LMFDB - Embedded newform 381.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(1,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, 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("381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.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:	$3.04230031701$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 14x^{7} + 26x^{6} + 59x^{5} - 99x^{4} - 66x^{3} + 102x^{2} - 24x + 1 $ x^9 - 2x^8 - 14x^7 + 26x^6 + 59x^5 - 99x^4 - 66x^3 + 102x^2 - 24x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.63041$ of defining polynomial
Character	$\chi$	$=$	381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.63041 q^{2} +1.00000 q^{3} +4.91907 q^{4} -3.66812 q^{5} +2.63041 q^{6} +1.33794 q^{7} +7.67834 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.63041 q^{2} +1.00000 q^{3} +4.91907 q^{4} -3.66812 q^{5} +2.63041 q^{6} +1.33794 q^{7} +7.67834 q^{8} +1.00000 q^{9} -9.64866 q^{10} +1.38143 q^{11} +4.91907 q^{12} -4.52573 q^{13} +3.51933 q^{14} -3.66812 q^{15} +10.3591 q^{16} -0.752137 q^{17} +2.63041 q^{18} +1.24786 q^{19} -18.0437 q^{20} +1.33794 q^{21} +3.63373 q^{22} -7.69718 q^{23} +7.67834 q^{24} +8.45509 q^{25} -11.9045 q^{26} +1.00000 q^{27} +6.58141 q^{28} -3.06562 q^{29} -9.64866 q^{30} -6.08837 q^{31} +11.8919 q^{32} +1.38143 q^{33} -1.97843 q^{34} -4.90772 q^{35} +4.91907 q^{36} +11.0375 q^{37} +3.28239 q^{38} -4.52573 q^{39} -28.1651 q^{40} +9.45678 q^{41} +3.51933 q^{42} +2.44720 q^{43} +6.79535 q^{44} -3.66812 q^{45} -20.2468 q^{46} -12.0044 q^{47} +10.3591 q^{48} -5.20992 q^{49} +22.2404 q^{50} -0.752137 q^{51} -22.2624 q^{52} -10.7628 q^{53} +2.63041 q^{54} -5.06725 q^{55} +10.2732 q^{56} +1.24786 q^{57} -8.06383 q^{58} +4.88252 q^{59} -18.0437 q^{60} +13.1655 q^{61} -16.0149 q^{62} +1.33794 q^{63} +10.5625 q^{64} +16.6009 q^{65} +3.63373 q^{66} +3.65390 q^{67} -3.69981 q^{68} -7.69718 q^{69} -12.9093 q^{70} +12.3713 q^{71} +7.67834 q^{72} +3.80234 q^{73} +29.0331 q^{74} +8.45509 q^{75} +6.13832 q^{76} +1.84827 q^{77} -11.9045 q^{78} +11.3394 q^{79} -37.9983 q^{80} +1.00000 q^{81} +24.8752 q^{82} +10.4561 q^{83} +6.58141 q^{84} +2.75893 q^{85} +6.43715 q^{86} -3.06562 q^{87} +10.6071 q^{88} -11.7099 q^{89} -9.64866 q^{90} -6.05516 q^{91} -37.8629 q^{92} -6.08837 q^{93} -31.5765 q^{94} -4.57731 q^{95} +11.8919 q^{96} +2.50120 q^{97} -13.7042 q^{98} +1.38143 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * 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 $

$2$	2.63041	1.85998	0.929991	−	0.367582i	$-0.119814\pi$
$2$	2.63041	1.85998	0.929991	+	0.367582i	$0.119814\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.91907	2.45953
$5$	−3.66812	−1.64043	−0.820216	−	0.572054i	$-0.806147\pi$
$5$	−3.66812	−1.64043	−0.820216	+	0.572054i	$0.806147\pi$
$6$	2.63041	1.07386
$7$	1.33794	0.505693	0.252847	−	0.967506i	$-0.418633\pi$
$7$	1.33794	0.505693	0.252847	+	0.967506i	$0.418633\pi$
$8$	7.67834	2.71470
$9$	1.00000	0.333333
$10$	−9.64866	−3.05117
$11$	1.38143	0.416517	0.208259	−	0.978074i	$-0.433220\pi$
$11$	1.38143	0.416517	0.208259	+	0.978074i	$0.433220\pi$
$12$	4.91907	1.42001
$13$	−4.52573	−1.25521	−0.627607	−	0.778531i	$-0.715965\pi$
$13$	−4.52573	−1.25521	−0.627607	+	0.778531i	$0.715965\pi$
$14$	3.51933	0.940580
$15$	−3.66812	−0.947104
$16$	10.3591	2.58977
$17$	−0.752137	−0.182420	−0.0912101	−	0.995832i	$-0.529073\pi$
$17$	−0.752137	−0.182420	−0.0912101	+	0.995832i	$0.529073\pi$
$18$	2.63041	0.619994
$19$	1.24786	0.286279	0.143140	−	0.989703i	$-0.454280\pi$
$19$	1.24786	0.286279	0.143140	+	0.989703i	$0.454280\pi$
$20$	−18.0437	−4.03470
$21$	1.33794	0.291962
$22$	3.63373	0.774714
$23$	−7.69718	−1.60497	−0.802487	−	0.596670i	$-0.796490\pi$
$23$	−7.69718	−1.60497	−0.802487	+	0.596670i	$0.796490\pi$
$24$	7.67834	1.56734
$25$	8.45509	1.69102
$26$	−11.9045	−2.33467
$27$	1.00000	0.192450
$28$	6.58141	1.24377
$29$	−3.06562	−0.569271	−0.284635	−	0.958636i	$-0.591873\pi$
$29$	−3.06562	−0.569271	−0.284635	+	0.958636i	$0.591873\pi$
$30$	−9.64866	−1.76160
$31$	−6.08837	−1.09350	−0.546752	−	0.837295i	$-0.684136\pi$
$31$	−6.08837	−1.09350	−0.546752	+	0.837295i	$0.684136\pi$
$32$	11.8919	2.10222
$33$	1.38143	0.240476
$34$	−1.97843	−0.339298
$35$	−4.90772	−0.829556
$36$	4.91907	0.819844
$37$	11.0375	1.81455	0.907274	−	0.420539i	$-0.138159\pi$
$37$	11.0375	1.81455	0.907274	+	0.420539i	$0.138159\pi$
$38$	3.28239	0.532474
$39$	−4.52573	−0.724698
$40$	−28.1651	−4.45329
$41$	9.45678	1.47690	0.738450	−	0.674308i	$-0.235558\pi$
$41$	9.45678	1.47690	0.738450	+	0.674308i	$0.235558\pi$
$42$	3.51933	0.543044
$43$	2.44720	0.373195	0.186597	−	0.982436i	$-0.440254\pi$
$43$	2.44720	0.373195	0.186597	+	0.982436i	$0.440254\pi$
$44$	6.79535	1.02444
$45$	−3.66812	−0.546811
$46$	−20.2468	−2.98522
$47$	−12.0044	−1.75102	−0.875510	−	0.483201i	$-0.839474\pi$
$47$	−12.0044	−1.75102	−0.875510	+	0.483201i	$0.839474\pi$
$48$	10.3591	1.49520
$49$	−5.20992	−0.744274
$50$	22.2404	3.14526
$51$	−0.752137	−0.105320
$52$	−22.2624	−3.08724
$53$	−10.7628	−1.47838	−0.739192	−	0.673495i	$-0.764792\pi$
$53$	−10.7628	−1.47838	−0.739192	+	0.673495i	$0.764792\pi$
$54$	2.63041	0.357954
$55$	−5.06725	−0.683268
$56$	10.2732	1.37281
$57$	1.24786	0.165283
$58$	−8.06383	−1.05883
$59$	4.88252	0.635650	0.317825	−	0.948149i	$-0.397048\pi$
$59$	4.88252	0.635650	0.317825	+	0.948149i	$0.397048\pi$
$60$	−18.0437	−2.32943
$61$	13.1655	1.68567	0.842835	−	0.538172i	$-0.180885\pi$
$61$	13.1655	1.68567	0.842835	+	0.538172i	$0.180885\pi$
$62$	−16.0149	−2.03390
$63$	1.33794	0.168564
$64$	10.5625	1.32032
