473669\pi$
$353$	3.10479	0.165251	0.0826256	+	0.996581i	$0.473669\pi$
$354$	−4.50868	−0.239633
$355$	−43.1399	−2.28963
$356$	−1.33424	−0.0707144
$357$	6.06028	0.320744
$358$	19.3119	1.02066
$359$	−0.513047	−0.0270776	−0.0135388	−	0.999908i	$-0.504310\pi$
$359$	−0.513047	−0.0270776	−0.0135388	+	0.999908i	$0.504310\pi$
$360$	−8.09320	−0.426549
$361$	−15.2496	−0.802613
$362$	−27.3660	−1.43833
$363$	3.24216	0.170169
$364$	1.41244	0.0740322
$365$	−8.78064	−0.459600
$366$	13.1182	0.685697
$367$	2.45004	0.127891	0.0639456	−	0.997953i	$-0.479632\pi$
$367$	2.45004	0.127891	0.0639456	+	0.997953i	$0.479632\pi$
$368$	−15.4284	−0.804262
$369$	−3.51151	−0.182802
$370$	−6.06976	−0.315552
$371$	11.1491	0.578832
$372$	−1.87775	−0.0973570
$373$	−28.9564	−1.49930	−0.749652	−	0.661832i	$-0.769779\pi$
$373$	−28.9564	−1.49930	−0.749652	+	0.661832i	$0.769779\pi$
$374$	−27.1120	−1.40193
$375$	9.18552	0.474338
$376$	−5.46346	−0.281756
$377$	5.90424	0.304084
$378$	1.60620	0.0826139
$379$	10.9005	0.559919	0.279959	−	0.960012i	$-0.409679\pi$
$379$	10.9005	0.559919	0.279959	+	0.960012i	$0.409679\pi$
$380$	3.98438	0.204395
$381$	−1.00000	−0.0512316
$382$	−22.3739	−1.14475
$383$	−16.5606	−0.846208	−0.423104	−	0.906081i	$-0.639059\pi$
$383$	−16.5606	−0.846208	−0.423104	+	0.906081i	$0.639059\pi$
$384$	13.6478	0.696462
$385$	9.88243	0.503655
$386$	37.8436	1.92619
$387$	5.82642	0.296174
$388$	−0.410536	−0.0208418
$389$	−12.9612	−0.657157	−0.328578	−	0.944477i	$-0.606569\pi$
$389$	−12.9612	−0.657157	−0.328578	+	0.944477i	$0.606569\pi$
$390$	−13.8814	−0.702911
$391$	−19.3844	−0.980312
$392$	2.28101	0.115208
$393$	16.9371	0.854366
$394$	10.4874	0.528346
$395$	10.7186	0.539313
$396$	−1.61511	−0.0811622
$397$	−31.8068	−1.59634	−0.798168	−	0.602435i	$-0.794197\pi$
$397$	−31.8068	−1.59634	−0.798168	+	0.602435i	$0.794197\pi$
$398$	−30.5615	−1.53191
$399$	1.93658	0.0969505
$400$	−36.6049	−1.83024
$401$	36.4319	1.81932	0.909660	−	0.415353i	$-0.136342\pi$
$401$	36.4319	1.81932	0.909660	+	0.415353i	$0.136342\pi$
$402$	9.60429	0.479019
$403$	7.88765	0.392912
$404$	6.49027	0.322903
$405$	−3.54808	−0.176306
$406$	−3.89334	−0.193223
$407$	2.96653	0.147046
$408$	13.8235	0.684367
$409$	−0.0186891	−0.000924115 0	−0.000462058	−	1.00000i	$-0.500147\pi$
$409$	−0.0186891	−0.000924115 0	−0.000462058		1.00000i	$0.500147\pi$
$410$	−20.0118	−0.988313
$411$	8.14622	0.401824
$412$	5.46455	0.269219
$413$	−2.80705	−0.138126
$414$	−5.13759	−0.252499
$415$	36.1689	1.77546
$416$	7.75913	0.380423
$417$	10.0461	0.491960
$418$	−8.66375	−0.423758
$419$	−20.4211	−0.997637	−0.498819	−	0.866706i	$-0.666233\pi$
$419$	−20.4211	−0.997637	−0.498819	+	0.866706i	$0.666233\pi$
$420$	2.05743	0.100392
$421$	20.7357	1.01060	0.505299	−	0.862944i	$-0.331382\pi$
$421$	20.7357	1.01060	0.505299	+	0.862944i	$0.331382\pi$
$422$	20.1852	0.982598
$423$	−2.39519	−0.116458
$424$	25.4312	1.23505
$425$	−45.9907	−2.23087
$426$	19.5292	0.946194
$427$	8.16721	0.395239
$428$	−3.80510	−0.183927
$429$	6.78439	0.327553
$430$	33.2043	1.60125
$431$	26.7720	1.28956	0.644782	−	0.764367i	$-0.276948\pi$
$431$	26.7720	1.28956	0.644782	+	0.764367i	$0.276948\pi$
$432$	4.82349	0.232070
$433$	−7.45697	−0.358359	−0.179179	−	0.983816i	$-0.557344\pi$
$433$	−7.45697	−0.358359	−0.179179	+	0.983816i	$0.557344\pi$
$434$	−5.20123	−0.249667
$435$	8.60037	0.412356
$436$	−8.98995	−0.430540
$437$	−6.19436	−0.296317
$438$	3.97495	0.189930
$439$	0.491516	0.0234588	0.0117294	−	0.999931i	$-0.496266\pi$
$439$	0.491516	0.0234588	0.0117294	+	0.999931i	$0.496266\pi$
