LMFDB - Embedded newform 2671.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} +O(q^{10})$	\(q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} -0.764466 q^{10} +0.901782 q^{11} -4.12299 q^{12} +0.278911 q^{13} +7.30756 q^{14} -0.382069 q^{15} +1.31691 q^{16} +4.78193 q^{17} +3.81052 q^{18} -6.54262 q^{19} +1.14386 q^{20} +3.65222 q^{21} -2.11743 q^{22} +0.624344 q^{23} +4.17002 q^{24} -4.89400 q^{25} -0.654898 q^{26} +5.42501 q^{27} -10.9342 q^{28} +4.53032 q^{29} +0.897119 q^{30} +10.5723 q^{31} +4.01465 q^{32} -1.05826 q^{33} -11.2282 q^{34} -1.01325 q^{35} -5.70161 q^{36} +2.02104 q^{37} +15.3624 q^{38} -0.327309 q^{39} -1.15690 q^{40} -5.23071 q^{41} -8.57560 q^{42} +7.56540 q^{43} +3.16827 q^{44} -0.528357 q^{45} -1.46599 q^{46} -10.7040 q^{47} -1.54543 q^{48} +2.68568 q^{49} +11.4914 q^{50} -5.61170 q^{51} +0.979913 q^{52} +1.60569 q^{53} -12.7382 q^{54} +0.293597 q^{55} +11.0589 q^{56} +7.67792 q^{57} -10.6374 q^{58} +8.21823 q^{59} -1.34234 q^{60} -12.1066 q^{61} -24.8243 q^{62} +5.05058 q^{63} -12.0604 q^{64} +0.0908065 q^{65} +2.48486 q^{66} +11.3945 q^{67} +16.8006 q^{68} -0.732683 q^{69} +2.37916 q^{70} -3.12791 q^{71} +5.76664 q^{72} -2.36889 q^{73} -4.74550 q^{74} +5.74322 q^{75} -22.9865 q^{76} -2.80651 q^{77} +0.768539 q^{78} +13.5492 q^{79} +0.428754 q^{80} -1.49785 q^{81} +12.2820 q^{82} -12.4417 q^{83} +12.8315 q^{84} +1.55687 q^{85} -17.7640 q^{86} -5.31644 q^{87} -3.20441 q^{88} -4.77624 q^{89} +1.24061 q^{90} -0.868023 q^{91} +2.19354 q^{92} -12.4068 q^{93} +25.1335 q^{94} -2.13011 q^{95} -4.71129 q^{96} +13.8789 q^{97} -6.30611 q^{98} -1.46345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	−2.34805	−1.66032	−0.830162	−	0.557523i	$-0.811752\pi$
$2$	−2.34805	−1.66032	−0.830162	+	0.557523i	$0.811752\pi$
$3$	−1.17352	−0.677534	−0.338767	−	0.940870i	$-0.610010\pi$
$3$	−1.17352	−0.677534	−0.338767	+	0.940870i	$0.610010\pi$
$4$	3.51335	1.75667
$5$	0.325575	0.145601	0.0728007	−	0.997347i	$-0.476806\pi$
$5$	0.325575	0.145601	0.0728007	+	0.997347i	$0.476806\pi$
$6$	2.75549	1.12493
$7$	−3.11218	−1.17629	−0.588147	−	0.808754i	$-0.700142\pi$
$7$	−3.11218	−1.17629	−0.588147	+	0.808754i	$0.700142\pi$
$8$	−3.55342	−1.25632
$9$	−1.62284	−0.540948
$10$	−0.764466	−0.241745
$11$	0.901782	0.271898	0.135949	−	0.990716i	$-0.456592\pi$
$11$	0.901782	0.271898	0.135949	+	0.990716i	$0.456592\pi$
$12$	−4.12299	−1.19021
$13$	0.278911	0.0773561	0.0386781	−	0.999252i	$-0.487685\pi$
$13$	0.278911	0.0773561	0.0386781	+	0.999252i	$0.487685\pi$
$14$	7.30756	1.95303
$15$	−0.382069	−0.0986499
$16$	1.31691	0.329228
$17$	4.78193	1.15979	0.579894	−	0.814692i	$-0.303094\pi$
$17$	4.78193	1.15979	0.579894	+	0.814692i	$0.303094\pi$
$18$	3.81052	0.898148
$19$	−6.54262	−1.50098	−0.750490	−	0.660881i	$-0.770183\pi$
$19$	−6.54262	−1.50098	−0.750490	+	0.660881i	$0.770183\pi$
$20$	1.14386	0.255774
$21$	3.65222	0.796979
$22$	−2.11743	−0.451438
$23$	0.624344	0.130185	0.0650924	−	0.997879i	$-0.479266\pi$
$23$	0.624344	0.130185	0.0650924	+	0.997879i	$0.479266\pi$
$24$	4.17002	0.851201
$25$	−4.89400	−0.978800
$26$	−0.654898	−0.128436
$27$	5.42501	1.04404
$28$	−10.9342	−2.06637
$29$	4.53032	0.841260	0.420630	−	0.907232i	$-0.361809\pi$
$29$	4.53032	0.841260	0.420630	+	0.907232i	$0.361809\pi$
$30$	0.897119	0.163791
$31$	10.5723	1.89884	0.949419	−	0.314013i	$-0.101674\pi$
$31$	10.5723	1.89884	0.949419	+	0.314013i	$0.101674\pi$
$32$	4.01465	0.709697
$33$	−1.05826	−0.184220
$34$	−11.2282	−1.92562
$35$	−1.01325	−0.171270
$36$	−5.70161	−0.950268
$37$	2.02104	0.332257	0.166128	−	0.986104i	$-0.446873\pi$
$37$	2.02104	0.332257	0.166128	+	0.986104i	$0.446873\pi$
$38$	15.3624	2.49211
$39$	−0.327309	−0.0524114
$40$	−1.15690	−0.182922
$41$	−5.23071	−0.816900	−0.408450	−	0.912781i	$-0.633931\pi$
$41$	−5.23071	−0.816900	−0.408450	+	0.912781i	$0.633931\pi$
$42$	−8.57560	−1.32324
$43$	7.56540	1.15371	0.576856	−	0.816846i	$-0.304279\pi$
$43$	7.56540	1.15371	0.576856	+	0.816846i	$0.304279\pi$
$44$	3.16827	0.477635
$45$	−0.528357	−0.0787627
$46$	−1.46599	−0.216149
$47$	−10.7040	−1.56134	−0.780669	−	0.624945i	$-0.785121\pi$
$47$	−10.7040	−1.56134	−0.780669	+	0.624945i	$0.785121\pi$
$48$	−1.54543	−0.223063
$49$	2.68568	0.383668
$50$	11.4914	1.62512
$51$	−5.61170	−0.785796
$52$	0.979913	0.135889
$53$	1.60569	0.220558	0.110279	−	0.993901i	$-0.464825\pi$
$53$	1.60569	0.220558	0.110279	+	0.993901i	$0.464825\pi$
$54$	−12.7382	−1.73345
$55$	0.293597	0.0395887
$56$	11.0589	1.47781
$57$	7.67792	1.01697
$58$	−10.6374	−1.39676
$59$	8.21823	1.06992	0.534961	−	0.844876i	$-0.320326\pi$
$59$	8.21823	1.06992	0.534961	+	0.844876i	$0.320326\pi$
$60$	−1.34234	−0.173296
$61$	−12.1066	−1.55009	−0.775046	−	0.631905i	$-0.782273\pi$
$61$	−12.1066	−1.55009	−0.775046	+	0.631905i	$0.782273\pi$
$62$	−24.8243	−3.15268
$63$	5.05058	0.636314
$64$	−12.0604	−1.50756
$65$	0.0908065	0.0112632
$66$	2.48486	0.305865
$67$	11.3945	1.39206	0.696030	−	0.718012i	$-0.254948\pi$
$67$	11.3945	1.39206	0.696030	+	0.718012i	$0.254948\pi$
$68$	16.8006	2.03737
$69$	−0.732683	−0.0882046
$70$	2.37916	0.284364
$71$	−3.12791	−0.371215	−0.185607	−	0.982624i	$-0.559425\pi$
$71$	−3.12791	−0.371215	−0.185607	+	0.982624i	$0.559425\pi$
$72$	5.76664	0.679605
$73$	−2.36889	−0.277257	−0.138629	−	0.990344i	$-0.544269\pi$
$73$	−2.36889	−0.277257	−0.138629	+	0.990344i	$0.544269\pi$
$74$	−4.74550	−0.551654
$75$	5.74322	0.663170
$76$	−22.9865	−2.63673
$77$	−2.80651	−0.319832
$78$	0.768539	0.0870199
