LMFDB - Embedded newform 2667.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.118870813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 $ x^7 - 9x^5 - 3x^4 + 20x^3 + 7x^2 - 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.69855$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +2.30993 q^{10} -5.62069 q^{11} -1.29302 q^{12} -3.65275 q^{13} +0.840819 q^{14} +2.74724 q^{15} +0.257957 q^{16} -5.86462 q^{17} +0.840819 q^{18} -2.05868 q^{19} -3.55225 q^{20} +1.00000 q^{21} -4.72598 q^{22} +2.78500 q^{23} -2.76884 q^{24} +2.54733 q^{25} -3.07130 q^{26} +1.00000 q^{27} -1.29302 q^{28} -4.83208 q^{29} +2.30993 q^{30} -6.87419 q^{31} +5.75457 q^{32} -5.62069 q^{33} -4.93108 q^{34} +2.74724 q^{35} -1.29302 q^{36} -8.71097 q^{37} -1.73097 q^{38} -3.65275 q^{39} -7.60666 q^{40} -4.09940 q^{41} +0.840819 q^{42} -2.48024 q^{43} +7.26768 q^{44} +2.74724 q^{45} +2.34168 q^{46} +12.6576 q^{47} +0.257957 q^{48} +1.00000 q^{49} +2.14185 q^{50} -5.86462 q^{51} +4.72310 q^{52} +4.92291 q^{53} +0.840819 q^{54} -15.4414 q^{55} -2.76884 q^{56} -2.05868 q^{57} -4.06291 q^{58} -9.41559 q^{59} -3.55225 q^{60} +4.96498 q^{61} -5.77995 q^{62} +1.00000 q^{63} +4.32264 q^{64} -10.0350 q^{65} -4.72598 q^{66} +4.57422 q^{67} +7.58309 q^{68} +2.78500 q^{69} +2.30993 q^{70} +2.13466 q^{71} -2.76884 q^{72} +9.59565 q^{73} -7.32435 q^{74} +2.54733 q^{75} +2.66192 q^{76} -5.62069 q^{77} -3.07130 q^{78} -10.0298 q^{79} +0.708669 q^{80} +1.00000 q^{81} -3.44685 q^{82} -5.06691 q^{83} -1.29302 q^{84} -16.1115 q^{85} -2.08543 q^{86} -4.83208 q^{87} +15.5628 q^{88} +2.73622 q^{89} +2.30993 q^{90} -3.65275 q^{91} -3.60107 q^{92} -6.87419 q^{93} +10.6428 q^{94} -5.65568 q^{95} +5.75457 q^{96} +14.0813 q^{97} +0.840819 q^{98} -5.62069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * 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 $

$2$	0.840819	0.594549	0.297274	−	0.954792i	$-0.403922\pi$
$2$	0.840819	0.594549	0.297274	+	0.954792i	$0.403922\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.29302	−0.646512
$5$	2.74724	1.22860	0.614302	−	0.789071i	$-0.289438\pi$
$5$	2.74724	1.22860	0.614302	+	0.789071i	$0.289438\pi$
$6$	0.840819	0.343263
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.76884	−0.978932
$9$	1.00000	0.333333
$10$	2.30993	0.730465
$11$	−5.62069	−1.69470	−0.847351	−	0.531034i	$-0.821804\pi$
$11$	−5.62069	−1.69470	−0.847351	+	0.531034i	$0.821804\pi$
$12$	−1.29302	−0.373264
$13$	−3.65275	−1.01309	−0.506546	−	0.862213i	$-0.669078\pi$
$13$	−3.65275	−1.01309	−0.506546	+	0.862213i	$0.669078\pi$
$14$	0.840819	0.224718
$15$	2.74724	0.709335
$16$	0.257957	0.0644892
$17$	−5.86462	−1.42238	−0.711189	−	0.703000i	$-0.751843\pi$
$17$	−5.86462	−1.42238	−0.711189	+	0.703000i	$0.751843\pi$
$18$	0.840819	0.198183
$19$	−2.05868	−0.472293	−0.236146	−	0.971718i	$-0.575884\pi$
$19$	−2.05868	−0.472293	−0.236146	+	0.971718i	$0.575884\pi$
$20$	−3.55225	−0.794307
$21$	1.00000	0.218218
$22$	−4.72598	−1.00758
$23$	2.78500	0.580713	0.290356	−	0.956919i	$-0.406226\pi$
$23$	2.78500	0.580713	0.290356	+	0.956919i	$0.406226\pi$
$24$	−2.76884	−0.565186
$25$	2.54733	0.509467
$26$	−3.07130	−0.602332
$27$	1.00000	0.192450
$28$	−1.29302	−0.244358
$29$	−4.83208	−0.897295	−0.448648	−	0.893709i	$-0.648094\pi$
$29$	−4.83208	−0.897295	−0.448648	+	0.893709i	$0.648094\pi$
$30$	2.30993	0.421734
$31$	−6.87419	−1.23464	−0.617321	−	0.786712i	$-0.711782\pi$
$31$	−6.87419	−1.23464	−0.617321	+	0.786712i	$0.711782\pi$
$32$	5.75457	1.01727
$33$	−5.62069	−0.978436
$34$	−4.93108	−0.845674
$35$	2.74724	0.464369
$36$	−1.29302	−0.215504
$37$	−8.71097	−1.43207	−0.716037	−	0.698062i	$-0.754046\pi$
$37$	−8.71097	−1.43207	−0.716037	+	0.698062i	$0.754046\pi$
$38$	−1.73097	−0.280801
$39$	−3.65275	−0.584909
$40$	−7.60666	−1.20272
$41$	−4.09940	−0.640219	−0.320109	−	0.947381i	$-0.603720\pi$
$41$	−4.09940	−0.640219	−0.320109	+	0.947381i	$0.603720\pi$
$42$	0.840819	0.129741
$43$	−2.48024	−0.378233	−0.189116	−	0.981955i	$-0.560562\pi$
$43$	−2.48024	−0.378233	−0.189116	+	0.981955i	$0.560562\pi$
$44$	7.26768	1.09564
$45$	2.74724	0.409535
$46$	2.34168	0.345262
$47$	12.6576	1.84630	0.923152	−	0.384434i	$-0.125603\pi$
$47$	12.6576	1.84630	0.923152	+	0.384434i	$0.125603\pi$
$48$	0.257957	0.0372328
$49$	1.00000	0.142857
$50$	2.14185	0.302903
$51$	−5.86462	−0.821211
$52$	4.72310	0.654975
$53$	4.92291	0.676214	0.338107	−	0.941108i	$-0.390213\pi$
$53$	4.92291	0.676214	0.338107	+	0.941108i	$0.390213\pi$
$54$	0.840819	0.114421
$55$	−15.4414	−2.08212
$56$	−2.76884	−0.370001
$57$	−2.05868	−0.272678
$58$	−4.06291	−0.533486
$59$	−9.41559	−1.22581	−0.612903	−	0.790158i	$-0.709998\pi$
$59$	−9.41559	−1.22581	−0.612903	+	0.790158i	$0.709998\pi$
$60$	−3.55225	−0.458593
$61$	4.96498	0.635701	0.317850	−	0.948141i	$-0.397039\pi$
$61$	4.96498	0.635701	0.317850	+	0.948141i	$0.397039\pi$
$62$	−5.77995	−0.734055
$63$	1.00000	0.125988
$64$	4.32264	0.540330
$65$	−10.0350	−1.24469
$66$	−4.72598	−0.581728
$67$	4.57422	0.558829	0.279415	−	0.960171i	$-0.409860\pi$
$67$	4.57422	0.558829	0.279415	+	0.960171i	$0.409860\pi$
$68$	7.58309	0.919585
$69$	2.78500	0.335275
$70$	2.30993	0.276090
$71$	2.13466	0.253338	0.126669	−	0.991945i	$-0.459571\pi$
$71$	2.13466	0.253338	0.126669	+	0.991945i	$0.459571\pi$
$72$	−2.76884	−0.326311
$73$	9.59565	1.12309	0.561543	−	0.827448i	$-0.310208\pi$
$73$	9.59565	1.12309	0.561543	+	0.827448i	$0.310208\pi$
$74$	−7.32435	−0.851438
$75$	2.54733	0.294141
$76$	2.66192	0.305343
$77$	−5.62069	−0.640537
