LMFDB - Embedded newform 8041.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64866 q^{2} +1.22889 q^{3} +5.01539 q^{4} -0.305577 q^{5} -3.25491 q^{6} -2.34072 q^{7} -7.98675 q^{8} -1.48983 q^{9} +O(q^{10})$	\(q-2.64866 q^{2} +1.22889 q^{3} +5.01539 q^{4} -0.305577 q^{5} -3.25491 q^{6} -2.34072 q^{7} -7.98675 q^{8} -1.48983 q^{9} +0.809369 q^{10} -1.00000 q^{11} +6.16336 q^{12} -0.268014 q^{13} +6.19978 q^{14} -0.375520 q^{15} +11.1234 q^{16} +1.00000 q^{17} +3.94606 q^{18} +2.78504 q^{19} -1.53259 q^{20} -2.87649 q^{21} +2.64866 q^{22} -2.45254 q^{23} -9.81482 q^{24} -4.90662 q^{25} +0.709878 q^{26} -5.51750 q^{27} -11.7396 q^{28} -5.07720 q^{29} +0.994624 q^{30} -7.06987 q^{31} -13.4886 q^{32} -1.22889 q^{33} -2.64866 q^{34} +0.715271 q^{35} -7.47210 q^{36} -7.59317 q^{37} -7.37662 q^{38} -0.329359 q^{39} +2.44057 q^{40} +7.50921 q^{41} +7.61883 q^{42} -1.00000 q^{43} -5.01539 q^{44} +0.455259 q^{45} +6.49593 q^{46} -1.35156 q^{47} +13.6694 q^{48} -1.52102 q^{49} +12.9960 q^{50} +1.22889 q^{51} -1.34420 q^{52} -5.03813 q^{53} +14.6140 q^{54} +0.305577 q^{55} +18.6948 q^{56} +3.42250 q^{57} +13.4478 q^{58} +10.9591 q^{59} -1.88338 q^{60} +6.27375 q^{61} +18.7257 q^{62} +3.48729 q^{63} +13.4798 q^{64} +0.0818989 q^{65} +3.25491 q^{66} +6.17499 q^{67} +5.01539 q^{68} -3.01389 q^{69} -1.89451 q^{70} -3.48195 q^{71} +11.8989 q^{72} -6.74516 q^{73} +20.1117 q^{74} -6.02969 q^{75} +13.9681 q^{76} +2.34072 q^{77} +0.872360 q^{78} +2.73092 q^{79} -3.39905 q^{80} -2.31089 q^{81} -19.8893 q^{82} -2.28648 q^{83} -14.4267 q^{84} -0.305577 q^{85} +2.64866 q^{86} -6.23931 q^{87} +7.98675 q^{88} +4.36714 q^{89} -1.20583 q^{90} +0.627347 q^{91} -12.3004 q^{92} -8.68807 q^{93} +3.57983 q^{94} -0.851043 q^{95} -16.5759 q^{96} -15.1278 q^{97} +4.02865 q^{98} +1.48983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−2.64866	−1.87288	−0.936442	−	0.350822i	$-0.885902\pi$
$2$	−2.64866	−1.87288	−0.936442	+	0.350822i	$0.885902\pi$
$3$	1.22889	0.709499	0.354749	−	0.934961i	$-0.384566\pi$
$3$	1.22889	0.709499	0.354749	+	0.934961i	$0.384566\pi$
$4$	5.01539	2.50770
$5$	−0.305577	−0.136658	−0.0683291	−	0.997663i	$-0.521767\pi$
$5$	−0.305577	−0.136658	−0.0683291	+	0.997663i	$0.521767\pi$
$6$	−3.25491	−1.32881
$7$	−2.34072	−0.884710	−0.442355	−	0.896840i	$-0.645857\pi$
$7$	−2.34072	−0.884710	−0.442355	+	0.896840i	$0.645857\pi$
$8$	−7.98675	−2.82374
$9$	−1.48983	−0.496611
$10$	0.809369	0.255945
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.16336	1.77921
$13$	−0.268014	−0.0743337	−0.0371669	−	0.999309i	$-0.511833\pi$
$13$	−0.268014	−0.0743337	−0.0371669	+	0.999309i	$0.511833\pi$
$14$	6.19978	1.65696
$15$	−0.375520	−0.0969588
$16$	11.1234	2.78085
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.94606	0.930096
$19$	2.78504	0.638932	0.319466	−	0.947598i	$-0.396497\pi$
$19$	2.78504	0.638932	0.319466	+	0.947598i	$0.396497\pi$
$20$	−1.53259	−0.342697
$21$	−2.87649	−0.627701
$22$	2.64866	0.564696
$23$	−2.45254	−0.511389	−0.255695	−	0.966758i	$-0.582304\pi$
$23$	−2.45254	−0.511389	−0.255695	+	0.966758i	$0.582304\pi$
$24$	−9.81482	−2.00344
$25$	−4.90662	−0.981325
$26$	0.709878	0.139218
$27$	−5.51750	−1.06184
$28$	−11.7396	−2.21858
$29$	−5.07720	−0.942812	−0.471406	−	0.881916i	$-0.656253\pi$
$29$	−5.07720	−0.942812	−0.471406	+	0.881916i	$0.656253\pi$
$30$	0.994624	0.181593
$31$	−7.06987	−1.26979	−0.634893	−	0.772600i	$-0.718956\pi$
$31$	−7.06987	−1.26979	−0.634893	+	0.772600i	$0.718956\pi$
$32$	−13.4886	−2.38446
$33$	−1.22889	−0.213922
$34$	−2.64866	−0.454241
$35$	0.715271	0.120903
$36$	−7.47210	−1.24535
$37$	−7.59317	−1.24831	−0.624155	−	0.781301i	$-0.714556\pi$
$37$	−7.59317	−1.24831	−0.624155	+	0.781301i	$0.714556\pi$
$38$	−7.37662	−1.19665
$39$	−0.329359	−0.0527397
$40$	2.44057	0.385887
$41$	7.50921	1.17274	0.586371	−	0.810043i	$-0.300556\pi$
$41$	7.50921	1.17274	0.586371	+	0.810043i	$0.300556\pi$
$42$	7.61883	1.17561
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.01539	−0.756099
$45$	0.455259	0.0678660
$46$	6.49593	0.957773
$47$	−1.35156	−0.197146	−0.0985729	−	0.995130i	$-0.531428\pi$
$47$	−1.35156	−0.197146	−0.0985729	+	0.995130i	$0.531428\pi$
$48$	13.6694	1.97301
$49$	−1.52102	−0.217288
$50$	12.9960	1.83791
$51$	1.22889	0.172079
$52$	−1.34420	−0.186406
$53$	−5.03813	−0.692041	−0.346020	−	0.938227i	$-0.612467\pi$
$53$	−5.03813	−0.692041	−0.346020	+	0.938227i	$0.612467\pi$
$54$	14.6140	1.98871
$55$	0.305577	0.0412040
$56$	18.6948	2.49819
$57$	3.42250	0.453321
$58$	13.4478	1.76578
$59$	10.9591	1.42675	0.713377	−	0.700781i	$-0.247165\pi$
$59$	10.9591	1.42675	0.713377	+	0.700781i	$0.247165\pi$
$60$	−1.88338	−0.243143
$61$	6.27375	0.803272	0.401636	−	0.915799i	$-0.368442\pi$
$61$	6.27375	0.803272	0.401636	+	0.915799i	$0.368442\pi$
$62$	18.7257	2.37816
$63$	3.48729	0.439357
$64$	13.4798	1.68498
$65$	0.0818989	0.0101583
$66$	3.25491	0.400651
$67$	6.17499	0.754395	0.377198	−	0.926133i	$-0.376888\pi$
$67$	6.17499	0.754395	0.377198	+	0.926133i	$0.376888\pi$
$68$	5.01539	0.608206
$69$	−3.01389	−0.362830
$70$	−1.89451	−0.226437
$71$	−3.48195	−0.413231	−0.206616	−	0.978422i	$-0.566245\pi$
$71$	−3.48195	−0.413231	−0.206616	+	0.978422i	$0.566245\pi$
$72$	11.8989	1.40230
$73$	−6.74516	−0.789461	−0.394731	−	0.918797i	$-0.629162\pi$
$73$	−6.74516	−0.789461	−0.394731	+	0.918797i	$0.629162\pi$
$74$	20.1117	2.33794
$75$	−6.02969	−0.696249
$76$	13.9681	1.60225
$77$	2.34072	0.266750
$78$	0.872360	0.0987753
$79$	2.73092	0.307252	0.153626	−	0.988129i	$-0.450905\pi$
