LMFDB - Embedded newform 4007.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37198 q^{2} +1.06086 q^{3} +3.62628 q^{4} +2.75167 q^{5} -2.51634 q^{6} +1.78055 q^{7} -3.85749 q^{8} -1.87457 q^{9} +O(q^{10})$	\(q-2.37198 q^{2} +1.06086 q^{3} +3.62628 q^{4} +2.75167 q^{5} -2.51634 q^{6} +1.78055 q^{7} -3.85749 q^{8} -1.87457 q^{9} -6.52689 q^{10} -0.928447 q^{11} +3.84698 q^{12} +0.274681 q^{13} -4.22342 q^{14} +2.91914 q^{15} +1.89733 q^{16} +1.61331 q^{17} +4.44644 q^{18} -7.95141 q^{19} +9.97830 q^{20} +1.88892 q^{21} +2.20225 q^{22} -1.17201 q^{23} -4.09227 q^{24} +2.57167 q^{25} -0.651536 q^{26} -5.17125 q^{27} +6.45676 q^{28} -9.59192 q^{29} -6.92413 q^{30} +1.26834 q^{31} +3.21456 q^{32} -0.984955 q^{33} -3.82675 q^{34} +4.89947 q^{35} -6.79771 q^{36} +0.0610377 q^{37} +18.8606 q^{38} +0.291399 q^{39} -10.6145 q^{40} -1.20569 q^{41} -4.48047 q^{42} +10.7484 q^{43} -3.36680 q^{44} -5.15819 q^{45} +2.77998 q^{46} -11.4740 q^{47} +2.01280 q^{48} -3.82965 q^{49} -6.09993 q^{50} +1.71151 q^{51} +0.996068 q^{52} +9.41522 q^{53} +12.2661 q^{54} -2.55478 q^{55} -6.86845 q^{56} -8.43536 q^{57} +22.7518 q^{58} -5.31749 q^{59} +10.5856 q^{60} -7.47755 q^{61} -3.00847 q^{62} -3.33776 q^{63} -11.4195 q^{64} +0.755830 q^{65} +2.33629 q^{66} -12.2619 q^{67} +5.85033 q^{68} -1.24334 q^{69} -11.6214 q^{70} +16.1915 q^{71} +7.23114 q^{72} -2.66305 q^{73} -0.144780 q^{74} +2.72818 q^{75} -28.8340 q^{76} -1.65314 q^{77} -0.691191 q^{78} -2.58260 q^{79} +5.22081 q^{80} +0.137725 q^{81} +2.85988 q^{82} +3.44977 q^{83} +6.84974 q^{84} +4.43930 q^{85} -25.4949 q^{86} -10.1757 q^{87} +3.58147 q^{88} -11.2417 q^{89} +12.2351 q^{90} +0.489082 q^{91} -4.25003 q^{92} +1.34553 q^{93} +27.2162 q^{94} -21.8796 q^{95} +3.41021 q^{96} +0.942699 q^{97} +9.08384 q^{98} +1.74044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.37198	−1.67724	−0.838621	−	0.544716i	$-0.816637\pi$
$2$	−2.37198	−1.67724	−0.838621	+	0.544716i	$0.816637\pi$
$3$	1.06086	0.612489	0.306245	−	0.951953i	$-0.400927\pi$
$3$	1.06086	0.612489	0.306245	+	0.951953i	$0.400927\pi$
$4$	3.62628	1.81314
$5$	2.75167	1.23058	0.615291	−	0.788300i	$-0.289038\pi$
$5$	2.75167	1.23058	0.615291	+	0.788300i	$0.289038\pi$
$6$	−2.51634	−1.02729
$7$	1.78055	0.672984	0.336492	−	0.941686i	$-0.390759\pi$
$7$	1.78055	0.672984	0.336492	+	0.941686i	$0.390759\pi$
$8$	−3.85749	−1.36383
$9$	−1.87457	−0.624857
$10$	−6.52689	−2.06398
$11$	−0.928447	−0.279937	−0.139969	−	0.990156i	$-0.544700\pi$
$11$	−0.928447	−0.279937	−0.139969	+	0.990156i	$0.544700\pi$
$12$	3.84698	1.11053
$13$	0.274681	0.0761827	0.0380914	−	0.999274i	$-0.487872\pi$
$13$	0.274681	0.0761827	0.0380914	+	0.999274i	$0.487872\pi$
$14$	−4.22342	−1.12876
$15$	2.91914	0.753719
$16$	1.89733	0.474332
$17$	1.61331	0.391286	0.195643	−	0.980675i	$-0.437321\pi$
$17$	1.61331	0.391286	0.195643	+	0.980675i	$0.437321\pi$
$18$	4.44644	1.04804
$19$	−7.95141	−1.82418	−0.912090	−	0.409991i	$-0.865532\pi$
$19$	−7.95141	−1.82418	−0.912090	+	0.409991i	$0.865532\pi$
$20$	9.97830	2.23122
$21$	1.88892	0.412196
$22$	2.20225	0.469522
$23$	−1.17201	−0.244381	−0.122190	−	0.992507i	$-0.538992\pi$
$23$	−1.17201	−0.244381	−0.122190	+	0.992507i	$0.538992\pi$
$24$	−4.09227	−0.835331
$25$	2.57167	0.514333
$26$	−0.651536	−0.127777
$27$	−5.17125	−0.995208
$28$	6.45676	1.22021
$29$	−9.59192	−1.78117	−0.890587	−	0.454812i	$-0.849706\pi$
$29$	−9.59192	−1.78117	−0.890587	+	0.454812i	$0.849706\pi$
$30$	−6.92413	−1.26417
$31$	1.26834	0.227801	0.113900	−	0.993492i	$-0.463666\pi$
$31$	1.26834	0.227801	0.113900	+	0.993492i	$0.463666\pi$
$32$	3.21456	0.568260
$33$	−0.984955	−0.171459
$34$	−3.82675	−0.656282
$35$	4.89947	0.828162
$36$	−6.79771	−1.13295
$37$	0.0610377	0.0100345	0.00501727	−	0.999987i	$-0.498403\pi$
$37$	0.0610377	0.0100345	0.00501727	+	0.999987i	$0.498403\pi$
$38$	18.8606	3.05959
$39$	0.291399	0.0466611
$40$	−10.6145	−1.67830
$41$	−1.20569	−0.188298	−0.0941489	−	0.995558i	$-0.530013\pi$
$41$	−1.20569	−0.188298	−0.0941489	+	0.995558i	$0.530013\pi$
$42$	−4.48047	−0.691351
$43$	10.7484	1.63911	0.819555	−	0.573000i	$-0.194220\pi$
$43$	10.7484	1.63911	0.819555	+	0.573000i	$0.194220\pi$
$44$	−3.36680	−0.507565
$45$	−5.15819	−0.768938
$46$	2.77998	0.409885
$47$	−11.4740	−1.67366	−0.836830	−	0.547462i	$-0.815594\pi$
$47$	−11.4740	−1.67366	−0.836830	+	0.547462i	$0.815594\pi$
$48$	2.01280	0.290523
$49$	−3.82965	−0.547093
$50$	−6.09993	−0.862661
$51$	1.71151	0.239659
$52$	0.996068	0.138130
$53$	9.41522	1.29328	0.646640	−	0.762795i	$-0.276174\pi$
$53$	9.41522	1.29328	0.646640	+	0.762795i	$0.276174\pi$
$54$	12.2661	1.66920
$55$	−2.55478	−0.344486
$56$	−6.86845	−0.917835
$57$	−8.43536	−1.11729
$58$	22.7518	2.98746
$59$	−5.31749	−0.692278	−0.346139	−	0.938183i	$-0.612507\pi$
$59$	−5.31749	−0.692278	−0.346139	+	0.938183i	$0.612507\pi$
$60$	10.5856	1.36660
$61$	−7.47755	−0.957402	−0.478701	−	0.877978i	$-0.658892\pi$
$61$	−7.47755	−0.957402	−0.478701	+	0.877978i	$0.658892\pi$
$62$	−3.00847	−0.382077
$63$	−3.33776	−0.420519
$64$	−11.4195	−1.42744
$65$	0.755830	0.0937491
$66$	2.33629	0.287577
$67$	−12.2619	−1.49803	−0.749015	−	0.662553i	$-0.769473\pi$
$67$	−12.2619	−1.49803	−0.749015	+	0.662553i	$0.769473\pi$
$68$	5.85033	0.709456
$69$	−1.24334	−0.149681
$70$	−11.6214	−1.38903
$71$	16.1915	1.92157	0.960787	−	0.277288i	$-0.0894355\pi$
$71$	16.1915	1.92157	0.960787	+	0.277288i	$0.0894355\pi$
$72$	7.23114	0.852198
$73$	−2.66305	−0.311687	−0.155843	−	0.987782i	$-0.549810\pi$
$73$	−2.66305	−0.311687	−0.155843	+	0.987782i	$0.549810\pi$