$65$	16.6009	2.05909
$66$	3.63373	0.447282
$67$	3.65390	0.446395	0.223198	−	0.974773i	$-0.428351\pi$
$67$	3.65390	0.446395	0.223198	+	0.974773i	$0.428351\pi$
$68$	−3.69981	−0.448668
$69$	−7.69718	−0.926632
$70$	−12.9093	−1.54296
$71$	12.3713	1.46820	0.734099	−	0.679042i	$-0.237605\pi$
$71$	12.3713	1.46820	0.734099	+	0.679042i	$0.237605\pi$
$72$	7.67834	0.904901
$73$	3.80234	0.445030	0.222515	−	0.974929i	$-0.428573\pi$
$73$	3.80234	0.445030	0.222515	+	0.974929i	$0.428573\pi$
$74$	29.0331	3.37503
$75$	8.45509	0.976309
$76$	6.13832	0.704113
$77$	1.84827	0.210630
$78$	−11.9045	−1.34792
$79$	11.3394	1.27578	0.637889	−	0.770129i	$-0.279808\pi$
$79$	11.3394	1.27578	0.637889	+	0.770129i	$0.279808\pi$
$80$	−37.9983	−4.24834
$81$	1.00000	0.111111
$82$	24.8752	2.74701
$83$	10.4561	1.14771	0.573854	−	0.818958i	$-0.305448\pi$
$83$	10.4561	1.14771	0.573854	+	0.818958i	$0.305448\pi$
$84$	6.58141	0.718090
$85$	2.75893	0.299248
$86$	6.43715	0.694136
$87$	−3.06562	−0.328669
$88$	10.6071	1.13072
$89$	−11.7099	−1.24124	−0.620621	−	0.784111i	$-0.713119\pi$
$89$	−11.7099	−1.24124	−0.620621	+	0.784111i	$0.713119\pi$
$90$	−9.64866	−1.01706
$91$	−6.05516	−0.634753
$92$	−37.8629	−3.94748
$93$	−6.08837	−0.631335
$94$	−31.5765	−3.25686
$95$	−4.57731	−0.469622
$96$	11.8919	1.21372
$97$	2.50120	0.253958	0.126979	−	0.991905i	$-0.459472\pi$
$97$	2.50120	0.253958	0.126979	+	0.991905i	$0.459472\pi$
$98$	−13.7042	−1.38434
$99$	1.38143	0.138839
$100$	41.5911	4.15911
$101$	11.0515	1.09966	0.549831	−	0.835276i	$-0.314692\pi$
$101$	11.0515	1.09966	0.549831	+	0.835276i	$0.314692\pi$
$102$	−1.97843	−0.195894
$103$	−7.72423	−0.761091	−0.380545	−	0.924762i	$-0.624264\pi$
$103$	−7.72423	−0.761091	−0.380545	+	0.924762i	$0.624264\pi$
$104$	−34.7501	−3.40753
$105$	−4.90772	−0.478944
$106$	−28.3106	−2.74977
$107$	4.99756	0.483133	0.241566	−	0.970384i	$-0.422339\pi$
$107$	4.99756	0.483133	0.241566	+	0.970384i	$0.422339\pi$
$108$	4.91907	0.473337
$109$	7.01073	0.671506	0.335753	−	0.941950i	$-0.391009\pi$
$109$	7.01073	0.671506	0.335753	+	0.941950i	$0.391009\pi$
$110$	−13.3290	−1.27087
$111$	11.0375	1.04763
$112$	13.8598	1.30963
$113$	1.21639	0.114428	0.0572141	−	0.998362i	$-0.481778\pi$
$113$	1.21639	0.114428	0.0572141	+	0.998362i	$0.481778\pi$
$114$	3.28239	0.307424
$115$	28.2342	2.63285
$116$	−15.0800	−1.40014
$117$	−4.52573	−0.418404
$118$	12.8430	1.18230
$119$	−1.00631	−0.0922486
$120$	−28.1651	−2.57111
$121$	−9.09165	−0.826513
$122$	34.6307	3.13532
$123$	9.45678	0.852689
$124$	−29.9491	−2.68951
$125$	−12.6737	−1.13357
$126$	3.51933	0.313527
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	3.99996	0.353550
$129$	2.44720	0.215464
$130$	43.6673	3.82987
$131$	−20.6161	−1.80123	−0.900617	−	0.434614i	$-0.856885\pi$
$131$	−20.6161	−1.80123	−0.900617	+	0.434614i	$0.856885\pi$
$132$	6.79535	0.591459
$133$	1.66956	0.144770
$134$	9.61126	0.830287
$135$	−3.66812	−0.315701
$136$	−5.77517	−0.495217
$137$	−14.6257	−1.24956	−0.624778	−	0.780802i	$-0.714811\pi$
$137$	−14.6257	−1.24956	−0.624778	+	0.780802i	$0.714811\pi$
$138$	−20.2468	−1.72352
$139$	1.45860	0.123717	0.0618586	−	0.998085i	$-0.480297\pi$
$139$	1.45860	0.123717	0.0618586	+	0.998085i	$0.480297\pi$
$140$	−24.1414	−2.04032
$141$	−12.0044	−1.01095
$142$	32.5415	2.73082
$143$	−6.25199	−0.522818
$144$	10.3591	0.863256
$145$	11.2450	0.933850
$146$	10.0017	0.827748
$147$	−5.20992	−0.429707
$148$	54.2940	4.46294
$149$	2.53291	0.207504	0.103752	−	0.994603i	$-0.466915\pi$
$149$	2.53291	0.207504	0.103752	+	0.994603i	$0.466915\pi$
$150$	22.2404	1.81592
$151$	−5.67936	−0.462180	−0.231090	−	0.972932i	$-0.574229\pi$
$151$	−5.67936	−0.462180	−0.231090	+	0.972932i	$0.574229\pi$
$152$	9.58152	0.777164
$153$	−0.752137	−0.0608067
$154$	4.86171	0.391768
$155$	22.3329	1.79382
$156$	−22.2624	−1.78242
$157$	4.85802	0.387712	0.193856	−	0.981030i	$-0.437901\pi$
$157$	4.85802	0.387712	0.193856	+	0.981030i	$0.437901\pi$
$158$	29.8272	2.37292
$159$	−10.7628	−0.853545
$160$	−43.6210	−3.44854
$161$	−10.2984	−0.811624
$162$	2.63041	0.206665
$163$	−21.7174	−1.70104	−0.850521	−	0.525941i	$-0.823713\pi$
$163$	−21.7174	−1.70104	−0.850521	+	0.525941i	$0.823713\pi$
$164$	46.5185	3.63249
$165$	−5.06725	−0.394485
$166$	27.5039	2.13471
$167$	0.243613	0.0188514	0.00942569	−	0.999956i	$-0.497000\pi$
$167$	0.243613	0.0188514	0.00942569	+	0.999956i	$0.497000\pi$
$168$	10.2732	0.792591
$169$	7.48228	0.575560
$170$	7.25712	0.556596
$171$	1.24786	0.0954264
$172$	12.0379	0.917885
$173$	−12.3947	−0.942352	−0.471176	−	0.882039i	$-0.656170\pi$
$173$	−12.3947	−0.942352	−0.471176	+	0.882039i	$0.656170\pi$
$174$	−8.06383	−0.611318
$175$	11.3124	0.855136
$176$	14.3103	1.07868
$177$	4.88252	0.366993
$178$	−30.8017	−2.30869
$179$	24.6260	1.84063	0.920316	−	0.391176i	$-0.127932\pi$
$179$	24.6260	1.84063	0.920316	+	0.391176i	$0.127932\pi$
$180$	−18.0437	−1.34490
$181$	18.5294	1.37728	0.688638	−	0.725105i	$-0.258209\pi$
$181$	18.5294	1.37728	0.688638	+	0.725105i	$0.258209\pi$
$182$	−15.9276	−1.18063
$183$	13.1655	0.973222
$184$	−59.1016	−4.35703
$185$	−40.4867	−2.97664
$186$	−16.0149	−1.17427
$187$	−1.03903	−0.0759811
$188$	−59.0503	−4.30669
$189$	1.33794	0.0973207
$190$	−12.0402	−0.873488
$191$	−9.42328	−0.681844	−0.340922	−	0.940092i	$-0.610739\pi$
$191$	−9.42328	−0.681844	−0.340922	+	0.940092i	$0.610739\pi$
$192$	10.5625	0.762286
$193$	−10.2111	−0.735012	−0.367506	−	0.930021i	$-0.619788\pi$
$193$	−10.2111	−0.735012	−0.367506	+	0.930021i	$0.619788\pi$
$194$	6.57918	0.472357
$195$	16.6009	1.18882
$196$	−25.6279	−1.83057
