LMFDB - Embedded newform 209.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, 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("209.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 $ x^7 - x^6 - 14x^5 + 10x^4 + 59x^3 - 27x^2 - 66*x + 30
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.78328$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78328 q^{2} -2.10880 q^{3} +5.74667 q^{4} -2.97131 q^{5} +5.86939 q^{6} -1.34513 q^{7} -10.4280 q^{8} +1.44705 q^{9} +O(q^{10})$	\(q-2.78328 q^{2} -2.10880 q^{3} +5.74667 q^{4} -2.97131 q^{5} +5.86939 q^{6} -1.34513 q^{7} -10.4280 q^{8} +1.44705 q^{9} +8.27000 q^{10} -1.00000 q^{11} -12.1186 q^{12} -3.44600 q^{13} +3.74387 q^{14} +6.26590 q^{15} +17.5308 q^{16} +4.36902 q^{17} -4.02754 q^{18} +1.00000 q^{19} -17.0751 q^{20} +2.83661 q^{21} +2.78328 q^{22} +8.16120 q^{23} +21.9907 q^{24} +3.82868 q^{25} +9.59120 q^{26} +3.27487 q^{27} -7.73000 q^{28} -1.36214 q^{29} -17.4398 q^{30} +2.69934 q^{31} -27.9372 q^{32} +2.10880 q^{33} -12.1602 q^{34} +3.99679 q^{35} +8.31569 q^{36} -1.17307 q^{37} -2.78328 q^{38} +7.26694 q^{39} +30.9849 q^{40} -3.36782 q^{41} -7.89509 q^{42} -3.18989 q^{43} -5.74667 q^{44} -4.29962 q^{45} -22.7149 q^{46} +6.44720 q^{47} -36.9691 q^{48} -5.19063 q^{49} -10.6563 q^{50} -9.21340 q^{51} -19.8030 q^{52} +9.21835 q^{53} -9.11490 q^{54} +2.97131 q^{55} +14.0270 q^{56} -2.10880 q^{57} +3.79121 q^{58} -4.84279 q^{59} +36.0081 q^{60} +0.802455 q^{61} -7.51302 q^{62} -1.94646 q^{63} +42.6955 q^{64} +10.2391 q^{65} -5.86939 q^{66} +10.2818 q^{67} +25.1073 q^{68} -17.2103 q^{69} -11.1242 q^{70} +2.41929 q^{71} -15.0898 q^{72} -2.83093 q^{73} +3.26498 q^{74} -8.07393 q^{75} +5.74667 q^{76} +1.34513 q^{77} -20.2259 q^{78} +11.4884 q^{79} -52.0895 q^{80} -11.2472 q^{81} +9.37360 q^{82} -4.47265 q^{83} +16.3010 q^{84} -12.9817 q^{85} +8.87835 q^{86} +2.87248 q^{87} +10.4280 q^{88} +8.70190 q^{89} +11.9671 q^{90} +4.63532 q^{91} +46.8997 q^{92} -5.69237 q^{93} -17.9444 q^{94} -2.97131 q^{95} +58.9141 q^{96} -15.2358 q^{97} +14.4470 q^{98} -1.44705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9} - 6 q^{10} - 7 q^{11} - 16 q^{12} - 4 q^{13} + 6 q^{14} + 12 q^{15} + 27 q^{16} + 2 q^{17} + 9 q^{18} + 7 q^{19} - 4 q^{20} - 14 q^{21} + q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} - 4 q^{27} + 26 q^{28} - 18 q^{29} - 42 q^{30} + 24 q^{31} - 49 q^{32} - 2 q^{33} - 6 q^{34} + 8 q^{35} + 29 q^{36} - q^{38} + 24 q^{39} - 2 q^{40} - 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} - 4 q^{46} + 8 q^{47} - 72 q^{48} + 17 q^{49} - 33 q^{50} - 24 q^{51} - 60 q^{52} + 2 q^{53} - 52 q^{54} - 2 q^{55} + 26 q^{56} + 2 q^{57} - 8 q^{58} - 10 q^{59} + 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} - 14 q^{65} + 2 q^{66} + 8 q^{67} - 18 q^{68} - 6 q^{69} - 66 q^{70} + 10 q^{71} + 53 q^{72} - 6 q^{73} + 26 q^{74} + 26 q^{75} + 15 q^{76} - 10 q^{77} + 22 q^{78} + 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} - 6 q^{84} - 12 q^{85} + 8 q^{86} + 6 q^{87} + 9 q^{88} + 20 q^{90} + 12 q^{91} + 2 q^{93} + 24 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9 - 6 * q^10 - 7 * q^11 - 16 * q^12 - 4 * q^13 + 6 * q^14 + 12 * q^15 + 27 * q^16 + 2 * q^17 + 9 * q^18 + 7 * q^19 - 4 * q^20 - 14 * q^21 + q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 - 4 * q^27 + 26 * q^28 - 18 * q^29 - 42 * q^30 + 24 * q^31 - 49 * q^32 - 2 * q^33 - 6 * q^34 + 8 * q^35 + 29 * q^36 - q^38 + 24 * q^39 - 2 * q^40 - 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 - 4 * q^46 + 8 * q^47 - 72 * q^48 + 17 * q^49 - 33 * q^50 - 24 * q^51 - 60 * q^52 + 2 * q^53 - 52 * q^54 - 2 * q^55 + 26 * q^56 + 2 * q^57 - 8 * q^58 - 10 * q^59 + 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 - 14 * q^65 + 2 * q^66 + 8 * q^67 - 18 * q^68 - 6 * q^69 - 66 * q^70 + 10 * q^71 + 53 * q^72 - 6 * q^73 + 26 * q^74 + 26 * q^75 + 15 * q^76 - 10 * q^77 + 22 * q^78 + 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 + 6 * q^87 + 9 * q^88 + 20 * q^90 + 12 * q^91 + 2 * q^93 + 24 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 19 * q^98 - 11 * 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 $

$2$	−2.78328	−1.96808	−0.984039	−	0.177952i	$-0.943053\pi$
$2$	−2.78328	−1.96808	−0.984039	+	0.177952i	$0.943053\pi$
$3$	−2.10880	−1.21752	−0.608759	−	0.793355i	$-0.708332\pi$
$3$	−2.10880	−1.21752	−0.608759	+	0.793355i	$0.708332\pi$
$4$	5.74667	2.87333
$5$	−2.97131	−1.32881	−0.664405	−	0.747373i	$-0.731315\pi$
$5$	−2.97131	−1.32881	−0.664405	+	0.747373i	$0.731315\pi$
$6$	5.86939	2.39617
$7$	−1.34513	−0.508411	−0.254205	−	0.967150i	$-0.581814\pi$
$7$	−1.34513	−0.508411	−0.254205	+	0.967150i	$0.581814\pi$
$8$	−10.4280	−3.68687
$9$	1.44705	0.482348
$10$	8.27000	2.61520
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−12.1186	−3.49833
$13$	−3.44600	−0.955749	−0.477875	−	0.878428i	$-0.658593\pi$
$13$	−3.44600	−0.955749	−0.477875	+	0.878428i	$0.658593\pi$
$14$	3.74387	1.00059
$15$	6.26590	1.61785
$16$	17.5308	4.38271
$17$	4.36902	1.05964	0.529822	−	0.848109i	$-0.322259\pi$
$17$	4.36902	1.05964	0.529822	+	0.848109i	$0.322259\pi$
$18$	−4.02754	−0.949300
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−17.0751	−3.81811
$21$	2.83661	0.618999
$22$	2.78328	0.593398
$23$	8.16120	1.70173	0.850863	−	0.525387i	$-0.176079\pi$
$23$	8.16120	1.70173	0.850863	+	0.525387i	$0.176079\pi$
$24$	21.9907	4.48882
$25$	3.82868	0.765736
$26$	9.59120	1.88099
$27$	3.27487	0.630250
$28$	−7.73000	−1.46083
$29$	−1.36214	−0.252942	−0.126471	−	0.991970i	$-0.540365\pi$
$29$	−1.36214	−0.252942	−0.126471	+	0.991970i	$0.540365\pi$
$30$	−17.4398	−3.18405
$31$	2.69934	0.484815	0.242408	−	0.970174i	$-0.422063\pi$
$31$	2.69934	0.484815	0.242408	+	0.970174i	$0.422063\pi$
$32$	−27.9372	−4.93865
$33$	2.10880	0.367095
$34$	−12.1602	−2.08546
$35$	3.99679	0.675581
$36$	8.31569	1.38595
$37$	−1.17307	−0.192851	−0.0964255	−	0.995340i	$-0.530741\pi$
$37$	−1.17307	−0.192851	−0.0964255	+	0.995340i	$0.530741\pi$
$38$	−2.78328	−0.451508
$39$	7.26694	1.16364
$40$	30.9849	4.89915
