LMFDB - Embedded newform 8007.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-0.679888 q^{2} -1.00000 q^{3} -1.53775 q^{4} +2.83101 q^{5} +0.679888 q^{6} -0.718741 q^{7} +2.40527 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.679888 q^{2} -1.00000 q^{3} -1.53775 q^{4} +2.83101 q^{5} +0.679888 q^{6} -0.718741 q^{7} +2.40527 q^{8} +1.00000 q^{9} -1.92477 q^{10} -0.429458 q^{11} +1.53775 q^{12} +0.378868 q^{13} +0.488663 q^{14} -2.83101 q^{15} +1.44019 q^{16} +1.00000 q^{17} -0.679888 q^{18} -0.638368 q^{19} -4.35339 q^{20} +0.718741 q^{21} +0.291983 q^{22} +4.51930 q^{23} -2.40527 q^{24} +3.01460 q^{25} -0.257588 q^{26} -1.00000 q^{27} +1.10525 q^{28} +0.186187 q^{29} +1.92477 q^{30} -6.25746 q^{31} -5.78972 q^{32} +0.429458 q^{33} -0.679888 q^{34} -2.03476 q^{35} -1.53775 q^{36} -2.51324 q^{37} +0.434019 q^{38} -0.378868 q^{39} +6.80935 q^{40} -3.44664 q^{41} -0.488663 q^{42} +8.07399 q^{43} +0.660400 q^{44} +2.83101 q^{45} -3.07262 q^{46} -7.10299 q^{47} -1.44019 q^{48} -6.48341 q^{49} -2.04959 q^{50} -1.00000 q^{51} -0.582606 q^{52} -6.64764 q^{53} +0.679888 q^{54} -1.21580 q^{55} -1.72877 q^{56} +0.638368 q^{57} -0.126586 q^{58} -2.16366 q^{59} +4.35339 q^{60} +1.34532 q^{61} +4.25437 q^{62} -0.718741 q^{63} +1.05598 q^{64} +1.07258 q^{65} -0.291983 q^{66} -0.865625 q^{67} -1.53775 q^{68} -4.51930 q^{69} +1.38341 q^{70} +8.28293 q^{71} +2.40527 q^{72} -14.5701 q^{73} +1.70872 q^{74} -3.01460 q^{75} +0.981652 q^{76} +0.308669 q^{77} +0.257588 q^{78} +15.3145 q^{79} +4.07718 q^{80} +1.00000 q^{81} +2.34333 q^{82} -8.22121 q^{83} -1.10525 q^{84} +2.83101 q^{85} -5.48941 q^{86} -0.186187 q^{87} -1.03296 q^{88} +10.9323 q^{89} -1.92477 q^{90} -0.272308 q^{91} -6.94957 q^{92} +6.25746 q^{93} +4.82923 q^{94} -1.80722 q^{95} +5.78972 q^{96} +4.45084 q^{97} +4.40799 q^{98} -0.429458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.679888	−0.480753	−0.240377	−	0.970680i	$-0.577271\pi$
$2$	−0.679888	−0.480753	−0.240377	+	0.970680i	$0.577271\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.53775	−0.768876
$5$	2.83101	1.26606	0.633032	−	0.774125i	$-0.281810\pi$
$5$	2.83101	1.26606	0.633032	+	0.774125i	$0.281810\pi$
$6$	0.679888	0.277563
$7$	−0.718741	−0.271658	−0.135829	−	0.990732i	$-0.543370\pi$
$7$	−0.718741	−0.271658	−0.135829	+	0.990732i	$0.543370\pi$
$8$	2.40527	0.850393
$9$	1.00000	0.333333
$10$	−1.92477	−0.608665
$11$	−0.429458	−0.129486	−0.0647432	−	0.997902i	$-0.520623\pi$
$11$	−0.429458	−0.129486	−0.0647432	+	0.997902i	$0.520623\pi$
$12$	1.53775	0.443911
$13$	0.378868	0.105079	0.0525396	−	0.998619i	$-0.483268\pi$
$13$	0.378868	0.105079	0.0525396	+	0.998619i	$0.483268\pi$
$14$	0.488663	0.130601
$15$	−2.83101	−0.730963
$16$	1.44019	0.360047
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.679888	−0.160251
$19$	−0.638368	−0.146452	−0.0732258	−	0.997315i	$-0.523329\pi$
$19$	−0.638368	−0.146452	−0.0732258	+	0.997315i	$0.523329\pi$
$20$	−4.35339	−0.973447
$21$	0.718741	0.156842
$22$	0.291983	0.0622510
$23$	4.51930	0.942339	0.471170	−	0.882043i	$-0.343832\pi$
$23$	4.51930	0.942339	0.471170	+	0.882043i	$0.343832\pi$
$24$	−2.40527	−0.490975
$25$	3.01460	0.602920
$26$	−0.257588	−0.0505172
$27$	−1.00000	−0.192450
$28$	1.10525	0.208872
$29$	0.186187	0.0345741	0.0172870	−	0.999851i	$-0.494497\pi$
$29$	0.186187	0.0345741	0.0172870	+	0.999851i	$0.494497\pi$
$30$	1.92477	0.351413
$31$	−6.25746	−1.12387	−0.561937	−	0.827180i	$-0.689944\pi$
$31$	−6.25746	−1.12387	−0.561937	+	0.827180i	$0.689944\pi$
$32$	−5.78972	−1.02349
$33$	0.429458	0.0747590
$34$	−0.679888	−0.116600
$35$	−2.03476	−0.343937
$36$	−1.53775	−0.256292
$37$	−2.51324	−0.413174	−0.206587	−	0.978428i	$-0.566236\pi$
$37$	−2.51324	−0.413174	−0.206587	+	0.978428i	$0.566236\pi$
$38$	0.434019	0.0704071
$39$	−0.378868	−0.0606675
$40$	6.80935	1.07665
$41$	−3.44664	−0.538275	−0.269138	−	0.963102i	$-0.586739\pi$
$41$	−3.44664	−0.538275	−0.269138	+	0.963102i	$0.586739\pi$
$42$	−0.488663	−0.0754023
$43$	8.07399	1.23127	0.615636	−	0.788031i	$-0.288899\pi$
$43$	8.07399	1.23127	0.615636	+	0.788031i	$0.288899\pi$
$44$	0.660400	0.0995590
$45$	2.83101	0.422022
$46$	−3.07262	−0.453033
$47$	−7.10299	−1.03608	−0.518039	−	0.855357i	$-0.673338\pi$
$47$	−7.10299	−1.03608	−0.518039	+	0.855357i	$0.673338\pi$
$48$	−1.44019	−0.207873
$49$	−6.48341	−0.926202
$50$	−2.04959	−0.289856
$51$	−1.00000	−0.140028
$52$	−0.582606	−0.0807929
$53$	−6.64764	−0.913123	−0.456562	−	0.889692i	$-0.650919\pi$
$53$	−6.64764	−0.913123	−0.456562	+	0.889692i	$0.650919\pi$
$54$	0.679888	0.0925210
$55$	−1.21580	−0.163938
$56$	−1.72877	−0.231016
$57$	0.638368	0.0845539
$58$	−0.126586	−0.0166216
$59$	−2.16366	−0.281685	−0.140842	−	0.990032i	$-0.544981\pi$
$59$	−2.16366	−0.281685	−0.140842	+	0.990032i	$0.544981\pi$
$60$	4.35339	0.562020
$61$	1.34532	0.172250	0.0861250	−	0.996284i	$-0.472552\pi$
$61$	1.34532	0.172250	0.0861250	+	0.996284i	$0.472552\pi$
$62$	4.25437	0.540306
$63$	−0.718741	−0.0905528
$64$	1.05598	0.131998
$65$	1.07258	0.133037
$66$	−0.291983	−0.0359406
$67$	−0.865625	−0.105753	−0.0528765	−	0.998601i	$-0.516839\pi$
$67$	−0.865625	−0.105753	−0.0528765	+	0.998601i	$0.516839\pi$
$68$	−1.53775	−0.186480
$69$	−4.51930	−0.544060
$70$	1.38341	0.165349
$71$	8.28293	0.983003	0.491502	−	0.870877i	$-0.336448\pi$
$71$	8.28293	0.983003	0.491502	+	0.870877i	$0.336448\pi$
$72$	2.40527	0.283464
$73$	−14.5701	−1.70530	−0.852650	−	0.522483i	$-0.825006\pi$
$73$	−14.5701	−1.70530	−0.852650	+	0.522483i	$0.825006\pi$
$74$	1.70872	0.198635
$75$	−3.01460	−0.348096
$76$	0.981652	0.112603
$77$	0.308669	0.0351761