$440$	22.5419	1.07464
$441$	1.00000	0.0476190
$442$	23.7100	1.12777
$443$	16.3582	0.777203	0.388602	−	0.921406i	$-0.372958\pi$
$443$	16.3582	0.777203	0.388602	+	0.921406i	$0.372958\pi$
$444$	0.617604	0.0293102
$445$	8.16385	0.387004
$446$	−44.9146	−2.12677
$447$	4.50378	0.213021
$448$	4.53050	0.214046
$449$	21.0828	0.994957	0.497478	−	0.867476i	$-0.334259\pi$
$449$	21.0828	0.994957	0.497478	+	0.867476i	$0.334259\pi$
$450$	−12.1892	−0.574606
$451$	9.78057	0.460549
$452$	8.62167	0.405529
$453$	13.3733	0.628334
$454$	27.6717	1.29870
$455$	−8.64238	−0.405161
$456$	4.41736	0.206862
$457$	9.58237	0.448245	0.224122	−	0.974561i	$-0.428049\pi$
$457$	9.58237	0.448245	0.224122	+	0.974561i	$0.428049\pi$
$458$	28.5369	1.33344
$459$	6.06028	0.282870
$460$	−6.58089	−0.306836
$461$	−26.0159	−1.21168	−0.605841	−	0.795586i	$-0.707163\pi$
$461$	−26.0159	−1.21168	−0.605841	+	0.795586i	$0.707163\pi$
$462$	−4.47373	−0.208137
$463$	−15.0319	−0.698590	−0.349295	−	0.937013i	$-0.613579\pi$
$463$	−15.0319	−0.698590	−0.349295	+	0.937013i	$0.613579\pi$
$464$	−11.6919	−0.542783
$465$	11.4895	0.532812
$466$	−22.5327	−1.04381
$467$	−7.12952	−0.329915	−0.164957	−	0.986301i	$-0.552749\pi$
$467$	−7.12952	−0.329915	−0.164957	+	0.986301i	$0.552749\pi$
$468$	1.41244	0.0652903
$469$	5.97952	0.276109
$470$	−13.6500	−0.629628
$471$	7.76796	0.357929
$472$	−6.40290	−0.294718
$473$	−16.2283	−0.746177
$474$	−4.85227	−0.222872
$475$	−14.6965	−0.674321
$476$	−3.51418	−0.161072
$477$	11.1491	0.510482
$478$	34.4414	1.57531
$479$	−2.79072	−0.127511	−0.0637557	−	0.997966i	$-0.520308\pi$
$479$	−2.79072	−0.127511	−0.0637557	+	0.997966i	$0.520308\pi$
$480$	11.3023	0.515876
$481$	−2.59429	−0.118290
$482$	7.34735	0.334662
$483$	−3.19860	−0.145541
$484$	−1.88004	−0.0854561
$485$	2.51196	0.114062
$486$	1.60620	0.0728586
$487$	32.2763	1.46258	0.731289	−	0.682067i	$-0.238919\pi$
$487$	32.2763	1.46258	0.731289	+	0.682067i	$0.238919\pi$
$488$	18.6295	0.843317
$489$	−11.3737	−0.514337
$490$	5.69892	0.257451
$491$	−30.0985	−1.35833	−0.679163	−	0.733987i	$-0.737657\pi$
$491$	−30.0985	−1.35833	−0.679163	+	0.733987i	$0.737657\pi$
$492$	2.03622	0.0918000
$493$	−14.6898	−0.661596
$494$	7.57662	0.340888
$495$	9.88243	0.444182
$496$	−15.6196	−0.701339
$497$	12.1587	0.545391
$498$	−16.3735	−0.733713
$499$	31.8366	1.42520	0.712602	−	0.701569i	$-0.247517\pi$
$499$	31.8366	1.42520	0.712602	+	0.701569i	$0.247517\pi$
$500$	−5.32642	−0.238205
$501$	−2.47601	−0.110620
$502$	−18.1418	−0.809707
$503$	−42.3948	−1.89029	−0.945145	−	0.326651i	$-0.894080\pi$
$503$	−42.3948	−1.89029	−0.945145	+	0.326651i	$0.894080\pi$
$504$	2.28101	0.101604
$505$	−39.7123	−1.76717
$506$	14.3097	0.636142
$507$	7.06692	0.313853
$508$	0.579871	0.0257276
$509$	15.5022	0.687125	0.343562	−	0.939130i	$-0.388366\pi$
$509$	15.5022	0.687125	0.343562	+	0.939130i	$0.388366\pi$
$510$	34.5370	1.52932
$511$	2.47476	0.109477
$512$	6.63978	0.293440
$513$	1.93658	0.0855023
$514$	43.6199	1.92399
$515$	−33.4362	−1.47337
$516$	−3.37857	−0.148733
$517$	6.67131	0.293404
$518$	1.71072	0.0751645
$519$	10.7831	0.473323
$520$	−19.7133	−0.864487
$521$	37.1898	1.62931	0.814657	−	0.579943i	$-0.196925\pi$
$521$	37.1898	1.62931	0.814657	+	0.579943i	$0.196925\pi$
$522$	−3.89334	−0.170407
$523$	−43.4445	−1.89970	−0.949848	−	0.312712i	$-0.898763\pi$
$523$	−43.4445	−1.89970	−0.949848	+	0.312712i	$0.898763\pi$
$524$	−9.82136	−0.429048
$525$	−7.58887	−0.331205
$526$	−1.85217	−0.0807586
$527$	−19.6246	−0.854859
$528$	−13.4348	−0.584676
$529$	−12.7689	−0.555172
