LMFDB - Embedded newform 671.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2661761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 3x^3 + 9*x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.36588$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54773 q^{2} -2.36588 q^{3} +0.395474 q^{4} +0.422675 q^{5} -3.66175 q^{6} +1.36588 q^{7} -2.48338 q^{8} +2.59739 q^{9} +O(q^{10})$	\(q+1.54773 q^{2} -2.36588 q^{3} +0.395474 q^{4} +0.422675 q^{5} -3.66175 q^{6} +1.36588 q^{7} -2.48338 q^{8} +2.59739 q^{9} +0.654188 q^{10} -1.00000 q^{11} -0.935644 q^{12} +0.691342 q^{13} +2.11402 q^{14} -1.00000 q^{15} -4.63455 q^{16} -6.98116 q^{17} +4.02007 q^{18} -2.82571 q^{19} +0.167157 q^{20} -3.23151 q^{21} -1.54773 q^{22} -1.09156 q^{23} +5.87537 q^{24} -4.82135 q^{25} +1.07001 q^{26} +0.952518 q^{27} +0.540170 q^{28} -0.882505 q^{29} -1.54773 q^{30} -2.77168 q^{31} -2.20629 q^{32} +2.36588 q^{33} -10.8050 q^{34} +0.577325 q^{35} +1.02720 q^{36} -8.28206 q^{37} -4.37344 q^{38} -1.63563 q^{39} -1.04966 q^{40} -2.27239 q^{41} -5.00152 q^{42} -0.00667303 q^{43} -0.395474 q^{44} +1.09785 q^{45} -1.68944 q^{46} +5.49887 q^{47} +10.9648 q^{48} -5.13437 q^{49} -7.46215 q^{50} +16.5166 q^{51} +0.273408 q^{52} +5.40346 q^{53} +1.47424 q^{54} -0.422675 q^{55} -3.39200 q^{56} +6.68530 q^{57} -1.36588 q^{58} +4.46026 q^{59} -0.395474 q^{60} -1.00000 q^{61} -4.28982 q^{62} +3.54773 q^{63} +5.85436 q^{64} +0.292213 q^{65} +3.66175 q^{66} -8.41643 q^{67} -2.76087 q^{68} +2.58249 q^{69} +0.893544 q^{70} +2.07775 q^{71} -6.45031 q^{72} +9.89906 q^{73} -12.8184 q^{74} +11.4067 q^{75} -1.11749 q^{76} -1.36588 q^{77} -2.53152 q^{78} +9.51894 q^{79} -1.95891 q^{80} -10.0457 q^{81} -3.51705 q^{82} +15.5956 q^{83} -1.27798 q^{84} -2.95077 q^{85} -0.0103281 q^{86} +2.08790 q^{87} +2.48338 q^{88} +1.19458 q^{89} +1.69918 q^{90} +0.944292 q^{91} -0.431682 q^{92} +6.55747 q^{93} +8.51078 q^{94} -1.19436 q^{95} +5.21981 q^{96} -10.4094 q^{97} -7.94663 q^{98} -2.59739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	1.54773	1.09441	0.547206	−	0.836998i	$-0.315691\pi$
$2$	1.54773	1.09441	0.547206	+	0.836998i	$0.315691\pi$
$3$	−2.36588	−1.36594	−0.682971	−	0.730445i	$-0.739313\pi$
$3$	−2.36588	−1.36594	−0.682971	+	0.730445i	$0.739313\pi$
$4$	0.395474	0.197737
$5$	0.422675	0.189026	0.0945131	−	0.995524i	$-0.469871\pi$
$5$	0.422675	0.189026	0.0945131	+	0.995524i	$0.469871\pi$
$6$	−3.66175	−1.49490
$7$	1.36588	0.516255	0.258127	−	0.966111i	$-0.416895\pi$
$7$	1.36588	0.516255	0.258127	+	0.966111i	$0.416895\pi$
$8$	−2.48338	−0.878006
$9$	2.59739	0.865798
$10$	0.654188	0.206873
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.935644	−0.270097
$13$	0.691342	0.191744	0.0958719	−	0.995394i	$-0.469436\pi$
$13$	0.691342	0.191744	0.0958719	+	0.995394i	$0.469436\pi$
$14$	2.11402	0.564995
$15$	−1.00000	−0.258199
$16$	−4.63455	−1.15864
$17$	−6.98116	−1.69318	−0.846591	−	0.532245i	$-0.821349\pi$
$17$	−6.98116	−1.69318	−0.846591	+	0.532245i	$0.821349\pi$
$18$	4.02007	0.947539
$19$	−2.82571	−0.648263	−0.324131	−	0.946012i	$-0.605072\pi$
$19$	−2.82571	−0.648263	−0.324131	+	0.946012i	$0.605072\pi$
$20$	0.167157	0.0373775
$21$	−3.23151	−0.705174
$22$	−1.54773	−0.329978
$23$	−1.09156	−0.227605	−0.113803	−	0.993503i	$-0.536303\pi$
$23$	−1.09156	−0.227605	−0.113803	+	0.993503i	$0.536303\pi$
$24$	5.87537	1.19931
$25$	−4.82135	−0.964269
$26$	1.07001	0.209847
$27$	0.952518	0.183312
$28$	0.540170	0.102083
$29$	−0.882505	−0.163877	−0.0819385	−	0.996637i	$-0.526111\pi$
$29$	−0.882505	−0.163877	−0.0819385	+	0.996637i	$0.526111\pi$
$30$	−1.54773	−0.282576
$31$	−2.77168	−0.497809	−0.248905	−	0.968528i	$-0.580071\pi$
$31$	−2.77168	−0.497809	−0.248905	+	0.968528i	$0.580071\pi$
$32$	−2.20629	−0.390020
$33$	2.36588	0.411847
$34$	−10.8050	−1.85304
$35$	0.577325	0.0975857
$36$	1.02720	0.171200
$37$	−8.28206	−1.36156	−0.680781	−	0.732487i	$-0.738360\pi$
$37$	−8.28206	−1.36156	−0.680781	+	0.732487i	$0.738360\pi$
$38$	−4.37344	−0.709466
$39$	−1.63563	−0.261911
$40$	−1.04966	−0.165966
$41$	−2.27239	−0.354888	−0.177444	−	0.984131i	$-0.556783\pi$
$41$	−2.27239	−0.354888	−0.177444	+	0.984131i	$0.556783\pi$
$42$	−5.00152	−0.771751
$43$	−0.00667303	−0.00101763	−0.000508814	−	1.00000i	$-0.500162\pi$
$43$	−0.00667303	−0.00101763	−0.000508814		1.00000i	$0.500162\pi$
$44$	−0.395474	−0.0596199
$45$	1.09785	0.163659
$46$	−1.68944	−0.249094
$47$	5.49887	0.802093	0.401047	−	0.916058i	$-0.368647\pi$
$47$	5.49887	0.802093	0.401047	+	0.916058i	$0.368647\pi$
$48$	10.9648	1.58263
$49$	−5.13437	−0.733481
$50$	−7.46215	−1.05531
$51$	16.5166	2.31279
$52$	0.273408	0.0379149
$53$	5.40346	0.742223	0.371111	−	0.928588i	$-0.378977\pi$
$53$	5.40346	0.742223	0.371111	+	0.928588i	$0.378977\pi$
$54$	1.47424	0.200619
$55$	−0.422675	−0.0569936
$56$	−3.39200	−0.453275
$57$	6.68530	0.885489
$58$	−1.36588	−0.179349
$59$	4.46026	0.580676	0.290338	−	0.956924i	$-0.406232\pi$
$59$	4.46026	0.580676	0.290338	+	0.956924i	$0.406232\pi$
$60$	−0.395474	−0.0510555
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.28982	−0.544808
$63$	3.54773	0.446972
$64$	5.85436	0.731795
$65$	0.292213	0.0362446
$66$	3.66175	0.450730
$67$	−8.41643	−1.02823	−0.514115	−	0.857721i	$-0.671880\pi$
$67$	−8.41643	−1.02823	−0.514115	+	0.857721i	$0.671880\pi$
$68$	−2.76087	−0.334804
$69$	2.58249	0.310896
$70$	0.893544	0.106799
$71$	2.07775	0.246584	0.123292	−	0.992370i	$-0.460655\pi$
$71$	2.07775	0.246584	0.123292	+	0.992370i	$0.460655\pi$
$72$	−6.45031	−0.760176
$73$	9.89906	1.15860	0.579299	−	0.815115i	$-0.303327\pi$
$73$	9.89906	1.15860	0.579299	+	0.815115i	$0.303327\pi$
