LMFDB - Embedded newform 2013.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} + \cdots + 1 $ x^12 - x^11 - 16x^10 + 13x^9 + 93x^8 - 59x^7 - 238x^6 + 108x^5 + 257x^4 - 71x^3 - 93x^2 + 13x + 1
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			1.7
Root			$0.188928$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.188928 q^{2} -1.00000 q^{3} -1.96431 q^{4} -1.33997 q^{5} -0.188928 q^{6} -0.912886 q^{7} -0.748968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.188928 q^{2} -1.00000 q^{3} -1.96431 q^{4} -1.33997 q^{5} -0.188928 q^{6} -0.912886 q^{7} -0.748968 q^{8} +1.00000 q^{9} -0.253157 q^{10} -1.00000 q^{11} +1.96431 q^{12} +5.78089 q^{13} -0.172470 q^{14} +1.33997 q^{15} +3.78711 q^{16} +3.08894 q^{17} +0.188928 q^{18} -6.38313 q^{19} +2.63211 q^{20} +0.912886 q^{21} -0.188928 q^{22} +7.04455 q^{23} +0.748968 q^{24} -3.20449 q^{25} +1.09217 q^{26} -1.00000 q^{27} +1.79319 q^{28} -9.45402 q^{29} +0.253157 q^{30} +7.73908 q^{31} +2.21343 q^{32} +1.00000 q^{33} +0.583586 q^{34} +1.22324 q^{35} -1.96431 q^{36} -8.78403 q^{37} -1.20595 q^{38} -5.78089 q^{39} +1.00359 q^{40} +8.00213 q^{41} +0.172470 q^{42} +10.8810 q^{43} +1.96431 q^{44} -1.33997 q^{45} +1.33091 q^{46} +10.0426 q^{47} -3.78711 q^{48} -6.16664 q^{49} -0.605417 q^{50} -3.08894 q^{51} -11.3554 q^{52} -3.34750 q^{53} -0.188928 q^{54} +1.33997 q^{55} +0.683723 q^{56} +6.38313 q^{57} -1.78613 q^{58} -11.0804 q^{59} -2.63211 q^{60} -1.00000 q^{61} +1.46213 q^{62} -0.912886 q^{63} -7.15604 q^{64} -7.74621 q^{65} +0.188928 q^{66} -14.0297 q^{67} -6.06762 q^{68} -7.04455 q^{69} +0.231104 q^{70} -15.6388 q^{71} -0.748968 q^{72} +2.96989 q^{73} -1.65955 q^{74} +3.20449 q^{75} +12.5384 q^{76} +0.912886 q^{77} -1.09217 q^{78} -16.1356 q^{79} -5.07461 q^{80} +1.00000 q^{81} +1.51183 q^{82} -8.28753 q^{83} -1.79319 q^{84} -4.13907 q^{85} +2.05573 q^{86} +9.45402 q^{87} +0.748968 q^{88} +16.6552 q^{89} -0.253157 q^{90} -5.27730 q^{91} -13.8377 q^{92} -7.73908 q^{93} +1.89733 q^{94} +8.55318 q^{95} -2.21343 q^{96} +2.95496 q^{97} -1.16505 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * q^98 - 12 * 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 $

$2$	0.188928	0.133592	0.0667961	−	0.997767i	$-0.478722\pi$
$2$	0.188928	0.133592	0.0667961	+	0.997767i	$0.478722\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96431	−0.982153
$5$	−1.33997	−0.599252	−0.299626	−	0.954057i	$-0.596862\pi$
$5$	−1.33997	−0.599252	−0.299626	+	0.954057i	$0.596862\pi$
$6$	−0.188928	−0.0771295
$7$	−0.912886	−0.345039	−0.172519	−	0.985006i	$-0.555191\pi$
$7$	−0.912886	−0.345039	−0.172519	+	0.985006i	$0.555191\pi$
$8$	−0.748968	−0.264800
$9$	1.00000	0.333333
$10$	−0.253157	−0.0800554
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.96431	0.567046
$13$	5.78089	1.60333	0.801666	−	0.597773i	$-0.203947\pi$
$13$	5.78089	1.60333	0.801666	+	0.597773i	$0.203947\pi$
$14$	−0.172470	−0.0460945
$15$	1.33997	0.345978
$16$	3.78711	0.946778
$17$	3.08894	0.749177	0.374588	−	0.927191i	$-0.377784\pi$
$17$	3.08894	0.749177	0.374588	+	0.927191i	$0.377784\pi$
$18$	0.188928	0.0445307
$19$	−6.38313	−1.46439	−0.732195	−	0.681095i	$-0.761504\pi$
$19$	−6.38313	−1.46439	−0.732195	+	0.681095i	$0.761504\pi$
$20$	2.63211	0.588557
$21$	0.912886	0.199208
$22$	−0.188928	−0.0402796
$23$	7.04455	1.46889	0.734445	−	0.678668i	$-0.237442\pi$
$23$	7.04455	1.46889	0.734445	+	0.678668i	$0.237442\pi$
$24$	0.748968	0.152883
$25$	−3.20449	−0.640898
$26$	1.09217	0.214193
$27$	−1.00000	−0.192450
$28$	1.79319	0.338881
$29$	−9.45402	−1.75557	−0.877784	−	0.479056i	$-0.840979\pi$
$29$	−9.45402	−1.75557	−0.877784	+	0.479056i	$0.840979\pi$
$30$	0.253157	0.0462200
$31$	7.73908	1.38998	0.694990	−	0.719019i	$-0.255409\pi$
$31$	7.73908	1.38998	0.694990	+	0.719019i	$0.255409\pi$
$32$	2.21343	0.391282
$33$	1.00000	0.174078
$34$	0.583586	0.100084
$35$	1.22324	0.206765
$36$	−1.96431	−0.327384
$37$	−8.78403	−1.44409	−0.722043	−	0.691849i	$-0.756797\pi$
$37$	−8.78403	−1.44409	−0.722043	+	0.691849i	$0.756797\pi$
$38$	−1.20595	−0.195631
$39$	−5.78089	−0.925684
$40$	1.00359	0.158682
$41$	8.00213	1.24972	0.624861	−	0.780736i	$-0.285155\pi$
$41$	8.00213	1.24972	0.624861	+	0.780736i	$0.285155\pi$
$42$	0.172470	0.0266127
$43$	10.8810	1.65934	0.829670	−	0.558254i	$-0.188529\pi$
$43$	10.8810	1.65934	0.829670	+	0.558254i	$0.188529\pi$
$44$	1.96431	0.296130
$45$	−1.33997	−0.199751
$46$	1.33091	0.196232
$47$	10.0426	1.46487	0.732433	−	0.680839i	$-0.238385\pi$
$47$	10.0426	1.46487	0.732433	+	0.680839i	$0.238385\pi$
$48$	−3.78711	−0.546622
$49$	−6.16664	−0.880948
$50$	−0.605417	−0.0856189
$51$	−3.08894	−0.432537
$52$	−11.3554	−1.57472
$53$	−3.34750	−0.459814	−0.229907	−	0.973213i	$-0.573842\pi$
$53$	−3.34750	−0.459814	−0.229907	+	0.973213i	$0.573842\pi$
$54$	−0.188928	−0.0257098
$55$	1.33997	0.180681
$56$	0.683723	0.0913663
$57$	6.38313	0.845466
$58$	−1.78613	−0.234530
$59$	−11.0804	−1.44254	−0.721271	−	0.692653i	$-0.756442\pi$
$59$	−11.0804	−1.44254	−0.721271	+	0.692653i	$0.756442\pi$
$60$	−2.63211	−0.339803
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	1.46213	0.185691
$63$	−0.912886	−0.115013
$64$	−7.15604	−0.894506
$65$	−7.74621	−0.960799
$66$	0.188928	0.0232554
$67$	−14.0297	−1.71400	−0.857000	−	0.515317i	$-0.827674\pi$
$67$	−14.0297	−1.71400	−0.857000	+	0.515317i	$0.827674\pi$
$68$	−6.06762	−0.735806
$69$	−7.04455	−0.848064
$70$	0.231104	0.0276222
$71$	−15.6388	−1.85599	−0.927993	−	0.372597i	$-0.878467\pi$
$71$	−15.6388	−1.85599	−0.927993	+	0.372597i	$0.878467\pi$
$72$	−0.748968	−0.0882668
$73$	2.96989	0.347599	0.173800	−	0.984781i	$-0.444395\pi$
