LMFDB - Embedded newform 1849.2.a.n.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.18520$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18520 q^{2} -2.30227 q^{3} -0.595300 q^{4} -3.24275 q^{5} -2.72866 q^{6} +2.76837 q^{7} -3.07595 q^{8} +2.30047 q^{9} +O(q^{10})$	\(q+1.18520 q^{2} -2.30227 q^{3} -0.595300 q^{4} -3.24275 q^{5} -2.72866 q^{6} +2.76837 q^{7} -3.07595 q^{8} +2.30047 q^{9} -3.84331 q^{10} +5.58012 q^{11} +1.37054 q^{12} +1.64410 q^{13} +3.28107 q^{14} +7.46570 q^{15} -2.45502 q^{16} -0.758169 q^{17} +2.72651 q^{18} -2.17868 q^{19} +1.93041 q^{20} -6.37355 q^{21} +6.61355 q^{22} -0.00141055 q^{23} +7.08168 q^{24} +5.51542 q^{25} +1.94858 q^{26} +1.61052 q^{27} -1.64801 q^{28} -4.68548 q^{29} +8.84835 q^{30} +4.03357 q^{31} +3.24222 q^{32} -12.8470 q^{33} -0.898582 q^{34} -8.97713 q^{35} -1.36947 q^{36} +1.99901 q^{37} -2.58217 q^{38} -3.78516 q^{39} +9.97454 q^{40} -7.00114 q^{41} -7.55393 q^{42} -3.32185 q^{44} -7.45983 q^{45} -0.00167179 q^{46} -7.86308 q^{47} +5.65212 q^{48} +0.663871 q^{49} +6.53688 q^{50} +1.74551 q^{51} -0.978731 q^{52} -3.94381 q^{53} +1.90879 q^{54} -18.0949 q^{55} -8.51537 q^{56} +5.01592 q^{57} -5.55324 q^{58} +3.64476 q^{59} -4.44433 q^{60} -8.55078 q^{61} +4.78059 q^{62} +6.36854 q^{63} +8.75271 q^{64} -5.33139 q^{65} -15.2262 q^{66} +9.38859 q^{67} +0.451338 q^{68} +0.00324748 q^{69} -10.6397 q^{70} -6.90767 q^{71} -7.07612 q^{72} -11.1085 q^{73} +2.36923 q^{74} -12.6980 q^{75} +1.29697 q^{76} +15.4478 q^{77} -4.48617 q^{78} +6.53961 q^{79} +7.96100 q^{80} -10.6093 q^{81} -8.29775 q^{82} -5.70753 q^{83} +3.79417 q^{84} +2.45855 q^{85} +10.7873 q^{87} -17.1642 q^{88} -8.63463 q^{89} -8.84140 q^{90} +4.55147 q^{91} +0.000839703 q^{92} -9.28638 q^{93} -9.31932 q^{94} +7.06491 q^{95} -7.46447 q^{96} -17.6655 q^{97} +0.786820 q^{98} +12.8369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.18520	0.838063	0.419032	−	0.907972i	$-0.362370\pi$
$2$	1.18520	0.838063	0.419032	+	0.907972i	$0.362370\pi$
$3$	−2.30227	−1.32922	−0.664609	−	0.747191i	$-0.731402\pi$
$3$	−2.30227	−1.32922	−0.664609	+	0.747191i	$0.731402\pi$
$4$	−0.595300	−0.297650
$5$	−3.24275	−1.45020	−0.725101	−	0.688643i	$-0.758207\pi$
$5$	−3.24275	−1.45020	−0.725101	+	0.688643i	$0.758207\pi$
$6$	−2.72866	−1.11397
$7$	2.76837	1.04635	0.523173	−	0.852227i	$-0.324748\pi$
$7$	2.76837	1.04635	0.523173	+	0.852227i	$0.324748\pi$
$8$	−3.07595	−1.08751
$9$	2.30047	0.766822
$10$	−3.84331	−1.21536
$11$	5.58012	1.68247	0.841234	−	0.540671i	$-0.181830\pi$
$11$	5.58012	1.68247	0.841234	+	0.540671i	$0.181830\pi$
$12$	1.37054	0.395642
$13$	1.64410	0.455990	0.227995	−	0.973662i	$-0.426783\pi$
$13$	1.64410	0.455990	0.227995	+	0.973662i	$0.426783\pi$
$14$	3.28107	0.876904
$15$	7.46570	1.92763
$16$	−2.45502	−0.613754
$17$	−0.758169	−0.183883	−0.0919415	−	0.995764i	$-0.529307\pi$
$17$	−0.758169	−0.183883	−0.0919415	+	0.995764i	$0.529307\pi$
$18$	2.72651	0.642645
$19$	−2.17868	−0.499823	−0.249912	−	0.968269i	$-0.580402\pi$
$19$	−2.17868	−0.499823	−0.249912	+	0.968269i	$0.580402\pi$
$20$	1.93041	0.431653
$21$	−6.37355	−1.39082
$22$	6.61355	1.41001
$23$	−0.00141055	−0.000294121 0	−0.000147060	−	1.00000i	$-0.500047\pi$
$23$	−0.00141055	−0.000294121 0	−0.000147060		1.00000i	$0.500047\pi$
$24$	7.08168	1.44554
$25$	5.51542	1.10308
$26$	1.94858	0.382149
$27$	1.61052	0.309945
$28$	−1.64801	−0.311445
$29$	−4.68548	−0.870073	−0.435036	−	0.900413i	$-0.643264\pi$
$29$	−4.68548	−0.870073	−0.435036	+	0.900413i	$0.643264\pi$
$30$	8.84835	1.61548
$31$	4.03357	0.724450	0.362225	−	0.932091i	$-0.382017\pi$
$31$	4.03357	0.724450	0.362225	+	0.932091i	$0.382017\pi$
$32$	3.24222	0.573148
$33$	−12.8470	−2.23637
$34$	−0.898582	−0.154106
$35$	−8.97713	−1.51741
$36$	−1.36947	−0.228245
$37$	1.99901	0.328636	0.164318	−	0.986407i	$-0.447458\pi$
$37$	1.99901	0.328636	0.164318	+	0.986407i	$0.447458\pi$
$38$	−2.58217	−0.418883
$39$	−3.78516	−0.606111
$40$	9.97454	1.57711
$41$	−7.00114	−1.09339	−0.546697	−	0.837330i	$-0.684115\pi$
$41$	−7.00114	−1.09339	−0.546697	+	0.837330i	$0.684115\pi$
$42$	−7.55393	−1.16560
$43$	0	0
$43$	0	0
$44$	−3.32185	−0.500787
$45$	−7.45983	−1.11205
$46$	−0.00167179	−0.000246492 0
$47$	−7.86308	−1.14695	−0.573474	−	0.819224i	$-0.694405\pi$
$47$	−7.86308	−1.14695	−0.573474	+	0.819224i	$0.694405\pi$
$48$	5.65212	0.815813
$49$	0.663871	0.0948388
$50$	6.53688	0.924455
$51$	1.74551	0.244421
$52$	−0.978731	−0.135726
$53$	−3.94381	−0.541724	−0.270862	−	0.962618i	$-0.587309\pi$
$53$	−3.94381	−0.541724	−0.270862	+	0.962618i	$0.587309\pi$
$54$	1.90879	0.259753
$55$	−18.0949	−2.43992
$56$	−8.51537	−1.13791
$57$	5.01592	0.664374
$58$	−5.55324	−0.729176
$59$	3.64476	0.474508	0.237254	−	0.971448i	$-0.423753\pi$
$59$	3.64476	0.474508	0.237254	+	0.971448i	$0.423753\pi$
$60$	−4.44433	−0.573761
$61$	−8.55078	−1.09482	−0.547408	−	0.836866i	$-0.684385\pi$
$61$	−8.55078	−1.09482	−0.547408	+	0.836866i	$0.684385\pi$
$62$	4.78059	0.607135
$63$	6.36854	0.802361
$64$	8.75271	1.09409
$65$	−5.33139	−0.661278
$66$	−15.2262	−1.87422
$67$	9.38859	1.14700	0.573500	−	0.819206i	$-0.305585\pi$
$67$	9.38859	1.14700	0.573500	+	0.819206i	$0.305585\pi$
$68$	0.451338	0.0547328
$69$	0.00324748	0.000390951 0
$70$	−10.6397	−1.27169
$71$	−6.90767	−0.819789	−0.409895	−	0.912133i	$-0.634435\pi$
$71$	−6.90767	−0.819789	−0.409895	+	0.912133i	$0.634435\pi$
$72$	−7.07612	−0.833929
$73$	−11.1085	−1.30015	−0.650076	−	0.759869i	$-0.725263\pi$
$73$	−11.1085	−1.30015	−0.650076	+	0.759869i	$0.725263\pi$
$74$	2.36923	0.275417
$75$	−12.6980	−1.46624
$76$	1.29697	0.148772
