LMFDB - Embedded newform 1334.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 22x^{6} + 151x^{4} - 332x^{2} + 6 $ x^8 - 22x^6 + 151x^4 - 332*x^2 + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.27484$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52651 q^{3} +1.00000 q^{4} +2.27484 q^{5} -2.52651 q^{6} +1.33106 q^{7} +1.00000 q^{8} +3.38328 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52651 q^{3} +1.00000 q^{4} +2.27484 q^{5} -2.52651 q^{6} +1.33106 q^{7} +1.00000 q^{8} +3.38328 q^{9} +2.27484 q^{10} +2.72172 q^{11} -2.52651 q^{12} +1.63729 q^{13} +1.33106 q^{14} -5.74741 q^{15} +1.00000 q^{16} -5.34308 q^{17} +3.38328 q^{18} +4.68951 q^{19} +2.27484 q^{20} -3.36295 q^{21} +2.72172 q^{22} -1.00000 q^{23} -2.52651 q^{24} +0.174882 q^{25} +1.63729 q^{26} -0.968356 q^{27} +1.33106 q^{28} -1.00000 q^{29} -5.74741 q^{30} +1.28851 q^{31} +1.00000 q^{32} -6.87647 q^{33} -5.34308 q^{34} +3.02795 q^{35} +3.38328 q^{36} +6.71008 q^{37} +4.68951 q^{38} -4.13664 q^{39} +2.27484 q^{40} -6.72031 q^{41} -3.36295 q^{42} +7.66918 q^{43} +2.72172 q^{44} +7.69640 q^{45} -1.00000 q^{46} +5.22508 q^{47} -2.52651 q^{48} -5.22827 q^{49} +0.174882 q^{50} +13.4994 q^{51} +1.63729 q^{52} -11.7594 q^{53} -0.968356 q^{54} +6.19147 q^{55} +1.33106 q^{56} -11.8481 q^{57} -1.00000 q^{58} +13.2848 q^{59} -5.74741 q^{60} +6.26597 q^{61} +1.28851 q^{62} +4.50336 q^{63} +1.00000 q^{64} +3.72457 q^{65} -6.87647 q^{66} -8.37331 q^{67} -5.34308 q^{68} +2.52651 q^{69} +3.02795 q^{70} +9.48799 q^{71} +3.38328 q^{72} +10.2351 q^{73} +6.71008 q^{74} -0.441841 q^{75} +4.68951 q^{76} +3.62279 q^{77} -4.13664 q^{78} +9.05742 q^{79} +2.27484 q^{80} -7.70327 q^{81} -6.72031 q^{82} +4.69227 q^{83} -3.36295 q^{84} -12.1546 q^{85} +7.66918 q^{86} +2.52651 q^{87} +2.72172 q^{88} +11.9360 q^{89} +7.69640 q^{90} +2.17934 q^{91} -1.00000 q^{92} -3.25544 q^{93} +5.22508 q^{94} +10.6679 q^{95} -2.52651 q^{96} +14.2260 q^{97} -5.22827 q^{98} +9.20834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.52651	−1.45868	−0.729342	−	0.684149i	$-0.760174\pi$
$3$	−2.52651	−1.45868	−0.729342	+	0.684149i	$0.760174\pi$
$4$	1.00000	0.500000
$5$	2.27484	1.01734	0.508669	−	0.860962i	$-0.330138\pi$
$5$	2.27484	1.01734	0.508669	+	0.860962i	$0.330138\pi$
$6$	−2.52651	−1.03145
$7$	1.33106	0.503095	0.251547	−	0.967845i	$-0.419061\pi$
$7$	1.33106	0.503095	0.251547	+	0.967845i	$0.419061\pi$
$8$	1.00000	0.353553
$9$	3.38328	1.12776
$10$	2.27484	0.719367
$11$	2.72172	0.820630	0.410315	−	0.911944i	$-0.365419\pi$
$11$	2.72172	0.820630	0.410315	+	0.911944i	$0.365419\pi$
$12$	−2.52651	−0.729342
$13$	1.63729	0.454103	0.227052	−	0.973883i	$-0.427091\pi$
$13$	1.63729	0.454103	0.227052	+	0.973883i	$0.427091\pi$
$14$	1.33106	0.355742
$15$	−5.74741	−1.48397
$16$	1.00000	0.250000
$17$	−5.34308	−1.29589	−0.647943	−	0.761689i	$-0.724371\pi$
$17$	−5.34308	−1.29589	−0.647943	+	0.761689i	$0.724371\pi$
$18$	3.38328	0.797446
$19$	4.68951	1.07585	0.537923	−	0.842994i	$-0.319209\pi$
$19$	4.68951	1.07585	0.537923	+	0.842994i	$0.319209\pi$
$20$	2.27484	0.508669
$21$	−3.36295	−0.733856
$22$	2.72172	0.580273
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.52651	−0.515723
$25$	0.174882	0.0349763
$26$	1.63729	0.321099
$27$	−0.968356	−0.186360
$28$	1.33106	0.251547
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−5.74741	−1.04933
$31$	1.28851	0.231423	0.115712	−	0.993283i	$-0.463085\pi$
$31$	1.28851	0.231423	0.115712	+	0.993283i	$0.463085\pi$
$32$	1.00000	0.176777
$33$	−6.87647	−1.19704
$34$	−5.34308	−0.916330
$35$	3.02795	0.511817
$36$	3.38328	0.563880
$37$	6.71008	1.10313	0.551565	−	0.834132i	$-0.314031\pi$
$37$	6.71008	1.10313	0.551565	+	0.834132i	$0.314031\pi$
$38$	4.68951	0.760738
$39$	−4.13664	−0.662393
$40$	2.27484	0.359683
$41$	−6.72031	−1.04954	−0.524768	−	0.851245i	$-0.675848\pi$
$41$	−6.72031	−1.04954	−0.524768	+	0.851245i	$0.675848\pi$
$42$	−3.36295	−0.518915
$43$	7.66918	1.16954	0.584770	−	0.811199i	$-0.301185\pi$
$43$	7.66918	1.16954	0.584770	+	0.811199i	$0.301185\pi$
$44$	2.72172	0.410315
$45$	7.69640	1.14731
$46$	−1.00000	−0.147442
$47$	5.22508	0.762156	0.381078	−	0.924543i	$-0.375553\pi$
$47$	5.22508	0.762156	0.381078	+	0.924543i	$0.375553\pi$
$48$	−2.52651	−0.364671
$49$	−5.22827	−0.746896
$50$	0.174882	0.0247320
$51$	13.4994	1.89029
$52$	1.63729	0.227052
$53$	−11.7594	−1.61528	−0.807640	−	0.589675i	$-0.799256\pi$
$53$	−11.7594	−1.61528	−0.807640	+	0.589675i	$0.799256\pi$
$54$	−0.968356	−0.131777
$55$	6.19147	0.834858
$56$	1.33106	0.177871
$57$	−11.8481	−1.56932
$58$	−1.00000	−0.131306
$59$	13.2848	1.72954	0.864769	−	0.502171i	$-0.167465\pi$
$59$	13.2848	1.72954	0.864769	+	0.502171i	$0.167465\pi$
$60$	−5.74741	−0.741987
$61$	6.26597	0.802276	0.401138	−	0.916018i	$-0.368615\pi$
$61$	6.26597	0.802276	0.401138	+	0.916018i	$0.368615\pi$
$62$	1.28851	0.163641
$63$	4.50336	0.567370
$64$	1.00000	0.125000
$65$	3.72457	0.461976
$66$	−6.87647	−0.846435
$67$	−8.37331	−1.02296	−0.511481	−	0.859295i	$-0.670903\pi$
$67$	−8.37331	−1.02296	−0.511481	+	0.859295i	$0.670903\pi$
$68$	−5.34308	−0.647943
$69$	2.52651	0.304157
$70$	3.02795	0.361909
$71$	9.48799	1.12602	0.563009	−	0.826451i	$-0.309644\pi$
$71$	9.48799	1.12602	0.563009	+	0.826451i	$0.309644\pi$
$72$	3.38328	0.398723
$73$	10.2351	1.19793	0.598963	−	0.800777i	$-0.295580\pi$
$73$	10.2351	1.19793	0.598963	+	0.800777i	$0.295580\pi$
$74$	6.71008	0.780031
$75$	−0.441841	−0.0510194
$76$	4.68951	0.537923
$77$	3.62279	0.412855
$78$	−4.13664	−0.468383