$197$	14.6155	1.04131	0.520656	−	0.853766i	$-0.325687\pi$
$197$	14.6155	1.04131	0.520656	+	0.853766i	$0.325687\pi$
$198$	3.63373	0.258238
$199$	1.64827	0.116843	0.0584215	−	0.998292i	$-0.481393\pi$
$199$	1.64827	0.116843	0.0584215	+	0.998292i	$0.481393\pi$
$200$	64.9211	4.59061
$201$	3.65390	0.257726
$202$	29.0699	2.04535
$203$	−4.10161	−0.287876
$204$	−3.69981	−0.259039
$205$	−34.6886	−2.42276
$206$	−20.3179	−1.41561
$207$	−7.69718	−0.534991
$208$	−46.8824	−3.25071
$209$	1.72384	0.119240
$210$	−12.9093	−0.890827
$211$	−12.3908	−0.853020	−0.426510	−	0.904483i	$-0.640257\pi$
$211$	−12.3908	−0.853020	−0.426510	+	0.904483i	$0.640257\pi$
$212$	−52.9429	−3.63613
$213$	12.3713	0.847665
$214$	13.1456	0.898618
$215$	−8.97663	−0.612201
$216$	7.67834	0.522445
$217$	−8.14587	−0.552978
$218$	18.4411	1.24899
$219$	3.80234	0.256938
$220$	−24.9261	−1.68052
$221$	3.40397	0.228976
$222$	29.0331	1.94857
$223$	0.220333	0.0147546	0.00737729	−	0.999973i	$-0.497652\pi$
$223$	0.220333	0.0147546	0.00737729	+	0.999973i	$0.497652\pi$
$224$	15.9107	1.06308
$225$	8.45509	0.563673
$226$	3.19960	0.212834
$227$	20.9448	1.39015	0.695077	−	0.718935i	$-0.255370\pi$
$227$	20.9448	1.39015	0.695077	+	0.718935i	$0.255370\pi$
$228$	6.13832	0.406520
$229$	−1.65368	−0.109278	−0.0546390	−	0.998506i	$-0.517401\pi$
$229$	−1.65368	−0.109278	−0.0546390	+	0.998506i	$0.517401\pi$
$230$	74.2675	4.89705
$231$	1.84827	0.121607
$232$	−23.5389	−1.54540
$233$	6.28169	0.411527	0.205764	−	0.978602i	$-0.434032\pi$
$233$	6.28169	0.411527	0.205764	+	0.978602i	$0.434032\pi$
$234$	−11.9045	−0.778224
$235$	44.0335	2.87243
$236$	24.0174	1.56340
$237$	11.3394	0.736570
$238$	−2.64702	−0.171581
$239$	5.20375	0.336603	0.168301	−	0.985736i	$-0.446172\pi$
$239$	5.20375	0.336603	0.168301	+	0.985736i	$0.446172\pi$
$240$	−37.9983	−2.45278
$241$	−7.16736	−0.461690	−0.230845	−	0.972991i	$-0.574149\pi$
$241$	−7.16736	−0.461690	−0.230845	+	0.972991i	$0.574149\pi$
$242$	−23.9148	−1.53730
$243$	1.00000	0.0641500
$244$	64.7620	4.14596
$245$	19.1106	1.22093
$246$	24.8752	1.58599
$247$	−5.64750	−0.359342
$248$	−46.7486	−2.96854
$249$	10.4561	0.662629
$250$	−33.3370	−2.10842
$251$	−7.56405	−0.477439	−0.238719	−	0.971089i	$-0.576728\pi$
$251$	−7.56405	−0.477439	−0.238719	+	0.971089i	$0.576728\pi$
$252$	6.58141	0.414590
$253$	−10.6331	−0.668499
$254$	−2.63041	−0.165047
$255$	2.75893	0.172771
$256$	−10.6035	−0.662721
$257$	1.11895	0.0697983	0.0348992	−	0.999391i	$-0.488889\pi$
$257$	1.11895	0.0697983	0.0348992	+	0.999391i	$0.488889\pi$
$258$	6.43715	0.400759
$259$	14.7675	0.917605
$260$	81.6610	5.06440
$261$	−3.06562	−0.189757
$262$	−54.2287	−3.35026
$263$	10.2466	0.631833	0.315917	−	0.948787i	$-0.397688\pi$
$263$	10.2466	0.631833	0.315917	+	0.948787i	$0.397688\pi$
$264$	10.6071	0.652822
$265$	39.4792	2.42519
$266$	4.39164	0.269269
$267$	−11.7099	−0.716631
$268$	17.9738	1.09792
$269$	−12.2123	−0.744600	−0.372300	−	0.928112i	$-0.621431\pi$
$269$	−12.2123	−0.744600	−0.372300	+	0.928112i	$0.621431\pi$
$270$	−9.64866	−0.587199
$271$	6.64444	0.403621	0.201811	−	0.979425i	$-0.435317\pi$
$271$	6.64444	0.403621	0.201811	+	0.979425i	$0.435317\pi$
$272$	−7.79144	−0.472426
$273$	−6.05516	−0.366475
$274$	−38.4716	−2.32415
$275$	11.6801	0.704338
$276$	−37.8629	−2.27908
$277$	8.74452	0.525407	0.262704	−	0.964877i	$-0.415386\pi$
$277$	8.74452	0.525407	0.262704	+	0.964877i	$0.415386\pi$
$278$	3.83673	0.230112
$279$	−6.08837	−0.364501
$280$	−37.6831	−2.25200
$281$	−24.5276	−1.46319	−0.731596	−	0.681739i	$-0.761224\pi$
$281$	−24.5276	−1.46319	−0.731596	+	0.681739i	$0.761224\pi$
$282$	−31.5765	−1.88035
$283$	3.74992	0.222909	0.111455	−	0.993770i	$-0.464449\pi$
$283$	3.74992	0.222909	0.111455	+	0.993770i	$0.464449\pi$
$284$	60.8550	3.61108
$285$	−4.57731	−0.271136
$286$	−16.4453	−0.972431
$287$	12.6526	0.746859
$288$	11.8919	0.700739
$289$	−16.4343	−0.966723
$290$	29.5791	1.73694
$291$	2.50120	0.146623
$292$	18.7040	1.09457
$293$	−20.2355	−1.18217	−0.591085	−	0.806609i	$-0.701300\pi$
$293$	−20.2355	−1.18217	−0.591085	+	0.806609i	$0.701300\pi$
$294$	−13.7042	−0.799247
$295$	−17.9097	−1.04274
$296$	84.7495	4.92596
$297$	1.38143	0.0801588
$298$	6.66259	0.385953
$299$	34.8354	2.01458
$300$	41.5911	2.40126
$301$	3.27421	0.188722
$302$	−14.9391	−0.859646
$303$	11.0515	0.634890
$304$	12.9267	0.741397
$305$	−48.2926	−2.76523
$306$	−1.97843	−0.113099
$307$	−15.7665	−0.899840	−0.449920	−	0.893069i	$-0.648548\pi$
$307$	−15.7665	−0.899840	−0.449920	+	0.893069i	$0.648548\pi$
$308$	9.09176	0.518051
$309$	−7.72423	−0.439416
$310$	58.7446	3.33647
$311$	3.12563	0.177238	0.0886191	−	0.996066i	$-0.471755\pi$
$311$	3.12563	0.177238	0.0886191	+	0.996066i	$0.471755\pi$
$312$	−34.7501	−1.96734
$313$	14.6877	0.830196	0.415098	−	0.909777i	$-0.363747\pi$
$313$	14.6877	0.830196	0.415098	+	0.909777i	$0.363747\pi$
$314$	12.7786	0.721137
$315$	−4.90772	−0.276519
$316$	55.7790	3.13782
$317$	−24.1867	−1.35846	−0.679230	−	0.733926i	$-0.737686\pi$
$317$	−24.1867	−1.35846	−0.679230	+	0.733926i	$0.737686\pi$
$318$	−28.3106	−1.58758
$319$	−4.23494	−0.237111
$320$	−38.7446	−2.16589
$321$	4.99756	0.278937
$322$	−27.0889	−1.50961
$323$	−0.938564	−0.0522231
$324$	4.91907	0.273281
$325$	−38.2655	−2.12259
$326$	−57.1258	−3.16391
$327$	7.01073	0.387694
$328$	72.6124	4.00935
$329$	−16.0611	−0.885479
$330$	−13.3290	−0.733735
$331$	−3.12592	−0.171816	−0.0859082	−	0.996303i	$-0.527379\pi$
$331$	−3.12592	−0.171816	−0.0859082	+	0.996303i	$0.527379\pi$
$332$	51.4343	2.82282
$333$	11.0375	0.604850
$334$	0.640804	0.0350632
$335$	−13.4029	−0.732281
$336$	13.8598	0.756114