$79$	13.5492	1.52440	0.762202	−	0.647340i	$-0.224119\pi$
$79$	13.5492	1.52440	0.762202	+	0.647340i	$0.224119\pi$
$80$	0.428754	0.0479361
$81$	−1.49785	−0.166428
$82$	12.2820	1.35632
$83$	−12.4417	−1.36565	−0.682826	−	0.730581i	$-0.739249\pi$
$83$	−12.4417	−1.36565	−0.682826	+	0.730581i	$0.739249\pi$
$84$	12.8315	1.40003
$85$	1.55687	0.168867
$86$	−17.7640	−1.91554
$87$	−5.31644	−0.569982
$88$	−3.20441	−0.341591
$89$	−4.77624	−0.506281	−0.253140	−	0.967430i	$-0.581463\pi$
$89$	−4.77624	−0.506281	−0.253140	+	0.967430i	$0.581463\pi$
$90$	1.24061	0.130772
$91$	−0.868023	−0.0909936
$92$	2.19354	0.228692
$93$	−12.4068	−1.28653
$94$	25.1335	2.59233
$95$	−2.13011	−0.218545
$96$	−4.71129	−0.480844
$97$	13.8789	1.40918	0.704592	−	0.709612i	$-0.251130\pi$
$97$	13.8789	1.40918	0.704592	+	0.709612i	$0.251130\pi$
$98$	−6.30611	−0.637013
$99$	−1.46345	−0.147082
$100$	−17.1943	−1.71943
$101$	−12.4264	−1.23647	−0.618237	−	0.785992i	$-0.712153\pi$
$101$	−12.4264	−1.23647	−0.618237	+	0.785992i	$0.712153\pi$
$102$	13.1766	1.30467
$103$	14.4547	1.42427	0.712133	−	0.702044i	$-0.247729\pi$
$103$	14.4547	1.42427	0.712133	+	0.702044i	$0.247729\pi$
$104$	−0.991089	−0.0971842
$105$	1.18907	0.116041
$106$	−3.77024	−0.366198
$107$	−8.28486	−0.800927	−0.400464	−	0.916313i	$-0.631151\pi$
$107$	−8.28486	−0.800927	−0.400464	+	0.916313i	$0.631151\pi$
$108$	19.0600	1.83405
$109$	2.46382	0.235991	0.117996	−	0.993014i	$-0.462353\pi$
$109$	2.46382	0.235991	0.117996	+	0.993014i	$0.462353\pi$
$110$	−0.689382	−0.0657300
$111$	−2.37174	−0.225115
$112$	−4.09847	−0.387269
$113$	−5.48211	−0.515713	−0.257857	−	0.966183i	$-0.583016\pi$
$113$	−5.48211	−0.515713	−0.257857	+	0.966183i	$0.583016\pi$
$114$	−18.0282	−1.68849
$115$	0.203271	0.0189551
$116$	15.9166	1.47782
$117$	−0.452629	−0.0418456
$118$	−19.2968	−1.77642
$119$	−14.8822	−1.36425
$120$	1.35765	0.123936
$121$	−10.1868	−0.926072
$122$	28.4269	2.57365
$123$	6.13836	0.553477
$124$	37.1441	3.33564
$125$	−3.22124	−0.288116
$126$	−11.8590	−1.05649
$127$	10.8580	0.963489	0.481744	−	0.876312i	$-0.340003\pi$
$127$	10.8580	0.963489	0.481744	+	0.876312i	$0.340003\pi$
$128$	20.2892	1.79333
$129$	−8.87817	−0.781680
$130$	−0.213218	−0.0187005
$131$	9.97166	0.871228	0.435614	−	0.900134i	$-0.356531\pi$
$131$	9.97166	0.871228	0.435614	+	0.900134i	$0.356531\pi$
$132$	−3.71804	−0.323614
$133$	20.3618	1.76559
$134$	−26.7549	−2.31127
$135$	1.76625	0.152014
$136$	−16.9922	−1.45707
$137$	20.5105	1.75233	0.876166	−	0.482009i	$-0.160093\pi$
$137$	20.5105	1.75233	0.876166	+	0.482009i	$0.160093\pi$
$138$	1.72038	0.146448
$139$	1.58378	0.134334	0.0671671	−	0.997742i	$-0.478604\pi$
$139$	1.58378	0.134334	0.0671671	+	0.997742i	$0.478604\pi$
$140$	−3.55989	−0.300866
$141$	12.5614	1.05786
$142$	7.34450	0.616337
$143$	0.251517	0.0210329
$144$	−2.13714	−0.178095
$145$	1.47496	0.122489
$146$	5.56227	0.460337
$147$	−3.15171	−0.259948
$148$	7.10061	0.583667
$149$	2.07286	0.169816	0.0849078	−	0.996389i	$-0.472940\pi$
$149$	2.07286	0.169816	0.0849078	+	0.996389i	$0.472940\pi$
$150$	−13.4854	−1.10108
$151$	1.07759	0.0876927	0.0438463	−	0.999038i	$-0.486039\pi$
$151$	1.07759	0.0876927	0.0438463	+	0.999038i	$0.486039\pi$
$152$	23.2487	1.88572
$153$	−7.76032	−0.627384
$154$	6.58983	0.531024
$155$	3.44207	0.276473
$156$	−1.14995	−0.0920697
$157$	−5.99232	−0.478239	−0.239119	−	0.970990i	$-0.576859\pi$
$157$	−5.99232	−0.478239	−0.239119	+	0.970990i	$0.576859\pi$
$158$	−31.8142	−2.53100
$159$	−1.88431	−0.149436
$160$	1.30707	0.103333
$161$	−1.94307	−0.153136
$162$	3.51703	0.276324
$163$	5.29279	0.414563	0.207282	−	0.978281i	$-0.433538\pi$
$163$	5.29279	0.414563	0.207282	+	0.978281i	$0.433538\pi$
$164$	−18.3773	−1.43503
$165$	−0.344543	−0.0268227
$166$	29.2137	2.26742
$167$	−0.147895	−0.0114445	−0.00572224	−	0.999984i	$-0.501821\pi$
$167$	−0.147895	−0.0114445	−0.00572224	+	0.999984i	$0.501821\pi$
$168$	−12.9779	−1.00126
$169$	−12.9222	−0.994016
$170$	−3.65562	−0.280373
$171$	10.6176	0.811952
$172$	26.5799	2.02670
$173$	−7.71964	−0.586913	−0.293457	−	0.955972i	$-0.594806\pi$
$173$	−7.71964	−0.586913	−0.293457	+	0.955972i	$0.594806\pi$
$174$	12.4833	0.946354
$175$	15.2310	1.15136
$176$	1.18757	0.0895164
$177$	−9.64429	−0.724909
$178$	11.2149	0.840590
$179$	−8.01095	−0.598766	−0.299383	−	0.954133i	$-0.596781\pi$
$179$	−8.01095	−0.598766	−0.299383	+	0.954133i	$0.596781\pi$
$180$	−1.85630	−0.138360
$181$	5.11607	0.380275	0.190137	−	0.981757i	$-0.439107\pi$
$181$	5.11607	0.380275	0.190137	+	0.981757i	$0.439107\pi$
$182$	2.03816	0.151079
$183$	14.2074	1.05024
$184$	−2.21856	−0.163554
$185$	0.657999	0.0483770
$186$	29.1318	2.13605
$187$	4.31226	0.315343
$188$	−37.6068	−2.74276
$189$	−16.8836	−1.22810
$190$	5.00161	0.362855
$191$	2.05663	0.148813	0.0744063	−	0.997228i	$-0.476294\pi$
$191$	2.05663	0.148813	0.0744063	+	0.997228i	$0.476294\pi$
$192$	14.1532	1.02142
$193$	−1.33651	−0.0962042	−0.0481021	−	0.998842i	$-0.515317\pi$
$193$	−1.33651	−0.0962042	−0.0481021	+	0.998842i	$0.515317\pi$
$194$	−32.5883	−2.33970
$195$	−0.106564	−0.00763117
$196$	9.43572	0.673980
$197$	−27.3001	−1.94505	−0.972525	−	0.232796i	$-0.925212\pi$
$197$	−27.3001	−1.94505	−0.972525	+	0.232796i	$0.925212\pi$
$198$	3.43626	0.244204
$199$	2.87597	0.203872	0.101936	−	0.994791i	$-0.467496\pi$
$199$	2.87597	0.203872	0.101936	+	0.994791i	$0.467496\pi$
$200$	17.3904	1.22969
$201$	−13.3717	−0.943168
$202$	29.1778	2.05295
$203$	−14.0992	−0.989569
$204$	−19.7159	−1.38039
$205$	−1.70299	−0.118942
$206$	−33.9405	−2.36474
