LMFDB - Embedded newform 9251.2.a.ba.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.982505 q^{2} -2.74351 q^{3} -1.03468 q^{4} -0.473482 q^{5} +2.69551 q^{6} +0.734426 q^{7} +2.98159 q^{8} +4.52686 q^{9} +O(q^{10})$	\(q-0.982505 q^{2} -2.74351 q^{3} -1.03468 q^{4} -0.473482 q^{5} +2.69551 q^{6} +0.734426 q^{7} +2.98159 q^{8} +4.52686 q^{9} +0.465198 q^{10} +1.00000 q^{11} +2.83867 q^{12} +4.26199 q^{13} -0.721577 q^{14} +1.29900 q^{15} -0.860058 q^{16} +5.99561 q^{17} -4.44766 q^{18} +0.434696 q^{19} +0.489905 q^{20} -2.01491 q^{21} -0.982505 q^{22} -0.899538 q^{23} -8.18003 q^{24} -4.77581 q^{25} -4.18743 q^{26} -4.18896 q^{27} -0.759900 q^{28} -1.27628 q^{30} +8.85266 q^{31} -5.11817 q^{32} -2.74351 q^{33} -5.89072 q^{34} -0.347738 q^{35} -4.68387 q^{36} +6.47264 q^{37} -0.427091 q^{38} -11.6928 q^{39} -1.41173 q^{40} -2.26494 q^{41} +1.97966 q^{42} +0.296004 q^{43} -1.03468 q^{44} -2.14339 q^{45} +0.883801 q^{46} -0.724577 q^{47} +2.35958 q^{48} -6.46062 q^{49} +4.69226 q^{50} -16.4490 q^{51} -4.40982 q^{52} -10.8562 q^{53} +4.11568 q^{54} -0.473482 q^{55} +2.18976 q^{56} -1.19260 q^{57} -5.23970 q^{59} -1.34406 q^{60} +7.03655 q^{61} -8.69778 q^{62} +3.32465 q^{63} +6.74874 q^{64} -2.01798 q^{65} +2.69551 q^{66} -8.99860 q^{67} -6.20357 q^{68} +2.46790 q^{69} +0.341654 q^{70} +2.22307 q^{71} +13.4973 q^{72} -16.9855 q^{73} -6.35940 q^{74} +13.1025 q^{75} -0.449774 q^{76} +0.734426 q^{77} +11.4883 q^{78} -10.6558 q^{79} +0.407222 q^{80} -2.08811 q^{81} +2.22531 q^{82} +11.6276 q^{83} +2.08479 q^{84} -2.83882 q^{85} -0.290825 q^{86} +2.98159 q^{88} -8.40633 q^{89} +2.10589 q^{90} +3.13012 q^{91} +0.930739 q^{92} -24.2874 q^{93} +0.711900 q^{94} -0.205821 q^{95} +14.0418 q^{96} -11.2266 q^{97} +6.34759 q^{98} +4.52686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.982505	−0.694736	−0.347368	−	0.937729i	$-0.612924\pi$
$2$	−0.982505	−0.694736	−0.347368	+	0.937729i	$0.612924\pi$
$3$	−2.74351	−1.58397	−0.791984	−	0.610542i	$-0.790952\pi$
$3$	−2.74351	−1.58397	−0.791984	+	0.610542i	$0.790952\pi$
$4$	−1.03468	−0.517342
$5$	−0.473482	−0.211748	−0.105874	−	0.994380i	$-0.533764\pi$
$5$	−0.473482	−0.211748	−0.105874	+	0.994380i	$0.533764\pi$
$6$	2.69551	1.10044
$7$	0.734426	0.277587	0.138794	−	0.990321i	$-0.455678\pi$
$7$	0.734426	0.277587	0.138794	+	0.990321i	$0.455678\pi$
$8$	2.98159	1.05415
$9$	4.52686	1.50895
$10$	0.465198	0.147109
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.83867	0.819454
$13$	4.26199	1.18206	0.591032	−	0.806648i	$-0.298721\pi$
$13$	4.26199	1.18206	0.591032	+	0.806648i	$0.298721\pi$
$14$	−0.721577	−0.192850
$15$	1.29900	0.335401
$16$	−0.860058	−0.215015
$17$	5.99561	1.45415	0.727075	−	0.686558i	$-0.240879\pi$
$17$	5.99561	1.45415	0.727075	+	0.686558i	$0.240879\pi$
$18$	−4.44766	−1.04832
$19$	0.434696	0.0997262	0.0498631	−	0.998756i	$-0.484121\pi$
$19$	0.434696	0.0997262	0.0498631	+	0.998756i	$0.484121\pi$
$20$	0.489905	0.109546
$21$	−2.01491	−0.439689
$22$	−0.982505	−0.209471
$23$	−0.899538	−0.187567	−0.0937834	−	0.995593i	$-0.529896\pi$
$23$	−0.899538	−0.187567	−0.0937834	+	0.995593i	$0.529896\pi$
$24$	−8.18003	−1.66974
$25$	−4.77581	−0.955163
$26$	−4.18743	−0.821222
$27$	−4.18896	−0.806166
$28$	−0.759900	−0.143608
$29$	0	0
$29$	0	0
$30$	−1.27628	−0.233015
$31$	8.85266	1.58998	0.794992	−	0.606620i	$-0.207475\pi$
$31$	8.85266	1.58998	0.794992	+	0.606620i	$0.207475\pi$
$32$	−5.11817	−0.904774
$33$	−2.74351	−0.477584
$34$	−5.89072	−1.01025
$35$	−0.347738	−0.0587784
$36$	−4.68387	−0.780646
$37$	6.47264	1.06410	0.532048	−	0.846714i	$-0.321423\pi$
$37$	6.47264	1.06410	0.532048	+	0.846714i	$0.321423\pi$
$38$	−0.427091	−0.0692834
$39$	−11.6928	−1.87235
$40$	−1.41173	−0.223214
$41$	−2.26494	−0.353724	−0.176862	−	0.984236i	$-0.556595\pi$
$41$	−2.26494	−0.353724	−0.176862	+	0.984236i	$0.556595\pi$
$42$	1.97966	0.305468
$43$	0.296004	0.0451402	0.0225701	−	0.999745i	$-0.492815\pi$
$43$	0.296004	0.0451402	0.0225701	+	0.999745i	$0.492815\pi$
$44$	−1.03468	−0.155985
$45$	−2.14339	−0.319517
$46$	0.883801	0.130309
$47$	−0.724577	−0.105690	−0.0528452	−	0.998603i	$-0.516829\pi$
$47$	−0.724577	−0.105690	−0.0528452	+	0.998603i	$0.516829\pi$
$48$	2.35958	0.340576
$49$	−6.46062	−0.922945
$50$	4.69226	0.663586
$51$	−16.4490	−2.30333
$52$	−4.40982	−0.611532
$53$	−10.8562	−1.49121	−0.745606	−	0.666387i	$-0.767840\pi$
$53$	−10.8562	−1.49121	−0.745606	+	0.666387i	$0.767840\pi$
$54$	4.11568	0.560073
$55$	−0.473482	−0.0638443
$56$	2.18976	0.292619
$57$	−1.19260	−0.157963
$58$	0	0
$59$	−5.23970	−0.682151	−0.341075	−	0.940036i	$-0.610791\pi$
$59$	−5.23970	−0.682151	−0.341075	+	0.940036i	$0.610791\pi$
$60$	−1.34406	−0.173517
$61$	7.03655	0.900938	0.450469	−	0.892792i	$-0.351257\pi$
$61$	7.03655	0.900938	0.450469	+	0.892792i	$0.351257\pi$
$62$	−8.69778	−1.10462
$63$	3.32465	0.418866
$64$	6.74874	0.843593
$65$	−2.01798	−0.250299
$66$	2.69551	0.331795
$67$	−8.99860	−1.09935	−0.549677	−	0.835377i	$-0.685249\pi$
$67$	−8.99860	−1.09935	−0.549677	+	0.835377i	$0.685249\pi$
$68$	−6.20357	−0.752293
$69$	2.46790	0.297100
$70$	0.341654	0.0408355
$71$	2.22307	0.263829	0.131915	−	0.991261i	$-0.457888\pi$
$71$	2.22307	0.263829	0.131915	+	0.991261i	$0.457888\pi$
$72$	13.4973	1.59067
$73$	−16.9855	−1.98800	−0.993999	−	0.109387i	$-0.965111\pi$
$73$	−16.9855	−1.98800	−0.993999	+	0.109387i	$0.965111\pi$
$74$	−6.35940	−0.739265
$75$	13.1025	1.51295
$76$	−0.449774	−0.0515926
$77$	0.734426	0.0836956
$78$	11.4883	1.30079