$74$	−0.144780	−0.0168303
$75$	2.72818	0.315024
$76$	−28.8340	−3.30749
$77$	−1.65314	−0.188393
$78$	−0.691191	−0.0782619
$79$	−2.58260	−0.290566	−0.145283	−	0.989390i	$-0.546409\pi$
$79$	−2.58260	−0.290566	−0.145283	+	0.989390i	$0.546409\pi$
$80$	5.22081	0.583704
$81$	0.137725	0.0153027
$82$	2.85988	0.315821
$83$	3.44977	0.378662	0.189331	−	0.981913i	$-0.439368\pi$
$83$	3.44977	0.378662	0.189331	+	0.981913i	$0.439368\pi$
$84$	6.84974	0.747367
$85$	4.43930	0.481510
$86$	−25.4949	−2.74918
$87$	−10.1757	−1.09095
$88$	3.58147	0.381786
$89$	−11.2417	−1.19162	−0.595809	−	0.803126i	$-0.703168\pi$
$89$	−11.2417	−1.19162	−0.595809	+	0.803126i	$0.703168\pi$
$90$	12.2351	1.28969
$91$	0.489082	0.0512698
$92$	−4.25003	−0.443096
$93$	1.34553	0.139525
$94$	27.2162	2.80713
$95$	−21.8796	−2.24480
$96$	3.41021	0.348053
$97$	0.942699	0.0957165	0.0478583	−	0.998854i	$-0.484760\pi$
$97$	0.942699	0.0957165	0.0478583	+	0.998854i	$0.484760\pi$
$98$	9.08384	0.917606
$99$	1.74044	0.174921
$100$	9.32557	0.932557
$101$	−14.2768	−1.42059	−0.710297	−	0.703902i	$-0.751439\pi$
$101$	−14.2768	−1.42059	−0.710297	+	0.703902i	$0.751439\pi$
$102$	−4.05965	−0.401965
$103$	0.616639	0.0607593	0.0303796	−	0.999538i	$-0.490328\pi$
$103$	0.616639	0.0607593	0.0303796	+	0.999538i	$0.490328\pi$
$104$	−1.05958	−0.103900
$105$	5.19767	0.507241
$106$	−22.3327	−2.16914
$107$	−18.4326	−1.78194	−0.890971	−	0.454059i	$-0.849975\pi$
$107$	−18.4326	−1.78194	−0.890971	+	0.454059i	$0.849975\pi$
$108$	−18.7524	−1.80445
$109$	−12.1077	−1.15971	−0.579856	−	0.814719i	$-0.696891\pi$
$109$	−12.1077	−1.15971	−0.579856	+	0.814719i	$0.696891\pi$
$110$	6.05987	0.577786
$111$	0.0647527	0.00614605
$112$	3.37828	0.319218
$113$	1.48805	0.139984	0.0699920	−	0.997548i	$-0.477703\pi$
$113$	1.48805	0.139984	0.0699920	+	0.997548i	$0.477703\pi$
$114$	20.0085	1.87397
$115$	−3.22498	−0.300731
$116$	−34.7829	−3.22952
$117$	−0.514908	−0.0476033
$118$	12.6130	1.16112
$119$	2.87259	0.263329
$120$	−11.2606	−1.02794
$121$	−10.1380	−0.921635
$122$	17.7366	1.60579
$123$	−1.27908	−0.115330
$124$	4.59935	0.413034
$125$	−6.68197	−0.597653
$126$	7.91710	0.705311
$127$	4.82251	0.427929	0.213964	−	0.976841i	$-0.431362\pi$
$127$	4.82251	0.427929	0.213964	+	0.976841i	$0.431362\pi$
$128$	20.6577	1.82590
$129$	11.4025	1.00394
$130$	−1.79281	−0.157240
$131$	−5.31053	−0.463983	−0.231992	−	0.972718i	$-0.574524\pi$
$131$	−5.31053	−0.463983	−0.231992	+	0.972718i	$0.574524\pi$
$132$	−3.57172	−0.310878
$133$	−14.1579	−1.22764
$134$	29.0849	2.51256
$135$	−14.2296	−1.22468
$136$	−6.22335	−0.533648
$137$	20.2409	1.72930	0.864650	−	0.502374i	$-0.167540\pi$
$137$	20.2409	1.72930	0.864650	+	0.502374i	$0.167540\pi$
$138$	2.94917	0.251050
$139$	−15.4975	−1.31448	−0.657239	−	0.753682i	$-0.728276\pi$
$139$	−15.4975	−1.31448	−0.657239	+	0.753682i	$0.728276\pi$
$140$	17.7668	1.50157
$141$	−12.1724	−1.02510
$142$	−38.4058	−3.22294
$143$	−0.255026	−0.0213264
$144$	−3.55667	−0.296389
$145$	−26.3938	−2.19188
$146$	6.31670	0.522774
$147$	−4.06273	−0.335088
$148$	0.221340	0.0181940
$149$	10.2414	0.839005	0.419502	−	0.907754i	$-0.362205\pi$
$149$	10.2414	0.839005	0.419502	+	0.907754i	$0.362205\pi$
$150$	−6.47119	−0.528370
$151$	−4.15410	−0.338056	−0.169028	−	0.985611i	$-0.554063\pi$
$151$	−4.15410	−0.338056	−0.169028	+	0.985611i	$0.554063\pi$
$152$	30.6725	2.48787
$153$	−3.02427	−0.244498
$154$	3.92122	0.315981
$155$	3.49005	0.280327
$156$	1.05669	0.0846030
$157$	12.3325	0.984240	0.492120	−	0.870527i	$-0.336222\pi$
$157$	12.3325	0.984240	0.492120	+	0.870527i	$0.336222\pi$
$158$	6.12588	0.487349
$159$	9.98825	0.792120
$160$	8.84541	0.699291
$161$	−2.08682	−0.164464
$162$	−0.326679	−0.0256664
$163$	12.5474	0.982791	0.491395	−	0.870937i	$-0.336487\pi$
$163$	12.5474	0.982791	0.491395	+	0.870937i	$0.336487\pi$
$164$	−4.37218	−0.341410
$165$	−2.71027	−0.210994
$166$	−8.18279	−0.635107
$167$	−0.447377	−0.0346191	−0.0173095	−	0.999850i	$-0.505510\pi$
$167$	−0.447377	−0.0346191	−0.0173095	+	0.999850i	$0.505510\pi$
$168$	−7.28648	−0.562164
$169$	−12.9246	−0.994196
$170$	−10.5299	−0.807609
$171$	14.9055	1.13985
$172$	38.9766	2.97193
$173$	16.6201	1.26360	0.631801	−	0.775131i	$-0.282316\pi$
$173$	16.6201	1.26360	0.631801	+	0.775131i	$0.282316\pi$
$174$	24.1366	1.82979
$175$	4.57897	0.346138
$176$	−1.76157	−0.132783
$177$	−5.64113	−0.424013
$178$	26.6651	1.99863
$179$	15.7084	1.17410	0.587050	−	0.809551i	$-0.300289\pi$
$179$	15.7084	1.17410	0.587050	+	0.809551i	$0.300289\pi$
$180$	−18.7050	−1.39419
$181$	14.7842	1.09890	0.549450	−	0.835527i	$-0.314837\pi$
$181$	14.7842	1.09890	0.549450	+	0.835527i	$0.314837\pi$
$182$	−1.16009	−0.0859918
$183$	−7.93266	−0.586399
$184$	4.52101	0.333293
$185$	0.167955	0.0123483
$186$	−3.19158	−0.234018
$187$	−1.49788	−0.109536
$188$	−41.6080	−3.03458
$189$	−9.20766	−0.669759
$190$	51.8980	3.76508
$191$	−2.16281	−0.156496	−0.0782478	−	0.996934i	$-0.524933\pi$
$191$	−2.16281	−0.156496	−0.0782478	+	0.996934i	$0.524933\pi$
$192$	−12.1146	−0.874292
$193$	8.51585	0.612984	0.306492	−	0.951873i	$-0.400845\pi$
$193$	8.51585	0.612984	0.306492	+	0.951873i	$0.400845\pi$
$194$	−2.23606	−0.160540
$195$	0.801831	0.0574203
$196$	−13.8874	−0.991954
$197$	7.51834	0.535659	0.267830	−	0.963466i	$-0.413694\pi$
$197$	7.51834	0.535659	0.267830	+	0.963466i	$0.413694\pi$
$198$	−4.12828	−0.293384
$199$	−2.78398	−0.197351	−0.0986755	−	0.995120i	$-0.531461\pi$
$199$	−2.78398	−0.197351	−0.0986755	+	0.995120i	$0.531461\pi$
$200$	−9.92017	−0.701462
$201$	−13.0082	−0.917527
