LMFDB - Embedded newform 8007.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06382 q^{2} -1.00000 q^{3} +2.25934 q^{4} -2.15851 q^{5} +2.06382 q^{6} +0.293019 q^{7} -0.535232 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.06382 q^{2} -1.00000 q^{3} +2.25934 q^{4} -2.15851 q^{5} +2.06382 q^{6} +0.293019 q^{7} -0.535232 q^{8} +1.00000 q^{9} +4.45478 q^{10} -1.28906 q^{11} -2.25934 q^{12} +6.19002 q^{13} -0.604738 q^{14} +2.15851 q^{15} -3.41406 q^{16} +1.00000 q^{17} -2.06382 q^{18} -7.51210 q^{19} -4.87682 q^{20} -0.293019 q^{21} +2.66039 q^{22} +8.06548 q^{23} +0.535232 q^{24} -0.340819 q^{25} -12.7751 q^{26} -1.00000 q^{27} +0.662030 q^{28} -2.92588 q^{29} -4.45478 q^{30} -0.441742 q^{31} +8.11646 q^{32} +1.28906 q^{33} -2.06382 q^{34} -0.632486 q^{35} +2.25934 q^{36} +4.74016 q^{37} +15.5036 q^{38} -6.19002 q^{39} +1.15531 q^{40} +7.73296 q^{41} +0.604738 q^{42} -9.62800 q^{43} -2.91243 q^{44} -2.15851 q^{45} -16.6457 q^{46} +0.0536453 q^{47} +3.41406 q^{48} -6.91414 q^{49} +0.703388 q^{50} -1.00000 q^{51} +13.9854 q^{52} +12.2265 q^{53} +2.06382 q^{54} +2.78246 q^{55} -0.156833 q^{56} +7.51210 q^{57} +6.03847 q^{58} +2.28956 q^{59} +4.87682 q^{60} -3.62474 q^{61} +0.911674 q^{62} +0.293019 q^{63} -9.92277 q^{64} -13.3612 q^{65} -2.66039 q^{66} -7.01439 q^{67} +2.25934 q^{68} -8.06548 q^{69} +1.30534 q^{70} -7.52304 q^{71} -0.535232 q^{72} -4.73694 q^{73} -9.78282 q^{74} +0.340819 q^{75} -16.9724 q^{76} -0.377720 q^{77} +12.7751 q^{78} -14.8451 q^{79} +7.36930 q^{80} +1.00000 q^{81} -15.9594 q^{82} +14.5272 q^{83} -0.662030 q^{84} -2.15851 q^{85} +19.8704 q^{86} +2.92588 q^{87} +0.689948 q^{88} -4.35953 q^{89} +4.45478 q^{90} +1.81379 q^{91} +18.2227 q^{92} +0.441742 q^{93} -0.110714 q^{94} +16.2150 q^{95} -8.11646 q^{96} -14.1859 q^{97} +14.2695 q^{98} -1.28906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.06382	−1.45934	−0.729670	−	0.683800i	$-0.760326\pi$
$2$	−2.06382	−1.45934	−0.729670	+	0.683800i	$0.760326\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.25934	1.12967
$5$	−2.15851	−0.965317	−0.482658	−	0.875809i	$-0.660329\pi$
$5$	−2.15851	−0.965317	−0.482658	+	0.875809i	$0.660329\pi$
$6$	2.06382	0.842550
$7$	0.293019	0.110751	0.0553754	−	0.998466i	$-0.482364\pi$
$7$	0.293019	0.110751	0.0553754	+	0.998466i	$0.482364\pi$
$8$	−0.535232	−0.189233
$9$	1.00000	0.333333
$10$	4.45478	1.40872
$11$	−1.28906	−0.388667	−0.194334	−	0.980935i	$-0.562254\pi$
$11$	−1.28906	−0.388667	−0.194334	+	0.980935i	$0.562254\pi$
$12$	−2.25934	−0.652216
$13$	6.19002	1.71680	0.858401	−	0.512980i	$-0.171458\pi$
$13$	6.19002	1.71680	0.858401	+	0.512980i	$0.171458\pi$
$14$	−0.604738	−0.161623
$15$	2.15851	0.557326
$16$	−3.41406	−0.853515
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.06382	−0.486446
$19$	−7.51210	−1.72339	−0.861697	−	0.507423i	$-0.830598\pi$
$19$	−7.51210	−1.72339	−0.861697	+	0.507423i	$0.830598\pi$
$20$	−4.87682	−1.09049
$21$	−0.293019	−0.0639420
$22$	2.66039	0.567197
$23$	8.06548	1.68177	0.840884	−	0.541215i	$-0.182035\pi$
$23$	8.06548	1.68177	0.840884	+	0.541215i	$0.182035\pi$
$24$	0.535232	0.109254
$25$	−0.340819	−0.0681638
$26$	−12.7751	−2.50540
$27$	−1.00000	−0.192450
$28$	0.662030	0.125112
$29$	−2.92588	−0.543322	−0.271661	−	0.962393i	$-0.587573\pi$
$29$	−2.92588	−0.543322	−0.271661	+	0.962393i	$0.587573\pi$
$30$	−4.45478	−0.813327
$31$	−0.441742	−0.0793391	−0.0396696	−	0.999213i	$-0.512631\pi$
$31$	−0.441742	−0.0793391	−0.0396696	+	0.999213i	$0.512631\pi$
$32$	8.11646	1.43480
$33$	1.28906	0.224397
$34$	−2.06382	−0.353942
$35$	−0.632486	−0.106910
$36$	2.25934	0.376557
$37$	4.74016	0.779278	0.389639	−	0.920968i	$-0.372600\pi$
$37$	4.74016	0.779278	0.389639	+	0.920968i	$0.372600\pi$
$38$	15.5036	2.51502
$39$	−6.19002	−0.991196
$40$	1.15531	0.182670
$41$	7.73296	1.20769	0.603843	−	0.797104i	$-0.293636\pi$
$41$	7.73296	1.20769	0.603843	+	0.797104i	$0.293636\pi$
$42$	0.604738	0.0933131
$43$	−9.62800	−1.46826	−0.734128	−	0.679011i	$-0.762409\pi$
$43$	−9.62800	−1.46826	−0.734128	+	0.679011i	$0.762409\pi$
$44$	−2.91243	−0.439066
$45$	−2.15851	−0.321772
$46$	−16.6457	−2.45427
$47$	0.0536453	0.00782498	0.00391249	−	0.999992i	$-0.498755\pi$
$47$	0.0536453	0.00782498	0.00391249	+	0.999992i	$0.498755\pi$
$48$	3.41406	0.492777
$49$	−6.91414	−0.987734
$50$	0.703388	0.0994741
$51$	−1.00000	−0.140028
$52$	13.9854	1.93942
$53$	12.2265	1.67944	0.839720	−	0.543020i	$-0.182719\pi$
$53$	12.2265	1.67944	0.839720	+	0.543020i	$0.182719\pi$
$54$	2.06382	0.280850
$55$	2.78246	0.375187
$56$	−0.156833	−0.0209577
$57$	7.51210	0.995002
$58$	6.03847	0.792891
$59$	2.28956	0.298075	0.149038	−	0.988832i	$-0.452382\pi$
$59$	2.28956	0.298075	0.149038	+	0.988832i	$0.452382\pi$
$60$	4.87682	0.629595
$61$	−3.62474	−0.464101	−0.232050	−	0.972704i	$-0.574543\pi$
$61$	−3.62474	−0.464101	−0.232050	+	0.972704i	$0.574543\pi$
$62$	0.911674	0.115783
$63$	0.293019	0.0369170
$64$	−9.92277	−1.24035
$65$	−13.3612	−1.65726
$66$	−2.66039	−0.327471
$67$	−7.01439	−0.856944	−0.428472	−	0.903555i	$-0.640948\pi$
$67$	−7.01439	−0.856944	−0.428472	+	0.903555i	$0.640948\pi$
$68$	2.25934	0.273985
$69$	−8.06548	−0.970970
$70$	1.30534	0.156017
$71$	−7.52304	−0.892820	−0.446410	−	0.894829i	$-0.647298\pi$
$71$	−7.52304	−0.892820	−0.446410	+	0.894829i	$0.647298\pi$
$72$	−0.535232	−0.0630777
$73$	−4.73694	−0.554417	−0.277209	−	0.960810i	$-0.589409\pi$
$73$	−4.73694	−0.554417	−0.277209	+	0.960810i	$0.589409\pi$
$74$	−9.78282	−1.13723
$75$	0.340819	0.0393544
$76$	−16.9724	−1.94687
$77$	−0.377720	−0.0430452
