LMFDB - Embedded newform 1014.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.692021 q^{5} -1.00000 q^{6} +0.356896 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.692021 q^{5} -1.00000 q^{6} +0.356896 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.692021 q^{10} +2.93900 q^{11} +1.00000 q^{12} -0.356896 q^{14} -0.692021 q^{15} +1.00000 q^{16} +6.71379 q^{17} -1.00000 q^{18} -7.20775 q^{19} -0.692021 q^{20} +0.356896 q^{21} -2.93900 q^{22} +2.39612 q^{23} -1.00000 q^{24} -4.52111 q^{25} +1.00000 q^{27} +0.356896 q^{28} +7.82908 q^{29} +0.692021 q^{30} -2.76271 q^{31} -1.00000 q^{32} +2.93900 q^{33} -6.71379 q^{34} -0.246980 q^{35} +1.00000 q^{36} +10.0978 q^{37} +7.20775 q^{38} +0.692021 q^{40} +4.89008 q^{41} -0.356896 q^{42} +6.59179 q^{43} +2.93900 q^{44} -0.692021 q^{45} -2.39612 q^{46} +4.98792 q^{47} +1.00000 q^{48} -6.87263 q^{49} +4.52111 q^{50} +6.71379 q^{51} -8.88769 q^{53} -1.00000 q^{54} -2.03385 q^{55} -0.356896 q^{56} -7.20775 q^{57} -7.82908 q^{58} +1.64310 q^{59} -0.692021 q^{60} -6.49396 q^{61} +2.76271 q^{62} +0.356896 q^{63} +1.00000 q^{64} -2.93900 q^{66} +13.5254 q^{67} +6.71379 q^{68} +2.39612 q^{69} +0.246980 q^{70} +6.81163 q^{71} -1.00000 q^{72} +3.18598 q^{73} -10.0978 q^{74} -4.52111 q^{75} -7.20775 q^{76} +1.04892 q^{77} +15.0465 q^{79} -0.692021 q^{80} +1.00000 q^{81} -4.89008 q^{82} -14.8267 q^{83} +0.356896 q^{84} -4.64609 q^{85} -6.59179 q^{86} +7.82908 q^{87} -2.93900 q^{88} +0.396125 q^{89} +0.692021 q^{90} +2.39612 q^{92} -2.76271 q^{93} -4.98792 q^{94} +4.98792 q^{95} -1.00000 q^{96} -0.417895 q^{97} +6.87263 q^{98} +2.93900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - q^{11} + 3 q^{12} + 3 q^{14} + 3 q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + 2 q^{25} + 3 q^{27} - 3 q^{28} + 13 q^{29} - 3 q^{30} + 9 q^{31} - 3 q^{32} - q^{33} - 12 q^{34} + 4 q^{35} + 3 q^{36} + 12 q^{37} + 4 q^{38} - 3 q^{40} + 14 q^{41} + 3 q^{42} - 8 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} - 4 q^{47} + 3 q^{48} - 4 q^{49} - 2 q^{50} + 12 q^{51} + 15 q^{53} - 3 q^{54} - 22 q^{55} + 3 q^{56} - 4 q^{57} - 13 q^{58} + 9 q^{59} + 3 q^{60} - 10 q^{61} - 9 q^{62} - 3 q^{63} + 3 q^{64} + q^{66} + 6 q^{67} + 12 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{72} - 5 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 5 q^{79} + 3 q^{80} + 3 q^{81} - 14 q^{82} + 7 q^{83} - 3 q^{84} + 26 q^{85} + 8 q^{86} + 13 q^{87} + q^{88} + 10 q^{89} - 3 q^{90} + 16 q^{92} + 9 q^{93} + 4 q^{94} - 4 q^{95} - 3 q^{96} - 7 q^{97} + 4 q^{98} - q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - q^11 + 3 * q^12 + 3 * q^14 + 3 * q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + 2 * q^25 + 3 * q^27 - 3 * q^28 + 13 * q^29 - 3 * q^30 + 9 * q^31 - 3 * q^32 - q^33 - 12 * q^34 + 4 * q^35 + 3 * q^36 + 12 * q^37 + 4 * q^38 - 3 * q^40 + 14 * q^41 + 3 * q^42 - 8 * q^43 - q^44 + 3 * q^45 - 16 * q^46 - 4 * q^47 + 3 * q^48 - 4 * q^49 - 2 * q^50 + 12 * q^51 + 15 * q^53 - 3 * q^54 - 22 * q^55 + 3 * q^56 - 4 * q^57 - 13 * q^58 + 9 * q^59 + 3 * q^60 - 10 * q^61 - 9 * q^62 - 3 * q^63 + 3 * q^64 + q^66 + 6 * q^67 + 12 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^72 - 5 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 5 * q^79 + 3 * q^80 + 3 * q^81 - 14 * q^82 + 7 * q^83 - 3 * q^84 + 26 * q^85 + 8 * q^86 + 13 * q^87 + q^88 + 10 * q^89 - 3 * q^90 + 16 * q^92 + 9 * q^93 + 4 * q^94 - 4 * q^95 - 3 * q^96 - 7 * q^97 + 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.692021	−0.309481	−0.154741	−	0.987955i	$-0.549454\pi$
$5$	−0.692021	−0.309481	−0.154741	+	0.987955i	$0.549454\pi$
$6$	−1.00000	−0.408248
$7$	0.356896	0.134894	0.0674470	−	0.997723i	$-0.478515\pi$
$7$	0.356896	0.134894	0.0674470	+	0.997723i	$0.478515\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.692021	0.218836
$11$	2.93900	0.886142	0.443071	−	0.896486i	$-0.353889\pi$
$11$	2.93900	0.886142	0.443071	+	0.896486i	$0.353889\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−0.356896	−0.0953844
$15$	−0.692021	−0.178679
$16$	1.00000	0.250000
$17$	6.71379	1.62833	0.814167	−	0.580631i	$-0.197194\pi$
$17$	6.71379	1.62833	0.814167	+	0.580631i	$0.197194\pi$
$18$	−1.00000	−0.235702
$19$	−7.20775	−1.65357	−0.826786	−	0.562517i	$-0.809833\pi$
$19$	−7.20775	−1.65357	−0.826786	+	0.562517i	$0.809833\pi$
$20$	−0.692021	−0.154741
$21$	0.356896	0.0778811
$22$	−2.93900	−0.626597
$23$	2.39612	0.499627	0.249813	−	0.968294i	$-0.419631\pi$
$23$	2.39612	0.499627	0.249813	+	0.968294i	$0.419631\pi$
$24$	−1.00000	−0.204124
$25$	−4.52111	−0.904221
$26$	0	0
$27$	1.00000	0.192450
$28$	0.356896	0.0674470
$29$	7.82908	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$29$	7.82908	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$30$	0.692021	0.126345
$31$	−2.76271	−0.496197	−0.248099	−	0.968735i	$-0.579806\pi$
$31$	−2.76271	−0.496197	−0.248099	+	0.968735i	$0.579806\pi$
$32$	−1.00000	−0.176777
$33$	2.93900	0.511614
$34$	−6.71379	−1.15141
$35$	−0.246980	−0.0417472
$36$	1.00000	0.166667
$37$	10.0978	1.66007	0.830037	−	0.557708i	$-0.188319\pi$
$37$	10.0978	1.66007	0.830037	+	0.557708i	$0.188319\pi$
$38$	7.20775	1.16925
$39$	0	0
$40$	0.692021	0.109418
$41$	4.89008	0.763703	0.381851	−	0.924224i	$-0.375287\pi$
$41$	4.89008	0.763703	0.381851	+	0.924224i	$0.375287\pi$
$42$	−0.356896	−0.0550702
$43$	6.59179	1.00524	0.502620	−	0.864508i	$-0.332370\pi$
$43$	6.59179	1.00524	0.502620	+	0.864508i	$0.332370\pi$
$44$	2.93900	0.443071
$45$	−0.692021	−0.103160
$46$	−2.39612	−0.353289
$47$	4.98792	0.727563	0.363781	−	0.931484i	$-0.381486\pi$
$47$	4.98792	0.727563	0.363781	+	0.931484i	$0.381486\pi$
$48$	1.00000	0.144338
$49$	−6.87263	−0.981804
$50$	4.52111	0.639381
$51$	6.71379	0.940119
$52$	0	0
$53$	−8.88769	−1.22082	−0.610409	−	0.792086i	$-0.708995\pi$
$53$	−8.88769	−1.22082	−0.610409	+	0.792086i	$0.708995\pi$
$54$	−1.00000	−0.136083
$55$	−2.03385	−0.274245
$56$	−0.356896	−0.0476922