$337$	3.44056	0.187419	0.0937096	−	0.995600i	$-0.470127\pi$
$337$	3.44056	0.187419	0.0937096	+	0.995600i	$0.470127\pi$
$338$	19.6815	1.07053
$339$	1.21639	0.0660652
$340$	13.5713	0.736010
$341$	−8.41067	−0.455463
$342$	3.28239	0.177491
$343$	−16.3361	−0.882068
$344$	18.7905	1.01311
$345$	28.2342	1.52008
$346$	−32.6032	−1.75276
$347$	22.1420	1.18864	0.594322	−	0.804227i	$-0.297421\pi$
$347$	22.1420	1.18864	0.594322	+	0.804227i	$0.297421\pi$
$348$	−15.0800	−0.808371
$349$	17.8504	0.955510	0.477755	−	0.878493i	$-0.341451\pi$
$349$	17.8504	0.955510	0.477755	+	0.878493i	$0.341451\pi$
$350$	29.7562	1.59054
$351$	−4.52573	−0.241566
$352$	16.4279	0.875609
$353$	−13.1795	−0.701472	−0.350736	−	0.936474i	$-0.614068\pi$
$353$	−13.1795	−0.701472	−0.350736	+	0.936474i	$0.614068\pi$
$354$	12.8430	0.682600
$355$	−45.3792	−2.40848
$356$	−57.6015	−3.05288
$357$	−1.00631	−0.0532598
$358$	64.7764	3.42354
$359$	−3.81524	−0.201360	−0.100680	−	0.994919i	$-0.532102\pi$
$359$	−3.81524	−0.201360	−0.100680	+	0.994919i	$0.532102\pi$
$360$	−28.1651	−1.48443
$361$	−17.4428	−0.918044
$362$	48.7398	2.56171
$363$	−9.09165	−0.477188
$364$	−29.7857	−1.56120
$365$	−13.9474	−0.730042
$366$	34.6307	1.81018
$367$	4.56241	0.238156	0.119078	−	0.992885i	$-0.462006\pi$
$367$	4.56241	0.238156	0.119078	+	0.992885i	$0.462006\pi$
$368$	−79.7357	−4.15651
$369$	9.45678	0.492300
$370$	−106.497	−5.53650
$371$	−14.4000	−0.747609
$372$	−29.9491	−1.55279
$373$	−15.8147	−0.818853	−0.409426	−	0.912343i	$-0.634271\pi$
$373$	−15.8147	−0.818853	−0.409426	+	0.912343i	$0.634271\pi$
$374$	−2.73307	−0.141323
$375$	−12.6737	−0.654466
$376$	−92.1738	−4.75350
$377$	13.8742	0.714556
$378$	3.51933	0.181015
$379$	−11.1383	−0.572136	−0.286068	−	0.958209i	$-0.592348\pi$
$379$	−11.1383	−0.572136	−0.286068	+	0.958209i	$0.592348\pi$
$380$	−22.5161	−1.15505
$381$	−1.00000	−0.0512316
$382$	−24.7871	−1.26822
$383$	8.77266	0.448262	0.224131	−	0.974559i	$-0.428046\pi$
$383$	8.77266	0.448262	0.224131	+	0.974559i	$0.428046\pi$
$384$	3.99996	0.204122
$385$	−6.77967	−0.345524
$386$	−26.8594	−1.36711
$387$	2.44720	0.124398
$388$	12.3036	0.624618
$389$	22.7816	1.15507	0.577537	−	0.816365i	$-0.304014\pi$
$389$	22.7816	1.15507	0.577537	+	0.816365i	$0.304014\pi$
$390$	43.6673	2.21118
$391$	5.78934	0.292779
$392$	−40.0035	−2.02048
$393$	−20.6161	−1.03994
$394$	38.4448	1.93682
$395$	−41.5941	−2.09283
$396$	6.79535	0.341479
$397$	−20.4760	−1.02766	−0.513829	−	0.857892i	$-0.671774\pi$
$397$	−20.4760	−1.02766	−0.513829	+	0.857892i	$0.671774\pi$
$398$	4.33564	0.217326
$399$	1.66956	0.0835827
$400$	87.5869	4.37934
$401$	−26.2751	−1.31212	−0.656058	−	0.754710i	$-0.727778\pi$
$401$	−26.2751	−1.31212	−0.656058	+	0.754710i	$0.727778\pi$
$402$	9.61126	0.479366
$403$	27.5544	1.37258
$404$	54.3629	2.70466
$405$	−3.66812	−0.182270
$406$	−10.7889	−0.535445
$407$	15.2475	0.755791
$408$	−5.77517	−0.285913
$409$	−23.8373	−1.17868	−0.589340	−	0.807885i	$-0.700612\pi$
$409$	−23.8373	−1.17868	−0.589340	+	0.807885i	$0.700612\pi$
$410$	−91.2452	−4.50628
$411$	−14.6257	−0.721432
$412$	−37.9960	−1.87193
$413$	6.53252	0.321444
$414$	−20.2468	−0.995074
$415$	−38.3542	−1.88274
$416$	−53.8197	−2.63873
$417$	1.45860	0.0714282
$418$	4.53440	0.221785
$419$	26.5853	1.29878	0.649389	−	0.760457i	$-0.275025\pi$
$419$	26.5853	1.29878	0.649389	+	0.760457i	$0.275025\pi$
$420$	−24.1414	−1.17798
$421$	−33.6982	−1.64235	−0.821176	−	0.570675i	$-0.806682\pi$
$421$	−33.6982	−1.64235	−0.821176	+	0.570675i	$0.806682\pi$
$422$	−32.5930	−1.58660
$423$	−12.0044	−0.583673
$424$	−82.6405	−4.01338
$425$	−6.35939	−0.308476
$426$	32.5415	1.57664
$427$	17.6146	0.852432
$428$	24.5833	1.18828
$429$	−6.25199	−0.301849
$430$	−23.6122	−1.13868
$431$	10.1188	0.487407	0.243704	−	0.969850i	$-0.421638\pi$
$431$	10.1188	0.487407	0.243704	+	0.969850i	$0.421638\pi$
$432$	10.3591	0.498401
$433$	34.4830	1.65715	0.828575	−	0.559879i	$-0.189152\pi$
$433$	34.4830	1.65715	0.828575	+	0.559879i	$0.189152\pi$
$434$	−21.4270	−1.02853
$435$	11.2450	0.539158
$436$	34.4862	1.65159
$437$	−9.60503	−0.459471
$438$	10.0017	0.477901
$439$	32.7837	1.56468	0.782340	−	0.622851i	$-0.214026\pi$
$439$	32.7837	1.56468	0.782340	+	0.622851i	$0.214026\pi$
$440$	−38.9081	−1.85487
$441$	−5.20992	−0.248091
$442$	8.95385	0.425891
$443$	1.54458	0.0733850	0.0366925	−	0.999327i	$-0.488318\pi$
$443$	1.54458	0.0733850	0.0366925	+	0.999327i	$0.488318\pi$
$444$	54.2940	2.57668
$445$	42.9531	2.03617
$446$	0.579566	0.0274433
$447$	2.53291	0.119802
$448$	14.1320	0.667676
$449$	−17.5195	−0.826797	−0.413398	−	0.910550i	$-0.635658\pi$
$449$	−17.5195	−0.826797	−0.413398	+	0.910550i	$0.635658\pi$
$450$	22.2404	1.04842
$451$	13.0639	0.615155
$452$	5.98350	0.281440
$453$	−5.67936	−0.266840
$454$	55.0934	2.58566
$455$	22.2110	1.04127
$456$	9.58152	0.448696
$457$	−9.93294	−0.464643	−0.232322	−	0.972639i	$-0.574632\pi$
$457$	−9.93294	−0.464643	−0.232322	+	0.972639i	$0.574632\pi$
$458$	−4.34985	−0.203255
$459$	−0.752137	−0.0351068
$460$	138.886	6.47558
$461$	−1.84652	−0.0860011	−0.0430005	−	0.999075i	$-0.513692\pi$
$461$	−1.84652	−0.0860011	−0.0430005	+	0.999075i	$0.513692\pi$
$462$	4.86171	0.226187
$463$	14.9364	0.694151	0.347076	−	0.937837i	$-0.387175\pi$
$463$	14.9364	0.694151	0.347076	+	0.937837i	$0.387175\pi$
$464$	−31.7569	−1.47428
$465$	22.3329	1.03566
$466$	16.5234	0.765433
$467$	17.0829	0.790501	0.395250	−	0.918573i	$-0.370658\pi$
$467$	17.0829	0.790501	0.395250	+	0.918573i	$0.370658\pi$
$468$	−22.2624	−1.02908
$469$	4.88870	0.225739
$470$	115.826	5.34266
$471$	4.85802	0.223846
$472$	37.4897	1.72560
$473$	3.38064	0.155442