$78$	12.7751	1.44649
$79$	−14.8451	−1.67021	−0.835105	−	0.550091i	$-0.814593\pi$
$79$	−14.8451	−1.67021	−0.835105	+	0.550091i	$0.814593\pi$
$80$	7.36930	0.823912
$81$	1.00000	0.111111
$82$	−15.9594	−1.76242
$83$	14.5272	1.59457	0.797284	−	0.603605i	$-0.206269\pi$
$83$	14.5272	1.59457	0.797284	+	0.603605i	$0.206269\pi$
$84$	−0.662030	−0.0722334
$85$	−2.15851	−0.234124
$86$	19.8704	2.14268
$87$	2.92588	0.313687
$88$	0.689948	0.0735488
$89$	−4.35953	−0.462109	−0.231054	−	0.972941i	$-0.574218\pi$
$89$	−4.35953	−0.462109	−0.231054	+	0.972941i	$0.574218\pi$
$90$	4.45478	0.469575
$91$	1.81379	0.190137
$92$	18.2227	1.89984
$93$	0.441742	0.0458065
$94$	−0.110714	−0.0114193
$95$	16.2150	1.66362
$96$	−8.11646	−0.828383
$97$	−14.1859	−1.44036	−0.720181	−	0.693787i	$-0.755941\pi$
$97$	−14.1859	−1.44036	−0.720181	+	0.693787i	$0.755941\pi$
$98$	14.2695	1.44144
$99$	−1.28906	−0.129556
$100$	−0.770027	−0.0770027
$101$	−16.0697	−1.59899	−0.799497	−	0.600670i	$-0.794901\pi$
$101$	−16.0697	−1.59899	−0.799497	+	0.600670i	$0.794901\pi$
$102$	2.06382	0.204348
$103$	15.6393	1.54099	0.770494	−	0.637447i	$-0.220009\pi$
$103$	15.6393	1.54099	0.770494	+	0.637447i	$0.220009\pi$
$104$	−3.31310	−0.324876
$105$	0.632486	0.0617243
$106$	−25.2333	−2.45087
$107$	10.9751	1.06100	0.530500	−	0.847685i	$-0.322004\pi$
$107$	10.9751	1.06100	0.530500	+	0.847685i	$0.322004\pi$
$108$	−2.25934	−0.217405
$109$	−8.50950	−0.815062	−0.407531	−	0.913191i	$-0.633610\pi$
$109$	−8.50950	−0.815062	−0.407531	+	0.913191i	$0.633610\pi$
$110$	−5.74249	−0.547525
$111$	−4.74016	−0.449916
$112$	−1.00039	−0.0945275
$113$	−11.8831	−1.11787	−0.558933	−	0.829213i	$-0.688789\pi$
$113$	−11.8831	−1.11787	−0.558933	+	0.829213i	$0.688789\pi$
$114$	−15.5036	−1.45205
$115$	−17.4094	−1.62344
$116$	−6.61055	−0.613774
$117$	6.19002	0.572267
$118$	−4.72523	−0.434993
$119$	0.293019	0.0268610
$120$	−1.15531	−0.105465
$121$	−9.33832	−0.848938
$122$	7.48080	0.677280
$123$	−7.73296	−0.697257
$124$	−0.998045	−0.0896271
$125$	11.5282	1.03112
$126$	−0.604738	−0.0538744
$127$	17.2822	1.53355	0.766774	−	0.641918i	$-0.221861\pi$
$127$	17.2822	1.53355	0.766774	+	0.641918i	$0.221861\pi$
$128$	4.24586	0.375285
$129$	9.62800	0.847698
$130$	27.5751	2.41850
$131$	10.0710	0.879911	0.439955	−	0.898020i	$-0.354994\pi$
$131$	10.0710	0.879911	0.439955	+	0.898020i	$0.354994\pi$
$132$	2.91243	0.253495
$133$	−2.20119	−0.190867
$134$	14.4764	1.25057
$135$	2.15851	0.185775
$136$	−0.535232	−0.0458958
$137$	−0.656209	−0.0560637	−0.0280319	−	0.999607i	$-0.508924\pi$
$137$	−0.656209	−0.0560637	−0.0280319	+	0.999607i	$0.508924\pi$
$138$	16.6457	1.41697
$139$	7.80493	0.662005	0.331003	−	0.943630i	$-0.392613\pi$
$139$	7.80493	0.662005	0.331003	+	0.943630i	$0.392613\pi$
$140$	−1.42900	−0.120773
$141$	−0.0536453	−0.00451775
$142$	15.5262	1.30293
$143$	−7.97932	−0.667264
$144$	−3.41406	−0.284505
$145$	6.31554	0.524477
$146$	9.77619	0.809083
$147$	6.91414	0.570269
$148$	10.7096	0.880327
$149$	−21.6006	−1.76959	−0.884796	−	0.465978i	$-0.845702\pi$
$149$	−21.6006	−1.76959	−0.884796	+	0.465978i	$0.845702\pi$
$150$	−0.703388	−0.0574314
$151$	17.0383	1.38656	0.693280	−	0.720668i	$-0.256165\pi$
$151$	17.0383	1.38656	0.693280	+	0.720668i	$0.256165\pi$
$152$	4.02072	0.326123
$153$	1.00000	0.0808452
$154$	0.779546	0.0628176
$155$	0.953505	0.0765874
$156$	−13.9854	−1.11972
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	30.6377	2.43740
$159$	−12.2265	−0.969625
$160$	−17.5195	−1.38504
$161$	2.36334	0.186257
$162$	−2.06382	−0.162149
$163$	14.4814	1.13427	0.567136	−	0.823624i	$-0.308051\pi$
$163$	14.4814	1.13427	0.567136	+	0.823624i	$0.308051\pi$
$164$	17.4714	1.36429
$165$	−2.78246	−0.216614
$166$	−29.9815	−2.32701
$167$	−17.9374	−1.38804	−0.694020	−	0.719955i	$-0.744162\pi$
$167$	−17.9374	−1.38804	−0.694020	+	0.719955i	$0.744162\pi$
$168$	0.156833	0.0121000
$169$	25.3163	1.94741
$170$	4.45478	0.341666
$171$	−7.51210	−0.574465
$172$	−21.7529	−1.65864
$173$	−0.286587	−0.0217888	−0.0108944	−	0.999941i	$-0.503468\pi$
$173$	−0.286587	−0.0217888	−0.0108944	+	0.999941i	$0.503468\pi$
$174$	−6.03847	−0.457776
$175$	−0.0998666	−0.00754920
$176$	4.40094	0.331733
$177$	−2.28956	−0.172094
$178$	8.99727	0.674374
$179$	14.9503	1.11744	0.558719	−	0.829357i	$-0.311293\pi$
$179$	14.9503	1.11744	0.558719	+	0.829357i	$0.311293\pi$
$180$	−4.87682	−0.363497
$181$	7.04602	0.523726	0.261863	−	0.965105i	$-0.415663\pi$
$181$	7.04602	0.523726	0.261863	+	0.965105i	$0.415663\pi$
$182$	−3.74334	−0.277475
$183$	3.62474	0.267949
$184$	−4.31691	−0.318247
$185$	−10.2317	−0.752250
$186$	−0.911674	−0.0668472
$187$	−1.28906	−0.0942656
$188$	0.121203	0.00883964
$189$	−0.293019	−0.0213140
$190$	−33.4647	−2.42779
$191$	−21.1728	−1.53201	−0.766004	−	0.642836i	$-0.777758\pi$
$191$	−21.1728	−1.53201	−0.766004	+	0.642836i	$0.777758\pi$
$192$	9.92277	0.716114
$193$	22.1752	1.59620	0.798102	−	0.602523i	$-0.205838\pi$
$193$	22.1752	1.59620	0.798102	+	0.602523i	$0.205838\pi$
$194$	29.2771	2.10198
$195$	13.3612	0.956818
$196$	−15.6214	−1.11581
$197$	22.7628	1.62178	0.810891	−	0.585197i	$-0.198983\pi$
$197$	22.7628	1.62178	0.810891	+	0.585197i	$0.198983\pi$
$198$	2.66039	0.189066
$199$	5.72693	0.405972	0.202986	−	0.979182i	$-0.434935\pi$
$199$	5.72693	0.405972	0.202986	+	0.979182i	$0.434935\pi$
$200$	0.182417	0.0128989
$201$	7.01439	0.494757
$202$	33.1649	2.33347
$203$	−0.857338	−0.0601734
$204$	−2.25934	−0.158186
$205$	−16.6917	−1.16580
$206$	−32.2767	−2.24882
$207$	8.06548	0.560590
$208$	−21.1331	−1.46532
$209$	9.68357	0.669827