$79$	9.05742	1.01904	0.509520	−	0.860459i	$-0.329823\pi$
$79$	9.05742	1.01904	0.509520	+	0.860459i	$0.329823\pi$
$80$	2.27484	0.254334
$81$	−7.70327	−0.855918
$82$	−6.72031	−0.742134
$83$	4.69227	0.515043	0.257522	−	0.966273i	$-0.417094\pi$
$83$	4.69227	0.515043	0.257522	+	0.966273i	$0.417094\pi$
$84$	−3.36295	−0.366928
$85$	−12.1546	−1.31835
$86$	7.66918	0.826989
$87$	2.52651	0.270871
$88$	2.72172	0.290137
$89$	11.9360	1.26521	0.632606	−	0.774474i	$-0.281985\pi$
$89$	11.9360	1.26521	0.632606	+	0.774474i	$0.281985\pi$
$90$	7.69640	0.811272
$91$	2.17934	0.228457
$92$	−1.00000	−0.104257
$93$	−3.25544	−0.337573
$94$	5.22508	0.538926
$95$	10.6679	1.09450
$96$	−2.52651	−0.257861
$97$	14.2260	1.44443	0.722217	−	0.691667i	$-0.243123\pi$
$97$	14.2260	1.44443	0.722217	+	0.691667i	$0.243123\pi$
$98$	−5.22827	−0.528135
$99$	9.20834	0.925473
$100$	0.174882	0.0174882
$101$	7.57190	0.753432	0.376716	−	0.926329i	$-0.377053\pi$
$101$	7.57190	0.753432	0.376716	+	0.926329i	$0.377053\pi$
$102$	13.4994	1.33664
$103$	−5.80246	−0.571733	−0.285867	−	0.958269i	$-0.592281\pi$
$103$	−5.80246	−0.571733	−0.285867	+	0.958269i	$0.592281\pi$
$104$	1.63729	0.160550
$105$	−7.65016	−0.746580
$106$	−11.7594	−1.14218
$107$	−10.3755	−1.00304	−0.501520	−	0.865146i	$-0.667226\pi$
$107$	−10.3755	−1.00304	−0.501520	+	0.865146i	$0.667226\pi$
$108$	−0.968356	−0.0931801
$109$	−2.61556	−0.250525	−0.125263	−	0.992124i	$-0.539977\pi$
$109$	−2.61556	−0.250525	−0.125263	+	0.992124i	$0.539977\pi$
$110$	6.19147	0.590334
$111$	−16.9531	−1.60912
$112$	1.33106	0.125774
$113$	0.734043	0.0690529	0.0345265	−	0.999404i	$-0.489008\pi$
$113$	0.734043	0.0690529	0.0345265	+	0.999404i	$0.489008\pi$
$114$	−11.8481	−1.10968
$115$	−2.27484	−0.212130
$116$	−1.00000	−0.0928477
$117$	5.53941	0.512119
$118$	13.2848	1.22297
$119$	−7.11197	−0.651953
$120$	−5.74741	−0.524664
$121$	−3.59223	−0.326566
$122$	6.26597	0.567295
$123$	16.9790	1.53094
$124$	1.28851	0.115712
$125$	−10.9764	−0.981755
$126$	4.50336	0.401191
$127$	−11.3892	−1.01063	−0.505316	−	0.862934i	$-0.668624\pi$
$127$	−11.3892	−1.01063	−0.505316	+	0.862934i	$0.668624\pi$
$128$	1.00000	0.0883883
$129$	−19.3763	−1.70599
$130$	3.72457	0.326667
$131$	−9.87851	−0.863089	−0.431545	−	0.902092i	$-0.642031\pi$
$131$	−9.87851	−0.863089	−0.431545	+	0.902092i	$0.642031\pi$
$132$	−6.87647	−0.598520
$133$	6.24203	0.541253
$134$	−8.37331	−0.723344
$135$	−2.20285	−0.189591
$136$	−5.34308	−0.458165
$137$	−15.1478	−1.29416	−0.647081	−	0.762421i	$-0.724010\pi$
$137$	−15.1478	−1.29416	−0.647081	+	0.762421i	$0.724010\pi$
$138$	2.52651	0.215071
$139$	−1.50917	−0.128007	−0.0640033	−	0.997950i	$-0.520387\pi$
$139$	−1.50917	−0.128007	−0.0640033	+	0.997950i	$0.520387\pi$
$140$	3.02795	0.255909
$141$	−13.2012	−1.11174
$142$	9.48799	0.796214
$143$	4.45626	0.372651
$144$	3.38328	0.281940
$145$	−2.27484	−0.188915
$146$	10.2351	0.847061
$147$	13.2093	1.08948
$148$	6.71008	0.551565
$149$	−4.24553	−0.347807	−0.173904	−	0.984763i	$-0.555638\pi$
$149$	−4.24553	−0.347807	−0.173904	+	0.984763i	$0.555638\pi$
$150$	−0.441841	−0.0360762
$151$	−2.62221	−0.213393	−0.106696	−	0.994292i	$-0.534027\pi$
$151$	−2.62221	−0.213393	−0.106696	+	0.994292i	$0.534027\pi$
$152$	4.68951	0.380369
$153$	−18.0771	−1.46145
$154$	3.62279	0.291932
$155$	2.93115	0.235436
$156$	−4.13664	−0.331197
$157$	−19.5518	−1.56040	−0.780201	−	0.625529i	$-0.784883\pi$
$157$	−19.5518	−1.56040	−0.780201	+	0.625529i	$0.784883\pi$
$158$	9.05742	0.720569
$159$	29.7104	2.35618
$160$	2.27484	0.179842
$161$	−1.33106	−0.104902
$162$	−7.70327	−0.605226
$163$	−2.80107	−0.219397	−0.109698	−	0.993965i	$-0.534989\pi$
$163$	−2.80107	−0.219397	−0.109698	+	0.993965i	$0.534989\pi$
$164$	−6.72031	−0.524768
$165$	−15.6429	−1.21779
$166$	4.69227	0.364191
$167$	−14.2911	−1.10587	−0.552937	−	0.833223i	$-0.686493\pi$
$167$	−14.2911	−1.10587	−0.552937	+	0.833223i	$0.686493\pi$
$168$	−3.36295	−0.259457
$169$	−10.3193	−0.793790
$170$	−12.1546	−0.932217
$171$	15.8659	1.21330
$172$	7.66918	0.584770
$173$	2.87566	0.218632	0.109316	−	0.994007i	$-0.465134\pi$
$173$	2.87566	0.218632	0.109316	+	0.994007i	$0.465134\pi$
$174$	2.52651	0.191535
$175$	0.232779	0.0175964
$176$	2.72172	0.205158
$177$	−33.5643	−2.52285
$178$	11.9360	0.894639
$179$	15.0520	1.12504	0.562519	−	0.826784i	$-0.309832\pi$
$179$	15.0520	1.12504	0.562519	+	0.826784i	$0.309832\pi$
$180$	7.69640	0.573656
$181$	3.22054	0.239381	0.119691	−	0.992811i	$-0.461810\pi$
$181$	3.22054	0.239381	0.119691	+	0.992811i	$0.461810\pi$
$182$	2.17934	0.161543
$183$	−15.8311	−1.17027
$184$	−1.00000	−0.0737210
$185$	15.2643	1.12226
$186$	−3.25544	−0.238700
$187$	−14.5424	−1.06344
$188$	5.22508	0.381078
$189$	−1.28894	−0.0937568
$190$	10.6679	0.773928
$191$	12.4630	0.901788	0.450894	−	0.892578i	$-0.351105\pi$
$191$	12.4630	0.901788	0.450894	+	0.892578i	$0.351105\pi$
$192$	−2.52651	−0.182336
$193$	10.1341	0.729472	0.364736	−	0.931111i	$-0.381159\pi$
$193$	10.1341	0.729472	0.364736	+	0.931111i	$0.381159\pi$
$194$	14.2260	1.02137
$195$	−9.41019	−0.673878
$196$	−5.22827	−0.373448
$197$	7.94915	0.566354	0.283177	−	0.959068i	$-0.408612\pi$
$197$	7.94915	0.566354	0.283177	+	0.959068i	$0.408612\pi$
$198$	9.20834	0.654408
$199$	−18.4253	−1.30614	−0.653068	−	0.757300i	$-0.726518\pi$
$199$	−18.4253	−1.30614	−0.653068	+	0.757300i	$0.726518\pi$
$200$	0.174882	0.0123660
$201$	21.1553	1.49218
$202$	7.57190	0.532757
$203$	−1.33106	−0.0934223
$204$	13.4994	0.945144
$205$	−15.2876	−1.06773
$206$	−5.80246	−0.404277
$207$	−3.38328	−0.235154