$78$	−3.07130	−0.347757
$79$	−10.0298	−1.12844	−0.564220	−	0.825624i	$-0.690823\pi$
$79$	−10.0298	−1.12844	−0.564220	+	0.825624i	$0.690823\pi$
$80$	0.708669	0.0792316
$81$	1.00000	0.111111
$82$	−3.44685	−0.380641
$83$	−5.06691	−0.556166	−0.278083	−	0.960557i	$-0.589699\pi$
$83$	−5.06691	−0.556166	−0.278083	+	0.960557i	$0.589699\pi$
$84$	−1.29302	−0.141080
$85$	−16.1115	−1.74754
$86$	−2.08543	−0.224878
$87$	−4.83208	−0.518054
$88$	15.5628	1.65900
$89$	2.73622	0.290039	0.145019	−	0.989429i	$-0.453676\pi$
$89$	2.73622	0.290039	0.145019	+	0.989429i	$0.453676\pi$
$90$	2.30993	0.243488
$91$	−3.65275	−0.382913
$92$	−3.60107	−0.375437
$93$	−6.87419	−0.712821
$94$	10.6428	1.09772
$95$	−5.65568	−0.580260
$96$	5.75457	0.587323
$97$	14.0813	1.42974	0.714872	−	0.699255i	$-0.246485\pi$
$97$	14.0813	1.42974	0.714872	+	0.699255i	$0.246485\pi$
$98$	0.840819	0.0849355
$99$	−5.62069	−0.564900
$100$	−3.29376	−0.329376
$101$	−2.91727	−0.290279	−0.145139	−	0.989411i	$-0.546363\pi$
$101$	−2.91727	−0.290279	−0.145139	+	0.989411i	$0.546363\pi$
$102$	−4.93108	−0.488250
$103$	17.2096	1.69571	0.847855	−	0.530228i	$-0.177894\pi$
$103$	17.2096	1.69571	0.847855	+	0.530228i	$0.177894\pi$
$104$	10.1139	0.991747
$105$	2.74724	0.268103
$106$	4.13928	0.402042
$107$	3.25655	0.314823	0.157411	−	0.987533i	$-0.449685\pi$
$107$	3.25655	0.314823	0.157411	+	0.987533i	$0.449685\pi$
$108$	−1.29302	−0.124421
$109$	9.69847	0.928945	0.464472	−	0.885588i	$-0.346244\pi$
$109$	9.69847	0.928945	0.464472	+	0.885588i	$0.346244\pi$
$110$	−12.9834	−1.23792
$111$	−8.71097	−0.826808
$112$	0.257957	0.0243746
$113$	1.89566	0.178329	0.0891645	−	0.996017i	$-0.471580\pi$
$113$	1.89566	0.178329	0.0891645	+	0.996017i	$0.471580\pi$
$114$	−1.73097	−0.162121
$115$	7.65107	0.713466
$116$	6.24800	0.580112
$117$	−3.65275	−0.337697
$118$	−7.91681	−0.728801
$119$	−5.86462	−0.537609
$120$	−7.60666	−0.694390
$121$	20.5921	1.87201
$122$	4.17465	0.377955
$123$	−4.09940	−0.369631
$124$	8.88849	0.798210
$125$	−6.73807	−0.602671
$126$	0.840819	0.0749061
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−7.87458	−0.696021
$129$	−2.48024	−0.218373
$130$	−8.43761	−0.740028
$131$	5.84500	0.510680	0.255340	−	0.966851i	$-0.417813\pi$
$131$	5.84500	0.510680	0.255340	+	0.966851i	$0.417813\pi$
$132$	7.26768	0.632571
$133$	−2.05868	−0.178510
$134$	3.84609	0.332251
$135$	2.74724	0.236445
$136$	16.2382	1.39241
$137$	−10.6774	−0.912233	−0.456117	−	0.889920i	$-0.650760\pi$
$137$	−10.6774	−0.912233	−0.456117	+	0.889920i	$0.650760\pi$
$138$	2.34168	0.199337
$139$	−21.7313	−1.84323	−0.921613	−	0.388111i	$-0.873128\pi$
$139$	−21.7313	−1.84323	−0.921613	+	0.388111i	$0.873128\pi$
$140$	−3.55225	−0.300220
$141$	12.6576	1.06596
$142$	1.79486	0.150622
$143$	20.5310	1.71689
$144$	0.257957	0.0214964
$145$	−13.2749	−1.10242
$146$	8.06821	0.667729
$147$	1.00000	0.0824786
$148$	11.2635	0.925853
$149$	−16.2091	−1.32790	−0.663952	−	0.747775i	$-0.731122\pi$
$149$	−16.2091	−1.32790	−0.663952	+	0.747775i	$0.731122\pi$
$150$	2.14185	0.174881
$151$	−22.1101	−1.79929	−0.899646	−	0.436621i	$-0.856175\pi$
$151$	−22.1101	−1.79929	−0.899646	+	0.436621i	$0.856175\pi$
$152$	5.70014	0.462342
$153$	−5.86462	−0.474126
$154$	−4.72598	−0.380830
$155$	−18.8851	−1.51688
$156$	4.72310	0.378150
$157$	23.2986	1.85943	0.929714	−	0.368282i	$-0.120054\pi$
$157$	23.2986	1.85943	0.929714	+	0.368282i	$0.120054\pi$
$158$	−8.43325	−0.670913
$159$	4.92291	0.390412
$160$	15.8092	1.24983
$161$	2.78500	0.219489
$162$	0.840819	0.0660610
$163$	−21.5951	−1.69146	−0.845731	−	0.533609i	$-0.820835\pi$
$163$	−21.5951	−1.69146	−0.845731	+	0.533609i	$0.820835\pi$
$164$	5.30062	0.413909
$165$	−15.4414	−1.20211
$166$	−4.26036	−0.330668
$167$	−3.26635	−0.252758	−0.126379	−	0.991982i	$-0.540336\pi$
$167$	−3.26635	−0.252758	−0.126379	+	0.991982i	$0.540336\pi$
$168$	−2.76884	−0.213620
$169$	0.342604	0.0263542
$170$	−13.5469	−1.03900
$171$	−2.05868	−0.157431
$172$	3.20701	0.244532
$173$	9.97561	0.758431	0.379216	−	0.925308i	$-0.376194\pi$
$173$	9.97561	0.758431	0.379216	+	0.925308i	$0.376194\pi$
$174$	−4.06291	−0.308008
$175$	2.54733	0.192560
$176$	−1.44989	−0.109290
$177$	−9.41559	−0.707719
$178$	2.30066	0.172442
$179$	21.3721	1.59743	0.798714	−	0.601711i	$-0.205514\pi$
$179$	21.3721	1.59743	0.798714	+	0.601711i	$0.205514\pi$
$180$	−3.55225	−0.264769
$181$	−23.7938	−1.76858	−0.884288	−	0.466942i	$-0.845356\pi$
$181$	−23.7938	−1.76858	−0.884288	+	0.466942i	$0.845356\pi$
$182$	−3.07130	−0.227660
$183$	4.96498	0.367022
$184$	−7.71121	−0.568478
$185$	−23.9311	−1.75945
$186$	−5.77995	−0.423807
$187$	32.9632	2.41051
$188$	−16.3666	−1.19366
$189$	1.00000	0.0727393
$190$	−4.75540	−0.344993
$191$	17.1115	1.23814	0.619072	−	0.785335i	$-0.287509\pi$
$191$	17.1115	1.23814	0.619072	+	0.785335i	$0.287509\pi$
$192$	4.32264	0.311959
$193$	−21.1983	−1.52589	−0.762945	−	0.646464i	$-0.776247\pi$
$193$	−21.1983	−1.52589	−0.762945	+	0.646464i	$0.776247\pi$
$194$	11.8399	0.850053
$195$	−10.0350	−0.718621
$196$	−1.29302	−0.0923588
$197$	9.64407	0.687111	0.343556	−	0.939132i	$-0.388369\pi$
$197$	9.64407	0.687111	0.343556	+	0.939132i	$0.388369\pi$
$198$	−4.72598	−0.335861
$199$	−8.11930	−0.575562	−0.287781	−	0.957696i	$-0.592918\pi$
$199$	−8.11930	−0.575562	−0.287781	+	0.957696i	$0.592918\pi$
$200$	−7.05315	−0.498733
$201$	4.57422	0.322640
$202$	−2.45289	−0.172585
$203$	−4.83208	−0.339146
$204$	7.58309	0.530922
$205$	−11.2620	−0.786575
$206$	14.4701	1.00818
$207$	2.78500	0.193571