$74$	−12.8184	−1.49011
$75$	11.4067	1.31714
$76$	−1.11749	−0.128185
$77$	−1.36588	−0.155657
$78$	−2.53152	−0.286639
$79$	9.51894	1.07096	0.535482	−	0.844546i	$-0.320130\pi$
$79$	9.51894	1.07096	0.535482	+	0.844546i	$0.320130\pi$
$80$	−1.95891	−0.219013
$81$	−10.0457	−1.11619
$82$	−3.51705	−0.388394
$83$	15.5956	1.71184	0.855922	−	0.517105i	$-0.172990\pi$
$83$	15.5956	1.71184	0.855922	+	0.517105i	$0.172990\pi$
$84$	−1.27798	−0.139439
$85$	−2.95077	−0.320056
$86$	−0.0103281	−0.00111370
$87$	2.08790	0.223847
$88$	2.48338	0.264729
$89$	1.19458	0.126625	0.0633127	−	0.997994i	$-0.479833\pi$
$89$	1.19458	0.126625	0.0633127	+	0.997994i	$0.479833\pi$
$90$	1.69918	0.179110
$91$	0.944292	0.0989887
$92$	−0.431682	−0.0450060
$93$	6.55747	0.679978
$94$	8.51078	0.877820
$95$	−1.19436	−0.122539
$96$	5.21981	0.532745
$97$	−10.4094	−1.05692	−0.528459	−	0.848959i	$-0.677230\pi$
$97$	−10.4094	−1.05692	−0.528459	+	0.848959i	$0.677230\pi$
$98$	−7.94663	−0.802730
$99$	−2.59739	−0.261048
$100$	−1.90672	−0.190672
$101$	−4.87420	−0.485001	−0.242501	−	0.970151i	$-0.577968\pi$
$101$	−4.87420	−0.485001	−0.242501	+	0.970151i	$0.577968\pi$
$102$	25.5633	2.53114
$103$	5.03129	0.495747	0.247874	−	0.968792i	$-0.420268\pi$
$103$	5.03129	0.495747	0.247874	+	0.968792i	$0.420268\pi$
$104$	−1.71686	−0.168352
$105$	−1.36588	−0.133296
$106$	8.36311	0.812298
$107$	−15.5222	−1.50059	−0.750294	−	0.661105i	$-0.770088\pi$
$107$	−15.5222	−1.50059	−0.750294	+	0.661105i	$0.770088\pi$
$108$	0.376696	0.0362476
$109$	−13.5177	−1.29476	−0.647379	−	0.762168i	$-0.724135\pi$
$109$	−13.5177	−1.29476	−0.647379	+	0.762168i	$0.724135\pi$
$110$	−0.654188	−0.0623744
$111$	19.5944	1.85982
$112$	−6.33024	−0.598152
$113$	17.6781	1.66302	0.831508	−	0.555512i	$-0.187478\pi$
$113$	17.6781	1.66302	0.831508	+	0.555512i	$0.187478\pi$
$114$	10.3470	0.969090
$115$	−0.461375	−0.0430234
$116$	−0.349008	−0.0324046
$117$	1.79569	0.166011
$118$	6.90329	0.635499
$119$	−9.53544	−0.874113
$120$	2.48338	0.226700
$121$	1.00000	0.0909091
$122$	−1.54773	−0.140125
$123$	5.37621	0.484756
$124$	−1.09613	−0.0984352
$125$	−4.15124	−0.371298
$126$	5.49094	0.489172
$127$	0.946356	0.0839755	0.0419878	−	0.999118i	$-0.486631\pi$
$127$	0.946356	0.0839755	0.0419878	+	0.999118i	$0.486631\pi$
$128$	13.4735	1.19090
$129$	0.0157876	0.00139002
$130$	0.452268	0.0396665
$131$	3.27232	0.285904	0.142952	−	0.989730i	$-0.454341\pi$
$131$	3.27232	0.285904	0.142952	+	0.989730i	$0.454341\pi$
$132$	0.935644	0.0814374
$133$	−3.85959	−0.334669
$134$	−13.0264	−1.12531
$135$	0.402606	0.0346508
$136$	17.3369	1.48662
$137$	−7.60856	−0.650043	−0.325021	−	0.945707i	$-0.605372\pi$
$137$	−7.60856	−0.650043	−0.325021	+	0.945707i	$0.605372\pi$
$138$	3.99701	0.340248
$139$	6.01301	0.510017	0.255008	−	0.966939i	$-0.417922\pi$
$139$	6.01301	0.510017	0.255008	+	0.966939i	$0.417922\pi$
$140$	0.228317	0.0192963
$141$	−13.0097	−1.09561
$142$	3.21580	0.269864
$143$	−0.691342	−0.0578130
$144$	−12.0377	−1.00315
$145$	−0.373013	−0.0309771
$146$	15.3211	1.26798
$147$	12.1473	1.00189
$148$	−3.27534	−0.269231
$149$	5.00949	0.410393	0.205197	−	0.978721i	$-0.434217\pi$
$149$	5.00949	0.410393	0.205197	+	0.978721i	$0.434217\pi$
$150$	17.6546	1.44149
$151$	−16.9389	−1.37846	−0.689232	−	0.724540i	$-0.742052\pi$
$151$	−16.9389	−1.37846	−0.689232	+	0.724540i	$0.742052\pi$
$152$	7.01730	0.569178
$153$	−18.1328	−1.46595
$154$	−2.11402	−0.170352
$155$	−1.17152	−0.0940990
$156$	−0.646851	−0.0517895
$157$	3.73938	0.298435	0.149218	−	0.988804i	$-0.452325\pi$
$157$	3.73938	0.298435	0.149218	+	0.988804i	$0.452325\pi$
$158$	14.7328	1.17208
$159$	−12.7840	−1.01383
$160$	−0.932543	−0.0737240
$161$	−1.49094	−0.117502
$162$	−15.5481	−1.22157
$163$	13.7402	1.07621	0.538107	−	0.842876i	$-0.319140\pi$
$163$	13.7402	1.07621	0.538107	+	0.842876i	$0.319140\pi$
$164$	−0.898672	−0.0701745
$165$	1.00000	0.0778499
$166$	24.1379	1.87346
$167$	7.29435	0.564454	0.282227	−	0.959348i	$-0.408927\pi$
$167$	7.29435	0.564454	0.282227	+	0.959348i	$0.408927\pi$
$168$	8.02506	0.619147
$169$	−12.5220	−0.963234
$170$	−4.56700	−0.350273
$171$	−7.33948	−0.561264
$172$	−0.00263901	−0.000201223 0
$173$	−19.1556	−1.45637	−0.728185	−	0.685380i	$-0.759636\pi$
$173$	−19.1556	−1.45637	−0.728185	+	0.685380i	$0.759636\pi$
$174$	3.23151	0.244980
$175$	−6.58539	−0.497808
$176$	4.63455	0.349342
$177$	−10.5524	−0.793170
$178$	1.84889	0.138580
$179$	2.77095	0.207110	0.103555	−	0.994624i	$-0.466978\pi$
$179$	2.77095	0.207110	0.103555	+	0.994624i	$0.466978\pi$
$180$	0.434173	0.0323613
$181$	12.3659	0.919148	0.459574	−	0.888139i	$-0.348002\pi$
$181$	12.3659	0.919148	0.459574	+	0.888139i	$0.348002\pi$
$182$	1.46151	0.108334
$183$	2.36588	0.174891
$184$	2.71075	0.199839
$185$	−3.50063	−0.257371
$186$	10.1492	0.744176
$187$	6.98116	0.510513
$188$	2.17466	0.158603
$189$	1.30103	0.0946357
$190$	−1.84855	−0.134108
$191$	−14.3068	−1.03521	−0.517603	−	0.855621i	$-0.673175\pi$
$191$	−14.3068	−1.03521	−0.517603	+	0.855621i	$0.673175\pi$
$192$	−13.8507	−0.999589
$193$	−9.81514	−0.706509	−0.353255	−	0.935527i	$-0.614925\pi$
$193$	−9.81514	−0.706509	−0.353255	+	0.935527i	$0.614925\pi$
$194$	−16.1110	−1.15670
$195$	−0.691342	−0.0495081
$196$	−2.03051	−0.145036
$197$	−2.26769	−0.161566	−0.0807832	−	0.996732i	$-0.525742\pi$
$197$	−2.26769	−0.161566	−0.0807832	+	0.996732i	$0.525742\pi$
$198$	−4.02007	−0.285694
$199$	−19.1563	−1.35795	−0.678977	−	0.734160i	$-0.737576\pi$
$199$	−19.1563	−1.35795	−0.678977	+	0.734160i	$0.737576\pi$
$200$	11.9732	0.846634
$201$	19.9123	1.40450
$202$	−7.54396	−0.530791
$203$	−1.20540	−0.0846023