$530$	63.5378	2.75990
$531$	−2.80705	−0.121816
$532$	−1.12297	−0.0486869
$533$	−8.55331	−0.370485
$534$	−3.69573	−0.159930
$535$	23.2824	1.00659
$536$	13.6393	0.589130
$537$	12.0233	0.518846
$538$	−25.5423	−1.10121
$539$	−2.78529	−0.119971
$540$	2.05743	0.0885376
$541$	−5.77004	−0.248074	−0.124037	−	0.992278i	$-0.539584\pi$
$541$	−5.77004	−0.248074	−0.124037	+	0.992278i	$0.539584\pi$
$542$	−5.69751	−0.244729
$543$	−17.0378	−0.731161
$544$	−19.3048	−0.827686
$545$	55.0072	2.35625
$546$	3.91236	0.167434
$547$	−34.9425	−1.49403	−0.747016	−	0.664806i	$-0.768514\pi$
$547$	−34.9425	−1.49403	−0.747016	+	0.664806i	$0.768514\pi$
$548$	−4.72376	−0.201789
$549$	8.16721	0.348568
$550$	33.9505	1.44766
$551$	−4.69419	−0.199979
$552$	−7.29604	−0.310540
$553$	−3.02097	−0.128465
$554$	−1.41242	−0.0600080
$555$	−3.77896	−0.160408
$556$	−5.82544	−0.247054
$557$	−17.9223	−0.759392	−0.379696	−	0.925111i	$-0.623971\pi$
$557$	−17.9223	−0.759392	−0.379696	+	0.925111i	$0.623971\pi$
$558$	−5.20123	−0.220186
$559$	14.1919	0.600255
$560$	17.1141	0.723204
$561$	−16.8796	−0.712658
$562$	−24.9288	−1.05156
$563$	17.5956	0.741568	0.370784	−	0.928719i	$-0.379089\pi$
$563$	17.5956	0.741568	0.370784	+	0.928719i	$0.379089\pi$
$564$	1.38890	0.0584834
$565$	−52.7537	−2.21937
$566$	43.5855	1.83203
$567$	1.00000	0.0419961
$568$	27.7340	1.16369
$569$	32.1201	1.34654	0.673272	−	0.739395i	$-0.264888\pi$
$569$	32.1201	1.34654	0.673272	+	0.739395i	$0.264888\pi$
$570$	11.0364	0.462265
$571$	17.9633	0.751739	0.375870	−	0.926673i	$-0.377344\pi$
$571$	17.9633	0.751739	0.375870	+	0.926673i	$0.377344\pi$
$572$	−3.93407	−0.164492
$573$	−13.9297	−0.581922
$574$	5.64018	0.235416
$575$	24.2738	1.01229
$576$	4.53050	0.188771
$577$	−29.0564	−1.20963	−0.604816	−	0.796365i	$-0.706753\pi$
$577$	−29.0564	−1.20963	−0.604816	+	0.796365i	$0.706753\pi$
$578$	−31.6854	−1.31794
$579$	23.5610	0.979162
$580$	−4.98711	−0.207078
$581$	−10.1939	−0.422916
$582$	−1.13715	−0.0471365
$583$	−31.0535	−1.28610
$584$	5.64494	0.233589
$585$	−8.64238	−0.357319
$586$	22.1955	0.916886
$587$	−6.10638	−0.252037	−0.126019	−	0.992028i	$-0.540220\pi$
$587$	−6.10638	−0.252037	−0.126019	+	0.992028i	$0.540220\pi$
$588$	−0.579871	−0.0239135
$589$	−6.27110	−0.258396
$590$	−15.9971	−0.658592
$591$	6.52931	0.268580
$592$	5.13736	0.211144
$593$	−9.02500	−0.370612	−0.185306	−	0.982681i	$-0.559328\pi$
$593$	−9.02500	−0.370612	−0.185306	+	0.982681i	$0.559328\pi$
$594$	−4.47373	−0.183559
$595$	21.5023	0.881510
$596$	−2.61161	−0.106976
$597$	−19.0272	−0.778733
$598$	−12.5141	−0.511739
$599$	5.06194	0.206825	0.103413	−	0.994639i	$-0.467024\pi$
$599$	5.06194	0.206825	0.103413	+	0.994639i	$0.467024\pi$
$600$	−17.3103	−0.706689
$601$	−8.99790	−0.367032	−0.183516	−	0.983017i	$-0.558748\pi$
$601$	−8.99790	−0.367032	−0.183516	+	0.983017i	$0.558748\pi$
$602$	−9.35838	−0.381419
$603$	5.97952	0.243505
$604$	−7.75481	−0.315539
$605$	11.5034	0.467682
$606$	17.9776	0.730288
$607$	12.7806	0.518749	0.259375	−	0.965777i	$-0.416484\pi$
$607$	12.7806	0.518749	0.259375	+	0.965777i	$0.416484\pi$
$608$	−6.16892	−0.250183
$609$	−2.42395	−0.0982235
$610$	46.5443	1.88452
$611$	−5.83419	−0.236026
$612$	−3.51418	−0.142052
$613$	−17.1381	−0.692201	−0.346101	−	0.938197i	$-0.612494\pi$
$613$	−17.1381	−0.692201	−0.346101	+	0.938197i	$0.612494\pi$
$614$	39.8438	1.60797
$615$	−12.4591	−0.502400
$616$	−6.35327	−0.255980
$617$	−45.8447	−1.84564	−0.922820	−	0.385232i	$-0.874121\pi$
$617$	−45.8447	−1.84564	−0.922820	+	0.385232i	$0.874121\pi$
$618$	15.1364	0.608874