$208$	−0.942252	−0.0653334
$209$	11.5712	0.800395
$210$	2.30993	0.159400
$211$	−10.1539	−0.699023	−0.349511	−	0.936932i	$-0.613652\pi$
$211$	−10.1539	−0.699023	−0.349511	+	0.936932i	$0.613652\pi$
$212$	−6.36544	−0.437180
$213$	2.13466	0.146264
$214$	2.73817	0.187178
$215$	−6.81382	−0.464698
$216$	−2.76884	−0.188395
$217$	−6.87419	−0.466651
$218$	8.15466	0.552303
$219$	9.59565	0.648414
$220$	19.9661	1.34611
$221$	21.4220	1.44100
$222$	−7.32435	−0.491578
$223$	22.3276	1.49517	0.747583	−	0.664168i	$-0.231214\pi$
$223$	22.3276	1.49517	0.747583	+	0.664168i	$0.231214\pi$
$224$	5.75457	0.384493
$225$	2.54733	0.169822
$226$	1.59391	0.106025
$227$	−23.3340	−1.54873	−0.774365	−	0.632739i	$-0.781931\pi$
$227$	−23.3340	−1.54873	−0.774365	+	0.632739i	$0.781931\pi$
$228$	2.66192	0.176290
$229$	−8.57841	−0.566877	−0.283439	−	0.958990i	$-0.591475\pi$
$229$	−8.57841	−0.566877	−0.283439	+	0.958990i	$0.591475\pi$
$230$	6.43316	0.424190
$231$	−5.62069	−0.369814
$232$	13.3793	0.878391
$233$	14.6183	0.957677	0.478839	−	0.877903i	$-0.341058\pi$
$233$	14.6183	0.957677	0.478839	+	0.877903i	$0.341058\pi$
$234$	−3.07130	−0.200777
$235$	34.7736	2.26838
$236$	12.1746	0.792498
$237$	−10.0298	−0.651505
$238$	−4.93108	−0.319635
$239$	5.05219	0.326799	0.163399	−	0.986560i	$-0.447754\pi$
$239$	5.05219	0.326799	0.163399	+	0.986560i	$0.447754\pi$
$240$	0.708669	0.0457444
$241$	−15.9324	−1.02629	−0.513147	−	0.858301i	$-0.671520\pi$
$241$	−15.9324	−1.02629	−0.513147	+	0.858301i	$0.671520\pi$
$242$	17.3143	1.11300
$243$	1.00000	0.0641500
$244$	−6.41984	−0.410988
$245$	2.74724	0.175515
$246$	−3.44685	−0.219763
$247$	7.51983	0.478475
$248$	19.0335	1.20863
$249$	−5.06691	−0.321103
$250$	−5.66549	−0.358317
$251$	−11.8771	−0.749678	−0.374839	−	0.927090i	$-0.622302\pi$
$251$	−11.8771	−0.749678	−0.374839	+	0.927090i	$0.622302\pi$
$252$	−1.29302	−0.0814528
$253$	−15.6536	−0.984134
$254$	−0.840819	−0.0527577
$255$	−16.1115	−1.00894
$256$	−15.2664	−0.954148
$257$	−19.3728	−1.20844	−0.604221	−	0.796817i	$-0.706516\pi$
$257$	−19.3728	−1.20844	−0.604221	+	0.796817i	$0.706516\pi$
$258$	−2.08543	−0.129833
$259$	−8.71097	−0.541273
$260$	12.9755	0.804705
$261$	−4.83208	−0.299098
$262$	4.91459	0.303624
$263$	−25.0402	−1.54405	−0.772024	−	0.635594i	$-0.780755\pi$
$263$	−25.0402	−1.54405	−0.772024	+	0.635594i	$0.780755\pi$
$264$	15.5628	0.957822
$265$	13.5244	0.830799
$266$	−1.73097	−0.106133
$267$	2.73622	0.167454
$268$	−5.91457	−0.361290
$269$	−20.8253	−1.26974	−0.634870	−	0.772619i	$-0.718946\pi$
$269$	−20.8253	−1.26974	−0.634870	+	0.772619i	$0.718946\pi$
$270$	2.30993	0.140578
$271$	14.7479	0.895871	0.447936	−	0.894066i	$-0.352159\pi$
$271$	14.7479	0.895871	0.447936	+	0.894066i	$0.352159\pi$
$272$	−1.51282	−0.0917280
$273$	−3.65275	−0.221075
$274$	−8.97778	−0.542367
$275$	−14.3178	−0.863394
$276$	−3.60107	−0.216759
$277$	−12.6554	−0.760389	−0.380195	−	0.924907i	$-0.624143\pi$
$277$	−12.6554	−0.760389	−0.380195	+	0.924907i	$0.624143\pi$
$278$	−18.2721	−1.09589
$279$	−6.87419	−0.411547
$280$	−7.60666	−0.454585
$281$	−30.2858	−1.80670	−0.903350	−	0.428903i	$-0.858900\pi$
$281$	−30.2858	−1.80670	−0.903350	+	0.428903i	$0.858900\pi$
$282$	10.6428	0.633768
$283$	−0.554307	−0.0329501	−0.0164751	−	0.999864i	$-0.505244\pi$
$283$	−0.554307	−0.0329501	−0.0164751	+	0.999864i	$0.505244\pi$
$284$	−2.76017	−0.163786
$285$	−5.65568	−0.335013
$286$	17.2628	1.02077
$287$	−4.09940	−0.241980
$288$	5.75457	0.339091
$289$	17.3937	1.02316
$290$	−11.1618	−0.655443
$291$	14.0813	0.825463
$292$	−12.4074	−0.726088
$293$	10.7329	0.627023	0.313512	−	0.949584i	$-0.398495\pi$
$293$	10.7329	0.627023	0.313512	+	0.949584i	$0.398495\pi$
$294$	0.840819	0.0490376
$295$	−25.8669	−1.50603
$296$	24.1192	1.40190
$297$	−5.62069	−0.326145
$298$	−13.6289	−0.789504
$299$	−10.1729	−0.588315
$300$	−3.29376	−0.190165
$301$	−2.48024	−0.142959
$302$	−18.5906	−1.06977
$303$	−2.91727	−0.167593
$304$	−0.531049	−0.0304578
$305$	13.6400	0.781024
$306$	−4.93108	−0.281891
$307$	5.96740	0.340577	0.170289	−	0.985394i	$-0.445530\pi$
$307$	5.96740	0.340577	0.170289	+	0.985394i	$0.445530\pi$
$308$	7.26768	0.414115
$309$	17.2096	0.979019
$310$	−15.8789	−0.901862
$311$	26.7130	1.51475	0.757377	−	0.652978i	$-0.226481\pi$
$311$	26.7130	1.51475	0.757377	+	0.652978i	$0.226481\pi$
$312$	10.1139	0.572585
$313$	−25.9107	−1.46456	−0.732279	−	0.681005i	$-0.761543\pi$
$313$	−25.9107	−1.46456	−0.732279	+	0.681005i	$0.761543\pi$
$314$	19.5899	1.10552
$315$	2.74724	0.154790
$316$	12.9688	0.729550
$317$	−6.29184	−0.353385	−0.176693	−	0.984266i	$-0.556540\pi$
$317$	−6.29184	−0.353385	−0.176693	+	0.984266i	$0.556540\pi$
$318$	4.13928	0.232119
$319$	27.1596	1.52065
$320$	11.8753	0.663851
$321$	3.25655	0.181763
$322$	2.34168	0.130497
$323$	12.0733	0.671779
$324$	−1.29302	−0.0718346
$325$	−9.30478	−0.516136
$326$	−18.1576	−1.00566
$327$	9.69847	0.536327
$328$	11.3506	0.626731
$329$	12.6576	0.697838
$330$	−12.9834	−0.714713
$331$	6.26075	0.344122	0.172061	−	0.985086i	$-0.444957\pi$
$331$	6.26075	0.344122	0.172061	+	0.985086i	$0.444957\pi$
$332$	6.55164	0.359568
$333$	−8.71097	−0.477358
$334$	−2.74641	−0.150277
$335$	12.5665	0.686580
$336$	0.257957	0.0140727
$337$	10.6291	0.579003	0.289502	−	0.957178i	$-0.406510\pi$
$337$	10.6291	0.579003	0.289502	+	0.957178i	$0.406510\pi$
$338$	0.288068	0.0156688
$339$	1.89566	0.102958
$340$	20.8326	1.12980
$341$	38.6377	2.09235
$342$	−1.73097	−0.0936003
$343$	1.00000	0.0539949
$344$	6.86738	0.370264
$345$	7.65107	0.411920
$346$	8.38768	0.450925
