LMFDB - Embedded newform 1511.2.a.b.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, 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("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$0$
Dimension:	$87$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44927 q^{2} +3.31595 q^{3} +0.100393 q^{4} +4.01615 q^{5} +4.80572 q^{6} -2.73727 q^{7} -2.75305 q^{8} +7.99552 q^{9} +O(q^{10})$	\(q+1.44927 q^{2} +3.31595 q^{3} +0.100393 q^{4} +4.01615 q^{5} +4.80572 q^{6} -2.73727 q^{7} -2.75305 q^{8} +7.99552 q^{9} +5.82049 q^{10} -3.14100 q^{11} +0.332897 q^{12} +2.87975 q^{13} -3.96705 q^{14} +13.3173 q^{15} -4.19071 q^{16} +5.61098 q^{17} +11.5877 q^{18} -4.56682 q^{19} +0.403192 q^{20} -9.07664 q^{21} -4.55217 q^{22} -6.25002 q^{23} -9.12898 q^{24} +11.1294 q^{25} +4.17355 q^{26} +16.5649 q^{27} -0.274802 q^{28} -1.47976 q^{29} +19.3005 q^{30} -4.74390 q^{31} -0.567379 q^{32} -10.4154 q^{33} +8.13184 q^{34} -10.9933 q^{35} +0.802693 q^{36} -9.14627 q^{37} -6.61857 q^{38} +9.54911 q^{39} -11.0566 q^{40} +3.97721 q^{41} -13.1545 q^{42} +11.8280 q^{43} -0.315334 q^{44} +32.1112 q^{45} -9.05799 q^{46} -7.58501 q^{47} -13.8962 q^{48} +0.492628 q^{49} +16.1296 q^{50} +18.6057 q^{51} +0.289106 q^{52} -6.48252 q^{53} +24.0071 q^{54} -12.6147 q^{55} +7.53583 q^{56} -15.1433 q^{57} -2.14457 q^{58} -1.31833 q^{59} +1.33696 q^{60} +11.4490 q^{61} -6.87521 q^{62} -21.8859 q^{63} +7.55913 q^{64} +11.5655 q^{65} -15.0948 q^{66} +13.7075 q^{67} +0.563302 q^{68} -20.7248 q^{69} -15.9322 q^{70} -7.06155 q^{71} -22.0121 q^{72} -8.64227 q^{73} -13.2554 q^{74} +36.9046 q^{75} -0.458476 q^{76} +8.59776 q^{77} +13.8393 q^{78} -13.1376 q^{79} -16.8305 q^{80} +30.9418 q^{81} +5.76406 q^{82} +1.62956 q^{83} -0.911229 q^{84} +22.5345 q^{85} +17.1419 q^{86} -4.90681 q^{87} +8.64733 q^{88} +5.19522 q^{89} +46.5379 q^{90} -7.88265 q^{91} -0.627457 q^{92} -15.7305 q^{93} -10.9927 q^{94} -18.3410 q^{95} -1.88140 q^{96} -18.7843 q^{97} +0.713953 q^{98} -25.1140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) $ 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * 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 $

$2$	1.44927	1.02479	0.512395	−	0.858750i	$-0.328758\pi$
$2$	1.44927	1.02479	0.512395	+	0.858750i	$0.328758\pi$
$3$	3.31595	1.91446	0.957232	−	0.289321i	$-0.0934294\pi$
$3$	3.31595	1.91446	0.957232	+	0.289321i	$0.0934294\pi$
$4$	0.100393	0.0501964
$5$	4.01615	1.79607	0.898037	−	0.439919i	$-0.144993\pi$
$5$	4.01615	1.79607	0.898037	+	0.439919i	$0.144993\pi$
$6$	4.80572	1.96193
$7$	−2.73727	−1.03459	−0.517295	−	0.855807i	$-0.673061\pi$
$7$	−2.73727	−1.03459	−0.517295	+	0.855807i	$0.673061\pi$
$8$	−2.75305	−0.973350
$9$	7.99552	2.66517
$10$	5.82049	1.84060
$11$	−3.14100	−0.947048	−0.473524	−	0.880781i	$-0.657018\pi$
$11$	−3.14100	−0.947048	−0.473524	+	0.880781i	$0.657018\pi$
$12$	0.332897	0.0960992
$13$	2.87975	0.798700	0.399350	−	0.916799i	$-0.369236\pi$
$13$	2.87975	0.798700	0.399350	+	0.916799i	$0.369236\pi$
$14$	−3.96705	−1.06024
$15$	13.3173	3.43852
$16$	−4.19071	−1.04768
$17$	5.61098	1.36086	0.680431	−	0.732812i	$-0.261793\pi$
$17$	5.61098	1.36086	0.680431	+	0.732812i	$0.261793\pi$
$18$	11.5877	2.73125
$19$	−4.56682	−1.04770	−0.523850	−	0.851810i	$-0.675505\pi$
$19$	−4.56682	−1.04770	−0.523850	+	0.851810i	$0.675505\pi$
$20$	0.403192	0.0901565
$21$	−9.07664	−1.98068
$22$	−4.55217	−0.970526
$23$	−6.25002	−1.30322	−0.651610	−	0.758554i	$-0.725906\pi$
$23$	−6.25002	−1.30322	−0.651610	+	0.758554i	$0.725906\pi$
$24$	−9.12898	−1.86344
$25$	11.1294	2.22589
$26$	4.17355	0.818500
$27$	16.5649	3.18792
$28$	−0.274802	−0.0519327
$29$	−1.47976	−0.274784	−0.137392	−	0.990517i	$-0.543872\pi$
$29$	−1.47976	−0.274784	−0.137392	+	0.990517i	$0.543872\pi$
$30$	19.3005	3.52377
$31$	−4.74390	−0.852030	−0.426015	−	0.904716i	$-0.640083\pi$
$31$	−4.74390	−0.852030	−0.426015	+	0.904716i	$0.640083\pi$
$32$	−0.567379	−0.100299
$33$	−10.4154	−1.81309
$34$	8.13184	1.39460
$35$	−10.9933	−1.85820
$36$	0.802693	0.133782
$37$	−9.14627	−1.50364	−0.751819	−	0.659370i	$-0.770823\pi$
$37$	−9.14627	−1.50364	−0.751819	+	0.659370i	$0.770823\pi$
$38$	−6.61857	−1.07367
$39$	9.54911	1.52908
$40$	−11.0566	−1.74821
$41$	3.97721	0.621135	0.310568	−	0.950551i	$-0.399481\pi$
$41$	3.97721	0.621135	0.310568	+	0.950551i	$0.399481\pi$
$42$	−13.1545	−2.02979
$43$	11.8280	1.80375	0.901873	−	0.432001i	$-0.142192\pi$
$43$	11.8280	1.80375	0.901873	+	0.432001i	$0.142192\pi$
$44$	−0.315334	−0.0475384
$45$	32.1112	4.78685
$46$	−9.05799	−1.33553
$47$	−7.58501	−1.10639	−0.553194	−	0.833053i	$-0.686591\pi$
$47$	−7.58501	−1.10639	−0.553194	+	0.833053i	$0.686591\pi$
$48$	−13.8962	−2.00574
$49$	0.492628	0.0703755
$50$	16.1296	2.28107
$51$	18.6057	2.60532
$52$	0.289106	0.0400918
$53$	−6.48252	−0.890442	−0.445221	−	0.895421i	$-0.646875\pi$
$53$	−6.48252	−0.890442	−0.445221	+	0.895421i	$0.646875\pi$
$54$	24.0071	3.26695
$55$	−12.6147	−1.70097
$56$	7.53583	1.00702
$57$	−15.1433	−2.00579
$58$	−2.14457	−0.281596
$59$	−1.31833	−0.171632	−0.0858158	−	0.996311i	$-0.527350\pi$
$59$	−1.31833	−0.171632	−0.0858158	+	0.996311i	$0.527350\pi$
$60$	1.33696	0.172601
$61$	11.4490	1.46589	0.732946	−	0.680287i	$-0.238145\pi$
$61$	11.4490	1.46589	0.732946	+	0.680287i	$0.238145\pi$
$62$	−6.87521	−0.873152
$63$	−21.8859	−2.75736
$64$	7.55913	0.944891
$65$	11.5655	1.43452
$66$	−15.0948	−1.85804
$67$	13.7075	1.67464	0.837320	−	0.546713i	$-0.184121\pi$
$67$	13.7075	1.67464	0.837320	+	0.546713i	$0.184121\pi$
$68$	0.563302	0.0683103
$69$	−20.7248	−2.49497
$70$	−15.9322	−1.90427