$207$	−1.01321	−0.0704232
$208$	0.367302	0.0254678
$209$	−5.90002	−0.408113
$210$	−2.79200	−0.192666
$211$	−7.27685	−0.500959	−0.250479	−	0.968122i	$-0.580588\pi$
$211$	−7.27685	−0.500959	−0.250479	+	0.968122i	$0.580588\pi$
$212$	5.64134	0.387449
$213$	3.67068	0.251511
$214$	19.4533	1.32980
$215$	2.46310	0.167982
$216$	−19.2773	−1.31166
$217$	−32.9029	−2.23359
$218$	−5.78518	−0.391822
$219$	2.77994	0.187851
$220$	1.03151	0.0695444
$221$	1.33373	0.0897167
$222$	5.56896	0.373764
$223$	−14.5339	−0.973262	−0.486631	−	0.873608i	$-0.661774\pi$
$223$	−14.5339	−0.973262	−0.486631	+	0.873608i	$0.661774\pi$
$224$	−12.4943	−0.834813
$225$	7.94220	0.529480
$226$	12.8723	0.856250
$227$	12.4510	0.826401	0.413200	−	0.910640i	$-0.364411\pi$
$227$	12.4510	0.826401	0.413200	+	0.910640i	$0.364411\pi$
$228$	26.9752	1.78648
$229$	−28.0256	−1.85198	−0.925992	−	0.377543i	$-0.876769\pi$
$229$	−28.0256	−1.85198	−0.925992	+	0.377543i	$0.876769\pi$
$230$	−0.477290	−0.0314716
$231$	3.29351	0.216697
$232$	−16.0981	−1.05689
$233$	−3.74643	−0.245437	−0.122718	−	0.992442i	$-0.539161\pi$
$233$	−3.74643	−0.245437	−0.122718	+	0.992442i	$0.539161\pi$
$234$	1.06280	0.0694772
$235$	−3.48495	−0.227333
$236$	28.8735	1.87951
$237$	−15.9003	−1.03283
$238$	34.9442	2.26510
$239$	−9.38154	−0.606842	−0.303421	−	0.952857i	$-0.598129\pi$
$239$	−9.38154	−0.606842	−0.303421	+	0.952857i	$0.598129\pi$
$240$	−0.503152	−0.0324783
$241$	−27.5267	−1.77315	−0.886576	−	0.462583i	$-0.846923\pi$
$241$	−27.5267	−1.77315	−0.886576	+	0.462583i	$0.846923\pi$
$242$	23.9191	1.53758
$243$	−14.5173	−0.931284
$244$	−42.5347	−2.72301
$245$	0.874389	0.0558626
$246$	−14.4132	−0.918951
$247$	−1.82481	−0.116110
$248$	−37.5677	−2.38555
$249$	14.6006	0.925275
$250$	7.56363	0.478366
$251$	−23.5481	−1.48634	−0.743170	−	0.669103i	$-0.766679\pi$
$251$	−23.5481	−1.48634	−0.743170	+	0.669103i	$0.766679\pi$
$252$	17.7445	1.11780
$253$	0.563023	0.0353969
$254$	−25.4951	−1.59970
$255$	−1.82703	−0.114413
$256$	−23.5193	−1.46996
$257$	6.13326	0.382582	0.191291	−	0.981533i	$-0.438733\pi$
$257$	6.13326	0.382582	0.191291	+	0.981533i	$0.438733\pi$
$258$	20.8464	1.29784
$259$	−6.28984	−0.390832
$260$	0.319035	0.0197857
$261$	−7.35200	−0.455077
$262$	−23.4140	−1.44652
$263$	−4.86356	−0.299900	−0.149950	−	0.988694i	$-0.547911\pi$
$263$	−4.86356	−0.299900	−0.149950	+	0.988694i	$0.547911\pi$
$264$	3.76045	0.231440
$265$	0.522772	0.0321136
$266$	−47.8106	−2.93146
$267$	5.60503	0.343022
$268$	40.0329	2.44540
$269$	−5.96648	−0.363783	−0.181891	−	0.983319i	$-0.558222\pi$
$269$	−5.96648	−0.363783	−0.181891	+	0.983319i	$0.558222\pi$
$270$	−4.14724	−0.252393
$271$	−23.8283	−1.44747	−0.723735	−	0.690078i	$-0.757576\pi$
$271$	−23.8283	−1.44747	−0.723735	+	0.690078i	$0.757576\pi$
$272$	6.29738	0.381835
$273$	1.01865	0.0616512
$274$	−48.1598	−2.90944
$275$	−4.41332	−0.266133
$276$	−2.57417	−0.154947
$277$	6.80659	0.408968	0.204484	−	0.978870i	$-0.434448\pi$
$277$	6.80659	0.408968	0.204484	+	0.978870i	$0.434448\pi$
$278$	−3.71879	−0.223038
$279$	−17.1571	−1.02717
$280$	3.60049	0.215171
$281$	−27.1593	−1.62019	−0.810094	−	0.586300i	$-0.800584\pi$
$281$	−27.1593	−1.62019	−0.810094	+	0.586300i	$0.800584\pi$
$282$	−29.4948	−1.75639
$283$	0.271762	0.0161546	0.00807729	−	0.999967i	$-0.497429\pi$
$283$	0.271762	0.0161546	0.00807729	+	0.999967i	$0.497429\pi$
$284$	−10.9894	−0.652103
$285$	2.49974	0.148072
$286$	−0.590576	−0.0349215
$287$	16.2789	0.960914
$288$	−6.51515	−0.383909
$289$	5.86683	0.345107
$290$	−3.46328	−0.203371
$291$	−16.2872	−0.954771
$292$	−8.32272	−0.487050
$293$	18.0364	1.05370	0.526849	−	0.849959i	$-0.323373\pi$
$293$	18.0364	1.05370	0.526849	+	0.849959i	$0.323373\pi$
$294$	7.40037	0.431598
$295$	2.67565	0.155782
$296$	−7.18159	−0.417422
$297$	4.89218	0.283873
$298$	−4.86719	−0.281949
$299$	0.174137	0.0100706
$300$	20.1779	1.16497
$301$	−23.5449	−1.35711
$302$	−2.53023	−0.145598
$303$	14.5827	0.837753
$304$	−8.61607	−0.494165
$305$	−3.94160	−0.225696
$306$	18.2216	1.04166
$307$	17.4149	0.993921	0.496961	−	0.867773i	$-0.334449\pi$
$307$	17.4149	0.993921	0.496961	+	0.867773i	$0.334449\pi$
$308$	−9.86025	−0.561840
$309$	−16.9630	−0.964989
$310$	−8.08215	−0.459035
$311$	−26.0417	−1.47669	−0.738345	−	0.674424i	$-0.764392\pi$
$311$	−26.0417	−1.47669	−0.738345	+	0.674424i	$0.764392\pi$
$312$	1.16307	0.0658456
$313$	−3.55307	−0.200832	−0.100416	−	0.994946i	$-0.532017\pi$
$313$	−3.55307	−0.200832	−0.100416	+	0.994946i	$0.532017\pi$
$314$	14.0703	0.794031
$315$	1.64434	0.0926482
$316$	47.6030	2.67788
$317$	−19.1080	−1.07321	−0.536605	−	0.843834i	$-0.680293\pi$
$317$	−19.1080	−1.07321	−0.536605	+	0.843834i	$0.680293\pi$
$318$	4.42447	0.248112
$319$	4.08536	0.228736
$320$	−3.92657	−0.219502
$321$	9.72247	0.542656
$322$	4.56244	0.254255
$323$	−31.2863	−1.74082
$324$	−5.26247	−0.292360
$325$	−1.36499	−0.0757162
$326$	−12.4277	−0.688309
$327$	−2.89135	−0.159892
$328$	18.5869	1.02629
$329$	33.3128	1.83659
$330$	0.809006	0.0445343
$331$	−18.4441	−1.01378	−0.506891	−	0.862010i	$-0.669205\pi$
$331$	−18.4441	−1.01378	−0.506891	+	0.862010i	$0.669205\pi$
$332$	−43.7119	−2.39900
$333$	−3.27983	−0.179733
$334$	0.347266	0.0190015
$335$	3.70976	0.202686
$336$	4.80966	0.262388
$337$	−1.17361	−0.0639307	−0.0319653	−	0.999489i	$-0.510177\pi$
$337$	−1.17361	−0.0639307	−0.0319653	+	0.999489i	$0.510177\pi$
$338$	30.3420	1.65039
$339$	6.43338	0.349413
$340$	5.46984	0.296644
$341$	9.53389	0.516289
$342$	−24.9308	−1.34810
$343$	13.4270	0.724987
$344$	−26.8830	−1.44944
