LMFDB - Embedded newform 8018.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +2.78011 q^{10} -5.50011 q^{11} -2.15742 q^{12} -5.88689 q^{13} +1.33229 q^{14} +5.99787 q^{15} +1.00000 q^{16} -2.24200 q^{17} -1.65446 q^{18} -1.00000 q^{19} -2.78011 q^{20} +2.87432 q^{21} +5.50011 q^{22} -6.52318 q^{23} +2.15742 q^{24} +2.72902 q^{25} +5.88689 q^{26} +2.90289 q^{27} -1.33229 q^{28} +7.17506 q^{29} -5.99787 q^{30} +3.81787 q^{31} -1.00000 q^{32} +11.8661 q^{33} +2.24200 q^{34} +3.70393 q^{35} +1.65446 q^{36} +0.00121348 q^{37} +1.00000 q^{38} +12.7005 q^{39} +2.78011 q^{40} -0.0230918 q^{41} -2.87432 q^{42} -10.2247 q^{43} -5.50011 q^{44} -4.59959 q^{45} +6.52318 q^{46} -1.06053 q^{47} -2.15742 q^{48} -5.22499 q^{49} -2.72902 q^{50} +4.83693 q^{51} -5.88689 q^{52} +10.3892 q^{53} -2.90289 q^{54} +15.2909 q^{55} +1.33229 q^{56} +2.15742 q^{57} -7.17506 q^{58} +13.1194 q^{59} +5.99787 q^{60} +2.45924 q^{61} -3.81787 q^{62} -2.20423 q^{63} +1.00000 q^{64} +16.3662 q^{65} -11.8661 q^{66} +6.44973 q^{67} -2.24200 q^{68} +14.0732 q^{69} -3.70393 q^{70} +2.95646 q^{71} -1.65446 q^{72} -7.06136 q^{73} -0.00121348 q^{74} -5.88764 q^{75} -1.00000 q^{76} +7.32777 q^{77} -12.7005 q^{78} +4.54943 q^{79} -2.78011 q^{80} -11.2261 q^{81} +0.0230918 q^{82} -2.00252 q^{83} +2.87432 q^{84} +6.23300 q^{85} +10.2247 q^{86} -15.4796 q^{87} +5.50011 q^{88} +10.2497 q^{89} +4.59959 q^{90} +7.84307 q^{91} -6.52318 q^{92} -8.23675 q^{93} +1.06053 q^{94} +2.78011 q^{95} +2.15742 q^{96} +3.39933 q^{97} +5.22499 q^{98} -9.09974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−2.15742	−1.24559	−0.622794	−	0.782386i	$-0.714002\pi$
$3$	−2.15742	−1.24559	−0.622794	+	0.782386i	$0.714002\pi$
$4$	1.00000	0.500000
$5$	−2.78011	−1.24330	−0.621652	−	0.783294i	$-0.713538\pi$
$5$	−2.78011	−1.24330	−0.621652	+	0.783294i	$0.713538\pi$
$6$	2.15742	0.880763
$7$	−1.33229	−0.503560	−0.251780	−	0.967784i	$-0.581016\pi$
$7$	−1.33229	−0.503560	−0.251780	+	0.967784i	$0.581016\pi$
$8$	−1.00000	−0.353553
$9$	1.65446	0.551488
$10$	2.78011	0.879148
$11$	−5.50011	−1.65835	−0.829173	−	0.558992i	$-0.811188\pi$
$11$	−5.50011	−1.65835	−0.829173	+	0.558992i	$0.811188\pi$
$12$	−2.15742	−0.622794
$13$	−5.88689	−1.63273	−0.816365	−	0.577536i	$-0.804014\pi$
$13$	−5.88689	−1.63273	−0.816365	+	0.577536i	$0.804014\pi$
$14$	1.33229	0.356071
$15$	5.99787	1.54864
$16$	1.00000	0.250000
$17$	−2.24200	−0.543764	−0.271882	−	0.962331i	$-0.587646\pi$
$17$	−2.24200	−0.543764	−0.271882	+	0.962331i	$0.587646\pi$
$18$	−1.65446	−0.389961
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.78011	−0.621652
$21$	2.87432	0.627228
$22$	5.50011	1.17263
$23$	−6.52318	−1.36018	−0.680089	−	0.733130i	$-0.738059\pi$
$23$	−6.52318	−1.36018	−0.680089	+	0.733130i	$0.738059\pi$
$24$	2.15742	0.440382
$25$	2.72902	0.545804
$26$	5.88689	1.15451
$27$	2.90289	0.558661
$28$	−1.33229	−0.251780
$29$	7.17506	1.33238	0.666188	−	0.745784i	$-0.267925\pi$
$29$	7.17506	1.33238	0.666188	+	0.745784i	$0.267925\pi$
$30$	−5.99787	−1.09506
$31$	3.81787	0.685710	0.342855	−	0.939388i	$-0.388606\pi$
$31$	3.81787	0.685710	0.342855	+	0.939388i	$0.388606\pi$
$32$	−1.00000	−0.176777
$33$	11.8661	2.06562
$34$	2.24200	0.384499
$35$	3.70393	0.626078
$36$	1.65446	0.275744
$37$	0.00121348	0.000199495 0	9.97474e−5	−	1.00000i	$-0.499968\pi$
$37$	0.00121348	0.000199495 0	9.97474e−5		1.00000i	$0.499968\pi$
$38$	1.00000	0.162221
$39$	12.7005	2.03371
$40$	2.78011	0.439574
$41$	−0.0230918	−0.00360634	−0.00180317	−	0.999998i	$-0.500574\pi$
$41$	−0.0230918	−0.00360634	−0.00180317	+	0.999998i	$0.500574\pi$
$42$	−2.87432	−0.443517
$43$	−10.2247	−1.55926	−0.779628	−	0.626243i	$-0.784592\pi$
$43$	−10.2247	−1.55926	−0.779628	+	0.626243i	$0.784592\pi$
$44$	−5.50011	−0.829173
$45$	−4.59959	−0.685667
$46$	6.52318	0.961791
$47$	−1.06053	−0.154695	−0.0773474	−	0.997004i	$-0.524645\pi$
$47$	−1.06053	−0.154695	−0.0773474	+	0.997004i	$0.524645\pi$
$48$	−2.15742	−0.311397
$49$	−5.22499	−0.746427
$50$	−2.72902	−0.385941
$51$	4.83693	0.677306
$52$	−5.88689	−0.816365
$53$	10.3892	1.42707	0.713534	−	0.700621i	$-0.247094\pi$
$53$	10.3892	1.42707	0.713534	+	0.700621i	$0.247094\pi$
$54$	−2.90289	−0.395033
$55$	15.2909	2.06183
$56$	1.33229	0.178035
$57$	2.15742	0.285757
$58$	−7.17506	−0.942132
$59$	13.1194	1.70800	0.853998	−	0.520276i	$-0.174171\pi$
$59$	13.1194	1.70800	0.853998	+	0.520276i	$0.174171\pi$
$60$	5.99787	0.774322
$61$	2.45924	0.314874	0.157437	−	0.987529i	$-0.449677\pi$
$61$	2.45924	0.314874	0.157437	+	0.987529i	$0.449677\pi$
$62$	−3.81787	−0.484870
$63$	−2.20423	−0.277707
$64$	1.00000	0.125000
$65$	16.3662	2.02998
$66$	−11.8661	−1.46061
$67$	6.44973	0.787960	0.393980	−	0.919119i	$-0.371098\pi$
$67$	6.44973	0.787960	0.393980	+	0.919119i	$0.371098\pi$
$68$	−2.24200	−0.271882
$69$	14.0732	1.69422
$70$	−3.70393	−0.442704
$71$	2.95646	0.350868	0.175434	−	0.984491i	$-0.443867\pi$
$71$	2.95646	0.350868	0.175434	+	0.984491i	$0.443867\pi$
$72$	−1.65446	−0.194980
$73$	−7.06136	−0.826470	−0.413235	−	0.910624i	$-0.635601\pi$
$73$	−7.06136	−0.826470	−0.413235	+	0.910624i	$0.635601\pi$
$74$	−0.00121348	−0.000141064 0
$75$	−5.88764	−0.679846
$76$	−1.00000	−0.114708
$77$	7.32777	0.835077
$78$	−12.7005	−1.43805
$79$	4.54943	0.511850	0.255925	−	0.966697i	$-0.417620\pi$
$79$	4.54943	0.511850	0.255925	+	0.966697i	$0.417620\pi$
$80$	−2.78011	−0.310826
$81$	−11.2261	−1.24735
$82$	0.0230918	0.00255006
$83$	−2.00252	−0.219806	−0.109903	−	0.993942i	$-0.535054\pi$