$73$	2.96989	0.347599	0.173800	+	0.984781i	$0.444395\pi$
$74$	−1.65955	−0.192919
$75$	3.20449	0.370022
$76$	12.5384	1.43825
$77$	0.912886	0.104033
$78$	−1.09217	−0.123664
$79$	−16.1356	−1.81540	−0.907698	−	0.419624i	$-0.862162\pi$
$79$	−16.1356	−1.81540	−0.907698	+	0.419624i	$0.862162\pi$
$80$	−5.07461	−0.567358
$81$	1.00000	0.111111
$82$	1.51183	0.166953
$83$	−8.28753	−0.909674	−0.454837	−	0.890575i	$-0.650303\pi$
$83$	−8.28753	−0.909674	−0.454837	+	0.890575i	$0.650303\pi$
$84$	−1.79319	−0.195653
$85$	−4.13907	−0.448945
$86$	2.05573	0.221675
$87$	9.45402	1.01358
$88$	0.748968	0.0798403
$89$	16.6552	1.76544	0.882722	−	0.469895i	$-0.155708\pi$
$89$	16.6552	1.76544	0.882722	+	0.469895i	$0.155708\pi$
$90$	−0.253157	−0.0266851
$91$	−5.27730	−0.553211
$92$	−13.8377	−1.44268
$93$	−7.73908	−0.802506
$94$	1.89733	0.195695
$95$	8.55318	0.877538
$96$	−2.21343	−0.225907
$97$	2.95496	0.300030	0.150015	−	0.988684i	$-0.452068\pi$
$97$	2.95496	0.300030	0.150015	+	0.988684i	$0.452068\pi$
$98$	−1.16505	−0.117688
$99$	−1.00000	−0.100504
$100$	6.29460	0.629460
$101$	−8.13212	−0.809176	−0.404588	−	0.914499i	$-0.632585\pi$
$101$	−8.13212	−0.809176	−0.404588	+	0.914499i	$0.632585\pi$
$102$	−0.583586	−0.0577837
$103$	−2.95362	−0.291029	−0.145515	−	0.989356i	$-0.546484\pi$
$103$	−2.95362	−0.291029	−0.145515	+	0.989356i	$0.546484\pi$
$104$	−4.32971	−0.424563
$105$	−1.22324	−0.119376
$106$	−0.632435	−0.0614276
$107$	−5.43795	−0.525707	−0.262853	−	0.964836i	$-0.584664\pi$
$107$	−5.43795	−0.525707	−0.262853	+	0.964836i	$0.584664\pi$
$108$	1.96431	0.189015
$109$	−12.9693	−1.24223	−0.621115	−	0.783719i	$-0.713320\pi$
$109$	−12.9693	−1.24223	−0.621115	+	0.783719i	$0.713320\pi$
$110$	0.253157	0.0241376
$111$	8.78403	0.833743
$112$	−3.45720	−0.326675
$113$	−4.05596	−0.381552	−0.190776	−	0.981634i	$-0.561100\pi$
$113$	−4.05596	−0.381552	−0.190776	+	0.981634i	$0.561100\pi$
$114$	1.20595	0.112948
$115$	−9.43947	−0.880235
$116$	18.5706	1.72424
$117$	5.78089	0.534444
$118$	−2.09339	−0.192712
$119$	−2.81985	−0.258495
$120$	−1.00359	−0.0916151
$121$	1.00000	0.0909091
$122$	−0.188928	−0.0171047
$123$	−8.00213	−0.721528
$124$	−15.2019	−1.36517
$125$	10.9937	0.983310
$126$	−0.172470	−0.0153648
$127$	11.1248	0.987164	0.493582	−	0.869699i	$-0.335687\pi$
$127$	11.1248	0.987164	0.493582	+	0.869699i	$0.335687\pi$
$128$	−5.77883	−0.510781
$129$	−10.8810	−0.958020
$130$	−1.46348	−0.128355
$131$	−10.9684	−0.958317	−0.479158	−	0.877728i	$-0.659058\pi$
$131$	−10.9684	−0.958317	−0.479158	+	0.877728i	$0.659058\pi$
$132$	−1.96431	−0.170971
$133$	5.82707	0.505271
$134$	−2.65060	−0.228977
$135$	1.33997	0.115326
$136$	−2.31351	−0.198382
$137$	9.44450	0.806898	0.403449	−	0.915002i	$-0.367811\pi$
$137$	9.44450	0.806898	0.403449	+	0.915002i	$0.367811\pi$
$138$	−1.33091	−0.113295
$139$	−5.72383	−0.485489	−0.242744	−	0.970090i	$-0.578048\pi$
$139$	−5.72383	−0.485489	−0.242744	+	0.970090i	$0.578048\pi$
$140$	−2.40281	−0.203075
$141$	−10.0426	−0.845741
$142$	−2.95461	−0.247945
$143$	−5.78089	−0.483423
$144$	3.78711	0.315593
$145$	12.6681	1.05203
$146$	0.561095	0.0464366
$147$	6.16664	0.508616
$148$	17.2545	1.41831
$149$	3.38560	0.277359	0.138679	−	0.990337i	$-0.455714\pi$
$149$	3.38560	0.277359	0.138679	+	0.990337i	$0.455714\pi$
$150$	0.605417	0.0494321
$151$	0.0659442	0.00536647	0.00268323	−	0.999996i	$-0.499146\pi$
$151$	0.0659442	0.00536647	0.00268323	+	0.999996i	$0.499146\pi$
$152$	4.78076	0.387771
$153$	3.08894	0.249726
$154$	0.172470	0.0138980
$155$	−10.3701	−0.832948
$156$	11.3554	0.909163
$157$	7.21978	0.576201	0.288100	−	0.957600i	$-0.406976\pi$
$157$	7.21978	0.576201	0.288100	+	0.957600i	$0.406976\pi$
$158$	−3.04847	−0.242523
$159$	3.34750	0.265474
$160$	−2.96592	−0.234477
$161$	−6.43088	−0.506824
$162$	0.188928	0.0148436
$163$	2.21336	0.173364	0.0866820	−	0.996236i	$-0.472374\pi$
$163$	2.21336	0.173364	0.0866820	+	0.996236i	$0.472374\pi$
$164$	−15.7186	−1.22742
$165$	−1.33997	−0.104316
$166$	−1.56575	−0.121525
$167$	−4.31720	−0.334075	−0.167037	−	0.985951i	$-0.553420\pi$
$167$	−4.31720	−0.334075	−0.167037	+	0.985951i	$0.553420\pi$
$168$	−0.683723	−0.0527504
$169$	20.4187	1.57067
$170$	−0.781986	−0.0599756
$171$	−6.38313	−0.488130
$172$	−21.3737	−1.62973
$173$	20.4365	1.55376	0.776878	−	0.629651i	$-0.216802\pi$
$173$	20.4365	1.55376	0.776878	+	0.629651i	$0.216802\pi$
$174$	1.78613	0.135406
$175$	2.92533	0.221134
$176$	−3.78711	−0.285464
$177$	11.0804	0.832852
$178$	3.14663	0.235850
$179$	11.9618	0.894069	0.447034	−	0.894517i	$-0.352480\pi$
$179$	11.9618	0.894069	0.447034	+	0.894517i	$0.352480\pi$
$180$	2.63211	0.196186
$181$	−12.9042	−0.959165	−0.479583	−	0.877497i	$-0.659212\pi$
$181$	−12.9042	−0.959165	−0.479583	+	0.877497i	$0.659212\pi$
$182$	−0.997029	−0.0739047
$183$	1.00000	0.0739221
$184$	−5.27615	−0.388963
$185$	11.7703	0.865370
$186$	−1.46213	−0.107209
$187$	−3.08894	−0.225885
$188$	−19.7268	−1.43872
$189$	0.912886	0.0664027
$190$	1.61593	0.117232
$191$	−17.6646	−1.27817	−0.639083	−	0.769138i	$-0.720686\pi$
$191$	−17.6646	−1.27817	−0.639083	+	0.769138i	$0.720686\pi$
$192$	7.15604	0.516443
$193$	−1.47701	−0.106318	−0.0531588	−	0.998586i	$-0.516929\pi$
$193$	−1.47701	−0.106318	−0.0531588	+	0.998586i	$0.516929\pi$
$194$	0.558274	0.0400817
$195$	7.74621	0.554718
$196$	12.1132	0.865226
$197$	−4.86491	−0.346611	−0.173305	−	0.984868i	$-0.555445\pi$
$197$	−4.86491	−0.346611	−0.173305	+	0.984868i	$0.555445\pi$
$198$	−0.188928	−0.0134265
$199$	−24.7175	−1.75218	−0.876088	−	0.482151i	$-0.839856\pi$
$199$	−24.7175	−1.75218	−0.876088	+	0.482151i	$0.839856\pi$
$200$	2.40006	0.169710