$345$	−0.238543	−0.0128427
$346$	18.1261	0.974466
$347$	19.5628	1.05018	0.525092	−	0.851045i	$-0.324031\pi$
$347$	19.5628	1.05018	0.525092	+	0.851045i	$0.324031\pi$
$348$	−18.6785	−1.00127
$349$	−5.17091	−0.276792	−0.138396	−	0.990377i	$-0.544195\pi$
$349$	−5.17091	−0.276792	−0.138396	+	0.990377i	$0.544195\pi$
$350$	−35.7632	−1.91163
$351$	1.51310	0.0807632
$352$	3.62034	0.192965
$353$	−9.92715	−0.528369	−0.264185	−	0.964472i	$-0.585103\pi$
$353$	−9.92715	−0.528369	−0.264185	+	0.964472i	$0.585103\pi$
$354$	22.6453	1.20358
$355$	−1.01837	−0.0540494
$356$	−16.7806	−0.889370
$357$	17.4646	0.924327
$358$	18.8101	0.994146
$359$	36.6829	1.93605	0.968026	−	0.250851i	$-0.0807104\pi$
$359$	36.6829	1.93605	0.968026	+	0.250851i	$0.0807104\pi$
$360$	1.87747	0.0989514
$361$	23.8059	1.25294
$362$	−12.0128	−0.631379
$363$	11.9544	0.627445
$364$	−3.04967	−0.159846
$365$	−0.771249	−0.0403690
$366$	−33.3597	−1.74374
$367$	−26.5453	−1.38565	−0.692827	−	0.721103i	$-0.743635\pi$
$367$	−26.5453	−1.38565	−0.692827	+	0.721103i	$0.743635\pi$
$368$	0.822208	0.0428605
$369$	8.48862	0.441900
$370$	−1.54502	−0.0803215
$371$	−4.99720	−0.259442
$372$	−43.5895	−2.26001
$373$	7.71020	0.399219	0.199610	−	0.979876i	$-0.436033\pi$
$373$	7.71020	0.399219	0.199610	+	0.979876i	$0.436033\pi$
$374$	−10.1254	−0.523572
$375$	3.78020	0.195208
$376$	38.0358	1.96154
$377$	1.26356	0.0650766
$378$	39.6436	2.03905
$379$	6.38638	0.328046	0.164023	−	0.986457i	$-0.447553\pi$
$379$	6.38638	0.328046	0.164023	+	0.986457i	$0.447553\pi$
$380$	−7.48382	−0.383912
$381$	−12.7421	−0.652796
$382$	−4.82907	−0.247077
$383$	−38.6132	−1.97304	−0.986522	−	0.163630i	$-0.947680\pi$
$383$	−38.6132	−1.97304	−0.986522	+	0.163630i	$0.947680\pi$
$384$	−23.8099	−1.21504
$385$	−0.913729	−0.0465679
$386$	3.13820	0.159730
$387$	−12.2775	−0.624098
$388$	48.7613	2.47548
$389$	7.80422	0.395690	0.197845	−	0.980233i	$-0.436606\pi$
$389$	7.80422	0.395690	0.197845	+	0.980233i	$0.436606\pi$
$390$	0.250217	0.0126702
$391$	2.98557	0.150987
$392$	−9.54334	−0.482011
$393$	−11.7020	−0.590287
$394$	64.1020	3.22941
$395$	4.41127	0.221955
$396$	−5.14161	−0.258376
$397$	−34.1848	−1.71568	−0.857842	−	0.513913i	$-0.828195\pi$
$397$	−34.1848	−1.71568	−0.857842	+	0.513913i	$0.828195\pi$
$398$	−6.75293	−0.338494
$399$	−23.8951	−1.19625
$400$	−6.44498	−0.322249
$401$	−29.4431	−1.47032	−0.735159	−	0.677894i	$-0.762893\pi$
$401$	−29.4431	−1.47032	−0.735159	+	0.677894i	$0.762893\pi$
$402$	31.3975	1.56596
$403$	2.94873	0.146887
$404$	−43.6583	−2.17208
$405$	−0.487663	−0.0242321
$406$	33.1056	1.64300
$407$	1.82254	0.0903398
$408$	19.9407	0.987213
$409$	5.74323	0.283985	0.141992	−	0.989868i	$-0.454649\pi$
$409$	5.74323	0.283985	0.141992	+	0.989868i	$0.454649\pi$
$410$	3.99870	0.197482
$411$	−24.0696	−1.18726
$412$	50.7845	2.50197
$413$	−25.5766	−1.25854
$414$	2.37908	0.116925
$415$	−4.05069	−0.198841
$416$	1.11973	0.0548994
$417$	−1.85860	−0.0910161
$418$	13.8536	0.677599
$419$	34.8874	1.70436	0.852181	−	0.523247i	$-0.175280\pi$
$419$	34.8874	1.70436	0.852181	+	0.523247i	$0.175280\pi$
$420$	4.17761	0.203847
$421$	25.5550	1.24547	0.622737	−	0.782432i	$-0.286021\pi$
$421$	25.5550	1.24547	0.622737	+	0.782432i	$0.286021\pi$
$422$	17.0864	0.831754
$423$	17.3709	0.844602
$424$	−5.70568	−0.277093
$425$	−23.4028	−1.13520
$426$	−8.61894	−0.417589
$427$	37.6780	1.82336
$428$	−29.1076	−1.40697
$429$	−0.295162	−0.0142505
$430$	−5.78349	−0.278905
$431$	−33.3519	−1.60650	−0.803251	−	0.595640i	$-0.796898\pi$
$431$	−33.3519	−1.60650	−0.803251	+	0.595640i	$0.796898\pi$
$432$	7.14427	0.343729
$433$	7.09935	0.341173	0.170586	−	0.985343i	$-0.445434\pi$
$433$	7.09935	0.341173	0.170586	+	0.985343i	$0.445434\pi$
$434$	77.2576	3.70848
$435$	−1.73090	−0.0829902
$436$	8.65626	0.414560
$437$	−4.08485	−0.195405
$438$	−6.52745	−0.311894
$439$	24.6379	1.17591	0.587953	−	0.808895i	$-0.299934\pi$
$439$	24.6379	1.17591	0.587953	+	0.808895i	$0.299934\pi$
$440$	−1.04327	−0.0497361
$441$	−4.35843	−0.207544
$442$	−3.13168	−0.148959
$443$	13.5680	0.644635	0.322318	−	0.946632i	$-0.395538\pi$
$443$	13.5680	0.644635	0.322318	+	0.946632i	$0.395538\pi$
$444$	−8.33273	−0.395454
$445$	−1.55502	−0.0737152
$446$	34.1264	1.61593
$447$	−2.43255	−0.115056
$448$	37.5343	1.77333
$449$	20.3828	0.961922	0.480961	−	0.876742i	$-0.340288\pi$
$449$	20.3828	0.961922	0.480961	+	0.876742i	$0.340288\pi$
$450$	−18.6487	−0.879107
$451$	−4.71696	−0.222113
$452$	−19.2605	−0.905940
$453$	−1.26457	−0.0594148
$454$	−29.2356	−1.37209
$455$	−0.282606	−0.0132488
$456$	−27.2829	−1.27764
$457$	0.759564	0.0355309	0.0177654	−	0.999842i	$-0.494345\pi$
$457$	0.759564	0.0355309	0.0177654	+	0.999842i	$0.494345\pi$
$458$	65.8056	3.07489
$459$	25.9420	1.21087
$460$	0.714161	0.0332979
$461$	−17.9079	−0.834055	−0.417028	−	0.908894i	$-0.636928\pi$
$461$	−17.9079	−0.834055	−0.417028	+	0.908894i	$0.636928\pi$
$462$	−7.73332	−0.359787
$463$	14.5297	0.675253	0.337626	−	0.941280i	$-0.390376\pi$
$463$	14.5297	0.675253	0.337626	+	0.941280i	$0.390376\pi$
$464$	5.96604	0.276966
$465$	−4.03934	−0.187320
$466$	8.79681	0.407504
$467$	17.9017	0.828391	0.414196	−	0.910188i	$-0.364063\pi$
$467$	17.9017	0.828391	0.414196	+	0.910188i	$0.364063\pi$
$468$	−1.59024	−0.0735091
$469$	−35.4618	−1.63747
$470$	8.18284	0.377446
$471$	7.03212	0.324023
$472$	−29.2028	−1.34417
$473$	6.82234	0.313692
$474$	37.3347	1.71484
$475$	32.0196	1.46916
$476$	−52.2864	−2.39654
$477$	−2.60578	−0.119311
$478$	22.0283	1.00755