$347$	24.2445	1.30151	0.650757	−	0.759286i	$-0.274452\pi$
$347$	24.2445	1.30151	0.650757	+	0.759286i	$0.274452\pi$
$348$	6.24800	0.334928
$349$	19.2656	1.03127	0.515633	−	0.856810i	$-0.327557\pi$
$349$	19.2656	1.03127	0.515633	+	0.856810i	$0.327557\pi$
$350$	2.14185	0.114487
$351$	−3.65275	−0.194970
$352$	−32.3446	−1.72397
$353$	2.47593	0.131780	0.0658902	−	0.997827i	$-0.479011\pi$
$353$	2.47593	0.131780	0.0658902	+	0.997827i	$0.479011\pi$
$354$	−7.91681	−0.420774
$355$	5.86443	0.311251
$356$	−3.53800	−0.187513
$357$	−5.86462	−0.310389
$358$	17.9701	0.949749
$359$	31.8474	1.68084	0.840422	−	0.541933i	$-0.182307\pi$
$359$	31.8474	1.68084	0.840422	+	0.541933i	$0.182307\pi$
$360$	−7.60666	−0.400906
$361$	−14.7619	−0.776940
$362$	−20.0062	−1.05150
$363$	20.5921	1.08081
$364$	4.72310	0.247557
$365$	26.3616	1.37983
$366$	4.17465	0.218213
$367$	9.45164	0.493372	0.246686	−	0.969095i	$-0.420658\pi$
$367$	9.45164	0.493372	0.246686	+	0.969095i	$0.420658\pi$
$368$	0.718409	0.0374497
$369$	−4.09940	−0.213406
$370$	−20.1217	−1.04608
$371$	4.92291	0.255585
$372$	8.88849	0.460847
$373$	−8.74070	−0.452576	−0.226288	−	0.974060i	$-0.572659\pi$
$373$	−8.74070	−0.452576	−0.226288	+	0.974060i	$0.572659\pi$
$374$	27.7161	1.43316
$375$	−6.73807	−0.347952
$376$	−35.0469	−1.80741
$377$	17.6504	0.909042
$378$	0.840819	0.0432471
$379$	−15.3774	−0.789882	−0.394941	−	0.918707i	$-0.629235\pi$
$379$	−15.3774	−0.789882	−0.394941	+	0.918707i	$0.629235\pi$
$380$	7.31292	0.375145
$381$	−1.00000	−0.0512316
$382$	14.3877	0.736137
$383$	19.4375	0.993210	0.496605	−	0.867977i	$-0.334580\pi$
$383$	19.4375	0.993210	0.496605	+	0.867977i	$0.334580\pi$
$384$	−7.87458	−0.401848
$385$	−15.4414	−0.786966
$386$	−17.8240	−0.907216
$387$	−2.48024	−0.126078
$388$	−18.2075	−0.924347
$389$	20.2992	1.02921	0.514604	−	0.857428i	$-0.327939\pi$
$389$	20.2992	1.02921	0.514604	+	0.857428i	$0.327939\pi$
$390$	−8.43761	−0.427255
$391$	−16.3330	−0.825993
$392$	−2.76884	−0.139847
$393$	5.84500	0.294841
$394$	8.10891	0.408521
$395$	−27.5543	−1.38641
$396$	7.26768	0.365215
$397$	−5.04735	−0.253319	−0.126660	−	0.991946i	$-0.540426\pi$
$397$	−5.04735	−0.253319	−0.126660	+	0.991946i	$0.540426\pi$
$398$	−6.82686	−0.342200
$399$	−2.05868	−0.103063
$400$	0.657102	0.0328551
$401$	0.828202	0.0413584	0.0206792	−	0.999786i	$-0.493417\pi$
$401$	0.828202	0.0413584	0.0206792	+	0.999786i	$0.493417\pi$
$402$	3.84609	0.191825
$403$	25.1097	1.25080
$404$	3.77209	0.187669
$405$	2.74724	0.136512
$406$	−4.06291	−0.201639
$407$	48.9616	2.42694
$408$	16.2382	0.803909
$409$	7.63539	0.377546	0.188773	−	0.982021i	$-0.439549\pi$
$409$	7.63539	0.377546	0.188773	+	0.982021i	$0.439549\pi$
$410$	−9.46934	−0.467657
$411$	−10.6774	−0.526678
$412$	−22.2524	−1.09630
$413$	−9.41559	−0.463311
$414$	2.34168	0.115087
$415$	−13.9200	−0.683308
$416$	−21.0200	−1.03059
$417$	−21.7313	−1.06419
$418$	9.72926	0.475874
$419$	−0.606948	−0.0296514	−0.0148257	−	0.999890i	$-0.504719\pi$
$419$	−0.606948	−0.0296514	−0.0148257	+	0.999890i	$0.504719\pi$
$420$	−3.55225	−0.173332
$421$	12.2074	0.594951	0.297476	−	0.954729i	$-0.403855\pi$
$421$	12.2074	0.594951	0.297476	+	0.954729i	$0.403855\pi$
$422$	−8.53759	−0.415603
$423$	12.6576	0.615435
$424$	−13.6307	−0.661967
$425$	−14.9391	−0.724655
$426$	1.79486	0.0869614
$427$	4.96498	0.240272
$428$	−4.21080	−0.203537
$429$	20.5310	0.991245
$430$	−5.72919	−0.276286
$431$	27.6025	1.32957	0.664783	−	0.747037i	$-0.268524\pi$
$431$	27.6025	1.32957	0.664783	+	0.747037i	$0.268524\pi$
$432$	0.257957	0.0124109
$433$	−21.0747	−1.01278	−0.506392	−	0.862304i	$-0.669021\pi$
$433$	−21.0747	−1.01278	−0.506392	+	0.862304i	$0.669021\pi$
$434$	−5.77995	−0.277447
$435$	−13.2749	−0.636483
$436$	−12.5403	−0.600574
$437$	−5.73341	−0.274266
$438$	8.06821	0.385514
$439$	−11.8630	−0.566189	−0.283094	−	0.959092i	$-0.591361\pi$
$439$	−11.8630	−0.566189	−0.283094	+	0.959092i	$0.591361\pi$
$440$	42.7547	2.03825
$441$	1.00000	0.0476190
$442$	18.0120	0.856745
$443$	11.0804	0.526446	0.263223	−	0.964735i	$-0.415214\pi$
$443$	11.0804	0.526446	0.263223	+	0.964735i	$0.415214\pi$
$444$	11.2635	0.534541
$445$	7.51705	0.356342
$446$	18.7735	0.888949
$447$	−16.2091	−0.766666
$448$	4.32264	0.204225
$449$	21.1462	0.997949	0.498974	−	0.866617i	$-0.333710\pi$
$449$	21.1462	0.997949	0.498974	+	0.866617i	$0.333710\pi$
$450$	2.14185	0.100968
$451$	23.0415	1.08498
$452$	−2.45114	−0.115292
$453$	−22.1101	−1.03882
$454$	−19.6196	−0.920796
$455$	−10.0350	−0.470448
$456$	5.70014	0.266933
$457$	−0.600191	−0.0280758	−0.0140379	−	0.999901i	$-0.504469\pi$
$457$	−0.600191	−0.0280758	−0.0140379	+	0.999901i	$0.504469\pi$
$458$	−7.21289	−0.337036
$459$	−5.86462	−0.273737
$460$	−9.89301	−0.461264
$461$	−31.0470	−1.44600	−0.723001	−	0.690847i	$-0.757238\pi$
$461$	−31.0470	−1.44600	−0.723001	+	0.690847i	$0.757238\pi$
$462$	−4.72598	−0.219873
$463$	9.93441	0.461691	0.230846	−	0.972990i	$-0.425851\pi$
$463$	9.93441	0.461691	0.230846	+	0.972990i	$0.425851\pi$
$464$	−1.24647	−0.0578658
$465$	−18.8851	−0.875774
$466$	12.2913	0.569386
$467$	−6.15650	−0.284889	−0.142444	−	0.989803i	$-0.545496\pi$
$467$	−6.15650	−0.284889	−0.142444	+	0.989803i	$0.545496\pi$
$468$	4.72310	0.218325
$469$	4.57422	0.211218
$470$	29.2383	1.34866
$471$	23.2986	1.07354
$472$	26.0702	1.19998
$473$	13.9407	0.640992
$474$	−8.43325	−0.387352
$475$	−5.24413	−0.240617
$476$	7.58309	0.347570
$477$	4.92291	0.225405
$478$	4.24798	0.194298
$479$	15.7671	0.720417	0.360209	−	0.932872i	$-0.382706\pi$