$79$	2.73092	0.307252	0.153626	+	0.988129i	$0.450905\pi$
$80$	−3.39905	−0.380025
$81$	−2.31089	−0.256766
$82$	−19.8893	−2.19641
$83$	−2.28648	−0.250974	−0.125487	−	0.992095i	$-0.540049\pi$
$83$	−2.28648	−0.250974	−0.125487	+	0.992095i	$0.540049\pi$
$84$	−14.4267	−1.57408
$85$	−0.305577	−0.0331445
$86$	2.64866	0.285612
$87$	−6.23931	−0.668924
$88$	7.98675	0.851390
$89$	4.36714	0.462916	0.231458	−	0.972845i	$-0.425650\pi$
$89$	4.36714	0.462916	0.231458	+	0.972845i	$0.425650\pi$
$90$	−1.20583	−0.127105
$91$	0.627347	0.0657638
$92$	−12.3004	−1.28241
$93$	−8.68807	−0.900911
$94$	3.57983	0.369231
$95$	−0.851043	−0.0873152
$96$	−16.5759	−1.69177
$97$	−15.1278	−1.53599	−0.767997	−	0.640453i	$-0.778747\pi$
$97$	−15.1278	−1.53599	−0.767997	+	0.640453i	$0.778747\pi$
$98$	4.02865	0.406955
$99$	1.48983	0.149734
$100$	−24.6086	−2.46086
$101$	11.7091	1.16510	0.582552	−	0.812794i	$-0.302054\pi$
$101$	11.7091	1.16510	0.582552	+	0.812794i	$0.302054\pi$
$102$	−3.25491	−0.322284
$103$	6.68433	0.658627	0.329313	−	0.944221i	$-0.393183\pi$
$103$	6.68433	0.658627	0.329313	+	0.944221i	$0.393183\pi$
$104$	2.14056	0.209899
$105$	0.878988	0.0857804
$106$	13.3443	1.29611
$107$	−4.08334	−0.394752	−0.197376	−	0.980328i	$-0.563242\pi$
$107$	−4.08334	−0.394752	−0.197376	+	0.980328i	$0.563242\pi$
$108$	−27.6725	−2.66278
$109$	−4.10865	−0.393538	−0.196769	−	0.980450i	$-0.563045\pi$
$109$	−4.10865	−0.393538	−0.196769	+	0.980450i	$0.563045\pi$
$110$	−0.809369	−0.0771703
$111$	−9.33115	−0.885674
$112$	−26.0368	−2.46024
$113$	12.4171	1.16810	0.584051	−	0.811717i	$-0.301467\pi$
$113$	12.4171	1.16810	0.584051	+	0.811717i	$0.301467\pi$
$114$	−9.06504	−0.849018
$115$	0.749438	0.0698855
$116$	−25.4641	−2.36429
$117$	0.399296	0.0369150
$118$	−29.0269	−2.67214
$119$	−2.34072	−0.214574
$120$	2.99918	0.273787
$121$	1.00000	0.0909091
$122$	−16.6170	−1.50444
$123$	9.22798	0.832059
$124$	−35.4582	−3.18424
$125$	3.02723	0.270764
$126$	−9.23664	−0.822865
$127$	7.54825	0.669799	0.334899	−	0.942254i	$-0.391298\pi$
$127$	7.54825	0.669799	0.334899	+	0.942254i	$0.391298\pi$
$128$	−8.72632	−0.771305
$129$	−1.22889	−0.108198
$130$	−0.216922	−0.0190253
$131$	−16.5869	−1.44920	−0.724601	−	0.689169i	$-0.757976\pi$
$131$	−16.5869	−1.44920	−0.724601	+	0.689169i	$0.757976\pi$
$132$	−6.16336	−0.536451
$133$	−6.51900	−0.565269
$134$	−16.3554	−1.41290
$135$	1.68602	0.145110
$136$	−7.98675	−0.684858
$137$	6.56763	0.561110	0.280555	−	0.959838i	$-0.409481\pi$
$137$	6.56763	0.561110	0.280555	+	0.959838i	$0.409481\pi$
$138$	7.98277	0.679539
$139$	−9.51047	−0.806668	−0.403334	−	0.915053i	$-0.632149\pi$
$139$	−9.51047	−0.806668	−0.403334	+	0.915053i	$0.632149\pi$
$140$	3.58736	0.303188
$141$	−1.66092	−0.139875
$142$	9.22250	0.773935
$143$	0.268014	0.0224125
$144$	−16.5720	−1.38100
$145$	1.55147	0.128843
$146$	17.8656	1.47857
$147$	−1.86916	−0.154166
$148$	−38.0827	−3.13038
$149$	17.3253	1.41934	0.709672	−	0.704533i	$-0.248843\pi$
$149$	17.3253	1.41934	0.709672	+	0.704533i	$0.248843\pi$
$150$	15.9706	1.30399
$151$	4.46772	0.363578	0.181789	−	0.983338i	$-0.441811\pi$
$151$	4.46772	0.363578	0.181789	+	0.983338i	$0.441811\pi$
$152$	−22.2434	−1.80418
$153$	−1.48983	−0.120446
$154$	−6.19978	−0.499592
$155$	2.16039	0.173526
$156$	−1.65187	−0.132255
$157$	20.9019	1.66815	0.834077	−	0.551648i	$-0.186001\pi$
$157$	20.9019	1.66815	0.834077	+	0.551648i	$0.186001\pi$
$158$	−7.23327	−0.575448
$159$	−6.19130	−0.491002
$160$	4.12179	0.325856
$161$	5.74071	0.452431
$162$	6.12077	0.480893
$163$	−17.1059	−1.33984	−0.669921	−	0.742433i	$-0.733672\pi$
$163$	−17.1059	−1.33984	−0.669921	+	0.742433i	$0.733672\pi$
$164$	37.6616	2.94088
$165$	0.375520	0.0292342
$166$	6.05610	0.470045
$167$	−12.0139	−0.929661	−0.464830	−	0.885400i	$-0.653885\pi$
$167$	−12.0139	−0.929661	−0.464830	+	0.885400i	$0.653885\pi$
$168$	22.9738	1.77247
$169$	−12.9282	−0.994475
$170$	0.809369	0.0620758
$171$	−4.14924	−0.317301
$172$	−5.01539	−0.382420
$173$	15.9146	1.20997	0.604983	−	0.796239i	$-0.293180\pi$
$173$	15.9146	1.20997	0.604983	+	0.796239i	$0.293180\pi$
$174$	16.5258	1.25282
$175$	11.4850	0.868188
$176$	−11.1234	−0.838457
$177$	13.4675	1.01228
$178$	−11.5671	−0.866989
$179$	−4.98079	−0.372282	−0.186141	−	0.982523i	$-0.559598\pi$
$179$	−4.98079	−0.372282	−0.186141	+	0.982523i	$0.559598\pi$
$180$	2.28330	0.170187
$181$	−7.45555	−0.554166	−0.277083	−	0.960846i	$-0.589368\pi$
$181$	−7.45555	−0.554166	−0.277083	+	0.960846i	$0.589368\pi$
$182$	−1.66163	−0.123168
$183$	7.70974	0.569921
$184$	19.5878	1.44403
$185$	2.32030	0.170592
$186$	23.0117	1.68730
$187$	−1.00000	−0.0731272
$188$	−6.77863	−0.494382
$189$	12.9149	0.939424
$190$	2.25412	0.163531
$191$	−0.00220239	−0.000159359 0	−7.96795e−5	−	1.00000i	$-0.500025\pi$
$191$	−0.00220239	−0.000159359 0	−7.96795e−5		1.00000i	$0.500025\pi$
$192$	16.5652	1.19549
$193$	−19.2693	−1.38703	−0.693516	−	0.720441i	$-0.743939\pi$
$193$	−19.2693	−1.38703	−0.693516	+	0.720441i	$0.743939\pi$
$194$	40.0684	2.87674
$195$	0.100645	0.00720731
$196$	−7.62849	−0.544892
$197$	3.37152	0.240211	0.120105	−	0.992761i	$-0.461677\pi$
$197$	3.37152	0.240211	0.120105	+	0.992761i	$0.461677\pi$
$198$	−3.94606	−0.280434
$199$	16.8674	1.19570	0.597850	−	0.801608i	$-0.296022\pi$
$199$	16.8674	1.19570	0.597850	+	0.801608i	$0.296022\pi$
$200$	39.1880	2.77101
$201$	7.58837	0.535243
$202$	−31.0135	−2.18210
$203$	11.8843	0.834115
$204$	6.16336	0.431521
$205$	−2.29464	−0.160265
$206$	−17.7045	−1.23353
$207$	3.65387	0.253962
$208$	−2.98122	−0.206711