$83$	−2.00252	−0.219806	−0.109903	+	0.993942i	$0.535054\pi$
$84$	2.87432	0.313614
$85$	6.23300	0.676064
$86$	10.2247	1.10256
$87$	−15.4796	−1.65959
$88$	5.50011	0.586314
$89$	10.2497	1.08647	0.543235	−	0.839581i	$-0.317199\pi$
$89$	10.2497	1.08647	0.543235	+	0.839581i	$0.317199\pi$
$90$	4.59959	0.484840
$91$	7.84307	0.822178
$92$	−6.52318	−0.680089
$93$	−8.23675	−0.854112
$94$	1.06053	0.109386
$95$	2.78011	0.285233
$96$	2.15742	0.220191
$97$	3.39933	0.345150	0.172575	−	0.984996i	$-0.444791\pi$
$97$	3.39933	0.345150	0.172575	+	0.984996i	$0.444791\pi$
$98$	5.22499	0.527804
$99$	−9.09974	−0.914558
$100$	2.72902	0.272902
$101$	−4.60039	−0.457756	−0.228878	−	0.973455i	$-0.573506\pi$
$101$	−4.60039	−0.457756	−0.228878	+	0.973455i	$0.573506\pi$
$102$	−4.83693	−0.478927
$103$	−11.1268	−1.09636	−0.548180	−	0.836360i	$-0.684679\pi$
$103$	−11.1268	−1.09636	−0.548180	+	0.836360i	$0.684679\pi$
$104$	5.88689	0.577257
$105$	−7.99093	−0.779835
$106$	−10.3892	−1.00909
$107$	0.319302	0.0308681	0.0154340	−	0.999881i	$-0.495087\pi$
$107$	0.319302	0.0308681	0.0154340	+	0.999881i	$0.495087\pi$
$108$	2.90289	0.279331
$109$	−8.01354	−0.767558	−0.383779	−	0.923425i	$-0.625378\pi$
$109$	−8.01354	−0.767558	−0.383779	+	0.923425i	$0.625378\pi$
$110$	−15.2909	−1.45793
$111$	−0.00261799	−0.000248488 0
$112$	−1.33229	−0.125890
$113$	7.93918	0.746855	0.373428	−	0.927659i	$-0.378182\pi$
$113$	7.93918	0.746855	0.373428	+	0.927659i	$0.378182\pi$
$114$	−2.15742	−0.202061
$115$	18.1352	1.69111
$116$	7.17506	0.666188
$117$	−9.73965	−0.900431
$118$	−13.1194	−1.20774
$119$	2.98700	0.273818
$120$	−5.99787	−0.547528
$121$	19.2512	1.75011
$122$	−2.45924	−0.222649
$123$	0.0498188	0.00449201
$124$	3.81787	0.342855
$125$	6.31358	0.564704
$126$	2.20423	0.196369
$127$	−15.8788	−1.40902	−0.704509	−	0.709695i	$-0.748833\pi$
$127$	−15.8788	−1.40902	−0.704509	+	0.709695i	$0.748833\pi$
$128$	−1.00000	−0.0883883
$129$	22.0590	1.94219
$130$	−16.3662	−1.43541
$131$	11.8312	1.03369	0.516847	−	0.856078i	$-0.327106\pi$
$131$	11.8312	1.03369	0.516847	+	0.856078i	$0.327106\pi$
$132$	11.8661	1.03281
$133$	1.33229	0.115525
$134$	−6.44973	−0.557172
$135$	−8.07035	−0.694585
$136$	2.24200	0.192250
$137$	−13.9862	−1.19492	−0.597459	−	0.801899i	$-0.703823\pi$
$137$	−13.9862	−1.19492	−0.597459	+	0.801899i	$0.703823\pi$
$138$	−14.0732	−1.19799
$139$	5.22721	0.443366	0.221683	−	0.975119i	$-0.428845\pi$
$139$	5.22721	0.443366	0.221683	+	0.975119i	$0.428845\pi$
$140$	3.70393	0.313039
$141$	2.28802	0.192686
$142$	−2.95646	−0.248101
$143$	32.3786	2.70763
$144$	1.65446	0.137872
$145$	−19.9475	−1.65655
$146$	7.06136	0.584403
$147$	11.2725	0.929740
$148$	0.00121348	9.97474e−5 0
$149$	−12.7346	−1.04326	−0.521630	−	0.853172i	$-0.674676\pi$
$149$	−12.7346	−1.04326	−0.521630	+	0.853172i	$0.674676\pi$
$150$	5.88764	0.480724
$151$	−15.3227	−1.24694	−0.623471	−	0.781846i	$-0.714278\pi$
$151$	−15.3227	−1.24694	−0.623471	+	0.781846i	$0.714278\pi$
$152$	1.00000	0.0811107
$153$	−3.70930	−0.299879
$154$	−7.32777	−0.590489
$155$	−10.6141	−0.852546
$156$	12.7005	1.01685
$157$	9.36503	0.747411	0.373705	−	0.927547i	$-0.378087\pi$
$157$	9.36503	0.747411	0.373705	+	0.927547i	$0.378087\pi$
$158$	−4.54943	−0.361933
$159$	−22.4139	−1.77754
$160$	2.78011	0.219787
$161$	8.69080	0.684931
$162$	11.2261	0.882009
$163$	−10.5985	−0.830135	−0.415068	−	0.909791i	$-0.636242\pi$
$163$	−10.5985	−0.830135	−0.415068	+	0.909791i	$0.636242\pi$
$164$	−0.0230918	−0.00180317
$165$	−32.9890	−2.56819
$166$	2.00252	0.155426
$167$	−24.5651	−1.90091	−0.950453	−	0.310869i	$-0.899380\pi$
$167$	−24.5651	−1.90091	−0.950453	+	0.310869i	$0.899380\pi$
$168$	−2.87432	−0.221759
$169$	21.6555	1.66581
$170$	−6.23300	−0.478049
$171$	−1.65446	−0.126520
$172$	−10.2247	−0.779628
$173$	18.5003	1.40655	0.703274	−	0.710919i	$-0.251721\pi$
$173$	18.5003	1.40655	0.703274	+	0.710919i	$0.251721\pi$
$174$	15.4796	1.17351
$175$	−3.63586	−0.274845
$176$	−5.50011	−0.414587
$177$	−28.3040	−2.12746
$178$	−10.2497	−0.768250
$179$	21.2926	1.59149	0.795743	−	0.605634i	$-0.207080\pi$
$179$	21.2926	1.59149	0.795743	+	0.605634i	$0.207080\pi$
$180$	−4.59959	−0.342833
$181$	−17.1761	−1.27669	−0.638346	−	0.769750i	$-0.720381\pi$
$181$	−17.1761	−1.27669	−0.638346	+	0.769750i	$0.720381\pi$
$182$	−7.84307	−0.581367
$183$	−5.30562	−0.392203
$184$	6.52318	0.480895
$185$	−0.00337361	−0.000248033 0
$186$	8.23675	0.603948
$187$	12.3312	0.901749
$188$	−1.06053	−0.0773474
$189$	−3.86750	−0.281319
$190$	−2.78011	−0.201690
$191$	8.30885	0.601208	0.300604	−	0.953749i	$-0.402812\pi$
$191$	8.30885	0.601208	0.300604	+	0.953749i	$0.402812\pi$
$192$	−2.15742	−0.155698
$193$	25.4097	1.82903	0.914515	−	0.404551i	$-0.132572\pi$
$193$	25.4097	1.82903	0.914515	+	0.404551i	$0.132572\pi$
$194$	−3.39933	−0.244058
$195$	−35.3088	−2.52852
$196$	−5.22499	−0.373214
$197$	1.65567	0.117962	0.0589808	−	0.998259i	$-0.481215\pi$
$197$	1.65567	0.117962	0.0589808	+	0.998259i	$0.481215\pi$
$198$	9.09974	0.646690
$199$	−13.4727	−0.955057	−0.477529	−	0.878616i	$-0.658467\pi$
$199$	−13.4727	−0.955057	−0.477529	+	0.878616i	$0.658467\pi$
$200$	−2.72902	−0.192971
$201$	−13.9148	−0.981473
$202$	4.60039	0.323682
$203$	−9.55930	−0.670931
$204$	4.83693	0.338653
$205$	0.0641978	0.00448377
$206$	11.1268	0.775243
$207$	−10.7924	−0.750121
$208$	−5.88689	−0.408182
$209$	5.50011	0.380451
$210$	7.99093	0.551427
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	10.3892	0.713534
$213$	−6.37833	−0.437036