$210$	−1.30534	−0.0900767
$211$	3.00066	0.206574	0.103287	−	0.994652i	$-0.467064\pi$
$211$	3.00066	0.206574	0.103287	+	0.994652i	$0.467064\pi$
$212$	27.6239	1.89721
$213$	7.52304	0.515470
$214$	−22.6505	−1.54836
$215$	20.7822	1.41733
$216$	0.535232	0.0364180
$217$	−0.129439	−0.00878688
$218$	17.5621	1.18945
$219$	4.73694	0.320093
$220$	6.28653	0.423838
$221$	6.19002	0.416385
$222$	9.78282	0.656580
$223$	7.28187	0.487630	0.243815	−	0.969822i	$-0.421601\pi$
$223$	7.28187	0.487630	0.243815	+	0.969822i	$0.421601\pi$
$224$	2.37828	0.158905
$225$	−0.340819	−0.0227213
$226$	24.5245	1.63134
$227$	1.16172	0.0771063	0.0385531	−	0.999257i	$-0.487725\pi$
$227$	1.16172	0.0771063	0.0385531	+	0.999257i	$0.487725\pi$
$228$	16.9724	1.12402
$229$	1.13226	0.0748220	0.0374110	−	0.999300i	$-0.488089\pi$
$229$	1.13226	0.0748220	0.0374110	+	0.999300i	$0.488089\pi$
$230$	35.9299	2.36915
$231$	0.377720	0.0248522
$232$	1.56602	0.102815
$233$	3.20761	0.210138	0.105069	−	0.994465i	$-0.466494\pi$
$233$	3.20761	0.210138	0.105069	+	0.994465i	$0.466494\pi$
$234$	−12.7751	−0.835132
$235$	−0.115794	−0.00755358
$236$	5.17289	0.336727
$237$	14.8451	0.964296
$238$	−0.604738	−0.0391994
$239$	22.0947	1.42919	0.714593	−	0.699540i	$-0.246612\pi$
$239$	22.0947	1.42919	0.714593	+	0.699540i	$0.246612\pi$
$240$	−7.36930	−0.475686
$241$	−15.5171	−0.999547	−0.499774	−	0.866156i	$-0.666583\pi$
$241$	−15.5171	−0.999547	−0.499774	+	0.866156i	$0.666583\pi$
$242$	19.2726	1.23889
$243$	−1.00000	−0.0641500
$244$	−8.18953	−0.524281
$245$	14.9243	0.953476
$246$	15.9594	1.01753
$247$	−46.5000	−2.95873
$248$	0.236434	0.0150136
$249$	−14.5272	−0.920624
$250$	−23.7922	−1.50475
$251$	23.7365	1.49823	0.749116	−	0.662439i	$-0.230478\pi$
$251$	23.7365	1.49823	0.749116	+	0.662439i	$0.230478\pi$
$252$	0.662030	0.0417040
$253$	−10.3969	−0.653648
$254$	−35.6673	−2.23797
$255$	2.15851	0.135171
$256$	11.0829	0.692679
$257$	−21.6538	−1.35073	−0.675363	−	0.737486i	$-0.736013\pi$
$257$	−21.6538	−1.35073	−0.675363	+	0.737486i	$0.736013\pi$
$258$	−19.8704	−1.23708
$259$	1.38896	0.0863057
$260$	−30.1876	−1.87215
$261$	−2.92588	−0.181107
$262$	−20.7848	−1.28409
$263$	−23.5115	−1.44978	−0.724891	−	0.688863i	$-0.758110\pi$
$263$	−23.5115	−1.44978	−0.724891	+	0.688863i	$0.758110\pi$
$264$	−0.689948	−0.0424634
$265$	−26.3911	−1.62119
$266$	4.54285	0.278540
$267$	4.35953	0.266799
$268$	−15.8479	−0.968065
$269$	−29.6392	−1.80713	−0.903565	−	0.428450i	$-0.859060\pi$
$269$	−29.6392	−1.80713	−0.903565	+	0.428450i	$0.859060\pi$
$270$	−4.45478	−0.271109
$271$	3.20609	0.194756	0.0973779	−	0.995247i	$-0.468954\pi$
$271$	3.20609	0.194756	0.0973779	+	0.995247i	$0.468954\pi$
$272$	−3.41406	−0.207008
$273$	−1.81379	−0.109776
$274$	1.35430	0.0818160
$275$	0.439337	0.0264930
$276$	−18.2227	−1.09688
$277$	−29.7448	−1.78719	−0.893595	−	0.448874i	$-0.851825\pi$
$277$	−29.7448	−1.78719	−0.893595	+	0.448874i	$0.851825\pi$
$278$	−16.1079	−0.966090
$279$	−0.441742	−0.0264464
$280$	0.338527	0.0202309
$281$	−2.39132	−0.142654	−0.0713270	−	0.997453i	$-0.522723\pi$
$281$	−2.39132	−0.142654	−0.0713270	+	0.997453i	$0.522723\pi$
$282$	0.110714	0.00659293
$283$	1.51036	0.0897816	0.0448908	−	0.998992i	$-0.485706\pi$
$283$	1.51036	0.0897816	0.0448908	+	0.998992i	$0.485706\pi$
$284$	−16.9971	−1.00859
$285$	−16.2150	−0.960492
$286$	16.4679	0.973765
$287$	2.26591	0.133752
$288$	8.11646	0.478267
$289$	1.00000	0.0588235
$290$	−13.0341	−0.765390
$291$	14.1859	0.831593
$292$	−10.7024	−0.626309
$293$	23.8958	1.39601	0.698003	−	0.716095i	$-0.254072\pi$
$293$	23.8958	1.39601	0.698003	+	0.716095i	$0.254072\pi$
$294$	−14.2695	−0.832215
$295$	−4.94204	−0.287737
$296$	−2.53709	−0.147465
$297$	1.28906	0.0747990
$298$	44.5797	2.58243
$299$	49.9254	2.88726
$300$	0.770027	0.0444575
$301$	−2.82119	−0.162611
$302$	−35.1640	−2.02346
$303$	16.0697	0.923180
$304$	25.6468	1.47094
$305$	7.82405	0.448004
$306$	−2.06382	−0.117981
$307$	2.68441	0.153207	0.0766037	−	0.997062i	$-0.475592\pi$
$307$	2.68441	0.153207	0.0766037	+	0.997062i	$0.475592\pi$
$308$	−0.853399	−0.0486269
$309$	−15.6393	−0.889690
$310$	−1.96786	−0.111767
$311$	18.3878	1.04268	0.521339	−	0.853350i	$-0.325433\pi$
$311$	18.3878	1.04268	0.521339	+	0.853350i	$0.325433\pi$
$312$	3.31310	0.187567
$313$	12.1742	0.688128	0.344064	−	0.938946i	$-0.388196\pi$
$313$	12.1742	0.688128	0.344064	+	0.938946i	$0.388196\pi$
$314$	−2.06382	−0.116468
$315$	−0.632486	−0.0356366
$316$	−33.5402	−1.88679
$317$	28.1787	1.58267	0.791336	−	0.611381i	$-0.209386\pi$
$317$	28.1787	1.58267	0.791336	+	0.611381i	$0.209386\pi$
$318$	25.2333	1.41501
$319$	3.77164	0.211171
$320$	21.4184	1.19733
$321$	−10.9751	−0.612569
$322$	−4.87750	−0.271813
$323$	−7.51210	−0.417984
$324$	2.25934	0.125519
$325$	−2.10968	−0.117024
$326$	−29.8870	−1.65529
$327$	8.50950	0.470576
$328$	−4.13893	−0.228534
$329$	0.0157191	0.000866623 0
$330$	5.74249	0.316114
$331$	−11.0726	−0.608607	−0.304304	−	0.952575i	$-0.598424\pi$
$331$	−11.0726	−0.608607	−0.304304	+	0.952575i	$0.598424\pi$
$332$	32.8219	1.80134
$333$	4.74016	0.259759
$334$	37.0196	2.02562
$335$	15.1407	0.827223
$336$	1.00039	0.0545755
$337$	−1.76951	−0.0963914	−0.0481957	−	0.998838i	$-0.515347\pi$
$337$	−1.76951	−0.0963914	−0.0481957	+	0.998838i	$0.515347\pi$
$338$	−52.2482	−2.84193
$339$	11.8831	0.645400
$340$	−4.87682	−0.264483
$341$	0.569433	0.0308365
$342$	15.5036	0.838339
$343$	−4.07711	−0.220143
$344$	5.15321	0.277843
$345$	17.4094	0.937293
$346$	0.591464	0.0317973
$347$	−2.64160	−0.141809	−0.0709043	−	0.997483i	$-0.522588\pi$