$209$	−2.78504	−0.192645
$210$	−2.32814	−0.160657
$211$	13.9706	0.961777	0.480889	−	0.876782i	$-0.340314\pi$
$211$	13.9706	0.961777	0.480889	+	0.876782i	$0.340314\pi$
$212$	−25.2682	−1.73543
$213$	−4.27893	−0.293187
$214$	10.8154	0.739324
$215$	0.305577	0.0208402
$216$	44.0669	2.99837
$217$	16.5486	1.12339
$218$	10.8824	0.737050
$219$	−8.28905	−0.560122
$220$	1.53259	0.103327
$221$	−0.268014	−0.0180286
$222$	24.7150	1.65877
$223$	−4.83975	−0.324094	−0.162047	−	0.986783i	$-0.551810\pi$
$223$	−4.83975	−0.324094	−0.162047	+	0.986783i	$0.551810\pi$
$224$	31.5730	2.10956
$225$	7.31005	0.487337
$226$	−32.8886	−2.18772
$227$	10.1641	0.674614	0.337307	−	0.941395i	$-0.390484\pi$
$227$	10.1641	0.674614	0.337307	+	0.941395i	$0.390484\pi$
$228$	17.1652	1.13679
$229$	−6.29198	−0.415785	−0.207893	−	0.978152i	$-0.566660\pi$
$229$	−6.29198	−0.415785	−0.207893	+	0.978152i	$0.566660\pi$
$230$	−1.98501	−0.130887
$231$	2.87649	0.189259
$232$	40.5503	2.66226
$233$	21.5526	1.41196	0.705981	−	0.708231i	$-0.250507\pi$
$233$	21.5526	1.41196	0.705981	+	0.708231i	$0.250507\pi$
$234$	−1.05760	−0.0691375
$235$	0.413007	0.0269416
$236$	54.9642	3.57786
$237$	3.35599	0.217995
$238$	6.19978	0.401872
$239$	26.5598	1.71801	0.859006	−	0.511966i	$-0.171083\pi$
$239$	26.5598	1.71801	0.859006	+	0.511966i	$0.171083\pi$
$240$	−4.17705	−0.269628
$241$	14.5493	0.937205	0.468603	−	0.883409i	$-0.344758\pi$
$241$	14.5493	0.937205	0.468603	+	0.883409i	$0.344758\pi$
$242$	−2.64866	−0.170262
$243$	13.7127	0.879669
$244$	31.4654	2.01436
$245$	0.464787	0.0296942
$246$	−24.4418	−1.55835
$247$	−0.746429	−0.0474942
$248$	56.4652	3.58555
$249$	−2.80983	−0.178066
$250$	−8.01811	−0.507110
$251$	−11.0650	−0.698418	−0.349209	−	0.937045i	$-0.613550\pi$
$251$	−11.0650	−0.698418	−0.349209	+	0.937045i	$0.613550\pi$
$252$	17.4901	1.10177
$253$	2.45254	0.154190
$254$	−19.9927	−1.25446
$255$	−0.375520	−0.0235160
$256$	−3.84659	−0.240412
$257$	−27.1089	−1.69100	−0.845502	−	0.533972i	$-0.820699\pi$
$257$	−27.1089	−1.69100	−0.845502	+	0.533972i	$0.820699\pi$
$258$	3.25491	0.202642
$259$	17.7735	1.10439
$260$	0.410755	0.0254739
$261$	7.56418	0.468211
$262$	43.9330	2.71419
$263$	−8.33979	−0.514254	−0.257127	−	0.966378i	$-0.582776\pi$
$263$	−8.33979	−0.514254	−0.257127	+	0.966378i	$0.582776\pi$
$264$	9.81482	0.604060
$265$	1.53954	0.0945730
$266$	17.2666	1.05868
$267$	5.36673	0.328439
$268$	30.9700	1.89179
$269$	−12.9135	−0.787349	−0.393675	−	0.919250i	$-0.628796\pi$
$269$	−12.9135	−0.787349	−0.393675	+	0.919250i	$0.628796\pi$
$270$	−4.46570	−0.271774
$271$	1.36880	0.0831487	0.0415744	−	0.999135i	$-0.486763\pi$
$271$	1.36880	0.0831487	0.0415744	+	0.999135i	$0.486763\pi$
$272$	11.1234	0.674454
$273$	0.770939	0.0466593
$274$	−17.3954	−1.05089
$275$	4.90662	0.295880
$276$	−15.1159	−0.909868
$277$	−15.5444	−0.933973	−0.466987	−	0.884264i	$-0.654660\pi$
$277$	−15.5444	−0.933973	−0.466987	+	0.884264i	$0.654660\pi$
$278$	25.1900	1.51080
$279$	10.5329	0.630590
$280$	−5.71269	−0.341398
$281$	1.08802	0.0649059	0.0324530	−	0.999473i	$-0.489668\pi$
$281$	1.08802	0.0649059	0.0324530	+	0.999473i	$0.489668\pi$
$282$	4.39921	0.261969
$283$	−7.45314	−0.443043	−0.221522	−	0.975155i	$-0.571102\pi$
$283$	−7.45314	−0.443043	−0.221522	+	0.975155i	$0.571102\pi$
$284$	−17.4633	−1.03626
$285$	−1.04584	−0.0619500
$286$	−0.709878	−0.0419759
$287$	−17.5770	−1.03754
$288$	20.0957	1.18415
$289$	1.00000	0.0588235
$290$	−4.10932	−0.241308
$291$	−18.5904	−1.08979
$292$	−33.8296	−1.97973
$293$	7.13715	0.416957	0.208479	−	0.978027i	$-0.433149\pi$
$293$	7.13715	0.416957	0.208479	+	0.978027i	$0.433149\pi$
$294$	4.95076	0.288734
$295$	−3.34885	−0.194977
$296$	60.6447	3.52490
$297$	5.51750	0.320158
$298$	−45.8888	−2.65827
$299$	0.657314	0.0380134
$300$	−30.2413	−1.74598
$301$	2.34072	0.134917
$302$	−11.8335	−0.680940
$303$	14.3892	0.826640
$304$	30.9791	1.77677
$305$	−1.91711	−0.109774
$306$	3.94606	0.225581
$307$	5.22192	0.298031	0.149015	−	0.988835i	$-0.452390\pi$
$307$	5.22192	0.298031	0.149015	+	0.988835i	$0.452390\pi$
$308$	11.7396	0.668929
$309$	8.21429	0.467295
$310$	−5.72213	−0.324995
$311$	−28.0808	−1.59232	−0.796158	−	0.605089i	$-0.793138\pi$
$311$	−28.0808	−1.59232	−0.796158	+	0.605089i	$0.793138\pi$
$312$	2.63051	0.148923
$313$	−22.9588	−1.29771	−0.648854	−	0.760913i	$-0.724751\pi$
$313$	−22.9588	−1.29771	−0.648854	+	0.760913i	$0.724751\pi$
$314$	−55.3620	−3.12426
$315$	−1.06563	−0.0600417
$316$	13.6966	0.770495
$317$	25.7950	1.44879	0.724396	−	0.689384i	$-0.242119\pi$
$317$	25.7950	1.44879	0.724396	+	0.689384i	$0.242119\pi$
$318$	16.3986	0.919590
$319$	5.07720	0.284268
$320$	−4.11912	−0.230266
$321$	−5.01797	−0.280076
$322$	−15.2052	−0.847351
$323$	2.78504	0.154964
$324$	−11.5900	−0.643891
$325$	1.31504	0.0729455
$326$	45.3078	2.50937
$327$	−5.04907	−0.279214
$328$	−59.9742	−3.31152
$329$	3.16364	0.174417
$330$	−0.994624	−0.0547522
$331$	12.0946	0.664777	0.332389	−	0.943142i	$-0.392145\pi$
$331$	12.0946	0.664777	0.332389	+	0.943142i	$0.392145\pi$
$332$	−11.4676	−0.629366
$333$	11.3126	0.619924
$334$	31.8206	1.74115
$335$	−1.88693	−0.103094
$336$	−31.9963	−1.74554
$337$	−8.40784	−0.458004	−0.229002	−	0.973426i	$-0.573546\pi$
$337$	−8.40784	−0.458004	−0.229002	+	0.973426i	$0.573546\pi$
$338$	34.2423	1.86254
$339$	15.2592	0.828767
$340$	−1.53259	−0.0831163
$341$	7.06987	0.382855
$342$	10.9899	0.594268
$343$	19.9453	1.07695
$344$	7.98675	0.430617
$345$	0.920976	0.0495837
$346$	−42.1524	−2.26613
$347$	−7.83360	−0.420530	−0.210265	−	0.977644i	$-0.567433\pi$