$474$	29.8272	1.37001
$475$	10.5508	0.484103
$476$	−4.95012	−0.226889
$477$	−10.7628	−0.492795
$478$	13.6880	0.626075
$479$	−28.3634	−1.29595	−0.647977	−	0.761659i	$-0.724385\pi$
$479$	−28.3634	−1.29595	−0.647977	+	0.761659i	$0.724385\pi$
$480$	−43.6210	−1.99102
$481$	−49.9527	−2.27765
$482$	−18.8531	−0.858735
$483$	−10.2984	−0.468592
$484$	−44.7224	−2.03284
$485$	−9.17469	−0.416601
$486$	2.63041	0.119318
$487$	−36.0777	−1.63484	−0.817419	−	0.576043i	$-0.804596\pi$
$487$	−36.0777	−1.63484	−0.817419	+	0.576043i	$0.804596\pi$
$488$	101.089	4.57610
$489$	−21.7174	−0.982097
$490$	50.2687	2.27091
$491$	27.4226	1.23756	0.618782	−	0.785563i	$-0.287627\pi$
$491$	27.4226	1.23756	0.618782	+	0.785563i	$0.287627\pi$
$492$	46.5185	2.09722
$493$	2.30576	0.103846
$494$	−14.8552	−0.668369
$495$	−5.06725	−0.227756
$496$	−63.0699	−2.83192
$497$	16.5520	0.742458
$498$	27.5039	1.23248
$499$	12.1417	0.543536	0.271768	−	0.962363i	$-0.412392\pi$
$499$	12.1417	0.543536	0.271768	+	0.962363i	$0.412392\pi$
$500$	−62.3426	−2.78805
$501$	0.243613	0.0108838
$502$	−19.8966	−0.888027
$503$	−32.4848	−1.44842	−0.724212	−	0.689577i	$-0.757796\pi$
$503$	−32.4848	−1.44842	−0.724212	+	0.689577i	$0.757796\pi$
$504$	10.2732	0.457603
$505$	−40.5381	−1.80392
$506$	−27.9695	−1.24340
$507$	7.48228	0.332300
$508$	−4.91907	−0.218248
$509$	12.7456	0.564937	0.282468	−	0.959277i	$-0.408847\pi$
$509$	12.7456	0.564937	0.282468	+	0.959277i	$0.408847\pi$
$510$	7.25712	0.321351
$511$	5.08730	0.225049
$512$	−35.8916	−1.58620
$513$	1.24786	0.0550945
$514$	2.94331	0.129824
$515$	28.3334	1.24852
$516$	12.0379	0.529941
$517$	−16.5832	−0.729329
$518$	38.8445	1.70673
$519$	−12.3947	−0.544067
$520$	127.468	5.58982
$521$	24.5222	1.07434	0.537169	−	0.843475i	$-0.319494\pi$
$521$	24.5222	1.07434	0.537169	+	0.843475i	$0.319494\pi$
$522$	−8.06383	−0.352944
$523$	−10.3012	−0.450439	−0.225219	−	0.974308i	$-0.572310\pi$
$523$	−10.3012	−0.450439	−0.225219	+	0.974308i	$0.572310\pi$
$524$	−101.412	−4.43019
$525$	11.3124	0.493713
$526$	26.9528	1.17520
$527$	4.57929	0.199477
$528$	14.3103	0.622778
$529$	36.2466	1.57594
$530$	103.847	4.51081
$531$	4.88252	0.211883
$532$	8.21269	0.356065
$533$	−42.7989	−1.85383
$534$	−30.8017	−1.33292
$535$	−18.3316	−0.792546
$536$	28.0559	1.21183
$537$	24.6260	1.06269
$538$	−32.1235	−1.38494
$539$	−7.19715	−0.310003
$540$	−18.0437	−0.776478
$541$	2.34002	0.100606	0.0503028	−	0.998734i	$-0.483981\pi$
$541$	2.34002	0.100606	0.0503028	+	0.998734i	$0.483981\pi$
$542$	17.4776	0.750728
$543$	18.5294	0.795171
$544$	−8.94437	−0.383487
$545$	−25.7162	−1.10156
$546$	−15.9276	−0.681636
$547$	−24.4579	−1.04575	−0.522873	−	0.852411i	$-0.675140\pi$
$547$	−24.4579	−1.04575	−0.522873	+	0.852411i	$0.675140\pi$
$548$	−71.9447	−3.07333
$549$	13.1655	0.561890
$550$	30.7235	1.31006
$551$	−3.82547	−0.162970
$552$	−59.1016	−2.51553
$553$	15.1714	0.645152
$554$	23.0017	0.977248
$555$	−40.4867	−1.71857
$556$	7.17497	0.304287
$557$	13.2343	0.560754	0.280377	−	0.959890i	$-0.409541\pi$
$557$	13.2343	0.560754	0.280377	+	0.959890i	$0.409541\pi$
$558$	−16.0149	−0.677966
$559$	−11.0754	−0.468439
$560$	−50.8394	−2.14836
$561$	−1.03903	−0.0438677
$562$	−64.5176	−2.72151
$563$	−13.9558	−0.588166	−0.294083	−	0.955780i	$-0.595014\pi$
$563$	−13.9558	−0.588166	−0.294083	+	0.955780i	$0.595014\pi$
$564$	−59.0503	−2.48647
$565$	−4.46186	−0.187712
$566$	9.86382	0.414607
$567$	1.33794	0.0561881
$568$	94.9908	3.98572
$569$	29.6212	1.24179	0.620893	−	0.783896i	$-0.286770\pi$
$569$	29.6212	1.24179	0.620893	+	0.783896i	$0.286770\pi$
$570$	−12.0402	−0.504309
$571$	0.524483	0.0219489	0.0109745	−	0.999940i	$-0.496507\pi$
$571$	0.524483	0.0219489	0.0109745	+	0.999940i	$0.496507\pi$
$572$	−30.7539	−1.28589
$573$	−9.42328	−0.393663
$574$	33.2815	1.38914
$575$	−65.0804	−2.71404
$576$	10.5625	0.440106
$577$	28.8344	1.20039	0.600196	−	0.799853i	$-0.295089\pi$
$577$	28.8344	1.20039	0.600196	+	0.799853i	$0.295089\pi$
$578$	−43.2289	−1.79809
$579$	−10.2111	−0.424360
$580$	55.3151	2.29683
$581$	13.9896	0.580388
$582$	6.57918	0.272716
$583$	−14.8681	−0.615772
$584$	29.1957	1.20813
$585$	16.6009	0.686364
$586$	−53.2277	−2.19882
$587$	12.0644	0.497952	0.248976	−	0.968510i	$-0.419906\pi$
$587$	12.0644	0.497952	0.248976	+	0.968510i	$0.419906\pi$
$588$	−25.6279	−1.05688
$589$	−7.59745	−0.313048
$590$	−47.1098	−1.93948
$591$	14.6155	0.601202
$592$	114.338	4.69926
$593$	37.0703	1.52230	0.761148	−	0.648578i	$-0.224636\pi$
$593$	37.0703	1.52230	0.761148	+	0.648578i	$0.224636\pi$
$594$	3.63373	0.149094
$595$	3.69128	0.151328
$596$	12.4595	0.510362
$597$	1.64827	0.0674594
$598$	91.6315	3.74709
$599$	15.0410	0.614560	0.307280	−	0.951619i	$-0.400581\pi$
$599$	15.0410	0.614560	0.307280	+	0.951619i	$0.400581\pi$
$600$	64.9211	2.65039
$601$	−19.5815	−0.798747	−0.399374	−	0.916788i	$-0.630772\pi$
$601$	−19.5815	−0.798747	−0.399374	+	0.916788i	$0.630772\pi$
$602$	8.61251	0.351020
$603$	3.65390	0.148798
$604$	−27.9372	−1.13675
$605$	33.3492	1.35584
$606$	29.0699	1.18088
$607$	16.3630	0.664152	0.332076	−	0.943253i	$-0.392251\pi$
$607$	16.3630	0.664152	0.332076	+	0.943253i	$0.392251\pi$
$608$	14.8395	0.601821
$609$	−4.10161	−0.166205
$610$	−127.029	−5.14327
$611$	54.3287	2.19790
$612$	−3.69981	−0.149556
$613$	36.0917	1.45773	0.728866	−	0.684657i	$-0.240048\pi$
$613$	36.0917	1.45773	0.728866	+	0.684657i	$0.240048\pi$
$614$	−41.4723	−1.67369
$615$	−34.6886	−1.39878
$616$	14.1917	0.571798
$617$	34.1824	1.37613	0.688066	−	0.725648i	$-0.258460\pi$
$617$	34.1824	1.37613	0.688066	+	0.725648i	$0.258460\pi$
$618$	−20.3179	−0.817306
