LMFDB - Embedded newform 4007.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53714 q^{2} -2.64168 q^{3} +4.43706 q^{4} +4.10471 q^{5} +6.70230 q^{6} -0.283767 q^{7} -6.18314 q^{8} +3.97846 q^{9} +O(q^{10})$	\(q-2.53714 q^{2} -2.64168 q^{3} +4.43706 q^{4} +4.10471 q^{5} +6.70230 q^{6} -0.283767 q^{7} -6.18314 q^{8} +3.97846 q^{9} -10.4142 q^{10} +1.99360 q^{11} -11.7213 q^{12} -2.69197 q^{13} +0.719956 q^{14} -10.8433 q^{15} +6.81336 q^{16} -1.86606 q^{17} -10.0939 q^{18} +1.34461 q^{19} +18.2129 q^{20} +0.749621 q^{21} -5.05804 q^{22} -1.84743 q^{23} +16.3339 q^{24} +11.8487 q^{25} +6.82989 q^{26} -2.58478 q^{27} -1.25909 q^{28} -3.63451 q^{29} +27.5110 q^{30} +8.20259 q^{31} -4.92014 q^{32} -5.26645 q^{33} +4.73445 q^{34} -1.16478 q^{35} +17.6527 q^{36} -6.52261 q^{37} -3.41146 q^{38} +7.11132 q^{39} -25.3800 q^{40} -0.646703 q^{41} -1.90189 q^{42} -2.23958 q^{43} +8.84573 q^{44} +16.3305 q^{45} +4.68719 q^{46} -0.855722 q^{47} -17.9987 q^{48} -6.91948 q^{49} -30.0617 q^{50} +4.92954 q^{51} -11.9444 q^{52} -7.59026 q^{53} +6.55795 q^{54} +8.18317 q^{55} +1.75457 q^{56} -3.55203 q^{57} +9.22123 q^{58} +4.50550 q^{59} -48.1125 q^{60} -7.72459 q^{61} -20.8111 q^{62} -1.12896 q^{63} -1.14367 q^{64} -11.0498 q^{65} +13.3617 q^{66} -0.0617335 q^{67} -8.27982 q^{68} +4.88033 q^{69} +2.95521 q^{70} -4.46755 q^{71} -24.5994 q^{72} +1.23929 q^{73} +16.5487 q^{74} -31.3004 q^{75} +5.96612 q^{76} -0.565719 q^{77} -18.0424 q^{78} -3.42912 q^{79} +27.9669 q^{80} -5.10722 q^{81} +1.64077 q^{82} +0.607703 q^{83} +3.32611 q^{84} -7.65965 q^{85} +5.68212 q^{86} +9.60119 q^{87} -12.3267 q^{88} -6.94814 q^{89} -41.4326 q^{90} +0.763893 q^{91} -8.19717 q^{92} -21.6686 q^{93} +2.17108 q^{94} +5.51925 q^{95} +12.9974 q^{96} -3.35310 q^{97} +17.5556 q^{98} +7.93147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * 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 $

$2$	−2.53714	−1.79403	−0.897013	−	0.442004i	$-0.854268\pi$
$2$	−2.53714	−1.79403	−0.897013	+	0.442004i	$0.854268\pi$
$3$	−2.64168	−1.52517	−0.762587	−	0.646886i	$-0.776071\pi$
$3$	−2.64168	−1.52517	−0.762587	+	0.646886i	$0.776071\pi$
$4$	4.43706	2.21853
$5$	4.10471	1.83568	0.917842	−	0.396946i	$-0.129930\pi$
$5$	4.10471	1.83568	0.917842	+	0.396946i	$0.129930\pi$
$6$	6.70230	2.73620
$7$	−0.283767	−0.107254	−0.0536269	−	0.998561i	$-0.517078\pi$
$7$	−0.283767	−0.107254	−0.0536269	+	0.998561i	$0.517078\pi$
$8$	−6.18314	−2.18607
$9$	3.97846	1.32615
$10$	−10.4142	−3.29326
$11$	1.99360	0.601094	0.300547	−	0.953767i	$-0.402831\pi$
$11$	1.99360	0.601094	0.300547	+	0.953767i	$0.402831\pi$
$12$	−11.7213	−3.38364
$13$	−2.69197	−0.746618	−0.373309	−	0.927707i	$-0.621777\pi$
$13$	−2.69197	−0.746618	−0.373309	+	0.927707i	$0.621777\pi$
$14$	0.719956	0.192416
$15$	−10.8433	−2.79974
$16$	6.81336	1.70334
$17$	−1.86606	−0.452587	−0.226293	−	0.974059i	$-0.572661\pi$
$17$	−1.86606	−0.452587	−0.226293	+	0.974059i	$0.572661\pi$
$18$	−10.0939	−2.37915
$19$	1.34461	0.308475	0.154238	−	0.988034i	$-0.450708\pi$
$19$	1.34461	0.308475	0.154238	+	0.988034i	$0.450708\pi$
$20$	18.2129	4.07252
$21$	0.749621	0.163581
$22$	−5.05804	−1.07838
$23$	−1.84743	−0.385217	−0.192608	−	0.981276i	$-0.561695\pi$
$23$	−1.84743	−0.385217	−0.192608	+	0.981276i	$0.561695\pi$
$24$	16.3339	3.33414
$25$	11.8487	2.36974
$26$	6.82989	1.33945
$27$	−2.58478	−0.497442
$28$	−1.25909	−0.237946
$29$	−3.63451	−0.674911	−0.337455	−	0.941342i	$-0.609566\pi$
$29$	−3.63451	−0.674911	−0.337455	+	0.941342i	$0.609566\pi$
$30$	27.5110	5.02280
$31$	8.20259	1.47323	0.736614	−	0.676313i	$-0.236423\pi$
$31$	8.20259	1.47323	0.736614	+	0.676313i	$0.236423\pi$
$32$	−4.92014	−0.869765
$33$	−5.26645	−0.916772
$34$	4.73445	0.811952
$35$	−1.16478	−0.196884
$36$	17.6527	2.94211
$37$	−6.52261	−1.07231	−0.536155	−	0.844119i	$-0.680124\pi$
$37$	−6.52261	−1.07231	−0.536155	+	0.844119i	$0.680124\pi$
$38$	−3.41146	−0.553412
$39$	7.11132	1.13872
$40$	−25.3800	−4.01294
$41$	−0.646703	−0.100998	−0.0504990	−	0.998724i	$-0.516081\pi$
$41$	−0.646703	−0.100998	−0.0504990	+	0.998724i	$0.516081\pi$
$42$	−1.90189	−0.293468
$43$	−2.23958	−0.341533	−0.170767	−	0.985312i	$-0.554624\pi$
$43$	−2.23958	−0.341533	−0.170767	+	0.985312i	$0.554624\pi$
$44$	8.84573	1.33354
$45$	16.3305	2.43440
$46$	4.68719	0.691089
$47$	−0.855722	−0.124820	−0.0624099	−	0.998051i	$-0.519879\pi$
$47$	−0.855722	−0.124820	−0.0624099	+	0.998051i	$0.519879\pi$
$48$	−17.9987	−2.59789
$49$	−6.91948	−0.988497
$50$	−30.0617	−4.25137
$51$	4.92954	0.690273
$52$	−11.9444	−1.65639
$53$	−7.59026	−1.04260	−0.521301	−	0.853373i	$-0.674553\pi$
$53$	−7.59026	−1.04260	−0.521301	+	0.853373i	$0.674553\pi$
$54$	6.55795	0.892423
$55$	8.18317	1.10342
$56$	1.75457	0.234465
$57$	−3.55203	−0.470478
$58$	9.22123	1.21081
$59$	4.50550	0.586566	0.293283	−	0.956026i	$-0.405252\pi$
$59$	4.50550	0.586566	0.293283	+	0.956026i	$0.405252\pi$
$60$	−48.1125	−6.21130
$61$	−7.72459	−0.989033	−0.494516	−	0.869168i	$-0.664655\pi$
$61$	−7.72459	−0.989033	−0.494516	+	0.869168i	$0.664655\pi$
$62$	−20.8111	−2.64301
$63$	−1.12896	−0.142235
$64$	−1.14367	−0.142959
$65$	−11.0498	−1.37055
$66$	13.3617	1.64471
$67$	−0.0617335	−0.00754194	−0.00377097	−	0.999993i	$-0.501200\pi$
$67$	−0.0617335	−0.00754194	−0.00377097	+	0.999993i	$0.501200\pi$
$68$	−8.27982	−1.00408
$69$	4.88033	0.587522
$70$	2.95521	0.353215
$71$	−4.46755	−0.530200	−0.265100	−	0.964221i	$-0.585405\pi$
$71$	−4.46755	−0.530200	−0.265100	+	0.964221i	$0.585405\pi$
$72$	−24.5994	−2.89907