$202$	33.8642	2.38268
$203$	−17.0789	−1.19870
$204$	6.20639	0.434534
$205$	−3.31767	−0.231716
$206$	−1.46265	−0.101908
$207$	2.19701	0.152703
$208$	0.521159	0.0361359
$209$	7.38246	0.510656
$210$	−12.3288	−0.850765
$211$	3.54400	0.243979	0.121990	−	0.992531i	$-0.461073\pi$
$211$	3.54400	0.243979	0.121990	+	0.992531i	$0.461073\pi$
$212$	34.1422	2.34489
$213$	17.1769	1.17694
$214$	43.7216	2.98875
$215$	29.5759	2.01706
$216$	19.9480	1.35729
$217$	2.25834	0.153306
$218$	28.7193	1.94512
$219$	−2.82513	−0.190905
$220$	−9.26432	−0.624600
$221$	0.443147	0.0298093
$222$	−0.153592	−0.0103084
$223$	−29.1949	−1.95504	−0.977518	−	0.210854i	$-0.932376\pi$
$223$	−29.1949	−1.95504	−0.977518	+	0.210854i	$0.932376\pi$
$224$	5.72369	0.382430
$225$	−4.82077	−0.321384
$226$	−3.52962	−0.234787
$227$	23.2516	1.54326	0.771632	−	0.636069i	$-0.219441\pi$
$227$	23.2516	1.54326	0.771632	+	0.636069i	$0.219441\pi$
$228$	−30.5889	−2.02580
$229$	−12.0030	−0.793182	−0.396591	−	0.917995i	$-0.629807\pi$
$229$	−12.0030	−0.793182	−0.396591	+	0.917995i	$0.629807\pi$
$230$	7.64957	0.504398
$231$	−1.75376	−0.115389
$232$	37.0007	2.42922
$233$	−20.3520	−1.33331	−0.666653	−	0.745368i	$-0.732274\pi$
$233$	−20.3520	−1.33331	−0.666653	+	0.745368i	$0.732274\pi$
$234$	1.22135	0.0798422
$235$	−31.5727	−2.05958
$236$	−19.2827	−1.25520
$237$	−2.73979	−0.177968
$238$	−6.81371	−0.441667
$239$	16.5870	1.07293	0.536463	−	0.843924i	$-0.319760\pi$
$239$	16.5870	1.07293	0.536463	+	0.843924i	$0.319760\pi$
$240$	5.53856	0.357513
$241$	−4.36927	−0.281449	−0.140725	−	0.990049i	$-0.544943\pi$
$241$	−4.36927	−0.281449	−0.140725	+	0.990049i	$0.544943\pi$
$242$	24.0471	1.54580
$243$	15.6599	1.00458
$244$	−27.1157	−1.73590
$245$	−10.5379	−0.673242
$246$	3.03394	0.193437
$247$	−2.18410	−0.138971
$248$	−4.89261	−0.310681
$249$	3.65974	0.231926
$250$	15.8495	1.00241
$251$	22.1689	1.39929	0.699643	−	0.714492i	$-0.253342\pi$
$251$	22.1689	1.39929	0.699643	+	0.714492i	$0.253342\pi$
$252$	−12.1037	−0.762458
$253$	1.08815	0.0684113
$254$	−11.4389	−0.717740
$255$	4.70949	0.294920
$256$	−26.1606	−1.63504
$257$	11.1517	0.695627	0.347813	−	0.937564i	$-0.386924\pi$
$257$	11.1517	0.695627	0.347813	+	0.937564i	$0.386924\pi$
$258$	−27.0466	−1.68385
$259$	0.108681	0.00675309
$260$	2.74085	0.169980
$261$	17.9807	1.11298
$262$	12.5965	0.778212
$263$	25.6318	1.58052	0.790261	−	0.612770i	$-0.209945\pi$
$263$	25.6318	1.58052	0.790261	+	0.612770i	$0.209945\pi$
$264$	3.79945	0.233840
$265$	25.9075	1.59149
$266$	33.5822	2.05905
$267$	−11.9259	−0.729853
$268$	−44.4650	−2.71613
$269$	−16.3535	−0.997093	−0.498546	−	0.866863i	$-0.666133\pi$
$269$	−16.3535	−0.997093	−0.498546	+	0.866863i	$0.666133\pi$
$270$	33.7522	2.05409
$271$	13.2467	0.804679	0.402339	−	0.915491i	$-0.368197\pi$
$271$	13.2467	0.804679	0.402339	+	0.915491i	$0.368197\pi$
$272$	3.06099	0.185599
$273$	0.518849	0.0314022
$274$	−48.0111	−2.90045
$275$	−2.38765	−0.143981
$276$	−4.50870	−0.271392
$277$	−29.7751	−1.78901	−0.894506	−	0.447056i	$-0.852473\pi$
$277$	−29.7751	−1.78901	−0.894506	+	0.447056i	$0.852473\pi$
$278$	36.7597	2.20470
$279$	−2.37759	−0.142343
$280$	−18.8997	−1.12947
$281$	−5.39714	−0.321966	−0.160983	−	0.986957i	$-0.551466\pi$
$281$	−5.39714	−0.321966	−0.160983	+	0.986957i	$0.551466\pi$
$282$	28.8726	1.71934
$283$	18.9195	1.12465	0.562324	−	0.826917i	$-0.309907\pi$
$283$	18.9195	1.12465	0.562324	+	0.826917i	$0.309907\pi$
$284$	58.7147	3.48408
$285$	−23.2113	−1.37492
$286$	0.604917	0.0357695
$287$	−2.14680	−0.126721
$288$	−6.02593	−0.355081
$289$	−14.3972	−0.846895
$290$	62.6054	3.67632
$291$	1.00007	0.0586254
$292$	−9.65696	−0.565131
$293$	−9.55818	−0.558395	−0.279198	−	0.960234i	$-0.590068\pi$
$293$	−9.55818	−0.558395	−0.279198	+	0.960234i	$0.590068\pi$
$294$	9.63670	0.562024
$295$	−14.6320	−0.851906
$296$	−0.235452	−0.0136854
$297$	4.80123	0.278596
$298$	−24.2923	−1.40721
$299$	−0.321928	−0.0186176
$300$	9.89315	0.571181
$301$	19.1380	1.10310
$302$	9.85344	0.567002
$303$	−15.1457	−0.870099
$304$	−15.0864	−0.865266
$305$	−20.5757	−1.17816
$306$	7.17350	0.410082
$307$	−22.1153	−1.26218	−0.631092	−	0.775708i	$-0.717393\pi$
$307$	−22.1153	−1.26218	−0.631092	+	0.775708i	$0.717393\pi$
$308$	−5.99476	−0.341583
$309$	0.654170	0.0372144
$310$	−8.27832	−0.470177
$311$	3.25543	0.184599	0.0922993	−	0.995731i	$-0.470578\pi$
$311$	3.25543	0.184599	0.0922993	+	0.995731i	$0.470578\pi$
$312$	−1.12407	−0.0636378
$313$	−3.43022	−0.193888	−0.0969439	−	0.995290i	$-0.530907\pi$
$313$	−3.43022	−0.193888	−0.0969439	+	0.995290i	$0.530907\pi$
$314$	−29.2524	−1.65081
$315$	−9.18441	−0.517483
$316$	−9.36524	−0.526836
$317$	1.74273	0.0978814	0.0489407	−	0.998802i	$-0.484415\pi$
$317$	1.74273	0.0978814	0.0489407	+	0.998802i	$0.484415\pi$
$318$	−23.6919	−1.32858
$319$	8.90559	0.498617
$320$	−31.4227	−1.75658
$321$	−19.5544	−1.09142
$322$	4.94989	0.275846
$323$	−12.8281	−0.713776
$324$	0.499427	0.0277460
$325$	0.706387	0.0391833
$326$	−29.7622	−1.64838
$327$	−12.8447	−0.710311
$328$	4.65096	0.256806
$329$	−20.4301	−1.12635
$330$	6.42869	0.353888
$331$	−29.7765	−1.63666	−0.818332	−	0.574745i	$-0.805101\pi$
$331$	−29.7765	−1.63666	−0.818332	+	0.574745i	$0.805101\pi$
$332$	12.5098	0.686566
$333$	−0.114420	−0.00627015
$334$	1.06117	0.0580645
$335$	−33.7406	−1.84345
$336$	3.58389	0.195517
$337$	−20.1527	−1.09779	−0.548893	−	0.835893i	$-0.684951\pi$
$337$	−20.1527	−1.09779	−0.548893	+	0.835893i	$0.684951\pi$
$338$	30.6567	1.66751
$339$	1.57862	0.0857387
$340$	16.0981	0.873044
$341$	−1.17759	−0.0637699