$619$	−31.5552	−1.26831	−0.634156	−	0.773205i	$-0.718652\pi$
$619$	−31.5552	−1.26831	−0.634156	+	0.773205i	$0.718652\pi$
$620$	109.857	4.41196
$621$	−7.69718	−0.308877
$622$	8.22169	0.329660
$623$	−15.6671	−0.627688
$624$	−46.8824	−1.87680
$625$	4.21308	0.168523
$626$	38.6346	1.54415
$627$	1.72384	0.0688434
$628$	23.8969	0.953590
$629$	−8.30169	−0.331010
$630$	−12.9093	−0.514319
$631$	3.43133	0.136599	0.0682996	−	0.997665i	$-0.478243\pi$
$631$	3.43133	0.136599	0.0682996	+	0.997665i	$0.478243\pi$
$632$	87.0675	3.46336
$633$	−12.3908	−0.492491
$634$	−63.6209	−2.52671
$635$	3.66812	0.145565
$636$	−52.9429	−2.09932
$637$	23.5787	0.934223
$638$	−11.1396	−0.441022
$639$	12.3713	0.489400
$640$	−14.6723	−0.579975
$641$	16.9053	0.667721	0.333861	−	0.942622i	$-0.391649\pi$
$641$	16.9053	0.667721	0.333861	+	0.942622i	$0.391649\pi$
$642$	13.1456	0.518817
$643$	16.5912	0.654292	0.327146	−	0.944974i	$-0.393913\pi$
$643$	16.5912	0.654292	0.327146	+	0.944974i	$0.393913\pi$
$644$	−50.6583	−1.99622
$645$	−8.97663	−0.353454
$646$	−2.46881	−0.0971340
$647$	−8.77451	−0.344961	−0.172481	−	0.985013i	$-0.555178\pi$
$647$	−8.77451	−0.344961	−0.172481	+	0.985013i	$0.555178\pi$
$648$	7.67834	0.301634
$649$	6.74487	0.264759
$650$	−100.654	−3.94797
$651$	−8.14587	−0.319262
$652$	−106.830	−4.18377
$653$	37.2018	1.45582	0.727909	−	0.685674i	$-0.240492\pi$
$653$	37.2018	1.45582	0.727909	+	0.685674i	$0.240492\pi$
$654$	18.4411	0.721104
$655$	75.6221	2.95480
$656$	97.9635	3.82483
$657$	3.80234	0.148343
$658$	−42.2474	−1.64697
$659$	4.04437	0.157546	0.0787731	−	0.996893i	$-0.474900\pi$
$659$	4.04437	0.157546	0.0787731	+	0.996893i	$0.474900\pi$
$660$	−24.9261	−0.970249
$661$	−36.0863	−1.40359	−0.701797	−	0.712377i	$-0.747619\pi$
$661$	−36.0863	−1.40359	−0.701797	+	0.712377i	$0.747619\pi$
$662$	−8.22247	−0.319575
$663$	3.40397	0.132199
$664$	80.2856	3.11569
$665$	−6.12416	−0.237485
$666$	29.0331	1.12501
$667$	23.5966	0.913664
$668$	1.19835	0.0463656
$669$	0.220333	0.00851856
$670$	−35.2552	−1.36203
$671$	18.1872	0.702111
$672$	15.9107	0.613768
$673$	−19.7896	−0.762834	−0.381417	−	0.924403i	$-0.624564\pi$
$673$	−19.7896	−0.762834	−0.381417	+	0.924403i	$0.624564\pi$
$674$	9.05009	0.348596
$675$	8.45509	0.325436
$676$	36.8058	1.41561
$677$	−39.9558	−1.53563	−0.767814	−	0.640673i	$-0.778655\pi$
$677$	−39.9558	−1.53563	−0.767814	+	0.640673i	$0.778655\pi$
$678$	3.19960	0.122880
$679$	3.34645	0.128425
$680$	21.1840	0.812369
$681$	20.9448	0.802606
$682$	−22.1235	−0.847153
$683$	−47.4373	−1.81514	−0.907569	−	0.419903i	$-0.862064\pi$
$683$	−47.4373	−1.81514	−0.907569	+	0.419903i	$0.862064\pi$
$684$	6.13832	0.234704
$685$	53.6487	2.04981
$686$	−42.9707	−1.64063
$687$	−1.65368	−0.0630917
$688$	25.3507	0.966488
$689$	48.7096	1.85569
$690$	74.2675	2.82732
$691$	−43.7086	−1.66275	−0.831376	−	0.555710i	$-0.812447\pi$
$691$	−43.7086	−1.66275	−0.831376	+	0.555710i	$0.812447\pi$
$692$	−60.9704	−2.31775
$693$	1.84827	0.0702100
$694$	58.2425	2.21085
$695$	−5.35033	−0.202950
$696$	−23.5389	−0.892238
$697$	−7.11280	−0.269416
$698$	46.9539	1.77723
$699$	6.28169	0.237595
$700$	55.6464	2.10324
$701$	−15.0798	−0.569555	−0.284778	−	0.958594i	$-0.591920\pi$
$701$	−15.0798	−0.569555	−0.284778	+	0.958594i	$0.591920\pi$
$702$	−11.9045	−0.449308
$703$	13.7732	0.519468
$704$	14.5914	0.549935
$705$	44.0335	1.65840
$706$	−34.6674	−1.30472
$707$	14.7862	0.556092
$708$	24.0174	0.902631
$709$	−27.4302	−1.03016	−0.515081	−	0.857141i	$-0.672238\pi$
$709$	−27.4302	−1.03016	−0.515081	+	0.857141i	$0.672238\pi$
$710$	−119.366	−4.47973
$711$	11.3394	0.425259
$712$	−89.9123	−3.36960
$713$	46.8633	1.75505
$714$	−2.64702	−0.0990622
$715$	22.9330	0.857647
$716$	121.137	4.52709
$717$	5.20375	0.194338
$718$	−10.0356	−0.374527
$719$	−1.14733	−0.0427883	−0.0213941	−	0.999771i	$-0.506810\pi$
$719$	−1.14733	−0.0427883	−0.0213941	+	0.999771i	$0.506810\pi$
$720$	−37.9983	−1.41611
$721$	−10.3345	−0.384878
$722$	−45.8818	−1.70755
$723$	−7.16736	−0.266557
$724$	91.1471	3.38745
$725$	−25.9201	−0.962647
$726$	−23.9148	−0.887561
$727$	−38.2066	−1.41701	−0.708503	−	0.705708i	$-0.750629\pi$
$727$	−38.2066	−1.41701	−0.708503	+	0.705708i	$0.750629\pi$
$728$	−46.4936	−1.72317
$729$	1.00000	0.0370370
$730$	−36.6875	−1.35786
$731$	−1.84063	−0.0680782
$732$	64.7620	2.39367
$733$	47.8758	1.76833	0.884167	−	0.467171i	$-0.154727\pi$
$733$	47.8758	1.76833	0.884167	+	0.467171i	$0.154727\pi$
$734$	12.0010	0.442966
$735$	19.1106	0.704905
$736$	−91.5344	−3.37400
$737$	5.04761	0.185931
$738$	24.8752	0.915670
$739$	5.84125	0.214874	0.107437	−	0.994212i	$-0.465736\pi$
$739$	5.84125	0.214874	0.107437	+	0.994212i	$0.465736\pi$
$740$	−199.157	−7.32115
$741$	−5.64750	−0.207466
$742$	−37.8778	−1.39054
$743$	42.4023	1.55559	0.777796	−	0.628517i	$-0.216338\pi$
$743$	42.4023	1.55559	0.777796	+	0.628517i	$0.216338\pi$
$744$	−46.7486	−1.71389
$745$	−9.29100	−0.340396
$746$	−41.5991	−1.52305
$747$	10.4561	0.382569
$748$	−5.11104	−0.186878
$749$	6.68643	0.244317
$750$	−33.3370	−1.21729
$751$	24.5064	0.894252	0.447126	−	0.894471i	$-0.352447\pi$
$751$	24.5064	0.894252	0.447126	+	0.894471i	$0.352447\pi$
$752$	−124.354	−4.53473
$753$	−7.56405	−0.275649
$754$	36.4948	1.32906
$755$	20.8326	0.758175
$756$	6.58141	0.239363
$757$	−26.7598	−0.972600	−0.486300	−	0.873792i	$-0.661654\pi$
$757$	−26.7598	−0.972600	−0.486300	+	0.873792i	$0.661654\pi$
$758$	−29.2983	−1.06416
$759$	−10.6331	−0.385958
$760$	−35.1461	−1.27488
$761$	38.4739	1.39468	0.697339	−	0.716742i	$-0.254367\pi$
$761$	38.4739	1.39468	0.697339	+	0.716742i	$0.254367\pi$