$479$	15.7671	0.720417	0.360209	+	0.932872i	$0.382706\pi$
$480$	15.8092	0.721587
$481$	31.8190	1.45082
$482$	−13.3962	−0.610182
$483$	2.78500	0.126722
$484$	−26.6261	−1.21028
$485$	38.6849	1.75659
$486$	0.840819	0.0381403
$487$	−6.30114	−0.285532	−0.142766	−	0.989756i	$-0.545600\pi$
$487$	−6.30114	−0.285532	−0.142766	+	0.989756i	$0.545600\pi$
$488$	−13.7472	−0.622308
$489$	−21.5951	−0.976566
$490$	2.30993	0.104352
$491$	−2.75670	−0.124408	−0.0622040	−	0.998063i	$-0.519813\pi$
$491$	−2.75670	−0.124408	−0.0622040	+	0.998063i	$0.519813\pi$
$492$	5.30062	0.238971
$493$	28.3383	1.27629
$494$	6.32282	0.284477
$495$	−15.4414	−0.694039
$496$	−1.77324	−0.0796210
$497$	2.13466	0.0957526
$498$	−4.26036	−0.190911
$499$	1.20293	0.0538506	0.0269253	−	0.999637i	$-0.491428\pi$
$499$	1.20293	0.0538506	0.0269253	+	0.999637i	$0.491428\pi$
$500$	8.71248	0.389634
$501$	−3.26635	−0.145930
$502$	−9.98652	−0.445720
$503$	29.0110	1.29354	0.646769	−	0.762686i	$-0.276120\pi$
$503$	29.0110	1.29354	0.646769	+	0.762686i	$0.276120\pi$
$504$	−2.76884	−0.123334
$505$	−8.01443	−0.356637
$506$	−13.1619	−0.585116
$507$	0.342604	0.0152156
$508$	1.29302	0.0573686
$509$	−9.23054	−0.409136	−0.204568	−	0.978852i	$-0.565579\pi$
$509$	−9.23054	−0.409136	−0.204568	+	0.978852i	$0.565579\pi$
$510$	−13.5469	−0.599866
$511$	9.59565	0.424487
$512$	2.91291	0.128734
$513$	−2.05868	−0.0908927
$514$	−16.2890	−0.718478
$515$	47.2789	2.08336
$516$	3.20701	0.141181
$517$	−71.1446	−3.12894
$518$	−7.32435	−0.321813
$519$	9.97561	0.437881
$520$	27.7853	1.21846
$521$	−29.3043	−1.28385	−0.641923	−	0.766769i	$-0.721863\pi$
$521$	−29.3043	−1.28385	−0.641923	+	0.766769i	$0.721863\pi$
$522$	−4.06291	−0.177829
$523$	5.55943	0.243097	0.121549	−	0.992585i	$-0.461214\pi$
$523$	5.55943	0.243097	0.121549	+	0.992585i	$0.461214\pi$
$524$	−7.55772	−0.330161
$525$	2.54733	0.111175
$526$	−21.0543	−0.918012
$527$	40.3145	1.75613
$528$	−1.44989	−0.0630985
$529$	−15.2438	−0.662773
$530$	11.3716	0.493951
$531$	−9.41559	−0.408602
$532$	2.66192	0.115409
$533$	14.9741	0.648600
$534$	2.30066	0.0995595
$535$	8.94654	0.386793
$536$	−12.6653	−0.547056
$537$	21.3721	0.922276
$538$	−17.5103	−0.754922
$539$	−5.62069	−0.242100
$540$	−3.55225	−0.152864
$541$	−12.1035	−0.520371	−0.260186	−	0.965559i	$-0.583784\pi$
$541$	−12.1035	−0.520371	−0.260186	+	0.965559i	$0.583784\pi$
$542$	12.4003	0.532639
$543$	−23.7938	−1.02109
$544$	−33.7483	−1.44695
$545$	26.6440	1.14130
$546$	−3.07130	−0.131440
$547$	27.7176	1.18512	0.592561	−	0.805526i	$-0.298117\pi$
$547$	27.7176	1.18512	0.592561	+	0.805526i	$0.298117\pi$
$548$	13.8062	0.589770
$549$	4.96498	0.211900
$550$	−12.0387	−0.513330
$551$	9.94769	0.423786
$552$	−7.71121	−0.328211
$553$	−10.0298	−0.426510
$554$	−10.6409	−0.452088
$555$	−23.9311	−1.01582
$556$	28.0991	1.19167
$557$	2.98048	0.126287	0.0631435	−	0.998004i	$-0.479887\pi$
$557$	2.98048	0.126287	0.0631435	+	0.998004i	$0.479887\pi$
$558$	−5.77995	−0.244685
$559$	9.05970	0.383185
$560$	0.708669	0.0299467
$561$	32.9632	1.39171
$562$	−25.4649	−1.07417
$563$	−36.8092	−1.55132	−0.775662	−	0.631149i	$-0.782584\pi$
$563$	−36.8092	−1.55132	−0.775662	+	0.631149i	$0.782584\pi$
$564$	−16.3666	−0.689159
$565$	5.20784	0.219096
$566$	−0.466072	−0.0195904
$567$	1.00000	0.0419961
$568$	−5.91052	−0.248000
$569$	−30.9224	−1.29633	−0.648167	−	0.761499i	$-0.724464\pi$
$569$	−30.9224	−1.29633	−0.648167	+	0.761499i	$0.724464\pi$
$570$	−4.75540	−0.199182
$571$	13.7621	0.575925	0.287963	−	0.957642i	$-0.407022\pi$
$571$	13.7621	0.575925	0.287963	+	0.957642i	$0.407022\pi$
$572$	−26.5470	−1.10999
$573$	17.1115	0.714842
$574$	−3.44685	−0.143869
$575$	7.09432	0.295854
$576$	4.32264	0.180110
$577$	35.2200	1.46623	0.733114	−	0.680106i	$-0.238066\pi$
$577$	35.2200	1.46623	0.733114	+	0.680106i	$0.238066\pi$
$578$	14.6250	0.608320
$579$	−21.1983	−0.880973
$580$	17.1648	0.712728
$581$	−5.06691	−0.210211
$582$	11.8399	0.490778
$583$	−27.6702	−1.14598
$584$	−26.5688	−1.09942
$585$	−10.0350	−0.414896
$586$	9.02443	0.372796
$587$	17.1613	0.708322	0.354161	−	0.935184i	$-0.384766\pi$
$587$	17.1613	0.708322	0.354161	+	0.935184i	$0.384766\pi$
$588$	−1.29302	−0.0533234
$589$	14.1517	0.583112
$590$	−21.7494	−0.895408
$591$	9.64407	0.396704
$592$	−2.24705	−0.0923533
$593$	−41.1163	−1.68845	−0.844223	−	0.535992i	$-0.819938\pi$
$593$	−41.1163	−1.68845	−0.844223	+	0.535992i	$0.819938\pi$
$594$	−4.72598	−0.193909
$595$	−16.1115	−0.660508
$596$	20.9588	0.858506
$597$	−8.11930	−0.332301
$598$	−8.55358	−0.349782
$599$	15.4682	0.632013	0.316007	−	0.948757i	$-0.397658\pi$
$599$	15.4682	0.632013	0.316007	+	0.948757i	$0.397658\pi$
$600$	−7.05315	−0.287944
$601$	−14.5724	−0.594421	−0.297210	−	0.954812i	$-0.596056\pi$
$601$	−14.5724	−0.594421	−0.297210	+	0.954812i	$0.596056\pi$
$602$	−2.08543	−0.0849959
$603$	4.57422	0.186276
$604$	28.5888	1.16326
$605$	56.5716	2.29996
$606$	−2.45289	−0.0996419
$607$	41.7362	1.69402	0.847009	−	0.531578i	$-0.178401\pi$
$607$	41.7362	1.69402	0.847009	+	0.531578i	$0.178401\pi$
$608$	−11.8468	−0.480451
$609$	−4.83208	−0.195806
$610$	11.4688	0.464357
$611$	−46.2352	−1.87048
$612$	7.58309	0.306528
$613$	−43.5236	−1.75790	−0.878951	−	0.476913i	$-0.841756\pi$
$613$	−43.5236	−1.75790	−0.878951	+	0.476913i	$0.841756\pi$
$614$	5.01750	0.202490
$615$	−11.2620	−0.454129
$616$	15.5628	0.627042
$617$	18.8239	0.757823	0.378912	−	0.925433i	$-0.376298\pi$
$617$	18.8239	0.757823	0.378912	+	0.925433i	$0.376298\pi$
$618$	14.4701	0.582075
