LMFDB - Embedded newform 2671.2.a.a.1.64

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			1.64
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)

$f(q)$	$=$	$q+0.716099 q^{2} -0.503376 q^{3} -1.48720 q^{4} -0.847397 q^{5} -0.360467 q^{6} +1.18461 q^{7} -2.49718 q^{8} -2.74661 q^{9} +O(q^{10})$	\(q+0.716099 q^{2} -0.503376 q^{3} -1.48720 q^{4} -0.847397 q^{5} -0.360467 q^{6} +1.18461 q^{7} -2.49718 q^{8} -2.74661 q^{9} -0.606820 q^{10} -1.22305 q^{11} +0.748622 q^{12} +4.75445 q^{13} +0.848297 q^{14} +0.426559 q^{15} +1.18617 q^{16} -1.01306 q^{17} -1.96685 q^{18} +6.87908 q^{19} +1.26025 q^{20} -0.596303 q^{21} -0.875827 q^{22} +4.16231 q^{23} +1.25702 q^{24} -4.28192 q^{25} +3.40466 q^{26} +2.89271 q^{27} -1.76175 q^{28} +7.11176 q^{29} +0.305459 q^{30} -4.57224 q^{31} +5.84378 q^{32} +0.615655 q^{33} -0.725450 q^{34} -1.00383 q^{35} +4.08477 q^{36} -1.71006 q^{37} +4.92610 q^{38} -2.39328 q^{39} +2.11611 q^{40} -9.71561 q^{41} -0.427012 q^{42} -11.1223 q^{43} +1.81893 q^{44} +2.32747 q^{45} +2.98063 q^{46} -5.30052 q^{47} -0.597090 q^{48} -5.59670 q^{49} -3.06628 q^{50} +0.509949 q^{51} -7.07083 q^{52} -10.2922 q^{53} +2.07147 q^{54} +1.03641 q^{55} -2.95818 q^{56} -3.46276 q^{57} +5.09273 q^{58} -4.70509 q^{59} -0.634380 q^{60} -4.82346 q^{61} -3.27418 q^{62} -3.25366 q^{63} +1.81239 q^{64} -4.02891 q^{65} +0.440870 q^{66} -4.97160 q^{67} +1.50662 q^{68} -2.09521 q^{69} -0.718844 q^{70} +6.67796 q^{71} +6.85879 q^{72} +14.5636 q^{73} -1.22458 q^{74} +2.15542 q^{75} -10.2306 q^{76} -1.44884 q^{77} -1.71382 q^{78} -15.4208 q^{79} -1.00516 q^{80} +6.78372 q^{81} -6.95734 q^{82} -12.3950 q^{83} +0.886823 q^{84} +0.858462 q^{85} -7.96470 q^{86} -3.57989 q^{87} +3.05419 q^{88} +4.44461 q^{89} +1.66670 q^{90} +5.63216 q^{91} -6.19020 q^{92} +2.30156 q^{93} -3.79570 q^{94} -5.82931 q^{95} -2.94162 q^{96} +18.7183 q^{97} -4.00780 q^{98} +3.35925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.716099	0.506359	0.253179	−	0.967419i	$-0.418524\pi$
$2$	0.716099	0.506359	0.253179	+	0.967419i	$0.418524\pi$
$3$	−0.503376	−0.290624	−0.145312	−	0.989386i	$-0.546419\pi$
$3$	−0.503376	−0.290624	−0.145312	+	0.989386i	$0.546419\pi$
$4$	−1.48720	−0.743601
$5$	−0.847397	−0.378967	−0.189484	−	0.981884i	$-0.560681\pi$
$5$	−0.847397	−0.378967	−0.189484	+	0.981884i	$0.560681\pi$
$6$	−0.360467	−0.147160
$7$	1.18461	0.447740	0.223870	−	0.974619i	$-0.428131\pi$
$7$	1.18461	0.447740	0.223870	+	0.974619i	$0.428131\pi$
$8$	−2.49718	−0.882888
$9$	−2.74661	−0.915538
$10$	−0.606820	−0.191893
$11$	−1.22305	−0.368764	−0.184382	−	0.982855i	$-0.559028\pi$
$11$	−1.22305	−0.368764	−0.184382	+	0.982855i	$0.559028\pi$
$12$	0.748622	0.216108
$13$	4.75445	1.31865	0.659324	−	0.751859i	$-0.270843\pi$
$13$	4.75445	1.31865	0.659324	+	0.751859i	$0.270843\pi$
$14$	0.848297	0.226717
$15$	0.426559	0.110137
$16$	1.18617	0.296543
$17$	−1.01306	−0.245703	−0.122851	−	0.992425i	$-0.539204\pi$
$17$	−1.01306	−0.245703	−0.122851	+	0.992425i	$0.539204\pi$
$18$	−1.96685	−0.463590
$19$	6.87908	1.57817	0.789084	−	0.614285i	$-0.210555\pi$
$19$	6.87908	1.57817	0.789084	+	0.614285i	$0.210555\pi$
$20$	1.26025	0.281800
$21$	−0.596303	−0.130124
$22$	−0.875827	−0.186727
$23$	4.16231	0.867902	0.433951	−	0.900937i	$-0.357119\pi$
$23$	4.16231	0.867902	0.433951	+	0.900937i	$0.357119\pi$
$24$	1.25702	0.256589
$25$	−4.28192	−0.856384
$26$	3.40466	0.667709
$27$	2.89271	0.556702
$28$	−1.76175	−0.332940
$29$	7.11176	1.32062	0.660310	−	0.750993i	$-0.270425\pi$
$29$	7.11176	1.32062	0.660310	+	0.750993i	$0.270425\pi$
$30$	0.305459	0.0557689
$31$	−4.57224	−0.821199	−0.410599	−	0.911816i	$-0.634680\pi$
$31$	−4.57224	−0.821199	−0.410599	+	0.911816i	$0.634680\pi$
$32$	5.84378	1.03304
$33$	0.615655	0.107172
$34$	−0.725450	−0.124414
$35$	−1.00383	−0.169679
$36$	4.08477	0.680794
$37$	−1.71006	−0.281133	−0.140566	−	0.990071i	$-0.544892\pi$
$37$	−1.71006	−0.281133	−0.140566	+	0.990071i	$0.544892\pi$
$38$	4.92610	0.799120
$39$	−2.39328	−0.383231
$40$	2.11611	0.334586
$41$	−9.71561	−1.51732	−0.758662	−	0.651485i	$-0.774146\pi$
$41$	−9.71561	−1.51732	−0.758662	+	0.651485i	$0.774146\pi$
$42$	−0.427012	−0.0658894
$43$	−11.1223	−1.69614	−0.848071	−	0.529883i	$-0.822236\pi$
$43$	−11.1223	−1.69614	−0.848071	+	0.529883i	$0.822236\pi$
$44$	1.81893	0.274213
$45$	2.32747	0.346959
$46$	2.98063	0.439470
$47$	−5.30052	−0.773160	−0.386580	−	0.922256i	$-0.626344\pi$
$47$	−5.30052	−0.773160	−0.386580	+	0.922256i	$0.626344\pi$
$48$	−0.597090	−0.0861826
$49$	−5.59670	−0.799529
$50$	−3.06628	−0.433637
$51$	0.509949	0.0714071
$52$	−7.07083	−0.980548
$53$	−10.2922	−1.41375	−0.706873	−	0.707340i	$-0.749895\pi$
$53$	−10.2922	−1.41375	−0.706873	+	0.707340i	$0.749895\pi$
$54$	2.07147	0.281891
$55$	1.03641	0.139750
$56$	−2.95818	−0.395304
$57$	−3.46276	−0.458654
$58$	5.09273	0.668708
$59$	−4.70509	−0.612551	−0.306276	−	0.951943i	$-0.599083\pi$
$59$	−4.70509	−0.612551	−0.306276	+	0.951943i	$0.599083\pi$
$60$	−0.634380	−0.0818981
$61$	−4.82346	−0.617581	−0.308791	−	0.951130i	$-0.599924\pi$
$61$	−4.82346	−0.617581	−0.308791	+	0.951130i	$0.599924\pi$
$62$	−3.27418	−0.415821
$63$	−3.25366	−0.409923
$64$	1.81239	0.226548
$65$	−4.02891	−0.499725
$66$	0.440870	0.0542674
$67$	−4.97160	−0.607378	−0.303689	−	0.952771i	$-0.598218\pi$
$67$	−4.97160	−0.607378	−0.303689	+	0.952771i	$0.598218\pi$
$68$	1.50662	0.182705
$69$	−2.09521	−0.252233
$70$	−0.718844	−0.0859183
$71$	6.67796	0.792529	0.396264	−	0.918136i	$-0.370306\pi$
$71$	6.67796	0.792529	0.396264	+	0.918136i	$0.370306\pi$
$72$	6.85879	0.808317
