LMFDB - Embedded newform 4334.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.181771 q^{3} +1.00000 q^{4} +4.29102 q^{5} -0.181771 q^{6} -3.68727 q^{7} -1.00000 q^{8} -2.96696 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.181771 q^{3} +1.00000 q^{4} +4.29102 q^{5} -0.181771 q^{6} -3.68727 q^{7} -1.00000 q^{8} -2.96696 q^{9} -4.29102 q^{10} +1.00000 q^{11} +0.181771 q^{12} +3.37616 q^{13} +3.68727 q^{14} +0.779983 q^{15} +1.00000 q^{16} -6.28286 q^{17} +2.96696 q^{18} +6.51670 q^{19} +4.29102 q^{20} -0.670238 q^{21} -1.00000 q^{22} +2.48130 q^{23} -0.181771 q^{24} +13.4129 q^{25} -3.37616 q^{26} -1.08462 q^{27} -3.68727 q^{28} -4.57428 q^{29} -0.779983 q^{30} +4.34436 q^{31} -1.00000 q^{32} +0.181771 q^{33} +6.28286 q^{34} -15.8221 q^{35} -2.96696 q^{36} +6.51544 q^{37} -6.51670 q^{38} +0.613687 q^{39} -4.29102 q^{40} +8.42548 q^{41} +0.670238 q^{42} +1.92583 q^{43} +1.00000 q^{44} -12.7313 q^{45} -2.48130 q^{46} -11.1529 q^{47} +0.181771 q^{48} +6.59595 q^{49} -13.4129 q^{50} -1.14204 q^{51} +3.37616 q^{52} -8.28386 q^{53} +1.08462 q^{54} +4.29102 q^{55} +3.68727 q^{56} +1.18455 q^{57} +4.57428 q^{58} +3.39391 q^{59} +0.779983 q^{60} -9.66643 q^{61} -4.34436 q^{62} +10.9400 q^{63} +1.00000 q^{64} +14.4872 q^{65} -0.181771 q^{66} -0.980061 q^{67} -6.28286 q^{68} +0.451028 q^{69} +15.8221 q^{70} -3.36075 q^{71} +2.96696 q^{72} +7.35486 q^{73} -6.51544 q^{74} +2.43807 q^{75} +6.51670 q^{76} -3.68727 q^{77} -0.613687 q^{78} +10.2239 q^{79} +4.29102 q^{80} +8.70373 q^{81} -8.42548 q^{82} -17.8528 q^{83} -0.670238 q^{84} -26.9599 q^{85} -1.92583 q^{86} -0.831471 q^{87} -1.00000 q^{88} +14.9767 q^{89} +12.7313 q^{90} -12.4488 q^{91} +2.48130 q^{92} +0.789678 q^{93} +11.1529 q^{94} +27.9633 q^{95} -0.181771 q^{96} +18.4715 q^{97} -6.59595 q^{98} -2.96696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.181771	0.104945	0.0524727	−	0.998622i	$-0.483290\pi$
$3$	0.181771	0.104945	0.0524727	+	0.998622i	$0.483290\pi$
$4$	1.00000	0.500000
$5$	4.29102	1.91900	0.959501	−	0.281704i	$-0.0908997\pi$
$5$	4.29102	1.91900	0.959501	+	0.281704i	$0.0908997\pi$
$6$	−0.181771	−0.0742077
$7$	−3.68727	−1.39366	−0.696828	−	0.717238i	$-0.745406\pi$
$7$	−3.68727	−1.39366	−0.696828	+	0.717238i	$0.745406\pi$
$8$	−1.00000	−0.353553
$9$	−2.96696	−0.988986
$10$	−4.29102	−1.35694
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.181771	0.0524727
$13$	3.37616	0.936378	0.468189	−	0.883628i	$-0.344907\pi$
$13$	3.37616	0.936378	0.468189	+	0.883628i	$0.344907\pi$
$14$	3.68727	0.985464
$15$	0.779983	0.201391
$16$	1.00000	0.250000
$17$	−6.28286	−1.52382	−0.761908	−	0.647685i	$-0.775737\pi$
$17$	−6.28286	−1.52382	−0.761908	+	0.647685i	$0.775737\pi$
$18$	2.96696	0.699319
$19$	6.51670	1.49503	0.747516	−	0.664243i	$-0.231246\pi$
$19$	6.51670	1.49503	0.747516	+	0.664243i	$0.231246\pi$
$20$	4.29102	0.959501
$21$	−0.670238	−0.146258
$22$	−1.00000	−0.213201
$23$	2.48130	0.517387	0.258693	−	0.965960i	$-0.416708\pi$
$23$	2.48130	0.517387	0.258693	+	0.965960i	$0.416708\pi$
$24$	−0.181771	−0.0371038
$25$	13.4129	2.68257
$26$	−3.37616	−0.662119
$27$	−1.08462	−0.208735
$28$	−3.68727	−0.696828
$29$	−4.57428	−0.849422	−0.424711	−	0.905329i	$-0.639624\pi$
$29$	−4.57428	−0.849422	−0.424711	+	0.905329i	$0.639624\pi$
$30$	−0.779983	−0.142405
$31$	4.34436	0.780270	0.390135	−	0.920758i	$-0.372428\pi$
$31$	4.34436	0.780270	0.390135	+	0.920758i	$0.372428\pi$
$32$	−1.00000	−0.176777
$33$	0.181771	0.0316423
$34$	6.28286	1.07750
$35$	−15.8221	−2.67443
$36$	−2.96696	−0.494493
$37$	6.51544	1.07113	0.535566	−	0.844493i	$-0.320098\pi$
$37$	6.51544	1.07113	0.535566	+	0.844493i	$0.320098\pi$
$38$	−6.51670	−1.05715
$39$	0.613687	0.0982686
$40$	−4.29102	−0.678470
$41$	8.42548	1.31584	0.657919	−	0.753089i	$-0.271437\pi$
$41$	8.42548	1.31584	0.657919	+	0.753089i	$0.271437\pi$
$42$	0.670238	0.103420
$43$	1.92583	0.293687	0.146843	−	0.989160i	$-0.453089\pi$
$43$	1.92583	0.293687	0.146843	+	0.989160i	$0.453089\pi$
$44$	1.00000	0.150756
$45$	−12.7313	−1.89787
$46$	−2.48130	−0.365848
$47$	−11.1529	−1.62681	−0.813406	−	0.581696i	$-0.802389\pi$
$47$	−11.1529	−1.62681	−0.813406	+	0.581696i	$0.802389\pi$
$48$	0.181771	0.0262364
$49$	6.59595	0.942279
$50$	−13.4129	−1.89686
$51$	−1.14204	−0.159918
$52$	3.37616	0.468189
$53$	−8.28386	−1.13788	−0.568938	−	0.822381i	$-0.692645\pi$
$53$	−8.28386	−1.13788	−0.568938	+	0.822381i	$0.692645\pi$
$54$	1.08462	0.147598
$55$	4.29102	0.578601
$56$	3.68727	0.492732
$57$	1.18455	0.156897
$58$	4.57428	0.600632
$59$	3.39391	0.441849	0.220925	−	0.975291i	$-0.429093\pi$
$59$	3.39391	0.441849	0.220925	+	0.975291i	$0.429093\pi$
$60$	0.779983	0.100695
$61$	−9.66643	−1.23766	−0.618830	−	0.785525i	$-0.712393\pi$
$61$	−9.66643	−1.23766	−0.618830	+	0.785525i	$0.712393\pi$
$62$	−4.34436	−0.551734
$63$	10.9400	1.37831
$64$	1.00000	0.125000
$65$	14.4872	1.79691
$66$	−0.181771	−0.0223745
$67$	−0.980061	−0.119734	−0.0598668	−	0.998206i	$-0.519068\pi$
$67$	−0.980061	−0.119734	−0.0598668	+	0.998206i	$0.519068\pi$
$68$	−6.28286	−0.761908
$69$	0.451028	0.0542974
$70$	15.8221	1.89111
$71$	−3.36075	−0.398847	−0.199424	−	0.979913i	$-0.563907\pi$
$71$	−3.36075	−0.398847	−0.199424	+	0.979913i	$0.563907\pi$
$72$	2.96696	0.349660
$73$	7.35486	0.860822	0.430411	−	0.902633i	$-0.358369\pi$
$73$	7.35486	0.860822	0.430411	+	0.902633i	$0.358369\pi$
$74$	−6.51544	−0.757405
$75$	2.43807	0.281524
$76$	6.51670	0.747516
$77$	−3.68727	−0.420203
$78$	−0.613687	−0.0694864
$79$	10.2239	1.15028	0.575142	−	0.818054i	$-0.304947\pi$