$201$	14.0297	0.989578
$202$	−1.53638	−0.108100
$203$	8.63045	0.605739
$204$	6.06762	0.424818
$205$	−10.7226	−0.748898
$206$	−0.558022	−0.0388792
$207$	7.04455	0.489630
$208$	21.8929	1.51800
$209$	6.38313	0.441530
$210$	−0.231104	−0.0159477
$211$	−19.9377	−1.37257	−0.686285	−	0.727332i	$-0.740760\pi$
$211$	−19.9377	−1.37257	−0.686285	+	0.727332i	$0.740760\pi$
$212$	6.57551	0.451608
$213$	15.6388	1.07155
$214$	−1.02738	−0.0702303
$215$	−14.5802	−0.994362
$216$	0.748968	0.0509608
$217$	−7.06490	−0.479597
$218$	−2.45026	−0.165952
$219$	−2.96989	−0.200687
$220$	−2.63211	−0.177457
$221$	17.8568	1.20118
$222$	1.65955	0.111382
$223$	2.57011	0.172108	0.0860538	−	0.996290i	$-0.472574\pi$
$223$	2.57011	0.172108	0.0860538	+	0.996290i	$0.472574\pi$
$224$	−2.02061	−0.135008
$225$	−3.20449	−0.213633
$226$	−0.766283	−0.0509724
$227$	−15.8132	−1.04956	−0.524781	−	0.851237i	$-0.675853\pi$
$227$	−15.8132	−1.04956	−0.524781	+	0.851237i	$0.675853\pi$
$228$	−12.5384	−0.830377
$229$	−7.47054	−0.493667	−0.246834	−	0.969058i	$-0.579390\pi$
$229$	−7.47054	−0.493667	−0.246834	+	0.969058i	$0.579390\pi$
$230$	−1.78338	−0.117593
$231$	−0.912886	−0.0600635
$232$	7.08076	0.464875
$233$	3.38309	0.221634	0.110817	−	0.993841i	$-0.464653\pi$
$233$	3.38309	0.221634	0.110817	+	0.993841i	$0.464653\pi$
$234$	1.09217	0.0713976
$235$	−13.4568	−0.877824
$236$	21.7652	1.41680
$237$	16.1356	1.04812
$238$	−0.532748	−0.0345329
$239$	9.79975	0.633893	0.316947	−	0.948443i	$-0.397342\pi$
$239$	9.79975	0.633893	0.316947	+	0.948443i	$0.397342\pi$
$240$	5.07461	0.327564
$241$	−27.2706	−1.75666	−0.878328	−	0.478058i	$-0.841341\pi$
$241$	−27.2706	−1.75666	−0.878328	+	0.478058i	$0.841341\pi$
$242$	0.188928	0.0121447
$243$	−1.00000	−0.0641500
$244$	1.96431	0.125752
$245$	8.26309	0.527910
$246$	−1.51183	−0.0963905
$247$	−36.9002	−2.34790
$248$	−5.79633	−0.368067
$249$	8.28753	0.525201
$250$	2.07703	0.131363
$251$	11.1707	0.705087	0.352543	−	0.935795i	$-0.385317\pi$
$251$	11.1707	0.705087	0.352543	+	0.935795i	$0.385317\pi$
$252$	1.79319	0.112960
$253$	−7.04455	−0.442887
$254$	2.10178	0.131877
$255$	4.13907	0.259199
$256$	13.2203	0.826269
$257$	−4.34515	−0.271043	−0.135522	−	0.990774i	$-0.543271\pi$
$257$	−4.34515	−0.271043	−0.135522	+	0.990774i	$0.543271\pi$
$258$	−2.05573	−0.127984
$259$	8.01882	0.498265
$260$	15.2159	0.943652
$261$	−9.45402	−0.585189
$262$	−2.07224	−0.128024
$263$	−2.95382	−0.182140	−0.0910701	−	0.995844i	$-0.529029\pi$
$263$	−2.95382	−0.182140	−0.0910701	+	0.995844i	$0.529029\pi$
$264$	−0.748968	−0.0460958
$265$	4.48553	0.275544
$266$	1.10090	0.0675003
$267$	−16.6552	−1.01928
$268$	27.5586	1.68341
$269$	14.5056	0.884421	0.442211	−	0.896911i	$-0.354194\pi$
$269$	14.5056	0.884421	0.442211	+	0.896911i	$0.354194\pi$
$270$	0.253157	0.0154067
$271$	−0.612616	−0.0372138	−0.0186069	−	0.999827i	$-0.505923\pi$
$271$	−0.612616	−0.0372138	−0.0186069	+	0.999827i	$0.505923\pi$
$272$	11.6981	0.709304
$273$	5.27730	0.319397
$274$	1.78433	0.107795
$275$	3.20449	0.193238
$276$	13.8377	0.832929
$277$	−8.29532	−0.498417	−0.249209	−	0.968450i	$-0.580170\pi$
$277$	−8.29532	−0.498417	−0.249209	+	0.968450i	$0.580170\pi$
$278$	−1.08139	−0.0648575
$279$	7.73908	0.463327
$280$	−0.916166	−0.0547514
$281$	27.5450	1.64320	0.821598	−	0.570067i	$-0.193083\pi$
$281$	27.5450	1.64320	0.821598	+	0.570067i	$0.193083\pi$
$282$	−1.89733	−0.112984
$283$	−17.0530	−1.01369	−0.506847	−	0.862036i	$-0.669189\pi$
$283$	−17.0530	−1.01369	−0.506847	+	0.862036i	$0.669189\pi$
$284$	30.7194	1.82286
$285$	−8.55318	−0.506647
$286$	−1.09217	−0.0645815
$287$	−7.30504	−0.431203
$288$	2.21343	0.130427
$289$	−7.45848	−0.438734
$290$	2.39335	0.140543
$291$	−2.95496	−0.173223
$292$	−5.83377	−0.341396
$293$	22.4254	1.31011	0.655054	−	0.755582i	$-0.272646\pi$
$293$	22.4254	1.31011	0.655054	+	0.755582i	$0.272646\pi$
$294$	1.16505	0.0679471
$295$	14.8473	0.864445
$296$	6.57896	0.382394
$297$	1.00000	0.0580259
$298$	0.639634	0.0370530
$299$	40.7238	2.35512
$300$	−6.29460	−0.363419
$301$	−9.93313	−0.572536
$302$	0.0124587	0.000716918 0
$303$	8.13212	0.467178
$304$	−24.1736	−1.38645
$305$	1.33997	0.0767263
$306$	0.583586	0.0333614
$307$	−19.7220	−1.12560	−0.562798	−	0.826594i	$-0.690275\pi$
$307$	−19.7220	−1.12560	−0.562798	+	0.826594i	$0.690275\pi$
$308$	−1.79319	−0.102176
$309$	2.95362	0.168026
$310$	−1.95921	−0.111275
$311$	−27.6646	−1.56872	−0.784358	−	0.620309i	$-0.787007\pi$
$311$	−27.6646	−1.56872	−0.784358	+	0.620309i	$0.787007\pi$
$312$	4.32971	0.245121
$313$	−0.806666	−0.0455955	−0.0227977	−	0.999740i	$-0.507257\pi$
$313$	−0.806666	−0.0455955	−0.0227977	+	0.999740i	$0.507257\pi$
$314$	1.36402	0.0769760
$315$	1.22324	0.0689216
$316$	31.6953	1.78300
$317$	27.5804	1.54907	0.774534	−	0.632533i	$-0.217985\pi$
$317$	27.5804	1.54907	0.774534	+	0.632533i	$0.217985\pi$
$318$	0.632435	0.0354652
$319$	9.45402	0.529324
$320$	9.58887	0.536034
$321$	5.43795	0.303517
$322$	−1.21497	−0.0677078
$323$	−19.7171	−1.09709
$324$	−1.96431	−0.109128
$325$	−18.5248	−1.02757
$326$	0.418166	0.0231601
$327$	12.9693	0.717202
$328$	−5.99334	−0.330927
$329$	−9.16777	−0.505436
$330$	−0.253157	−0.0139358
$331$	1.25583	0.0690268	0.0345134	−	0.999404i	$-0.489012\pi$
$331$	1.25583	0.0690268	0.0345134	+	0.999404i	$0.489012\pi$
$332$	16.2792	0.893439
$333$	−8.78403	−0.481362
$334$	−0.815640	−0.0446298
$335$	18.7993	1.02712
$336$	3.45720	0.188606
$337$	9.30865	0.507075	0.253537	−	0.967326i	$-0.418406\pi$
$337$	9.30865	0.507075	0.253537	+	0.967326i	$0.418406\pi$
$338$	3.85767	0.209830
$339$	4.05596	0.220289
$340$	8.13041	0.440933
$341$	−7.73908	−0.419095