$73$	14.5636	1.70454	0.852269	−	0.523105i	$-0.175226\pi$
$73$	14.5636	1.70454	0.852269	+	0.523105i	$0.175226\pi$
$74$	−1.22458	−0.142354
$75$	2.15542	0.248886
$76$	−10.2306	−1.17353
$77$	−1.44884	−0.165110
$78$	−1.71382	−0.194052
$79$	−15.4208	−1.73498	−0.867489	−	0.497457i	$-0.834267\pi$
$79$	−15.4208	−1.73498	−0.867489	+	0.497457i	$0.834267\pi$
$80$	−1.00516	−0.112380
$81$	6.78372	0.753746
$82$	−6.95734	−0.768310
$83$	−12.3950	−1.36052	−0.680262	−	0.732969i	$-0.738134\pi$
$83$	−12.3950	−1.36052	−0.680262	+	0.732969i	$0.738134\pi$
$84$	0.886823	0.0967603
$85$	0.858462	0.0931133
$86$	−7.96470	−0.858856
$87$	−3.57989	−0.383804
$88$	3.05419	0.325577
$89$	4.44461	0.471128	0.235564	−	0.971859i	$-0.424306\pi$
$89$	4.44461	0.471128	0.235564	+	0.971859i	$0.424306\pi$
$90$	1.66670	0.175686
$91$	5.63216	0.590411
$92$	−6.19020	−0.645373
$93$	2.30156	0.238660
$94$	−3.79570	−0.391496
$95$	−5.82931	−0.598074
$96$	−2.94162	−0.300228
$97$	18.7183	1.90055	0.950277	−	0.311405i	$-0.100800\pi$
$97$	18.7183	1.90055	0.950277	+	0.311405i	$0.100800\pi$
$98$	−4.00780	−0.404849
$99$	3.35925	0.337617
$100$	6.36808	0.636808
$101$	−1.15493	−0.114920	−0.0574598	−	0.998348i	$-0.518300\pi$
$101$	−1.15493	−0.114920	−0.0574598	+	0.998348i	$0.518300\pi$
$102$	0.365174	0.0361576
$103$	−2.31279	−0.227886	−0.113943	−	0.993487i	$-0.536348\pi$
$103$	−2.31279	−0.227886	−0.113943	+	0.993487i	$0.536348\pi$
$104$	−11.8727	−1.16422
$105$	0.505306	0.0493128
$106$	−7.37026	−0.715863
$107$	−16.5656	−1.60145	−0.800726	−	0.599031i	$-0.795553\pi$
$107$	−16.5656	−1.60145	−0.800726	+	0.599031i	$0.795553\pi$
$108$	−4.30204	−0.413964
$109$	−12.5494	−1.20202	−0.601008	−	0.799243i	$-0.705234\pi$
$109$	−12.5494	−1.20202	−0.601008	+	0.799243i	$0.705234\pi$
$110$	0.742173	0.0707634
$111$	0.860805	0.0817040
$112$	1.40515	0.132774
$113$	18.2088	1.71294	0.856468	−	0.516200i	$-0.172654\pi$
$113$	18.2088	1.71294	0.856468	+	0.516200i	$0.172654\pi$
$114$	−2.47968	−0.232244
$115$	−3.52713	−0.328907
$116$	−10.5766	−0.982014
$117$	−13.0586	−1.20727
$118$	−3.36932	−0.310171
$119$	−1.20008	−0.110011
$120$	−1.06520	−0.0972387
$121$	−9.50414	−0.864013
$122$	−3.45408	−0.312718
$123$	4.89061	0.440971
$124$	6.79984	0.610644
$125$	7.86547	0.703509
$126$	−2.32994	−0.207568
$127$	10.7598	0.954774	0.477387	−	0.878693i	$-0.341584\pi$
$127$	10.7598	0.954774	0.477387	+	0.878693i	$0.341584\pi$
$128$	−10.3897	−0.918330
$129$	5.59872	0.492940
$130$	−2.88510	−0.253040
$131$	5.71972	0.499734	0.249867	−	0.968280i	$-0.419613\pi$
$131$	5.71972	0.499734	0.249867	+	0.968280i	$0.419613\pi$
$132$	−0.915604	−0.0796931
$133$	8.14901	0.706609
$134$	−3.56016	−0.307551
$135$	−2.45127	−0.210972
$136$	2.52979	0.216928
$137$	−18.1492	−1.55059	−0.775294	−	0.631601i	$-0.782398\pi$
$137$	−18.1492	−1.55059	−0.775294	+	0.631601i	$0.782398\pi$
$138$	−1.50038	−0.127721
$139$	−5.21919	−0.442686	−0.221343	−	0.975196i	$-0.571044\pi$
$139$	−5.21919	−0.442686	−0.221343	+	0.975196i	$0.571044\pi$
$140$	1.49290	0.126173
$141$	2.66815	0.224699
$142$	4.78209	0.401304
$143$	−5.81495	−0.486270
$144$	−3.25795	−0.271496
$145$	−6.02648	−0.500472
$146$	10.4290	0.863107
$147$	2.81725	0.232363
$148$	2.54321	0.209050
$149$	−13.6092	−1.11491	−0.557456	−	0.830206i	$-0.688223\pi$
$149$	−13.6092	−1.11491	−0.557456	+	0.830206i	$0.688223\pi$
$150$	1.54349	0.126026
$151$	14.7563	1.20085	0.600427	−	0.799679i	$-0.294997\pi$
$151$	14.7563	1.20085	0.600427	+	0.799679i	$0.294997\pi$
$152$	−17.1783	−1.39335
$153$	2.78248	0.224950
$154$	−1.03751	−0.0836051
$155$	3.87450	0.311207
$156$	3.55929	0.284971
$157$	14.7054	1.17362	0.586810	−	0.809724i	$-0.300383\pi$
$157$	14.7054	1.17362	0.586810	+	0.809724i	$0.300383\pi$
$158$	−11.0428	−0.878521
$159$	5.18086	0.410869
$160$	−4.95200	−0.391490
$161$	4.93071	0.388594
$162$	4.85782	0.381666
$163$	9.71194	0.760698	0.380349	−	0.924843i	$-0.375804\pi$
$163$	9.71194	0.760698	0.380349	+	0.924843i	$0.375804\pi$
$164$	14.4491	1.12828
$165$	−0.521704	−0.0406146
$166$	−8.87602	−0.688913
$167$	−6.67751	−0.516722	−0.258361	−	0.966048i	$-0.583182\pi$
$167$	−6.67751	−0.516722	−0.258361	+	0.966048i	$0.583182\pi$
$168$	1.48908	0.114885
$169$	9.60482	0.738833
$170$	0.614744	0.0471487
$171$	−18.8942	−1.44487
$172$	16.5412	1.26125
$173$	−9.39875	−0.714574	−0.357287	−	0.933995i	$-0.616298\pi$
$173$	−9.39875	−0.714574	−0.357287	+	0.933995i	$0.616298\pi$
$174$	−2.56356	−0.194343
$175$	−5.07239	−0.383437
$176$	−1.45075	−0.109354
$177$	2.36843	0.178022
$178$	3.18279	0.238560
$179$	13.2739	0.992137	0.496069	−	0.868283i	$-0.334776\pi$
$179$	13.2739	0.992137	0.496069	+	0.868283i	$0.334776\pi$
$180$	−3.46142	−0.257999
$181$	16.3083	1.21219	0.606094	−	0.795393i	$-0.292736\pi$
$181$	16.3083	1.21219	0.606094	+	0.795393i	$0.292736\pi$
$182$	4.03319	0.298960
$183$	2.42802	0.179484
$184$	−10.3941	−0.766260
$185$	1.44910	0.106540
$186$	1.64814	0.120848
$187$	1.23902	0.0906063
$188$	7.88294	0.574923
$189$	3.42672	0.249257
$190$	−4.17436	−0.302840
$191$	−16.4471	−1.19007	−0.595033	−	0.803701i	$-0.702861\pi$
$191$	−16.4471	−1.19007	−0.595033	+	0.803701i	$0.702861\pi$
$192$	−0.912312	−0.0658404
$193$	−24.4568	−1.76044	−0.880219	−	0.474568i	$-0.842604\pi$
$193$	−24.4568	−1.76044	−0.880219	+	0.474568i	$0.842604\pi$
$194$	13.4042	0.962362
$195$	2.02806	0.145232
$196$	8.32343	0.594531
$197$	−18.3161	−1.30497	−0.652483	−	0.757803i	$-0.726273\pi$
$197$	−18.3161	−1.30497	−0.652483	+	0.757803i	$0.726273\pi$
$198$	2.40556	0.170956
$199$	−18.7398	−1.32843	−0.664214	−	0.747542i	$-0.731234\pi$
$199$	−18.7398	−1.32843	−0.664214	+	0.747542i	$0.731234\pi$
$200$	10.6927	0.756091
