LMFDB - Embedded newform 4017.2.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.856339 q^{2} -1.00000 q^{3} -1.26668 q^{4} +1.28941 q^{5} +0.856339 q^{6} +1.75524 q^{7} +2.79739 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.856339 q^{2} -1.00000 q^{3} -1.26668 q^{4} +1.28941 q^{5} +0.856339 q^{6} +1.75524 q^{7} +2.79739 q^{8} +1.00000 q^{9} -1.10417 q^{10} -3.35053 q^{11} +1.26668 q^{12} +1.00000 q^{13} -1.50308 q^{14} -1.28941 q^{15} +0.137853 q^{16} -2.31076 q^{17} -0.856339 q^{18} +1.56504 q^{19} -1.63327 q^{20} -1.75524 q^{21} +2.86919 q^{22} +7.81736 q^{23} -2.79739 q^{24} -3.33743 q^{25} -0.856339 q^{26} -1.00000 q^{27} -2.22334 q^{28} -6.34364 q^{29} +1.10417 q^{30} -1.96684 q^{31} -5.71283 q^{32} +3.35053 q^{33} +1.97879 q^{34} +2.26322 q^{35} -1.26668 q^{36} -4.02909 q^{37} -1.34020 q^{38} -1.00000 q^{39} +3.60697 q^{40} -5.49241 q^{41} +1.50308 q^{42} +8.96229 q^{43} +4.24406 q^{44} +1.28941 q^{45} -6.69431 q^{46} -4.45621 q^{47} -0.137853 q^{48} -3.91913 q^{49} +2.85797 q^{50} +2.31076 q^{51} -1.26668 q^{52} +11.3450 q^{53} +0.856339 q^{54} -4.32019 q^{55} +4.91009 q^{56} -1.56504 q^{57} +5.43231 q^{58} -14.5459 q^{59} +1.63327 q^{60} -6.75499 q^{61} +1.68428 q^{62} +1.75524 q^{63} +4.61641 q^{64} +1.28941 q^{65} -2.86919 q^{66} +5.10218 q^{67} +2.92700 q^{68} -7.81736 q^{69} -1.93808 q^{70} -8.96266 q^{71} +2.79739 q^{72} +1.05839 q^{73} +3.45027 q^{74} +3.33743 q^{75} -1.98241 q^{76} -5.88099 q^{77} +0.856339 q^{78} +13.3733 q^{79} +0.177749 q^{80} +1.00000 q^{81} +4.70336 q^{82} +13.2453 q^{83} +2.22334 q^{84} -2.97950 q^{85} -7.67476 q^{86} +6.34364 q^{87} -9.37273 q^{88} +9.75592 q^{89} -1.10417 q^{90} +1.75524 q^{91} -9.90212 q^{92} +1.96684 q^{93} +3.81602 q^{94} +2.01797 q^{95} +5.71283 q^{96} -4.23298 q^{97} +3.35610 q^{98} -3.35053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.856339	−0.605523	−0.302762	−	0.953066i	$-0.597909\pi$
$2$	−0.856339	−0.605523	−0.302762	+	0.953066i	$0.597909\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.26668	−0.633342
$5$	1.28941	0.576640	0.288320	−	0.957534i	$-0.406903\pi$
$5$	1.28941	0.576640	0.288320	+	0.957534i	$0.406903\pi$
$6$	0.856339	0.349599
$7$	1.75524	0.663419	0.331709	−	0.943382i	$-0.392375\pi$
$7$	1.75524	0.663419	0.331709	+	0.943382i	$0.392375\pi$
$8$	2.79739	0.989026
$9$	1.00000	0.333333
$10$	−1.10417	−0.349169
$11$	−3.35053	−1.01022	−0.505111	−	0.863054i	$-0.668549\pi$
$11$	−3.35053	−1.01022	−0.505111	+	0.863054i	$0.668549\pi$
$12$	1.26668	0.365660
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.50308	−0.401716
$15$	−1.28941	−0.332923
$16$	0.137853	0.0344634
$17$	−2.31076	−0.560441	−0.280220	−	0.959936i	$-0.590408\pi$
$17$	−2.31076	−0.560441	−0.280220	+	0.959936i	$0.590408\pi$
$18$	−0.856339	−0.201841
$19$	1.56504	0.359045	0.179522	−	0.983754i	$-0.442545\pi$
$19$	1.56504	0.359045	0.179522	+	0.983754i	$0.442545\pi$
$20$	−1.63327	−0.365210
$21$	−1.75524	−0.383025
$22$	2.86919	0.611713
$23$	7.81736	1.63003	0.815016	−	0.579439i	$-0.196728\pi$
$23$	7.81736	1.63003	0.815016	+	0.579439i	$0.196728\pi$
$24$	−2.79739	−0.571015
$25$	−3.33743	−0.667487
$26$	−0.856339	−0.167942
$27$	−1.00000	−0.192450
$28$	−2.22334	−0.420171
$29$	−6.34364	−1.17798	−0.588992	−	0.808139i	$-0.700475\pi$
$29$	−6.34364	−1.17798	−0.588992	+	0.808139i	$0.700475\pi$
$30$	1.10417	0.201593
$31$	−1.96684	−0.353255	−0.176628	−	0.984278i	$-0.556519\pi$
$31$	−1.96684	−0.353255	−0.176628	+	0.984278i	$0.556519\pi$
$32$	−5.71283	−1.00989
$33$	3.35053	0.583252
$34$	1.97879	0.339360
$35$	2.26322	0.382554
$36$	−1.26668	−0.211114
$37$	−4.02909	−0.662379	−0.331189	−	0.943564i	$-0.607450\pi$
$37$	−4.02909	−0.662379	−0.331189	+	0.943564i	$0.607450\pi$
$38$	−1.34020	−0.217410
$39$	−1.00000	−0.160128
$40$	3.60697	0.570312
$41$	−5.49241	−0.857770	−0.428885	−	0.903359i	$-0.641093\pi$
$41$	−5.49241	−0.857770	−0.428885	+	0.903359i	$0.641093\pi$
$42$	1.50308	0.231931
$43$	8.96229	1.36674	0.683368	−	0.730074i	$-0.260514\pi$
$43$	8.96229	1.36674	0.683368	+	0.730074i	$0.260514\pi$
$44$	4.24406	0.639816
$45$	1.28941	0.192213
$46$	−6.69431	−0.987022
$47$	−4.45621	−0.650005	−0.325002	−	0.945713i	$-0.605365\pi$
$47$	−4.45621	−0.650005	−0.325002	+	0.945713i	$0.605365\pi$
$48$	−0.137853	−0.0198974
$49$	−3.91913	−0.559875
$50$	2.85797	0.404179
$51$	2.31076	0.323571
$52$	−1.26668	−0.175657
$53$	11.3450	1.55836	0.779179	−	0.626802i	$-0.215636\pi$
$53$	11.3450	1.55836	0.779179	+	0.626802i	$0.215636\pi$
$54$	0.856339	0.116533
$55$	−4.32019	−0.582535
$56$	4.91009	0.656139
$57$	−1.56504	−0.207295
$58$	5.43231	0.713297
$59$	−14.5459	−1.89372	−0.946861	−	0.321644i	$-0.895765\pi$
$59$	−14.5459	−1.89372	−0.946861	+	0.321644i	$0.895765\pi$
$60$	1.63327	0.210854
$61$	−6.75499	−0.864888	−0.432444	−	0.901661i	$-0.642349\pi$
$61$	−6.75499	−0.864888	−0.432444	+	0.901661i	$0.642349\pi$
$62$	1.68428	0.213904
$63$	1.75524	0.221140
$64$	4.61641	0.577051
$65$	1.28941	0.159931
$66$	−2.86919	−0.353173
$67$	5.10218	0.623331	0.311666	−	0.950192i	$-0.399113\pi$
$67$	5.10218	0.623331	0.311666	+	0.950192i	$0.399113\pi$
$68$	2.92700	0.354951
$69$	−7.81736	−0.941099
$70$	−1.93808	−0.231645
$71$	−8.96266	−1.06367	−0.531836	−	0.846847i	$-0.678498\pi$
$71$	−8.96266	−1.06367	−0.531836	+	0.846847i	$0.678498\pi$
$72$	2.79739	0.329675
$73$	1.05839	0.123875	0.0619375	−	0.998080i	$-0.480272\pi$
$73$	1.05839	0.123875	0.0619375	+	0.998080i	$0.480272\pi$
$74$	3.45027	0.401086
$75$	3.33743	0.385374
$76$	−1.98241	−0.227398
$77$	−5.88099	−0.670201
$78$	0.856339	0.0969613