$71$	−7.06155	−0.838051	−0.419026	−	0.907974i	$-0.637628\pi$
$71$	−7.06155	−0.838051	−0.419026	+	0.907974i	$0.637628\pi$
$72$	−22.0121	−2.59415
$73$	−8.64227	−1.01150	−0.505751	−	0.862680i	$-0.668784\pi$
$73$	−8.64227	−1.01150	−0.505751	+	0.862680i	$0.668784\pi$
$74$	−13.2554	−1.54091
$75$	36.9046	4.26138
$76$	−0.458476	−0.0525908
$77$	8.59776	0.979806
$78$	13.8393	1.56699
$79$	−13.1376	−1.47810	−0.739049	−	0.673651i	$-0.764725\pi$
$79$	−13.1376	−1.47810	−0.739049	+	0.673651i	$0.764725\pi$
$80$	−16.8305	−1.88171
$81$	30.9418	3.43798
$82$	5.76406	0.636534
$83$	1.62956	0.178867	0.0894335	−	0.995993i	$-0.471494\pi$
$83$	1.62956	0.178867	0.0894335	+	0.995993i	$0.471494\pi$
$84$	−0.911229	−0.0994232
$85$	22.5345	2.44421
$86$	17.1419	1.84846
$87$	−4.90681	−0.526065
$88$	8.64733	0.921809
$89$	5.19522	0.550692	0.275346	−	0.961345i	$-0.411208\pi$
$89$	5.19522	0.550692	0.275346	+	0.961345i	$0.411208\pi$
$90$	46.5379	4.90552
$91$	−7.88265	−0.826326
$92$	−0.627457	−0.0654169
$93$	−15.7305	−1.63118
$94$	−10.9927	−1.13382
$95$	−18.3410	−1.88175
$96$	−1.88140	−0.192020
$97$	−18.7843	−1.90725	−0.953626	−	0.300993i	$-0.902682\pi$
$97$	−18.7843	−1.90725	−0.953626	+	0.300993i	$0.902682\pi$
$98$	0.713953	0.0721202
$99$	−25.1140	−2.52405
$100$	1.11731	0.111731
$101$	0.0334589	0.00332929	0.00166464	−	0.999999i	$-0.499470\pi$
$101$	0.0334589	0.00332929	0.00166464	+	0.999999i	$0.499470\pi$
$102$	26.9648	2.66991
$103$	2.38873	0.235368	0.117684	−	0.993051i	$-0.462453\pi$
$103$	2.38873	0.235368	0.117684	+	0.993051i	$0.462453\pi$
$104$	−7.92810	−0.777414
$105$	−36.4531	−3.55746
$106$	−9.39494	−0.912517
$107$	−0.312589	−0.0302191	−0.0151095	−	0.999886i	$-0.504810\pi$
$107$	−0.312589	−0.0302191	−0.0151095	+	0.999886i	$0.504810\pi$
$108$	1.66300	0.160022
$109$	−9.98341	−0.956237	−0.478118	−	0.878295i	$-0.658681\pi$
$109$	−9.98341	−0.956237	−0.478118	+	0.878295i	$0.658681\pi$
$110$	−18.2822	−1.74314
$111$	−30.3286	−2.87866
$112$	11.4711	1.08392
$113$	1.18355	0.111339	0.0556696	−	0.998449i	$-0.482271\pi$
$113$	1.18355	0.111339	0.0556696	+	0.998449i	$0.482271\pi$
$114$	−21.9468	−2.05551
$115$	−25.1010	−2.34068
$116$	−0.148557	−0.0137932
$117$	23.0251	2.12867
$118$	−1.91062	−0.175886
$119$	−15.3587	−1.40793
$120$	−36.6633	−3.34689
$121$	−1.13411	−0.103101
$122$	16.5927	1.50223
$123$	13.1882	1.18914
$124$	−0.476253	−0.0427688
$125$	24.6167	2.20178
$126$	−31.7186	−2.82572
$127$	12.1911	1.08178	0.540892	−	0.841092i	$-0.318087\pi$
$127$	12.1911	1.08178	0.540892	+	0.841092i	$0.318087\pi$
$128$	12.0900	1.06861
$129$	39.2209	3.45321
$130$	16.7616	1.47009
$131$	3.33321	0.291224	0.145612	−	0.989342i	$-0.453485\pi$
$131$	3.33321	0.291224	0.145612	+	0.989342i	$0.453485\pi$
$132$	−1.04563	−0.0910105
$133$	12.5006	1.08394
$134$	19.8659	1.71616
$135$	66.5271	5.72574
$136$	−15.4473	−1.32459
$137$	−2.52813	−0.215993	−0.107997	−	0.994151i	$-0.534444\pi$
$137$	−2.52813	−0.215993	−0.107997	+	0.994151i	$0.534444\pi$
$138$	−30.0358	−2.55682
$139$	−4.53037	−0.384261	−0.192130	−	0.981369i	$-0.561540\pi$
$139$	−4.53037	−0.384261	−0.192130	+	0.981369i	$0.561540\pi$
$140$	−1.10364	−0.0932749
$141$	−25.1515	−2.11814
$142$	−10.2341	−0.858827
$143$	−9.04531	−0.756407
$144$	−33.5069	−2.79224
$145$	−5.94293	−0.493533
$146$	−12.5250	−1.03658
$147$	1.63353	0.134731
$148$	−0.918219	−0.0754772
$149$	8.23046	0.674266	0.337133	−	0.941457i	$-0.390543\pi$
$149$	8.23046	0.674266	0.337133	+	0.941457i	$0.390543\pi$
$150$	53.4849	4.36702
$151$	−1.93095	−0.157139	−0.0785694	−	0.996909i	$-0.525035\pi$
$151$	−1.93095	−0.157139	−0.0785694	+	0.996909i	$0.525035\pi$
$152$	12.5727	1.01978
$153$	44.8627	3.62693
$154$	12.4605	1.00410
$155$	−19.0522	−1.53031
$156$	0.958662	0.0767544
$157$	15.3575	1.22566	0.612829	−	0.790215i	$-0.290031\pi$
$157$	15.3575	1.22566	0.612829	+	0.790215i	$0.290031\pi$
$158$	−19.0400	−1.51474
$159$	−21.4957	−1.70472
$160$	−2.27868	−0.180145
$161$	17.1080	1.34830
$162$	44.8432	3.52321
$163$	11.7774	0.922477	0.461239	−	0.887276i	$-0.347405\pi$
$163$	11.7774	0.922477	0.461239	+	0.887276i	$0.347405\pi$
$164$	0.399283	0.0311788
$165$	−41.8298	−3.25644
$166$	2.36167	0.183301
$167$	1.78286	0.137962	0.0689808	−	0.997618i	$-0.478025\pi$
$167$	1.78286	0.137962	0.0689808	+	0.997618i	$0.478025\pi$
$168$	24.9884	1.92790
$169$	−4.70703	−0.362079
$170$	32.6586	2.50480
$171$	−36.5141	−2.79230
$172$	1.18744	0.0905416
$173$	24.5464	1.86623	0.933115	−	0.359577i	$-0.117079\pi$
$173$	24.5464	1.86623	0.933115	+	0.359577i	$0.117079\pi$
$174$	−7.11130	−0.539106
$175$	−30.4642	−2.30288
$176$	13.1630	0.992200
$177$	−4.37151	−0.328582
$178$	7.52929	0.564344
$179$	−7.21411	−0.539208	−0.269604	−	0.962971i	$-0.586893\pi$
$179$	−7.21411	−0.539208	−0.269604	+	0.962971i	$0.586893\pi$
$180$	3.22373	0.240283
$181$	−10.6725	−0.793277	−0.396639	−	0.917975i	$-0.629823\pi$
$181$	−10.6725	−0.793277	−0.396639	+	0.917975i	$0.629823\pi$
$182$	−11.4241	−0.846812
$183$	37.9643	2.80640
$184$	17.2066	1.26849
$185$	−36.7327	−2.70065
$186$	−22.7978	−1.67162
$187$	−17.6241	−1.28880
$188$	−0.761480	−0.0555366
$189$	−45.3426	−3.29819
$190$	−26.5811	−1.92840
$191$	22.4814	1.62669	0.813347	−	0.581779i	$-0.197643\pi$
$191$	22.4814	1.62669	0.813347	+	0.581779i	$0.197643\pi$
$192$	25.0657	1.80896
$193$	−2.26734	−0.163206	−0.0816032	−	0.996665i	$-0.526004\pi$
$193$	−2.26734	−0.163206	−0.0816032	+	0.996665i	$0.526004\pi$
$194$	−27.2235	−1.95453
$195$	38.3506	2.74635
$196$	0.0494563	0.00353260
$197$	−2.25618	−0.160746	−0.0803731	−	0.996765i	$-0.525611\pi$
$197$	−2.25618	−0.160746	−0.0803731	+	0.996765i	$0.525611\pi$