$619$	−29.5177	−1.18642	−0.593209	−	0.805049i	$-0.702139\pi$
$619$	−29.5177	−1.18642	−0.593209	+	0.805049i	$0.702139\pi$
$620$	24.4188	0.980684
$621$	2.78500	0.111758
$622$	22.4608	0.900595
$623$	2.73622	0.109624
$624$	−0.942252	−0.0377203
$625$	−31.2478	−1.24991
$626$	−21.7862	−0.870751
$627$	11.5712	0.462108
$628$	−30.1256	−1.20214
$629$	51.0865	2.03695
$630$	2.30993	0.0920299
$631$	−24.2239	−0.964337	−0.482169	−	0.876078i	$-0.660151\pi$
$631$	−24.2239	−0.964337	−0.482169	+	0.876078i	$0.660151\pi$
$632$	27.7709	1.10467
$633$	−10.1539	−0.403581
$634$	−5.29030	−0.210105
$635$	−2.74724	−0.109021
$636$	−6.36544	−0.252406
$637$	−3.65275	−0.144727
$638$	22.8363	0.904099
$639$	2.13466	0.0844458
$640$	−21.6334	−0.855134
$641$	28.0303	1.10713	0.553564	−	0.832806i	$-0.313267\pi$
$641$	28.0303	1.10713	0.553564	+	0.832806i	$0.313267\pi$
$642$	2.73817	0.108067
$643$	−42.3142	−1.66871	−0.834354	−	0.551229i	$-0.814159\pi$
$643$	−42.3142	−1.66871	−0.834354	+	0.551229i	$0.814159\pi$
$644$	−3.60107	−0.141902
$645$	−6.81382	−0.268294
$646$	10.1515	0.399405
$647$	−28.5548	−1.12260	−0.561302	−	0.827611i	$-0.689699\pi$
$647$	−28.5548	−1.12260	−0.561302	+	0.827611i	$0.689699\pi$
$648$	−2.76884	−0.108770
$649$	52.9221	2.07737
$650$	−7.82364	−0.306868
$651$	−6.87419	−0.269421
$652$	27.9230	1.09355
$653$	−0.00473242	−0.000185194 0	−9.25970e−5	−	1.00000i	$-0.500029\pi$
$653$	−0.00473242	−0.000185194 0	−9.25970e−5		1.00000i	$0.500029\pi$
$654$	8.15466	0.318872
$655$	16.0576	0.627423
$656$	−1.05747	−0.0412872
$657$	9.59565	0.374362
$658$	10.6428	0.414899
$659$	1.08891	0.0424181	0.0212090	−	0.999775i	$-0.493248\pi$
$659$	1.08891	0.0424181	0.0212090	+	0.999775i	$0.493248\pi$
$660$	19.9661	0.777178
$661$	−34.1649	−1.32886	−0.664431	−	0.747350i	$-0.731326\pi$
$661$	−34.1649	−1.32886	−0.664431	+	0.747350i	$0.731326\pi$
$662$	5.26415	0.204597
$663$	21.4220	0.831962
$664$	14.0295	0.544449
$665$	−5.65568	−0.219318
$666$	−7.32435	−0.283813
$667$	−13.4574	−0.521071
$668$	4.22347	0.163411
$669$	22.3276	0.863235
$670$	10.5661	0.408205
$671$	−27.9066	−1.07732
$672$	5.75457	0.221987
$673$	−5.87608	−0.226506	−0.113253	−	0.993566i	$-0.536127\pi$
$673$	−5.87608	−0.226506	−0.113253	+	0.993566i	$0.536127\pi$
$674$	8.93714	0.344246
$675$	2.54733	0.0980469
$676$	−0.442995	−0.0170383
$677$	−3.17149	−0.121890	−0.0609452	−	0.998141i	$-0.519411\pi$
$677$	−3.17149	−0.121890	−0.0609452	+	0.998141i	$0.519411\pi$
$678$	1.59391	0.0612137
$679$	14.0813	0.540393
$680$	44.6102	1.71072
$681$	−23.3340	−0.894160
$682$	32.4873	1.24400
$683$	16.1790	0.619074	0.309537	−	0.950887i	$-0.399826\pi$
$683$	16.1790	0.619074	0.309537	+	0.950887i	$0.399826\pi$
$684$	2.66192	0.101781
$685$	−29.3334	−1.12077
$686$	0.840819	0.0321026
$687$	−8.57841	−0.327287
$688$	−0.639794	−0.0243919
$689$	−17.9822	−0.685067
$690$	6.43316	0.244906
$691$	−20.6251	−0.784617	−0.392309	−	0.919834i	$-0.628323\pi$
$691$	−20.6251	−0.784617	−0.392309	+	0.919834i	$0.628323\pi$
$692$	−12.8987	−0.490335
$693$	−5.62069	−0.213512
$694$	20.3852	0.773813
$695$	−59.7011	−2.26459
$696$	13.3793	0.507139
$697$	24.0414	0.910634
$698$	16.1989	0.613138
$699$	14.6183	0.552915
$700$	−3.29376	−0.124493
$701$	−4.12137	−0.155662	−0.0778311	−	0.996967i	$-0.524799\pi$
$701$	−4.12137	−0.155662	−0.0778311	+	0.996967i	$0.524799\pi$
$702$	−3.07130	−0.115919
$703$	17.9331	0.676358
$704$	−24.2962	−0.915697
$705$	34.7736	1.30965
$706$	2.08181	0.0783498
$707$	−2.91727	−0.109715
$708$	12.1746	0.457549
$709$	−0.871563	−0.0327322	−0.0163661	−	0.999866i	$-0.505210\pi$
$709$	−0.871563	−0.0327322	−0.0163661	+	0.999866i	$0.505210\pi$
$710$	4.93092	0.185054
$711$	−10.0298	−0.376147
$712$	−7.57614	−0.283928
$713$	−19.1446	−0.716972
$714$	−4.93108	−0.184541
$715$	56.4036	2.10937
$716$	−27.6347	−1.03276
$717$	5.05219	0.188677
$718$	26.7779	0.999343
$719$	−40.4977	−1.51031	−0.755154	−	0.655547i	$-0.772438\pi$
$719$	−40.4977	−1.51031	−0.755154	+	0.655547i	$0.772438\pi$
$720$	0.708669	0.0264105
$721$	17.2096	0.640918
$722$	−12.4120	−0.461929
$723$	−15.9324	−0.592531
$724$	30.7659	1.14340
$725$	−12.3089	−0.457142
$726$	17.3143	0.642592
$727$	20.3846	0.756022	0.378011	−	0.925801i	$-0.376608\pi$
$727$	20.3846	0.756022	0.378011	+	0.925801i	$0.376608\pi$
$728$	10.1139	0.374845
$729$	1.00000	0.0370370
$730$	22.1653	0.820375
$731$	14.5457	0.537991
$732$	−6.41984	−0.237284
$733$	−45.0929	−1.66554	−0.832772	−	0.553617i	$-0.813247\pi$
$733$	−45.0929	−1.66554	−0.832772	+	0.553617i	$0.813247\pi$
$734$	7.94712	0.293334
$735$	2.74724	0.101334
$736$	16.0265	0.590743
$737$	−25.7102	−0.947049
$738$	−3.44685	−0.126880
$739$	−18.1927	−0.669230	−0.334615	−	0.942355i	$-0.608606\pi$
$739$	−18.1927	−0.669230	−0.334615	+	0.942355i	$0.608606\pi$
$740$	30.9435	1.13751
$741$	7.51983	0.276248
$742$	4.13928	0.151958
$743$	33.9156	1.24424	0.622122	−	0.782921i	$-0.286271\pi$
$743$	33.9156	1.24424	0.622122	+	0.782921i	$0.286271\pi$
$744$	19.0335	0.697803
$745$	−44.5304	−1.63147
$746$	−7.34935	−0.269079
$747$	−5.06691	−0.185389
$748$	−42.6222	−1.55842
$749$	3.25655	0.118992
$750$	−5.66549	−0.206875
$751$	26.1611	0.954631	0.477316	−	0.878732i	$-0.341610\pi$
$751$	26.1611	0.954631	0.477316	+	0.878732i	$0.341610\pi$
$752$	3.26512	0.119067
$753$	−11.8771	−0.432827
$754$	14.8408	0.540470
$755$	−60.7417	−2.21062
$756$	−1.29302	−0.0470268
$757$	−8.54392	−0.310534	−0.155267	−	0.987873i	$-0.549624\pi$
$757$	−8.54392	−0.310534	−0.155267	+	0.987873i	$0.549624\pi$
$758$	−12.9296	−0.469623
$759$	−15.6536	−0.568190