$479$	−35.7490	−1.63341	−0.816706	−	0.577053i	$-0.804202\pi$
$479$	−35.7490	−1.63341	−0.816706	+	0.577053i	$0.804202\pi$
$480$	−1.53388	−0.0700116
$481$	0.563691	0.0257021
$482$	64.6342	2.94401
$483$	2.28024	0.103755
$484$	−35.7897	−1.62681
$485$	4.51861	0.205179
$486$	34.0873	1.54623
$487$	−36.3886	−1.64893	−0.824463	−	0.565915i	$-0.808523\pi$
$487$	−36.3886	−1.64893	−0.824463	+	0.565915i	$0.808523\pi$
$488$	43.0198	1.94742
$489$	−6.21121	−0.280881
$490$	−2.05311	−0.0927501
$491$	−23.0643	−1.04088	−0.520439	−	0.853899i	$-0.674232\pi$
$491$	−23.0643	−1.04088	−0.520439	+	0.853899i	$0.674232\pi$
$492$	21.5662	0.972279
$493$	21.6637	0.975682
$494$	4.28475	0.192780
$495$	−0.476463	−0.0214154
$496$	13.9228	0.625151
$497$	9.73463	0.436658
$498$	−34.2830	−1.53626
$499$	−37.3057	−1.67003	−0.835015	−	0.550227i	$-0.814541\pi$
$499$	−37.3057	−1.67003	−0.835015	+	0.550227i	$0.814541\pi$
$500$	−11.3173	−0.506126
$501$	0.173559	0.00775403
$502$	55.2920	2.46780
$503$	15.4181	0.687461	0.343730	−	0.939068i	$-0.388309\pi$
$503$	15.4181	0.687461	0.343730	+	0.939068i	$0.388309\pi$
$504$	−17.9468	−0.799415
$505$	−4.04572	−0.180032
$506$	−1.32201	−0.0587704
$507$	15.1645	0.673480
$508$	38.1478	1.69254
$509$	3.86699	0.171401	0.0857006	−	0.996321i	$-0.472687\pi$
$509$	3.86699	0.171401	0.0857006	+	0.996321i	$0.472687\pi$
$510$	4.28996	0.189962
$511$	7.37241	0.326136
$512$	14.6460	0.647270
$513$	−35.4938	−1.56709
$514$	−14.4012	−0.635211
$515$	4.70609	0.207375
$516$	−31.1921	−1.37316
$517$	−9.65267	−0.424524
$518$	14.7689	0.648907
$519$	9.05917	0.397654
$520$	−0.322673	−0.0141502
$521$	1.18885	0.0520844	0.0260422	−	0.999661i	$-0.491710\pi$
$521$	1.18885	0.0520844	0.0260422	+	0.999661i	$0.491710\pi$
$522$	17.2629	0.755576
$523$	−32.9351	−1.44015	−0.720075	−	0.693896i	$-0.755893\pi$
$523$	−32.9351	−1.44015	−0.720075	+	0.693896i	$0.755893\pi$
$524$	35.0339	1.53046
$525$	−17.8740	−0.780084
$526$	11.4199	0.497931
$527$	50.5559	2.20225
$528$	−1.39364	−0.0606504
$529$	−22.6102	−0.983052
$530$	−1.22750	−0.0533190
$531$	−13.3369	−0.578772
$532$	71.5382	3.10157
$533$	−1.45890	−0.0631922
$534$	−13.1609	−0.569528
$535$	−2.69734	−0.116616
$536$	−40.4894	−1.74888
$537$	9.40104	0.405685
$538$	14.0096	0.603997
$539$	2.42190	0.104318
$540$	6.20544	0.267040
$541$	−25.3091	−1.08812	−0.544062	−	0.839045i	$-0.683114\pi$
$541$	−25.3091	−1.08812	−0.544062	+	0.839045i	$0.683114\pi$
$542$	55.9502	2.40327
$543$	−6.00383	−0.257649
$544$	19.1978	0.823098
$545$	0.802158	0.0343607
$546$	−2.39183	−0.102361
$547$	−21.1335	−0.903604	−0.451802	−	0.892118i	$-0.649219\pi$
$547$	−21.1335	−0.903604	−0.451802	+	0.892118i	$0.649219\pi$
$548$	72.0606	3.07828
$549$	19.6471	0.838519
$550$	10.3627	0.441867
$551$	−29.6402	−1.26271
$552$	2.60353	0.110813
$553$	−42.1676	−1.79315
$554$	−15.9822	−0.679020
$555$	−0.772177	−0.0327771
$556$	5.56436	0.235981
$557$	−43.0616	−1.82458	−0.912290	−	0.409546i	$-0.865687\pi$
$557$	−43.0616	−1.82458	−0.912290	+	0.409546i	$0.865687\pi$
$558$	40.2859	1.70544
$559$	2.11008	0.0892467
$560$	−1.33436	−0.0563870
$561$	−5.06053	−0.213656
$562$	63.7714	2.69003
$563$	16.5865	0.699039	0.349520	−	0.936929i	$-0.386345\pi$
$563$	16.5865	0.699039	0.349520	+	0.936929i	$0.386345\pi$
$564$	44.1325	1.85831
$565$	−1.78483	−0.0750886
$566$	−0.638112	−0.0268218
$567$	4.66159	0.195768
$568$	11.1148	0.466366
$569$	28.8352	1.20884	0.604418	−	0.796667i	$-0.293406\pi$
$569$	28.8352	1.20884	0.604418	+	0.796667i	$0.293406\pi$
$570$	−5.86951	−0.245847
$571$	−35.5671	−1.48844	−0.744218	−	0.667937i	$-0.767178\pi$
$571$	−35.5671	−1.48844	−0.744218	+	0.667937i	$0.767178\pi$
$572$	0.883668	0.0369480
$573$	−2.41350	−0.100826
$574$	−38.2238	−1.59543
$575$	−3.05554	−0.127425
$576$	19.5722	0.815508
$577$	12.2153	0.508531	0.254266	−	0.967134i	$-0.418166\pi$
$577$	12.2153	0.508531	0.254266	+	0.967134i	$0.418166\pi$
$578$	−13.7756	−0.572990
$579$	1.56843	0.0651816
$580$	5.18204	0.215172
$581$	38.7208	1.60641
$582$	38.2431	1.58523
$583$	1.44798	0.0599693
$584$	8.41764	0.348324
$585$	−0.147365	−0.00609278
$586$	−42.3504	−1.74948
$587$	15.0470	0.621055	0.310528	−	0.950564i	$-0.399494\pi$
$587$	15.0470	0.621055	0.310528	+	0.950564i	$0.399494\pi$
$588$	−11.0730	−0.456644
$589$	−69.1704	−2.85012
$590$	−6.28256	−0.258649
$591$	32.0373	1.31784
$592$	2.66153	0.109388
$593$	32.5019	1.33469	0.667347	−	0.744747i	$-0.267430\pi$
$593$	32.5019	1.33469	0.667347	+	0.744747i	$0.267430\pi$
$594$	−11.4871	−0.471321
$595$	−4.84528	−0.198637
$596$	7.28269	0.298311
$597$	−3.37502	−0.138130
$598$	−0.408882	−0.0167204
$599$	6.73077	0.275012	0.137506	−	0.990501i	$-0.456091\pi$
$599$	6.73077	0.275012	0.137506	+	0.990501i	$0.456091\pi$
$600$	−20.4081	−0.833156
$601$	42.1103	1.71772	0.858858	−	0.512213i	$-0.171174\pi$
$601$	42.1103	1.71772	0.858858	+	0.512213i	$0.171174\pi$
$602$	55.2847	2.25323
$603$	−18.4915	−0.753032
$604$	3.78593	0.154047
$605$	−3.31656	−0.134837
$606$	−34.2409	−1.39094
$607$	27.2151	1.10463	0.552314	−	0.833636i	$-0.313745\pi$
$607$	27.2151	1.10463	0.552314	+	0.833636i	$0.313745\pi$
$608$	−26.2664	−1.06524
$609$	16.5457	0.670467
$610$	9.25509	0.374728
$611$	−2.98547	−0.120779
$612$	−27.2647	−1.10211
$613$	16.9023	0.682676	0.341338	−	0.939941i	$-0.389120\pi$
$613$	16.9023	0.682676	0.341338	+	0.939941i	$0.389120\pi$
$614$	−40.8911	−1.65023
$615$	1.99849	0.0805871
$616$	9.97270	0.401812
$617$	6.68079	0.268958	0.134479	−	0.990916i	$-0.457064\pi$
$617$	6.68079	0.268958	0.134479	+	0.990916i	$0.457064\pi$
$618$	39.8299	1.60219