$79$	13.3733	1.50462	0.752308	−	0.658811i	$-0.228940\pi$
$79$	13.3733	1.50462	0.752308	+	0.658811i	$0.228940\pi$
$80$	0.177749	0.0198730
$81$	1.00000	0.111111
$82$	4.70336	0.519400
$83$	13.2453	1.45386	0.726930	−	0.686711i	$-0.240946\pi$
$83$	13.2453	1.45386	0.726930	+	0.686711i	$0.240946\pi$
$84$	2.22334	0.242586
$85$	−2.97950	−0.323173
$86$	−7.67476	−0.827591
$87$	6.34364	0.680110
$88$	−9.37273	−0.999137
$89$	9.75592	1.03413	0.517063	−	0.855948i	$-0.327025\pi$
$89$	9.75592	1.03413	0.517063	+	0.855948i	$0.327025\pi$
$90$	−1.10417	−0.116390
$91$	1.75524	0.183999
$92$	−9.90212	−1.03237
$93$	1.96684	0.203952
$94$	3.81602	0.393593
$95$	2.01797	0.207040
$96$	5.71283	0.583063
$97$	−4.23298	−0.429794	−0.214897	−	0.976637i	$-0.568942\pi$
$97$	−4.23298	−0.429794	−0.214897	+	0.976637i	$0.568942\pi$
$98$	3.35610	0.339017
$99$	−3.35053	−0.336741
$100$	4.22747	0.422747
$101$	0.598375	0.0595405	0.0297703	−	0.999557i	$-0.490522\pi$
$101$	0.598375	0.0595405	0.0297703	+	0.999557i	$0.490522\pi$
$102$	−1.97879	−0.195930
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.79739	0.274307
$105$	−2.26322	−0.220868
$106$	−9.71518	−0.943622
$107$	−9.75471	−0.943024	−0.471512	−	0.881860i	$-0.656292\pi$
$107$	−9.75471	−0.943024	−0.471512	+	0.881860i	$0.656292\pi$
$108$	1.26668	0.121887
$109$	−10.8096	−1.03537	−0.517687	−	0.855570i	$-0.673207\pi$
$109$	−10.8096	−1.03537	−0.517687	+	0.855570i	$0.673207\pi$
$110$	3.69955	0.352738
$111$	4.02909	0.382425
$112$	0.241966	0.0228637
$113$	0.345677	0.0325186	0.0162593	−	0.999868i	$-0.494824\pi$
$113$	0.345677	0.0325186	0.0162593	+	0.999868i	$0.494824\pi$
$114$	1.34020	0.125522
$115$	10.0797	0.939941
$116$	8.03539	0.746067
$117$	1.00000	0.0924500
$118$	12.4563	1.14669
$119$	−4.05594	−0.371807
$120$	−3.60697	−0.329270
$121$	0.226051	0.0205501
$122$	5.78456	0.523710
$123$	5.49241	0.495234
$124$	2.49137	0.223731
$125$	−10.7503	−0.961539
$126$	−1.50308	−0.133905
$127$	−11.7862	−1.04585	−0.522926	−	0.852378i	$-0.675160\pi$
$127$	−11.7862	−1.04585	−0.522926	+	0.852378i	$0.675160\pi$
$128$	7.47244	0.660477
$129$	−8.96229	−0.789086
$130$	−1.10417	−0.0968420
$131$	−1.13413	−0.0990892	−0.0495446	−	0.998772i	$-0.515777\pi$
$131$	−1.13413	−0.0990892	−0.0495446	+	0.998772i	$0.515777\pi$
$132$	−4.24406	−0.369398
$133$	2.74702	0.238197
$134$	−4.36920	−0.377441
$135$	−1.28941	−0.110974
$136$	−6.46408	−0.554291
$137$	10.9932	0.939213	0.469606	−	0.882876i	$-0.344396\pi$
$137$	10.9932	0.939213	0.469606	+	0.882876i	$0.344396\pi$
$138$	6.69431	0.569857
$139$	−6.35873	−0.539341	−0.269670	−	0.962953i	$-0.586915\pi$
$139$	−6.35873	−0.539341	−0.269670	+	0.962953i	$0.586915\pi$
$140$	−2.86678	−0.242287
$141$	4.45621	0.375280
$142$	7.67508	0.644078
$143$	−3.35053	−0.280185
$144$	0.137853	0.0114878
$145$	−8.17953	−0.679273
$146$	−0.906339	−0.0750091
$147$	3.91913	0.323244
$148$	5.10359	0.419512
$149$	−8.62247	−0.706380	−0.353190	−	0.935552i	$-0.614903\pi$
$149$	−8.62247	−0.706380	−0.353190	+	0.935552i	$0.614903\pi$
$150$	−2.85797	−0.233353
$151$	0.197957	0.0161095	0.00805474	−	0.999968i	$-0.497436\pi$
$151$	0.197957	0.0161095	0.00805474	+	0.999968i	$0.497436\pi$
$152$	4.37802	0.355105
$153$	−2.31076	−0.186814
$154$	5.03612	0.405822
$155$	−2.53606	−0.203701
$156$	1.26668	0.101416
$157$	14.8978	1.18897	0.594486	−	0.804106i	$-0.297356\pi$
$157$	14.8978	1.18897	0.594486	+	0.804106i	$0.297356\pi$
$158$	−11.4521	−0.911080
$159$	−11.3450	−0.899718
$160$	−7.36615	−0.582345
$161$	13.7214	1.08139
$162$	−0.856339	−0.0672804
$163$	−4.37211	−0.342450	−0.171225	−	0.985232i	$-0.554773\pi$
$163$	−4.37211	−0.342450	−0.171225	+	0.985232i	$0.554773\pi$
$164$	6.95714	0.543262
$165$	4.32019	0.336327
$166$	−11.3425	−0.880346
$167$	−5.91365	−0.457612	−0.228806	−	0.973472i	$-0.573482\pi$
$167$	−5.91365	−0.457612	−0.228806	+	0.973472i	$0.573482\pi$
$168$	−4.91009	−0.378822
$169$	1.00000	0.0769231
$170$	2.55147	0.195688
$171$	1.56504	0.119682
$172$	−11.3524	−0.865611
$173$	22.3043	1.69576	0.847882	−	0.530185i	$-0.177878\pi$
$173$	22.3043	1.69576	0.847882	+	0.530185i	$0.177878\pi$
$174$	−5.43231	−0.411822
$175$	−5.85800	−0.442823
$176$	−0.461882	−0.0348157
$177$	14.5459	1.09334
$178$	−8.35437	−0.626187
$179$	−7.44119	−0.556181	−0.278090	−	0.960555i	$-0.589701\pi$
$179$	−7.44119	−0.556181	−0.278090	+	0.960555i	$0.589701\pi$
$180$	−1.63327	−0.121737
$181$	14.9922	1.11436	0.557182	−	0.830390i	$-0.311883\pi$
$181$	14.9922	1.11436	0.557182	+	0.830390i	$0.311883\pi$
$182$	−1.50308	−0.111416
$183$	6.75499	0.499343
$184$	21.8682	1.61214
$185$	−5.19514	−0.381954
$186$	−1.68428	−0.123498
$187$	7.74226	0.566170
$188$	5.64460	0.411675
$189$	−1.75524	−0.127675
$190$	−1.72807	−0.125367
$191$	−21.2326	−1.53633	−0.768167	−	0.640250i	$-0.778831\pi$
$191$	−21.2326	−1.53633	−0.768167	+	0.640250i	$0.778831\pi$
$192$	−4.61641	−0.333161
$193$	0.358592	0.0258120	0.0129060	−	0.999917i	$-0.495892\pi$
$193$	0.358592	0.0258120	0.0129060	+	0.999917i	$0.495892\pi$
$194$	3.62487	0.260251
$195$	−1.28941	−0.0923363
$196$	4.96429	0.354592
$197$	7.28990	0.519384	0.259692	−	0.965691i	$-0.416379\pi$
$197$	7.28990	0.519384	0.259692	+	0.965691i	$0.416379\pi$
$198$	2.86919	0.203904
$199$	15.1708	1.07543	0.537716	−	0.843126i	$-0.319287\pi$
$199$	15.1708	1.07543	0.537716	+	0.843126i	$0.319287\pi$
$200$	−9.33610	−0.660162
$201$	−5.10218	−0.359880
$202$	−0.512412	−0.0360532
$203$	−11.1346	−0.781497
$204$	−2.92700	−0.204931
$205$	−7.08194	−0.494624
$206$	−0.856339	−0.0596640
$207$	7.81736	0.543344
$208$	0.137853	0.00955842
$209$	−5.24371	−0.362715