$347$	−7.83360	−0.420530	−0.210265	+	0.977644i	$0.567433\pi$
$348$	−31.2926	−1.67746
$349$	27.2955	1.46109	0.730546	−	0.682863i	$-0.239265\pi$
$349$	27.2955	1.46109	0.730546	+	0.682863i	$0.239265\pi$
$350$	−30.4200	−1.62602
$351$	1.47877	0.0789308
$352$	13.4886	0.718943
$353$	13.0599	0.695108	0.347554	−	0.937660i	$-0.387012\pi$
$353$	13.0599	0.695108	0.347554	+	0.937660i	$0.387012\pi$
$354$	−35.6708	−1.89588
$355$	1.06400	0.0564714
$356$	21.9029	1.16085
$357$	−2.87649	−0.152240
$358$	13.1924	0.697241
$359$	33.2463	1.75467	0.877337	−	0.479875i	$-0.159318\pi$
$359$	33.2463	1.75467	0.877337	+	0.479875i	$0.159318\pi$
$360$	−3.63604	−0.191636
$361$	−11.2436	−0.591766
$362$	19.7472	1.03789
$363$	1.22889	0.0644999
$364$	3.14639	0.164916
$365$	2.06116	0.107886
$366$	−20.4205	−1.06740
$367$	−6.15987	−0.321542	−0.160771	−	0.986992i	$-0.551398\pi$
$367$	−6.15987	−0.321542	−0.160771	+	0.986992i	$0.551398\pi$
$368$	−27.2805	−1.42209
$369$	−11.1875	−0.582397
$370$	−6.14567	−0.319498
$371$	11.7929	0.612255
$372$	−43.5741	−2.25921
$373$	12.2775	0.635704	0.317852	−	0.948140i	$-0.397038\pi$
$373$	12.2775	0.635704	0.317852	+	0.948140i	$0.397038\pi$
$374$	2.64866	0.136959
$375$	3.72013	0.192107
$376$	10.7946	0.556689
$377$	1.36076	0.0700827
$378$	−34.2073	−1.75943
$379$	−25.0356	−1.28599	−0.642995	−	0.765870i	$-0.722308\pi$
$379$	−25.0356	−1.28599	−0.642995	+	0.765870i	$0.722308\pi$
$380$	−4.26832	−0.218960
$381$	9.27595	0.475221
$382$	0.00583337	0.000298461 0
$383$	1.90900	0.0975454	0.0487727	−	0.998810i	$-0.484469\pi$
$383$	1.90900	0.0975454	0.0487727	+	0.998810i	$0.484469\pi$
$384$	−10.7237	−0.547240
$385$	−0.715271	−0.0364536
$386$	51.0377	2.59775
$387$	1.48983	0.0757325
$388$	−75.8718	−3.85181
$389$	−2.30376	−0.116805	−0.0584026	−	0.998293i	$-0.518601\pi$
$389$	−2.30376	−0.116805	−0.0584026	+	0.998293i	$0.518601\pi$
$390$	−0.266573	−0.0134985
$391$	−2.45254	−0.124030
$392$	12.1480	0.613565
$393$	−20.3834	−1.02821
$394$	−8.93001	−0.449887
$395$	−0.834505	−0.0419885
$396$	7.47210	0.375487
$397$	0.285991	0.0143535	0.00717674	−	0.999974i	$-0.497716\pi$
$397$	0.285991	0.0143535	0.00717674	+	0.999974i	$0.497716\pi$
$398$	−44.6760	−2.23941
$399$	−8.01113	−0.401058
$400$	−54.5783	−2.72891
$401$	19.2094	0.959272	0.479636	−	0.877467i	$-0.340769\pi$
$401$	19.2094	0.959272	0.479636	+	0.877467i	$0.340769\pi$
$402$	−20.0990	−1.00245
$403$	1.89482	0.0943879
$404$	58.7260	2.92173
$405$	0.706155	0.0350891
$406$	−31.4775	−1.56220
$407$	7.59317	0.376379
$408$	−9.81482	−0.485906
$409$	1.05361	0.0520977	0.0260489	−	0.999661i	$-0.491707\pi$
$409$	1.05361	0.0520977	0.0260489	+	0.999661i	$0.491707\pi$
$410$	6.07772	0.300157
$411$	8.07088	0.398107
$412$	33.5245	1.65164
$413$	−25.6522	−1.26226
$414$	−9.67786	−0.475641
$415$	0.698695	0.0342976
$416$	3.61512	0.177246
$417$	−11.6873	−0.572330
$418$	7.37662	0.360802
$419$	9.92785	0.485007	0.242504	−	0.970151i	$-0.422031\pi$
$419$	9.92785	0.485007	0.242504	+	0.970151i	$0.422031\pi$
$420$	4.40847	0.215111
$421$	11.0239	0.537274	0.268637	−	0.963241i	$-0.413427\pi$
$421$	11.0239	0.537274	0.268637	+	0.963241i	$0.413427\pi$
$422$	−37.0034	−1.80130
$423$	2.01361	0.0979049
$424$	40.2383	1.95414
$425$	−4.90662	−0.238006
$426$	11.3334	0.549106
$427$	−14.6851	−0.710663
$428$	−20.4796	−0.989918
$429$	0.329359	0.0159016
$430$	−0.809369	−0.0390312
$431$	−28.4669	−1.37120	−0.685600	−	0.727978i	$-0.740460\pi$
$431$	−28.4669	−1.37120	−0.685600	+	0.727978i	$0.740460\pi$
$432$	−61.3733	−2.95283
$433$	8.86759	0.426149	0.213075	−	0.977036i	$-0.431652\pi$
$433$	8.86759	0.426149	0.213075	+	0.977036i	$0.431652\pi$
$434$	−43.8316	−2.10398
$435$	1.90659	0.0914139
$436$	−20.6065	−0.986873
$437$	−6.83041	−0.326743
$438$	21.9549	1.04904
$439$	29.7520	1.41999	0.709993	−	0.704209i	$-0.248698\pi$
$439$	29.7520	1.41999	0.709993	+	0.704209i	$0.248698\pi$
$440$	−2.44057	−0.116349
$441$	2.26606	0.107908
$442$	0.709878	0.0337654
$443$	6.95523	0.330453	0.165227	−	0.986256i	$-0.447164\pi$
$443$	6.95523	0.330453	0.165227	+	0.986256i	$0.447164\pi$
$444$	−46.7994	−2.22100
$445$	−1.33450	−0.0632613
$446$	12.8189	0.606990
$447$	21.2908	1.00702
$448$	−31.5525	−1.49072
$449$	0.697151	0.0329006	0.0164503	−	0.999865i	$-0.494763\pi$
$449$	0.697151	0.0329006	0.0164503	+	0.999865i	$0.494763\pi$
$450$	−19.3618	−0.912726
$451$	−7.50921	−0.353595
$452$	62.2766	2.92924
$453$	5.49033	0.257958
$454$	−26.9212	−1.26347
$455$	−0.191703	−0.00898716
$456$	−27.3347	−1.28006
$457$	−1.47388	−0.0689453	−0.0344726	−	0.999406i	$-0.510975\pi$
$457$	−1.47388	−0.0689453	−0.0344726	+	0.999406i	$0.510975\pi$
$458$	16.6653	0.778718
$459$	−5.51750	−0.257535
$460$	3.75873	0.175252
$461$	17.2361	0.802767	0.401383	−	0.915910i	$-0.368529\pi$
$461$	17.2361	0.802767	0.401383	+	0.915910i	$0.368529\pi$
$462$	−7.61883	−0.354460
$463$	12.5775	0.584526	0.292263	−	0.956338i	$-0.405592\pi$
$463$	12.5775	0.584526	0.292263	+	0.956338i	$0.405592\pi$
$464$	−56.4756	−2.62182
$465$	2.65487	0.123117
$466$	−57.0856	−2.64444
$467$	21.2580	0.983704	0.491852	−	0.870679i	$-0.336320\pi$
$467$	21.2580	0.983704	0.491852	+	0.870679i	$0.336320\pi$
$468$	2.00263	0.0925715
$469$	−14.4539	−0.667421
$470$	−1.09391	−0.0504585
$471$	25.6861	1.18355
$472$	−87.5276	−4.02878
$473$	1.00000	0.0459800
$474$	−8.88888	−0.408280
$475$	−13.6651	−0.626999
$476$	−11.7396	−0.538086
$477$	7.50598	0.343675
$478$	−70.3479	−3.21764
$479$	6.12803	0.279997	0.139998	−	0.990152i	$-0.455290\pi$
$479$	6.12803	0.279997	0.139998	+	0.990152i	$0.455290\pi$
