LMFDB - Embedded newform 4003.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, 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("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +O(q^{10})$	\(q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +9.64388 q^{10} -4.34035 q^{11} -4.60163 q^{12} +2.56321 q^{13} -8.99086 q^{14} +4.55944 q^{15} +3.88114 q^{16} -1.43730 q^{17} +4.06751 q^{18} -3.57623 q^{19} -15.6962 q^{20} -4.25071 q^{21} +10.6140 q^{22} +7.56025 q^{23} +5.59838 q^{24} +10.5523 q^{25} -6.26814 q^{26} +5.39150 q^{27} +14.6333 q^{28} -10.0757 q^{29} -11.1498 q^{30} -3.66806 q^{31} +0.193461 q^{32} +5.01811 q^{33} +3.51480 q^{34} -14.4992 q^{35} -6.62019 q^{36} -0.492301 q^{37} +8.74543 q^{38} -2.96346 q^{39} +19.0961 q^{40} +6.34905 q^{41} +10.3948 q^{42} +2.05250 q^{43} -17.2751 q^{44} +6.55950 q^{45} -18.4880 q^{46} +5.80507 q^{47} -4.48718 q^{48} +6.51738 q^{49} -25.8048 q^{50} +1.66173 q^{51} +10.2019 q^{52} -3.51286 q^{53} -13.1845 q^{54} +17.1168 q^{55} -17.8030 q^{56} +4.13467 q^{57} +24.6393 q^{58} -8.67947 q^{59} +18.1471 q^{60} +7.65206 q^{61} +8.96998 q^{62} -6.11533 q^{63} -8.23537 q^{64} -10.1084 q^{65} -12.2714 q^{66} +0.0212825 q^{67} -5.72061 q^{68} -8.74079 q^{69} +35.4567 q^{70} -0.157222 q^{71} +8.05418 q^{72} -13.0624 q^{73} +1.20389 q^{74} -12.2000 q^{75} -14.2339 q^{76} -15.9577 q^{77} +7.24692 q^{78} -1.22358 q^{79} -15.3058 q^{80} -1.24345 q^{81} -15.5262 q^{82} +9.74164 q^{83} -16.9183 q^{84} +5.66817 q^{85} -5.01924 q^{86} +11.6490 q^{87} +21.0171 q^{88} +11.9571 q^{89} -16.0408 q^{90} +9.42389 q^{91} +30.0907 q^{92} +4.24084 q^{93} -14.1959 q^{94} +14.1034 q^{95} -0.223671 q^{96} +3.79864 q^{97} -15.9378 q^{98} +7.21936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.44543	−1.72918	−0.864590	−	0.502478i	$-0.832422\pi$
$2$	−2.44543	−1.72918	−0.864590	+	0.502478i	$0.832422\pi$
$3$	−1.15615	−0.667505	−0.333752	−	0.942661i	$-0.608315\pi$
$3$	−1.15615	−0.667505	−0.333752	+	0.942661i	$0.608315\pi$
$4$	3.98012	1.99006
$5$	−3.94364	−1.76365	−0.881824	−	0.471579i	$-0.843684\pi$
$5$	−3.94364	−1.76365	−0.881824	+	0.471579i	$0.843684\pi$
$6$	2.82729	1.15424
$7$	3.67660	1.38962	0.694812	−	0.719191i	$-0.255488\pi$
$7$	3.67660	1.38962	0.694812	+	0.719191i	$0.255488\pi$
$8$	−4.84225	−1.71199
$9$	−1.66331	−0.554438
$10$	9.64388	3.04966
$11$	−4.34035	−1.30867	−0.654333	−	0.756207i	$-0.727050\pi$
$11$	−4.34035	−1.30867	−0.654333	+	0.756207i	$0.727050\pi$
$12$	−4.60163	−1.32838
$13$	2.56321	0.710906	0.355453	−	0.934694i	$-0.384327\pi$
$13$	2.56321	0.710906	0.355453	+	0.934694i	$0.384327\pi$
$14$	−8.99086	−2.40291
$15$	4.55944	1.17724
$16$	3.88114	0.970284
$17$	−1.43730	−0.348595	−0.174298	−	0.984693i	$-0.555765\pi$
$17$	−1.43730	−0.348595	−0.174298	+	0.984693i	$0.555765\pi$
$18$	4.06751	0.958722
$19$	−3.57623	−0.820444	−0.410222	−	0.911986i	$-0.634549\pi$
$19$	−3.57623	−0.820444	−0.410222	+	0.911986i	$0.634549\pi$
$20$	−15.6962	−3.50977
$21$	−4.25071	−0.927580
$22$	10.6140	2.26292
$23$	7.56025	1.57642	0.788210	−	0.615406i	$-0.211008\pi$
$23$	7.56025	1.57642	0.788210	+	0.615406i	$0.211008\pi$
$24$	5.59838	1.14276
$25$	10.5523	2.11045
$26$	−6.26814	−1.22928
$27$	5.39150	1.03759
$28$	14.6333	2.76544
$29$	−10.0757	−1.87100	−0.935501	−	0.353324i	$-0.885051\pi$
$29$	−10.0757	−1.87100	−0.935501	+	0.353324i	$0.885051\pi$
$30$	−11.1498	−2.03566
$31$	−3.66806	−0.658803	−0.329402	−	0.944190i	$-0.606847\pi$
$31$	−3.66806	−0.658803	−0.329402	+	0.944190i	$0.606847\pi$
$32$	0.193461	0.0341994
$33$	5.01811	0.873540
$34$	3.51480	0.602784
$35$	−14.4992	−2.45081
$36$	−6.62019	−1.10336
$37$	−0.492301	−0.0809339	−0.0404669	−	0.999181i	$-0.512885\pi$
$37$	−0.492301	−0.0809339	−0.0404669	+	0.999181i	$0.512885\pi$
$38$	8.74543	1.41870
$39$	−2.96346	−0.474533
$40$	19.0961	3.01936