$210$	1.93808	0.133740
$211$	−15.1507	−1.04301	−0.521507	−	0.853247i	$-0.674630\pi$
$211$	−15.1507	−1.04301	−0.521507	+	0.853247i	$0.674630\pi$
$212$	−14.3705	−0.986973
$213$	8.96266	0.614111
$214$	8.35334	0.571023
$215$	11.5560	0.788115
$216$	−2.79739	−0.190338
$217$	−3.45229	−0.234356
$218$	9.25670	0.626943
$219$	−1.05839	−0.0715192
$220$	5.47232	0.368943
$221$	−2.31076	−0.155438
$222$	−3.45027	−0.231567
$223$	−20.9079	−1.40010	−0.700049	−	0.714095i	$-0.746838\pi$
$223$	−20.9079	−1.40010	−0.700049	+	0.714095i	$0.746838\pi$
$224$	−10.0274	−0.669983
$225$	−3.33743	−0.222496
$226$	−0.296017	−0.0196908
$227$	−2.61929	−0.173849	−0.0869243	−	0.996215i	$-0.527704\pi$
$227$	−2.61929	−0.173849	−0.0869243	+	0.996215i	$0.527704\pi$
$228$	1.98241	0.131288
$229$	−6.95646	−0.459696	−0.229848	−	0.973227i	$-0.573823\pi$
$229$	−6.95646	−0.459696	−0.229848	+	0.973227i	$0.573823\pi$
$230$	−8.63168	−0.569156
$231$	5.88099	0.386941
$232$	−17.7456	−1.16506
$233$	−13.7416	−0.900239	−0.450120	−	0.892968i	$-0.648619\pi$
$233$	−13.7416	−0.900239	−0.450120	+	0.892968i	$0.648619\pi$
$234$	−0.856339	−0.0559806
$235$	−5.74586	−0.374819
$236$	18.4251	1.19937
$237$	−13.3733	−0.868691
$238$	3.47326	0.225138
$239$	−20.4718	−1.32421	−0.662107	−	0.749409i	$-0.730337\pi$
$239$	−20.4718	−1.32421	−0.662107	+	0.749409i	$0.730337\pi$
$240$	−0.177749	−0.0114737
$241$	9.75215	0.628191	0.314096	−	0.949391i	$-0.398299\pi$
$241$	9.75215	0.628191	0.314096	+	0.949391i	$0.398299\pi$
$242$	−0.193576	−0.0124435
$243$	−1.00000	−0.0641500
$244$	8.55643	0.547770
$245$	−5.05334	−0.322846
$246$	−4.70336	−0.299876
$247$	1.56504	0.0995811
$248$	−5.50202	−0.349379
$249$	−13.2453	−0.839387
$250$	9.20593	0.582234
$251$	−18.6092	−1.17460	−0.587301	−	0.809368i	$-0.699810\pi$
$251$	−18.6092	−1.17460	−0.587301	+	0.809368i	$0.699810\pi$
$252$	−2.22334	−0.140057
$253$	−26.1923	−1.64670
$254$	10.0929	0.633288
$255$	2.97950	0.186584
$256$	−15.6318	−0.976985
$257$	−8.03121	−0.500973	−0.250487	−	0.968120i	$-0.580591\pi$
$257$	−8.03121	−0.500973	−0.250487	+	0.968120i	$0.580591\pi$
$258$	7.67476	0.477810
$259$	−7.07203	−0.439435
$260$	−1.63327	−0.101291
$261$	−6.34364	−0.392662
$262$	0.971198	0.0600008
$263$	−24.1393	−1.48849	−0.744246	−	0.667906i	$-0.767191\pi$
$263$	−24.1393	−1.48849	−0.744246	+	0.667906i	$0.767191\pi$
$264$	9.37273	0.576852
$265$	14.6283	0.898611
$266$	−2.35238	−0.144234
$267$	−9.75592	−0.597052
$268$	−6.46285	−0.394782
$269$	−11.4748	−0.699631	−0.349815	−	0.936819i	$-0.613756\pi$
$269$	−11.4748	−0.699631	−0.349815	+	0.936819i	$0.613756\pi$
$270$	1.10417	0.0671976
$271$	−7.64921	−0.464657	−0.232328	−	0.972637i	$-0.574634\pi$
$271$	−7.64921	−0.464657	−0.232328	+	0.972637i	$0.574634\pi$
$272$	−0.318546	−0.0193147
$273$	−1.75524	−0.106232
$274$	−9.41391	−0.568715
$275$	11.1822	0.674310
$276$	9.90212	0.596037
$277$	11.6751	0.701489	0.350745	−	0.936471i	$-0.385929\pi$
$277$	11.6751	0.701489	0.350745	+	0.936471i	$0.385929\pi$
$278$	5.44523	0.326583
$279$	−1.96684	−0.117752
$280$	6.33110	0.378356
$281$	−21.5397	−1.28495	−0.642476	−	0.766306i	$-0.722093\pi$
$281$	−21.5397	−1.28495	−0.642476	+	0.766306i	$0.722093\pi$
$282$	−3.81602	−0.227241
$283$	−18.1903	−1.08130	−0.540651	−	0.841247i	$-0.681822\pi$
$283$	−18.1903	−1.08130	−0.540651	+	0.841247i	$0.681822\pi$
$284$	11.3529	0.673668
$285$	−2.01797	−0.119534
$286$	2.86919	0.169659
$287$	−9.64050	−0.569061
$288$	−5.71283	−0.336632
$289$	−11.6604	−0.685906
$290$	7.00445	0.411315
$291$	4.23298	0.248142
$292$	−1.34064	−0.0784552
$293$	−27.1140	−1.58402	−0.792010	−	0.610508i	$-0.790965\pi$
$293$	−27.1140	−1.58402	−0.792010	+	0.610508i	$0.790965\pi$
$294$	−3.35610	−0.195732
$295$	−18.7556	−1.09200
$296$	−11.2709	−0.655110
$297$	3.35053	0.194417
$298$	7.38376	0.427730
$299$	7.81736	0.452089
$300$	−4.22747	−0.244073
$301$	15.7310	0.906719
$302$	−0.169518	−0.00975466
$303$	−0.598375	−0.0343757
$304$	0.215746	0.0123739
$305$	−8.70992	−0.498729
$306$	1.97879	0.113120
$307$	9.56563	0.545940	0.272970	−	0.962023i	$-0.411994\pi$
$307$	9.56563	0.545940	0.272970	+	0.962023i	$0.411994\pi$
$308$	7.44935	0.424466
$309$	−1.00000	−0.0568880
$310$	2.17173	0.123346
$311$	−33.3675	−1.89210	−0.946049	−	0.324023i	$-0.894964\pi$
$311$	−33.3675	−1.89210	−0.946049	+	0.324023i	$0.894964\pi$
$312$	−2.79739	−0.158371
$313$	9.86778	0.557760	0.278880	−	0.960326i	$-0.410037\pi$
$313$	9.86778	0.557760	0.278880	+	0.960326i	$0.410037\pi$
$314$	−12.7575	−0.719950
$315$	2.26322	0.127518
$316$	−16.9398	−0.952936
$317$	−4.72199	−0.265214	−0.132607	−	0.991169i	$-0.542335\pi$
$317$	−4.72199	−0.265214	−0.132607	+	0.991169i	$0.542335\pi$
$318$	9.71518	0.544800
$319$	21.2546	1.19003
$320$	5.95243	0.332751
$321$	9.75471	0.544455
$322$	−11.7501	−0.654809
$323$	−3.61643	−0.201223
$324$	−1.26668	−0.0703713
$325$	−3.33743	−0.185127
$326$	3.74401	0.207362
$327$	10.8096	0.597773
$328$	−15.3644	−0.848357
$329$	−7.82172	−0.431225
$330$	−3.69955	−0.203654
$331$	−9.75227	−0.536033	−0.268017	−	0.963414i	$-0.586368\pi$
$331$	−9.75227	−0.536033	−0.268017	+	0.963414i	$0.586368\pi$
$332$	−16.7776	−0.920790
$333$	−4.02909	−0.220793
$334$	5.06409	0.277095
$335$	6.57879	0.359438
$336$	−0.241966	−0.0132003
$337$	13.9497	0.759886	0.379943	−	0.925010i	$-0.375944\pi$
$337$	13.9497	0.759886	0.379943	+	0.925010i	$0.375944\pi$
$338$	−0.856339	−0.0465787
$339$	−0.345677	−0.0187746
$340$	3.77409	0.204679
$341$	6.58997	0.356867
$342$	−1.34020	−0.0724700
$343$	−19.1657	−1.03485
$344$	25.0710	1.35174
$345$	−10.0797	−0.542675
$346$	−19.1000	−1.02682