$41$	−3.36782	−0.525965	−0.262983	−	0.964801i	$-0.584706\pi$
$41$	−3.36782	−0.525965	−0.262983	+	0.964801i	$0.584706\pi$
$42$	−7.89509	−1.21824
$43$	−3.18989	−0.486453	−0.243226	−	0.969970i	$-0.578206\pi$
$43$	−3.18989	−0.486453	−0.243226	+	0.969970i	$0.578206\pi$
$44$	−5.74667	−0.866342
$45$	−4.29962	−0.640950
$46$	−22.7149	−3.34913
$47$	6.44720	0.940421	0.470211	−	0.882554i	$-0.344178\pi$
$47$	6.44720	0.940421	0.470211	+	0.882554i	$0.344178\pi$
$48$	−36.9691	−5.33602
$49$	−5.19063	−0.741518
$50$	−10.6563	−1.50703
$51$	−9.21340	−1.29013
$52$	−19.8030	−2.74619
$53$	9.21835	1.26624	0.633119	−	0.774055i	$-0.281774\pi$
$53$	9.21835	1.26624	0.633119	+	0.774055i	$0.281774\pi$
$54$	−9.11490	−1.24038
$55$	2.97131	0.400651
$56$	14.0270	1.87444
$57$	−2.10880	−0.279318
$58$	3.79121	0.497810
$59$	−4.84279	−0.630477	−0.315239	−	0.949012i	$-0.602085\pi$
$59$	−4.84279	−0.630477	−0.315239	+	0.949012i	$0.602085\pi$
$60$	36.0081	4.64862
$61$	0.802455	0.102744	0.0513719	−	0.998680i	$-0.483641\pi$
$61$	0.802455	0.102744	0.0513719	+	0.998680i	$0.483641\pi$
$62$	−7.51302	−0.954155
$63$	−1.94646	−0.245231
$64$	42.6955	5.33694
$65$	10.2391	1.27001
$66$	−5.86939	−0.722472
$67$	10.2818	1.25612	0.628058	−	0.778166i	$-0.283850\pi$
$67$	10.2818	1.25612	0.628058	+	0.778166i	$0.283850\pi$
$68$	25.1073	3.04471
$69$	−17.2103	−2.07188
$70$	−11.1242	−1.32960
$71$	2.41929	0.287117	0.143558	−	0.989642i	$-0.454146\pi$
$71$	2.41929	0.287117	0.143558	+	0.989642i	$0.454146\pi$
$72$	−15.0898	−1.77835
$73$	−2.83093	−0.331335	−0.165667	−	0.986182i	$-0.552978\pi$
$73$	−2.83093	−0.331335	−0.165667	+	0.986182i	$0.552978\pi$
$74$	3.26498	0.379546
$75$	−8.07393	−0.932297
$76$	5.74667	0.659188
$77$	1.34513	0.153292
$78$	−20.2259	−2.29014
$79$	11.4884	1.29254	0.646272	−	0.763107i	$-0.276327\pi$
$79$	11.4884	1.29254	0.646272	+	0.763107i	$0.276327\pi$
$80$	−52.0895	−5.82379
$81$	−11.2472	−1.24969
$82$	9.37360	1.03514
$83$	−4.47265	−0.490937	−0.245468	−	0.969405i	$-0.578942\pi$
$83$	−4.47265	−0.490937	−0.245468	+	0.969405i	$0.578942\pi$
$84$	16.3010	1.77859
$85$	−12.9817	−1.40806
$86$	8.87835	0.957378
$87$	2.87248	0.307962
$88$	10.4280	1.11163
$89$	8.70190	0.922400	0.461200	−	0.887296i	$-0.347419\pi$
$89$	8.70190	0.922400	0.461200	+	0.887296i	$0.347419\pi$
$90$	11.9671	1.26144
$91$	4.63532	0.485913
$92$	46.8997	4.88963
$93$	−5.69237	−0.590271
$94$	−17.9444	−1.85082
$95$	−2.97131	−0.304850
$96$	58.9141	6.01289
$97$	−15.2358	−1.54696	−0.773480	−	0.633820i	$-0.781486\pi$
$97$	−15.2358	−1.54696	−0.773480	+	0.633820i	$0.781486\pi$
$98$	14.4470	1.45937
$99$	−1.44705	−0.145434
$100$	22.0022	2.20022
$101$	−12.0030	−1.19435	−0.597173	−	0.802113i	$-0.703709\pi$
$101$	−12.0030	−1.19435	−0.597173	+	0.802113i	$0.703709\pi$
$102$	25.6435	2.53909
$103$	−0.316628	−0.0311983	−0.0155991	−	0.999878i	$-0.504966\pi$
$103$	−0.316628	−0.0311983	−0.0155991	+	0.999878i	$0.504966\pi$
$104$	35.9350	3.52372
$105$	−8.42845	−0.822532
$106$	−25.6573	−2.49205
$107$	−8.30461	−0.802837	−0.401418	−	0.915895i	$-0.631483\pi$
$107$	−8.30461	−0.802837	−0.401418	+	0.915895i	$0.631483\pi$
$108$	18.8196	1.81092
$109$	19.3664	1.85497	0.927484	−	0.373863i	$-0.121967\pi$
$109$	19.3664	1.85497	0.927484	+	0.373863i	$0.121967\pi$
$110$	−8.27000	−0.788513
$111$	2.47377	0.234800
$112$	−23.5812	−2.22822
$113$	−2.94347	−0.276898	−0.138449	−	0.990370i	$-0.544212\pi$
$113$	−2.94347	−0.276898	−0.138449	+	0.990370i	$0.544212\pi$
$114$	5.86939	0.549719
$115$	−24.2494	−2.26127
$116$	−7.82774	−0.726788
$117$	−4.98652	−0.461004
$118$	13.4788	1.24083
$119$	−5.87690	−0.538734
$120$	−65.3410	−5.96479
$121$	1.00000	0.0909091
$122$	−2.23346	−0.202208
$123$	7.10207	0.640372
$124$	15.5122	1.39304
$125$	3.48035	0.311292
$126$	5.41756	0.482634
$127$	15.8170	1.40353	0.701764	−	0.712409i	$-0.252396\pi$
$127$	15.8170	1.40353	0.701764	+	0.712409i	$0.252396\pi$
$128$	−62.9593	−5.56487
$129$	6.72684	0.592265
$130$	−28.4984	−2.49948
$131$	2.01458	0.176015	0.0880075	−	0.996120i	$-0.471950\pi$
$131$	2.01458	0.176015	0.0880075	+	0.996120i	$0.471950\pi$
$132$	12.1186	1.05479
$133$	−1.34513	−0.116637
$134$	−28.6170	−2.47214
$135$	−9.73066	−0.837482
$136$	−45.5603	−3.90676
$137$	−1.93459	−0.165283	−0.0826417	−	0.996579i	$-0.526336\pi$
$137$	−1.93459	−0.165283	−0.0826417	+	0.996579i	$0.526336\pi$
$138$	47.9013	4.07763
$139$	4.13447	0.350681	0.175340	−	0.984508i	$-0.443897\pi$
$139$	4.13447	0.350681	0.175340	+	0.984508i	$0.443897\pi$
$140$	22.9682	1.94117
$141$	−13.5959	−1.14498
$142$	−6.73357	−0.565068
$143$	3.44600	0.288169
$144$	25.3679	2.11399
$145$	4.04733	0.336112
$146$	7.87927	0.652093
$147$	10.9460	0.902812
$148$	−6.74123	−0.554125
$149$	0.735641	0.0602661	0.0301330	−	0.999546i	$-0.490407\pi$
$149$	0.735641	0.0602661	0.0301330	+	0.999546i	$0.490407\pi$
$150$	22.4720	1.83483
$151$	10.4650	0.851628	0.425814	−	0.904811i	$-0.359988\pi$
$151$	10.4650	0.851628	0.425814	+	0.904811i	$0.359988\pi$
$152$	−10.4280	−0.845825
$153$	6.32217	0.511117
$154$	−3.74387	−0.301690
$155$	−8.02057	−0.644227
$156$	41.7607	3.34353
$157$	2.40102	0.191622	0.0958111	−	0.995400i	$-0.469456\pi$
$157$	2.40102	0.191622	0.0958111	+	0.995400i	$0.469456\pi$
$158$	−31.9754	−2.54383
$159$	−19.4397	−1.54167
$160$	83.0101	6.56253
$161$	−10.9779	−0.865176
$162$	31.3041	2.45948
$163$	11.8694	0.929682	0.464841	−	0.885394i	$-0.346111\pi$
$163$	11.8694	0.929682	0.464841	+	0.885394i	$0.346111\pi$
$164$	−19.3537	−1.51127
$165$	−6.26590	−0.487800
$166$	12.4486	0.966202
$167$	21.4056	1.65641	0.828206	−	0.560424i	$-0.189362\pi$
$167$	21.4056	1.65641	0.828206	+	0.560424i	$0.189362\pi$
$168$	−29.5803	−2.28217
$169$	−1.12506	−0.0865433
$170$	36.1318	2.77118
$171$	1.44705	0.110658
$172$	−18.3312	−1.39774
$173$	−3.41185	−0.259398	−0.129699	−	0.991553i	$-0.541401\pi$
$173$	−3.41185	−0.259398	−0.129699	+	0.991553i	$0.541401\pi$
$174$	−7.99491	−0.606093
$175$	−5.15007	−0.389309
$176$	−17.5308	−1.32144
$177$	10.2125	0.767617
$178$	−24.2199	−1.81535
$179$	22.2079	1.65990	0.829948	−	0.557841i	$-0.188370\pi$
$179$	22.2079	1.65990	0.829948	+	0.557841i	$0.188370\pi$