$201$	2.50259	0.176519
$202$	−0.827044	−0.0581906
$203$	8.42464	0.591294
$204$	−0.758397	−0.0530984
$205$	8.23298	0.575016
$206$	−1.65619	−0.115392
$207$	−11.4323	−0.794597
$208$	5.63960	0.391036
$209$	−8.41347	−0.581972
$210$	0.361849	0.0249700
$211$	−1.96347	−0.135171	−0.0675854	−	0.997713i	$-0.521530\pi$
$211$	−1.96347	−0.135171	−0.0675854	+	0.997713i	$0.521530\pi$
$212$	15.3066	1.05126
$213$	−3.36153	−0.230328
$214$	−11.8626	−0.810909
$215$	9.42504	0.642782
$216$	−7.22362	−0.491505
$217$	−5.41631	−0.367683
$218$	−8.98663	−0.608651
$219$	−7.33095	−0.495380
$220$	−1.54135	−0.103918
$221$	−4.81653	−0.323995
$222$	0.616422	0.0413715
$223$	29.2257	1.95710	0.978548	−	0.206020i	$-0.0660514\pi$
$223$	29.2257	1.95710	0.978548	+	0.206020i	$0.0660514\pi$
$224$	6.92259	0.462535
$225$	11.7608	0.784051
$226$	13.0393	0.867360
$227$	−26.3291	−1.74752	−0.873762	−	0.486354i	$-0.838327\pi$
$227$	−26.3291	−1.74752	−0.873762	+	0.486354i	$0.838327\pi$
$228$	5.14983	0.341056
$229$	2.93007	0.193625	0.0968123	−	0.995303i	$-0.469135\pi$
$229$	2.93007	0.193625	0.0968123	+	0.995303i	$0.469135\pi$
$230$	−2.52578	−0.166545
$231$	0.729310	0.0479851
$232$	−17.7594	−1.16596
$233$	−21.9080	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$233$	−21.9080	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$234$	−9.35129	−0.611313
$235$	4.49164	0.293003
$236$	6.99742	0.455493
$237$	7.76247	0.504227
$238$	−0.859374	−0.0557049
$239$	−12.0528	−0.779634	−0.389817	−	0.920892i	$-0.627462\pi$
$239$	−12.0528	−0.779634	−0.389817	+	0.920892i	$0.627462\pi$
$240$	0.505973	0.0326604
$241$	1.06712	0.0687395	0.0343697	−	0.999409i	$-0.489058\pi$
$241$	1.06712	0.0687395	0.0343697	+	0.999409i	$0.489058\pi$
$242$	−6.80591	−0.437501
$243$	−12.0929	−0.775759
$244$	7.17346	0.459234
$245$	4.74263	0.302995
$246$	3.50216	0.223290
$247$	32.7063	2.08105
$248$	11.4177	0.725026
$249$	6.23932	0.395401
$250$	5.63246	0.356228
$251$	12.2786	0.775019	0.387510	−	0.921866i	$-0.373335\pi$
$251$	12.2786	0.775019	0.387510	+	0.921866i	$0.373335\pi$
$252$	4.83885	0.304819
$253$	−5.09073	−0.320051
$254$	7.70506	0.483458
$255$	−0.432129	−0.0270610
$256$	−11.0648	−0.691553
$257$	−3.81331	−0.237868	−0.118934	−	0.992902i	$-0.537948\pi$
$257$	−3.81331	−0.237868	−0.118934	+	0.992902i	$0.537948\pi$
$258$	4.00924	0.249604
$259$	−2.02575	−0.125874
$260$	5.99180	0.371596
$261$	−19.5332	−1.20908
$262$	4.09589	0.253045
$263$	−1.17248	−0.0722982	−0.0361491	−	0.999346i	$-0.511509\pi$
$263$	−1.17248	−0.0722982	−0.0361491	+	0.999346i	$0.511509\pi$
$264$	−1.53740	−0.0946207
$265$	8.72160	0.535764
$266$	5.83550	0.357798
$267$	−2.23731	−0.136921
$268$	7.39378	0.451647
$269$	−14.2650	−0.869750	−0.434875	−	0.900491i	$-0.643207\pi$
$269$	−14.2650	−0.869750	−0.434875	+	0.900491i	$0.643207\pi$
$270$	−1.75535	−0.106827
$271$	−12.6776	−0.770110	−0.385055	−	0.922894i	$-0.625817\pi$
$271$	−12.6776	−0.770110	−0.385055	+	0.922894i	$0.625817\pi$
$272$	−1.20166	−0.0728614
$273$	−2.83510	−0.171588
$274$	−12.9966	−0.785154
$275$	5.23701	0.315804
$276$	3.11600	0.187561
$277$	−6.19163	−0.372019	−0.186010	−	0.982548i	$-0.559556\pi$
$277$	−6.19163	−0.372019	−0.186010	+	0.982548i	$0.559556\pi$
$278$	−3.73746	−0.224158
$279$	12.5582	0.751838
$280$	2.50676	0.149807
$281$	17.2092	1.02662	0.513308	−	0.858205i	$-0.328420\pi$
$281$	17.2092	1.02662	0.513308	+	0.858205i	$0.328420\pi$
$282$	1.91066	0.113778
$283$	−11.9693	−0.711504	−0.355752	−	0.934580i	$-0.615775\pi$
$283$	−11.9693	−0.711504	−0.355752	+	0.934580i	$0.615775\pi$
$284$	−9.93148	−0.589325
$285$	2.93433	0.173815
$286$	−4.16408	−0.246227
$287$	−11.5092	−0.679366
$288$	−16.0506	−0.945791
$289$	−15.9737	−0.939630
$290$	−4.31556	−0.253418
$291$	−9.42234	−0.552347
$292$	−21.6590	−1.26750
$293$	−14.2233	−0.830936	−0.415468	−	0.909608i	$-0.636382\pi$
$293$	−14.2233	−0.830936	−0.415468	+	0.909608i	$0.636382\pi$
$294$	2.01743	0.117659
$295$	3.98708	0.232137
$296$	4.27034	0.248208
$297$	−3.53793	−0.205292
$298$	−9.74557	−0.564546
$299$	19.7895	1.14446
$300$	−3.20554	−0.185072
$301$	−13.1756	−0.759430
$302$	10.5670	0.608063
$303$	0.581363	0.0333985
$304$	8.15977	0.467995
$305$	4.08739	0.234043
$306$	1.99253	0.113905
$307$	32.2496	1.84058	0.920292	−	0.391232i	$-0.127951\pi$
$307$	32.2496	1.84058	0.920292	+	0.391232i	$0.127951\pi$
$308$	2.15471	0.122776
$309$	1.16420	0.0662293
$310$	2.77453	0.157583
$311$	20.8076	1.17989	0.589946	−	0.807443i	$-0.299149\pi$
$311$	20.8076	1.17989	0.589946	+	0.807443i	$0.299149\pi$
$312$	5.97645	0.338350
$313$	0.00200241	0.000113183 0	5.65915e−5	−	1.00000i	$-0.499982\pi$
$313$	0.00200241	0.000113183 0	5.65915e−5		1.00000i	$0.499982\pi$
$314$	10.5305	0.594273
$315$	2.75714	0.155347
$316$	22.9339	1.29013
$317$	−15.7582	−0.885066	−0.442533	−	0.896752i	$-0.645920\pi$
$317$	−15.7582	−0.885066	−0.442533	+	0.896752i	$0.645920\pi$
$318$	3.71001	0.208047
$319$	−8.69805	−0.486998
$320$	−1.53581	−0.0858544
$321$	8.33870	0.465421
$322$	3.53088	0.196768
$323$	−6.96890	−0.387760
$324$	−10.0888	−0.560486
$325$	−20.3582	−1.12927
$326$	6.95471	0.385186
$327$	6.31707	0.349335
$328$	24.2617	1.33963
$329$	−6.27904	−0.346175
$330$	−0.373592	−0.0205656
$331$	12.9273	0.710548	0.355274	−	0.934762i	$-0.384388\pi$
$331$	12.9273	0.710548	0.355274	+	0.934762i	$0.384388\pi$
$332$	18.4338	1.01169
$333$	4.69688	0.257387
$334$	−4.78176	−0.261647
$335$	4.21292	0.230176
$336$	−0.707318	−0.0385874
$337$	−0.993668	−0.0541286	−0.0270643	−	0.999634i	$-0.508616\pi$
$337$	−0.993668	−0.0541286	−0.0270643	+	0.999634i	$0.508616\pi$
$338$	6.87801	0.374114
$339$	−9.16586	−0.497821