$342$	−35.3555	−1.91180
$343$	−19.2827	−1.04117
$344$	−41.4617	−2.23547
$345$	−3.42126	−0.184194
$346$	−39.4224	−2.11936
$347$	23.4396	1.25831	0.629153	−	0.777282i	$-0.283402\pi$
$347$	23.4396	1.25831	0.629153	+	0.777282i	$0.283402\pi$
$348$	−36.8999	−1.97804
$349$	2.11237	0.113073	0.0565363	−	0.998401i	$-0.481994\pi$
$349$	2.11237	0.113073	0.0565363	+	0.998401i	$0.481994\pi$
$350$	−10.8612	−0.580557
$351$	−1.42044	−0.0758176
$352$	−2.98455	−0.159077
$353$	24.1933	1.28768	0.643839	−	0.765161i	$-0.277341\pi$
$353$	24.1933	1.28768	0.643839	+	0.765161i	$0.277341\pi$
$354$	13.3806	0.711172
$355$	44.5535	2.36466
$356$	−40.7655	−2.16057
$357$	3.04742	0.161286
$358$	−37.2599	−1.96925
$359$	−4.37065	−0.230674	−0.115337	−	0.993326i	$-0.536795\pi$
$359$	−4.37065	−0.230674	−0.115337	+	0.993326i	$0.536795\pi$
$360$	19.8977	1.04870
$361$	44.2250	2.32763
$362$	−35.0678	−1.84312
$363$	−10.7550	−0.564492
$364$	1.77355	0.0929592
$365$	−7.32783	−0.383556
$366$	18.8161	0.983532
$367$	16.2536	0.848431	0.424216	−	0.905561i	$-0.360550\pi$
$367$	16.2536	0.848431	0.424216	+	0.905561i	$0.360550\pi$
$368$	−2.22368	−0.115917
$369$	2.26016	0.117659
$370$	−0.398387	−0.0207111
$371$	16.7643	0.870357
$372$	4.87928	0.252979
$373$	10.8715	0.562905	0.281452	−	0.959575i	$-0.409184\pi$
$373$	10.8715	0.562905	0.281452	+	0.959575i	$0.409184\pi$
$374$	3.55293	0.183718
$375$	−7.08865	−0.366056
$376$	44.2610	2.28259
$377$	−2.63472	−0.135695
$378$	21.8404	1.12335
$379$	35.2353	1.80992	0.904959	−	0.425499i	$-0.139901\pi$
$379$	35.2353	1.80992	0.904959	+	0.425499i	$0.139901\pi$
$380$	−79.3416	−4.07014
$381$	5.11602	0.262102
$382$	5.13014	0.262481
$383$	4.38853	0.224244	0.112122	−	0.993694i	$-0.464235\pi$
$383$	4.38853	0.224244	0.112122	+	0.993694i	$0.464235\pi$
$384$	21.9150	1.11835
$385$	−4.54890	−0.231833
$386$	−20.1994	−1.02812
$387$	−20.1486	−1.02421
$388$	3.41849	0.173547
$389$	−26.7997	−1.35880	−0.679399	−	0.733769i	$-0.737760\pi$
$389$	−26.7997	−1.35880	−0.679399	+	0.733769i	$0.737760\pi$
$390$	−1.90193	−0.0963078
$391$	−1.89082	−0.0956228
$392$	14.7728	0.746140
$393$	−5.63374	−0.284185
$394$	−17.8333	−0.898430
$395$	−7.10646	−0.357565
$396$	6.31131	0.317155
$397$	8.27675	0.415398	0.207699	−	0.978193i	$-0.433403\pi$
$397$	8.27675	0.415398	0.207699	+	0.978193i	$0.433403\pi$
$398$	6.60353	0.331005
$399$	−15.0196	−0.751919
$400$	4.87929	0.243964
$401$	−19.3558	−0.966584	−0.483292	−	0.875459i	$-0.660559\pi$
$401$	−19.3558	−0.966584	−0.483292	+	0.875459i	$0.660559\pi$
$402$	30.8551	1.53891
$403$	0.348389	0.0173545
$404$	−51.7716	−2.57573
$405$	0.378972	0.0188313
$406$	40.5107	2.01051
$407$	−0.0566703	−0.00280904
$408$	−6.60212	−0.326853
$409$	−7.85318	−0.388315	−0.194157	−	0.980970i	$-0.562197\pi$
$409$	−7.85318	−0.388315	−0.194157	+	0.980970i	$0.562197\pi$
$410$	7.86944	0.388644
$411$	21.4729	1.05918
$412$	2.23610	0.110165
$413$	−9.46805	−0.465892
$414$	−5.21126	−0.256120
$415$	9.49263	0.465975
$416$	0.882979	0.0432916
$417$	−16.4407	−0.805104
$418$	−17.5110	−0.856493
$419$	33.6026	1.64159	0.820797	−	0.571220i	$-0.193530\pi$
$419$	33.6026	1.64159	0.820797	+	0.571220i	$0.193530\pi$
$420$	18.8482	0.919697
$421$	18.9360	0.922882	0.461441	−	0.887171i	$-0.347333\pi$
$421$	18.9360	0.922882	0.461441	+	0.887171i	$0.347333\pi$
$422$	−8.40629	−0.409212
$423$	21.5089	1.04580
$424$	−36.3191	−1.76381
$425$	4.14891	0.201251
$426$	−40.7433	−1.97402
$427$	−13.3141	−0.644316
$428$	−66.8416	−3.23091
$429$	−0.270548	−0.0130622
$430$	−70.1534	−3.38310
$431$	−14.1153	−0.679911	−0.339956	−	0.940441i	$-0.610412\pi$
$431$	−14.1153	−0.679911	−0.339956	+	0.940441i	$0.610412\pi$
$432$	−9.81155	−0.472058
$433$	15.7197	0.755439	0.377720	−	0.925920i	$-0.376708\pi$
$433$	15.7197	0.755439	0.377720	+	0.925920i	$0.376708\pi$
$434$	−5.35673	−0.257131
$435$	−28.0002	−1.34250
$436$	−43.9060	−2.10272
$437$	9.31913	0.445794
$438$	6.70115	0.320193
$439$	16.4489	0.785064	0.392532	−	0.919738i	$-0.371599\pi$
$439$	16.4489	0.785064	0.392532	+	0.919738i	$0.371599\pi$
$440$	9.85502	0.469820
$441$	7.17894	0.341854
$442$	−1.05113	−0.0499973
$443$	−21.2134	−1.00788	−0.503940	−	0.863738i	$-0.668117\pi$
$443$	−21.2134	−1.00788	−0.503940	+	0.863738i	$0.668117\pi$
$444$	0.234811	0.0111436
$445$	−30.9334	−1.46638
$446$	69.2496	3.27907
$447$	10.8647	0.513882
$448$	−20.3330	−0.960645
$449$	15.9824	0.754255	0.377127	−	0.926161i	$-0.376912\pi$
$449$	15.9824	0.754255	0.377127	+	0.926161i	$0.376912\pi$
$450$	11.4347	0.539039
$451$	1.11942	0.0527116
$452$	5.39608	0.253810
$453$	−4.40693	−0.207056
$454$	−55.1523	−2.58843
$455$	1.34579	0.0630917
$456$	32.5393	1.52379
$457$	−17.3437	−0.811304	−0.405652	−	0.914028i	$-0.632956\pi$
$457$	−17.3437	−0.811304	−0.405652	+	0.914028i	$0.632956\pi$
$458$	28.4709	1.33036
$459$	−8.34285	−0.389411
$460$	−11.6947	−0.545266
$461$	20.3795	0.949167	0.474584	−	0.880210i	$-0.342599\pi$
$461$	20.3795	0.949167	0.474584	+	0.880210i	$0.342599\pi$
$462$	4.15988	0.193535
$463$	−17.3638	−0.806966	−0.403483	−	0.914987i	$-0.632201\pi$
$463$	−17.3638	−0.806966	−0.403483	+	0.914987i	$0.632201\pi$
$464$	−18.1990	−0.844867
$465$	3.70246	0.171698
$466$	48.2745	2.23627
$467$	−10.4241	−0.482371	−0.241185	−	0.970479i	$-0.577536\pi$
$467$	−10.4241	−0.482371	−0.241185	+	0.970479i	$0.577536\pi$
$468$	−1.86720	−0.0863113
$469$	−21.8329	−1.00815
$470$	74.8898	3.45441
$471$	13.0831	0.602837
$472$	20.5122	0.944149
$473$	−9.97929	−0.458848
$474$	6.49872	0.298496
$475$	−20.4484	−0.938236
$476$	10.4168	0.477453
$477$	−17.6495	−0.808115
$478$	−39.3440	−1.79955