$77$	15.4478	1.76044
$78$	−4.48617	−0.507959
$79$	6.53961	0.735763	0.367882	−	0.929873i	$-0.380083\pi$
$79$	6.53961	0.735763	0.367882	+	0.929873i	$0.380083\pi$
$80$	7.96100	0.890067
$81$	−10.6093	−1.17881
$82$	−8.29775	−0.916334
$83$	−5.70753	−0.626482	−0.313241	−	0.949674i	$-0.601415\pi$
$83$	−5.70753	−0.626482	−0.313241	+	0.949674i	$0.601415\pi$
$84$	3.79417	0.413978
$85$	2.45855	0.266667
$86$	0	0
$87$	10.7873	1.15652
$88$	−17.1642	−1.82971
$89$	−8.63463	−0.915269	−0.457635	−	0.889140i	$-0.651303\pi$
$89$	−8.63463	−0.915269	−0.457635	+	0.889140i	$0.651303\pi$
$90$	−8.84140	−0.931965
$91$	4.55147	0.477123
$92$	0.000839703 0	8.75451e−5 0
$93$	−9.28638	−0.962953
$94$	−9.31932	−0.961214
$95$	7.06491	0.724844
$96$	−7.46447	−0.761839
$97$	−17.6655	−1.79366	−0.896832	−	0.442371i	$-0.854137\pi$
$97$	−17.6655	−1.79366	−0.896832	+	0.442371i	$0.854137\pi$
$98$	0.786820	0.0794809
$99$	12.8369	1.29015
$100$	−3.28333	−0.328333
$101$	10.1012	1.00511	0.502553	−	0.864546i	$-0.332394\pi$
$101$	10.1012	1.00511	0.502553	+	0.864546i	$0.332394\pi$
$102$	2.06878	0.204840
$103$	−13.9468	−1.37422	−0.687110	−	0.726553i	$-0.741121\pi$
$103$	−13.9468	−1.37422	−0.687110	+	0.726553i	$0.741121\pi$
$104$	−5.05716	−0.495895
$105$	20.6678	2.01697
$106$	−4.67421	−0.453999
$107$	−7.47180	−0.722326	−0.361163	−	0.932503i	$-0.617620\pi$
$107$	−7.47180	−0.722326	−0.361163	+	0.932503i	$0.617620\pi$
$108$	−0.958743	−0.0922551
$109$	−7.61766	−0.729639	−0.364820	−	0.931078i	$-0.618869\pi$
$109$	−7.61766	−0.729639	−0.364820	+	0.931078i	$0.618869\pi$
$110$	−21.4461	−2.04481
$111$	−4.60227	−0.436829
$112$	−6.79639	−0.642199
$113$	−6.45052	−0.606814	−0.303407	−	0.952861i	$-0.598124\pi$
$113$	−6.45052	−0.606814	−0.303407	+	0.952861i	$0.598124\pi$
$114$	5.94486	0.556787
$115$	0.00457407	0.000426534 0
$116$	2.78927	0.258977
$117$	3.78219	0.349663
$118$	4.31977	0.397667
$119$	−2.09889	−0.192405
$120$	−22.9641	−2.09633
$121$	20.1377	1.83070
$122$	−10.1344	−0.917524
$123$	16.1185	1.45336
$124$	−2.40118	−0.215633
$125$	−1.67139	−0.149494
$126$	7.54800	0.672429
$127$	7.65176	0.678984	0.339492	−	0.940609i	$-0.389745\pi$
$127$	7.65176	0.678984	0.339492	+	0.940609i	$0.389745\pi$
$128$	3.88928	0.343767
$129$	0	0
$130$	−6.31877	−0.554193
$131$	17.4448	1.52416	0.762080	−	0.647483i	$-0.224178\pi$
$131$	17.4448	1.52416	0.762080	+	0.647483i	$0.224178\pi$
$132$	7.64780	0.665655
$133$	−6.03139	−0.522988
$134$	11.1274	0.961258
$135$	−5.22251	−0.449482
$136$	2.33209	0.199975
$137$	2.60242	0.222340	0.111170	−	0.993801i	$-0.464540\pi$
$137$	2.60242	0.222340	0.111170	+	0.993801i	$0.464540\pi$
$138$	0.00384891	0.000327641 0
$139$	7.94294	0.673712	0.336856	−	0.941556i	$-0.390637\pi$
$139$	7.94294	0.673712	0.336856	+	0.941556i	$0.390637\pi$
$140$	5.34409	0.451658
$141$	18.1030	1.52454
$142$	−8.18697	−0.687035
$143$	9.17425	0.767189
$144$	−5.64768	−0.470640
$145$	15.1939	1.26178
$146$	−13.1658	−1.08961
$147$	−1.52841	−0.126061
$148$	−1.19001	−0.0978185
$149$	−18.6637	−1.52899	−0.764496	−	0.644629i	$-0.777012\pi$
$149$	−18.6637	−1.52899	−0.764496	+	0.644629i	$0.777012\pi$
$150$	−15.0497	−1.22880
$151$	9.34975	0.760872	0.380436	−	0.924807i	$-0.375774\pi$
$151$	9.34975	0.760872	0.380436	+	0.924807i	$0.375774\pi$
$152$	6.70151	0.543564
$153$	−1.74414	−0.141006
$154$	18.3088	1.47536
$155$	−13.0798	−1.05060
$156$	2.25331	0.180409
$157$	1.48255	0.118320	0.0591600	−	0.998249i	$-0.481158\pi$
$157$	1.48255	0.118320	0.0591600	+	0.998249i	$0.481158\pi$
$158$	7.75074	0.616616
$159$	9.07974	0.720070
$160$	−10.5137	−0.831180
$161$	−0.00390493	−0.000307752 0
$162$	−12.5741	−0.987914
$163$	14.5394	1.13881	0.569407	−	0.822056i	$-0.307173\pi$
$163$	14.5394	1.13881	0.569407	+	0.822056i	$0.307173\pi$
$164$	4.16778	0.325449
$165$	41.6595	3.24318
$166$	−6.76456	−0.525032
$167$	7.93560	0.614075	0.307038	−	0.951697i	$-0.400662\pi$
$167$	7.93560	0.614075	0.307038	+	0.951697i	$0.400662\pi$
$168$	19.6047	1.51254
$169$	−10.2969	−0.792073
$170$	2.91388	0.223484
$171$	−5.01198	−0.383275
$172$	0	0
$173$	−1.73137	−0.131634	−0.0658169	−	0.997832i	$-0.520965\pi$
$173$	−1.73137	−0.131634	−0.0658169	+	0.997832i	$0.520965\pi$
$174$	12.7851	0.969234
$175$	15.2687	1.15421
$176$	−13.6993	−1.03262
$177$	−8.39124	−0.630725
$178$	−10.2338	−0.767053
$179$	−8.14405	−0.608715	−0.304358	−	0.952558i	$-0.598442\pi$
$179$	−8.14405	−0.608715	−0.304358	+	0.952558i	$0.598442\pi$
$180$	4.44084	0.331001
$181$	−12.8700	−0.956620	−0.478310	−	0.878191i	$-0.658750\pi$
$181$	−12.8700	−0.956620	−0.478310	+	0.878191i	$0.658750\pi$
$182$	5.39440	0.399860
$183$	19.6862	1.45525
$184$	0.00433879	0.000319860 0
$185$	−6.48230	−0.476588
$186$	−11.0062	−0.807015
$187$	−4.23067	−0.309377
$188$	4.68089	0.341389
$189$	4.45851	0.324309
$190$	8.37333	0.607465
$191$	−14.7575	−1.06782	−0.533909	−	0.845542i	$-0.679277\pi$
$191$	−14.7575	−1.06782	−0.533909	+	0.845542i	$0.679277\pi$
$192$	−20.1511	−1.45428
$193$	17.4834	1.25848	0.629241	−	0.777210i	$-0.283366\pi$
$193$	17.4834	1.25848	0.629241	+	0.777210i	$0.283366\pi$
$194$	−20.9372	−1.50320
$195$	12.2743	0.878983
$196$	−0.395203	−0.0282288
$197$	−2.73256	−0.194687	−0.0973436	−	0.995251i	$-0.531035\pi$
$197$	−2.73256	−0.194687	−0.0973436	+	0.995251i	$0.531035\pi$
$198$	15.2143	1.08123
$199$	−3.89720	−0.276265	−0.138133	−	0.990414i	$-0.544110\pi$
$199$	−3.89720	−0.276265	−0.138133	+	0.990414i	$0.544110\pi$
$200$	−16.9652	−1.19962
$201$	−21.6151	−1.52461
$202$	11.9719	0.842343
$203$	−12.9712	−0.910397
$204$	−1.03910	−0.0727519
$205$	22.7029	1.58564
$206$	−16.5298	−1.15168
$207$	−0.00324493	−0.000225538 0