$57$	−7.20775	−0.954690
$58$	−7.82908	−1.02801
$59$	1.64310	0.213914	0.106957	−	0.994264i	$-0.465889\pi$
$59$	1.64310	0.213914	0.106957	+	0.994264i	$0.465889\pi$
$60$	−0.692021	−0.0893396
$61$	−6.49396	−0.831466	−0.415733	−	0.909487i	$-0.636475\pi$
$61$	−6.49396	−0.831466	−0.415733	+	0.909487i	$0.636475\pi$
$62$	2.76271	0.350864
$63$	0.356896	0.0449647
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.93900	−0.361766
$67$	13.5254	1.65239	0.826196	−	0.563382i	$-0.190500\pi$
$67$	13.5254	1.65239	0.826196	+	0.563382i	$0.190500\pi$
$68$	6.71379	0.814167
$69$	2.39612	0.288459
$70$	0.246980	0.0295197
$71$	6.81163	0.808391	0.404196	−	0.914673i	$-0.367551\pi$
$71$	6.81163	0.808391	0.404196	+	0.914673i	$0.367551\pi$
$72$	−1.00000	−0.117851
$73$	3.18598	0.372891	0.186445	−	0.982465i	$-0.440303\pi$
$73$	3.18598	0.372891	0.186445	+	0.982465i	$0.440303\pi$
$74$	−10.0978	−1.17385
$75$	−4.52111	−0.522052
$76$	−7.20775	−0.826786
$77$	1.04892	0.119535
$78$	0	0
$79$	15.0465	1.69287	0.846433	−	0.532495i	$-0.178745\pi$
$79$	15.0465	1.69287	0.846433	+	0.532495i	$0.178745\pi$
$80$	−0.692021	−0.0773704
$81$	1.00000	0.111111
$82$	−4.89008	−0.540019
$83$	−14.8267	−1.62744	−0.813720	−	0.581256i	$-0.802561\pi$
$83$	−14.8267	−1.62744	−0.813720	+	0.581256i	$0.802561\pi$
$84$	0.356896	0.0389405
$85$	−4.64609	−0.503939
$86$	−6.59179	−0.710811
$87$	7.82908	0.839366
$88$	−2.93900	−0.313299
$89$	0.396125	0.0419891	0.0209946	−	0.999780i	$-0.493317\pi$
$89$	0.396125	0.0419891	0.0209946	+	0.999780i	$0.493317\pi$
$90$	0.692021	0.0729455
$91$	0	0
$92$	2.39612	0.249813
$93$	−2.76271	−0.286480
$94$	−4.98792	−0.514465
$95$	4.98792	0.511750
$96$	−1.00000	−0.102062
$97$	−0.417895	−0.0424308	−0.0212154	−	0.999775i	$-0.506754\pi$
$97$	−0.417895	−0.0424308	−0.0212154	+	0.999775i	$0.506754\pi$
$98$	6.87263	0.694240
$99$	2.93900	0.295381
$100$	−4.52111	−0.452111
$101$	10.0151	0.996536	0.498268	−	0.867023i	$-0.333970\pi$
$101$	10.0151	0.996536	0.498268	+	0.867023i	$0.333970\pi$
$102$	−6.71379	−0.664764
$103$	−9.62565	−0.948443	−0.474222	−	0.880406i	$-0.657270\pi$
$103$	−9.62565	−0.948443	−0.474222	+	0.880406i	$0.657270\pi$
$104$	0	0
$105$	−0.246980	−0.0241027
$106$	8.88769	0.863249
$107$	−6.63102	−0.641045	−0.320523	−	0.947241i	$-0.603859\pi$
$107$	−6.63102	−0.641045	−0.320523	+	0.947241i	$0.603859\pi$
$108$	1.00000	0.0962250
$109$	12.9879	1.24402	0.622008	−	0.783011i	$-0.286317\pi$
$109$	12.9879	1.24402	0.622008	+	0.783011i	$0.286317\pi$
$110$	2.03385	0.193920
$111$	10.0978	0.958444
$112$	0.356896	0.0337235
$113$	0.792249	0.0745285	0.0372643	−	0.999305i	$-0.488136\pi$
$113$	0.792249	0.0745285	0.0372643	+	0.999305i	$0.488136\pi$
$114$	7.20775	0.675068
$115$	−1.65817	−0.154625
$116$	7.82908	0.726912
$117$	0	0
$118$	−1.64310	−0.151260
$119$	2.39612	0.219652
$120$	0.692021	0.0631726
$121$	−2.36227	−0.214752
$122$	6.49396	0.587935
$123$	4.89008	0.440924
$124$	−2.76271	−0.248099
$125$	6.58881	0.589321
$126$	−0.356896	−0.0317948
$127$	−18.2174	−1.61654	−0.808268	−	0.588815i	$-0.799595\pi$
$127$	−18.2174	−1.61654	−0.808268	+	0.588815i	$0.799595\pi$
$128$	−1.00000	−0.0883883
$129$	6.59179	0.580375
$130$	0	0
$131$	2.73556	0.239007	0.119504	−	0.992834i	$-0.461870\pi$
$131$	2.73556	0.239007	0.119504	+	0.992834i	$0.461870\pi$
$132$	2.93900	0.255807
$133$	−2.57242	−0.223057
$134$	−13.5254	−1.16842
$135$	−0.692021	−0.0595597
$136$	−6.71379	−0.575703
$137$	−7.64742	−0.653363	−0.326681	−	0.945135i	$-0.605930\pi$
$137$	−7.64742	−0.653363	−0.326681	+	0.945135i	$0.605930\pi$
$138$	−2.39612	−0.203972
$139$	3.38404	0.287031	0.143515	−	0.989648i	$-0.454159\pi$
$139$	3.38404	0.287031	0.143515	+	0.989648i	$0.454159\pi$
$140$	−0.246980	−0.0208736
$141$	4.98792	0.420059
$142$	−6.81163	−0.571619
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.41789	−0.449932
$146$	−3.18598	−0.263674
$147$	−6.87263	−0.566845
$148$	10.0978	0.830037
$149$	20.8170	1.70540	0.852698	−	0.522405i	$-0.174965\pi$
$149$	20.8170	1.70540	0.852698	+	0.522405i	$0.174965\pi$
$150$	4.52111	0.369147
$151$	0.895461	0.0728715	0.0364358	−	0.999336i	$-0.488400\pi$
$151$	0.895461	0.0728715	0.0364358	+	0.999336i	$0.488400\pi$
$152$	7.20775	0.584626
$153$	6.71379	0.542778
$154$	−1.04892	−0.0845242
$155$	1.91185	0.153564
$156$	0	0
$157$	8.59179	0.685700	0.342850	−	0.939390i	$-0.388608\pi$
$157$	8.59179	0.685700	0.342850	+	0.939390i	$0.388608\pi$
$158$	−15.0465	−1.19704
$159$	−8.88769	−0.704840
$160$	0.692021	0.0547091
$161$	0.855167	0.0673966
$162$	−1.00000	−0.0785674
$163$	−1.72587	−0.135181	−0.0675904	−	0.997713i	$-0.521531\pi$
$163$	−1.72587	−0.135181	−0.0675904	+	0.997713i	$0.521531\pi$
$164$	4.89008	0.381851
$165$	−2.03385	−0.158335
$166$	14.8267	1.15077
$167$	−21.1400	−1.63587	−0.817933	−	0.575314i	$-0.804880\pi$
$167$	−21.1400	−1.63587	−0.817933	+	0.575314i	$0.804880\pi$
$168$	−0.356896	−0.0275351
$169$	0	0
$170$	4.64609	0.356339
$171$	−7.20775	−0.551190
$172$	6.59179	0.502620
$173$	9.35450	0.711210	0.355605	−	0.934636i	$-0.384275\pi$
$173$	9.35450	0.711210	0.355605	+	0.934636i	$0.384275\pi$
$174$	−7.82908	−0.593521
$175$	−1.61356	−0.121974
$176$	2.93900	0.221536
$177$	1.64310	0.123503
$178$	−0.396125	−0.0296908
$179$	3.17523	0.237328	0.118664	−	0.992934i	$-0.462139\pi$
$179$	3.17523	0.237328	0.118664	+	0.992934i	$0.462139\pi$
$180$	−0.692021	−0.0515802
$181$	−19.7995	−1.47169	−0.735844	−	0.677151i	$-0.763214\pi$
$181$	−19.7995	−1.47169	−0.735844	+	0.677151i	$0.763214\pi$
$182$	0	0
$183$	−6.49396	−0.480047
$184$	−2.39612	−0.176645
$185$	−6.98792	−0.513762
$186$	2.76271	0.202572
$187$	19.7318	1.44294
$188$	4.98792	0.363781
$189$	0.356896	0.0259604
$190$	−4.98792	−0.361862
$191$	15.2620	1.10432	0.552161	−	0.833737i	$-0.313803\pi$
$191$	15.2620	1.10432	0.552161	+	0.833737i	$0.313803\pi$
$192$	1.00000	0.0721688
$193$	−4.76809	−0.343214	−0.171607	−	0.985165i	$-0.554896\pi$
$193$	−4.76809	−0.343214	−0.171607	+	0.985165i	$0.554896\pi$
$194$	0.417895	0.0300031
$195$	0	0