$204$	6.53189	0.457324
$205$	−0.960484	−0.0670831
$206$	7.78708	0.542552
$207$	−2.83520	−0.197060
$208$	−3.20406	−0.222162
$209$	2.82571	0.195459
$210$	−2.11402	−0.145881
$211$	19.8390	1.36577	0.682885	−	0.730526i	$-0.260725\pi$
$211$	19.8390	1.36577	0.682885	+	0.730526i	$0.260725\pi$
$212$	2.13693	0.146765
$213$	−4.91572	−0.336819
$214$	−24.0242	−1.64226
$215$	−0.00282053	−0.000192358 0
$216$	−2.36546	−0.160949
$217$	−3.78579	−0.256996
$218$	−20.9217	−1.41700
$219$	−23.4200	−1.58258
$220$	−0.167157	−0.0112697
$221$	−4.82638	−0.324657
$222$	30.3268	2.03540
$223$	−18.7507	−1.25564	−0.627820	−	0.778358i	$-0.716053\pi$
$223$	−18.7507	−1.25564	−0.627820	+	0.778358i	$0.716053\pi$
$224$	−3.01352	−0.201350
$225$	−12.5229	−0.834862
$226$	27.3610	1.82002
$227$	6.72472	0.446335	0.223168	−	0.974780i	$-0.428360\pi$
$227$	6.72472	0.446335	0.223168	+	0.974780i	$0.428360\pi$
$228$	2.64386	0.175094
$229$	0.837138	0.0553196	0.0276598	−	0.999617i	$-0.491194\pi$
$229$	0.837138	0.0553196	0.0276598	+	0.999617i	$0.491194\pi$
$230$	−0.714084	−0.0470853
$231$	3.23151	0.212618
$232$	2.19159	0.143885
$233$	−14.1523	−0.927150	−0.463575	−	0.886058i	$-0.653434\pi$
$233$	−14.1523	−0.927150	−0.463575	+	0.886058i	$0.653434\pi$
$234$	2.77924	0.181685
$235$	2.32424	0.151617
$236$	1.76392	0.114821
$237$	−22.5207	−1.46288
$238$	−14.7583	−0.956639
$239$	−17.6284	−1.14029	−0.570143	−	0.821545i	$-0.693112\pi$
$239$	−17.6284	−1.14029	−0.570143	+	0.821545i	$0.693112\pi$
$240$	4.63455	0.299159
$241$	−25.8972	−1.66818	−0.834092	−	0.551625i	$-0.814008\pi$
$241$	−25.8972	−1.66818	−0.834092	+	0.551625i	$0.814008\pi$
$242$	1.54773	0.0994920
$243$	20.9094	1.34134
$244$	−0.395474	−0.0253176
$245$	−2.17017	−0.138647
$246$	8.32093	0.530523
$247$	−1.95353	−0.124300
$248$	6.88313	0.437079
$249$	−36.8974	−2.33828
$250$	−6.42501	−0.406353
$251$	−8.19954	−0.517551	−0.258775	−	0.965938i	$-0.583319\pi$
$251$	−8.19954	−0.517551	−0.258775	+	0.965938i	$0.583319\pi$
$252$	1.40304	0.0883829
$253$	1.09156	0.0686256
$254$	1.46471	0.0919038
$255$	6.98116	0.437178
$256$	9.14472	0.571545
$257$	18.5352	1.15619	0.578096	−	0.815969i	$-0.303796\pi$
$257$	18.5352	1.15619	0.578096	+	0.815969i	$0.303796\pi$
$258$	0.0244350	0.00152126
$259$	−11.3123	−0.702913
$260$	0.115563	0.00716690
$261$	−2.29221	−0.141884
$262$	5.06468	0.312897
$263$	−0.204989	−0.0126401	−0.00632007	−	0.999980i	$-0.502012\pi$
$263$	−0.204989	−0.0126401	−0.00632007	+	0.999980i	$0.502012\pi$
$264$	−5.87537	−0.361604
$265$	2.28391	0.140300
$266$	−5.97360	−0.366265
$267$	−2.82624	−0.172963
$268$	−3.32848	−0.203319
$269$	14.5941	0.889819	0.444909	−	0.895576i	$-0.353236\pi$
$269$	14.5941	0.889819	0.444909	+	0.895576i	$0.353236\pi$
$270$	0.623126	0.0379222
$271$	−0.982037	−0.0596545	−0.0298273	−	0.999555i	$-0.509496\pi$
$271$	−0.982037	−0.0596545	−0.0298273	+	0.999555i	$0.509496\pi$
$272$	32.3545	1.96178
$273$	−2.23408	−0.135213
$274$	−11.7760	−0.711414
$275$	4.82135	0.290738
$276$	1.02131	0.0614756
$277$	−18.2313	−1.09541	−0.547707	−	0.836670i	$-0.684499\pi$
$277$	−18.2313	−1.09541	−0.547707	+	0.836670i	$0.684499\pi$
$278$	9.30652	0.558168
$279$	−7.19915	−0.431002
$280$	−1.43371	−0.0856808
$281$	−15.9521	−0.951623	−0.475812	−	0.879547i	$-0.657846\pi$
$281$	−15.9521	−0.951623	−0.475812	+	0.879547i	$0.657846\pi$
$282$	−20.1355	−1.19905
$283$	21.2072	1.26064	0.630318	−	0.776337i	$-0.282925\pi$
$283$	21.2072	1.26064	0.630318	+	0.776337i	$0.282925\pi$
$284$	0.821697	0.0487587
$285$	2.82571	0.167381
$286$	−1.07001	−0.0632712
$287$	−3.10382	−0.183213
$288$	−5.73059	−0.337678
$289$	31.7367	1.86686
$290$	−0.577325	−0.0339017
$291$	24.6275	1.44369
$292$	3.91482	0.229098
$293$	12.6145	0.736946	0.368473	−	0.929638i	$-0.379881\pi$
$293$	12.6145	0.736946	0.368473	+	0.929638i	$0.379881\pi$
$294$	18.8008	1.09648
$295$	1.88524	0.109763
$296$	20.5675	1.19546
$297$	−0.952518	−0.0552707
$298$	7.75335	0.449139
$299$	−0.754640	−0.0436420
$300$	4.51106	0.260446
$301$	−0.00911457	−0.000525355 0
$302$	−26.2168	−1.50861
$303$	11.5318	0.662484
$304$	13.0959	0.751101
$305$	−0.422675	−0.0242023
$306$	−28.0648	−1.60436
$307$	2.82296	0.161115	0.0805574	−	0.996750i	$-0.474330\pi$
$307$	2.82296	0.161115	0.0805574	+	0.996750i	$0.474330\pi$
$308$	−0.540170	−0.0307791
$309$	−11.9034	−0.677162
$310$	−1.81320	−0.102983
$311$	1.20268	0.0681978	0.0340989	−	0.999418i	$-0.489144\pi$
$311$	1.20268	0.0681978	0.0340989	+	0.999418i	$0.489144\pi$
$312$	4.06189	0.229960
$313$	2.49200	0.140856	0.0704282	−	0.997517i	$-0.477563\pi$
$313$	2.49200	0.140856	0.0704282	+	0.997517i	$0.477563\pi$
$314$	5.78756	0.326611
$315$	1.49954	0.0844895
$316$	3.76449	0.211769
$317$	17.8571	1.00295	0.501477	−	0.865171i	$-0.332790\pi$
$317$	17.8571	1.00295	0.501477	+	0.865171i	$0.332790\pi$
$318$	−19.7861	−1.10955
$319$	0.882505	0.0494108
$320$	2.47449	0.138328
$321$	36.7237	2.04972
$322$	−2.30757	−0.128596
$323$	19.7268	1.09763
$324$	−3.97282	−0.220712
$325$	−3.33320	−0.184893
$326$	21.2661	1.17782
$327$	31.9812	1.76857
$328$	5.64320	0.311594
$329$	7.51081	0.414084
$330$	1.54773	0.0851998
$331$	13.1705	0.723918	0.361959	−	0.932194i	$-0.382108\pi$
$331$	13.1705	0.723918	0.361959	+	0.932194i	$0.382108\pi$
$332$	6.16767	0.338495
$333$	−21.5118	−1.17884
$334$	11.2897	0.617745
$335$	−3.55742	−0.194363
$336$	14.9766	0.817041
$337$	−26.8052	−1.46017	−0.730086	−	0.683356i	$-0.760520\pi$
$337$	−26.8052	−1.46017	−0.730086	+	0.683356i	$0.760520\pi$
$338$	−19.3808	−1.05417
$339$	−41.8243	−2.27158
$340$	−1.16695	−0.0632868
$341$	2.77168	0.150095
$342$	−11.3596	−0.614254
$343$	−16.5741	−0.894918