$79$	−10.6558	−1.19888	−0.599438	−	0.800421i	$-0.704609\pi$
$79$	−10.6558	−1.19888	−0.599438	+	0.800421i	$0.704609\pi$
$80$	0.407222	0.0455288
$81$	−2.08811	−0.232012
$82$	2.22531	0.245745
$83$	11.6276	1.27629	0.638147	−	0.769914i	$-0.279701\pi$
$83$	11.6276	1.27629	0.638147	+	0.769914i	$0.279701\pi$
$84$	2.08479	0.227470
$85$	−2.83882	−0.307913
$86$	−0.290825	−0.0313605
$87$	0	0
$88$	2.98159	0.317839
$89$	−8.40633	−0.891069	−0.445534	−	0.895265i	$-0.646986\pi$
$89$	−8.40633	−0.891069	−0.445534	+	0.895265i	$0.646986\pi$
$90$	2.10589	0.221980
$91$	3.13012	0.328126
$92$	0.930739	0.0970362
$93$	−24.2874	−2.51848
$94$	0.711900	0.0734269
$95$	−0.205821	−0.0211168
$96$	14.0418	1.43313
$97$	−11.2266	−1.13989	−0.569945	−	0.821683i	$-0.693035\pi$
$97$	−11.2266	−1.13989	−0.569945	+	0.821683i	$0.693035\pi$
$98$	6.34759	0.641203
$99$	4.52686	0.454967
$100$	4.94146	0.494146
$101$	11.2363	1.11806	0.559029	−	0.829148i	$-0.311174\pi$
$101$	11.2363	1.11806	0.559029	+	0.829148i	$0.311174\pi$
$102$	16.1613	1.60020
$103$	−8.72226	−0.859430	−0.429715	−	0.902965i	$-0.641386\pi$
$103$	−8.72226	−0.859430	−0.429715	+	0.902965i	$0.641386\pi$
$104$	12.7075	1.24608
$105$	0.954023	0.0931031
$106$	10.6663	1.03600
$107$	−2.26769	−0.219226	−0.109613	−	0.993974i	$-0.534961\pi$
$107$	−2.26769	−0.219226	−0.109613	+	0.993974i	$0.534961\pi$
$108$	4.33426	0.417064
$109$	−12.1128	−1.16020	−0.580099	−	0.814546i	$-0.696986\pi$
$109$	−12.1128	−1.16020	−0.580099	+	0.814546i	$0.696986\pi$
$110$	0.465198	0.0443549
$111$	−17.7578	−1.68549
$112$	−0.631650	−0.0596853
$113$	−7.43535	−0.699458	−0.349729	−	0.936851i	$-0.613726\pi$
$113$	−7.43535	−0.699458	−0.349729	+	0.936851i	$0.613726\pi$
$114$	1.17173	0.109743
$115$	0.425915	0.0397168
$116$	0	0
$117$	19.2935	1.78368
$118$	5.14803	0.473914
$119$	4.40334	0.403653
$120$	3.87310	0.353564
$121$	1.00000	0.0909091
$122$	−6.91345	−0.625914
$123$	6.21388	0.560287
$124$	−9.15971	−0.822566
$125$	4.62867	0.414001
$126$	−3.26648	−0.291001
$127$	−3.05342	−0.270947	−0.135474	−	0.990781i	$-0.543256\pi$
$127$	−3.05342	−0.270947	−0.135474	+	0.990781i	$0.543256\pi$
$128$	3.60567	0.318699
$129$	−0.812091	−0.0715006
$130$	1.98267	0.173892
$131$	−0.207440	−0.0181241	−0.00906205	−	0.999959i	$-0.502885\pi$
$131$	−0.207440	−0.0181241	−0.00906205	+	0.999959i	$0.502885\pi$
$132$	2.83867	0.247075
$133$	0.319253	0.0276827
$134$	8.84117	0.763761
$135$	1.98340	0.170704
$136$	17.8765	1.53290
$137$	8.34972	0.713365	0.356682	−	0.934226i	$-0.383908\pi$
$137$	8.34972	0.713365	0.356682	+	0.934226i	$0.383908\pi$
$138$	−2.42472	−0.206406
$139$	5.40904	0.458789	0.229394	−	0.973334i	$-0.426325\pi$
$139$	5.40904	0.458789	0.229394	+	0.973334i	$0.426325\pi$
$140$	0.359799	0.0304086
$141$	1.98789	0.167410
$142$	−2.18417	−0.183292
$143$	4.26199	0.356406
$144$	−3.89337	−0.324447
$145$	0	0
$146$	16.6883	1.38113
$147$	17.7248	1.46192
$148$	−6.69714	−0.550502
$149$	16.9992	1.39263	0.696313	−	0.717738i	$-0.254823\pi$
$149$	16.9992	1.39263	0.696313	+	0.717738i	$0.254823\pi$
$150$	−12.8733	−1.05110
$151$	−5.41293	−0.440498	−0.220249	−	0.975444i	$-0.570687\pi$
$151$	−5.41293	−0.440498	−0.220249	+	0.975444i	$0.570687\pi$
$152$	1.29609	0.105127
$153$	27.1413	2.19425
$154$	−0.721577	−0.0581464
$155$	−4.19157	−0.336675
$156$	12.0984	0.968647
$157$	−8.42541	−0.672421	−0.336210	−	0.941787i	$-0.609145\pi$
$157$	−8.42541	−0.672421	−0.336210	+	0.941787i	$0.609145\pi$
$158$	10.4694	0.832901
$159$	29.7841	2.36203
$160$	2.42336	0.191584
$161$	−0.660645	−0.0520661
$162$	2.05158	0.161187
$163$	20.6571	1.61799	0.808995	−	0.587815i	$-0.200012\pi$
$163$	20.6571	1.61799	0.808995	+	0.587815i	$0.200012\pi$
$164$	2.34350	0.182996
$165$	1.29900	0.101127
$166$	−11.4242	−0.886688
$167$	5.78081	0.447332	0.223666	−	0.974666i	$-0.428197\pi$
$167$	5.78081	0.447332	0.223666	+	0.974666i	$0.428197\pi$
$168$	−6.00763	−0.463499
$169$	5.16460	0.397277
$170$	2.78915	0.213918
$171$	1.96781	0.150482
$172$	−0.306271	−0.0233529
$173$	−13.2637	−1.00842	−0.504211	−	0.863581i	$-0.668216\pi$
$173$	−13.2637	−1.00842	−0.504211	+	0.863581i	$0.668216\pi$
$174$	0	0
$175$	−3.50748	−0.265141
$176$	−0.860058	−0.0648293
$177$	14.3752	1.08050
$178$	8.25926	0.619057
$179$	−21.6527	−1.61840	−0.809200	−	0.587533i	$-0.800099\pi$
$179$	−21.6527	−1.61840	−0.809200	+	0.587533i	$0.800099\pi$
$180$	2.21773	0.165300
$181$	−16.8694	−1.25389	−0.626946	−	0.779063i	$-0.715695\pi$
$181$	−16.8694	−1.25389	−0.626946	+	0.779063i	$0.715695\pi$
$182$	−3.07536	−0.227961
$183$	−19.3049	−1.42706
$184$	−2.68206	−0.197724
$185$	−3.06468	−0.225320
$186$	23.8625	1.74968
$187$	5.99561	0.438443
$188$	0.749709	0.0546781
$189$	−3.07649	−0.223781
$190$	0.202220	0.0146706
$191$	−19.1615	−1.38648	−0.693239	−	0.720708i	$-0.743817\pi$
$191$	−19.1615	−1.38648	−0.693239	+	0.720708i	$0.743817\pi$
$192$	−18.5153	−1.33622
$193$	10.3581	0.745595	0.372798	−	0.927913i	$-0.378399\pi$
$193$	10.3581	0.745595	0.372798	+	0.927913i	$0.378399\pi$
$194$	11.0302	0.791922
$195$	5.53635	0.396466
$196$	6.68470	0.477479
$197$	−4.75638	−0.338878	−0.169439	−	0.985541i	$-0.554196\pi$
$197$	−4.75638	−0.338878	−0.169439	+	0.985541i	$0.554196\pi$
$198$	−4.44766	−0.316082
$199$	11.3806	0.806747	0.403374	−	0.915035i	$-0.367838\pi$
$199$	11.3806	0.806747	0.403374	+	0.915035i	$0.367838\pi$
$200$	−14.2395	−1.00689
$201$	24.6878	1.74134
$202$	−11.0398	−0.776755
$203$	0	0
$204$	17.0196	1.19161
$205$	1.07241	0.0749002
$206$	8.56966	0.597077
$207$	−4.07209	−0.283030
$208$	−3.66556	−0.254161