$78$	0.257588	0.0291661
$79$	15.3145	1.72302	0.861511	−	0.507740i	$-0.169519\pi$
$79$	15.3145	1.72302	0.861511	+	0.507740i	$0.169519\pi$
$80$	4.07718	0.455843
$81$	1.00000	0.111111
$82$	2.34333	0.258777
$83$	−8.22121	−0.902395	−0.451198	−	0.892424i	$-0.649003\pi$
$83$	−8.22121	−0.902395	−0.451198	+	0.892424i	$0.649003\pi$
$84$	−1.10525	−0.120592
$85$	2.83101	0.307066
$86$	−5.48941	−0.591938
$87$	−0.186187	−0.0199614
$88$	−1.03296	−0.110114
$89$	10.9323	1.15883	0.579413	−	0.815034i	$-0.303282\pi$
$89$	10.9323	1.15883	0.579413	+	0.815034i	$0.303282\pi$
$90$	−1.92477	−0.202888
$91$	−0.272308	−0.0285457
$92$	−6.94957	−0.724542
$93$	6.25746	0.648869
$94$	4.82923	0.498098
$95$	−1.80722	−0.185417
$96$	5.78972	0.590910
$97$	4.45084	0.451914	0.225957	−	0.974137i	$-0.427449\pi$
$97$	4.45084	0.451914	0.225957	+	0.974137i	$0.427449\pi$
$98$	4.40799	0.445275
$99$	−0.429458	−0.0431621
$100$	−4.63571	−0.463571
$101$	3.98240	0.396263	0.198132	−	0.980175i	$-0.436513\pi$
$101$	3.98240	0.396263	0.198132	+	0.980175i	$0.436513\pi$
$102$	0.679888	0.0673189
$103$	−4.57714	−0.450999	−0.225499	−	0.974243i	$-0.572401\pi$
$103$	−4.57714	−0.450999	−0.225499	+	0.974243i	$0.572401\pi$
$104$	0.911283	0.0893586
$105$	2.03476	0.198572
$106$	4.51965	0.438987
$107$	−8.32575	−0.804881	−0.402440	−	0.915446i	$-0.631838\pi$
$107$	−8.32575	−0.804881	−0.402440	+	0.915446i	$0.631838\pi$
$108$	1.53775	0.147970
$109$	−9.24800	−0.885798	−0.442899	−	0.896572i	$-0.646050\pi$
$109$	−9.24800	−0.885798	−0.442899	+	0.896572i	$0.646050\pi$
$110$	0.826606	0.0788138
$111$	2.51324	0.238546
$112$	−1.03512	−0.0978098
$113$	−18.9921	−1.78662	−0.893311	−	0.449438i	$-0.851624\pi$
$113$	−18.9921	−1.78662	−0.893311	+	0.449438i	$0.851624\pi$
$114$	−0.434019	−0.0406496
$115$	12.7942	1.19306
$116$	−0.286310	−0.0265832
$117$	0.378868	0.0350264
$118$	1.47105	0.135421
$119$	−0.718741	−0.0658868
$120$	−6.80935	−0.621606
$121$	−10.8156	−0.983233
$122$	−0.914664	−0.0828098
$123$	3.44664	0.310773
$124$	9.62243	0.864120
$125$	−5.62068	−0.502729
$126$	0.488663	0.0435336
$127$	10.6495	0.944988	0.472494	−	0.881334i	$-0.343354\pi$
$127$	10.6495	0.944988	0.472494	+	0.881334i	$0.343354\pi$
$128$	10.8615	0.960029
$129$	−8.07399	−0.710875
$130$	−0.729234	−0.0639580
$131$	−13.6032	−1.18852	−0.594259	−	0.804274i	$-0.702555\pi$
$131$	−13.6032	−1.18852	−0.594259	+	0.804274i	$0.702555\pi$
$132$	−0.660400	−0.0574804
$133$	0.458821	0.0397848
$134$	0.588528	0.0508411
$135$	−2.83101	−0.243654
$136$	2.40527	0.206251
$137$	4.09508	0.349866	0.174933	−	0.984580i	$-0.444029\pi$
$137$	4.09508	0.349866	0.174933	+	0.984580i	$0.444029\pi$
$138$	3.07262	0.261559
$139$	2.19787	0.186421	0.0932106	−	0.995646i	$-0.470287\pi$
$139$	2.19787	0.186421	0.0932106	+	0.995646i	$0.470287\pi$
$140$	3.12896	0.264445
$141$	7.10299	0.598179
$142$	−5.63146	−0.472582
$143$	−0.162708	−0.0136063
$144$	1.44019	0.120016
$145$	0.527097	0.0437730
$146$	9.90602	0.819828
$147$	6.48341	0.534743
$148$	3.86474	0.317679
$149$	−4.63030	−0.379329	−0.189664	−	0.981849i	$-0.560740\pi$
$149$	−4.63030	−0.379329	−0.189664	+	0.981849i	$0.560740\pi$
$150$	2.04959	0.167348
$151$	11.4592	0.932536	0.466268	−	0.884643i	$-0.345598\pi$
$151$	11.4592	0.932536	0.466268	+	0.884643i	$0.345598\pi$
$152$	−1.53545	−0.124541
$153$	1.00000	0.0808452
$154$	−0.209860	−0.0169110
$155$	−17.7149	−1.42290
$156$	0.582606	0.0466458
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−10.4122	−0.828348
$159$	6.64764	0.527192
$160$	−16.3907	−1.29580
$161$	−3.24821	−0.255994
$162$	−0.679888	−0.0534170
$163$	20.8302	1.63155	0.815773	−	0.578372i	$-0.196312\pi$
$163$	20.8302	1.63155	0.815773	+	0.578372i	$0.196312\pi$
$164$	5.30008	0.413867
$165$	1.21580	0.0946497
$166$	5.58950	0.433829
$167$	−13.8738	−1.07358	−0.536792	−	0.843715i	$-0.680364\pi$
$167$	−13.8738	−1.07358	−0.536792	+	0.843715i	$0.680364\pi$
$168$	1.72877	0.133377
$169$	−12.8565	−0.988958
$170$	−1.92477	−0.147623
$171$	−0.638368	−0.0488172
$172$	−12.4158	−0.946696
$173$	−6.14498	−0.467194	−0.233597	−	0.972333i	$-0.575050\pi$
$173$	−6.14498	−0.467194	−0.233597	+	0.972333i	$0.575050\pi$
$174$	0.126586	0.00959649
$175$	−2.16672	−0.163788
$176$	−0.618500	−0.0466212
$177$	2.16366	0.162631
$178$	−7.43277	−0.557109
$179$	2.12163	0.158578	0.0792889	−	0.996852i	$-0.474735\pi$
$179$	2.12163	0.158578	0.0792889	+	0.996852i	$0.474735\pi$
$180$	−4.35339	−0.324482
$181$	11.6003	0.862242	0.431121	−	0.902294i	$-0.358118\pi$
$181$	11.6003	0.862242	0.431121	+	0.902294i	$0.358118\pi$
$182$	0.185139	0.0137234
$183$	−1.34532	−0.0994486
$184$	10.8702	0.801359
$185$	−7.11499	−0.523104
$186$	−4.25437	−0.311946
$187$	−0.429458	−0.0314051
$188$	10.9226	0.796615
$189$	0.718741	0.0522807
$190$	1.22871	0.0891400
$191$	−23.8352	−1.72466	−0.862329	−	0.506349i	$-0.830995\pi$
$191$	−23.8352	−1.72466	−0.862329	+	0.506349i	$0.830995\pi$
$192$	−1.05598	−0.0762089
$193$	4.70784	0.338878	0.169439	−	0.985541i	$-0.445804\pi$
$193$	4.70784	0.338878	0.169439	+	0.985541i	$0.445804\pi$
$194$	−3.02607	−0.217259
$195$	−1.07258	−0.0768090
$196$	9.96988	0.712135
$197$	−4.70724	−0.335377	−0.167689	−	0.985840i	$-0.553630\pi$
$197$	−4.70724	−0.335377	−0.167689	+	0.985840i	$0.553630\pi$
$198$	0.291983	0.0207503
$199$	−5.48329	−0.388700	−0.194350	−	0.980932i	$-0.562260\pi$
$199$	−5.48329	−0.388700	−0.194350	+	0.980932i	$0.562260\pi$
$200$	7.25095	0.512719
$201$	0.865625	0.0610565
$202$	−2.70758	−0.190505
$203$	−0.133820	−0.00939234
$204$	1.53775	0.107664
$205$	−9.75747	−0.681491
$206$	3.11194	0.216819
$207$	4.51930	0.314113
$208$	0.545642	0.0378335