$344$	0.0165717	0.000893484 0
$345$	1.09156	0.0587675
$346$	−29.6477	−1.59387
$347$	1.77497	0.0952851	0.0476426	−	0.998864i	$-0.484829\pi$
$347$	1.77497	0.0952851	0.0476426	+	0.998864i	$0.484829\pi$
$348$	0.825711	0.0442627
$349$	31.3758	1.67951	0.839753	−	0.542968i	$-0.182700\pi$
$349$	31.3758	1.67951	0.839753	+	0.542968i	$0.182700\pi$
$350$	−10.1924	−0.544807
$351$	0.658516	0.0351490
$352$	2.20629	0.117595
$353$	25.7264	1.36928	0.684640	−	0.728881i	$-0.259959\pi$
$353$	25.7264	1.36928	0.684640	+	0.728881i	$0.259959\pi$
$354$	−16.3324	−0.868055
$355$	0.878215	0.0466108
$356$	0.472426	0.0250385
$357$	22.5597	1.19399
$358$	4.28868	0.226664
$359$	−15.9563	−0.842141	−0.421070	−	0.907028i	$-0.638346\pi$
$359$	−15.9563	−0.842141	−0.421070	+	0.907028i	$0.638346\pi$
$360$	−2.72639	−0.143693
$361$	−11.0154	−0.579756
$362$	19.1391	1.00593
$363$	−2.36588	−0.124177
$364$	0.373443	0.0195737
$365$	4.18409	0.219005
$366$	3.66175	0.191403
$367$	−36.0792	−1.88332	−0.941659	−	0.336570i	$-0.890733\pi$
$367$	−36.0792	−1.88332	−0.941659	+	0.336570i	$0.890733\pi$
$368$	5.05887	0.263712
$369$	−5.90230	−0.307261
$370$	−5.41803	−0.281670
$371$	7.38049	0.383176
$372$	2.59331	0.134457
$373$	4.83912	0.250560	0.125280	−	0.992121i	$-0.460017\pi$
$373$	4.83912	0.250560	0.125280	+	0.992121i	$0.460017\pi$
$374$	10.8050	0.558712
$375$	9.82135	0.507172
$376$	−13.6558	−0.704243
$377$	−0.610113	−0.0314224
$378$	2.01364	0.103570
$379$	−7.13651	−0.366578	−0.183289	−	0.983059i	$-0.558674\pi$
$379$	−7.13651	−0.366578	−0.183289	+	0.983059i	$0.558674\pi$
$380$	−0.472338	−0.0242304
$381$	−2.23897	−0.114706
$382$	−22.1431	−1.13294
$383$	23.8902	1.22073	0.610365	−	0.792120i	$-0.291023\pi$
$383$	23.8902	1.22073	0.610365	+	0.792120i	$0.291023\pi$
$384$	−31.8768	−1.62671
$385$	−0.577325	−0.0294232
$386$	−15.1912	−0.773212
$387$	−0.0173325	−0.000881060 0
$388$	−4.11666	−0.208992
$389$	−26.8388	−1.36078	−0.680391	−	0.732849i	$-0.738190\pi$
$389$	−26.8388	−1.36078	−0.680391	+	0.732849i	$0.738190\pi$
$390$	−1.07001	−0.0541822
$391$	7.62034	0.385377
$392$	12.7506	0.644001
$393$	−7.74193	−0.390528
$394$	−3.50978	−0.176820
$395$	4.02342	0.202440
$396$	−1.02720	−0.0516188
$397$	18.1033	0.908577	0.454288	−	0.890855i	$-0.349894\pi$
$397$	18.1033	0.908577	0.454288	+	0.890855i	$0.349894\pi$
$398$	−29.6488	−1.48616
$399$	9.13132	0.457138
$400$	22.3448	1.11724
$401$	−16.9938	−0.848627	−0.424314	−	0.905515i	$-0.639485\pi$
$401$	−16.9938	−0.848627	−0.424314	+	0.905515i	$0.639485\pi$
$402$	30.8189	1.53711
$403$	−1.91618	−0.0954518
$404$	−1.92762	−0.0959027
$405$	−4.24608	−0.210990
$406$	−1.86563	−0.0925897
$407$	8.28206	0.410527
$408$	−41.0169	−2.03064
$409$	−6.46314	−0.319582	−0.159791	−	0.987151i	$-0.551082\pi$
$409$	−6.46314	−0.319582	−0.159791	+	0.987151i	$0.551082\pi$
$410$	−1.48657	−0.0734166
$411$	18.0009	0.887921
$412$	1.98974	0.0980276
$413$	6.09218	0.299777
$414$	−4.38814	−0.215665
$415$	6.59189	0.323583
$416$	−1.52530	−0.0747839
$417$	−14.2261	−0.696653
$418$	4.37344	0.213912
$419$	−8.37098	−0.408949	−0.204475	−	0.978872i	$-0.565549\pi$
$419$	−8.37098	−0.408949	−0.204475	+	0.978872i	$0.565549\pi$
$420$	−0.540170	−0.0263576
$421$	−18.4572	−0.899548	−0.449774	−	0.893142i	$-0.648495\pi$
$421$	−18.4572	−0.899548	−0.449774	+	0.893142i	$0.648495\pi$
$422$	30.7054	1.49472
$423$	14.2827	0.694451
$424$	−13.4188	−0.651676
$425$	33.6586	1.63268
$426$	−7.60821	−0.368619
$427$	−1.36588	−0.0660996
$428$	−6.13862	−0.296722
$429$	1.63563	0.0789692
$430$	−0.00436542	−0.000210519 0
$431$	26.6306	1.28275	0.641377	−	0.767226i	$-0.278364\pi$
$431$	26.6306	1.28275	0.641377	+	0.767226i	$0.278364\pi$
$432$	−4.41449	−0.212392
$433$	−22.2520	−1.06936	−0.534681	−	0.845054i	$-0.679568\pi$
$433$	−22.2520	−1.06936	−0.534681	+	0.845054i	$0.679568\pi$
$434$	−5.85939	−0.281260
$435$	0.882505	0.0423129
$436$	−5.34589	−0.256022
$437$	3.08443	0.147548
$438$	−36.2479	−1.73199
$439$	15.0500	0.718298	0.359149	−	0.933280i	$-0.383067\pi$
$439$	15.0500	0.718298	0.359149	+	0.933280i	$0.383067\pi$
$440$	1.04966	0.0500407
$441$	−13.3360	−0.635047
$442$	−7.46994	−0.355309
$443$	8.71671	0.414143	0.207072	−	0.978326i	$-0.433607\pi$
$443$	8.71671	0.414143	0.207072	+	0.978326i	$0.433607\pi$
$444$	7.74907	0.367754
$445$	0.504921	0.0239355
$446$	−29.0211	−1.37419
$447$	−11.8519	−0.560574
$448$	7.99636	0.377792
$449$	6.65276	0.313963	0.156982	−	0.987602i	$-0.449824\pi$
$449$	6.65276	0.313963	0.156982	+	0.987602i	$0.449824\pi$
$450$	−19.3821	−0.913683
$451$	2.27239	0.107003
$452$	6.99123	0.328840
$453$	40.0753	1.88290
$454$	10.4081	0.488475
$455$	0.399129	0.0187115
$456$	−16.6021	−0.777465
$457$	−14.4594	−0.676382	−0.338191	−	0.941077i	$-0.609815\pi$
$457$	−14.4594	−0.676382	−0.338191	+	0.941077i	$0.609815\pi$
$458$	1.29566	0.0605424
$459$	−6.64968	−0.310381
$460$	−0.182462	−0.00850731
$461$	−11.0567	−0.514962	−0.257481	−	0.966283i	$-0.582893\pi$
$461$	−11.0567	−0.514962	−0.257481	+	0.966283i	$0.582893\pi$
$462$	5.00152	0.232692
$463$	−35.5539	−1.65233	−0.826166	−	0.563427i	$-0.809483\pi$
$463$	−35.5539	−1.65233	−0.826166	+	0.563427i	$0.809483\pi$
$464$	4.09001	0.189874
$465$	2.77168	0.128534
$466$	−21.9040	−1.01468
$467$	20.6585	0.955961	0.477980	−	0.878371i	$-0.341369\pi$
$467$	20.6585	0.955961	0.477980	+	0.878371i	$0.341369\pi$
$468$	0.710148	0.0328266
$469$	−11.4958	−0.530829
$470$	3.59730	0.165931
$471$	−8.84693	−0.407645
$472$	−11.0765	−0.509837
$473$	0.00667303	0.000306826 0
$474$	−34.8560	−1.60099
$475$	13.6237	0.625100
$476$	−3.77102	−0.172844
$477$	14.0349	0.642615
$478$	−27.2840	−1.24794
$479$	28.0497	1.28162	0.640812	−	0.767697i	$-0.278598\pi$