$208$	−4.03628	−0.279866
$209$	−12.1573	−0.840936
$210$	24.4955	1.69035
$211$	−10.0532	−0.692092	−0.346046	−	0.938218i	$-0.612476\pi$
$211$	−10.0532	−0.692092	−0.346046	+	0.938218i	$0.612476\pi$
$212$	2.34775	0.161244
$213$	15.9033	1.08968
$214$	−8.85557	−0.605355
$215$	0	0
$216$	−4.95388	−0.337069
$217$	11.1664	0.758025
$218$	−9.02845	−0.611484
$219$	25.5748	1.72819
$220$	10.7719	0.726242
$221$	−1.24650	−0.0838489
$222$	−5.45462	−0.366090
$223$	−14.9829	−1.00333	−0.501664	−	0.865063i	$-0.667279\pi$
$223$	−14.9829	−1.00333	−0.501664	+	0.865063i	$0.667279\pi$
$224$	8.97565	0.599711
$225$	12.6880	0.845870
$226$	−7.64516	−0.508548
$227$	−8.88345	−0.589615	−0.294808	−	0.955557i	$-0.595256\pi$
$227$	−8.88345	−0.589615	−0.294808	+	0.955557i	$0.595256\pi$
$228$	−2.98598	−0.197751
$229$	20.2878	1.34065	0.670327	−	0.742066i	$-0.266154\pi$
$229$	20.2878	1.34065	0.670327	+	0.742066i	$0.266154\pi$
$230$	0.00542119	0.000357463 0
$231$	−35.5651	−2.34001
$232$	14.4123	0.946215
$233$	10.2023	0.668375	0.334188	−	0.942507i	$-0.391538\pi$
$233$	10.2023	0.668375	0.334188	+	0.942507i	$0.391538\pi$
$234$	4.48265	0.293040
$235$	25.4980	1.66331
$236$	−2.16973	−0.141237
$237$	−15.0560	−0.977990
$238$	−2.48761	−0.161248
$239$	−7.98940	−0.516792	−0.258396	−	0.966039i	$-0.583194\pi$
$239$	−7.98940	−0.516792	−0.258396	+	0.966039i	$0.583194\pi$
$240$	−18.3284	−1.18309
$241$	−8.40852	−0.541640	−0.270820	−	0.962630i	$-0.587295\pi$
$241$	−8.40852	−0.541640	−0.270820	+	0.962630i	$0.587295\pi$
$242$	23.8672	1.53424
$243$	19.5939	1.25695
$244$	5.09028	0.325872
$245$	−2.15277	−0.137535
$246$	19.1037	1.21801
$247$	−3.58196	−0.227915
$248$	−12.4071	−0.787849
$249$	13.1403	0.832732
$250$	−1.98093	−0.125285
$251$	−18.2941	−1.15471	−0.577356	−	0.816493i	$-0.695915\pi$
$251$	−18.2941	−1.15471	−0.577356	+	0.816493i	$0.695915\pi$
$252$	−3.79119	−0.238823
$253$	−0.00787105	−0.000494849 0
$254$	9.06886	0.569031
$255$	−5.66026	−0.354459
$256$	−12.8958	−0.805990
$257$	19.1765	1.19620	0.598098	−	0.801423i	$-0.295923\pi$
$257$	19.1765	1.19620	0.598098	+	0.801423i	$0.295923\pi$
$258$	0	0
$259$	5.53401	0.343866
$260$	3.17378	0.196830
$261$	−10.7788	−0.667191
$262$	20.6756	1.27734
$263$	−13.9076	−0.857577	−0.428789	−	0.903405i	$-0.641060\pi$
$263$	−13.9076	−0.857577	−0.428789	+	0.903405i	$0.641060\pi$
$264$	39.5166	2.43208
$265$	12.7888	0.785610
$266$	−7.14840	−0.438297
$267$	19.8793	1.21659
$268$	−5.58903	−0.341405
$269$	−27.0907	−1.65175	−0.825875	−	0.563854i	$-0.809318\pi$
$269$	−27.0907	−1.65175	−0.825875	+	0.563854i	$0.809318\pi$
$270$	−6.18972	−0.376694
$271$	20.2820	1.23205	0.616023	−	0.787728i	$-0.288743\pi$
$271$	20.2820	1.23205	0.616023	+	0.787728i	$0.288743\pi$
$272$	1.86132	0.112859
$273$	−10.4787	−0.634201
$274$	3.08439	0.186335
$275$	30.7767	1.85590
$276$	−0.00193323	−0.000116367 0
$277$	17.4577	1.04893	0.524466	−	0.851432i	$-0.324265\pi$
$277$	17.4577	1.04893	0.524466	+	0.851432i	$0.324265\pi$
$278$	9.41398	0.564613
$279$	9.27909	0.555524
$280$	27.6132	1.65020
$281$	15.4044	0.918952	0.459476	−	0.888190i	$-0.348037\pi$
$281$	15.4044	0.918952	0.459476	+	0.888190i	$0.348037\pi$
$282$	21.4556	1.27766
$283$	−16.2175	−0.964033	−0.482017	−	0.876162i	$-0.660096\pi$
$283$	−16.2175	−0.964033	−0.482017	+	0.876162i	$0.660096\pi$
$284$	4.11214	0.244011
$285$	−16.2654	−0.963476
$286$	10.8733	0.642953
$287$	−19.3817	−1.14407
$288$	7.45861	0.439503
$289$	−16.4252	−0.966187
$290$	18.0078	1.05745
$291$	40.6709	2.38417
$292$	6.61290	0.386990
$293$	−20.2742	−1.18443	−0.592216	−	0.805779i	$-0.701747\pi$
$293$	−20.2742	−1.18443	−0.592216	+	0.805779i	$0.701747\pi$
$294$	−1.81148	−0.105647
$295$	−11.8191	−0.688132
$296$	−6.14886	−0.357395
$297$	8.98688	0.521472
$298$	−22.1202	−1.28139
$299$	−0.00231909	−0.000134116 0
$300$	7.55913	0.436427
$301$	0	0
$302$	11.0813	0.637659
$303$	−23.2557	−1.33601
$304$	5.34869	0.306769
$305$	27.7280	1.58770
$306$	−2.06716	−0.118172
$307$	8.29541	0.473444	0.236722	−	0.971577i	$-0.423927\pi$
$307$	8.29541	0.473444	0.236722	+	0.971577i	$0.423927\pi$
$308$	−9.19610	−0.523996
$309$	32.1094	1.82664
$310$	−15.5022	−0.880468
$311$	−29.9812	−1.70008	−0.850039	−	0.526720i	$-0.823422\pi$
$311$	−29.9812	−1.70008	−0.850039	+	0.526720i	$0.823422\pi$
$312$	11.6430	0.659153
$313$	−6.53698	−0.369492	−0.184746	−	0.982786i	$-0.559146\pi$
$313$	−6.53698	−0.369492	−0.184746	+	0.982786i	$0.559146\pi$
$314$	1.75711	0.0991597
$315$	−20.6516	−1.16358
$316$	−3.89303	−0.219000
$317$	−7.83698	−0.440169	−0.220084	−	0.975481i	$-0.570633\pi$
$317$	−7.83698	−0.440169	−0.220084	+	0.975481i	$0.570633\pi$
$318$	10.7613	0.603464
$319$	−26.1455	−1.46387
$320$	−28.3828	−1.58665
$321$	17.2021	0.960129
$322$	−0.00462813	−0.000257915 0
$323$	1.65181	0.0919090
$324$	6.31569	0.350872
$325$	9.06789	0.502996
$326$	17.2321	0.954398
$327$	17.5379	0.969850
$328$	21.5352	1.18908
$329$	−21.7679	−1.20010
$330$	49.3748	2.71799
$331$	−24.2612	−1.33352	−0.666759	−	0.745274i	$-0.732319\pi$
$331$	−24.2612	−1.33352	−0.666759	+	0.745274i	$0.732319\pi$
$332$	3.39769	0.186473
$333$	4.59866	0.252005
$334$	9.40528	0.514634
$335$	−30.4449	−1.66338
$336$	15.6472	0.853623
$337$	−33.1345	−1.80495	−0.902476	−	0.430740i	$-0.858252\pi$
$337$	−33.1345	−1.80495	−0.902476	+	0.430740i	$0.858252\pi$
$338$	−12.2039	−0.663807
$339$	14.8509	0.806588
$340$	−1.46358	−0.0793736
$341$	22.5078	1.21886
$342$	−5.94019	−0.321209
$343$	−17.5407	−0.947111
$344$	0	0
$345$	−0.0105308	−0.000566957 0
$346$	−2.05202	−0.110317
$347$	−3.65484	−0.196202	−0.0981011	−	0.995176i	$-0.531277\pi$