$79$	10.2239	1.15028	0.575142	+	0.818054i	$0.304947\pi$
$80$	4.29102	0.479751
$81$	8.70373	0.967081
$82$	−8.42548	−0.930438
$83$	−17.8528	−1.95960	−0.979799	−	0.199984i	$-0.935911\pi$
$83$	−17.8528	−1.95960	−0.979799	+	0.199984i	$0.935911\pi$
$84$	−0.670238	−0.0731290
$85$	−26.9599	−2.92421
$86$	−1.92583	−0.207668
$87$	−0.831471	−0.0891430
$88$	−1.00000	−0.106600
$89$	14.9767	1.58753	0.793763	−	0.608227i	$-0.208119\pi$
$89$	14.9767	1.58753	0.793763	+	0.608227i	$0.208119\pi$
$90$	12.7313	1.34199
$91$	−12.4488	−1.30499
$92$	2.48130	0.258693
$93$	0.789678	0.0818858
$94$	11.1529	1.15033
$95$	27.9633	2.86897
$96$	−0.181771	−0.0185519
$97$	18.4715	1.87550	0.937750	−	0.347311i	$-0.112905\pi$
$97$	18.4715	1.87550	0.937750	+	0.347311i	$0.112905\pi$
$98$	−6.59595	−0.666292
$99$	−2.96696	−0.298191
$100$	13.4129	1.34129
$101$	14.1046	1.40346	0.701731	−	0.712442i	$-0.252411\pi$
$101$	14.1046	1.40346	0.701731	+	0.712442i	$0.252411\pi$
$102$	1.14204	0.113079
$103$	0.789092	0.0777516	0.0388758	−	0.999244i	$-0.487622\pi$
$103$	0.789092	0.0777516	0.0388758	+	0.999244i	$0.487622\pi$
$104$	−3.37616	−0.331060
$105$	−2.87601	−0.280669
$106$	8.28386	0.804599
$107$	−1.54860	−0.149709	−0.0748545	−	0.997194i	$-0.523849\pi$
$107$	−1.54860	−0.149709	−0.0748545	+	0.997194i	$0.523849\pi$
$108$	−1.08462	−0.104368
$109$	6.11800	0.585998	0.292999	−	0.956113i	$-0.405347\pi$
$109$	6.11800	0.585998	0.292999	+	0.956113i	$0.405347\pi$
$110$	−4.29102	−0.409133
$111$	1.18432	0.112411
$112$	−3.68727	−0.348414
$113$	20.7352	1.95060	0.975300	−	0.220883i	$-0.0708939\pi$
$113$	20.7352	1.95060	0.975300	+	0.220883i	$0.0708939\pi$
$114$	−1.18455	−0.110943
$115$	10.6473	0.992866
$116$	−4.57428	−0.424711
$117$	−10.0169	−0.926065
$118$	−3.39391	−0.312434
$119$	23.1666	2.12368
$120$	−0.779983	−0.0712024
$121$	1.00000	0.0909091
$122$	9.66643	0.875157
$123$	1.53151	0.138091
$124$	4.34436	0.390135
$125$	36.0997	3.22886
$126$	−10.9400	−0.974611
$127$	−2.62171	−0.232639	−0.116320	−	0.993212i	$-0.537110\pi$
$127$	−2.62171	−0.232639	−0.116320	+	0.993212i	$0.537110\pi$
$128$	−1.00000	−0.0883883
$129$	0.350061	0.0308211
$130$	−14.4872	−1.27061
$131$	14.0879	1.23086	0.615432	−	0.788190i	$-0.288982\pi$
$131$	14.0879	1.23086	0.615432	+	0.788190i	$0.288982\pi$
$132$	0.181771	0.0158211
$133$	−24.0288	−2.08356
$134$	0.980061	0.0846644
$135$	−4.65413	−0.400563
$136$	6.28286	0.538751
$137$	0.779585	0.0666045	0.0333022	−	0.999445i	$-0.489398\pi$
$137$	0.779585	0.0666045	0.0333022	+	0.999445i	$0.489398\pi$
$138$	−0.451028	−0.0383941
$139$	−6.88259	−0.583773	−0.291887	−	0.956453i	$-0.594283\pi$
$139$	−6.88259	−0.583773	−0.291887	+	0.956453i	$0.594283\pi$
$140$	−15.8221	−1.33722
$141$	−2.02727	−0.170727
$142$	3.36075	0.282028
$143$	3.37616	0.282329
$144$	−2.96696	−0.247247
$145$	−19.6283	−1.63004
$146$	−7.35486	−0.608693
$147$	1.19895	0.0988879
$148$	6.51544	0.535566
$149$	−9.69903	−0.794575	−0.397288	−	0.917694i	$-0.630048\pi$
$149$	−9.69903	−0.794575	−0.397288	+	0.917694i	$0.630048\pi$
$150$	−2.43807	−0.199067
$151$	−18.4788	−1.50378	−0.751890	−	0.659288i	$-0.770858\pi$
$151$	−18.4788	−1.50378	−0.751890	+	0.659288i	$0.770858\pi$
$152$	−6.51670	−0.528574
$153$	18.6410	1.50703
$154$	3.68727	0.297129
$155$	18.6417	1.49734
$156$	0.613687	0.0491343
$157$	−0.144765	−0.0115535	−0.00577675	−	0.999983i	$-0.501839\pi$
$157$	−0.144765	−0.0115535	−0.00577675	+	0.999983i	$0.501839\pi$
$158$	−10.2239	−0.813373
$159$	−1.50576	−0.119415
$160$	−4.29102	−0.339235
$161$	−9.14922	−0.721059
$162$	−8.70373	−0.683829
$163$	2.85014	0.223240	0.111620	−	0.993751i	$-0.464396\pi$
$163$	2.85014	0.223240	0.111620	+	0.993751i	$0.464396\pi$
$164$	8.42548	0.657919
$165$	0.779983	0.0607216
$166$	17.8528	1.38565
$167$	1.93980	0.150106	0.0750532	−	0.997180i	$-0.476087\pi$
$167$	1.93980	0.150106	0.0750532	+	0.997180i	$0.476087\pi$
$168$	0.670238	0.0517100
$169$	−1.60156	−0.123197
$170$	26.9599	2.06773
$171$	−19.3348	−1.47857
$172$	1.92583	0.146843
$173$	−13.8555	−1.05341	−0.526707	−	0.850047i	$-0.676574\pi$
$173$	−13.8555	−1.05341	−0.526707	+	0.850047i	$0.676574\pi$
$174$	0.831471	0.0630337
$175$	−49.4568	−3.73858
$176$	1.00000	0.0753778
$177$	0.616914	0.0463701
$178$	−14.9767	−1.12255
$179$	17.5739	1.31353	0.656767	−	0.754093i	$-0.271923\pi$
$179$	17.5739	1.31353	0.656767	+	0.754093i	$0.271923\pi$
$180$	−12.7313	−0.948934
$181$	16.2398	1.20709	0.603547	−	0.797327i	$-0.293753\pi$
$181$	16.2398	1.20709	0.603547	+	0.797327i	$0.293753\pi$
$182$	12.4488	0.922767
$183$	−1.75708	−0.129887
$184$	−2.48130	−0.182924
$185$	27.9579	2.05551
$186$	−0.789678	−0.0579020
$187$	−6.28286	−0.459448
$188$	−11.1529	−0.813406
$189$	3.99928	0.290905
$190$	−27.9633	−2.02867
$191$	9.02576	0.653081	0.326540	−	0.945183i	$-0.394117\pi$
$191$	9.02576	0.653081	0.326540	+	0.945183i	$0.394117\pi$
$192$	0.181771	0.0131182
$193$	17.8095	1.28196	0.640980	−	0.767558i	$-0.278528\pi$
$193$	17.8095	1.28196	0.640980	+	0.767558i	$0.278528\pi$
$194$	−18.4715	−1.32618
$195$	2.63334	0.188578
$196$	6.59595	0.471140
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	2.96696	0.210853
$199$	1.72121	0.122013	0.0610066	−	0.998137i	$-0.480569\pi$
$199$	1.72121	0.122013	0.0610066	+	0.998137i	$0.480569\pi$
$200$	−13.4129	−0.948432
$201$	−0.178147	−0.0125655
$202$	−14.1046	−0.992398
$203$	16.8666	1.18380
$204$	−1.14204	−0.0799588
$205$	36.1539	2.52510
$206$	−0.789092	−0.0549787
$207$	−7.36191	−0.511688
$208$	3.37616	0.234094
$209$	6.51670	0.450769
$210$	2.87601	0.198463