$347$	−15.4233	−0.827964	−0.413982	−	0.910285i	$-0.635862\pi$
$347$	−15.4233	−0.827964	−0.413982	+	0.910285i	$0.635862\pi$
$348$	−8.03539	−0.430742
$349$	−16.5690	−0.886920	−0.443460	−	0.896294i	$-0.646249\pi$
$349$	−16.5690	−0.886920	−0.443460	+	0.896294i	$0.646249\pi$
$350$	5.01644	0.268140
$351$	−1.00000	−0.0533761
$352$	19.1410	1.02022
$353$	4.68814	0.249525	0.124762	−	0.992187i	$-0.460183\pi$
$353$	4.68814	0.249525	0.124762	+	0.992187i	$0.460183\pi$
$354$	−12.4563	−0.662043
$355$	−11.5565	−0.613356
$356$	−12.3577	−0.654955
$357$	4.05594	0.214663
$358$	6.37218	0.336780
$359$	2.07794	0.109669	0.0548347	−	0.998495i	$-0.482537\pi$
$359$	2.07794	0.109669	0.0548347	+	0.998495i	$0.482537\pi$
$360$	3.60697	0.190104
$361$	−16.5507	−0.871087
$362$	−12.8384	−0.674773
$363$	−0.226051	−0.0118646
$364$	−2.22334	−0.116534
$365$	1.36469	0.0714312
$366$	−5.78456	−0.302364
$367$	16.9108	0.882736	0.441368	−	0.897326i	$-0.354493\pi$
$367$	16.9108	0.882736	0.441368	+	0.897326i	$0.354493\pi$
$368$	1.07765	0.0561764
$369$	−5.49241	−0.285923
$370$	4.44880	0.231282
$371$	19.9132	1.03384
$372$	−2.49137	−0.129171
$373$	12.4609	0.645202	0.322601	−	0.946535i	$-0.395443\pi$
$373$	12.4609	0.645202	0.322601	+	0.946535i	$0.395443\pi$
$374$	−6.63000	−0.342829
$375$	10.7503	0.555145
$376$	−12.4657	−0.642872
$377$	−6.34364	−0.326714
$378$	1.50308	0.0773102
$379$	−7.00082	−0.359608	−0.179804	−	0.983702i	$-0.557546\pi$
$379$	−7.00082	−0.359608	−0.179804	+	0.983702i	$0.557546\pi$
$380$	−2.55613	−0.131127
$381$	11.7862	0.603823
$382$	18.1823	0.930286
$383$	0.741120	0.0378694	0.0189347	−	0.999821i	$-0.493973\pi$
$383$	0.741120	0.0378694	0.0189347	+	0.999821i	$0.493973\pi$
$384$	−7.47244	−0.381326
$385$	−7.58298	−0.386465
$386$	−0.307077	−0.0156298
$387$	8.96229	0.455579
$388$	5.36185	0.272207
$389$	−7.65766	−0.388259	−0.194129	−	0.980976i	$-0.562188\pi$
$389$	−7.65766	−0.388259	−0.194129	+	0.980976i	$0.562188\pi$
$390$	1.10417	0.0559118
$391$	−18.0640	−0.913536
$392$	−10.9633	−0.553731
$393$	1.13413	0.0572092
$394$	−6.24263	−0.314499
$395$	17.2436	0.867622
$396$	4.24406	0.213272
$397$	22.5199	1.13024	0.565120	−	0.825008i	$-0.308830\pi$
$397$	22.5199	1.13024	0.565120	+	0.825008i	$0.308830\pi$
$398$	−12.9914	−0.651199
$399$	−2.74702	−0.137523
$400$	−0.460077	−0.0230038
$401$	−5.84611	−0.291941	−0.145970	−	0.989289i	$-0.546630\pi$
$401$	−5.84611	−0.291941	−0.145970	+	0.989289i	$0.546630\pi$
$402$	4.36920	0.217916
$403$	−1.96684	−0.0979754
$404$	−0.757952	−0.0377095
$405$	1.28941	0.0640711
$406$	9.53501	0.473215
$407$	13.4996	0.669150
$408$	6.46408	0.320020
$409$	31.4783	1.55650	0.778252	−	0.627952i	$-0.216107\pi$
$409$	31.4783	1.55650	0.778252	+	0.627952i	$0.216107\pi$
$410$	6.06454	0.299507
$411$	−10.9932	−0.542255
$412$	−1.26668	−0.0624050
$413$	−25.5317	−1.25633
$414$	−6.69431	−0.329007
$415$	17.0786	0.838354
$416$	−5.71283	−0.280094
$417$	6.35873	0.311388
$418$	4.49040	0.219632
$419$	−32.3469	−1.58025	−0.790124	−	0.612947i	$-0.789984\pi$
$419$	−32.3469	−1.58025	−0.790124	+	0.612947i	$0.789984\pi$
$420$	2.86678	0.139885
$421$	14.6518	0.714086	0.357043	−	0.934088i	$-0.383785\pi$
$421$	14.6518	0.714086	0.357043	+	0.934088i	$0.383785\pi$
$422$	12.9741	0.631569
$423$	−4.45621	−0.216668
$424$	31.7364	1.54126
$425$	7.71200	0.374087
$426$	−7.67508	−0.371859
$427$	−11.8566	−0.573783
$428$	12.3561	0.597256
$429$	3.35053	0.161765
$430$	−9.89588	−0.477222
$431$	−19.2526	−0.927363	−0.463682	−	0.886002i	$-0.653472\pi$
$431$	−19.2526	−0.927363	−0.463682	+	0.886002i	$0.653472\pi$
$432$	−0.137853	−0.00663248
$433$	20.3904	0.979899	0.489950	−	0.871751i	$-0.337015\pi$
$433$	20.3904	0.979899	0.489950	+	0.871751i	$0.337015\pi$
$434$	2.95633	0.141908
$435$	8.17953	0.392178
$436$	13.6924	0.655745
$437$	12.2345	0.585254
$438$	0.906339	0.0433065
$439$	31.5935	1.50787	0.753937	−	0.656947i	$-0.228152\pi$
$439$	31.5935	1.50787	0.753937	+	0.656947i	$0.228152\pi$
$440$	−12.0853	−0.576142
$441$	−3.91913	−0.186625
$442$	1.97879	0.0941215
$443$	−15.7853	−0.749984	−0.374992	−	0.927028i	$-0.622355\pi$
$443$	−15.7853	−0.749984	−0.374992	+	0.927028i	$0.622355\pi$
$444$	−5.10359	−0.242205
$445$	12.5793	0.596318
$446$	17.9043	0.847792
$447$	8.62247	0.407829
$448$	8.10291	0.382827
$449$	−14.2683	−0.673361	−0.336680	−	0.941619i	$-0.609304\pi$
$449$	−14.2683	−0.673361	−0.336680	+	0.941619i	$0.609304\pi$
$450$	2.85797	0.134726
$451$	18.4025	0.866539
$452$	−0.437864	−0.0205954
$453$	−0.197957	−0.00930081
$454$	2.24300	0.105269
$455$	2.26322	0.106101
$456$	−4.37802	−0.205020
$457$	−11.2287	−0.525256	−0.262628	−	0.964897i	$-0.584589\pi$
$457$	−11.2287	−0.525256	−0.262628	+	0.964897i	$0.584589\pi$
$458$	5.95709	0.278357
$459$	2.31076	0.107857
$460$	−12.7678	−0.595304
$461$	26.2477	1.22248	0.611240	−	0.791446i	$-0.290671\pi$
$461$	26.2477	1.22248	0.611240	+	0.791446i	$0.290671\pi$
$462$	−5.03612	−0.234302
$463$	3.67713	0.170891	0.0854453	−	0.996343i	$-0.472769\pi$
$463$	3.67713	0.170891	0.0854453	+	0.996343i	$0.472769\pi$
$464$	−0.874493	−0.0405973
$465$	2.53606	0.117607
$466$	11.7674	0.545116
$467$	0.143037	0.00661895	0.00330948	−	0.999995i	$-0.498947\pi$
$467$	0.143037	0.00661895	0.00330948	+	0.999995i	$0.498947\pi$
$468$	−1.26668	−0.0585525
$469$	8.95557	0.413530
$470$	4.92040	0.226961
$471$	−14.8978	−0.686453
$472$	−40.6907	−1.87294
$473$	−30.0284	−1.38071
$474$	11.4521	0.526012
$475$	−5.22322	−0.239658
$476$	5.13759	0.235481
$477$	11.3450	0.519453
$478$	17.5308	0.801842
$479$	−37.2907	−1.70385	−0.851927	−	0.523661i	$-0.824566\pi$