$209$	0.274152	0.0189635
$210$	−1.38341	−0.0954643
$211$	21.7913	1.50018	0.750088	−	0.661338i	$-0.230011\pi$
$211$	21.7913	1.50018	0.750088	+	0.661338i	$0.230011\pi$
$212$	10.2224	0.702079
$213$	−8.28293	−0.567537
$214$	5.66058	0.386949
$215$	22.8575	1.55887
$216$	−2.40527	−0.163658
$217$	4.49749	0.305310
$218$	6.28760	0.425850
$219$	14.5701	0.984555
$220$	1.86960	0.126048
$221$	0.378868	0.0254854
$222$	−1.70872	−0.114682
$223$	2.80160	0.187609	0.0938043	−	0.995591i	$-0.470097\pi$
$223$	2.80160	0.187609	0.0938043	+	0.995591i	$0.470097\pi$
$224$	4.16130	0.278039
$225$	3.01460	0.200973
$226$	12.9125	0.858925
$227$	6.03767	0.400734	0.200367	−	0.979721i	$-0.435786\pi$
$227$	6.03767	0.400734	0.200367	+	0.979721i	$0.435786\pi$
$228$	−0.981652	−0.0650115
$229$	2.73774	0.180915	0.0904574	−	0.995900i	$-0.471167\pi$
$229$	2.73774	0.180915	0.0904574	+	0.995900i	$0.471167\pi$
$230$	−8.69860	−0.573569
$231$	−0.308669	−0.0203089
$232$	0.447831	0.0294016
$233$	24.2203	1.58673	0.793364	−	0.608748i	$-0.208328\pi$
$233$	24.2203	1.58673	0.793364	+	0.608748i	$0.208328\pi$
$234$	−0.257588	−0.0168391
$235$	−20.1086	−1.31174
$236$	3.32718	0.216581
$237$	−15.3145	−0.994787
$238$	0.488663	0.0316753
$239$	−2.77953	−0.179793	−0.0898963	−	0.995951i	$-0.528654\pi$
$239$	−2.77953	−0.179793	−0.0898963	+	0.995951i	$0.528654\pi$
$240$	−4.07718	−0.263181
$241$	−15.8841	−1.02319	−0.511593	−	0.859228i	$-0.670944\pi$
$241$	−15.8841	−1.02319	−0.511593	+	0.859228i	$0.670944\pi$
$242$	7.35337	0.472693
$243$	−1.00000	−0.0641500
$244$	−2.06876	−0.132439
$245$	−18.3546	−1.17263
$246$	−2.34333	−0.149405
$247$	−0.241858	−0.0153890
$248$	−15.0509	−0.955734
$249$	8.22121	0.520998
$250$	3.82143	0.241688
$251$	15.1490	0.956196	0.478098	−	0.878307i	$-0.341326\pi$
$251$	15.1490	0.956196	0.478098	+	0.878307i	$0.341326\pi$
$252$	1.10525	0.0696239
$253$	−1.94085	−0.122020
$254$	−7.24045	−0.454306
$255$	−2.83101	−0.177285
$256$	−9.49655	−0.593535
$257$	27.6303	1.72353	0.861767	−	0.507305i	$-0.169358\pi$
$257$	27.6303	1.72353	0.861767	+	0.507305i	$0.169358\pi$
$258$	5.48941	0.341756
$259$	1.80637	0.112242
$260$	−1.64936	−0.102289
$261$	0.186187	0.0115247
$262$	9.24865	0.571384
$263$	5.70827	0.351987	0.175994	−	0.984391i	$-0.443686\pi$
$263$	5.70827	0.351987	0.175994	+	0.984391i	$0.443686\pi$
$264$	1.03296	0.0635745
$265$	−18.8195	−1.15607
$266$	−0.311947	−0.0191267
$267$	−10.9323	−0.669048
$268$	1.33112	0.0813109
$269$	−18.4091	−1.12242	−0.561211	−	0.827673i	$-0.689664\pi$
$269$	−18.4091	−1.12242	−0.561211	+	0.827673i	$0.689664\pi$
$270$	1.92477	0.117138
$271$	−11.0865	−0.673457	−0.336729	−	0.941602i	$-0.609321\pi$
$271$	−11.0865	−0.673457	−0.336729	+	0.941602i	$0.609321\pi$
$272$	1.44019	0.0873242
$273$	0.272308	0.0164808
$274$	−2.78420	−0.168199
$275$	−1.29464	−0.0780699
$276$	6.94957	0.418315
$277$	−6.92138	−0.415866	−0.207933	−	0.978143i	$-0.566674\pi$
$277$	−6.92138	−0.415866	−0.207933	+	0.978143i	$0.566674\pi$
$278$	−1.49431	−0.0896226
$279$	−6.25746	−0.374624
$280$	−4.89416	−0.292482
$281$	−32.8998	−1.96264	−0.981320	−	0.192381i	$-0.938379\pi$
$281$	−32.8998	−1.96264	−0.981320	+	0.192381i	$0.938379\pi$
$282$	−4.82923	−0.287577
$283$	6.93094	0.412002	0.206001	−	0.978552i	$-0.433955\pi$
$283$	6.93094	0.412002	0.206001	+	0.978552i	$0.433955\pi$
$284$	−12.7371	−0.755808
$285$	1.80722	0.107051
$286$	0.110623	0.00654128
$287$	2.47724	0.146227
$288$	−5.78972	−0.341162
$289$	1.00000	0.0588235
$290$	−0.358367	−0.0210440
$291$	−4.45084	−0.260913
$292$	22.4052	1.31116
$293$	22.2634	1.30064	0.650320	−	0.759660i	$-0.274635\pi$
$293$	22.2634	1.30064	0.650320	+	0.759660i	$0.274635\pi$
$294$	−4.40799	−0.257079
$295$	−6.12534	−0.356631
$296$	−6.04502	−0.351360
$297$	0.429458	0.0249197
$298$	3.14808	0.182363
$299$	1.71222	0.0990203
$300$	4.63571	0.267643
$301$	−5.80310	−0.334485
$302$	−7.79097	−0.448320
$303$	−3.98240	−0.228783
$304$	−0.919370	−0.0527295
$305$	3.80860	0.218080
$306$	−0.679888	−0.0388666
$307$	−5.72048	−0.326485	−0.163242	−	0.986586i	$-0.552195\pi$
$307$	−5.72048	−0.326485	−0.163242	+	0.986586i	$0.552195\pi$
$308$	−0.474656	−0.0270460
$309$	4.57714	0.260384
$310$	12.0442	0.684062
$311$	29.0522	1.64740	0.823701	−	0.567025i	$-0.191906\pi$
$311$	29.0522	1.64740	0.823701	+	0.567025i	$0.191906\pi$
$312$	−0.911283	−0.0515912
$313$	28.7950	1.62759	0.813793	−	0.581154i	$-0.197399\pi$
$313$	28.7950	1.62759	0.813793	+	0.581154i	$0.197399\pi$
$314$	−0.679888	−0.0383683
$315$	−2.03476	−0.114646
$316$	−23.5500	−1.32479
$317$	−24.9129	−1.39925	−0.699624	−	0.714512i	$-0.746649\pi$
$317$	−24.9129	−1.39925	−0.699624	+	0.714512i	$0.746649\pi$
$318$	−4.51965	−0.253449
$319$	−0.0799595	−0.00447687
$320$	2.98949	0.167118
$321$	8.32575	0.464698
$322$	2.20842	0.123070
$323$	−0.638368	−0.0355197
$324$	−1.53775	−0.0854307
$325$	1.14214	0.0633544
$326$	−14.1622	−0.784371
$327$	9.24800	0.511416
$328$	−8.29012	−0.457745
$329$	5.10521	0.281459
$330$	−0.826606	−0.0455032
$331$	−2.98838	−0.164256	−0.0821282	−	0.996622i	$-0.526172\pi$
$331$	−2.98838	−0.164256	−0.0821282	+	0.996622i	$0.526172\pi$
$332$	12.6422	0.693830
$333$	−2.51324	−0.137725
$334$	9.43260	0.516129
$335$	−2.45059	−0.133890
$336$	1.03512	0.0564705
$337$	−1.39673	−0.0760845	−0.0380422	−	0.999276i	$-0.512112\pi$
$337$	−1.39673	−0.0760845	−0.0380422	+	0.999276i	$0.512112\pi$
$338$	8.74095	0.475445
$339$	18.9921	1.03151
$340$	−4.35339	−0.236096
$341$	2.68731	0.145526
$342$	0.434019	0.0234690
$343$	9.69108	0.523269
$344$	19.4202	1.04707
$345$	−12.7942	−0.688815
$346$	4.17790	0.224605
$347$	20.9576	1.12507	0.562533	−	0.826775i	$-0.309827\pi$