$41$	6.34905	0.991555	0.495777	−	0.868450i	$-0.334883\pi$
$41$	6.34905	0.991555	0.495777	+	0.868450i	$0.334883\pi$
$42$	10.3948	1.60395
$43$	2.05250	0.313003	0.156501	−	0.987678i	$-0.449978\pi$
$43$	2.05250	0.313003	0.156501	+	0.987678i	$0.449978\pi$
$44$	−17.2751	−2.60432
$45$	6.55950	0.977833
$46$	−18.4880	−2.72591
$47$	5.80507	0.846757	0.423379	−	0.905953i	$-0.360844\pi$
$47$	5.80507	0.846757	0.423379	+	0.905953i	$0.360844\pi$
$48$	−4.48718	−0.647669
$49$	6.51738	0.931055
$50$	−25.8048	−3.64935
$51$	1.66173	0.232689
$52$	10.2019	1.41475
$53$	−3.51286	−0.482528	−0.241264	−	0.970459i	$-0.577562\pi$
$53$	−3.51286	−0.482528	−0.241264	+	0.970459i	$0.577562\pi$
$54$	−13.1845	−1.79419
$55$	17.1168	2.30803
$56$	−17.8030	−2.37903
$57$	4.13467	0.547650
$58$	24.6393	3.23530
$59$	−8.67947	−1.12997	−0.564986	−	0.825101i	$-0.691118\pi$
$59$	−8.67947	−1.12997	−0.564986	+	0.825101i	$0.691118\pi$
$60$	18.1471	2.34279
$61$	7.65206	0.979746	0.489873	−	0.871794i	$-0.337043\pi$
$61$	7.65206	0.979746	0.489873	+	0.871794i	$0.337043\pi$
$62$	8.96998	1.13919
$63$	−6.11533	−0.770460
$64$	−8.23537	−1.02942
$65$	−10.1084	−1.25379
$66$	−12.2714	−1.51051
$67$	0.0212825	0.00260007	0.00130004	−	0.999999i	$-0.499586\pi$
$67$	0.0212825	0.00260007	0.00130004	+	0.999999i	$0.499586\pi$
$68$	−5.72061	−0.693726
$69$	−8.74079	−1.05227
$70$	35.4567	4.23789
$71$	−0.157222	−0.0186589	−0.00932943	−	0.999956i	$-0.502970\pi$
$71$	−0.157222	−0.0186589	−0.00932943	+	0.999956i	$0.502970\pi$
$72$	8.05418	0.949194
$73$	−13.0624	−1.52884	−0.764418	−	0.644720i	$-0.776974\pi$
$73$	−13.0624	−1.52884	−0.764418	+	0.644720i	$0.776974\pi$
$74$	1.20389	0.139949
$75$	−12.2000	−1.40874
$76$	−14.2339	−1.63273
$77$	−15.9577	−1.81855
$78$	7.24692	0.820553
$79$	−1.22358	−0.137663	−0.0688317	−	0.997628i	$-0.521927\pi$
$79$	−1.22358	−0.137663	−0.0688317	+	0.997628i	$0.521927\pi$
$80$	−15.3058	−1.71124
$81$	−1.24345	−0.138161
$82$	−15.5262	−1.71458
$83$	9.74164	1.06928	0.534642	−	0.845079i	$-0.320446\pi$
$83$	9.74164	1.06928	0.534642	+	0.845079i	$0.320446\pi$
$84$	−16.9183	−1.84594
$85$	5.66817	0.614799
$86$	−5.01924	−0.541238
$87$	11.6490	1.24890
$88$	21.0171	2.24043
$89$	11.9571	1.26745	0.633727	−	0.773557i	$-0.281524\pi$
$89$	11.9571	1.26745	0.633727	+	0.773557i	$0.281524\pi$
$90$	−16.0408	−1.69085
$91$	9.42389	0.987892
$92$	30.0907	3.13717
$93$	4.24084	0.439754
$94$	−14.1959	−1.46419
$95$	14.1034	1.44697
$96$	−0.223671	−0.0228283
$97$	3.79864	0.385694	0.192847	−	0.981229i	$-0.438228\pi$
$97$	3.79864	0.385694	0.192847	+	0.981229i	$0.438228\pi$
$98$	−15.9378	−1.60996
$99$	7.21936	0.725573
$100$	41.9993	4.19993
$101$	−7.78154	−0.774292	−0.387146	−	0.922018i	$-0.626539\pi$
$101$	−7.78154	−0.774292	−0.387146	+	0.922018i	$0.626539\pi$
$102$	−4.06365	−0.402361
$103$	−12.3739	−1.21923	−0.609617	−	0.792696i	$-0.708677\pi$
$103$	−12.3739	−1.21923	−0.609617	+	0.792696i	$0.708677\pi$
$104$	−12.4117	−1.21707
$105$	16.7632	1.63593
$106$	8.59045	0.834378
$107$	12.8460	1.24187	0.620937	−	0.783861i	$-0.286752\pi$
$107$	12.8460	1.24187	0.620937	+	0.783861i	$0.286752\pi$
$108$	21.4588	2.06488
$109$	16.2967	1.56094	0.780470	−	0.625193i	$-0.214980\pi$
$109$	16.2967	1.56094	0.780470	+	0.625193i	$0.214980\pi$
$110$	−41.8579	−3.99099
$111$	0.569175	0.0540237
$112$	14.2694	1.34833
$113$	16.5689	1.55867	0.779335	−	0.626607i	$-0.215557\pi$
$113$	16.5689	1.55867	0.779335	+	0.626607i	$0.215557\pi$
$114$	−10.1110	−0.946986
$115$	−29.8149	−2.78025
$116$	−40.1023	−3.72341
$117$	−4.26342	−0.394153
$118$	21.2250	1.95392
$119$	−5.28436	−0.484416
$120$	−22.0780	−2.01543
$121$	7.83866	0.712605
$122$	−18.7126	−1.69416
$123$	−7.34047	−0.661868
$124$	−14.5993	−1.31106
$125$	−21.8961	−1.95845
$126$	14.9546	1.33226
$127$	−0.990646	−0.0879057	−0.0439528	−	0.999034i	$-0.513995\pi$
$127$	−0.990646	−0.0879057	−0.0439528	+	0.999034i	$0.513995\pi$