$347$	−2.64160	−0.141809	−0.0709043	+	0.997483i	$0.522588\pi$
$348$	6.61055	0.354363
$349$	−8.26314	−0.442316	−0.221158	−	0.975238i	$-0.570984\pi$
$349$	−8.26314	−0.442316	−0.221158	+	0.975238i	$0.570984\pi$
$350$	0.206106	0.0110168
$351$	−6.19002	−0.330399
$352$	−10.4626	−0.557660
$353$	−23.2195	−1.23585	−0.617924	−	0.786238i	$-0.712026\pi$
$353$	−23.2195	−1.23585	−0.617924	+	0.786238i	$0.712026\pi$
$354$	4.72523	0.251143
$355$	16.2386	0.861854
$356$	−9.84966	−0.522031
$357$	−0.293019	−0.0155082
$358$	−30.8547	−1.63072
$359$	24.9482	1.31671	0.658357	−	0.752706i	$-0.271252\pi$
$359$	24.9482	1.31671	0.658357	+	0.752706i	$0.271252\pi$
$360$	1.15531	0.0608900
$361$	37.4317	1.97009
$362$	−14.5417	−0.764294
$363$	9.33832	0.490134
$364$	4.09798	0.214792
$365$	10.2248	0.535188
$366$	−7.48080	−0.391028
$367$	−8.26694	−0.431531	−0.215765	−	0.976445i	$-0.569225\pi$
$367$	−8.26694	−0.431531	−0.215765	+	0.976445i	$0.569225\pi$
$368$	−27.5360	−1.43541
$369$	7.73296	0.402562
$370$	21.1164	1.09779
$371$	3.58260	0.185999
$372$	0.998045	0.0517462
$373$	−8.36167	−0.432951	−0.216476	−	0.976288i	$-0.569456\pi$
$373$	−8.36167	−0.432951	−0.216476	+	0.976288i	$0.569456\pi$
$374$	2.66039	0.137566
$375$	−11.5282	−0.595315
$376$	−0.0287127	−0.00148075
$377$	−18.1112	−0.932775
$378$	0.604738	0.0311044
$379$	8.27555	0.425087	0.212543	−	0.977152i	$-0.431825\pi$
$379$	8.27555	0.425087	0.212543	+	0.977152i	$0.431825\pi$
$380$	36.6351	1.87934
$381$	−17.2822	−0.885394
$382$	43.6967	2.23572
$383$	−27.0729	−1.38336	−0.691681	−	0.722203i	$-0.743130\pi$
$383$	−27.0729	−1.38336	−0.691681	+	0.722203i	$0.743130\pi$
$384$	−4.24586	−0.216671
$385$	0.815315	0.0415523
$386$	−45.7655	−2.32940
$387$	−9.62800	−0.489419
$388$	−32.0508	−1.62713
$389$	−36.2016	−1.83549	−0.917746	−	0.397168i	$-0.869993\pi$
$389$	−36.2016	−1.83549	−0.917746	+	0.397168i	$0.869993\pi$
$390$	−27.5751	−1.39632
$391$	8.06548	0.407889
$392$	3.70067	0.186912
$393$	−10.0710	−0.508017
$394$	−46.9782	−2.36673
$395$	32.0434	1.61228
$396$	−2.91243	−0.146355
$397$	9.36447	0.469989	0.234995	−	0.971997i	$-0.424493\pi$
$397$	9.36447	0.469989	0.234995	+	0.971997i	$0.424493\pi$
$398$	−11.8193	−0.592450
$399$	2.20119	0.110197
$400$	1.16358	0.0581789
$401$	−17.9196	−0.894862	−0.447431	−	0.894318i	$-0.647661\pi$
$401$	−17.9196	−0.894862	−0.447431	+	0.894318i	$0.647661\pi$
$402$	−14.4764	−0.722018
$403$	−2.73439	−0.136210
$404$	−36.3069	−1.80634
$405$	−2.15851	−0.107257
$406$	1.76939	0.0878133
$407$	−6.11037	−0.302880
$408$	0.535232	0.0264980
$409$	−1.79978	−0.0889935	−0.0444967	−	0.999010i	$-0.514168\pi$
$409$	−1.79978	−0.0889935	−0.0444967	+	0.999010i	$0.514168\pi$
$410$	34.4486	1.70130
$411$	0.656209	0.0323684
$412$	35.3346	1.74081
$413$	0.670885	0.0330121
$414$	−16.6457	−0.818090
$415$	−31.3572	−1.53926
$416$	50.2410	2.46327
$417$	−7.80493	−0.382209
$418$	−19.9851	−0.977504
$419$	12.4289	0.607192	0.303596	−	0.952801i	$-0.401813\pi$
$419$	12.4289	0.607192	0.303596	+	0.952801i	$0.401813\pi$
$420$	1.42900	0.0697281
$421$	−25.5304	−1.24427	−0.622137	−	0.782908i	$-0.713735\pi$
$421$	−25.5304	−1.24427	−0.622137	+	0.782908i	$0.713735\pi$
$422$	−6.19281	−0.301461
$423$	0.0536453	0.00260833
$424$	−6.54402	−0.317806
$425$	−0.340819	−0.0165322
$426$	−15.5262	−0.752245
$427$	−1.06212	−0.0513995
$428$	24.7964	1.19858
$429$	7.97932	0.385245
$430$	−42.8906	−2.06837
$431$	6.81896	0.328458	0.164229	−	0.986422i	$-0.447486\pi$
$431$	6.81896	0.328458	0.164229	+	0.986422i	$0.447486\pi$
$432$	3.41406	0.164259
$433$	14.6254	0.702852	0.351426	−	0.936216i	$-0.385697\pi$
$433$	14.6254	0.702852	0.351426	+	0.936216i	$0.385697\pi$
$434$	0.267138	0.0128230
$435$	−6.31554	−0.302807
$436$	−19.2259	−0.920752
$437$	−60.5887	−2.89835
$438$	−9.77619	−0.467124
$439$	1.24439	0.0593916	0.0296958	−	0.999559i	$-0.490546\pi$
$439$	1.24439	0.0593916	0.0296958	+	0.999559i	$0.490546\pi$
$440$	−1.48926	−0.0709978
$441$	−6.91414	−0.329245
$442$	−12.7751	−0.607648
$443$	19.9592	0.948289	0.474144	−	0.880447i	$-0.342757\pi$
$443$	19.9592	0.948289	0.474144	+	0.880447i	$0.342757\pi$
$444$	−10.7096	−0.508257
$445$	9.41010	0.446081
$446$	−15.0284	−0.711618
$447$	21.6006	1.02167
$448$	−2.90756	−0.137369
$449$	−25.7704	−1.21618	−0.608091	−	0.793867i	$-0.708064\pi$
$449$	−25.7704	−1.21618	−0.608091	+	0.793867i	$0.708064\pi$
$450$	0.703388	0.0331580
$451$	−9.96827	−0.469388
$452$	−26.8479	−1.26282
$453$	−17.0383	−0.800531
$454$	−2.39758	−0.112524
$455$	−3.91510	−0.183543
$456$	−4.02072	−0.188287
$457$	4.56115	0.213362	0.106681	−	0.994293i	$-0.465978\pi$
$457$	4.56115	0.213362	0.106681	+	0.994293i	$0.465978\pi$
$458$	−2.33678	−0.109191
$459$	−1.00000	−0.0466760
$460$	−39.3339	−1.83395
$461$	−22.5530	−1.05040	−0.525200	−	0.850979i	$-0.676009\pi$
$461$	−22.5530	−1.05040	−0.525200	+	0.850979i	$0.676009\pi$
$462$	−0.779546	−0.0362678
$463$	12.4966	0.580767	0.290384	−	0.956910i	$-0.406217\pi$
$463$	12.4966	0.580767	0.290384	+	0.956910i	$0.406217\pi$
$464$	9.98912	0.463733
$465$	−0.953505	−0.0442177
$466$	−6.61993	−0.306662
$467$	−35.4047	−1.63833	−0.819166	−	0.573556i	$-0.805564\pi$
$467$	−35.4047	−1.63833	−0.819166	+	0.573556i	$0.805564\pi$
$468$	13.9854	0.646473
$469$	−2.05535	−0.0949074
$470$	0.238978	0.0110232
$471$	−1.00000	−0.0460776
$472$	−1.22545	−0.0564057
$473$	12.4111	0.570663
$474$	−30.6377	−1.40723
$475$	2.56027	0.117473
$476$	0.662030	0.0303441
$477$	12.2265	0.559813
$478$	−45.5994	−2.08567
$479$	−33.0229	−1.50886	−0.754428	−	0.656383i	$-0.772086\pi$
$479$	−33.0229	−1.50886	−0.754428	+	0.656383i	$0.772086\pi$