$342$	−1.20595	−0.0652104
$343$	12.0196	0.649000
$344$	−8.14954	−0.439394
$345$	9.43947	0.508204
$346$	3.86102	0.207570
$347$	4.07377	0.218691	0.109346	−	0.994004i	$-0.465124\pi$
$347$	4.07377	0.218691	0.109346	+	0.994004i	$0.465124\pi$
$348$	−18.5706	−0.995489
$349$	−7.75144	−0.414925	−0.207462	−	0.978243i	$-0.566520\pi$
$349$	−7.75144	−0.414925	−0.207462	+	0.978243i	$0.566520\pi$
$350$	0.552677	0.0295418
$351$	−5.78089	−0.308561
$352$	−2.21343	−0.117976
$353$	5.73190	0.305078	0.152539	−	0.988297i	$-0.451255\pi$
$353$	5.73190	0.305078	0.152539	+	0.988297i	$0.451255\pi$
$354$	2.09339	0.111263
$355$	20.9555	1.11220
$356$	−32.7159	−1.73394
$357$	2.81985	0.149242
$358$	2.25992	0.119441
$359$	−15.6034	−0.823514	−0.411757	−	0.911294i	$-0.635085\pi$
$359$	−15.6034	−0.823514	−0.411757	+	0.911294i	$0.635085\pi$
$360$	1.00359	0.0528940
$361$	21.7443	1.14444
$362$	−2.43797	−0.128137
$363$	−1.00000	−0.0524864
$364$	10.3662	0.543338
$365$	−3.97956	−0.208299
$366$	0.188928	0.00987542
$367$	0.783228	0.0408842	0.0204421	−	0.999791i	$-0.493493\pi$
$367$	0.783228	0.0408842	0.0204421	+	0.999791i	$0.493493\pi$
$368$	26.6785	1.39071
$369$	8.00213	0.416574
$370$	2.22374	0.115607
$371$	3.05588	0.158654
$372$	15.2019	0.788183
$373$	−31.9258	−1.65305	−0.826527	−	0.562897i	$-0.809687\pi$
$373$	−31.9258	−1.65305	−0.826527	+	0.562897i	$0.809687\pi$
$374$	−0.583586	−0.0301765
$375$	−10.9937	−0.567715
$376$	−7.52160	−0.387897
$377$	−54.6527	−2.81476
$378$	0.172470	0.00887089
$379$	4.12048	0.211655	0.105827	−	0.994385i	$-0.466251\pi$
$379$	4.12048	0.211655	0.105827	+	0.994385i	$0.466251\pi$
$380$	−16.8011	−0.861876
$381$	−11.1248	−0.569939
$382$	−3.33734	−0.170753
$383$	−7.79173	−0.398139	−0.199069	−	0.979985i	$-0.563792\pi$
$383$	−7.79173	−0.398139	−0.199069	+	0.979985i	$0.563792\pi$
$384$	5.77883	0.294900
$385$	−1.22324	−0.0623420
$386$	−0.279049	−0.0142032
$387$	10.8810	0.553113
$388$	−5.80444	−0.294676
$389$	21.1087	1.07025	0.535127	−	0.844771i	$-0.320264\pi$
$389$	21.1087	1.07025	0.535127	+	0.844771i	$0.320264\pi$
$390$	1.46348	0.0741060
$391$	21.7602	1.10046
$392$	4.61862	0.233275
$393$	10.9684	0.553285
$394$	−0.919118	−0.0463045
$395$	21.6212	1.08788
$396$	1.96431	0.0987101
$397$	17.2021	0.863348	0.431674	−	0.902030i	$-0.357923\pi$
$397$	17.2021	0.863348	0.431674	+	0.902030i	$0.357923\pi$
$398$	−4.66982	−0.234077
$399$	−5.82707	−0.291718
$400$	−12.1358	−0.606788
$401$	−1.36379	−0.0681044	−0.0340522	−	0.999420i	$-0.510841\pi$
$401$	−1.36379	−0.0681044	−0.0340522	+	0.999420i	$0.510841\pi$
$402$	2.65060	0.132200
$403$	44.7388	2.22860
$404$	15.9740	0.794735
$405$	−1.33997	−0.0665835
$406$	1.63053	0.0809220
$407$	8.78403	0.435408
$408$	2.31351	0.114536
$409$	−6.41076	−0.316992	−0.158496	−	0.987360i	$-0.550664\pi$
$409$	−6.41076	−0.316992	−0.158496	+	0.987360i	$0.550664\pi$
$410$	−2.02580	−0.100047
$411$	−9.44450	−0.465863
$412$	5.80182	0.285835
$413$	10.1151	0.497732
$414$	1.33091	0.0654108
$415$	11.1050	0.545124
$416$	12.7956	0.627355
$417$	5.72383	0.280297
$418$	1.20595	0.0589850
$419$	10.1744	0.497051	0.248525	−	0.968625i	$-0.420054\pi$
$419$	10.1744	0.497051	0.248525	+	0.968625i	$0.420054\pi$
$420$	2.40281	0.117245
$421$	−35.7079	−1.74029	−0.870147	−	0.492792i	$-0.835976\pi$
$421$	−35.7079	−1.74029	−0.870147	+	0.492792i	$0.835976\pi$
$422$	−3.76680	−0.183365
$423$	10.0426	0.488289
$424$	2.50717	0.121759
$425$	−9.89846	−0.480146
$426$	2.95461	0.143151
$427$	0.912886	0.0441777
$428$	10.6818	0.516325
$429$	5.78089	0.279104
$430$	−2.75461	−0.132839
$431$	−14.0872	−0.678554	−0.339277	−	0.940686i	$-0.610182\pi$
$431$	−14.0872	−0.678554	−0.339277	+	0.940686i	$0.610182\pi$
$432$	−3.78711	−0.182207
$433$	4.30378	0.206827	0.103413	−	0.994638i	$-0.467024\pi$
$433$	4.30378	0.206827	0.103413	+	0.994638i	$0.467024\pi$
$434$	−1.33476	−0.0640704
$435$	−12.6681	−0.607388
$436$	25.4756	1.22006
$437$	−44.9663	−2.15103
$438$	−0.561095	−0.0268102
$439$	0.316453	0.0151035	0.00755175	−	0.999971i	$-0.497596\pi$
$439$	0.316453	0.0151035	0.00755175	+	0.999971i	$0.497596\pi$
$440$	−1.00359	−0.0478444
$441$	−6.16664	−0.293649
$442$	3.37365	0.160468
$443$	−2.87540	−0.136614	−0.0683072	−	0.997664i	$-0.521760\pi$
$443$	−2.87540	−0.136614	−0.0683072	+	0.997664i	$0.521760\pi$
$444$	−17.2545	−0.818863
$445$	−22.3174	−1.05795
$446$	0.485566	0.0229922
$447$	−3.38560	−0.160133
$448$	6.53266	0.308639
$449$	−0.511009	−0.0241160	−0.0120580	−	0.999927i	$-0.503838\pi$
$449$	−0.511009	−0.0241160	−0.0120580	+	0.999927i	$0.503838\pi$
$450$	−0.605417	−0.0285396
$451$	−8.00213	−0.376806
$452$	7.96714	0.374743
$453$	−0.0659442	−0.00309833
$454$	−2.98756	−0.140213
$455$	7.07141	0.331513
$456$	−4.78076	−0.223880
$457$	−19.6806	−0.920618	−0.460309	−	0.887759i	$-0.652261\pi$
$457$	−19.6806	−0.920618	−0.460309	+	0.887759i	$0.652261\pi$
$458$	−1.41139	−0.0659501
$459$	−3.08894	−0.144179
$460$	18.5420	0.864526
$461$	−13.6635	−0.636373	−0.318187	−	0.948028i	$-0.603074\pi$
$461$	−13.6635	−0.636373	−0.318187	+	0.948028i	$0.603074\pi$
$462$	−0.172470	−0.00802402
$463$	−23.4673	−1.09062	−0.545310	−	0.838235i	$-0.683588\pi$
$463$	−23.4673	−1.09062	−0.545310	+	0.838235i	$0.683588\pi$
$464$	−35.8034	−1.66213
$465$	10.3701	0.480903
$466$	0.639161	0.0296085
$467$	−36.7528	−1.70072	−0.850359	−	0.526203i	$-0.823615\pi$
$467$	−36.7528	−1.70072	−0.850359	+	0.526203i	$0.823615\pi$
$468$	−11.3554	−0.524906
$469$	12.8075	0.591396
$470$	−2.54236	−0.117270
$471$	−7.21978	−0.332670
$472$	8.29885	0.381985
$473$	−10.8810	−0.500310
$474$	3.04847	0.140021
$475$	20.4546	0.938524
$476$	5.53904	0.253882
$477$	−3.34750	−0.153271