$73$	1.23929	0.145048	0.0725238	−	0.997367i	$-0.476895\pi$
$73$	1.23929	0.145048	0.0725238	+	0.997367i	$0.476895\pi$
$74$	16.5487	1.92375
$75$	−31.3004	−3.61426
$76$	5.96612	0.684361
$77$	−0.565719	−0.0644696
$78$	−18.0424	−2.04290
$79$	−3.42912	−0.385806	−0.192903	−	0.981218i	$-0.561790\pi$
$79$	−3.42912	−0.385806	−0.192903	+	0.981218i	$0.561790\pi$
$80$	27.9669	3.12680
$81$	−5.10722	−0.567469
$82$	1.64077	0.181193
$83$	0.607703	0.0667041	0.0333521	−	0.999444i	$-0.489382\pi$
$83$	0.607703	0.0667041	0.0333521	+	0.999444i	$0.489382\pi$
$84$	3.32611	0.362909
$85$	−7.65965	−0.830806
$86$	5.68212	0.612719
$87$	9.60119	1.02936
$88$	−12.3267	−1.31403
$89$	−6.94814	−0.736502	−0.368251	−	0.929726i	$-0.620043\pi$
$89$	−6.94814	−0.736502	−0.368251	+	0.929726i	$0.620043\pi$
$90$	−41.4326	−4.36738
$91$	0.763893	0.0800777
$92$	−8.19717	−0.854615
$93$	−21.6686	−2.24693
$94$	2.17108	0.223930
$95$	5.51925	0.566263
$96$	12.9974	1.32654
$97$	−3.35310	−0.340456	−0.170228	−	0.985405i	$-0.554450\pi$
$97$	−3.35310	−0.340456	−0.170228	+	0.985405i	$0.554450\pi$
$98$	17.5556	1.77339
$99$	7.93147	0.797143
$100$	52.5733	5.25733
$101$	−8.92806	−0.888375	−0.444188	−	0.895934i	$-0.646508\pi$
$101$	−8.92806	−0.888375	−0.444188	+	0.895934i	$0.646508\pi$
$102$	−12.5069	−1.23837
$103$	−15.0022	−1.47821	−0.739105	−	0.673590i	$-0.764751\pi$
$103$	−15.0022	−1.47821	−0.739105	+	0.673590i	$0.764751\pi$
$104$	16.6448	1.63216
$105$	3.07698	0.300283
$106$	19.2575	1.87045
$107$	−7.90994	−0.764683	−0.382342	−	0.924021i	$-0.624882\pi$
$107$	−7.90994	−0.764683	−0.382342	+	0.924021i	$0.624882\pi$
$108$	−11.4688	−1.10359
$109$	2.56766	0.245937	0.122969	−	0.992411i	$-0.460759\pi$
$109$	2.56766	0.245937	0.122969	+	0.992411i	$0.460759\pi$
$110$	−20.7618	−1.97956
$111$	17.2306	1.63546
$112$	−1.93341	−0.182690
$113$	11.6426	1.09524	0.547621	−	0.836727i	$-0.315534\pi$
$113$	11.6426	1.09524	0.547621	+	0.836727i	$0.315534\pi$
$114$	9.01198	0.844050
$115$	−7.58319	−0.707136
$116$	−16.1265	−1.49731
$117$	−10.7099	−0.990131
$118$	−11.4311	−1.05232
$119$	0.529527	0.0485417
$120$	67.0459	6.12043
$121$	−7.02555	−0.638687
$122$	19.5983	1.77435
$123$	1.70838	0.154039
$124$	36.3954	3.26840
$125$	28.1119	2.51440
$126$	2.86432	0.255174
$127$	6.07715	0.539260	0.269630	−	0.962964i	$-0.413099\pi$
$127$	6.07715	0.539260	0.269630	+	0.962964i	$0.413099\pi$
$128$	12.7419	1.12624
$129$	5.91625	0.520897
$130$	28.0348	2.45881
$131$	6.28746	0.549338	0.274669	−	0.961539i	$-0.411432\pi$
$131$	6.28746	0.549338	0.274669	+	0.961539i	$0.411432\pi$
$132$	−23.3676	−2.03388
$133$	−0.381557	−0.0330851
$134$	0.156626	0.0135304
$135$	−10.6098	−0.913146
$136$	11.5381	0.989387
$137$	−8.99794	−0.768746	−0.384373	−	0.923178i	$-0.625582\pi$
$137$	−8.99794	−0.768746	−0.384373	+	0.923178i	$0.625582\pi$
$138$	−12.3821	−1.05403
$139$	15.1729	1.28695	0.643475	−	0.765467i	$-0.277492\pi$
$139$	15.1729	1.28695	0.643475	+	0.765467i	$0.277492\pi$
$140$	−5.16821	−0.436793
$141$	2.26054	0.190372
$142$	11.3348	0.951193
$143$	−5.36672	−0.448787
$144$	27.1067	2.25889
$145$	−14.9186	−1.23892
$146$	−3.14424	−0.260219
$147$	18.2790	1.50763
$148$	−28.9412	−2.37895
$149$	9.41599	0.771388	0.385694	−	0.922627i	$-0.373962\pi$
$149$	9.41599	0.771388	0.385694	+	0.922627i	$0.373962\pi$
$150$	79.4133	6.48407
$151$	−14.1507	−1.15157	−0.575783	−	0.817603i	$-0.695303\pi$
$151$	−14.1507	−1.15157	−0.575783	+	0.817603i	$0.695303\pi$
$152$	−8.31393	−0.674349
$153$	−7.42406	−0.600200
$154$	1.43530	0.115660
$155$	33.6693	2.70438
$156$	31.5533	2.52629
$157$	1.25751	0.100360	0.0501799	−	0.998740i	$-0.484021\pi$
$157$	1.25751	0.100360	0.0501799	+	0.998740i	$0.484021\pi$
$158$	8.70014	0.692146
$159$	20.0510	1.59015
$160$	−20.1958	−1.59661
$161$	0.524241	0.0413160
$162$	12.9577	1.01805
$163$	13.0536	1.02244	0.511220	−	0.859450i	$-0.329194\pi$
$163$	13.0536	1.02244	0.511220	+	0.859450i	$0.329194\pi$
$164$	−2.86946	−0.224067
$165$	−21.6173	−1.68290
$166$	−1.54183	−0.119669
$167$	−12.9670	−1.00342	−0.501708	−	0.865037i	$-0.667295\pi$
$167$	−12.9670	−1.00342	−0.501708	+	0.865037i	$0.667295\pi$
$168$	−4.63502	−0.357599
$169$	−5.75330	−0.442561
$170$	19.4336	1.49049
$171$	5.34949	0.409085
$172$	−9.93715	−0.757701
$173$	−24.7280	−1.88004	−0.940018	−	0.341126i	$-0.889192\pi$
$173$	−24.7280	−1.88004	−0.940018	+	0.341126i	$0.889192\pi$
$174$	−24.3595	−1.84669
$175$	−3.36227	−0.254163
$176$	13.5831	1.02387
$177$	−11.9021	−0.894616
$178$	17.6284	1.32130
$179$	3.01169	0.225105	0.112552	−	0.993646i	$-0.464097\pi$
$179$	3.01169	0.225105	0.112552	+	0.993646i	$0.464097\pi$
$180$	72.4591	5.40079
$181$	7.75076	0.576109	0.288055	−	0.957614i	$-0.406992\pi$
$181$	7.75076	0.576109	0.288055	+	0.957614i	$0.406992\pi$
$182$	−1.93810	−0.143661
$183$	20.4059	1.50845
$184$	11.4230	0.842112
$185$	−26.7734	−1.96842
$186$	54.9762	4.03105
$187$	−3.72018	−0.272047
$188$	−3.79689	−0.276916
$189$	0.733477	0.0533526
$190$	−14.0031	−1.01589
$191$	5.91207	0.427782	0.213891	−	0.976857i	$-0.431386\pi$
$191$	5.91207	0.427782	0.213891	+	0.976857i	$0.431386\pi$
$192$	3.02122	0.218038
$193$	2.92522	0.210562	0.105281	−	0.994443i	$-0.466426\pi$
$193$	2.92522	0.210562	0.105281	+	0.994443i	$0.466426\pi$
$194$	8.50727	0.610786
$195$	29.1899	2.09033
$196$	−30.7021	−2.19301
$197$	9.77869	0.696703	0.348352	−	0.937364i	$-0.386742\pi$
$197$	9.77869	0.696703	0.348352	+	0.937364i	$0.386742\pi$
$198$	−20.1232	−1.43009
$199$	10.2219	0.724612	0.362306	−	0.932059i	$-0.381990\pi$
$199$	10.2219	0.724612	0.362306	+	0.932059i	$0.381990\pi$
$200$	−73.2621	−5.18041