$340$	−1.27671	−0.0692391
$341$	5.59209	0.302829
$342$	−13.5301	−0.731624
$343$	−14.9222	−0.805721
$344$	27.7745	1.49750
$345$	1.77547	0.0955882
$346$	−6.73044	−0.361831
$347$	21.5185	1.15517	0.577587	−	0.816329i	$-0.303994\pi$
$347$	21.5185	1.15517	0.577587	+	0.816329i	$0.303994\pi$
$348$	5.32402	0.285397
$349$	20.5427	1.09962	0.549812	−	0.835288i	$-0.314699\pi$
$349$	20.5427	1.09962	0.549812	+	0.835288i	$0.314699\pi$
$350$	−3.63234	−0.194157
$351$	13.7532	0.734094
$352$	−7.14725	−0.380950
$353$	1.37446	0.0731551	0.0365775	−	0.999331i	$-0.488354\pi$
$353$	1.37446	0.0731551	0.0365775	+	0.999331i	$0.488354\pi$
$354$	1.69603	0.0901431
$355$	−5.65889	−0.300343
$356$	−6.61004	−0.350331
$357$	0.604089	0.0319718
$358$	9.50543	0.502377
$359$	10.9577	0.578327	0.289163	−	0.957280i	$-0.406623\pi$
$359$	10.9577	0.578327	0.289163	+	0.957280i	$0.406623\pi$
$360$	−5.81212	−0.306326
$361$	28.3217	1.49062
$362$	11.6784	0.613802
$363$	4.78416	0.251103
$364$	−8.37616	−0.439030
$365$	−12.3411	−0.645964
$366$	1.73870	0.0908833
$367$	−33.2039	−1.73323	−0.866614	−	0.498979i	$-0.833708\pi$
$367$	−33.2039	−1.73323	−0.866614	+	0.498979i	$0.833708\pi$
$368$	4.93722	0.257370
$369$	26.6850	1.38917
$370$	1.03770	0.0539475
$371$	−12.1923	−0.632990
$372$	−3.42288	−0.177468
$373$	−33.1506	−1.71647	−0.858236	−	0.513255i	$-0.828440\pi$
$373$	−33.1506	−1.71647	−0.858236	+	0.513255i	$0.828440\pi$
$374$	0.887263	0.0458793
$375$	−3.95929	−0.204457
$376$	13.2364	0.682614
$377$	33.8125	1.74143
$378$	2.45387	0.126214
$379$	−13.4835	−0.692599	−0.346300	−	0.938124i	$-0.612562\pi$
$379$	−13.4835	−0.692599	−0.346300	+	0.938124i	$0.612562\pi$
$380$	8.66936	0.444729
$381$	−5.41620	−0.277481
$382$	−11.7777	−0.602601
$383$	−4.36055	−0.222814	−0.111407	−	0.993775i	$-0.535536\pi$
$383$	−4.36055	−0.222814	−0.111407	+	0.993775i	$0.535536\pi$
$384$	5.22994	0.266889
$385$	1.22774	0.0625715
$386$	−17.5135	−0.891413
$387$	30.5488	1.55288
$388$	−27.8379	−1.41325
$389$	−14.1329	−0.716566	−0.358283	−	0.933613i	$-0.616638\pi$
$389$	−14.1329	−0.716566	−0.358283	+	0.933613i	$0.616638\pi$
$390$	1.45229	0.0735396
$391$	−4.21666	−0.213246
$392$	13.9760	0.705894
$393$	−2.87917	−0.145235
$394$	−13.1161	−0.660781
$395$	13.0676	0.657500
$396$	−4.99588	−0.251053
$397$	−11.2433	−0.564287	−0.282144	−	0.959372i	$-0.591045\pi$
$397$	−11.2433	−0.564287	−0.282144	+	0.959372i	$0.591045\pi$
$398$	−13.4195	−0.672661
$399$	−4.10202	−0.205358
$400$	−5.07909	−0.253955
$401$	32.2221	1.60909	0.804547	−	0.593889i	$-0.202408\pi$
$401$	32.2221	1.60909	0.804547	+	0.593889i	$0.202408\pi$
$402$	1.79210	0.0893818
$403$	−21.7385	−1.08287
$404$	1.71761	0.0854544
$405$	−5.74850	−0.285645
$406$	6.03288	0.299407
$407$	2.09150	0.103672
$408$	−1.27344	−0.0630445
$409$	39.7902	1.96750	0.983750	−	0.179545i	$-0.0574624\pi$
$409$	39.7902	1.96750	0.983750	+	0.179545i	$0.0574624\pi$
$410$	5.89563	0.291164
$411$	9.13585	0.450638
$412$	3.43959	0.169456
$413$	−5.57369	−0.274263
$414$	−8.18663	−0.402351
$415$	10.5034	0.515594
$416$	27.7840	1.36222
$417$	2.62721	0.128655
$418$	−6.02488	−0.294687
$419$	−9.04420	−0.441838	−0.220919	−	0.975292i	$-0.570906\pi$
$419$	−9.04420	−0.441838	−0.220919	+	0.975292i	$0.570906\pi$
$420$	−0.751491	−0.0366690
$421$	−20.5201	−1.00009	−0.500043	−	0.866000i	$-0.666683\pi$
$421$	−20.5201	−1.00009	−0.500043	+	0.866000i	$0.666683\pi$
$422$	−1.40604	−0.0684449
$423$	14.5585	0.707857
$424$	25.7016	1.24818
$425$	4.33783	0.210416
$426$	−2.40719	−0.116629
$427$	−5.71391	−0.276516
$428$	24.6363	1.19084
$429$	2.92710	0.141322
$430$	6.74926	0.325478
$431$	6.55886	0.315929	0.157965	−	0.987445i	$-0.449507\pi$
$431$	6.55886	0.315929	0.157965	+	0.987445i	$0.449507\pi$
$432$	3.43125	0.165086
$433$	9.90555	0.476030	0.238015	−	0.971261i	$-0.423503\pi$
$433$	9.90555	0.476030	0.238015	+	0.971261i	$0.423503\pi$
$434$	−3.87862	−0.186180
$435$	3.03359	0.145449
$436$	18.6635	0.893820
$437$	28.6329	1.36970
$438$	−5.24969	−0.250840
$439$	25.3628	1.21050	0.605250	−	0.796035i	$-0.293073\pi$
$439$	25.3628	1.21050	0.605250	+	0.796035i	$0.293073\pi$
$440$	−2.58811	−0.123383
$441$	15.3720	0.731999
$442$	−3.44912	−0.164058
$443$	−0.194136	−0.00922368	−0.00461184	−	0.999989i	$-0.501468\pi$
$443$	−0.194136	−0.00922368	−0.00461184	+	0.999989i	$0.501468\pi$
$444$	−1.28019	−0.0607551
$445$	−3.76635	−0.178542
$446$	20.9285	0.990992
$447$	6.85057	0.324021
$448$	2.14697	0.101435
$449$	−1.15851	−0.0546737	−0.0273368	−	0.999626i	$-0.508703\pi$
$449$	−1.15851	−0.0546737	−0.0273368	+	0.999626i	$0.508703\pi$
$450$	8.42188	0.397011
$451$	11.8827	0.559535
$452$	−27.0801	−1.27374
$453$	−7.42799	−0.348997
$454$	−18.8543	−0.884874
$455$	−4.77268	−0.223747
$456$	8.64715	0.404940
$457$	−0.277298	−0.0129715	−0.00648574	−	0.999979i	$-0.502064\pi$
$457$	−0.277298	−0.0129715	−0.00648574	+	0.999979i	$0.502064\pi$
$458$	2.09822	0.0980435
$459$	−2.93048	−0.136783
$460$	5.24555	0.244575
$461$	5.75271	0.267930	0.133965	−	0.990986i	$-0.457229\pi$
$461$	5.75271	0.267930	0.133965	+	0.990986i	$0.457229\pi$
$462$	0.522259	0.0242977
$463$	18.6240	0.865529	0.432765	−	0.901507i	$-0.357538\pi$
$463$	18.6240	0.865529	0.432765	+	0.901507i	$0.357538\pi$
$464$	8.43577	0.391621
$465$	−1.95033	−0.0904445
$466$	−15.6883	−0.726747
$467$	23.4883	1.08691	0.543455	−	0.839438i	$-0.317116\pi$
$467$	23.4883	1.08691	0.543455	+	0.839438i	$0.317116\pi$
$468$	19.4208	0.897728
$469$	−5.88940	−0.271947
$470$	3.21646	0.148364
$471$	−7.40236	−0.341083
$472$	11.7495	0.540814
$473$	13.6032	0.625476
$474$	5.55870	0.255320
$475$	−29.4556	−1.35152
$476$	1.78475	0.0818041
$477$	28.2688	1.29434