$480$	5.06522	0.231195
$481$	2.03508	0.0927914
$482$	−38.5362	−1.75528
$483$	7.05469	0.320999
$484$	5.01539	0.227972
$485$	4.62270	0.209906
$486$	−36.3202	−1.64752
$487$	18.4294	0.835117	0.417559	−	0.908650i	$-0.362886\pi$
$487$	18.4294	0.835117	0.417559	+	0.908650i	$0.362886\pi$
$488$	−50.1069	−2.26823
$489$	−21.0213	−0.950616
$490$	−1.23106	−0.0556137
$491$	32.0801	1.44775	0.723877	−	0.689929i	$-0.242358\pi$
$491$	32.0801	1.44775	0.723877	+	0.689929i	$0.242358\pi$
$492$	46.2819	2.08655
$493$	−5.07720	−0.228665
$494$	1.97704	0.0889511
$495$	−0.455259	−0.0204624
$496$	−78.6409	−3.53108
$497$	8.15028	0.365590
$498$	7.44227	0.333496
$499$	2.01780	0.0903291	0.0451646	−	0.998980i	$-0.485619\pi$
$499$	2.01780	0.0903291	0.0451646	+	0.998980i	$0.485619\pi$
$500$	15.1828	0.678994
$501$	−14.7637	−0.659593
$502$	29.3075	1.30806
$503$	24.3600	1.08616	0.543079	−	0.839682i	$-0.317258\pi$
$503$	24.3600	1.08616	0.543079	+	0.839682i	$0.317258\pi$
$504$	−27.8521	−1.24063
$505$	−3.57804	−0.159221
$506$	−6.49593	−0.288779
$507$	−15.8873	−0.705579
$508$	37.8574	1.67965
$509$	−16.7090	−0.740613	−0.370307	−	0.928910i	$-0.620747\pi$
$509$	−16.7090	−0.740613	−0.370307	+	0.928910i	$0.620747\pi$
$510$	0.994624	0.0440427
$511$	15.7886	0.698444
$512$	27.6409	1.22157
$513$	−15.3665	−0.678446
$514$	71.8021	3.16706
$515$	−2.04258	−0.0900067
$516$	−6.16336	−0.271327
$517$	1.35156	0.0594417
$518$	−47.0759	−2.06840
$519$	19.5573	0.858469
$520$	−0.654106	−0.0286844
$521$	10.7142	0.469399	0.234700	−	0.972068i	$-0.424589\pi$
$521$	10.7142	0.469399	0.234700	+	0.972068i	$0.424589\pi$
$522$	−20.0349	−0.876905
$523$	−19.4558	−0.850743	−0.425371	−	0.905019i	$-0.639857\pi$
$523$	−19.4558	−0.850743	−0.425371	+	0.905019i	$0.639857\pi$
$524$	−83.1897	−3.63416
$525$	14.1138	0.615978
$526$	22.0893	0.963138
$527$	−7.06987	−0.307968
$528$	−13.6694	−0.594884
$529$	−16.9851	−0.738481
$530$	−4.07771	−0.177124
$531$	−16.3272	−0.708542
$532$	−32.6954	−1.41752
$533$	−2.01257	−0.0871742
$534$	−14.2146	−0.615128
$535$	1.24778	0.0539460
$536$	−49.3181	−2.13022
$537$	−6.12084	−0.264134
$538$	34.2034	1.47461
$539$	1.52102	0.0655148
$540$	8.45606	0.363891
$541$	−15.9516	−0.685814	−0.342907	−	0.939369i	$-0.611412\pi$
$541$	−15.9516	−0.685814	−0.342907	+	0.939369i	$0.611412\pi$
$542$	−3.62549	−0.155728
$543$	−9.16203	−0.393180
$544$	−13.4886	−0.578317
$545$	1.25551	0.0537801
$546$	−2.04195	−0.0873875
$547$	2.05413	0.0878280	0.0439140	−	0.999035i	$-0.486017\pi$
$547$	2.05413	0.0878280	0.0439140	+	0.999035i	$0.486017\pi$
$548$	32.9392	1.40709
$549$	−9.34685	−0.398914
$550$	−12.9960	−0.554150
$551$	−14.1402	−0.602392
$552$	24.0712	1.02454
$553$	−6.39232	−0.271829
$554$	41.1719	1.74922
$555$	2.85138	0.121035
$556$	−47.6988	−2.02288
$557$	23.1470	0.980769	0.490384	−	0.871506i	$-0.336856\pi$
$557$	23.1470	0.980769	0.490384	+	0.871506i	$0.336856\pi$
$558$	−27.8981	−1.18102
$559$	0.268014	0.0113358
$560$	7.95623	0.336212
$561$	−1.22889	−0.0518837
$562$	−2.88180	−0.121561
$563$	−2.41209	−0.101658	−0.0508288	−	0.998707i	$-0.516186\pi$
$563$	−2.41209	−0.101658	−0.0508288	+	0.998707i	$0.516186\pi$
$564$	−8.33017	−0.350764
$565$	−3.79437	−0.159631
$566$	19.7408	0.829769
$567$	5.40916	0.227163
$568$	27.8095	1.16686
$569$	−9.59879	−0.402402	−0.201201	−	0.979550i	$-0.564484\pi$
$569$	−9.59879	−0.402402	−0.201201	+	0.979550i	$0.564484\pi$
$570$	2.77006	0.116025
$571$	−23.3290	−0.976290	−0.488145	−	0.872763i	$-0.662326\pi$
$571$	−23.3290	−0.976290	−0.488145	+	0.872763i	$0.662326\pi$
$572$	1.34420	0.0562036
$573$	−0.00270649	−0.000113065 0
$574$	46.5554	1.94319
$575$	12.0337	0.501839
$576$	−20.0827	−0.836779
$577$	2.79422	0.116325	0.0581624	−	0.998307i	$-0.481476\pi$
$577$	2.79422	0.116325	0.0581624	+	0.998307i	$0.481476\pi$
$578$	−2.64866	−0.110170
$579$	−23.6798	−0.984098
$580$	7.78125	0.323099
$581$	5.35201	0.222039
$582$	49.2395	2.04104
$583$	5.03813	0.208658
$584$	53.8719	2.22924
$585$	−0.122016	−0.00504473
$586$	−18.9039	−0.780912
$587$	−10.8416	−0.447479	−0.223740	−	0.974649i	$-0.571827\pi$
$587$	−10.8416	−0.447479	−0.223740	+	0.974649i	$0.571827\pi$
$588$	−9.37456	−0.386600
$589$	−19.6898	−0.811306
$590$	8.86995	0.365170
$591$	4.14322	0.170429
$592$	−84.4617	−3.47136
$593$	−7.81014	−0.320724	−0.160362	−	0.987058i	$-0.551266\pi$
$593$	−7.81014	−0.320724	−0.160362	+	0.987058i	$0.551266\pi$
$594$	−14.6140	−0.599619
$595$	0.715271	0.0293232
$596$	86.8932	3.55928
$597$	20.7282	0.848347
$598$	−1.74100	−0.0711948
$599$	−11.2999	−0.461700	−0.230850	−	0.972989i	$-0.574151\pi$
$599$	−11.2999	−0.461700	−0.230850	+	0.972989i	$0.574151\pi$
$600$	48.1576	1.96603
$601$	−44.1176	−1.79960	−0.899798	−	0.436307i	$-0.856286\pi$
$601$	−44.1176	−1.79960	−0.899798	+	0.436307i	$0.856286\pi$
$602$	−6.19978	−0.252684
$603$	−9.19971	−0.374641
$604$	22.4074	0.911743
$605$	−0.305577	−0.0124235
$606$	−38.1122	−1.54820
$607$	31.2184	1.26712	0.633558	−	0.773695i	$-0.281594\pi$
$607$	31.2184	1.26712	0.633558	+	0.773695i	$0.281594\pi$
$608$	−37.5661	−1.52351
$609$	14.6045	0.591804
$610$	5.07778	0.205593
$611$	0.362238	0.0146546
$612$	−7.47210	−0.302042
$613$	−38.9756	−1.57421	−0.787104	−	0.616820i	$-0.788421\pi$
$613$	−38.9756	−1.57421	−0.787104	+	0.616820i	$0.788421\pi$
$614$	−13.8311	−0.558177
$615$	−2.81986	−0.113708
$616$	−18.6948	−0.753234
$617$	37.8751	1.52480	0.762398	−	0.647108i	$-0.224022\pi$
$617$	37.8751	1.52480	0.762398	+	0.647108i	$0.224022\pi$
$618$	−21.7569	−0.875189
$619$	24.9471	1.00271	0.501355	−	0.865242i	$-0.332835\pi$