$214$	−0.319302	−0.0218270
$215$	28.4259	1.93863
$216$	−2.90289	−0.197517
$217$	−5.08653	−0.345296
$218$	8.01354	0.542746
$219$	15.2343	1.02944
$220$	15.2909	1.03091
$221$	13.1984	0.887820
$222$	0.00261799	0.000175708 0
$223$	−2.73815	−0.183360	−0.0916802	−	0.995789i	$-0.529224\pi$
$223$	−2.73815	−0.183360	−0.0916802	+	0.995789i	$0.529224\pi$
$224$	1.33229	0.0890177
$225$	4.51506	0.301004
$226$	−7.93918	−0.528106
$227$	11.9544	0.793440	0.396720	−	0.917940i	$-0.370148\pi$
$227$	11.9544	0.793440	0.396720	+	0.917940i	$0.370148\pi$
$228$	2.15742	0.142879
$229$	23.1719	1.53124	0.765620	−	0.643293i	$-0.222432\pi$
$229$	23.1719	1.53124	0.765620	+	0.643293i	$0.222432\pi$
$230$	−18.1352	−1.19580
$231$	−15.8091	−1.04016
$232$	−7.17506	−0.471066
$233$	0.0624516	0.00409134	0.00204567	−	0.999998i	$-0.499349\pi$
$233$	0.0624516	0.00409134	0.00204567	+	0.999998i	$0.499349\pi$
$234$	9.73965	0.636701
$235$	2.94840	0.192333
$236$	13.1194	0.853998
$237$	−9.81503	−0.637554
$238$	−2.98700	−0.193618
$239$	4.02893	0.260610	0.130305	−	0.991474i	$-0.458404\pi$
$239$	4.02893	0.260610	0.130305	+	0.991474i	$0.458404\pi$
$240$	5.99787	0.387161
$241$	−15.1865	−0.978246	−0.489123	−	0.872215i	$-0.662683\pi$
$241$	−15.1865	−0.978246	−0.489123	+	0.872215i	$0.662683\pi$
$242$	−19.2512	−1.23752
$243$	15.5108	0.995021
$244$	2.45924	0.157437
$245$	14.5261	0.928036
$246$	−0.0498188	−0.00317633
$247$	5.88689	0.374574
$248$	−3.81787	−0.242435
$249$	4.32029	0.273787
$250$	−6.31358	−0.399306
$251$	8.49005	0.535887	0.267944	−	0.963435i	$-0.413656\pi$
$251$	8.49005	0.535887	0.267944	+	0.963435i	$0.413656\pi$
$252$	−2.20423	−0.138854
$253$	35.8782	2.25565
$254$	15.8788	0.996327
$255$	−13.4472	−0.842097
$256$	1.00000	0.0625000
$257$	0.782274	0.0487969	0.0243985	−	0.999702i	$-0.492233\pi$
$257$	0.782274	0.0487969	0.0243985	+	0.999702i	$0.492233\pi$
$258$	−22.0590	−1.37333
$259$	−0.00161671	−0.000100458 0
$260$	16.3662	1.01499
$261$	11.8709	0.734789
$262$	−11.8312	−0.730932
$263$	29.1044	1.79465	0.897327	−	0.441366i	$-0.145506\pi$
$263$	29.1044	1.79465	0.897327	+	0.441366i	$0.145506\pi$
$264$	−11.8661	−0.730305
$265$	−28.8832	−1.77428
$266$	−1.33229	−0.0816882
$267$	−22.1130	−1.35329
$268$	6.44973	0.393980
$269$	9.47053	0.577428	0.288714	−	0.957415i	$-0.406772\pi$
$269$	9.47053	0.577428	0.288714	+	0.957415i	$0.406772\pi$
$270$	8.07035	0.491146
$271$	10.9255	0.663675	0.331838	−	0.943336i	$-0.392331\pi$
$271$	10.9255	0.663675	0.331838	+	0.943336i	$0.392331\pi$
$272$	−2.24200	−0.135941
$273$	−16.9208	−1.02409
$274$	13.9862	0.844935
$275$	−15.0099	−0.905131
$276$	14.0732	0.847110
$277$	25.6386	1.54047	0.770236	−	0.637759i	$-0.220138\pi$
$277$	25.6386	1.54047	0.770236	+	0.637759i	$0.220138\pi$
$278$	−5.22721	−0.313507
$279$	6.31653	0.378161
$280$	−3.70393	−0.221352
$281$	1.68999	0.100817	0.0504083	−	0.998729i	$-0.483948\pi$
$281$	1.68999	0.100817	0.0504083	+	0.998729i	$0.483948\pi$
$282$	−2.28802	−0.136249
$283$	0.713173	0.0423937	0.0211969	−	0.999775i	$-0.493252\pi$
$283$	0.713173	0.0423937	0.0211969	+	0.999775i	$0.493252\pi$
$284$	2.95646	0.175434
$285$	−5.99787	−0.355283
$286$	−32.3786	−1.91458
$287$	0.0307651	0.00181601
$288$	−1.65446	−0.0974902
$289$	−11.9735	−0.704321
$290$	19.9475	1.17136
$291$	−7.33379	−0.429914
$292$	−7.06136	−0.413235
$293$	2.86164	0.167179	0.0835894	−	0.996500i	$-0.473362\pi$
$293$	2.86164	0.167179	0.0835894	+	0.996500i	$0.473362\pi$
$294$	−11.2725	−0.657426
$295$	−36.4733	−2.12356
$296$	−0.00121348	−7.05321e−5 0
$297$	−15.9662	−0.926454
$298$	12.7346	0.737696
$299$	38.4013	2.22080
$300$	−5.88764	−0.339923
$301$	13.6223	0.785179
$302$	15.3227	0.881722
$303$	9.92498	0.570175
$304$	−1.00000	−0.0573539
$305$	−6.83697	−0.391484
$306$	3.70930	0.212047
$307$	−1.59554	−0.0910623	−0.0455311	−	0.998963i	$-0.514498\pi$
$307$	−1.59554	−0.0910623	−0.0455311	+	0.998963i	$0.514498\pi$
$308$	7.32777	0.417539
$309$	24.0053	1.36561
$310$	10.6141	0.602841
$311$	−15.4563	−0.876446	−0.438223	−	0.898866i	$-0.644392\pi$
$311$	−15.4563	−0.876446	−0.438223	+	0.898866i	$0.644392\pi$
$312$	−12.7005	−0.719024
$313$	−20.3537	−1.15046	−0.575230	−	0.817992i	$-0.695087\pi$
$313$	−20.3537	−1.15046	−0.575230	+	0.817992i	$0.695087\pi$
$314$	−9.36503	−0.528499
$315$	6.12801	0.345274
$316$	4.54943	0.255925
$317$	15.3337	0.861225	0.430612	−	0.902537i	$-0.358298\pi$
$317$	15.3337	0.861225	0.430612	+	0.902537i	$0.358298\pi$
$318$	22.4139	1.25691
$319$	−39.4636	−2.20954
$320$	−2.78011	−0.155413
$321$	−0.688869	−0.0384489
$322$	−8.69080	−0.484319
$323$	2.24200	0.124748
$324$	−11.2261	−0.623675
$325$	−16.0654	−0.891150
$326$	10.5985	0.586994
$327$	17.2886	0.956061
$328$	0.0230918	0.00127503
$329$	1.41294	0.0778981
$330$	32.9890	1.81598
$331$	19.1231	1.05110	0.525552	−	0.850762i	$-0.323859\pi$
$331$	19.1231	1.05110	0.525552	+	0.850762i	$0.323859\pi$
$332$	−2.00252	−0.109903
$333$	0.00200766	0.000110019 0
$334$	24.5651	1.34414
$335$	−17.9310	−0.979673
$336$	2.87432	0.156807
$337$	12.7409	0.694042	0.347021	−	0.937857i	$-0.387193\pi$
$337$	12.7409	0.694042	0.347021	+	0.937857i	$0.387193\pi$
$338$	−21.6555	−1.17790
$339$	−17.1281	−0.930273
$340$	6.23300	0.338032
$341$	−20.9987	−1.13714
$342$	1.65446	0.0894631
$343$	16.2873	0.879431
$344$	10.2247	0.551280
$345$	−39.1252	−2.10643
$346$	−18.5003	−0.994580
$347$	−13.0802	−0.702179	−0.351090	−	0.936342i	$-0.614189\pi$
$347$	−13.0802	−0.702179	−0.351090	+	0.936342i	$0.614189\pi$
$348$	−15.4796	−0.829795