$211$	10.9705	0.755241	0.377620	−	0.925960i	$-0.376742\pi$
$211$	10.9705	0.755241	0.377620	+	0.925960i	$0.376742\pi$
$212$	−8.28386	−0.568938
$213$	−0.610886	−0.0418572
$214$	1.54860	0.105860
$215$	8.26379	0.563586
$216$	1.08462	0.0737990
$217$	−16.0188	−1.08743
$218$	−6.11800	−0.414363
$219$	1.33690	0.0903394
$220$	4.29102	0.289301
$221$	−21.2119	−1.42687
$222$	−1.18432	−0.0794862
$223$	13.2188	0.885199	0.442599	−	0.896719i	$-0.354056\pi$
$223$	13.2188	0.885199	0.442599	+	0.896719i	$0.354056\pi$
$224$	3.68727	0.246366
$225$	−39.7954	−2.65303
$226$	−20.7352	−1.37928
$227$	15.1519	1.00567	0.502833	−	0.864384i	$-0.332291\pi$
$227$	15.1519	1.00567	0.502833	+	0.864384i	$0.332291\pi$
$228$	1.18455	0.0784485
$229$	4.49543	0.297067	0.148533	−	0.988907i	$-0.452545\pi$
$229$	4.49543	0.297067	0.148533	+	0.988907i	$0.452545\pi$
$230$	−10.6473	−0.702062
$231$	−0.670238	−0.0440984
$232$	4.57428	0.300316
$233$	−10.8812	−0.712851	−0.356425	−	0.934324i	$-0.616005\pi$
$233$	−10.8812	−0.712851	−0.356425	+	0.934324i	$0.616005\pi$
$234$	10.0169	0.654827
$235$	−47.8572	−3.12186
$236$	3.39391	0.220925
$237$	1.85842	0.120717
$238$	−23.1666	−1.50167
$239$	22.1608	1.43346	0.716730	−	0.697351i	$-0.245638\pi$
$239$	22.1608	1.43346	0.716730	+	0.697351i	$0.245638\pi$
$240$	0.779983	0.0503477
$241$	−14.2880	−0.920373	−0.460187	−	0.887822i	$-0.652217\pi$
$241$	−14.2880	−0.920373	−0.460187	+	0.887822i	$0.652217\pi$
$242$	−1.00000	−0.0642824
$243$	4.83594	0.310226
$244$	−9.66643	−0.618830
$245$	28.3034	1.80824
$246$	−1.53151	−0.0976453
$247$	22.0014	1.39992
$248$	−4.34436	−0.275867
$249$	−3.24512	−0.205651
$250$	−36.0997	−2.28315
$251$	−25.6773	−1.62074	−0.810369	−	0.585921i	$-0.800733\pi$
$251$	−25.6773	−1.62074	−0.810369	+	0.585921i	$0.800733\pi$
$252$	10.9400	0.689154
$253$	2.48130	0.155998
$254$	2.62171	0.164501
$255$	−4.90052	−0.306882
$256$	1.00000	0.0625000
$257$	2.44200	0.152328	0.0761639	−	0.997095i	$-0.475733\pi$
$257$	2.44200	0.152328	0.0761639	+	0.997095i	$0.475733\pi$
$258$	−0.350061	−0.0217938
$259$	−24.0242	−1.49279
$260$	14.4872	0.898456
$261$	13.5717	0.840067
$262$	−14.0879	−0.870352
$263$	−29.7851	−1.83663	−0.918314	−	0.395853i	$-0.870449\pi$
$263$	−29.7851	−1.83663	−0.918314	+	0.395853i	$0.870449\pi$
$264$	−0.181771	−0.0111872
$265$	−35.5462	−2.18359
$266$	24.0288	1.47330
$267$	2.72233	0.166604
$268$	−0.980061	−0.0598668
$269$	0.965597	0.0588735	0.0294367	−	0.999567i	$-0.490629\pi$
$269$	0.965597	0.0588735	0.0294367	+	0.999567i	$0.490629\pi$
$270$	4.65413	0.283241
$271$	−6.61910	−0.402082	−0.201041	−	0.979583i	$-0.564432\pi$
$271$	−6.61910	−0.402082	−0.201041	+	0.979583i	$0.564432\pi$
$272$	−6.28286	−0.380954
$273$	−2.26283	−0.136953
$274$	−0.779585	−0.0470965
$275$	13.4129	0.808825
$276$	0.451028	0.0271487
$277$	21.1372	1.27001	0.635007	−	0.772507i	$-0.280997\pi$
$277$	21.1372	1.27001	0.635007	+	0.772507i	$0.280997\pi$
$278$	6.88259	0.412790
$279$	−12.8895	−0.771676
$280$	15.8221	0.945554
$281$	−16.3632	−0.976148	−0.488074	−	0.872802i	$-0.662300\pi$
$281$	−16.3632	−0.976148	−0.488074	+	0.872802i	$0.662300\pi$
$282$	2.02727	0.120722
$283$	−30.7709	−1.82914	−0.914571	−	0.404426i	$-0.867471\pi$
$283$	−30.7709	−1.82914	−0.914571	+	0.404426i	$0.867471\pi$
$284$	−3.36075	−0.199424
$285$	5.08291	0.301086
$286$	−3.37616	−0.199636
$287$	−31.0670	−1.83383
$288$	2.96696	0.174830
$289$	22.4743	1.32202
$290$	19.6283	1.15261
$291$	3.35759	0.196825
$292$	7.35486	0.430411
$293$	11.7087	0.684029	0.342014	−	0.939695i	$-0.388891\pi$
$293$	11.7087	0.684029	0.342014	+	0.939695i	$0.388891\pi$
$294$	−1.19895	−0.0699243
$295$	14.5633	0.847909
$296$	−6.51544	−0.378702
$297$	−1.08462	−0.0629360
$298$	9.69903	0.561850
$299$	8.37726	0.484469
$300$	2.43807	0.140762
$301$	−7.10107	−0.409299
$302$	18.4788	1.06333
$303$	2.56381	0.147287
$304$	6.51670	0.373758
$305$	−41.4788	−2.37507
$306$	−18.6410	−1.06563
$307$	34.1800	1.95075	0.975377	−	0.220545i	$-0.0707837\pi$
$307$	34.1800	1.95075	0.975377	+	0.220545i	$0.0707837\pi$
$308$	−3.68727	−0.210102
$309$	0.143434	0.00815968
$310$	−18.6417	−1.05878
$311$	−23.7251	−1.34533	−0.672664	−	0.739948i	$-0.734850\pi$
$311$	−23.7251	−1.34533	−0.672664	+	0.739948i	$0.734850\pi$
$312$	−0.613687	−0.0347432
$313$	16.8968	0.955065	0.477532	−	0.878614i	$-0.341531\pi$
$313$	16.8968	0.955065	0.477532	+	0.878614i	$0.341531\pi$
$314$	0.144765	0.00816956
$315$	46.9437	2.64498
$316$	10.2239	0.575142
$317$	7.48373	0.420328	0.210164	−	0.977666i	$-0.432600\pi$
$317$	7.48373	0.420328	0.210164	+	0.977666i	$0.432600\pi$
$318$	1.50576	0.0844391
$319$	−4.57428	−0.256110
$320$	4.29102	0.239875
$321$	−0.281491	−0.0157113
$322$	9.14922	0.509866
$323$	−40.9435	−2.27816
$324$	8.70373	0.483540
$325$	45.2839	2.51190
$326$	−2.85014	−0.157855
$327$	1.11207	0.0614978
$328$	−8.42548	−0.465219
$329$	41.1236	2.26722
$330$	−0.779983	−0.0429366
$331$	−10.5010	−0.577188	−0.288594	−	0.957451i	$-0.593188\pi$
$331$	−10.5010	−0.577188	−0.288594	+	0.957451i	$0.593188\pi$
$332$	−17.8528	−0.979799
$333$	−19.3311	−1.05934
$334$	−1.93980	−0.106141
$335$	−4.20546	−0.229769
$336$	−0.670238	−0.0365645
$337$	−18.4051	−1.00259	−0.501295	−	0.865277i	$-0.667143\pi$
$337$	−18.4051	−1.00259	−0.501295	+	0.865277i	$0.667143\pi$
$338$	1.60156	0.0871133
$339$	3.76905	0.204707
$340$	−26.9599	−1.46210
$341$	4.34436	0.235260
$342$	19.3348	1.04550
$343$	1.48983	0.0804432
$344$	−1.92583	−0.103834
$345$	1.93537	0.104197
$346$	13.8555	0.744876
$347$	1.35989	0.0730028	0.0365014	−	0.999334i	$-0.488379\pi$
$347$	1.35989	0.0730028	0.0365014	+	0.999334i	$0.488379\pi$