$479$	−37.2907	−1.70385	−0.851927	+	0.523661i	$0.824566\pi$
$480$	7.36615	0.336217
$481$	−4.02909	−0.183711
$482$	−8.35115	−0.380384
$483$	−13.7214	−0.624343
$484$	−0.286334	−0.0130152
$485$	−5.45803	−0.247837
$486$	0.856339	0.0388443
$487$	23.8548	1.08096	0.540482	−	0.841356i	$-0.318242\pi$
$487$	23.8548	1.08096	0.540482	+	0.841356i	$0.318242\pi$
$488$	−18.8963	−0.855397
$489$	4.37211	0.197714
$490$	4.32738	0.195491
$491$	−13.4939	−0.608972	−0.304486	−	0.952517i	$-0.598485\pi$
$491$	−13.4939	−0.608972	−0.304486	+	0.952517i	$0.598485\pi$
$492$	−6.95714	−0.313652
$493$	14.6586	0.660191
$494$	−1.34020	−0.0602987
$495$	−4.32019	−0.194178
$496$	−0.271136	−0.0121744
$497$	−15.7316	−0.705660
$498$	11.3425	0.508268
$499$	−5.73036	−0.256526	−0.128263	−	0.991740i	$-0.540940\pi$
$499$	−5.73036	−0.256526	−0.128263	+	0.991740i	$0.540940\pi$
$500$	13.6173	0.608983
$501$	5.91365	0.264202
$502$	15.9358	0.711249
$503$	−37.7329	−1.68243	−0.841214	−	0.540702i	$-0.818159\pi$
$503$	−37.7329	−1.68243	−0.841214	+	0.540702i	$0.818159\pi$
$504$	4.91009	0.218713
$505$	0.771548	0.0343334
$506$	22.4295	0.997112
$507$	−1.00000	−0.0444116
$508$	14.9293	0.662382
$509$	11.2932	0.500564	0.250282	−	0.968173i	$-0.419477\pi$
$509$	11.2932	0.500564	0.250282	+	0.968173i	$0.419477\pi$
$510$	−2.55147	−0.112981
$511$	1.85773	0.0821810
$512$	−1.55879	−0.0688896
$513$	−1.56504	−0.0690982
$514$	6.87744	0.303351
$515$	1.28941	0.0568180
$516$	11.3524	0.499761
$517$	14.9307	0.656649
$518$	6.05606	0.266088
$519$	−22.3043	−0.979050
$520$	3.60697	0.158176
$521$	−23.6653	−1.03680	−0.518398	−	0.855140i	$-0.673471\pi$
$521$	−23.6653	−1.03680	−0.518398	+	0.855140i	$0.673471\pi$
$522$	5.43231	0.237766
$523$	−24.9527	−1.09111	−0.545553	−	0.838076i	$-0.683680\pi$
$523$	−24.9527	−1.09111	−0.545553	+	0.838076i	$0.683680\pi$
$524$	1.43658	0.0627573
$525$	5.85800	0.255664
$526$	20.6714	0.901317
$527$	4.54490	0.197979
$528$	0.461882	0.0201008
$529$	38.1111	1.65700
$530$	−12.5268	−0.544130
$531$	−14.5459	−0.631240
$532$	−3.47961	−0.150860
$533$	−5.49241	−0.237903
$534$	8.35437	0.361529
$535$	−12.5778	−0.543785
$536$	14.2728	0.616491
$537$	7.44119	0.321111
$538$	9.82631	0.423643
$539$	13.1312	0.565599
$540$	1.63327	0.0702847
$541$	6.11903	0.263078	0.131539	−	0.991311i	$-0.458008\pi$
$541$	6.11903	0.263078	0.131539	+	0.991311i	$0.458008\pi$
$542$	6.55032	0.281360
$543$	−14.9922	−0.643378
$544$	13.2010	0.565986
$545$	−13.9380	−0.597038
$546$	1.50308	0.0643260
$547$	1.13260	0.0484266	0.0242133	−	0.999707i	$-0.492292\pi$
$547$	1.13260	0.0484266	0.0242133	+	0.999707i	$0.492292\pi$
$548$	−13.9249	−0.594843
$549$	−6.75499	−0.288296
$550$	−9.57573	−0.408310
$551$	−9.92805	−0.422949
$552$	−21.8682	−0.930772
$553$	23.4734	0.998191
$554$	−9.99785	−0.424768
$555$	5.19514	0.220521
$556$	8.05450	0.341587
$557$	−8.98778	−0.380824	−0.190412	−	0.981704i	$-0.560982\pi$
$557$	−8.98778	−0.380824	−0.190412	+	0.981704i	$0.560982\pi$
$558$	1.68428	0.0713015
$559$	8.96229	0.379065
$560$	0.311993	0.0131841
$561$	−7.74226	−0.326878
$562$	18.4453	0.778068
$563$	38.4063	1.61863	0.809317	−	0.587373i	$-0.199838\pi$
$563$	38.4063	1.61863	0.809317	+	0.587373i	$0.199838\pi$
$564$	−5.64460	−0.237681
$565$	0.445718	0.0187515
$566$	15.5771	0.654753
$567$	1.75524	0.0737132
$568$	−25.0720	−1.05200
$569$	44.1918	1.85262	0.926309	−	0.376765i	$-0.122964\pi$
$569$	44.1918	1.85262	0.926309	+	0.376765i	$0.122964\pi$
$570$	1.72807	0.0723808
$571$	3.19644	0.133767	0.0668835	−	0.997761i	$-0.478694\pi$
$571$	3.19644	0.133767	0.0668835	+	0.997761i	$0.478694\pi$
$572$	4.24406	0.177453
$573$	21.2326	0.887003
$574$	8.25554	0.344580
$575$	−26.0899	−1.08802
$576$	4.61641	0.192350
$577$	−11.4522	−0.476760	−0.238380	−	0.971172i	$-0.576616\pi$
$577$	−11.4522	−0.476760	−0.238380	+	0.971172i	$0.576616\pi$
$578$	9.98526	0.415332
$579$	−0.358592	−0.0149026
$580$	10.3609	0.430212
$581$	23.2487	0.964519
$582$	−3.62487	−0.150256
$583$	−38.0118	−1.57429
$584$	2.96072	0.122516
$585$	1.28941	0.0533104
$586$	23.2188	0.959160
$587$	−31.1328	−1.28499	−0.642495	−	0.766290i	$-0.722100\pi$
$587$	−31.1328	−1.28499	−0.642495	+	0.766290i	$0.722100\pi$
$588$	−4.96429	−0.204724
$589$	−3.07819	−0.126835
$590$	16.0612	0.661228
$591$	−7.28990	−0.299867
$592$	−0.555425	−0.0228278
$593$	34.9428	1.43493	0.717464	−	0.696595i	$-0.245303\pi$
$593$	34.9428	1.43493	0.717464	+	0.696595i	$0.245303\pi$
$594$	−2.86919	−0.117724
$595$	−5.22975	−0.214399
$596$	10.9219	0.447380
$597$	−15.1708	−0.620901
$598$	−6.69431	−0.273751
$599$	−23.3679	−0.954787	−0.477394	−	0.878690i	$-0.658418\pi$
$599$	−23.3679	−0.954787	−0.477394	+	0.878690i	$0.658418\pi$
$600$	9.33610	0.381145
$601$	−23.2541	−0.948554	−0.474277	−	0.880376i	$-0.657291\pi$
$601$	−23.2541	−0.948554	−0.474277	+	0.880376i	$0.657291\pi$
$602$	−13.4711	−0.549039
$603$	5.10218	0.207777
$604$	−0.250748	−0.0102028
$605$	0.291471	0.0118500
$606$	0.512412	0.0208153
$607$	−3.17515	−0.128875	−0.0644377	−	0.997922i	$-0.520525\pi$
$607$	−3.17515	−0.128875	−0.0644377	+	0.997922i	$0.520525\pi$
$608$	−8.94080	−0.362597
$609$	11.1346	0.451198
$610$	7.45865	0.301992
$611$	−4.45621	−0.180279
$612$	2.92700	0.118317
$613$	39.5075	1.59569	0.797847	−	0.602860i	$-0.205972\pi$
$613$	39.5075	1.59569	0.797847	+	0.602860i	$0.205972\pi$
$614$	−8.19143	−0.330579
$615$	7.08194	0.285572
$616$	−16.4514	−0.662846
$617$	−9.34020	−0.376022	−0.188011	−	0.982167i	$-0.560204\pi$
$617$	−9.34020	−0.376022	−0.188011	+	0.982167i	$0.560204\pi$
$618$	0.856339	0.0344470