$479$	−33.9845	−1.55279	−0.776395	−	0.630247i	$-0.782954\pi$
$479$	−33.9845	−1.55279	−0.776395	+	0.630247i	$0.782954\pi$
$480$	9.38376	0.428308
$481$	0.0167659	0.000764459 0
$482$	10.3638	0.472059
$483$	−2.21383	−0.100733
$484$	−36.7631	−1.67105
$485$	2.59399	0.117787
$486$	−37.1448	−1.68492
$487$	−26.6363	−1.20701	−0.603504	−	0.797360i	$-0.706229\pi$
$487$	−26.6363	−1.20701	−0.603504	+	0.797360i	$0.706229\pi$
$488$	28.8446	1.30573
$489$	13.3111	0.601949
$490$	24.9957	1.12919
$491$	35.4972	1.60197	0.800984	−	0.598686i	$-0.204310\pi$
$491$	35.4972	1.60197	0.800984	+	0.598686i	$0.204310\pi$
$492$	−4.63828	−0.209110
$493$	−15.4748	−0.696949
$494$	5.18064	0.233088
$495$	4.78911	0.215254
$496$	2.40646	0.108053
$497$	28.8297	1.29319
$498$	−8.68081	−0.388997
$499$	−5.59753	−0.250580	−0.125290	−	0.992120i	$-0.539986\pi$
$499$	−5.59753	−0.250580	−0.125290	+	0.992120i	$0.539986\pi$
$500$	−24.2307	−1.08363
$501$	−0.474605	−0.0212038
$502$	−52.5841	−2.34694
$503$	−5.00451	−0.223140	−0.111570	−	0.993757i	$-0.535588\pi$
$503$	−5.00451	−0.223140	−0.111570	+	0.993757i	$0.535588\pi$
$504$	12.8754	0.573515
$505$	−39.2850	−1.74816
$506$	−2.58106	−0.114742
$507$	−13.7112	−0.608935
$508$	17.4878	0.775894
$509$	23.9450	1.06134	0.530671	−	0.847578i	$-0.321940\pi$
$509$	23.9450	1.06134	0.530671	+	0.847578i	$0.321940\pi$
$510$	−11.1708	−0.494652
$511$	−4.74169	−0.209760
$512$	20.7369	0.916451
$513$	41.1187	1.81544
$514$	−26.4517	−1.16673
$515$	1.69679	0.0747693
$516$	41.3488	1.82028
$517$	10.6530	0.468520
$518$	−0.257788	−0.0113266
$519$	17.6316	0.773942
$520$	−2.91561	−0.127858
$521$	−21.0755	−0.923336	−0.461668	−	0.887053i	$-0.652749\pi$
$521$	−21.0755	−0.923336	−0.461668	+	0.887053i	$0.652749\pi$
$522$	−42.6499	−1.86673
$523$	−34.8043	−1.52188	−0.760942	−	0.648820i	$-0.775263\pi$
$523$	−34.8043	−1.52188	−0.760942	+	0.648820i	$0.775263\pi$
$524$	−19.2574	−0.841266
$525$	4.85766	0.212006
$526$	−60.7980	−2.65092
$527$	2.04623	0.0891353
$528$	−1.86878	−0.0813282
$529$	−21.6264	−0.940278
$530$	−61.4521	−2.66931
$531$	9.96801	0.432575
$532$	−51.3404	−2.22589
$533$	−0.331181	−0.0143450
$534$	28.2880	1.22414
$535$	−50.7202	−2.19283
$536$	47.3002	2.04306
$537$	16.6644	0.719124
$538$	38.7902	1.67236
$539$	3.55562	0.153152
$540$	−51.6003	−2.22052
$541$	−41.9037	−1.80158	−0.900791	−	0.434254i	$-0.857012\pi$
$541$	−41.9037	−1.80158	−0.900791	+	0.434254i	$0.857012\pi$
$542$	−31.4208	−1.34964
$543$	15.6840	0.673065
$544$	5.18611	0.222352
$545$	−33.3165	−1.42712
$546$	−1.23070	−0.0526690
$547$	11.5202	0.492569	0.246285	−	0.969198i	$-0.420790\pi$
$547$	11.5202	0.492569	0.246285	+	0.969198i	$0.420790\pi$
$548$	73.3992	3.13546
$549$	14.0172	0.598239
$550$	5.66346	0.241491
$551$	76.2693	3.24918
$552$	4.79617	0.204139
$553$	−4.59845	−0.195546
$554$	70.6259	3.00060
$555$	0.178178	0.00756322
$556$	−56.1981	−2.38333
$557$	−4.63438	−0.196365	−0.0981826	−	0.995168i	$-0.531303\pi$
$557$	−4.63438	−0.196365	−0.0981826	+	0.995168i	$0.531303\pi$
$558$	5.63960	0.238743
$559$	2.95237	0.124872
$560$	9.29590	0.392824
$561$	−1.58904	−0.0670894
$562$	12.8019	0.540015
$563$	−40.8567	−1.72191	−0.860953	−	0.508685i	$-0.830132\pi$
$563$	−40.8567	−1.72191	−0.860953	+	0.508685i	$0.830132\pi$
$564$	−44.1404	−1.85865
$565$	4.09462	0.172262
$566$	−44.8766	−1.88631
$567$	0.245225	0.0102985
$568$	−62.4584	−2.62070
$569$	−31.8050	−1.33334	−0.666668	−	0.745355i	$-0.732280\pi$
$569$	−31.8050	−1.33334	−0.666668	+	0.745355i	$0.732280\pi$
$570$	55.0566	2.30607
$571$	−35.2861	−1.47668	−0.738338	−	0.674431i	$-0.764389\pi$
$571$	−35.2861	−1.47668	−0.738338	+	0.674431i	$0.764389\pi$
$572$	−0.924796	−0.0386677
$573$	−2.29445	−0.0958518
$574$	5.09216	0.212542
$575$	−3.01401	−0.125693
$576$	21.4067	0.891946
$577$	38.8359	1.61676	0.808379	−	0.588663i	$-0.200345\pi$
$577$	38.8359	1.61676	0.808379	+	0.588663i	$0.200345\pi$
$578$	34.1499	1.42045
$579$	9.03415	0.375446
$580$	−95.7111	−3.97419
$581$	6.14249	0.254833
$582$	−2.37215	−0.0983289
$583$	−8.74153	−0.362037
$584$	10.2727	0.425087
$585$	−1.41686	−0.0585798
$586$	22.6718	0.936563
$587$	−13.1307	−0.541963	−0.270982	−	0.962585i	$-0.587348\pi$
$587$	−13.1307	−0.541963	−0.270982	+	0.962585i	$0.587348\pi$
$588$	−14.7326	−0.607561
$589$	−10.0851	−0.415549
$590$	34.7067	1.42885
$591$	7.97592	0.328086
$592$	0.115809	0.00475970
$593$	−29.0930	−1.19471	−0.597353	−	0.801978i	$-0.703781\pi$
$593$	−29.0930	−1.19471	−0.597353	+	0.801978i	$0.703781\pi$
$594$	−11.3884	−0.467272
$595$	7.90439	0.324049
$596$	37.1380	1.52123
$597$	−2.95342	−0.120875
$598$	0.763606	0.0312262
$599$	−6.13200	−0.250547	−0.125273	−	0.992122i	$-0.539981\pi$
$599$	−6.13200	−0.250547	−0.125273	+	0.992122i	$0.539981\pi$
$600$	−10.5239	−0.429638
$601$	34.3762	1.40224	0.701118	−	0.713046i	$-0.252685\pi$
$601$	34.3762	1.40224	0.701118	+	0.713046i	$0.252685\pi$
$602$	−45.3949	−1.85016
$603$	22.9858	0.936054
$604$	−15.0639	−0.612942
$605$	−27.8964	−1.13415
$606$	35.9253	1.45937
$607$	−38.6864	−1.57023	−0.785116	−	0.619349i	$-0.787397\pi$
$607$	−38.6864	−1.57023	−0.785116	+	0.619349i	$0.787397\pi$
$608$	−25.5603	−1.03661
$609$	−18.1183	−0.734192
$610$	48.8051	1.97606
$611$	−3.15170	−0.127504
$612$	−10.9668	−0.443308
$613$	−12.4308	−0.502077	−0.251039	−	0.967977i	$-0.580772\pi$
$613$	−12.4308	−0.502077	−0.251039	+	0.967977i	$0.580772\pi$
$614$	52.4569	2.11699
$615$	−3.51959	−0.141924
$616$	6.37699	0.256936
$617$	22.4610	0.904244	0.452122	−	0.891956i	$-0.350667\pi$
$617$	22.4610	0.904244	0.452122	+	0.891956i	$0.350667\pi$