$201$	0.163080	0.0115028
$202$	22.6517	1.59377
$203$	1.03135	0.0723868
$204$	21.8726	1.53139
$205$	−2.65453	−0.185400
$206$	38.0626	2.65195
$207$	−7.34995	−0.510857
$208$	−18.3414	−1.27174
$209$	2.68062	0.185422
$210$	−7.80672	−0.538715
$211$	−23.5099	−1.61849	−0.809243	−	0.587474i	$-0.800123\pi$
$211$	−23.5099	−1.61849	−0.809243	+	0.587474i	$0.800123\pi$
$212$	−33.6784	−2.31304
$213$	11.8018	0.808648
$214$	20.0686	1.37186
$215$	−9.19284	−0.626947
$216$	15.9821	1.08744
$217$	−2.32762	−0.158009
$218$	−6.51451	−0.441218
$219$	−3.27380	−0.221223
$220$	36.3092	2.44796
$221$	5.02338	0.337909
$222$	−43.7165	−2.93406
$223$	−20.8776	−1.39807	−0.699035	−	0.715087i	$-0.746387\pi$
$223$	−20.8776	−1.39807	−0.699035	+	0.715087i	$0.746387\pi$
$224$	1.39617	0.0932857
$225$	47.1395	3.14263
$226$	−29.5388	−1.96489
$227$	−19.4167	−1.28873	−0.644365	−	0.764718i	$-0.722878\pi$
$227$	−19.4167	−1.28873	−0.644365	+	0.764718i	$0.722878\pi$
$228$	−15.7606	−1.04377
$229$	9.21209	0.608752	0.304376	−	0.952552i	$-0.401552\pi$
$229$	9.21209	0.608752	0.304376	+	0.952552i	$0.401552\pi$
$230$	19.2396	1.26862
$231$	1.49445	0.0983274
$232$	22.4727	1.47540
$233$	28.8376	1.88921	0.944606	−	0.328208i	$-0.106445\pi$
$233$	28.8376	1.88921	0.944606	+	0.328208i	$0.106445\pi$
$234$	27.1725	1.77632
$235$	−3.51249	−0.229130
$236$	19.9912	1.30131
$237$	9.05862	0.588421
$238$	−1.34348	−0.0870850
$239$	14.4234	0.932970	0.466485	−	0.884529i	$-0.345520\pi$
$239$	14.4234	0.932970	0.466485	+	0.884529i	$0.345520\pi$
$240$	−73.8796	−4.76891
$241$	−10.3333	−0.665628	−0.332814	−	0.942992i	$-0.607998\pi$
$241$	−10.3333	−0.665628	−0.332814	+	0.942992i	$0.607998\pi$
$242$	17.8248	1.14582
$243$	21.2460	1.36293
$244$	−34.2745	−2.19420
$245$	−28.4025	−1.81457
$246$	−4.33439	−0.276351
$247$	−3.61965	−0.230313
$248$	−50.7178	−3.22058
$249$	−1.60536	−0.101735
$250$	−71.3236	−4.51090
$251$	14.0819	0.888841	0.444420	−	0.895818i	$-0.353410\pi$
$251$	14.0819	0.888841	0.444420	+	0.895818i	$0.353410\pi$
$252$	−5.00925	−0.315553
$253$	−3.68305	−0.231551
$254$	−15.4186	−0.967446
$255$	20.2343	1.26712
$256$	−30.0406	−1.87754
$257$	9.56915	0.596907	0.298453	−	0.954424i	$-0.403529\pi$
$257$	9.56915	0.596907	0.298453	+	0.954424i	$0.403529\pi$
$258$	−15.0103	−0.934503
$259$	1.85090	0.115009
$260$	−49.0284	−3.04062
$261$	−14.4597	−0.895036
$262$	−15.9521	−0.985526
$263$	2.72597	0.168090	0.0840451	−	0.996462i	$-0.473216\pi$
$263$	2.72597	0.168090	0.0840451	+	0.996462i	$0.473216\pi$
$264$	32.5632	2.00413
$265$	−31.1558	−1.91389
$266$	0.968061	0.0593556
$267$	18.3548	1.12329
$268$	−0.273915	−0.0167320
$269$	−4.64244	−0.283054	−0.141527	−	0.989934i	$-0.545201\pi$
$269$	−4.64244	−0.283054	−0.141527	+	0.989934i	$0.545201\pi$
$270$	26.9185	1.63821
$271$	−26.2446	−1.59425	−0.797123	−	0.603816i	$-0.793646\pi$
$271$	−26.2446	−1.59425	−0.797123	+	0.603816i	$0.793646\pi$
$272$	−12.7142	−0.770909
$273$	−2.01796	−0.122132
$274$	22.8290	1.37915
$275$	23.6215	1.42443
$276$	21.6543	1.30344
$277$	−15.6750	−0.941822	−0.470911	−	0.882181i	$-0.656075\pi$
$277$	−15.6750	−0.941822	−0.470911	+	0.882181i	$0.656075\pi$
$278$	−38.4957	−2.30882
$279$	32.6337	1.95373
$280$	7.20202	0.430403
$281$	−1.85547	−0.110688	−0.0553440	−	0.998467i	$-0.517626\pi$
$281$	−1.85547	−0.110688	−0.0553440	+	0.998467i	$0.517626\pi$
$282$	−5.73530	−0.341532
$283$	29.6319	1.76143	0.880716	−	0.473645i	$-0.157062\pi$
$283$	29.6319	1.76143	0.880716	+	0.473645i	$0.157062\pi$
$284$	−19.8228	−1.17626
$285$	−14.5801	−0.863649
$286$	13.6161	0.805136
$287$	0.183513	0.0108324
$288$	−19.5746	−1.15344
$289$	−13.5178	−0.795165
$290$	37.8505	2.22266
$291$	8.85781	0.519254
$292$	5.49879	0.321792
$293$	−20.9497	−1.22390	−0.611948	−	0.790898i	$-0.709614\pi$
$293$	−20.9497	−1.22390	−0.611948	+	0.790898i	$0.709614\pi$
$294$	−46.3764	−2.70473
$295$	18.4938	1.07675
$296$	40.3302	2.34415
$297$	−5.15303	−0.299009
$298$	−23.8897	−1.38389
$299$	4.97324	0.287610
$300$	−138.882	−8.01833
$301$	0.635520	0.0366307
$302$	35.9022	2.06594
$303$	23.5851	1.35493
$304$	9.16133	0.525438
$305$	−31.7072	−1.81555
$306$	18.8358	1.07677
$307$	2.68639	0.153320	0.0766601	−	0.997057i	$-0.475574\pi$
$307$	2.68639	0.153320	0.0766601	+	0.997057i	$0.475574\pi$
$308$	−2.51013	−0.143028
$309$	39.6310	2.25453
$310$	−85.4235	−4.85173
$311$	24.5963	1.39473	0.697365	−	0.716716i	$-0.254355\pi$
$311$	24.5963	1.39473	0.697365	+	0.716716i	$0.254355\pi$
$312$	−43.9703	−2.48933
$313$	−19.0663	−1.07769	−0.538845	−	0.842405i	$-0.681139\pi$
$313$	−19.0663	−1.07769	−0.538845	+	0.842405i	$0.681139\pi$
$314$	−3.19046	−0.180048
$315$	−4.63405	−0.261099
$316$	−15.2152	−0.855921
$317$	13.8601	0.778462	0.389231	−	0.921140i	$-0.372741\pi$
$317$	13.8601	0.778462	0.389231	+	0.921140i	$0.372741\pi$
$318$	−50.8721	−2.85277
$319$	−7.24576	−0.405685
$320$	−4.69445	−0.262428
$321$	20.8955	1.16627
$322$	−1.33007	−0.0741220
$323$	−2.50913	−0.139612
$324$	−22.6610	−1.25895
$325$	−31.8963	−1.76929
$326$	−33.1188	−1.83428
$327$	−6.78294	−0.375097
$328$	3.99866	0.220789
$329$	0.242826	0.0133874
$330$	54.8460	3.01917
$331$	−4.64378	−0.255245	−0.127623	−	0.991823i	$-0.540735\pi$
$331$	−4.64378	−0.255245	−0.127623	+	0.991823i	$0.540735\pi$
$332$	2.69641	0.147985
$333$	−25.9500	−1.42205
$334$	32.8990	1.80016
$335$	−0.253398	−0.0138446
$336$	5.10744	0.278634
$337$	2.63488	0.143531	0.0717655	−	0.997422i	$-0.477137\pi$
$337$	2.63488	0.143531	0.0717655	+	0.997422i	$0.477137\pi$
$338$	14.5969	0.793967
$339$	−30.7559	−1.67043
$340$	−33.9863	−1.84317