$760$	15.6596	0.568035
$761$	6.45289	0.233917	0.116959	−	0.993137i	$-0.462686\pi$
$761$	6.45289	0.233917	0.116959	+	0.993137i	$0.462686\pi$
$762$	−0.840819	−0.0304597
$763$	9.69847	0.351108
$764$	−22.1255	−0.800474
$765$	−16.1115	−0.582513
$766$	16.3434	0.590512
$767$	34.3928	1.24185
$768$	−15.2664	−0.550878
$769$	−12.6368	−0.455695	−0.227847	−	0.973697i	$-0.573169\pi$
$769$	−12.6368	−0.455695	−0.227847	+	0.973697i	$0.573169\pi$
$770$	−12.9834	−0.467890
$771$	−19.3728	−0.697694
$772$	27.4099	0.986505
$773$	1.63697	0.0588776	0.0294388	−	0.999567i	$-0.490628\pi$
$773$	1.63697	0.0588776	0.0294388	+	0.999567i	$0.490628\pi$
$774$	−2.08543	−0.0749593
$775$	−17.5109	−0.629009
$776$	−38.9890	−1.39962
$777$	−8.71097	−0.312504
$778$	17.0679	0.611914
$779$	8.43934	0.302371
$780$	12.9755	0.464597
$781$	−11.9983	−0.429331
$782$	−13.7331	−0.491093
$783$	−4.83208	−0.172685
$784$	0.257957	0.00921274
$785$	64.0068	2.28450
$786$	4.91459	0.175297
$787$	32.4089	1.15525	0.577626	−	0.816301i	$-0.303979\pi$
$787$	32.4089	1.15525	0.577626	+	0.816301i	$0.303979\pi$
$788$	−12.4700	−0.444225
$789$	−25.0402	−0.891456
$790$	−23.1682	−0.824286
$791$	1.89566	0.0674020
$792$	15.5628	0.552999
$793$	−18.1359	−0.644023
$794$	−4.24391	−0.150611
$795$	13.5244	0.479662
$796$	10.4985	0.372108
$797$	28.3883	1.00557	0.502783	−	0.864413i	$-0.332310\pi$
$797$	28.3883	1.00557	0.502783	+	0.864413i	$0.332310\pi$
$798$	−1.73097	−0.0612758
$799$	−74.2322	−2.62614
$800$	14.6588	0.518267
$801$	2.73622	0.0966795
$802$	0.696368	0.0245896
$803$	−53.9342	−1.90330
$804$	−5.91457	−0.208591
$805$	7.65107	0.269665
$806$	21.1127	0.743664
$807$	−20.8253	−0.733085
$808$	8.07743	0.284163
$809$	0.0199237	0.000700480 0	0.000350240	−	1.00000i	$-0.499889\pi$
$809$	0.0199237	0.000700480 0	0.000350240		1.00000i	$0.499889\pi$
$810$	2.30993	0.0811628
$811$	8.52421	0.299326	0.149663	−	0.988737i	$-0.452181\pi$
$811$	8.52421	0.299326	0.149663	+	0.988737i	$0.452181\pi$
$812$	6.24800	0.219262
$813$	14.7479	0.517232
$814$	41.1679	1.44293
$815$	−59.3271	−2.07814
$816$	−1.51282	−0.0529592
$817$	5.10601	0.178637
$818$	6.41998	0.224469
$819$	−3.65275	−0.127638
$820$	14.5621	0.508530
$821$	−21.9384	−0.765655	−0.382828	−	0.923820i	$-0.625050\pi$
$821$	−21.9384	−0.765655	−0.382828	+	0.923820i	$0.625050\pi$
$822$	−8.97778	−0.313136
$823$	16.5378	0.576471	0.288236	−	0.957559i	$-0.406931\pi$
$823$	16.5378	0.576471	0.288236	+	0.957559i	$0.406931\pi$
$824$	−47.6505	−1.65998
$825$	−14.3178	−0.498481
$826$	−7.91681	−0.275461
$827$	−0.791654	−0.0275285	−0.0137643	−	0.999905i	$-0.504381\pi$
$827$	−0.791654	−0.0275285	−0.0137643	+	0.999905i	$0.504381\pi$
$828$	−3.60107	−0.125146
$829$	−41.5550	−1.44326	−0.721632	−	0.692277i	$-0.756608\pi$
$829$	−41.5550	−1.44326	−0.721632	+	0.692277i	$0.756608\pi$
$830$	−11.7042	−0.406260
$831$	−12.6554	−0.439011
$832$	−15.7895	−0.547403
$833$	−5.86462	−0.203197
$834$	−18.2721	−0.632711
$835$	−8.97345	−0.310539
$836$	−14.9618	−0.517465
$837$	−6.87419	−0.237607
$838$	−0.510334	−0.0176292
$839$	44.5008	1.53634	0.768169	−	0.640247i	$-0.221168\pi$
$839$	44.5008	1.53634	0.768169	+	0.640247i	$0.221168\pi$
$840$	−7.60666	−0.262455
$841$	−5.65097	−0.194861
$842$	10.2642	0.353728
$843$	−30.2858	−1.04310
$844$	13.1292	0.451926
$845$	0.941216	0.0323788
$846$	10.6428	0.365906
$847$	20.5921	0.707554
$848$	1.26990	0.0436085
$849$	−0.554307	−0.0190238
$850$	−12.5611	−0.430843
$851$	−24.2600	−0.831623
$852$	−2.76017	−0.0945617
$853$	−18.5412	−0.634838	−0.317419	−	0.948285i	$-0.602816\pi$
$853$	−18.5412	−0.634838	−0.317419	+	0.948285i	$0.602816\pi$
$854$	4.17465	0.142854
$855$	−5.65568	−0.193420
$856$	−9.01686	−0.308190
$857$	37.2675	1.27304	0.636518	−	0.771262i	$-0.280374\pi$
$857$	37.2675	1.27304	0.636518	+	0.771262i	$0.280374\pi$
$858$	17.2628	0.589344
$859$	−16.3924	−0.559303	−0.279651	−	0.960102i	$-0.590219\pi$
$859$	−16.3924	−0.559303	−0.279651	+	0.960102i	$0.590219\pi$
$860$	8.81042	0.300433
$861$	−4.09940	−0.139707
$862$	23.2087	0.790491
$863$	−47.5599	−1.61896	−0.809479	−	0.587149i	$-0.800250\pi$
$863$	−47.5599	−1.61896	−0.809479	+	0.587149i	$0.800250\pi$
$864$	5.75457	0.195774
$865$	27.4054	0.931812
$866$	−17.7200	−0.602149
$867$	17.3937	0.590723
$868$	8.88849	0.301695
$869$	56.3744	1.91237
$870$	−11.1618	−0.378420
$871$	−16.7085	−0.566145
$872$	−26.8535	−0.909373
$873$	14.0813	0.476581
$874$	−4.82076	−0.163065
$875$	−6.73807	−0.227788
$876$	−12.4074	−0.419207
$877$	−22.3076	−0.753275	−0.376637	−	0.926361i	$-0.622920\pi$
$877$	−22.3076	−0.753275	−0.376637	+	0.926361i	$0.622920\pi$
$878$	−9.97462	−0.336627
$879$	10.7329	0.362012
$880$	−3.98321	−0.134274
$881$	20.9990	0.707474	0.353737	−	0.935345i	$-0.384911\pi$
$881$	20.9990	0.707474	0.353737	+	0.935345i	$0.384911\pi$
$882$	0.840819	0.0283118
$883$	24.4512	0.822849	0.411425	−	0.911444i	$-0.365031\pi$
$883$	24.4512	0.822849	0.411425	+	0.911444i	$0.365031\pi$
$884$	−27.6992	−0.931623
$885$	−25.8669	−0.869507
$886$	9.31662	0.312998
$887$	17.1615	0.576227	0.288113	−	0.957596i	$-0.406972\pi$
$887$	17.1615	0.576227	0.288113	+	0.957596i	$0.406972\pi$
$888$	24.1192	0.809389
$889$	−1.00000	−0.0335389
$890$	6.32048	0.211863
$891$	−5.62069	−0.188300
$892$	−28.8701	−0.966643
$893$	−26.0579	−0.871996
$894$	−13.6289	−0.455820
$895$	58.7144	1.96261
$896$	−7.87458	−0.263071
$897$	−10.1729	−0.339664
$898$	17.7801	0.593329
$899$	33.2167	1.10784
$900$	−3.29376	−0.109792
$901$	−28.8710	−0.961833
$902$	19.3737	0.645073
$903$	−2.48024	−0.0825372
$904$	−5.24878	−0.174572