$209$	0.434696	0.0300686
$210$	−0.937332	−0.0646820
$211$	12.5619	0.864797	0.432399	−	0.901683i	$-0.357667\pi$
$211$	12.5619	0.864797	0.432399	+	0.901683i	$0.357667\pi$
$212$	11.2327	0.771467
$213$	−6.09901	−0.417897
$214$	2.22802	0.152304
$215$	−0.140153	−0.00955833
$216$	−12.4898	−0.849822
$217$	6.50162	0.441359
$218$	11.9009	0.806031
$219$	46.5998	3.14893
$220$	0.489905	0.0330294
$221$	25.5533	1.71890
$222$	17.4471	1.17097
$223$	9.05692	0.606496	0.303248	−	0.952912i	$-0.401929\pi$
$223$	9.05692	0.606496	0.303248	+	0.952912i	$0.401929\pi$
$224$	−3.75892	−0.251153
$225$	−21.6195	−1.44130
$226$	7.30526	0.485939
$227$	−4.75628	−0.315685	−0.157843	−	0.987464i	$-0.550454\pi$
$227$	−4.75628	−0.315685	−0.157843	+	0.987464i	$0.550454\pi$
$228$	1.23396	0.0817210
$229$	−2.05454	−0.135768	−0.0678840	−	0.997693i	$-0.521625\pi$
$229$	−2.05454	−0.135768	−0.0678840	+	0.997693i	$0.521625\pi$
$230$	−0.418464	−0.0275927
$231$	−2.01491	−0.132571
$232$	0	0
$233$	−20.4376	−1.33891	−0.669454	−	0.742853i	$-0.733472\pi$
$233$	−20.4376	−1.33891	−0.669454	+	0.742853i	$0.733472\pi$
$234$	−18.9559	−1.23919
$235$	0.343074	0.0223797
$236$	5.42144	0.352905
$237$	29.2344	1.89898
$238$	−4.32630	−0.280432
$239$	−12.5765	−0.813508	−0.406754	−	0.913538i	$-0.633339\pi$
$239$	−12.5765	−0.813508	−0.406754	+	0.913538i	$0.633339\pi$
$240$	−1.11722	−0.0721162
$241$	29.5538	1.90373	0.951865	−	0.306518i	$-0.0991638\pi$
$241$	29.5538	1.90373	0.951865	+	0.306518i	$0.0991638\pi$
$242$	−0.982505	−0.0631578
$243$	18.2956	1.17367
$244$	−7.28061	−0.466094
$245$	3.05899	0.195431
$246$	−6.10517	−0.389251
$247$	1.85267	0.117883
$248$	26.3950	1.67608
$249$	−31.9005	−2.02161
$250$	−4.54769	−0.287621
$251$	25.9797	1.63982	0.819912	−	0.572490i	$-0.194022\pi$
$251$	25.9797	1.63982	0.819912	+	0.572490i	$0.194022\pi$
$252$	−3.43996	−0.216697
$253$	−0.899538	−0.0565535
$254$	3.00000	0.188237
$255$	7.78833	0.487724
$256$	−17.0401	−1.06500
$257$	12.3905	0.772895	0.386448	−	0.922311i	$-0.373702\pi$
$257$	12.3905	0.772895	0.386448	+	0.922311i	$0.373702\pi$
$258$	0.797883	0.0496740
$259$	4.75368	0.295379
$260$	2.08797	0.129490
$261$	0	0
$262$	0.203811	0.0125915
$263$	16.8090	1.03649	0.518243	−	0.855233i	$-0.326586\pi$
$263$	16.8090	1.03649	0.518243	+	0.855233i	$0.326586\pi$
$264$	−8.18003	−0.503446
$265$	5.14021	0.315761
$266$	−0.313667	−0.0192322
$267$	23.0629	1.41142
$268$	9.31072	0.568743
$269$	−10.9157	−0.665541	−0.332770	−	0.943008i	$-0.607983\pi$
$269$	−10.9157	−0.665541	−0.332770	+	0.943008i	$0.607983\pi$
$270$	−1.94870	−0.118594
$271$	−4.27834	−0.259890	−0.129945	−	0.991521i	$-0.541480\pi$
$271$	−4.27834	−0.259890	−0.129945	+	0.991521i	$0.541480\pi$
$272$	−5.15658	−0.312664
$273$	−8.58753	−0.519741
$274$	−8.20364	−0.495600
$275$	−4.77581	−0.287992
$276$	−2.55349	−0.153702
$277$	−7.57621	−0.455210	−0.227605	−	0.973754i	$-0.573090\pi$
$277$	−7.57621	−0.455210	−0.227605	+	0.973754i	$0.573090\pi$
$278$	−5.31440	−0.318737
$279$	40.0747	2.39921
$280$	−1.03681	−0.0619614
$281$	−18.3677	−1.09573	−0.547864	−	0.836567i	$-0.684559\pi$
$281$	−18.3677	−1.09573	−0.547864	+	0.836567i	$0.684559\pi$
$282$	−1.95311	−0.116306
$283$	−28.3100	−1.68285	−0.841426	−	0.540372i	$-0.818284\pi$
$283$	−28.3100	−1.68285	−0.841426	+	0.540372i	$0.818284\pi$
$284$	−2.30017	−0.136490
$285$	0.564672	0.0334483
$286$	−4.18743	−0.247608
$287$	−1.66343	−0.0981891
$288$	−23.1693	−1.36526
$289$	18.9474	1.11455
$290$	0	0
$291$	30.8003	1.80555
$292$	17.5746	1.02848
$293$	−14.8781	−0.869190	−0.434595	−	0.900626i	$-0.643109\pi$
$293$	−14.8781	−0.869190	−0.434595	+	0.900626i	$0.643109\pi$
$294$	−17.4147	−1.01565
$295$	2.48090	0.144444
$296$	19.2988	1.12172
$297$	−4.18896	−0.243068
$298$	−16.7018	−0.967507
$299$	−3.83383	−0.221716
$300$	−13.5570	−0.782712
$301$	0.217393	0.0125303
$302$	5.31823	0.306030
$303$	−30.8270	−1.77097
$304$	−0.373864	−0.0214426
$305$	−3.33168	−0.190772
$306$	−26.6665	−1.52442
$307$	−23.3470	−1.33248	−0.666241	−	0.745736i	$-0.732098\pi$
$307$	−23.3470	−1.33248	−0.666241	+	0.745736i	$0.732098\pi$
$308$	−0.759900	−0.0432993
$309$	23.9296	1.36131
$310$	4.11824	0.233900
$311$	13.3687	0.758068	0.379034	−	0.925383i	$-0.376256\pi$
$311$	13.3687	0.758068	0.379034	+	0.925383i	$0.376256\pi$
$312$	−34.8633	−1.97374
$313$	14.1749	0.801211	0.400606	−	0.916251i	$-0.368800\pi$
$313$	14.1749	0.801211	0.400606	+	0.916251i	$0.368800\pi$
$314$	8.27800	0.467155
$315$	−1.57416	−0.0886939
$316$	11.0254	0.620229
$317$	−20.4559	−1.14892	−0.574458	−	0.818534i	$-0.694787\pi$
$317$	−20.4559	−1.14892	−0.574458	+	0.818534i	$0.694787\pi$
$318$	−29.2630	−1.64099
$319$	0	0
$320$	−3.19541	−0.178629
$321$	6.22144	0.347247
$322$	0.649087	0.0361722
$323$	2.60627	0.145017
$324$	2.16054	0.120030
$325$	−20.3545	−1.12906
$326$	−20.2957	−1.12408
$327$	33.2317	1.83772
$328$	−6.75312	−0.372879
$329$	−0.532149	−0.0293383
$330$	−1.27628	−0.0702568
$331$	−28.0328	−1.54082	−0.770411	−	0.637548i	$-0.779949\pi$
$331$	−28.0328	−1.54082	−0.770411	+	0.637548i	$0.779949\pi$
$332$	−12.0309	−0.660281
$333$	29.3008	1.60567
$334$	−5.67967	−0.310778
$335$	4.26068	0.232786
$336$	1.73294	0.0945395
$337$	6.52102	0.355222	0.177611	−	0.984101i	$-0.443163\pi$
$337$	6.52102	0.355222	0.177611	+	0.984101i	$0.443163\pi$
$338$	−5.07424	−0.276002
$339$	20.3990	1.10792
$340$	2.93728	0.159296
$341$	8.85266	0.479398
$342$	−1.93338	−0.104545
$343$	−9.88583	−0.533785
$344$	0.882563	0.0475846
$345$	−1.16850	−0.0629101
$346$	13.0317	0.700586