$349$	−14.1564	−0.757774	−0.378887	−	0.925443i	$-0.623693\pi$
$349$	−14.1564	−0.757774	−0.378887	+	0.925443i	$0.623693\pi$
$350$	3.63586	0.194345
$351$	−17.0890	−0.912143
$352$	5.50011	0.293157
$353$	−15.0701	−0.802102	−0.401051	−	0.916056i	$-0.631355\pi$
$353$	−15.0701	−0.802102	−0.401051	+	0.916056i	$0.631355\pi$
$354$	28.3040	1.50434
$355$	−8.21929	−0.436235
$356$	10.2497	0.543235
$357$	−6.44422	−0.341064
$358$	−21.2926	−1.12535
$359$	22.9899	1.21336	0.606679	−	0.794947i	$-0.292501\pi$
$359$	22.9899	1.21336	0.606679	+	0.794947i	$0.292501\pi$
$360$	4.59959	0.242420
$361$	1.00000	0.0526316
$362$	17.1761	0.902758
$363$	−41.5330	−2.17992
$364$	7.84307	0.411089
$365$	19.6314	1.02755
$366$	5.30562	0.277329
$367$	−27.3145	−1.42581	−0.712903	−	0.701263i	$-0.752620\pi$
$367$	−27.3145	−1.42581	−0.712903	+	0.701263i	$0.752620\pi$
$368$	−6.52318	−0.340044
$369$	−0.0382046	−0.00198885
$370$	0.00337361	0.000175386 0
$371$	−13.8415	−0.718614
$372$	−8.23675	−0.427056
$373$	21.8061	1.12908	0.564538	−	0.825407i	$-0.309054\pi$
$373$	21.8061	1.12908	0.564538	+	0.825407i	$0.309054\pi$
$374$	−12.3312	−0.637633
$375$	−13.6211	−0.703388
$376$	1.06053	0.0546929
$377$	−42.2388	−2.17541
$378$	3.86750	0.198923
$379$	−30.5595	−1.56973	−0.784867	−	0.619664i	$-0.787269\pi$
$379$	−30.5595	−1.56973	−0.784867	+	0.619664i	$0.787269\pi$
$380$	2.78011	0.142617
$381$	34.2573	1.75506
$382$	−8.30885	−0.425118
$383$	11.4871	0.586963	0.293481	−	0.955965i	$-0.405186\pi$
$383$	11.4871	0.586963	0.293481	+	0.955965i	$0.405186\pi$
$384$	2.15742	0.110095
$385$	−20.3720	−1.03825
$386$	−25.4097	−1.29332
$387$	−16.9164	−0.859910
$388$	3.39933	0.172575
$389$	−15.0418	−0.762651	−0.381326	−	0.924441i	$-0.624532\pi$
$389$	−15.0418	−0.762651	−0.381326	+	0.924441i	$0.624532\pi$
$390$	35.3088	1.78793
$391$	14.6250	0.739616
$392$	5.22499	0.263902
$393$	−25.5248	−1.28756
$394$	−1.65567	−0.0834115
$395$	−12.6479	−0.636385
$396$	−9.09974	−0.457279
$397$	28.2545	1.41805	0.709026	−	0.705182i	$-0.249135\pi$
$397$	28.2545	1.41805	0.709026	+	0.705182i	$0.249135\pi$
$398$	13.4727	0.675328
$399$	−2.87432	−0.143896
$400$	2.72902	0.136451
$401$	−0.492403	−0.0245894	−0.0122947	−	0.999924i	$-0.503914\pi$
$401$	−0.492403	−0.0245894	−0.0122947	+	0.999924i	$0.503914\pi$
$402$	13.9148	0.694006
$403$	−22.4754	−1.11958
$404$	−4.60039	−0.228878
$405$	31.2099	1.55083
$406$	9.55930	0.474420
$407$	−0.00667427	−0.000330831 0
$408$	−4.83693	−0.239464
$409$	8.21722	0.406316	0.203158	−	0.979146i	$-0.434880\pi$
$409$	8.21722	0.406316	0.203158	+	0.979146i	$0.434880\pi$
$410$	−0.0641978	−0.00317050
$411$	30.1740	1.48838
$412$	−11.1268	−0.548180
$413$	−17.4789	−0.860079
$414$	10.7924	0.530416
$415$	5.56724	0.273285
$416$	5.88689	0.288629
$417$	−11.2773	−0.552251
$418$	−5.50011	−0.269019
$419$	−26.8072	−1.30962	−0.654808	−	0.755795i	$-0.727251\pi$
$419$	−26.8072	−1.30962	−0.654808	+	0.755795i	$0.727251\pi$
$420$	−7.99093	−0.389917
$421$	−29.2489	−1.42550	−0.712752	−	0.701416i	$-0.752552\pi$
$421$	−29.2489	−1.42550	−0.712752	+	0.701416i	$0.752552\pi$
$422$	1.00000	0.0486792
$423$	−1.75461	−0.0853123
$424$	−10.3892	−0.504545
$425$	−6.11845	−0.296788
$426$	6.37833	0.309031
$427$	−3.27644	−0.158558
$428$	0.319302	0.0154340
$429$	−69.8542	−3.37259
$430$	−28.4259	−1.37082
$431$	0.974703	0.0469498	0.0234749	−	0.999724i	$-0.492527\pi$
$431$	0.974703	0.0469498	0.0234749	+	0.999724i	$0.492527\pi$
$432$	2.90289	0.139665
$433$	−7.32945	−0.352231	−0.176115	−	0.984370i	$-0.556353\pi$
$433$	−7.32945	−0.352231	−0.176115	+	0.984370i	$0.556353\pi$
$434$	5.08653	0.244161
$435$	43.0351	2.06337
$436$	−8.01354	−0.383779
$437$	6.52318	0.312046
$438$	−15.2343	−0.727924
$439$	−19.3320	−0.922665	−0.461333	−	0.887227i	$-0.652629\pi$
$439$	−19.3320	−0.922665	−0.461333	+	0.887227i	$0.652629\pi$
$440$	−15.2909	−0.728966
$441$	−8.64456	−0.411646
$442$	−13.1984	−0.627783
$443$	−30.3823	−1.44350	−0.721752	−	0.692152i	$-0.756663\pi$
$443$	−30.3823	−1.44350	−0.721752	+	0.692152i	$0.756663\pi$
$444$	−0.00261799	−0.000124244 0
$445$	−28.4954	−1.35081
$446$	2.73815	0.129655
$447$	27.4739	1.29947
$448$	−1.33229	−0.0629450
$449$	38.4172	1.81302	0.906509	−	0.422186i	$-0.138737\pi$
$449$	38.4172	1.81302	0.906509	+	0.422186i	$0.138737\pi$
$450$	−4.51506	−0.212842
$451$	0.127008	0.00598055
$452$	7.93918	0.373428
$453$	33.0575	1.55318
$454$	−11.9544	−0.561047
$455$	−21.8046	−1.02222
$456$	−2.15742	−0.101030
$457$	−1.48137	−0.0692958	−0.0346479	−	0.999400i	$-0.511031\pi$
$457$	−1.48137	−0.0692958	−0.0346479	+	0.999400i	$0.511031\pi$
$458$	−23.1719	−1.08275
$459$	−6.50827	−0.303780
$460$	18.1352	0.845557
$461$	−38.6136	−1.79841	−0.899207	−	0.437523i	$-0.855856\pi$
$461$	−38.6136	−1.79841	−0.899207	+	0.437523i	$0.855856\pi$
$462$	15.8091	0.735505
$463$	−4.78767	−0.222502	−0.111251	−	0.993792i	$-0.535486\pi$
$463$	−4.78767	−0.222502	−0.111251	+	0.993792i	$0.535486\pi$
$464$	7.17506	0.333094
$465$	22.8991	1.06192
$466$	−0.0624516	−0.00289301
$467$	−16.0814	−0.744157	−0.372078	−	0.928201i	$-0.621355\pi$
$467$	−16.0814	−0.744157	−0.372078	+	0.928201i	$0.621355\pi$
$468$	−9.73965	−0.450215
$469$	−8.59294	−0.396785
$470$	−2.94840	−0.136000
$471$	−20.2043	−0.930966
$472$	−13.1194	−0.603868
$473$	56.2371	2.58579
$474$	9.81503	0.450819
$475$	−2.72902	−0.125216
$476$	2.98700	0.136909
$477$	17.1886	0.787010
$478$	−4.02893	−0.184279
$479$	5.35999	0.244904	0.122452	−	0.992474i	$-0.460924\pi$
$479$	5.35999	0.244904	0.122452	+	0.992474i	$0.460924\pi$
$480$	−5.99787	−0.273764