$478$	−8.63104	−0.394774
$479$	−19.6968	−0.899972	−0.449986	−	0.893036i	$-0.648571\pi$
$479$	−19.6968	−0.899972	−0.449986	+	0.893036i	$0.648571\pi$
$480$	2.49272	0.113777
$481$	−8.13041	−0.370715
$482$	0.764167	0.0348068
$483$	−2.48200	−0.112935
$484$	14.1346	0.642481
$485$	−15.8618	−0.720248
$486$	−8.65971	−0.392812
$487$	−9.81100	−0.444579	−0.222289	−	0.974981i	$-0.571353\pi$
$487$	−9.81100	−0.444579	−0.222289	+	0.974981i	$0.571353\pi$
$488$	12.0451	0.545255
$489$	−4.88876	−0.221077
$490$	3.39619	0.153424
$491$	−8.11650	−0.366292	−0.183146	−	0.983086i	$-0.558628\pi$
$491$	−8.11650	−0.366292	−0.183146	+	0.983086i	$0.558628\pi$
$492$	−7.27332	−0.327906
$493$	−7.20462	−0.324480
$494$	23.4209	1.05376
$495$	−2.84662	−0.127946
$496$	−5.42346	−0.243521
$497$	7.91077	0.354847
$498$	4.46798	0.200215
$499$	−9.53156	−0.426691	−0.213346	−	0.976977i	$-0.568436\pi$
$499$	−9.53156	−0.426691	−0.213346	+	0.976977i	$0.568436\pi$
$500$	−11.6975	−0.523130
$501$	3.36130	0.150172
$502$	8.79271	0.392438
$503$	−22.1566	−0.987913	−0.493957	−	0.869487i	$-0.664450\pi$
$503$	−22.1566	−0.987913	−0.493957	+	0.869487i	$0.664450\pi$
$504$	8.12498	0.361915
$505$	0.978683	0.0435508
$506$	−3.64547	−0.162061
$507$	−4.83484	−0.214723
$508$	−16.0019	−0.709971
$509$	4.55976	0.202108	0.101054	−	0.994881i	$-0.467779\pi$
$509$	4.55976	0.202108	0.101054	+	0.994881i	$0.467779\pi$
$510$	−0.309447	−0.0137026
$511$	17.2521	0.763189
$512$	12.8559	0.568156
$513$	19.8992	0.878569
$514$	−2.73071	−0.120446
$515$	1.95985	0.0863614
$516$	−8.32643	−0.366550
$517$	6.48281	0.285114
$518$	−1.45064	−0.0637375
$519$	4.73111	0.207672
$520$	10.0609	0.441201
$521$	−12.9743	−0.568412	−0.284206	−	0.958763i	$-0.591730\pi$
$521$	−12.9743	−0.568412	−0.284206	+	0.958763i	$0.591730\pi$
$522$	−13.9877	−0.612227
$523$	−11.8516	−0.518236	−0.259118	−	0.965846i	$-0.583432\pi$
$523$	−11.8516	−0.518236	−0.259118	+	0.965846i	$0.583432\pi$
$524$	−8.50637	−0.371603
$525$	2.55332	0.111436
$526$	−0.839612	−0.0366088
$527$	4.63194	0.201771
$528$	0.730273	0.0317811
$529$	−5.67517	−0.246746
$530$	6.24554	0.271289
$531$	12.9231	0.560813
$532$	−12.1192	−0.525435
$533$	−46.1924	−2.00082
$534$	−1.60214	−0.0693313
$535$	14.0376	0.606898
$536$	12.4150	0.536246
$537$	−6.68176	−0.288339
$538$	−10.2151	−0.440405
$539$	6.84506	0.294838
$540$	3.64553	0.156879
$541$	28.8357	1.23974	0.619872	−	0.784703i	$-0.287184\pi$
$541$	28.8357	1.23974	0.619872	+	0.784703i	$0.287184\pi$
$542$	−9.07843	−0.389952
$543$	−8.20922	−0.352291
$544$	−5.92009	−0.253822
$545$	10.6343	0.455525
$546$	−2.03021	−0.0868850
$547$	3.18638	0.136240	0.0681198	−	0.997677i	$-0.478300\pi$
$547$	3.18638	0.136240	0.0681198	+	0.997677i	$0.478300\pi$
$548$	26.9915	1.15302
$549$	13.2482	0.565419
$550$	3.75022	0.159910
$551$	48.9223	2.08416
$552$	5.23212	0.222694
$553$	−18.2676	−0.776818
$554$	−4.43382	−0.188375
$555$	−0.729443	−0.0309631
$556$	7.76198	0.329181
$557$	−45.8285	−1.94182	−0.970908	−	0.239453i	$-0.923032\pi$
$557$	−45.8285	−1.94182	−0.970908	+	0.239453i	$0.923032\pi$
$558$	8.99290	0.380700
$559$	−52.8807	−2.23661
$560$	−1.19072	−0.0503170
$561$	−0.623694	−0.0263324
$562$	12.3235	0.519836
$563$	−2.80420	−0.118183	−0.0590915	−	0.998253i	$-0.518820\pi$
$563$	−2.80420	−0.118183	−0.0590915	+	0.998253i	$0.518820\pi$
$564$	−3.96808	−0.167086
$565$	−15.4301	−0.649147
$566$	−8.57124	−0.360276
$567$	8.03605	0.337482
$568$	−16.6761	−0.699714
$569$	−16.4204	−0.688379	−0.344190	−	0.938900i	$-0.611846\pi$
$569$	−16.4204	−0.688379	−0.344190	+	0.938900i	$0.611846\pi$
$570$	2.10128	0.0880127
$571$	9.83121	0.411423	0.205712	−	0.978613i	$-0.434049\pi$
$571$	9.83121	0.411423	0.205712	+	0.978613i	$0.434049\pi$
$572$	8.64800	0.361591
$573$	8.27905	0.345862
$574$	−8.24172	−0.344003
$575$	−17.8227	−0.743257
$576$	−4.97792	−0.207413
$577$	36.3920	1.51502	0.757510	−	0.652823i	$-0.226416\pi$
$577$	36.3920	1.51502	0.757510	+	0.652823i	$0.226416\pi$
$578$	−11.4388	−0.475790
$579$	12.3110	0.511626
$580$	8.96259	0.372151
$581$	−14.6832	−0.609160
$582$	−6.74733	−0.279686
$583$	12.5879	0.521339
$584$	−36.3679	−1.50491
$585$	11.0659	0.457517
$586$	−10.1853	−0.420752
$587$	30.1628	1.24495	0.622475	−	0.782639i	$-0.286127\pi$
$587$	30.1628	1.24495	0.622475	+	0.782639i	$0.286127\pi$
$588$	−4.18981	−0.172785
$589$	−31.4528	−1.29599
$590$	2.85515	0.117545
$591$	9.21987	0.379255
$592$	−2.02843	−0.0833679
$593$	−17.4944	−0.718408	−0.359204	−	0.933259i	$-0.616952\pi$
$593$	−17.4944	−0.718408	−0.359204	+	0.933259i	$0.616952\pi$
$594$	−2.53351	−0.103951
$595$	1.01694	0.0416905
$596$	20.2397	0.829050
$597$	9.43316	0.386074
$598$	14.1713	0.579506
$599$	17.0383	0.696167	0.348084	−	0.937464i	$-0.386833\pi$
$599$	17.0383	0.696167	0.348084	+	0.937464i	$0.386833\pi$
$600$	−5.38247	−0.219738
$601$	−23.1408	−0.943932	−0.471966	−	0.881617i	$-0.656455\pi$
$601$	−23.1408	−0.943932	−0.471966	+	0.881617i	$0.656455\pi$
$602$	−9.43505	−0.384544
$603$	13.6551	0.556077
$604$	−21.9457	−0.892956
$605$	8.05378	0.327433
$606$	0.416314	0.0169116
$607$	19.1910	0.778938	0.389469	−	0.921040i	$-0.372659\pi$
$607$	19.1910	0.778938	0.389469	+	0.921040i	$0.372659\pi$
$608$	40.1998	1.63032
$609$	−4.24076	−0.171844
$610$	2.92698	0.118510
$611$	−25.2011	−1.01953
$612$	−4.13810	−0.167273
$613$	−18.2030	−0.735211	−0.367606	−	0.929982i	$-0.619822\pi$
$613$	−18.2030	−0.735211	−0.367606	+	0.929982i	$0.619822\pi$
$614$	23.0939	0.931996
$615$	−4.14428	−0.167114
$616$	3.61801	0.145774
$617$	−39.3088	−1.58251	−0.791256	−	0.611486i	$-0.790572\pi$
$617$	−39.3088	−1.58251	−0.791256	+	0.611486i	$0.790572\pi$