$478$	1.85145	0.0846832
$479$	8.48544	0.387710	0.193855	−	0.981030i	$-0.437901\pi$
$479$	8.48544	0.387710	0.193855	+	0.981030i	$0.437901\pi$
$480$	2.96592	0.135375
$481$	−50.7795	−2.31535
$482$	−5.15219	−0.234676
$483$	6.43088	0.292615
$484$	−1.96431	−0.0892866
$485$	−3.95954	−0.179794
$486$	−0.188928	−0.00856995
$487$	−0.497479	−0.0225429	−0.0112715	−	0.999936i	$-0.503588\pi$
$487$	−0.497479	−0.0225429	−0.0112715	+	0.999936i	$0.503588\pi$
$488$	0.748968	0.0339042
$489$	−2.21336	−0.100092
$490$	1.56113	0.0705246
$491$	12.9744	0.585524	0.292762	−	0.956185i	$-0.405426\pi$
$491$	12.9744	0.585524	0.292762	+	0.956185i	$0.405426\pi$
$492$	15.7186	0.708651
$493$	−29.2029	−1.31523
$494$	−6.97147	−0.313661
$495$	1.33997	0.0602270
$496$	29.3088	1.31600
$497$	14.2765	0.640387
$498$	1.56575	0.0701627
$499$	19.4116	0.868981	0.434491	−	0.900676i	$-0.356928\pi$
$499$	19.4116	0.868981	0.434491	+	0.900676i	$0.356928\pi$
$500$	−21.5951	−0.965761
$501$	4.31720	0.192878
$502$	2.11045	0.0941941
$503$	−10.6466	−0.474709	−0.237355	−	0.971423i	$-0.576280\pi$
$503$	−10.6466	−0.474709	−0.237355	+	0.971423i	$0.576280\pi$
$504$	0.683723	0.0304554
$505$	10.8968	0.484900
$506$	−1.33091	−0.0591663
$507$	−20.4187	−0.906828
$508$	−21.8525	−0.969546
$509$	−11.4627	−0.508075	−0.254038	−	0.967194i	$-0.581759\pi$
$509$	−11.4627	−0.508075	−0.254038	+	0.967194i	$0.581759\pi$
$510$	0.781986	0.0346269
$511$	−2.71117	−0.119935
$512$	14.0553	0.621165
$513$	6.38313	0.281822
$514$	−0.820921	−0.0362093
$515$	3.95776	0.174400
$516$	21.3737	0.940923
$517$	−10.0426	−0.441674
$518$	1.51498	0.0665644
$519$	−20.4365	−0.897062
$520$	5.80166	0.254420
$521$	4.09976	0.179614	0.0898068	−	0.995959i	$-0.471375\pi$
$521$	4.09976	0.179614	0.0898068	+	0.995959i	$0.471375\pi$
$522$	−1.78613	−0.0781768
$523$	24.0544	1.05182	0.525912	−	0.850539i	$-0.323724\pi$
$523$	24.0544	1.05182	0.525912	+	0.850539i	$0.323724\pi$
$524$	21.5454	0.941214
$525$	−2.92533	−0.127672
$526$	−0.558059	−0.0243325
$527$	23.9055	1.04134
$528$	3.78711	0.164813
$529$	26.6257	1.15764
$530$	0.847443	0.0368106
$531$	−11.0804	−0.480847
$532$	−11.4461	−0.496253
$533$	46.2595	2.00372
$534$	−3.14663	−0.136168
$535$	7.28668	0.315031
$536$	10.5078	0.453868
$537$	−11.9618	−0.516191
$538$	2.74051	0.118152
$539$	6.16664	0.265616
$540$	−2.63211	−0.113268
$541$	22.0309	0.947180	0.473590	−	0.880745i	$-0.342958\pi$
$541$	22.0309	0.947180	0.473590	+	0.880745i	$0.342958\pi$
$542$	−0.115740	−0.00497147
$543$	12.9042	0.553774
$544$	6.83714	0.293140
$545$	17.3784	0.744409
$546$	0.997029	0.0426689
$547$	17.0557	0.729250	0.364625	−	0.931154i	$-0.381197\pi$
$547$	17.0557	0.729250	0.364625	+	0.931154i	$0.381197\pi$
$548$	−18.5519	−0.792498
$549$	−1.00000	−0.0426790
$550$	0.605417	0.0258151
$551$	60.3462	2.57084
$552$	5.27615	0.224568
$553$	14.7300	0.626382
$554$	−1.56722	−0.0665847
$555$	−11.7703	−0.499622
$556$	11.2434	0.476824
$557$	14.2050	0.601884	0.300942	−	0.953642i	$-0.402699\pi$
$557$	14.2050	0.601884	0.300942	+	0.953642i	$0.402699\pi$
$558$	1.46213	0.0618969
$559$	62.9020	2.66047
$560$	4.63254	0.195760
$561$	3.08894	0.130415
$562$	5.20402	0.219518
$563$	−2.83423	−0.119449	−0.0597243	−	0.998215i	$-0.519022\pi$
$563$	−2.83423	−0.119449	−0.0597243	+	0.998215i	$0.519022\pi$
$564$	19.7268	0.830647
$565$	5.43485	0.228646
$566$	−3.22178	−0.135422
$567$	−0.912886	−0.0383376
$568$	11.7130	0.491466
$569$	−3.03834	−0.127374	−0.0636870	−	0.997970i	$-0.520286\pi$
$569$	−3.03834	−0.127374	−0.0636870	+	0.997970i	$0.520286\pi$
$570$	−1.61593	−0.0676841
$571$	−36.7092	−1.53623	−0.768117	−	0.640310i	$-0.778806\pi$
$571$	−36.7092	−1.53623	−0.768117	+	0.640310i	$0.778806\pi$
$572$	11.3554	0.474795
$573$	17.6646	0.737949
$574$	−1.38013	−0.0576053
$575$	−22.5742	−0.941408
$576$	−7.15604	−0.298169
$577$	−34.2000	−1.42377	−0.711883	−	0.702298i	$-0.752157\pi$
$577$	−34.2000	−1.42377	−0.711883	+	0.702298i	$0.752157\pi$
$578$	−1.40911	−0.0586115
$579$	1.47701	0.0613825
$580$	−24.8840	−1.03325
$581$	7.56557	0.313873
$582$	−0.558274	−0.0231412
$583$	3.34750	0.138639
$584$	−2.22435	−0.0920444
$585$	−7.74621	−0.320266
$586$	4.23679	0.175020
$587$	8.17818	0.337550	0.168775	−	0.985655i	$-0.446019\pi$
$587$	8.17818	0.337550	0.168775	+	0.985655i	$0.446019\pi$
$588$	−12.1132	−0.499539
$589$	−49.3995	−2.03547
$590$	2.80508	0.115483
$591$	4.86491	0.200116
$592$	−33.2661	−1.36723
$593$	24.4614	1.00451	0.502255	−	0.864719i	$-0.332504\pi$
$593$	24.4614	1.00451	0.502255	+	0.864719i	$0.332504\pi$
$594$	0.188928	0.00775181
$595$	3.77850	0.154904
$596$	−6.65035	−0.272409
$597$	24.7175	1.01162
$598$	7.69387	0.314626
$599$	−19.4585	−0.795052	−0.397526	−	0.917591i	$-0.630131\pi$
$599$	−19.4585	−0.795052	−0.397526	+	0.917591i	$0.630131\pi$
$600$	−2.40006	−0.0979820
$601$	10.6191	0.433161	0.216581	−	0.976265i	$-0.430510\pi$
$601$	10.6191	0.433161	0.216581	+	0.976265i	$0.430510\pi$
$602$	−1.87665	−0.0764864
$603$	−14.0297	−0.571333
$604$	−0.129535	−0.00527069
$605$	−1.33997	−0.0544774
$606$	1.53638	0.0624114
$607$	−28.0148	−1.13709	−0.568543	−	0.822653i	$-0.692493\pi$
$607$	−28.0148	−1.13709	−0.568543	+	0.822653i	$0.692493\pi$
$608$	−14.1286	−0.572990
$609$	−8.63045	−0.349723
$610$	0.253157	0.0102500
$611$	58.0553	2.34867
$612$	−6.06762	−0.245269
$613$	−40.0262	−1.61664	−0.808321	−	0.588742i	$-0.799623\pi$
$613$	−40.0262	−1.61664	−0.808321	+	0.588742i	$0.799623\pi$
$614$	−3.72605	−0.150371
$615$	10.7226	0.432377
$616$	−0.683723	−0.0275480
$617$	−14.7964	−0.595681	−0.297841	−	0.954616i	$-0.596266\pi$
$617$	−14.7964	−0.595681	−0.297841	+	0.954616i	$0.596266\pi$
$618$	0.558022	0.0224469