$619$	5.51341	0.221603	0.110801	−	0.993843i	$-0.464658\pi$
$619$	5.51341	0.221603	0.110801	+	0.993843i	$0.464658\pi$
$620$	3.21238	0.129012
$621$	−7.81736	−0.313700
$622$	28.5739	1.14571
$623$	17.1240	0.686058
$624$	−0.137853	−0.00551856
$625$	2.82562	0.113025
$626$	−8.45017	−0.337737
$627$	5.24371	0.209414
$628$	−18.8708	−0.753025
$629$	9.31025	0.371224
$630$	−1.93808	−0.0772151
$631$	29.0337	1.15581	0.577906	−	0.816104i	$-0.303870\pi$
$631$	29.0337	1.15581	0.577906	+	0.816104i	$0.303870\pi$
$632$	37.4104	1.48811
$633$	15.1507	0.602185
$634$	4.04363	0.160593
$635$	−15.1971	−0.603080
$636$	14.3705	0.569829
$637$	−3.91913	−0.155281
$638$	−18.2011	−0.720589
$639$	−8.96266	−0.354557
$640$	9.63501	0.380857
$641$	29.4694	1.16397	0.581985	−	0.813200i	$-0.302276\pi$
$641$	29.4694	1.16397	0.581985	+	0.813200i	$0.302276\pi$
$642$	−8.35334	−0.329680
$643$	−13.8802	−0.547382	−0.273691	−	0.961818i	$-0.588245\pi$
$643$	−13.8802	−0.547382	−0.273691	+	0.961818i	$0.588245\pi$
$644$	−17.3806	−0.684892
$645$	−11.5560	−0.455018
$646$	3.09689	0.121845
$647$	36.5234	1.43588	0.717941	−	0.696104i	$-0.245085\pi$
$647$	36.5234	1.43588	0.717941	+	0.696104i	$0.245085\pi$
$648$	2.79739	0.109892
$649$	48.7366	1.91308
$650$	2.85797	0.112099
$651$	3.45229	0.135306
$652$	5.53808	0.216888
$653$	−24.1451	−0.944869	−0.472435	−	0.881366i	$-0.656625\pi$
$653$	−24.1451	−0.944869	−0.472435	+	0.881366i	$0.656625\pi$
$654$	−9.25670	−0.361966
$655$	−1.46235	−0.0571388
$656$	−0.757148	−0.0295616
$657$	1.05839	0.0412916
$658$	6.69804	0.261117
$659$	−20.2929	−0.790501	−0.395250	−	0.918573i	$-0.629342\pi$
$659$	−20.2929	−0.790501	−0.395250	+	0.918573i	$0.629342\pi$
$660$	−5.47232	−0.213010
$661$	8.17203	0.317855	0.158928	−	0.987290i	$-0.449196\pi$
$661$	8.17203	0.317855	0.158928	+	0.987290i	$0.449196\pi$
$662$	8.35125	0.324581
$663$	2.31076	0.0897424
$664$	37.0522	1.43791
$665$	3.54203	0.137354
$666$	3.45027	0.133695
$667$	−49.5905	−1.92015
$668$	7.49072	0.289825
$669$	20.9079	0.808347
$670$	−5.63367	−0.217648
$671$	22.6328	0.873730
$672$	10.0274	0.386815
$673$	−23.9609	−0.923624	−0.461812	−	0.886978i	$-0.652800\pi$
$673$	−23.9609	−0.923624	−0.461812	+	0.886978i	$0.652800\pi$
$674$	−11.9456	−0.460129
$675$	3.33743	0.128458
$676$	−1.26668	−0.0487186
$677$	50.5675	1.94347	0.971734	−	0.236079i	$-0.0758623\pi$
$677$	50.5675	1.94347	0.971734	+	0.236079i	$0.0758623\pi$
$678$	0.296017	0.0113685
$679$	−7.42991	−0.285134
$680$	−8.33483	−0.319626
$681$	2.61929	0.100372
$682$	−5.64325	−0.216091
$683$	25.1439	0.962103	0.481052	−	0.876692i	$-0.340255\pi$
$683$	25.1439	0.962103	0.481052	+	0.876692i	$0.340255\pi$
$684$	−1.98241	−0.0757993
$685$	14.1747	0.541588
$686$	16.4123	0.626626
$687$	6.95646	0.265406
$688$	1.23548	0.0471024
$689$	11.3450	0.432211
$690$	8.63168	0.328602
$691$	−4.07984	−0.155204	−0.0776022	−	0.996984i	$-0.524726\pi$
$691$	−4.07984	−0.155204	−0.0776022	+	0.996984i	$0.524726\pi$
$692$	−28.2525	−1.07400
$693$	−5.88099	−0.223400
$694$	13.2075	0.501351
$695$	−8.19899	−0.311005
$696$	17.7456	0.672646
$697$	12.6916	0.480729
$698$	14.1887	0.537051
$699$	13.7416	0.519753
$700$	7.42023	0.280458
$701$	27.6876	1.04575	0.522873	−	0.852411i	$-0.324860\pi$
$701$	27.6876	1.04575	0.522873	+	0.852411i	$0.324860\pi$
$702$	0.856339	0.0323204
$703$	−6.30569	−0.237824
$704$	−15.4674	−0.582950
$705$	5.74586	0.216402
$706$	−4.01464	−0.151093
$707$	1.05029	0.0395003
$708$	−18.4251	−0.692458
$709$	1.66018	0.0623492	0.0311746	−	0.999514i	$-0.490075\pi$
$709$	1.66018	0.0623492	0.0311746	+	0.999514i	$0.490075\pi$
$710$	9.89629	0.371401
$711$	13.3733	0.501539
$712$	27.2911	1.02278
$713$	−15.3755	−0.575818
$714$	−3.47326	−0.129983
$715$	−4.32019	−0.161566
$716$	9.42563	0.352252
$717$	20.4718	0.764535
$718$	−1.77942	−0.0664073
$719$	10.5683	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$719$	10.5683	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$720$	0.177749	0.00662432
$721$	1.75524	0.0653686
$722$	14.1730	0.527463
$723$	−9.75215	−0.362686
$724$	−18.9904	−0.705773
$725$	21.1715	0.786289
$726$	0.193576	0.00718428
$727$	−21.7537	−0.806799	−0.403400	−	0.915024i	$-0.632172\pi$
$727$	−21.7537	−0.806799	−0.403400	+	0.915024i	$0.632172\pi$
$728$	4.91009	0.181980
$729$	1.00000	0.0370370
$730$	−1.16864	−0.0432533
$731$	−20.7097	−0.765975
$732$	−8.55643	−0.316255
$733$	−18.2093	−0.672576	−0.336288	−	0.941759i	$-0.609172\pi$
$733$	−18.2093	−0.672576	−0.336288	+	0.941759i	$0.609172\pi$
$734$	−14.4814	−0.534517
$735$	5.05334	0.186395
$736$	−44.6592	−1.64616
$737$	−17.0950	−0.629703
$738$	4.70336	0.173133
$739$	8.04546	0.295957	0.147979	−	0.988991i	$-0.452723\pi$
$739$	8.04546	0.295957	0.147979	+	0.988991i	$0.452723\pi$
$740$	6.58059	0.241907
$741$	−1.56504	−0.0574932
$742$	−17.0525	−0.626017
$743$	30.4334	1.11649	0.558247	−	0.829675i	$-0.311474\pi$
$743$	30.4334	1.11649	0.558247	+	0.829675i	$0.311474\pi$
$744$	5.50202	0.201714
$745$	−11.1179	−0.407327
$746$	−10.6708	−0.390685
$747$	13.2453	0.484620
$748$	−9.80699	−0.358579
$749$	−17.1219	−0.625620
$750$	−9.20593	−0.336153
$751$	17.4806	0.637875	0.318938	−	0.947776i	$-0.396674\pi$
$751$	17.4806	0.637875	0.318938	+	0.947776i	$0.396674\pi$
$752$	−0.614304	−0.0224013
$753$	18.6092	0.678157
$754$	5.43231	0.197833
$755$	0.255246	0.00928937
$756$	2.22334	0.0808619
$757$	14.2801	0.519018	0.259509	−	0.965741i	$-0.416439\pi$
$757$	14.2801	0.519018	0.259509	+	0.965741i	$0.416439\pi$
$758$	5.99507	0.217751
$759$	26.1923	0.950720
$760$	5.64505	0.204768
$761$	−25.3070	−0.917378	−0.458689	−	0.888597i	$-0.651681\pi$