$198$	−36.3970	−2.58662
$199$	−3.70076	−0.262340	−0.131170	−	0.991360i	$-0.541873\pi$
$199$	−3.70076	−0.262340	−0.131170	+	0.991360i	$0.541873\pi$
$200$	−30.6399	−2.16657
$201$	45.4534	3.20604
$202$	0.0484911	0.00341182
$203$	4.05049	0.284289
$204$	1.86788	0.130778
$205$	15.9730	1.11561
$206$	3.46192	0.241203
$207$	−49.9722	−3.47331
$208$	−12.0682	−0.836779
$209$	14.3444	0.992222
$210$	−52.8305	−3.64565
$211$	18.0944	1.24567	0.622836	−	0.782353i	$-0.285980\pi$
$211$	18.0944	1.24567	0.622836	+	0.782353i	$0.285980\pi$
$212$	−0.650798	−0.0446970
$213$	−23.4157	−1.60442
$214$	−0.453026	−0.0309682
$215$	47.5028	3.23966
$216$	−45.6040	−3.10296
$217$	12.9853	0.881501
$218$	−14.4687	−0.979943
$219$	−28.6573	−1.93648
$220$	−1.26643	−0.0853825
$221$	16.1582	1.08692
$222$	−43.9544	−2.95002
$223$	−23.0004	−1.54022	−0.770112	−	0.637909i	$-0.779800\pi$
$223$	−23.0004	−1.54022	−0.770112	+	0.637909i	$0.779800\pi$
$224$	1.55307	0.103769
$225$	88.9856	5.93237
$226$	1.71529	0.114099
$227$	−5.22139	−0.346556	−0.173278	−	0.984873i	$-0.555436\pi$
$227$	−5.22139	−0.346556	−0.173278	+	0.984873i	$0.555436\pi$
$228$	−1.52028	−0.100683
$229$	16.8354	1.11252	0.556258	−	0.831010i	$-0.312237\pi$
$229$	16.8354	1.11252	0.556258	+	0.831010i	$0.312237\pi$
$230$	−36.3782	−2.39871
$231$	28.5097	1.87580
$232$	4.07385	0.267461
$233$	0.00347835	0.000227874 0	0.000113937	−	1.00000i	$-0.499964\pi$
$233$	0.00347835	0.000227874 0	0.000113937		1.00000i	$0.499964\pi$
$234$	33.3697	2.18145
$235$	−30.4625	−1.98715
$236$	−0.132350	−0.00861528
$237$	−43.5637	−2.82977
$238$	−22.2590	−1.44284
$239$	3.65467	0.236401	0.118200	−	0.992990i	$-0.462287\pi$
$239$	3.65467	0.236401	0.118200	+	0.992990i	$0.462287\pi$
$240$	−55.8091	−3.60246
$241$	3.83708	0.247168	0.123584	−	0.992334i	$-0.460561\pi$
$241$	3.83708	0.247168	0.123584	+	0.992334i	$0.460561\pi$
$242$	−1.64363	−0.105657
$243$	52.9068	3.39397
$244$	1.14940	0.0735825
$245$	1.97847	0.126400
$246$	19.1133	1.21862
$247$	−13.1513	−0.836798
$248$	13.0602	0.829323
$249$	5.40352	0.342434
$250$	35.6763	2.25637
$251$	−12.1118	−0.764487	−0.382244	−	0.924062i	$-0.624848\pi$
$251$	−12.1118	−0.764487	−0.382244	+	0.924062i	$0.624848\pi$
$252$	−2.19718	−0.138410
$253$	19.6313	1.23421
$254$	17.6682	1.10860
$255$	74.7233	4.67935
$256$	2.40346	0.150216
$257$	10.1603	0.633782	0.316891	−	0.948462i	$-0.397361\pi$
$257$	10.1603	0.633782	0.316891	+	0.948462i	$0.397361\pi$
$258$	56.8418	3.53882
$259$	25.0358	1.55565
$260$	1.16109	0.0720079
$261$	−11.8314	−0.732348
$262$	4.83074	0.298444
$263$	−14.7563	−0.909915	−0.454958	−	0.890513i	$-0.650346\pi$
$263$	−14.7563	−0.909915	−0.454958	+	0.890513i	$0.650346\pi$
$264$	28.6741	1.76477
$265$	−26.0347	−1.59930
$266$	18.1168	1.11081
$267$	17.2271	1.05428
$268$	1.37614	0.0840609
$269$	10.5782	0.644963	0.322481	−	0.946576i	$-0.395483\pi$
$269$	10.5782	0.644963	0.322481	+	0.946576i	$0.395483\pi$
$270$	96.4159	5.86768
$271$	−7.69980	−0.467730	−0.233865	−	0.972269i	$-0.575137\pi$
$271$	−7.69980	−0.467730	−0.233865	+	0.972269i	$0.575137\pi$
$272$	−23.5140	−1.42574
$273$	−26.1385	−1.58197
$274$	−3.66396	−0.221348
$275$	−34.9575	−2.10802
$276$	−2.08062	−0.125238
$277$	−12.6505	−0.760093	−0.380046	−	0.924967i	$-0.624092\pi$
$277$	−12.6505	−0.760093	−0.380046	+	0.924967i	$0.624092\pi$
$278$	−6.56574	−0.393787
$279$	−37.9300	−2.27081
$280$	30.2650	1.80868
$281$	16.6648	0.994141	0.497070	−	0.867710i	$-0.334409\pi$
$281$	16.6648	0.994141	0.497070	+	0.867710i	$0.334409\pi$
$282$	−36.4514	−2.17065
$283$	23.7578	1.41225	0.706127	−	0.708086i	$-0.250441\pi$
$283$	23.7578	1.41225	0.706127	+	0.708086i	$0.250441\pi$
$284$	−0.708928	−0.0420672
$285$	−60.8179	−3.60254
$286$	−13.1091	−0.775159
$287$	−10.8867	−0.642620
$288$	−4.53650	−0.267316
$289$	14.4831	0.851945
$290$	−8.61292	−0.505768
$291$	−62.2877	−3.65137
$292$	−0.867622	−0.0507737
$293$	27.6652	1.61622	0.808108	−	0.589034i	$-0.200492\pi$
$293$	27.6652	1.61622	0.808108	+	0.589034i	$0.200492\pi$
$294$	2.36743	0.138071
$295$	−5.29459	−0.308263
$296$	25.1801	1.46357
$297$	−52.0304	−3.01911
$298$	11.9282	0.690981
$299$	−17.9985	−1.04088
$300$	3.70496	0.213906
$301$	−32.3763	−1.86614
$302$	−2.79848	−0.161034
$303$	0.110948	0.00637380
$304$	19.1382	1.09765
$305$	45.9808	2.63285
$306$	65.0183	3.71685
$307$	9.99271	0.570314	0.285157	−	0.958481i	$-0.407954\pi$
$307$	9.99271	0.570314	0.285157	+	0.958481i	$0.407954\pi$
$308$	0.863153	0.0491827
$309$	7.92091	0.450605
$310$	−27.6118	−1.56825
$311$	0.529920	0.0300490	0.0150245	−	0.999887i	$-0.495217\pi$
$311$	0.529920	0.0300490	0.0150245	+	0.999887i	$0.495217\pi$
$312$	−26.2892	−1.48833
$313$	−14.7922	−0.836102	−0.418051	−	0.908423i	$-0.637287\pi$
$313$	−14.7922	−0.836102	−0.418051	+	0.908423i	$0.637287\pi$
$314$	22.2572	1.25604
$315$	−87.8969	−4.95243
$316$	−1.31892	−0.0741952
$317$	12.7172	0.714271	0.357136	−	0.934053i	$-0.383753\pi$
$317$	12.7172	0.714271	0.357136	+	0.934053i	$0.383753\pi$
$318$	−31.1531	−1.74698
$319$	4.64792	0.260234
$320$	30.3586	1.69709
$321$	−1.03653	−0.0578534
$322$	24.7941	1.38172
$323$	−25.6243	−1.42578
$324$	3.10634	0.172574
$325$	32.0500	1.77781
$326$	17.0687	0.945346
$327$	−33.1045	−1.83068
$328$	−10.9495	−0.604582
$329$	20.7622	1.14466
$330$	−60.6228	−3.33717
$331$	−23.1441	−1.27212	−0.636058	−	0.771641i	$-0.719436\pi$
$331$	−23.1441	−1.27212	−0.636058	+	0.771641i	$0.719436\pi$
$332$	0.163596	0.00897847
$333$	−73.1292	−4.00746
$334$	2.58385	0.141382
$335$	55.0514	3.00778
$336$	38.0375	2.07512
$337$	−18.7999	−1.02410	−0.512048	−	0.858957i	$-0.671113\pi$