$480$	17.5195	0.799652
$481$	29.3417	1.33786
$482$	32.0245	1.45868
$483$	−2.36334	−0.107536
$484$	−21.0984	−0.959020
$485$	30.6205	1.39040
$486$	2.06382	0.0936166
$487$	−14.4930	−0.656743	−0.328371	−	0.944549i	$-0.606500\pi$
$487$	−14.4930	−0.656743	−0.328371	+	0.944549i	$0.606500\pi$
$488$	1.94008	0.0878232
$489$	−14.4814	−0.654872
$490$	−30.8010	−1.39145
$491$	37.2606	1.68155	0.840773	−	0.541388i	$-0.182101\pi$
$491$	37.2606	1.68155	0.840773	+	0.541388i	$0.182101\pi$
$492$	−17.4714	−0.787671
$493$	−2.92588	−0.131775
$494$	95.9675	4.31778
$495$	2.78246	0.125062
$496$	1.50813	0.0677171
$497$	−2.20439	−0.0988806
$498$	29.9815	1.34350
$499$	−35.2355	−1.57736	−0.788679	−	0.614806i	$-0.789234\pi$
$499$	−35.2355	−1.57736	−0.788679	+	0.614806i	$0.789234\pi$
$500$	26.0462	1.16482
$501$	17.9374	0.801386
$502$	−48.9877	−2.18643
$503$	−23.4710	−1.04652	−0.523261	−	0.852173i	$-0.675285\pi$
$503$	−23.4710	−1.04652	−0.523261	+	0.852173i	$0.675285\pi$
$504$	−0.156833	−0.00698592
$505$	34.6866	1.54354
$506$	21.4573	0.953895
$507$	−25.3163	−1.12434
$508$	39.0464	1.73240
$509$	−9.84430	−0.436341	−0.218171	−	0.975911i	$-0.570009\pi$
$509$	−9.84430	−0.436341	−0.218171	+	0.975911i	$0.570009\pi$
$510$	−4.45478	−0.197261
$511$	−1.38802	−0.0614022
$512$	−31.3647	−1.38614
$513$	7.51210	0.331667
$514$	44.6894	1.97117
$515$	−33.7577	−1.48754
$516$	21.7529	0.957619
$517$	−0.0691522	−0.00304131
$518$	−2.86656	−0.125949
$519$	0.286587	0.0125798
$520$	7.15136	0.313608
$521$	−3.24054	−0.141971	−0.0709853	−	0.997477i	$-0.522614\pi$
$521$	−3.24054	−0.141971	−0.0709853	+	0.997477i	$0.522614\pi$
$522$	6.03847	0.264297
$523$	−4.57640	−0.200112	−0.100056	−	0.994982i	$-0.531902\pi$
$523$	−4.57640	−0.200112	−0.100056	+	0.994982i	$0.531902\pi$
$524$	22.7539	0.994009
$525$	0.0998666	0.00435853
$526$	48.5235	2.11572
$527$	−0.441742	−0.0192426
$528$	−4.40094	−0.191526
$529$	42.0520	1.82835
$530$	54.4664	2.36587
$531$	2.28956	0.0993584
$532$	−4.97324	−0.215617
$533$	47.8671	2.07336
$534$	−8.99727	−0.389350
$535$	−23.6898	−1.02420
$536$	3.75433	0.162162
$537$	−14.9503	−0.645153
$538$	61.1698	2.63722
$539$	8.91276	0.383900
$540$	4.87682	0.209865
$541$	8.45340	0.363440	0.181720	−	0.983350i	$-0.441834\pi$
$541$	8.45340	0.363440	0.181720	+	0.983350i	$0.441834\pi$
$542$	−6.61678	−0.284215
$543$	−7.04602	−0.302374
$544$	8.11646	0.347990
$545$	18.3679	0.786793
$546$	3.74334	0.160200
$547$	10.8474	0.463803	0.231902	−	0.972739i	$-0.425505\pi$
$547$	10.8474	0.463803	0.231902	+	0.972739i	$0.425505\pi$
$548$	−1.48260	−0.0633335
$549$	−3.62474	−0.154700
$550$	−0.906712	−0.0386623
$551$	21.9795	0.936357
$552$	4.31691	0.183740
$553$	−4.34991	−0.184977
$554$	61.3878	2.60812
$555$	10.2317	0.434311
$556$	17.6340	0.747848
$557$	25.1125	1.06405	0.532026	−	0.846728i	$-0.321431\pi$
$557$	25.1125	1.06405	0.532026	+	0.846728i	$0.321431\pi$
$558$	0.911674	0.0385942
$559$	−59.5974	−2.52070
$560$	2.15935	0.0912490
$561$	1.28906	0.0544243
$562$	4.93524	0.208181
$563$	16.3875	0.690653	0.345326	−	0.938483i	$-0.387768\pi$
$563$	16.3875	0.690653	0.345326	+	0.938483i	$0.387768\pi$
$564$	−0.121203	−0.00510357
$565$	25.6498	1.07909
$566$	−3.11711	−0.131022
$567$	0.293019	0.0123057
$568$	4.02657	0.168951
$569$	−11.1240	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$569$	−11.1240	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$570$	33.4647	1.40168
$571$	31.8292	1.33201	0.666005	−	0.745948i	$-0.268003\pi$
$571$	31.8292	1.33201	0.666005	+	0.745948i	$0.268003\pi$
$572$	−18.0280	−0.753789
$573$	21.1728	0.884505
$574$	−4.67641	−0.195190
$575$	−2.74887	−0.114636
$576$	−9.92277	−0.413449
$577$	−11.0513	−0.460073	−0.230037	−	0.973182i	$-0.573885\pi$
$577$	−11.0513	−0.460073	−0.230037	+	0.973182i	$0.573885\pi$
$578$	−2.06382	−0.0858435
$579$	−22.1752	−0.921568
$580$	14.2690	0.592487
$581$	4.25675	0.176600
$582$	−29.2771	−1.21358
$583$	−15.7607	−0.652743
$584$	2.53537	0.104914
$585$	−13.3612	−0.552419
$586$	−49.3165	−2.03725
$587$	38.4053	1.58516	0.792579	−	0.609770i	$-0.208738\pi$
$587$	38.4053	1.58516	0.792579	+	0.609770i	$0.208738\pi$
$588$	15.6214	0.644216
$589$	3.31841	0.136733
$590$	10.1995	0.419906
$591$	−22.7628	−0.936336
$592$	−16.1832	−0.665125
$593$	−11.5093	−0.472630	−0.236315	−	0.971677i	$-0.575940\pi$
$593$	−11.5093	−0.472630	−0.236315	+	0.971677i	$0.575940\pi$
$594$	−2.66039	−0.109157
$595$	−0.632486	−0.0259294
$596$	−48.8032	−1.99906
$597$	−5.72693	−0.234388
$598$	−103.037	−4.21350
$599$	41.1188	1.68007	0.840033	−	0.542535i	$-0.182535\pi$
$599$	41.1188	1.68007	0.840033	+	0.542535i	$0.182535\pi$
$600$	−0.182417	−0.00744716
$601$	2.67697	0.109196	0.0545979	−	0.998508i	$-0.482612\pi$
$601$	2.67697	0.109196	0.0545979	+	0.998508i	$0.482612\pi$
$602$	5.82242	0.237304
$603$	−7.01439	−0.285648
$604$	38.4954	1.56636
$605$	20.1569	0.819494
$606$	−33.1649	−1.34723
$607$	−25.3102	−1.02731	−0.513655	−	0.857997i	$-0.671709\pi$
$607$	−25.3102	−1.02731	−0.513655	+	0.857997i	$0.671709\pi$
$608$	−60.9717	−2.47273
$609$	0.857338	0.0347411
$610$	−16.1474	−0.653790
$611$	0.332065	0.0134339
$612$	2.25934	0.0913284
$613$	6.27593	0.253482	0.126741	−	0.991936i	$-0.459548\pi$
$613$	6.27593	0.253482	0.126741	+	0.991936i	$0.459548\pi$
$614$	−5.54013	−0.223581
$615$	16.6917	0.673074
$616$	0.202168	0.00814559
$617$	−17.0342	−0.685770	−0.342885	−	0.939377i	$-0.611404\pi$
$617$	−17.0342	−0.685770	−0.342885	+	0.939377i	$0.611404\pi$
$618$	32.2767	1.29836
$619$	−38.9292	−1.56470	−0.782349	−	0.622840i	$-0.785979\pi$
$619$	−38.9292	−1.56470	−0.782349	+	0.622840i	$0.785979\pi$