$619$	−4.86331	−0.195473	−0.0977364	−	0.995212i	$-0.531160\pi$
$619$	−4.86331	−0.195473	−0.0977364	+	0.995212i	$0.531160\pi$
$620$	20.3701	0.818082
$621$	−7.04455	−0.282688
$622$	−5.22662	−0.209568
$623$	−15.2043	−0.609147
$624$	−21.8929	−0.876417
$625$	1.29118	0.0516472
$626$	−0.152402	−0.00609120
$627$	−6.38313	−0.254917
$628$	−14.1818	−0.565917
$629$	−27.1333	−1.08188
$630$	0.231104	0.00920740
$631$	−32.3971	−1.28971	−0.644853	−	0.764307i	$-0.723081\pi$
$631$	−32.3971	−1.28971	−0.644853	+	0.764307i	$0.723081\pi$
$632$	12.0850	0.480717
$633$	19.9377	0.792454
$634$	5.21070	0.206943
$635$	−14.9068	−0.591559
$636$	−6.57551	−0.260736
$637$	−35.6487	−1.41245
$638$	1.78613	0.0707135
$639$	−15.6388	−0.618662
$640$	7.74345	0.306087
$641$	34.3316	1.35602	0.678008	−	0.735054i	$-0.262843\pi$
$641$	34.3316	1.35602	0.678008	+	0.735054i	$0.262843\pi$
$642$	1.02738	0.0405475
$643$	−42.4036	−1.67224	−0.836118	−	0.548550i	$-0.815180\pi$
$643$	−42.4036	−1.67224	−0.836118	+	0.548550i	$0.815180\pi$
$644$	12.6322	0.497779
$645$	14.5802	0.574095
$646$	−3.72510	−0.146562
$647$	−27.9751	−1.09982	−0.549908	−	0.835225i	$-0.685337\pi$
$647$	−27.9751	−1.09982	−0.549908	+	0.835225i	$0.685337\pi$
$648$	−0.748968	−0.0294223
$649$	11.0804	0.434943
$650$	−3.49985	−0.137276
$651$	7.06490	0.276895
$652$	−4.34772	−0.170270
$653$	−25.1449	−0.983994	−0.491997	−	0.870597i	$-0.663733\pi$
$653$	−25.1449	−0.983994	−0.491997	+	0.870597i	$0.663733\pi$
$654$	2.45026	0.0958126
$655$	14.6973	0.574273
$656$	30.3050	1.18321
$657$	2.96989	0.115866
$658$	−1.73205	−0.0675223
$659$	−0.221591	−0.00863196	−0.00431598	−	0.999991i	$-0.501374\pi$
$659$	−0.221591	−0.00863196	−0.00431598	+	0.999991i	$0.501374\pi$
$660$	2.63211	0.102455
$661$	−1.23876	−0.0481822	−0.0240911	−	0.999710i	$-0.507669\pi$
$661$	−1.23876	−0.0481822	−0.0240911	+	0.999710i	$0.507669\pi$
$662$	0.237262	0.00922145
$663$	−17.8568	−0.693501
$664$	6.20709	0.240882
$665$	−7.80808	−0.302784
$666$	−1.65955	−0.0643062
$667$	−66.5994	−2.57874
$668$	8.48030	0.328113
$669$	−2.57011	−0.0993664
$670$	3.55172	0.137215
$671$	1.00000	0.0386046
$672$	2.02061	0.0779467
$673$	30.9749	1.19400	0.596998	−	0.802243i	$-0.296360\pi$
$673$	30.9749	1.19400	0.596998	+	0.802243i	$0.296360\pi$
$674$	1.75866	0.0677412
$675$	3.20449	0.123341
$676$	−40.1087	−1.54264
$677$	35.1446	1.35072	0.675359	−	0.737489i	$-0.263989\pi$
$677$	35.1446	1.35072	0.675359	+	0.737489i	$0.263989\pi$
$678$	0.766283	0.0294289
$679$	−2.69754	−0.103522
$680$	3.10003	0.118881
$681$	15.8132	0.605965
$682$	−1.46213	−0.0559878
$683$	−43.4525	−1.66266	−0.831332	−	0.555776i	$-0.812421\pi$
$683$	−43.4525	−1.66266	−0.831332	+	0.555776i	$0.812421\pi$
$684$	12.5384	0.479418
$685$	−12.6553	−0.483535
$686$	2.27085	0.0867013
$687$	7.47054	0.285019
$688$	41.2076	1.57103
$689$	−19.3515	−0.737234
$690$	1.78338	0.0678921
$691$	48.9612	1.86257	0.931286	−	0.364289i	$-0.118688\pi$
$691$	48.9612	1.86257	0.931286	+	0.364289i	$0.118688\pi$
$692$	−40.1435	−1.52603
$693$	0.912886	0.0346777
$694$	0.769649	0.0292155
$695$	7.66974	0.290930
$696$	−7.08076	−0.268396
$697$	24.7181	0.936263
$698$	−1.46446	−0.0554307
$699$	−3.38309	−0.127960
$700$	−5.74625	−0.217188
$701$	−25.7797	−0.973686	−0.486843	−	0.873489i	$-0.661852\pi$
$701$	−25.7797	−0.973686	−0.486843	+	0.873489i	$0.661852\pi$
$702$	−1.09217	−0.0412214
$703$	56.0696	2.11470
$704$	7.15604	0.269704
$705$	13.4568	0.506812
$706$	1.08292	0.0407561
$707$	7.42370	0.279197
$708$	−21.7652	−0.817988
$709$	−23.5130	−0.883048	−0.441524	−	0.897249i	$-0.645562\pi$
$709$	−23.5130	−0.883048	−0.441524	+	0.897249i	$0.645562\pi$
$710$	3.95908	0.148582
$711$	−16.1356	−0.605132
$712$	−12.4742	−0.467490
$713$	54.5184	2.04173
$714$	0.532748	0.0199376
$715$	7.74621	0.289692
$716$	−23.4967	−0.878112
$717$	−9.79975	−0.365978
$718$	−2.94791	−0.110015
$719$	−17.8431	−0.665435	−0.332717	−	0.943027i	$-0.607966\pi$
$719$	−17.8431	−0.665435	−0.332717	+	0.943027i	$0.607966\pi$
$720$	−5.07461	−0.189119
$721$	2.69632	0.100416
$722$	4.10810	0.152888
$723$	27.2706	1.01421
$724$	25.3479	0.942047
$725$	30.2953	1.12514
$726$	−0.188928	−0.00701177
$727$	−16.4832	−0.611328	−0.305664	−	0.952139i	$-0.598878\pi$
$727$	−16.4832	−0.611328	−0.305664	+	0.952139i	$0.598878\pi$
$728$	3.95253	0.146491
$729$	1.00000	0.0370370
$730$	−0.751849	−0.0278272
$731$	33.6108	1.24314
$732$	−1.96431	−0.0726028
$733$	−8.48088	−0.313248	−0.156624	−	0.987658i	$-0.550061\pi$
$733$	−8.48088	−0.313248	−0.156624	+	0.987658i	$0.550061\pi$
$734$	0.147974	0.00546181
$735$	−8.26309	−0.304789
$736$	15.5926	0.574751
$737$	14.0297	0.516790
$738$	1.51183	0.0556511
$739$	10.0368	0.369210	0.184605	−	0.982813i	$-0.440899\pi$
$739$	10.0368	0.369210	0.184605	+	0.982813i	$0.440899\pi$
$740$	−23.1205	−0.849926
$741$	36.9002	1.35556
$742$	0.577342	0.0211949
$743$	−13.0278	−0.477944	−0.238972	−	0.971026i	$-0.576810\pi$
$743$	−13.0278	−0.477944	−0.238972	+	0.971026i	$0.576810\pi$
$744$	5.79633	0.212504
$745$	−4.53659	−0.166208
$746$	−6.03167	−0.220835
$747$	−8.28753	−0.303225
$748$	6.06762	0.221854
$749$	4.96423	0.181389
$750$	−2.07703	−0.0758423
$751$	−0.704894	−0.0257219	−0.0128610	−	0.999917i	$-0.504094\pi$
$751$	−0.704894	−0.0257219	−0.0128610	+	0.999917i	$0.504094\pi$
$752$	38.0325	1.38690
$753$	−11.1707	−0.407082
$754$	−10.3254	−0.376030
$755$	−0.0883631	−0.00321586
$756$	−1.79319	−0.0652176
$757$	52.9627	1.92496	0.962482	−	0.271347i	$-0.0874691\pi$
$757$	52.9627	1.92496	0.962482	+	0.271347i	$0.0874691\pi$
$758$	0.778474	0.0282755
$759$	7.04455	0.255701
$760$	−6.40606	−0.232372
$761$	−42.7541	−1.54984	−0.774918	−	0.632061i	$-0.782209\pi$