$337$	−18.7999	−1.02410	−0.512048	+	0.858957i	$0.671113\pi$
$338$	−6.82177	−0.371055
$339$	3.92460	0.213155
$340$	2.26230	0.122690
$341$	14.9006	0.806913
$342$	−52.9189	−2.86153
$343$	17.8124	0.961780
$344$	−32.5630	−1.75568
$345$	−83.2337	−4.48115
$346$	35.5745	1.91250
$347$	−6.41344	−0.344292	−0.172146	−	0.985071i	$-0.555070\pi$
$347$	−6.41344	−0.344292	−0.172146	+	0.985071i	$0.555070\pi$
$348$	−0.492608	−0.0264065
$349$	−5.61211	−0.300409	−0.150205	−	0.988655i	$-0.547993\pi$
$349$	−5.61211	−0.300409	−0.150205	+	0.988655i	$0.547993\pi$
$350$	−44.1510	−2.35997
$351$	47.7028	2.54619
$352$	1.78214	0.0949884
$353$	28.5929	1.52185	0.760924	−	0.648841i	$-0.224746\pi$
$353$	28.5929	1.52185	0.760924	+	0.648841i	$0.224746\pi$
$354$	−6.33551	−0.336728
$355$	−28.3602	−1.50520
$356$	0.521562	0.0276427
$357$	−50.9288	−2.69544
$358$	−10.4552	−0.552575
$359$	−6.32484	−0.333812	−0.166906	−	0.985973i	$-0.553378\pi$
$359$	−6.32484	−0.333812	−0.166906	+	0.985973i	$0.553378\pi$
$360$	−88.4037	−4.65928
$361$	1.85585	0.0976761
$362$	−15.4673	−0.812943
$363$	−3.76064	−0.197383
$364$	−0.791361	−0.0414786
$365$	−34.7086	−1.81673
$366$	55.0206	2.87597
$367$	−4.38267	−0.228774	−0.114387	−	0.993436i	$-0.536490\pi$
$367$	−4.38267	−0.228774	−0.114387	+	0.993436i	$0.536490\pi$
$368$	26.1920	1.36535
$369$	31.7999	1.65543
$370$	−53.2358	−2.76760
$371$	17.7444	0.921242
$372$	−1.57923	−0.0818794
$373$	−20.2166	−1.04678	−0.523388	−	0.852095i	$-0.675332\pi$
$373$	−20.2166	−1.04678	−0.523388	+	0.852095i	$0.675332\pi$
$374$	−25.5421	−1.32075
$375$	81.6276	4.21523
$376$	20.8819	1.07690
$377$	−4.26134	−0.219470
$378$	−65.7138	−3.37995
$379$	−6.08345	−0.312486	−0.156243	−	0.987719i	$-0.549938\pi$
$379$	−6.08345	−0.312486	−0.156243	+	0.987719i	$0.549938\pi$
$380$	−1.84131	−0.0944570
$381$	40.4250	2.07104
$382$	32.5816	1.66702
$383$	34.8663	1.78159	0.890793	−	0.454410i	$-0.150150\pi$
$383$	34.8663	1.78159	0.890793	+	0.454410i	$0.150150\pi$
$384$	40.0898	2.04583
$385$	34.5299	1.75980
$386$	−3.28599	−0.167252
$387$	94.5707	4.80730
$388$	−1.88580	−0.0957372
$389$	−8.13106	−0.412261	−0.206130	−	0.978525i	$-0.566087\pi$
$389$	−8.13106	−0.412261	−0.206130	+	0.978525i	$0.566087\pi$
$390$	55.5805	2.81443
$391$	−35.0687	−1.77350
$392$	−1.35623	−0.0685000
$393$	11.0528	0.557538
$394$	−3.26982	−0.164731
$395$	−52.7626	−2.65478
$396$	−2.52126	−0.126698
$397$	−3.29094	−0.165168	−0.0825839	−	0.996584i	$-0.526317\pi$
$397$	−3.29094	−0.165168	−0.0825839	+	0.996584i	$0.526317\pi$
$398$	−5.36341	−0.268843
$399$	41.4514	2.07516
$400$	−46.6402	−2.33201
$401$	−26.1611	−1.30642	−0.653212	−	0.757175i	$-0.726579\pi$
$401$	−26.1611	−1.30642	−0.653212	+	0.757175i	$0.726579\pi$
$402$	65.8745	3.28552
$403$	−13.6613	−0.680516
$404$	0.00335903	0.000167118 0
$405$	124.267	6.17487
$406$	5.87027	0.291337
$407$	28.7284	1.42402
$408$	−51.2225	−2.53589
$409$	−8.38345	−0.414535	−0.207268	−	0.978284i	$-0.566457\pi$
$409$	−8.38345	−0.414535	−0.207268	+	0.978284i	$0.566457\pi$
$410$	23.1493	1.14326
$411$	−8.38317	−0.413511
$412$	0.239811	0.0118146
$413$	3.60861	0.177568
$414$	−72.4234	−3.55941
$415$	6.54453	0.321258
$416$	−1.63391	−0.0801091
$417$	−15.0225	−0.735654
$418$	20.7889	1.01682
$419$	8.05698	0.393609	0.196805	−	0.980443i	$-0.436944\pi$
$419$	8.05698	0.393609	0.196805	+	0.980443i	$0.436944\pi$
$420$	−3.65963	−0.178572
$421$	24.4147	1.18990	0.594951	−	0.803762i	$-0.297171\pi$
$421$	24.4147	1.18990	0.594951	+	0.803762i	$0.297171\pi$
$422$	26.2238	1.27655
$423$	−60.6461	−2.94871
$424$	17.8467	0.866712
$425$	62.4469	3.02912
$426$	−33.9358	−1.64419
$427$	−31.3389	−1.51660
$428$	−0.0313816	−0.00151689
$429$	−29.9938	−1.44811
$430$	68.8445	3.31998
$431$	12.7548	0.614379	0.307190	−	0.951648i	$-0.400611\pi$
$431$	12.7548	0.614379	0.307190	+	0.951648i	$0.400611\pi$
$432$	−69.4187	−3.33991
$433$	27.9638	1.34385	0.671927	−	0.740617i	$-0.265467\pi$
$433$	27.9638	1.34385	0.671927	+	0.740617i	$0.265467\pi$
$434$	18.8193	0.903354
$435$	−19.7064	−0.944852
$436$	−1.00226	−0.0479996
$437$	28.5427	1.36538
$438$	−41.5323	−1.98449
$439$	41.0119	1.95739	0.978696	−	0.205316i	$-0.0658220\pi$
$439$	41.0119	1.95739	0.978696	+	0.205316i	$0.0658220\pi$
$440$	34.7290	1.65564
$441$	3.93882	0.187563
$442$	23.4177	1.11387
$443$	12.7756	0.606988	0.303494	−	0.952833i	$-0.401847\pi$
$443$	12.7756	0.606988	0.303494	+	0.952833i	$0.401847\pi$
$444$	−3.04477	−0.144498
$445$	20.8647	0.989084
$446$	−33.3339	−1.57841
$447$	27.2918	1.29086
$448$	−20.6913	−0.977574
$449$	−34.7460	−1.63976	−0.819881	−	0.572533i	$-0.805961\pi$
$449$	−34.7460	−1.63976	−0.819881	+	0.572533i	$0.805961\pi$
$450$	128.964	6.07944
$451$	−12.4924	−0.588245
$452$	0.118820	0.00558882
$453$	−6.40295	−0.300837
$454$	−7.56722	−0.355147
$455$	−31.6579	−1.48414
$456$	41.6904	1.95233
$457$	−7.20621	−0.337092	−0.168546	−	0.985694i	$-0.553907\pi$
$457$	−7.20621	−0.337092	−0.168546	+	0.985694i	$0.553907\pi$
$458$	24.3991	1.14010
$459$	92.9453	4.33831
$460$	−2.51996	−0.117494
$461$	23.6215	1.10016	0.550081	−	0.835112i	$-0.314597\pi$
$461$	23.6215	1.10016	0.550081	+	0.835112i	$0.314597\pi$
$462$	41.3184	1.92231
$463$	−8.72642	−0.405551	−0.202776	−	0.979225i	$-0.564996\pi$
$463$	−8.72642	−0.405551	−0.202776	+	0.979225i	$0.564996\pi$
$464$	6.20123	0.287885
$465$	−63.1761	−2.92972
$466$	0.00504108	0.000233524 0
$467$	−3.59066	−0.166156	−0.0830779	−	0.996543i	$-0.526475\pi$
$467$	−3.59066	−0.166156	−0.0830779	+	0.996543i	$0.526475\pi$
$468$	2.31156	0.106852
$469$	−37.5211	−1.73256
$470$	−44.1485	−2.03642
$471$	50.9246	2.34648
$472$	3.62942	0.167058