$180$	−24.7085	−1.84166
$181$	−15.1315	−1.12472	−0.562359	−	0.826893i	$-0.690106\pi$
$181$	−15.1315	−1.12472	−0.562359	+	0.826893i	$0.690106\pi$
$182$	−12.9014	−0.956315
$183$	−1.69222	−0.125092
$184$	−85.1052	−6.27404
$185$	3.48555	0.256262
$186$	15.8435	1.16170
$187$	−4.36902	−0.319494
$188$	37.0499	2.70214
$189$	−4.40513	−0.320426
$190$	8.27000	0.599969
$191$	−3.30482	−0.239128	−0.119564	−	0.992826i	$-0.538150\pi$
$191$	−3.30482	−0.239128	−0.119564	+	0.992826i	$0.538150\pi$
$192$	−90.0364	−6.49782
$193$	−3.08205	−0.221851	−0.110925	−	0.993829i	$-0.535381\pi$
$193$	−3.08205	−0.221851	−0.110925	+	0.993829i	$0.535381\pi$
$194$	42.4055	3.04454
$195$	−21.5923	−1.54626
$196$	−29.8288	−2.13063
$197$	13.7142	0.977094	0.488547	−	0.872537i	$-0.337527\pi$
$197$	13.7142	0.977094	0.488547	+	0.872537i	$0.337527\pi$
$198$	4.02754	0.286225
$199$	10.8031	0.765810	0.382905	−	0.923788i	$-0.374924\pi$
$199$	10.8031	0.765810	0.382905	+	0.923788i	$0.374924\pi$
$200$	−39.9256	−2.82317
$201$	−21.6822	−1.52934
$202$	33.4078	2.35057
$203$	1.83225	0.128599
$204$	−52.9463	−3.70698
$205$	10.0068	0.698908
$206$	0.881265	0.0614006
$207$	11.8096	0.820825
$208$	−60.4113	−4.18877
$209$	−1.00000	−0.0691714
$210$	23.4588	1.61881
$211$	6.83161	0.470307	0.235154	−	0.971958i	$-0.424441\pi$
$211$	6.83161	0.470307	0.235154	+	0.971958i	$0.424441\pi$
$212$	52.9748	3.63832
$213$	−5.10180	−0.349570
$214$	23.1141	1.58005
$215$	9.47814	0.646404
$216$	−34.1505	−2.32365
$217$	−3.63096	−0.246485
$218$	−53.9023	−3.65072
$219$	5.96986	0.403406
$220$	17.0751	1.15120
$221$	−15.0557	−1.01275
$222$	−6.88519	−0.462104
$223$	−24.1323	−1.61602	−0.808009	−	0.589171i	$-0.799455\pi$
$223$	−24.1323	−1.61602	−0.808009	+	0.589171i	$0.799455\pi$
$224$	37.5792	2.51086
$225$	5.54028	0.369352
$226$	8.19250	0.544957
$227$	4.74633	0.315025	0.157513	−	0.987517i	$-0.449653\pi$
$227$	4.74633	0.315025	0.157513	+	0.987517i	$0.449653\pi$
$228$	−12.1186	−0.802573
$229$	21.3091	1.40814	0.704071	−	0.710130i	$-0.251364\pi$
$229$	21.3091	1.40814	0.704071	+	0.710130i	$0.251364\pi$
$230$	67.4931	4.45036
$231$	−2.83661	−0.186635
$232$	14.2044	0.932564
$233$	2.75817	0.180694	0.0903468	−	0.995910i	$-0.471202\pi$
$233$	2.75817	0.180694	0.0903468	+	0.995910i	$0.471202\pi$
$234$	13.8789	0.907292
$235$	−19.1566	−1.24964
$236$	−27.8299	−1.81157
$237$	−24.2267	−1.57369
$238$	16.3571	1.06027
$239$	19.0865	1.23460	0.617302	−	0.786726i	$-0.288226\pi$
$239$	19.0865	1.23460	0.617302	+	0.786726i	$0.288226\pi$
$240$	109.847	7.09056
$241$	9.69921	0.624781	0.312391	−	0.949954i	$-0.398870\pi$
$241$	9.69921	0.624781	0.312391	+	0.949954i	$0.398870\pi$
$242$	−2.78328	−0.178916
$243$	13.8935	0.891268
$244$	4.61144	0.295217
$245$	15.4230	0.985337
$246$	−19.7671	−1.26030
$247$	−3.44600	−0.219264
$248$	−28.1488	−1.78745
$249$	9.43192	0.597724
$250$	−9.68679	−0.612647
$251$	−27.5354	−1.73802	−0.869011	−	0.494793i	$-0.835244\pi$
$251$	−27.5354	−1.73802	−0.869011	+	0.494793i	$0.835244\pi$
$252$	−11.1857	−0.704631
$253$	−8.16120	−0.513090
$254$	−44.0231	−2.76226
$255$	27.3759	1.71434
$256$	89.8425	5.61516
$257$	18.3975	1.14760	0.573801	−	0.818994i	$-0.305468\pi$
$257$	18.3975	1.14760	0.573801	+	0.818994i	$0.305468\pi$
$258$	−18.7227	−1.16562
$259$	1.57793	0.0980476
$260$	58.8409	3.64916
$261$	−1.97107	−0.122006
$262$	−5.60716	−0.346411
$263$	−15.9534	−0.983726	−0.491863	−	0.870673i	$-0.663684\pi$
$263$	−15.9534	−0.983726	−0.491863	+	0.870673i	$0.663684\pi$
$264$	−21.9907	−1.35343
$265$	−27.3906	−1.68259
$266$	3.74387	0.229552
$267$	−18.3506	−1.12304
$268$	59.0858	3.60924
$269$	5.39659	0.329036	0.164518	−	0.986374i	$-0.447393\pi$
$269$	5.39659	0.329036	0.164518	+	0.986374i	$0.447393\pi$
$270$	27.0832	1.64823
$271$	13.8386	0.840634	0.420317	−	0.907377i	$-0.361919\pi$
$271$	13.8386	0.840634	0.420317	+	0.907377i	$0.361919\pi$
$272$	76.5926	4.64411
$273$	−9.77497	−0.591608
$274$	5.38452	0.325291
$275$	−3.82868	−0.230878
$276$	−98.9021	−5.95321
$277$	27.6769	1.66294	0.831472	−	0.555566i	$-0.187498\pi$
$277$	27.6769	1.66294	0.831472	+	0.555566i	$0.187498\pi$
$278$	−11.5074	−0.690167
$279$	3.90606	0.233850
$280$	−41.6787	−2.49078
$281$	19.0977	1.13928	0.569638	−	0.821896i	$-0.307083\pi$
$281$	19.0977	1.13928	0.569638	+	0.821896i	$0.307083\pi$
$282$	37.8412	2.25341
$283$	−2.72601	−0.162044	−0.0810221	−	0.996712i	$-0.525818\pi$
$283$	−2.72601	−0.162044	−0.0810221	+	0.996712i	$0.525818\pi$
$284$	13.9028	0.824982
$285$	6.26590	0.371160
$286$	−9.59120	−0.567140
$287$	4.53015	0.267406
$288$	−40.4264	−2.38215
$289$	2.08835	0.122844
$290$	−11.2649	−0.661495
$291$	32.1293	1.88345
$292$	−16.2684	−0.952035
$293$	−5.24410	−0.306363	−0.153182	−	0.988198i	$-0.548952\pi$
$293$	−5.24410	−0.306363	−0.153182	+	0.988198i	$0.548952\pi$
$294$	−30.4658	−1.77680
$295$	14.3894	0.837785
$296$	12.2328	0.711016
$297$	−3.27487	−0.190027
$298$	−2.04750	−0.118608
$299$	−28.1235	−1.62642
$300$	−46.3982	−2.67880
$301$	4.29081	0.247318
$302$	−29.1270	−1.67607
$303$	25.3120	1.45414
$304$	17.5308	1.00546
$305$	−2.38434	−0.136527
$306$	−17.5964	−1.00592
$307$	−19.5218	−1.11417	−0.557084	−	0.830456i	$-0.688080\pi$
$307$	−19.5218	−1.11417	−0.557084	+	0.830456i	$0.688080\pi$
$308$	7.73000	0.440458
$309$	0.667705	0.0379844
$310$	22.3235	1.26789
$311$	−0.793022	−0.0449681	−0.0224841	−	0.999747i	$-0.507158\pi$
$311$	−0.793022	−0.0449681	−0.0224841	+	0.999747i	$0.507158\pi$
$312$	−75.7799	−4.29019
$313$	−13.3412	−0.754087	−0.377044	−	0.926195i	$-0.623059\pi$
$313$	−13.3412	−0.754087	−0.377044	+	0.926195i	$0.623059\pi$
$314$	−6.68271	−0.377127
$315$	5.78354	0.325866
$316$	66.0199	3.71391
$317$	−11.2812	−0.633614	−0.316807	−	0.948490i	$-0.602611\pi$
$317$	−11.2812	−0.633614	−0.316807	+	0.948490i	$0.602611\pi$
$318$	54.1061	3.03412
$319$	1.36214	0.0762650
$320$	−126.862	−7.09178
$321$	17.5128	0.977468
$322$	30.5545	1.70273
$323$	4.36902	0.243099
$324$	−64.6339	−3.59077
$325$	−13.1937	−0.731852
$326$	−33.0359	−1.82969
$327$	−40.8400	−2.25846
$328$	35.1197	1.93916
$329$	−8.67232	−0.478120
$330$	17.4398	0.960029
$331$	−2.01592	−0.110805	−0.0554025	−	0.998464i	$-0.517644\pi$