$128$	19.7521	1.74585
$129$	−2.37300	−0.208931
$130$	24.7193	2.16802
$131$	18.4777	1.61440	0.807201	−	0.590277i	$-0.200981\pi$
$131$	18.4777	1.61440	0.807201	+	0.590277i	$0.200981\pi$
$132$	19.9727	1.73840
$133$	−13.1484	−1.14011
$134$	−0.0520448	−0.00449599
$135$	−21.2621	−1.82995
$136$	6.95975	0.596793
$137$	9.07582	0.775400	0.387700	−	0.921786i	$-0.373270\pi$
$137$	9.07582	0.775400	0.387700	+	0.921786i	$0.373270\pi$
$138$	21.3750	1.81956
$139$	−11.6227	−0.985822	−0.492911	−	0.870080i	$-0.664067\pi$
$139$	−11.6227	−0.985822	−0.492911	+	0.870080i	$0.664067\pi$
$140$	−57.7085	−4.87726
$141$	−6.71155	−0.565214
$142$	0.384476	0.0322645
$143$	−11.1252	−0.930338
$144$	−6.45554	−0.537962
$145$	39.7347	3.29979
$146$	31.9431	2.64363
$147$	−7.53509	−0.621483
$148$	−1.95942	−0.161063
$149$	10.0783	0.825649	0.412824	−	0.910811i	$-0.364542\pi$
$149$	10.0783	0.825649	0.412824	+	0.910811i	$0.364542\pi$
$150$	29.8343	2.43596
$151$	−2.89948	−0.235957	−0.117978	−	0.993016i	$-0.537641\pi$
$151$	−2.89948	−0.235957	−0.117978	+	0.993016i	$0.537641\pi$
$152$	17.3170	1.40460
$153$	2.39067	0.193274
$154$	39.0235	3.14460
$155$	14.4655	1.16190
$156$	−11.7949	−0.944350
$157$	11.2788	0.900145	0.450072	−	0.892992i	$-0.351398\pi$
$157$	11.2788	0.900145	0.450072	+	0.892992i	$0.351398\pi$
$158$	2.99217	0.238045
$159$	4.06140	0.322090
$160$	−0.762941	−0.0603158
$161$	27.7960	2.19063
$162$	3.04078	0.238906
$163$	0.268052	0.0209954	0.0104977	−	0.999945i	$-0.496658\pi$
$163$	0.268052	0.0209954	0.0104977	+	0.999945i	$0.496658\pi$
$164$	25.2700	1.97326
$165$	−19.7896	−1.54062
$166$	−23.8225	−1.84898
$167$	14.8715	1.15079	0.575397	−	0.817874i	$-0.304847\pi$
$167$	14.8715	1.15079	0.575397	+	0.817874i	$0.304847\pi$
$168$	20.5830	1.58801
$169$	−6.42997	−0.494613
$170$	−13.8611	−1.06310
$171$	5.94839	0.454885
$172$	8.16919	0.622895
$173$	−18.7577	−1.42612	−0.713059	−	0.701104i	$-0.752691\pi$
$173$	−18.7577	−1.42612	−0.713059	+	0.701104i	$0.752691\pi$
$174$	−28.4868	−2.15958
$175$	38.7965	2.93274
$176$	−16.8455	−1.26978
$177$	10.0348	0.754261
$178$	−29.2403	−2.19166
$179$	−6.32143	−0.472486	−0.236243	−	0.971694i	$-0.575916\pi$
$179$	−6.32143	−0.472486	−0.236243	+	0.971694i	$0.575916\pi$
$180$	26.1076	1.94595
$181$	−1.36262	−0.101283	−0.0506415	−	0.998717i	$-0.516127\pi$
$181$	−1.36262	−0.101283	−0.0506415	+	0.998717i	$0.516127\pi$
$182$	−23.0454	−1.70824
$183$	−8.84694	−0.653985
$184$	−36.6086	−2.69882
$185$	1.94146	0.142739
$186$	−10.3707	−0.760414
$187$	6.23837	0.456195
$188$	23.1049	1.68510
$189$	19.8224	1.44187
$190$	−34.4888	−2.50208
$191$	−21.9818	−1.59055	−0.795274	−	0.606250i	$-0.792673\pi$
$191$	−21.9818	−1.59055	−0.795274	+	0.606250i	$0.792673\pi$
$192$	9.52133	0.687143
$193$	6.34397	0.456649	0.228324	−	0.973585i	$-0.426675\pi$
$193$	6.34397	0.456649	0.228324	+	0.973585i	$0.426675\pi$
$194$	−9.28931	−0.666934
$195$	11.6868	0.836909
$196$	25.9400	1.85286
$197$	−15.7382	−1.12130	−0.560649	−	0.828053i	$-0.689448\pi$
$197$	−15.7382	−1.12130	−0.560649	+	0.828053i	$0.689448\pi$
$198$	−17.6544	−1.25465
$199$	7.17962	0.508950	0.254475	−	0.967079i	$-0.418097\pi$
$199$	7.17962	0.508950	0.254475	+	0.967079i	$0.418097\pi$
$200$	−51.0968	−3.61309
$201$	−0.0246058	−0.00173556
$202$	19.0292	1.33889
$203$	−37.0441	−2.59999
$204$	6.61390	0.463065
$205$	−25.0383	−1.74875
$206$	30.2594	2.10827
$207$	−12.5751	−0.874027
$208$	9.94816	0.689780
$209$	15.5221	1.07369
$210$	−40.9933	−2.82881
$211$	16.8062	1.15699	0.578494	−	0.815687i	$-0.303641\pi$
$211$	16.8062	1.15699	0.578494	+	0.815687i	$0.303641\pi$
$212$	−13.9816	−0.960261
$213$	0.181773	0.0124549
$214$	−31.4141	−2.14742
$215$	−8.09430	−0.552027
$216$	−26.1070	−1.77636
$217$	−13.4860	−0.915489
$218$	−39.8524	−2.69914
$219$	15.1021	1.02051
$220$	68.1269	4.59311
$221$	−3.68409	−0.247818
$222$	−1.39188	−0.0934167