$620$	2.15429	0.0865185
$621$	−8.06548	−0.323657
$622$	−37.9491	−1.52162
$623$	−1.27743	−0.0511790
$624$	21.1331	0.846000
$625$	−23.1797	−0.927190
$626$	−25.1254	−1.00421
$627$	−9.68357	−0.386725
$628$	2.25934	0.0901575
$629$	4.74016	0.189003
$630$	1.30534	0.0520058
$631$	0.535771	0.0213287	0.0106644	−	0.999943i	$-0.496605\pi$
$631$	0.535771	0.0213287	0.0106644	+	0.999943i	$0.496605\pi$
$632$	7.94560	0.316059
$633$	−3.00066	−0.119265
$634$	−58.1557	−2.30966
$635$	−37.3039	−1.48036
$636$	−27.6239	−1.09536
$637$	−42.7986	−1.69574
$638$	−7.78398	−0.308171
$639$	−7.52304	−0.297607
$640$	−9.16475	−0.362268
$641$	−29.7177	−1.17378	−0.586890	−	0.809667i	$-0.699648\pi$
$641$	−29.7177	−1.17378	−0.586890	+	0.809667i	$0.699648\pi$
$642$	22.6505	0.893946
$643$	46.7397	1.84323	0.921616	−	0.388103i	$-0.126869\pi$
$643$	46.7397	1.84323	0.921616	+	0.388103i	$0.126869\pi$
$644$	5.33959	0.210409
$645$	−20.7822	−0.818297
$646$	15.5036	0.609981
$647$	−0.176487	−0.00693842	−0.00346921	−	0.999994i	$-0.501104\pi$
$647$	−0.176487	−0.00693842	−0.00346921	+	0.999994i	$0.501104\pi$
$648$	−0.535232	−0.0210259
$649$	−2.95139	−0.115852
$650$	4.35398	0.170777
$651$	0.129439	0.00507311
$652$	32.7185	1.28135
$653$	11.2640	0.440794	0.220397	−	0.975410i	$-0.429265\pi$
$653$	11.2640	0.440794	0.220397	+	0.975410i	$0.429265\pi$
$654$	−17.5621	−0.686730
$655$	−21.7385	−0.849393
$656$	−26.4008	−1.03078
$657$	−4.73694	−0.184806
$658$	−0.0324414	−0.00126470
$659$	−32.5436	−1.26772	−0.633859	−	0.773448i	$-0.718530\pi$
$659$	−32.5436	−1.26772	−0.633859	+	0.773448i	$0.718530\pi$
$660$	−6.28653	−0.244703
$661$	1.02361	0.0398138	0.0199069	−	0.999802i	$-0.493663\pi$
$661$	1.02361	0.0398138	0.0199069	+	0.999802i	$0.493663\pi$
$662$	22.8519	0.888164
$663$	−6.19002	−0.240400
$664$	−7.77543	−0.301745
$665$	4.75130	0.184247
$666$	−9.78282	−0.379077
$667$	−23.5986	−0.913741
$668$	−40.5268	−1.56803
$669$	−7.28187	−0.281533
$670$	−31.2476	−1.20720
$671$	4.67252	0.180381
$672$	−2.37828	−0.0917441
$673$	−1.17824	−0.0454179	−0.0227089	−	0.999742i	$-0.507229\pi$
$673$	−1.17824	−0.0454179	−0.0227089	+	0.999742i	$0.507229\pi$
$674$	3.65195	0.140668
$675$	0.340819	0.0131181
$676$	57.1981	2.19993
$677$	11.3031	0.434413	0.217206	−	0.976126i	$-0.430306\pi$
$677$	11.3031	0.434413	0.217206	+	0.976126i	$0.430306\pi$
$678$	−24.5245	−0.941857
$679$	−4.15675	−0.159521
$680$	1.15531	0.0443040
$681$	−1.16172	−0.0445173
$682$	−1.17521	−0.0450009
$683$	36.2459	1.38691	0.693456	−	0.720499i	$-0.256087\pi$
$683$	36.2459	1.38691	0.693456	+	0.720499i	$0.256087\pi$
$684$	−16.9724	−0.648956
$685$	1.41644	0.0541192
$686$	8.41441	0.321264
$687$	−1.13226	−0.0431985
$688$	32.8706	1.25318
$689$	75.6823	2.88326
$690$	−35.9299	−1.36783
$691$	6.27030	0.238533	0.119267	−	0.992862i	$-0.461946\pi$
$691$	6.27030	0.238533	0.119267	+	0.992862i	$0.461946\pi$
$692$	−0.647499	−0.0246142
$693$	−0.377720	−0.0143484
$694$	5.45178	0.206947
$695$	−16.8470	−0.639045
$696$	−1.56602	−0.0593600
$697$	7.73296	0.292907
$698$	17.0536	0.645488
$699$	−3.20761	−0.121323
$700$	−0.225633	−0.00852811
$701$	−9.39587	−0.354877	−0.177439	−	0.984132i	$-0.556781\pi$
$701$	−9.39587	−0.354877	−0.177439	+	0.984132i	$0.556781\pi$
$702$	12.7751	0.482164
$703$	−35.6086	−1.34300
$704$	12.7911	0.482082
$705$	0.115794	0.00436106
$706$	47.9207	1.80352
$707$	−4.70873	−0.177090
$708$	−5.17289	−0.194409
$709$	−35.1732	−1.32096	−0.660478	−	0.750845i	$-0.729646\pi$
$709$	−35.1732	−1.32096	−0.660478	+	0.750845i	$0.729646\pi$
$710$	−33.5134	−1.25774
$711$	−14.8451	−0.556736
$712$	2.33336	0.0874464
$713$	−3.56286	−0.133430
$714$	0.604738	0.0226318
$715$	17.2235	0.644121
$716$	33.7778	1.26234
$717$	−22.0947	−0.825141
$718$	−51.4884	−1.92153
$719$	−41.5829	−1.55078	−0.775391	−	0.631482i	$-0.782447\pi$
$719$	−41.5829	−1.55078	−0.775391	+	0.631482i	$0.782447\pi$
$720$	7.36930	0.274637
$721$	4.58262	0.170666
$722$	−77.2521	−2.87503
$723$	15.5171	0.577089
$724$	15.9194	0.591638
$725$	0.997195	0.0370349
$726$	−19.2726	−0.715272
$727$	−44.7834	−1.66092	−0.830462	−	0.557075i	$-0.811924\pi$
$727$	−44.7834	−1.66092	−0.830462	+	0.557075i	$0.811924\pi$
$728$	−0.970801	−0.0359803
$729$	1.00000	0.0370370
$730$	−21.1020	−0.781021
$731$	−9.62800	−0.356104
$732$	8.18953	0.302694
$733$	0.963975	0.0356052	0.0178026	−	0.999842i	$-0.494333\pi$
$733$	0.963975	0.0356052	0.0178026	+	0.999842i	$0.494333\pi$
$734$	17.0615	0.629750
$735$	−14.9243	−0.550490
$736$	65.4631	2.41300
$737$	9.04200	0.333066
$738$	−15.9594	−0.587474
$739$	−6.62952	−0.243871	−0.121935	−	0.992538i	$-0.538910\pi$
$739$	−6.62952	−0.243871	−0.121935	+	0.992538i	$0.538910\pi$
$740$	−23.1169	−0.849794
$741$	46.5000	1.70822
$742$	−7.39384	−0.271436
$743$	−38.1787	−1.40064	−0.700321	−	0.713828i	$-0.746960\pi$
$743$	−38.1787	−1.40064	−0.700321	+	0.713828i	$0.746960\pi$
$744$	−0.236434	−0.00866811
$745$	46.6252	1.70822
$746$	17.2570	0.631822
$747$	14.5272	0.531522
$748$	−2.91243	−0.106489
$749$	3.21591	0.117507
$750$	23.7922	0.868767
$751$	−34.8578	−1.27198	−0.635990	−	0.771697i	$-0.719408\pi$
$751$	−34.8578	−1.27198	−0.635990	+	0.771697i	$0.719408\pi$
$752$	−0.183148	−0.00667873
$753$	−23.7365	−0.865005
$754$	37.3782	1.36124
$755$	−36.7775	−1.33847
$756$	−0.662030	−0.0240778
$757$	−14.5801	−0.529921	−0.264961	−	0.964259i	$-0.585359\pi$
$757$	−14.5801	−0.529921	−0.264961	+	0.964259i	$0.585359\pi$
$758$	−17.0792	−0.620346
$759$	10.3969	0.377384
$760$	−8.67878	−0.314812
$761$	−47.6935	−1.72889	−0.864444	−	0.502730i	$-0.832329\pi$