$479$	28.0497	1.28162	0.640812	+	0.767697i	$0.278598\pi$
$480$	2.20629	0.100703
$481$	−5.72574	−0.261071
$482$	−40.0819	−1.82568
$483$	3.52738	0.160501
$484$	0.395474	0.0179761
$485$	−4.39981	−0.199785
$486$	32.3622	1.46798
$487$	−19.2288	−0.871340	−0.435670	−	0.900107i	$-0.643488\pi$
$487$	−19.2288	−0.871340	−0.435670	+	0.900107i	$0.643488\pi$
$488$	2.48338	0.112417
$489$	−32.5076	−1.47005
$490$	−3.35884	−0.151737
$491$	1.78235	0.0804363	0.0402181	−	0.999191i	$-0.487195\pi$
$491$	1.78235	0.0804363	0.0402181	+	0.999191i	$0.487195\pi$
$492$	2.12615	0.0958543
$493$	6.16091	0.277474
$494$	−3.02355	−0.136036
$495$	−1.09785	−0.0493449
$496$	12.8455	0.576780
$497$	2.83796	0.127300
$498$	−57.1073	−2.55904
$499$	−33.7716	−1.51182	−0.755912	−	0.654673i	$-0.772806\pi$
$499$	−33.7716	−1.51182	−0.755912	+	0.654673i	$0.772806\pi$
$500$	−1.64171	−0.0734194
$501$	−17.2576	−0.771012
$502$	−12.6907	−0.566413
$503$	−30.5958	−1.36420	−0.682099	−	0.731260i	$-0.738933\pi$
$503$	−30.5958	−1.36420	−0.682099	+	0.731260i	$0.738933\pi$
$504$	−8.81035	−0.392444
$505$	−2.06021	−0.0916780
$506$	1.68944	0.0751047
$507$	29.6257	1.31572
$508$	0.374259	0.0166051
$509$	−33.0724	−1.46591	−0.732954	−	0.680278i	$-0.761859\pi$
$509$	−33.0724	−1.46591	−0.732954	+	0.680278i	$0.761859\pi$
$510$	10.8050	0.478452
$511$	13.5209	0.598131
$512$	−12.7935	−0.565399
$513$	−2.69154	−0.118834
$514$	28.6875	1.26535
$515$	2.12660	0.0937092
$516$	0.00624359	0.000274859 0
$517$	−5.49887	−0.241840
$518$	−17.5084	−0.769276
$519$	45.3198	1.98932
$520$	−0.725676	−0.0318230
$521$	−33.8751	−1.48410	−0.742048	−	0.670347i	$-0.766145\pi$
$521$	−33.8751	−1.48410	−0.742048	+	0.670347i	$0.766145\pi$
$522$	−3.54773	−0.155280
$523$	18.1631	0.794219	0.397109	−	0.917771i	$-0.370013\pi$
$523$	18.1631	0.794219	0.397109	+	0.917771i	$0.370013\pi$
$524$	1.29412	0.0565338
$525$	15.5802	0.679977
$526$	−0.317267	−0.0138335
$527$	19.3496	0.842881
$528$	−10.9648	−0.477181
$529$	−21.8085	−0.948196
$530$	3.53488	0.153546
$531$	11.5851	0.502748
$532$	−1.52637	−0.0661763
$533$	−1.57100	−0.0680476
$534$	−4.37426	−0.189293
$535$	−6.56085	−0.283650
$536$	20.9012	0.902793
$537$	−6.55573	−0.282901
$538$	22.5878	0.973828
$539$	5.13437	0.221153
$540$	0.159220	0.00685174
$541$	6.68740	0.287514	0.143757	−	0.989613i	$-0.454082\pi$
$541$	6.68740	0.287514	0.143757	+	0.989613i	$0.454082\pi$
$542$	−1.51993	−0.0652866
$543$	−29.2562	−1.25550
$544$	15.4024	0.660374
$545$	−5.71359	−0.244743
$546$	−3.45776	−0.147978
$547$	41.9803	1.79495	0.897473	−	0.441069i	$-0.145401\pi$
$547$	41.9803	1.79495	0.897473	+	0.441069i	$0.145401\pi$
$548$	−3.00899	−0.128537
$549$	−2.59739	−0.110854
$550$	7.46215	0.318187
$551$	2.49370	0.106235
$552$	−6.41331	−0.272968
$553$	13.0017	0.552891
$554$	−28.2172	−1.19883
$555$	8.28206	0.351554
$556$	2.37799	0.100849
$557$	2.05083	0.0868967	0.0434483	−	0.999056i	$-0.486166\pi$
$557$	2.05083	0.0868967	0.0434483	+	0.999056i	$0.486166\pi$
$558$	−11.1424	−0.471694
$559$	−0.00461335	−0.000195124 0
$560$	−2.67564	−0.113066
$561$	−16.5166	−0.697332
$562$	−24.6896	−1.04147
$563$	21.0209	0.885925	0.442963	−	0.896540i	$-0.353927\pi$
$563$	21.0209	0.885925	0.442963	+	0.896540i	$0.353927\pi$
$564$	−5.14499	−0.216643
$565$	7.47210	0.314354
$566$	32.8230	1.37965
$567$	−13.7213	−0.576239
$568$	−5.15984	−0.216502
$569$	21.4394	0.898786	0.449393	−	0.893334i	$-0.351640\pi$
$569$	21.4394	0.898786	0.449393	+	0.893334i	$0.351640\pi$
$570$	4.37344	0.183183
$571$	−3.44489	−0.144164	−0.0720821	−	0.997399i	$-0.522964\pi$
$571$	−3.44489	−0.144164	−0.0720821	+	0.997399i	$0.522964\pi$
$572$	−0.273408	−0.0114318
$573$	33.8482	1.41403
$574$	−4.80388	−0.200510
$575$	5.26277	0.219473
$576$	15.2061	0.633586
$577$	27.8944	1.16126	0.580629	−	0.814168i	$-0.302807\pi$
$577$	27.8944	1.16126	0.580629	+	0.814168i	$0.302807\pi$
$578$	49.1198	2.04312
$579$	23.2215	0.965051
$580$	−0.147517	−0.00612531
$581$	21.3018	0.883747
$582$	38.1167	1.57999
$583$	−5.40346	−0.223789
$584$	−24.5831	−1.01726
$585$	0.758994	0.0313805
$586$	19.5238	0.806522
$587$	−0.960679	−0.0396514	−0.0198257	−	0.999803i	$-0.506311\pi$
$587$	−0.960679	−0.0396514	−0.0198257	+	0.999803i	$0.506311\pi$
$588$	4.80394	0.198111
$589$	7.83198	0.322711
$590$	2.91785	0.120126
$591$	5.36509	0.220690
$592$	38.3836	1.57756
$593$	28.1799	1.15721	0.578606	−	0.815607i	$-0.303597\pi$
$593$	28.1799	1.15721	0.578606	+	0.815607i	$0.303597\pi$
$594$	−1.47424	−0.0604889
$595$	−4.03040	−0.165230
$596$	1.98112	0.0811499
$597$	45.3215	1.85489
$598$	−1.16798	−0.0477623
$599$	17.5169	0.715722	0.357861	−	0.933775i	$-0.383506\pi$
$599$	17.5169	0.715722	0.357861	+	0.933775i	$0.383506\pi$
$600$	−28.3272	−1.15645
$601$	−41.9789	−1.71236	−0.856178	−	0.516680i	$-0.827168\pi$
$601$	−41.9789	−1.71236	−0.856178	+	0.516680i	$0.827168\pi$
$602$	−0.0141069	−0.000574955 0
$603$	−21.8608	−0.890240
$604$	−6.69888	−0.272573
$605$	0.422675	0.0171842
$606$	17.8481	0.725030
$607$	2.58751	0.105024	0.0525119	−	0.998620i	$-0.483277\pi$
$607$	2.58751	0.105024	0.0525119	+	0.998620i	$0.483277\pi$
$608$	6.23433	0.252835
$609$	2.85183	0.115562
$610$	−0.654188	−0.0264873
$611$	3.80161	0.153796
$612$	−7.17106	−0.289873
$613$	−8.46890	−0.342056	−0.171028	−	0.985266i	$-0.554709\pi$
$613$	−8.46890	−0.342056	−0.171028	+	0.985266i	$0.554709\pi$
$614$	4.36918	0.176326
$615$	2.27239	0.0916317
$616$	3.39200	0.136667
$617$	32.5956	1.31225	0.656125	−	0.754652i	$-0.272194\pi$
$617$	32.5956	1.31225	0.656125	+	0.754652i	$0.272194\pi$
$618$	−18.4233	−0.741094
$619$	0.882619	0.0354754	0.0177377	−	0.999843i	$-0.494354\pi$