$223$	16.1410	1.08088	0.540439	−	0.841383i	$-0.318258\pi$
$223$	16.1410	1.08088	0.540439	+	0.841383i	$0.318258\pi$
$224$	0.711279	0.0475243
$225$	−17.5517	−1.17012
$226$	−40.5180	−2.69522
$227$	−8.36879	−0.555456	−0.277728	−	0.960660i	$-0.589581\pi$
$227$	−8.36879	−0.555456	−0.277728	+	0.960660i	$0.589581\pi$
$228$	16.4565	1.08986
$229$	1.20796	0.0798240	0.0399120	−	0.999203i	$-0.487292\pi$
$229$	1.20796	0.0798240	0.0399120	+	0.999203i	$0.487292\pi$
$230$	72.9101	4.80755
$231$	18.4496	1.21389
$232$	48.7888	3.20314
$233$	−20.9223	−1.37066	−0.685331	−	0.728231i	$-0.740343\pi$
$233$	−20.9223	−1.37066	−0.685331	+	0.728231i	$0.740343\pi$
$234$	10.4259	0.681561
$235$	−22.8931	−1.49338
$236$	−34.5454	−2.24871
$237$	1.41464	0.0918909
$238$	12.9225	0.837643
$239$	14.4069	0.931906	0.465953	−	0.884809i	$-0.345711\pi$
$239$	14.4069	0.931906	0.465953	+	0.884809i	$0.345711\pi$
$240$	17.6958	1.14226
$241$	1.60754	0.103551	0.0517754	−	0.998659i	$-0.483512\pi$
$241$	1.60754	0.103551	0.0517754	+	0.998659i	$0.483512\pi$
$242$	−19.1689	−1.23222
$243$	−14.7369	−0.945371
$244$	30.4561	1.94975
$245$	−25.7022	−1.64205
$246$	17.9506	1.14449
$247$	−9.16663	−0.583259
$248$	17.7617	1.12787
$249$	−11.2628	−0.713752
$250$	53.5455	3.38651
$251$	13.7490	0.867832	0.433916	−	0.900953i	$-0.357132\pi$
$251$	13.7490	0.867832	0.433916	+	0.900953i	$0.357132\pi$
$252$	−24.3398	−1.53326
$253$	−32.8141	−2.06301
$254$	2.42256	0.152005
$255$	−6.55327	−0.410382
$256$	−31.8316	−1.98947
$257$	−10.7570	−0.671001	−0.335501	−	0.942040i	$-0.608905\pi$
$257$	−10.7570	−0.671001	−0.335501	+	0.942040i	$0.608905\pi$
$258$	5.80300	0.361279
$259$	−1.81000	−0.112468
$260$	−40.2325	−2.49511
$261$	16.7590	1.03735
$262$	−45.1858	−2.79159
$263$	−7.44899	−0.459324	−0.229662	−	0.973270i	$-0.573762\pi$
$263$	−7.44899	−0.459324	−0.229662	+	0.973270i	$0.573762\pi$
$264$	−24.2989	−1.49550
$265$	13.8534	0.851010
$266$	32.1534	1.97145
$267$	−13.8243	−0.846031
$268$	0.0847069	0.00517430
$269$	8.37834	0.510837	0.255418	−	0.966831i	$-0.417787\pi$
$269$	8.37834	0.510837	0.255418	+	0.966831i	$0.417787\pi$
$270$	51.9950	3.16431
$271$	1.00504	0.0610516	0.0305258	−	0.999534i	$-0.490282\pi$
$271$	1.00504	0.0610516	0.0305258	+	0.999534i	$0.490282\pi$
$272$	−5.57834	−0.338236
$273$	−10.8954	−0.659422
$274$	−22.1943	−1.34081
$275$	−45.8006	−2.76188
$276$	−34.7894	−2.09408
$277$	23.3188	1.40109	0.700546	−	0.713607i	$-0.252940\pi$
$277$	23.3188	1.40109	0.700546	+	0.713607i	$0.252940\pi$
$278$	28.4224	1.70466
$279$	6.10113	0.365265
$280$	70.2086	4.19577
$281$	2.68923	0.160426	0.0802130	−	0.996778i	$-0.474440\pi$
$281$	2.68923	0.160426	0.0802130	+	0.996778i	$0.474440\pi$
$282$	16.4126	0.977357
$283$	−15.9997	−0.951085	−0.475543	−	0.879693i	$-0.657748\pi$
$283$	−15.9997	−0.951085	−0.475543	+	0.879693i	$0.657748\pi$
$284$	−0.625764	−0.0371323
$285$	−16.3056	−0.965862
$286$	27.2059	1.60872
$287$	23.3429	1.37789
$288$	−0.321786	−0.0189614
$289$	−14.9342	−0.878481
$290$	−97.1684	−5.70593
$291$	−4.39181	−0.257452
$292$	−51.9899	−3.04248
$293$	20.6283	1.20512	0.602560	−	0.798074i	$-0.294148\pi$
$293$	20.6283	1.20512	0.602560	+	0.798074i	$0.294148\pi$
$294$	18.4265	1.07466
$295$	34.2287	1.99287
$296$	2.38385	0.138558
$297$	−23.4010	−1.35786
$298$	−24.6458	−1.42770
$299$	19.3785	1.12069
$300$	−48.5576	−2.80348
$301$	7.54621	0.434956
$302$	7.09048	0.408012
$303$	8.99664	0.516843
$304$	−13.8798	−0.796064
$305$	−30.1769	−1.72793
$306$	−5.84622	−0.334206
$307$	−16.2859	−0.929484	−0.464742	−	0.885446i	$-0.653853\pi$
$307$	−16.2859	−0.929484	−0.464742	+	0.885446i	$0.653853\pi$
$308$	−63.5138	−3.61903
$309$	14.3061	0.813844
$310$	−35.3744	−2.00913
$311$	−23.8103	−1.35016	−0.675080	−	0.737744i	$-0.735891\pi$
$311$	−23.8103	−1.35016	−0.675080	+	0.737744i	$0.735891\pi$
$312$	14.3498	0.812398
$313$	6.58466	0.372187	0.186094	−	0.982532i	$-0.440417\pi$