$761$	−25.3070	−0.917378	−0.458689	+	0.888597i	$0.651681\pi$
$762$	−10.0929	−0.365629
$763$	−18.9735	−0.686887
$764$	26.8949	0.973024
$765$	−2.97950	−0.107724
$766$	−0.634650	−0.0229308
$767$	−14.5459	−0.525224
$768$	15.6318	0.564063
$769$	−54.2086	−1.95481	−0.977406	−	0.211369i	$-0.932208\pi$
$769$	−54.2086	−1.95481	−0.977406	+	0.211369i	$0.932208\pi$
$770$	6.49360	0.234013
$771$	8.03121	0.289237
$772$	−0.454223	−0.0163478
$773$	11.9395	0.429436	0.214718	−	0.976676i	$-0.431117\pi$
$773$	11.9395	0.429436	0.214718	+	0.976676i	$0.431117\pi$
$774$	−7.67476	−0.275864
$775$	6.56421	0.235793
$776$	−11.8413	−0.425078
$777$	7.07203	0.253708
$778$	6.55755	0.235100
$779$	−8.59584	−0.307978
$780$	1.63327	0.0584804
$781$	30.0297	1.07455
$782$	15.4689	0.553167
$783$	6.34364	0.226703
$784$	−0.540265	−0.0192952
$785$	19.2093	0.685608
$786$	−0.971198	−0.0346415
$787$	−13.1508	−0.468776	−0.234388	−	0.972143i	$-0.575309\pi$
$787$	−13.1508	−0.468776	−0.234388	+	0.972143i	$0.575309\pi$
$788$	−9.23400	−0.328948
$789$	24.1393	0.859381
$790$	−14.7664	−0.525365
$791$	0.606747	0.0215734
$792$	−9.37273	−0.333046
$793$	−6.75499	−0.239877
$794$	−19.2847	−0.684387
$795$	−14.6283	−0.518813
$796$	−19.2166	−0.681116
$797$	−1.45989	−0.0517121	−0.0258561	−	0.999666i	$-0.508231\pi$
$797$	−1.45989	−0.0517121	−0.0258561	+	0.999666i	$0.508231\pi$
$798$	2.35238	0.0832735
$799$	10.2972	0.364289
$800$	19.0662	0.674091
$801$	9.75592	0.344708
$802$	5.00626	0.176777
$803$	−3.54616	−0.125141
$804$	6.46285	0.227927
$805$	17.6924	0.623575
$806$	1.68428	0.0593264
$807$	11.4748	0.403932
$808$	1.67389	0.0588871
$809$	−10.2561	−0.360586	−0.180293	−	0.983613i	$-0.557705\pi$
$809$	−10.2561	−0.360586	−0.180293	+	0.983613i	$0.557705\pi$
$810$	−1.10417	−0.0387965
$811$	14.7173	0.516794	0.258397	−	0.966039i	$-0.416806\pi$
$811$	14.7173	0.516794	0.258397	+	0.966039i	$0.416806\pi$
$812$	14.1040	0.494955
$813$	7.64921	0.268270
$814$	−11.5602	−0.405186
$815$	−5.63743	−0.197470
$816$	0.318546	0.0111513
$817$	14.0263	0.490720
$818$	−26.9561	−0.942499
$819$	1.75524	0.0613331
$820$	8.97058	0.313266
$821$	−46.2596	−1.61447	−0.807236	−	0.590229i	$-0.799037\pi$
$821$	−46.2596	−1.61447	−0.807236	+	0.590229i	$0.799037\pi$
$822$	9.41391	0.328348
$823$	−8.27584	−0.288478	−0.144239	−	0.989543i	$-0.546073\pi$
$823$	−8.27584	−0.288478	−0.144239	+	0.989543i	$0.546073\pi$
$824$	2.79739	0.0974517
$825$	−11.1822	−0.389313
$826$	21.8638	0.760737
$827$	50.3825	1.75197	0.875985	−	0.482338i	$-0.160212\pi$
$827$	50.3825	1.75197	0.875985	+	0.482338i	$0.160212\pi$
$828$	−9.90212	−0.344122
$829$	−25.6495	−0.890845	−0.445422	−	0.895321i	$-0.646946\pi$
$829$	−25.6495	−0.890845	−0.445422	+	0.895321i	$0.646946\pi$
$830$	−14.6250	−0.507643
$831$	−11.6751	−0.405005
$832$	4.61641	0.160045
$833$	9.05615	0.313777
$834$	−5.44523	−0.188553
$835$	−7.62509	−0.263877
$836$	6.64212	0.229723
$837$	1.96684	0.0679840
$838$	27.6999	0.956877
$839$	−0.142760	−0.00492864	−0.00246432	−	0.999997i	$-0.500784\pi$
$839$	−0.142760	−0.00492864	−0.00246432	+	0.999997i	$0.500784\pi$
$840$	−6.33110	−0.218444
$841$	11.2418	0.387648
$842$	−12.5469	−0.432396
$843$	21.5397	0.741867
$844$	19.1911	0.660584
$845$	1.28941	0.0443569
$846$	3.81602	0.131198
$847$	0.396773	0.0136333
$848$	1.56395	0.0537063
$849$	18.1903	0.624290
$850$	−6.60408	−0.226518
$851$	−31.4969	−1.07970
$852$	−11.3529	−0.388942
$853$	−9.38000	−0.321165	−0.160583	−	0.987022i	$-0.551337\pi$
$853$	−9.38000	−0.321165	−0.160583	+	0.987022i	$0.551337\pi$
$854$	10.1533	0.347439
$855$	2.01797	0.0690132
$856$	−27.2877	−0.932675
$857$	−28.1179	−0.960489	−0.480244	−	0.877135i	$-0.659452\pi$
$857$	−28.1179	−0.960489	−0.480244	+	0.877135i	$0.659452\pi$
$858$	−2.86919	−0.0979525
$859$	−28.1497	−0.960455	−0.480227	−	0.877144i	$-0.659446\pi$
$859$	−28.1497	−0.960455	−0.480227	+	0.877144i	$0.659446\pi$
$860$	−14.6378	−0.499146
$861$	9.64050	0.328547
$862$	16.4867	0.561540
$863$	26.8278	0.913228	0.456614	−	0.889665i	$-0.349062\pi$
$863$	26.8278	0.913228	0.456614	+	0.889665i	$0.349062\pi$
$864$	5.71283	0.194354
$865$	28.7593	0.977845
$866$	−17.4611	−0.593352
$867$	11.6604	0.396008
$868$	4.37295	0.148428
$869$	−44.8077	−1.52000
$870$	−7.00445	−0.237473
$871$	5.10218	0.172881
$872$	−30.2387	−1.02401
$873$	−4.23298	−0.143265
$874$	−10.4769	−0.354385
$875$	−18.8694	−0.637903
$876$	1.34064	0.0452961
$877$	5.37965	0.181658	0.0908289	−	0.995867i	$-0.471048\pi$
$877$	5.37965	0.181658	0.0908289	+	0.995867i	$0.471048\pi$
$878$	−27.0547	−0.913052
$879$	27.1140	0.914534
$880$	−0.595554	−0.0200761
$881$	25.8879	0.872186	0.436093	−	0.899902i	$-0.356362\pi$
$881$	25.8879	0.872186	0.436093	+	0.899902i	$0.356362\pi$
$882$	3.35610	0.113006
$883$	9.11790	0.306842	0.153421	−	0.988161i	$-0.450971\pi$
$883$	9.11790	0.306842	0.153421	+	0.988161i	$0.450971\pi$
$884$	2.92700	0.0984456
$885$	18.7556	0.630464
$886$	13.5176	0.454133
$887$	−15.3421	−0.515136	−0.257568	−	0.966260i	$-0.582921\pi$
$887$	−15.3421	−0.515136	−0.257568	+	0.966260i	$0.582921\pi$
$888$	11.2709	0.378228
$889$	−20.6875	−0.693838
$890$	−10.7722	−0.361084
$891$	−3.35053	−0.112247
$892$	26.4837	0.886740
$893$	−6.97414	−0.233381
$894$	−7.38376	−0.246950
$895$	−9.59471	−0.320716
$896$	13.1159	0.438173
$897$	−7.81736	−0.261014
$898$	12.2185	0.407736
$899$	12.4769	0.416130
$900$	4.22747	0.140916
$901$	−26.2156	−0.873367
$902$	−15.7588	−0.524709
$903$	−15.7310	−0.523494
$904$	0.966993	0.0321617
$905$	19.3311	0.642587
$906$	0.169518	0.00563186
$907$	−24.1193	−0.800868	−0.400434	−	0.916326i	$-0.631141\pi$