$618$	0.833686	0.0335358
$619$	−25.4463	−1.02277	−0.511387	−	0.859351i	$-0.670868\pi$
$619$	−25.4463	−1.02277	−0.511387	+	0.859351i	$0.670868\pi$
$620$	−5.76217	−0.231414
$621$	12.0403	0.483162
$622$	14.9003	0.597448
$623$	5.26513	0.210943
$624$	−2.83884	−0.113645
$625$	14.7444	0.589777
$626$	0.00143393	5.73112e−5 0
$627$	4.23514	0.169135
$628$	−21.8699	−0.872705
$629$	1.73239	0.0690750
$630$	1.97439	0.0786615
$631$	−24.2068	−0.963656	−0.481828	−	0.876266i	$-0.660027\pi$
$631$	−24.2068	−0.963656	−0.481828	+	0.876266i	$0.660027\pi$
$632$	38.5086	1.53179
$633$	0.988363	0.0392839
$634$	−11.2844	−0.448161
$635$	−9.11778	−0.361828
$636$	−7.70499	−0.305523
$637$	−26.6093	−1.05430
$638$	−6.22867	−0.246595
$639$	−18.3418	−0.725590
$640$	8.80421	0.348017
$641$	−2.92497	−0.115529	−0.0577646	−	0.998330i	$-0.518397\pi$
$641$	−2.92497	−0.115529	−0.0577646	+	0.998330i	$0.518397\pi$
$642$	5.97134	0.235670
$643$	11.8694	0.468082	0.234041	−	0.972227i	$-0.424805\pi$
$643$	11.8694	0.468082	0.234041	+	0.972227i	$0.424805\pi$
$644$	−7.33296	−0.288959
$645$	−4.74434	−0.186808
$646$	−4.99043	−0.196346
$647$	−26.3549	−1.03612	−0.518058	−	0.855345i	$-0.673345\pi$
$647$	−26.3549	−1.03612	−0.518058	+	0.855345i	$0.673345\pi$
$648$	−16.9402	−0.665473
$649$	5.75458	0.225887
$650$	−14.5785	−0.571815
$651$	2.72644	0.106858
$652$	−14.4436	−0.565656
$653$	−9.40243	−0.367945	−0.183973	−	0.982931i	$-0.558896\pi$
$653$	−9.40243	−0.367945	−0.183973	+	0.982931i	$0.558896\pi$
$654$	4.52365	0.176889
$655$	−4.84687	−0.189383
$656$	−11.5244	−0.449952
$657$	−40.0005	−1.56057
$658$	−4.49641	−0.175289
$659$	−22.7971	−0.888050	−0.444025	−	0.896014i	$-0.646450\pi$
$659$	−22.7971	−0.888050	−0.444025	+	0.896014i	$0.646450\pi$
$660$	0.775880	0.0302011
$661$	−18.8306	−0.732426	−0.366213	−	0.930531i	$-0.619346\pi$
$661$	−18.8306	−0.732426	−0.366213	+	0.930531i	$0.619346\pi$
$662$	9.25722	0.359792
$663$	2.42453	0.0941609
$664$	30.9525	1.20119
$665$	−6.90545	−0.267782
$666$	3.36343	0.130330
$667$	29.6013	1.14617
$668$	9.93081	0.384235
$669$	−14.7115	−0.568779
$670$	3.01687	0.116552
$671$	5.89935	0.227742
$672$	−3.48467	−0.134424
$673$	−26.0031	−1.00234	−0.501172	−	0.865348i	$-0.667098\pi$
$673$	−26.0031	−1.00234	−0.501172	+	0.865348i	$0.667098\pi$
$674$	−0.711565	−0.0274085
$675$	−12.3863	−0.476750
$676$	−14.2843	−0.549397
$677$	−22.3760	−0.859979	−0.429990	−	0.902834i	$-0.641483\pi$
$677$	−22.3760	−0.859979	−0.429990	+	0.902834i	$0.641483\pi$
$678$	−6.56366	−0.252076
$679$	22.1738	0.850954
$680$	−2.14374	−0.0822085
$681$	13.2534	0.507873
$682$	4.00449	0.153340
$683$	−16.2358	−0.621247	−0.310624	−	0.950533i	$-0.600538\pi$
$683$	−16.2358	−0.621247	−0.310624	+	0.950533i	$0.600538\pi$
$684$	28.0994	1.07441
$685$	15.3795	0.587622
$686$	−10.6857	−0.407984
$687$	−1.47493	−0.0562720
$688$	−13.1930	−0.502979
$689$	−48.9339	−1.86423
$690$	1.27141	0.0484019
$691$	37.1736	1.41415	0.707075	−	0.707138i	$-0.250014\pi$
$691$	37.1736	1.41415	0.707075	+	0.707138i	$0.250014\pi$
$692$	13.9778	0.531358
$693$	3.97940	0.151165
$694$	15.4094	0.584933
$695$	4.42272	0.167763
$696$	8.93964	0.338856
$697$	9.84247	0.372810
$698$	14.7106	0.556804
$699$	11.0280	0.417116
$700$	7.54367	0.285124
$701$	47.3401	1.78801	0.894006	−	0.448054i	$-0.147883\pi$
$701$	47.3401	1.78801	0.894006	+	0.448054i	$0.147883\pi$
$702$	9.84869	0.371715
$703$	−11.7637	−0.443675
$704$	−2.21664	−0.0835429
$705$	−2.26099	−0.0851537
$706$	0.984250	0.0370427
$707$	−1.36814	−0.0514541
$708$	−3.52234	−0.132377
$709$	14.0401	0.527286	0.263643	−	0.964620i	$-0.415076\pi$
$709$	14.0401	0.527286	0.263643	+	0.964620i	$0.415076\pi$
$710$	−4.05233	−0.152081
$711$	42.3550	1.58844
$712$	−11.0990	−0.415953
$713$	−19.0311	−0.712720
$714$	0.432588	0.0161892
$715$	4.92757	0.184281
$716$	−19.7410	−0.737754
$717$	6.06711	0.226581
$718$	7.84682	0.292841
$719$	−38.1796	−1.42386	−0.711929	−	0.702251i	$-0.752178\pi$
$719$	−38.1796	−1.42386	−0.711929	+	0.702251i	$0.752178\pi$
$720$	2.76078	0.102888
$721$	−2.73975	−0.102034
$722$	20.2812	0.754787
$723$	−0.537164	−0.0199774
$724$	−24.2538	−0.901384
$725$	−30.4520	−1.13096
$726$	3.42593	0.127148
$727$	−6.25319	−0.231918	−0.115959	−	0.993254i	$-0.536994\pi$
$727$	−6.25319	−0.231918	−0.115959	+	0.993254i	$0.536994\pi$
$728$	−14.0645	−0.521267
$729$	−14.2639	−0.528292
$730$	−8.83747	−0.327090
$731$	11.2676	0.416746
$732$	−3.61095	−0.133464
$733$	45.0148	1.66266	0.831329	−	0.555780i	$-0.187580\pi$
$733$	45.0148	1.66266	0.831329	+	0.555780i	$0.187580\pi$
$734$	−23.7773	−0.877635
$735$	−2.38733	−0.0880579
$736$	24.3236	0.896581
$737$	6.08053	0.223979
$738$	19.1091	0.703417
$739$	32.9438	1.21186	0.605930	−	0.795518i	$-0.292801\pi$
$739$	32.9438	1.21186	0.605930	+	0.795518i	$0.292801\pi$
$740$	−2.15511	−0.0792233
$741$	−16.4635	−0.604803
$742$	−8.73087	−0.320520
$743$	22.0178	0.807754	0.403877	−	0.914813i	$-0.367662\pi$
$743$	22.0178	0.807754	0.403877	+	0.914813i	$0.367662\pi$
$744$	−5.74741	−0.210710
$745$	11.5324	0.422516
$746$	−23.7391	−0.869151
$747$	34.0441	1.24561
$748$	−1.84268	−0.0673749
$749$	−19.6237	−0.717034
$750$	−2.83524	−0.103528
$751$	30.8457	1.12557	0.562787	−	0.826602i	$-0.309729\pi$
$751$	30.8457	1.12557	0.562787	+	0.826602i	$0.309729\pi$
$752$	−6.28733	−0.229275
$753$	−6.18076	−0.225239
$754$	24.2131	0.881790
$755$	−12.5045	−0.455085
$756$	−5.09623	−0.185348
$757$	27.0381	0.982717	0.491359	−	0.870957i	$-0.336500\pi$
$757$	27.0381	0.982717	0.491359	+	0.870957i	$0.336500\pi$
$758$	−9.65551	−0.350704
$759$	2.56255	0.0930146
$760$	14.5569	0.528033
$761$	−1.70744	−0.0618948	−0.0309474	−	0.999521i	$-0.509852\pi$