$313$	6.58466	0.372187	0.186094	+	0.982532i	$0.440417\pi$
$314$	−27.5815	−1.55651
$315$	24.1167	1.35882
$316$	−4.86999	−0.273958
$317$	2.90341	0.163072	0.0815359	−	0.996670i	$-0.474017\pi$
$317$	2.90341	0.163072	0.0815359	+	0.996670i	$0.474017\pi$
$318$	−9.93186	−0.556951
$319$	43.7319	2.44852
$320$	32.4773	1.81554
$321$	−14.8520	−0.828956
$322$	−67.9731	−3.78800
$323$	5.14010	0.286003
$324$	−4.94909	−0.274950
$325$	27.0477	1.50033
$326$	−0.655501	−0.0363049
$327$	−18.8414	−1.04193
$328$	−30.7437	−1.69754
$329$	21.3429	1.17667
$330$	48.3940	2.66400
$331$	−23.5568	−1.29480	−0.647399	−	0.762151i	$-0.724143\pi$
$331$	−23.5568	−1.29480	−0.647399	+	0.762151i	$0.724143\pi$
$332$	38.7729	2.12794
$333$	0.818851	0.0448728
$334$	−36.3673	−1.98993
$335$	−0.0839304	−0.00458561
$336$	−16.4976	−0.900016
$337$	27.4114	1.49320	0.746598	−	0.665275i	$-0.231686\pi$
$337$	27.4114	1.49320	0.746598	+	0.665275i	$0.231686\pi$
$338$	15.7240	0.855274
$339$	−19.1562	−1.04042
$340$	22.5600	1.22349
$341$	15.9207	0.862153
$342$	−14.5464	−0.786578
$343$	−1.77438	−0.0958078
$344$	−9.93871	−0.535859
$345$	34.4705	1.85583
$346$	45.8705	2.46601
$347$	−34.1393	−1.83269	−0.916346	−	0.400388i	$-0.868875\pi$
$347$	−34.1393	−1.83269	−0.916346	+	0.400388i	$0.868875\pi$
$348$	46.3644	2.48539
$349$	−1.72055	−0.0920988	−0.0460494	−	0.998939i	$-0.514663\pi$
$349$	−1.72055	−0.0920988	−0.0460494	+	0.998939i	$0.514663\pi$
$350$	−94.8740	−5.07123
$351$	13.8195	0.737632
$352$	−0.839690	−0.0447556
$353$	26.1787	1.39335	0.696677	−	0.717385i	$-0.254661\pi$
$353$	26.1787	1.39335	0.696677	+	0.717385i	$0.254661\pi$
$354$	−24.5394	−1.30425
$355$	0.620028	0.0329077
$356$	47.5909	2.52231
$357$	6.10952	0.323350
$358$	15.4586	0.817012
$359$	18.9369	0.999451	0.499725	−	0.866184i	$-0.333434\pi$
$359$	18.9369	0.999451	0.499725	+	0.866184i	$0.333434\pi$
$360$	−31.7628	−1.67404
$361$	−6.21055	−0.326871
$362$	3.33220	0.175137
$363$	−9.06268	−0.475667
$364$	37.5082	1.96597
$365$	51.5133	2.69633
$366$	21.6346	1.13086
$367$	−30.5112	−1.59267	−0.796337	−	0.604853i	$-0.793232\pi$
$367$	−30.5112	−1.59267	−0.796337	+	0.604853i	$0.793232\pi$
$368$	29.3423	1.52958
$369$	−10.5605	−0.549755
$370$	−4.74770	−0.246821
$371$	−12.9154	−0.670533
$372$	16.8791	0.875138
$373$	−14.8881	−0.770876	−0.385438	−	0.922734i	$-0.625950\pi$
$373$	−14.8881	−0.770876	−0.385438	+	0.922734i	$0.625950\pi$
$374$	−15.2555	−0.788842
$375$	25.3153	1.30728
$376$	−28.1096	−1.44964
$377$	−25.8260	−1.33011
$378$	−48.4742	−2.49324
$379$	−29.6533	−1.52319	−0.761593	−	0.648055i	$-0.775583\pi$
$379$	−29.6533	−1.52319	−0.761593	+	0.648055i	$0.775583\pi$
$380$	56.1331	2.87957
$381$	1.14534	0.0586774
$382$	53.7550	2.75034
$383$	22.2739	1.13815	0.569073	−	0.822287i	$-0.307302\pi$
$383$	22.2739	1.13815	0.569073	+	0.822287i	$0.307302\pi$
$384$	−22.8364	−1.16537
$385$	62.9315	3.20729
$386$	−15.5137	−0.789627
$387$	−3.41395	−0.173541
$388$	15.1191	0.767554
$389$	−19.8382	−1.00583	−0.502917	−	0.864335i	$-0.667740\pi$
$389$	−19.8382	−1.00583	−0.502917	+	0.864335i	$0.667740\pi$
$390$	−28.5792	−1.44717
$391$	−10.8663	−0.549533
$392$	−31.5588	−1.59396
$393$	−21.3630	−1.07762
$394$	38.4866	1.93893
$395$	4.82535	0.242790
$396$	28.7340	1.44394
$397$	12.5398	0.629353	0.314676	−	0.949199i	$-0.398104\pi$
$397$	12.5398	0.629353	0.314676	+	0.949199i	$0.398104\pi$
$398$	−17.5572	−0.880065
$399$	15.2015	0.761028
$400$	40.9548	2.04774
$401$	−28.3753	−1.41700	−0.708498	−	0.705713i	$-0.750627\pi$
$401$	−28.3753	−1.41700	−0.708498	+	0.705713i	$0.750627\pi$
$402$	0.0601717	0.00300109
$403$	−9.40200	−0.468347
$404$	−30.9715	−1.54089
$405$	4.90373	0.243668
$406$	90.5888	4.49585
$407$	2.13676	0.105915
$408$	−8.04652	−0.398362
$409$	−32.7730	−1.62052	−0.810261	−	0.586070i	$-0.800675\pi$
$409$	−32.7730	−1.62052	−0.810261	+	0.586070i	$0.800675\pi$