$208$	1.63729	0.113526
$209$	12.7635	0.882872
$210$	−7.65016	−0.527912
$211$	−4.50954	−0.310450	−0.155225	−	0.987879i	$-0.549610\pi$
$211$	−4.50954	−0.310450	−0.155225	+	0.987879i	$0.549610\pi$
$212$	−11.7594	−0.807640
$213$	−23.9715	−1.64250
$214$	−10.3755	−0.709257
$215$	17.4461	1.18982
$216$	−0.968356	−0.0658883
$217$	1.71509	0.116428
$218$	−2.61556	−0.177148
$219$	−25.8591	−1.74739
$220$	6.19147	0.417429
$221$	−8.74818	−0.588466
$222$	−16.9531	−1.13782
$223$	8.58839	0.575121	0.287561	−	0.957762i	$-0.407156\pi$
$223$	8.58839	0.575121	0.287561	+	0.957762i	$0.407156\pi$
$224$	1.33106	0.0889354
$225$	0.591673	0.0394449
$226$	0.734043	0.0488278
$227$	−25.4490	−1.68911	−0.844556	−	0.535468i	$-0.820135\pi$
$227$	−25.4490	−1.68911	−0.844556	+	0.535468i	$0.820135\pi$
$228$	−11.8481	−0.784660
$229$	11.7705	0.777817	0.388909	−	0.921276i	$-0.372852\pi$
$229$	11.7705	0.777817	0.388909	+	0.921276i	$0.372852\pi$
$230$	−2.27484	−0.149998
$231$	−9.15302	−0.602225
$232$	−1.00000	−0.0656532
$233$	−9.84846	−0.645194	−0.322597	−	0.946536i	$-0.604556\pi$
$233$	−9.84846	−0.645194	−0.322597	+	0.946536i	$0.604556\pi$
$234$	5.53941	0.362123
$235$	11.8862	0.775370
$236$	13.2848	0.864769
$237$	−22.8837	−1.48646
$238$	−7.11197	−0.461001
$239$	8.85331	0.572673	0.286337	−	0.958129i	$-0.407562\pi$
$239$	8.85331	0.572673	0.286337	+	0.958129i	$0.407562\pi$
$240$	−5.74741	−0.370994
$241$	9.00091	0.579800	0.289900	−	0.957057i	$-0.406378\pi$
$241$	9.00091	0.579800	0.289900	+	0.957057i	$0.406378\pi$
$242$	−3.59223	−0.230917
$243$	22.3675	1.43487
$244$	6.26597	0.401138
$245$	−11.8935	−0.759845
$246$	16.9790	1.08254
$247$	7.67809	0.488545
$248$	1.28851	0.0818205
$249$	−11.8551	−0.751285
$250$	−10.9764	−0.694206
$251$	−16.0024	−1.01006	−0.505030	−	0.863102i	$-0.668519\pi$
$251$	−16.0024	−1.01006	−0.505030	+	0.863102i	$0.668519\pi$
$252$	4.50336	0.283685
$253$	−2.72172	−0.171113
$254$	−11.3892	−0.714625
$255$	30.7088	1.92306
$256$	1.00000	0.0625000
$257$	21.9581	1.36971	0.684855	−	0.728679i	$-0.259865\pi$
$257$	21.9581	1.36971	0.684855	+	0.728679i	$0.259865\pi$
$258$	−19.3763	−1.20632
$259$	8.93154	0.554979
$260$	3.72457	0.230988
$261$	−3.38328	−0.209420
$262$	−9.87851	−0.610296
$263$	−23.7605	−1.46514	−0.732568	−	0.680694i	$-0.761678\pi$
$263$	−23.7605	−1.46514	−0.732568	+	0.680694i	$0.761678\pi$
$264$	−6.87647	−0.423218
$265$	−26.7508	−1.64329
$266$	6.24203	0.382723
$267$	−30.1564	−1.84554
$268$	−8.37331	−0.511481
$269$	−27.6821	−1.68781	−0.843904	−	0.536495i	$-0.819748\pi$
$269$	−27.6821	−1.68781	−0.843904	+	0.536495i	$0.819748\pi$
$270$	−2.20285	−0.134061
$271$	24.2712	1.47437	0.737186	−	0.675690i	$-0.236154\pi$
$271$	24.2712	1.47437	0.737186	+	0.675690i	$0.236154\pi$
$272$	−5.34308	−0.323972
$273$	−5.50614	−0.333246
$274$	−15.1478	−0.915111
$275$	0.475979	0.0287026
$276$	2.52651	0.152078
$277$	−7.76532	−0.466573	−0.233286	−	0.972408i	$-0.574948\pi$
$277$	−7.76532	−0.466573	−0.233286	+	0.972408i	$0.574948\pi$
$278$	−1.50917	−0.0905143
$279$	4.35939	0.260990
$280$	3.02795	0.180955
$281$	−8.40852	−0.501610	−0.250805	−	0.968038i	$-0.580695\pi$
$281$	−8.40852	−0.501610	−0.250805	+	0.968038i	$0.580695\pi$
$282$	−13.2012	−0.786122
$283$	−28.2349	−1.67839	−0.839195	−	0.543830i	$-0.816974\pi$
$283$	−28.2349	−1.67839	−0.839195	+	0.543830i	$0.816974\pi$
$284$	9.48799	0.563009
$285$	−26.9525	−1.59653
$286$	4.45626	0.263504
$287$	−8.94516	−0.528016
$288$	3.38328	0.199362
$289$	11.5485	0.679321
$290$	−2.27484	−0.133583
$291$	−35.9422	−2.10697
$292$	10.2351	0.598963
$293$	8.42638	0.492274	0.246137	−	0.969235i	$-0.420839\pi$
$293$	8.42638	0.492274	0.246137	+	0.969235i	$0.420839\pi$
$294$	13.2093	0.770382
$295$	30.2208	1.75952
$296$	6.71008	0.390015
$297$	−2.63560	−0.152933
$298$	−4.24553	−0.245937
$299$	−1.63729	−0.0946871
$300$	−0.441841	−0.0255097
$301$	10.2082	0.588389
$302$	−2.62221	−0.150891
$303$	−19.1305	−1.09902
$304$	4.68951	0.268962
$305$	14.2541	0.816186
$306$	−18.0771	−1.03340
$307$	−16.3683	−0.934189	−0.467095	−	0.884207i	$-0.654699\pi$
$307$	−16.3683	−0.934189	−0.467095	+	0.884207i	$0.654699\pi$
$308$	3.62279	0.206427
$309$	14.6600	0.833978
$310$	2.93115	0.166478
$311$	6.81694	0.386553	0.193276	−	0.981144i	$-0.438089\pi$
$311$	6.81694	0.386553	0.193276	+	0.981144i	$0.438089\pi$
$312$	−4.13664	−0.234191
$313$	18.1589	1.02640	0.513202	−	0.858268i	$-0.328459\pi$
$313$	18.1589	1.02640	0.513202	+	0.858268i	$0.328459\pi$
$314$	−19.5518	−1.10337
$315$	10.2444	0.577207
$316$	9.05742	0.509520
$317$	−34.9606	−1.96358	−0.981792	−	0.189959i	$-0.939164\pi$
$317$	−34.9606	−1.96358	−0.981792	+	0.189959i	$0.939164\pi$
$318$	29.7104	1.66607
$319$	−2.72172	−0.152387
$320$	2.27484	0.127167
$321$	26.2139	1.46312
$322$	−1.33106	−0.0741773
$323$	−25.0564	−1.39417
$324$	−7.70327	−0.427959
$325$	0.286332	0.0158829
$326$	−2.80107	−0.155137
$327$	6.60825	0.365437
$328$	−6.72031	−0.371067
$329$	6.95491	0.383437
$330$	−15.6429	−0.861111
$331$	5.00360	0.275023	0.137511	−	0.990500i	$-0.456090\pi$
$331$	5.00360	0.275023	0.137511	+	0.990500i	$0.456090\pi$
$332$	4.69227	0.257522
$333$	22.7020	1.24406
$334$	−14.2911	−0.781972
$335$	−19.0479	−1.04070
$336$	−3.36295	−0.183464
$337$	−12.0562	−0.656741	−0.328371	−	0.944549i	$-0.606499\pi$
$337$	−12.0562	−0.656741	−0.328371	+	0.944549i	$0.606499\pi$
$338$	−10.3193	−0.561294
$339$	−1.85457	−0.100726
$340$	−12.1546	−0.659177
$341$	3.50697	0.189913
$342$	15.8659	0.857930
$343$	−16.2766	−0.878854
$344$	7.66918	0.413495
$345$	5.74741	0.309430