$341$	16.3527	0.885548
$342$	−13.5724	−0.733910
$343$	3.94989	0.213274
$344$	13.8477	0.746616
$345$	20.0324	1.07851
$346$	62.7383	3.37283
$347$	−4.23813	−0.227515	−0.113757	−	0.993509i	$-0.536289\pi$
$347$	−4.23813	−0.227515	−0.113757	+	0.993509i	$0.536289\pi$
$348$	42.6010	2.28366
$349$	−28.3217	−1.51602	−0.758012	−	0.652241i	$-0.773829\pi$
$349$	−28.3217	−1.51602	−0.758012	+	0.652241i	$0.773829\pi$
$350$	8.53052	0.455976
$351$	6.95816	0.371399
$352$	−9.80879	−0.522810
$353$	−7.16279	−0.381237	−0.190618	−	0.981664i	$-0.561049\pi$
$353$	−7.16279	−0.381237	−0.190618	+	0.981664i	$0.561049\pi$
$354$	30.1972	1.60496
$355$	−18.3380	−0.973281
$356$	−30.8293	−1.63395
$357$	−1.39884	−0.0740345
$358$	−7.64107	−0.403843
$359$	30.3429	1.60144	0.800718	−	0.599042i	$-0.204452\pi$
$359$	30.3429	1.60144	0.800718	+	0.599042i	$0.204452\pi$
$360$	−100.974	−5.32177
$361$	−17.1920	−0.904843
$362$	−19.6647	−1.03355
$363$	18.5592	0.974108
$364$	3.38944	0.177655
$365$	5.08692	0.266261
$366$	−51.7725	−2.70619
$367$	2.72026	0.141997	0.0709983	−	0.997476i	$-0.477382\pi$
$367$	2.72026	0.141997	0.0709983	+	0.997476i	$0.477382\pi$
$368$	−12.5872	−0.656155
$369$	−2.57288	−0.133939
$370$	67.9279	3.53140
$371$	2.15386	0.111823
$372$	−96.1448	−4.98488
$373$	27.8856	1.44386	0.721930	−	0.691966i	$-0.243255\pi$
$373$	27.8856	1.44386	0.721930	+	0.691966i	$0.243255\pi$
$374$	9.43861	0.488059
$375$	−74.2625	−3.83490
$376$	5.29105	0.272865
$377$	9.78398	0.503901
$378$	−1.86093	−0.0957159
$379$	−1.32368	−0.0679931	−0.0339965	−	0.999422i	$-0.510824\pi$
$379$	−1.32368	−0.0679931	−0.0339965	+	0.999422i	$0.510824\pi$
$380$	24.4892	1.25627
$381$	−16.0539	−0.822465
$382$	−14.9997	−0.767453
$383$	−10.6787	−0.545657	−0.272828	−	0.962063i	$-0.587959\pi$
$383$	−10.6787	−0.545657	−0.272828	+	0.962063i	$0.587959\pi$
$384$	−33.6601	−1.71771
$385$	−2.32211	−0.118346
$386$	−7.42168	−0.377753
$387$	−8.91009	−0.452926
$388$	−14.8779	−0.755310
$389$	1.91710	0.0972009	0.0486004	−	0.998818i	$-0.484524\pi$
$389$	1.91710	0.0972009	0.0486004	+	0.998818i	$0.484524\pi$
$390$	−74.0588	−3.75011
$391$	3.44743	0.174344
$392$	42.7841	2.16092
$393$	−16.6094	−0.837836
$394$	−24.8099	−1.24990
$395$	−14.0755	−0.708218
$396$	35.1924	1.76848
$397$	−12.3019	−0.617414	−0.308707	−	0.951157i	$-0.599896\pi$
$397$	−12.3019	−0.617414	−0.308707	+	0.951157i	$0.599896\pi$
$398$	−25.9344	−1.29997
$399$	1.00795	0.0504606
$400$	80.7293	4.03647
$401$	35.1609	1.75585	0.877925	−	0.478797i	$-0.158927\pi$
$401$	35.1609	1.75585	0.877925	+	0.478797i	$0.158927\pi$
$402$	−0.413756	−0.0206363
$403$	−22.0811	−1.09994
$404$	−39.6143	−1.97089
$405$	−20.9637	−1.04169
$406$	−2.61668	−0.129864
$407$	−13.0035	−0.644559
$408$	−30.4800	−1.50899
$409$	−27.1229	−1.34114	−0.670570	−	0.741847i	$-0.733950\pi$
$409$	−27.1229	−1.34114	−0.670570	+	0.741847i	$0.733950\pi$
$410$	6.73490	0.332613
$411$	23.7697	1.17247
$412$	−66.5656	−3.27945
$413$	−1.27851	−0.0629115
$414$	18.6478	0.916490
$415$	2.49445	0.122448
$416$	13.2449	0.649383
$417$	−40.0819	−1.96282
$418$	−6.80110	−0.332652
$419$	−0.426437	−0.0208328	−0.0104164	−	0.999946i	$-0.503316\pi$
$419$	−0.426437	−0.0208328	−0.0104164	+	0.999946i	$0.503316\pi$
$420$	13.6527	0.666186
$421$	−19.9784	−0.973686	−0.486843	−	0.873489i	$-0.661852\pi$
$421$	−19.9784	−0.973686	−0.486843	+	0.873489i	$0.661852\pi$
$422$	59.6477	2.90361
$423$	−3.40446	−0.165530
$424$	46.9316	2.27920
$425$	−22.1104	−1.07251
$426$	−29.9428	−1.45073
$427$	2.19199	0.106078
$428$	−35.0969	−1.69647
$429$	14.1771	0.684479
$430$	23.3235	1.12476
$431$	37.3997	1.80148	0.900740	−	0.434359i	$-0.143025\pi$
$431$	37.3997	1.80148	0.900740	+	0.434359i	$0.143025\pi$
$432$	−17.6111	−0.847313
$433$	−12.6397	−0.607423	−0.303712	−	0.952764i	$-0.598226\pi$
$433$	−12.6397	−0.607423	−0.303712	+	0.952764i	$0.598226\pi$
$434$	5.90550	0.283473
$435$	39.4102	1.88957
$436$	11.3929	0.545619
$437$	−2.48408	−0.118830
$438$	8.30606	0.396879
$439$	−25.9761	−1.23977	−0.619885	−	0.784693i	$-0.712821\pi$
$439$	−25.9761	−1.23977	−0.619885	+	0.784693i	$0.712821\pi$
$440$	−50.5977	−2.41215
$441$	−27.5289	−1.31090
$442$	−12.7450	−0.606218
$443$	36.9041	1.75337	0.876683	−	0.481068i	$-0.159751\pi$
$443$	36.9041	1.75337	0.876683	+	0.481068i	$0.159751\pi$
$444$	76.4533	3.62831
$445$	−28.5201	−1.35198
$446$	52.9694	2.50817
$447$	−24.8740	−1.17650
$448$	0.324537	0.0153329
$449$	2.55861	0.120748	0.0603742	−	0.998176i	$-0.480771\pi$
$449$	2.55861	0.120748	0.0603742	+	0.998176i	$0.480771\pi$
$450$	−119.599	−5.63797
$451$	−1.28927	−0.0607092
$452$	51.6588	2.42982
$453$	37.3815	1.75634
$454$	49.2627	2.31201
$455$	3.13556	0.146997
$456$	21.9627	1.02850
$457$	−10.2036	−0.477304	−0.238652	−	0.971105i	$-0.576706\pi$
$457$	−10.2036	−0.477304	−0.238652	+	0.971105i	$0.576706\pi$
$458$	−23.3723	−1.09212
$459$	4.82337	0.225135
$460$	−33.6471	−1.56880
$461$	−28.6993	−1.33666	−0.668329	−	0.743866i	$-0.732990\pi$
$461$	−28.6993	−1.33666	−0.668329	+	0.743866i	$0.732990\pi$
$462$	−3.79161	−0.176402
$463$	0.980434	0.0455646	0.0227823	−	0.999740i	$-0.492748\pi$
$463$	0.980434	0.0455646	0.0227823	+	0.999740i	$0.492748\pi$
$464$	−24.7632	−1.14960
$465$	−88.9434	−4.12465
$466$	−73.1648	−3.38929
$467$	9.61048	0.444720	0.222360	−	0.974965i	$-0.428624\pi$
$467$	9.61048	0.444720	0.222360	+	0.974965i	$0.428624\pi$
$468$	−47.5204	−2.19663
$469$	0.0175179	0.000808903 0
$470$	8.91167	0.411065
$471$	−3.32192	−0.153066
$472$	−27.8582	−1.28228
$473$	−4.46483	−0.205293
$474$	−22.9830	−1.05564
$475$	15.9319	0.731004
$476$	2.34954	0.107691