$473$	−37.1516	−1.70823
$474$	−63.1357	−2.89992
$475$	−50.8261	−2.33206
$476$	−1.54191	−0.0706732
$477$	−51.8311	−2.37318
$478$	5.29661	0.242261
$479$	−1.25828	−0.0574924	−0.0287462	−	0.999587i	$-0.509151\pi$
$479$	−1.25828	−0.0574924	−0.0287462	+	0.999587i	$0.509151\pi$
$480$	−7.55598	−0.344882
$481$	−26.3390	−1.20095
$482$	5.56098	0.253296
$483$	56.7292	2.58127
$484$	−0.113856	−0.00517528
$485$	−75.4403	−3.42557
$486$	76.6764	3.47811
$487$	−13.1375	−0.595316	−0.297658	−	0.954673i	$-0.596205\pi$
$487$	−13.1375	−0.595316	−0.297658	+	0.954673i	$0.596205\pi$
$488$	−31.5196	−1.42683
$489$	39.0533	1.76605
$490$	2.86734	0.129533
$491$	−16.4237	−0.741192	−0.370596	−	0.928794i	$-0.620847\pi$
$491$	−16.4237	−0.741192	−0.370596	+	0.928794i	$0.620847\pi$
$492$	1.32400	0.0596906
$493$	−8.30289	−0.373943
$494$	−19.0598	−0.857543
$495$	−100.861	−4.53338
$496$	19.8803	0.892651
$497$	19.3293	0.867039
$498$	7.83118	0.350924
$499$	24.3662	1.09078	0.545391	−	0.838182i	$-0.316381\pi$
$499$	24.3662	1.09078	0.545391	+	0.838182i	$0.316381\pi$
$500$	2.47134	0.110521
$501$	5.91186	0.264123
$502$	−17.5532	−0.783439
$503$	−21.6281	−0.964348	−0.482174	−	0.876075i	$-0.660153\pi$
$503$	−21.6281	−0.964348	−0.482174	+	0.876075i	$0.660153\pi$
$504$	60.2529	2.68388
$505$	0.134376	0.00597965
$506$	28.4512	1.26481
$507$	−15.6083	−0.693187
$508$	1.22390	0.0543017
$509$	−40.9721	−1.81605	−0.908027	−	0.418911i	$-0.862412\pi$
$509$	−40.9721	−1.81605	−0.908027	+	0.418911i	$0.862412\pi$
$510$	108.294	4.79536
$511$	23.6562	1.04649
$512$	−20.6967	−0.914675
$513$	−75.6489	−3.33998
$514$	14.7250	0.649494
$515$	9.59348	0.422739
$516$	3.93750	0.173339
$517$	23.8245	1.04780
$518$	36.2837	1.59421
$519$	81.3947	3.57283
$520$	−31.8404	−1.39629
$521$	−6.92813	−0.303527	−0.151763	−	0.988417i	$-0.548495\pi$
$521$	−6.92813	−0.303527	−0.151763	+	0.988417i	$0.548495\pi$
$522$	−17.1470	−0.750504
$523$	36.3530	1.58961	0.794803	−	0.606868i	$-0.207574\pi$
$523$	36.3530	1.58961	0.794803	+	0.606868i	$0.207574\pi$
$524$	0.334631	0.0146184
$525$	−101.018	−4.40878
$526$	−21.3860	−0.932473
$527$	−26.6179	−1.15949
$528$	43.6479	1.89953
$529$	16.0628	0.698382
$530$	−37.7314	−1.63895
$531$	−10.5407	−0.457428
$532$	1.25497	0.0544099
$533$	11.4534	0.496101
$534$	24.9667	1.08042
$535$	−1.25540	−0.0542757
$536$	−37.7375	−1.63001
$537$	−23.9216	−1.03229
$538$	15.3307	0.660952
$539$	−1.54735	−0.0666489
$540$	6.67884	0.287411
$541$	−40.7573	−1.75229	−0.876146	−	0.482046i	$-0.839894\pi$
$541$	−40.7573	−1.75229	−0.876146	+	0.482046i	$0.839894\pi$
$542$	−11.1591	−0.479325
$543$	−35.3893	−1.51870
$544$	−3.18355	−0.136494
$545$	−40.0948	−1.71747
$546$	−37.8818	−1.62119
$547$	13.2921	0.568327	0.284164	−	0.958776i	$-0.408284\pi$
$547$	13.2921	0.568327	0.284164	+	0.958776i	$0.408284\pi$
$548$	−0.253806	−0.0108421
$549$	91.5406	3.90686
$550$	−50.6630	−2.16028
$551$	6.75779	0.287892
$552$	57.0563	2.42848
$553$	35.9612	1.52923
$554$	−18.3340	−0.778936
$555$	−121.804	−5.17029
$556$	−0.454816	−0.0192885
$557$	−20.7146	−0.877707	−0.438853	−	0.898559i	$-0.644615\pi$
$557$	−20.7146	−0.877707	−0.438853	+	0.898559i	$0.644615\pi$
$558$	−54.9709	−2.32710
$559$	34.0616	1.44065
$560$	46.0695	1.94679
$561$	−58.4406	−2.46736
$562$	24.1519	1.01879
$563$	12.7123	0.535760	0.267880	−	0.963452i	$-0.413677\pi$
$563$	12.7123	0.535760	0.267880	+	0.963452i	$0.413677\pi$
$564$	−2.52503	−0.106323
$565$	4.75331	0.199973
$566$	34.4315	1.44726
$567$	−84.6960	−3.55690
$568$	19.4408	0.815717
$569$	5.32161	0.223093	0.111547	−	0.993759i	$-0.464420\pi$
$569$	5.32161	0.223093	0.111547	+	0.993759i	$0.464420\pi$
$570$	−88.1417	−3.69185
$571$	19.5317	0.817376	0.408688	−	0.912674i	$-0.365986\pi$
$571$	19.5317	0.817376	0.408688	+	0.912674i	$0.365986\pi$
$572$	−0.908084	−0.0379689
$573$	74.5470	3.11425
$574$	−15.7778	−0.658551
$575$	−69.5592	−2.90082
$576$	60.4392	2.51830
$577$	−12.1179	−0.504473	−0.252237	−	0.967666i	$-0.581166\pi$
$577$	−12.1179	−0.504473	−0.252237	+	0.967666i	$0.581166\pi$
$578$	20.9899	0.873065
$579$	−7.51837	−0.312453
$580$	−0.596627	−0.0247736
$581$	−4.46053	−0.185054
$582$	−90.2718	−3.74189
$583$	20.3616	0.843291
$584$	23.7926	0.984545
$585$	92.4723	3.82326
$586$	40.0944	1.65628
$587$	32.6594	1.34800	0.673998	−	0.738733i	$-0.264575\pi$
$587$	32.6594	1.34800	0.673998	+	0.738733i	$0.264575\pi$
$588$	0.163995	0.00676303
$589$	21.6645	0.892672
$590$	−7.67331	−0.315905
$591$	−7.48138	−0.307743
$592$	38.3293	1.57533
$593$	−27.9810	−1.14904	−0.574520	−	0.818490i	$-0.694811\pi$
$593$	−27.9810	−1.14904	−0.574520	+	0.818490i	$0.694811\pi$
$594$	−75.4063	−3.09396
$595$	−61.6829	−2.52875
$596$	0.826279	0.0338457
$597$	−12.2715	−0.502240
$598$	−26.0848	−1.06669
$599$	−10.3632	−0.423428	−0.211714	−	0.977332i	$-0.567905\pi$
$599$	−10.3632	−0.423428	−0.211714	+	0.977332i	$0.567905\pi$
$600$	−101.600	−4.14781
$601$	−26.3017	−1.07287	−0.536434	−	0.843942i	$-0.680229\pi$
$601$	−26.3017	−1.07287	−0.536434	+	0.843942i	$0.680229\pi$
$602$	−46.9221	−1.91240
$603$	109.599	4.46321
$604$	−0.193854	−0.00788780
$605$	−4.55474	−0.185177
$606$	0.160794	0.00653181
$607$	−25.0808	−1.01800	−0.508999	−	0.860767i	$-0.669984\pi$
$607$	−25.0808	−1.01800	−0.508999	+	0.860767i	$0.669984\pi$
$608$	2.59112	0.105084
$609$	13.4312	0.544261
$610$	66.6387	2.69812
$611$	−21.8429	−0.883671
$612$	4.50389	0.182059
$613$	17.0545	0.688825	0.344413	−	0.938818i	$-0.388078\pi$
$613$	17.0545	0.688825	0.344413	+	0.938818i	$0.388078\pi$
$614$	14.4822	0.584453
$615$	52.9658	2.13579
$616$	−23.6701	−0.953694
$617$	−9.29734	−0.374297	−0.187148	−	0.982332i	$-0.559925\pi$