$346$	2.87566	0.154596
$347$	12.0763	0.648292	0.324146	−	0.946007i	$-0.394923\pi$
$347$	12.0763	0.648292	0.324146	+	0.946007i	$0.394923\pi$
$348$	2.52651	0.135435
$349$	3.72959	0.199640	0.0998202	−	0.995005i	$-0.468173\pi$
$349$	3.72959	0.199640	0.0998202	+	0.995005i	$0.468173\pi$
$350$	0.232779	0.0124425
$351$	−1.58548	−0.0846268
$352$	2.72172	0.145068
$353$	−12.6477	−0.673168	−0.336584	−	0.941653i	$-0.609272\pi$
$353$	−12.6477	−0.673168	−0.336584	+	0.941653i	$0.609272\pi$
$354$	−33.5643	−1.78392
$355$	21.5836	1.14554
$356$	11.9360	0.632606
$357$	17.9685	0.950994
$358$	15.0520	0.795522
$359$	16.9800	0.896171	0.448086	−	0.893991i	$-0.352106\pi$
$359$	16.9800	0.896171	0.448086	+	0.893991i	$0.352106\pi$
$360$	7.69640	0.405636
$361$	2.99147	0.157446
$362$	3.22054	0.169268
$363$	9.07581	0.476357
$364$	2.17934	0.114228
$365$	23.2831	1.21869
$366$	−15.8311	−0.827504
$367$	6.57419	0.343170	0.171585	−	0.985169i	$-0.445111\pi$
$367$	6.57419	0.343170	0.171585	+	0.985169i	$0.445111\pi$
$368$	−1.00000	−0.0521286
$369$	−22.7367	−1.18362
$370$	15.2643	0.793555
$371$	−15.6525	−0.812639
$372$	−3.25544	−0.168787
$373$	−15.2797	−0.791153	−0.395577	−	0.918433i	$-0.629455\pi$
$373$	−15.2797	−0.791153	−0.395577	+	0.918433i	$0.629455\pi$
$374$	−14.5424	−0.751968
$375$	27.7319	1.43207
$376$	5.22508	0.269463
$377$	−1.63729	−0.0843249
$378$	−1.28894	−0.0662961
$379$	−6.21271	−0.319125	−0.159563	−	0.987188i	$-0.551008\pi$
$379$	−6.21271	−0.319125	−0.159563	+	0.987188i	$0.551008\pi$
$380$	10.6679	0.547250
$381$	28.7751	1.47419
$382$	12.4630	0.637660
$383$	−3.33221	−0.170268	−0.0851339	−	0.996370i	$-0.527132\pi$
$383$	−3.33221	−0.170268	−0.0851339	+	0.996370i	$0.527132\pi$
$384$	−2.52651	−0.128931
$385$	8.24124	0.420013
$386$	10.1341	0.515814
$387$	25.9470	1.31896
$388$	14.2260	0.722217
$389$	−25.5372	−1.29479	−0.647393	−	0.762156i	$-0.724141\pi$
$389$	−25.5372	−1.29479	−0.647393	+	0.762156i	$0.724141\pi$
$390$	−9.41019	−0.476503
$391$	5.34308	0.270211
$392$	−5.22827	−0.264068
$393$	24.9582	1.25897
$394$	7.94915	0.400472
$395$	20.6041	1.03671
$396$	9.20834	0.462737
$397$	19.6657	0.986993	0.493497	−	0.869748i	$-0.335719\pi$
$397$	19.6657	0.986993	0.493497	+	0.869748i	$0.335719\pi$
$398$	−18.4253	−0.923577
$399$	−15.7706	−0.789517
$400$	0.174882	0.00874408
$401$	−25.5515	−1.27598	−0.637991	−	0.770044i	$-0.720234\pi$
$401$	−25.5515	−1.27598	−0.637991	+	0.770044i	$0.720234\pi$
$402$	21.1553	1.05513
$403$	2.10967	0.105090
$404$	7.57190	0.376716
$405$	−17.5237	−0.870758
$406$	−1.33106	−0.0660596
$407$	18.2630	0.905262
$408$	13.4994	0.668318
$409$	−13.7634	−0.680557	−0.340278	−	0.940325i	$-0.610521\pi$
$409$	−13.7634	−0.680557	−0.340278	+	0.940325i	$0.610521\pi$
$410$	−15.2876	−0.755001
$411$	38.2711	1.88777
$412$	−5.80246	−0.285867
$413$	17.6829	0.870121
$414$	−3.38328	−0.166279
$415$	10.6741	0.523973
$416$	1.63729	0.0802749
$417$	3.81295	0.186721
$418$	12.7635	0.624285
$419$	−30.1116	−1.47105	−0.735524	−	0.677498i	$-0.763064\pi$
$419$	−30.1116	−1.47105	−0.735524	+	0.677498i	$0.763064\pi$
$420$	−7.65016	−0.373290
$421$	−7.67995	−0.374298	−0.187149	−	0.982332i	$-0.559925\pi$
$421$	−7.67995	−0.374298	−0.187149	+	0.982332i	$0.559925\pi$
$422$	−4.50954	−0.219521
$423$	17.6779	0.859528
$424$	−11.7594	−0.571088
$425$	−0.934406	−0.0453253
$426$	−23.9715	−1.16143
$427$	8.34041	0.403621
$428$	−10.3755	−0.501520
$429$	−11.2588	−0.543580
$430$	17.4461	0.841327
$431$	34.0466	1.63997	0.819984	−	0.572387i	$-0.193982\pi$
$431$	34.0466	1.63997	0.819984	+	0.572387i	$0.193982\pi$
$432$	−0.968356	−0.0465900
$433$	17.6946	0.850349	0.425174	−	0.905111i	$-0.360213\pi$
$433$	17.6946	0.850349	0.425174	+	0.905111i	$0.360213\pi$
$434$	1.71509	0.0823269
$435$	5.74741	0.275567
$436$	−2.61556	−0.125263
$437$	−4.68951	−0.224330
$438$	−25.8591	−1.23559
$439$	−10.6834	−0.509893	−0.254946	−	0.966955i	$-0.582058\pi$
$439$	−10.6834	−0.509893	−0.254946	+	0.966955i	$0.582058\pi$
$440$	6.19147	0.295167
$441$	−17.6887	−0.842319
$442$	−8.74818	−0.416108
$443$	7.86945	0.373889	0.186944	−	0.982370i	$-0.440142\pi$
$443$	7.86945	0.373889	0.186944	+	0.982370i	$0.440142\pi$
$444$	−16.9531	−0.804559
$445$	27.1524	1.28715
$446$	8.58839	0.406672
$447$	10.7264	0.507341
$448$	1.33106	0.0628868
$449$	−31.8692	−1.50400	−0.752001	−	0.659162i	$-0.770911\pi$
$449$	−31.8692	−1.50400	−0.752001	+	0.659162i	$0.770911\pi$
$450$	0.591673	0.0278917
$451$	−18.2908	−0.861281
$452$	0.734043	0.0345265
$453$	6.62506	0.311273
$454$	−25.4490	−1.19438
$455$	4.95764	0.232418
$456$	−11.8481	−0.554838
$457$	−17.5067	−0.818931	−0.409466	−	0.912326i	$-0.634285\pi$
$457$	−17.5067	−0.818931	−0.409466	+	0.912326i	$0.634285\pi$
$458$	11.7705	0.550000
$459$	5.17400	0.241502
$460$	−2.27484	−0.106065
$461$	40.9670	1.90803	0.954013	−	0.299766i	$-0.0969088\pi$
$461$	40.9670	1.90803	0.954013	+	0.299766i	$0.0969088\pi$
$462$	−9.15302	−0.425837
$463$	34.9144	1.62261	0.811305	−	0.584623i	$-0.198758\pi$
$463$	34.9144	1.62261	0.811305	+	0.584623i	$0.198758\pi$
$464$	−1.00000	−0.0464238
$465$	−7.40559	−0.343426
$466$	−9.84846	−0.456221
$467$	−20.9403	−0.969000	−0.484500	−	0.874791i	$-0.660998\pi$
$467$	−20.9403	−0.969000	−0.484500	+	0.874791i	$0.660998\pi$
$468$	5.53941	0.256060
$469$	−11.1454	−0.514647
$470$	11.8862	0.548270
$471$	49.3979	2.27613
$472$	13.2848	0.611484
$473$	20.8734	0.959759
$474$	−22.8837	−1.05108
$475$	0.820109	0.0376292
$476$	−7.11197	−0.325977
$477$	−39.7854	−1.82165
$478$	8.85331	0.404941
$479$	9.23258	0.421848	0.210924	−	0.977503i	$-0.432353\pi$