$347$	−3.65484	−0.196202	−0.0981011	+	0.995176i	$0.531277\pi$
$348$	−6.42167	−0.344237
$349$	−5.58223	−0.298810	−0.149405	−	0.988776i	$-0.547736\pi$
$349$	−5.58223	−0.298810	−0.149405	+	0.988776i	$0.547736\pi$
$350$	18.0965	0.967299
$351$	2.64785	0.141332
$352$	18.0919	0.964303
$353$	−4.10575	−0.218527	−0.109264	−	0.994013i	$-0.534849\pi$
$353$	−4.10575	−0.218527	−0.109264	+	0.994013i	$0.534849\pi$
$354$	−9.94530	−0.528587
$355$	22.3998	1.18886
$356$	5.14020	0.272430
$357$	4.83223	0.255748
$358$	−9.65233	−0.510142
$359$	2.66385	0.140592	0.0702962	−	0.997526i	$-0.477606\pi$
$359$	2.66385	0.140592	0.0702962	+	0.997526i	$0.477606\pi$
$360$	22.9461	1.20936
$361$	−14.2534	−0.750177
$362$	−15.2535	−0.801708
$363$	−46.3625	−2.43340
$364$	−2.70949	−0.142016
$365$	36.0221	1.88548
$366$	23.3321	1.21959
$367$	−2.75378	−0.143746	−0.0718731	−	0.997414i	$-0.522898\pi$
$367$	−2.75378	−0.143746	−0.0718731	+	0.997414i	$0.522898\pi$
$368$	0.00346293	0.000180518 0
$369$	−16.1059	−0.838439
$370$	−7.68282	−0.399411
$371$	−10.9179	−0.566831
$372$	5.52818	0.286623
$373$	33.4700	1.73301	0.866506	−	0.499166i	$-0.166360\pi$
$373$	33.4700	1.73301	0.866506	+	0.499166i	$0.166360\pi$
$374$	−5.01419	−0.259278
$375$	3.84800	0.198710
$376$	24.1864	1.24732
$377$	−7.70339	−0.396745
$378$	5.28423	0.271791
$379$	−16.2487	−0.834639	−0.417319	−	0.908760i	$-0.637030\pi$
$379$	−16.2487	−0.834639	−0.417319	+	0.908760i	$0.637030\pi$
$380$	−4.20574	−0.215750
$381$	−17.6164	−0.902518
$382$	−17.4906	−0.894899
$383$	−34.5710	−1.76649	−0.883247	−	0.468908i	$-0.844648\pi$
$383$	−34.5710	−1.76649	−0.883247	+	0.468908i	$0.844648\pi$
$384$	−8.95419	−0.456942
$385$	−50.0934	−2.55300
$386$	20.7213	1.05469
$387$	0	0
$388$	10.5163	0.533884
$389$	18.6035	0.943233	0.471616	−	0.881804i	$-0.343671\pi$
$389$	18.6035	0.943233	0.471616	+	0.881804i	$0.343671\pi$
$390$	14.5475	0.736643
$391$	0.00106944	5.40838e−5 0
$392$	−2.04204	−0.103138
$393$	−40.1627	−2.02594
$394$	−3.23864	−0.163160
$395$	−21.2063	−1.06700
$396$	−7.64179	−0.384014
$397$	30.3896	1.52521	0.762604	−	0.646866i	$-0.223921\pi$
$397$	30.3896	1.52521	0.762604	+	0.646866i	$0.223921\pi$
$398$	−4.61896	−0.231528
$399$	13.8859	0.695165
$400$	−13.5405	−0.677023
$401$	−37.8025	−1.88777	−0.943883	−	0.330279i	$-0.892857\pi$
$401$	−37.8025	−1.88777	−0.943883	+	0.330279i	$0.892857\pi$
$402$	−25.6182	−1.27772
$403$	6.63157	0.330342
$404$	−6.01325	−0.299170
$405$	34.4032	1.70951
$406$	−15.3734	−0.762970
$407$	11.1547	0.552919
$408$	−5.36911	−0.265811
$409$	4.27094	0.211184	0.105592	−	0.994410i	$-0.466326\pi$
$409$	4.27094	0.211184	0.105592	+	0.994410i	$0.466326\pi$
$410$	26.9075	1.32887
$411$	−5.99149	−0.295539
$412$	8.30255	0.409037
$413$	10.0901	0.496499
$414$	−0.00384589	−0.000189015 0
$415$	18.5081	0.908526
$416$	5.33051	0.261350
$417$	−18.2868	−0.895510
$418$	−14.4088	−0.704758
$419$	12.1865	0.595350	0.297675	−	0.954667i	$-0.403789\pi$
$419$	12.1865	0.595350	0.297675	+	0.954667i	$0.403789\pi$
$420$	−12.3036	−0.600352
$421$	−9.90977	−0.482973	−0.241486	−	0.970404i	$-0.577635\pi$
$421$	−9.90977	−0.482973	−0.241486	+	0.970404i	$0.577635\pi$
$422$	−11.9151	−0.580017
$423$	−18.0887	−0.879505
$424$	12.1310	0.589132
$425$	−4.18162	−0.202839
$426$	18.8487	0.913220
$427$	−23.6717	−1.14556
$428$	4.44796	0.215000
$429$	−21.1216	−1.01976
$430$	0	0
$431$	−20.4652	−0.985772	−0.492886	−	0.870094i	$-0.664058\pi$
$431$	−20.4652	−0.985772	−0.492886	+	0.870094i	$0.664058\pi$
$432$	−3.95385	−0.190230
$433$	−1.38022	−0.0663293	−0.0331646	−	0.999450i	$-0.510559\pi$
$433$	−1.38022	−0.0663293	−0.0331646	+	0.999450i	$0.510559\pi$
$434$	13.2344	0.635273
$435$	−34.9804	−1.67718
$436$	4.53480	0.217177
$437$	0.00307314	0.000147008 0
$438$	30.3113	1.44833
$439$	−10.2864	−0.490945	−0.245473	−	0.969404i	$-0.578943\pi$
$439$	−10.2864	−0.490945	−0.245473	+	0.969404i	$0.578943\pi$
$440$	55.6591	2.65344
$441$	1.52721	0.0727244
$442$	−1.47736	−0.0702706
$443$	5.47233	0.259998	0.129999	−	0.991514i	$-0.458503\pi$
$443$	5.47233	0.259998	0.129999	+	0.991514i	$0.458503\pi$
$444$	2.73974	0.130022
$445$	28.0000	1.32732
$446$	−17.7577	−0.840852
$447$	42.9690	2.03236
$448$	24.2307	1.14479
$449$	27.9847	1.32068	0.660341	−	0.750966i	$-0.270412\pi$
$449$	27.9847	1.32068	0.660341	+	0.750966i	$0.270412\pi$
$450$	15.0379	0.708892
$451$	−39.0672	−1.83960
$452$	3.84000	0.180618
$453$	−21.5257	−1.01137
$454$	−10.5287	−0.494135
$455$	−14.7593	−0.691925
$456$	−15.4287	−0.722515
$457$	36.8380	1.72321	0.861603	−	0.507582i	$-0.169461\pi$
$457$	36.8380	1.72321	0.861603	+	0.507582i	$0.169461\pi$
$458$	24.0451	1.12355
$459$	−1.22105	−0.0569935
$460$	−0.00272295	−0.000126958 0
$461$	13.1790	0.613808	0.306904	−	0.951740i	$-0.400707\pi$
$461$	13.1790	0.613808	0.306904	+	0.951740i	$0.400707\pi$
$462$	−42.1518	−1.96108
$463$	28.8275	1.33973	0.669864	−	0.742484i	$-0.266352\pi$
$463$	28.8275	1.33973	0.669864	+	0.742484i	$0.266352\pi$
$464$	11.5029	0.534011
$465$	30.1134	1.39648
$466$	12.0918	0.560140
$467$	−3.24820	−0.150309	−0.0751544	−	0.997172i	$-0.523945\pi$
$467$	−3.24820	−0.150309	−0.0751544	+	0.997172i	$0.523945\pi$
$468$	−2.25154	−0.104077
$469$	25.9911	1.20016
$470$	30.2202	1.39395
$471$	−3.41323	−0.157273
$472$	−11.2111	−0.516033
$473$	0	0
$474$	−17.8443	−0.819617
$475$	−12.0163	−0.551347
$476$	1.24947	0.0572694
$477$	−9.07261	−0.415406
$478$	−9.46904	−0.433104
$479$	−22.3259	−1.02010	−0.510049	−	0.860145i	$-0.670373\pi$
$479$	−22.3259	−1.02010	−0.510049	+	0.860145i	$0.670373\pi$
$480$	24.2054	1.10482
$481$	3.28657	0.149855
$482$	−9.96578	−0.453929
$483$	0.00899023	0.000409069 0