$348$	−0.831471	−0.0445715
$349$	28.2420	1.51176	0.755879	−	0.654711i	$-0.227210\pi$
$349$	28.2420	1.51176	0.755879	+	0.654711i	$0.227210\pi$
$350$	49.4568	2.64358
$351$	−3.66185	−0.195455
$352$	−1.00000	−0.0533002
$353$	15.3466	0.816818	0.408409	−	0.912799i	$-0.366084\pi$
$353$	15.3466	0.816818	0.408409	+	0.912799i	$0.366084\pi$
$354$	−0.616914	−0.0327886
$355$	−14.4210	−0.765389
$356$	14.9767	0.793763
$357$	4.21101	0.222870
$358$	−17.5739	−0.928809
$359$	−23.8278	−1.25758	−0.628792	−	0.777574i	$-0.716450\pi$
$359$	−23.8278	−1.25758	−0.628792	+	0.777574i	$0.716450\pi$
$360$	12.7313	0.670997
$361$	23.4673	1.23512
$362$	−16.2398	−0.853545
$363$	0.181771	0.00954050
$364$	−12.4488	−0.652495
$365$	31.5599	1.65192
$366$	1.75708	0.0918438
$367$	15.5015	0.809170	0.404585	−	0.914500i	$-0.367416\pi$
$367$	15.5015	0.809170	0.404585	+	0.914500i	$0.367416\pi$
$368$	2.48130	0.129347
$369$	−24.9980	−1.30135
$370$	−27.9579	−1.45346
$371$	30.5448	1.58581
$372$	0.789678	0.0409429
$373$	5.54119	0.286912	0.143456	−	0.989657i	$-0.454178\pi$
$373$	5.54119	0.286912	0.143456	+	0.989657i	$0.454178\pi$
$374$	6.28286	0.324879
$375$	6.56188	0.338854
$376$	11.1529	0.575165
$377$	−15.4435	−0.795380
$378$	−3.99928	−0.205701
$379$	−3.41599	−0.175467	−0.0877337	−	0.996144i	$-0.527962\pi$
$379$	−3.41599	−0.175467	−0.0877337	+	0.996144i	$0.527962\pi$
$380$	27.9633	1.43449
$381$	−0.476551	−0.0244144
$382$	−9.02576	−0.461798
$383$	−13.8478	−0.707590	−0.353795	−	0.935323i	$-0.615109\pi$
$383$	−13.8478	−0.707590	−0.353795	+	0.935323i	$0.615109\pi$
$384$	−0.181771	−0.00927596
$385$	−15.8221	−0.806371
$386$	−17.8095	−0.906482
$387$	−5.71387	−0.290452
$388$	18.4715	0.937750
$389$	24.6771	1.25118	0.625590	−	0.780152i	$-0.284858\pi$
$389$	24.6771	1.25118	0.625590	+	0.780152i	$0.284858\pi$
$390$	−2.63334	−0.133345
$391$	−15.5896	−0.788402
$392$	−6.59595	−0.333146
$393$	2.56077	0.129174
$394$	1.00000	0.0503793
$395$	43.8711	2.20740
$396$	−2.96696	−0.149095
$397$	−26.1274	−1.31130	−0.655649	−	0.755066i	$-0.727605\pi$
$397$	−26.1274	−1.31130	−0.655649	+	0.755066i	$0.727605\pi$
$398$	−1.72121	−0.0862764
$399$	−4.36774	−0.218660
$400$	13.4129	0.670643
$401$	8.30355	0.414660	0.207330	−	0.978271i	$-0.433523\pi$
$401$	8.30355	0.414660	0.207330	+	0.978271i	$0.433523\pi$
$402$	0.178147	0.00888515
$403$	14.6672	0.730627
$404$	14.1046	0.701731
$405$	37.3479	1.85583
$406$	−16.8666	−0.837075
$407$	6.51544	0.322959
$408$	1.14204	0.0565394
$409$	16.3116	0.806557	0.403278	−	0.915077i	$-0.367871\pi$
$409$	16.3116	0.806557	0.403278	+	0.915077i	$0.367871\pi$
$410$	−36.1539	−1.78551
$411$	0.141706	0.00698984
$412$	0.789092	0.0388758
$413$	−12.5142	−0.615786
$414$	7.36191	0.361818
$415$	−76.6067	−3.76047
$416$	−3.37616	−0.165530
$417$	−1.25105	−0.0612644
$418$	−6.51670	−0.318742
$419$	5.59083	0.273130	0.136565	−	0.990631i	$-0.456394\pi$
$419$	5.59083	0.273130	0.136565	+	0.990631i	$0.456394\pi$
$420$	−2.87601	−0.140335
$421$	7.57118	0.368997	0.184498	−	0.982833i	$-0.440934\pi$
$421$	7.57118	0.368997	0.184498	+	0.982833i	$0.440934\pi$
$422$	−10.9705	−0.534036
$423$	33.0901	1.60890
$424$	8.28386	0.402300
$425$	−84.2710	−4.08775
$426$	0.610886	0.0295975
$427$	35.6427	1.72487
$428$	−1.54860	−0.0748545
$429$	0.613687	0.0296291
$430$	−8.26379	−0.398515
$431$	−7.79827	−0.375629	−0.187815	−	0.982204i	$-0.560140\pi$
$431$	−7.79827	−0.375629	−0.187815	+	0.982204i	$0.560140\pi$
$432$	−1.08462	−0.0521838
$433$	7.90811	0.380039	0.190020	−	0.981780i	$-0.439145\pi$
$433$	7.90811	0.380039	0.190020	+	0.981780i	$0.439145\pi$
$434$	16.0188	0.768928
$435$	−3.56786	−0.171066
$436$	6.11800	0.292999
$437$	16.1699	0.773510
$438$	−1.33690	−0.0638796
$439$	32.7133	1.56132	0.780661	−	0.624955i	$-0.214883\pi$
$439$	32.7133	1.56132	0.780661	+	0.624955i	$0.214883\pi$
$440$	−4.29102	−0.204566
$441$	−19.5699	−0.931901
$442$	21.2119	1.00895
$443$	−22.6380	−1.07556	−0.537782	−	0.843084i	$-0.680737\pi$
$443$	−22.6380	−1.07556	−0.537782	+	0.843084i	$0.680737\pi$
$444$	1.18432	0.0562053
$445$	64.2653	3.04647
$446$	−13.2188	−0.625930
$447$	−1.76300	−0.0833871
$448$	−3.68727	−0.174207
$449$	34.3159	1.61947	0.809735	−	0.586796i	$-0.199611\pi$
$449$	34.3159	1.61947	0.809735	+	0.586796i	$0.199611\pi$
$450$	39.7954	1.87597
$451$	8.42548	0.396740
$452$	20.7352	0.975300
$453$	−3.35890	−0.157815
$454$	−15.1519	−0.711113
$455$	−53.4181	−2.50428
$456$	−1.18455	−0.0554714
$457$	11.6889	0.546786	0.273393	−	0.961902i	$-0.411854\pi$
$457$	11.6889	0.546786	0.273393	+	0.961902i	$0.411854\pi$
$458$	−4.49543	−0.210058
$459$	6.81451	0.318074
$460$	10.6473	0.496433
$461$	−14.5879	−0.679426	−0.339713	−	0.940529i	$-0.610330\pi$
$461$	−14.5879	−0.679426	−0.339713	+	0.940529i	$0.610330\pi$
$462$	0.670238	0.0311823
$463$	−1.30476	−0.0606373	−0.0303186	−	0.999540i	$-0.509652\pi$
$463$	−1.30476	−0.0606373	−0.0303186	+	0.999540i	$0.509652\pi$
$464$	−4.57428	−0.212356
$465$	3.38852	0.157139
$466$	10.8812	0.504061
$467$	−3.69447	−0.170960	−0.0854798	−	0.996340i	$-0.527242\pi$
$467$	−3.69447	−0.170960	−0.0854798	+	0.996340i	$0.527242\pi$
$468$	−10.0169	−0.463032
$469$	3.61375	0.166867
$470$	47.8572	2.20749
$471$	−0.0263141	−0.00121249
$472$	−3.39391	−0.156217
$473$	1.92583	0.0885499
$474$	−1.85842	−0.0853599
$475$	87.4075	4.01053
$476$	23.1666	1.06184
$477$	24.5779	1.12534
$478$	−22.1608	−1.01361
$479$	26.9717	1.23237	0.616184	−	0.787603i	$-0.288678\pi$
$479$	26.9717	1.23237	0.616184	+	0.787603i	$0.288678\pi$
$480$	−0.779983	−0.0356012
$481$	21.9972	1.00298