$617$	−9.29734	−0.374297	−0.187148	+	0.982332i	$0.559925\pi$
$618$	11.4796	0.461775
$619$	20.2709	0.814758	0.407379	−	0.913259i	$-0.366443\pi$
$619$	20.2709	0.814758	0.407379	+	0.913259i	$0.366443\pi$
$620$	−1.91270	−0.0768160
$621$	−103.531	−4.15456
$622$	0.767999	0.0307939
$623$	−14.2207	−0.569740
$624$	−40.0175	−1.60198
$625$	43.2170	1.72868
$626$	−21.4379	−0.856830
$627$	47.5653	1.89957
$628$	1.54178	0.0615236
$629$	−51.3195	−2.04624
$630$	−127.387	−5.07520
$631$	−4.43816	−0.176680	−0.0883402	−	0.996090i	$-0.528156\pi$
$631$	−4.43816	−0.176680	−0.0883402	+	0.996090i	$0.528156\pi$
$632$	36.1685	1.43871
$633$	60.0002	2.38479
$634$	18.4308	0.731979
$635$	48.9612	1.94297
$636$	−2.15801	−0.0855708
$637$	1.41865	0.0562089
$638$	6.73611	0.266685
$639$	−56.4608	−2.23355
$640$	48.5552	1.91931
$641$	−23.5955	−0.931966	−0.465983	−	0.884794i	$-0.654299\pi$
$641$	−23.5955	−0.931966	−0.465983	+	0.884794i	$0.654299\pi$
$642$	−1.50221	−0.0592876
$643$	27.3975	1.08045	0.540226	−	0.841520i	$-0.318339\pi$
$643$	27.3975	1.08045	0.540226	+	0.841520i	$0.318339\pi$
$644$	1.71752	0.0676797
$645$	157.517	6.20222
$646$	−37.1366	−1.46112
$647$	−10.2375	−0.402476	−0.201238	−	0.979542i	$-0.564496\pi$
$647$	−10.2375	−0.402476	−0.201238	+	0.979542i	$0.564496\pi$
$648$	−85.1844	−3.34636
$649$	4.14087	0.162543
$650$	46.4492	1.82189
$651$	43.0587	1.68760
$652$	1.18237	0.0463050
$653$	−31.7703	−1.24327	−0.621634	−	0.783308i	$-0.713531\pi$
$653$	−31.7703	−1.24327	−0.621634	+	0.783308i	$0.713531\pi$
$654$	−47.9774	−1.87607
$655$	13.3867	0.523061
$656$	−16.6673	−0.650749
$657$	−69.0995	−2.69583
$658$	30.0901	1.17303
$659$	22.5092	0.876833	0.438417	−	0.898772i	$-0.355539\pi$
$659$	22.5092	0.876833	0.438417	+	0.898772i	$0.355539\pi$
$660$	−4.19941	−0.163462
$661$	9.96472	0.387583	0.193791	−	0.981043i	$-0.437922\pi$
$661$	9.96472	0.387583	0.193791	+	0.981043i	$0.437922\pi$
$662$	−33.5422	−1.30365
$663$	53.5799	2.08087
$664$	−4.48625	−0.174100
$665$	50.2042	1.94684
$666$	−105.984	−4.10680
$667$	9.24853	0.358104
$668$	0.178986	0.00692517
$669$	−76.2683	−2.94870
$670$	79.7845	3.08234
$671$	−35.9613	−1.38827
$672$	5.14990	0.198662
$673$	30.6455	1.18130	0.590648	−	0.806930i	$-0.298872\pi$
$673$	30.6455	1.18130	0.590648	+	0.806930i	$0.298872\pi$
$674$	−27.2462	−1.04949
$675$	184.358	7.09594
$676$	−0.472551	−0.0181751
$677$	−8.23806	−0.316614	−0.158307	−	0.987390i	$-0.550604\pi$
$677$	−8.23806	−0.316614	−0.158307	+	0.987390i	$0.550604\pi$
$678$	5.68781	0.218439
$679$	51.4175	1.97322
$680$	−62.0386	−2.37907
$681$	−17.3139	−0.663469
$682$	21.5950	0.826917
$683$	−2.91806	−0.111656	−0.0558281	−	0.998440i	$-0.517780\pi$
$683$	−2.91806	−0.111656	−0.0558281	+	0.998440i	$0.517780\pi$
$684$	−3.66575	−0.140164
$685$	−10.1534	−0.387940
$686$	25.8150	0.985623
$687$	55.8254	2.12987
$688$	−49.5675	−1.88974
$689$	−18.6680	−0.711196
$690$	−120.628	−4.59224
$691$	−8.76492	−0.333433	−0.166717	−	0.986005i	$-0.553317\pi$
$691$	−8.76492	−0.333433	−0.166717	+	0.986005i	$0.553317\pi$
$692$	2.46428	0.0936780
$693$	68.7436	2.61135
$694$	−9.29483	−0.352827
$695$	−18.1946	−0.690161
$696$	13.5087	0.512045
$697$	22.3160	0.845280
$698$	−8.13348	−0.307857
$699$	0.0115340	0.000436257 0
$700$	−3.05839	−0.115596
$701$	−18.8367	−0.711451	−0.355725	−	0.934591i	$-0.615766\pi$
$701$	−18.8367	−0.711451	−0.355725	+	0.934591i	$0.615766\pi$
$702$	69.1344	2.60931
$703$	41.7694	1.57536
$704$	−23.7432	−0.894857
$705$	−101.012	−3.80434
$706$	41.4389	1.55958
$707$	−0.0915860	−0.00344445
$708$	−0.438868	−0.0164937
$709$	−5.36253	−0.201394	−0.100697	−	0.994917i	$-0.532107\pi$
$709$	−5.36253	−0.201394	−0.100697	+	0.994917i	$0.532107\pi$
$710$	−41.1017	−1.54252
$711$	−105.042	−3.93939
$712$	−14.3027	−0.536016
$713$	29.6495	1.11038
$714$	−73.8098	−2.76226
$715$	−36.3273	−1.35856
$716$	−0.724244	−0.0270663
$717$	12.1187	0.452581
$718$	−9.16641	−0.342088
$719$	−12.7385	−0.475067	−0.237533	−	0.971379i	$-0.576339\pi$
$719$	−12.7385	−0.475067	−0.237533	+	0.971379i	$0.576339\pi$
$720$	−134.569	−5.01507
$721$	−6.53859	−0.243510
$722$	2.68963	0.100098
$723$	12.7236	0.473195
$724$	−1.07144	−0.0398197
$725$	−16.4689	−0.611638
$726$	−5.45020	−0.202276
$727$	4.44421	0.164827	0.0824134	−	0.996598i	$-0.473737\pi$
$727$	4.44421	0.164827	0.0824134	+	0.996598i	$0.473737\pi$
$728$	21.7013	0.804305
$729$	82.6109	3.05966
$730$	−50.3023	−1.86177
$731$	66.3664	2.45465
$732$	3.81134	0.140871
$733$	40.1474	1.48288	0.741438	−	0.671021i	$-0.234144\pi$
$733$	40.1474	1.48288	0.741438	+	0.671021i	$0.234144\pi$
$734$	−6.35169	−0.234445
$735$	6.56050	0.241988
$736$	3.54613	0.130712
$737$	−43.0553	−1.58596
$738$	46.0867	1.69647
$739$	25.5966	0.941586	0.470793	−	0.882244i	$-0.343968\pi$
$739$	25.5966	0.941586	0.470793	+	0.882244i	$0.343968\pi$
$740$	−3.68770	−0.135563
$741$	−43.6091	−1.60202
$742$	25.7164	0.944080
$743$	−0.0935795	−0.00343310	−0.00171655	−	0.999999i	$-0.500546\pi$
$743$	−0.0935795	−0.00343310	−0.00171655	+	0.999999i	$0.500546\pi$
$744$	43.3069	1.58771
$745$	33.0547	1.21103
$746$	−29.2994	−1.07273
$747$	13.0291	0.476712
$748$	−1.76933	−0.0646932
$749$	0.855639	0.0312644
$750$	118.301	4.31973
$751$	−3.52705	−0.128704	−0.0643519	−	0.997927i	$-0.520498\pi$
$751$	−3.52705	−0.128704	−0.0643519	+	0.997927i	$0.520498\pi$
$752$	31.7865	1.15914
$753$	−40.1620	−1.46358
$754$	−6.17584	−0.224911
$755$	−7.75499	−0.282233
$756$	−4.55207	−0.165557
$757$	−5.87876	−0.213667	−0.106834	−	0.994277i	$-0.534071\pi$
$757$	−5.87876	−0.213667	−0.106834	+	0.994277i	$0.534071\pi$
$758$	−8.81658	−0.320233