$619$	30.2690	1.21661	0.608307	−	0.793702i	$-0.291849\pi$
$619$	30.2690	1.21661	0.608307	+	0.793702i	$0.291849\pi$
$620$	12.0932	0.485674
$621$	3.38708	0.135919
$622$	61.1473	2.45178
$623$	14.8645	0.595535
$624$	−0.431038	−0.0172553
$625$	23.4213	0.936850
$626$	8.34280	0.333445
$627$	6.92381	0.276510
$628$	−21.0531	−0.840110
$629$	9.66446	0.385347
$630$	−3.86100	−0.153826
$631$	17.3959	0.692518	0.346259	−	0.938139i	$-0.387452\pi$
$631$	17.3959	0.692518	0.346259	+	0.938139i	$0.387452\pi$
$632$	−48.1459	−1.91514
$633$	8.53955	0.339417
$634$	44.8665	1.78188
$635$	3.53508	0.140285
$636$	−6.62025	−0.262510
$637$	0.749066	0.0296791
$638$	−9.59264	−0.379776
$639$	5.07611	0.200808
$640$	6.60566	0.261112
$641$	17.7232	0.700023	0.350012	−	0.936745i	$-0.386178\pi$
$641$	17.7232	0.700023	0.350012	+	0.936745i	$0.386178\pi$
$642$	−22.8289	−0.900984
$643$	29.0692	1.14638	0.573189	−	0.819423i	$-0.305706\pi$
$643$	29.0692	1.14638	0.573189	+	0.819423i	$0.305706\pi$
$644$	−6.82669	−0.269009
$645$	−2.89051	−0.113814
$646$	73.4620	2.89032
$647$	−38.8368	−1.52683	−0.763416	−	0.645908i	$-0.776479\pi$
$647$	−38.8368	−1.52683	−0.763416	+	0.645908i	$0.776479\pi$
$648$	5.32249	0.209087
$649$	7.41106	0.290909
$650$	3.20507	0.125713
$651$	38.6123	1.51333
$652$	18.5954	0.728252
$653$	7.84953	0.307176	0.153588	−	0.988135i	$-0.450917\pi$
$653$	7.84953	0.307176	0.153588	+	0.988135i	$0.450917\pi$
$654$	6.78905	0.265473
$655$	3.24652	0.126852
$656$	−6.88839	−0.268947
$657$	3.84433	0.149982
$658$	−78.2201	−3.04934
$659$	−27.6785	−1.07820	−0.539100	−	0.842242i	$-0.681236\pi$
$659$	−27.6785	−1.07820	−0.539100	+	0.842242i	$0.681236\pi$
$660$	−1.21050	−0.0471187
$661$	13.3687	0.519983	0.259992	−	0.965611i	$-0.416280\pi$
$661$	13.3687	0.519983	0.259992	+	0.965611i	$0.416280\pi$
$662$	43.3078	1.68320
$663$	−1.56517	−0.0607861
$664$	44.2105	1.71570
$665$	6.62930	0.257073
$666$	7.70121	0.298416
$667$	2.82848	0.109519
$668$	−0.519608	−0.0201042
$669$	17.0559	0.659418
$670$	−8.71071	−0.336524
$671$	−10.9175	−0.421466
$672$	14.6624	0.565614
$673$	20.5707	0.792944	0.396472	−	0.918047i	$-0.370234\pi$
$673$	20.5707	0.792944	0.396472	+	0.918047i	$0.370234\pi$
$674$	2.75570	0.106146
$675$	−26.5500	−1.02191
$676$	−45.4002	−1.74616
$677$	−41.3070	−1.58756	−0.793778	−	0.608207i	$-0.791889\pi$
$677$	−41.3070	−1.58756	−0.793778	+	0.608207i	$0.791889\pi$
$678$	−15.1059	−0.580139
$679$	−43.1935	−1.65762
$680$	−5.53222	−0.212151
$681$	−14.6115	−0.559915
$682$	−22.3861	−0.857207
$683$	−46.8947	−1.79438	−0.897188	−	0.441648i	$-0.854394\pi$
$683$	−46.8947	−1.79438	−0.897188	+	0.441648i	$0.854394\pi$
$684$	37.3035	1.42633
$685$	6.67771	0.255142
$686$	−31.5272	−1.20371
$687$	32.8887	1.25478
$688$	9.96298	0.379835
$689$	0.447845	0.0170615
$690$	0.560111	0.0213231
$691$	−47.2198	−1.79633	−0.898163	−	0.439662i	$-0.855098\pi$
$691$	−47.2198	−1.79633	−0.898163	+	0.439662i	$0.855098\pi$
$692$	−27.1218	−1.03101
$693$	4.55453	0.173012
$694$	−45.9344	−1.74365
$695$	0.515638	0.0195593
$696$	18.8915	0.716081
$697$	−25.0129	−0.947430
$698$	12.1416	0.459565
$699$	4.39652	0.166292
$700$	53.5119	2.02256
$701$	−3.96292	−0.149678	−0.0748388	−	0.997196i	$-0.523844\pi$
$701$	−3.96292	−0.149678	−0.0748388	+	0.997196i	$0.523844\pi$
$702$	−3.55283	−0.134093
$703$	−13.2229	−0.498711
$704$	−10.8759	−0.409901
$705$	4.08967	0.154026
$706$	23.3095	0.877264
$707$	38.6732	1.45446
$708$	−33.8837	−1.27343
$709$	42.5890	1.59946	0.799731	−	0.600358i	$-0.204975\pi$
$709$	42.5890	1.59946	0.799731	+	0.600358i	$0.204975\pi$
$710$	2.39118	0.0897395
$711$	−21.9882	−0.824622
$712$	16.9720	0.636052
$713$	6.60074	0.247200
$714$	−41.0079	−1.53468
$715$	0.0818877	0.00306243
$716$	−28.1452	−1.05184
$717$	11.0095	0.411156
$718$	−86.1334	−3.21447
$719$	26.7342	0.997017	0.498508	−	0.866885i	$-0.333881\pi$
$719$	26.7342	0.997017	0.498508	+	0.866885i	$0.333881\pi$
$720$	−0.695800	−0.0259309
$721$	−44.9857	−1.67536
$722$	−55.8975	−2.08029
$723$	32.3032	1.20137
$724$	17.9745	0.668019
$725$	−22.1714	−0.823425
$726$	−28.0696	−1.04176
$727$	27.3724	1.01519	0.507594	−	0.861597i	$-0.330535\pi$
$727$	27.3724	1.01519	0.507594	+	0.861597i	$0.330535\pi$
$728$	3.08445	0.114317
$729$	21.5299	0.797404
$730$	1.81093	0.0670257
$731$	36.1772	1.33806
$732$	49.9155	1.84493
$733$	28.0429	1.03579	0.517895	−	0.855444i	$-0.326716\pi$
$733$	28.0429	1.03579	0.517895	+	0.855444i	$0.326716\pi$
$734$	62.3298	2.30063
$735$	−1.02612	−0.0378488
$736$	2.50653	0.0923918
$737$	10.2754	0.378498
$738$	−19.9317	−0.733697
$739$	8.35865	0.307478	0.153739	−	0.988111i	$-0.450868\pi$
$739$	8.35865	0.307478	0.153739	+	0.988111i	$0.450868\pi$
$740$	2.31178	0.0849827
$741$	2.14146	0.0786685
$742$	11.7337	0.430757
$743$	25.6522	0.941086	0.470543	−	0.882377i	$-0.344058\pi$
$743$	25.6522	0.941086	0.470543	+	0.882377i	$0.344058\pi$
$744$	44.0866	1.61629
$745$	0.674872	0.0247254
$746$	−18.1040	−0.662833
$747$	20.1909	0.738746
$748$	15.1505	0.553955
$749$	25.7840	0.942126
$750$	−8.87609	−0.324109
$751$	−15.6703	−0.571817	−0.285908	−	0.958257i	$-0.592295\pi$
$751$	−15.6703	−0.571817	−0.285908	+	0.958257i	$0.592295\pi$
$752$	−14.0962	−0.514037
$753$	27.6342	1.00705
$754$	−2.96690	−0.108048
$755$	0.350835	0.0127682
$756$	−59.3181	−2.15738
$757$	1.03102	0.0374729	0.0187364	−	0.999824i	$-0.494036\pi$
$757$	1.03102	0.0374729	0.0187364	+	0.999824i	$0.494036\pi$
$758$	−14.9955	−0.544663
$759$	−0.660720	−0.0239826
$760$	7.56918	0.274563
$761$	−2.42703	−0.0879798	−0.0439899	−	0.999032i	$-0.514007\pi$