$619$	46.5262	1.87005	0.935023	−	0.354587i	$-0.115378\pi$
$619$	46.5262	1.87005	0.935023	+	0.354587i	$0.115378\pi$
$620$	−6.66242	−0.267569
$621$	−3.19860	−0.128355
$622$	23.0954	0.926042
$623$	−2.30092	−0.0921845
$624$	11.7490	0.470337
$625$	−5.35340	−0.214136
$626$	−8.73690	−0.349197
$627$	−5.39395	−0.215414
$628$	−4.50441	−0.179746
$629$	6.45463	0.257363
$630$	5.69892	0.227050
$631$	−13.7725	−0.548273	−0.274136	−	0.961691i	$-0.588392\pi$
$631$	−13.7725	−0.548273	−0.274136	+	0.961691i	$0.588392\pi$
$632$	−6.89085	−0.274103
$633$	12.5670	0.499495
$634$	1.29693	0.0515076
$635$	−3.54808	−0.140801
$636$	−6.46503	−0.256355
$637$	2.43579	0.0965096
$638$	10.8441	0.429322
$639$	12.1587	0.480989
$640$	48.4235	1.91411
$641$	−0.860650	−0.0339937	−0.0169968	−	0.999856i	$-0.505411\pi$
$641$	−0.860650	−0.0339937	−0.0169968	+	0.999856i	$0.505411\pi$
$642$	−10.5398	−0.415974
$643$	−41.6792	−1.64367	−0.821834	−	0.569727i	$-0.807049\pi$
$643$	−41.6792	−1.64367	−0.821834	+	0.569727i	$0.807049\pi$
$644$	1.85478	0.0730884
$645$	20.6726	0.813983
$646$	−18.8507	−0.741672
$647$	19.3518	0.760798	0.380399	−	0.924822i	$-0.375787\pi$
$647$	19.3518	0.760798	0.380399	+	0.924822i	$0.375787\pi$
$648$	2.28101	0.0896065
$649$	7.81845	0.306901
$650$	−29.6904	−1.16455
$651$	−3.23823	−0.126916
$652$	6.59529	0.258291
$653$	8.67139	0.339338	0.169669	−	0.985501i	$-0.445730\pi$
$653$	8.67139	0.339338	0.169669	+	0.985501i	$0.445730\pi$
$654$	−24.9015	−0.973724
$655$	60.0944	2.34808
$656$	16.9377	0.661308
$657$	2.47476	0.0965495
$658$	3.84715	0.149978
$659$	22.3147	0.869257	0.434629	−	0.900610i	$-0.356880\pi$
$659$	22.3147	0.869257	0.434629	+	0.900610i	$0.356880\pi$
$660$	−5.73053	−0.223061
$661$	−0.0803059	−0.00312354	−0.00156177	−	0.999999i	$-0.500497\pi$
$661$	−0.0803059	−0.00312354	−0.00156177	+	0.999999i	$0.500497\pi$
$662$	7.39759	0.287516
$663$	14.7616	0.573292
$664$	−23.2525	−0.902370
$665$	6.87116	0.266452
$666$	1.71072	0.0662889
$667$	7.75325	0.300207
$668$	1.43577	0.0555515
$669$	−27.9633	−1.08112
$670$	34.0768	1.31650
$671$	−22.7481	−0.878179
$672$	−3.18546	−0.122882
$673$	36.2767	1.39836	0.699182	−	0.714944i	$-0.253548\pi$
$673$	36.2767	1.39836	0.699182	+	0.714944i	$0.253548\pi$
$674$	−5.96308	−0.229689
$675$	−7.58887	−0.292096
$676$	−4.09790	−0.157612
$677$	10.2419	0.393629	0.196815	−	0.980441i	$-0.436940\pi$
$677$	10.2419	0.393629	0.196815	+	0.980441i	$0.436940\pi$
$678$	23.8814	0.917158
$679$	−0.707978	−0.0271697
$680$	49.0470	1.88087
$681$	17.2281	0.660180
$682$	14.4869	0.554734
$683$	2.86486	0.109621	0.0548104	−	0.998497i	$-0.482545\pi$
$683$	2.86486	0.109621	0.0548104	+	0.998497i	$0.482545\pi$
$684$	−1.12297	−0.0429378
$685$	28.9034	1.10434
$686$	−1.60620	−0.0613249
$687$	17.7667	0.677844
$688$	−28.1037	−1.07144
$689$	27.1569	1.03459
$690$	−18.2286	−0.693950
$691$	−4.83501	−0.183932	−0.0919662	−	0.995762i	$-0.529315\pi$
$691$	−4.83501	−0.183932	−0.0919662	+	0.995762i	$0.529315\pi$
$692$	−6.25278	−0.237695
$693$	−2.78529	−0.105804
$694$	8.65649	0.328596
$695$	35.6444	1.35207
$696$	−5.52905	−0.209578
$697$	21.2807	0.806065
$698$	−26.2032	−0.991804
$699$	−14.0286	−0.530610
$700$	4.40057	0.166326
$701$	−25.9468	−0.979998	−0.489999	−	0.871723i	$-0.663003\pi$
$701$	−25.9468	−0.979998	−0.489999	+	0.871723i	$0.663003\pi$
$702$	3.91236	0.147663
$703$	2.06260	0.0777925
$704$	−12.6187	−0.475587
$705$	−8.49834	−0.320066
$706$	−4.98691	−0.187685
$707$	11.1926	0.420942
$708$	1.62773	0.0611737
$709$	−25.5065	−0.957918	−0.478959	−	0.877837i	$-0.658986\pi$