$759$	65.0965	2.36285
$760$	50.4937	1.83160
$761$	24.9285	0.903659	0.451829	−	0.892104i	$-0.350772\pi$
$761$	24.9285	0.903659	0.451829	+	0.892104i	$0.350772\pi$
$762$	58.5869	2.12238
$763$	27.3272	0.989313
$764$	2.25697	0.0816541
$765$	180.175	6.51425
$766$	50.5308	1.82575
$767$	−3.79645	−0.137082
$768$	7.96974	0.287583
$769$	27.3551	0.986450	0.493225	−	0.869902i	$-0.335818\pi$
$769$	27.3551	0.986450	0.493225	+	0.869902i	$0.335818\pi$
$770$	50.0432	1.80343
$771$	33.6910	1.21335
$772$	−0.227624	−0.00819237
$773$	22.4134	0.806152	0.403076	−	0.915166i	$-0.367941\pi$
$773$	22.4134	0.806152	0.403076	+	0.915166i	$0.367941\pi$
$774$	137.059	4.92648
$775$	−52.7969	−1.89652
$776$	51.7140	1.85642
$777$	83.0174	2.97823
$778$	−11.7841	−0.422481
$779$	−18.1632	−0.650764
$780$	3.85013	0.137857
$781$	22.1803	0.793675
$782$	−50.8242	−1.81747
$783$	−24.5121	−0.875990
$784$	−2.06446	−0.0737308
$785$	61.6778	2.20138
$786$	16.0185	0.571360
$787$	−26.6724	−0.950769	−0.475384	−	0.879778i	$-0.657691\pi$
$787$	−26.6724	−0.950769	−0.475384	+	0.879778i	$0.657691\pi$
$788$	−0.226504	−0.00806888
$789$	−48.9313	−1.74200
$790$	−76.4675	−2.72059
$791$	−3.23969	−0.115190
$792$	69.1400	2.45678
$793$	32.9702	1.17081
$794$	−4.76948	−0.169262
$795$	−86.3298	−3.06180
$796$	−0.371529	−0.0131685
$797$	−0.635216	−0.0225005	−0.0112502	−	0.999937i	$-0.503581\pi$
$797$	−0.635216	−0.0225005	−0.0112502	+	0.999937i	$0.503581\pi$
$798$	60.0744	2.12661
$799$	−42.5593	−1.50564
$800$	−6.31461	−0.223255
$801$	41.5385	1.46769
$802$	−37.9146	−1.33881
$803$	27.1454	0.957940
$804$	4.56320	0.160932
$805$	68.7081	2.42164
$806$	−19.7989	−0.697386
$807$	35.0767	1.23476
$808$	−0.0921141	−0.00324056
$809$	16.2533	0.571437	0.285718	−	0.958314i	$-0.407768\pi$
$809$	16.2533	0.571437	0.285718	+	0.958314i	$0.407768\pi$
$810$	180.097	6.32795
$811$	−24.9061	−0.874570	−0.437285	−	0.899323i	$-0.644060\pi$
$811$	−24.9061	−0.874570	−0.437285	+	0.899323i	$0.644060\pi$
$812$	0.406640	0.0142703
$813$	−25.5322	−0.895452
$814$	41.6354	1.45932
$815$	47.2998	1.65684
$816$	−77.9711	−2.72953
$817$	−54.0162	−1.88979
$818$	−12.1499	−0.424812
$819$	−63.0259	−2.20230
$820$	1.60358	0.0559994
$821$	16.5448	0.577418	0.288709	−	0.957417i	$-0.406774\pi$
$821$	16.5448	0.577418	0.288709	+	0.957417i	$0.406774\pi$
$822$	−12.1495	−0.423763
$823$	−8.08311	−0.281760	−0.140880	−	0.990027i	$-0.544993\pi$
$823$	−8.08311	−0.281760	−0.140880	+	0.990027i	$0.544993\pi$
$824$	−6.57629	−0.229096
$825$	−115.917	−4.03573
$826$	5.22986	0.181970
$827$	−21.6559	−0.753051	−0.376525	−	0.926406i	$-0.622881\pi$
$827$	−21.6559	−0.753051	−0.376525	+	0.926406i	$0.622881\pi$
$828$	−5.01685	−0.174348
$829$	21.2354	0.737534	0.368767	−	0.929522i	$-0.379780\pi$
$829$	21.2354	0.737534	0.368767	+	0.929522i	$0.379780\pi$
$830$	9.48481	0.329223
$831$	−41.9483	−1.45517
$832$	21.7684	0.754684
$833$	2.76413	0.0957713
$834$	−21.7717	−0.753891
$835$	7.16021	0.247789
$836$	1.44007	0.0498060
$837$	−78.5822	−2.71620
$838$	11.6768	0.403367
$839$	−37.9669	−1.31076	−0.655381	−	0.755299i	$-0.727492\pi$
$839$	−37.9669	−1.31076	−0.655381	+	0.755299i	$0.727492\pi$
$840$	100.357	3.46265
$841$	−26.8103	−0.924494
$842$	35.3836	1.21940
$843$	55.2598	1.90325
$844$	1.81655	0.0625282
$845$	−18.9041	−0.650321
$846$	−87.8928	−3.02182
$847$	3.10435	0.106667
$848$	27.1663	0.932895
$849$	78.7796	2.70371
$850$	90.5027	3.10422
$851$	57.1644	1.95957
$852$	−2.35077	−0.0805361
$853$	41.9841	1.43751	0.718755	−	0.695264i	$-0.244712\pi$
$853$	41.9841	1.43751	0.718755	+	0.695264i	$0.244712\pi$
$854$	−45.4187	−1.55419
$855$	−146.646	−5.01519
$856$	0.860572	0.0294138
$857$	−23.2984	−0.795857	−0.397929	−	0.917416i	$-0.630271\pi$
$857$	−23.2984	−0.795857	−0.397929	+	0.917416i	$0.630271\pi$
$858$	−43.4692	−1.48401
$859$	33.7193	1.15049	0.575244	−	0.817982i	$-0.304907\pi$
$859$	33.7193	1.15049	0.575244	+	0.817982i	$0.304907\pi$
$860$	4.76894	0.162619
$861$	−36.0997	−1.23027
$862$	18.4853	0.629610
$863$	35.8842	1.22151	0.610756	−	0.791819i	$-0.290866\pi$
$863$	35.8842	1.22151	0.610756	+	0.791819i	$0.290866\pi$
$864$	−9.39859	−0.319746
$865$	98.5820	3.35189
$866$	40.5272	1.37717
$867$	48.0251	1.63102
$868$	1.30363	0.0442482
$869$	41.2653	1.39983
$870$	−28.5600	−0.968275
$871$	39.4743	1.33753
$872$	27.4848	0.930753
$873$	−150.190	−5.08316
$874$	41.3662	1.39923
$875$	−67.3824	−2.27794
$876$	−2.87699	−0.0972045
$877$	−38.1117	−1.28694	−0.643471	−	0.765471i	$-0.722506\pi$
$877$	−38.1117	−1.28694	−0.643471	+	0.765471i	$0.722506\pi$
$878$	59.4375	2.00592
$879$	91.7363	3.09419
$880$	52.8646	1.78207
$881$	33.8172	1.13933	0.569666	−	0.821876i	$-0.307073\pi$
$881$	33.8172	1.13933	0.569666	+	0.821876i	$0.307073\pi$
$882$	5.70843	0.192213
$883$	18.0429	0.607192	0.303596	−	0.952801i	$-0.401813\pi$
$883$	18.0429	0.607192	0.303596	+	0.952801i	$0.401813\pi$
$884$	1.62217	0.0545594
$885$	−17.5566	−0.590159
$886$	18.5153	0.622035
$887$	10.0518	0.337505	0.168752	−	0.985658i	$-0.446026\pi$
$887$	10.0518	0.337505	0.168752	+	0.985658i	$0.446026\pi$
$888$	83.4961	2.80194
$889$	−33.3703	−1.11920
$890$	30.2387	1.01360
$891$	−97.1883	−3.25593
$892$	−2.30908	−0.0773137
$893$	34.6394	1.15916
$894$	39.5533	1.32286
$895$	−28.9729	−0.968458
$896$	−33.0935	−1.10558
$897$	−59.6822	−1.99273
$898$	−50.3564	−1.68041
$899$	7.01983	0.234124
$900$	8.93351	0.297784
$901$	−36.3732	−1.21177
$902$	−18.1049	−0.602828
$903$	−107.358	−3.57265
$904$	−3.25838	−0.108372
$905$	−42.8621	−1.42479
$906$	−9.27962	−0.308295
$907$	6.83792	0.227049	0.113525	−	0.993535i	$-0.463786\pi$