$762$	−2.63041	−0.0952898
$763$	9.37993	0.339576
$764$	−46.3537	−1.67702
$765$	2.75893	0.0997493
$766$	23.0757	0.833759
$767$	−22.0970	−0.797876
$768$	−10.6035	−0.382622
$769$	14.6657	0.528858	0.264429	−	0.964405i	$-0.414817\pi$
$769$	14.6657	0.528858	0.264429	+	0.964405i	$0.414817\pi$
$770$	−17.8333	−0.642669
$771$	1.11895	0.0402981
$772$	−50.2292	−1.80779
$773$	−19.3561	−0.696191	−0.348095	−	0.937459i	$-0.613172\pi$
$773$	−19.3561	−0.696191	−0.348095	+	0.937459i	$0.613172\pi$
$774$	6.43715	0.231379
$775$	−51.4777	−1.84913
$776$	19.2050	0.689421
$777$	14.7675	0.529780
$778$	59.9250	2.14842
$779$	11.8008	0.422806
$780$	81.6610	2.92393
$781$	17.0900	0.611530
$782$	15.2283	0.544564
$783$	−3.06562	−0.109556
$784$	−53.9699	−1.92750
$785$	−17.8198	−0.636015
$786$	−54.2287	−1.93427
$787$	−11.3979	−0.406291	−0.203146	−	0.979149i	$-0.565117\pi$
$787$	−11.3979	−0.406291	−0.203146	+	0.979149i	$0.565117\pi$
$788$	71.8947	2.56114
$789$	10.2466	0.364789
$790$	−109.410	−3.89262
$791$	1.62745	0.0578656
$792$	10.6071	0.376907
$793$	−59.5836	−2.11588
$794$	−53.8602	−1.91143
$795$	39.4792	1.40018
$796$	8.10797	0.287379
$797$	−7.69745	−0.272658	−0.136329	−	0.990664i	$-0.543530\pi$
$797$	−7.69745	−0.272658	−0.136329	+	0.990664i	$0.543530\pi$
$798$	4.39164	0.155462
$799$	9.02894	0.319421
$800$	100.547	3.55489
$801$	−11.7099	−0.413747
$802$	−69.1144	−2.44051
$803$	5.25267	0.185363
$804$	17.9738	0.633886
$805$	37.7756	1.33141
$806$	72.4793	2.55297
$807$	−12.2123	−0.429895
$808$	84.8570	2.98526
$809$	36.1970	1.27262	0.636309	−	0.771434i	$-0.280460\pi$
$809$	36.1970	1.27262	0.636309	+	0.771434i	$0.280460\pi$
$810$	−9.64866	−0.339019
$811$	28.1126	0.987168	0.493584	−	0.869698i	$-0.335687\pi$
$811$	28.1126	0.987168	0.493584	+	0.869698i	$0.335687\pi$
$812$	−20.1761	−0.708041
$813$	6.64444	0.233031
$814$	40.1072	1.40576
$815$	79.6622	2.79044
$816$	−7.79144	−0.272755
$817$	3.05377	0.106838
$818$	−62.7020	−2.19233
$819$	−6.05516	−0.211584
$820$	−170.635	−5.95885
$821$	−11.6835	−0.407757	−0.203879	−	0.978996i	$-0.565355\pi$
$821$	−11.6835	−0.407757	−0.203879	+	0.978996i	$0.565355\pi$
$822$	−38.4716	−1.34185
$823$	3.02177	0.105332	0.0526661	−	0.998612i	$-0.483228\pi$
$823$	3.02177	0.105332	0.0526661	+	0.998612i	$0.483228\pi$
$824$	−59.3093	−2.06614
$825$	11.6801	0.406650
$826$	17.1832	0.597880
$827$	9.34432	0.324934	0.162467	−	0.986714i	$-0.448055\pi$
$827$	9.34432	0.324934	0.162467	+	0.986714i	$0.448055\pi$
$828$	−37.8629	−1.31583
$829$	−7.45902	−0.259062	−0.129531	−	0.991575i	$-0.541347\pi$
$829$	−7.45902	−0.259062	−0.129531	+	0.991575i	$0.541347\pi$
$830$	−100.887	−3.50185
$831$	8.74452	0.303344
$832$	−47.8033	−1.65728
$833$	3.91858	0.135771
$834$	3.83673	0.132855
$835$	−0.893603	−0.0309244
$836$	8.47966	0.293275
$837$	−6.08837	−0.210445
$838$	69.9303	2.41570
$839$	20.2000	0.697382	0.348691	−	0.937238i	$-0.386626\pi$
$839$	20.2000	0.697382	0.348691	+	0.937238i	$0.386626\pi$
$840$	−37.6831	−1.30019
$841$	−19.6020	−0.675931
$842$	−88.6403	−3.05475
$843$	−24.5276	−0.844774
$844$	−60.9513	−2.09803
$845$	−27.4459	−0.944167
$846$	−31.5765	−1.08562
$847$	−12.1641	−0.417962
$848$	−111.493	−3.82867
$849$	3.74992	0.128697
$850$	−16.7278	−0.573759
$851$	−84.9574	−2.91230
$852$	60.8550	2.08486
$853$	−30.3153	−1.03797	−0.518987	−	0.854782i	$-0.673691\pi$
$853$	−30.3153	−1.03797	−0.518987	+	0.854782i	$0.673691\pi$
$854$	46.3338	1.58551
$855$	−4.57731	−0.156541
$856$	38.3730	1.31156
$857$	5.96282	0.203686	0.101843	−	0.994800i	$-0.467526\pi$
$857$	5.96282	0.203686	0.101843	+	0.994800i	$0.467526\pi$
$858$	−16.4453	−0.561434
$859$	15.6304	0.533304	0.266652	−	0.963793i	$-0.414083\pi$
$859$	15.6304	0.533304	0.266652	+	0.963793i	$0.414083\pi$
$860$	−44.1566	−1.50573
$861$	12.6526	0.431199
$862$	26.6167	0.906569
$863$	−22.4550	−0.764378	−0.382189	−	0.924084i	$-0.624830\pi$
$863$	−22.4550	−0.764378	−0.382189	+	0.924084i	$0.624830\pi$
$864$	11.8919	0.404572
$865$	45.4653	1.54586
$866$	90.7046	3.08227
$867$	−16.4343	−0.558138
$868$	−40.0701	−1.36007
$869$	15.6645	0.531383
$870$	29.5791	1.00282
$871$	−16.5366	−0.560321
$872$	53.8308	1.82294
$873$	2.50120	0.0846527
$874$	−25.2652	−0.854607
$875$	−16.9566	−0.573238
$876$	18.7040	0.631948
$877$	20.9196	0.706405	0.353202	−	0.935547i	$-0.385093\pi$
$877$	20.9196	0.706405	0.353202	+	0.935547i	$0.385093\pi$
$878$	86.2346	2.91028
$879$	−20.2355	−0.682527
$880$	−52.4920	−1.76951
$881$	−6.80598	−0.229299	−0.114650	−	0.993406i	$-0.536575\pi$
$881$	−6.80598	−0.229299	−0.114650	+	0.993406i	$0.536575\pi$
$882$	−13.7042	−0.461446
$883$	−9.21708	−0.310179	−0.155090	−	0.987900i	$-0.549567\pi$
$883$	−9.21708	−0.310179	−0.155090	+	0.987900i	$0.549567\pi$
$884$	16.7444	0.563174
$885$	−17.9097	−0.602027
$886$	4.06287	0.136495
$887$	50.3315	1.68997	0.844983	−	0.534793i	$-0.179610\pi$
$887$	50.3315	1.68997	0.844983	+	0.534793i	$0.179610\pi$
$888$	84.7495	2.84401
$889$	−1.33794	−0.0448730
$890$	112.984	3.78725
$891$	1.38143	0.0462797
$892$	1.08383	0.0362894
$893$	−14.9798	−0.501281
$894$	6.66259	0.222830
$895$	−90.3310	−3.01943
$896$	5.35170	0.178788
$897$	34.8354	1.16312
$898$	−46.0835	−1.53783
$899$	18.6646	0.622500
$900$	41.5911	1.38637
$901$	8.09510	0.269687
$902$	34.3634	1.14418
$903$	3.27421	0.108959
$904$	9.33985	0.310639
$905$	−67.9678	−2.25933
$906$	−14.9391	−0.496317
$907$	10.1396	0.336681	0.168341	−	0.985729i	$-0.446159\pi$
$907$	10.1396	0.336681	0.168341	+	0.985729i	$0.446159\pi$
$908$	103.029	3.41913
$909$	11.0515	0.366554
$910$	58.4241	1.93674
$911$	38.4215	1.27296	0.636481	−	0.771293i	$-0.280389\pi$