$618$	−1.55168	−0.0624176
$619$	14.6684	0.589575	0.294787	−	0.955563i	$-0.404751\pi$
$619$	14.6684	0.589575	0.294787	+	0.955563i	$0.404751\pi$
$620$	12.6559	0.508272
$621$	6.06075	0.243210
$622$	−7.72181	−0.309616
$623$	−20.0164	−0.801940
$624$	0.552878	0.0221328
$625$	−31.2449	−1.24979
$626$	8.13641	0.325197
$627$	7.83178	0.312771
$628$	44.7210	1.78456
$629$	0.0984731	0.00392638
$630$	21.7852	0.867943
$631$	−42.5097	−1.69228	−0.846142	−	0.532958i	$-0.821081\pi$
$631$	−42.5097	−1.69228	−0.846142	+	0.532958i	$0.821081\pi$
$632$	9.96237	0.396282
$633$	3.75970	0.149435
$634$	−4.13371	−0.164171
$635$	13.2699	0.526602
$636$	36.2202	1.43622
$637$	−1.05193	−0.0416790
$638$	−21.1238	−0.836301
$639$	−30.3520	−1.20071
$640$	56.8432	2.24692
$641$	40.6171	1.60428	0.802140	−	0.597136i	$-0.203695\pi$
$641$	40.6171	1.60428	0.802140	+	0.597136i	$0.203695\pi$
$642$	46.3826	1.83058
$643$	12.1274	0.478260	0.239130	−	0.970988i	$-0.423138\pi$
$643$	12.1274	0.478260	0.239130	+	0.970988i	$0.423138\pi$
$644$	−7.56738	−0.298196
$645$	31.3760	1.23543
$646$	30.4280	1.19718
$647$	−12.4708	−0.490278	−0.245139	−	0.969488i	$-0.578834\pi$
$647$	−12.4708	−0.490278	−0.245139	+	0.969488i	$0.578834\pi$
$648$	−0.531271	−0.0208703
$649$	4.93701	0.193794
$650$	−1.67553	−0.0657198
$651$	2.39579	0.0938984
$652$	45.5004	1.78194
$653$	−10.2829	−0.402402	−0.201201	−	0.979550i	$-0.564484\pi$
$653$	−10.2829	−0.402402	−0.201201	+	0.979550i	$0.564484\pi$
$654$	30.4672	1.19136
$655$	−14.6128	−0.570970
$656$	−2.28760	−0.0893156
$657$	4.99208	0.194760
$658$	48.4597	1.88916
$659$	37.1571	1.44743	0.723717	−	0.690097i	$-0.242432\pi$
$659$	37.1571	1.44743	0.723717	+	0.690097i	$0.242432\pi$
$660$	−9.82817	−0.382561
$661$	−42.0846	−1.63690	−0.818450	−	0.574578i	$-0.805166\pi$
$661$	−42.0846	−1.63690	−0.818450	+	0.574578i	$0.805166\pi$
$662$	70.6292	2.74508
$663$	0.470118	0.0182579
$664$	−13.3075	−0.516430
$665$	−38.9577	−1.51072
$666$	0.271401	0.0105166
$667$	11.2418	0.435285
$668$	−1.62231	−0.0627691
$669$	−30.9718	−1.19744
$670$	80.0320	3.09191
$671$	6.94251	0.268013
$672$	6.07205	0.234234
$673$	−40.7528	−1.57090	−0.785452	−	0.618922i	$-0.787570\pi$
$673$	−40.7528	−1.57090	−0.785452	+	0.618922i	$0.787570\pi$
$674$	47.8017	1.84125
$675$	−13.2987	−0.511868
$676$	−46.8680	−1.80261
$677$	4.94661	0.190114	0.0950568	−	0.995472i	$-0.469697\pi$
$677$	4.94661	0.190114	0.0950568	+	0.995472i	$0.469697\pi$
$678$	−3.74444	−0.143805
$679$	1.67852	0.0644157
$680$	−17.1246	−0.656697
$681$	24.6668	0.945233
$682$	2.79321	0.106957
$683$	−26.9424	−1.03092	−0.515462	−	0.856913i	$-0.672380\pi$
$683$	−26.9424	−1.03092	−0.515462	+	0.856913i	$0.672380\pi$
$684$	54.0514	2.06671
$685$	55.6963	2.12805
$686$	45.7382	1.74629
$687$	−12.7336	−0.485816
$688$	20.3932	0.777482
$689$	2.58618	0.0985256
$690$	8.11514	0.308938
$691$	45.1013	1.71573	0.857867	−	0.513873i	$-0.171790\pi$
$691$	45.1013	1.71573	0.857867	+	0.513873i	$0.171790\pi$
$692$	60.2690	2.29108
$693$	3.09894	0.117719
$694$	−55.5983	−2.11048
$695$	−42.6439	−1.61757
$696$	39.2527	1.48787
$697$	−1.94517	−0.0736784
$698$	−5.01050	−0.189650
$699$	−21.5907	−0.816635
$700$	16.6046	0.627596
$701$	49.3381	1.86348	0.931738	−	0.363133i	$-0.118293\pi$
$701$	49.3381	1.86348	0.931738	+	0.363133i	$0.118293\pi$
$702$	3.36926	0.127164
$703$	−0.485336	−0.0183048
$704$	10.6024	0.399594
$705$	−33.4943	−1.26147
$706$	−57.3859	−2.15975
$707$	−25.4205	−0.956037
$708$	−20.4563	−0.768794
$709$	−10.6945	−0.401640	−0.200820	−	0.979628i	$-0.564361\pi$
$709$	−10.6945	−0.401640	−0.200820	+	0.979628i	$0.564361\pi$
$710$	−105.680	−3.96610
$711$	4.84127	0.181562
$712$	43.3647	1.62516
$713$	−1.48651	−0.0556701
$714$	−7.22841	−0.270516
$715$	−0.701748	−0.0262439
$716$	56.9630	2.12881
$717$	17.5966	0.657155
$718$	10.3671	0.386896
$719$	−11.0211	−0.411019	−0.205510	−	0.978655i	$-0.565885\pi$
$719$	−11.0211	−0.411019	−0.205510	+	0.978655i	$0.565885\pi$
$720$	−9.78677	−0.364731
$721$	1.09796	0.0408900
$722$	−104.901	−3.90400
$723$	−4.63520	−0.172385
$724$	53.6116	1.99246
$725$	−24.6672	−0.916117
$726$	25.5106	0.946789
$727$	6.00254	0.222622	0.111311	−	0.993786i	$-0.464495\pi$
$727$	6.00254	0.222622	0.111311	+	0.993786i	$0.464495\pi$
$728$	−1.88663	−0.0699232
$729$	16.1998	0.599992
$730$	17.3814	0.643316
$731$	17.3405	0.641362
$732$	−28.7660	−1.06322
$733$	−28.3259	−1.04624	−0.523120	−	0.852259i	$-0.675232\pi$
$733$	−28.3259	−1.04624	−0.523120	+	0.852259i	$0.675232\pi$
$734$	−38.5532	−1.42302
$735$	−11.1793	−0.412354
$736$	−3.76750	−0.138872
$737$	11.3845	0.419354
$738$	−5.36105	−0.197343
$739$	36.8596	1.35590	0.677951	−	0.735107i	$-0.262868\pi$
$739$	36.8596	1.35590	0.677951	+	0.735107i	$0.262868\pi$
$740$	0.609053	0.0223892
$741$	−2.31703	−0.0851182
$742$	−39.7644	−1.45980
$743$	6.63581	0.243444	0.121722	−	0.992564i	$-0.461158\pi$
$743$	6.63581	0.243444	0.121722	+	0.992564i	$0.461158\pi$
$744$	−5.19039	−0.190289
$745$	28.1808	1.03246
$746$	−25.7869	−0.944127
$747$	−6.46685	−0.236609
$748$	−5.43172	−0.198603
$749$	−32.8201	−1.19922
$750$	16.8141	0.613965
$751$	−10.4902	−0.382795	−0.191397	−	0.981513i	$-0.561302\pi$
$751$	−10.4902	−0.382795	−0.191397	+	0.981513i	$0.561302\pi$
$752$	−21.7700	−0.793870
$753$	23.5181	0.857048
$754$	6.24949	0.227593
$755$	−11.4307	−0.416006
$756$	−33.3895	−1.21437
$757$	35.0830	1.27511	0.637557	−	0.770403i	$-0.279945\pi$
$757$	35.0830	1.27511	0.637557	+	0.770403i	$0.279945\pi$
$758$	−83.5774	−3.03567
$759$	1.15438	0.0419012
$760$	84.4005	3.06153
$761$	43.0733	1.56141	0.780704	−	0.624901i	$-0.214861\pi$