$347$	−26.5949	−1.42769	−0.713844	−	0.700305i	$-0.753047\pi$
$347$	−26.5949	−1.42769	−0.713844	+	0.700305i	$0.753047\pi$
$348$	0	0
$349$	−31.1655	−1.66825	−0.834124	−	0.551577i	$-0.814026\pi$
$349$	−31.1655	−1.66825	−0.834124	+	0.551577i	$0.814026\pi$
$350$	3.44612	0.184203
$351$	−17.8533	−0.952941
$352$	−5.11817	−0.272799
$353$	−19.3696	−1.03094	−0.515469	−	0.856908i	$-0.672382\pi$
$353$	−19.3696	−1.03094	−0.515469	+	0.856908i	$0.672382\pi$
$354$	−14.1237	−0.750665
$355$	−1.05258	−0.0558652
$356$	8.69790	0.460988
$357$	−12.0806	−0.639374
$358$	21.2739	1.12436
$359$	−33.9595	−1.79231	−0.896157	−	0.443738i	$-0.853652\pi$
$359$	−33.9595	−1.79231	−0.896157	+	0.443738i	$0.853652\pi$
$360$	−6.39071	−0.336820
$361$	−18.8110	−0.990055
$362$	16.5742	0.871123
$363$	−2.74351	−0.143997
$364$	−3.23869	−0.169753
$365$	8.04231	0.420954
$366$	18.9671	0.991428
$367$	9.08041	0.473994	0.236997	−	0.971510i	$-0.423837\pi$
$367$	9.08041	0.473994	0.236997	+	0.971510i	$0.423837\pi$
$368$	0.773656	0.0403296
$369$	−10.2531	−0.533753
$370$	3.01106	0.156538
$371$	−7.97307	−0.413941
$372$	25.1298	1.30292
$373$	−19.6889	−1.01945	−0.509726	−	0.860337i	$-0.670253\pi$
$373$	−19.6889	−1.01945	−0.509726	+	0.860337i	$0.670253\pi$
$374$	−5.89072	−0.304602
$375$	−12.6988	−0.655764
$376$	−2.16039	−0.111414
$377$	0	0
$378$	3.02266	0.155469
$379$	24.6098	1.26412	0.632060	−	0.774919i	$-0.282209\pi$
$379$	24.6098	1.26412	0.632060	+	0.774919i	$0.282209\pi$
$380$	0.212960	0.0109246
$381$	8.37709	0.429172
$382$	18.8263	0.963235
$383$	20.9941	1.07275	0.536373	−	0.843981i	$-0.319794\pi$
$383$	20.9941	1.07275	0.536373	+	0.843981i	$0.319794\pi$
$384$	−9.89220	−0.504809
$385$	−0.347738	−0.0177224
$386$	−10.1769	−0.517991
$387$	1.33997	0.0681145
$388$	11.6160	0.589713
$389$	−15.6991	−0.795976	−0.397988	−	0.917391i	$-0.630291\pi$
$389$	−15.6991	−0.795976	−0.397988	+	0.917391i	$0.630291\pi$
$390$	−5.43949	−0.275439
$391$	−5.39329	−0.272750
$392$	−19.2629	−0.972925
$393$	0.569114	0.0287080
$394$	4.67317	0.235431
$395$	5.04535	0.253859
$396$	−4.68387	−0.235374
$397$	7.81619	0.392283	0.196142	−	0.980576i	$-0.437159\pi$
$397$	7.81619	0.392283	0.196142	+	0.980576i	$0.437159\pi$
$398$	−11.1815	−0.560476
$399$	−0.875873	−0.0438485
$400$	4.10748	0.205374
$401$	−23.2939	−1.16324	−0.581620	−	0.813461i	$-0.697581\pi$
$401$	−23.2939	−1.16324	−0.581620	+	0.813461i	$0.697581\pi$
$402$	−24.2559	−1.20977
$403$	37.7300	1.87946
$404$	−11.6261	−0.578419
$405$	0.988683	0.0491280
$406$	0	0
$407$	6.47264	0.320837
$408$	−49.0443	−2.42806
$409$	9.24661	0.457215	0.228608	−	0.973519i	$-0.426583\pi$
$409$	9.24661	0.457215	0.228608	+	0.973519i	$0.426583\pi$
$410$	−1.05365	−0.0520358
$411$	−22.9076	−1.12995
$412$	9.02479	0.444619
$413$	−3.84817	−0.189356
$414$	4.00084	0.196631
$415$	−5.50546	−0.270252
$416$	−21.8136	−1.06950
$417$	−14.8398	−0.726706
$418$	−0.427091	−0.0208897
$419$	7.10143	0.346928	0.173464	−	0.984840i	$-0.444504\pi$
$419$	7.10143	0.346928	0.173464	+	0.984840i	$0.444504\pi$
$420$	−0.987113	−0.0481662
$421$	29.9740	1.46084	0.730421	−	0.682997i	$-0.239324\pi$
$421$	29.9740	1.46084	0.730421	+	0.682997i	$0.239324\pi$
$422$	−12.3421	−0.600805
$423$	−3.28006	−0.159482
$424$	−32.3687	−1.57196
$425$	−28.6339	−1.38895
$426$	5.99231	0.290328
$427$	5.16783	0.250089
$428$	2.34634	0.113415
$429$	−11.6928	−0.564535
$430$	0.137701	0.00664051
$431$	29.2994	1.41130	0.705652	−	0.708559i	$-0.250654\pi$
$431$	29.2994	1.41130	0.705652	+	0.708559i	$0.250654\pi$
$432$	3.60275	0.173338
$433$	−33.3147	−1.60100	−0.800502	−	0.599330i	$-0.795434\pi$
$433$	−33.3147	−1.60100	−0.800502	+	0.599330i	$0.795434\pi$
$434$	−6.38788	−0.306628
$435$	0	0
$436$	12.5330	0.600220
$437$	−0.391026	−0.0187053
$438$	−45.7846	−2.18767
$439$	6.97129	0.332721	0.166361	−	0.986065i	$-0.446798\pi$
$439$	6.97129	0.332721	0.166361	+	0.986065i	$0.446798\pi$
$440$	−1.41173	−0.0673016
$441$	−29.2463	−1.39268
$442$	−25.1062	−1.19418
$443$	−24.4979	−1.16393	−0.581965	−	0.813214i	$-0.697716\pi$
$443$	−24.4979	−1.16393	−0.581965	+	0.813214i	$0.697716\pi$
$444$	18.3737	0.871977
$445$	3.98025	0.188682
$446$	−8.89846	−0.421354
$447$	−46.6374	−2.20587
$448$	4.95646	0.234171
$449$	−37.9144	−1.78929	−0.894646	−	0.446776i	$-0.852572\pi$
$449$	−37.9144	−1.78929	−0.894646	+	0.446776i	$0.852572\pi$
$450$	21.2412	1.00132
$451$	−2.26494	−0.106652
$452$	7.69324	0.361859
$453$	14.8504	0.697735
$454$	4.67307	0.219318
$455$	−1.48206	−0.0694799
$456$	−3.55583	−0.166517
$457$	21.1474	0.989235	0.494618	−	0.869111i	$-0.335308\pi$
$457$	21.1474	0.989235	0.494618	+	0.869111i	$0.335308\pi$
$458$	2.01860	0.0943229
$459$	−25.1154	−1.17229
$460$	−0.440688	−0.0205472
$461$	−32.6493	−1.52063	−0.760314	−	0.649556i	$-0.774955\pi$
$461$	−32.6493	−1.52063	−0.760314	+	0.649556i	$0.774955\pi$
$462$	1.97966	0.0921019
$463$	38.0777	1.76962	0.884810	−	0.465951i	$-0.154288\pi$
$463$	38.0777	1.76962	0.884810	+	0.465951i	$0.154288\pi$
$464$	0	0
$465$	11.4996	0.533283
$466$	20.0800	0.930188
$467$	10.9771	0.507959	0.253980	−	0.967210i	$-0.418260\pi$
$467$	10.9771	0.507959	0.253980	+	0.967210i	$0.418260\pi$
$468$	−19.9626	−0.922774
$469$	−6.60881	−0.305167
$470$	−0.337072	−0.0155480
$471$	23.1152	1.06509
$472$	−15.6226	−0.719090
$473$	0.296004	0.0136103
$474$	−28.7230	−1.31929
$475$	−2.07603	−0.0952548
$476$	−4.55607	−0.208827
$477$	−49.1444	−2.25017
$478$	12.3565	0.565173
$479$	35.2847	1.61220	0.806100	−	0.591779i	$-0.201574\pi$
$479$	35.2847	1.61220	0.806100	+	0.591779i	$0.201574\pi$