$484$	−11.9880	−0.544908
$485$	57.2849	2.60117
$486$	23.2226	1.05340
$487$	−13.5253	−0.612889	−0.306444	−	0.951889i	$-0.599139\pi$
$487$	−13.5253	−0.612889	−0.306444	+	0.951889i	$0.599139\pi$
$488$	26.3018	1.19063
$489$	−33.4737	−1.51373
$490$	−2.55146	−0.115263
$491$	10.0559	0.453818	0.226909	−	0.973916i	$-0.427138\pi$
$491$	10.0559	0.453818	0.226909	+	0.973916i	$0.427138\pi$
$492$	−9.59538	−0.432593
$493$	3.55239	0.159992
$494$	−4.24534	−0.191007
$495$	−41.6267	−1.87098
$496$	−9.90248	−0.444634
$497$	−19.1230	−0.857783
$498$	15.5739	0.697882
$499$	24.5349	1.09833	0.549166	−	0.835713i	$-0.314945\pi$
$499$	24.5349	1.09833	0.549166	+	0.835713i	$0.314945\pi$
$500$	0.994979	0.0444968
$501$	−18.2699	−0.816240
$502$	−21.6821	−0.967721
$503$	−19.5869	−0.873335	−0.436668	−	0.899623i	$-0.643841\pi$
$503$	−19.5869	−0.873335	−0.436668	+	0.899623i	$0.643841\pi$
$504$	−19.5893	−0.872578
$505$	−32.7557	−1.45761
$506$	−0.00932877	−0.000414714 0
$507$	23.7064	1.05284
$508$	−4.55509	−0.202100
$509$	−4.27192	−0.189349	−0.0946747	−	0.995508i	$-0.530181\pi$
$509$	−4.27192	−0.189349	−0.0946747	+	0.995508i	$0.530181\pi$
$510$	−6.70854	−0.297059
$511$	−30.7524	−1.36041
$512$	−23.0627	−1.01924
$513$	−3.50880	−0.154917
$514$	22.7280	1.00249
$515$	45.2260	1.99290
$516$	0	0
$517$	−43.8769	−1.92970
$518$	6.55890	0.288182
$519$	3.98610	0.174970
$520$	16.3991	0.719148
$521$	−3.57614	−0.156674	−0.0783368	−	0.996927i	$-0.524961\pi$
$521$	−3.57614	−0.156674	−0.0783368	+	0.996927i	$0.524961\pi$
$522$	−12.7750	−0.559148
$523$	0.689388	0.0301448	0.0150724	−	0.999886i	$-0.495202\pi$
$523$	0.689388	0.0301448	0.0150724	+	0.999886i	$0.495202\pi$
$524$	−10.3849	−0.453667
$525$	−35.1528	−1.53419
$526$	−16.4833	−0.718704
$527$	−3.05813	−0.133214
$528$	31.5395	1.37258
$529$	−23.0000	−1.00000
$530$	15.1573	0.658391
$531$	8.38465	0.363863
$532$	3.59049	0.155667
$533$	−11.5106	−0.498577
$534$	23.5609	1.01958
$535$	24.2292	1.04752
$536$	−28.8788	−1.24738
$537$	18.7498	0.809115
$538$	−32.1079	−1.38427
$539$	3.70448	0.159563
$540$	3.10896	0.133788
$541$	−39.9802	−1.71888	−0.859441	−	0.511234i	$-0.829188\pi$
$541$	−39.9802	−1.71888	−0.859441	+	0.511234i	$0.829188\pi$
$542$	24.0383	1.03253
$543$	29.6303	1.27156
$544$	−2.45815	−0.105392
$545$	24.7022	1.05812
$546$	−12.4194	−0.531501
$547$	38.0125	1.62530	0.812649	−	0.582753i	$-0.198025\pi$
$547$	38.0125	1.62530	0.812649	+	0.582753i	$0.198025\pi$
$548$	−1.54922	−0.0661796
$549$	−19.6708	−0.839528
$550$	36.4766	1.55537
$551$	10.2082	0.434882
$552$	−0.00998909	−0.000425164 0
$553$	18.1040	0.769862
$554$	20.6909	0.879071
$555$	14.9240	0.633490
$556$	−4.72844	−0.200530
$557$	37.6975	1.59729	0.798647	−	0.601800i	$-0.205549\pi$
$557$	37.6975	1.59729	0.798647	+	0.601800i	$0.205549\pi$
$558$	10.9976	0.465564
$559$	0	0
$560$	22.0390	0.931318
$561$	9.74016	0.411230
$562$	18.2573	0.770140
$563$	−36.3191	−1.53067	−0.765335	−	0.643632i	$-0.777427\pi$
$563$	−36.3191	−1.53067	−0.765335	+	0.643632i	$0.777427\pi$
$564$	−10.7767	−0.453781
$565$	20.9174	0.880003
$566$	−19.2210	−0.807921
$567$	−29.3703	−1.23344
$568$	21.2476	0.891532
$569$	28.7826	1.20663	0.603316	−	0.797502i	$-0.293846\pi$
$569$	28.7826	1.20663	0.603316	+	0.797502i	$0.293846\pi$
$570$	−19.2777	−0.807454
$571$	−18.1320	−0.758801	−0.379400	−	0.925233i	$-0.623870\pi$
$571$	−18.1320	−0.758801	−0.379400	+	0.925233i	$0.623870\pi$
$572$	−5.46143	−0.228354
$573$	33.9759	1.41936
$574$	−22.9713	−0.958802
$575$	−0.00777980	−0.000324440 0
$576$	20.1353	0.838971
$577$	−13.3145	−0.554291	−0.277145	−	0.960828i	$-0.589388\pi$
$577$	−13.3145	−0.554291	−0.277145	+	0.960828i	$0.589388\pi$
$578$	−19.4671	−0.809726
$579$	−40.2516	−1.67280
$580$	−9.04491	−0.375569
$581$	−15.8005	−0.655517
$582$	48.2032	1.99809
$583$	−22.0069	−0.911434
$584$	34.1692	1.41393
$585$	−12.2647	−0.507082
$586$	−24.0290	−0.992630
$587$	−6.62581	−0.273476	−0.136738	−	0.990607i	$-0.543662\pi$
$587$	−6.62581	−0.273476	−0.136738	+	0.990607i	$0.543662\pi$
$588$	0.909865	0.0375222
$589$	−8.78785	−0.362097
$590$	−14.0079	−0.576698
$591$	6.29111	0.258782
$592$	−4.90761	−0.201701
$593$	4.31501	0.177196	0.0885982	−	0.996067i	$-0.471761\pi$
$593$	4.31501	0.177196	0.0885982	+	0.996067i	$0.471761\pi$
$594$	10.6513	0.437026
$595$	6.80618	0.279026
$596$	11.1105	0.455105
$597$	8.97242	0.367217
$598$	−0.00274858	−0.000112398 0
$599$	22.4522	0.917372	0.458686	−	0.888598i	$-0.348320\pi$
$599$	22.4522	0.917372	0.458686	+	0.888598i	$0.348320\pi$
$600$	39.0585	1.59456
$601$	3.82446	0.156003	0.0780015	−	0.996953i	$-0.475146\pi$
$601$	3.82446	0.156003	0.0780015	+	0.996953i	$0.475146\pi$
$602$	0	0
$603$	21.5981	0.879544
$604$	−5.56591	−0.226474
$605$	−65.3015	−2.65488
$606$	−27.5627	−1.11966
$607$	23.2407	0.943309	0.471655	−	0.881783i	$-0.343657\pi$
$607$	23.2407	0.943309	0.471655	+	0.881783i	$0.343657\pi$
$608$	−7.06374	−0.286473
$609$	29.8632	1.21012
$610$	32.8633	1.33060
$611$	−12.9277	−0.522997
$612$	1.03829	0.0419703
$613$	3.30764	0.133594	0.0667972	−	0.997767i	$-0.478722\pi$
$613$	3.30764	0.133594	0.0667972	+	0.997767i	$0.478722\pi$
$614$	9.83173	0.396776
$615$	−52.2684	−2.10767
$616$	−47.5167	−1.91450
$617$	−35.0051	−1.40925	−0.704627	−	0.709578i	$-0.748886\pi$
$617$	−35.0051	−1.40925	−0.704627	+	0.709578i	$0.748886\pi$
$618$	38.0561	1.53084
$619$	17.9849	0.722873	0.361436	−	0.932397i	$-0.382286\pi$
$619$	17.9849	0.722873	0.361436	+	0.932397i	$0.382286\pi$
$620$	7.78644	0.312711
$621$	−0.00227172	−9.11611e−5 0
$622$	−35.5337	−1.42477
$623$	−23.9039	−0.957688
$624$	9.29263	0.372003
$625$	−22.1572	−0.886289