$619$	24.9471	1.00271	0.501355	+	0.865242i	$0.332835\pi$
$620$	10.8352	0.435152
$621$	13.5319	0.543015
$622$	74.3765	2.98222
$623$	−10.2223	−0.409547
$624$	−3.66359	−0.146661
$625$	23.6081	0.944322
$626$	60.8100	2.43046
$627$	−3.42250	−0.136681
$628$	104.831	4.18323
$629$	−7.59317	−0.302759
$630$	2.82250	0.112451
$631$	−7.54870	−0.300509	−0.150255	−	0.988647i	$-0.548009\pi$
$631$	−7.54870	−0.300509	−0.150255	+	0.988647i	$0.548009\pi$
$632$	−21.8112	−0.867601
$633$	17.1683	0.682380
$634$	−68.3222	−2.71342
$635$	−2.30657	−0.0915334
$636$	−31.0518	−1.23128
$637$	0.407653	0.0161518
$638$	−13.4478	−0.532402
$639$	5.18753	0.205215
$640$	2.66656	0.105405
$641$	28.7321	1.13485	0.567425	−	0.823425i	$-0.307940\pi$
$641$	28.7321	1.13485	0.567425	+	0.823425i	$0.307940\pi$
$642$	13.2909	0.524550
$643$	33.0609	1.30380	0.651898	−	0.758307i	$-0.273973\pi$
$643$	33.0609	1.30380	0.651898	+	0.758307i	$0.273973\pi$
$644$	28.7919	1.13456
$645$	0.375520	0.0147861
$646$	−7.37662	−0.290229
$647$	−35.9405	−1.41297	−0.706483	−	0.707730i	$-0.749719\pi$
$647$	−35.9405	−1.41297	−0.706483	+	0.707730i	$0.749719\pi$
$648$	18.4565	0.725041
$649$	−10.9591	−0.430182
$650$	−3.48310	−0.136618
$651$	20.3364	0.797045
$652$	−85.7931	−3.35992
$653$	−42.8042	−1.67506	−0.837529	−	0.546394i	$-0.816000\pi$
$653$	−42.8042	−1.67506	−0.837529	+	0.546394i	$0.816000\pi$
$654$	13.3733	0.522936
$655$	5.06856	0.198045
$656$	83.5278	3.26121
$657$	10.0492	0.392055
$658$	−8.37939	−0.326663
$659$	−12.9986	−0.506355	−0.253178	−	0.967420i	$-0.581476\pi$
$659$	−12.9986	−0.506355	−0.253178	+	0.967420i	$0.581476\pi$
$660$	1.88338	0.0733104
$661$	51.3583	1.99761	0.998803	−	0.0489147i	$-0.0155762\pi$
$661$	51.3583	1.99761	0.998803	+	0.0489147i	$0.0155762\pi$
$662$	−32.0344	−1.24505
$663$	−0.329359	−0.0127913
$664$	18.2615	0.708685
$665$	1.99206	0.0772486
$666$	−29.9631	−1.16105
$667$	12.4520	0.482144
$668$	−60.2543	−2.33131
$669$	−5.94751	−0.229944
$670$	4.99784	0.193084
$671$	−6.27375	−0.242196
$672$	38.7997	1.49673
$673$	−47.1410	−1.81715	−0.908576	−	0.417720i	$-0.862829\pi$
$673$	−47.1410	−1.81715	−0.908576	+	0.417720i	$0.862829\pi$
$674$	22.2695	0.857789
$675$	27.0723	1.04201
$676$	−64.8399	−2.49384
$677$	−14.3021	−0.549676	−0.274838	−	0.961491i	$-0.588624\pi$
$677$	−14.3021	−0.549676	−0.274838	+	0.961491i	$0.588624\pi$
$678$	−40.4164	−1.55218
$679$	35.4100	1.35891
$680$	2.44057	0.0935914
$681$	12.4905	0.478638
$682$	−18.7257	−0.717043
$683$	−3.73565	−0.142941	−0.0714703	−	0.997443i	$-0.522769\pi$
$683$	−3.73565	−0.142941	−0.0714703	+	0.997443i	$0.522769\pi$
$684$	−20.8101	−0.795694
$685$	−2.00691	−0.0766803
$686$	−52.8284	−2.01700
$687$	−7.73213	−0.294999
$688$	−11.1234	−0.424075
$689$	1.35029	0.0514419
$690$	−2.43935	−0.0928645
$691$	−8.10503	−0.308330	−0.154165	−	0.988045i	$-0.549269\pi$
$691$	−8.10503	−0.308330	−0.154165	+	0.988045i	$0.549269\pi$
$692$	79.8180	3.03423
$693$	−3.48729	−0.132471
$694$	20.7485	0.787604
$695$	2.90618	0.110238
$696$	49.8318	1.88887
$697$	7.50921	0.284432
$698$	−72.2964	−2.73646
$699$	26.4858	1.00178
$700$	57.6020	2.17715
$701$	11.5512	0.436284	0.218142	−	0.975917i	$-0.430000\pi$
$701$	11.5512	0.436284	0.218142	+	0.975917i	$0.430000\pi$
$702$	−3.91675	−0.147828
$703$	−21.1473	−0.797584
$704$	−13.4798	−0.508040
$705$	0.507539	0.0191150
$706$	−34.5912	−1.30186
$707$	−27.4079	−1.03078
$708$	67.5448	2.53849
$709$	41.5861	1.56180	0.780900	−	0.624656i	$-0.214761\pi$
$709$	41.5861	1.56180	0.780900	+	0.624656i	$0.214761\pi$
$710$	−2.81818	−0.105764
$711$	−4.06861	−0.152585
$712$	−34.8793	−1.30716
$713$	17.3391	0.649354
$714$	7.61883	0.285128
$715$	−0.0818989	−0.00306284
$716$	−24.9806	−0.933571
$717$	32.6390	1.21893
$718$	−88.0581	−3.28630
$719$	27.6226	1.03015	0.515075	−	0.857145i	$-0.327764\pi$
$719$	27.6226	1.03015	0.515075	+	0.857145i	$0.327764\pi$
$720$	5.06402	0.188725
$721$	−15.6462	−0.582694
$722$	29.7804	1.10831
$723$	17.8795	0.664946
$724$	−37.3925	−1.38968
$725$	24.9119	0.925204
$726$	−3.25491	−0.120801
$727$	18.4052	0.682610	0.341305	−	0.939953i	$-0.389131\pi$
$727$	18.4052	0.682610	0.341305	+	0.939953i	$0.389131\pi$
$728$	−5.01046	−0.185700
$729$	23.7840	0.880890
$730$	−5.45932	−0.202059
$731$	−1.00000	−0.0369863
$732$	38.6674	1.42919
$733$	29.3185	1.08290	0.541452	−	0.840732i	$-0.317875\pi$
$733$	29.3185	1.08290	0.541452	+	0.840732i	$0.317875\pi$
$734$	16.3154	0.602212
$735$	0.571171	0.0210680
$736$	33.0812	1.21939
$737$	−6.17499	−0.227459
$738$	29.6318	1.09076
$739$	−20.9128	−0.769290	−0.384645	−	0.923065i	$-0.625676\pi$
$739$	−20.9128	−0.769290	−0.384645	+	0.923065i	$0.625676\pi$
$740$	11.6372	0.427792
$741$	−0.917278	−0.0336970
$742$	−31.2353	−1.14668
$743$	0.238240	0.00874018	0.00437009	−	0.999990i	$-0.498609\pi$
$743$	0.238240	0.00874018	0.00437009	+	0.999990i	$0.498609\pi$
$744$	69.3895	2.54394
$745$	−5.29421	−0.193965
$746$	−32.5189	−1.19060
$747$	3.40647	0.124636
$748$	−5.01539	−0.183381
$749$	9.55798	0.349241
$750$	−9.85336	−0.359794
$751$	−10.1566	−0.370619	−0.185310	−	0.982680i	$-0.559329\pi$
$751$	−10.1566	−0.370619	−0.185310	+	0.982680i	$0.559329\pi$
$752$	−15.0340	−0.548232
$753$	−13.5977	−0.495527
$754$	−3.60419	−0.131257
$755$	−1.36523	−0.0496859
$756$	64.7736	2.35579
$757$	16.0606	0.583731	0.291865	−	0.956459i	$-0.405724\pi$
$757$	16.0606	0.583731	0.291865	+	0.956459i	$0.405724\pi$
$758$	66.3107	2.40851
$759$	3.01389	0.109397
$760$	6.79707	0.246556
$761$	7.26178	0.263239	0.131620	−	0.991300i	$-0.457982\pi$
$761$	7.26178	0.263239	0.131620	+	0.991300i	$0.457982\pi$