$347$	20.9576	1.12507	0.562533	+	0.826775i	$0.309827\pi$
$348$	0.286310	0.0153478
$349$	−28.9516	−1.54974	−0.774872	−	0.632118i	$-0.782186\pi$
$349$	−28.9516	−1.54974	−0.774872	+	0.632118i	$0.782186\pi$
$350$	1.47312	0.0787418
$351$	−0.378868	−0.0202225
$352$	2.48644	0.132528
$353$	22.3323	1.18863	0.594315	−	0.804232i	$-0.297423\pi$
$353$	22.3323	1.18863	0.594315	+	0.804232i	$0.297423\pi$
$354$	−1.47105	−0.0781853
$355$	23.4490	1.24455
$356$	−16.8112	−0.890994
$357$	0.718741	0.0380398
$358$	−1.44247	−0.0762368
$359$	−30.9727	−1.63468	−0.817338	−	0.576159i	$-0.804551\pi$
$359$	−30.9727	−1.63468	−0.817338	+	0.576159i	$0.804551\pi$
$360$	6.80935	0.358884
$361$	−18.5925	−0.978552
$362$	−7.88689	−0.414526
$363$	10.8156	0.567670
$364$	0.418743	0.0219481
$365$	−41.2480	−2.15902
$366$	0.914664	0.0478102
$367$	−16.8503	−0.879578	−0.439789	−	0.898101i	$-0.644947\pi$
$367$	−16.8503	−0.879578	−0.439789	+	0.898101i	$0.644947\pi$
$368$	6.50864	0.339287
$369$	−3.44664	−0.179425
$370$	4.83739	0.251484
$371$	4.77793	0.248058
$372$	−9.62243	−0.498900
$373$	−30.5087	−1.57968	−0.789841	−	0.613311i	$-0.789837\pi$
$373$	−30.5087	−1.57968	−0.789841	+	0.613311i	$0.789837\pi$
$374$	0.291983	0.0150981
$375$	5.62068	0.290251
$376$	−17.0846	−0.881073
$377$	0.0705404	0.00363302
$378$	−0.488663	−0.0251341
$379$	−22.4492	−1.15314	−0.576570	−	0.817048i	$-0.695609\pi$
$379$	−22.4492	−1.15314	−0.576570	+	0.817048i	$0.695609\pi$
$380$	2.77906	0.142563
$381$	−10.6495	−0.545589
$382$	16.2053	0.829135
$383$	31.0325	1.58569	0.792843	−	0.609426i	$-0.208600\pi$
$383$	31.0325	1.58569	0.792843	+	0.609426i	$0.208600\pi$
$384$	−10.8615	−0.554273
$385$	0.873843	0.0445352
$386$	−3.20081	−0.162917
$387$	8.07399	0.410424
$388$	−6.84429	−0.347466
$389$	27.3300	1.38569	0.692843	−	0.721088i	$-0.256358\pi$
$389$	27.3300	1.38569	0.692843	+	0.721088i	$0.256358\pi$
$390$	0.729234	0.0369262
$391$	4.51930	0.228551
$392$	−15.5944	−0.787636
$393$	13.6032	0.686191
$394$	3.20040	0.161234
$395$	43.3556	2.18146
$396$	0.660400	0.0331863
$397$	−19.3606	−0.971680	−0.485840	−	0.874048i	$-0.661486\pi$
$397$	−19.3606	−0.971680	−0.485840	+	0.874048i	$0.661486\pi$
$398$	3.72802	0.186869
$399$	−0.458821	−0.0229698
$400$	4.34159	0.217080
$401$	−30.5280	−1.52449	−0.762247	−	0.647286i	$-0.775904\pi$
$401$	−30.5280	−1.52449	−0.762247	+	0.647286i	$0.775904\pi$
$402$	−0.588528	−0.0293531
$403$	−2.37076	−0.118096
$404$	−6.12394	−0.304678
$405$	2.83101	0.140674
$406$	0.0909828	0.00451540
$407$	1.07933	0.0535003
$408$	−2.40527	−0.119079
$409$	16.9179	0.836537	0.418269	−	0.908323i	$-0.362637\pi$
$409$	16.9179	0.836537	0.418269	+	0.908323i	$0.362637\pi$
$410$	6.63398	0.327629
$411$	−4.09508	−0.201995
$412$	7.03851	0.346762
$413$	1.55511	0.0765220
$414$	−3.07262	−0.151011
$415$	−23.2743	−1.14249
$416$	−2.19354	−0.107547
$417$	−2.19787	−0.107630
$418$	−0.186393	−0.00911676
$419$	−14.4811	−0.707448	−0.353724	−	0.935350i	$-0.615085\pi$
$419$	−14.4811	−0.707448	−0.353724	+	0.935350i	$0.615085\pi$
$420$	−3.12896	−0.152677
$421$	−15.8786	−0.773877	−0.386938	−	0.922106i	$-0.626467\pi$
$421$	−15.8786	−0.773877	−0.386938	+	0.922106i	$0.626467\pi$
$422$	−14.8157	−0.721215
$423$	−7.10299	−0.345359
$424$	−15.9894	−0.776514
$425$	3.01460	0.146230
$426$	5.63146	0.272845
$427$	−0.966933	−0.0467932
$428$	12.8029	0.618854
$429$	0.162708	0.00785561
$430$	−15.5406	−0.749432
$431$	−24.5578	−1.18291	−0.591455	−	0.806338i	$-0.701446\pi$
$431$	−24.5578	−1.18291	−0.591455	+	0.806338i	$0.701446\pi$
$432$	−1.44019	−0.0692911
$433$	−13.9349	−0.669669	−0.334835	−	0.942277i	$-0.608680\pi$
$433$	−13.9349	−0.669669	−0.334835	+	0.942277i	$0.608680\pi$
$434$	−3.05779	−0.146779
$435$	−0.527097	−0.0252724
$436$	14.2211	0.681069
$437$	−2.88498	−0.138007
$438$	−9.90602	−0.473328
$439$	27.9449	1.33374	0.666869	−	0.745175i	$-0.267634\pi$
$439$	27.9449	1.33374	0.666869	+	0.745175i	$0.267634\pi$
$440$	−2.92433	−0.139412
$441$	−6.48341	−0.308734
$442$	−0.257588	−0.0122522
$443$	−2.07028	−0.0983621	−0.0491811	−	0.998790i	$-0.515661\pi$
$443$	−2.07028	−0.0983621	−0.0491811	+	0.998790i	$0.515661\pi$
$444$	−3.86474	−0.183412
$445$	30.9495	1.46715
$446$	−1.90477	−0.0901935
$447$	4.63030	0.219005
$448$	−0.758977	−0.0358583
$449$	−21.3110	−1.00573	−0.502865	−	0.864365i	$-0.667721\pi$
$449$	−21.3110	−1.00573	−0.502865	+	0.864365i	$0.667721\pi$
$450$	−2.04959	−0.0966186
$451$	1.48019	0.0696993
$452$	29.2051	1.37369
$453$	−11.4592	−0.538400
$454$	−4.10494	−0.192654
$455$	−0.770906	−0.0361406
$456$	1.53545	0.0719041
$457$	−24.3298	−1.13810	−0.569050	−	0.822303i	$-0.692689\pi$
$457$	−24.3298	−1.13810	−0.569050	+	0.822303i	$0.692689\pi$
$458$	−1.86136	−0.0869754
$459$	−1.00000	−0.0466760
$460$	−19.6743	−0.917318
$461$	1.25464	0.0584342	0.0292171	−	0.999573i	$-0.490699\pi$
$461$	1.25464	0.0584342	0.0292171	+	0.999573i	$0.490699\pi$
$462$	0.209860	0.00976357
$463$	14.4595	0.671992	0.335996	−	0.941863i	$-0.390927\pi$
$463$	14.4595	0.671992	0.335996	+	0.941863i	$0.390927\pi$
$464$	0.268144	0.0124483
$465$	17.7149	0.821510
$466$	−16.4671	−0.762825
$467$	−15.2834	−0.707233	−0.353617	−	0.935390i	$-0.615048\pi$
$467$	−15.2834	−0.707233	−0.353617	+	0.935390i	$0.615048\pi$
$468$	−0.582606	−0.0269310
$469$	0.622160	0.0287287
$470$	13.6716	0.630624
$471$	−1.00000	−0.0460776
$472$	−5.20420	−0.239543
$473$	−3.46744	−0.159433
$474$	10.4122	0.478247
$475$	−1.92443	−0.0882987
$476$	1.10525	0.0506588
$477$	−6.64764	−0.304374
$478$	1.88977	0.0864359
$479$	−10.0857	−0.460829	−0.230415	−	0.973093i	$-0.574008\pi$
$479$	−10.0857	−0.460829	−0.230415	+	0.973093i	$0.574008\pi$