$761$	43.0733	1.56141	0.780704	+	0.624901i	$0.214861\pi$
$762$	−12.1351	−0.439608
$763$	−21.5584	−0.780468
$764$	−7.84295	−0.283748
$765$	−8.32179	−0.300875
$766$	−10.4095	−0.376111
$767$	−1.46061	−0.0527397
$768$	−27.7528	−1.00144
$769$	38.3731	1.38377	0.691884	−	0.722009i	$-0.256781\pi$
$769$	38.3731	1.38377	0.691884	+	0.722009i	$0.256781\pi$
$770$	10.7899	0.388841
$771$	11.8305	0.426064
$772$	30.8808	1.11143
$773$	−12.4723	−0.448598	−0.224299	−	0.974520i	$-0.572009\pi$
$773$	−12.4723	−0.448598	−0.224299	+	0.974520i	$0.572009\pi$
$774$	47.7920	1.71785
$775$	3.26175	0.117165
$776$	−3.63645	−0.130541
$777$	0.115295	0.00413619
$778$	63.5683	2.27903
$779$	9.58698	0.343489
$780$	2.90766	0.104111
$781$	−15.0329	−0.537920
$782$	4.48498	0.160383
$783$	49.6022	1.77264
$784$	−7.26609	−0.259503
$785$	33.9349	1.21119
$786$	13.3631	0.476646
$787$	36.9367	1.31665	0.658326	−	0.752733i	$-0.271265\pi$
$787$	36.9367	1.31665	0.658326	+	0.752733i	$0.271265\pi$
$788$	27.2636	0.971224
$789$	27.1918	0.968053
$790$	16.8564	0.599723
$791$	2.64955	0.0942070
$792$	−6.71373	−0.238562
$793$	−2.05394	−0.0729375
$794$	−19.6323	−0.696723
$795$	27.4843	0.974769
$796$	−10.0955	−0.357825
$797$	50.8525	1.80129	0.900644	−	0.434557i	$-0.143095\pi$
$797$	50.8525	1.80129	0.900644	+	0.434557i	$0.143095\pi$
$798$	35.6261	1.26115
$799$	−18.5112	−0.654881
$800$	8.26678	0.292275
$801$	21.0734	0.744590
$802$	45.9116	1.62119
$803$	2.47250	0.0872527
$804$	−47.1713	−1.66360
$805$	−5.74223	−0.202387
$806$	−0.826370	−0.0291076
$807$	−17.3489	−0.610709
$808$	55.0726	1.93745
$809$	39.8269	1.40024	0.700120	−	0.714026i	$-0.253130\pi$
$809$	39.8269	1.40024	0.700120	+	0.714026i	$0.253130\pi$
$810$	−0.898913	−0.0315846
$811$	−20.6010	−0.723401	−0.361700	−	0.932294i	$-0.617804\pi$
$811$	−20.6010	−0.723401	−0.361700	+	0.932294i	$0.617804\pi$
$812$	−61.9327	−2.17341
$813$	14.0529	0.492857
$814$	0.134421	0.00471144
$815$	34.5263	1.20940
$816$	3.24729	0.113678
$817$	−85.4647	−2.99003
$818$	18.6276	0.651298
$819$	−0.916819	−0.0320363
$820$	−12.0308	−0.420133
$821$	−22.0460	−0.769409	−0.384705	−	0.923040i	$-0.625697\pi$
$821$	−22.0460	−0.769409	−0.384705	+	0.923040i	$0.625697\pi$
$822$	−50.9331	−1.77650
$823$	30.0411	1.04717	0.523583	−	0.851975i	$-0.324595\pi$
$823$	30.0411	1.04717	0.523583	+	0.851975i	$0.324595\pi$
$824$	−2.37868	−0.0828653
$825$	−2.53297	−0.0881868
$826$	22.4580	0.781414
$827$	−2.00976	−0.0698862	−0.0349431	−	0.999389i	$-0.511125\pi$
$827$	−2.00976	−0.0698862	−0.0349431	+	0.999389i	$0.511125\pi$
$828$	7.96697	0.276872
$829$	−30.3566	−1.05433	−0.527163	−	0.849764i	$-0.676744\pi$
$829$	−30.3566	−1.05433	−0.527163	+	0.849764i	$0.676744\pi$
$830$	−22.5163	−0.781552
$831$	−31.5873	−1.09575
$832$	−3.13672	−0.108746
$833$	−6.17843	−0.214070
$834$	38.9970	1.35035
$835$	−1.23103	−0.0426016
$836$	26.7709	0.925889
$837$	−6.55890	−0.226709
$838$	−79.7046	−2.75335
$839$	−37.7547	−1.30344	−0.651719	−	0.758460i	$-0.725952\pi$
$839$	−37.7547	−1.30344	−0.651719	+	0.758460i	$0.725952\pi$
$840$	−20.0500	−0.691789
$841$	63.0049	2.17258
$842$	−44.9157	−1.54790
$843$	−5.72562	−0.197201
$844$	12.8515	0.442368
$845$	−35.5640	−1.22344
$846$	−51.0186	−1.75406
$847$	−18.0512	−0.620246
$848$	17.8637	0.613443
$849$	20.0710	0.688835
$850$	−9.84111	−0.337547
$851$	−0.0715368	−0.00245225
$852$	62.2883	2.13396
$853$	−11.7867	−0.403569	−0.201785	−	0.979430i	$-0.564674\pi$
$853$	−11.7867	−0.403569	−0.201785	+	0.979430i	$0.564674\pi$
$854$	31.5808	1.08067
$855$	41.0149	1.40268
$856$	71.1034	2.43026
$857$	−43.7306	−1.49381	−0.746904	−	0.664932i	$-0.768460\pi$
$857$	−43.7306	−1.49381	−0.746904	+	0.664932i	$0.768460\pi$
$858$	0.641734	0.0219084
$859$	34.1861	1.16641	0.583207	−	0.812323i	$-0.301798\pi$
$859$	34.1861	1.16641	0.583207	+	0.812323i	$0.301798\pi$
$860$	107.250	3.65721
$861$	−2.27746	−0.0776155
$862$	33.4812	1.14038
$863$	−24.4079	−0.830855	−0.415427	−	0.909626i	$-0.636368\pi$
$863$	−24.4079	−0.830855	−0.415427	+	0.909626i	$0.636368\pi$
$864$	−16.6233	−0.565537
$865$	45.7329	1.55497
$866$	−37.2867	−1.26705
$867$	−15.2735	−0.518714
$868$	8.18937	0.277965
$869$	2.39781	0.0813401
$870$	66.4157	2.25170
$871$	−3.36811	−0.114124
$872$	46.7055	1.58165
$873$	−1.76715	−0.0598091
$874$	−22.1048	−0.747704
$875$	−11.8976	−0.402211
$876$	−10.2447	−0.346137
$877$	22.0781	0.745524	0.372762	−	0.927927i	$-0.378411\pi$
$877$	22.0781	0.745524	0.372762	+	0.927927i	$0.378411\pi$
$878$	−39.0165	−1.31674
$879$	−10.1399	−0.342011
$880$	−4.84724	−0.163401
$881$	−32.0825	−1.08089	−0.540444	−	0.841380i	$-0.681744\pi$
$881$	−32.0825	−1.08089	−0.540444	+	0.841380i	$0.681744\pi$
$882$	−17.0283	−0.573372
$883$	45.4919	1.53093	0.765463	−	0.643480i	$-0.222510\pi$
$883$	45.4919	1.53093	0.765463	+	0.643480i	$0.222510\pi$
$884$	1.60697	0.0540483
$885$	−15.5225	−0.521783
$886$	50.3178	1.69046
$887$	−17.9109	−0.601390	−0.300695	−	0.953720i	$-0.597219\pi$
$887$	−17.9109	−0.601390	−0.300695	+	0.953720i	$0.597219\pi$
$888$	−0.249783	−0.00838216
$889$	8.58672	0.287989
$890$	73.3733	2.45948
$891$	−0.127870	−0.00428380
$892$	−105.869	−3.54475
$893$	91.2348	3.05306
$894$	−25.7708	−0.861903
$895$	43.2242	1.44483
$896$	36.7821	1.22880
$897$	−0.341522	−0.0114031
$898$	−37.9098	−1.26507
$899$	−12.1658	−0.405753
$900$	−17.4814	−0.582714
$901$	15.1897	0.506043
$902$	−2.65525	−0.0884100
$903$	20.3028	0.675634
$904$	−5.74014	−0.190914
$905$	40.6812	1.35229
$906$	10.4531	0.347282
$907$	25.4200	0.844057	0.422028	−	0.906583i	$-0.361318\pi$