$481$	−0.00714362	−0.000325721 0
$482$	15.1865	0.691725
$483$	−18.7497	−0.853141
$484$	19.2512	0.875056
$485$	−9.45052	−0.429126
$486$	−15.5108	−0.703586
$487$	−1.50511	−0.0682029	−0.0341014	−	0.999418i	$-0.510857\pi$
$487$	−1.50511	−0.0682029	−0.0341014	+	0.999418i	$0.510857\pi$
$488$	−2.45924	−0.111325
$489$	22.8653	1.03401
$490$	−14.5261	−0.656220
$491$	10.0401	0.453102	0.226551	−	0.973999i	$-0.427255\pi$
$491$	10.0401	0.453102	0.226551	+	0.973999i	$0.427255\pi$
$492$	0.0498188	0.00224600
$493$	−16.0865	−0.724498
$494$	−5.88689	−0.264864
$495$	25.2983	1.13707
$496$	3.81787	0.171427
$497$	−3.93888	−0.176683
$498$	−4.32029	−0.193597
$499$	15.9373	0.713453	0.356727	−	0.934209i	$-0.383893\pi$
$499$	15.9373	0.713453	0.356727	+	0.934209i	$0.383893\pi$
$500$	6.31358	0.282352
$501$	52.9973	2.36774
$502$	−8.49005	−0.378929
$503$	41.3289	1.84277	0.921383	−	0.388656i	$-0.127061\pi$
$503$	41.3289	1.84277	0.921383	+	0.388656i	$0.127061\pi$
$504$	2.20423	0.0981843
$505$	12.7896	0.569130
$506$	−35.8782	−1.59498
$507$	−46.7200	−2.07491
$508$	−15.8788	−0.704509
$509$	18.4331	0.817031	0.408516	−	0.912751i	$-0.366047\pi$
$509$	18.4331	0.817031	0.408516	+	0.912751i	$0.366047\pi$
$510$	13.4472	0.595452
$511$	9.40782	0.416177
$512$	−1.00000	−0.0441942
$513$	−2.90289	−0.128166
$514$	−0.782274	−0.0345046
$515$	30.9338	1.36311
$516$	22.0590	0.971094
$517$	5.83306	0.256538
$518$	0.00161671	7.10343e−5 0
$519$	−39.9128	−1.75198
$520$	−16.3662	−0.717706
$521$	−40.0811	−1.75599	−0.877993	−	0.478674i	$-0.841118\pi$
$521$	−40.0811	−1.75599	−0.877993	+	0.478674i	$0.841118\pi$
$522$	−11.8709	−0.519574
$523$	−3.41281	−0.149232	−0.0746158	−	0.997212i	$-0.523773\pi$
$523$	−3.41281	−0.149232	−0.0746158	+	0.997212i	$0.523773\pi$
$524$	11.8312	0.516847
$525$	7.84407	0.342343
$526$	−29.1044	−1.26901
$527$	−8.55965	−0.372864
$528$	11.8661	0.516404
$529$	19.5519	0.850082
$530$	28.8832	1.25460
$531$	21.7055	0.941939
$532$	1.33229	0.0577623
$533$	0.135939	0.00588817
$534$	22.1130	0.956922
$535$	−0.887695	−0.0383784
$536$	−6.44973	−0.278586
$537$	−45.9372	−1.98234
$538$	−9.47053	−0.408304
$539$	28.7380	1.23783
$540$	−8.07035	−0.347293
$541$	38.3046	1.64684	0.823422	−	0.567430i	$-0.192062\pi$
$541$	38.3046	1.64684	0.823422	+	0.567430i	$0.192062\pi$
$542$	−10.9255	−0.469289
$543$	37.0561	1.59023
$544$	2.24200	0.0961248
$545$	22.2785	0.954308
$546$	16.9208	0.724144
$547$	−2.03295	−0.0869226	−0.0434613	−	0.999055i	$-0.513839\pi$
$547$	−2.03295	−0.0869226	−0.0434613	+	0.999055i	$0.513839\pi$
$548$	−13.9862	−0.597459
$549$	4.06873	0.173649
$550$	15.0099	0.640025
$551$	−7.17506	−0.305668
$552$	−14.0732	−0.598997
$553$	−6.06118	−0.257747
$554$	−25.6386	−1.08928
$555$	0.00727829	0.000308946 0
$556$	5.22721	0.221683
$557$	−26.4962	−1.12268	−0.561339	−	0.827586i	$-0.689714\pi$
$557$	−26.4962	−1.12268	−0.561339	+	0.827586i	$0.689714\pi$
$558$	−6.31653	−0.267400
$559$	60.1918	2.54584
$560$	3.70393	0.156520
$561$	−26.6037	−1.12321
$562$	−1.68999	−0.0712881
$563$	−7.76923	−0.327434	−0.163717	−	0.986507i	$-0.552348\pi$
$563$	−7.76923	−0.327434	−0.163717	+	0.986507i	$0.552348\pi$
$564$	2.28802	0.0963429
$565$	−22.0718	−0.928568
$566$	−0.713173	−0.0299769
$567$	14.9565	0.628115
$568$	−2.95646	−0.124050
$569$	13.2614	0.555949	0.277974	−	0.960588i	$-0.410337\pi$
$569$	13.2614	0.555949	0.277974	+	0.960588i	$0.410337\pi$
$570$	5.99787	0.251223
$571$	−9.12816	−0.382002	−0.191001	−	0.981590i	$-0.561173\pi$
$571$	−9.12816	−0.382002	−0.191001	+	0.981590i	$0.561173\pi$
$572$	32.3786	1.35382
$573$	−17.9257	−0.748857
$574$	−0.0307651	−0.00128411
$575$	−17.8019	−0.742390
$576$	1.65446	0.0689360
$577$	−18.3659	−0.764581	−0.382291	−	0.924042i	$-0.624865\pi$
$577$	−18.3659	−0.764581	−0.382291	+	0.924042i	$0.624865\pi$
$578$	11.9735	0.498030
$579$	−54.8194	−2.27822
$580$	−19.9475	−0.828273
$581$	2.66795	0.110685
$582$	7.33379	0.303995
$583$	−57.1418	−2.36657
$584$	7.06136	0.292201
$585$	27.0773	1.11951
$586$	−2.86164	−0.118213
$587$	14.5419	0.600210	0.300105	−	0.953906i	$-0.402978\pi$
$587$	14.5419	0.600210	0.300105	+	0.953906i	$0.402978\pi$
$588$	11.2725	0.464870
$589$	−3.81787	−0.157313
$590$	36.4733	1.50158
$591$	−3.57198	−0.146932
$592$	0.00121348	4.98737e−5 0
$593$	−12.0601	−0.495249	−0.247625	−	0.968856i	$-0.579650\pi$
$593$	−12.0601	−0.495249	−0.247625	+	0.968856i	$0.579650\pi$
$594$	15.9662	0.655102
$595$	−8.30419	−0.340439
$596$	−12.7346	−0.521630
$597$	29.0664	1.18961
$598$	−38.4013	−1.57034
$599$	−9.07245	−0.370690	−0.185345	−	0.982673i	$-0.559340\pi$
$599$	−9.07245	−0.370690	−0.185345	+	0.982673i	$0.559340\pi$
$600$	5.88764	0.240362
$601$	−0.942780	−0.0384568	−0.0192284	−	0.999815i	$-0.506121\pi$
$601$	−0.942780	−0.0384568	−0.0192284	+	0.999815i	$0.506121\pi$
$602$	−13.6223	−0.555205
$603$	10.6708	0.434550
$604$	−15.3227	−0.623471
$605$	−53.5206	−2.17592
$606$	−9.92498	−0.403175
$607$	22.7710	0.924245	0.462122	−	0.886816i	$-0.347088\pi$
$607$	22.7710	0.924245	0.462122	+	0.886816i	$0.347088\pi$
$608$	1.00000	0.0405554
$609$	20.6234	0.835703
$610$	6.83697	0.276821
$611$	6.24325	0.252575
$612$	−3.70930	−0.149940
$613$	48.0768	1.94180	0.970902	−	0.239476i	$-0.0769755\pi$
$613$	48.0768	1.94180	0.970902	+	0.239476i	$0.0769755\pi$
$614$	1.59554	0.0643908
$615$	−0.138502	−0.00558493
$616$	−7.32777	−0.295244
$617$	8.23906	0.331692	0.165846	−	0.986152i	$-0.446965\pi$
$617$	8.23906	0.331692	0.165846	+	0.986152i	$0.446965\pi$
$618$	−24.0053	−0.965633