$482$	14.2880	0.650802
$483$	−1.66306	−0.0756719
$484$	1.00000	0.0454545
$485$	79.2617	3.59909
$486$	−4.83594	−0.219363
$487$	−20.4504	−0.926695	−0.463348	−	0.886177i	$-0.653352\pi$
$487$	−20.4504	−0.926695	−0.463348	+	0.886177i	$0.653352\pi$
$488$	9.66643	0.437579
$489$	0.518073	0.0234280
$490$	−28.3034	−1.27862
$491$	−3.77837	−0.170515	−0.0852577	−	0.996359i	$-0.527171\pi$
$491$	−3.77837	−0.170515	−0.0852577	+	0.996359i	$0.527171\pi$
$492$	1.53151	0.0690456
$493$	28.7395	1.29436
$494$	−22.0014	−0.989890
$495$	−12.7313	−0.572229
$496$	4.34436	0.195067
$497$	12.3920	0.555856
$498$	3.24512	0.145417
$499$	−33.5503	−1.50192	−0.750960	−	0.660348i	$-0.770409\pi$
$499$	−33.5503	−1.50192	−0.750960	+	0.660348i	$0.770409\pi$
$500$	36.0997	1.61443
$501$	0.352600	0.0157530
$502$	25.6773	1.14603
$503$	4.07342	0.181625	0.0908123	−	0.995868i	$-0.471054\pi$
$503$	4.07342	0.181625	0.0908123	+	0.995868i	$0.471054\pi$
$504$	−10.9400	−0.487305
$505$	60.5232	2.69325
$506$	−2.48130	−0.110307
$507$	−0.291117	−0.0129289
$508$	−2.62171	−0.116320
$509$	−22.0789	−0.978631	−0.489315	−	0.872107i	$-0.662753\pi$
$509$	−22.0789	−0.978631	−0.489315	+	0.872107i	$0.662753\pi$
$510$	4.90052	0.216999
$511$	−27.1194	−1.19969
$512$	−1.00000	−0.0441942
$513$	−7.06814	−0.312066
$514$	−2.44200	−0.107712
$515$	3.38601	0.149205
$516$	0.350061	0.0154106
$517$	−11.1529	−0.490503
$518$	24.0242	1.05556
$519$	−2.51853	−0.110551
$520$	−14.4872	−0.635304
$521$	11.4920	0.503474	0.251737	−	0.967796i	$-0.418998\pi$
$521$	11.4920	0.503474	0.251737	+	0.967796i	$0.418998\pi$
$522$	−13.5717	−0.594017
$523$	−41.3753	−1.80922	−0.904608	−	0.426245i	$-0.859836\pi$
$523$	−41.3753	−1.80922	−0.904608	+	0.426245i	$0.859836\pi$
$524$	14.0879	0.615432
$525$	−8.98981	−0.392347
$526$	29.7851	1.29869
$527$	−27.2950	−1.18899
$528$	0.181771	0.00791056
$529$	−16.8432	−0.732311
$530$	35.5462	1.54403
$531$	−10.0696	−0.436983
$532$	−24.0288	−1.04178
$533$	28.4457	1.23212
$534$	−2.72233	−0.117807
$535$	−6.64508	−0.287292
$536$	0.980061	0.0423322
$537$	3.19442	0.137850
$538$	−0.965597	−0.0416298
$539$	6.59595	0.284108
$540$	−4.65413	−0.200282
$541$	−8.60355	−0.369895	−0.184948	−	0.982748i	$-0.559212\pi$
$541$	−8.60355	−0.369895	−0.184948	+	0.982748i	$0.559212\pi$
$542$	6.61910	0.284315
$543$	2.95192	0.126679
$544$	6.28286	0.269375
$545$	26.2525	1.12453
$546$	2.26283	0.0968402
$547$	21.4333	0.916424	0.458212	−	0.888843i	$-0.348490\pi$
$547$	21.4333	0.916424	0.458212	+	0.888843i	$0.348490\pi$
$548$	0.779585	0.0333022
$549$	28.6799	1.22403
$550$	−13.4129	−0.571926
$551$	−29.8092	−1.26991
$552$	−0.451028	−0.0191970
$553$	−37.6984	−1.60310
$554$	−21.1372	−0.898035
$555$	5.08193	0.215716
$556$	−6.88259	−0.291887
$557$	−41.5647	−1.76115	−0.880577	−	0.473903i	$-0.842845\pi$
$557$	−41.5647	−1.76115	−0.880577	+	0.473903i	$0.842845\pi$
$558$	12.8895	0.545658
$559$	6.50192	0.275002
$560$	−15.8221	−0.668608
$561$	−1.14204	−0.0482170
$562$	16.3632	0.690241
$563$	−22.9100	−0.965543	−0.482771	−	0.875746i	$-0.660370\pi$
$563$	−22.9100	−0.965543	−0.482771	+	0.875746i	$0.660370\pi$
$564$	−2.02727	−0.0853633
$565$	88.9750	3.74321
$566$	30.7709	1.29340
$567$	−32.0930	−1.34778
$568$	3.36075	0.141014
$569$	28.6820	1.20241	0.601207	−	0.799093i	$-0.294687\pi$
$569$	28.6820	1.20241	0.601207	+	0.799093i	$0.294687\pi$
$570$	−5.08291	−0.212900
$571$	−31.2592	−1.30816	−0.654079	−	0.756426i	$-0.726944\pi$
$571$	−31.2592	−1.30816	−0.654079	+	0.756426i	$0.726944\pi$
$572$	3.37616	0.141164
$573$	1.64062	0.0685379
$574$	31.0670	1.29671
$575$	33.2813	1.38793
$576$	−2.96696	−0.123623
$577$	−36.1337	−1.50427	−0.752134	−	0.659011i	$-0.770975\pi$
$577$	−36.1337	−1.50427	−0.752134	+	0.659011i	$0.770975\pi$
$578$	−22.4743	−0.934807
$579$	3.23726	0.134536
$580$	−19.6283	−0.815022
$581$	65.8280	2.73101
$582$	−3.35759	−0.139176
$583$	−8.28386	−0.343082
$584$	−7.35486	−0.304346
$585$	−42.9828	−1.77712
$586$	−11.7087	−0.483681
$587$	−11.5499	−0.476717	−0.238358	−	0.971177i	$-0.576609\pi$
$587$	−11.5499	−0.476717	−0.238358	+	0.971177i	$0.576609\pi$
$588$	1.19895	0.0494440
$589$	28.3109	1.16653
$590$	−14.5633	−0.599563
$591$	−0.181771	−0.00747706
$592$	6.51544	0.267783
$593$	26.8828	1.10395	0.551973	−	0.833862i	$-0.313875\pi$
$593$	26.8828	1.10395	0.551973	+	0.833862i	$0.313875\pi$
$594$	1.08462	0.0445025
$595$	99.4083	4.07534
$596$	−9.69903	−0.397288
$597$	0.312866	0.0128047
$598$	−8.37726	−0.342572
$599$	−21.7105	−0.887065	−0.443532	−	0.896258i	$-0.646275\pi$
$599$	−21.7105	−0.887065	−0.443532	+	0.896258i	$0.646275\pi$
$600$	−2.43807	−0.0995337
$601$	30.6251	1.24922	0.624612	−	0.780936i	$-0.285257\pi$
$601$	30.6251	1.24922	0.624612	+	0.780936i	$0.285257\pi$
$602$	7.10107	0.289418
$603$	2.90780	0.118415
$604$	−18.4788	−0.751890
$605$	4.29102	0.174455
$606$	−2.56381	−0.104148
$607$	18.7022	0.759097	0.379548	−	0.925172i	$-0.376079\pi$
$607$	18.7022	0.759097	0.379548	+	0.925172i	$0.376079\pi$
$608$	−6.51670	−0.264287
$609$	3.06586	0.124235
$610$	41.4788	1.67943
$611$	−37.6538	−1.52331
$612$	18.6410	0.753517
$613$	−6.84223	−0.276355	−0.138178	−	0.990407i	$-0.544124\pi$
$613$	−6.84223	−0.276355	−0.138178	+	0.990407i	$0.544124\pi$
$614$	−34.1800	−1.37939
$615$	6.57173	0.264998
$616$	3.68727	0.148564
$617$	−36.6369	−1.47494	−0.737472	−	0.675377i	$-0.763981\pi$
$617$	−36.6369	−1.47494	−0.737472	+	0.675377i	$0.763981\pi$
$618$	−0.143434	−0.00576976
$619$	40.0534	1.60988	0.804941	−	0.593355i	$-0.202197\pi$
$619$	40.0534	1.60988	0.804941	+	0.593355i	$0.202197\pi$