$761$	−42.7541	−1.54984	−0.774918	+	0.632061i	$0.782209\pi$
$762$	−2.10178	−0.0761395
$763$	11.8395	0.428618
$764$	34.6987	1.25535
$765$	−4.13907	−0.149648
$766$	−1.47207	−0.0531882
$767$	−64.0544	−2.31287
$768$	−13.2203	−0.477047
$769$	34.3109	1.23728	0.618642	−	0.785673i	$-0.287683\pi$
$769$	34.3109	1.23728	0.618642	+	0.785673i	$0.287683\pi$
$770$	−0.231104	−0.00832840
$771$	4.34515	0.156487
$772$	2.90130	0.104420
$773$	9.34776	0.336216	0.168108	−	0.985769i	$-0.446234\pi$
$773$	9.34776	0.336216	0.168108	+	0.985769i	$0.446234\pi$
$774$	2.05573	0.0738916
$775$	−24.7998	−0.890835
$776$	−2.21317	−0.0794481
$777$	−8.01882	−0.287674
$778$	3.98803	0.142978
$779$	−51.0786	−1.83008
$780$	−15.2159	−0.544818
$781$	15.6388	0.559601
$782$	4.11110	0.147013
$783$	9.45402	0.337859
$784$	−23.3537	−0.834062
$785$	−9.67426	−0.345289
$786$	2.07224	0.0739145
$787$	21.6265	0.770901	0.385451	−	0.922728i	$-0.374046\pi$
$787$	21.6265	0.770901	0.385451	+	0.922728i	$0.374046\pi$
$788$	9.55618	0.340425
$789$	2.95382	0.105159
$790$	4.08484	0.145332
$791$	3.70263	0.131650
$792$	0.748968	0.0266134
$793$	−5.78089	−0.205286
$794$	3.24996	0.115337
$795$	−4.48553	−0.159086
$796$	48.5527	1.72091
$797$	13.4312	0.475756	0.237878	−	0.971295i	$-0.423548\pi$
$797$	13.4312	0.475756	0.237878	+	0.971295i	$0.423548\pi$
$798$	−1.10090	−0.0389713
$799$	31.0210	1.09744
$800$	−7.09290	−0.250772
$801$	16.6552	0.588481
$802$	−0.257658	−0.00909822
$803$	−2.96989	−0.104805
$804$	−27.5586	−0.971917
$805$	8.61716	0.303715
$806$	8.45241	0.297724
$807$	−14.5056	−0.510621
$808$	6.09070	0.214270
$809$	−31.2517	−1.09875	−0.549376	−	0.835575i	$-0.685134\pi$
$809$	−31.2517	−1.09875	−0.549376	+	0.835575i	$0.685134\pi$
$810$	−0.253157	−0.00889504
$811$	19.0933	0.670455	0.335228	−	0.942137i	$-0.391187\pi$
$811$	19.0933	0.670455	0.335228	+	0.942137i	$0.391187\pi$
$812$	−16.9528	−0.594928
$813$	0.612616	0.0214854
$814$	1.65955	0.0581671
$815$	−2.96583	−0.103889
$816$	−11.6981	−0.409517
$817$	−69.4549	−2.42992
$818$	−1.21117	−0.0423476
$819$	−5.27730	−0.184404
$820$	21.0625	0.735533
$821$	34.7513	1.21283	0.606415	−	0.795148i	$-0.292607\pi$
$821$	34.7513	1.21283	0.606415	+	0.795148i	$0.292607\pi$
$822$	−1.78433	−0.0622357
$823$	−37.2319	−1.29782	−0.648912	−	0.760864i	$-0.724776\pi$
$823$	−37.2319	−1.29782	−0.648912	+	0.760864i	$0.724776\pi$
$824$	2.21217	0.0770646
$825$	−3.20449	−0.111566
$826$	1.91103	0.0664932
$827$	40.7001	1.41528	0.707641	−	0.706573i	$-0.249760\pi$
$827$	40.7001	1.41528	0.707641	+	0.706573i	$0.249760\pi$
$828$	−13.8377	−0.480892
$829$	27.8172	0.966130	0.483065	−	0.875585i	$-0.339524\pi$
$829$	27.8172	0.966130	0.483065	+	0.875585i	$0.339524\pi$
$830$	2.09805	0.0728243
$831$	8.29532	0.287761
$832$	−41.3683	−1.43419
$833$	−19.0483	−0.659986
$834$	1.08139	0.0374455
$835$	5.78491	0.200195
$836$	−12.5384	−0.433650
$837$	−7.73908	−0.267502
$838$	1.92222	0.0664021
$839$	33.1766	1.14538	0.572691	−	0.819771i	$-0.305899\pi$
$839$	33.1766	1.14538	0.572691	+	0.819771i	$0.305899\pi$
$840$	0.916166	0.0316107
$841$	60.3786	2.08202
$842$	−6.74621	−0.232490
$843$	−27.5450	−0.948700
$844$	39.1638	1.34807
$845$	−27.3604	−0.941228
$846$	1.89733	0.0652316
$847$	−0.912886	−0.0313671
$848$	−12.6773	−0.435342
$849$	17.0530	0.585256
$850$	−1.87010	−0.0641437
$851$	−61.8795	−2.12120
$852$	−30.7194	−1.05243
$853$	−33.1586	−1.13533	−0.567665	−	0.823260i	$-0.692153\pi$
$853$	−33.1586	−1.13533	−0.567665	+	0.823260i	$0.692153\pi$
$854$	0.172470	0.00590179
$855$	8.55318	0.292513
$856$	4.07285	0.139207
$857$	−8.51148	−0.290746	−0.145373	−	0.989377i	$-0.546438\pi$
$857$	−8.51148	−0.290746	−0.145373	+	0.989377i	$0.546438\pi$
$858$	1.09217	0.0372862
$859$	26.5055	0.904355	0.452178	−	0.891928i	$-0.350647\pi$
$859$	26.5055	0.904355	0.452178	+	0.891928i	$0.350647\pi$
$860$	28.6400	0.976616
$861$	7.30504	0.248955
$862$	−2.66146	−0.0906496
$863$	20.9587	0.713444	0.356722	−	0.934211i	$-0.383894\pi$
$863$	20.9587	0.713444	0.356722	+	0.934211i	$0.383894\pi$
$864$	−2.21343	−0.0753023
$865$	−27.3842	−0.931091
$866$	0.813105	0.0276304
$867$	7.45848	0.253303
$868$	13.8776	0.471038
$869$	16.1356	0.547363
$870$	−2.39335	−0.0811423
$871$	−81.1042	−2.74811
$872$	9.71357	0.328943
$873$	2.95496	0.100010
$874$	−8.49538	−0.287361
$875$	−10.0360	−0.339280
$876$	5.83377	0.197105
$877$	51.1399	1.72687	0.863435	−	0.504460i	$-0.168308\pi$
$877$	51.1399	1.72687	0.863435	+	0.504460i	$0.168308\pi$
$878$	0.0597869	0.00201771
$879$	−22.4254	−0.756391
$880$	5.07461	0.171065
$881$	−44.4489	−1.49752	−0.748760	−	0.662841i	$-0.769350\pi$
$881$	−44.4489	−1.49752	−0.748760	+	0.662841i	$0.769350\pi$
$882$	−1.16505	−0.0392293
$883$	−34.7181	−1.16836	−0.584179	−	0.811625i	$-0.698584\pi$
$883$	−34.7181	−1.16836	−0.584179	+	0.811625i	$0.698584\pi$
$884$	−35.0762	−1.17974
$885$	−14.8473	−0.499088
$886$	−0.543243	−0.0182506
$887$	18.4050	0.617980	0.308990	−	0.951065i	$-0.400009\pi$
$887$	18.4050	0.617980	0.308990	+	0.951065i	$0.400009\pi$
$888$	−6.57896	−0.220775
$889$	−10.1557	−0.340610
$890$	−4.21638	−0.141333
$891$	−1.00000	−0.0335013
$892$	−5.04849	−0.169036
$893$	−64.1033	−2.14514
$894$	−0.639634	−0.0213925
$895$	−16.0284	−0.535772
$896$	5.27542	0.176239
$897$	−40.7238	−1.35973
$898$	−0.0965439	−0.00322171
$899$	−73.1655	−2.44021
$900$	6.29460	0.209820
$901$	−10.3402	−0.344482
$902$	−1.51183	−0.0503383
$903$	9.93313	0.330554
$904$	3.03778	0.101035
$905$	17.2913	0.574781
$906$	−0.0124587	−0.000413913 0
$907$	23.9890	0.796541	0.398271	−	0.917268i	$-0.369611\pi$
$907$	23.9890	0.796541	0.398271	+	0.917268i	$0.369611\pi$
$908$	31.0620	1.03083