$761$	−47.6935	−1.72889	−0.864444	+	0.502730i	$0.832329\pi$
$762$	35.6673	1.29209
$763$	−2.49345	−0.0902689
$764$	−47.8365	−1.73066
$765$	−2.15851	−0.0780412
$766$	55.8736	2.01879
$767$	14.1724	0.511736
$768$	−11.0829	−0.399918
$769$	−53.6534	−1.93479	−0.967396	−	0.253270i	$-0.918494\pi$
$769$	−53.6534	−1.93479	−0.967396	+	0.253270i	$0.918494\pi$
$770$	−1.68266	−0.0606389
$771$	21.6538	0.779842
$772$	50.1013	1.80318
$773$	−17.7258	−0.637552	−0.318776	−	0.947830i	$-0.603272\pi$
$773$	−17.7258	−0.637552	−0.318776	+	0.947830i	$0.603272\pi$
$774$	19.8704	0.714228
$775$	0.150554	0.00540806
$776$	7.59276	0.272564
$777$	−1.38896	−0.0498286
$778$	74.7134	2.67861
$779$	−58.0908	−2.08132
$780$	30.1876	1.08089
$781$	9.69767	0.347010
$782$	−16.6457	−0.595248
$783$	2.92588	0.104562
$784$	23.6053	0.843046
$785$	−2.15851	−0.0770407
$786$	20.7848	0.741369
$787$	−33.9747	−1.21107	−0.605534	−	0.795819i	$-0.707041\pi$
$787$	−33.9747	−1.21107	−0.605534	+	0.795819i	$0.707041\pi$
$788$	51.4289	1.83208
$789$	23.5115	0.837032
$790$	−66.1318	−2.35286
$791$	−3.48197	−0.123805
$792$	0.689948	0.0245163
$793$	−22.4372	−0.796768
$794$	−19.3266	−0.685874
$795$	26.3911	0.935995
$796$	12.9391	0.458614
$797$	1.63756	0.0580052	0.0290026	−	0.999579i	$-0.490767\pi$
$797$	1.63756	0.0580052	0.0290026	+	0.999579i	$0.490767\pi$
$798$	−4.54285	−0.160815
$799$	0.0536453	0.00189784
$800$	−2.76625	−0.0978015
$801$	−4.35953	−0.154036
$802$	36.9828	1.30591
$803$	6.10622	0.215484
$804$	15.8479	0.558913
$805$	−5.10130	−0.179797
$806$	5.64327	0.198776
$807$	29.6392	1.04335
$808$	8.60102	0.302583
$809$	1.99965	0.0703038	0.0351519	−	0.999382i	$-0.488808\pi$
$809$	1.99965	0.0703038	0.0351519	+	0.999382i	$0.488808\pi$
$810$	4.45478	0.156525
$811$	29.6891	1.04252	0.521262	−	0.853397i	$-0.325462\pi$
$811$	29.6891	1.04252	0.521262	+	0.853397i	$0.325462\pi$
$812$	−1.93702	−0.0679761
$813$	−3.20609	−0.112442
$814$	12.6107	0.442004
$815$	−31.2583	−1.09493
$816$	3.41406	0.119516
$817$	72.3265	2.53038
$818$	3.71442	0.129872
$819$	1.81379	0.0633791
$820$	−37.7122	−1.31697
$821$	1.70089	0.0593614	0.0296807	−	0.999559i	$-0.490551\pi$
$821$	1.70089	0.0593614	0.0296807	+	0.999559i	$0.490551\pi$
$822$	−1.35430	−0.0472365
$823$	11.9482	0.416487	0.208243	−	0.978077i	$-0.433225\pi$
$823$	11.9482	0.416487	0.208243	+	0.978077i	$0.433225\pi$
$824$	−8.37067	−0.291606
$825$	−0.439337	−0.0152958
$826$	−1.38458	−0.0481758
$827$	−10.3654	−0.360440	−0.180220	−	0.983626i	$-0.557681\pi$
$827$	−10.3654	−0.360440	−0.180220	+	0.983626i	$0.557681\pi$
$828$	18.2227	0.633282
$829$	−29.4497	−1.02283	−0.511415	−	0.859334i	$-0.670879\pi$
$829$	−29.4497	−1.02283	−0.511415	+	0.859334i	$0.670879\pi$
$830$	64.7154	2.24631
$831$	29.7448	1.03183
$832$	−61.4221	−2.12943
$833$	−6.91414	−0.239561
$834$	16.1079	0.557772
$835$	38.7182	1.33990
$836$	21.8785	0.756684
$837$	0.441742	0.0152688
$838$	−25.6510	−0.886099
$839$	12.3335	0.425801	0.212901	−	0.977074i	$-0.431709\pi$
$839$	12.3335	0.425801	0.212901	+	0.977074i	$0.431709\pi$
$840$	−0.338527	−0.0116803
$841$	−20.4392	−0.704802
$842$	52.6900	1.81582
$843$	2.39132	0.0823613
$844$	6.77951	0.233360
$845$	−54.6455	−1.87986
$846$	−0.110714	−0.00380643
$847$	−2.73631	−0.0940206
$848$	−41.7420	−1.43343
$849$	−1.51036	−0.0518354
$850$	0.703388	0.0241260
$851$	38.2317	1.31056
$852$	16.9971	0.582311
$853$	31.4593	1.07715	0.538573	−	0.842579i	$-0.318964\pi$
$853$	31.4593	1.07715	0.538573	+	0.842579i	$0.318964\pi$
$854$	2.19202	0.0750094
$855$	16.2150	0.554540
$856$	−5.87422	−0.200777
$857$	−6.32478	−0.216050	−0.108025	−	0.994148i	$-0.534453\pi$
$857$	−6.32478	−0.216050	−0.108025	+	0.994148i	$0.534453\pi$
$858$	−16.4679	−0.562203
$859$	−23.0049	−0.784918	−0.392459	−	0.919770i	$-0.628375\pi$
$859$	−23.0049	−0.784918	−0.392459	+	0.919770i	$0.628375\pi$
$860$	46.9540	1.60112
$861$	−2.26591	−0.0772219
$862$	−14.0731	−0.479331
$863$	−32.6335	−1.11086	−0.555428	−	0.831565i	$-0.687446\pi$
$863$	−32.6335	−1.11086	−0.555428	+	0.831565i	$0.687446\pi$
$864$	−8.11646	−0.276128
$865$	0.618603	0.0210331
$866$	−30.1841	−1.02570
$867$	−1.00000	−0.0339618
$868$	−0.292446	−0.00992628
$869$	19.1363	0.649156
$870$	13.0341	0.441898
$871$	−43.4192	−1.47120
$872$	4.55456	0.154237
$873$	−14.1859	−0.480120
$874$	125.044	4.22968
$875$	3.37799	0.114197
$876$	10.7024	0.361600
$877$	−40.2673	−1.35973	−0.679865	−	0.733337i	$-0.737962\pi$
$877$	−40.2673	−1.35973	−0.679865	+	0.733337i	$0.737962\pi$
$878$	−2.56820	−0.0866724
$879$	−23.8958	−0.805984
$880$	−9.49949	−0.320228
$881$	−4.46309	−0.150365	−0.0751827	−	0.997170i	$-0.523954\pi$
$881$	−4.46309	−0.150365	−0.0751827	+	0.997170i	$0.523954\pi$
$882$	14.2695	0.480480
$883$	−41.1638	−1.38527	−0.692636	−	0.721287i	$-0.743551\pi$
$883$	−41.1638	−1.38527	−0.692636	+	0.721287i	$0.743551\pi$
$884$	13.9854	0.470378
$885$	4.94204	0.166125
$886$	−41.1921	−1.38387
$887$	−9.02729	−0.303107	−0.151553	−	0.988449i	$-0.548428\pi$
$887$	−9.02729	−0.303107	−0.151553	+	0.988449i	$0.548428\pi$
$888$	2.53709	0.0851391
$889$	5.06402	0.169842
$890$	−19.4207	−0.650984
$891$	−1.28906	−0.0431852
$892$	16.4522	0.550861
$893$	−0.402989	−0.0134855
$894$	−44.5797	−1.49097
$895$	−32.2704	−1.07868
$896$	1.24412	0.0415631
$897$	−49.9254	−1.66696
$898$	53.1855	1.77482
$899$	1.29248	0.0431067
$900$	−0.770027	−0.0256676
$901$	12.2265	0.407324
$902$	20.5727	0.684996
$903$	2.82119	0.0938833
$904$	6.36020	0.211537
$905$	−15.2089	−0.505562
$906$	35.1640	1.16825
$907$	−12.0246	−0.399271	−0.199636	−	0.979870i	$-0.563976\pi$
$907$	−12.0246	−0.399271	−0.199636	+	0.979870i	$0.563976\pi$