$480$	−6.64853	−0.303462
$481$	27.5864	1.25783
$482$	−29.0368	−1.32259
$483$	1.81249	0.0824710
$484$	−1.03468	−0.0470311
$485$	5.31560	0.241369
$486$	−17.9756	−0.815388
$487$	−7.98025	−0.361619	−0.180810	−	0.983518i	$-0.557872\pi$
$487$	−7.98025	−0.361619	−0.180810	+	0.983518i	$0.557872\pi$
$488$	20.9801	0.949726
$489$	−56.6731	−2.56284
$490$	−3.00547	−0.135773
$491$	20.8866	0.942599	0.471299	−	0.881973i	$-0.343785\pi$
$491$	20.8866	0.942599	0.471299	+	0.881973i	$0.343785\pi$
$492$	−6.42941	−0.289860
$493$	0	0
$494$	−1.82026	−0.0818974
$495$	−2.14339	−0.0963381
$496$	−7.61380	−0.341870
$497$	1.63268	0.0732356
$498$	31.3424	1.40448
$499$	6.77678	0.303370	0.151685	−	0.988429i	$-0.451530\pi$
$499$	6.77678	0.303370	0.151685	+	0.988429i	$0.451530\pi$
$500$	−4.78922	−0.214180
$501$	−15.8597	−0.708560
$502$	−25.5252	−1.13924
$503$	−1.60619	−0.0716166	−0.0358083	−	0.999359i	$-0.511401\pi$
$503$	−1.60619	−0.0716166	−0.0358083	+	0.999359i	$0.511401\pi$
$504$	9.91274	0.441548
$505$	−5.32021	−0.236746
$506$	0.883801	0.0392897
$507$	−14.1691	−0.629274
$508$	3.15933	0.140172
$509$	36.3201	1.60986	0.804930	−	0.593370i	$-0.202203\pi$
$509$	36.3201	1.60986	0.804930	+	0.593370i	$0.202203\pi$
$510$	−7.65207	−0.338839
$511$	−12.4746	−0.551843
$512$	9.53061	0.421198
$513$	−1.82093	−0.0803959
$514$	−12.1737	−0.536958
$515$	4.12983	0.181982
$516$	0.840258	0.0369903
$517$	−0.724577	−0.0318669
$518$	−4.67051	−0.205211
$519$	36.3892	1.59731
$520$	−6.01679	−0.263854
$521$	28.5067	1.24890	0.624450	−	0.781065i	$-0.285323\pi$
$521$	28.5067	1.24890	0.624450	+	0.781065i	$0.285323\pi$
$522$	0	0
$523$	−18.7176	−0.818462	−0.409231	−	0.912431i	$-0.634203\pi$
$523$	−18.7176	−0.818462	−0.409231	+	0.912431i	$0.634203\pi$
$524$	0.214635	0.00937636
$525$	9.62283	0.419975
$526$	−16.5149	−0.720084
$527$	53.0771	2.31208
$528$	2.35958	0.102688
$529$	−22.1908	−0.964819
$530$	−5.05028	−0.219370
$531$	−23.7194	−1.02933
$532$	−0.330326	−0.0143214
$533$	−9.65315	−0.418124
$534$	−22.6594	−0.980567
$535$	1.07371	0.0464205
$536$	−26.8302	−1.15889
$537$	59.4045	2.56349
$538$	10.7247	0.462375
$539$	−6.46062	−0.278279
$540$	−2.05219	−0.0883123
$541$	7.25912	0.312094	0.156047	−	0.987750i	$-0.450125\pi$
$541$	7.25912	0.312094	0.156047	+	0.987750i	$0.450125\pi$
$542$	4.20348	0.180555
$543$	46.2814	1.98612
$544$	−30.6866	−1.31568
$545$	5.73520	0.245669
$546$	8.43728	0.361082
$547$	10.3835	0.443967	0.221984	−	0.975050i	$-0.428747\pi$
$547$	10.3835	0.443967	0.221984	+	0.975050i	$0.428747\pi$
$548$	−8.63933	−0.369054
$549$	31.8535	1.35947
$550$	4.69226	0.200079
$551$	0	0
$552$	7.35826	0.313188
$553$	−7.82593	−0.332792
$554$	7.44366	0.316251
$555$	8.40799	0.356899
$556$	−5.59665	−0.237351
$557$	−22.7512	−0.963998	−0.481999	−	0.876172i	$-0.660089\pi$
$557$	−22.7512	−0.963998	−0.481999	+	0.876172i	$0.660089\pi$
$558$	−39.3736	−1.66682
$559$	1.26157	0.0533586
$560$	0.299075	0.0126382
$561$	−16.4490	−0.694479
$562$	18.0464	0.761241
$563$	−7.23992	−0.305126	−0.152563	−	0.988294i	$-0.548753\pi$
$563$	−7.23992	−0.305126	−0.152563	+	0.988294i	$0.548753\pi$
$564$	−2.05684	−0.0866084
$565$	3.52050	0.148109
$566$	27.8147	1.16914
$567$	−1.53356	−0.0644036
$568$	6.62827	0.278116
$569$	−9.48599	−0.397673	−0.198837	−	0.980033i	$-0.563716\pi$
$569$	−9.48599	−0.397673	−0.198837	+	0.980033i	$0.563716\pi$
$570$	−0.554793	−0.0232377
$571$	−46.9716	−1.96570	−0.982851	−	0.184404i	$-0.940965\pi$
$571$	−46.9716	−1.96570	−0.982851	+	0.184404i	$0.940965\pi$
$572$	−4.40982	−0.184384
$573$	52.5698	2.19614
$574$	1.63433	0.0682155
$575$	4.29603	0.179157
$576$	30.5506	1.27294
$577$	−5.75635	−0.239640	−0.119820	−	0.992796i	$-0.538232\pi$
$577$	−5.75635	−0.239640	−0.119820	+	0.992796i	$0.538232\pi$
$578$	−18.6159	−0.774320
$579$	−28.4177	−1.18100
$580$	0	0
$581$	8.53961	0.354283
$582$	−30.2615	−1.25438
$583$	−10.8562	−0.449617
$584$	−50.6437	−2.09565
$585$	−9.13511	−0.377690
$586$	14.6178	0.603857
$587$	−38.5199	−1.58989	−0.794943	−	0.606684i	$-0.792499\pi$
$587$	−38.5199	−1.58989	−0.794943	+	0.606684i	$0.792499\pi$
$588$	−18.3396	−0.756311
$589$	3.84822	0.158563
$590$	−2.43750	−0.100350
$591$	13.0492	0.536772
$592$	−5.56685	−0.228796
$593$	36.6924	1.50677	0.753387	−	0.657577i	$-0.228419\pi$
$593$	36.6924	1.50677	0.753387	+	0.657577i	$0.228419\pi$
$594$	4.11568	0.168868
$595$	−2.08490	−0.0854726
$596$	−17.5888	−0.720464
$597$	−31.2227	−1.27786
$598$	3.76675	0.154034
$599$	−9.47372	−0.387086	−0.193543	−	0.981092i	$-0.561998\pi$
$599$	−9.47372	−0.387086	−0.193543	+	0.981092i	$0.561998\pi$
$600$	39.0663	1.59488
$601$	−28.9295	−1.18006	−0.590029	−	0.807382i	$-0.700884\pi$
$601$	−28.9295	−1.18006	−0.590029	+	0.807382i	$0.700884\pi$
$602$	−0.213590	−0.00870527
$603$	−40.7354	−1.65887
$604$	5.60068	0.227888
$605$	−0.473482	−0.0192498
$606$	30.2877	1.23035
$607$	14.5554	0.590784	0.295392	−	0.955376i	$-0.404550\pi$
$607$	14.5554	0.590784	0.295392	+	0.955376i	$0.404550\pi$
$608$	−2.22485	−0.0902296
$609$	0	0
$610$	3.27339	0.132536
$611$	−3.08814	−0.124933
$612$	−28.0827	−1.13518
$613$	−44.2228	−1.78614	−0.893071	−	0.449915i	$-0.851454\pi$
$613$	−44.2228	−1.78614	−0.893071	+	0.449915i	$0.851454\pi$
$614$	22.9385	0.925723
$615$	−2.94216	−0.118639
$616$	2.18976	0.0882279
$617$	28.6977	1.15533	0.577663	−	0.816275i	$-0.303965\pi$
$617$	28.6977	1.15533	0.577663	+	0.816275i	$0.303965\pi$
$618$	−23.5110	−0.945750
$619$	−22.8729	−0.919340	−0.459670	−	0.888090i	$-0.652032\pi$
$619$	−22.8729	−0.919340	−0.459670	+	0.888090i	$0.652032\pi$