$762$	−24.5688	−0.890035
$763$	9.61722	0.348167
$764$	−0.0110458	−0.000399624 0
$765$	0.455259	0.0164599
$766$	−5.05629	−0.182691
$767$	−2.93719	−0.106056
$768$	−4.72703	−0.170572
$769$	−28.2645	−1.01924	−0.509622	−	0.860399i	$-0.670215\pi$
$769$	−28.2645	−1.01924	−0.509622	+	0.860399i	$0.670215\pi$
$770$	1.89451	0.0682733
$771$	−33.3138	−1.19977
$772$	−96.6430	−3.47826
$773$	−5.00944	−0.180177	−0.0900886	−	0.995934i	$-0.528715\pi$
$773$	−5.00944	−0.180177	−0.0900886	+	0.995934i	$0.528715\pi$
$774$	−3.94606	−0.141838
$775$	34.6892	1.24607
$776$	120.822	4.33725
$777$	21.8416	0.783565
$778$	6.10187	0.218763
$779$	20.9134	0.749302
$780$	0.504772	0.0180737
$781$	3.48195	0.124594
$782$	6.49593	0.232294
$783$	28.0135	1.00112
$784$	−16.9188	−0.604244
$785$	−6.38714	−0.227967
$786$	53.9887	1.92571
$787$	−17.5022	−0.623886	−0.311943	−	0.950101i	$-0.600980\pi$
$787$	−17.5022	−0.623886	−0.311943	+	0.950101i	$0.600980\pi$
$788$	16.9095	0.602376
$789$	−10.2487	−0.364862
$790$	2.21032	0.0786396
$791$	−29.0650	−1.03343
$792$	−11.8989	−0.422810
$793$	−1.68145	−0.0597102
$794$	−0.757492	−0.0268824
$795$	1.89192	0.0670994
$796$	84.5967	2.99845
$797$	46.9875	1.66438	0.832191	−	0.554489i	$-0.187086\pi$
$797$	46.9875	1.66438	0.832191	+	0.554489i	$0.187086\pi$
$798$	21.2187	0.751135
$799$	−1.35156	−0.0478149
$800$	66.1833	2.33993
$801$	−6.50632	−0.229889
$802$	−50.8792	−1.79661
$803$	6.74516	0.238032
$804$	38.0587	1.34223
$805$	−1.75423	−0.0618284
$806$	−5.01874	−0.176778
$807$	−15.8692	−0.558623
$808$	−93.5180	−3.28995
$809$	39.8733	1.40187	0.700935	−	0.713225i	$-0.252766\pi$
$809$	39.8733	1.40187	0.700935	+	0.713225i	$0.252766\pi$
$810$	−1.87036	−0.0657179
$811$	14.4861	0.508677	0.254338	−	0.967115i	$-0.418142\pi$
$811$	14.4861	0.508677	0.254338	+	0.967115i	$0.418142\pi$
$812$	59.6045	2.09171
$813$	1.68210	0.0589939
$814$	−20.1117	−0.704915
$815$	5.22718	0.183100
$816$	13.6694	0.478525
$817$	−2.78504	−0.0974361
$818$	−2.79066	−0.0975730
$819$	−0.934642	−0.0326590
$820$	−11.5085	−0.401895
$821$	−14.3373	−0.500374	−0.250187	−	0.968198i	$-0.580492\pi$
$821$	−14.3373	−0.500374	−0.250187	+	0.968198i	$0.580492\pi$
$822$	−21.3770	−0.745609
$823$	−45.5240	−1.58687	−0.793433	−	0.608658i	$-0.791708\pi$
$823$	−45.5240	−1.58687	−0.793433	+	0.608658i	$0.791708\pi$
$824$	−53.3861	−1.85979
$825$	6.02969	0.209927
$826$	67.9440	2.36407
$827$	−17.9070	−0.622686	−0.311343	−	0.950298i	$-0.600779\pi$
$827$	−17.9070	−0.622686	−0.311343	+	0.950298i	$0.600779\pi$
$828$	18.3256	0.636859
$829$	42.9478	1.49164	0.745820	−	0.666148i	$-0.232058\pi$
$829$	42.9478	1.49164	0.745820	+	0.666148i	$0.232058\pi$
$830$	−1.85060	−0.0642354
$831$	−19.1023	−0.662653
$832$	−3.61278	−0.125251
$833$	−1.52102	−0.0527001
$834$	30.9557	1.07191
$835$	3.67116	0.127046
$836$	−13.9681	−0.483096
$837$	39.0080	1.34831
$838$	−26.2955	−0.908362
$839$	46.3224	1.59923	0.799613	−	0.600515i	$-0.205038\pi$
$839$	46.3224	1.59923	0.799613	+	0.600515i	$0.205038\pi$
$840$	−7.02025	−0.242222
$841$	−3.22207	−0.111106
$842$	−29.1987	−1.00625
$843$	1.33706	0.0460507
$844$	70.0682	2.41185
$845$	3.95055	0.135903
$846$	−5.33336	−0.183365
$847$	−2.34072	−0.0804282
$848$	−56.0411	−1.92446
$849$	−9.15908	−0.314339
$850$	12.9960	0.445758
$851$	18.6225	0.638372
$852$	−21.4605	−0.735225
$853$	57.9110	1.98284	0.991418	−	0.130729i	$-0.0417317\pi$
$853$	57.9110	1.98284	0.991418	+	0.130729i	$0.0417317\pi$
$854$	38.8959	1.33099
$855$	1.26791	0.0433617
$856$	32.6126	1.11468
$857$	−29.7489	−1.01620	−0.508101	−	0.861297i	$-0.669652\pi$
$857$	−29.7489	−1.01620	−0.508101	+	0.861297i	$0.669652\pi$
$858$	−0.872360	−0.0297819
$859$	38.6130	1.31746	0.658729	−	0.752381i	$-0.271095\pi$
$859$	38.6130	1.31746	0.658729	+	0.752381i	$0.271095\pi$
$860$	1.53259	0.0522608
$861$	−21.6001	−0.736131
$862$	75.3990	2.56810
$863$	−53.2115	−1.81134	−0.905670	−	0.423983i	$-0.860632\pi$
$863$	−53.2115	−1.81134	−0.905670	+	0.423983i	$0.860632\pi$
$864$	74.4232	2.53193
$865$	−4.86314	−0.165352
$866$	−23.4872	−0.798128
$867$	1.22889	0.0417352
$868$	82.9977	2.81713
$869$	−2.73092	−0.0926400
$870$	−5.04990	−0.171208
$871$	−1.65498	−0.0560770
$872$	32.8148	1.11125
$873$	22.5379	0.762792
$874$	18.0914	0.611951
$875$	−7.08592	−0.239548
$876$	−41.5728	−1.40462
$877$	37.9204	1.28048	0.640241	−	0.768174i	$-0.278835\pi$
$877$	37.9204	1.28048	0.640241	+	0.768174i	$0.278835\pi$
$878$	−78.8029	−2.65947
$879$	8.77076	0.295831
$880$	3.39905	0.114582
$881$	−28.5273	−0.961108	−0.480554	−	0.876965i	$-0.659564\pi$
$881$	−28.5273	−0.961108	−0.480554	+	0.876965i	$0.659564\pi$
$882$	−6.00202	−0.202099
$883$	−22.2546	−0.748928	−0.374464	−	0.927242i	$-0.622173\pi$
$883$	−22.2546	−0.748928	−0.374464	+	0.927242i	$0.622173\pi$
$884$	−1.34420	−0.0452102
$885$	−4.11536	−0.138336
$886$	−18.4220	−0.618900
$887$	23.2626	0.781080	0.390540	−	0.920586i	$-0.372288\pi$
$887$	23.2626	0.781080	0.390540	+	0.920586i	$0.372288\pi$
$888$	74.5256	2.50091
$889$	−17.6684	−0.592578
$890$	3.53463	0.118481
$891$	2.31089	0.0774178
$892$	−24.2733	−0.812729
$893$	−3.76416	−0.125963
$894$	−56.3922	−1.88604
$895$	1.52202	0.0508754
$896$	20.4259	0.682381
$897$	0.807765	0.0269705
$898$	−1.84652	−0.0616190
$899$	35.8951	1.19717
$900$	36.6628	1.22209
$901$	−5.03813	−0.167845
$902$	19.8893	0.662242
$903$	2.87649	0.0957235
$904$	−99.1722	−3.29842
$905$	2.27824	0.0757313
$906$	−14.5420	−0.483126
$907$	−1.81109	−0.0601363	−0.0300681	−	0.999548i	$-0.509572\pi$
$907$	−1.81109	−0.0601363	−0.0300681	+	0.999548i	$0.509572\pi$