$905$	−65.3672	−2.17288
$906$	−18.5906	−0.617630
$907$	31.9309	1.06025	0.530124	−	0.847920i	$-0.322145\pi$
$907$	31.9309	1.06025	0.530124	+	0.847920i	$0.322145\pi$
$908$	30.1714	1.00127
$909$	−2.91727	−0.0967596
$910$	−8.43761	−0.279704
$911$	37.7485	1.25067	0.625333	−	0.780358i	$-0.284963\pi$
$911$	37.7485	1.25067	0.625333	+	0.780358i	$0.284963\pi$
$912$	−0.531049	−0.0175848
$913$	28.4795	0.942535
$914$	−0.504652	−0.0166924
$915$	13.6400	0.450925
$916$	11.0921	0.366493
$917$	5.84500	0.193019
$918$	−4.93108	−0.162750
$919$	48.2941	1.59308	0.796538	−	0.604588i	$-0.206662\pi$
$919$	48.2941	1.59308	0.796538	+	0.604588i	$0.206662\pi$
$920$	−21.1845	−0.698434
$921$	5.96740	0.196632
$922$	−26.1049	−0.859718
$923$	−7.79739	−0.256654
$924$	7.26768	0.239089
$925$	−22.1897	−0.729594
$926$	8.35304	0.274498
$927$	17.2096	0.565237
$928$	−27.8066	−0.912795
$929$	59.7282	1.95962	0.979810	−	0.199932i	$-0.0640720\pi$
$929$	59.7282	1.95962	0.979810	+	0.199932i	$0.0640720\pi$
$930$	−15.8789	−0.520690
$931$	−2.05868	−0.0674704
$932$	−18.9018	−0.619149
$933$	26.7130	0.874543
$934$	−5.17650	−0.169380
$935$	90.5578	2.96156
$936$	10.1139	0.330582
$937$	−27.0530	−0.883782	−0.441891	−	0.897069i	$-0.645692\pi$
$937$	−27.0530	−0.883782	−0.441891	+	0.897069i	$0.645692\pi$
$938$	3.84609	0.125579
$939$	−25.9107	−0.845563
$940$	−44.9630	−1.46653
$941$	32.2760	1.05217	0.526084	−	0.850433i	$-0.323660\pi$
$941$	32.2760	1.05217	0.526084	+	0.850433i	$0.323660\pi$
$942$	19.5899	0.638273
$943$	−11.4168	−0.371783
$944$	−2.42882	−0.0790512
$945$	2.74724	0.0893678
$946$	11.7216	0.381101
$947$	4.40313	0.143083	0.0715413	−	0.997438i	$-0.477208\pi$
$947$	4.40313	0.143083	0.0715413	+	0.997438i	$0.477208\pi$
$948$	12.9688	0.421206
$949$	−35.0505	−1.13779
$950$	−4.40937	−0.143059
$951$	−6.29184	−0.204027
$952$	16.2382	0.526282
$953$	17.0635	0.552741	0.276370	−	0.961051i	$-0.410868\pi$
$953$	17.0635	0.552741	0.276370	+	0.961051i	$0.410868\pi$
$954$	4.13928	0.134014
$955$	47.0094	1.52119
$956$	−6.53260	−0.211279
$957$	27.1596	0.877946
$958$	13.2573	0.428323
$959$	−10.6774	−0.344792
$960$	11.8753	0.383274
$961$	16.2545	0.524340
$962$	26.7540	0.862584
$963$	3.25655	0.104941
$964$	20.6009	0.663511
$965$	−58.2369	−1.87471
$966$	2.34168	0.0753423
$967$	−26.9109	−0.865398	−0.432699	−	0.901539i	$-0.642439\pi$
$967$	−26.9109	−0.865398	−0.432699	+	0.901539i	$0.642439\pi$
$968$	−57.0163	−1.83257
$969$	12.0733	0.387852
$970$	32.5270	1.04438
$971$	−28.9843	−0.930151	−0.465076	−	0.885271i	$-0.653973\pi$
$971$	−28.9843	−0.930151	−0.465076	+	0.885271i	$0.653973\pi$
$972$	−1.29302	−0.0414737
$973$	−21.7313	−0.696674
$974$	−5.29812	−0.169763
$975$	−9.30478	−0.297991
$976$	1.28075	0.0409958
$977$	−50.2194	−1.60666	−0.803330	−	0.595534i	$-0.796941\pi$
$977$	−50.2194	−1.60666	−0.803330	+	0.595534i	$0.796941\pi$
$978$	−18.1576	−0.580616
$979$	−15.3794	−0.491529
$980$	−3.55225	−0.113472
$981$	9.69847	0.309648
$982$	−2.31788	−0.0739667
$983$	−1.32859	−0.0423756	−0.0211878	−	0.999776i	$-0.506745\pi$
$983$	−1.32859	−0.0423756	−0.0211878	+	0.999776i	$0.506745\pi$
$984$	11.3506	0.361843
$985$	26.4946	0.844187
$986$	23.8274	0.758819
$987$	12.6576	0.402897
$988$	−9.72332	−0.309340
$989$	−6.90747	−0.219645
$990$	−12.9834	−0.412640
$991$	−38.1866	−1.21304	−0.606518	−	0.795070i	$-0.707434\pi$
$991$	−38.1866	−1.21304	−0.606518	+	0.795070i	$0.707434\pi$
$992$	−39.5580	−1.25597
$993$	6.26075	0.198679
$994$	1.79486	0.0569296
$995$	−22.3057	−0.707138
$996$	6.55164	0.207597
$997$	34.2759	1.08553	0.542764	−	0.839885i	$-0.317378\pi$
$997$	34.2759	1.08553	0.542764	+	0.839885i	$0.317378\pi$
$998$	1.01145	0.0320168
$999$	−8.71097	−0.275603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.j.1.6	✓	7
3.2	odd	2		8001.2.a.l.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.j.1.6	✓	7	1.1	even	1	trivial
8001.2.a.l.1.2		7	3.2	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +2.30993 q^{10} -5.62069 q^{11} -1.29302 q^{12} -3.65275 q^{13} +0.840819 q^{14} +2.74724 q^{15} +0.257957 q^{16} -5.86462 q^{17} +0.840819 q^{18} -2.05868 q^{19} -3.55225 q^{20} +1.00000 q^{21} -4.72598 q^{22} +2.78500 q^{23} -2.76884 q^{24} +2.54733 q^{25} -3.07130 q^{26} +1.00000 q^{27} -1.29302 q^{28} -4.83208 q^{29} +2.30993 q^{30} -6.87419 q^{31} +5.75457 q^{32} -5.62069 q^{33} -4.93108 q^{34} +2.74724 q^{35} -1.29302 q^{36} -8.71097 q^{37} -1.73097 q^{38} -3.65275 q^{39} -7.60666 q^{40} -4.09940 q^{41} +0.840819 q^{42} -2.48024 q^{43} +7.26768 q^{44} +2.74724 q^{45} +2.34168 q^{46} +12.6576 q^{47} +0.257957 q^{48} +1.00000 q^{49} +2.14185 q^{50} -5.86462 q^{51} +4.72310 q^{52} +4.92291 q^{53} +0.840819 q^{54} -15.4414 q^{55} -2.76884 q^{56} -2.05868 q^{57} -4.06291 q^{58} -9.41559 q^{59} -3.55225 q^{60} +4.96498 q^{61} -5.77995 q^{62} +1.00000 q^{63} +4.32264 q^{64} -10.0350 q^{65} -4.72598 q^{66} +4.57422 q^{67} +7.58309 q^{68} +2.78500 q^{69} +2.30993 q^{70} +2.13466 q^{71} -2.76884 q^{72} +9.59565 q^{73} -7.32435 q^{74} +2.54733 q^{75} +2.66192 q^{76} -5.62069 q^{77} -3.07130 q^{78} -10.0298 q^{79} +0.708669 q^{80} +1.00000 q^{81} -3.44685 q^{82} -5.06691 q^{83} -1.29302 q^{84} -16.1115 q^{85} -2.08543 q^{86} -4.83208 q^{87} +15.5628 q^{88} +2.73622 q^{89} +2.30993 q^{90} -3.65275 q^{91} -3.60107 q^{92} -6.87419 q^{93} +10.6428 q^{94} -5.65568 q^{95} +5.75457 q^{96} +14.0813 q^{97} +0.840819 q^{98} -5.62069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * q^99

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