$909$	−8.13212	−0.269725
$910$	1.33599	0.0442875
$911$	44.6361	1.47886	0.739430	−	0.673234i	$-0.235095\pi$
$911$	44.6361	1.47886	0.739430	+	0.673234i	$0.235095\pi$
$912$	24.1736	0.800468
$913$	8.28753	0.274277
$914$	−3.71821	−0.122987
$915$	−1.33997	−0.0442980
$916$	14.6744	0.484857
$917$	10.0129	0.330656
$918$	−0.583586	−0.0192612
$919$	−2.84110	−0.0937193	−0.0468596	−	0.998901i	$-0.514921\pi$
$919$	−2.84110	−0.0937193	−0.0468596	+	0.998901i	$0.514921\pi$
$920$	7.06986	0.233086
$921$	19.7220	0.649864
$922$	−2.58142	−0.0850146
$923$	−90.4064	−2.97576
$924$	1.79319	0.0589916
$925$	28.1483	0.925511
$926$	−4.43364	−0.145698
$927$	−2.95362	−0.0970097
$928$	−20.9258	−0.686923
$929$	−26.0639	−0.855128	−0.427564	−	0.903985i	$-0.640628\pi$
$929$	−26.0639	−0.855128	−0.427564	+	0.903985i	$0.640628\pi$
$930$	1.95921	0.0642449
$931$	39.3624	1.29005
$932$	−6.64543	−0.217678
$933$	27.6646	0.905698
$934$	−6.94363	−0.227203
$935$	4.13907	0.135362
$936$	−4.32971	−0.141521
$937$	10.0548	0.328477	0.164238	−	0.986421i	$-0.447483\pi$
$937$	10.0548	0.328477	0.164238	+	0.986421i	$0.447483\pi$
$938$	2.41970	0.0790059
$939$	0.806666	0.0263246
$940$	26.4332	0.862157
$941$	27.9026	0.909597	0.454799	−	0.890594i	$-0.349711\pi$
$941$	27.9026	0.909597	0.454799	+	0.890594i	$0.349711\pi$
$942$	−1.36402	−0.0444421
$943$	56.3714	1.83571
$944$	−41.9626	−1.36577
$945$	−1.22324	−0.0397919
$946$	−2.05573	−0.0668375
$947$	4.44494	0.144441	0.0722206	−	0.997389i	$-0.476991\pi$
$947$	4.44494	0.144441	0.0722206	+	0.997389i	$0.476991\pi$
$948$	−31.6953	−1.02941
$949$	17.1686	0.557317
$950$	3.86445	0.125379
$951$	−27.5804	−0.894354
$952$	2.11198	0.0684495
$953$	−16.7457	−0.542446	−0.271223	−	0.962517i	$-0.587428\pi$
$953$	−16.7457	−0.542446	−0.271223	+	0.962517i	$0.587428\pi$
$954$	−0.632435	−0.0204759
$955$	23.6700	0.765943
$956$	−19.2497	−0.622580
$957$	−9.45402	−0.305605
$958$	1.60314	0.0517950
$959$	−8.62176	−0.278411
$960$	−9.58887	−0.309479
$961$	28.8934	0.932046
$962$	−9.59367	−0.309312
$963$	−5.43795	−0.175236
$964$	53.5679	1.72531
$965$	1.97915	0.0637110
$966$	1.21497	0.0390911
$967$	9.55119	0.307145	0.153573	−	0.988137i	$-0.450922\pi$
$967$	9.55119	0.307145	0.153573	+	0.988137i	$0.450922\pi$
$968$	−0.748968	−0.0240728
$969$	19.7171	0.633403
$970$	−0.748069	−0.0240190
$971$	32.6303	1.04716	0.523578	−	0.851978i	$-0.324597\pi$
$971$	32.6303	1.04716	0.523578	+	0.851978i	$0.324597\pi$
$972$	1.96431	0.0630052
$973$	5.22521	0.167512
$974$	−0.0939877	−0.00301156
$975$	18.5248	0.593269
$976$	−3.78711	−0.121222
$977$	−36.9074	−1.18077	−0.590386	−	0.807121i	$-0.701025\pi$
$977$	−36.9074	−1.18077	−0.590386	+	0.807121i	$0.701025\pi$
$978$	−0.418166	−0.0133715
$979$	−16.6552	−0.532302
$980$	−16.2312	−0.518488
$981$	−12.9693	−0.414077
$982$	2.45122	0.0782215
$983$	−20.4490	−0.652223	−0.326111	−	0.945331i	$-0.605738\pi$
$983$	−20.4490	−0.652223	−0.326111	+	0.945331i	$0.605738\pi$
$984$	5.99334	0.191061
$985$	6.51883	0.207707
$986$	−5.51724	−0.175705
$987$	9.16777	0.291813
$988$	72.4832	2.30600
$989$	76.6519	2.43739
$990$	0.253157	0.00804587
$991$	−46.1894	−1.46725	−0.733627	−	0.679552i	$-0.762174\pi$
$991$	−46.1894	−1.46725	−0.733627	+	0.679552i	$0.762174\pi$
$992$	17.1299	0.543875
$993$	−1.25583	−0.0398526
$994$	2.69722	0.0855507
$995$	33.1206	1.04999
$996$	−16.2792	−0.515827
$997$	−35.4822	−1.12373	−0.561866	−	0.827228i	$-0.689916\pi$
$997$	−35.4822	−1.12373	−0.561866	+	0.827228i	$0.689916\pi$
$998$	3.66739	0.116089
$999$	8.78403	0.277914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.d.1.7	✓	12
3.2	odd	2		6039.2.a.e.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.d.1.7	✓	12	1.1	even	1	trivial
6039.2.a.e.1.6		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+0.188928 q^{2} -1.00000 q^{3} -1.96431 q^{4} -1.33997 q^{5} -0.188928 q^{6} -0.912886 q^{7} -0.748968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.188928 q^{2} -1.00000 q^{3} -1.96431 q^{4} -1.33997 q^{5} -0.188928 q^{6} -0.912886 q^{7} -0.748968 q^{8} +1.00000 q^{9} -0.253157 q^{10} -1.00000 q^{11} +1.96431 q^{12} +5.78089 q^{13} -0.172470 q^{14} +1.33997 q^{15} +3.78711 q^{16} +3.08894 q^{17} +0.188928 q^{18} -6.38313 q^{19} +2.63211 q^{20} +0.912886 q^{21} -0.188928 q^{22} +7.04455 q^{23} +0.748968 q^{24} -3.20449 q^{25} +1.09217 q^{26} -1.00000 q^{27} +1.79319 q^{28} -9.45402 q^{29} +0.253157 q^{30} +7.73908 q^{31} +2.21343 q^{32} +1.00000 q^{33} +0.583586 q^{34} +1.22324 q^{35} -1.96431 q^{36} -8.78403 q^{37} -1.20595 q^{38} -5.78089 q^{39} +1.00359 q^{40} +8.00213 q^{41} +0.172470 q^{42} +10.8810 q^{43} +1.96431 q^{44} -1.33997 q^{45} +1.33091 q^{46} +10.0426 q^{47} -3.78711 q^{48} -6.16664 q^{49} -0.605417 q^{50} -3.08894 q^{51} -11.3554 q^{52} -3.34750 q^{53} -0.188928 q^{54} +1.33997 q^{55} +0.683723 q^{56} +6.38313 q^{57} -1.78613 q^{58} -11.0804 q^{59} -2.63211 q^{60} -1.00000 q^{61} +1.46213 q^{62} -0.912886 q^{63} -7.15604 q^{64} -7.74621 q^{65} +0.188928 q^{66} -14.0297 q^{67} -6.06762 q^{68} -7.04455 q^{69} +0.231104 q^{70} -15.6388 q^{71} -0.748968 q^{72} +2.96989 q^{73} -1.65955 q^{74} +3.20449 q^{75} +12.5384 q^{76} +0.912886 q^{77} -1.09217 q^{78} -16.1356 q^{79} -5.07461 q^{80} +1.00000 q^{81} +1.51183 q^{82} -8.28753 q^{83} -1.79319 q^{84} -4.13907 q^{85} +2.05573 q^{86} +9.45402 q^{87} +0.748968 q^{88} +16.6552 q^{89} -0.253157 q^{90} -5.27730 q^{91} -13.8377 q^{92} -7.73908 q^{93} +1.89733 q^{94} +8.55318 q^{95} -2.21343 q^{96} +2.95496 q^{97} -1.16505 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * q^98 - 12 * q^99

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