$331$	−2.01592	−0.110805	−0.0554025	+	0.998464i	$0.517644\pi$
$332$	−25.7028	−1.41062
$333$	−1.69748	−0.0930214
$334$	−59.5777	−3.25995
$335$	−30.5503	−1.66914
$336$	49.7281	2.71289
$337$	24.2228	1.31950	0.659750	−	0.751485i	$-0.270662\pi$
$337$	24.2228	1.31950	0.659750	+	0.751485i	$0.270662\pi$
$338$	3.13137	0.170324
$339$	6.20719	0.337128
$340$	−74.6016	−4.04584
$341$	−2.69934	−0.146177
$342$	−4.02754	−0.217784
$343$	16.3980	0.885407
$344$	33.2642	1.79349
$345$	51.1373	2.75314
$346$	9.49614	0.510516
$347$	13.9060	0.746515	0.373258	−	0.927728i	$-0.378241\pi$
$347$	13.9060	0.746515	0.373258	+	0.927728i	$0.378241\pi$
$348$	16.5072	0.884876
$349$	2.80678	0.150244	0.0751218	−	0.997174i	$-0.476065\pi$
$349$	2.80678	0.150244	0.0751218	+	0.997174i	$0.476065\pi$
$350$	14.3341	0.766190
$351$	−11.2852	−0.602361
$352$	27.9372	1.48906
$353$	33.1125	1.76240	0.881201	−	0.472742i	$-0.156736\pi$
$353$	33.1125	1.76240	0.881201	+	0.472742i	$0.156736\pi$
$354$	−28.4242	−1.51073
$355$	−7.18846	−0.381524
$356$	50.0069	2.65036
$357$	12.3932	0.655918
$358$	−61.8109	−3.26681
$359$	−34.4747	−1.81951	−0.909753	−	0.415150i	$-0.863729\pi$
$359$	−34.4747	−1.81951	−0.909753	+	0.415150i	$0.863729\pi$
$360$	44.8366	2.36310
$361$	1.00000	0.0526316
$362$	42.1154	2.21353
$363$	−2.10880	−0.110683
$364$	26.6376	1.39619
$365$	8.41156	0.440281
$366$	4.70992	0.246192
$367$	−18.1330	−0.946533	−0.473267	−	0.880919i	$-0.656925\pi$
$367$	−18.1330	−0.946533	−0.473267	+	0.880919i	$0.656925\pi$
$368$	143.073	7.45817
$369$	−4.87339	−0.253699
$370$	−9.70126	−0.504345
$371$	−12.3999	−0.643769
$372$	−32.7121	−1.69605
$373$	−19.4690	−1.00807	−0.504034	−	0.863684i	$-0.668151\pi$
$373$	−19.4690	−1.00807	−0.504034	+	0.863684i	$0.668151\pi$
$374$	12.1602	0.628790
$375$	−7.33936	−0.379003
$376$	−67.2316	−3.46721
$377$	4.69393	0.241749
$378$	12.2607	0.630623
$379$	8.24163	0.423344	0.211672	−	0.977341i	$-0.432109\pi$
$379$	8.24163	0.423344	0.211672	+	0.977341i	$0.432109\pi$
$380$	−17.0751	−0.875935
$381$	−33.3549	−1.70882
$382$	9.19825	0.470623
$383$	−16.6259	−0.849546	−0.424773	−	0.905300i	$-0.639646\pi$
$383$	−16.6259	−0.849546	−0.424773	+	0.905300i	$0.639646\pi$
$384$	132.769	6.77532
$385$	−3.99679	−0.203695
$386$	8.57821	0.436619
$387$	−4.61591	−0.234640
$388$	−87.5550	−4.44493
$389$	1.96261	0.0995083	0.0497542	−	0.998761i	$-0.484156\pi$
$389$	1.96261	0.0995083	0.0497542	+	0.998761i	$0.484156\pi$
$390$	60.0976	3.04316
$391$	35.6564	1.80322
$392$	54.1280	2.73388
$393$	−4.24836	−0.214301
$394$	−38.1704	−1.92300
$395$	−34.1355	−1.71755
$396$	−8.31569	−0.417879
$397$	12.1527	0.609926	0.304963	−	0.952364i	$-0.401356\pi$
$397$	12.1527	0.609926	0.304963	+	0.952364i	$0.401356\pi$
$398$	−30.0680	−1.50717
$399$	2.83661	0.142008
$400$	67.1200	3.35600
$401$	10.6511	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$401$	10.6511	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$402$	60.3477	3.00987
$403$	−9.30192	−0.463362
$404$	−68.9773	−3.43175
$405$	33.4189	1.66060
$406$	−5.09967	−0.253092
$407$	1.17307	0.0581468
$408$	96.0776	4.75655
$409$	−33.5066	−1.65679	−0.828397	−	0.560141i	$-0.810747\pi$
$409$	−33.5066	−1.65679	−0.828397	+	0.560141i	$0.810747\pi$
$410$	−27.8519	−1.37551
$411$	4.07967	0.201235
$412$	−1.81955	−0.0896430
$413$	6.51417	0.320541
$414$	−32.8695	−1.61545
$415$	13.2896	0.652362
$416$	96.2717	4.72011
$417$	−8.71877	−0.426960
$418$	2.78328	0.136135
$419$	−14.8963	−0.727734	−0.363867	−	0.931451i	$-0.618544\pi$
$419$	−14.8963	−0.727734	−0.363867	+	0.931451i	$0.618544\pi$
$420$	−48.4355	−2.36341
$421$	−28.5728	−1.39255	−0.696277	−	0.717774i	$-0.745161\pi$
$421$	−28.5728	−1.39255	−0.696277	+	0.717774i	$0.745161\pi$
$422$	−19.0143	−0.925601
$423$	9.32940	0.453611
$424$	−96.1292	−4.66845
$425$	16.7276	0.811408
$426$	14.1998	0.687980
$427$	−1.07940	−0.0522361
$428$	−47.7238	−2.30682
$429$	−7.26694	−0.350851
$430$	−26.3803	−1.27217
$431$	−22.1774	−1.06825	−0.534124	−	0.845406i	$-0.679359\pi$
$431$	−22.1774	−1.06825	−0.534124	+	0.845406i	$0.679359\pi$
$432$	57.4113	2.76220
$433$	14.8364	0.712991	0.356495	−	0.934297i	$-0.383972\pi$
$433$	14.8364	0.712991	0.356495	+	0.934297i	$0.383972\pi$
$434$	10.1060	0.485102
$435$	−8.53501	−0.409223
$436$	111.292	5.32994
$437$	8.16120	0.390403
$438$	−16.6158	−0.793934
$439$	−15.4371	−0.736773	−0.368386	−	0.929673i	$-0.620090\pi$
$439$	−15.4371	−0.736773	−0.368386	+	0.929673i	$0.620090\pi$
$440$	−30.9849	−1.47715
$441$	−7.51108	−0.357670
$442$	41.9042	1.99318
$443$	−0.598596	−0.0284402	−0.0142201	−	0.999899i	$-0.504527\pi$
$443$	−0.598596	−0.0284402	−0.0142201	+	0.999899i	$0.504527\pi$
$444$	14.2159	0.674657
$445$	−25.8560	−1.22569
$446$	67.1670	3.18045
$447$	−1.55132	−0.0733750
$448$	−57.4310	−2.71336
$449$	12.5396	0.591780	0.295890	−	0.955222i	$-0.404384\pi$
$449$	12.5396	0.591780	0.295890	+	0.955222i	$0.404384\pi$
$450$	−15.4202	−0.726913
$451$	3.36782	0.158584
$452$	−16.9151	−0.795620
$453$	−22.0686	−1.03687
$454$	−13.2104	−0.619994
$455$	−13.7730	−0.645687
$456$	21.9907	1.02981
$457$	−13.6683	−0.639374	−0.319687	−	0.947523i	$-0.603578\pi$
$457$	−13.6683	−0.639374	−0.319687	+	0.947523i	$0.603578\pi$
$458$	−59.3091	−2.77133
$459$	14.3080	0.667840
$460$	−139.353	−6.49739
$461$	−33.1958	−1.54608	−0.773041	−	0.634357i	$-0.781265\pi$
$461$	−33.1958	−1.54608	−0.773041	+	0.634357i	$0.781265\pi$
$462$	7.89509	0.367313
$463$	−25.3243	−1.17692	−0.588460	−	0.808526i	$-0.700266\pi$
$463$	−25.3243	−1.17692	−0.588460	+	0.808526i	$0.700266\pi$
$464$	−23.8794	−1.10857
$465$	16.9138	0.784358
$466$	−7.67676	−0.355619
$467$	−13.0891	−0.605691	−0.302845	−	0.953040i	$-0.597937\pi$
$467$	−13.0891	−0.605691	−0.302845	+	0.953040i	$0.597937\pi$
$468$	−28.6559	−1.32462
$469$	−13.8303	−0.638623
$470$	53.3184	2.45939
$471$	−5.06327	−0.233303
$472$	50.5007	2.32449
$473$	3.18989	0.146671
$474$	67.4298	3.09716
$475$	3.82868	0.175672
$476$	−33.7726	−1.54796
$477$	13.3394	0.610768
$478$	−53.1232	−2.42980
$479$	35.6473	1.62877	0.814383	−	0.580328i	$-0.197076\pi$
$479$	35.6473	1.62877	0.814383	+	0.580328i	$0.197076\pi$