$479$	9.23258	0.421848	0.210924	+	0.977503i	$0.432353\pi$
$480$	−5.74741	−0.262332
$481$	10.9864	0.500935
$482$	9.00091	0.409980
$483$	3.36295	0.153020
$484$	−3.59223	−0.163283
$485$	32.3619	1.46948
$486$	22.3675	1.01461
$487$	40.6871	1.84371	0.921855	−	0.387535i	$-0.126673\pi$
$487$	40.6871	1.84371	0.921855	+	0.387535i	$0.126673\pi$
$488$	6.26597	0.283647
$489$	7.07695	0.320031
$490$	−11.8935	−0.537292
$491$	−8.44462	−0.381100	−0.190550	−	0.981677i	$-0.561027\pi$
$491$	−8.44462	−0.381100	−0.190550	+	0.981677i	$0.561027\pi$
$492$	16.9790	0.765471
$493$	5.34308	0.240640
$494$	7.67809	0.345454
$495$	20.9475	0.941519
$496$	1.28851	0.0578558
$497$	12.6291	0.566493
$498$	−11.8551	−0.531239
$499$	14.5022	0.649210	0.324605	−	0.945850i	$-0.394769\pi$
$499$	14.5022	0.649210	0.324605	+	0.945850i	$0.394769\pi$
$500$	−10.9764	−0.490878
$501$	36.1066	1.61312
$502$	−16.0024	−0.714220
$503$	−26.0048	−1.15950	−0.579749	−	0.814795i	$-0.696850\pi$
$503$	−26.0048	−1.15950	−0.579749	+	0.814795i	$0.696850\pi$
$504$	4.50336	0.200595
$505$	17.2248	0.766495
$506$	−2.72172	−0.120995
$507$	26.0718	1.15789
$508$	−11.3892	−0.505316
$509$	5.30400	0.235096	0.117548	−	0.993067i	$-0.462497\pi$
$509$	5.30400	0.235096	0.117548	+	0.993067i	$0.462497\pi$
$510$	30.7088	1.35981
$511$	13.6235	0.602670
$512$	1.00000	0.0441942
$513$	−4.54111	−0.200495
$514$	21.9581	0.968531
$515$	−13.1996	−0.581646
$516$	−19.3763	−0.852994
$517$	14.2212	0.625448
$518$	8.93154	0.392429
$519$	−7.26539	−0.318915
$520$	3.72457	0.163333
$521$	15.3537	0.672656	0.336328	−	0.941745i	$-0.390815\pi$
$521$	15.3537	0.672656	0.336328	+	0.941745i	$0.390815\pi$
$522$	−3.38328	−0.148082
$523$	40.3553	1.76461	0.882306	−	0.470676i	$-0.155990\pi$
$523$	40.3553	1.76461	0.882306	+	0.470676i	$0.155990\pi$
$524$	−9.87851	−0.431545
$525$	−0.588118	−0.0256676
$526$	−23.7605	−1.03601
$527$	−6.88461	−0.299898
$528$	−6.87647	−0.299260
$529$	1.00000	0.0434783
$530$	−26.7508	−1.16198
$531$	44.9463	1.95050
$532$	6.24203	0.270626
$533$	−11.0031	−0.476598
$534$	−30.1564	−1.30500
$535$	−23.6026	−1.02043
$536$	−8.37331	−0.361672
$537$	−38.0290	−1.64107
$538$	−27.6821	−1.19346
$539$	−14.2299	−0.612925
$540$	−2.20285	−0.0947956
$541$	5.71398	0.245663	0.122831	−	0.992428i	$-0.460803\pi$
$541$	5.71398	0.245663	0.122831	+	0.992428i	$0.460803\pi$
$542$	24.2712	1.04254
$543$	−8.13675	−0.349181
$544$	−5.34308	−0.229083
$545$	−5.94997	−0.254869
$546$	−5.50614	−0.235641
$547$	−18.0837	−0.773205	−0.386603	−	0.922246i	$-0.626351\pi$
$547$	−18.0837	−0.773205	−0.386603	+	0.922246i	$0.626351\pi$
$548$	−15.1478	−0.647081
$549$	21.1995	0.904774
$550$	0.475979	0.0202958
$551$	−4.68951	−0.199780
$552$	2.52651	0.107536
$553$	12.0560	0.512673
$554$	−7.76532	−0.329917
$555$	−38.5656	−1.63702
$556$	−1.50917	−0.0640033
$557$	−6.35325	−0.269196	−0.134598	−	0.990900i	$-0.542974\pi$
$557$	−6.35325	−0.269196	−0.134598	+	0.990900i	$0.542974\pi$
$558$	4.35939	0.184548
$559$	12.5567	0.531091
$560$	3.02795	0.127954
$561$	36.7415	1.55123
$562$	−8.40852	−0.354692
$563$	19.7667	0.833067	0.416533	−	0.909120i	$-0.363245\pi$
$563$	19.7667	0.833067	0.416533	+	0.909120i	$0.363245\pi$
$564$	−13.2012	−0.555872
$565$	1.66983	0.0702502
$566$	−28.2349	−1.18680
$567$	−10.2535	−0.430608
$568$	9.48799	0.398107
$569$	16.7398	0.701771	0.350885	−	0.936418i	$-0.385881\pi$
$569$	16.7398	0.701771	0.350885	+	0.936418i	$0.385881\pi$
$570$	−26.9525	−1.12892
$571$	25.4767	1.06617	0.533084	−	0.846063i	$-0.321033\pi$
$571$	25.4767	1.06617	0.533084	+	0.846063i	$0.321033\pi$
$572$	4.45626	0.186325
$573$	−31.4878	−1.31542
$574$	−8.94516	−0.373364
$575$	−0.174882	−0.00729307
$576$	3.38328	0.140970
$577$	−32.8891	−1.36919	−0.684595	−	0.728924i	$-0.740021\pi$
$577$	−32.8891	−1.36919	−0.684595	+	0.728924i	$0.740021\pi$
$578$	11.5485	0.480353
$579$	−25.6041	−1.06407
$580$	−2.27484	−0.0944574
$581$	6.24571	0.259116
$582$	−35.9422	−1.48985
$583$	−32.0059	−1.32555
$584$	10.2351	0.423531
$585$	12.6013	0.520998
$586$	8.42638	0.348090
$587$	−1.04143	−0.0429843	−0.0214922	−	0.999769i	$-0.506842\pi$
$587$	−1.04143	−0.0429843	−0.0214922	+	0.999769i	$0.506842\pi$
$588$	13.2093	0.544742
$589$	6.04248	0.248976
$590$	30.2208	1.24417
$591$	−20.0836	−0.826131
$592$	6.71008	0.275782
$593$	10.3840	0.426420	0.213210	−	0.977006i	$-0.431608\pi$
$593$	10.3840	0.426420	0.213210	+	0.977006i	$0.431608\pi$
$594$	−2.63560	−0.108140
$595$	−16.1786	−0.663257
$596$	−4.24553	−0.173904
$597$	46.5518	1.90524
$598$	−1.63729	−0.0669539
$599$	−36.1458	−1.47688	−0.738438	−	0.674321i	$-0.764436\pi$
$599$	−36.1458	−1.47688	−0.738438	+	0.674321i	$0.764436\pi$
$600$	−0.441841	−0.0180381
$601$	−30.6671	−1.25094	−0.625468	−	0.780250i	$-0.715092\pi$
$601$	−30.6671	−1.25094	−0.625468	+	0.780250i	$0.715092\pi$
$602$	10.2082	0.416054
$603$	−28.3292	−1.15365
$604$	−2.62221	−0.106696
$605$	−8.17173	−0.332228
$606$	−19.1305	−0.777124
$607$	−40.3470	−1.63763	−0.818817	−	0.574054i	$-0.805370\pi$
$607$	−40.3470	−1.63763	−0.818817	+	0.574054i	$0.805370\pi$
$608$	4.68951	0.190185
$609$	3.36295	0.136274
$610$	14.2541	0.577130
$611$	8.55498	0.346098
$612$	−18.0771	−0.730724
$613$	3.84480	0.155290	0.0776450	−	0.996981i	$-0.475260\pi$
$613$	3.84480	0.155290	0.0776450	+	0.996981i	$0.475260\pi$
$614$	−16.3683	−0.660572
$615$	38.6244	1.55748
$616$	3.62279	0.145966
$617$	−43.9231	−1.76828	−0.884138	−	0.467226i	$-0.845254\pi$
$617$	−43.9231	−1.76828	−0.884138	+	0.467226i	$0.845254\pi$
$618$	14.6600	0.589712
$619$	10.6846	0.429451	0.214725	−	0.976674i	$-0.431114\pi$