$908$	50.9769	1.69173
$909$	−17.4447	−0.578604
$910$	0.507755	0.0168319
$911$	30.3251	1.00472	0.502358	−	0.864660i	$-0.332466\pi$
$911$	30.3251	1.00472	0.502358	+	0.864660i	$0.332466\pi$
$912$	38.0698	1.26062
$913$	2.28648	0.0756714
$914$	3.90381	0.129127
$915$	−2.35592	−0.0778843
$916$	−31.5567	−1.04266
$917$	38.8253	1.28212
$918$	14.6140	0.482333
$919$	5.66088	0.186735	0.0933676	−	0.995632i	$-0.470237\pi$
$919$	5.66088	0.186735	0.0933676	+	0.995632i	$0.470237\pi$
$920$	−5.98558	−0.197339
$921$	6.41716	0.211452
$922$	−45.6526	−1.50349
$923$	0.933211	0.0307170
$924$	14.4267	0.474604
$925$	37.2568	1.22500
$926$	−33.3135	−1.09475
$927$	−9.95854	−0.327081
$928$	68.4841	2.24810
$929$	38.4670	1.26206	0.631030	−	0.775758i	$-0.282632\pi$
$929$	38.4670	1.26206	0.631030	+	0.775758i	$0.282632\pi$
$930$	−7.03186	−0.230584
$931$	−4.23609	−0.138832
$932$	108.095	3.54077
$933$	−34.5082	−1.12975
$934$	−56.3052	−1.84236
$935$	0.305577	0.00999343
$936$	−3.18908	−0.104238
$937$	−29.2167	−0.954466	−0.477233	−	0.878777i	$-0.658360\pi$
$937$	−29.2167	−0.954466	−0.477233	+	0.878777i	$0.658360\pi$
$938$	38.2836	1.25000
$939$	−28.2138	−0.920722
$940$	2.07139	0.0675613
$941$	2.50868	0.0817805	0.0408902	−	0.999164i	$-0.486981\pi$
$941$	2.50868	0.0817805	0.0408902	+	0.999164i	$0.486981\pi$
$942$	−68.0338	−2.21666
$943$	−18.4166	−0.599727
$944$	121.902	3.96758
$945$	−3.94651	−0.128380
$946$	−2.64866	−0.0861153
$947$	−30.5531	−0.992843	−0.496422	−	0.868082i	$-0.665353\pi$
$947$	−30.5531	−0.992843	−0.496422	+	0.868082i	$0.665353\pi$
$948$	16.8316	0.546666
$949$	1.80780	0.0586836
$950$	36.1943	1.17430
$951$	31.6992	1.02792
$952$	18.6948	0.605901
$953$	−1.83896	−0.0595698	−0.0297849	−	0.999556i	$-0.509482\pi$
$953$	−1.83896	−0.0595698	−0.0297849	+	0.999556i	$0.509482\pi$
$954$	−19.8808	−0.643664
$955$	0.000672998 0	2.17777e−5 0
$956$	133.208	4.30825
$957$	6.23931	0.201688
$958$	−16.2311	−0.524401
$959$	−15.3730	−0.496420
$960$	−5.06194	−0.163373
$961$	18.9830	0.612355
$962$	−5.39022	−0.173788
$963$	6.08350	0.196038
$964$	72.9707	2.35023
$965$	5.88824	0.189549
$966$	−18.6855	−0.601195
$967$	−27.5789	−0.886878	−0.443439	−	0.896305i	$-0.646242\pi$
$967$	−27.5789	−0.886878	−0.443439	+	0.896305i	$0.646242\pi$
$968$	−7.98675	−0.256704
$969$	3.42250	0.109947
$970$	−12.2440	−0.393130
$971$	57.4764	1.84451	0.922253	−	0.386587i	$-0.126346\pi$
$971$	57.4764	1.84451	0.922253	+	0.386587i	$0.126346\pi$
$972$	68.7745	2.20594
$973$	22.2614	0.713667
$974$	−48.8133	−1.56408
$975$	1.61604	0.0517547
$976$	69.7854	2.23378
$977$	−8.73018	−0.279303	−0.139652	−	0.990201i	$-0.544598\pi$
$977$	−8.73018	−0.279303	−0.139652	+	0.990201i	$0.544598\pi$
$978$	55.6782	1.78039
$979$	−4.36714	−0.139575
$980$	2.33109	0.0744639
$981$	6.12121	0.195435
$982$	−84.9692	−2.71148
$983$	−26.8766	−0.857230	−0.428615	−	0.903487i	$-0.640998\pi$
$983$	−26.8766	−0.857230	−0.428615	+	0.903487i	$0.640998\pi$
$984$	−73.7015	−2.34952
$985$	−1.03026	−0.0328268
$986$	13.4478	0.428264
$987$	3.88776	0.123749
$988$	−3.74364	−0.119101
$989$	2.45254	0.0779861
$990$	1.20583	0.0383236
$991$	27.4695	0.872598	0.436299	−	0.899802i	$-0.356289\pi$
$991$	27.4695	0.872598	0.436299	+	0.899802i	$0.356289\pi$
$992$	95.3623	3.02776
$993$	14.8629	0.471659
$994$	−21.5873	−0.684708
$995$	−5.15429	−0.163402
$996$	−14.0924	−0.446534
$997$	−6.13159	−0.194190	−0.0970948	−	0.995275i	$-0.530955\pi$
$997$	−6.13159	−0.194190	−0.0970948	+	0.995275i	$0.530955\pi$
$998$	−5.34446	−0.169176
$999$	41.8953	1.32551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.2	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.2	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64866 q^{2} +1.22889 q^{3} +5.01539 q^{4} -0.305577 q^{5} -3.25491 q^{6} -2.34072 q^{7} -7.98675 q^{8} -1.48983 q^{9} +O(q^{10})\)	\(q-2.64866 q^{2} +1.22889 q^{3} +5.01539 q^{4} -0.305577 q^{5} -3.25491 q^{6} -2.34072 q^{7} -7.98675 q^{8} -1.48983 q^{9} +0.809369 q^{10} -1.00000 q^{11} +6.16336 q^{12} -0.268014 q^{13} +6.19978 q^{14} -0.375520 q^{15} +11.1234 q^{16} +1.00000 q^{17} +3.94606 q^{18} +2.78504 q^{19} -1.53259 q^{20} -2.87649 q^{21} +2.64866 q^{22} -2.45254 q^{23} -9.81482 q^{24} -4.90662 q^{25} +0.709878 q^{26} -5.51750 q^{27} -11.7396 q^{28} -5.07720 q^{29} +0.994624 q^{30} -7.06987 q^{31} -13.4886 q^{32} -1.22889 q^{33} -2.64866 q^{34} +0.715271 q^{35} -7.47210 q^{36} -7.59317 q^{37} -7.37662 q^{38} -0.329359 q^{39} +2.44057 q^{40} +7.50921 q^{41} +7.61883 q^{42} -1.00000 q^{43} -5.01539 q^{44} +0.455259 q^{45} +6.49593 q^{46} -1.35156 q^{47} +13.6694 q^{48} -1.52102 q^{49} +12.9960 q^{50} +1.22889 q^{51} -1.34420 q^{52} -5.03813 q^{53} +14.6140 q^{54} +0.305577 q^{55} +18.6948 q^{56} +3.42250 q^{57} +13.4478 q^{58} +10.9591 q^{59} -1.88338 q^{60} +6.27375 q^{61} +18.7257 q^{62} +3.48729 q^{63} +13.4798 q^{64} +0.0818989 q^{65} +3.25491 q^{66} +6.17499 q^{67} +5.01539 q^{68} -3.01389 q^{69} -1.89451 q^{70} -3.48195 q^{71} +11.8989 q^{72} -6.74516 q^{73} +20.1117 q^{74} -6.02969 q^{75} +13.9681 q^{76} +2.34072 q^{77} +0.872360 q^{78} +2.73092 q^{79} -3.39905 q^{80} -2.31089 q^{81} -19.8893 q^{82} -2.28648 q^{83} -14.4267 q^{84} -0.305577 q^{85} +2.64866 q^{86} -6.23931 q^{87} +7.98675 q^{88} +4.36714 q^{89} -1.20583 q^{90} +0.627347 q^{91} -12.3004 q^{92} -8.68807 q^{93} +3.57983 q^{94} -0.851043 q^{95} -16.5759 q^{96} -15.1278 q^{97} +4.02865 q^{98} +1.48983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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