$480$	−175.052	−7.98999
$481$	4.04239	0.184317
$482$	−26.9956	−1.22962
$483$	23.1501	1.05337
$484$	5.74667	0.261212
$485$	45.2703	2.05562
$486$	−38.6695	−1.75408
$487$	35.3242	1.60069	0.800347	−	0.599538i	$-0.204649\pi$
$487$	35.3242	1.60069	0.800347	+	0.599538i	$0.204649\pi$
$488$	−8.36802	−0.378803
$489$	−25.0302	−1.13190
$490$	−42.9265	−1.93922
$491$	−11.5208	−0.519926	−0.259963	−	0.965619i	$-0.583710\pi$
$491$	−11.5208	−0.519926	−0.259963	+	0.965619i	$0.583710\pi$
$492$	40.8132	1.84000
$493$	−5.95120	−0.268029
$494$	9.59120	0.431529
$495$	4.29962	0.193254
$496$	47.3216	2.12480
$497$	−3.25425	−0.145973
$498$	−26.2517	−1.17637
$499$	29.8138	1.33465	0.667324	−	0.744768i	$-0.267440\pi$
$499$	29.8138	1.33465	0.667324	+	0.744768i	$0.267440\pi$
$500$	20.0004	0.894445
$501$	−45.1401	−2.01671
$502$	76.6389	3.42056
$503$	31.8285	1.41916	0.709581	−	0.704624i	$-0.248884\pi$
$503$	31.8285	1.41916	0.709581	+	0.704624i	$0.248884\pi$
$504$	20.2978	0.904135
$505$	35.6647	1.58706
$506$	22.7149	1.00980
$507$	2.37253	0.105368
$508$	90.8948	4.03281
$509$	38.3440	1.69957	0.849784	−	0.527131i	$-0.176732\pi$
$509$	38.3440	1.69957	0.849784	+	0.527131i	$0.176732\pi$
$510$	−76.1948	−3.37396
$511$	3.80796	0.168454
$512$	−124.139	−5.48620
$513$	3.27487	0.144589
$514$	−51.2054	−2.25857
$515$	0.940800	0.0414566
$516$	38.6569	1.70177
$517$	−6.44720	−0.283548
$518$	−4.39182	−0.192965
$519$	7.19491	0.315822
$520$	−106.774	−4.68235
$521$	19.9328	0.873270	0.436635	−	0.899639i	$-0.356170\pi$
$521$	19.9328	0.873270	0.436635	+	0.899639i	$0.356170\pi$
$522$	5.48605	0.240118
$523$	4.09116	0.178894	0.0894469	−	0.995992i	$-0.471490\pi$
$523$	4.09116	0.178894	0.0894469	+	0.995992i	$0.471490\pi$
$524$	11.5771	0.505750
$525$	10.8605	0.473990
$526$	44.4027	1.93605
$527$	11.7935	0.513731
$528$	36.9691	1.60887
$529$	43.6051	1.89587
$530$	76.2357	3.31147
$531$	−7.00773	−0.304110
$532$	−7.73000	−0.335138
$533$	11.6055	0.502691
$534$	51.0749	2.21023
$535$	24.6756	1.06682
$536$	−107.219	−4.63113
$537$	−46.8321	−2.02095
$538$	−15.0202	−0.647568
$539$	5.19063	0.223576
$540$	−55.9189	−2.40637
$541$	10.9993	0.472897	0.236448	−	0.971644i	$-0.424017\pi$
$541$	10.9993	0.472897	0.236448	+	0.971644i	$0.424017\pi$
$542$	−38.5167	−1.65443
$543$	31.9094	1.36936
$544$	−122.058	−5.23321
$545$	−57.5437	−2.46490
$546$	27.2065	1.16433
$547$	−8.58461	−0.367052	−0.183526	−	0.983015i	$-0.558751\pi$
$547$	−8.58461	−0.367052	−0.183526	+	0.983015i	$0.558751\pi$
$548$	−11.1175	−0.474914
$549$	1.16119	0.0495583
$550$	10.6563	0.454386
$551$	−1.36214	−0.0580289
$552$	179.470	7.63875
$553$	−15.4534	−0.657143
$554$	−77.0327	−3.27281
$555$	−7.35033	−0.312004
$556$	23.7594	1.00762
$557$	−33.0043	−1.39844	−0.699218	−	0.714908i	$-0.746468\pi$
$557$	−33.0043	−1.39844	−0.699218	+	0.714908i	$0.746468\pi$
$558$	−10.8717	−0.460235
$559$	10.9924	0.464927
$560$	70.0671	2.96088
$561$	9.21340	0.388990
$562$	−53.1544	−2.24218
$563$	−6.07578	−0.256064	−0.128032	−	0.991770i	$-0.540866\pi$
$563$	−6.07578	−0.256064	−0.128032	+	0.991770i	$0.540866\pi$
$564$	−78.1310	−3.28991
$565$	8.74595	0.367945
$566$	7.58724	0.318916
$567$	15.1289	0.635355
$568$	−25.2284	−1.05856
$569$	3.77407	0.158217	0.0791086	−	0.996866i	$-0.474793\pi$
$569$	3.77407	0.158217	0.0791086	+	0.996866i	$0.474793\pi$
$570$	−17.4398	−0.730472
$571$	4.70221	0.196781	0.0983907	−	0.995148i	$-0.468631\pi$
$571$	4.70221	0.196781	0.0983907	+	0.995148i	$0.468631\pi$
$572$	19.8030	0.828006
$573$	6.96921	0.291143
$574$	−12.6087	−0.526277
$575$	31.2466	1.30307
$576$	61.7824	2.57426
$577$	−4.08561	−0.170086	−0.0850430	−	0.996377i	$-0.527103\pi$
$577$	−4.08561	−0.170086	−0.0850430	+	0.996377i	$0.527103\pi$
$578$	−5.81246	−0.241766
$579$	6.49943	0.270107
$580$	23.2586	0.965763
$581$	6.01628	0.249597
$582$	−89.4249	−3.70678
$583$	−9.21835	−0.381785
$584$	29.5210	1.22159
$585$	14.8165	0.612587
$586$	14.5958	0.602947
$587$	−4.81323	−0.198663	−0.0993317	−	0.995054i	$-0.531670\pi$
$587$	−4.81323	−0.198663	−0.0993317	+	0.995054i	$0.531670\pi$
$588$	62.9031	2.59408
$589$	2.69934	0.111224
$590$	−40.0498	−1.64883
$591$	−28.9205	−1.18963
$592$	−20.5648	−0.845210
$593$	27.4494	1.12721	0.563606	−	0.826044i	$-0.309414\pi$
$593$	27.4494	1.12721	0.563606	+	0.826044i	$0.309414\pi$
$594$	9.11490	0.373989
$595$	17.4621	0.715875
$596$	4.22749	0.173165
$597$	−22.7815	−0.932387
$598$	78.2757	3.20093
$599$	18.6290	0.761162	0.380581	−	0.924748i	$-0.375724\pi$
$599$	18.6290	0.761162	0.380581	+	0.924748i	$0.375724\pi$
$600$	84.1952	3.43726
$601$	−5.20057	−0.212135	−0.106068	−	0.994359i	$-0.533826\pi$
$601$	−5.20057	−0.212135	−0.106068	+	0.994359i	$0.533826\pi$
$602$	−11.9425	−0.486741
$603$	14.8782	0.605886
$604$	60.1388	2.44701
$605$	−2.97131	−0.120801
$606$	−70.4504	−2.86185
$607$	38.5202	1.56349	0.781743	−	0.623601i	$-0.214331\pi$
$607$	38.5202	1.56349	0.781743	+	0.623601i	$0.214331\pi$
$608$	−27.9372	−1.13300
$609$	−3.86385	−0.156571
$610$	6.63630	0.268696
$611$	−22.2171	−0.898807
$612$	36.3314	1.46861
$613$	38.0655	1.53745	0.768726	−	0.639578i	$-0.220891\pi$
$613$	38.0655	1.53745	0.768726	+	0.639578i	$0.220891\pi$
$614$	54.3347	2.19277
$615$	−21.1024	−0.850933
$616$	−14.0270	−0.565166
$617$	−40.8903	−1.64618	−0.823092	−	0.567909i	$-0.807753\pi$
$617$	−40.8903	−1.64618	−0.823092	+	0.567909i	$0.807753\pi$
$618$	−1.85841	−0.0747564
$619$	−1.48232	−0.0595796	−0.0297898	−	0.999556i	$-0.509484\pi$
$619$	−1.48232	−0.0595796	−0.0297898	+	0.999556i	$0.509484\pi$
$620$	−46.0915	−1.85108
$621$	26.7269	1.07251
$622$	2.20720	0.0885008
$623$	−11.7052	−0.468958
$624$	127.395	5.09990
$625$	−29.4846	−1.17938
$626$	37.1323	1.48410
$627$	2.10880	0.0842174
$628$	13.7978	0.550594
$629$	−5.12516	−0.204353
$630$	−16.0972	−0.641329
$631$	−45.9250	−1.82824	−0.914122	−	0.405439i	$-0.867119\pi$
$631$	−45.9250	−1.82824	−0.914122	+	0.405439i	$0.867119\pi$
$632$	−119.801	−4.76544
$633$	−14.4065	−0.572607
$634$	31.3987	1.24700
$635$	−46.9971	−1.86502
$636$	−111.713	−4.42972
$637$	17.8869	0.708706
$638$	−3.79121	−0.150095
$639$	3.50082	0.138490
$640$	187.072	7.39465