$761$	−1.70744	−0.0618948	−0.0309474	+	0.999521i	$0.509852\pi$
$762$	−3.87854	−0.140505
$763$	−14.8661	−0.538190
$764$	24.4601	0.884935
$765$	−2.35786	−0.0852487
$766$	−3.12259	−0.112824
$767$	−22.3701	−0.807739
$768$	5.56978	0.200982
$769$	14.0928	0.508200	0.254100	−	0.967178i	$-0.418221\pi$
$769$	14.0928	0.508200	0.254100	+	0.967178i	$0.418221\pi$
$770$	0.879184	0.0316836
$771$	1.91953	0.0691302
$772$	36.3722	1.30906
$773$	13.8883	0.499527	0.249764	−	0.968307i	$-0.419647\pi$
$773$	13.8883	0.499527	0.249764	+	0.968307i	$0.419647\pi$
$774$	21.8760	0.786315
$775$	19.5780	0.703261
$776$	−46.7430	−1.67798
$777$	1.01972	0.0365821
$778$	−10.1206	−0.362839
$779$	−66.8344	−2.39459
$780$	−3.01613	−0.107995
$781$	−8.16750	−0.292256
$782$	−3.01955	−0.107979
$783$	20.5722	0.735192
$784$	−6.63865	−0.237095
$785$	−12.4613	−0.444764
$786$	−2.06177	−0.0735410
$787$	37.7794	1.34669	0.673345	−	0.739328i	$-0.264857\pi$
$787$	37.7794	1.34669	0.673345	+	0.739328i	$0.264857\pi$
$788$	27.2397	0.970374
$789$	0.590198	0.0210116
$790$	9.35767	0.332931
$791$	21.5702	0.766950
$792$	−8.38867	−0.298078
$793$	−22.9329	−0.814372
$794$	−8.05135	−0.285732
$795$	−4.39025	−0.155706
$796$	27.8698	0.987820
$797$	22.7897	0.807252	0.403626	−	0.914924i	$-0.367750\pi$
$797$	22.7897	0.807252	0.403626	+	0.914924i	$0.367750\pi$
$798$	−2.93745	−0.103985
$799$	5.36973	0.189967
$800$	−25.0226	−0.884683
$801$	−12.2076	−0.431336
$802$	23.0742	0.814779
$803$	−17.8120	−0.628572
$804$	−3.72185	−0.131260
$805$	−4.17827	−0.147265
$806$	−15.5669	−0.548322
$807$	7.18064	0.252770
$808$	2.88407	0.101461
$809$	−25.6347	−0.901267	−0.450633	−	0.892709i	$-0.648802\pi$
$809$	−25.6347	−0.901267	−0.450633	+	0.892709i	$0.648802\pi$
$810$	−4.11650	−0.144639
$811$	23.6009	0.828740	0.414370	−	0.910108i	$-0.364002\pi$
$811$	23.6009	0.828740	0.414370	+	0.910108i	$0.364002\pi$
$812$	−12.5291	−0.439687
$813$	6.38160	0.223813
$814$	1.49772	0.0524950
$815$	−8.22987	−0.288280
$816$	0.604887	0.0211753
$817$	−76.5114	−2.67680
$818$	28.4938	0.996261
$819$	−15.4694	−0.540544
$820$	−12.2441	−0.427582
$821$	16.3781	0.571599	0.285799	−	0.958289i	$-0.407741\pi$
$821$	16.3781	0.571599	0.285799	+	0.958289i	$0.407741\pi$
$822$	6.54218	0.228185
$823$	11.9797	0.417585	0.208793	−	0.977960i	$-0.433047\pi$
$823$	11.9797	0.417585	0.208793	+	0.977960i	$0.433047\pi$
$824$	5.77547	0.201198
$825$	−2.63619	−0.0917802
$826$	−3.99132	−0.138876
$827$	−27.7577	−0.965231	−0.482616	−	0.875832i	$-0.660313\pi$
$827$	−27.7577	−0.965231	−0.482616	+	0.875832i	$0.660313\pi$
$828$	17.0021	0.590863
$829$	54.2156	1.88299	0.941493	−	0.337033i	$-0.109423\pi$
$829$	54.2156	1.88299	0.941493	+	0.337033i	$0.109423\pi$
$830$	7.52151	0.261076
$831$	3.11672	0.108118
$832$	8.61690	0.298737
$833$	5.66978	0.196446
$834$	1.88135	0.0651457
$835$	5.65851	0.195821
$836$	12.5125	0.432755
$837$	−13.2262	−0.457163
$838$	−6.47655	−0.223729
$839$	15.6720	0.541056	0.270528	−	0.962712i	$-0.412802\pi$
$839$	15.6720	0.541056	0.270528	+	0.962712i	$0.412802\pi$
$840$	−1.26184	−0.0435376
$841$	21.5771	0.744038
$842$	−14.6944	−0.506403
$843$	−8.66270	−0.298359
$844$	2.92007	0.100513
$845$	−8.13910	−0.279993
$846$	10.4253	0.358430
$847$	−11.2587	−0.386853
$848$	−12.2084	−0.419237
$849$	6.02508	0.206780
$850$	3.10632	0.106546
$851$	−7.11781	−0.243996
$852$	4.99927	0.171272
$853$	−38.0677	−1.30341	−0.651707	−	0.758471i	$-0.725947\pi$
$853$	−38.0677	−1.30341	−0.651707	+	0.758471i	$0.725947\pi$
$854$	−4.09173	−0.140016
$855$	16.0109	0.547560
$856$	41.3672	1.41390
$857$	41.6241	1.42185	0.710927	−	0.703266i	$-0.248276\pi$
$857$	41.6241	1.42185	0.710927	+	0.703266i	$0.248276\pi$
$858$	2.09610	0.0715596
$859$	4.39079	0.149812	0.0749058	−	0.997191i	$-0.476134\pi$
$859$	4.39079	0.149812	0.0749058	+	0.997191i	$0.476134\pi$
$860$	−14.0169	−0.477973
$861$	5.79345	0.197440
$862$	4.69679	0.159973
$863$	−8.09814	−0.275664	−0.137832	−	0.990456i	$-0.544013\pi$
$863$	−8.09814	−0.275664	−0.137832	+	0.990456i	$0.544013\pi$
$864$	16.9044	0.575098
$865$	7.96447	0.270800
$866$	7.09336	0.241042
$867$	8.04079	0.273079
$868$	8.05515	0.273410
$869$	18.8605	0.639798
$870$	2.17235	0.0736495
$871$	−23.6373	−0.800918
$872$	31.3382	1.06124
$873$	−51.4119	−1.74003
$874$	20.5040	0.693557
$875$	9.31750	0.314989
$876$	10.9026	0.368365
$877$	2.33144	0.0787272	0.0393636	−	0.999225i	$-0.487467\pi$
$877$	2.33144	0.0787272	0.0393636	+	0.999225i	$0.487467\pi$
$878$	18.1623	0.612947
$879$	7.15969	0.241490
$880$	1.22936	0.0414418
$881$	58.3602	1.96621	0.983103	−	0.183053i	$-0.0585980\pi$
$881$	58.3602	1.96621	0.983103	+	0.183053i	$0.0585980\pi$
$882$	11.0079	0.370654
$883$	25.7574	0.866807	0.433404	−	0.901200i	$-0.357312\pi$
$883$	25.7574	0.866807	0.433404	+	0.901200i	$0.357312\pi$
$884$	7.16316	0.240923
$885$	−2.00700	−0.0674646
$886$	−0.139021	−0.00467049
$887$	37.3144	1.25289	0.626447	−	0.779464i	$-0.284508\pi$
$887$	37.3144	1.25289	0.626447	+	0.779464i	$0.284508\pi$
$888$	−2.14959	−0.0721354
$889$	12.7461	0.427490
$890$	−2.69708	−0.0904064
$891$	−8.29684	−0.277955
$892$	−43.4645	−1.45530
$893$	−36.4627	−1.22018
$894$	4.90569	0.164071
$895$	−11.2483	−0.375988
$896$	−12.3077	−0.411173
$897$	−9.96157	−0.332607
$898$	−0.829612	−0.0276845
$899$	−32.5167	−1.08449
$900$	−17.4906	−0.583021
$901$	10.4266	0.347361
$902$	8.50920	0.283325
$903$	6.63229	0.220709
$904$	−45.4706	−1.51233
$905$	−13.8196	−0.459380
$906$	−5.31918	−0.176718
$907$	7.45901	0.247672	0.123836	−	0.992303i	$-0.460480\pi$
$907$	7.45901	0.247672	0.123836	+	0.992303i	$0.460480\pi$
$908$	39.1567	1.29946
$909$	3.17214	0.105213