$410$	61.2295	3.02391
$411$	−10.4930	−0.517583
$412$	−49.2495	−2.42635
$413$	−31.9109	−1.57024
$414$	30.7514	1.51135
$415$	−38.4175	−1.88584
$416$	0.495881	0.0243126
$417$	13.4376	0.658041
$418$	−37.9582	−1.85660
$419$	−37.7606	−1.84473	−0.922363	−	0.386325i	$-0.873744\pi$
$419$	−37.7606	−1.84473	−0.922363	+	0.386325i	$0.873744\pi$
$420$	66.7198	3.25559
$421$	19.6401	0.957201	0.478601	−	0.878033i	$-0.341144\pi$
$421$	19.6401	0.957201	0.478601	+	0.878033i	$0.341144\pi$
$422$	−41.0984	−2.00064
$423$	−9.65565	−0.469474
$424$	17.0101	0.826086
$425$	−15.1667	−0.735695
$426$	−0.444513	−0.0215367
$427$	28.1336	1.36148
$428$	51.1288	2.47140
$429$	12.8624	0.621005
$430$	19.7940	0.954554
$431$	−18.4192	−0.887222	−0.443611	−	0.896219i	$-0.646303\pi$
$431$	−18.4192	−0.887222	−0.443611	+	0.896219i	$0.646303\pi$
$432$	20.9251	1.00676
$433$	7.03845	0.338246	0.169123	−	0.985595i	$-0.445906\pi$
$433$	7.03845	0.338246	0.169123	+	0.985595i	$0.445906\pi$
$434$	32.9790	1.58304
$435$	−45.9394	−2.20262
$436$	64.8628	3.10637
$437$	−27.0372	−1.29337
$438$	−36.9311	−1.76464
$439$	−8.01432	−0.382502	−0.191251	−	0.981541i	$-0.561255\pi$
$439$	−8.01432	−0.382502	−0.191251	+	0.981541i	$0.561255\pi$
$440$	−82.8837	−3.95133
$441$	−10.8404	−0.516212
$442$	9.00917	0.428523
$443$	−3.17399	−0.150801	−0.0754005	−	0.997153i	$-0.524024\pi$
$443$	−3.17399	−0.150801	−0.0754005	+	0.997153i	$0.524024\pi$
$444$	2.26539	0.107511
$445$	−47.1546	−2.23534
$446$	−39.4716	−1.86903
$447$	−11.6521	−0.551124
$448$	−30.2781	−1.43051
$449$	−34.3893	−1.62293	−0.811467	−	0.584398i	$-0.801331\pi$
$449$	−34.3893	−1.62293	−0.811467	+	0.584398i	$0.801331\pi$
$450$	42.9215	2.02334
$451$	−27.5571	−1.29761
$452$	65.9462	3.10185
$453$	3.35225	0.157502
$454$	20.4653	0.960483
$455$	−37.1644	−1.74229
$456$	−20.0211	−0.937574
$457$	−0.434926	−0.0203450	−0.0101725	−	0.999948i	$-0.503238\pi$
$457$	−0.434926	−0.0203450	−0.0101725	+	0.999948i	$0.503238\pi$
$458$	−2.95397	−0.138030
$459$	−7.74918	−0.361701
$460$	−118.667	−5.53287
$461$	7.34963	0.342307	0.171153	−	0.985244i	$-0.445251\pi$
$461$	7.34963	0.342307	0.171153	+	0.985244i	$0.445251\pi$
$462$	−45.1171	−2.09904
$463$	−12.5653	−0.583961	−0.291981	−	0.956424i	$-0.594314\pi$
$463$	−12.5653	−0.583961	−0.291981	+	0.956424i	$0.594314\pi$
$464$	−39.1050	−1.81540
$465$	−16.7243	−0.775572
$466$	51.1639	2.37012
$467$	−38.9070	−1.80040	−0.900201	−	0.435475i	$-0.856580\pi$
$467$	−38.9070	−1.80040	−0.900201	+	0.435475i	$0.856580\pi$
$468$	−16.9689	−0.784389
$469$	0.0782472	0.00361312
$470$	55.9835	2.58232
$471$	−13.0400	−0.600851
$472$	42.0282	1.93450
$473$	−8.90856	−0.409616
$474$	−3.45941	−0.158896
$475$	−37.7374	−1.73151
$476$	−21.0324	−0.964019
$477$	5.84298	0.267532
$478$	−35.2311	−1.61143
$479$	−24.7758	−1.13204	−0.566018	−	0.824393i	$-0.691517\pi$
$479$	−24.7758	−1.13204	−0.566018	+	0.824393i	$0.691517\pi$
$480$	0.882075	0.0402610
$481$	−1.26187	−0.0575364
$482$	−3.93113	−0.179058
$483$	−32.1364	−1.46226
$484$	31.1988	1.41813
$485$	−14.9805	−0.680228
$486$	36.0380	1.63472
$487$	−2.14050	−0.0969953	−0.0484977	−	0.998823i	$-0.515443\pi$
$487$	−2.14050	−0.0969953	−0.0484977	+	0.998823i	$0.515443\pi$
$488$	−37.0532	−1.67732
$489$	−0.309909	−0.0140145
$490$	62.8529	2.83940
$491$	−34.0031	−1.53454	−0.767268	−	0.641326i	$-0.778385\pi$
$491$	−34.0031	−1.53454	−0.767268	+	0.641326i	$0.778385\pi$
$492$	−29.2160	−1.31716
$493$	14.4817	0.652222
$494$	22.4163	1.00856
$495$	−28.4705	−1.27966
$496$	−14.2362	−0.639226
$497$	−0.578044	−0.0259288
$498$	27.5424	1.23421
$499$	−23.0993	−1.03407	−0.517034	−	0.855965i	$-0.672964\pi$
$499$	−23.0993	−1.03407	−0.517034	+	0.855965i	$0.672964\pi$
$500$	−87.1494	−3.89744
$501$	−17.1938	−0.768161
$502$	−33.6223	−1.50064
$503$	43.1977	1.92609	0.963045	−	0.269340i	$-0.0868054\pi$
$503$	43.1977	1.92609	0.963045	+	0.269340i	$0.0868054\pi$