$641$	10.0510	0.396991	0.198496	−	0.980102i	$-0.436394\pi$
$641$	10.0510	0.396991	0.198496	+	0.980102i	$0.436394\pi$
$642$	−48.7430	−1.92373
$643$	35.4842	1.39936	0.699680	−	0.714457i	$-0.253326\pi$
$643$	35.4842	1.39936	0.699680	+	0.714457i	$0.253326\pi$
$644$	−63.0861	−2.48594
$645$	−19.9875	−0.787008
$646$	−12.1602	−0.478438
$647$	13.6898	0.538201	0.269101	−	0.963112i	$-0.413274\pi$
$647$	13.6898	0.538201	0.269101	+	0.963112i	$0.413274\pi$
$648$	117.286	4.60743
$649$	4.84279	0.190096
$650$	36.7217	1.44034
$651$	7.65697	0.300100
$652$	68.2094	2.67129
$653$	3.90898	0.152970	0.0764852	−	0.997071i	$-0.475630\pi$
$653$	3.90898	0.152970	0.0764852	+	0.997071i	$0.475630\pi$
$654$	113.669	4.44482
$655$	−5.98595	−0.233891
$656$	−59.0407	−2.30515
$657$	−4.09648	−0.159819
$658$	24.1375	0.940978
$659$	15.0568	0.586529	0.293265	−	0.956031i	$-0.405258\pi$
$659$	15.0568	0.586529	0.293265	+	0.956031i	$0.405258\pi$
$660$	−36.0081	−1.40161
$661$	−10.1127	−0.393340	−0.196670	−	0.980470i	$-0.563013\pi$
$661$	−10.1127	−0.393340	−0.196670	+	0.980470i	$0.563013\pi$
$662$	5.61087	0.218073
$663$	31.7494	1.23304
$664$	46.6409	1.81002
$665$	3.99679	0.154989
$666$	4.72457	0.183073
$667$	−11.1167	−0.430439
$668$	123.011	4.75942
$669$	50.8902	1.96753
$670$	85.0301	3.28500
$671$	−0.802455	−0.0309784
$672$	−79.2470	−3.05702
$673$	−33.9676	−1.30936	−0.654678	−	0.755908i	$-0.727196\pi$
$673$	−33.9676	−1.30936	−0.654678	+	0.755908i	$0.727196\pi$
$674$	−67.4189	−2.59688
$675$	12.5385	0.482605
$676$	−6.46536	−0.248668
$677$	6.65874	0.255916	0.127958	−	0.991780i	$-0.459158\pi$
$677$	6.65874	0.255916	0.127958	+	0.991780i	$0.459158\pi$
$678$	−17.2764	−0.663495
$679$	20.4941	0.786491
$680$	135.374	5.19135
$681$	−10.0091	−0.383548
$682$	7.51302	0.287688
$683$	−51.3716	−1.96568	−0.982841	−	0.184457i	$-0.940947\pi$
$683$	−51.3716	−1.96568	−0.982841	+	0.184457i	$0.940947\pi$
$684$	8.31569	0.317958
$685$	5.74827	0.219630
$686$	−45.6402	−1.74255
$687$	−44.9366	−1.71444
$688$	−55.9214	−2.13198
$689$	−31.7665	−1.21021
$690$	−142.329	−5.41839
$691$	20.5978	0.783578	0.391789	−	0.920055i	$-0.371856\pi$
$691$	20.5978	0.783578	0.391789	+	0.920055i	$0.371856\pi$
$692$	−19.6068	−0.745337
$693$	1.94646	0.0739400
$694$	−38.7045	−1.46920
$695$	−12.2848	−0.465988
$696$	−29.9543	−1.13541
$697$	−14.7141	−0.557336
$698$	−7.81207	−0.295691
$699$	−5.81643	−0.219998
$700$	−29.5957	−1.11861
$701$	15.0717	0.569249	0.284624	−	0.958639i	$-0.408131\pi$
$701$	15.0717	0.569249	0.284624	+	0.958639i	$0.408131\pi$
$702$	31.4100	1.18549
$703$	−1.17307	−0.0442431
$704$	−42.6955	−1.60915
$705$	40.3976	1.52146
$706$	−92.1615	−3.46854
$707$	16.1456	0.607218
$708$	58.6877	2.20562
$709$	45.2616	1.69984	0.849918	−	0.526914i	$-0.176651\pi$
$709$	45.2616	1.69984	0.849918	+	0.526914i	$0.176651\pi$
$710$	20.0075	0.750868
$711$	16.6242	0.623457
$712$	−90.7437	−3.40076
$713$	22.0298	0.825023
$714$	−34.4938	−1.29090
$715$	−10.2391	−0.382922
$716$	127.621	4.76943
$717$	−40.2497	−1.50315
$718$	95.9529	3.58093
$719$	−32.6509	−1.21767	−0.608836	−	0.793296i	$-0.708363\pi$
$719$	−32.6509	−1.21767	−0.608836	+	0.793296i	$0.708363\pi$
$720$	−75.3759	−2.80910
$721$	0.425905	0.0158615
$722$	−2.78328	−0.103583
$723$	−20.4537	−0.760682
$724$	−86.9559	−3.23169
$725$	−5.21519	−0.193687
$726$	5.86939	0.217834
$727$	41.6968	1.54645	0.773225	−	0.634132i	$-0.218642\pi$
$727$	41.6968	1.54645	0.773225	+	0.634132i	$0.218642\pi$
$728$	−48.3372	−1.79150
$729$	4.44298	0.164555
$730$	−23.4117	−0.866507
$731$	−13.9367	−0.515467
$732$	−9.72461	−0.359432
$733$	22.9042	0.845985	0.422992	−	0.906133i	$-0.360980\pi$
$733$	22.9042	0.845985	0.422992	+	0.906133i	$0.360980\pi$
$734$	50.4692	1.86285
$735$	−32.5240	−1.19967
$736$	−228.001	−8.40423
$737$	−10.2818	−0.378733
$738$	13.5640	0.499299
$739$	33.6635	1.23833	0.619167	−	0.785260i	$-0.287471\pi$
$739$	33.6635	1.23833	0.619167	+	0.785260i	$0.287471\pi$
$740$	20.0303	0.736327
$741$	7.26694	0.266958
$742$	34.5123	1.26699
$743$	−8.11846	−0.297837	−0.148919	−	0.988849i	$-0.547579\pi$
$743$	−8.11846	−0.297837	−0.148919	+	0.988849i	$0.547579\pi$
$744$	59.3602	2.17625
$745$	−2.18582	−0.0800822
$746$	54.1878	1.98396
$747$	−6.47212	−0.236803
$748$	−25.1073	−0.918014
$749$	11.1708	0.408171
$750$	20.4275	0.745908
$751$	−48.3687	−1.76500	−0.882499	−	0.470314i	$-0.844141\pi$
$751$	−48.3687	−1.76500	−0.882499	+	0.470314i	$0.844141\pi$
$752$	113.025	4.12159
$753$	58.0668	2.11607
$754$	−13.0645	−0.475782
$755$	−31.0947	−1.13165
$756$	−25.3148	−0.920690
$757$	17.5568	0.638114	0.319057	−	0.947735i	$-0.396634\pi$
$757$	17.5568	0.638114	0.319057	+	0.947735i	$0.396634\pi$
$758$	−22.9388	−0.833174
$759$	17.2103	0.624696
$760$	30.9849	1.12394
$761$	−19.3297	−0.700701	−0.350351	−	0.936619i	$-0.613938\pi$
$761$	−19.3297	−0.700701	−0.350351	+	0.936619i	$0.613938\pi$
$762$	92.8360	3.36309
$763$	−26.0503	−0.943086
$764$	−18.9917	−0.687095
$765$	−18.7851	−0.679178
$766$	46.2747	1.67197
$767$	16.6883	0.602578
$768$	−189.460	−6.83655
$769$	8.30997	0.299665	0.149833	−	0.988711i	$-0.452127\pi$
$769$	8.30997	0.299665	0.149833	+	0.988711i	$0.452127\pi$
$770$	11.1242	0.400889
$771$	−38.7966	−1.39723
$772$	−17.7115	−0.637451
$773$	−15.7782	−0.567503	−0.283752	−	0.958898i	$-0.591579\pi$
$773$	−15.7782	−0.567503	−0.283752	+	0.958898i	$0.591579\pi$
$774$	12.8474	0.461790
$775$	10.3349	0.371241
$776$	158.879	5.70344
$777$	−3.32753	−0.119375
$778$	−5.46250	−0.195840
$779$	−3.36782	−0.120665
$780$	−124.084	−4.44292
$781$	−2.41929	−0.0865689
$782$	−99.2420	−3.54889
$783$	−4.46082	−0.159417
$784$	−90.9961	−3.24986
$785$	−7.13417	−0.254629
$786$	11.8244	0.421762
$787$	0.522446	0.0186232	0.00931160	−	0.999957i	$-0.497036\pi$
$787$	0.522446	0.0186232	0.00931160	+	0.999957i	$0.497036\pi$
$788$	78.8108	2.80752
$789$	33.6425	1.19770
$790$	95.0089	3.38027
$791$	3.95934	0.140778
$792$	15.0898	0.536194
$793$	−2.76526	−0.0981973
$794$	−33.8244	−1.20038
$795$	57.7613	2.04858
$796$	62.0817	2.20043
$797$	−27.9594	−0.990373	−0.495187	−	0.868787i	$-0.664900\pi$
$797$	−27.9594	−0.990373	−0.495187	+	0.868787i	$0.664900\pi$