$907$	25.4200	0.844057	0.422028	+	0.906583i	$0.361318\pi$
$908$	84.3168	2.79815
$909$	26.7629	0.887668
$910$	−3.19219	−0.105820
$911$	16.1759	0.535931	0.267966	−	0.963428i	$-0.413649\pi$
$911$	16.1759	0.535931	0.267966	+	0.963428i	$0.413649\pi$
$912$	−16.0046	−0.529966
$913$	−3.20293	−0.106002
$914$	41.1389	1.36075
$915$	−21.8280	−0.721612
$916$	−43.5263	−1.43815
$917$	−9.45566	−0.312253
$918$	19.7891	0.653136
$919$	3.26868	0.107824	0.0539118	−	0.998546i	$-0.482831\pi$
$919$	3.26868	0.107824	0.0539118	+	0.998546i	$0.482831\pi$
$920$	12.4403	0.410145
$921$	−23.4612	−0.773074
$922$	−48.3397	−1.59198
$923$	4.44749	0.146391
$924$	−6.35962	−0.209216
$925$	0.156969	0.00516110
$926$	41.1866	1.35348
$927$	−1.15593	−0.0379659
$928$	−30.8338	−1.01217
$929$	−23.9458	−0.785636	−0.392818	−	0.919616i	$-0.628500\pi$
$929$	−23.9458	−0.785636	−0.392818	+	0.919616i	$0.628500\pi$
$930$	−8.78216	−0.287978
$931$	30.4511	0.997995
$932$	−73.8021	−2.41747
$933$	3.45356	0.113065
$934$	24.7258	0.809052
$935$	−4.12166	−0.134793
$936$	1.98625	0.0649227
$937$	9.97607	0.325904	0.162952	−	0.986634i	$-0.447898\pi$
$937$	9.97607	0.325904	0.162952	+	0.986634i	$0.447898\pi$
$938$	51.7871	1.69091
$939$	−3.63900	−0.118754
$940$	−114.491	−3.73430
$941$	9.65315	0.314684	0.157342	−	0.987544i	$-0.449708\pi$
$941$	9.65315	0.314684	0.157342	+	0.987544i	$0.449708\pi$
$942$	−31.0328	−1.01110
$943$	1.41308	0.0460164
$944$	−10.0890	−0.328370
$945$	−25.3364	−0.824193
$946$	23.6706	0.769599
$947$	53.3362	1.73319	0.866597	−	0.499009i	$-0.166303\pi$
$947$	53.3362	1.73319	0.866597	+	0.499009i	$0.166303\pi$
$948$	−9.93523	−0.322681
$949$	−0.731489	−0.0237451
$950$	48.5031	1.57365
$951$	1.84880	0.0599513
$952$	−11.0810	−0.359136
$953$	−20.7581	−0.672421	−0.336210	−	0.941787i	$-0.609145\pi$
$953$	−20.7581	−0.672421	−0.336210	+	0.941787i	$0.609145\pi$
$954$	41.8642	1.35540
$955$	−5.95133	−0.192581
$956$	60.1491	1.94536
$957$	9.44760	0.305398
$958$	80.6104	2.60440
$959$	36.0400	1.16379
$960$	−33.3352	−1.07589
$961$	−29.3913	−0.948107
$962$	−0.0397683	−0.00128218
$963$	34.5531	1.11346
$964$	−15.8442	−0.510307
$965$	23.4328	0.754328
$966$	5.25115	0.168953
$967$	27.4841	0.883829	0.441914	−	0.897057i	$-0.354299\pi$
$967$	27.4841	0.883829	0.441914	+	0.897057i	$0.354299\pi$
$968$	39.1072	1.25695
$969$	−13.6089	−0.437180
$970$	−6.15289	−0.197557
$971$	−0.823985	−0.0264430	−0.0132215	−	0.999913i	$-0.504209\pi$
$971$	−0.823985	−0.0264430	−0.0132215	+	0.999913i	$0.504209\pi$
$972$	56.7870	1.82144
$973$	−27.5940	−0.884623
$974$	63.1808	2.02444
$975$	0.749380	0.0239994
$976$	−14.1874	−0.454126
$977$	−42.7702	−1.36834	−0.684170	−	0.729323i	$-0.739835\pi$
$977$	−42.7702	−1.36834	−0.684170	+	0.729323i	$0.739835\pi$
$978$	−31.5736	−1.00961
$979$	10.4373	0.333578
$980$	−38.2134	−1.22068
$981$	22.6968	0.724654
$982$	−84.1987	−2.68689
$983$	55.9328	1.78398	0.891989	−	0.452057i	$-0.149310\pi$
$983$	55.9328	1.78398	0.891989	+	0.452057i	$0.149310\pi$
$984$	4.93402	0.157291
$985$	20.6880	0.659173
$986$	36.7058	1.16895
$987$	−21.6735	−0.689876
$988$	−7.92015	−0.251974
$989$	−12.5972	−0.400567
$990$	−11.3597	−0.361033
$991$	−25.7381	−0.817599	−0.408799	−	0.912624i	$-0.634052\pi$
$991$	−25.7381	−0.817599	−0.408799	+	0.912624i	$0.634052\pi$
$992$	4.07716	0.129450
$993$	−31.5888	−1.00244
$994$	−68.3834	−2.16899
$995$	−7.66058	−0.242857
$996$	13.2712	0.420515
$997$	−48.0077	−1.52042	−0.760210	−	0.649678i	$-0.774904\pi$
$997$	−48.0077	−1.52042	−0.760210	+	0.649678i	$0.774904\pi$
$998$	13.2772	0.420283
$999$	−0.315641	−0.00998645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.16	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.16	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37198 q^{2} +1.06086 q^{3} +3.62628 q^{4} +2.75167 q^{5} -2.51634 q^{6} +1.78055 q^{7} -3.85749 q^{8} -1.87457 q^{9} +O(q^{10})\)	\(q-2.37198 q^{2} +1.06086 q^{3} +3.62628 q^{4} +2.75167 q^{5} -2.51634 q^{6} +1.78055 q^{7} -3.85749 q^{8} -1.87457 q^{9} -6.52689 q^{10} -0.928447 q^{11} +3.84698 q^{12} +0.274681 q^{13} -4.22342 q^{14} +2.91914 q^{15} +1.89733 q^{16} +1.61331 q^{17} +4.44644 q^{18} -7.95141 q^{19} +9.97830 q^{20} +1.88892 q^{21} +2.20225 q^{22} -1.17201 q^{23} -4.09227 q^{24} +2.57167 q^{25} -0.651536 q^{26} -5.17125 q^{27} +6.45676 q^{28} -9.59192 q^{29} -6.92413 q^{30} +1.26834 q^{31} +3.21456 q^{32} -0.984955 q^{33} -3.82675 q^{34} +4.89947 q^{35} -6.79771 q^{36} +0.0610377 q^{37} +18.8606 q^{38} +0.291399 q^{39} -10.6145 q^{40} -1.20569 q^{41} -4.48047 q^{42} +10.7484 q^{43} -3.36680 q^{44} -5.15819 q^{45} +2.77998 q^{46} -11.4740 q^{47} +2.01280 q^{48} -3.82965 q^{49} -6.09993 q^{50} +1.71151 q^{51} +0.996068 q^{52} +9.41522 q^{53} +12.2661 q^{54} -2.55478 q^{55} -6.86845 q^{56} -8.43536 q^{57} +22.7518 q^{58} -5.31749 q^{59} +10.5856 q^{60} -7.47755 q^{61} -3.00847 q^{62} -3.33776 q^{63} -11.4195 q^{64} +0.755830 q^{65} +2.33629 q^{66} -12.2619 q^{67} +5.85033 q^{68} -1.24334 q^{69} -11.6214 q^{70} +16.1915 q^{71} +7.23114 q^{72} -2.66305 q^{73} -0.144780 q^{74} +2.72818 q^{75} -28.8340 q^{76} -1.65314 q^{77} -0.691191 q^{78} -2.58260 q^{79} +5.22081 q^{80} +0.137725 q^{81} +2.85988 q^{82} +3.44977 q^{83} +6.84974 q^{84} +4.43930 q^{85} -25.4949 q^{86} -10.1757 q^{87} +3.58147 q^{88} -11.2417 q^{89} +12.2351 q^{90} +0.489082 q^{91} -4.25003 q^{92} +1.34553 q^{93} +27.2162 q^{94} -21.8796 q^{95} +3.41021 q^{96} +0.942699 q^{97} +9.08384 q^{98} +1.74044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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