$619$	−1.67620	−0.0673721	−0.0336860	−	0.999432i	$-0.510725\pi$
$619$	−1.67620	−0.0673721	−0.0336860	+	0.999432i	$0.510725\pi$
$620$	−10.6141	−0.426273
$621$	−18.9361	−0.759878
$622$	15.4563	0.619741
$623$	−13.6557	−0.547103
$624$	12.7005	0.508427
$625$	−31.1976	−1.24790
$626$	20.3537	0.813498
$627$	−11.8661	−0.473885
$628$	9.36503	0.373705
$629$	−0.00272062	−0.000108478 0
$630$	−6.12801	−0.244146
$631$	−40.8749	−1.62721	−0.813603	−	0.581421i	$-0.802497\pi$
$631$	−40.8749	−1.62721	−0.813603	+	0.581421i	$0.802497\pi$
$632$	−4.54943	−0.180966
$633$	2.15742	0.0857498
$634$	−15.3337	−0.608978
$635$	44.1449	1.75184
$636$	−22.4139	−0.888769
$637$	30.7590	1.21871
$638$	39.4636	1.56238
$639$	4.89136	0.193499
$640$	2.78011	0.109894
$641$	−26.2565	−1.03707	−0.518535	−	0.855056i	$-0.673522\pi$
$641$	−26.2565	−1.03707	−0.518535	+	0.855056i	$0.673522\pi$
$642$	0.688869	0.0271875
$643$	−24.4264	−0.963282	−0.481641	−	0.876369i	$-0.659959\pi$
$643$	−24.4264	−0.963282	−0.481641	+	0.876369i	$0.659959\pi$
$644$	8.69080	0.342466
$645$	−61.3265	−2.41473
$646$	−2.24200	−0.0882102
$647$	−29.1756	−1.14701	−0.573505	−	0.819202i	$-0.694417\pi$
$647$	−29.1756	−1.14701	−0.573505	+	0.819202i	$0.694417\pi$
$648$	11.2261	0.441004
$649$	−72.1580	−2.83245
$650$	16.0654	0.630138
$651$	10.9738	0.430097
$652$	−10.5985	−0.415068
$653$	−36.8413	−1.44171	−0.720855	−	0.693086i	$-0.756251\pi$
$653$	−36.8413	−1.44171	−0.720855	+	0.693086i	$0.756251\pi$
$654$	−17.2886	−0.676037
$655$	−32.8919	−1.28519
$656$	−0.0230918	−0.000901584 0
$657$	−11.6828	−0.455788
$658$	−1.41294	−0.0550823
$659$	−16.2993	−0.634930	−0.317465	−	0.948270i	$-0.602832\pi$
$659$	−16.2993	−0.634930	−0.317465	+	0.948270i	$0.602832\pi$
$660$	−32.9890	−1.28409
$661$	45.4371	1.76730	0.883648	−	0.468151i	$-0.155080\pi$
$661$	45.4371	1.76730	0.883648	+	0.468151i	$0.155080\pi$
$662$	−19.1231	−0.743242
$663$	−28.4745	−1.10586
$664$	2.00252	0.0777130
$665$	−3.70393	−0.143632
$666$	−0.00200766	−7.77951e−5 0
$667$	−46.8042	−1.81227
$668$	−24.5651	−0.950453
$669$	5.90735	0.228391
$670$	17.9310	0.692734
$671$	−13.5261	−0.522170
$672$	−2.87432	−0.110879
$673$	−42.1124	−1.62331	−0.811657	−	0.584134i	$-0.801434\pi$
$673$	−42.1124	−1.62331	−0.811657	+	0.584134i	$0.801434\pi$
$674$	−12.7409	−0.490762
$675$	7.92203	0.304919
$676$	21.6555	0.832903
$677$	−31.4073	−1.20708	−0.603539	−	0.797333i	$-0.706243\pi$
$677$	−31.4073	−1.20708	−0.603539	+	0.797333i	$0.706243\pi$
$678$	17.1281	0.657803
$679$	−4.52891	−0.173804
$680$	−6.23300	−0.239025
$681$	−25.7906	−0.988299
$682$	20.9987	0.804083
$683$	9.75667	0.373329	0.186664	−	0.982424i	$-0.440232\pi$
$683$	9.75667	0.373329	0.186664	+	0.982424i	$0.440232\pi$
$684$	−1.65446	−0.0632600
$685$	38.8831	1.48565
$686$	−16.2873	−0.621852
$687$	−49.9914	−1.90729
$688$	−10.2247	−0.389814
$689$	−61.1601	−2.33002
$690$	39.1252	1.48947
$691$	21.8118	0.829761	0.414881	−	0.909876i	$-0.363823\pi$
$691$	21.8118	0.829761	0.414881	+	0.909876i	$0.363823\pi$
$692$	18.5003	0.703274
$693$	12.1235	0.460535
$694$	13.0802	0.496516
$695$	−14.5322	−0.551239
$696$	15.4796	0.586754
$697$	0.0517718	0.00196100
$698$	14.1564	0.535827
$699$	−0.134734	−0.00509612
$700$	−3.63586	−0.137422
$701$	−4.43796	−0.167620	−0.0838098	−	0.996482i	$-0.526709\pi$
$701$	−4.43796	−0.167620	−0.0838098	+	0.996482i	$0.526709\pi$
$702$	17.0890	0.644982
$703$	−0.00121348	−4.57672e−5 0
$704$	−5.50011	−0.207293
$705$	−6.36094	−0.239567
$706$	15.0701	0.567172
$707$	6.12908	0.230508
$708$	−28.3040	−1.06373
$709$	−18.3684	−0.689839	−0.344920	−	0.938632i	$-0.612094\pi$
$709$	−18.3684	−0.689839	−0.344920	+	0.938632i	$0.612094\pi$
$710$	8.21929	0.308465
$711$	7.52686	0.282279
$712$	−10.2497	−0.384125
$713$	−24.9047	−0.932687
$714$	6.44422	0.241169
$715$	−90.0160	−3.36641
$716$	21.2926	0.795743
$717$	−8.69210	−0.324612
$718$	−22.9899	−0.857974
$719$	41.4738	1.54671	0.773356	−	0.633972i	$-0.218577\pi$
$719$	41.4738	1.54671	0.773356	+	0.633972i	$0.218577\pi$
$720$	−4.59959	−0.171417
$721$	14.8242	0.552083
$722$	−1.00000	−0.0372161
$723$	32.7636	1.21849
$724$	−17.1761	−0.638346
$725$	19.5809	0.727215
$726$	41.5330	1.54144
$727$	20.1418	0.747018	0.373509	−	0.927627i	$-0.378155\pi$
$727$	20.1418	0.747018	0.373509	+	0.927627i	$0.378155\pi$
$728$	−7.84307	−0.290684
$729$	0.215012	0.00796340
$730$	−19.6314	−0.726590
$731$	22.9238	0.847867
$732$	−5.30562	−0.196101
$733$	51.9726	1.91965	0.959825	−	0.280599i	$-0.0905330\pi$
$733$	51.9726	1.91965	0.959825	+	0.280599i	$0.0905330\pi$
$734$	27.3145	1.00820
$735$	−31.3388	−1.15595
$736$	6.52318	0.240448
$737$	−35.4742	−1.30671
$738$	0.0382046	0.00140633
$739$	−37.8111	−1.39090	−0.695452	−	0.718573i	$-0.744796\pi$
$739$	−37.8111	−1.39090	−0.695452	+	0.718573i	$0.744796\pi$
$740$	−0.00337361	−0.000124016 0
$741$	−12.7005	−0.466565
$742$	13.8415	0.508137
$743$	0.661684	0.0242748	0.0121374	−	0.999926i	$-0.496136\pi$
$743$	0.661684	0.0242748	0.0121374	+	0.999926i	$0.496136\pi$
$744$	8.23675	0.301974
$745$	35.4036	1.29709
$746$	−21.8061	−0.798378
$747$	−3.31310	−0.121220
$748$	12.3312	0.450875
$749$	−0.425404	−0.0155439
$750$	13.6211	0.497371
$751$	−1.74926	−0.0638315	−0.0319158	−	0.999491i	$-0.510161\pi$
$751$	−1.74926	−0.0638315	−0.0319158	+	0.999491i	$0.510161\pi$
$752$	−1.06053	−0.0386737
$753$	−18.3166	−0.667494
$754$	42.2388	1.53825
$755$	42.5988	1.55033
$756$	−3.86750	−0.140660
$757$	−28.9312	−1.05152	−0.525761	−	0.850632i	$-0.676220\pi$
$757$	−28.9312	−1.05152	−0.525761	+	0.850632i	$0.676220\pi$