$709$	−25.5065	−0.957918	−0.478959	+	0.877837i	$0.658986\pi$
$710$	69.2912	2.60045
$711$	−3.02097	−0.113295
$712$	−5.24842	−0.196693
$713$	10.3578	0.387903
$714$	−9.73400	−0.364286
$715$	24.0715	0.900225
$716$	−6.97199	−0.260555
$717$	21.4428	0.800796
$718$	0.824054	0.0307534
$719$	39.6442	1.47848	0.739240	−	0.673442i	$-0.235185\pi$
$719$	39.6442	1.47848	0.739240	+	0.673442i	$0.235185\pi$
$720$	17.1141	0.637806
$721$	9.42373	0.350958
$722$	24.4939	0.911570
$723$	4.57437	0.170123
$724$	9.87971	0.367177
$725$	18.3951	0.683175
$726$	−5.20755	−0.193270
$727$	15.1557	0.562094	0.281047	−	0.959694i	$-0.409318\pi$
$727$	15.1557	0.562094	0.281047	+	0.959694i	$0.409318\pi$
$728$	5.55606	0.205921
$729$	1.00000	0.0370370
$730$	14.1034	0.521992
$731$	−35.3097	−1.30598
$732$	−4.73593	−0.175045
$733$	−8.36022	−0.308792	−0.154396	−	0.988009i	$-0.549343\pi$
$733$	−8.36022	−0.308792	−0.154396	+	0.988009i	$0.549343\pi$
$734$	−3.93525	−0.145253
$735$	3.54808	0.130873
$736$	10.1890	0.375573
$737$	−16.6547	−0.613484
$738$	5.64018	0.207618
$739$	−24.2136	−0.890712	−0.445356	−	0.895354i	$-0.646923\pi$
$739$	−24.2136	−0.890712	−0.445356	+	0.895354i	$0.646923\pi$
$740$	2.19131	0.0805541
$741$	4.71712	0.173288
$742$	−17.9076	−0.657410
$743$	28.8264	1.05754	0.528768	−	0.848766i	$-0.322654\pi$
$743$	28.8264	1.05754	0.528768	+	0.848766i	$0.322654\pi$
$744$	−7.38642	−0.270799
$745$	15.9798	0.585454
$746$	46.5097	1.70284
$747$	−10.1939	−0.372977
$748$	9.78800	0.357885
$749$	−6.56198	−0.239770
$750$	−14.7538	−0.538731
$751$	−11.1065	−0.405283	−0.202641	−	0.979253i	$-0.564953\pi$
$751$	−11.1065	−0.405283	−0.202641	+	0.979253i	$0.564953\pi$
$752$	11.5532	0.421302
$753$	−11.2949	−0.411607
$754$	−9.48338	−0.345364
$755$	47.4497	1.72687
$756$	−0.579871	−0.0210897
$757$	−15.6799	−0.569897	−0.284949	−	0.958543i	$-0.591977\pi$
$757$	−15.6799	−0.569897	−0.284949	+	0.958543i	$0.591977\pi$
$758$	−17.5083	−0.635930
$759$	8.90903	0.323377
$760$	15.6732	0.568525
$761$	26.4513	0.958857	0.479429	−	0.877581i	$-0.340844\pi$
$761$	26.4513	0.958857	0.479429	+	0.877581i	$0.340844\pi$
$762$	1.60620	0.0581864
$763$	−15.5034	−0.561259
$764$	8.07743	0.292231
$765$	21.5023	0.777419
$766$	26.5996	0.961083
$767$	−6.83739	−0.246884
$768$	−12.8601	−0.464048
$769$	−8.07969	−0.291361	−0.145681	−	0.989332i	$-0.546537\pi$
$769$	−8.07969	−0.291361	−0.145681	+	0.989332i	$0.546537\pi$
$770$	−15.8731	−0.572028
$771$	27.1572	0.978043
$772$	−13.6623	−0.491718
$773$	42.2559	1.51984	0.759919	−	0.650018i	$-0.225239\pi$
$773$	42.2559	1.51984	0.759919	+	0.650018i	$0.225239\pi$
$774$	−9.35838	−0.336380
$775$	24.5745	0.882742
$776$	−1.61490	−0.0579717
$777$	1.06507	0.0382092
$778$	20.8182	0.746368
$779$	6.80033	0.243647
$780$	5.01147	0.179439
$781$	−33.8654	−1.21180
$782$	31.1352	1.11339
$783$	−2.42395	−0.0866249
$784$	−4.82349	−0.172268
$785$	27.5613	0.983707
$786$	−27.2044	−0.970349
$787$	−32.9478	−1.17446	−0.587231	−	0.809420i	$-0.699782\pi$
$787$	−32.9478	−1.17446	−0.587231	+	0.809420i	$0.699782\pi$
$788$	−3.78616	−0.134876
$789$	−1.15314	−0.0410529
$790$	−17.2162	−0.612526
$791$	14.8683	0.528654
$792$	−6.35327	−0.225754
$793$	19.8936	0.706444
$794$	51.0879	1.81304
$795$	39.5579	1.40297
$796$	11.0333	0.391067
$797$	−10.7795	−0.381831	−0.190915	−	0.981607i	$-0.561146\pi$
$797$	−10.7795	−0.381831	−0.190915	+	0.981607i	$0.561146\pi$
$798$	−3.11054	−0.110112
$799$	14.5155	0.513523
$800$	24.1741	0.854683
$801$	−2.30092	−0.0812991
$802$	−58.5168	−2.06630
$803$	−6.89292	−0.243246
$804$	−3.46735	−0.122284