$196$	−6.87263	−0.490902
$197$	−12.2349	−0.871700	−0.435850	−	0.900019i	$-0.643552\pi$
$197$	−12.2349	−0.871700	−0.435850	+	0.900019i	$0.643552\pi$
$198$	−2.93900	−0.208866
$199$	−11.8485	−0.839915	−0.419958	−	0.907544i	$-0.637955\pi$
$199$	−11.8485	−0.839915	−0.419958	+	0.907544i	$0.637955\pi$
$200$	4.52111	0.319690
$201$	13.5254	0.954009
$202$	−10.0151	−0.704658
$203$	2.79417	0.196112
$204$	6.71379	0.470059
$205$	−3.38404	−0.236352
$206$	9.62565	0.670651
$207$	2.39612	0.166542
$208$	0	0
$209$	−21.1836	−1.46530
$210$	0.246980	0.0170432
$211$	−17.2620	−1.18837	−0.594184	−	0.804329i	$-0.702525\pi$
$211$	−17.2620	−1.18837	−0.594184	+	0.804329i	$0.702525\pi$
$212$	−8.88769	−0.610409
$213$	6.81163	0.466725
$214$	6.63102	0.453287
$215$	−4.56166	−0.311103
$216$	−1.00000	−0.0680414
$217$	−0.985999	−0.0669340
$218$	−12.9879	−0.879653
$219$	3.18598	0.215289
$220$	−2.03385	−0.137122
$221$	0	0
$222$	−10.0978	−0.677722
$223$	−6.76809	−0.453225	−0.226612	−	0.973985i	$-0.572765\pi$
$223$	−6.76809	−0.453225	−0.226612	+	0.973985i	$0.572765\pi$
$224$	−0.356896	−0.0238461
$225$	−4.52111	−0.301407
$226$	−0.792249	−0.0526996
$227$	−23.6799	−1.57169	−0.785846	−	0.618422i	$-0.787772\pi$
$227$	−23.6799	−1.57169	−0.785846	+	0.618422i	$0.787772\pi$
$228$	−7.20775	−0.477345
$229$	8.29829	0.548366	0.274183	−	0.961677i	$-0.411593\pi$
$229$	8.29829	0.548366	0.274183	+	0.961677i	$0.411593\pi$
$230$	1.65817	0.109336
$231$	1.04892	0.0690137
$232$	−7.82908	−0.514005
$233$	−23.9651	−1.57000	−0.785002	−	0.619493i	$-0.787338\pi$
$233$	−23.9651	−1.57000	−0.785002	+	0.619493i	$0.787338\pi$
$234$	0	0
$235$	−3.45175	−0.225167
$236$	1.64310	0.106957
$237$	15.0465	0.977377
$238$	−2.39612	−0.155318
$239$	−12.6160	−0.816058	−0.408029	−	0.912969i	$-0.633784\pi$
$239$	−12.6160	−0.816058	−0.408029	+	0.912969i	$0.633784\pi$
$240$	−0.692021	−0.0446698
$241$	−26.3937	−1.70017	−0.850085	−	0.526646i	$-0.823449\pi$
$241$	−26.3937	−1.70017	−0.850085	+	0.526646i	$0.823449\pi$
$242$	2.36227	0.151853
$243$	1.00000	0.0641500
$244$	−6.49396	−0.415733
$245$	4.75600	0.303850
$246$	−4.89008	−0.311780
$247$	0	0
$248$	2.76271	0.175432
$249$	−14.8267	−0.939603
$250$	−6.58881	−0.416713
$251$	−30.0344	−1.89576	−0.947879	−	0.318632i	$-0.896777\pi$
$251$	−30.0344	−1.89576	−0.947879	+	0.318632i	$0.896777\pi$
$252$	0.356896	0.0224823
$253$	7.04221	0.442740
$254$	18.2174	1.14306
$255$	−4.64609	−0.290949
$256$	1.00000	0.0625000
$257$	11.2620	0.702507	0.351254	−	0.936280i	$-0.385756\pi$
$257$	11.2620	0.702507	0.351254	+	0.936280i	$0.385756\pi$
$258$	−6.59179	−0.410387
$259$	3.60388	0.223934
$260$	0	0
$261$	7.82908	0.484608
$262$	−2.73556	−0.169004
$263$	−5.54958	−0.342202	−0.171101	−	0.985254i	$-0.554732\pi$
$263$	−5.54958	−0.342202	−0.171101	+	0.985254i	$0.554732\pi$
$264$	−2.93900	−0.180883
$265$	6.15047	0.377821
$266$	2.57242	0.157725
$267$	0.396125	0.0242424
$268$	13.5254	0.826196
$269$	16.6872	1.01744	0.508719	−	0.860932i	$-0.330119\pi$
$269$	16.6872	1.01744	0.508719	+	0.860932i	$0.330119\pi$
$270$	0.692021	0.0421151
$271$	6.61356	0.401745	0.200873	−	0.979617i	$-0.435622\pi$
$271$	6.61356	0.401745	0.200873	+	0.979617i	$0.435622\pi$
$272$	6.71379	0.407083
$273$	0	0
$274$	7.64742	0.461997
$275$	−13.2875	−0.801269
$276$	2.39612	0.144230
$277$	−21.7995	−1.30981	−0.654904	−	0.755712i	$-0.727291\pi$
$277$	−21.7995	−1.30981	−0.654904	+	0.755712i	$0.727291\pi$
$278$	−3.38404	−0.202961
$279$	−2.76271	−0.165399
$280$	0.246980	0.0147599
$281$	−20.5918	−1.22840	−0.614202	−	0.789149i	$-0.710522\pi$
$281$	−20.5918	−1.22840	−0.614202	+	0.789149i	$0.710522\pi$
$282$	−4.98792	−0.297026
$283$	−13.0121	−0.773488	−0.386744	−	0.922187i	$-0.626400\pi$
$283$	−13.0121	−0.773488	−0.386744	+	0.922187i	$0.626400\pi$
$284$	6.81163	0.404196
$285$	4.98792	0.295459
$286$	0	0
$287$	1.74525	0.103019
$288$	−1.00000	−0.0589256
$289$	28.0750	1.65147
$290$	5.41789	0.318150
$291$	−0.417895	−0.0244974
$292$	3.18598	0.186445
$293$	14.9390	0.872746	0.436373	−	0.899766i	$-0.356263\pi$
$293$	14.9390	0.872746	0.436373	+	0.899766i	$0.356263\pi$
$294$	6.87263	0.400820
$295$	−1.13706	−0.0662024
$296$	−10.0978	−0.586925
$297$	2.93900	0.170538
$298$	−20.8170	−1.20590
$299$	0	0
$300$	−4.52111	−0.261026
$301$	2.35258	0.135601
$302$	−0.895461	−0.0515280
$303$	10.0151	0.575350
$304$	−7.20775	−0.413393
$305$	4.49396	0.257323
$306$	−6.71379	−0.383802
$307$	−26.0301	−1.48562	−0.742809	−	0.669503i	$-0.766507\pi$
$307$	−26.0301	−1.48562	−0.742809	+	0.669503i	$0.766507\pi$
$308$	1.04892	0.0597676
$309$	−9.62565	−0.547584
$310$	−1.91185	−0.108586
$311$	−4.81163	−0.272842	−0.136421	−	0.990651i	$-0.543560\pi$
$311$	−4.81163	−0.272842	−0.136421	+	0.990651i	$0.543560\pi$
$312$	0	0
$313$	−26.0411	−1.47193	−0.735966	−	0.677018i	$-0.763272\pi$
$313$	−26.0411	−1.47193	−0.735966	+	0.677018i	$0.763272\pi$
$314$	−8.59179	−0.484863
$315$	−0.246980	−0.0139157
$316$	15.0465	0.846433
$317$	11.5211	0.647090	0.323545	−	0.946213i	$-0.395125\pi$
$317$	11.5211	0.647090	0.323545	+	0.946213i	$0.395125\pi$
$318$	8.88769	0.498397
$319$	23.0097	1.28830
$320$	−0.692021	−0.0386852
$321$	−6.63102	−0.370108
$322$	−0.855167	−0.0476566
$323$	−48.3913	−2.69257
$324$	1.00000	0.0555556
$325$	0	0
$326$	1.72587	0.0955873
$327$	12.9879	0.718234
$328$	−4.89008	−0.270010
$329$	1.78017	0.0981438
$330$	2.03385	0.111960
$331$	−3.43834	−0.188988	−0.0944940	−	0.995525i	$-0.530123\pi$
$331$	−3.43834	−0.188988	−0.0944940	+	0.995525i	$0.530123\pi$
$332$	−14.8267	−0.813720
$333$	10.0978	0.553358
$334$	21.1400	1.15673
$335$	−9.35988	−0.511385
$336$	0.356896	0.0194703
$337$	8.20105	0.446739	0.223370	−	0.974734i	$-0.428294\pi$
$337$	8.20105	0.446739	0.223370	+	0.974734i	$0.428294\pi$
$338$	0	0
$339$	0.792249	0.0430291
$340$	−4.64609	−0.251970
$341$	−8.11960	−0.439701
$342$	7.20775	0.389751
$343$	−4.95108	−0.267333
$344$	−6.59179	−0.355406
$345$	−1.65817	−0.0892729
$346$	−9.35450	−0.502901
$347$	7.86294	0.422105	0.211052	−	0.977475i	$-0.432311\pi$