$626$	−7.74763	−0.309658
$627$	27.9894	1.11779
$628$	−0.882560	−0.0352180
$629$	−1.51559	−0.0604305
$630$	−24.4763	−0.975157
$631$	25.1767	1.00227	0.501135	−	0.865369i	$-0.332916\pi$
$631$	25.1767	1.00227	0.501135	+	0.865369i	$0.332916\pi$
$632$	−20.1155	−0.800152
$633$	23.1453	0.919942
$634$	−9.28840	−0.368889
$635$	−24.8127	−0.984663
$636$	−5.40517	−0.214329
$637$	1.09147	0.0432456
$638$	−30.9877	−1.22682
$639$	−15.8909	−0.628633
$640$	−12.6120	−0.498532
$641$	36.3233	1.43468	0.717342	−	0.696721i	$-0.245359\pi$
$641$	36.3233	1.43468	0.717342	+	0.696721i	$0.245359\pi$
$642$	20.3880	0.804648
$643$	3.32782	0.131236	0.0656182	−	0.997845i	$-0.479098\pi$
$643$	3.32782	0.131236	0.0656182	+	0.997845i	$0.479098\pi$
$644$	0.00232461	9.16024e−5 0
$645$	0	0
$646$	1.95772	0.0770255
$647$	−42.1142	−1.65568	−0.827840	−	0.560965i	$-0.810430\pi$
$647$	−42.1142	−1.65568	−0.827840	+	0.560965i	$0.810430\pi$
$648$	32.6335	1.28197
$649$	20.3382	0.798344
$650$	10.7473	0.421542
$651$	−25.7081	−1.00758
$652$	−8.65531	−0.338968
$653$	23.8691	0.934071	0.467036	−	0.884239i	$-0.345322\pi$
$653$	23.8691	0.934071	0.467036	+	0.884239i	$0.345322\pi$
$654$	20.7860	0.812796
$655$	−56.5691	−2.21034
$656$	17.1879	0.671075
$657$	−25.5547	−0.996985
$658$	−25.7993	−1.00576
$659$	−4.78100	−0.186241	−0.0931206	−	0.995655i	$-0.529684\pi$
$659$	−4.78100	−0.186241	−0.0931206	+	0.995655i	$0.529684\pi$
$660$	−24.7999	−0.965335
$661$	−14.3106	−0.556617	−0.278309	−	0.960492i	$-0.589774\pi$
$661$	−14.3106	−0.556617	−0.278309	+	0.960492i	$0.589774\pi$
$662$	−28.7544	−1.11757
$663$	2.86979	0.111453
$664$	17.5561	0.681308
$665$	19.5583	0.758438
$666$	5.45033	0.211196
$667$	0.00660913	0.000255906 0
$668$	−4.72407	−0.182780
$669$	34.4947	1.33364
$670$	−36.0832	−1.39402
$671$	−47.7143	−1.84199
$672$	−20.6644	−0.797147
$673$	23.1738	0.893284	0.446642	−	0.894713i	$-0.352620\pi$
$673$	23.1738	0.893284	0.446642	+	0.894713i	$0.352620\pi$
$674$	−39.2710	−1.51266
$675$	8.88269	0.341895
$676$	6.12978	0.235761
$677$	14.1464	0.543691	0.271846	−	0.962341i	$-0.412366\pi$
$677$	14.1464	0.543691	0.271846	+	0.962341i	$0.412366\pi$
$678$	17.6013	0.675972
$679$	−48.9047	−1.87679
$680$	−7.56239	−0.290004
$681$	20.4521	0.783727
$682$	26.6762	1.02149
$683$	47.6110	1.82178	0.910892	−	0.412646i	$-0.135395\pi$
$683$	47.6110	1.82178	0.910892	+	0.412646i	$0.135395\pi$
$684$	2.98363	0.114082
$685$	−8.43901	−0.322438
$686$	−20.7893	−0.793739
$687$	−46.7080	−1.78202
$688$	0	0
$689$	−6.48401	−0.247021
$690$	−0.0124811	−0.000475146 0
$691$	41.3547	1.57321	0.786604	−	0.617458i	$-0.211837\pi$
$691$	41.3547	1.57321	0.786604	+	0.617458i	$0.211837\pi$
$692$	1.03069	0.0391808
$693$	35.5372	1.34995
$694$	−4.33172	−0.164430
$695$	−25.7570	−0.977018
$696$	−33.1811	−1.25773
$697$	5.30805	0.201057
$698$	−6.61606	−0.250422
$699$	−23.4885	−0.888417
$700$	−9.08948	−0.343550
$701$	47.8317	1.80658	0.903288	−	0.429034i	$-0.141146\pi$
$701$	47.8317	1.80658	0.903288	+	0.429034i	$0.141146\pi$
$702$	3.13823	0.118445
$703$	−4.35521	−0.164260
$704$	48.8411	1.84077
$705$	−58.7033	−2.21090
$706$	−4.86614	−0.183140
$707$	27.9639	1.05169
$708$	4.99531	0.187735
$709$	29.1562	1.09498	0.547492	−	0.836811i	$-0.315583\pi$
$709$	29.1562	1.09498	0.547492	+	0.836811i	$0.315583\pi$
$710$	26.5483	0.996340
$711$	15.0441	0.564199
$712$	26.5597	0.995367
$713$	−0.00568956	−0.000213076 0
$714$	5.72715	0.214333
$715$	−29.7498	−1.11258
$716$	4.84816	0.181184
$717$	18.3938	0.686929
$718$	3.15719	0.117825
$719$	1.94522	0.0725446	0.0362723	−	0.999342i	$-0.488452\pi$
$719$	1.94522	0.0725446	0.0362723	+	0.999342i	$0.488452\pi$
$720$	18.3140	0.682523
$721$	−38.6099	−1.43791
$722$	−16.8931	−0.628696
$723$	19.3587	0.719958
$724$	7.66152	0.284738
$725$	−25.8424	−0.959764
$726$	−54.9488	−2.03934
$727$	9.40356	0.348759	0.174379	−	0.984679i	$-0.444208\pi$
$727$	9.40356	0.348759	0.174379	+	0.984679i	$0.444208\pi$
$728$	−14.0001	−0.518878
$729$	−13.2827	−0.491950
$730$	42.6934	1.58015
$731$	0	0
$732$	−11.7192	−0.433155
$733$	−12.5611	−0.463956	−0.231978	−	0.972721i	$-0.574520\pi$
$733$	−12.5611	−0.463956	−0.231978	+	0.972721i	$0.574520\pi$
$734$	−3.26378	−0.120468
$735$	4.95626	0.182815
$736$	−0.00457332	−0.000168575 0
$737$	52.3894	1.92979
$738$	−19.0887	−0.702665
$739$	41.7821	1.53698	0.768489	−	0.639863i	$-0.221009\pi$
$739$	41.7821	1.53698	0.768489	+	0.639863i	$0.221009\pi$
$740$	3.85891	0.141856
$741$	8.24665	0.302948
$742$	−12.9399	−0.475040
$743$	1.58027	0.0579743	0.0289872	−	0.999580i	$-0.490772\pi$
$743$	1.58027	0.0579743	0.0289872	+	0.999580i	$0.490772\pi$
$744$	28.5644	1.04722
$745$	60.5218	2.21735
$746$	39.6687	1.45237
$747$	−13.1300	−0.480400
$748$	2.51852	0.0920862
$749$	−20.6847	−0.755802
$750$	4.56065	0.166531
$751$	6.19164	0.225936	0.112968	−	0.993599i	$-0.463964\pi$
$751$	6.19164	0.225936	0.112968	+	0.993599i	$0.463964\pi$
$752$	19.3040	0.703944
$753$	42.1180	1.53486
$754$	−9.13006	−0.332497
$755$	−30.3189	−1.10342
$756$	−2.65415	−0.0965307
$757$	−5.71950	−0.207879	−0.103939	−	0.994584i	$-0.533145\pi$
$757$	−5.71950	−0.207879	−0.103939	+	0.994584i	$0.533145\pi$
$758$	−19.2579	−0.699480
$759$	0.0181213	0.000657762 0
$760$	−21.7313	−0.788277
$761$	17.0825	0.619240	0.309620	−	0.950860i	$-0.399798\pi$
$761$	17.0825	0.619240	0.309620	+	0.950860i	$0.399798\pi$
$762$	−20.8790	−0.756367
$763$	−21.0885	−0.763455
$764$	8.78517	0.317836
$765$	5.65582	0.204486
$766$	−40.9735	−1.48043
$767$	5.99234	0.216371
$768$	29.6898	1.07134
$769$	−2.38761	−0.0860993	−0.0430497	−	0.999073i	$-0.513707\pi$
$769$	−2.38761	−0.0860993	−0.0430497	+	0.999073i	$0.513707\pi$