$805$	−11.3489	−0.399996
$806$	−12.6691	−0.446251
$807$	−15.9024	−0.559790
$808$	25.5304	0.898158
$809$	−11.5058	−0.404521	−0.202260	−	0.979332i	$-0.564829\pi$
$809$	−11.5058	−0.404521	−0.202260	+	0.979332i	$0.564829\pi$
$810$	5.69892	0.200240
$811$	7.28050	0.255653	0.127826	−	0.991797i	$-0.459200\pi$
$811$	7.28050	0.255653	0.127826	+	0.991797i	$0.459200\pi$
$812$	1.40558	0.0493261
$813$	−3.54720	−0.124406
$814$	−4.76484	−0.167008
$815$	−40.3549	−1.41357
$816$	−29.2317	−1.02331
$817$	−11.2834	−0.394755
$818$	0.0300184	0.00104957
$819$	2.43579	0.0851134
$820$	7.22468	0.252297
$821$	−23.7546	−0.829041	−0.414521	−	0.910040i	$-0.636051\pi$
$821$	−23.7546	−0.829041	−0.414521	+	0.910040i	$0.636051\pi$
$822$	−13.0844	−0.456372
$823$	54.5319	1.90086	0.950431	−	0.310936i	$-0.100642\pi$
$823$	54.5319	1.90086	0.950431	+	0.310936i	$0.100642\pi$
$824$	21.4956	0.748835
$825$	21.1372	0.735903
$826$	4.50868	0.156877
$827$	16.7507	0.582478	0.291239	−	0.956650i	$-0.405932\pi$
$827$	16.7507	0.582478	0.291239	+	0.956650i	$0.405932\pi$
$828$	1.85478	0.0644579
$829$	17.2568	0.599355	0.299677	−	0.954041i	$-0.403121\pi$
$829$	17.2568	0.599355	0.299677	+	0.954041i	$0.403121\pi$
$830$	−58.0944	−2.01649
$831$	−0.879357	−0.0305046
$832$	11.0353	0.382582
$833$	−6.06028	−0.209976
$834$	−16.1360	−0.558745
$835$	−8.78509	−0.304021
$836$	3.12779	0.108177
$837$	−3.23823	−0.111930
$838$	32.8004	1.13307
$839$	−4.63330	−0.159959	−0.0799796	−	0.996797i	$-0.525486\pi$
$839$	−4.63330	−0.159959	−0.0799796	+	0.996797i	$0.525486\pi$
$840$	8.09320	0.279242
$841$	−23.1245	−0.797395
$842$	−33.3057	−1.14779
$843$	−15.5204	−0.534550
$844$	−7.28726	−0.250838
$845$	25.0740	0.862572
$846$	3.84715	0.132268
$847$	−3.24216	−0.111402
$848$	−53.7776	−1.84673
$849$	27.1358	0.931298
$850$	73.8701	2.53372
$851$	−3.40674	−0.116782
$852$	−7.05046	−0.241545
$853$	−36.0413	−1.23403	−0.617016	−	0.786951i	$-0.711659\pi$
$853$	−36.0413	−1.23403	−0.617016	+	0.786951i	$0.711659\pi$
$854$	−13.1182	−0.448894
$855$	6.87116	0.234989
$856$	−14.9679	−0.511594
$857$	−38.5445	−1.31665	−0.658327	−	0.752732i	$-0.728736\pi$
$857$	−38.5445	−1.31665	−0.658327	+	0.752732i	$0.728736\pi$
$858$	−10.8971	−0.372020
$859$	−29.3488	−1.00137	−0.500685	−	0.865630i	$-0.666918\pi$
$859$	−29.3488	−1.00137	−0.500685	+	0.865630i	$0.666918\pi$
$860$	−11.9874	−0.408768
$861$	3.51151	0.119672
$862$	−43.0012	−1.46463
$863$	−2.89395	−0.0985111	−0.0492555	−	0.998786i	$-0.515685\pi$
$863$	−2.89395	−0.0985111	−0.0492555	+	0.998786i	$0.515685\pi$
$864$	−3.18546	−0.108372
$865$	38.2591	1.30085
$866$	11.9774	0.407007
$867$	−19.7270	−0.669963
$868$	1.87775	0.0637351
$869$	8.41427	0.285434
$870$	−13.8139	−0.468335
$871$	14.5649	0.493512
$872$	−35.3633	−1.19755
$873$	−0.707978	−0.0239614
$874$	9.94937	0.336542
$875$	−9.18552	−0.310527
$876$	−1.43504	−0.0484855
$877$	−20.8638	−0.704519	−0.352259	−	0.935902i	$-0.614587\pi$
$877$	−20.8638	−0.704519	−0.352259	+	0.935902i	$0.614587\pi$
$878$	−0.789471	−0.0266434
$879$	13.8186	0.466091
$880$	−47.6678	−1.60688
$881$	−37.4032	−1.26015	−0.630074	−	0.776535i	$-0.716975\pi$
$881$	−37.4032	−1.26015	−0.630074	+	0.776535i	$0.716975\pi$
$882$	−1.60620	−0.0540835
$883$	0.668193	0.0224865	0.0112433	−	0.999937i	$-0.496421\pi$
$883$	0.668193	0.0224865	0.0112433	+	0.999937i	$0.496421\pi$
$884$	−8.55981	−0.287897
$885$	−9.95964	−0.334790
$886$	−26.2746	−0.882711
$887$	15.8528	0.532286	0.266143	−	0.963934i	$-0.414251\pi$
$887$	15.8528	0.532286	0.266143	+	0.963934i	$0.414251\pi$
$888$	2.42944	0.0815266
$889$	1.00000	0.0335389