$910$	−3.41771	−0.113296
$911$	36.3790	1.20529	0.602645	−	0.798010i	$-0.294114\pi$
$911$	36.3790	1.20529	0.602645	+	0.798010i	$0.294114\pi$
$912$	−4.10743	−0.136011
$913$	15.1597	0.501712
$914$	−0.198573	−0.00656822
$915$	−2.05749	−0.0680186
$916$	−4.35761	−0.143979
$917$	6.77562	0.223751
$918$	−2.09851	−0.0692613
$919$	−59.6251	−1.96685	−0.983425	−	0.181318i	$-0.941964\pi$
$919$	−59.6251	−1.96685	−0.983425	+	0.181318i	$0.941964\pi$
$920$	8.80789	0.290387
$921$	−16.2337	−0.534918
$922$	4.11951	0.135669
$923$	31.7501	1.04507
$924$	−1.08463	−0.0356818
$925$	7.32235	0.240757
$926$	13.3366	0.438268
$927$	6.35234	0.208638
$928$	41.5596	1.36426
$929$	−21.9293	−0.719478	−0.359739	−	0.933053i	$-0.617134\pi$
$929$	−21.9293	−0.719478	−0.359739	+	0.933053i	$0.617134\pi$
$930$	−1.39663	−0.0457973
$931$	−38.5002	−1.26179
$932$	32.5816	1.06725
$933$	−10.4741	−0.342905
$934$	16.8200	0.550367
$935$	−1.04994	−0.0343368
$936$	32.6098	1.06589
$937$	−1.80895	−0.0590958	−0.0295479	−	0.999563i	$-0.509407\pi$
$937$	−1.80895	−0.0590958	−0.0295479	+	0.999563i	$0.509407\pi$
$938$	−4.21740	−0.137703
$939$	−0.00100797	−3.28937e−5 0
$940$	−6.67998	−0.217877
$941$	−13.5363	−0.441271	−0.220635	−	0.975356i	$-0.570813\pi$
$941$	−13.5363	−0.441271	−0.220635	+	0.975356i	$0.570813\pi$
$942$	−5.30082	−0.172710
$943$	−40.4394	−1.31689
$944$	−5.58105	−0.181648
$945$	−2.90380	−0.0944605
$946$	9.74125	0.316715
$947$	43.3702	1.40934	0.704670	−	0.709535i	$-0.251095\pi$
$947$	43.3702	1.40934	0.704670	+	0.709535i	$0.251095\pi$
$948$	−11.5444	−0.374943
$949$	69.2418	2.24768
$950$	−21.0932	−0.684353
$951$	7.93228	0.257222
$952$	2.99681	0.0971271
$953$	−21.3317	−0.691000	−0.345500	−	0.938419i	$-0.612291\pi$
$953$	−21.3317	−0.691000	−0.345500	+	0.938419i	$0.612291\pi$
$954$	20.2432	0.655399
$955$	13.9372	0.450997
$956$	17.9250	0.579736
$957$	4.37839	0.141533
$958$	−14.1049	−0.455708
$959$	−21.4996	−0.694260
$960$	0.773090	0.0249514
$961$	−10.0946	−0.325633
$962$	−5.82218	−0.187715
$963$	45.4992	1.46619
$964$	−1.58703	−0.0511147
$965$	20.7246	0.667148
$966$	−1.77736	−0.0571856
$967$	7.69924	0.247591	0.123795	−	0.992308i	$-0.460493\pi$
$967$	7.69924	0.247591	0.123795	+	0.992308i	$0.460493\pi$
$968$	23.7336	0.762826
$969$	3.50798	0.112692
$970$	−11.3586	−0.364704
$971$	−19.7709	−0.634478	−0.317239	−	0.948346i	$-0.602756\pi$
$971$	−19.7709	−0.634478	−0.317239	+	0.948346i	$0.602756\pi$
$972$	17.9846	0.576855
$973$	−6.18269	−0.198208
$974$	−7.02565	−0.225116
$975$	10.2478	0.328193
$976$	−5.72146	−0.183139
$977$	−27.7044	−0.886343	−0.443172	−	0.896437i	$-0.646147\pi$
$977$	−27.7044	−0.886343	−0.443172	+	0.896437i	$0.646147\pi$
$978$	−3.50084	−0.111944
$979$	−5.43600	−0.173735
$980$	−7.05325	−0.225308
$981$	34.4684	1.10049
$982$	−5.81222	−0.185475
$983$	−54.8219	−1.74855	−0.874274	−	0.485433i	$-0.838662\pi$
$983$	−54.8219	−1.74855	−0.874274	+	0.485433i	$0.838662\pi$
$984$	−12.2127	−0.389328
$985$	15.5210	0.494540
$986$	−5.15922	−0.164303
$987$	3.16072	0.100607
$988$	−48.6408	−1.54747
$989$	−46.2946	−1.47208
$990$	−2.03846	−0.0647866
$991$	−56.9512	−1.80911	−0.904557	−	0.426352i	$-0.859799\pi$
$991$	−56.9512	−1.80911	−0.904557	+	0.426352i	$0.859799\pi$
$992$	−26.7192	−0.848335
$993$	−6.50728	−0.206502
$994$	5.66490	0.179680
$995$	15.8800	0.503431
$996$	−9.27913	−0.294021
$997$	−10.7748	−0.341241	−0.170621	−	0.985337i	$-0.554577\pi$
$997$	−10.7748	−0.341241	−0.170621	+	0.985337i	$0.554577\pi$
$998$	−6.82554	−0.216059
$999$	−4.94671	−0.156507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.64	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.64	✓	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)

\(f(q)\)	\(=\)	\(q+0.716099 q^{2} -0.503376 q^{3} -1.48720 q^{4} -0.847397 q^{5} -0.360467 q^{6} +1.18461 q^{7} -2.49718 q^{8} -2.74661 q^{9} +O(q^{10})\)	\(q+0.716099 q^{2} -0.503376 q^{3} -1.48720 q^{4} -0.847397 q^{5} -0.360467 q^{6} +1.18461 q^{7} -2.49718 q^{8} -2.74661 q^{9} -0.606820 q^{10} -1.22305 q^{11} +0.748622 q^{12} +4.75445 q^{13} +0.848297 q^{14} +0.426559 q^{15} +1.18617 q^{16} -1.01306 q^{17} -1.96685 q^{18} +6.87908 q^{19} +1.26025 q^{20} -0.596303 q^{21} -0.875827 q^{22} +4.16231 q^{23} +1.25702 q^{24} -4.28192 q^{25} +3.40466 q^{26} +2.89271 q^{27} -1.76175 q^{28} +7.11176 q^{29} +0.305459 q^{30} -4.57224 q^{31} +5.84378 q^{32} +0.615655 q^{33} -0.725450 q^{34} -1.00383 q^{35} +4.08477 q^{36} -1.71006 q^{37} +4.92610 q^{38} -2.39328 q^{39} +2.11611 q^{40} -9.71561 q^{41} -0.427012 q^{42} -11.1223 q^{43} +1.81893 q^{44} +2.32747 q^{45} +2.98063 q^{46} -5.30052 q^{47} -0.597090 q^{48} -5.59670 q^{49} -3.06628 q^{50} +0.509949 q^{51} -7.07083 q^{52} -10.2922 q^{53} +2.07147 q^{54} +1.03641 q^{55} -2.95818 q^{56} -3.46276 q^{57} +5.09273 q^{58} -4.70509 q^{59} -0.634380 q^{60} -4.82346 q^{61} -3.27418 q^{62} -3.25366 q^{63} +1.81239 q^{64} -4.02891 q^{65} +0.440870 q^{66} -4.97160 q^{67} +1.50662 q^{68} -2.09521 q^{69} -0.718844 q^{70} +6.67796 q^{71} +6.85879 q^{72} +14.5636 q^{73} -1.22458 q^{74} +2.15542 q^{75} -10.2306 q^{76} -1.44884 q^{77} -1.71382 q^{78} -15.4208 q^{79} -1.00516 q^{80} +6.78372 q^{81} -6.95734 q^{82} -12.3950 q^{83} +0.886823 q^{84} +0.858462 q^{85} -7.96470 q^{86} -3.57989 q^{87} +3.05419 q^{88} +4.44461 q^{89} +1.66670 q^{90} +5.63216 q^{91} -6.19020 q^{92} +2.30156 q^{93} -3.79570 q^{94} -5.82931 q^{95} -2.94162 q^{96} +18.7183 q^{97} -4.00780 q^{98} +3.35925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 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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