$477$	−30.1975	−1.38265
$478$	−36.5941	−1.67377
$479$	4.71164	0.215280	0.107640	−	0.994190i	$-0.465671\pi$
$479$	4.71164	0.215280	0.107640	+	0.994190i	$0.465671\pi$
$480$	53.3507	2.43511
$481$	17.5587	0.800606
$482$	26.2170	1.19415
$483$	−1.38488	−0.0630141
$484$	−31.1728	−1.41694
$485$	−13.7635	−0.624969
$486$	−53.9040	−2.44513
$487$	16.2134	0.734700	0.367350	−	0.930083i	$-0.380265\pi$
$487$	16.2134	0.734700	0.367350	+	0.930083i	$0.380265\pi$
$488$	47.7623	2.16210
$489$	−34.4835	−1.55940
$490$	72.0609	3.25538
$491$	−20.0314	−0.904003	−0.452002	−	0.892017i	$-0.649290\pi$
$491$	−20.0314	−0.904003	−0.452002	+	0.892017i	$0.649290\pi$
$492$	7.58018	0.341741
$493$	6.78221	0.305456
$494$	9.18355	0.413188
$495$	32.5564	1.46330
$496$	55.8872	2.50941
$497$	1.26774	0.0568661
$498$	4.07301	0.182516
$499$	−34.7209	−1.55432	−0.777161	−	0.629301i	$-0.783341\pi$
$499$	−34.7209	−1.55432	−0.777161	+	0.629301i	$0.783341\pi$
$500$	124.734	5.57827
$501$	34.2546	1.53038
$502$	−35.7277	−1.59460
$503$	−16.1120	−0.718401	−0.359200	−	0.933260i	$-0.616951\pi$
$503$	−16.1120	−0.718401	−0.359200	+	0.933260i	$0.616951\pi$
$504$	6.98050	0.310936
$505$	−36.6471	−1.63078
$506$	9.34440	0.415409
$507$	15.1984	0.674983
$508$	26.9647	1.19636
$509$	44.3692	1.96663	0.983314	−	0.181916i	$-0.0582300\pi$
$509$	44.3692	1.96663	0.983314	+	0.181916i	$0.0582300\pi$
$510$	−51.3372	−2.27325
$511$	−0.351669	−0.0155569
$512$	50.7333	2.24212
$513$	−3.47553	−0.153448
$514$	−24.2782	−1.07087
$515$	−61.5797	−2.71353
$516$	26.2508	1.15563
$517$	−1.70597	−0.0750284
$518$	−4.69599	−0.206330
$519$	65.3234	2.86738
$520$	68.3223	2.99613
$521$	−7.48693	−0.328008	−0.164004	−	0.986460i	$-0.552441\pi$
$521$	−7.48693	−0.328008	−0.164004	+	0.986460i	$0.552441\pi$
$522$	36.6863	1.60572
$523$	−16.8239	−0.735657	−0.367829	−	0.929894i	$-0.619899\pi$
$523$	−16.8239	−0.735657	−0.367829	+	0.929894i	$0.619899\pi$
$524$	27.8978	1.21872
$525$	8.88202	0.387643
$526$	−6.91615	−0.301558
$527$	−15.3065	−0.666763
$528$	−35.8823	−1.56157
$529$	−19.5870	−0.851608
$530$	79.0466	3.43356
$531$	17.9250	0.777878
$532$	−1.69299	−0.0734003
$533$	1.74090	0.0754069
$534$	−46.5685	−2.01522
$535$	−32.4681	−1.40372
$536$	0.381707	0.0164872
$537$	−7.95592	−0.343323
$538$	11.7785	0.507807
$539$	−13.7947	−0.594179
$540$	−47.0763	−2.02584
$541$	−16.3069	−0.701089	−0.350545	−	0.936546i	$-0.614004\pi$
$541$	−16.3069	−0.701089	−0.350545	+	0.936546i	$0.614004\pi$
$542$	66.5861	2.86012
$543$	−20.4750	−0.878667
$544$	9.18128	0.393644
$545$	10.5395	0.451463
$546$	5.11983	0.219109
$547$	−0.940666	−0.0402200	−0.0201100	−	0.999798i	$-0.506402\pi$
$547$	−0.940666	−0.0402200	−0.0201100	+	0.999798i	$0.506402\pi$
$548$	−39.9244	−1.70549
$549$	−30.7320	−1.31161
$550$	−59.9311	−2.55547
$551$	−4.88700	−0.208193
$552$	−30.1758	−1.28437
$553$	0.973071	0.0413792
$554$	39.7697	1.68965
$555$	70.7268	3.00219
$556$	67.3231	2.85513
$557$	−25.3273	−1.07315	−0.536577	−	0.843851i	$-0.680283\pi$
$557$	−25.3273	−1.07315	−0.536577	+	0.843851i	$0.680283\pi$
$558$	−82.7961	−3.50504
$559$	6.02889	0.254995
$560$	−7.93609	−0.335361
$561$	9.82753	0.414919
$562$	4.70758	0.198577
$563$	−35.5814	−1.49958	−0.749788	−	0.661678i	$-0.769845\pi$
$563$	−35.5814	−1.49958	−0.749788	+	0.661678i	$0.769845\pi$
$564$	10.0302	0.422346
$565$	47.7894	2.01052
$566$	−75.1801	−3.16005
$567$	1.44926	0.0608633
$568$	27.6235	1.15906
$569$	−37.3078	−1.56402	−0.782012	−	0.623264i	$-0.785806\pi$
$569$	−37.3078	−1.56402	−0.782012	+	0.623264i	$0.785806\pi$
$570$	36.9916	1.54941
$571$	0.177921	0.00744575	0.00372287	−	0.999993i	$-0.498815\pi$
$571$	0.177921	0.00744575	0.00372287	+	0.999993i	$0.498815\pi$
$572$	−23.8124	−0.995648
$573$	−15.6178	−0.652443
$574$	−0.465597	−0.0194337
$575$	−21.8897	−0.912862
$576$	−4.55006	−0.189586
$577$	46.4523	1.93384	0.966918	−	0.255088i	$-0.0821045\pi$
$577$	46.4523	1.93384	0.966918	+	0.255088i	$0.0821045\pi$
$578$	34.2965	1.42655
$579$	−7.72749	−0.321143
$580$	−66.1947	−2.74859
$581$	−0.172446	−0.00715427
$582$	−22.4735	−0.931555
$583$	−15.1319	−0.626701
$584$	−7.66269	−0.317084
$585$	−43.9611	−1.81757
$586$	53.1523	2.19570
$587$	3.41754	0.141057	0.0705285	−	0.997510i	$-0.477531\pi$
$587$	3.41754	0.141057	0.0705285	+	0.997510i	$0.477531\pi$
$588$	81.1051	3.34472
$589$	11.0293	0.454454
$590$	−46.9213	−1.93172
$591$	−25.8322	−1.06259
$592$	−44.4409	−1.82651
$593$	−10.0328	−0.411996	−0.205998	−	0.978552i	$-0.566044\pi$
$593$	−10.0328	−0.411996	−0.205998	+	0.978552i	$0.566044\pi$
$594$	13.0739	0.536430
$595$	2.17356	0.0891072
$596$	41.7793	1.71135
$597$	−27.0030	−1.10516
$598$	−12.6178	−0.515979
$599$	36.7854	1.50301	0.751505	−	0.659727i	$-0.229328\pi$
$599$	36.7854	1.50301	0.751505	+	0.659727i	$0.229328\pi$
$600$	193.535	7.90103
$601$	7.63927	0.311612	0.155806	−	0.987788i	$-0.450203\pi$
$601$	7.63927	0.311612	0.155806	+	0.987788i	$0.450203\pi$
$602$	−1.61240	−0.0657165
$603$	−0.245604	−0.0100018
$604$	−62.7874	−2.55478
$605$	−28.8379	−1.17243
$606$	−59.8385	−2.43077
$607$	−14.1760	−0.575387	−0.287693	−	0.957723i	$-0.592888\pi$
$607$	−14.1760	−0.575387	−0.287693	+	0.957723i	$0.592888\pi$
$608$	−6.61567	−0.268301
$609$	−2.72450	−0.110402
$610$	80.4456	3.25715
$611$	2.30358	0.0931928
$612$	−32.9410	−1.33156
$613$	16.4515	0.664471	0.332235	−	0.943196i	$-0.392197\pi$
$613$	16.4515	0.664471	0.332235	+	0.943196i	$0.392197\pi$
$614$	−6.81573	−0.275060
$615$	7.01241	0.282768
$616$	3.49792	0.140935
$617$	29.5083	1.18796	0.593979	−	0.804481i	$-0.297556\pi$