$770$	−59.3707	−2.13957
$771$	−44.1495	−1.59001
$772$	−10.4079	−0.374587
$773$	1.76858	0.0636114	0.0318057	−	0.999494i	$-0.489874\pi$
$773$	1.76858	0.0636114	0.0318057	+	0.999494i	$0.489874\pi$
$774$	0	0
$775$	22.2468	0.799130
$776$	54.3383	1.95063
$777$	−12.7408	−0.457074
$778$	22.0488	0.790489
$779$	15.2532	0.546504
$780$	−7.30691	−0.261629
$781$	−38.5456	−1.37927
$782$	0.00126750	4.53256e−5 0
$783$	−7.54606	−0.269674
$784$	−1.62982	−0.0582077
$785$	−4.80752	−0.171588
$786$	−47.6009	−1.69787
$787$	32.9843	1.17576	0.587882	−	0.808947i	$-0.299962\pi$
$787$	32.9843	1.17576	0.587882	+	0.808947i	$0.299962\pi$
$788$	1.62670	0.0579487
$789$	32.0190	1.13991
$790$	−25.1337	−0.894217
$791$	−17.8574	−0.634937
$792$	−39.4856	−1.40306
$793$	−14.0583	−0.499225
$794$	36.0177	1.27822
$795$	−29.4433	−1.04425
$796$	2.32000	0.0822303
$797$	−22.5809	−0.799855	−0.399927	−	0.916547i	$-0.630965\pi$
$797$	−22.5809	−0.799855	−0.399927	+	0.916547i	$0.630965\pi$
$798$	16.4576	0.582592
$799$	5.96154	0.210904
$800$	17.8822	0.632231
$801$	−19.8637	−0.701849
$802$	−44.8035	−1.58207
$803$	−61.9867	−2.18746
$804$	12.8675	0.453801
$805$	0.0126627	0.000446302 0
$806$	7.85974	0.276848
$807$	62.3702	2.19554
$808$	−31.0708	−1.09307
$809$	−10.7635	−0.378424	−0.189212	−	0.981936i	$-0.560593\pi$
$809$	−10.7635	−0.378424	−0.189212	+	0.981936i	$0.560593\pi$
$810$	40.7746	1.43267
$811$	18.8879	0.663243	0.331621	−	0.943413i	$-0.392404\pi$
$811$	18.8879	0.663243	0.331621	+	0.943413i	$0.392404\pi$
$812$	7.72173	0.270980
$813$	−46.6948	−1.63766
$814$	13.2206	0.463381
$815$	−47.1477	−1.65151
$816$	−4.28526	−0.150014
$817$	0	0
$818$	5.06192	0.176986
$819$	10.4705	0.365869
$820$	−13.5151	−0.471967
$821$	−47.3249	−1.65165	−0.825824	−	0.563927i	$-0.809290\pi$
$821$	−47.3249	−1.65165	−0.825824	+	0.563927i	$0.809290\pi$
$822$	−7.10112	−0.247680
$823$	1.10335	0.0384605	0.0192302	−	0.999815i	$-0.493878\pi$
$823$	1.10335	0.0384605	0.0192302	+	0.999815i	$0.493878\pi$
$824$	42.8997	1.49448
$825$	−70.8564	−2.46690
$826$	11.9587	0.416098
$827$	22.0439	0.766543	0.383271	−	0.923636i	$-0.374797\pi$
$827$	22.0439	0.766543	0.383271	+	0.923636i	$0.374797\pi$
$828$	0.00193171	6.71315e−5 0
$829$	−51.2405	−1.77966	−0.889828	−	0.456297i	$-0.849176\pi$
$829$	−51.2405	−1.77966	−0.889828	+	0.456297i	$0.849176\pi$
$830$	21.9358	0.761402
$831$	−40.1924	−1.39426
$832$	14.3903	0.498894
$833$	−0.503327	−0.0174392
$834$	−21.6736	−0.750494
$835$	−25.7332	−0.890533
$836$	7.23723	0.250305
$837$	6.49614	0.224539
$838$	14.4435	0.498941
$839$	−11.1830	−0.386081	−0.193041	−	0.981191i	$-0.561835\pi$
$839$	−11.1830	−0.386081	−0.193041	+	0.981191i	$0.561835\pi$
$840$	−63.5732	−2.19348
$841$	−7.04623	−0.242974
$842$	−11.7451	−0.404761
$843$	−35.4652	−1.22149
$844$	5.98469	0.206001
$845$	33.3904	1.14867
$846$	−21.4388	−0.737080
$847$	55.7486	1.91554
$848$	9.68213	0.332486
$849$	37.3372	1.28141
$850$	−4.95606	−0.169991
$851$	−0.00281971	−9.66585e−5 0
$852$	−9.46727	−0.324343
$853$	20.9439	0.717105	0.358553	−	0.933510i	$-0.383270\pi$
$853$	20.9439	0.717105	0.358553	+	0.933510i	$0.383270\pi$
$854$	−28.0557	−0.960047
$855$	16.2526	0.555827
$856$	22.9829	0.785538
$857$	7.87648	0.269055	0.134528	−	0.990910i	$-0.457048\pi$
$857$	7.87648	0.269055	0.134528	+	0.990910i	$0.457048\pi$
$858$	−25.0334	−0.854625
$859$	−42.8104	−1.46067	−0.730337	−	0.683087i	$-0.760637\pi$
$859$	−42.8104	−1.46067	−0.730337	+	0.683087i	$0.760637\pi$
$860$	0	0
$861$	44.6221	1.52072
$862$	−24.2553	−0.826139
$863$	0.682436	0.0232304	0.0116152	−	0.999933i	$-0.496303\pi$
$863$	0.682436	0.0232304	0.0116152	+	0.999933i	$0.496303\pi$
$864$	5.22165	0.177644
$865$	5.61441	0.190896
$866$	−1.63584	−0.0555881
$867$	37.8153	1.28427
$868$	−6.64737	−0.225626
$869$	36.4918	1.23790
$870$	−41.4588	−1.40558
$871$	15.4358	0.523021
$872$	23.4315	0.793492
$873$	−40.6390	−1.37542
$874$	0.00364229	0.000123202 0
$875$	−4.62702	−0.156422
$876$	−15.2247	−0.514395
$877$	34.7501	1.17343	0.586714	−	0.809795i	$-0.300421\pi$
$877$	34.7501	1.17343	0.586714	+	0.809795i	$0.300421\pi$
$878$	−12.1915	−0.411443
$879$	46.6768	1.57437
$880$	44.4233	1.49751
$881$	−3.88988	−0.131053	−0.0655267	−	0.997851i	$-0.520873\pi$
$881$	−3.88988	−0.131053	−0.0655267	+	0.997851i	$0.520873\pi$
$882$	1.81005	0.0609477
$883$	−37.3663	−1.25748	−0.628738	−	0.777618i	$-0.716428\pi$
$883$	−37.3663	−1.25748	−0.628738	+	0.777618i	$0.716428\pi$
$884$	0.742044	0.0249576
$885$	27.2107	0.914678
$886$	6.48580	0.217895
$887$	−0.299473	−0.0100553	−0.00502766	−	0.999987i	$-0.501600\pi$
$887$	−0.299473	−0.0100553	−0.00502766	+	0.999987i	$0.501600\pi$
$888$	14.1564	0.475057
$889$	21.1829	0.710451
$890$	33.1855	1.11238
$891$	−59.2009	−1.98330
$892$	8.91932	0.298641
$893$	17.1311	0.573271
$894$	50.9269	1.70325
$895$	26.4091	0.882760
$896$	10.7670	0.359699
$897$	0.00533917	0.000178270 0
$898$	33.1675	1.10681
$899$	−18.8992	−0.630324
$900$	−7.55320	−0.251773
$901$	2.99008	0.0996139
$902$	−46.3024	−1.54170
$903$	0	0
$904$	19.8415	0.659918
$905$	41.7342	1.38729
$906$	−25.5123	−0.847588
$907$	−31.0927	−1.03242	−0.516208	−	0.856463i	$-0.672657\pi$
$907$	−31.0927	−1.03242	−0.516208	+	0.856463i	$0.672657\pi$
$908$	5.28832	0.175499
$909$	23.2375	0.770738
$910$	−17.4927	−0.579877
$911$	−29.4772	−0.976625	−0.488312	−	0.872669i	$-0.662387\pi$
$911$	−29.4772	−0.976625	−0.488312	+	0.872669i	$0.662387\pi$
$912$	−12.3142	−0.407762
$913$	−31.8487	−1.05404
$914$	43.6604	1.44416
$915$	−63.8375	−2.11040
$916$	−12.0773	−0.399046
$917$	48.2937	1.59480
$918$	−1.44718	−0.0477642