$504$	29.6120	1.31902
$505$	30.6875	1.36558
$506$	80.2446	3.56731
$507$	7.43402	0.330156
$508$	−3.94290	−0.174938
$509$	−8.00645	−0.354880	−0.177440	−	0.984132i	$-0.556782\pi$
$509$	−8.00645	−0.354880	−0.177440	+	0.984132i	$0.556782\pi$
$510$	16.0256	0.709623
$511$	−48.0252	−2.12451
$512$	38.3377	1.69430
$513$	−19.2813	−0.851288
$514$	26.3054	1.16028
$515$	48.7981	2.15030
$516$	−9.44483	−0.415785
$517$	−25.1961	−1.10812
$518$	4.42621	0.194477
$519$	21.6867	0.951940
$520$	48.9472	2.14648
$521$	4.99808	0.218970	0.109485	−	0.993988i	$-0.465080\pi$
$521$	4.99808	0.218970	0.109485	+	0.993988i	$0.465080\pi$
$522$	−40.9829	−1.79377
$523$	−17.2405	−0.753872	−0.376936	−	0.926239i	$-0.623022\pi$
$523$	−17.2405	−0.753872	−0.376936	+	0.926239i	$0.623022\pi$
$524$	73.5434	3.21276
$525$	−44.8546	−1.95762
$526$	18.2160	0.794254
$527$	5.27209	0.229656
$528$	19.4760	0.847582
$529$	34.1573	1.48510
$530$	−33.8776	−1.47155
$531$	14.4367	0.626498
$532$	−52.3322	−2.26889
$533$	16.2739	0.704902
$534$	33.8063	1.46294
$535$	−50.6601	−2.19023
$536$	−0.103055	−0.00445131
$537$	7.30853	0.315386
$538$	−20.4886	−0.883328
$539$	−28.2877	−1.21844
$540$	−84.6258	−3.64172
$541$	8.62014	0.370609	0.185304	−	0.982681i	$-0.440673\pi$
$541$	8.62014	0.370609	0.185304	+	0.982681i	$0.440673\pi$
$542$	−2.45774	−0.105569
$543$	1.57540	0.0676069
$544$	−0.278061	−0.0119218
$545$	−64.2682	−2.75295
$546$	26.6440	1.14026
$547$	−44.9978	−1.92397	−0.961983	−	0.273110i	$-0.911948\pi$
$547$	−44.9978	−1.92397	−0.961983	+	0.273110i	$0.911948\pi$
$548$	36.1229	1.54309
$549$	−12.7278	−0.543208
$550$	112.002	4.77578
$551$	36.0329	1.53505
$552$	42.3251	1.80148
$553$	−4.49861	−0.191300
$554$	−57.0246	−2.42274
$555$	−2.24462	−0.0952788
$556$	−46.2597	−1.96185
$557$	30.0011	1.27119	0.635594	−	0.772024i	$-0.280755\pi$
$557$	30.0011	1.27119	0.635594	+	0.772024i	$0.280755\pi$
$558$	−14.9199	−0.631609
$559$	5.26098	0.222516
$560$	−56.2733	−2.37798
$561$	−7.21250	−0.304512
$562$	−6.57632	−0.277405
$563$	−7.71352	−0.325086	−0.162543	−	0.986701i	$-0.551970\pi$
$563$	−7.71352	−0.325086	−0.162543	+	0.986701i	$0.551970\pi$
$564$	−26.7128	−1.12481
$565$	−65.3417	−2.74895
$566$	39.1262	1.64460
$567$	−4.57168	−0.191992
$568$	0.761310	0.0319439
$569$	−26.3693	−1.10546	−0.552730	−	0.833361i	$-0.686414\pi$
$569$	−26.3693	−1.10546	−0.552730	+	0.833361i	$0.686414\pi$
$570$	39.8743	1.67015
$571$	10.5608	0.441954	0.220977	−	0.975279i	$-0.429075\pi$
$571$	10.5608	0.441954	0.220977	+	0.975279i	$0.429075\pi$
$572$	−44.2798	−1.85143
$573$	25.4143	1.06170
$574$	−57.0834	−2.38262
$575$	79.7778	3.32696
$576$	13.6980	0.570750
$577$	−27.1978	−1.13226	−0.566129	−	0.824317i	$-0.691560\pi$
$577$	−27.1978	−1.13226	−0.566129	+	0.824317i	$0.691560\pi$
$578$	36.5205	1.51905
$579$	−7.33459	−0.304815
$580$	158.149	6.56678
$581$	35.8161	1.48590
$582$	10.7399	0.445181
$583$	15.2470	0.631468
$584$	63.2514	2.61736
$585$	16.8134	0.695147
$586$	−50.4451	−2.08387
$587$	20.5705	0.849034	0.424517	−	0.905420i	$-0.360444\pi$
$587$	20.5705	0.849034	0.424517	+	0.905420i	$0.360444\pi$
$588$	−29.9906	−1.23679
$589$	13.1178	0.540511
$590$	−83.7038	−3.44603
$591$	18.1957	0.748472
$592$	−1.91069	−0.0785288
$593$	−33.3908	−1.37120	−0.685598	−	0.727981i	$-0.740459\pi$
$593$	−33.3908	−1.37120	−0.685598	+	0.727981i	$0.740459\pi$
$594$	57.2255	2.34799
$595$	20.8396	0.854340
$596$	40.1130	1.64309
$597$	−8.30073	−0.339726
$598$	−47.3887	−1.93787
$599$	38.7384	1.58281	0.791405	−	0.611292i	$-0.209350\pi$
$599$	38.7384	1.58281	0.791405	+	0.611292i	$0.209350\pi$
$600$	59.0756	2.41175
$601$	2.64984	0.108089	0.0540446	−	0.998539i	$-0.482789\pi$
$601$	2.64984	0.108089	0.0540446	+	0.998539i	$0.482789\pi$
$602$	−18.4537	−0.752118
$603$	−0.0353994	−0.00144158
$604$	−11.5403	−0.469568
$605$	−30.9128	−1.25678
$606$	−22.0006	−0.893715