$620$	18.6417	0.748670
$621$	−2.69127	−0.107997
$622$	23.7251	0.951291
$623$	−55.2231	−2.21247
$624$	0.613687	0.0245672
$625$	87.8404	3.51361
$626$	−16.8968	−0.675333
$627$	1.18455	0.0473062
$628$	−0.144765	−0.00577675
$629$	−40.9356	−1.63221
$630$	−46.9437	−1.87028
$631$	12.0401	0.479311	0.239655	−	0.970858i	$-0.422966\pi$
$631$	12.0401	0.479311	0.239655	+	0.970858i	$0.422966\pi$
$632$	−10.2239	−0.406687
$633$	1.99412	0.0792591
$634$	−7.48373	−0.297217
$635$	−11.2498	−0.446435
$636$	−1.50576	−0.0597074
$637$	22.2690	0.882329
$638$	4.57428	0.181097
$639$	9.97120	0.394455
$640$	−4.29102	−0.169617
$641$	−11.0238	−0.435413	−0.217707	−	0.976014i	$-0.569858\pi$
$641$	−11.0238	−0.435413	−0.217707	+	0.976014i	$0.569858\pi$
$642$	0.281491	0.0111096
$643$	−28.9534	−1.14181	−0.570906	−	0.821016i	$-0.693408\pi$
$643$	−28.9534	−1.14181	−0.570906	+	0.821016i	$0.693408\pi$
$644$	−9.14922	−0.360530
$645$	1.50212	0.0591458
$646$	40.9435	1.61090
$647$	−12.0795	−0.474893	−0.237447	−	0.971401i	$-0.576311\pi$
$647$	−12.0795	−0.474893	−0.237447	+	0.971401i	$0.576311\pi$
$648$	−8.70373	−0.341915
$649$	3.39391	0.133223
$650$	−45.2839	−1.77618
$651$	−2.91176	−0.114121
$652$	2.85014	0.111620
$653$	28.0387	1.09724	0.548619	−	0.836073i	$-0.315154\pi$
$653$	28.0387	1.09724	0.548619	+	0.836073i	$0.315154\pi$
$654$	−1.11207	−0.0434855
$655$	60.4513	2.36203
$656$	8.42548	0.328960
$657$	−21.8216	−0.851341
$658$	−41.1236	−1.60317
$659$	2.17244	0.0846261	0.0423131	−	0.999104i	$-0.486527\pi$
$659$	2.17244	0.0846261	0.0423131	+	0.999104i	$0.486527\pi$
$660$	0.779983	0.0303608
$661$	−44.8840	−1.74578	−0.872892	−	0.487913i	$-0.837758\pi$
$661$	−44.8840	−1.74578	−0.872892	+	0.487913i	$0.837758\pi$
$662$	10.5010	0.408134
$663$	−3.85571	−0.149743
$664$	17.8528	0.692823
$665$	−103.108	−3.99836
$666$	19.3311	0.749063
$667$	−11.3502	−0.439480
$668$	1.93980	0.0750532
$669$	2.40280	0.0928976
$670$	4.20546	0.162471
$671$	−9.66643	−0.373168
$672$	0.670238	0.0258550
$673$	13.8966	0.535673	0.267837	−	0.963464i	$-0.413691\pi$
$673$	13.8966	0.535673	0.267837	+	0.963464i	$0.413691\pi$
$674$	18.4051	0.708938
$675$	−14.5478	−0.559947
$676$	−1.60156	−0.0615984
$677$	24.9229	0.957865	0.478933	−	0.877852i	$-0.341024\pi$
$677$	24.9229	0.957865	0.478933	+	0.877852i	$0.341024\pi$
$678$	−3.76905	−0.144750
$679$	−68.1095	−2.61380
$680$	26.9599	1.03386
$681$	2.75417	0.105540
$682$	−4.34436	−0.166354
$683$	−15.8956	−0.608227	−0.304114	−	0.952636i	$-0.598360\pi$
$683$	−15.8956	−0.608227	−0.304114	+	0.952636i	$0.598360\pi$
$684$	−19.3348	−0.739284
$685$	3.34522	0.127814
$686$	−1.48983	−0.0568820
$687$	0.817139	0.0311758
$688$	1.92583	0.0734217
$689$	−27.9676	−1.06548
$690$	−1.93537	−0.0736783
$691$	−46.3338	−1.76262	−0.881311	−	0.472537i	$-0.843338\pi$
$691$	−46.3338	−1.76262	−0.881311	+	0.472537i	$0.843338\pi$
$692$	−13.8555	−0.526707
$693$	10.9400	0.415575
$694$	−1.35989	−0.0516208
$695$	−29.5333	−1.12026
$696$	0.831471	0.0315168
$697$	−52.9361	−2.00510
$698$	−28.2420	−1.06897
$699$	−1.97788	−0.0748105
$700$	−49.4568	−1.86929
$701$	−27.3456	−1.03283	−0.516415	−	0.856339i	$-0.672734\pi$
$701$	−27.3456	−1.03283	−0.516415	+	0.856339i	$0.672734\pi$
$702$	3.66185	0.138208
$703$	42.4592	1.60138
$704$	1.00000	0.0376889
$705$	−8.69904	−0.327625
$706$	−15.3466	−0.577577
$707$	−52.0075	−1.95594
$708$	0.616914	0.0231850
$709$	−10.5599	−0.396587	−0.198294	−	0.980143i	$-0.563540\pi$
$709$	−10.5599	−0.396587	−0.198294	+	0.980143i	$0.563540\pi$
$710$	14.4210	0.541212
$711$	−30.3340	−1.13761
$712$	−14.9767	−0.561275
$713$	10.7797	0.403701
$714$	−4.21101	−0.157593
$715$	14.4872	0.541789
$716$	17.5739	0.656767
$717$	4.02818	0.150435
$718$	23.8278	0.889246
$719$	22.9105	0.854418	0.427209	−	0.904153i	$-0.359497\pi$
$719$	22.9105	0.854418	0.427209	+	0.904153i	$0.359497\pi$
$720$	−12.7313	−0.474467
$721$	−2.90960	−0.108359
$722$	−23.4673	−0.873364
$723$	−2.59715	−0.0965890
$724$	16.2398	0.603547
$725$	−61.3541	−2.27864
$726$	−0.181771	−0.00674615
$727$	25.0193	0.927914	0.463957	−	0.885858i	$-0.346429\pi$
$727$	25.0193	0.927914	0.463957	+	0.885858i	$0.346429\pi$
$728$	12.4488	0.461383
$729$	−25.2321	−0.934524
$730$	−31.5599	−1.16808
$731$	−12.0997	−0.447525
$732$	−1.75708	−0.0649434
$733$	−49.7329	−1.83693	−0.918463	−	0.395506i	$-0.870569\pi$
$733$	−49.7329	−1.83693	−0.918463	+	0.395506i	$0.870569\pi$
$734$	−15.5015	−0.572169
$735$	5.14473	0.189766
$736$	−2.48130	−0.0914619
$737$	−0.980061	−0.0361010
$738$	24.9980	0.920191
$739$	−43.6674	−1.60633	−0.803166	−	0.595755i	$-0.796853\pi$
$739$	−43.6674	−1.60633	−0.803166	+	0.595755i	$0.796853\pi$
$740$	27.9579	1.02775
$741$	3.99921	0.146915
$742$	−30.5448	−1.12134
$743$	−2.83421	−0.103977	−0.0519886	−	0.998648i	$-0.516556\pi$
$743$	−2.83421	−0.103977	−0.0519886	+	0.998648i	$0.516556\pi$
$744$	−0.789678	−0.0289510
$745$	−41.6187	−1.52479
$746$	−5.54119	−0.202878
$747$	52.9685	1.93802
$748$	−6.28286	−0.229724
$749$	5.71011	0.208643
$750$	−6.56188	−0.239606
$751$	16.2294	0.592220	0.296110	−	0.955154i	$-0.404311\pi$
$751$	16.2294	0.592220	0.296110	+	0.955154i	$0.404311\pi$
$752$	−11.1529	−0.406703
$753$	−4.66739	−0.170089
$754$	15.4435	0.562419
$755$	−79.2927	−2.88576
$756$	3.99928	0.145453
$757$	−33.4596	−1.21611	−0.608055	−	0.793895i	$-0.708050\pi$
$757$	−33.4596	−1.21611	−0.608055	+	0.793895i	$0.708050\pi$
$758$	3.41599	0.124074
$759$	0.451028	0.0163713
$760$	−27.9633	−1.01433
$761$	−4.84081	−0.175479	−0.0877396	−	0.996143i	$-0.527964\pi$
$761$	−4.84081	−0.175479	−0.0877396	+	0.996143i	$0.527964\pi$