$761$	−2.42703	−0.0879798	−0.0439899	+	0.999032i	$0.514007\pi$
$762$	29.9191	1.08385
$763$	−7.66786	−0.277595
$764$	7.22566	0.261415
$765$	−2.52656	−0.0913481
$766$	90.6658	3.27589
$767$	2.29216	0.0827651
$768$	27.6004	0.995945
$769$	−8.01305	−0.288958	−0.144479	−	0.989508i	$-0.546151\pi$
$769$	−8.01305	−0.288958	−0.144479	+	0.989508i	$0.546151\pi$
$770$	2.14548	0.0773178
$771$	−7.19753	−0.259213
$772$	−4.69563	−0.168999
$773$	25.4058	0.913784	0.456892	−	0.889522i	$-0.348963\pi$
$773$	25.4058	0.913784	0.456892	+	0.889522i	$0.348963\pi$
$774$	28.8281	1.03620
$775$	−51.7407	−1.85858
$776$	−49.3174	−1.77039
$777$	7.38127	0.264802
$778$	−18.3247	−0.656973
$779$	34.2226	1.22615
$780$	−0.374395	−0.0134055
$781$	−2.82070	−0.100932
$782$	−7.01027	−0.250687
$783$	24.5771	0.878312
$784$	3.53681	0.126314
$785$	−1.95095	−0.0696323
$786$	27.4768	0.980067
$787$	−14.9432	−0.532667	−0.266333	−	0.963881i	$-0.585812\pi$
$787$	−14.9432	−0.532667	−0.266333	+	0.963881i	$0.585812\pi$
$788$	−95.9147	−3.41682
$789$	5.70750	0.203192
$790$	−10.3579	−0.368517
$791$	17.0613	0.606630
$792$	5.20025	0.184783
$793$	−3.37667	−0.119909
$794$	80.2676	2.84859
$795$	−0.613485	−0.0217581
$796$	10.1043	0.358137
$797$	−19.5066	−0.690961	−0.345480	−	0.938426i	$-0.612284\pi$
$797$	−19.5066	−0.690961	−0.345480	+	0.938426i	$0.612284\pi$
$798$	56.1069	1.98616
$799$	−51.1857	−1.81082
$800$	−19.6477	−0.694652
$801$	7.75109	0.273871
$802$	69.1340	2.44120
$803$	−2.13622	−0.0753856
$804$	−46.9795	−1.65684
$805$	−0.632615	−0.0222968
$806$	−6.92377	−0.243879
$807$	7.00180	0.246475
$808$	44.1562	1.55341
$809$	−50.5381	−1.77683	−0.888413	−	0.459046i	$-0.848191\pi$
$809$	−50.5381	−1.77683	−0.888413	+	0.459046i	$0.848191\pi$
$810$	1.14506	0.0402332
$811$	−0.446678	−0.0156850	−0.00784249	−	0.999969i	$-0.502496\pi$
$811$	−0.446678	−0.0156850	−0.00784249	+	0.999969i	$0.502496\pi$
$812$	−49.5353	−1.73835
$813$	27.9631	0.980710
$814$	−4.27941	−0.149993
$815$	1.72320	0.0603610
$816$	−7.39013	−0.258706
$817$	−49.4976	−1.73170
$818$	−13.4854	−0.471506
$819$	1.40867	0.0492228
$820$	−5.98318	−0.208942
$821$	1.74179	0.0607887	0.0303944	−	0.999538i	$-0.490324\pi$
$821$	1.74179	0.0607887	0.0303944	+	0.999538i	$0.490324\pi$
$822$	56.5166	1.97124
$823$	0.906348	0.0315933	0.0157966	−	0.999875i	$-0.494972\pi$
$823$	0.906348	0.0315933	0.0157966	+	0.999875i	$0.494972\pi$
$824$	−51.3637	−1.78934
$825$	5.17914	0.180314
$826$	60.0553	2.08959
$827$	−33.4505	−1.16319	−0.581593	−	0.813480i	$-0.697570\pi$
$827$	−33.4505	−1.16319	−0.581593	+	0.813480i	$0.697570\pi$
$828$	−3.55977	−0.123711
$829$	−11.8970	−0.413199	−0.206600	−	0.978426i	$-0.566240\pi$
$829$	−11.8970	−0.413199	−0.206600	+	0.978426i	$0.566240\pi$
$830$	9.51124	0.330140
$831$	−7.98769	−0.277090
$832$	−3.36380	−0.116619
$833$	12.8427	0.444974
$834$	4.36409	0.151116
$835$	−0.0481510	−0.00166633
$836$	−20.7288	−0.716921
$837$	57.3548	1.98247
$838$	−81.9175	−2.82979
$839$	−0.0212549	−0.000733802 0	−0.000366901	−	1.00000i	$-0.500117\pi$
$839$	−0.0212549	−0.000733802 0	−0.000366901		1.00000i	$0.500117\pi$
$840$	−4.22526	−0.145785
$841$	−8.47619	−0.292282
$842$	−60.0044	−2.06789
$843$	31.8721	1.09773
$844$	−25.5661	−0.880021
$845$	−4.20714	−0.144730
$846$	−40.7878	−1.40231
$847$	31.7031	1.08933
$848$	2.11455	0.0726141
$849$	−0.318919	−0.0109453
$850$	54.9509	1.88480
$851$	1.26182	0.0432548
$852$	12.8964	0.441822
$853$	−3.98662	−0.136499	−0.0682496	−	0.997668i	$-0.521741\pi$
$853$	−3.98662	−0.136499	−0.0682496	+	0.997668i	$0.521741\pi$
$854$	−88.4698	−3.02738
$855$	3.45684	0.118221
$856$	29.4396	1.00622
$857$	−51.6879	−1.76563	−0.882813	−	0.469725i	$-0.844353\pi$
$857$	−51.6879	−1.76563	−0.882813	+	0.469725i	$0.844353\pi$
$858$	0.693054	0.0236605
$859$	16.2703	0.555135	0.277568	−	0.960706i	$-0.410472\pi$
$859$	16.2703	0.555135	0.277568	+	0.960706i	$0.410472\pi$
$860$	8.65373	0.295090
$861$	−19.1037	−0.651052
$862$	78.3119	2.66731
$863$	−21.2682	−0.723977	−0.361989	−	0.932183i	$-0.617902\pi$
$863$	−21.2682	−0.723977	−0.361989	+	0.932183i	$0.617902\pi$
$864$	21.7796	0.740955
$865$	−2.51332	−0.0854554
$866$	−16.6696	−0.566457
$867$	−6.88486	−0.233822
$868$	−115.599	−3.92369
$869$	12.2184	0.414481
$870$	4.06424	0.137791
$871$	3.17806	0.107684
$872$	−8.75499	−0.296481
$873$	−22.5232	−0.762295
$874$	9.59144	0.324435
$875$	10.0251	0.338909
$876$	9.76691	0.329993
$877$	−30.9034	−1.04353	−0.521767	−	0.853088i	$-0.674727\pi$
$877$	−30.9034	−1.04353	−0.521767	+	0.853088i	$0.674727\pi$
$878$	−57.8512	−1.95238
$879$	−21.1661	−0.713916
$880$	0.386642	0.0130337
$881$	−2.04031	−0.0687400	−0.0343700	−	0.999409i	$-0.510942\pi$
$881$	−2.04031	−0.0687400	−0.0343700	+	0.999409i	$0.510942\pi$
$882$	10.2338	0.344591
$883$	−29.3945	−0.989204	−0.494602	−	0.869119i	$-0.664686\pi$
$883$	−29.3945	−0.989204	−0.494602	+	0.869119i	$0.664686\pi$
$884$	4.68587	0.157603
$885$	−3.13994	−0.105548
$886$	−31.8584	−1.07030
$887$	−15.2813	−0.513095	−0.256548	−	0.966532i	$-0.582585\pi$
$887$	−15.2813	−0.513095	−0.256548	+	0.966532i	$0.582585\pi$
$888$	8.42777	0.282817
$889$	−33.7920	−1.13335
$890$	3.65128	0.122391
$891$	−1.35074	−0.0452514
$892$	−51.0627	−1.70970
$893$	70.0322	2.34354
$894$	5.71176	0.191030
$895$	−2.60816	−0.0871812
$896$	−63.1438	−2.10949
$897$	−0.204354	−0.00682317
$898$	−47.8598	−1.59710
$899$	47.8958	1.59742
$900$	27.9037	0.930123
$901$	7.67829	0.255801
$902$	11.0757	0.368779
$903$	27.6305	0.919485
$904$	19.4802	0.647902
$905$	1.66566	0.0553685