$619$	10.6846	0.429451	0.214725	+	0.976674i	$0.431114\pi$
$620$	2.93115	0.117718
$621$	0.968356	0.0388588
$622$	6.81694	0.273334
$623$	15.8875	0.636521
$624$	−4.13664	−0.165598
$625$	−25.8438	−1.03375
$626$	18.1589	0.725777
$627$	−32.2473	−1.28783
$628$	−19.5518	−0.780201
$629$	−35.8524	−1.42953
$630$	10.2444	0.408147
$631$	−8.07391	−0.321417	−0.160709	−	0.987002i	$-0.551378\pi$
$631$	−8.07391	−0.321417	−0.160709	+	0.987002i	$0.551378\pi$
$632$	9.05742	0.360285
$633$	11.3934	0.452848
$634$	−34.9606	−1.38846
$635$	−25.9087	−1.02815
$636$	29.7104	1.17809
$637$	−8.56021	−0.339168
$638$	−2.72172	−0.107754
$639$	32.1005	1.26988
$640$	2.27484	0.0899208
$641$	27.8226	1.09893	0.549464	−	0.835518i	$-0.314832\pi$
$641$	27.8226	1.09893	0.549464	+	0.835518i	$0.314832\pi$
$642$	26.2139	1.03458
$643$	−48.9411	−1.93005	−0.965025	−	0.262158i	$-0.915566\pi$
$643$	−48.9411	−1.93005	−0.965025	+	0.262158i	$0.915566\pi$
$644$	−1.33106	−0.0524512
$645$	−44.0779	−1.73557
$646$	−25.0564	−0.985830
$647$	−12.6844	−0.498676	−0.249338	−	0.968416i	$-0.580213\pi$
$647$	−12.6844	−0.498676	−0.249338	+	0.968416i	$0.580213\pi$
$648$	−7.70327	−0.302613
$649$	36.1576	1.41931
$650$	0.286332	0.0112309
$651$	−4.33320	−0.169831
$652$	−2.80107	−0.109698
$653$	−10.5033	−0.411026	−0.205513	−	0.978654i	$-0.565886\pi$
$653$	−10.5033	−0.411026	−0.205513	+	0.978654i	$0.565886\pi$
$654$	6.60825	0.258403
$655$	−22.4720	−0.878053
$656$	−6.72031	−0.262384
$657$	34.6281	1.35097
$658$	6.95491	0.271131
$659$	−48.0316	−1.87104	−0.935522	−	0.353268i	$-0.885070\pi$
$659$	−48.0316	−1.87104	−0.935522	+	0.353268i	$0.885070\pi$
$660$	−15.6429	−0.608897
$661$	40.4997	1.57525	0.787627	−	0.616152i	$-0.211309\pi$
$661$	40.4997	1.57525	0.787627	+	0.616152i	$0.211309\pi$
$662$	5.00360	0.194470
$663$	22.1024	0.858386
$664$	4.69227	0.182095
$665$	14.1996	0.550637
$666$	22.7020	0.879687
$667$	1.00000	0.0387202
$668$	−14.2911	−0.552937
$669$	−21.6987	−0.838920
$670$	−19.0479	−0.735885
$671$	17.0542	0.658372
$672$	−3.36295	−0.129729
$673$	3.38606	0.130523	0.0652615	−	0.997868i	$-0.479212\pi$
$673$	3.38606	0.130523	0.0652615	+	0.997868i	$0.479212\pi$
$674$	−12.0562	−0.464386
$675$	−0.169348	−0.00651819
$676$	−10.3193	−0.396895
$677$	16.0723	0.617707	0.308853	−	0.951110i	$-0.400055\pi$
$677$	16.0723	0.617707	0.308853	+	0.951110i	$0.400055\pi$
$678$	−1.85457	−0.0712243
$679$	18.9357	0.726687
$680$	−12.1546	−0.466109
$681$	64.2973	2.46388
$682$	3.50697	0.134289
$683$	−13.0138	−0.497959	−0.248980	−	0.968509i	$-0.580095\pi$
$683$	−13.0138	−0.497959	−0.248980	+	0.968509i	$0.580095\pi$
$684$	15.8659	0.606648
$685$	−34.4587	−1.31660
$686$	−16.2766	−0.621444
$687$	−29.7384	−1.13459
$688$	7.66918	0.292385
$689$	−19.2536	−0.733504
$690$	5.74741	0.218800
$691$	14.6292	0.556520	0.278260	−	0.960506i	$-0.410242\pi$
$691$	14.6292	0.556520	0.278260	+	0.960506i	$0.410242\pi$
$692$	2.87566	0.109316
$693$	12.2569	0.465601
$694$	12.0763	0.458412
$695$	−3.43313	−0.130226
$696$	2.52651	0.0957673
$697$	35.9071	1.36008
$698$	3.72959	0.141167
$699$	24.8823	0.941134
$700$	0.232779	0.00879820
$701$	−13.6856	−0.516897	−0.258449	−	0.966025i	$-0.583211\pi$
$701$	−13.6856	−0.516897	−0.258449	+	0.966025i	$0.583211\pi$
$702$	−1.58548	−0.0598402
$703$	31.4669	1.18680
$704$	2.72172	0.102579
$705$	−30.0307	−1.13102
$706$	−12.6477	−0.476002
$707$	10.0787	0.379048
$708$	−33.5643	−1.26142
$709$	16.6434	0.625055	0.312528	−	0.949909i	$-0.398824\pi$
$709$	16.6434	0.625055	0.312528	+	0.949909i	$0.398824\pi$
$710$	21.5836	0.810019
$711$	30.6438	1.14923
$712$	11.9360	0.447320
$713$	−1.28851	−0.0482551
$714$	17.9685	0.672454
$715$	10.1373	0.379112
$716$	15.0520	0.562519
$717$	−22.3680	−0.835349
$718$	16.9800	0.633689
$719$	20.8118	0.776150	0.388075	−	0.921628i	$-0.373140\pi$
$719$	20.8118	0.776150	0.388075	+	0.921628i	$0.373140\pi$
$720$	7.69640	0.286828
$721$	−7.72344	−0.287636
$722$	2.99147	0.111331
$723$	−22.7409	−0.845745
$724$	3.22054	0.119691
$725$	−0.174882	−0.00649494
$726$	9.07581	0.336835
$727$	7.13595	0.264658	0.132329	−	0.991206i	$-0.457754\pi$
$727$	7.13595	0.264658	0.132329	+	0.991206i	$0.457754\pi$
$728$	2.17934	0.0807717
$729$	−33.4020	−1.23711
$730$	23.2831	0.861747
$731$	−40.9770	−1.51559
$732$	−15.8311	−0.585133
$733$	−7.12220	−0.263065	−0.131532	−	0.991312i	$-0.541990\pi$
$733$	−7.12220	−0.263065	−0.131532	+	0.991312i	$0.541990\pi$
$734$	6.57419	0.242658
$735$	30.0490	1.10837
$736$	−1.00000	−0.0368605
$737$	−22.7898	−0.839474
$738$	−22.7367	−0.836948
$739$	−25.1689	−0.925853	−0.462927	−	0.886397i	$-0.653201\pi$
$739$	−25.1689	−0.925853	−0.462927	+	0.886397i	$0.653201\pi$
$740$	15.2643	0.561128
$741$	−19.3988	−0.712633
$742$	−15.6525	−0.574623
$743$	−8.57215	−0.314482	−0.157241	−	0.987560i	$-0.550260\pi$
$743$	−8.57215	−0.314482	−0.157241	+	0.987560i	$0.550260\pi$
$744$	−3.25544	−0.119350
$745$	−9.65788	−0.353837
$746$	−15.2797	−0.559430
$747$	15.8752	0.580845
$748$	−14.5424	−0.531722
$749$	−13.8105	−0.504625
$750$	27.7319	1.01263
$751$	13.8249	0.504476	0.252238	−	0.967665i	$-0.418833\pi$
$751$	13.8249	0.504476	0.252238	+	0.967665i	$0.418833\pi$
$752$	5.22508	0.190539
$753$	40.4302	1.47336
$754$	−1.63729	−0.0596267
$755$	−5.96511	−0.217092
$756$	−1.28894	−0.0468784
$757$	−16.7112	−0.607380	−0.303690	−	0.952771i	$-0.598219\pi$
$757$	−16.7112	−0.607380	−0.303690	+	0.952771i	$0.598219\pi$
$758$	−6.21271	−0.225656
$759$	6.87647	0.249600
$760$	10.6679	0.386964
$761$	−32.9304	−1.19372	−0.596862	−	0.802344i	$-0.703586\pi$