$617$	29.5083	1.18796	0.593979	+	0.804481i	$0.297556\pi$
$618$	−100.549	−4.04468
$619$	−27.1768	−1.09233	−0.546164	−	0.837678i	$-0.683912\pi$
$619$	−27.1768	−1.09233	−0.546164	+	0.837678i	$0.683912\pi$
$620$	149.393	5.99975
$621$	4.77522	0.191623
$622$	−62.4043	−2.50218
$623$	1.97165	0.0789927
$624$	48.4520	1.93963
$625$	56.1478	2.24591
$626$	48.3737	1.93340
$627$	−7.08133	−0.282801
$628$	5.57962	0.222651
$629$	12.1716	0.485313
$630$	11.7572	0.468418
$631$	15.2024	0.605199	0.302600	−	0.953118i	$-0.402146\pi$
$631$	15.2024	0.605199	0.302600	+	0.953118i	$0.402146\pi$
$632$	21.2027	0.843399
$633$	62.1055	2.46847
$634$	−35.1650	−1.39658
$635$	24.9450	0.989911
$636$	88.9675	3.52779
$637$	18.6270	0.738029
$638$	18.3835	0.727809
$639$	−17.7740	−0.703128
$640$	52.3020	2.06742
$641$	−16.9304	−0.668711	−0.334356	−	0.942447i	$-0.608519\pi$
$641$	−16.9304	−0.668711	−0.334356	+	0.942447i	$0.608519\pi$
$642$	−53.0148	−2.09233
$643$	22.4145	0.883940	0.441970	−	0.897030i	$-0.354280\pi$
$643$	22.4145	0.883940	0.441970	+	0.897030i	$0.354280\pi$
$644$	2.32609	0.0916607
$645$	24.2845	0.956203
$646$	6.36600	0.250467
$647$	−10.0868	−0.396552	−0.198276	−	0.980146i	$-0.563534\pi$
$647$	−10.0868	−0.396552	−0.198276	+	0.980146i	$0.563534\pi$
$648$	31.5787	1.24053
$649$	8.98218	0.352581
$650$	80.9252	3.17415
$651$	6.14884	0.240992
$652$	57.9197	2.26831
$653$	32.5132	1.27234	0.636170	−	0.771549i	$-0.280518\pi$
$653$	32.5132	1.27234	0.636170	+	0.771549i	$0.280518\pi$
$654$	17.2092	0.672934
$655$	25.8082	1.00841
$656$	−4.40622	−0.172034
$657$	4.93046	0.192355
$658$	−0.616082	−0.0240174
$659$	−31.7947	−1.23854	−0.619272	−	0.785176i	$-0.712572\pi$
$659$	−31.7947	−1.23854	−0.619272	+	0.785176i	$0.712572\pi$
$660$	−95.9171	−3.73357
$661$	11.9653	0.465398	0.232699	−	0.972549i	$-0.425244\pi$
$661$	11.9653	0.465398	0.232699	+	0.972549i	$0.425244\pi$
$662$	11.7819	0.457916
$663$	−13.2702	−0.515370
$664$	−3.75752	−0.145820
$665$	−1.56618	−0.0607339
$666$	65.8386	2.55119
$667$	6.71451	0.259987
$668$	−57.5353	−2.22611
$669$	55.1520	2.13230
$670$	0.642906	0.0248376
$671$	−15.3998	−0.594501
$672$	−3.68824	−0.142277
$673$	−21.5641	−0.831234	−0.415617	−	0.909540i	$-0.636434\pi$
$673$	−21.5641	−0.831234	−0.415617	+	0.909540i	$0.636434\pi$
$674$	−6.68505	−0.257498
$675$	−30.6263	−1.17881
$676$	−25.5277	−0.981835
$677$	42.5225	1.63427	0.817136	−	0.576445i	$-0.195561\pi$
$677$	42.5225	1.63427	0.817136	+	0.576445i	$0.195561\pi$
$678$	78.0320	2.99680
$679$	0.951499	0.0365152
$680$	47.3607	1.81620
$681$	51.2926	1.96554
$682$	−41.4890	−1.58870
$683$	−24.6219	−0.942131	−0.471065	−	0.882098i	$-0.656130\pi$
$683$	−24.6219	−0.942131	−0.471065	+	0.882098i	$0.656130\pi$
$684$	23.7360	0.907568
$685$	−36.9340	−1.41117
$686$	−10.0214	−0.382619
$687$	−24.3354	−0.928453
$688$	−15.2591	−0.581747
$689$	20.4327	0.778425
$690$	−50.8248	−1.93487
$691$	−35.8677	−1.36447	−0.682236	−	0.731132i	$-0.738992\pi$
$691$	−35.8677	−1.36447	−0.682236	+	0.731132i	$0.738992\pi$
$692$	−109.720	−4.17091
$693$	−2.25069	−0.0854967
$694$	10.7527	0.408168
$695$	62.2804	2.36243
$696$	−59.3656	−2.25025
$697$	1.20679	0.0457103
$698$	71.8559	2.71979
$699$	−76.1795	−2.88137
$700$	−14.9186	−0.563869
$701$	−44.7874	−1.69160	−0.845799	−	0.533502i	$-0.820876\pi$
$701$	−44.7874	−1.69160	−0.845799	+	0.533502i	$0.820876\pi$
$702$	−17.6538	−0.666300
$703$	−8.77037	−0.330781
$704$	−2.28003	−0.0859319
$705$	9.27888	0.349463
$706$	18.1730	0.683949
$707$	2.53349	0.0952817
$708$	−52.8102	−1.98473
$709$	1.59885	0.0600461	0.0300231	−	0.999549i	$-0.490442\pi$
$709$	1.59885	0.0600461	0.0300231	+	0.999549i	$0.490442\pi$
$710$	46.5260	1.74609
$711$	−13.6426	−0.511638
$712$	42.9614	1.61005
$713$	−15.1537	−0.567512
$714$	3.54905	0.132820
$715$	−22.0288	−0.823832
$716$	13.3631	0.499401
$717$	−38.1019	−1.42294
$718$	−76.9840	−2.87302
$719$	34.0444	1.26964	0.634821	−	0.772659i	$-0.281074\pi$
$719$	34.0444	1.26964	0.634821	+	0.772659i	$0.281074\pi$
$720$	111.265	4.14661
$721$	4.25713	0.158544
$722$	43.6185	1.62331
$723$	27.2973	1.01520
$724$	34.3906	1.27811
$725$	−43.0641	−1.59936
$726$	−47.0873	−1.74757
$727$	8.41653	0.312152	0.156076	−	0.987745i	$-0.450116\pi$
$727$	8.41653	0.312152	0.156076	+	0.987745i	$0.450116\pi$
$728$	−4.72326	−0.175056
$729$	−40.8034	−1.51124
$730$	−12.9062	−0.477680
$731$	4.17920	0.154573
$732$	90.5421	3.34653
$733$	−41.4797	−1.53209	−0.766044	−	0.642788i	$-0.777778\pi$
$733$	−41.4797	−1.53209	−0.766044	+	0.642788i	$0.777778\pi$
$734$	−6.90167	−0.254745
$735$	75.0302	2.76753
$736$	9.08963	0.335048
$737$	−0.123072	−0.00453341
$738$	6.52775	0.240290
$739$	−1.91173	−0.0703241	−0.0351621	−	0.999382i	$-0.511195\pi$
$739$	−1.91173	−0.0703241	−0.0351621	+	0.999382i	$0.511195\pi$
$740$	−118.795	−4.36700
$741$	9.56196	0.351267
$742$	−5.46465	−0.200614
$743$	36.3157	1.33229	0.666146	−	0.745821i	$-0.267943\pi$
$743$	36.3157	1.33229	0.666146	+	0.745821i	$0.267943\pi$
$744$	133.980	4.91195
$745$	38.6500	1.41602
$746$	−70.7494	−2.59032
$747$	2.41772	0.0884599
$748$	−16.5067	−0.603544
$749$	2.24458	0.0820152
$750$	188.414	6.87991
$751$	−0.358196	−0.0130708	−0.00653539	−	0.999979i	$-0.502080\pi$
$751$	−0.358196	−0.0130708	−0.00653539	+	0.999979i	$0.502080\pi$
$752$	−5.83034	−0.212611
$753$	−37.1998	−1.35564
$754$	−24.8233	−0.904011
$755$	−58.0845	−2.11391
$756$	3.25448	0.118364
$757$	−2.31885	−0.0842801	−0.0421400	−	0.999112i	$-0.513418\pi$
$757$	−2.31885	−0.0842801	−0.0421400	+	0.999112i	$0.513418\pi$
$758$	3.35836	0.121981
$759$	9.72943	0.353156
$760$	−34.1263	−1.23789