$480$	16.3907	0.748131
$481$	−0.952186	−0.0434159
$482$	10.7994	0.491900
$483$	3.24821	0.147798
$484$	16.6317	0.755985
$485$	12.6004	0.572153
$486$	0.679888	0.0308403
$487$	−22.0015	−0.996983	−0.498491	−	0.866895i	$-0.666112\pi$
$487$	−22.0015	−0.996983	−0.498491	+	0.866895i	$0.666112\pi$
$488$	3.23585	0.146480
$489$	−20.8302	−0.941974
$490$	12.4791	0.563746
$491$	−8.16399	−0.368436	−0.184218	−	0.982885i	$-0.558975\pi$
$491$	−8.16399	−0.368436	−0.184218	+	0.982885i	$0.558975\pi$
$492$	−5.30008	−0.238946
$493$	0.186187	0.00838545
$494$	0.164436	0.00739832
$495$	−1.21580	−0.0546460
$496$	−9.01192	−0.404647
$497$	−5.95328	−0.267041
$498$	−5.58950	−0.250472
$499$	12.4086	0.555484	0.277742	−	0.960656i	$-0.410414\pi$
$499$	12.4086	0.555484	0.277742	+	0.960656i	$0.410414\pi$
$500$	8.64321	0.386536
$501$	13.8738	0.619834
$502$	−10.2996	−0.459694
$503$	−16.7390	−0.746354	−0.373177	−	0.927760i	$-0.621732\pi$
$503$	−16.7390	−0.746354	−0.373177	+	0.927760i	$0.621732\pi$
$504$	−1.72877	−0.0770055
$505$	11.2742	0.501695
$506$	1.31956	0.0586616
$507$	12.8565	0.570975
$508$	−16.3763	−0.726579
$509$	−20.4864	−0.908042	−0.454021	−	0.890991i	$-0.650011\pi$
$509$	−20.4864	−0.908042	−0.454021	+	0.890991i	$0.650011\pi$
$510$	1.92477	0.0852301
$511$	10.4721	0.463259
$512$	−15.2664	−0.674685
$513$	0.638368	0.0281846
$514$	−18.7855	−0.828594
$515$	−12.9579	−0.570994
$516$	12.4158	0.546575
$517$	3.05043	0.134158
$518$	−1.22813	−0.0539607
$519$	6.14498	0.269735
$520$	2.57985	0.113134
$521$	−23.6032	−1.03408	−0.517038	−	0.855962i	$-0.672965\pi$
$521$	−23.6032	−1.03408	−0.517038	+	0.855962i	$0.672965\pi$
$522$	−0.126586	−0.00554053
$523$	−38.9296	−1.70227	−0.851136	−	0.524945i	$-0.824086\pi$
$523$	−38.9296	−1.70227	−0.851136	+	0.524945i	$0.824086\pi$
$524$	20.9184	0.913823
$525$	2.16672	0.0945633
$526$	−3.88098	−0.169219
$527$	−6.25746	−0.272579
$528$	0.618500	0.0269167
$529$	−2.57592	−0.111996
$530$	12.7952	0.555786
$531$	−2.16366	−0.0938949
$532$	−0.705553	−0.0305896
$533$	−1.30582	−0.0565615
$534$	7.43277	0.321647
$535$	−23.5703	−1.01903
$536$	−2.08207	−0.0899315
$537$	−2.12163	−0.0915550
$538$	12.5161	0.539608
$539$	2.78435	0.119930
$540$	4.35339	0.187340
$541$	7.59909	0.326710	0.163355	−	0.986567i	$-0.447768\pi$
$541$	7.59909	0.326710	0.163355	+	0.986567i	$0.447768\pi$
$542$	7.53758	0.323767
$543$	−11.6003	−0.497815
$544$	−5.78972	−0.248232
$545$	−26.1812	−1.12148
$546$	−0.185139	−0.00792322
$547$	−4.33054	−0.185161	−0.0925803	−	0.995705i	$-0.529511\pi$
$547$	−4.33054	−0.185161	−0.0925803	+	0.995705i	$0.529511\pi$
$548$	−6.29722	−0.269004
$549$	1.34532	0.0574167
$550$	0.880212	0.0375324
$551$	−0.118856	−0.00506343
$552$	−10.8702	−0.462665
$553$	−11.0072	−0.468073
$554$	4.70576	0.199929
$555$	7.11499	0.302015
$556$	−3.37979	−0.143335
$557$	−39.9471	−1.69261	−0.846306	−	0.532697i	$-0.821178\pi$
$557$	−39.9471	−1.69261	−0.846306	+	0.532697i	$0.821178\pi$
$558$	4.25437	0.180102
$559$	3.05898	0.129381
$560$	−2.93044	−0.123834
$561$	0.429458	0.0181317
$562$	22.3682	0.943546
$563$	−22.0055	−0.927423	−0.463711	−	0.885986i	$-0.653483\pi$
$563$	−22.0055	−0.927423	−0.463711	+	0.885986i	$0.653483\pi$
$564$	−10.9226	−0.459926
$565$	−53.7667	−2.26198
$566$	−4.71226	−0.198071
$567$	−0.718741	−0.0301843
$568$	19.9227	0.835939
$569$	20.8760	0.875170	0.437585	−	0.899177i	$-0.355834\pi$
$569$	20.8760	0.875170	0.437585	+	0.899177i	$0.355834\pi$
$570$	−1.22871	−0.0514650
$571$	−31.4722	−1.31707	−0.658535	−	0.752550i	$-0.728824\pi$
$571$	−31.4722	−1.31707	−0.658535	+	0.752550i	$0.728824\pi$
$572$	0.250205	0.0104616
$573$	23.8352	0.995731
$574$	−1.68425	−0.0702991
$575$	13.6239	0.568156
$576$	1.05598	0.0439992
$577$	−17.9758	−0.748344	−0.374172	−	0.927359i	$-0.622073\pi$
$577$	−17.9758	−0.748344	−0.374172	+	0.927359i	$0.622073\pi$
$578$	−0.679888	−0.0282796
$579$	−4.70784	−0.195651
$580$	−0.810545	−0.0336560
$581$	5.90892	0.245143
$582$	3.02607	0.125435
$583$	2.85488	0.118237
$584$	−35.0451	−1.45017
$585$	1.07258	0.0443457
$586$	−15.1366	−0.625287
$587$	−24.7451	−1.02134	−0.510670	−	0.859777i	$-0.670603\pi$
$587$	−24.7451	−1.02134	−0.510670	+	0.859777i	$0.670603\pi$
$588$	−9.96988	−0.411151
$589$	3.99456	0.164593
$590$	4.16454	0.171452
$591$	4.70724	0.193630
$592$	−3.61953	−0.148762
$593$	14.7552	0.605923	0.302961	−	0.953003i	$-0.402025\pi$
$593$	14.7552	0.605923	0.302961	+	0.953003i	$0.402025\pi$
$594$	−0.291983	−0.0119802
$595$	−2.03476	−0.0834170
$596$	7.12025	0.291657
$597$	5.48329	0.224416
$598$	−1.16412	−0.0476043
$599$	43.1852	1.76450	0.882249	−	0.470784i	$-0.156029\pi$
$599$	43.1852	1.76450	0.882249	+	0.470784i	$0.156029\pi$
$600$	−7.25095	−0.296019
$601$	−10.0408	−0.409574	−0.204787	−	0.978807i	$-0.565650\pi$
$601$	−10.0408	−0.409574	−0.204787	+	0.978807i	$0.565650\pi$
$602$	3.94546	0.160805
$603$	−0.865625	−0.0352510
$604$	−17.6214	−0.717005
$605$	−30.6189	−1.24484
$606$	2.70758	0.109988
$607$	−14.5418	−0.590235	−0.295117	−	0.955461i	$-0.595359\pi$
$607$	−14.5418	−0.590235	−0.295117	+	0.955461i	$0.595359\pi$
$608$	3.69597	0.149891
$609$	0.133820	0.00542267
$610$	−2.58942	−0.104843
$611$	−2.69110	−0.108870
$612$	−1.53775	−0.0621600
$613$	−28.1964	−1.13884	−0.569421	−	0.822046i	$-0.692833\pi$
$613$	−28.1964	−1.13884	−0.569421	+	0.822046i	$0.692833\pi$
$614$	3.88928	0.156959
$615$	9.75747	0.393459
$616$	0.742433	0.0299135
$617$	49.4674	1.99148	0.995741	−	0.0921924i	$-0.0293875\pi$
$617$	49.4674	1.99148	0.995741	+	0.0921924i	$0.0293875\pi$
$618$	−3.11194	−0.125181
$619$	−2.43738	−0.0979664	−0.0489832	−	0.998800i	$-0.515598\pi$