$620$	4.33696	0.174176
$621$	3.76813	0.151210
$622$	−13.1348	−0.526657
$623$	−6.17383	−0.247349
$624$	10.0565	0.402583
$625$	21.6875	0.867499
$626$	−13.9269	−0.556630
$627$	−1.19260	−0.0476277
$628$	8.71764	0.347872
$629$	38.8075	1.54736
$630$	1.54662	0.0616188
$631$	43.6391	1.73724	0.868622	−	0.495476i	$-0.165006\pi$
$631$	43.6391	1.73724	0.868622	+	0.495476i	$0.165006\pi$
$632$	−31.7714	−1.26380
$633$	−34.4637	−1.36981
$634$	20.0980	0.798193
$635$	1.44574	0.0573724
$636$	−30.8171	−1.22198
$637$	−27.5351	−1.09098
$638$	0	0
$639$	10.0635	0.398106
$640$	−1.70722	−0.0674838
$641$	−36.8687	−1.45622	−0.728112	−	0.685458i	$-0.759602\pi$
$641$	−36.8687	−1.45622	−0.728112	+	0.685458i	$0.759602\pi$
$642$	−6.11259	−0.241245
$643$	24.2144	0.954921	0.477460	−	0.878653i	$-0.341557\pi$
$643$	24.2144	0.954921	0.477460	+	0.878653i	$0.341557\pi$
$644$	0.683559	0.0269360
$645$	0.384510	0.0151401
$646$	−2.56067	−0.100748
$647$	37.5584	1.47657	0.738287	−	0.674487i	$-0.235635\pi$
$647$	37.5584	1.47657	0.738287	+	0.674487i	$0.235635\pi$
$648$	−6.22589	−0.244576
$649$	−5.23970	−0.205676
$650$	19.9984	0.784401
$651$	−17.8373	−0.699098
$652$	−21.3736	−0.837055
$653$	−1.32896	−0.0520061	−0.0260031	−	0.999662i	$-0.508278\pi$
$653$	−1.32896	−0.0520061	−0.0260031	+	0.999662i	$0.508278\pi$
$654$	−32.6503	−1.27673
$655$	0.0982190	0.00383774
$656$	1.94798	0.0760558
$657$	−76.8909	−2.99980
$658$	0.522838	0.0203824
$659$	−18.7406	−0.730030	−0.365015	−	0.931002i	$-0.618936\pi$
$659$	−18.7406	−0.730030	−0.365015	+	0.931002i	$0.618936\pi$
$660$	−1.34406	−0.0523174
$661$	−41.9503	−1.63168	−0.815839	−	0.578279i	$-0.803724\pi$
$661$	−41.9503	−1.63168	−0.815839	+	0.578279i	$0.803724\pi$
$662$	27.5423	1.07046
$663$	−70.1057	−2.72268
$664$	34.6688	1.34541
$665$	−0.151160	−0.00586175
$666$	−28.7881	−1.11552
$667$	0	0
$668$	−5.98131	−0.231424
$669$	−24.8478	−0.960670
$670$	−4.18614	−0.161725
$671$	7.03655	0.271643
$672$	10.3126	0.397819
$673$	−30.4494	−1.17374	−0.586870	−	0.809681i	$-0.699640\pi$
$673$	−30.4494	−1.17374	−0.586870	+	0.809681i	$0.699640\pi$
$674$	−6.40693	−0.246786
$675$	20.0057	0.770020
$676$	−5.34373	−0.205528
$677$	39.4408	1.51583	0.757916	−	0.652352i	$-0.226218\pi$
$677$	39.4408	1.51583	0.757916	+	0.652352i	$0.226218\pi$
$678$	−20.0421	−0.769711
$679$	−8.24512	−0.316419
$680$	−8.46419	−0.324587
$681$	13.0489	0.500036
$682$	−8.69778	−0.333055
$683$	35.0840	1.34245	0.671226	−	0.741253i	$-0.265768\pi$
$683$	35.0840	1.34245	0.671226	+	0.741253i	$0.265768\pi$
$684$	−2.03606	−0.0778508
$685$	−3.95344	−0.151053
$686$	9.71288	0.370839
$687$	5.63666	0.215052
$688$	−0.254581	−0.00970580
$689$	−46.2690	−1.76271
$690$	1.14806	0.0437059
$691$	−8.71400	−0.331496	−0.165748	−	0.986168i	$-0.553004\pi$
$691$	−8.71400	−0.331496	−0.165748	+	0.986168i	$0.553004\pi$
$692$	13.7238	0.521699
$693$	3.32465	0.126293
$694$	26.1296	0.991865
$695$	−2.56108	−0.0971474
$696$	0	0
$697$	−13.5797	−0.514367
$698$	30.6202	1.15899
$699$	56.0707	2.12079
$700$	3.62914	0.137169
$701$	22.8721	0.863868	0.431934	−	0.901905i	$-0.357831\pi$
$701$	22.8721	0.863868	0.431934	+	0.901905i	$0.357831\pi$
$702$	17.5410	0.662042
$703$	2.81363	0.106118
$704$	6.74874	0.254353
$705$	−0.941229	−0.0354487
$706$	19.0307	0.716229
$707$	8.25227	0.310358
$708$	−14.8738	−0.558991
$709$	−5.07431	−0.190570	−0.0952849	−	0.995450i	$-0.530376\pi$
$709$	−5.07431	−0.190570	−0.0952849	+	0.995450i	$0.530376\pi$
$710$	1.03417	0.0388116
$711$	−48.2375	−1.80905
$712$	−25.0642	−0.939322
$713$	−7.96330	−0.298228
$714$	11.8693	0.444196
$715$	−2.01798	−0.0754681
$716$	22.4037	0.837267
$717$	34.5038	1.28857
$718$	33.3654	1.24518
$719$	49.8410	1.85876	0.929378	−	0.369129i	$-0.120344\pi$
$719$	49.8410	1.85876	0.929378	+	0.369129i	$0.120344\pi$
$720$	1.84344	0.0687009
$721$	−6.40586	−0.238567
$722$	18.4819	0.687826
$723$	−81.0813	−3.01545
$724$	17.4545	0.648691
$725$	0	0
$726$	2.69551	0.100040
$727$	−28.7056	−1.06463	−0.532315	−	0.846546i	$-0.678678\pi$
$727$	−28.7056	−1.06463	−0.532315	+	0.846546i	$0.678678\pi$
$728$	9.33274	0.345894
$729$	−43.9300	−1.62704
$730$	−7.90161	−0.292452
$731$	1.77473	0.0656406
$732$	19.9745	0.738277
$733$	−1.08250	−0.0399831	−0.0199916	−	0.999800i	$-0.506364\pi$
$733$	−1.08250	−0.0399831	−0.0199916	+	0.999800i	$0.506364\pi$
$734$	−8.92155	−0.329300
$735$	−8.39237	−0.309557
$736$	4.60399	0.169705
$737$	−8.99860	−0.331468
$738$	10.0737	0.370817
$739$	−31.9120	−1.17390	−0.586951	−	0.809622i	$-0.699672\pi$
$739$	−31.9120	−1.17390	−0.586951	+	0.809622i	$0.699672\pi$
$740$	3.17098	0.116567
$741$	−5.08283	−0.186723
$742$	7.83358	0.287580
$743$	26.4619	0.970794	0.485397	−	0.874294i	$-0.338675\pi$
$743$	26.4619	0.970794	0.485397	+	0.874294i	$0.338675\pi$
$744$	−72.4150	−2.65486
$745$	−8.04880	−0.294885
$746$	19.3444	0.708250
$747$	52.6365	1.92587
$748$	−6.20357	−0.226825
$749$	−1.66545	−0.0608543
$750$	12.4767	0.455583
$751$	−19.8579	−0.724624	−0.362312	−	0.932057i	$-0.618013\pi$
$751$	−19.8579	−0.724624	−0.362312	+	0.932057i	$0.618013\pi$
$752$	0.623179	0.0227250
$753$	−71.2756	−2.59743
$754$	0	0
$755$	2.56293	0.0932744
$756$	3.18319	0.115772
$757$	38.6445	1.40456	0.702279	−	0.711901i	$-0.252166\pi$
$757$	38.6445	1.40456	0.702279	+	0.711901i	$0.252166\pi$
$758$	−24.1792	−0.878230
$759$	2.46790	0.0895789
$760$	−0.613674	−0.0222603
$761$	7.97618	0.289136	0.144568	−	0.989495i	$-0.453821\pi$
$761$	7.97618	0.289136	0.144568	+	0.989495i	$0.453821\pi$
$762$	−8.23053	−0.298161