$762$	0.476551	0.0172636
$763$	−22.5587	−0.816680
$764$	9.02576	0.326540
$765$	79.9888	2.89200
$766$	13.8478	0.500342
$767$	11.4584	0.413738
$768$	0.181771	0.00655909
$769$	−32.4947	−1.17179	−0.585894	−	0.810388i	$-0.699256\pi$
$769$	−32.4947	−1.17179	−0.585894	+	0.810388i	$0.699256\pi$
$770$	15.8221	0.570191
$771$	0.443885	0.0159861
$772$	17.8095	0.640980
$773$	32.4460	1.16700	0.583500	−	0.812113i	$-0.301683\pi$
$773$	32.4460	1.16700	0.583500	+	0.812113i	$0.301683\pi$
$774$	5.71387	0.205381
$775$	58.2702	2.09313
$776$	−18.4715	−0.663089
$777$	−4.36690	−0.156662
$778$	−24.6771	−0.884717
$779$	54.9063	1.96722
$780$	2.63334	0.0942889
$781$	−3.36075	−0.120257
$782$	15.5896	0.557485
$783$	4.96135	0.177304
$784$	6.59595	0.235570
$785$	−0.621189	−0.0221712
$786$	−2.56077	−0.0913395
$787$	20.2982	0.723552	0.361776	−	0.932265i	$-0.382171\pi$
$787$	20.2982	0.723552	0.361776	+	0.932265i	$0.382171\pi$
$788$	−1.00000	−0.0356235
$789$	−5.41406	−0.192746
$790$	−43.8711	−1.56087
$791$	−76.4561	−2.71847
$792$	2.96696	0.105426
$793$	−32.6354	−1.15892
$794$	26.1274	0.927227
$795$	−6.46126	−0.229157
$796$	1.72121	0.0610066
$797$	−25.7052	−0.910525	−0.455263	−	0.890357i	$-0.650455\pi$
$797$	−25.7052	−0.910525	−0.455263	+	0.890357i	$0.650455\pi$
$798$	4.36774	0.154616
$799$	70.0719	2.47896
$800$	−13.4129	−0.474216
$801$	−44.4352	−1.57004
$802$	−8.30355	−0.293209
$803$	7.35486	0.259548
$804$	−0.178147	−0.00628275
$805$	−39.2595	−1.38371
$806$	−14.6672	−0.516631
$807$	0.175517	0.00617850
$808$	−14.1046	−0.496199
$809$	30.7289	1.08037	0.540185	−	0.841547i	$-0.318354\pi$
$809$	30.7289	1.08037	0.540185	+	0.841547i	$0.318354\pi$
$810$	−37.3479	−1.31227
$811$	−33.2425	−1.16730	−0.583651	−	0.812004i	$-0.698377\pi$
$811$	−33.2425	−1.16730	−0.583651	+	0.812004i	$0.698377\pi$
$812$	16.8666	0.591902
$813$	−1.20316	−0.0421967
$814$	−6.51544	−0.228366
$815$	12.2300	0.428398
$816$	−1.14204	−0.0399794
$817$	12.5501	0.439071
$818$	−16.3116	−0.570322
$819$	36.9351	1.29062
$820$	36.1539	1.26255
$821$	11.1017	0.387450	0.193725	−	0.981056i	$-0.437943\pi$
$821$	11.1017	0.387450	0.193725	+	0.981056i	$0.437943\pi$
$822$	−0.141706	−0.00494256
$823$	27.8480	0.970721	0.485361	−	0.874314i	$-0.338688\pi$
$823$	27.8480	0.970721	0.485361	+	0.874314i	$0.338688\pi$
$824$	−0.789092	−0.0274893
$825$	2.43807	0.0848826
$826$	12.5142	0.435426
$827$	56.5862	1.96770	0.983848	−	0.179006i	$-0.0572883\pi$
$827$	56.5862	1.96770	0.983848	+	0.179006i	$0.0572883\pi$
$828$	−7.36191	−0.255844
$829$	−18.6655	−0.648279	−0.324140	−	0.946009i	$-0.605075\pi$
$829$	−18.6655	−0.648279	−0.324140	+	0.946009i	$0.605075\pi$
$830$	76.6067	2.65906
$831$	3.84213	0.133282
$832$	3.37616	0.117047
$833$	−41.4414	−1.43586
$834$	1.25105	0.0433205
$835$	8.32373	0.288055
$836$	6.51670	0.225385
$837$	−4.71198	−0.162870
$838$	−5.59083	−0.193132
$839$	−12.2945	−0.424452	−0.212226	−	0.977221i	$-0.568071\pi$
$839$	−12.2945	−0.424452	−0.212226	+	0.977221i	$0.568071\pi$
$840$	2.87601	0.0992316
$841$	−8.07597	−0.278482
$842$	−7.57118	−0.260920
$843$	−2.97436	−0.102442
$844$	10.9705	0.377620
$845$	−6.87232	−0.236415
$846$	−33.0901	−1.13766
$847$	−3.68727	−0.126696
$848$	−8.28386	−0.284469
$849$	−5.59326	−0.191960
$850$	84.2710	2.89047
$851$	16.1668	0.554189
$852$	−0.610886	−0.0209286
$853$	−50.3600	−1.72429	−0.862146	−	0.506660i	$-0.830880\pi$
$853$	−50.3600	−1.72429	−0.862146	+	0.506660i	$0.830880\pi$
$854$	−35.6427	−1.21967
$855$	−82.9659	−2.83737
$856$	1.54860	0.0529301
$857$	−29.0078	−0.990886	−0.495443	−	0.868640i	$-0.664994\pi$
$857$	−29.0078	−0.990886	−0.495443	+	0.868640i	$0.664994\pi$
$858$	−0.613687	−0.0209509
$859$	37.5645	1.28168	0.640842	−	0.767673i	$-0.278585\pi$
$859$	37.5645	1.28168	0.640842	+	0.767673i	$0.278585\pi$
$860$	8.26379	0.281793
$861$	−5.64708	−0.192452
$862$	7.79827	0.265610
$863$	−36.5109	−1.24285	−0.621423	−	0.783475i	$-0.713445\pi$
$863$	−36.5109	−1.24285	−0.621423	+	0.783475i	$0.713445\pi$
$864$	1.08462	0.0368995
$865$	−59.4542	−2.02150
$866$	−7.90811	−0.268728
$867$	4.08517	0.138740
$868$	−16.0188	−0.543714
$869$	10.2239	0.346823
$870$	3.56786	0.120962
$871$	−3.30884	−0.112116
$872$	−6.11800	−0.207182
$873$	−54.8043	−1.85484
$874$	−16.1699	−0.546954
$875$	−133.109	−4.49992
$876$	1.33690	0.0451697
$877$	39.6131	1.33764	0.668820	−	0.743424i	$-0.266800\pi$
$877$	39.6131	1.33764	0.668820	+	0.743424i	$0.266800\pi$
$878$	−32.7133	−1.10402
$879$	2.12830	0.0717857
$880$	4.29102	0.144650
$881$	24.9868	0.841827	0.420914	−	0.907101i	$-0.361710\pi$
$881$	24.9868	0.841827	0.420914	+	0.907101i	$0.361710\pi$
$882$	19.5699	0.658954
$883$	−27.1997	−0.915343	−0.457672	−	0.889121i	$-0.651316\pi$
$883$	−27.1997	−0.915343	−0.457672	+	0.889121i	$0.651316\pi$
$884$	−21.2119	−0.713434
$885$	2.64719	0.0889843
$886$	22.6380	0.760538
$887$	−35.3256	−1.18612	−0.593059	−	0.805159i	$-0.702080\pi$
$887$	−35.3256	−1.18612	−0.593059	+	0.805159i	$0.702080\pi$
$888$	−1.18432	−0.0397431
$889$	9.66695	0.324219
$890$	−64.2653	−2.15418
$891$	8.70373	0.291586
$892$	13.2188	0.442599
$893$	−72.6799	−2.43214
$894$	1.76300	0.0589636
$895$	75.4099	2.52068
$896$	3.68727	0.123183
$897$	1.52274	0.0508429
$898$	−34.3159	−1.14514
$899$	−19.8723	−0.662779
$900$	−39.7954	−1.32651
$901$	52.0463	1.73391
$902$	−8.42548	−0.280538
$903$	−1.29077	−0.0429541
$904$	−20.7352	−0.689641
$905$	69.6853	2.31642
$906$	3.35890	0.111592
$907$	−15.9580	−0.529875	−0.264938	−	0.964266i	$-0.585351\pi$
$907$	−15.9580	−0.529875	−0.264938	+	0.964266i	$0.585351\pi$
$908$	15.1519	0.502833