$619$	0.882619	0.0354754	0.0177377	+	0.999843i	$0.494354\pi$
$620$	−0.463307	−0.0186068
$621$	−1.03973	−0.0417228
$622$	1.86143	0.0746365
$623$	1.63166	0.0653710
$624$	7.58043	0.303460
$625$	22.3521	0.894084
$626$	3.85695	0.154155
$627$	−6.68530	−0.266985
$628$	1.47883	0.0590116
$629$	57.8185	2.30537
$630$	2.32088	0.0924663
$631$	−19.5118	−0.776753	−0.388377	−	0.921501i	$-0.626964\pi$
$631$	−19.5118	−0.776753	−0.388377	+	0.921501i	$0.626964\pi$
$632$	−23.6391	−0.940314
$633$	−46.9366	−1.86556
$634$	27.6380	1.09765
$635$	0.400002	0.0158736
$636$	−5.05572	−0.200472
$637$	−3.54961	−0.140641
$638$	1.36588	0.0540758
$639$	5.39674	0.213492
$640$	5.69494	0.225112
$641$	−11.9737	−0.472934	−0.236467	−	0.971640i	$-0.575989\pi$
$641$	−11.9737	−0.472934	−0.236467	+	0.971640i	$0.575989\pi$
$642$	56.8384	2.24323
$643$	−29.4944	−1.16314	−0.581572	−	0.813495i	$-0.697562\pi$
$643$	−29.4944	−1.16314	−0.581572	+	0.813495i	$0.697562\pi$
$644$	−0.589627	−0.0232346
$645$	0.00667303	0.000262750 0
$646$	30.5317	1.20125
$647$	−44.5496	−1.75142	−0.875712	−	0.482834i	$-0.839608\pi$
$647$	−44.5496	−1.75142	−0.875712	+	0.482834i	$0.839608\pi$
$648$	24.9473	0.980023
$649$	−4.46026	−0.175080
$650$	−5.15890	−0.202349
$651$	8.95673	0.351042
$652$	5.43388	0.212807
$653$	−19.0693	−0.746238	−0.373119	−	0.927783i	$-0.621712\pi$
$653$	−19.0693	−0.746238	−0.373119	+	0.927783i	$0.621712\pi$
$654$	49.4984	1.93554
$655$	1.38313	0.0540434
$656$	10.5315	0.411186
$657$	25.7118	1.00311
$658$	11.6247	0.453179
$659$	9.28102	0.361537	0.180769	−	0.983526i	$-0.442142\pi$
$659$	9.28102	0.361537	0.180769	+	0.983526i	$0.442142\pi$
$660$	0.395474	0.0153938
$661$	−33.9953	−1.32226	−0.661131	−	0.750270i	$-0.729923\pi$
$661$	−33.9953	−1.32226	−0.661131	+	0.750270i	$0.729923\pi$
$662$	20.3845	0.792264
$663$	11.4186	0.443463
$664$	−38.7298	−1.50301
$665$	−1.63135	−0.0632611
$666$	−33.2945	−1.29013
$667$	0.963305	0.0372993
$668$	2.88473	0.111613
$669$	44.3620	1.71513
$670$	−5.50593	−0.212713
$671$	1.00000	0.0386046
$672$	7.12964	0.275032
$673$	19.5899	0.755136	0.377568	−	0.925982i	$-0.376760\pi$
$673$	19.5899	0.755136	0.377568	+	0.925982i	$0.376760\pi$
$674$	−41.4872	−1.59803
$675$	−4.59242	−0.176762
$676$	−4.95214	−0.190467
$677$	34.1231	1.31146	0.655729	−	0.754996i	$-0.272361\pi$
$677$	34.1231	1.31146	0.655729	+	0.754996i	$0.272361\pi$
$678$	−64.7328	−2.48605
$679$	−14.2180	−0.545638
$680$	7.32786	0.281011
$681$	−15.9099	−0.609668
$682$	4.28982	0.164266
$683$	−3.15037	−0.120545	−0.0602727	−	0.998182i	$-0.519197\pi$
$683$	−3.15037	−0.120545	−0.0602727	+	0.998182i	$0.519197\pi$
$684$	−2.90257	−0.110983
$685$	−3.21595	−0.122875
$686$	−25.6523	−0.979408
$687$	−1.98057	−0.0755634
$688$	0.0309265	0.00117906
$689$	3.73564	0.142317
$690$	1.68944	0.0643158
$691$	11.7105	0.445490	0.222745	−	0.974877i	$-0.428498\pi$
$691$	11.7105	0.445490	0.222745	+	0.974877i	$0.428498\pi$
$692$	−7.57553	−0.287978
$693$	−3.54773	−0.134767
$694$	2.74717	0.104281
$695$	2.54155	0.0964065
$696$	−5.18505	−0.196539
$697$	15.8639	0.600890
$698$	48.5613	1.83807
$699$	33.4827	1.26643
$700$	−2.60435	−0.0984351
$701$	4.32291	0.163274	0.0816370	−	0.996662i	$-0.473985\pi$
$701$	4.32291	0.163274	0.0816370	+	0.996662i	$0.473985\pi$
$702$	1.01921	0.0384675
$703$	23.4027	0.882650
$704$	−5.85436	−0.220644
$705$	−5.49887	−0.207100
$706$	39.8176	1.49856
$707$	−6.65758	−0.250384
$708$	−4.17322	−0.156839
$709$	10.9229	0.410219	0.205109	−	0.978739i	$-0.434245\pi$
$709$	10.9229	0.410219	0.205109	+	0.978739i	$0.434245\pi$
$710$	1.35924	0.0510114
$711$	24.7244	0.927239
$712$	−2.96660	−0.111178
$713$	3.02545	0.113304
$714$	34.9164	1.30671
$715$	−0.292213	−0.0109282
$716$	1.09584	0.0409534
$717$	41.7067	1.55757
$718$	−24.6961	−0.921649
$719$	−36.9263	−1.37712	−0.688560	−	0.725179i	$-0.741757\pi$
$719$	−36.9263	−1.37712	−0.688560	+	0.725179i	$0.741757\pi$
$720$	−5.08806	−0.189621
$721$	6.87214	0.255932
$722$	−17.0488	−0.634491
$723$	61.2697	2.27864
$724$	4.89038	0.181750
$725$	4.25486	0.158022
$726$	−3.66175	−0.135900
$727$	28.5623	1.05932	0.529658	−	0.848211i	$-0.322320\pi$
$727$	28.5623	1.05932	0.529658	+	0.848211i	$0.322320\pi$
$728$	−2.34503	−0.0869126
$729$	−19.3321	−0.716003
$730$	6.47585	0.239682
$731$	0.0465855	0.00172303
$732$	0.935644	0.0345824
$733$	−27.4747	−1.01480	−0.507401	−	0.861710i	$-0.669394\pi$
$733$	−27.4747	−1.01480	−0.507401	+	0.861710i	$0.669394\pi$
$734$	−55.8409	−2.06112
$735$	5.13437	0.189384
$736$	2.40829	0.0887706
$737$	8.41643	0.310023
$738$	−9.13517	−0.336270
$739$	−10.6009	−0.389960	−0.194980	−	0.980807i	$-0.562464\pi$
$739$	−10.6009	−0.389960	−0.194980	+	0.980807i	$0.562464\pi$
$740$	−1.38441	−0.0508918
$741$	4.62183	0.169787
$742$	11.4230	0.419352
$743$	−11.5633	−0.424218	−0.212109	−	0.977246i	$-0.568033\pi$
$743$	−11.5633	−0.424218	−0.212109	+	0.977246i	$0.568033\pi$
$744$	−16.2847	−0.597025
$745$	2.11739	0.0775751
$746$	7.48966	0.274216
$747$	40.5080	1.48211
$748$	2.76087	0.100947
$749$	−21.2015	−0.774685
$750$	15.2008	0.555055
$751$	−17.6860	−0.645372	−0.322686	−	0.946506i	$-0.604586\pi$
$751$	−17.6860	−0.645372	−0.322686	+	0.946506i	$0.604586\pi$
$752$	−25.4848	−0.929335
$753$	19.3991	0.706944
$754$	−0.944292	−0.0343891
$755$	−7.15964	−0.260566
$756$	0.514522	0.0187130
$757$	33.1688	1.20554	0.602771	−	0.797914i	$-0.294063\pi$
$757$	33.1688	1.20554	0.602771	+	0.797914i	$0.294063\pi$
$758$	−11.0454	−0.401187
$759$	−2.58249	−0.0937386
$760$	2.96604	0.107590
$761$	4.53113	0.164253	0.0821266	−	0.996622i	$-0.473829\pi$
$761$	4.53113	0.164253	0.0821266	+	0.996622i	$0.473829\pi$
$762$	−3.46532	−0.125535