$763$	−8.89598	−0.322056
$764$	19.8261	0.717283
$765$	−12.8509	−0.464626
$766$	−20.6268	−0.745276
$767$	−22.3316	−0.806346
$768$	46.7497	1.68693
$769$	22.2494	0.802333	0.401167	−	0.916005i	$-0.368605\pi$
$769$	22.2494	0.802333	0.401167	+	0.916005i	$0.368605\pi$
$770$	0.341654	0.0123124
$771$	−33.9934	−1.22424
$772$	−10.7174	−0.385728
$773$	1.16167	0.0417823	0.0208912	−	0.999782i	$-0.493350\pi$
$773$	1.16167	0.0417823	0.0208912	+	0.999782i	$0.493350\pi$
$774$	−1.31653	−0.0473215
$775$	−42.2786	−1.51869
$776$	−33.4732	−1.20162
$777$	−13.0418	−0.467871
$778$	15.4244	0.552993
$779$	−0.984560	−0.0352755
$780$	−5.72837	−0.205109
$781$	2.22307	0.0795476
$782$	5.29893	0.189489
$783$	0	0
$784$	5.55651	0.198447
$785$	3.98928	0.142383
$786$	−0.559157	−0.0199445
$787$	−29.7863	−1.06177	−0.530883	−	0.847445i	$-0.678140\pi$
$787$	−29.7863	−1.06177	−0.530883	+	0.847445i	$0.678140\pi$
$788$	4.92136	0.175316
$789$	−46.1156	−1.64176
$790$	−4.95708	−0.176365
$791$	−5.46071	−0.194161
$792$	13.4973	0.479604
$793$	29.9898	1.06497
$794$	−7.67944	−0.272533
$795$	−14.1022	−0.500154
$796$	−11.7753	−0.417364
$797$	−50.8784	−1.80220	−0.901102	−	0.433607i	$-0.857241\pi$
$797$	−50.8784	−1.80220	−0.901102	+	0.433607i	$0.857241\pi$
$798$	0.860550	0.0304631
$799$	−4.34429	−0.153690
$800$	24.4434	0.864206
$801$	−38.0543	−1.34458
$802$	22.8863	0.808144
$803$	−16.9855	−0.599404
$804$	−25.5441	−0.900870
$805$	0.312803	0.0110249
$806$	−37.0699	−1.30573
$807$	29.9473	1.05419
$808$	33.5022	1.17860
$809$	−13.1133	−0.461039	−0.230520	−	0.973068i	$-0.574043\pi$
$809$	−13.1133	−0.461039	−0.230520	+	0.973068i	$0.574043\pi$
$810$	−0.971385	−0.0341310
$811$	−15.8504	−0.556582	−0.278291	−	0.960497i	$-0.589768\pi$
$811$	−15.8504	−0.556582	−0.278291	+	0.960497i	$0.589768\pi$
$812$	0	0
$813$	11.7377	0.411658
$814$	−6.35940	−0.222897
$815$	−9.78077	−0.342606
$816$	14.1471	0.495249
$817$	0.128672	0.00450166
$818$	−9.08483	−0.317644
$819$	14.1696	0.495127
$820$	−1.10960	−0.0387490
$821$	−13.9231	−0.485918	−0.242959	−	0.970037i	$-0.578118\pi$
$821$	−13.9231	−0.485918	−0.242959	+	0.970037i	$0.578118\pi$
$822$	22.5068	0.785015
$823$	15.4241	0.537650	0.268825	−	0.963189i	$-0.413365\pi$
$823$	15.4241	0.537650	0.268825	+	0.963189i	$0.413365\pi$
$824$	−26.0062	−0.905970
$825$	13.1025	0.456171
$826$	3.78085	0.131552
$827$	−2.83424	−0.0985562	−0.0492781	−	0.998785i	$-0.515692\pi$
$827$	−2.83424	−0.0985562	−0.0492781	+	0.998785i	$0.515692\pi$
$828$	4.21332	0.146423
$829$	10.1435	0.352297	0.176149	−	0.984364i	$-0.443636\pi$
$829$	10.1435	0.352297	0.176149	+	0.984364i	$0.443636\pi$
$830$	5.40914	0.187754
$831$	20.7854	0.721038
$832$	28.7631	0.997182
$833$	−38.7354	−1.34210
$834$	14.5801	0.504869
$835$	−2.73711	−0.0947216
$836$	−0.449774	−0.0155558
$837$	−37.0835	−1.28179
$838$	−6.97719	−0.241023
$839$	16.7036	0.576673	0.288336	−	0.957529i	$-0.406898\pi$
$839$	16.7036	0.576673	0.288336	+	0.957529i	$0.406898\pi$
$840$	2.84451	0.0981448
$841$	0	0
$842$	−29.4496	−1.01490
$843$	50.3922	1.73560
$844$	−12.9976	−0.447396
$845$	−2.44534	−0.0841224
$846$	3.22267	0.110798
$847$	0.734426	0.0252352
$848$	9.33695	0.320632
$849$	77.6687	2.66558
$850$	28.1330	0.964953
$851$	−5.82239	−0.199589
$852$	6.31055	0.216196
$853$	12.1797	0.417025	0.208513	−	0.978020i	$-0.433138\pi$
$853$	12.1797	0.417025	0.208513	+	0.978020i	$0.433138\pi$
$854$	−5.07742	−0.173746
$855$	−0.931723	−0.0318643
$856$	−6.76132	−0.231097
$857$	47.9590	1.63825	0.819125	−	0.573616i	$-0.194460\pi$
$857$	47.9590	1.63825	0.819125	+	0.573616i	$0.194460\pi$
$858$	11.4883	0.392203
$859$	23.3663	0.797247	0.398623	−	0.917115i	$-0.369488\pi$
$859$	23.3663	0.797247	0.398623	+	0.917115i	$0.369488\pi$
$860$	0.145014	0.00494493
$861$	4.56364	0.155528
$862$	−28.7868	−0.980483
$863$	−19.1115	−0.650564	−0.325282	−	0.945617i	$-0.605459\pi$
$863$	−19.1115	−0.650564	−0.325282	+	0.945617i	$0.605459\pi$
$864$	21.4398	0.729398
$865$	6.28013	0.213531
$866$	32.7319	1.11227
$867$	−51.9824	−1.76542
$868$	−6.72713	−0.228334
$869$	−10.6558	−0.361474
$870$	0	0
$871$	−38.3520	−1.29951
$872$	−36.1155	−1.22302
$873$	−50.8213	−1.72004
$874$	0.384185	0.0129953
$875$	3.39942	0.114921
$876$	−48.2161	−1.62907
$877$	−17.1568	−0.579344	−0.289672	−	0.957126i	$-0.593546\pi$
$877$	−17.1568	−0.579344	−0.289672	+	0.957126i	$0.593546\pi$
$878$	−6.84932	−0.231153
$879$	40.8184	1.37677
$880$	0.407222	0.0137275
$881$	8.59566	0.289595	0.144798	−	0.989461i	$-0.453747\pi$
$881$	8.59566	0.289595	0.144798	+	0.989461i	$0.453747\pi$
$882$	28.7346	0.967546
$883$	21.7462	0.731816	0.365908	−	0.930651i	$-0.380758\pi$
$883$	21.7462	0.731816	0.365908	+	0.930651i	$0.380758\pi$
$884$	−26.4396	−0.889259
$885$	−6.80639	−0.228794
$886$	24.0693	0.808623
$887$	−40.1246	−1.34725	−0.673627	−	0.739072i	$-0.735264\pi$
$887$	−40.1246	−1.34725	−0.673627	+	0.739072i	$0.735264\pi$
$888$	−52.9464	−1.77677
$889$	−2.24251	−0.0752114
$890$	−3.91061	−0.131084
$891$	−2.08811	−0.0699543
$892$	−9.37105	−0.313766
$893$	−0.314971	−0.0105401
$894$	45.8215	1.53250
$895$	10.2522	0.342693
$896$	2.64810	0.0884668
$897$	10.5182	0.351191
$898$	37.2511	1.24308
$899$	0	0
$900$	22.3693	0.745644
$901$	−65.0895	−2.16845
$902$	2.22531	0.0740948
$903$	−0.596421	−0.0198476
$904$	−22.1692	−0.737335
$905$	7.98735	0.265509
$906$	−14.5906	−0.484741
$907$	−40.8175	−1.35532	−0.677661	−	0.735374i	$-0.737006\pi$
$907$	−40.8175	−1.35532	−0.677661	+	0.735374i	$0.737006\pi$
$908$	4.92125	0.163317
$909$	50.8654	1.68710
$910$	1.45613	0.0482701