$909$	−41.8478	−1.38801
$910$	53.4181	1.77079
$911$	32.2740	1.06929	0.534643	−	0.845078i	$-0.320446\pi$
$911$	32.2740	1.06929	0.534643	+	0.845078i	$0.320446\pi$
$912$	1.18455	0.0392242
$913$	−17.8528	−0.590841
$914$	−11.6889	−0.386636
$915$	−7.53965	−0.249253
$916$	4.49543	0.148533
$917$	−51.9458	−1.71540
$918$	−6.81451	−0.224912
$919$	−5.36875	−0.177099	−0.0885494	−	0.996072i	$-0.528223\pi$
$919$	−5.36875	−0.177099	−0.0885494	+	0.996072i	$0.528223\pi$
$920$	−10.6473	−0.351031
$921$	6.21292	0.204723
$922$	14.5879	0.480427
$923$	−11.3464	−0.373472
$924$	−0.670238	−0.0220492
$925$	87.3907	2.87339
$926$	1.30476	0.0428770
$927$	−2.34120	−0.0768952
$928$	4.57428	0.150158
$929$	−10.3901	−0.340887	−0.170444	−	0.985367i	$-0.554520\pi$
$929$	−10.3901	−0.340887	−0.170444	+	0.985367i	$0.554520\pi$
$930$	−3.38852	−0.111114
$931$	42.9838	1.40874
$932$	−10.8812	−0.356425
$933$	−4.31254	−0.141186
$934$	3.69447	0.120887
$935$	−26.9599	−0.881682
$936$	10.0169	0.327413
$937$	−0.683433	−0.0223268	−0.0111634	−	0.999938i	$-0.503553\pi$
$937$	−0.683433	−0.0223268	−0.0111634	+	0.999938i	$0.503553\pi$
$938$	−3.61375	−0.117993
$939$	3.07135	0.100230
$940$	−47.8572	−1.56093
$941$	−49.5232	−1.61441	−0.807206	−	0.590270i	$-0.799021\pi$
$941$	−49.5232	−1.61441	−0.807206	+	0.590270i	$0.799021\pi$
$942$	0.0263141	0.000857359 0
$943$	20.9061	0.680797
$944$	3.39391	0.110462
$945$	17.1610	0.558248
$946$	−1.92583	−0.0626143
$947$	−18.2062	−0.591623	−0.295811	−	0.955246i	$-0.595590\pi$
$947$	−18.2062	−0.591623	−0.295811	+	0.955246i	$0.595590\pi$
$948$	1.85842	0.0603585
$949$	24.8312	0.806054
$950$	−87.4075	−2.83587
$951$	1.36032	0.0441115
$952$	−23.1666	−0.750833
$953$	56.4740	1.82937	0.914686	−	0.404166i	$-0.132438\pi$
$953$	56.4740	1.82937	0.914686	+	0.404166i	$0.132438\pi$
$954$	−24.5779	−0.795738
$955$	38.7297	1.25326
$956$	22.1608	0.716730
$957$	−0.831471	−0.0268776
$958$	−26.9717	−0.871415
$959$	−2.87454	−0.0928238
$960$	0.779983	0.0251738
$961$	−12.1266	−0.391179
$962$	−21.9972	−0.709217
$963$	4.59464	0.148060
$964$	−14.2880	−0.460187
$965$	76.4211	2.46008
$966$	1.66306	0.0535081
$967$	17.3789	0.558869	0.279434	−	0.960165i	$-0.409853\pi$
$967$	17.3789	0.558869	0.279434	+	0.960165i	$0.409853\pi$
$968$	−1.00000	−0.0321412
$969$	−7.44233	−0.239082
$970$	−79.2617	−2.54494
$971$	−26.7295	−0.857791	−0.428896	−	0.903354i	$-0.641097\pi$
$971$	−26.7295	−0.857791	−0.428896	+	0.903354i	$0.641097\pi$
$972$	4.83594	0.155113
$973$	25.3780	0.813580
$974$	20.4504	0.655272
$975$	8.23130	0.263613
$976$	−9.66643	−0.309415
$977$	−55.2805	−1.76858	−0.884291	−	0.466937i	$-0.845357\pi$
$977$	−55.2805	−1.76858	−0.884291	+	0.466937i	$0.845357\pi$
$978$	−0.518073	−0.0165661
$979$	14.9767	0.478657
$980$	28.3034	0.904118
$981$	−18.1519	−0.579544
$982$	3.77837	0.120573
$983$	12.3759	0.394729	0.197365	−	0.980330i	$-0.436762\pi$
$983$	12.3759	0.394729	0.197365	+	0.980330i	$0.436762\pi$
$984$	−1.53151	−0.0488226
$985$	−4.29102	−0.136723
$986$	−28.7395	−0.915253
$987$	7.47508	0.237934
$988$	22.0014	0.699958
$989$	4.77857	0.151950
$990$	12.7313	0.404627
$991$	56.2234	1.78600	0.892998	−	0.450060i	$-0.148597\pi$
$991$	56.2234	1.78600	0.892998	+	0.450060i	$0.148597\pi$
$992$	−4.34436	−0.137934
$993$	−1.90878	−0.0605733
$994$	−12.3920	−0.393050
$995$	7.38574	0.234144
$996$	−3.24512	−0.102826
$997$	35.3581	1.11980	0.559902	−	0.828559i	$-0.310839\pi$
$997$	35.3581	1.11980	0.559902	+	0.828559i	$0.310839\pi$
$998$	33.5503	1.06202
$999$	−7.06678	−0.223583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.h.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.h.1.15	✓	27	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.181771 q^{3} +1.00000 q^{4} +4.29102 q^{5} -0.181771 q^{6} -3.68727 q^{7} -1.00000 q^{8} -2.96696 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.181771 q^{3} +1.00000 q^{4} +4.29102 q^{5} -0.181771 q^{6} -3.68727 q^{7} -1.00000 q^{8} -2.96696 q^{9} -4.29102 q^{10} +1.00000 q^{11} +0.181771 q^{12} +3.37616 q^{13} +3.68727 q^{14} +0.779983 q^{15} +1.00000 q^{16} -6.28286 q^{17} +2.96696 q^{18} +6.51670 q^{19} +4.29102 q^{20} -0.670238 q^{21} -1.00000 q^{22} +2.48130 q^{23} -0.181771 q^{24} +13.4129 q^{25} -3.37616 q^{26} -1.08462 q^{27} -3.68727 q^{28} -4.57428 q^{29} -0.779983 q^{30} +4.34436 q^{31} -1.00000 q^{32} +0.181771 q^{33} +6.28286 q^{34} -15.8221 q^{35} -2.96696 q^{36} +6.51544 q^{37} -6.51670 q^{38} +0.613687 q^{39} -4.29102 q^{40} +8.42548 q^{41} +0.670238 q^{42} +1.92583 q^{43} +1.00000 q^{44} -12.7313 q^{45} -2.48130 q^{46} -11.1529 q^{47} +0.181771 q^{48} +6.59595 q^{49} -13.4129 q^{50} -1.14204 q^{51} +3.37616 q^{52} -8.28386 q^{53} +1.08462 q^{54} +4.29102 q^{55} +3.68727 q^{56} +1.18455 q^{57} +4.57428 q^{58} +3.39391 q^{59} +0.779983 q^{60} -9.66643 q^{61} -4.34436 q^{62} +10.9400 q^{63} +1.00000 q^{64} +14.4872 q^{65} -0.181771 q^{66} -0.980061 q^{67} -6.28286 q^{68} +0.451028 q^{69} +15.8221 q^{70} -3.36075 q^{71} +2.96696 q^{72} +7.35486 q^{73} -6.51544 q^{74} +2.43807 q^{75} +6.51670 q^{76} -3.68727 q^{77} -0.613687 q^{78} +10.2239 q^{79} +4.29102 q^{80} +8.70373 q^{81} -8.42548 q^{82} -17.8528 q^{83} -0.670238 q^{84} -26.9599 q^{85} -1.92583 q^{86} -0.831471 q^{87} -1.00000 q^{88} +14.9767 q^{89} +12.7313 q^{90} -12.4488 q^{91} +2.48130 q^{92} +0.789678 q^{93} +11.1529 q^{94} +27.9633 q^{95} -0.181771 q^{96} +18.4715 q^{97} -6.59595 q^{98} -2.96696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

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