$798$	−7.89509	−0.279483
$799$	28.1680	0.996511
$800$	−106.963	−3.78170
$801$	12.5920	0.444918
$802$	−29.6450	−1.04680
$803$	2.83093	0.0999012
$804$	−124.600	−4.39431
$805$	32.6186	1.14966
$806$	25.8899	0.911933
$807$	−11.3803	−0.400607
$808$	125.168	4.40339
$809$	−31.5433	−1.10900	−0.554501	−	0.832183i	$-0.687091\pi$
$809$	−31.5433	−1.10900	−0.554501	+	0.832183i	$0.687091\pi$
$810$	−93.0143	−3.26819
$811$	26.2360	0.921272	0.460636	−	0.887589i	$-0.347621\pi$
$811$	26.2360	0.921272	0.460636	+	0.887589i	$0.347621\pi$
$812$	10.5293	0.369507
$813$	−29.1828	−1.02349
$814$	−3.26498	−0.114437
$815$	−35.2676	−1.23537
$816$	−161.519	−5.65428
$817$	−3.18989	−0.111600
$818$	93.2583	3.26070
$819$	6.70751	0.234380
$820$	57.5060	2.00820
$821$	−12.3014	−0.429323	−0.214662	−	0.976688i	$-0.568865\pi$
$821$	−12.3014	−0.429323	−0.214662	+	0.976688i	$0.568865\pi$
$822$	−11.3549	−0.396047
$823$	16.8071	0.585859	0.292930	−	0.956134i	$-0.405370\pi$
$823$	16.8071	0.585859	0.292930	+	0.956134i	$0.405370\pi$
$824$	3.30181	0.115024
$825$	8.07393	0.281098
$826$	−18.1308	−0.630851
$827$	−17.8940	−0.622235	−0.311117	−	0.950371i	$-0.600703\pi$
$827$	−17.8940	−0.622235	−0.311117	+	0.950371i	$0.600703\pi$
$828$	67.8659	2.35850
$829$	−19.7370	−0.685495	−0.342747	−	0.939428i	$-0.611357\pi$
$829$	−19.7370	−0.685495	−0.342747	+	0.939428i	$0.611357\pi$
$830$	−36.9888	−1.28390
$831$	−58.3651	−2.02466
$832$	−147.129	−5.10078
$833$	−22.6780	−0.785745
$834$	24.2668	0.840291
$835$	−63.6025	−2.20106
$836$	−5.74667	−0.198753
$837$	8.83999	0.305555
$838$	41.4607	1.43224
$839$	−3.99991	−0.138092	−0.0690460	−	0.997613i	$-0.521996\pi$
$839$	−3.99991	−0.138092	−0.0690460	+	0.997613i	$0.521996\pi$
$840$	87.8921	3.03257
$841$	−27.1446	−0.936020
$842$	79.5262	2.74065
$843$	−40.2734	−1.38709
$844$	39.2590	1.35135
$845$	3.34291	0.115000
$846$	−25.9664	−0.892742
$847$	−1.34513	−0.0462192
$848$	161.605	5.54955
$849$	5.74861	0.197292
$850$	−46.5576	−1.59691
$851$	−9.57363	−0.328180
$852$	−29.3183	−1.00443
$853$	12.8329	0.439391	0.219696	−	0.975568i	$-0.429494\pi$
$853$	12.8329	0.439391	0.219696	+	0.975568i	$0.429494\pi$
$854$	3.00429	0.102805
$855$	−4.29962	−0.147044
$856$	86.6007	2.95995
$857$	−31.1557	−1.06426	−0.532130	−	0.846663i	$-0.678608\pi$
$857$	−31.1557	−1.06426	−0.532130	+	0.846663i	$0.678608\pi$
$858$	20.2259	0.690502
$859$	−6.48922	−0.221409	−0.110705	−	0.993853i	$-0.535311\pi$
$859$	−6.48922	−0.221409	−0.110705	+	0.993853i	$0.535311\pi$
$860$	54.4677	1.85733
$861$	−9.55319	−0.325572
$862$	61.7261	2.10240
$863$	−33.1425	−1.12818	−0.564091	−	0.825712i	$-0.690773\pi$
$863$	−33.1425	−1.12818	−0.564091	+	0.825712i	$0.690773\pi$
$864$	−91.4909	−3.11258
$865$	10.1377	0.344691
$866$	−41.2938	−1.40322
$867$	−4.40391	−0.149565
$868$	−20.8659	−0.708234
$869$	−11.4884	−0.389717
$870$	23.7554	0.805382
$871$	−35.4310	−1.20053
$872$	−201.954	−6.83902
$873$	−22.0469	−0.746174
$874$	−22.7149	−0.768344
$875$	−4.68152	−0.158264
$876$	34.3068	1.15912
$877$	−15.7117	−0.530548	−0.265274	−	0.964173i	$-0.585462\pi$
$877$	−15.7117	−0.530548	−0.265274	+	0.964173i	$0.585462\pi$
$878$	42.9658	1.45003
$879$	11.0588	0.373003
$880$	52.0895	1.75594
$881$	−33.2110	−1.11891	−0.559453	−	0.828862i	$-0.688989\pi$
$881$	−33.2110	−1.11891	−0.559453	+	0.828862i	$0.688989\pi$
$882$	20.9055	0.703923
$883$	31.7783	1.06942	0.534712	−	0.845034i	$-0.320420\pi$
$883$	31.7783	1.06942	0.534712	+	0.845034i	$0.320420\pi$
$884$	−86.5198	−2.90998
$885$	−30.3444	−1.02002
$886$	1.66606	0.0559725
$887$	−21.5202	−0.722577	−0.361289	−	0.932454i	$-0.617663\pi$
$887$	−21.5202	−0.722577	−0.361289	+	0.932454i	$0.617663\pi$
$888$	−25.7965	−0.865674
$889$	−21.2759	−0.713569
$890$	71.9647	2.41226
$891$	11.2472	0.376795
$892$	−138.680	−4.64336
$893$	6.44720	0.215747
$894$	4.31777	0.144408
$895$	−65.9865	−2.20569
$896$	84.6883	2.82924
$897$	59.3069	1.98020
$898$	−34.9012	−1.16467
$899$	−3.67686	−0.122630
$900$	31.8381	1.06127
$901$	40.2752	1.34176
$902$	−9.37360	−0.312107
$903$	−9.04846	−0.301114
$904$	30.6946	1.02089
$905$	44.9605	1.49454
$906$	61.4231	2.04065
$907$	−10.9491	−0.363558	−0.181779	−	0.983339i	$-0.558186\pi$
$907$	−10.9491	−0.363558	−0.181779	+	0.983339i	$0.558186\pi$
$908$	27.2756	0.905172
$909$	−17.3689	−0.576091
$910$	38.3341	1.27076
$911$	32.4243	1.07426	0.537132	−	0.843498i	$-0.319508\pi$
$911$	32.4243	1.07426	0.537132	+	0.843498i	$0.319508\pi$
$912$	−36.9691	−1.22417
$913$	4.47265	0.148023
$914$	38.0426	1.25834
$915$	5.02810	0.166224
$916$	122.456	4.04606
$917$	−2.70987	−0.0894879
$918$	−39.8232	−1.31436
$919$	−8.76890	−0.289259	−0.144630	−	0.989486i	$-0.546199\pi$
$919$	−8.76890	−0.289259	−0.144630	+	0.989486i	$0.546199\pi$
$920$	252.874	8.33701
$921$	41.1676	1.35652
$922$	92.3932	3.04281
$923$	−8.33688	−0.274412
$924$	−16.3010	−0.536265
$925$	−4.49130	−0.147673
$926$	70.4847	2.31627
$927$	−0.458175	−0.0150484
$928$	38.0543	1.24919
$929$	17.3701	0.569894	0.284947	−	0.958543i	$-0.408024\pi$
$929$	17.3701	0.569894	0.284947	+	0.958543i	$0.408024\pi$
$930$	−47.0759	−1.54368
$931$	−5.19063	−0.170116
$932$	15.8503	0.519193
$933$	1.67233	0.0547495
$934$	36.4306	1.19205
$935$	12.9817	0.424548
$936$	51.9996	1.69966
$937$	−58.0831	−1.89749	−0.948746	−	0.316039i	$-0.897647\pi$
$937$	−58.0831	−1.89749	−0.948746	+	0.316039i	$0.897647\pi$
$938$	38.4936	1.25686
$939$	28.1339	0.918115
$940$	−110.087	−3.59064
$941$	49.5931	1.61669	0.808345	−	0.588709i	$-0.200364\pi$
$941$	49.5931	1.61669	0.808345	+	0.588709i	$0.200364\pi$
$942$	14.0925	0.459159
$943$	−27.4854	−0.895049
$944$	−84.8981	−2.76320
$945$	13.0890	0.425785
$946$	−8.87835	−0.288660
$947$	−3.87525	−0.125929	−0.0629644	−	0.998016i	$-0.520055\pi$
$947$	−3.87525	−0.125929	−0.0629644	+	0.998016i	$0.520055\pi$
$948$	−139.223	−4.52175
$949$	9.75538	0.316673
$950$	−10.6563	−0.345736
$951$	23.7898	0.771436
$952$	61.2845	1.98624
$953$	53.5635	1.73509	0.867546	−	0.497358i	$-0.165696\pi$
$953$	53.5635	1.73509	0.867546	+	0.497358i	$0.165696\pi$
$954$	−37.1272	−1.20204
$955$	9.81965	0.317756
$956$	109.684	3.54743