$911$	14.5963	0.483597	0.241798	−	0.970326i	$-0.422263\pi$
$911$	14.5963	0.483597	0.241798	+	0.970326i	$0.422263\pi$
$912$	1.02570	0.0339644
$913$	11.6276	0.384817
$914$	−20.7775	−0.687257
$915$	9.14051	0.302176
$916$	2.12580	0.0702385
$917$	−0.152349	−0.00503102
$918$	24.6760	0.814430
$919$	−35.9892	−1.18718	−0.593588	−	0.804769i	$-0.702289\pi$
$919$	−35.9892	−1.18718	−0.593588	+	0.804769i	$0.702289\pi$
$920$	1.26991	0.0418675
$921$	64.0527	2.11061
$922$	32.0780	1.05643
$923$	9.47470	0.311863
$924$	2.08479	0.0685847
$925$	−30.9121	−1.01638
$926$	−37.4115	−1.22942
$927$	−39.4845	−1.29684
$928$	0	0
$929$	−17.1620	−0.563068	−0.281534	−	0.959551i	$-0.590843\pi$
$929$	−17.1620	−0.563068	−0.281534	+	0.959551i	$0.590843\pi$
$930$	−11.2984	−0.370491
$931$	−2.80841	−0.0920419
$932$	21.1464	0.692674
$933$	−36.6771	−1.20075
$934$	−10.7850	−0.352898
$935$	−2.83882	−0.0928392
$936$	57.5252	1.88027
$937$	−2.09072	−0.0683009	−0.0341505	−	0.999417i	$-0.510873\pi$
$937$	−2.09072	−0.0683009	−0.0341505	+	0.999417i	$0.510873\pi$
$938$	6.49319	0.212010
$939$	−38.8889	−1.26909
$940$	−0.354974	−0.0115780
$941$	35.7828	1.16649	0.583243	−	0.812298i	$-0.301784\pi$
$941$	35.7828	1.16649	0.583243	+	0.812298i	$0.301784\pi$
$942$	−22.7108	−0.739958
$943$	2.03740	0.0663468
$944$	4.50645	0.146672
$945$	1.45666	0.0473852
$946$	−0.290825	−0.00945555
$947$	−3.76091	−0.122213	−0.0611066	−	0.998131i	$-0.519463\pi$
$947$	−3.76091	−0.122213	−0.0611066	+	0.998131i	$0.519463\pi$
$948$	−30.2484	−0.982423
$949$	−72.3920	−2.34994
$950$	2.03971	0.0661769
$951$	56.1209	1.81985
$952$	13.1290	0.425512
$953$	35.0570	1.13561	0.567803	−	0.823164i	$-0.307793\pi$
$953$	35.0570	1.13561	0.567803	+	0.823164i	$0.307793\pi$
$954$	48.2846	1.56327
$955$	9.07262	0.293583
$956$	13.0127	0.420862
$957$	0	0
$958$	−34.6674	−1.12005
$959$	6.13226	0.198021
$960$	8.76665	0.282942
$961$	47.3695	1.52805
$962$	−27.1037	−0.873859
$963$	−10.2655	−0.330802
$964$	−30.5789	−0.984880
$965$	−4.90439	−0.157878
$966$	−1.78078	−0.0572956
$967$	−43.0406	−1.38409	−0.692046	−	0.721853i	$-0.743291\pi$
$967$	−43.0406	−1.38409	−0.692046	+	0.721853i	$0.743291\pi$
$968$	2.98159	0.0958320
$969$	−7.15034	−0.229702
$970$	−5.22260	−0.167688
$971$	−35.7519	−1.14733	−0.573667	−	0.819088i	$-0.694480\pi$
$971$	−35.7519	−1.14733	−0.573667	+	0.819088i	$0.694480\pi$
$972$	−18.9302	−0.607187
$973$	3.97254	0.127354
$974$	7.84063	0.251230
$975$	55.8428	1.78840
$976$	−6.05185	−0.193715
$977$	24.0334	0.768898	0.384449	−	0.923146i	$-0.374391\pi$
$977$	24.0334	0.768898	0.384449	+	0.923146i	$0.374391\pi$
$978$	55.6815	1.78050
$979$	−8.40633	−0.268667
$980$	−3.16509	−0.101105
$981$	−54.8331	−1.75069
$982$	−20.5212	−0.654857
$983$	15.0631	0.480439	0.240219	−	0.970719i	$-0.422781\pi$
$983$	15.0631	0.480439	0.240219	+	0.970719i	$0.422781\pi$
$984$	18.5273	0.590628
$985$	2.25206	0.0717567
$986$	0	0
$987$	1.45996	0.0464709
$988$	−1.91693	−0.0609858
$989$	−0.266267	−0.00846680
$990$	2.10589	0.0669295
$991$	3.75603	0.119314	0.0596571	−	0.998219i	$-0.480999\pi$
$991$	3.75603	0.119314	0.0596571	+	0.998219i	$0.480999\pi$
$992$	−45.3094	−1.43858
$993$	76.9083	2.44061
$994$	−1.60411	−0.0508794
$995$	−5.38850	−0.170827
$996$	33.0069	1.04586
$997$	−19.7052	−0.624070	−0.312035	−	0.950071i	$-0.601011\pi$
$997$	−19.7052	−0.624070	−0.312035	+	0.950071i	$0.601011\pi$
$998$	−6.65822	−0.210762
$999$	−27.1137	−0.857838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.14	✓	40
29.28	even	2		9251.2.a.bb.1.27	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.14	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.27	yes	40	29.28	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-0.982505 q^{2} -2.74351 q^{3} -1.03468 q^{4} -0.473482 q^{5} +2.69551 q^{6} +0.734426 q^{7} +2.98159 q^{8} +4.52686 q^{9} +O(q^{10})\)	\(q-0.982505 q^{2} -2.74351 q^{3} -1.03468 q^{4} -0.473482 q^{5} +2.69551 q^{6} +0.734426 q^{7} +2.98159 q^{8} +4.52686 q^{9} +0.465198 q^{10} +1.00000 q^{11} +2.83867 q^{12} +4.26199 q^{13} -0.721577 q^{14} +1.29900 q^{15} -0.860058 q^{16} +5.99561 q^{17} -4.44766 q^{18} +0.434696 q^{19} +0.489905 q^{20} -2.01491 q^{21} -0.982505 q^{22} -0.899538 q^{23} -8.18003 q^{24} -4.77581 q^{25} -4.18743 q^{26} -4.18896 q^{27} -0.759900 q^{28} -1.27628 q^{30} +8.85266 q^{31} -5.11817 q^{32} -2.74351 q^{33} -5.89072 q^{34} -0.347738 q^{35} -4.68387 q^{36} +6.47264 q^{37} -0.427091 q^{38} -11.6928 q^{39} -1.41173 q^{40} -2.26494 q^{41} +1.97966 q^{42} +0.296004 q^{43} -1.03468 q^{44} -2.14339 q^{45} +0.883801 q^{46} -0.724577 q^{47} +2.35958 q^{48} -6.46062 q^{49} +4.69226 q^{50} -16.4490 q^{51} -4.40982 q^{52} -10.8562 q^{53} +4.11568 q^{54} -0.473482 q^{55} +2.18976 q^{56} -1.19260 q^{57} -5.23970 q^{59} -1.34406 q^{60} +7.03655 q^{61} -8.69778 q^{62} +3.32465 q^{63} +6.74874 q^{64} -2.01798 q^{65} +2.69551 q^{66} -8.99860 q^{67} -6.20357 q^{68} +2.46790 q^{69} +0.341654 q^{70} +2.22307 q^{71} +13.4973 q^{72} -16.9855 q^{73} -6.35940 q^{74} +13.1025 q^{75} -0.449774 q^{76} +0.734426 q^{77} +11.4883 q^{78} -10.6558 q^{79} +0.407222 q^{80} -2.08811 q^{81} +2.22531 q^{82} +11.6276 q^{83} +2.08479 q^{84} -2.83882 q^{85} -0.290825 q^{86} +2.98159 q^{88} -8.40633 q^{89} +2.10589 q^{90} +3.13012 q^{91} +0.930739 q^{92} -24.2874 q^{93} +0.711900 q^{94} -0.205821 q^{95} +14.0418 q^{96} -11.2266 q^{97} +6.34759 q^{98} +4.52686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

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