$761$	−29.4489	−1.06752	−0.533761	−	0.845635i	$-0.679222\pi$
$761$	−29.4489	−1.06752	−0.533761	+	0.845635i	$0.679222\pi$
$762$	40.7309	1.47552
$763$	−0.728618	−0.0263777
$764$	26.2322	0.949048
$765$	−30.4736	−1.10178
$766$	27.0933	0.978922
$767$	−12.1287	−0.437941
$768$	79.3577	2.86358
$769$	30.2813	1.09197	0.545986	−	0.837794i	$-0.316155\pi$
$769$	30.2813	1.09197	0.545986	+	0.837794i	$0.316155\pi$
$770$	5.89152	0.212316
$771$	−25.2786	−0.910387
$772$	12.9794	0.467137
$773$	13.0603	0.469745	0.234873	−	0.972026i	$-0.424533\pi$
$773$	13.0603	0.469745	0.234873	+	0.972026i	$0.424533\pi$
$774$	22.6061	0.812560
$775$	97.1898	3.49116
$776$	20.7327	0.744260
$777$	−4.88949	−0.175409
$778$	−4.86395	−0.174381
$779$	−0.869564	−0.0311554
$780$	129.517	4.63747
$781$	−8.90651	−0.318700
$782$	−8.74659	−0.312778
$783$	9.39441	0.335729
$784$	−47.1449	−1.68375
$785$	5.16170	0.184229
$786$	42.1404	1.50310
$787$	−40.2375	−1.43431	−0.717155	−	0.696914i	$-0.754556\pi$
$787$	−40.2375	−1.43431	−0.717155	+	0.696914i	$0.754556\pi$
$788$	43.3886	1.54566
$789$	−7.20113	−0.256367
$790$	35.7116	1.27056
$791$	−3.30378	−0.117469
$792$	−49.0414	−1.74261
$793$	20.7944	0.738430
$794$	31.2115	1.10766
$795$	82.3037	2.91901
$796$	45.3552	1.60757
$797$	37.2675	1.32008	0.660041	−	0.751229i	$-0.270539\pi$
$797$	37.2675	1.32008	0.660041	+	0.751229i	$0.270539\pi$
$798$	−2.55730	−0.0905276
$799$	1.59683	0.0564918
$800$	−58.2971	−2.06111
$801$	−27.6429	−0.976715
$802$	−89.2079	−3.15004
$803$	2.47064	0.0871871
$804$	0.723595	0.0255192
$805$	2.15186	0.0758431
$806$	56.0228	1.97332
$807$	12.2638	0.431707
$808$	55.2035	1.94205
$809$	21.0812	0.741174	0.370587	−	0.928798i	$-0.379156\pi$
$809$	21.0812	0.741174	0.370587	+	0.928798i	$0.379156\pi$
$810$	53.1877	1.86883
$811$	12.2360	0.429666	0.214833	−	0.976651i	$-0.431079\pi$
$811$	12.2360	0.429666	0.214833	+	0.976651i	$0.431079\pi$
$812$	4.57617	0.160592
$813$	69.3298	2.43150
$814$	32.9916	1.15636
$815$	53.5814	1.87688
$816$	33.5867	1.17577
$817$	−3.01137	−0.105354
$818$	68.8144	2.40604
$819$	3.03912	0.106195
$820$	−11.7783	−0.411316
$821$	−31.1343	−1.08660	−0.543298	−	0.839540i	$-0.682824\pi$
$821$	−31.1343	−1.08660	−0.543298	+	0.839540i	$0.682824\pi$
$822$	−60.3069	−2.10344
$823$	−25.2751	−0.881036	−0.440518	−	0.897744i	$-0.645205\pi$
$823$	−25.2751	−0.881036	−0.440518	+	0.897744i	$0.645205\pi$
$824$	92.7608	3.23147
$825$	−62.4005	−2.17251
$826$	3.24376	0.112865
$827$	23.3593	0.812284	0.406142	−	0.913810i	$-0.366874\pi$
$827$	23.3593	0.812284	0.406142	+	0.913810i	$0.366874\pi$
$828$	−32.6122	−1.13335
$829$	44.4594	1.54414	0.772069	−	0.635539i	$-0.219222\pi$
$829$	44.4594	1.54414	0.772069	+	0.635539i	$0.219222\pi$
$830$	−6.32875	−0.219674
$831$	41.4084	1.43644
$832$	3.07874	0.106736
$833$	12.9122	0.447380
$834$	101.693	3.52135
$835$	−53.2258	−1.84196
$836$	11.8941	0.411365
$837$	−21.2019	−0.732845
$838$	1.08193	0.0373746
$839$	27.3657	0.944770	0.472385	−	0.881392i	$-0.343393\pi$
$839$	27.3657	0.944770	0.472385	+	0.881392i	$0.343393\pi$
$840$	−19.0254	−0.656439
$841$	−15.7904	−0.544495
$842$	50.6878	1.74682
$843$	4.90155	0.168818
$844$	−104.315	−3.59066
$845$	−23.6156	−0.812403
$846$	8.63757	0.296966
$847$	1.99362	0.0685016
$848$	−51.7152	−1.77591
$849$	−78.2779	−2.68649
$850$	56.0970	1.92411
$851$	12.0501	0.413072
$852$	52.3654	1.79401
$853$	−32.5423	−1.11423	−0.557113	−	0.830437i	$-0.688091\pi$
$853$	−32.5423	−1.11423	−0.557113	+	0.830437i	$0.688091\pi$
$854$	−5.56136	−0.190306
$855$	21.9581	0.750952
$856$	48.9083	1.67165
$857$	−28.5595	−0.975574	−0.487787	−	0.872963i	$-0.662196\pi$
$857$	−28.5595	−0.975574	−0.487787	+	0.872963i	$0.662196\pi$
$858$	−35.9693	−1.22797
$859$	−31.5403	−1.07614	−0.538070	−	0.842900i	$-0.680846\pi$
$859$	−31.5403	−1.07614	−0.538070	+	0.842900i	$0.680846\pi$
$860$	−40.7892	−1.39090
$861$	−0.484782	−0.0165213
$862$	−94.8881	−3.23190
$863$	−47.2320	−1.60779	−0.803897	−	0.594768i	$-0.797244\pi$
$863$	−47.2320	−1.60779	−0.803897	+	0.594768i	$0.797244\pi$
$864$	12.7175	0.432658
$865$	−101.501	−3.45115
$866$	32.0685	1.08973
$867$	35.7097	1.21277
$868$	−10.3278	−0.350549
$869$	−6.83629	−0.231905
$870$	−99.9889	−3.38994
$871$	0.166185	0.00563095
$872$	−15.8762	−0.537637
$873$	−13.3402	−0.451497
$874$	6.30245	0.213184
$875$	−7.97722	−0.269679
$876$	−14.5260	−0.490789
$877$	−6.36667	−0.214987	−0.107494	−	0.994206i	$-0.534283\pi$
$877$	−6.36667	−0.214987	−0.107494	+	0.994206i	$0.534283\pi$
$878$	65.9048	2.22418
$879$	55.3424	1.86665
$880$	55.7549	1.87950
$881$	20.7402	0.698757	0.349378	−	0.936982i	$-0.386393\pi$
$881$	20.7402	0.698757	0.349378	+	0.936982i	$0.386393\pi$
$882$	69.8445	2.35179
$883$	−15.2022	−0.511594	−0.255797	−	0.966731i	$-0.582338\pi$
$883$	−15.2022	−0.511594	−0.255797	+	0.966731i	$0.582338\pi$
$884$	22.2890	0.749662
$885$	−48.8547	−1.64223
$886$	−93.6307	−3.14558
$887$	21.1758	0.711012	0.355506	−	0.934674i	$-0.384308\pi$
$887$	21.1758	0.711012	0.355506	+	0.934674i	$0.384308\pi$
$888$	−106.539	−3.57523
$889$	−1.72450	−0.0578377
$890$	72.3595	2.42549
$891$	−10.1818	−0.341102
$892$	−92.6353	−3.10166
$893$	−1.15061	−0.0385038
$894$	63.1088	2.11067
$895$	12.3621	0.413221
$896$	−3.61574	−0.120793
$897$	−13.1377	−0.438655
$898$	−6.49154	−0.216626
$899$	−29.8124	−0.994298
$900$	209.161	6.97202
$901$	14.1639	0.471868
$902$	3.27105	0.108914
$903$	−1.67884	−0.0558682
$904$	−71.9877	−2.39428
$905$	31.8146	1.05755
$906$	−94.8420	−3.15092
$907$	−40.3294	−1.33911	−0.669557	−	0.742761i	$-0.733516\pi$