$919$	16.1056	0.531276	0.265638	−	0.964073i	$-0.414417\pi$
$919$	16.1056	0.531276	0.265638	+	0.964073i	$0.414417\pi$
$920$	−0.0140696	−0.000463861 0
$921$	−19.0983	−0.629311
$922$	15.6198	0.514410
$923$	−11.3569	−0.373816
$924$	21.1719	0.696505
$925$	11.0254	0.362513
$926$	34.1664	1.12278
$927$	−32.0842	−1.05378
$928$	−15.1913	−0.498680
$929$	22.6030	0.741579	0.370789	−	0.928717i	$-0.379087\pi$
$929$	22.6030	0.741579	0.370789	+	0.928717i	$0.379087\pi$
$930$	35.6904	1.17033
$931$	−1.44636	−0.0474026
$932$	−6.07344	−0.198942
$933$	69.0249	2.25978
$934$	−3.84977	−0.125968
$935$	13.7190	0.448659
$936$	−11.6338	−0.380263
$937$	32.7020	1.06833	0.534164	−	0.845381i	$-0.320627\pi$
$937$	32.7020	1.06833	0.534164	+	0.845381i	$0.320627\pi$
$938$	30.8047	1.00581
$939$	15.0499	0.491136
$940$	−15.1790	−0.495083
$941$	0.292595	0.00953833	0.00476916	−	0.999989i	$-0.498482\pi$
$941$	0.292595	0.00953833	0.00476916	+	0.999989i	$0.498482\pi$
$942$	−4.04536	−0.131805
$943$	0.00987548	0.000321590 0
$944$	−8.94795	−0.291231
$945$	−14.4578	−0.470313
$946$	0	0
$947$	13.5390	0.439959	0.219979	−	0.975504i	$-0.429401\pi$
$947$	13.5390	0.439959	0.219979	+	0.975504i	$0.429401\pi$
$948$	8.96282	0.291099
$949$	−18.2635	−0.592857
$950$	−14.2418	−0.462064
$951$	18.0429	0.585081
$952$	6.45609	0.209243
$953$	13.8132	0.447454	0.223727	−	0.974652i	$-0.428178\pi$
$953$	13.8132	0.447454	0.223727	+	0.974652i	$0.428178\pi$
$954$	−10.7529	−0.348137
$955$	47.8550	1.54855
$956$	4.75610	0.153823
$957$	60.1942	1.94580
$958$	−26.4607	−0.854906
$959$	7.20447	0.232645
$960$	65.3451	2.10900
$961$	−14.7303	−0.475172
$962$	3.89524	0.125588
$963$	−17.1886	−0.553895
$964$	5.00560	0.161219
$965$	−56.6943	−1.82505
$966$	0.0106552	0.000342826 0
$967$	−11.4904	−0.369506	−0.184753	−	0.982785i	$-0.559149\pi$
$967$	−11.4904	−0.369506	−0.184753	+	0.982785i	$0.559149\pi$
$968$	−61.9425	−1.99091
$969$	−3.80291	−0.122167
$970$	67.8941	2.17995
$971$	49.2629	1.58092	0.790460	−	0.612513i	$-0.209841\pi$
$971$	49.2629	1.58092	0.790460	+	0.612513i	$0.209841\pi$
$972$	−11.6642	−0.374130
$973$	21.9890	0.704935
$974$	−16.0302	−0.513640
$975$	−20.8768	−0.668592
$976$	20.9923	0.671947
$977$	−34.4225	−1.10127	−0.550636	−	0.834745i	$-0.685615\pi$
$977$	−34.4225	−1.10127	−0.550636	+	0.834745i	$0.685615\pi$
$978$	−39.6730	−1.26860
$979$	−48.1823	−1.53991
$980$	1.28154	0.0409374
$981$	−17.5242	−0.559504
$982$	11.9183	0.380328
$983$	46.7913	1.49241	0.746205	−	0.665716i	$-0.231874\pi$
$983$	46.7913	1.49241	0.746205	+	0.665716i	$0.231874\pi$
$984$	−49.5799	−1.58055
$985$	8.86102	0.282336
$986$	4.21029	0.134083
$987$	50.1157	1.59520
$988$	2.13234	0.0678388
$989$	0	0
$990$	−49.3360	−1.56800
$991$	23.3864	0.742894	0.371447	−	0.928454i	$-0.378862\pi$
$991$	23.3864	0.742894	0.371447	+	0.928454i	$0.378862\pi$
$992$	13.0777	0.415217
$993$	55.8560	1.77254
$994$	−22.6646	−0.718876
$995$	12.6376	0.400640
$996$	−7.82242	−0.247863
$997$	−49.6128	−1.57125	−0.785627	−	0.618701i	$-0.787659\pi$
$997$	−49.6128	−1.57125	−0.785627	+	0.618701i	$0.787659\pi$
$998$	29.0788	0.920472
$999$	3.21945	0.101859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.14		18
43.17	even	21		43.2.g.a.31.1	yes	36
43.38	even	21		43.2.g.a.25.1	✓	36
43.42	odd	2		1849.2.a.o.1.5		18
129.17	odd	42		387.2.y.c.289.3		36
129.38	odd	42		387.2.y.c.154.3		36
172.103	odd	42		688.2.bg.c.289.2		36
172.167	odd	42		688.2.bg.c.369.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.1	✓	36	43.38	even	21
43.2.g.a.31.1	yes	36	43.17	even	21
387.2.y.c.154.3		36	129.38	odd	42
387.2.y.c.289.3		36	129.17	odd	42
688.2.bg.c.289.2		36	172.103	odd	42
688.2.bg.c.369.2		36	172.167	odd	42
1849.2.a.n.1.14		18	1.1	even	1	trivial
1849.2.a.o.1.5		18	43.42	odd	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18520 q^{2} -2.30227 q^{3} -0.595300 q^{4} -3.24275 q^{5} -2.72866 q^{6} +2.76837 q^{7} -3.07595 q^{8} +2.30047 q^{9} +O(q^{10})\)	\(q+1.18520 q^{2} -2.30227 q^{3} -0.595300 q^{4} -3.24275 q^{5} -2.72866 q^{6} +2.76837 q^{7} -3.07595 q^{8} +2.30047 q^{9} -3.84331 q^{10} +5.58012 q^{11} +1.37054 q^{12} +1.64410 q^{13} +3.28107 q^{14} +7.46570 q^{15} -2.45502 q^{16} -0.758169 q^{17} +2.72651 q^{18} -2.17868 q^{19} +1.93041 q^{20} -6.37355 q^{21} +6.61355 q^{22} -0.00141055 q^{23} +7.08168 q^{24} +5.51542 q^{25} +1.94858 q^{26} +1.61052 q^{27} -1.64801 q^{28} -4.68548 q^{29} +8.84835 q^{30} +4.03357 q^{31} +3.24222 q^{32} -12.8470 q^{33} -0.898582 q^{34} -8.97713 q^{35} -1.36947 q^{36} +1.99901 q^{37} -2.58217 q^{38} -3.78516 q^{39} +9.97454 q^{40} -7.00114 q^{41} -7.55393 q^{42} -3.32185 q^{44} -7.45983 q^{45} -0.00167179 q^{46} -7.86308 q^{47} +5.65212 q^{48} +0.663871 q^{49} +6.53688 q^{50} +1.74551 q^{51} -0.978731 q^{52} -3.94381 q^{53} +1.90879 q^{54} -18.0949 q^{55} -8.51537 q^{56} +5.01592 q^{57} -5.55324 q^{58} +3.64476 q^{59} -4.44433 q^{60} -8.55078 q^{61} +4.78059 q^{62} +6.36854 q^{63} +8.75271 q^{64} -5.33139 q^{65} -15.2262 q^{66} +9.38859 q^{67} +0.451338 q^{68} +0.00324748 q^{69} -10.6397 q^{70} -6.90767 q^{71} -7.07612 q^{72} -11.1085 q^{73} +2.36923 q^{74} -12.6980 q^{75} +1.29697 q^{76} +15.4478 q^{77} -4.48617 q^{78} +6.53961 q^{79} +7.96100 q^{80} -10.6093 q^{81} -8.29775 q^{82} -5.70753 q^{83} +3.79417 q^{84} +2.45855 q^{85} +10.7873 q^{87} -17.1642 q^{88} -8.63463 q^{89} -8.84140 q^{90} +4.55147 q^{91} +0.000839703 q^{92} -9.28638 q^{93} -9.31932 q^{94} +7.06491 q^{95} -7.46447 q^{96} -17.6655 q^{97} +0.786820 q^{98} +12.8369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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