$908$	2.62473	0.0871047
$909$	−16.0697	−0.532998
$910$	8.08005	0.267851
$911$	47.4623	1.57250	0.786248	−	0.617911i	$-0.212021\pi$
$911$	47.4623	1.57250	0.786248	+	0.617911i	$0.212021\pi$
$912$	−25.6468	−0.849249
$913$	−18.7265	−0.619756
$914$	−9.41338	−0.311367
$915$	−7.82405	−0.258655
$916$	2.55817	0.0845242
$917$	2.95101	0.0974509
$918$	2.06382	0.0681161
$919$	−45.3124	−1.49472	−0.747359	−	0.664421i	$-0.768678\pi$
$919$	−45.3124	−1.49472	−0.747359	+	0.664421i	$0.768678\pi$
$920$	9.31810	0.307209
$921$	−2.68441	−0.0884543
$922$	46.5453	1.53289
$923$	−46.5677	−1.53279
$924$	0.853399	0.0280748
$925$	−1.61554	−0.0531185
$926$	−25.7907	−0.847536
$927$	15.6393	0.513663
$928$	−23.7478	−0.779559
$929$	39.1200	1.28348	0.641742	−	0.766920i	$-0.278212\pi$
$929$	39.1200	1.28348	0.641742	+	0.766920i	$0.278212\pi$
$930$	1.96786	0.0645287
$931$	51.9397	1.70226
$932$	7.24709	0.237386
$933$	−18.3878	−0.601990
$934$	73.0688	2.39088
$935$	2.78246	0.0909962
$936$	−3.31310	−0.108292
$937$	−16.6849	−0.545072	−0.272536	−	0.962146i	$-0.587862\pi$
$937$	−16.6849	−0.545072	−0.272536	+	0.962146i	$0.587862\pi$
$938$	4.24187	0.138502
$939$	−12.1742	−0.397291
$940$	−0.261619	−0.00853305
$941$	53.4238	1.74157	0.870783	−	0.491668i	$-0.163613\pi$
$941$	53.4238	1.74157	0.870783	+	0.491668i	$0.163613\pi$
$942$	2.06382	0.0672428
$943$	62.3700	2.03105
$944$	−7.81669	−0.254412
$945$	0.632486	0.0205748
$946$	−25.6142	−0.832791
$947$	14.4240	0.468715	0.234358	−	0.972150i	$-0.424701\pi$
$947$	14.4240	0.468715	0.234358	+	0.972150i	$0.424701\pi$
$948$	33.5402	1.08934
$949$	−29.3218	−0.951824
$950$	−5.28392	−0.171433
$951$	−28.1787	−0.913756
$952$	−0.156833	−0.00508300
$953$	−50.0710	−1.62196	−0.810980	−	0.585074i	$-0.801065\pi$
$953$	−50.0710	−1.62196	−0.810980	+	0.585074i	$0.801065\pi$
$954$	−25.2333	−0.816958
$955$	45.7017	1.47887
$956$	49.9194	1.61451
$957$	−3.77164	−0.121920
$958$	68.1533	2.20193
$959$	−0.192282	−0.00620911
$960$	−21.4184	−0.691277
$961$	−30.8049	−0.993705
$962$	−60.5558	−1.95240
$963$	10.9751	0.353667
$964$	−35.0585	−1.12916
$965$	−47.8654	−1.54084
$966$	4.87750	0.156931
$967$	−48.0872	−1.54638	−0.773190	−	0.634174i	$-0.781340\pi$
$967$	−48.0872	−1.54638	−0.773190	+	0.634174i	$0.781340\pi$
$968$	4.99817	0.160647
$969$	7.51210	0.241323
$970$	−63.1951	−2.02907
$971$	0.324851	0.0104250	0.00521249	−	0.999986i	$-0.498341\pi$
$971$	0.324851	0.0104250	0.00521249	+	0.999986i	$0.498341\pi$
$972$	−2.25934	−0.0724684
$973$	2.28699	0.0733177
$974$	29.9110	0.958410
$975$	2.10968	0.0675637
$976$	12.3751	0.396117
$977$	32.4901	1.03945	0.519724	−	0.854334i	$-0.326035\pi$
$977$	32.4901	1.03945	0.519724	+	0.854334i	$0.326035\pi$
$978$	29.8870	0.955681
$979$	5.61971	0.179607
$980$	33.7190	1.07711
$981$	−8.50950	−0.271687
$982$	−76.8990	−2.45395
$983$	18.5034	0.590168	0.295084	−	0.955471i	$-0.404652\pi$
$983$	18.5034	0.590168	0.295084	+	0.955471i	$0.404652\pi$
$984$	4.13893	0.131944
$985$	−49.1338	−1.56553
$986$	6.03847	0.192304
$987$	−0.0157191	−0.000500345 0
$988$	−105.059	−3.34238
$989$	−77.6544	−2.46927
$990$	−5.74249	−0.182508
$991$	−30.8164	−0.978914	−0.489457	−	0.872027i	$-0.662805\pi$
$991$	−30.8164	−0.978914	−0.489457	+	0.872027i	$0.662805\pi$
$992$	−3.58538	−0.113836
$993$	11.0726	0.351380
$994$	4.54947	0.144300
$995$	−12.3617	−0.391891
$996$	−32.8219	−1.04000
$997$	51.7862	1.64008	0.820042	−	0.572303i	$-0.193950\pi$
$997$	51.7862	1.64008	0.820042	+	0.572303i	$0.193950\pi$
$998$	72.7196	2.30190
$999$	−4.74016	−0.149972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.7	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.7	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.06382 q^{2} -1.00000 q^{3} +2.25934 q^{4} -2.15851 q^{5} +2.06382 q^{6} +0.293019 q^{7} -0.535232 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.06382 q^{2} -1.00000 q^{3} +2.25934 q^{4} -2.15851 q^{5} +2.06382 q^{6} +0.293019 q^{7} -0.535232 q^{8} +1.00000 q^{9} +4.45478 q^{10} -1.28906 q^{11} -2.25934 q^{12} +6.19002 q^{13} -0.604738 q^{14} +2.15851 q^{15} -3.41406 q^{16} +1.00000 q^{17} -2.06382 q^{18} -7.51210 q^{19} -4.87682 q^{20} -0.293019 q^{21} +2.66039 q^{22} +8.06548 q^{23} +0.535232 q^{24} -0.340819 q^{25} -12.7751 q^{26} -1.00000 q^{27} +0.662030 q^{28} -2.92588 q^{29} -4.45478 q^{30} -0.441742 q^{31} +8.11646 q^{32} +1.28906 q^{33} -2.06382 q^{34} -0.632486 q^{35} +2.25934 q^{36} +4.74016 q^{37} +15.5036 q^{38} -6.19002 q^{39} +1.15531 q^{40} +7.73296 q^{41} +0.604738 q^{42} -9.62800 q^{43} -2.91243 q^{44} -2.15851 q^{45} -16.6457 q^{46} +0.0536453 q^{47} +3.41406 q^{48} -6.91414 q^{49} +0.703388 q^{50} -1.00000 q^{51} +13.9854 q^{52} +12.2265 q^{53} +2.06382 q^{54} +2.78246 q^{55} -0.156833 q^{56} +7.51210 q^{57} +6.03847 q^{58} +2.28956 q^{59} +4.87682 q^{60} -3.62474 q^{61} +0.911674 q^{62} +0.293019 q^{63} -9.92277 q^{64} -13.3612 q^{65} -2.66039 q^{66} -7.01439 q^{67} +2.25934 q^{68} -8.06548 q^{69} +1.30534 q^{70} -7.52304 q^{71} -0.535232 q^{72} -4.73694 q^{73} -9.78282 q^{74} +0.340819 q^{75} -16.9724 q^{76} -0.377720 q^{77} +12.7751 q^{78} -14.8451 q^{79} +7.36930 q^{80} +1.00000 q^{81} -15.9594 q^{82} +14.5272 q^{83} -0.662030 q^{84} -2.15851 q^{85} +19.8704 q^{86} +2.92588 q^{87} +0.689948 q^{88} -4.35953 q^{89} +4.45478 q^{90} +1.81379 q^{91} +18.2227 q^{92} +0.441742 q^{93} -0.110714 q^{94} +16.2150 q^{95} -8.11646 q^{96} -14.1859 q^{97} +14.2695 q^{98} -1.28906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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