$907$	6.83792	0.227049	0.113525	+	0.993535i	$0.463786\pi$
$908$	−0.524190	−0.0173959
$909$	0.267522	0.00887313
$910$	−45.8809	−1.52094
$911$	−44.1850	−1.46391	−0.731957	−	0.681351i	$-0.761393\pi$
$911$	−44.1850	−1.46391	−0.731957	+	0.681351i	$0.761393\pi$
$912$	63.4613	2.10141
$913$	−5.11844	−0.169396
$914$	−10.4438	−0.345449
$915$	152.470	5.04050
$916$	1.69015	0.0558443
$917$	−9.12389	−0.301298
$918$	134.703	4.44587
$919$	41.1994	1.35904	0.679522	−	0.733655i	$-0.262187\pi$
$919$	41.1994	1.35904	0.679522	+	0.733655i	$0.262187\pi$
$920$	69.1043	2.27830
$921$	33.1353	1.09185
$922$	34.2340	1.12744
$923$	−20.3355	−0.669351
$924$	2.86217	0.0941585
$925$	−101.793	−3.34692
$926$	−12.6470	−0.415605
$927$	19.0991	0.627298
$928$	0.839585	0.0275607
$929$	11.7731	0.386265	0.193132	−	0.981173i	$-0.438135\pi$
$929$	11.7731	0.386265	0.193132	+	0.981173i	$0.438135\pi$
$930$	−91.5594	−3.00235
$931$	−2.24975	−0.0737324
$932$	0.000349201 0	1.14385e−5 0
$933$	1.75719	0.0575277
$934$	−5.20385	−0.170275
$935$	−70.7809	−2.31478
$936$	−63.3893	−2.07194
$937$	54.0741	1.76652	0.883262	−	0.468879i	$-0.155342\pi$
$937$	54.0741	1.76652	0.883262	+	0.468879i	$0.155342\pi$
$938$	−54.3784	−1.77552
$939$	−49.0501	−1.60069
$940$	−3.05821	−0.0997480
$941$	4.74013	0.154524	0.0772620	−	0.997011i	$-0.475382\pi$
$941$	4.74013	0.154524	0.0772620	+	0.997011i	$0.475382\pi$
$942$	73.8036	2.40465
$943$	−24.8576	−0.809476
$944$	5.52472	0.179814
$945$	−182.102	−5.92379
$946$	−53.8429	−1.75058
$947$	−5.08375	−0.165200	−0.0825998	−	0.996583i	$-0.526322\pi$
$947$	−5.08375	−0.165200	−0.0825998	+	0.996583i	$0.526322\pi$
$948$	−4.37348	−0.142044
$949$	−24.8876	−0.807886
$950$	−73.6609	−2.38987
$951$	42.1697	1.36745
$952$	42.2834	1.37041
$953$	11.8328	0.383302	0.191651	−	0.981463i	$-0.438616\pi$
$953$	11.8328	0.383302	0.191651	+	0.981463i	$0.438616\pi$
$954$	−75.1174	−2.43202
$955$	90.2884	2.92166
$956$	0.366902	0.0118665
$957$	15.4123	0.498208
$958$	−1.82360	−0.0589177
$959$	6.92018	0.223464
$960$	100.667	3.24903
$961$	−8.49542	−0.274046
$962$	−38.1724	−1.23073
$963$	−2.49931	−0.0805391
$964$	0.385215	0.0124069
$965$	−9.10595	−0.293131
$966$	82.2161	2.64526
$967$	40.5606	1.30434	0.652171	−	0.758072i	$-0.273858\pi$
$967$	40.5606	1.30434	0.652171	+	0.758072i	$0.273858\pi$
$968$	3.12225	0.100353
$969$	−84.9690	−2.72960
$970$	−109.334	−3.51049
$971$	48.4653	1.55533	0.777663	−	0.628681i	$-0.216405\pi$
$971$	48.4653	1.55533	0.777663	+	0.628681i	$0.216405\pi$
$972$	5.31146	0.170365
$973$	12.4008	0.397552
$974$	−19.0398	−0.610074
$975$	106.276	3.40356
$976$	−47.9793	−1.53578
$977$	−9.65781	−0.308981	−0.154490	−	0.987994i	$-0.549374\pi$
$977$	−9.65781	−0.308981	−0.154490	+	0.987994i	$0.549374\pi$
$978$	56.5989	1.80983
$979$	−16.3182	−0.521531
$980$	0.198624	0.00634481
$981$	−79.8226	−2.54854
$982$	−23.8025	−0.759567
$983$	27.7287	0.884407	0.442204	−	0.896915i	$-0.354197\pi$
$983$	27.7287	0.884407	0.442204	+	0.896915i	$0.354197\pi$
$984$	−36.3078	−1.15745
$985$	−9.06115	−0.288712
$986$	−12.0332	−0.383214
$987$	68.8464	2.19140
$988$	−1.32030	−0.0420042
$989$	−73.9250	−2.35068
$990$	−146.176	−4.64576
$991$	−34.4294	−1.09368	−0.546842	−	0.837236i	$-0.684170\pi$
$991$	−34.4294	−1.09368	−0.546842	+	0.837236i	$0.684170\pi$
$992$	2.69159	0.0854581
$993$	−76.7448	−2.43542
$994$	28.0135	0.888534
$995$	−14.8628	−0.471182
$996$	0.542475	0.0171890
$997$	25.0350	0.792867	0.396434	−	0.918063i	$-0.370248\pi$
$997$	25.0350	0.792867	0.396434	+	0.918063i	$0.370248\pi$
$998$	35.3133	1.11782
$999$	−151.507	−4.79347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.b.1.61	✓	87

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.b.1.61	✓	87	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q+1.44927 q^{2} +3.31595 q^{3} +0.100393 q^{4} +4.01615 q^{5} +4.80572 q^{6} -2.73727 q^{7} -2.75305 q^{8} +7.99552 q^{9} +O(q^{10})\)	\(q+1.44927 q^{2} +3.31595 q^{3} +0.100393 q^{4} +4.01615 q^{5} +4.80572 q^{6} -2.73727 q^{7} -2.75305 q^{8} +7.99552 q^{9} +5.82049 q^{10} -3.14100 q^{11} +0.332897 q^{12} +2.87975 q^{13} -3.96705 q^{14} +13.3173 q^{15} -4.19071 q^{16} +5.61098 q^{17} +11.5877 q^{18} -4.56682 q^{19} +0.403192 q^{20} -9.07664 q^{21} -4.55217 q^{22} -6.25002 q^{23} -9.12898 q^{24} +11.1294 q^{25} +4.17355 q^{26} +16.5649 q^{27} -0.274802 q^{28} -1.47976 q^{29} +19.3005 q^{30} -4.74390 q^{31} -0.567379 q^{32} -10.4154 q^{33} +8.13184 q^{34} -10.9933 q^{35} +0.802693 q^{36} -9.14627 q^{37} -6.61857 q^{38} +9.54911 q^{39} -11.0566 q^{40} +3.97721 q^{41} -13.1545 q^{42} +11.8280 q^{43} -0.315334 q^{44} +32.1112 q^{45} -9.05799 q^{46} -7.58501 q^{47} -13.8962 q^{48} +0.492628 q^{49} +16.1296 q^{50} +18.6057 q^{51} +0.289106 q^{52} -6.48252 q^{53} +24.0071 q^{54} -12.6147 q^{55} +7.53583 q^{56} -15.1433 q^{57} -2.14457 q^{58} -1.31833 q^{59} +1.33696 q^{60} +11.4490 q^{61} -6.87521 q^{62} -21.8859 q^{63} +7.55913 q^{64} +11.5655 q^{65} -15.0948 q^{66} +13.7075 q^{67} +0.563302 q^{68} -20.7248 q^{69} -15.9322 q^{70} -7.06155 q^{71} -22.0121 q^{72} -8.64227 q^{73} -13.2554 q^{74} +36.9046 q^{75} -0.458476 q^{76} +8.59776 q^{77} +13.8393 q^{78} -13.1376 q^{79} -16.8305 q^{80} +30.9418 q^{81} +5.76406 q^{82} +1.62956 q^{83} -0.911229 q^{84} +22.5345 q^{85} +17.1419 q^{86} -4.90681 q^{87} +8.64733 q^{88} +5.19522 q^{89} +46.5379 q^{90} -7.88265 q^{91} -0.627457 q^{92} -15.7305 q^{93} -10.9927 q^{94} -18.3410 q^{95} -1.88140 q^{96} -18.7843 q^{97} +0.713953 q^{98} -25.1140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * q^99

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