$619$	−2.43738	−0.0979664	−0.0489832	+	0.998800i	$0.515598\pi$
$620$	27.2412	1.09403
$621$	−4.51930	−0.181353
$622$	−19.7523	−0.791993
$623$	−7.85752	−0.314805
$624$	−0.545642	−0.0218432
$625$	−30.9852	−1.23941
$626$	−19.5773	−0.782468
$627$	−0.274152	−0.0109486
$628$	−1.53775	−0.0613630
$629$	−2.51324	−0.100209
$630$	1.38341	0.0551163
$631$	−1.98037	−0.0788371	−0.0394186	−	0.999223i	$-0.512551\pi$
$631$	−1.98037	−0.0788371	−0.0394186	+	0.999223i	$0.512551\pi$
$632$	36.8357	1.46525
$633$	−21.7913	−0.866127
$634$	16.9380	0.672693
$635$	30.1488	1.19642
$636$	−10.2224	−0.405345
$637$	−2.45636	−0.0973245
$638$	0.0543635	0.00215227
$639$	8.28293	0.327668
$640$	30.7489	1.21546
$641$	−39.3039	−1.55241	−0.776205	−	0.630481i	$-0.782858\pi$
$641$	−39.3039	−1.55241	−0.776205	+	0.630481i	$0.782858\pi$
$642$	−5.66058	−0.223405
$643$	−8.63358	−0.340475	−0.170238	−	0.985403i	$-0.554454\pi$
$643$	−8.63358	−0.340475	−0.170238	+	0.985403i	$0.554454\pi$
$644$	4.99494	0.196828
$645$	−22.8575	−0.900014
$646$	0.434019	0.0170762
$647$	−7.05587	−0.277395	−0.138697	−	0.990335i	$-0.544292\pi$
$647$	−7.05587	−0.277395	−0.138697	+	0.990335i	$0.544292\pi$
$648$	2.40527	0.0944881
$649$	0.929201	0.0364743
$650$	−0.776525	−0.0304578
$651$	−4.49749	−0.176271
$652$	−32.0317	−1.25446
$653$	−26.2059	−1.02552	−0.512759	−	0.858533i	$-0.671376\pi$
$653$	−26.2059	−1.02552	−0.512759	+	0.858533i	$0.671376\pi$
$654$	−6.28760	−0.245865
$655$	−38.5108	−1.50474
$656$	−4.96381	−0.193804
$657$	−14.5701	−0.568433
$658$	−3.47097	−0.135312
$659$	39.6598	1.54492	0.772462	−	0.635060i	$-0.219025\pi$
$659$	39.6598	1.54492	0.772462	+	0.635060i	$0.219025\pi$
$660$	−1.86960	−0.0727739
$661$	−2.50604	−0.0974737	−0.0487368	−	0.998812i	$-0.515520\pi$
$661$	−2.50604	−0.0974737	−0.0487368	+	0.998812i	$0.515520\pi$
$662$	2.03176	0.0789668
$663$	−0.378868	−0.0147140
$664$	−19.7743	−0.767391
$665$	1.29893	0.0503702
$666$	1.70872	0.0662115
$667$	0.841436	0.0325805
$668$	21.3344	0.825453
$669$	−2.80160	−0.108316
$670$	1.66613	0.0643681
$671$	−0.577756	−0.0223040
$672$	−4.16130	−0.160526
$673$	−11.8171	−0.455516	−0.227758	−	0.973718i	$-0.573139\pi$
$673$	−11.8171	−0.455516	−0.227758	+	0.973718i	$0.573139\pi$
$674$	0.949617	0.0365779
$675$	−3.01460	−0.116032
$676$	19.7701	0.760387
$677$	−1.00614	−0.0386692	−0.0193346	−	0.999813i	$-0.506155\pi$
$677$	−1.00614	−0.0386692	−0.0193346	+	0.999813i	$0.506155\pi$
$678$	−12.9125	−0.495900
$679$	−3.19900	−0.122766
$680$	6.80935	0.261127
$681$	−6.03767	−0.231364
$682$	−1.82707	−0.0699622
$683$	−12.0613	−0.461513	−0.230757	−	0.973011i	$-0.574120\pi$
$683$	−12.0613	−0.461513	−0.230757	+	0.973011i	$0.574120\pi$
$684$	0.981652	0.0375344
$685$	11.5932	0.442954
$686$	−6.58884	−0.251563
$687$	−2.73774	−0.104451
$688$	11.6281	0.443316
$689$	−2.51858	−0.0959502
$690$	8.69860	0.331150
$691$	23.4844	0.893387	0.446694	−	0.894687i	$-0.352601\pi$
$691$	23.4844	0.893387	0.446694	+	0.894687i	$0.352601\pi$
$692$	9.44946	0.359215
$693$	0.308669	0.0117254
$694$	−14.2488	−0.540879
$695$	6.22220	0.236021
$696$	−0.447831	−0.0169750
$697$	−3.44664	−0.130551
$698$	19.6839	0.745045
$699$	−24.2203	−0.916098
$700$	3.33187	0.125933
$701$	−18.3792	−0.694173	−0.347087	−	0.937833i	$-0.612829\pi$
$701$	−18.3792	−0.694173	−0.347087	+	0.937833i	$0.612829\pi$
$702$	0.257588	0.00972203
$703$	1.60437	0.0605100
$704$	−0.453499	−0.0170919
$705$	20.1086	0.757334
$706$	−15.1835	−0.571438
$707$	−2.86231	−0.107648
$708$	−3.32718	−0.125043
$709$	39.4936	1.48321	0.741607	−	0.670834i	$-0.234064\pi$
$709$	39.4936	1.48321	0.741607	+	0.670834i	$0.234064\pi$
$710$	−15.9427	−0.598319
$711$	15.3145	0.574340
$712$	26.2953	0.985458
$713$	−28.2794	−1.05907
$714$	−0.488663	−0.0182878
$715$	−0.460627	−0.0172265
$716$	−3.26254	−0.121927
$717$	2.77953	0.103803
$718$	21.0580	0.785876
$719$	41.9602	1.56485	0.782425	−	0.622745i	$-0.213983\pi$
$719$	41.9602	1.56485	0.782425	+	0.622745i	$0.213983\pi$
$720$	4.07718	0.151948
$721$	3.28978	0.122518
$722$	12.6408	0.470442
$723$	15.8841	0.590737
$724$	−17.8384	−0.662957
$725$	0.561280	0.0208454
$726$	−7.35337	−0.272909
$727$	−34.3974	−1.27573	−0.637864	−	0.770149i	$-0.720182\pi$
$727$	−34.3974	−1.27573	−0.637864	+	0.770149i	$0.720182\pi$
$728$	−0.654976	−0.0242750
$729$	1.00000	0.0370370
$730$	28.0440	1.03796
$731$	8.07399	0.298627
$732$	2.06876	0.0764637
$733$	34.8273	1.28638	0.643188	−	0.765708i	$-0.277611\pi$
$733$	34.8273	1.28638	0.643188	+	0.765708i	$0.277611\pi$
$734$	11.4563	0.422860
$735$	18.3546	0.677019
$736$	−26.1655	−0.964472
$737$	0.371749	0.0136936
$738$	2.34333	0.0862592
$739$	−10.1268	−0.372519	−0.186260	−	0.982501i	$-0.559637\pi$
$739$	−10.1268	−0.372519	−0.186260	+	0.982501i	$0.559637\pi$
$740$	10.9411	0.402203
$741$	0.241858	0.00888486
$742$	−3.24845	−0.119255
$743$	24.4788	0.898041	0.449021	−	0.893521i	$-0.351773\pi$
$743$	24.4788	0.898041	0.449021	+	0.893521i	$0.351773\pi$
$744$	15.0509	0.551793
$745$	−13.1084	−0.480255
$746$	20.7425	0.759438
$747$	−8.22121	−0.300798
$748$	0.660400	0.0241466
$749$	5.98406	0.218653
$750$	−3.82143	−0.139539
$751$	−28.5125	−1.04043	−0.520217	−	0.854034i	$-0.674149\pi$
$751$	−28.5125	−1.04043	−0.520217	+	0.854034i	$0.674149\pi$
$752$	−10.2296	−0.373037
$753$	−15.1490	−0.552060
$754$	−0.0479596	−0.00174658
$755$	32.4411	1.18065
$756$	−1.10525	−0.0401974
$757$	−4.09308	−0.148766	−0.0743828	−	0.997230i	$-0.523699\pi$
$757$	−4.09308	−0.148766	−0.0743828	+	0.997230i	$0.523699\pi$
$758$	15.2630	0.554376
$759$	1.94085	0.0704483
$760$	−4.34687	−0.157678
$761$	5.32001	0.192850	0.0964250	−	0.995340i	$-0.469259\pi$