$890$	−13.1128	−0.439541
$891$	−2.78529	−0.0933107
$892$	16.2151	0.542921
$893$	4.63849	0.155221
$894$	−7.23396	−0.241940
$895$	42.6598	1.42596
$896$	−13.6478	−0.455941
$897$	−7.79113	−0.260138
$898$	−33.8631	−1.13003
$899$	7.84931	0.261789
$900$	4.40057	0.146686
$901$	−67.5666	−2.25097
$902$	−15.7095	−0.523070
$903$	−5.82642	−0.193891
$904$	33.9146	1.12798
$905$	−60.4514	−2.00947
$906$	−21.4802	−0.713633
$907$	−3.26158	−0.108299	−0.0541496	−	0.998533i	$-0.517245\pi$
$907$	−3.26158	−0.108299	−0.0541496	+	0.998533i	$0.517245\pi$
$908$	−9.99005	−0.331531
$909$	11.1926	0.371236
$910$	13.8814	0.460163
$911$	50.2514	1.66490	0.832451	−	0.554099i	$-0.186937\pi$
$911$	50.2514	1.66490	0.832451	+	0.554099i	$0.186937\pi$
$912$	−9.34110	−0.309315
$913$	28.3931	0.939674
$914$	−15.3912	−0.509095
$915$	28.9779	0.957981
$916$	−10.3024	−0.340401
$917$	−16.9371	−0.559314
$918$	−9.73400	−0.321270
$919$	22.1516	0.730713	0.365356	−	0.930868i	$-0.380947\pi$
$919$	22.1516	0.730713	0.365356	+	0.930868i	$0.380947\pi$
$920$	−25.8869	−0.853466
$921$	24.8063	0.817395
$922$	41.7867	1.37617
$923$	29.6160	0.974822
$924$	1.61511	0.0531332
$925$	−8.08269	−0.265757
$926$	24.1442	0.793426
$927$	9.42373	0.309516
$928$	7.72141	0.253468
$929$	17.8794	0.586605	0.293302	−	0.956020i	$-0.405246\pi$
$929$	17.8794	0.586605	0.293302	+	0.956020i	$0.405246\pi$
$930$	−18.4544	−0.605143
$931$	−1.93658	−0.0634690
$932$	8.13477	0.266463
$933$	14.3789	0.470745
$934$	11.4514	0.374702
$935$	−59.8903	−1.95862
$936$	5.55606	0.181606
$937$	−41.2241	−1.34673	−0.673366	−	0.739310i	$-0.735152\pi$
$937$	−41.2241	−1.34673	−0.673366	+	0.739310i	$0.735152\pi$
$938$	−9.60429	−0.313591
$939$	−5.43949	−0.177511
$940$	4.92794	0.160732
$941$	18.6993	0.609581	0.304791	−	0.952419i	$-0.401414\pi$
$941$	18.6993	0.609581	0.304791	+	0.952419i	$0.401414\pi$
$942$	−12.4769	−0.406519
$943$	−11.2319	−0.365762
$944$	13.5398	0.440682
$945$	3.54808	0.115419
$946$	26.0658	0.847473
$947$	35.5049	1.15376	0.576878	−	0.816830i	$-0.304271\pi$
$947$	35.5049	1.15376	0.576878	+	0.816830i	$0.304271\pi$
$948$	1.75177	0.0568949
$949$	6.02799	0.195677
$950$	23.6055	0.765862
$951$	0.807453	0.0261835
$952$	−13.8235	−0.448024
$953$	8.77896	0.284378	0.142189	−	0.989839i	$-0.454586\pi$
$953$	8.77896	0.284378	0.142189	+	0.989839i	$0.454586\pi$
$954$	−17.9076	−0.579781
$955$	−49.4237	−1.59931
$956$	−12.4341	−0.402146
$957$	6.75141	0.218242
$958$	4.48245	0.144821
$959$	−8.14622	−0.263055
$960$	16.0746	0.518804
$961$	−20.5139	−0.661738
$962$	4.16695	0.134348
$963$	−6.56198	−0.211457
$964$	−2.65255	−0.0854327
$965$	83.5963	2.69106
$966$	5.13759	0.165299
$967$	27.9391	0.898461	0.449230	−	0.893416i	$-0.351698\pi$
$967$	27.9391	0.898461	0.449230	+	0.893416i	$0.351698\pi$
$968$	−7.39540	−0.237697
$969$	−11.7362	−0.377022
$970$	−4.03471	−0.129547
$971$	59.3843	1.90573	0.952867	−	0.303389i	$-0.0981181\pi$
$971$	59.3843	1.90573	0.952867	+	0.303389i	$0.0981181\pi$
$972$	−0.579871	−0.0185994
$973$	−10.0461	−0.322063
$974$	−51.8421	−1.66113
$975$	−18.4849	−0.591991
$976$	−39.3945	−1.26099
$977$	−15.7565	−0.504094	−0.252047	−	0.967715i	$-0.581104\pi$
$977$	−15.7565	−0.504094	−0.252047	+	0.967715i	$0.581104\pi$
$978$	18.2684	0.584160
$979$	6.40873	0.204824
$980$	−2.05743	−0.0657221
$981$	−15.5034	−0.494984
$982$	48.3442	1.54272
$983$	−38.6686	−1.23334	−0.616668	−	0.787223i	$-0.711518\pi$
$983$	−38.6686	−1.23334	−0.616668	+	0.787223i	$0.711518\pi$
$984$	8.00978	0.255343
$985$	23.1665	0.738146
$986$	23.5947	0.751410
$987$	2.39519	0.0762398