$906$	2.96928	0.0986477
$907$	23.9857	0.796432	0.398216	−	0.917292i	$-0.369629\pi$
$907$	23.9857	0.796432	0.398216	+	0.917292i	$0.369629\pi$
$908$	43.7446	1.45172
$909$	20.1661	0.668867
$910$	0.663574	0.0219973
$911$	35.7417	1.18418	0.592088	−	0.805873i	$-0.298304\pi$
$911$	35.7417	1.18418	0.592088	+	0.805873i	$0.298304\pi$
$912$	10.1112	0.334814
$913$	−11.2197	−0.371317
$914$	−1.78350	−0.0589928
$915$	4.62557	0.152916
$916$	−98.4637	−3.25333
$917$	−31.0336	−1.02482
$918$	−60.9132	−2.01044
$919$	52.8337	1.74282	0.871411	−	0.490553i	$-0.163205\pi$
$919$	52.8337	1.74282	0.871411	+	0.490553i	$0.163205\pi$
$920$	−0.722306	−0.0238137
$921$	−20.4368	−0.673416
$922$	42.0487	1.38480
$923$	−0.872411	−0.0287157
$924$	11.5712	0.380665
$925$	−9.89097	−0.325213
$926$	−34.1165	−1.12114
$927$	−23.4578	−0.770454
$928$	18.1877	0.597039
$929$	2.84065	0.0931987	0.0465994	−	0.998914i	$-0.485162\pi$
$929$	2.84065	0.0931987	0.0465994	+	0.998914i	$0.485162\pi$
$930$	9.48459	0.311012
$931$	−17.5714	−0.575879
$932$	−13.1625	−0.431152
$933$	30.5605	1.00051
$934$	−42.0341	−1.37540
$935$	1.40396	0.0459144
$936$	1.60838	0.0525716
$937$	−32.7325	−1.06933	−0.534663	−	0.845066i	$-0.679561\pi$
$937$	−32.7325	−1.06933	−0.534663	+	0.845066i	$0.679561\pi$
$938$	83.2661	2.71873
$939$	4.16961	0.136070
$940$	−12.2438	−0.399350
$941$	−44.1617	−1.43963	−0.719815	−	0.694166i	$-0.755773\pi$
$941$	−44.1617	−1.43963	−0.719815	+	0.694166i	$0.755773\pi$
$942$	−16.5118	−0.537983
$943$	−3.26576	−0.106348
$944$	10.8227	0.352249
$945$	−5.49688	−0.178814
$946$	−16.0192	−0.520830
$947$	16.5346	0.537303	0.268652	−	0.963237i	$-0.413422\pi$
$947$	16.5346	0.537303	0.268652	+	0.963237i	$0.413422\pi$
$948$	−55.8632	−1.81435
$949$	−0.660710	−0.0214475
$950$	−75.1837	−2.43928
$951$	22.4236	0.727136
$952$	52.8828	1.71394
$953$	−42.5360	−1.37788	−0.688939	−	0.724820i	$-0.741923\pi$
$953$	−42.5360	−1.37788	−0.688939	+	0.724820i	$0.741923\pi$
$954$	6.11851	0.198094
$955$	0.669587	0.0216673
$956$	−32.9606	−1.06602
$957$	−4.79427	−0.154977
$958$	83.9405	2.71199
$959$	−63.8325	−2.06126
$960$	4.60793	0.148720
$961$	80.7731	2.60558
$962$	−1.32358	−0.0426738
$963$	13.4450	0.433260
$964$	−96.7109	−3.11485
$965$	−0.435134	−0.0140075
$966$	−5.35413	−0.172266
$967$	1.77649	0.0571280	0.0285640	−	0.999592i	$-0.490907\pi$
$967$	1.77649	0.0571280	0.0285640	+	0.999592i	$0.490907\pi$
$968$	36.1979	1.16344
$969$	36.7153	1.17946
$970$	−10.6099	−0.340664
$971$	17.6973	0.567933	0.283966	−	0.958834i	$-0.408350\pi$
$971$	17.6973	0.567933	0.283966	+	0.958834i	$0.408350\pi$
$972$	−51.0042	−1.63596
$973$	−4.92901	−0.158017
$974$	85.4424	2.73775
$975$	1.60185	0.0513003
$976$	−15.9434	−0.510334
$977$	9.86596	0.315640	0.157820	−	0.987468i	$-0.449553\pi$
$977$	9.86596	0.315640	0.157820	+	0.987468i	$0.449553\pi$
$978$	14.5842	0.466353
$979$	−4.30713	−0.137657
$980$	3.07203	0.0981324
$981$	−3.99840	−0.127659
$982$	54.1562	1.72819
$983$	−36.7320	−1.17157	−0.585785	−	0.810467i	$-0.699214\pi$
$983$	−36.7320	−1.17157	−0.585785	+	0.810467i	$0.699214\pi$
$984$	−21.8122	−0.695346
$985$	−8.88822	−0.283202
$986$	−50.8674	−1.61995
$987$	−39.0933	−1.24435
$988$	−6.41120	−0.203967
$989$	4.72342	0.150196
$990$	1.11876	0.0355565
$991$	16.2178	0.515177	0.257588	−	0.966255i	$-0.417072\pi$
$991$	16.2178	0.515177	0.257588	+	0.966255i	$0.417072\pi$
$992$	42.4440	1.34760
$993$	21.6446	0.686871
$994$	−22.8574	−0.724993
$995$	0.936343	0.0296841
$996$	51.2970	1.62541
$997$	41.8714	1.32608	0.663040	−	0.748584i	$-0.269266\pi$
$997$	41.8714	1.32608	0.663040	+	0.748584i	$0.269266\pi$
$998$	87.5956	2.77279
$999$	10.9642	0.346891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.13	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.13	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} +O(q^{10})\)	\(q-2.34805 q^{2} -1.17352 q^{3} +3.51335 q^{4} +0.325575 q^{5} +2.75549 q^{6} -3.11218 q^{7} -3.55342 q^{8} -1.62284 q^{9} -0.764466 q^{10} +0.901782 q^{11} -4.12299 q^{12} +0.278911 q^{13} +7.30756 q^{14} -0.382069 q^{15} +1.31691 q^{16} +4.78193 q^{17} +3.81052 q^{18} -6.54262 q^{19} +1.14386 q^{20} +3.65222 q^{21} -2.11743 q^{22} +0.624344 q^{23} +4.17002 q^{24} -4.89400 q^{25} -0.654898 q^{26} +5.42501 q^{27} -10.9342 q^{28} +4.53032 q^{29} +0.897119 q^{30} +10.5723 q^{31} +4.01465 q^{32} -1.05826 q^{33} -11.2282 q^{34} -1.01325 q^{35} -5.70161 q^{36} +2.02104 q^{37} +15.3624 q^{38} -0.327309 q^{39} -1.15690 q^{40} -5.23071 q^{41} -8.57560 q^{42} +7.56540 q^{43} +3.16827 q^{44} -0.528357 q^{45} -1.46599 q^{46} -10.7040 q^{47} -1.54543 q^{48} +2.68568 q^{49} +11.4914 q^{50} -5.61170 q^{51} +0.979913 q^{52} +1.60569 q^{53} -12.7382 q^{54} +0.293597 q^{55} +11.0589 q^{56} +7.67792 q^{57} -10.6374 q^{58} +8.21823 q^{59} -1.34234 q^{60} -12.1066 q^{61} -24.8243 q^{62} +5.05058 q^{63} -12.0604 q^{64} +0.0908065 q^{65} +2.48486 q^{66} +11.3945 q^{67} +16.8006 q^{68} -0.732683 q^{69} +2.37916 q^{70} -3.12791 q^{71} +5.76664 q^{72} -2.36889 q^{73} -4.74550 q^{74} +5.74322 q^{75} -22.9865 q^{76} -2.80651 q^{77} +0.768539 q^{78} +13.5492 q^{79} +0.428754 q^{80} -1.49785 q^{81} +12.2820 q^{82} -12.4417 q^{83} +12.8315 q^{84} +1.55687 q^{85} -17.7640 q^{86} -5.31644 q^{87} -3.20441 q^{88} -4.77624 q^{89} +1.24061 q^{90} -0.868023 q^{91} +2.19354 q^{92} -12.4068 q^{93} +25.1335 q^{94} -2.13011 q^{95} -4.71129 q^{96} +13.8789 q^{97} -6.30611 q^{98} -1.46345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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