$761$	5.32001	0.192850	0.0964250	+	0.995340i	$0.469259\pi$
$762$	7.24045	0.262294
$763$	6.64692	0.240635
$764$	36.6527	1.32605
$765$	2.83101	0.102355
$766$	−21.0986	−0.762324
$767$	−0.819743	−0.0295992
$768$	9.49655	0.342677
$769$	−30.5613	−1.10207	−0.551034	−	0.834483i	$-0.685767\pi$
$769$	−30.5613	−1.10207	−0.551034	+	0.834483i	$0.685767\pi$
$770$	−0.594115	−0.0214104
$771$	−27.6303	−0.995082
$772$	−7.23950	−0.260555
$773$	4.52245	0.162661	0.0813306	−	0.996687i	$-0.474083\pi$
$773$	4.52245	0.162661	0.0813306	+	0.996687i	$0.474083\pi$
$774$	−5.48941	−0.197313
$775$	−18.8638	−0.677606
$776$	10.7055	0.384305
$777$	−1.80637	−0.0648030
$778$	−18.5813	−0.666173
$779$	2.20023	0.0788313
$780$	1.64936	0.0590566
$781$	−3.55717	−0.127285
$782$	−3.07262	−0.109877
$783$	−0.186187	−0.00665379
$784$	−9.33733	−0.333476
$785$	2.83101	0.101043
$786$	−9.24865	−0.329889
$787$	−14.8878	−0.530692	−0.265346	−	0.964153i	$-0.585486\pi$
$787$	−14.8878	−0.530692	−0.265346	+	0.964153i	$0.585486\pi$
$788$	7.23858	0.257864
$789$	−5.70827	−0.203220
$790$	−29.4769	−1.04874
$791$	13.6504	0.485351
$792$	−1.03296	−0.0367048
$793$	0.509698	0.0180999
$794$	13.1630	0.467138
$795$	18.8195	0.667459
$796$	8.43194	0.298862
$797$	−12.0899	−0.428247	−0.214124	−	0.976807i	$-0.568690\pi$
$797$	−12.0899	−0.428247	−0.214124	+	0.976807i	$0.568690\pi$
$798$	0.311947	0.0110428
$799$	−7.10299	−0.251286
$800$	−17.4537	−0.617081
$801$	10.9323	0.386275
$802$	20.7556	0.732906
$803$	6.25723	0.220813
$804$	−1.33112	−0.0469449
$805$	−9.19569	−0.324106
$806$	1.61185	0.0567749
$807$	18.4091	0.648031
$808$	9.57876	0.336980
$809$	−35.2820	−1.24045	−0.620224	−	0.784425i	$-0.712958\pi$
$809$	−35.2820	−1.24045	−0.620224	+	0.784425i	$0.712958\pi$
$810$	−1.92477	−0.0676294
$811$	22.0707	0.775008	0.387504	−	0.921868i	$-0.373337\pi$
$811$	22.0707	0.775008	0.387504	+	0.921868i	$0.373337\pi$
$812$	0.205782	0.00722155
$813$	11.0865	0.388821
$814$	−0.733822	−0.0257205
$815$	58.9704	2.06564
$816$	−1.44019	−0.0504167
$817$	−5.15418	−0.180322
$818$	−11.5023	−0.402168
$819$	−0.272308	−0.00951522
$820$	15.0046	0.523982
$821$	−5.62965	−0.196476	−0.0982381	−	0.995163i	$-0.531321\pi$
$821$	−5.62965	−0.196476	−0.0982381	+	0.995163i	$0.531321\pi$
$822$	2.78420	0.0971100
$823$	−27.8511	−0.970829	−0.485414	−	0.874284i	$-0.661331\pi$
$823$	−27.8511	−0.970829	−0.485414	+	0.874284i	$0.661331\pi$
$824$	−11.0093	−0.383526
$825$	1.29464	0.0450737
$826$	−1.05730	−0.0367882
$827$	0.651170	0.0226434	0.0113217	−	0.999936i	$-0.496396\pi$
$827$	0.651170	0.0226434	0.0113217	+	0.999936i	$0.496396\pi$
$828$	−6.94957	−0.241514
$829$	−6.11435	−0.212360	−0.106180	−	0.994347i	$-0.533862\pi$
$829$	−6.11435	−0.212360	−0.106180	+	0.994347i	$0.533862\pi$
$830$	15.8239	0.549256
$831$	6.92138	0.240100
$832$	0.400078	0.0138702
$833$	−6.48341	−0.224637
$834$	1.49431	0.0517437
$835$	−39.2767	−1.35923
$836$	−0.421578	−0.0145806
$837$	6.25746	0.216290
$838$	9.84553	0.340108
$839$	−7.92873	−0.273730	−0.136865	−	0.990590i	$-0.543703\pi$
$839$	−7.92873	−0.273730	−0.136865	+	0.990590i	$0.543703\pi$
$840$	4.89416	0.168864
$841$	−28.9653	−0.998805
$842$	10.7957	0.372044
$843$	32.8998	1.13313
$844$	−33.5097	−1.15345
$845$	−36.3967	−1.25209
$846$	4.82923	0.166033
$847$	7.77359	0.267104
$848$	−9.57385	−0.328767
$849$	−6.93094	−0.237869
$850$	−2.04959	−0.0703004
$851$	−11.3581	−0.389350
$852$	12.7371	0.436366
$853$	9.38918	0.321480	0.160740	−	0.986997i	$-0.448612\pi$
$853$	9.38918	0.321480	0.160740	+	0.986997i	$0.448612\pi$
$854$	0.657406	0.0224960
$855$	−1.80722	−0.0618058
$856$	−20.0257	−0.684465
$857$	25.1258	0.858280	0.429140	−	0.903238i	$-0.358817\pi$
$857$	25.1258	0.858280	0.429140	+	0.903238i	$0.358817\pi$
$858$	−0.110623	−0.00377661
$859$	55.9138	1.90775	0.953876	−	0.300200i	$-0.0970533\pi$
$859$	55.9138	1.90775	0.953876	+	0.300200i	$0.0970533\pi$
$860$	−35.1492	−1.19858
$861$	−2.47724	−0.0844242
$862$	16.6966	0.568688
$863$	36.7073	1.24953	0.624765	−	0.780813i	$-0.285195\pi$
$863$	36.7073	1.24953	0.624765	+	0.780813i	$0.285195\pi$
$864$	5.78972	0.196970
$865$	−17.3965	−0.591498
$866$	9.47418	0.321946
$867$	−1.00000	−0.0339618
$868$	−6.91603	−0.234745
$869$	−6.57695	−0.223108
$870$	0.358367	0.0121498
$871$	−0.327958	−0.0111124
$872$	−22.2440	−0.753276
$873$	4.45084	0.150638
$874$	1.96146	0.0663474
$875$	4.03981	0.136570
$876$	−22.4052	−0.757001
$877$	12.1176	0.409181	0.204591	−	0.978848i	$-0.434414\pi$
$877$	12.1176	0.409181	0.204591	+	0.978848i	$0.434414\pi$
$878$	−18.9994	−0.641199
$879$	−22.2634	−0.750925
$880$	−1.75098	−0.0590254
$881$	−1.27770	−0.0430466	−0.0215233	−	0.999768i	$-0.506852\pi$
$881$	−1.27770	−0.0430466	−0.0215233	+	0.999768i	$0.506852\pi$
$882$	4.40799	0.148425
$883$	−33.1075	−1.11416	−0.557078	−	0.830460i	$-0.688078\pi$
$883$	−33.1075	−1.11416	−0.557078	+	0.830460i	$0.688078\pi$
$884$	−0.582606	−0.0195952
$885$	6.12534	0.205901
$886$	1.40756	0.0472879
$887$	36.0648	1.21094	0.605469	−	0.795869i	$-0.292985\pi$
$887$	36.0648	1.21094	0.605469	+	0.795869i	$0.292985\pi$
$888$	6.04502	0.202858
$889$	−7.65421	−0.256714
$890$	−21.0422	−0.705337
$891$	−0.429458	−0.0143874
$892$	−4.30816	−0.144248
$893$	4.53432	0.151735
$894$	−3.14808	−0.105288
$895$	6.00634	0.200770
$896$	−7.80659	−0.260800
$897$	−1.71222	−0.0571694
$898$	14.4891	0.483508
$899$	−1.16506	−0.0388569
$900$	−4.63571	−0.154524
$901$	−6.64764	−0.221465
$902$	−1.00636	−0.0335082
$903$	5.80310	0.193115
$904$	−45.6811	−1.51933
$905$	32.8405	1.09165
$906$	7.79097	0.258838
$907$	−48.1800	−1.59979	−0.799895	−	0.600140i	$-0.795112\pi$
$907$	−48.1800	−1.59979	−0.799895	+	0.600140i	$0.795112\pi$