$758$	30.5595	1.10997
$759$	−77.4044	−2.80960
$760$	−2.78011	−0.100845
$761$	14.8160	0.537079	0.268540	−	0.963269i	$-0.413459\pi$
$761$	14.8160	0.537079	0.268540	+	0.963269i	$0.413459\pi$
$762$	−34.2573	−1.24101
$763$	10.6764	0.386512
$764$	8.30885	0.300604
$765$	10.3123	0.372841
$766$	−11.4871	−0.415045
$767$	−77.2323	−2.78870
$768$	−2.15742	−0.0778492
$769$	33.2703	1.19976	0.599880	−	0.800090i	$-0.295215\pi$
$769$	33.2703	1.19976	0.599880	+	0.800090i	$0.295215\pi$
$770$	20.3720	0.734157
$771$	−1.68769	−0.0607808
$772$	25.4097	0.914515
$773$	11.0643	0.397957	0.198978	−	0.980004i	$-0.436238\pi$
$773$	11.0643	0.397957	0.198978	+	0.980004i	$0.436238\pi$
$774$	16.9164	0.608048
$775$	10.4190	0.374263
$776$	−3.39933	−0.122029
$777$	0.00348793	0.000125129 0
$778$	15.0418	0.539276
$779$	0.0230918	0.000827350 0
$780$	−35.3088	−1.26426
$781$	−16.2609	−0.581860
$782$	−14.6250	−0.522987
$783$	20.8284	0.744346
$784$	−5.22499	−0.186607
$785$	−26.0358	−0.929259
$786$	25.5248	0.910439
$787$	16.0464	0.571993	0.285996	−	0.958231i	$-0.407675\pi$
$787$	16.0464	0.571993	0.285996	+	0.958231i	$0.407675\pi$
$788$	1.65567	0.0589808
$789$	−62.7904	−2.23540
$790$	12.6479	0.449992
$791$	−10.5773	−0.376086
$792$	9.09974	0.323345
$793$	−14.4773	−0.514104
$794$	−28.2545	−1.00271
$795$	62.3131	2.21002
$796$	−13.4727	−0.477529
$797$	41.5438	1.47156	0.735778	−	0.677223i	$-0.236817\pi$
$797$	41.5438	1.47156	0.735778	+	0.677223i	$0.236817\pi$
$798$	2.87432	0.101750
$799$	2.37771	0.0841175
$800$	−2.72902	−0.0964854
$801$	16.9578	0.599175
$802$	0.492403	0.0173874
$803$	38.8383	1.37057
$804$	−13.9148	−0.490736
$805$	−24.1614	−0.851577
$806$	22.4754	0.791662
$807$	−20.4319	−0.719238
$808$	4.60039	0.161841
$809$	29.7877	1.04728	0.523641	−	0.851939i	$-0.324573\pi$
$809$	29.7877	1.04728	0.523641	+	0.851939i	$0.324573\pi$
$810$	−31.2099	−1.09660
$811$	46.3916	1.62903	0.814515	−	0.580142i	$-0.197003\pi$
$811$	46.3916	1.62903	0.814515	+	0.580142i	$0.197003\pi$
$812$	−9.55930	−0.335466
$813$	−23.5708	−0.826666
$814$	0.00667427	0.000233933 0
$815$	29.4649	1.03211
$816$	4.83693	0.169326
$817$	10.2247	0.357718
$818$	−8.21722	−0.287309
$819$	12.9761	0.453421
$820$	0.0641978	0.00224188
$821$	0.984358	0.0343543	0.0171772	−	0.999852i	$-0.494532\pi$
$821$	0.984358	0.0343543	0.0171772	+	0.999852i	$0.494532\pi$
$822$	−30.1740	−1.05244
$823$	−11.9961	−0.418157	−0.209078	−	0.977899i	$-0.567046\pi$
$823$	−11.9961	−0.418157	−0.209078	+	0.977899i	$0.567046\pi$
$824$	11.1268	0.387622
$825$	32.3827	1.12742
$826$	17.4789	0.608168
$827$	−17.9525	−0.624270	−0.312135	−	0.950038i	$-0.601044\pi$
$827$	−17.9525	−0.624270	−0.312135	+	0.950038i	$0.601044\pi$
$828$	−10.7924	−0.375061
$829$	33.9311	1.17848	0.589239	−	0.807959i	$-0.299428\pi$
$829$	33.9311	1.17848	0.589239	+	0.807959i	$0.299428\pi$
$830$	−5.56724	−0.193242
$831$	−55.3132	−1.91879
$832$	−5.88689	−0.204091
$833$	11.7144	0.405880
$834$	11.2773	0.390501
$835$	68.2937	2.36340
$836$	5.50011	0.190225
$837$	11.0829	0.383079
$838$	26.8072	0.926039
$839$	−20.1454	−0.695496	−0.347748	−	0.937588i	$-0.613054\pi$
$839$	−20.1454	−0.695496	−0.347748	+	0.937588i	$0.613054\pi$
$840$	7.99093	0.275713
$841$	22.4815	0.775224
$842$	29.2489	1.00798
$843$	−3.64603	−0.125576
$844$	−1.00000	−0.0344214
$845$	−60.2047	−2.07110
$846$	1.75461	0.0603249
$847$	−25.6483	−0.881287
$848$	10.3892	0.356767
$849$	−1.53861	−0.0528051
$850$	6.11845	0.209861
$851$	−0.00791575	−0.000271348 0
$852$	−6.37833	−0.218518
$853$	9.31580	0.318967	0.159483	−	0.987201i	$-0.449017\pi$
$853$	9.31580	0.318967	0.159483	+	0.987201i	$0.449017\pi$
$854$	3.27644	0.112117
$855$	4.59959	0.157303
$856$	−0.319302	−0.0109135
$857$	13.1804	0.450233	0.225116	−	0.974332i	$-0.427724\pi$
$857$	13.1804	0.450233	0.225116	+	0.974332i	$0.427724\pi$
$858$	69.8542	2.38478
$859$	15.0053	0.511975	0.255987	−	0.966680i	$-0.417599\pi$
$859$	15.0053	0.511975	0.255987	+	0.966680i	$0.417599\pi$
$860$	28.4259	0.969314
$861$	−0.0663733	−0.00226199
$862$	−0.974703	−0.0331985
$863$	−47.7992	−1.62710	−0.813552	−	0.581493i	$-0.802469\pi$
$863$	−47.7992	−1.62710	−0.813552	+	0.581493i	$0.802469\pi$
$864$	−2.90289	−0.0987583
$865$	−51.4328	−1.74877
$866$	7.32945	0.249065
$867$	25.8318	0.877293
$868$	−5.08653	−0.172648
$869$	−25.0224	−0.848825
$870$	−43.0351	−1.45903
$871$	−37.9689	−1.28653
$872$	8.01354	0.271373
$873$	5.62407	0.190346
$874$	−6.52318	−0.220650
$875$	−8.41155	−0.284362
$876$	15.2343	0.514720
$877$	−37.1911	−1.25585	−0.627927	−	0.778273i	$-0.716096\pi$
$877$	−37.1911	−1.25585	−0.627927	+	0.778273i	$0.716096\pi$
$878$	19.3320	0.652423
$879$	−6.17376	−0.208236
$880$	15.2909	0.515457
$881$	7.44719	0.250902	0.125451	−	0.992100i	$-0.459962\pi$
$881$	7.44719	0.250902	0.125451	+	0.992100i	$0.459962\pi$
$882$	8.64456	0.291077
$883$	−15.0947	−0.507976	−0.253988	−	0.967207i	$-0.581742\pi$
$883$	−15.0947	−0.507976	−0.253988	+	0.967207i	$0.581742\pi$
$884$	13.1984	0.443910
$885$	78.6883	2.64508
$886$	30.3823	1.02071
$887$	−6.63936	−0.222928	−0.111464	−	0.993768i	$-0.535554\pi$
$887$	−6.63936	−0.222928	−0.111464	+	0.993768i	$0.535554\pi$
$888$	0.00261799	8.78538e−5 0
$889$	21.1553	0.709526
$890$	28.4954	0.955168
$891$	61.7450	2.06854
$892$	−2.73815	−0.0916802
$893$	1.06053	0.0354894
$894$	−27.4739	−0.918864
$895$	−59.1959	−1.97870
$896$	1.33229	0.0445088
$897$	−82.8477	−2.76620
$898$	−38.4172	−1.28200
$899$	27.3935	0.913623
$900$	4.51506	0.150502
$901$	−23.2926	−0.775988
$902$	−0.127008	−0.00422889