$957$	−2.87248	−0.0928539
$958$	−99.2165	−3.20554
$959$	2.60227	0.0840318
$960$	267.526	8.63437
$961$	−23.7136	−0.764954
$962$	−11.2511	−0.362751
$963$	−12.0171	−0.387247
$964$	55.7381	1.79520
$965$	9.15772	0.294797
$966$	−64.4334	−2.07311
$967$	35.2841	1.13466	0.567329	−	0.823491i	$-0.307977\pi$
$967$	35.2841	1.13466	0.567329	+	0.823491i	$0.307977\pi$
$968$	−10.4280	−0.335170
$969$	−9.21340	−0.295977
$970$	−126.000	−4.04562
$971$	−12.0373	−0.386295	−0.193147	−	0.981170i	$-0.561870\pi$
$971$	−12.0373	−0.386295	−0.193147	+	0.981170i	$0.561870\pi$
$972$	79.8412	2.56091
$973$	−5.56139	−0.178290
$974$	−98.3173	−3.15029
$975$	27.8228	0.891043
$976$	14.0677	0.450296
$977$	−48.2203	−1.54270	−0.771352	−	0.636409i	$-0.780419\pi$
$977$	−48.2203	−1.54270	−0.771352	+	0.636409i	$0.780419\pi$
$978$	69.6661	2.22768
$979$	−8.70190	−0.278114
$980$	88.6306	2.83120
$981$	28.0241	0.894741
$982$	32.0657	1.02326
$983$	25.5262	0.814159	0.407080	−	0.913393i	$-0.366547\pi$
$983$	25.5262	0.814159	0.407080	+	0.913393i	$0.366547\pi$
$984$	−74.0606	−2.36097
$985$	−40.7491	−1.29837
$986$	16.5639	0.527501
$987$	18.2882	0.582120
$988$	−19.8030	−0.630018
$989$	−26.0333	−0.827810
$990$	−11.9671	−0.380338
$991$	19.3464	0.614558	0.307279	−	0.951619i	$-0.400581\pi$
$991$	19.3464	0.614558	0.307279	+	0.951619i	$0.400581\pi$
$992$	−75.4120	−2.39433
$993$	4.25117	0.134907
$994$	9.05751	0.287287
$995$	−32.0993	−1.01762
$996$	54.2021	1.71746
$997$	16.9925	0.538157	0.269078	−	0.963118i	$-0.413281\pi$
$997$	16.9925	0.538157	0.269078	+	0.963118i	$0.413281\pi$
$998$	−82.9802	−2.62669
$999$	−3.84165	−0.121544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.a.d.1.1	✓	7
3.2	odd	2		1881.2.a.p.1.7		7
4.3	odd	2		3344.2.a.ba.1.6		7
5.4	even	2		5225.2.a.n.1.7		7
11.10	odd	2		2299.2.a.q.1.7		7
19.18	odd	2		3971.2.a.i.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.d.1.1	✓	7	1.1	even	1	trivial
1881.2.a.p.1.7		7	3.2	odd	2
2299.2.a.q.1.7		7	11.10	odd	2
3344.2.a.ba.1.6		7	4.3	odd	2
3971.2.a.i.1.7		7	19.18	odd	2
5225.2.a.n.1.7		7	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78328 q^{2} -2.10880 q^{3} +5.74667 q^{4} -2.97131 q^{5} +5.86939 q^{6} -1.34513 q^{7} -10.4280 q^{8} +1.44705 q^{9} +O(q^{10})\)	\(q-2.78328 q^{2} -2.10880 q^{3} +5.74667 q^{4} -2.97131 q^{5} +5.86939 q^{6} -1.34513 q^{7} -10.4280 q^{8} +1.44705 q^{9} +8.27000 q^{10} -1.00000 q^{11} -12.1186 q^{12} -3.44600 q^{13} +3.74387 q^{14} +6.26590 q^{15} +17.5308 q^{16} +4.36902 q^{17} -4.02754 q^{18} +1.00000 q^{19} -17.0751 q^{20} +2.83661 q^{21} +2.78328 q^{22} +8.16120 q^{23} +21.9907 q^{24} +3.82868 q^{25} +9.59120 q^{26} +3.27487 q^{27} -7.73000 q^{28} -1.36214 q^{29} -17.4398 q^{30} +2.69934 q^{31} -27.9372 q^{32} +2.10880 q^{33} -12.1602 q^{34} +3.99679 q^{35} +8.31569 q^{36} -1.17307 q^{37} -2.78328 q^{38} +7.26694 q^{39} +30.9849 q^{40} -3.36782 q^{41} -7.89509 q^{42} -3.18989 q^{43} -5.74667 q^{44} -4.29962 q^{45} -22.7149 q^{46} +6.44720 q^{47} -36.9691 q^{48} -5.19063 q^{49} -10.6563 q^{50} -9.21340 q^{51} -19.8030 q^{52} +9.21835 q^{53} -9.11490 q^{54} +2.97131 q^{55} +14.0270 q^{56} -2.10880 q^{57} +3.79121 q^{58} -4.84279 q^{59} +36.0081 q^{60} +0.802455 q^{61} -7.51302 q^{62} -1.94646 q^{63} +42.6955 q^{64} +10.2391 q^{65} -5.86939 q^{66} +10.2818 q^{67} +25.1073 q^{68} -17.2103 q^{69} -11.1242 q^{70} +2.41929 q^{71} -15.0898 q^{72} -2.83093 q^{73} +3.26498 q^{74} -8.07393 q^{75} +5.74667 q^{76} +1.34513 q^{77} -20.2259 q^{78} +11.4884 q^{79} -52.0895 q^{80} -11.2472 q^{81} +9.37360 q^{82} -4.47265 q^{83} +16.3010 q^{84} -12.9817 q^{85} +8.87835 q^{86} +2.87248 q^{87} +10.4280 q^{88} +8.70190 q^{89} +11.9671 q^{90} +4.63532 q^{91} +46.8997 q^{92} -5.69237 q^{93} -17.9444 q^{94} -2.97131 q^{95} +58.9141 q^{96} -15.2358 q^{97} +14.4470 q^{98} -1.44705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9	\( 7 q - q^{2} + 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} - 9 q^{8} + 11 q^{9} - 6 q^{10} - 7 q^{11} - 16 q^{12} - 4 q^{13} + 6 q^{14} + 12 q^{15} + 27 q^{16} + 2 q^{17} + 9 q^{18} + 7 q^{19} - 4 q^{20} - 14 q^{21} + q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} - 4 q^{27} + 26 q^{28} - 18 q^{29} - 42 q^{30} + 24 q^{31} - 49 q^{32} - 2 q^{33} - 6 q^{34} + 8 q^{35} + 29 q^{36} - q^{38} + 24 q^{39} - 2 q^{40} - 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} - 4 q^{46} + 8 q^{47} - 72 q^{48} + 17 q^{49} - 33 q^{50} - 24 q^{51} - 60 q^{52} + 2 q^{53} - 52 q^{54} - 2 q^{55} + 26 q^{56} + 2 q^{57} - 8 q^{58} - 10 q^{59} + 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} - 14 q^{65} + 2 q^{66} + 8 q^{67} - 18 q^{68} - 6 q^{69} - 66 q^{70} + 10 q^{71} + 53 q^{72} - 6 q^{73} + 26 q^{74} + 26 q^{75} + 15 q^{76} - 10 q^{77} + 22 q^{78} + 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} - 6 q^{84} - 12 q^{85} + 8 q^{86} + 6 q^{87} + 9 q^{88} + 20 q^{90} + 12 q^{91} + 2 q^{93} + 24 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q - q^2 + 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 - 9 * q^8 + 11 * q^9 - 6 * q^10 - 7 * q^11 - 16 * q^12 - 4 * q^13 + 6 * q^14 + 12 * q^15 + 27 * q^16 + 2 * q^17 + 9 * q^18 + 7 * q^19 - 4 * q^20 - 14 * q^21 + q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 - 4 * q^27 + 26 * q^28 - 18 * q^29 - 42 * q^30 + 24 * q^31 - 49 * q^32 - 2 * q^33 - 6 * q^34 + 8 * q^35 + 29 * q^36 - q^38 + 24 * q^39 - 2 * q^40 - 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 - 4 * q^46 + 8 * q^47 - 72 * q^48 + 17 * q^49 - 33 * q^50 - 24 * q^51 - 60 * q^52 + 2 * q^53 - 52 * q^54 - 2 * q^55 + 26 * q^56 + 2 * q^57 - 8 * q^58 - 10 * q^59 + 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 - 14 * q^65 + 2 * q^66 + 8 * q^67 - 18 * q^68 - 6 * q^69 - 66 * q^70 + 10 * q^71 + 53 * q^72 - 6 * q^73 + 26 * q^74 + 26 * q^75 + 15 * q^76 - 10 * q^77 + 22 * q^78 + 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 + 6 * q^87 + 9 * q^88 + 20 * q^90 + 12 * q^91 + 2 * q^93 + 24 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 19 * q^98 - 11 * q^99

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