$908$	−9.28444	−0.308115
$909$	3.98240	0.132088
$910$	0.524130	0.0173747
$911$	−1.54363	−0.0511429	−0.0255714	−	0.999673i	$-0.508141\pi$
$911$	−1.54363	−0.0511429	−0.0255714	+	0.999673i	$0.508141\pi$
$912$	0.919370	0.0304434
$913$	3.53066	0.116848
$914$	16.5415	0.547145
$915$	−3.80860	−0.125908
$916$	−4.20996	−0.139101
$917$	9.77718	0.322871
$918$	0.679888	0.0224396
$919$	−16.4866	−0.543842	−0.271921	−	0.962320i	$-0.587659\pi$
$919$	−16.4866	−0.543842	−0.271921	+	0.962320i	$0.587659\pi$
$920$	30.7735	1.01457
$921$	5.72048	0.188496
$922$	−0.853012	−0.0280924
$923$	3.13814	0.103293
$924$	0.474656	0.0156150
$925$	−7.57641	−0.249111
$926$	−9.83087	−0.323062
$927$	−4.57714	−0.150333
$928$	−1.07797	−0.0353861
$929$	15.6325	0.512887	0.256443	−	0.966559i	$-0.417449\pi$
$929$	15.6325	0.512887	0.256443	+	0.966559i	$0.417449\pi$
$930$	−12.0442	−0.394944
$931$	4.13880	0.135644
$932$	−37.2449	−1.22000
$933$	−29.0522	−0.951127
$934$	10.3910	0.340005
$935$	−1.21580	−0.0397608
$936$	0.911283	0.0297862
$937$	−49.7700	−1.62592	−0.812958	−	0.582323i	$-0.802144\pi$
$937$	−49.7700	−1.62592	−0.812958	+	0.582323i	$0.802144\pi$
$938$	−0.422999	−0.0138114
$939$	−28.7950	−0.939688
$940$	30.9221	1.00857
$941$	36.2374	1.18130	0.590652	−	0.806926i	$-0.298871\pi$
$941$	36.2374	1.18130	0.590652	+	0.806926i	$0.298871\pi$
$942$	0.679888	0.0221519
$943$	−15.5764	−0.507238
$944$	−3.11608	−0.101420
$945$	2.03476	0.0661907
$946$	2.35747	0.0766479
$947$	17.1312	0.556688	0.278344	−	0.960481i	$-0.410214\pi$
$947$	17.1312	0.556688	0.278344	+	0.960481i	$0.410214\pi$
$948$	23.5500	0.764868
$949$	−5.52015	−0.179191
$950$	1.30839	0.0424499
$951$	24.9129	0.807856
$952$	−1.72877	−0.0560297
$953$	−32.1535	−1.04155	−0.520776	−	0.853693i	$-0.674357\pi$
$953$	−32.1535	−1.04155	−0.520776	+	0.853693i	$0.674357\pi$
$954$	4.51965	0.146329
$955$	−67.4777	−2.18353
$956$	4.27423	0.138238
$957$	0.0799595	0.00258472
$958$	6.85717	0.221545
$959$	−2.94330	−0.0950442
$960$	−2.98949	−0.0964854
$961$	8.15584	0.263092
$962$	0.647380	0.0208724
$963$	−8.32575	−0.268294
$964$	24.4258	0.786703
$965$	13.3279	0.429042
$966$	−2.20842	−0.0710546
$967$	−20.5522	−0.660913	−0.330457	−	0.943821i	$-0.607203\pi$
$967$	−20.5522	−0.660913	−0.330457	+	0.943821i	$0.607203\pi$
$968$	−26.0144	−0.836135
$969$	0.638368	0.0205073
$970$	−8.56683	−0.275064
$971$	17.0104	0.545890	0.272945	−	0.962030i	$-0.412002\pi$
$971$	17.0104	0.545890	0.272945	+	0.962030i	$0.412002\pi$
$972$	1.53775	0.0493234
$973$	−1.57970	−0.0506429
$974$	14.9585	0.479303
$975$	−1.14214	−0.0365777
$976$	1.93751	0.0620181
$977$	15.9463	0.510166	0.255083	−	0.966919i	$-0.417897\pi$
$977$	15.9463	0.510166	0.255083	+	0.966919i	$0.417897\pi$
$978$	14.1622	0.452857
$979$	−4.69498	−0.150052
$980$	28.2248	0.901609
$981$	−9.24800	−0.295266
$982$	5.55060	0.177127
$983$	−19.9780	−0.637198	−0.318599	−	0.947890i	$-0.603212\pi$
$983$	−19.9780	−0.637198	−0.318599	+	0.947890i	$0.603212\pi$
$984$	8.29012	0.264279
$985$	−13.3262	−0.424609
$986$	−0.126586	−0.00403133
$987$	−5.10521	−0.162501
$988$	0.371917	0.0118323
$989$	36.4888	1.16028
$990$	0.826606	0.0262713
$991$	−11.1410	−0.353905	−0.176952	−	0.984219i	$-0.556624\pi$
$991$	−11.1410	−0.353905	−0.176952	+	0.984219i	$0.556624\pi$
$992$	36.2289	1.15027
$993$	2.98838	0.0948335
$994$	4.04756	0.128381
$995$	−15.5232	−0.492120
$996$	−12.6422	−0.400583
$997$	−14.2972	−0.452798	−0.226399	−	0.974035i	$-0.572695\pi$
$997$	−14.2972	−0.452798	−0.226399	+	0.974035i	$0.572695\pi$
$998$	−8.43644	−0.267051
$999$	2.51324	0.0795153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.17	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-0.679888 q^{2} -1.00000 q^{3} -1.53775 q^{4} +2.83101 q^{5} +0.679888 q^{6} -0.718741 q^{7} +2.40527 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.679888 q^{2} -1.00000 q^{3} -1.53775 q^{4} +2.83101 q^{5} +0.679888 q^{6} -0.718741 q^{7} +2.40527 q^{8} +1.00000 q^{9} -1.92477 q^{10} -0.429458 q^{11} +1.53775 q^{12} +0.378868 q^{13} +0.488663 q^{14} -2.83101 q^{15} +1.44019 q^{16} +1.00000 q^{17} -0.679888 q^{18} -0.638368 q^{19} -4.35339 q^{20} +0.718741 q^{21} +0.291983 q^{22} +4.51930 q^{23} -2.40527 q^{24} +3.01460 q^{25} -0.257588 q^{26} -1.00000 q^{27} +1.10525 q^{28} +0.186187 q^{29} +1.92477 q^{30} -6.25746 q^{31} -5.78972 q^{32} +0.429458 q^{33} -0.679888 q^{34} -2.03476 q^{35} -1.53775 q^{36} -2.51324 q^{37} +0.434019 q^{38} -0.378868 q^{39} +6.80935 q^{40} -3.44664 q^{41} -0.488663 q^{42} +8.07399 q^{43} +0.660400 q^{44} +2.83101 q^{45} -3.07262 q^{46} -7.10299 q^{47} -1.44019 q^{48} -6.48341 q^{49} -2.04959 q^{50} -1.00000 q^{51} -0.582606 q^{52} -6.64764 q^{53} +0.679888 q^{54} -1.21580 q^{55} -1.72877 q^{56} +0.638368 q^{57} -0.126586 q^{58} -2.16366 q^{59} +4.35339 q^{60} +1.34532 q^{61} +4.25437 q^{62} -0.718741 q^{63} +1.05598 q^{64} +1.07258 q^{65} -0.291983 q^{66} -0.865625 q^{67} -1.53775 q^{68} -4.51930 q^{69} +1.38341 q^{70} +8.28293 q^{71} +2.40527 q^{72} -14.5701 q^{73} +1.70872 q^{74} -3.01460 q^{75} +0.981652 q^{76} +0.308669 q^{77} +0.257588 q^{78} +15.3145 q^{79} +4.07718 q^{80} +1.00000 q^{81} +2.34333 q^{82} -8.22121 q^{83} -1.10525 q^{84} +2.83101 q^{85} -5.48941 q^{86} -0.186187 q^{87} -1.03296 q^{88} +10.9323 q^{89} -1.92477 q^{90} -0.272308 q^{91} -6.94957 q^{92} +6.25746 q^{93} +4.82923 q^{94} -1.80722 q^{95} +5.78972 q^{96} +4.45084 q^{97} +4.40799 q^{98} -0.429458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 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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