$907$	−40.3294	−1.33911	−0.669557	+	0.742761i	$0.733516\pi$
$908$	−86.1528	−2.85908
$909$	−35.5200	−1.17812
$910$	−7.95534	−0.263717
$911$	−50.2224	−1.66394	−0.831972	−	0.554818i	$-0.812788\pi$
$911$	−50.2224	−1.66394	−0.831972	+	0.554818i	$0.812788\pi$
$912$	−24.2013	−0.801384
$913$	1.21152	0.0400954
$914$	25.8879	0.856296
$915$	83.7603	2.76903
$916$	40.8746	1.35053
$917$	−1.78417	−0.0589186
$918$	−12.2375	−0.403899
$919$	−9.61705	−0.317237	−0.158619	−	0.987340i	$-0.550704\pi$
$919$	−9.61705	−0.317237	−0.158619	+	0.987340i	$0.550704\pi$
$920$	46.8880	1.54585
$921$	−7.09657	−0.233840
$922$	72.8139	2.39800
$923$	12.0265	0.395857
$924$	6.63094	0.218142
$925$	−77.2843	−2.54109
$926$	−2.48749	−0.0817441
$927$	−59.6857	−1.96034
$928$	17.8823	0.587014
$929$	11.8880	0.390031	0.195016	−	0.980800i	$-0.437524\pi$
$929$	11.8880	0.390031	0.195016	+	0.980800i	$0.437524\pi$
$930$	225.661	7.39973
$931$	−9.30401	−0.304927
$932$	127.954	4.19127
$933$	−64.9756	−2.12721
$934$	−24.3831	−0.797839
$935$	−15.2703	−0.499392
$936$	66.2209	2.16450
$937$	−3.15537	−0.103081	−0.0515407	−	0.998671i	$-0.516413\pi$
$937$	−3.15537	−0.103081	−0.0515407	+	0.998671i	$0.516413\pi$
$938$	−0.0444454	−0.00145119
$939$	50.3670	1.64366
$940$	−15.5851	−0.508331
$941$	−56.1797	−1.83140	−0.915702	−	0.401857i	$-0.868365\pi$
$941$	−56.1797	−1.83140	−0.915702	+	0.401857i	$0.868365\pi$
$942$	8.42817	0.274605
$943$	1.19474	0.0389061
$944$	30.6976	0.999122
$945$	3.01071	0.0979385
$946$	11.3279	0.368302
$947$	−11.2254	−0.364775	−0.182388	−	0.983227i	$-0.558383\pi$
$947$	−11.2254	−0.364775	−0.182388	+	0.983227i	$0.558383\pi$
$948$	40.1936	1.30543
$949$	−3.33612	−0.108295
$950$	−40.4213	−1.31144
$951$	−36.6140	−1.18729
$952$	−3.27414	−0.106116
$953$	−7.94610	−0.257399	−0.128700	−	0.991684i	$-0.541080\pi$
$953$	−7.94610	−0.257399	−0.128700	+	0.991684i	$0.541080\pi$
$954$	76.6153	2.48051
$955$	24.2674	0.785273
$956$	63.9973	2.06982
$957$	19.1410	0.618739
$958$	−11.9541	−0.386218
$959$	2.55332	0.0824510
$960$	12.4012	0.400248
$961$	36.2825	1.17040
$962$	−44.5487	−1.43631
$963$	−31.4694	−1.01409
$964$	−45.8496	−1.47671
$965$	12.0072	0.386525
$966$	3.51362	0.113049
$967$	1.68352	0.0541384	0.0270692	−	0.999634i	$-0.491383\pi$
$967$	1.68352	0.0541384	0.0270692	+	0.999634i	$0.491383\pi$
$968$	43.4400	1.39621
$969$	6.62831	0.212932
$970$	34.9199	1.12121
$971$	−30.5430	−0.980172	−0.490086	−	0.871674i	$-0.663035\pi$
$971$	−30.5430	−0.980172	−0.490086	+	0.871674i	$0.663035\pi$
$972$	94.2697	3.02370
$973$	−4.30557	−0.138030
$974$	−41.1356	−1.31807
$975$	84.2597	2.69847
$976$	−52.6304	−1.68466
$977$	−40.3423	−1.29066	−0.645332	−	0.763902i	$-0.723281\pi$
$977$	−40.3423	−1.29066	−0.645332	+	0.763902i	$0.723281\pi$
$978$	87.4893	2.79760
$979$	−13.8518	−0.442706
$980$	−126.023	−4.02567
$981$	10.2153	0.326151
$982$	50.8223	1.62181
$983$	18.4508	0.588489	0.294245	−	0.955730i	$-0.404932\pi$
$983$	18.4508	0.588489	0.294245	+	0.955730i	$0.404932\pi$
$984$	−10.5632	−0.336741
$985$	40.1387	1.27893
$986$	−17.2074	−0.547995
$987$	−0.641467	−0.0204181
$988$	−16.0606	−0.510956
$989$	4.13748	0.131564
$990$	−82.6000	−2.62520
$991$	−23.6025	−0.749758	−0.374879	−	0.927074i	$-0.622316\pi$
$991$	−23.6025	−0.749758	−0.374879	+	0.927074i	$0.622316\pi$
$992$	−40.3578	−1.28136
$993$	12.2674	0.389293
$994$	−3.21644	−0.102019
$995$	41.9580	1.33016
$996$	−7.12306	−0.225703
$997$	39.3342	1.24573	0.622864	−	0.782330i	$-0.285969\pi$
$997$	39.3342	1.24573	0.622864	+	0.782330i	$0.285969\pi$
$998$	88.0917	2.78850
$999$	16.8595	0.533412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.8	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.8	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53714 q^{2} -2.64168 q^{3} +4.43706 q^{4} +4.10471 q^{5} +6.70230 q^{6} -0.283767 q^{7} -6.18314 q^{8} +3.97846 q^{9} +O(q^{10})\)	\(q-2.53714 q^{2} -2.64168 q^{3} +4.43706 q^{4} +4.10471 q^{5} +6.70230 q^{6} -0.283767 q^{7} -6.18314 q^{8} +3.97846 q^{9} -10.4142 q^{10} +1.99360 q^{11} -11.7213 q^{12} -2.69197 q^{13} +0.719956 q^{14} -10.8433 q^{15} +6.81336 q^{16} -1.86606 q^{17} -10.0939 q^{18} +1.34461 q^{19} +18.2129 q^{20} +0.749621 q^{21} -5.05804 q^{22} -1.84743 q^{23} +16.3339 q^{24} +11.8487 q^{25} +6.82989 q^{26} -2.58478 q^{27} -1.25909 q^{28} -3.63451 q^{29} +27.5110 q^{30} +8.20259 q^{31} -4.92014 q^{32} -5.26645 q^{33} +4.73445 q^{34} -1.16478 q^{35} +17.6527 q^{36} -6.52261 q^{37} -3.41146 q^{38} +7.11132 q^{39} -25.3800 q^{40} -0.646703 q^{41} -1.90189 q^{42} -2.23958 q^{43} +8.84573 q^{44} +16.3305 q^{45} +4.68719 q^{46} -0.855722 q^{47} -17.9987 q^{48} -6.91948 q^{49} -30.0617 q^{50} +4.92954 q^{51} -11.9444 q^{52} -7.59026 q^{53} +6.55795 q^{54} +8.18317 q^{55} +1.75457 q^{56} -3.55203 q^{57} +9.22123 q^{58} +4.50550 q^{59} -48.1125 q^{60} -7.72459 q^{61} -20.8111 q^{62} -1.12896 q^{63} -1.14367 q^{64} -11.0498 q^{65} +13.3617 q^{66} -0.0617335 q^{67} -8.27982 q^{68} +4.88033 q^{69} +2.95521 q^{70} -4.46755 q^{71} -24.5994 q^{72} +1.23929 q^{73} +16.5487 q^{74} -31.3004 q^{75} +5.96612 q^{76} -0.565719 q^{77} -18.0424 q^{78} -3.42912 q^{79} +27.9669 q^{80} -5.10722 q^{81} +1.64077 q^{82} +0.607703 q^{83} +3.32611 q^{84} -7.65965 q^{85} +5.68212 q^{86} +9.60119 q^{87} -12.3267 q^{88} -6.94814 q^{89} -41.4326 q^{90} +0.763893 q^{91} -8.19717 q^{92} -21.6686 q^{93} +2.17108 q^{94} +5.51925 q^{95} +12.9974 q^{96} -3.35310 q^{97} +17.5556 q^{98} +7.93147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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