$907$	−24.1193	−0.800868	−0.400434	+	0.916326i	$0.631141\pi$
$908$	3.31782	0.110106
$909$	0.598375	0.0198468
$910$	−1.93808	−0.0642468
$911$	−37.1785	−1.23178	−0.615889	−	0.787833i	$-0.711203\pi$
$911$	−37.1785	−1.23178	−0.615889	+	0.787833i	$0.711203\pi$
$912$	−0.215746	−0.00714407
$913$	−44.3788	−1.46872
$914$	9.61556	0.318055
$915$	8.70992	0.287941
$916$	8.81164	0.291145
$917$	−1.99067	−0.0657377
$918$	−1.97879	−0.0653098
$919$	49.1962	1.62283	0.811416	−	0.584469i	$-0.198697\pi$
$919$	49.1962	1.62283	0.811416	+	0.584469i	$0.198697\pi$
$920$	28.1970	0.929627
$921$	−9.56563	−0.315198
$922$	−22.4770	−0.740240
$923$	−8.96266	−0.295010
$924$	−7.44935	−0.245066
$925$	13.4468	0.442129
$926$	−3.14887	−0.103478
$927$	1.00000	0.0328443
$928$	36.2401	1.18964
$929$	−54.6480	−1.79294	−0.896472	−	0.443101i	$-0.853878\pi$
$929$	−54.6480	−1.79294	−0.896472	+	0.443101i	$0.853878\pi$
$930$	−2.17173	−0.0712137
$931$	−6.13359	−0.201020
$932$	17.4062	0.570159
$933$	33.3675	1.09240
$934$	−0.122488	−0.00400793
$935$	9.98291	0.326476
$936$	2.79739	0.0914355
$937$	−44.5514	−1.45543	−0.727716	−	0.685878i	$-0.759418\pi$
$937$	−44.5514	−1.45543	−0.727716	+	0.685878i	$0.759418\pi$
$938$	−7.66900	−0.250402
$939$	−9.86778	−0.322023
$940$	7.27818	0.237388
$941$	−4.36800	−0.142393	−0.0711963	−	0.997462i	$-0.522682\pi$
$941$	−4.36800	−0.142393	−0.0711963	+	0.997462i	$0.522682\pi$
$942$	12.7575	0.415663
$943$	−42.9361	−1.39819
$944$	−2.00521	−0.0652640
$945$	−2.26322	−0.0736225
$946$	25.7145	0.836051
$947$	50.8633	1.65284	0.826418	−	0.563057i	$-0.190375\pi$
$947$	50.8633	1.65284	0.826418	+	0.563057i	$0.190375\pi$
$948$	16.9398	0.550178
$949$	1.05839	0.0343567
$950$	4.47284	0.145118
$951$	4.72199	0.153121
$952$	−11.3460	−0.367727
$953$	−11.1109	−0.359917	−0.179959	−	0.983674i	$-0.557596\pi$
$953$	−11.1109	−0.359917	−0.179959	+	0.983674i	$0.557596\pi$
$954$	−9.71518	−0.314541
$955$	−27.3774	−0.885911
$956$	25.9313	0.838680
$957$	−21.2546	−0.687062
$958$	31.9335	1.03172
$959$	19.2957	0.623092
$960$	−5.95243	−0.192114
$961$	−27.1315	−0.875211
$962$	3.45027	0.111241
$963$	−9.75471	−0.314341
$964$	−12.3529	−0.397860
$965$	0.462371	0.0148842
$966$	11.7501	0.378054
$967$	23.0461	0.741113	0.370557	−	0.928810i	$-0.379167\pi$
$967$	23.0461	0.741113	0.370557	+	0.928810i	$0.379167\pi$
$968$	0.632351	0.0203245
$969$	3.61643	0.116176
$970$	4.67393	0.150071
$971$	0.0373002	0.00119702	0.000598510	−	1.00000i	$-0.499809\pi$
$971$	0.0373002	0.00119702	0.000598510		1.00000i	$0.499809\pi$
$972$	1.26668	0.0406289
$973$	−11.1611	−0.357809
$974$	−20.4278	−0.654548
$975$	3.33743	0.106883
$976$	−0.931199	−0.0298070
$977$	13.7426	0.439665	0.219833	−	0.975538i	$-0.429449\pi$
$977$	13.7426	0.439665	0.219833	+	0.975538i	$0.429449\pi$
$978$	−3.74401	−0.119720
$979$	−32.6875	−1.04470
$980$	6.40099	0.204472
$981$	−10.8096	−0.345125
$982$	11.5554	0.368747
$983$	−43.0668	−1.37362	−0.686810	−	0.726837i	$-0.740989\pi$
$983$	−43.0668	−1.37362	−0.686810	+	0.726837i	$0.740989\pi$
$984$	15.3644	0.489799
$985$	9.39964	0.299498
$986$	−12.5527	−0.399761
$987$	7.82172	0.248968
$988$	−1.98241	−0.0630689
$989$	70.0614	2.22782
$990$	3.69955	0.117579
$991$	−53.4309	−1.69729	−0.848645	−	0.528963i	$-0.822581\pi$
$991$	−53.4309	−1.69729	−0.848645	+	0.528963i	$0.822581\pi$
$992$	11.2362	0.356751
$993$	9.75227	0.309479
$994$	13.4716	0.427294
$995$	19.5614	0.620137
$996$	16.7776	0.531619
$997$	10.8114	0.342401	0.171201	−	0.985236i	$-0.445235\pi$
$997$	10.8114	0.342401	0.171201	+	0.985236i	$0.445235\pi$
$998$	4.90713	0.155333
$999$	4.02909	0.127475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.11	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.856339 q^{2} -1.00000 q^{3} -1.26668 q^{4} +1.28941 q^{5} +0.856339 q^{6} +1.75524 q^{7} +2.79739 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.856339 q^{2} -1.00000 q^{3} -1.26668 q^{4} +1.28941 q^{5} +0.856339 q^{6} +1.75524 q^{7} +2.79739 q^{8} +1.00000 q^{9} -1.10417 q^{10} -3.35053 q^{11} +1.26668 q^{12} +1.00000 q^{13} -1.50308 q^{14} -1.28941 q^{15} +0.137853 q^{16} -2.31076 q^{17} -0.856339 q^{18} +1.56504 q^{19} -1.63327 q^{20} -1.75524 q^{21} +2.86919 q^{22} +7.81736 q^{23} -2.79739 q^{24} -3.33743 q^{25} -0.856339 q^{26} -1.00000 q^{27} -2.22334 q^{28} -6.34364 q^{29} +1.10417 q^{30} -1.96684 q^{31} -5.71283 q^{32} +3.35053 q^{33} +1.97879 q^{34} +2.26322 q^{35} -1.26668 q^{36} -4.02909 q^{37} -1.34020 q^{38} -1.00000 q^{39} +3.60697 q^{40} -5.49241 q^{41} +1.50308 q^{42} +8.96229 q^{43} +4.24406 q^{44} +1.28941 q^{45} -6.69431 q^{46} -4.45621 q^{47} -0.137853 q^{48} -3.91913 q^{49} +2.85797 q^{50} +2.31076 q^{51} -1.26668 q^{52} +11.3450 q^{53} +0.856339 q^{54} -4.32019 q^{55} +4.91009 q^{56} -1.56504 q^{57} +5.43231 q^{58} -14.5459 q^{59} +1.63327 q^{60} -6.75499 q^{61} +1.68428 q^{62} +1.75524 q^{63} +4.61641 q^{64} +1.28941 q^{65} -2.86919 q^{66} +5.10218 q^{67} +2.92700 q^{68} -7.81736 q^{69} -1.93808 q^{70} -8.96266 q^{71} +2.79739 q^{72} +1.05839 q^{73} +3.45027 q^{74} +3.33743 q^{75} -1.98241 q^{76} -5.88099 q^{77} +0.856339 q^{78} +13.3733 q^{79} +0.177749 q^{80} +1.00000 q^{81} +4.70336 q^{82} +13.2453 q^{83} +2.22334 q^{84} -2.97950 q^{85} -7.67476 q^{86} +6.34364 q^{87} -9.37273 q^{88} +9.75592 q^{89} -1.10417 q^{90} +1.75524 q^{91} -9.90212 q^{92} +1.96684 q^{93} +3.81602 q^{94} +2.01797 q^{95} +5.71283 q^{96} -4.23298 q^{97} +3.35610 q^{98} -3.35053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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