$988$	−2.73532	−0.0870221
$989$	18.6364	0.592603
$990$	−15.8731	−0.504481
$991$	41.4853	1.31783	0.658913	−	0.752219i	$-0.271017\pi$
$991$	41.4853	1.31783	0.658913	+	0.752219i	$0.271017\pi$
$992$	10.3153	0.327510
$993$	4.60565	0.146156
$994$	−19.5292	−0.619429
$995$	−67.5102	−2.14022
$996$	5.91117	0.187303
$997$	60.2478	1.90807	0.954034	−	0.299698i	$-0.0968859\pi$
$997$	60.2478	1.90807	0.954034	+	0.299698i	$0.0968859\pi$
$998$	−51.1359	−1.61868
$999$	1.06507	0.0336974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.p.1.6	✓	18
3.2	odd	2		8001.2.a.u.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.6	✓	18	1.1	even	1	trivial
8001.2.a.u.1.13		18	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.60620 q^{2} -1.00000 q^{3} +0.579871 q^{4} -3.54808 q^{5} +1.60620 q^{6} +1.00000 q^{7} +2.28101 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.60620 q^{2} -1.00000 q^{3} +0.579871 q^{4} -3.54808 q^{5} +1.60620 q^{6} +1.00000 q^{7} +2.28101 q^{8} +1.00000 q^{9} +5.69892 q^{10} -2.78529 q^{11} -0.579871 q^{12} +2.43579 q^{13} -1.60620 q^{14} +3.54808 q^{15} -4.82349 q^{16} -6.06028 q^{17} -1.60620 q^{18} -1.93658 q^{19} -2.05743 q^{20} -1.00000 q^{21} +4.47373 q^{22} +3.19860 q^{23} -2.28101 q^{24} +7.58887 q^{25} -3.91236 q^{26} -1.00000 q^{27} +0.579871 q^{28} +2.42395 q^{29} -5.69892 q^{30} +3.23823 q^{31} +3.18546 q^{32} +2.78529 q^{33} +9.73400 q^{34} -3.54808 q^{35} +0.579871 q^{36} -1.06507 q^{37} +3.11054 q^{38} -2.43579 q^{39} -8.09320 q^{40} -3.51151 q^{41} +1.60620 q^{42} +5.82642 q^{43} -1.61511 q^{44} -3.54808 q^{45} -5.13759 q^{46} -2.39519 q^{47} +4.82349 q^{48} +1.00000 q^{49} -12.1892 q^{50} +6.06028 q^{51} +1.41244 q^{52} +11.1491 q^{53} +1.60620 q^{54} +9.88243 q^{55} +2.28101 q^{56} +1.93658 q^{57} -3.89334 q^{58} -2.80705 q^{59} +2.05743 q^{60} +8.16721 q^{61} -5.20123 q^{62} +1.00000 q^{63} +4.53050 q^{64} -8.64238 q^{65} -4.47373 q^{66} +5.97952 q^{67} -3.51418 q^{68} -3.19860 q^{69} +5.69892 q^{70} +12.1587 q^{71} +2.28101 q^{72} +2.47476 q^{73} +1.71072 q^{74} -7.58887 q^{75} -1.12297 q^{76} -2.78529 q^{77} +3.91236 q^{78} -3.02097 q^{79} +17.1141 q^{80} +1.00000 q^{81} +5.64018 q^{82} -10.1939 q^{83} -0.579871 q^{84} +21.5023 q^{85} -9.35838 q^{86} -2.42395 q^{87} -6.35327 q^{88} -2.30092 q^{89} +5.69892 q^{90} +2.43579 q^{91} +1.85478 q^{92} -3.23823 q^{93} +3.84715 q^{94} +6.87116 q^{95} -3.18546 q^{96} -0.707978 q^{97} -1.60620 q^{98} -2.78529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19} - 21 q^{20} - 18 q^{21} + 5 q^{22} - 14 q^{23} + 21 q^{24} + 28 q^{25} - 8 q^{26} - 18 q^{27} + 22 q^{28} - 17 q^{29} + 4 q^{30} + 5 q^{31} - 53 q^{32} + 9 q^{33} - 19 q^{34} - 10 q^{35} + 22 q^{36} - 15 q^{37} - 22 q^{38} + 25 q^{39} - q^{40} - 17 q^{41} + 6 q^{42} + q^{43} - 33 q^{44} - 10 q^{45} + 10 q^{46} - 31 q^{47} - 34 q^{48} + 18 q^{49} - 35 q^{50} + 17 q^{51} - 70 q^{52} - 35 q^{53} + 6 q^{54} + 4 q^{55} - 21 q^{56} + 5 q^{57} + 3 q^{58} - 46 q^{59} + 21 q^{60} - 5 q^{61} - 10 q^{62} + 18 q^{63} + 63 q^{64} - 12 q^{65} - 5 q^{66} + 6 q^{67} - 56 q^{68} + 14 q^{69} - 4 q^{70} - 22 q^{71} - 21 q^{72} - 16 q^{73} + 18 q^{74} - 28 q^{75} + 32 q^{76} - 9 q^{77} + 8 q^{78} + 46 q^{79} - 30 q^{80} + 18 q^{81} - 12 q^{82} - 46 q^{83} - 22 q^{84} + 4 q^{85} + 18 q^{86} + 17 q^{87} + 30 q^{88} - 42 q^{89} - 4 q^{90} - 25 q^{91} - 48 q^{92} - 5 q^{93} + 3 q^{94} - 2 q^{95} + 53 q^{96} - 35 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

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