$761$	−32.9304	−1.19372	−0.596862	+	0.802344i	$0.703586\pi$
$762$	28.7751	1.04241
$763$	−3.48148	−0.126038
$764$	12.4630	0.450894
$765$	−41.1225	−1.48679
$766$	−3.33221	−0.120398
$767$	21.7511	0.785388
$768$	−2.52651	−0.0911678
$769$	27.5882	0.994858	0.497429	−	0.867505i	$-0.334278\pi$
$769$	27.5882	0.994858	0.497429	+	0.867505i	$0.334278\pi$
$770$	8.24124	0.296994
$771$	−55.4775	−1.99797
$772$	10.1341	0.364736
$773$	25.6813	0.923693	0.461847	−	0.886960i	$-0.347187\pi$
$773$	25.6813	0.923693	0.461847	+	0.886960i	$0.347187\pi$
$774$	25.9470	0.932644
$775$	0.225337	0.00809433
$776$	14.2260	0.510684
$777$	−22.5657	−0.809539
$778$	−25.5372	−0.915552
$779$	−31.5149	−1.12914
$780$	−9.41019	−0.336939
$781$	25.8237	0.924044
$782$	5.34308	0.191068
$783$	0.968356	0.0346062
$784$	−5.22827	−0.186724
$785$	−44.4771	−1.58746
$786$	24.9582	0.890229
$787$	31.6230	1.12724	0.563620	−	0.826034i	$-0.309408\pi$
$787$	31.6230	1.12724	0.563620	+	0.826034i	$0.309408\pi$
$788$	7.94915	0.283177
$789$	60.0313	2.13717
$790$	20.6041	0.733063
$791$	0.977057	0.0347402
$792$	9.20834	0.327204
$793$	10.2592	0.364316
$794$	19.6657	0.697910
$795$	67.5862	2.39704
$796$	−18.4253	−0.653068
$797$	20.5270	0.727103	0.363551	−	0.931574i	$-0.381564\pi$
$797$	20.5270	0.727103	0.363551	+	0.931574i	$0.381564\pi$
$798$	−15.7706	−0.558273
$799$	−27.9180	−0.987668
$800$	0.174882	0.00618300
$801$	40.3827	1.42685
$802$	−25.5515	−0.902256
$803$	27.8570	0.983054
$804$	21.1553	0.746089
$805$	−3.02795	−0.106721
$806$	2.10967	0.0743099
$807$	69.9392	2.46198
$808$	7.57190	0.266379
$809$	−36.8660	−1.29614	−0.648069	−	0.761581i	$-0.724423\pi$
$809$	−36.8660	−1.29614	−0.648069	+	0.761581i	$0.724423\pi$
$810$	−17.5237	−0.615719
$811$	−12.8835	−0.452401	−0.226201	−	0.974081i	$-0.572631\pi$
$811$	−12.8835	−0.452401	−0.226201	+	0.974081i	$0.572631\pi$
$812$	−1.33106	−0.0467112
$813$	−61.3216	−2.15064
$814$	18.2630	0.640117
$815$	−6.37198	−0.223201
$816$	13.4994	0.472572
$817$	35.9647	1.25824
$818$	−13.7634	−0.481226
$819$	7.37331	0.257644
$820$	−15.2876	−0.533866
$821$	−25.7933	−0.900191	−0.450096	−	0.892980i	$-0.648610\pi$
$821$	−25.7933	−0.900191	−0.450096	+	0.892980i	$0.648610\pi$
$822$	38.2711	1.33486
$823$	−8.64098	−0.301206	−0.150603	−	0.988594i	$-0.548121\pi$
$823$	−8.64098	−0.301206	−0.150603	+	0.988594i	$0.548121\pi$
$824$	−5.80246	−0.202138
$825$	−1.20257	−0.0418681
$826$	17.6829	0.615268
$827$	−11.0032	−0.382619	−0.191309	−	0.981530i	$-0.561273\pi$
$827$	−11.0032	−0.382619	−0.191309	+	0.981530i	$0.561273\pi$
$828$	−3.38328	−0.117577
$829$	−15.9824	−0.555091	−0.277546	−	0.960712i	$-0.589521\pi$
$829$	−15.9824	−0.555091	−0.277546	+	0.960712i	$0.589521\pi$
$830$	10.6741	0.370505
$831$	19.6192	0.680582
$832$	1.63729	0.0567629
$833$	27.9350	0.967892
$834$	3.81295	0.132032
$835$	−32.5098	−1.12505
$836$	12.7635	0.441436
$837$	−1.24774	−0.0431281
$838$	−30.1116	−1.04019
$839$	42.6283	1.47169	0.735846	−	0.677149i	$-0.236785\pi$
$839$	42.6283	1.47169	0.735846	+	0.677149i	$0.236785\pi$
$840$	−7.65016	−0.263956
$841$	1.00000	0.0344828
$842$	−7.67995	−0.264669
$843$	21.2443	0.731691
$844$	−4.50954	−0.155225
$845$	−23.4747	−0.807553
$846$	17.6779	0.607778
$847$	−4.78148	−0.164294
$848$	−11.7594	−0.403820
$849$	71.3359	2.44824
$850$	−0.934406	−0.0320499
$851$	−6.71008	−0.230018
$852$	−23.9715	−0.821252
$853$	56.5218	1.93527	0.967635	−	0.252355i	$-0.0812050\pi$
$853$	56.5218	1.93527	0.967635	+	0.252355i	$0.0812050\pi$
$854$	8.34041	0.285403
$855$	36.0923	1.23433
$856$	−10.3755	−0.354629
$857$	−36.4911	−1.24651	−0.623257	−	0.782017i	$-0.714191\pi$
$857$	−36.4911	−1.24651	−0.623257	+	0.782017i	$0.714191\pi$
$858$	−11.2588	−0.384369
$859$	−26.5306	−0.905212	−0.452606	−	0.891711i	$-0.649506\pi$
$859$	−26.5306	−0.905212	−0.452606	+	0.891711i	$0.649506\pi$
$860$	17.4461	0.594908
$861$	22.6001	0.770208
$862$	34.0466	1.15963
$863$	−51.7921	−1.76302	−0.881511	−	0.472163i	$-0.843473\pi$
$863$	−51.7921	−1.76302	−0.881511	+	0.472163i	$0.843473\pi$
$864$	−0.968356	−0.0329441
$865$	6.54165	0.222423
$866$	17.6946	0.601287
$867$	−29.1774	−0.990915
$868$	1.71509	0.0582139
$869$	24.6518	0.836254
$870$	5.74741	0.194855
$871$	−13.7096	−0.464530
$872$	−2.61556	−0.0885741
$873$	48.1306	1.62897
$874$	−4.68951	−0.158625
$875$	−14.6102	−0.493916
$876$	−25.8591	−0.873697
$877$	−6.69317	−0.226012	−0.113006	−	0.993594i	$-0.536048\pi$
$877$	−6.69317	−0.226012	−0.113006	+	0.993594i	$0.536048\pi$
$878$	−10.6834	−0.360549
$879$	−21.2894	−0.718072
$880$	6.19147	0.208715
$881$	15.7237	0.529744	0.264872	−	0.964284i	$-0.414670\pi$
$881$	15.7237	0.529744	0.264872	+	0.964284i	$0.414670\pi$
$882$	−17.6887	−0.595609
$883$	19.5945	0.659409	0.329704	−	0.944084i	$-0.393051\pi$
$883$	19.5945	0.659409	0.329704	+	0.944084i	$0.393051\pi$
$884$	−8.74818	−0.294233
$885$	−76.3533	−2.56659
$886$	7.86945	0.264379
$887$	−21.3703	−0.717545	−0.358772	−	0.933425i	$-0.616805\pi$
$887$	−21.3703	−0.717545	−0.358772	+	0.933425i	$0.616805\pi$
$888$	−16.9531	−0.568909
$889$	−15.1598	−0.508444
$890$	27.1524	0.910151
$891$	−20.9662	−0.702393
$892$	8.58839	0.287561
$893$	24.5030	0.819963
$894$	10.7264	0.358744
$895$	34.2408	1.14454
$896$	1.33106	0.0444677
$897$	4.13664	0.138119
$898$	−31.8692	−1.06349
$899$	−1.28851	−0.0429742
$900$	0.591673	0.0197224
$901$	62.8315	2.09322
$902$	−18.2908	−0.609018
$903$	−25.7911	−0.858273
$904$	0.734043	0.0244139
$905$	7.32621	0.243531
$906$	6.62506	0.220103
$907$	26.7826	0.889301	0.444650	−	0.895704i	$-0.353328\pi$