$763$	−18.4635	−0.668425
$764$	−5.65797	−0.204698
$765$	−7.66431	−0.277104
$766$	36.9756	1.33598
$767$	3.08357	0.111341
$768$	−21.6353	−0.780698
$769$	−39.1574	−1.41205	−0.706026	−	0.708186i	$-0.749514\pi$
$769$	−39.1574	−1.41205	−0.706026	+	0.708186i	$0.749514\pi$
$770$	−0.893544	−0.0322011
$771$	−43.8520	−1.57929
$772$	−3.88163	−0.139703
$773$	21.7780	0.783302	0.391651	−	0.920114i	$-0.371904\pi$
$773$	21.7780	0.783302	0.391651	+	0.920114i	$0.371904\pi$
$774$	−0.0268261	−0.000964243 0
$775$	13.3632	0.480022
$776$	25.8505	0.927980
$777$	26.7636	0.960139
$778$	−41.5393	−1.48926
$779$	6.42112	0.230061
$780$	−0.273408	−0.00978957
$781$	−2.07775	−0.0743478
$782$	11.7942	0.421761
$783$	−0.840602	−0.0300407
$784$	23.7955	0.849838
$785$	1.58054	0.0564121
$786$	−11.9824	−0.427399
$787$	−7.40337	−0.263902	−0.131951	−	0.991256i	$-0.542124\pi$
$787$	−7.40337	−0.263902	−0.131951	+	0.991256i	$0.542124\pi$
$788$	−0.896813	−0.0319477
$789$	0.484979	0.0172657
$790$	6.22718	0.221553
$791$	24.1462	0.858540
$792$	6.45031	0.229202
$793$	−0.691342	−0.0245503
$794$	28.0190	0.994357
$795$	−5.40346	−0.191641
$796$	−7.57582	−0.268518
$797$	−17.5955	−0.623264	−0.311632	−	0.950203i	$-0.600876\pi$
$797$	−17.5955	−0.623264	−0.311632	+	0.950203i	$0.600876\pi$
$798$	14.1328	0.500297
$799$	−38.3886	−1.35809
$800$	10.6373	0.376084
$801$	3.10280	0.109632
$802$	−26.3018	−0.928748
$803$	−9.89906	−0.349330
$804$	7.87479	0.277722
$805$	−0.630183	−0.0222110
$806$	−2.96574	−0.104464
$807$	−34.5279	−1.21544
$808$	12.1045	0.425834
$809$	51.4596	1.80922	0.904612	−	0.426236i	$-0.140161\pi$
$809$	51.4596	1.80922	0.904612	+	0.426236i	$0.140161\pi$
$810$	−6.57180	−0.230909
$811$	8.45892	0.297033	0.148516	−	0.988910i	$-0.452550\pi$
$811$	8.45892	0.297033	0.148516	+	0.988910i	$0.452550\pi$
$812$	−0.476703	−0.0167290
$813$	2.32338	0.0814846
$814$	12.8184	0.449285
$815$	5.80764	0.203433
$816$	−76.5470	−2.67968
$817$	0.0188561	0.000659690 0
$818$	−10.0032	−0.349754
$819$	2.45270	0.0857042
$820$	−0.379846	−0.0132648
$821$	−38.2631	−1.33539	−0.667695	−	0.744435i	$-0.732719\pi$
$821$	−38.2631	−1.33539	−0.667695	+	0.744435i	$0.732719\pi$
$822$	27.8606	0.971751
$823$	22.5391	0.785665	0.392832	−	0.919610i	$-0.371495\pi$
$823$	22.5391	0.785665	0.392832	+	0.919610i	$0.371495\pi$
$824$	−12.4946	−0.435269
$825$	−11.4067	−0.397131
$826$	9.42907	0.328079
$827$	−24.7959	−0.862239	−0.431119	−	0.902295i	$-0.641881\pi$
$827$	−24.7959	−0.862239	−0.431119	+	0.902295i	$0.641881\pi$
$828$	−1.12125	−0.0389661
$829$	−41.3694	−1.43682	−0.718409	−	0.695621i	$-0.755129\pi$
$829$	−41.3694	−1.43682	−0.718409	+	0.695621i	$0.755129\pi$
$830$	10.2025	0.354133
$831$	43.1332	1.49627
$832$	4.04737	0.140317
$833$	35.8439	1.24192
$834$	−22.0181	−0.762425
$835$	3.08314	0.106697
$836$	1.11749	0.0386494
$837$	−2.64008	−0.0912544
$838$	−12.9560	−0.447559
$839$	12.5463	0.433145	0.216573	−	0.976267i	$-0.430512\pi$
$839$	12.5463	0.433145	0.216573	+	0.976267i	$0.430512\pi$
$840$	3.39200	0.117035
$841$	−28.2212	−0.973144
$842$	−28.5668	−0.984476
$843$	37.7408	1.29986
$844$	7.84579	0.270063
$845$	−5.29276	−0.182077
$846$	22.1059	0.760015
$847$	1.36588	0.0469322
$848$	−25.0426	−0.859967
$849$	−50.1736	−1.72195
$850$	52.0945	1.78683
$851$	9.04035	0.309899
$852$	−1.94404	−0.0666016
$853$	57.6827	1.97502	0.987509	−	0.157562i	$-0.0503634\pi$
$853$	57.6827	1.97502	0.987509	+	0.157562i	$0.0503634\pi$
$854$	−2.11402	−0.0723402
$855$	−3.10222	−0.106094
$856$	38.5474	1.31752
$857$	32.6451	1.11514	0.557568	−	0.830131i	$-0.311734\pi$
$857$	32.6451	1.11514	0.557568	+	0.830131i	$0.311734\pi$
$858$	2.53152	0.0864248
$859$	−47.0676	−1.60592	−0.802962	−	0.596030i	$-0.796744\pi$
$859$	−47.0676	−1.60592	−0.802962	+	0.596030i	$0.796744\pi$
$860$	−0.00111545	−3.80364e−5 0
$861$	7.34326	0.250258
$862$	41.2171	1.40386
$863$	−33.3117	−1.13394	−0.566972	−	0.823737i	$-0.691885\pi$
$863$	−33.3117	−1.13394	−0.566972	+	0.823737i	$0.691885\pi$
$864$	−2.10153	−0.0714954
$865$	−8.09659	−0.275292
$866$	−34.4401	−1.17032
$867$	−75.0852	−2.55003
$868$	−1.49718	−0.0508176
$869$	−9.51894	−0.322908
$870$	1.36588	0.0463077
$871$	−5.81864	−0.197157
$872$	33.5695	1.13681
$873$	−27.0374	−0.915077
$874$	4.77386	0.161478
$875$	−5.67010	−0.191684
$876$	−9.26200	−0.312934
$877$	−11.7341	−0.396233	−0.198117	−	0.980178i	$-0.563482\pi$
$877$	−11.7341	−0.396233	−0.198117	+	0.980178i	$0.563482\pi$
$878$	23.2934	0.786114
$879$	−29.8444	−1.00663
$880$	1.95891	0.0660348
$881$	50.6721	1.70719	0.853593	−	0.520941i	$-0.174419\pi$
$881$	50.6721	1.70719	0.853593	+	0.520941i	$0.174419\pi$
$882$	−20.6405	−0.695002
$883$	27.7935	0.935327	0.467663	−	0.883907i	$-0.345096\pi$
$883$	27.7935	0.935327	0.467663	+	0.883907i	$0.345096\pi$
$884$	−1.90871	−0.0641967
$885$	−4.46026	−0.149930
$886$	13.4911	0.453243
$887$	3.70999	0.124569	0.0622846	−	0.998058i	$-0.480161\pi$
$887$	3.70999	0.124569	0.0622846	+	0.998058i	$0.480161\pi$
$888$	−48.6602	−1.63293
$889$	1.29261	0.0433527
$890$	0.781482	0.0261953
$891$	10.0457	0.336544
$892$	−7.41542	−0.248287
$893$	−15.5382	−0.519967
$894$	−18.3435	−0.613498
$895$	1.17121	0.0391493
$896$	18.4033	0.614810
$897$	1.78539	0.0596124
$898$	10.2967	0.343605
$899$	2.44602	0.0815795
$900$	−4.95249	−0.165083
$901$	−37.7225	−1.25672
$902$	3.51705	0.117105
$903$	0.0215640	0.000717605 0
$904$	−43.9014	−1.46014
$905$	5.22675	0.173743
$906$	62.0259	2.06067
$907$	−11.6086	−0.385456	−0.192728	−	0.981252i	$-0.561733\pi$
$907$	−11.6086	−0.385456	−0.192728	+	0.981252i	$0.561733\pi$
$908$	2.65945	0.0882570
$909$	−12.6602	−0.419913
$910$	0.617745	0.0204780