$347$	7.86294	0.422105	0.211052	+	0.977475i	$0.432311\pi$
$348$	7.82908	0.419683
$349$	18.7245	1.00230	0.501151	−	0.865360i	$-0.332910\pi$
$349$	18.7245	1.00230	0.501151	+	0.865360i	$0.332910\pi$
$350$	1.61356	0.0862486
$351$	0	0
$352$	−2.93900	−0.156649
$353$	31.5448	1.67896	0.839480	−	0.543391i	$-0.182860\pi$
$353$	31.5448	1.67896	0.839480	+	0.543391i	$0.182860\pi$
$354$	−1.64310	−0.0873300
$355$	−4.71379	−0.250182
$356$	0.396125	0.0209946
$357$	2.39612	0.126816
$358$	−3.17523	−0.167816
$359$	−2.39612	−0.126463	−0.0632313	−	0.997999i	$-0.520141\pi$
$359$	−2.39612	−0.126463	−0.0632313	+	0.997999i	$0.520141\pi$
$360$	0.692021	0.0364727
$361$	32.9517	1.73430
$362$	19.7995	1.04064
$363$	−2.36227	−0.123987
$364$	0	0
$365$	−2.20477	−0.115403
$366$	6.49396	0.339445
$367$	−0.00431187	−0.000225078 0	−0.000112539	−	1.00000i	$-0.500036\pi$
$367$	−0.00431187	−0.000225078 0	−0.000112539		1.00000i	$0.500036\pi$
$368$	2.39612	0.124907
$369$	4.89008	0.254568
$370$	6.98792	0.363285
$371$	−3.17198	−0.164681
$372$	−2.76271	−0.143240
$373$	−32.3129	−1.67310	−0.836549	−	0.547892i	$-0.815430\pi$
$373$	−32.3129	−1.67310	−0.836549	+	0.547892i	$0.815430\pi$
$374$	−19.7318	−1.02031
$375$	6.58881	0.340245
$376$	−4.98792	−0.257232
$377$	0	0
$378$	−0.356896	−0.0183567
$379$	−19.7560	−1.01480	−0.507399	−	0.861711i	$-0.669393\pi$
$379$	−19.7560	−1.01480	−0.507399	+	0.861711i	$0.669393\pi$
$380$	4.98792	0.255875
$381$	−18.2174	−0.933308
$382$	−15.2620	−0.780874
$383$	−28.8116	−1.47221	−0.736103	−	0.676870i	$-0.763336\pi$
$383$	−28.8116	−1.47221	−0.736103	+	0.676870i	$0.763336\pi$
$384$	−1.00000	−0.0510310
$385$	−0.725873	−0.0369939
$386$	4.76809	0.242689
$387$	6.59179	0.335080
$388$	−0.417895	−0.0212154
$389$	34.7821	1.76352	0.881761	−	0.471697i	$-0.156358\pi$
$389$	34.7821	1.76352	0.881761	+	0.471697i	$0.156358\pi$
$390$	0	0
$391$	16.0871	0.813559
$392$	6.87263	0.347120
$393$	2.73556	0.137991
$394$	12.2349	0.616385
$395$	−10.4125	−0.523911
$396$	2.93900	0.147690
$397$	5.15346	0.258645	0.129322	−	0.991603i	$-0.458720\pi$
$397$	5.15346	0.258645	0.129322	+	0.991603i	$0.458720\pi$
$398$	11.8485	0.593910
$399$	−2.57242	−0.128782
$400$	−4.52111	−0.226055
$401$	−13.3250	−0.665417	−0.332708	−	0.943030i	$-0.607962\pi$
$401$	−13.3250	−0.665417	−0.332708	+	0.943030i	$0.607962\pi$
$402$	−13.5254	−0.674587
$403$	0	0
$404$	10.0151	0.498268
$405$	−0.692021	−0.0343868
$406$	−2.79417	−0.138672
$407$	29.6775	1.47106
$408$	−6.71379	−0.332382
$409$	24.0237	1.18789	0.593947	−	0.804504i	$-0.297569\pi$
$409$	24.0237	1.18789	0.593947	+	0.804504i	$0.297569\pi$
$410$	3.38404	0.167126
$411$	−7.64742	−0.377219
$412$	−9.62565	−0.474222
$413$	0.586417	0.0288557
$414$	−2.39612	−0.117763
$415$	10.2604	0.503663
$416$	0	0
$417$	3.38404	0.165717
$418$	21.1836	1.03612
$419$	13.8049	0.674415	0.337207	−	0.941430i	$-0.390518\pi$
$419$	13.8049	0.674415	0.337207	+	0.941430i	$0.390518\pi$
$420$	−0.246980	−0.0120514
$421$	−7.72587	−0.376536	−0.188268	−	0.982118i	$-0.560287\pi$
$421$	−7.72587	−0.376536	−0.188268	+	0.982118i	$0.560287\pi$
$422$	17.2620	0.840303
$423$	4.98792	0.242521
$424$	8.88769	0.431624
$425$	−30.3538	−1.47237
$426$	−6.81163	−0.330024
$427$	−2.31767	−0.112160
$428$	−6.63102	−0.320523
$429$	0	0
$430$	4.56166	0.219983
$431$	−0.640120	−0.0308335	−0.0154168	−	0.999881i	$-0.504907\pi$
$431$	−0.640120	−0.0308335	−0.0154168	+	0.999881i	$0.504907\pi$
$432$	1.00000	0.0481125
$433$	21.2760	1.02246	0.511231	−	0.859443i	$-0.329190\pi$
$433$	21.2760	1.02246	0.511231	+	0.859443i	$0.329190\pi$
$434$	0.985999	0.0473295
$435$	−5.41789	−0.259768
$436$	12.9879	0.622008
$437$	−17.2707	−0.826168
$438$	−3.18598	−0.152232
$439$	12.7181	0.607002	0.303501	−	0.952831i	$-0.401844\pi$
$439$	12.7181	0.607002	0.303501	+	0.952831i	$0.401844\pi$
$440$	2.03385	0.0969601
$441$	−6.87263	−0.327268
$442$	0	0
$443$	22.5972	1.07362	0.536812	−	0.843702i	$-0.319628\pi$
$443$	22.5972	1.07362	0.536812	+	0.843702i	$0.319628\pi$
$444$	10.0978	0.479222
$445$	−0.274127	−0.0129949
$446$	6.76809	0.320478
$447$	20.8170	0.984610
$448$	0.356896	0.0168617
$449$	−11.6474	−0.549676	−0.274838	−	0.961491i	$-0.588624\pi$
$449$	−11.6474	−0.549676	−0.274838	+	0.961491i	$0.588624\pi$
$450$	4.52111	0.213127
$451$	14.3720	0.676749
$452$	0.792249	0.0372643
$453$	0.895461	0.0420724
$454$	23.6799	1.11135
$455$	0	0
$456$	7.20775	0.337534
$457$	21.1890	0.991178	0.495589	−	0.868557i	$-0.334952\pi$
$457$	21.1890	0.991178	0.495589	+	0.868557i	$0.334952\pi$
$458$	−8.29829	−0.387754
$459$	6.71379	0.313373
$460$	−1.65817	−0.0773126
$461$	−24.0694	−1.12102	−0.560511	−	0.828147i	$-0.689395\pi$
$461$	−24.0694	−1.12102	−0.560511	+	0.828147i	$0.689395\pi$
$462$	−1.04892	−0.0488001
$463$	18.1715	0.844502	0.422251	−	0.906479i	$-0.361240\pi$
$463$	18.1715	0.844502	0.422251	+	0.906479i	$0.361240\pi$
$464$	7.82908	0.363456
$465$	1.91185	0.0886601
$466$	23.9651	1.11016
$467$	−2.93123	−0.135641	−0.0678206	−	0.997698i	$-0.521605\pi$
$467$	−2.93123	−0.135641	−0.0678206	+	0.997698i	$0.521605\pi$
$468$	0	0
$469$	4.82717	0.222898
$470$	3.45175	0.159217
$471$	8.59179	0.395889
$472$	−1.64310	−0.0756300
$473$	19.3733	0.890785
$474$	−15.0465	−0.691110
$475$	32.5870	1.49519
$476$	2.39612	0.109826
$477$	−8.88769	−0.406939
$478$	12.6160	0.577040
$479$	30.7090	1.40313	0.701565	−	0.712605i	$-0.252485\pi$
$479$	30.7090	1.40313	0.701565	+	0.712605i	$0.252485\pi$
$480$	0.692021	0.0315863
$481$	0	0
$482$	26.3937	1.20220
$483$	0.855167	0.0389114
$484$	−2.36227	−0.107376
$485$	0.289192	0.0131315
$486$	−1.00000	−0.0453609
$487$	−24.1497	−1.09433	−0.547164	−	0.837025i	$-0.684293\pi$
$487$	−24.1497	−1.09433	−0.547164	+	0.837025i	$0.684293\pi$
$488$	6.49396	0.293968
$489$	−1.72587	−0.0780467
$490$	−4.75600	−0.214854
$491$	14.5972	0.658761	0.329381	−	0.944197i	$-0.393160\pi$
$491$	14.5972	0.658761	0.329381	+	0.944197i	$0.393160\pi$
$492$	4.89008	0.220462
$493$	52.5628	2.36731
$494$	0	0
$495$	−2.03385	−0.0914148