$903$	−29.3891	−0.978009
$904$	−7.93918	−0.264053
$905$	47.7516	1.58732
$906$	−33.0575	−1.09826
$907$	−7.26465	−0.241219	−0.120609	−	0.992700i	$-0.538485\pi$
$907$	−7.26465	−0.241219	−0.120609	+	0.992700i	$0.538485\pi$
$908$	11.9544	0.396720
$909$	−7.61118	−0.252447
$910$	21.8046	0.722816
$911$	24.7731	0.820770	0.410385	−	0.911912i	$-0.365394\pi$
$911$	24.7731	0.820770	0.410385	+	0.911912i	$0.365394\pi$
$912$	2.15742	0.0714393
$913$	11.0141	0.364514
$914$	1.48137	0.0489995
$915$	14.7502	0.487627
$916$	23.1719	0.765620
$917$	−15.7626	−0.520527
$918$	6.50827	0.214805
$919$	−21.0392	−0.694019	−0.347009	−	0.937862i	$-0.612803\pi$
$919$	−21.0392	−0.694019	−0.347009	+	0.937862i	$0.612803\pi$
$920$	−18.1352	−0.597899
$921$	3.44225	0.113426
$922$	38.6136	1.27167
$923$	−17.4044	−0.572872
$924$	−15.8091	−0.520081
$925$	0.00331161	0.000108885 0
$926$	4.78767	0.157333
$927$	−18.4089	−0.604629
$928$	−7.17506	−0.235533
$929$	−0.464932	−0.0152539	−0.00762697	−	0.999971i	$-0.502428\pi$
$929$	−0.464932	−0.0152539	−0.00762697	+	0.999971i	$0.502428\pi$
$930$	−22.8991	−0.750891
$931$	5.22499	0.171242
$932$	0.0624516	0.00204567
$933$	33.3457	1.09169
$934$	16.0814	0.526198
$935$	−34.2822	−1.12115
$936$	9.73965	0.318350
$937$	39.4858	1.28995	0.644973	−	0.764206i	$-0.276869\pi$
$937$	39.4858	1.28995	0.644973	+	0.764206i	$0.276869\pi$
$938$	8.59294	0.280569
$939$	43.9115	1.43300
$940$	2.94840	0.0961663
$941$	49.5049	1.61381	0.806907	−	0.590678i	$-0.201140\pi$
$941$	49.5049	1.61381	0.806907	+	0.590678i	$0.201140\pi$
$942$	20.2043	0.658292
$943$	0.150632	0.00490526
$944$	13.1194	0.426999
$945$	10.7521	0.349765
$946$	−56.2371	−1.82843
$947$	−49.1586	−1.59744	−0.798720	−	0.601703i	$-0.794489\pi$
$947$	−49.1586	−1.59744	−0.798720	+	0.601703i	$0.794489\pi$
$948$	−9.81503	−0.318777
$949$	41.5695	1.34940
$950$	2.72902	0.0885410
$951$	−33.0812	−1.07273
$952$	−2.98700	−0.0968092
$953$	12.7431	0.412791	0.206395	−	0.978469i	$-0.433827\pi$
$953$	12.7431	0.412791	0.206395	+	0.978469i	$0.433827\pi$
$954$	−17.1886	−0.556500
$955$	−23.0995	−0.747484
$956$	4.02893	0.130305
$957$	85.1397	2.75217
$958$	−5.35999	−0.173174
$959$	18.6337	0.601713
$960$	5.99787	0.193580
$961$	−16.4239	−0.529802
$962$	0.00714362	0.000230320 0
$963$	0.528274	0.0170234
$964$	−15.1865	−0.489123
$965$	−70.6418	−2.27404
$966$	18.7497	0.603262
$967$	−39.0003	−1.25417	−0.627083	−	0.778953i	$-0.715751\pi$
$967$	−39.0003	−1.25417	−0.627083	+	0.778953i	$0.715751\pi$
$968$	−19.2512	−0.618758
$969$	−4.83693	−0.155385
$970$	9.45052	0.303438
$971$	−6.69225	−0.214764	−0.107382	−	0.994218i	$-0.534247\pi$
$971$	−6.69225	−0.214764	−0.107382	+	0.994218i	$0.534247\pi$
$972$	15.5108	0.497511
$973$	−6.96419	−0.223262
$974$	1.50511	0.0482267
$975$	34.6599	1.11001
$976$	2.45924	0.0787185
$977$	35.5370	1.13693	0.568465	−	0.822707i	$-0.307537\pi$
$977$	35.5370	1.13693	0.568465	+	0.822707i	$0.307537\pi$
$978$	−22.8653	−0.731153
$979$	−56.3747	−1.80174
$980$	14.5261	0.464018
$981$	−13.2581	−0.423299
$982$	−10.0401	−0.320392
$983$	−21.5663	−0.687857	−0.343928	−	0.938996i	$-0.611758\pi$
$983$	−21.5663	−0.687857	−0.343928	+	0.938996i	$0.611758\pi$
$984$	−0.0498188	−0.00158816
$985$	−4.60295	−0.146662
$986$	16.0865	0.512297
$987$	−3.04831	−0.0970289
$988$	5.88689	0.187287
$989$	66.6977	2.12086
$990$	−25.2983	−0.804032
$991$	23.0864	0.733365	0.366682	−	0.930346i	$-0.380494\pi$
$991$	23.0864	0.733365	0.366682	+	0.930346i	$0.380494\pi$
$992$	−3.81787	−0.121218
$993$	−41.2567	−1.30924
$994$	3.93888	0.124934
$995$	37.4557	1.18743
$996$	4.32029	0.136894
$997$	−43.6392	−1.38207	−0.691034	−	0.722823i	$-0.742844\pi$
$997$	−43.6392	−1.38207	−0.691034	+	0.722823i	$0.742844\pi$
$998$	−15.9373	−0.504488
$999$	0.00352260	0.000111450 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.8	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.8	✓	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +2.78011 q^{10} -5.50011 q^{11} -2.15742 q^{12} -5.88689 q^{13} +1.33229 q^{14} +5.99787 q^{15} +1.00000 q^{16} -2.24200 q^{17} -1.65446 q^{18} -1.00000 q^{19} -2.78011 q^{20} +2.87432 q^{21} +5.50011 q^{22} -6.52318 q^{23} +2.15742 q^{24} +2.72902 q^{25} +5.88689 q^{26} +2.90289 q^{27} -1.33229 q^{28} +7.17506 q^{29} -5.99787 q^{30} +3.81787 q^{31} -1.00000 q^{32} +11.8661 q^{33} +2.24200 q^{34} +3.70393 q^{35} +1.65446 q^{36} +0.00121348 q^{37} +1.00000 q^{38} +12.7005 q^{39} +2.78011 q^{40} -0.0230918 q^{41} -2.87432 q^{42} -10.2247 q^{43} -5.50011 q^{44} -4.59959 q^{45} +6.52318 q^{46} -1.06053 q^{47} -2.15742 q^{48} -5.22499 q^{49} -2.72902 q^{50} +4.83693 q^{51} -5.88689 q^{52} +10.3892 q^{53} -2.90289 q^{54} +15.2909 q^{55} +1.33229 q^{56} +2.15742 q^{57} -7.17506 q^{58} +13.1194 q^{59} +5.99787 q^{60} +2.45924 q^{61} -3.81787 q^{62} -2.20423 q^{63} +1.00000 q^{64} +16.3662 q^{65} -11.8661 q^{66} +6.44973 q^{67} -2.24200 q^{68} +14.0732 q^{69} -3.70393 q^{70} +2.95646 q^{71} -1.65446 q^{72} -7.06136 q^{73} -0.00121348 q^{74} -5.88764 q^{75} -1.00000 q^{76} +7.32777 q^{77} -12.7005 q^{78} +4.54943 q^{79} -2.78011 q^{80} -11.2261 q^{81} +0.0230918 q^{82} -2.00252 q^{83} +2.87432 q^{84} +6.23300 q^{85} +10.2247 q^{86} -15.4796 q^{87} +5.50011 q^{88} +10.2497 q^{89} +4.59959 q^{90} +7.84307 q^{91} -6.52318 q^{92} -8.23675 q^{93} +1.06053 q^{94} +2.78011 q^{95} +2.15742 q^{96} +3.39933 q^{97} +5.22499 q^{98} -9.09974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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