$911$	38.4215	1.27296	0.636481	+	0.771293i	$0.280389\pi$
$912$	12.9267	0.428046
$913$	14.4444	0.478040
$914$	−26.1277	−0.864228
$915$	−48.2926	−1.59650
$916$	−8.13454	−0.268773
$917$	−27.5830	−0.910872
$918$	−1.97843	−0.0652980
$919$	43.9146	1.44861	0.724304	−	0.689481i	$-0.242161\pi$
$919$	43.9146	1.44861	0.724304	+	0.689481i	$0.242161\pi$
$920$	216.792	7.14741
$921$	−15.7665	−0.519523
$922$	−4.85711	−0.159960
$923$	−55.9891	−1.84290
$924$	9.09176	0.299097
$925$	93.3228	3.06843
$926$	39.2888	1.29111
$927$	−7.72423	−0.253697
$928$	−36.4561	−1.19673
$929$	−10.6262	−0.348634	−0.174317	−	0.984690i	$-0.555772\pi$
$929$	−10.6262	−0.348634	−0.174317	+	0.984690i	$0.555772\pi$
$930$	58.7446	1.92631
$931$	−6.50126	−0.213070
$932$	30.9000	1.01216
$933$	3.12563	0.102329
$934$	44.9350	1.47032
$935$	3.81127	0.124642
$936$	−34.7501	−1.13584
$937$	−9.98042	−0.326046	−0.163023	−	0.986622i	$-0.552124\pi$
$937$	−9.98042	−0.326046	−0.163023	+	0.986622i	$0.552124\pi$
$938$	12.8593	0.419870
$939$	14.6877	0.479314
$940$	216.604	7.06483
$941$	38.3582	1.25044	0.625220	−	0.780448i	$-0.285009\pi$
$941$	38.3582	1.25044	0.625220	+	0.780448i	$0.285009\pi$
$942$	12.7786	0.416349
$943$	−72.7906	−2.37039
$944$	50.5784	1.64619
$945$	−4.90772	−0.159648
$946$	8.89248	0.289119
$947$	36.2627	1.17838	0.589189	−	0.807995i	$-0.299447\pi$
$947$	36.2627	1.17838	0.589189	+	0.807995i	$0.299447\pi$
$948$	55.7790	1.81162
$949$	−17.2084	−0.558608
$950$	27.7529	0.900423
$951$	−24.1867	−0.784307
$952$	−7.72682	−0.250428
$953$	−19.7443	−0.639582	−0.319791	−	0.947488i	$-0.603613\pi$
$953$	−19.7443	−0.639582	−0.319791	+	0.947488i	$0.603613\pi$
$954$	−28.3106	−0.916589
$955$	34.5657	1.11852
$956$	25.5976	0.827885
$957$	−4.23494	−0.136896
$958$	−74.6073	−2.41045
$959$	−19.5683	−0.631892
$960$	−38.7446	−1.25048
$961$	6.06829	0.195751
$962$	−131.396	−4.23638
$963$	4.99756	0.161044
$964$	−35.2567	−1.13554
$965$	37.4556	1.20574
$966$	−27.0889	−0.871572
$967$	−35.1364	−1.12991	−0.564956	−	0.825121i	$-0.691107\pi$
$967$	−35.1364	−1.12991	−0.564956	+	0.825121i	$0.691107\pi$
$968$	−69.8088	−2.24374
$969$	−0.938564	−0.0301510
$970$	−24.1332	−0.774870
$971$	−5.30519	−0.170252	−0.0851258	−	0.996370i	$-0.527129\pi$
$971$	−5.30519	−0.170252	−0.0851258	+	0.996370i	$0.527129\pi$
$972$	4.91907	0.157779
$973$	1.95152	0.0625630
$974$	−94.8993	−3.04077
$975$	−38.2655	−1.22548
$976$	136.382	4.36549
$977$	−12.7815	−0.408915	−0.204457	−	0.978875i	$-0.565543\pi$
$977$	−12.7815	−0.408915	−0.204457	+	0.978875i	$0.565543\pi$
$978$	−57.1258	−1.82668
$979$	−16.1764	−0.516999
$980$	94.0063	3.00292
$981$	7.01073	0.223835
$982$	72.1326	2.30184
$983$	0.782612	0.0249614	0.0124807	−	0.999922i	$-0.496027\pi$
$983$	0.782612	0.0249614	0.0124807	+	0.999922i	$0.496027\pi$
$984$	72.6124	2.31480
$985$	−53.6114	−1.70820
$986$	6.06511	0.193152
$987$	−16.0611	−0.511231
$988$	−27.7804	−0.883812
$989$	−18.8366	−0.598968
$990$	−13.3290	−0.423622
$991$	46.1556	1.46618	0.733091	−	0.680131i	$-0.238077\pi$
$991$	46.1556	1.46618	0.733091	+	0.680131i	$0.238077\pi$
$992$	−72.4025	−2.29878
$993$	−3.12592	−0.0991982
$994$	43.5385	1.38096
$995$	−6.04606	−0.191673
$996$	51.4343	1.62976
$997$	9.80980	0.310679	0.155340	−	0.987861i	$-0.450353\pi$
$997$	9.80980	0.310679	0.155340	+	0.987861i	$0.450353\pi$
$998$	31.9376	1.01097
$999$	11.0375	0.349210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.a.e.1.9	✓	9
3.2	odd	2		1143.2.a.j.1.1		9
4.3	odd	2		6096.2.a.bk.1.3		9
5.4	even	2		9525.2.a.p.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.e.1.9	✓	9	1.1	even	1	trivial
1143.2.a.j.1.1		9	3.2	odd	2
6096.2.a.bk.1.3		9	4.3	odd	2
9525.2.a.p.1.1		9	5.4	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:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.63041 q^{2} +1.00000 q^{3} +4.91907 q^{4} -3.66812 q^{5} +2.63041 q^{6} +1.33794 q^{7} +7.67834 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.63041 q^{2} +1.00000 q^{3} +4.91907 q^{4} -3.66812 q^{5} +2.63041 q^{6} +1.33794 q^{7} +7.67834 q^{8} +1.00000 q^{9} -9.64866 q^{10} +1.38143 q^{11} +4.91907 q^{12} -4.52573 q^{13} +3.51933 q^{14} -3.66812 q^{15} +10.3591 q^{16} -0.752137 q^{17} +2.63041 q^{18} +1.24786 q^{19} -18.0437 q^{20} +1.33794 q^{21} +3.63373 q^{22} -7.69718 q^{23} +7.67834 q^{24} +8.45509 q^{25} -11.9045 q^{26} +1.00000 q^{27} +6.58141 q^{28} -3.06562 q^{29} -9.64866 q^{30} -6.08837 q^{31} +11.8919 q^{32} +1.38143 q^{33} -1.97843 q^{34} -4.90772 q^{35} +4.91907 q^{36} +11.0375 q^{37} +3.28239 q^{38} -4.52573 q^{39} -28.1651 q^{40} +9.45678 q^{41} +3.51933 q^{42} +2.44720 q^{43} +6.79535 q^{44} -3.66812 q^{45} -20.2468 q^{46} -12.0044 q^{47} +10.3591 q^{48} -5.20992 q^{49} +22.2404 q^{50} -0.752137 q^{51} -22.2624 q^{52} -10.7628 q^{53} +2.63041 q^{54} -5.06725 q^{55} +10.2732 q^{56} +1.24786 q^{57} -8.06383 q^{58} +4.88252 q^{59} -18.0437 q^{60} +13.1655 q^{61} -16.0149 q^{62} +1.33794 q^{63} +10.5625 q^{64} +16.6009 q^{65} +3.63373 q^{66} +3.65390 q^{67} -3.69981 q^{68} -7.69718 q^{69} -12.9093 q^{70} +12.3713 q^{71} +7.67834 q^{72} +3.80234 q^{73} +29.0331 q^{74} +8.45509 q^{75} +6.13832 q^{76} +1.84827 q^{77} -11.9045 q^{78} +11.3394 q^{79} -37.9983 q^{80} +1.00000 q^{81} +24.8752 q^{82} +10.4561 q^{83} +6.58141 q^{84} +2.75893 q^{85} +6.43715 q^{86} -3.06562 q^{87} +10.6071 q^{88} -11.7099 q^{89} -9.64866 q^{90} -6.05516 q^{91} -37.8629 q^{92} -6.08837 q^{93} -31.5765 q^{94} -4.57731 q^{95} +11.8919 q^{96} +2.50120 q^{97} -13.7042 q^{98} +1.38143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * q^99

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