$911$	−3.49920	−0.115934	−0.0579669	−	0.998319i	$-0.518462\pi$
$911$	−3.49920	−0.115934	−0.0579669	+	0.998319i	$0.518462\pi$
$912$	−30.9833	−1.02596
$913$	−15.5956	−0.516140
$914$	−22.3793	−0.740240
$915$	1.00000	0.0330590
$916$	0.331066	0.0109387
$917$	4.46960	0.147599
$918$	−10.2919	−0.339684
$919$	−9.12642	−0.301053	−0.150526	−	0.988606i	$-0.548097\pi$
$919$	−9.12642	−0.301053	−0.150526	+	0.988606i	$0.548097\pi$
$920$	1.14577	0.0377748
$921$	−6.67878	−0.220073
$922$	−17.1128	−0.563581
$923$	1.43644	0.0472809
$924$	1.27798	0.0420424
$925$	39.9307	1.31291
$926$	−55.0280	−1.80833
$927$	13.0682	0.429217
$928$	1.94706	0.0639153
$929$	22.5335	0.739301	0.369650	−	0.929171i	$-0.379477\pi$
$929$	22.5335	0.739301	0.369650	+	0.929171i	$0.379477\pi$
$930$	4.28982	0.140669
$931$	14.5082	0.475488
$932$	−5.59688	−0.183332
$933$	−2.84540	−0.0931543
$934$	31.9738	1.04621
$935$	2.95077	0.0965004
$936$	−4.45937	−0.145759
$937$	−38.3033	−1.25131	−0.625656	−	0.780099i	$-0.715169\pi$
$937$	−38.3033	−1.25131	−0.625656	+	0.780099i	$0.715169\pi$
$938$	−17.7925	−0.580945
$939$	−5.89579	−0.192402
$940$	0.919176	0.0299802
$941$	21.7093	0.707703	0.353852	−	0.935302i	$-0.384872\pi$
$941$	21.7093	0.707703	0.353852	+	0.935302i	$0.384872\pi$
$942$	−13.6927	−0.446132
$943$	2.48045	0.0807744
$944$	−20.6713	−0.672793
$945$	0.549912	0.0178886
$946$	0.0103281	0.000335794 0
$947$	3.10873	0.101020	0.0505101	−	0.998724i	$-0.483915\pi$
$947$	3.10873	0.101020	0.0505101	+	0.998724i	$0.483915\pi$
$948$	−8.90635	−0.289265
$949$	6.84364	0.222154
$950$	21.0859	0.684116
$951$	−42.2478	−1.36998
$952$	23.6801	0.767476
$953$	−41.5239	−1.34509	−0.672545	−	0.740056i	$-0.734799\pi$
$953$	−41.5239	−1.34509	−0.672545	+	0.740056i	$0.734799\pi$
$954$	21.7223	0.703286
$955$	−6.04714	−0.195681
$956$	−6.97158	−0.225477
$957$	−2.08790	−0.0674923
$958$	43.4135	1.40263
$959$	−10.3924	−0.335588
$960$	−5.85436	−0.188949
$961$	−23.3178	−0.752186
$962$	−8.86191	−0.285720
$963$	−40.3173	−1.29921
$964$	−10.2417	−0.329862
$965$	−4.14862	−0.133549
$966$	5.45944	0.175655
$967$	−43.4014	−1.39569	−0.697847	−	0.716246i	$-0.745859\pi$
$967$	−43.4014	−1.39569	−0.697847	+	0.716246i	$0.745859\pi$
$968$	−2.48338	−0.0798187
$969$	−46.6712	−1.49929
$970$	−6.80973	−0.218647
$971$	−53.0809	−1.70345	−0.851723	−	0.523993i	$-0.824442\pi$
$971$	−53.0809	−1.70345	−0.851723	+	0.523993i	$0.824442\pi$
$972$	8.26914	0.265233
$973$	8.21305	0.263298
$974$	−29.7610	−0.953604
$975$	7.88596	0.252553
$976$	4.63455	0.148348
$977$	−34.4139	−1.10100	−0.550500	−	0.834835i	$-0.685563\pi$
$977$	−34.4139	−1.10100	−0.550500	+	0.834835i	$0.685563\pi$
$978$	−50.3131	−1.60884
$979$	−1.19458	−0.0381790
$980$	−0.858246	−0.0274157
$981$	−35.1107	−1.12100
$982$	2.75860	0.0880304
$983$	21.4468	0.684045	0.342023	−	0.939692i	$-0.388888\pi$
$983$	21.4468	0.684045	0.342023	+	0.939692i	$0.388888\pi$
$984$	−13.3512	−0.425619
$985$	−0.958498	−0.0305403
$986$	9.53544	0.303670
$987$	−17.7697	−0.565615
$988$	−0.772572	−0.0245788
$989$	0.00728400	0.000231618 0
$990$	−1.69918	−0.0540036
$991$	−33.1547	−1.05320	−0.526598	−	0.850115i	$-0.676532\pi$
$991$	−33.1547	−1.05320	−0.526598	+	0.850115i	$0.676532\pi$
$992$	6.11512	0.194155
$993$	−31.1599	−0.988830
$994$	4.39241	0.139319
$995$	−8.09690	−0.256689
$996$	−14.5920	−0.462364
$997$	−5.79512	−0.183533	−0.0917666	−	0.995781i	$-0.529251\pi$
$997$	−5.79512	−0.183533	−0.0917666	+	0.995781i	$0.529251\pi$
$998$	−52.2694	−1.65456
$999$	−7.88881	−0.249591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.b.1.5	✓	6
3.2	odd	2		6039.2.a.b.1.2		6
11.10	odd	2		7381.2.a.h.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.b.1.5	✓	6	1.1	even	1	trivial
6039.2.a.b.1.2		6	3.2	odd	2
7381.2.a.h.1.2		6	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+1.54773 q^{2} -2.36588 q^{3} +0.395474 q^{4} +0.422675 q^{5} -3.66175 q^{6} +1.36588 q^{7} -2.48338 q^{8} +2.59739 q^{9} +O(q^{10})\)	\(q+1.54773 q^{2} -2.36588 q^{3} +0.395474 q^{4} +0.422675 q^{5} -3.66175 q^{6} +1.36588 q^{7} -2.48338 q^{8} +2.59739 q^{9} +0.654188 q^{10} -1.00000 q^{11} -0.935644 q^{12} +0.691342 q^{13} +2.11402 q^{14} -1.00000 q^{15} -4.63455 q^{16} -6.98116 q^{17} +4.02007 q^{18} -2.82571 q^{19} +0.167157 q^{20} -3.23151 q^{21} -1.54773 q^{22} -1.09156 q^{23} +5.87537 q^{24} -4.82135 q^{25} +1.07001 q^{26} +0.952518 q^{27} +0.540170 q^{28} -0.882505 q^{29} -1.54773 q^{30} -2.77168 q^{31} -2.20629 q^{32} +2.36588 q^{33} -10.8050 q^{34} +0.577325 q^{35} +1.02720 q^{36} -8.28206 q^{37} -4.37344 q^{38} -1.63563 q^{39} -1.04966 q^{40} -2.27239 q^{41} -5.00152 q^{42} -0.00667303 q^{43} -0.395474 q^{44} +1.09785 q^{45} -1.68944 q^{46} +5.49887 q^{47} +10.9648 q^{48} -5.13437 q^{49} -7.46215 q^{50} +16.5166 q^{51} +0.273408 q^{52} +5.40346 q^{53} +1.47424 q^{54} -0.422675 q^{55} -3.39200 q^{56} +6.68530 q^{57} -1.36588 q^{58} +4.46026 q^{59} -0.395474 q^{60} -1.00000 q^{61} -4.28982 q^{62} +3.54773 q^{63} +5.85436 q^{64} +0.292213 q^{65} +3.66175 q^{66} -8.41643 q^{67} -2.76087 q^{68} +2.58249 q^{69} +0.893544 q^{70} +2.07775 q^{71} -6.45031 q^{72} +9.89906 q^{73} -12.8184 q^{74} +11.4067 q^{75} -1.11749 q^{76} -1.36588 q^{77} -2.53152 q^{78} +9.51894 q^{79} -1.95891 q^{80} -10.0457 q^{81} -3.51705 q^{82} +15.5956 q^{83} -1.27798 q^{84} -2.95077 q^{85} -0.0103281 q^{86} +2.08790 q^{87} +2.48338 q^{88} +1.19458 q^{89} +1.69918 q^{90} +0.944292 q^{91} -0.431682 q^{92} +6.55747 q^{93} +8.51078 q^{94} -1.19436 q^{95} +5.21981 q^{96} -10.4094 q^{97} -7.94663 q^{98} -2.59739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

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