$907$	26.7826	0.889301	0.444650	+	0.895704i	$0.353328\pi$
$908$	−25.4490	−0.844556
$909$	25.6178	0.849690
$910$	4.95764	0.164344
$911$	13.8633	0.459312	0.229656	−	0.973272i	$-0.426240\pi$
$911$	13.8633	0.459312	0.229656	+	0.973272i	$0.426240\pi$
$912$	−11.8481	−0.392330
$913$	12.7711	0.422660
$914$	−17.5067	−0.579072
$915$	−36.0131	−1.19056
$916$	11.7705	0.388909
$917$	−13.1489	−0.434216
$918$	5.17400	0.170767
$919$	6.35554	0.209650	0.104825	−	0.994491i	$-0.466572\pi$
$919$	6.35554	0.209650	0.104825	+	0.994491i	$0.466572\pi$
$920$	−2.27484	−0.0749991
$921$	41.3548	1.36269
$922$	40.9670	1.34918
$923$	15.5346	0.511328
$924$	−9.15302	−0.301112
$925$	1.17347	0.0385834
$926$	34.9144	1.14736
$927$	−19.6313	−0.644778
$928$	−1.00000	−0.0328266
$929$	−18.4358	−0.604860	−0.302430	−	0.953172i	$-0.597798\pi$
$929$	−18.4358	−0.604860	−0.302430	+	0.953172i	$0.597798\pi$
$930$	−7.40559	−0.242839
$931$	−24.5180	−0.803545
$932$	−9.84846	−0.322597
$933$	−17.2231	−0.563859
$934$	−20.9403	−0.685187
$935$	−33.0815	−1.08188
$936$	5.53941	0.181061
$937$	−15.6935	−0.512683	−0.256342	−	0.966586i	$-0.582517\pi$
$937$	−15.6935	−0.512683	−0.256342	+	0.966586i	$0.582517\pi$
$938$	−11.1454	−0.363910
$939$	−45.8788	−1.49720
$940$	11.8862	0.387685
$941$	0.525287	0.0171239	0.00856194	−	0.999963i	$-0.497275\pi$
$941$	0.525287	0.0171239	0.00856194	+	0.999963i	$0.497275\pi$
$942$	49.3979	1.60947
$943$	6.72031	0.218843
$944$	13.2848	0.432384
$945$	−2.93213	−0.0953824
$946$	20.8734	0.678652
$947$	0.525385	0.0170727	0.00853636	−	0.999964i	$-0.497283\pi$
$947$	0.525385	0.0170727	0.00853636	+	0.999964i	$0.497283\pi$
$948$	−22.8837	−0.743228
$949$	16.7578	0.543982
$950$	0.820109	0.0266078
$951$	88.3285	2.86425
$952$	−7.11197	−0.230500
$953$	57.7274	1.86997	0.934987	−	0.354683i	$-0.115411\pi$
$953$	57.7274	1.86997	0.934987	+	0.354683i	$0.115411\pi$
$954$	−39.7854	−1.28810
$955$	28.3512	0.917423
$956$	8.85331	0.286337
$957$	6.87647	0.222285
$958$	9.23258	0.298291
$959$	−20.1627	−0.651086
$960$	−5.74741	−0.185497
$961$	−29.3397	−0.946443
$962$	10.9864	0.354214
$963$	−35.1033	−1.13119
$964$	9.00091	0.289900
$965$	23.0535	0.742119
$966$	3.36295	0.108201
$967$	52.6328	1.69256	0.846279	−	0.532740i	$-0.178838\pi$
$967$	52.6328	1.69256	0.846279	+	0.532740i	$0.178838\pi$
$968$	−3.59223	−0.115459
$969$	63.3053	2.03366
$970$	32.3619	1.03908
$971$	44.1596	1.41715	0.708574	−	0.705637i	$-0.249339\pi$
$971$	44.1596	1.41715	0.708574	+	0.705637i	$0.249339\pi$
$972$	22.3675	0.717437
$973$	−2.00881	−0.0643994
$974$	40.6871	1.30370
$975$	−0.723423	−0.0231681
$976$	6.26597	0.200569
$977$	−20.3758	−0.651881	−0.325941	−	0.945390i	$-0.605681\pi$
$977$	−20.3758	−0.651881	−0.325941	+	0.945390i	$0.605681\pi$
$978$	7.07695	0.226296
$979$	32.4864	1.03827
$980$	−11.8935	−0.379923
$981$	−8.84917	−0.282532
$982$	−8.44462	−0.269479
$983$	29.4474	0.939226	0.469613	−	0.882872i	$-0.344393\pi$
$983$	29.4474	0.939226	0.469613	+	0.882872i	$0.344393\pi$
$984$	16.9790	0.541269
$985$	18.0830	0.576173
$986$	5.34308	0.170158
$987$	−17.5717	−0.559313
$988$	7.67809	0.244273
$989$	−7.66918	−0.243866
$990$	20.9475	0.665754
$991$	30.5855	0.971582	0.485791	−	0.874075i	$-0.338532\pi$
$991$	30.5855	0.971582	0.485791	+	0.874075i	$0.338532\pi$
$992$	1.28851	0.0409102
$993$	−12.6417	−0.401171
$994$	12.6291	0.400571
$995$	−41.9146	−1.32878
$996$	−11.8551	−0.375643
$997$	−3.54887	−0.112394	−0.0561970	−	0.998420i	$-0.517897\pi$
$997$	−3.54887	−0.112394	−0.0561970	+	0.998420i	$0.517897\pi$
$998$	14.5022	0.459060
$999$	−6.49774	−0.205579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.i.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.i.1.2	✓	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52651 q^{3} +1.00000 q^{4} +2.27484 q^{5} -2.52651 q^{6} +1.33106 q^{7} +1.00000 q^{8} +3.38328 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52651 q^{3} +1.00000 q^{4} +2.27484 q^{5} -2.52651 q^{6} +1.33106 q^{7} +1.00000 q^{8} +3.38328 q^{9} +2.27484 q^{10} +2.72172 q^{11} -2.52651 q^{12} +1.63729 q^{13} +1.33106 q^{14} -5.74741 q^{15} +1.00000 q^{16} -5.34308 q^{17} +3.38328 q^{18} +4.68951 q^{19} +2.27484 q^{20} -3.36295 q^{21} +2.72172 q^{22} -1.00000 q^{23} -2.52651 q^{24} +0.174882 q^{25} +1.63729 q^{26} -0.968356 q^{27} +1.33106 q^{28} -1.00000 q^{29} -5.74741 q^{30} +1.28851 q^{31} +1.00000 q^{32} -6.87647 q^{33} -5.34308 q^{34} +3.02795 q^{35} +3.38328 q^{36} +6.71008 q^{37} +4.68951 q^{38} -4.13664 q^{39} +2.27484 q^{40} -6.72031 q^{41} -3.36295 q^{42} +7.66918 q^{43} +2.72172 q^{44} +7.69640 q^{45} -1.00000 q^{46} +5.22508 q^{47} -2.52651 q^{48} -5.22827 q^{49} +0.174882 q^{50} +13.4994 q^{51} +1.63729 q^{52} -11.7594 q^{53} -0.968356 q^{54} +6.19147 q^{55} +1.33106 q^{56} -11.8481 q^{57} -1.00000 q^{58} +13.2848 q^{59} -5.74741 q^{60} +6.26597 q^{61} +1.28851 q^{62} +4.50336 q^{63} +1.00000 q^{64} +3.72457 q^{65} -6.87647 q^{66} -8.37331 q^{67} -5.34308 q^{68} +2.52651 q^{69} +3.02795 q^{70} +9.48799 q^{71} +3.38328 q^{72} +10.2351 q^{73} +6.71008 q^{74} -0.441841 q^{75} +4.68951 q^{76} +3.62279 q^{77} -4.13664 q^{78} +9.05742 q^{79} +2.27484 q^{80} -7.70327 q^{81} -6.72031 q^{82} +4.69227 q^{83} -3.36295 q^{84} -12.1546 q^{85} +7.66918 q^{86} +2.52651 q^{87} +2.72172 q^{88} +11.9360 q^{89} +7.69640 q^{90} +2.17934 q^{91} -1.00000 q^{92} -3.25544 q^{93} +5.22508 q^{94} +10.6679 q^{95} -2.52651 q^{96} +14.2260 q^{97} -5.22827 q^{98} +9.20834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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