$496$	−2.76271	−0.124049
$497$	2.43104	0.109047
$498$	14.8267	0.664400
$499$	−6.85517	−0.306879	−0.153440	−	0.988158i	$-0.549035\pi$
$499$	−6.85517	−0.306879	−0.153440	+	0.988158i	$0.549035\pi$
$500$	6.58881	0.294661
$501$	−21.1400	−0.944468
$502$	30.0344	1.34050
$503$	−26.7332	−1.19197	−0.595987	−	0.802994i	$-0.703239\pi$
$503$	−26.7332	−1.19197	−0.595987	+	0.802994i	$0.703239\pi$
$504$	−0.356896	−0.0158974
$505$	−6.93064	−0.308409
$506$	−7.04221	−0.313065
$507$	0	0
$508$	−18.2174	−0.808268
$509$	20.6595	0.915716	0.457858	−	0.889025i	$-0.348617\pi$
$509$	20.6595	0.915716	0.457858	+	0.889025i	$0.348617\pi$
$510$	4.64609	0.205732
$511$	1.13706	0.0503007
$512$	−1.00000	−0.0441942
$513$	−7.20775	−0.318230
$514$	−11.2620	−0.496748
$515$	6.66115	0.293525
$516$	6.59179	0.290188
$517$	14.6595	0.644724
$518$	−3.60388	−0.158345
$519$	9.35450	0.410617
$520$	0	0
$521$	−15.0965	−0.661390	−0.330695	−	0.943738i	$-0.607283\pi$
$521$	−15.0965	−0.661390	−0.330695	+	0.943738i	$0.607283\pi$
$522$	−7.82908	−0.342670
$523$	0.0349168	0.00152680	0.000763402	−	1.00000i	$-0.499757\pi$
$523$	0.0349168	0.00152680	0.000763402		1.00000i	$0.499757\pi$
$524$	2.73556	0.119504
$525$	−1.61356	−0.0704217
$526$	5.54958	0.241973
$527$	−18.5483	−0.807975
$528$	2.93900	0.127904
$529$	−17.2586	−0.750373
$530$	−6.15047	−0.267159
$531$	1.64310	0.0713046
$532$	−2.57242	−0.111528
$533$	0	0
$534$	−0.396125	−0.0171420
$535$	4.58881	0.198392
$536$	−13.5254	−0.584209
$537$	3.17523	0.137021
$538$	−16.6872	−0.719438
$539$	−20.1987	−0.870018
$540$	−0.692021	−0.0297799
$541$	−13.0858	−0.562600	−0.281300	−	0.959620i	$-0.590766\pi$
$541$	−13.0858	−0.562600	−0.281300	+	0.959620i	$0.590766\pi$
$542$	−6.61356	−0.284077
$543$	−19.7995	−0.849680
$544$	−6.71379	−0.287851
$545$	−8.98792	−0.385000
$546$	0	0
$547$	−5.97584	−0.255508	−0.127754	−	0.991806i	$-0.540777\pi$
$547$	−5.97584	−0.255508	−0.127754	+	0.991806i	$0.540777\pi$
$548$	−7.64742	−0.326681
$549$	−6.49396	−0.277155
$550$	13.2875	0.566582
$551$	−56.4301	−2.40400
$552$	−2.39612	−0.101986
$553$	5.37004	0.228357
$554$	21.7995	0.926174
$555$	−6.98792	−0.296621
$556$	3.38404	0.143515
$557$	10.4397	0.442343	0.221171	−	0.975235i	$-0.429012\pi$
$557$	10.4397	0.442343	0.221171	+	0.975235i	$0.429012\pi$
$558$	2.76271	0.116955
$559$	0	0
$560$	−0.246980	−0.0104368
$561$	19.7318	0.833079
$562$	20.5918	0.868612
$563$	−5.66056	−0.238564	−0.119282	−	0.992860i	$-0.538059\pi$
$563$	−5.66056	−0.238564	−0.119282	+	0.992860i	$0.538059\pi$
$564$	4.98792	0.210029
$565$	−0.548253	−0.0230652
$566$	13.0121	0.546939
$567$	0.356896	0.0149882
$568$	−6.81163	−0.285809
$569$	20.6568	0.865980	0.432990	−	0.901399i	$-0.357459\pi$
$569$	20.6568	0.865980	0.432990	+	0.901399i	$0.357459\pi$
$570$	−4.98792	−0.208921
$571$	44.3672	1.85671	0.928354	−	0.371697i	$-0.121224\pi$
$571$	44.3672	1.85671	0.928354	+	0.371697i	$0.121224\pi$
$572$	0	0
$573$	15.2620	0.637581
$574$	−1.74525	−0.0728454
$575$	−10.8331	−0.451773
$576$	1.00000	0.0416667
$577$	−29.4426	−1.22571	−0.612857	−	0.790194i	$-0.709980\pi$
$577$	−29.4426	−1.22571	−0.612857	+	0.790194i	$0.709980\pi$
$578$	−28.0750	−1.16777
$579$	−4.76809	−0.198155
$580$	−5.41789	−0.224966
$581$	−5.29159	−0.219532
$582$	0.417895	0.0173223
$583$	−26.1209	−1.08182
$584$	−3.18598	−0.131837
$585$	0	0
$586$	−14.9390	−0.617124
$587$	19.5636	0.807475	0.403738	−	0.914875i	$-0.367711\pi$
$587$	19.5636	0.807475	0.403738	+	0.914875i	$0.367711\pi$
$588$	−6.87263	−0.283422
$589$	19.9129	0.820498
$590$	1.13706	0.0468122
$591$	−12.2349	−0.503276
$592$	10.0978	0.415018
$593$	10.8793	0.446761	0.223380	−	0.974731i	$-0.428291\pi$
$593$	10.8793	0.446761	0.223380	+	0.974731i	$0.428291\pi$
$594$	−2.93900	−0.120589
$595$	−1.65817	−0.0679783
$596$	20.8170	0.852698
$597$	−11.8485	−0.484925
$598$	0	0
$599$	16.0543	0.655961	0.327980	−	0.944685i	$-0.393632\pi$
$599$	16.0543	0.655961	0.327980	+	0.944685i	$0.393632\pi$
$600$	4.52111	0.184573
$601$	12.8955	0.526017	0.263008	−	0.964794i	$-0.415285\pi$
$601$	12.8955	0.526017	0.263008	+	0.964794i	$0.415285\pi$
$602$	−2.35258	−0.0958842
$603$	13.5254	0.550798
$604$	0.895461	0.0364358
$605$	1.63474	0.0664618
$606$	−10.0151	−0.406834
$607$	44.4741	1.80515	0.902574	−	0.430534i	$-0.141675\pi$
$607$	44.4741	1.80515	0.902574	+	0.430534i	$0.141675\pi$
$608$	7.20775	0.292313
$609$	2.79417	0.113225
$610$	−4.49396	−0.181955
$611$	0	0
$612$	6.71379	0.271389
$613$	−42.0253	−1.69739	−0.848694	−	0.528884i	$-0.822610\pi$
$613$	−42.0253	−1.69739	−0.848694	+	0.528884i	$0.822610\pi$
$614$	26.0301	1.05049
$615$	−3.38404	−0.136458
$616$	−1.04892	−0.0422621
$617$	16.6655	0.670926	0.335463	−	0.942053i	$-0.391107\pi$
$617$	16.6655	0.670926	0.335463	+	0.942053i	$0.391107\pi$
$618$	9.62565	0.387200
$619$	−39.7512	−1.59774	−0.798868	−	0.601506i	$-0.794568\pi$
$619$	−39.7512	−1.59774	−0.798868	+	0.601506i	$0.794568\pi$
$620$	1.91185	0.0767819
$621$	2.39612	0.0961532
$622$	4.81163	0.192929
$623$	0.141375	0.00566408
$624$	0	0
$625$	18.0459	0.721837
$626$	26.0411	1.04081
$627$	−21.1836	−0.845991
$628$	8.59179	0.342850
$629$	67.7948	2.70315
$630$	0.246980	0.00983990
$631$	−14.5767	−0.580290	−0.290145	−	0.956983i	$-0.593704\pi$
$631$	−14.5767	−0.580290	−0.290145	+	0.956983i	$0.593704\pi$
$632$	−15.0465	−0.598519
$633$	−17.2620	−0.686105
$634$	−11.5211	−0.457562
$635$	12.6069	0.500288
$636$	−8.88769	−0.352420
$637$	0	0
$638$	−23.0097	−0.910962
$639$	6.81163	0.269464
$640$	0.692021	0.0273546
$641$	38.4349	1.51809	0.759043	−	0.651040i	$-0.225667\pi$
$641$	38.4349	1.51809	0.759043	+	0.651040i	$0.225667\pi$
$642$	6.63102	0.261706
$643$	1.04221	0.0411009	0.0205504	−	0.999789i	$-0.493458\pi$
$643$	1.04221	0.0411009	0.0205504	+	0.999789i	$0.493458\pi$
$644$	0.855167	0.0336983
$645$	−4.56166	−0.179615
$646$	48.3913	1.90393
$647$	−28.1608	−1.10711	−0.553557	−	0.832811i	$-0.686730\pi$
$647$	−28.1608	−1.10711	−0.553557	+	0.832811i	$0.686730\pi$
$648$	−1.00000	−0.0392837
$649$	4.82908	0.189558
$650$	0	0
$651$	−0.985999	−0.0386444
$652$	−1.72587	−0.0675904
$653$	10.6203	0.415603	0.207802	−	0.978171i	$-0.433369\pi$
$653$	10.6203	0.415603	0.207802	+	0.978171i	$0.433369\pi$
$654$	−12.9879	−0.507868
$655$	−1.89307	−0.0739683
$656$	4.89008	0.190926
$657$	3.18598	0.124297
$658$	−1.78017	−0.0693982
$659$	−40.3629	−1.57231	−0.786157	−	0.618027i	$-0.787932\pi$
$659$	−40.3629	−1.57231	−0.786157	+	0.618027i	$0.787932\pi$
$660$	−2.03385	−0.0791676
$661$	31.9168	1.24142	0.620709	−	0.784041i	$-0.286845\pi$
$661$	31.9168	1.24142	0.620709	+	0.784041i	$0.286845\pi$
$662$	3.43834	0.133635
$663$	0	0
$664$	14.8267	0.575387
$665$	1.78017	0.0690319
$666$	−10.0978	−0.391283
$667$	18.7595	0.726369
$668$	−21.1400	−0.817933
$669$	−6.76809	−0.261669
$670$	9.35988	0.361604
$671$	−19.0858	−0.736797
$672$	−0.356896	−0.0137676
$673$	3.82802	0.147559	0.0737797	−	0.997275i	$-0.476494\pi$
$673$	3.82802	0.147559	0.0737797	+	0.997275i	$0.476494\pi$
$674$	−8.20105	−0.315892
$675$	−4.52111	−0.174017
$676$	0	0
$677$	1.78927	0.0687670	0.0343835	−	0.999409i	$-0.489053\pi$
$677$	1.78927	0.0687670	0.0343835	+	0.999409i	$0.489053\pi$
$678$	−0.792249	−0.0304261
$679$	−0.149145	−0.00572366
$680$	4.64609	0.178169
$681$	−23.6799	−0.907417
$682$	8.11960	0.310916
$683$	−0.759725	−0.0290701	−0.0145350	−	0.999894i	$-0.504627\pi$
$683$	−0.759725	−0.0290701	−0.0145350	+	0.999894i	$0.504627\pi$
$684$	−7.20775	−0.275595
$685$	5.29218	0.202204
$686$	4.95108	0.189033
$687$	8.29829	0.316600
$688$	6.59179	0.251310
$689$	0	0
$690$	1.65817	0.0631254
$691$	−4.65950	−0.177256	−0.0886278	−	0.996065i	$-0.528248\pi$
$691$	−4.65950	−0.177256	−0.0886278	+	0.996065i	$0.528248\pi$
$692$	9.35450	0.355605
$693$	1.04892	0.0398451
$694$	−7.86294	−0.298473
$695$	−2.34183	−0.0888307
$696$	−7.82908	−0.296761
$697$	32.8310	1.24356
$698$	−18.7245	−0.708734
$699$	−23.9651	−0.906443
$700$	−1.61356	−0.0609870
$701$	−24.3284	−0.918872	−0.459436	−	0.888211i	$-0.651948\pi$
$701$	−24.3284	−0.918872	−0.459436	+	0.888211i	$0.651948\pi$
$702$	0	0
$703$	−72.7827	−2.74505
$704$	2.93900	0.110768
$705$	−3.45175	−0.130000
$706$	−31.5448	−1.18720
$707$	3.57434	0.134427
$708$	1.64310	0.0617516
$709$	29.3927	1.10386	0.551932	−	0.833889i	$-0.313891\pi$
$709$	29.3927	1.10386	0.551932	+	0.833889i	$0.313891\pi$
$710$	4.71379	0.176905
$711$	15.0465	0.564289
$712$	−0.396125	−0.0148454
$713$	−6.61979	−0.247913
$714$	−2.39612	−0.0896727
$715$	0	0
$716$	3.17523	0.118664
$717$	−12.6160	−0.471152
$718$	2.39612	0.0894226
$719$	−51.4878	−1.92017	−0.960086	−	0.279704i	$-0.909764\pi$
$719$	−51.4878	−1.92017	−0.960086	+	0.279704i	$0.909764\pi$
$720$	−0.692021	−0.0257901
$721$	−3.43535	−0.127939
$722$	−32.9517	−1.22633
$723$	−26.3937	−0.981593
$724$	−19.7995	−0.735844
$725$	−35.3961	−1.31458
$726$	2.36227	0.0876722
$727$	−3.67324	−0.136233	−0.0681164	−	0.997677i	$-0.521699\pi$
$727$	−3.67324	−0.136233	−0.0681164	+	0.997677i	$0.521699\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.20477	0.0816021
$731$	44.2559	1.63686
$732$	−6.49396	−0.240024
$733$	−18.3612	−0.678187	−0.339093	−	0.940753i	$-0.610120\pi$
$733$	−18.3612	−0.678187	−0.339093	+	0.940753i	$0.610120\pi$
$734$	0.00431187	0.000159154 0
$735$	4.75600	0.175428
$736$	−2.39612	−0.0883223
$737$	39.7512	1.46425
$738$	−4.89008	−0.180006
$739$	−1.68233	−0.0618856	−0.0309428	−	0.999521i	$-0.509851\pi$
$739$	−1.68233	−0.0618856	−0.0309428	+	0.999521i	$0.509851\pi$
$740$	−6.98792	−0.256881
$741$	0	0
$742$	3.17198	0.116447
$743$	−48.2935	−1.77172	−0.885858	−	0.463956i	$-0.846430\pi$
$743$	−48.2935	−1.77172	−0.885858	+	0.463956i	$0.846430\pi$
$744$	2.76271	0.101286
$745$	−14.4058	−0.527788
$746$	32.3129	1.18306
$747$	−14.8267	−0.542480
$748$	19.7318	0.721468
$749$	−2.36658	−0.0864731
$750$	−6.58881	−0.240589
$751$	11.7011	0.426980	0.213490	−	0.976945i	$-0.431517\pi$
$751$	11.7011	0.426980	0.213490	+	0.976945i	$0.431517\pi$
$752$	4.98792	0.181891
$753$	−30.0344	−1.09452
$754$	0	0
$755$	−0.619678	−0.0225524
$756$	0.356896	0.0129802
$757$	25.1836	0.915313	0.457657	−	0.889129i	$-0.348689\pi$
$757$	25.1836	0.915313	0.457657	+	0.889129i	$0.348689\pi$
$758$	19.7560	0.717570
$759$	7.04221	0.255616
$760$	−4.98792	−0.180931
$761$	−22.4155	−0.812561	−0.406281	−	0.913748i	$-0.633174\pi$
$761$	−22.4155	−0.812561	−0.406281	+	0.913748i	$0.633174\pi$
$762$	18.2174	0.659948
$763$	4.63533	0.167810
$764$	15.2620	0.552161
$765$	−4.64609	−0.167980
$766$	28.8116	1.04101
$767$	0	0
$768$	1.00000	0.0360844
$769$	0.132751	0.00478714	0.00239357	−	0.999997i	$-0.499238\pi$
$769$	0.132751	0.00478714	0.00239357	+	0.999997i	$0.499238\pi$
$770$	0.725873	0.0261587
$771$	11.2620	0.405593
$772$	−4.76809	−0.171607
$773$	48.0694	1.72893	0.864467	−	0.502689i	$-0.167656\pi$
$773$	48.0694	1.72893	0.864467	+	0.502689i	$0.167656\pi$
$774$	−6.59179	−0.236937
$775$	12.4905	0.448672
$776$	0.417895	0.0150015
$777$	3.60388	0.129288
$778$	−34.7821	−1.24700
$779$	−35.2465	−1.26284
$780$	0	0
$781$	20.0194	0.716350
$782$	−16.0871	−0.575273
$783$	7.82908	0.279789
$784$	−6.87263	−0.245451
$785$	−5.94571	−0.212211
$786$	−2.73556	−0.0975743
$787$	−6.20908	−0.221330	−0.110665	−	0.993858i	$-0.535298\pi$
$787$	−6.20908	−0.221330	−0.110665	+	0.993858i	$0.535298\pi$
$788$	−12.2349	−0.435850
$789$	−5.54958	−0.197570
$790$	10.4125	0.370461
$791$	0.282750	0.0100534
$792$	−2.93900	−0.104433
$793$	0	0
$794$	−5.15346	−0.182889
$795$	6.15047	0.218135
$796$	−11.8485	−0.419958
$797$	0.327830	0.0116123	0.00580616	−	0.999983i	$-0.498152\pi$
$797$	0.327830	0.0116123	0.00580616	+	0.999983i	$0.498152\pi$
$798$	2.57242	0.0910626
$799$	33.4878	1.18471
$800$	4.52111	0.159845
$801$	0.396125	0.0139964
$802$	13.3250	0.470521
$803$	9.36360	0.330434
$804$	13.5254	0.477005
$805$	−0.591794	−0.0208580
$806$	0	0
$807$	16.6872	0.587419
$808$	−10.0151	−0.352329
$809$	−37.4383	−1.31626	−0.658131	−	0.752904i	$-0.728653\pi$
$809$	−37.4383	−1.31626	−0.658131	+	0.752904i	$0.728653\pi$
$810$	0.692021	0.0243152
$811$	−17.1448	−0.602037	−0.301018	−	0.953618i	$-0.597327\pi$
$811$	−17.1448	−0.602037	−0.301018	+	0.953618i	$0.597327\pi$
$812$	2.79417	0.0980561
$813$	6.61356	0.231948
$814$	−29.6775	−1.04020
$815$	1.19434	0.0418360
$816$	6.71379	0.235030
$817$	−47.5120	−1.66223
$818$	−24.0237	−0.839969
$819$	0	0
$820$	−3.38404	−0.118176
$821$	17.7885	0.620824	0.310412	−	0.950602i	$-0.399533\pi$
$821$	17.7885	0.620824	0.310412	+	0.950602i	$0.399533\pi$
$822$	7.64742	0.266734
$823$	12.2301	0.426315	0.213157	−	0.977018i	$-0.431625\pi$
$823$	12.2301	0.426315	0.213157	+	0.977018i	$0.431625\pi$
$824$	9.62565	0.335325
$825$	−13.2875	−0.462613
$826$	−0.586417	−0.0204041
$827$	−20.5623	−0.715020	−0.357510	−	0.933909i	$-0.616374\pi$
$827$	−20.5623	−0.715020	−0.357510	+	0.933909i	$0.616374\pi$
$828$	2.39612	0.0832711
$829$	−25.4470	−0.883809	−0.441905	−	0.897062i	$-0.645697\pi$
$829$	−25.4470	−0.883809	−0.441905	+	0.897062i	$0.645697\pi$
$830$	−10.2604	−0.356143
$831$	−21.7995	−0.756218
$832$	0	0
$833$	−46.1414	−1.59870
$834$	−3.38404	−0.117180
$835$	14.6294	0.506270
$836$	−21.1836	−0.732650
$837$	−2.76271	−0.0954932
$838$	−13.8049	−0.476883
$839$	−5.76676	−0.199091	−0.0995453	−	0.995033i	$-0.531739\pi$
$839$	−5.76676	−0.199091	−0.0995453	+	0.995033i	$0.531739\pi$
$840$	0.246980	0.00852161
$841$	32.2946	1.11361
$842$	7.72587	0.266251
$843$	−20.5918	−0.709219
$844$	−17.2620	−0.594184
$845$	0	0
$846$	−4.98792	−0.171488
$847$	−0.843085	−0.0289688
$848$	−8.88769	−0.305205
$849$	−13.0121	−0.446573
$850$	30.3538	1.04113
$851$	24.1957	0.829417
$852$	6.81163	0.233362
$853$	21.1728	0.724944	0.362472	−	0.931995i	$-0.381933\pi$
$853$	21.1728	0.724944	0.362472	+	0.931995i	$0.381933\pi$
$854$	2.31767	0.0793089
$855$	4.98792	0.170583
$856$	6.63102	0.226644
$857$	12.0086	0.410207	0.205103	−	0.978740i	$-0.434247\pi$
$857$	12.0086	0.410207	0.205103	+	0.978740i	$0.434247\pi$
$858$	0	0
$859$	−1.66296	−0.0567393	−0.0283697	−	0.999598i	$-0.509032\pi$
$859$	−1.66296	−0.0567393	−0.0283697	+	0.999598i	$0.509032\pi$
$860$	−4.56166	−0.155551
$861$	1.74525	0.0594780
$862$	0.640120	0.0218026
$863$	23.8323	0.811262	0.405631	−	0.914037i	$-0.367052\pi$
$863$	23.8323	0.811262	0.405631	+	0.914037i	$0.367052\pi$
$864$	−1.00000	−0.0340207
$865$	−6.47352	−0.220106
$866$	−21.2760	−0.722989
$867$	28.0750	0.953477
$868$	−0.985999	−0.0334670
$869$	44.2218	1.50012
$870$	5.41789	0.183684
$871$	0	0
$872$	−12.9879	−0.439826
$873$	−0.417895	−0.0141436
$874$	17.2707	0.584189
$875$	2.35152	0.0794959
$876$	3.18598	0.107644
$877$	42.3177	1.42897	0.714483	−	0.699653i	$-0.246662\pi$
$877$	42.3177	1.42897	0.714483	+	0.699653i	$0.246662\pi$
$878$	−12.7181	−0.429215
$879$	14.9390	0.503880
$880$	−2.03385	−0.0685611
$881$	22.2741	0.750434	0.375217	−	0.926937i	$-0.377568\pi$
$881$	22.2741	0.750434	0.375217	+	0.926937i	$0.377568\pi$
$882$	6.87263	0.231413
$883$	−8.54229	−0.287471	−0.143735	−	0.989616i	$-0.545911\pi$
$883$	−8.54229	−0.287471	−0.143735	+	0.989616i	$0.545911\pi$
$884$	0	0
$885$	−1.13706	−0.0382220
$886$	−22.5972	−0.759167
$887$	−18.9142	−0.635078	−0.317539	−	0.948245i	$-0.602856\pi$
$887$	−18.9142	−0.635078	−0.317539	+	0.948245i	$0.602856\pi$
$888$	−10.0978	−0.338861
$889$	−6.50173	−0.218061
$890$	0.274127	0.00918875
$891$	2.93900	0.0984602
$892$	−6.76809	−0.226612
$893$	−35.9517	−1.20308
$894$	−20.8170	−0.696225
$895$	−2.19733	−0.0734485
$896$	−0.356896	−0.0119231
$897$	0	0
$898$	11.6474	0.388679
$899$	−21.6295	−0.721384
$900$	−4.52111	−0.150704
$901$	−59.6701	−1.98790
$902$	−14.3720	−0.478534
$903$	2.35258	0.0782891
$904$	−0.792249	−0.0263498
$905$	13.7017	0.455460
$906$	−0.895461	−0.0297497
$907$	13.9517	0.463258	0.231629	−	0.972804i	$-0.425595\pi$
$907$	13.9517	0.463258	0.231629	+	0.972804i	$0.425595\pi$
$908$	−23.6799	−0.785846
$909$	10.0151	0.332179
$910$	0	0
$911$	45.0422	1.49232	0.746158	−	0.665769i	$-0.231897\pi$
$911$	45.0422	1.49232	0.746158	+	0.665769i	$0.231897\pi$
$912$	−7.20775	−0.238672
$913$	−43.5757	−1.44214
$914$	−21.1890	−0.700869
$915$	4.49396	0.148566
$916$	8.29829	0.274183
$917$	0.976311	0.0322406
$918$	−6.71379	−0.221588
$919$	39.9976	1.31940	0.659700	−	0.751529i	$-0.270683\pi$
$919$	39.9976	1.31940	0.659700	+	0.751529i	$0.270683\pi$
$920$	1.65817	0.0546682
$921$	−26.0301	−0.857722
$922$	24.0694	0.792682
$923$	0	0
$924$	1.04892	0.0345068
$925$	−45.6534	−1.50107
$926$	−18.1715	−0.597153
$927$	−9.62565	−0.316148
$928$	−7.82908	−0.257002
$929$	−34.6848	−1.13797	−0.568986	−	0.822347i	$-0.692664\pi$
$929$	−34.6848	−1.13797	−0.568986	+	0.822347i	$0.692664\pi$
$930$	−1.91185	−0.0626922
$931$	49.5362	1.62348
$932$	−23.9651	−0.785002
$933$	−4.81163	−0.157526
$934$	2.93123	0.0959128
$935$	−13.6549	−0.446562
$936$	0	0
$937$	−19.1260	−0.624821	−0.312410	−	0.949947i	$-0.601136\pi$
$937$	−19.1260	−0.624821	−0.312410	+	0.949947i	$0.601136\pi$
$938$	−4.82717	−0.157613
$939$	−26.0411	−0.849821
$940$	−3.45175	−0.112584
$941$	22.5972	0.736647	0.368323	−	0.929698i	$-0.379932\pi$
$941$	22.5972	0.736647	0.368323	+	0.929698i	$0.379932\pi$
$942$	−8.59179	−0.279936
$943$	11.7172	0.381566
$944$	1.64310	0.0534785
$945$	−0.246980	−0.00803425
$946$	−19.3733	−0.629880
$947$	27.4359	0.891548	0.445774	−	0.895145i	$-0.352928\pi$
$947$	27.4359	0.891548	0.445774	+	0.895145i	$0.352928\pi$
$948$	15.0465	0.488688
$949$	0	0
$950$	−32.5870	−1.05726
$951$	11.5211	0.373597
$952$	−2.39612	−0.0776588
$953$	−1.84787	−0.0598584	−0.0299292	−	0.999552i	$-0.509528\pi$
$953$	−1.84787	−0.0598584	−0.0299292	+	0.999552i	$0.509528\pi$
$954$	8.88769	0.287750
$955$	−10.5617	−0.341767
$956$	−12.6160	−0.408029
$957$	23.0097	0.743798
$958$	−30.7090	−0.992163
$959$	−2.72933	−0.0881347
$960$	−0.692021	−0.0223349
$961$	−23.3674	−0.753788
$962$	0	0
$963$	−6.63102	−0.213682
$964$	−26.3937	−0.850085
$965$	3.29962	0.106218
$966$	−0.855167	−0.0275145
$967$	8.88471	0.285713	0.142856	−	0.989743i	$-0.454371\pi$
$967$	8.88471	0.285713	0.142856	+	0.989743i	$0.454371\pi$
$968$	2.36227	0.0759263
$969$	−48.3913	−1.55455
$970$	−0.289192	−0.00928540
$971$	35.0863	1.12597	0.562987	−	0.826466i	$-0.309652\pi$
$971$	35.0863	1.12597	0.562987	+	0.826466i	$0.309652\pi$
$972$	1.00000	0.0320750
$973$	1.20775	0.0387187
$974$	24.1497	0.773807
$975$	0	0
$976$	−6.49396	−0.207867
$977$	8.33704	0.266726	0.133363	−	0.991067i	$-0.457422\pi$
$977$	8.33704	0.266726	0.133363	+	0.991067i	$0.457422\pi$
$978$	1.72587	0.0551873
$979$	1.16421	0.0372083
$980$	4.75600	0.151925
$981$	12.9879	0.414672
$982$	−14.5972	−0.465814
$983$	55.6051	1.77353	0.886763	−	0.462224i	$-0.152949\pi$
$983$	55.6051	1.77353	0.886763	+	0.462224i	$0.152949\pi$
$984$	−4.89008	−0.155890
$985$	8.46681	0.269775
$986$	−52.5628	−1.67394
$987$	1.78017	0.0566634
$988$	0	0
$989$	15.7948	0.502244
$990$	2.03385	0.0646401
$991$	−43.5967	−1.38489	−0.692447	−	0.721468i	$-0.743468\pi$
$991$	−43.5967	−1.38489	−0.692447	+	0.721468i	$0.743468\pi$
$992$	2.76271	0.0877161
$993$	−3.43834	−0.109112
$994$	−2.43104	−0.0771079
$995$	8.19939	0.259938
$996$	−14.8267	−0.469802
$997$	22.4590	0.711285	0.355643	−	0.934622i	$-0.384262\pi$
$997$	22.4590	0.711285	0.355643	+	0.934622i	$0.384262\pi$
$998$	6.85517	0.216997
$999$	10.0978	0.319481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.m.1.1	✓	3
3.2	odd	2		3042.2.a.be.1.3		3
4.3	odd	2		8112.2.a.ce.1.1		3
13.2	odd	12		1014.2.i.g.823.3		12
13.3	even	3		1014.2.e.m.529.1		6
13.4	even	6		1014.2.e.k.991.3		6
13.5	odd	4		1014.2.b.g.337.6		6
13.6	odd	12		1014.2.i.g.361.6		12
13.7	odd	12		1014.2.i.g.361.1		12
13.8	odd	4		1014.2.b.g.337.1		6
13.9	even	3		1014.2.e.m.991.1		6
13.10	even	6		1014.2.e.k.529.3		6
13.11	odd	12		1014.2.i.g.823.4		12
13.12	even	2		1014.2.a.o.1.3	yes	3
39.5	even	4		3042.2.b.r.1351.1		6
39.8	even	4		3042.2.b.r.1351.6		6
39.38	odd	2		3042.2.a.bd.1.1		3
52.51	odd	2		8112.2.a.bz.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.1	✓	3	1.1	even	1	trivial
1014.2.a.o.1.3	yes	3	13.12	even	2
1014.2.b.g.337.1		6	13.8	odd	4
1014.2.b.g.337.6		6	13.5	odd	4
1014.2.e.k.529.3		6	13.10	even	6
1014.2.e.k.991.3		6	13.4	even	6
1014.2.e.m.529.1		6	13.3	even	3
1014.2.e.m.991.1		6	13.9	even	3
1014.2.i.g.361.1		12	13.7	odd	12
1014.2.i.g.361.6		12	13.6	odd	12
1014.2.i.g.823.3		12	13.2	odd	12
1014.2.i.g.823.4		12	13.11	odd	12
3042.2.a.bd.1.1		3	39.38	odd	2
3042.2.a.be.1.3		3	3.2	odd	2
3042.2.b.r.1351.1		6	39.5	even	4
3042.2.b.r.1351.6		6	39.8	even	4
8112.2.a.bz.1.3		3	52.51	odd	2
8112.2.a.ce.1.1		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.692021 q^{5} -1.00000 q^{6} +0.356896 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.692021 q^{5} -1.00000 q^{6} +0.356896 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.692021 q^{10} +2.93900 q^{11} +1.00000 q^{12} -0.356896 q^{14} -0.692021 q^{15} +1.00000 q^{16} +6.71379 q^{17} -1.00000 q^{18} -7.20775 q^{19} -0.692021 q^{20} +0.356896 q^{21} -2.93900 q^{22} +2.39612 q^{23} -1.00000 q^{24} -4.52111 q^{25} +1.00000 q^{27} +0.356896 q^{28} +7.82908 q^{29} +0.692021 q^{30} -2.76271 q^{31} -1.00000 q^{32} +2.93900 q^{33} -6.71379 q^{34} -0.246980 q^{35} +1.00000 q^{36} +10.0978 q^{37} +7.20775 q^{38} +0.692021 q^{40} +4.89008 q^{41} -0.356896 q^{42} +6.59179 q^{43} +2.93900 q^{44} -0.692021 q^{45} -2.39612 q^{46} +4.98792 q^{47} +1.00000 q^{48} -6.87263 q^{49} +4.52111 q^{50} +6.71379 q^{51} -8.88769 q^{53} -1.00000 q^{54} -2.03385 q^{55} -0.356896 q^{56} -7.20775 q^{57} -7.82908 q^{58} +1.64310 q^{59} -0.692021 q^{60} -6.49396 q^{61} +2.76271 q^{62} +0.356896 q^{63} +1.00000 q^{64} -2.93900 q^{66} +13.5254 q^{67} +6.71379 q^{68} +2.39612 q^{69} +0.246980 q^{70} +6.81163 q^{71} -1.00000 q^{72} +3.18598 q^{73} -10.0978 q^{74} -4.52111 q^{75} -7.20775 q^{76} +1.04892 q^{77} +15.0465 q^{79} -0.692021 q^{80} +1.00000 q^{81} -4.89008 q^{82} -14.8267 q^{83} +0.356896 q^{84} -4.64609 q^{85} -6.59179 q^{86} +7.82908 q^{87} -2.93900 q^{88} +0.396125 q^{89} +0.692021 q^{90} +2.39612 q^{92} -2.76271 q^{93} -4.98792 q^{94} +4.98792 q^{95} -1.00000 q^{96} -0.417895 q^{97} +6.87263 q^{98} +2.93900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - q^{11} + 3 q^{12} + 3 q^{14} + 3 q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + 2 q^{25} + 3 q^{27} - 3 q^{28} + 13 q^{29} - 3 q^{30} + 9 q^{31} - 3 q^{32} - q^{33} - 12 q^{34} + 4 q^{35} + 3 q^{36} + 12 q^{37} + 4 q^{38} - 3 q^{40} + 14 q^{41} + 3 q^{42} - 8 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} - 4 q^{47} + 3 q^{48} - 4 q^{49} - 2 q^{50} + 12 q^{51} + 15 q^{53} - 3 q^{54} - 22 q^{55} + 3 q^{56} - 4 q^{57} - 13 q^{58} + 9 q^{59} + 3 q^{60} - 10 q^{61} - 9 q^{62} - 3 q^{63} + 3 q^{64} + q^{66} + 6 q^{67} + 12 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{72} - 5 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 5 q^{79} + 3 q^{80} + 3 q^{81} - 14 q^{82} + 7 q^{83} - 3 q^{84} + 26 q^{85} + 8 q^{86} + 13 q^{87} + q^{88} + 10 q^{89} - 3 q^{90} + 16 q^{92} + 9 q^{93} + 4 q^{94} - 4 q^{95} - 3 q^{96} - 7 q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - q^11 + 3 * q^12 + 3 * q^14 + 3 * q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + 2 * q^25 + 3 * q^27 - 3 * q^28 + 13 * q^29 - 3 * q^30 + 9 * q^31 - 3 * q^32 - q^33 - 12 * q^34 + 4 * q^35 + 3 * q^36 + 12 * q^37 + 4 * q^38 - 3 * q^40 + 14 * q^41 + 3 * q^42 - 8 * q^43 - q^44 + 3 * q^45 - 16 * q^46 - 4 * q^47 + 3 * q^48 - 4 * q^49 - 2 * q^50 + 12 * q^51 + 15 * q^53 - 3 * q^54 - 22 * q^55 + 3 * q^56 - 4 * q^57 - 13 * q^58 + 9 * q^59 + 3 * q^60 - 10 * q^61 - 9 * q^62 - 3 * q^63 + 3 * q^64 + q^66 + 6 * q^67 + 12 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^72 - 5 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 5 * q^79 + 3 * q^80 + 3 * q^81 - 14 * q^82 + 7 * q^83 - 3 * q^84 + 26 * q^85 + 8 * q^86 + 13 * q^87 + q^88 + 10 * q^89 - 3 * q^90 + 16 * q^92 + 9 * q^93 + 4 * q^94 - 4 * q^95 - 3 * q^96 - 7 * q^97 + 4 * q^98 - q^99

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