$607$	−11.3306	−0.459897	−0.229948	−	0.973203i	$-0.573856\pi$
$607$	−11.3306	−0.459897	−0.229948	+	0.973203i	$0.573856\pi$
$608$	−0.691862	−0.0280587
$609$	42.8287	1.73550
$610$	73.7956	2.98790
$611$	14.8796	0.601965
$612$	9.51517	0.384628
$613$	−19.0320	−0.768696	−0.384348	−	0.923188i	$-0.625574\pi$
$613$	−19.0320	−0.768696	−0.384348	+	0.923188i	$0.625574\pi$
$614$	39.8259	1.60724
$615$	28.9481	1.16730
$616$	77.2714	3.11335
$617$	36.6963	1.47734	0.738669	−	0.674068i	$-0.235454\pi$
$617$	36.6963	1.47734	0.738669	+	0.674068i	$0.235454\pi$
$618$	−34.9845	−1.40728
$619$	−34.4101	−1.38306	−0.691530	−	0.722348i	$-0.743063\pi$
$619$	−34.4101	−1.38306	−0.691530	+	0.722348i	$0.743063\pi$
$620$	57.5745	2.31225
$621$	40.7611	1.63568
$622$	58.2265	2.33467
$623$	43.9616	1.76128
$624$	−11.5016	−0.460432
$625$	33.5891	1.34356
$626$	−16.1023	−0.643579
$627$	−17.9459	−0.716691
$628$	44.8909	1.79134
$629$	0.707583	0.0282132
$630$	−58.9756	−2.34964
$631$	27.8881	1.11021	0.555104	−	0.831781i	$-0.312678\pi$
$631$	27.8881	1.11021	0.555104	+	0.831781i	$0.312678\pi$
$632$	5.92487	0.235679
$633$	−19.4305	−0.772295
$634$	−7.10008	−0.281980
$635$	3.90675	0.155035
$636$	16.1649	0.640979
$637$	16.7054	0.661892
$638$	−106.943	−4.23392
$639$	0.261510	0.0103452
$640$	−77.8950	−3.07907
$641$	39.2139	1.54886	0.774428	−	0.632663i	$-0.218038\pi$
$641$	39.2139	1.54886	0.774428	+	0.632663i	$0.218038\pi$
$642$	36.3194	1.43341
$643$	27.3908	1.08019	0.540093	−	0.841605i	$-0.318389\pi$
$643$	27.3908	1.08019	0.540093	+	0.841605i	$0.318389\pi$
$644$	110.632	4.35949
$645$	9.35825	0.368481
$646$	−12.5698	−0.494551
$647$	10.1515	0.399098	0.199549	−	0.979888i	$-0.436052\pi$
$647$	10.1515	0.399098	0.199549	+	0.979888i	$0.436052\pi$
$648$	6.02111	0.236532
$649$	37.6720	1.47875
$650$	−66.1431	−2.59435
$651$	15.5919	0.611093
$652$	1.06688	0.0417822
$653$	−27.0495	−1.05853	−0.529264	−	0.848457i	$-0.677532\pi$
$653$	−27.0495	−1.05853	−0.529264	+	0.848457i	$0.677532\pi$
$654$	46.0754	1.80169
$655$	−72.8693	−2.84724
$656$	24.6415	0.962090
$657$	21.7268	0.847645
$658$	−52.1926	−2.03468
$659$	−14.5738	−0.567715	−0.283857	−	0.958866i	$-0.591614\pi$
$659$	−14.5738	−0.567715	−0.283857	+	0.958866i	$0.591614\pi$
$660$	−78.7650	−3.06592
$661$	−17.1929	−0.668725	−0.334362	−	0.942445i	$-0.608521\pi$
$661$	−17.1929	−0.668725	−0.334362	+	0.942445i	$0.608521\pi$
$662$	57.6064	2.23894
$663$	4.25936	0.165420
$664$	−47.1715	−1.83061
$665$	51.8524	2.01075
$666$	−2.00244	−0.0775931
$667$	−76.1744	−2.94949
$668$	59.1906	2.29015
$669$	−18.6614	−0.721491
$670$	0.205246	0.00792934
$671$	−33.2126	−1.28216
$672$	−0.822347	−0.0317227
$673$	−12.8796	−0.496471	−0.248235	−	0.968700i	$-0.579851\pi$
$673$	−12.8796	−0.496471	−0.248235	+	0.968700i	$0.579851\pi$
$674$	−67.0327	−2.58200
$675$	56.8926	2.18980
$676$	−25.5921	−0.984310
$677$	−1.75429	−0.0674229	−0.0337115	−	0.999432i	$-0.510733\pi$
$677$	−1.75429	−0.0674229	−0.0337115	+	0.999432i	$0.510733\pi$
$678$	46.8450	1.79907
$679$	13.9661	0.535969
$680$	−27.4467	−1.05253
$681$	9.67559	0.370769
$682$	−38.9329	−1.49082
$683$	36.0142	1.37804	0.689022	−	0.724741i	$-0.258040\pi$
$683$	36.0142	1.37804	0.689022	+	0.724741i	$0.258040\pi$
$684$	23.6753	0.905249
$685$	−35.7918	−1.36753
$686$	4.33913	0.165669
$687$	−1.39658	−0.0532829
$688$	7.96602	0.303702
$689$	−9.00419	−0.343032
$690$	−84.2952	−3.20906
$691$	25.1211	0.955651	0.477825	−	0.878455i	$-0.341425\pi$
$691$	25.1211	0.955651	0.477825	+	0.878455i	$0.341425\pi$
$692$	−74.6578	−2.83806
$693$	26.5427	1.00827
$694$	83.4851	3.16905
$695$	45.8356	1.73864
$696$	−56.4073	−2.13811
$697$	−9.12546	−0.345651
$698$	4.20748	0.159255
$699$	24.1893	0.914924
$700$	154.415	5.83633
$701$	−24.9904	−0.943873	−0.471937	−	0.881632i	$-0.656445\pi$
$701$	−24.9904	−0.943873	−0.471937	+	0.881632i	$0.656445\pi$
$702$	−33.7947	−1.27550
$703$	1.76058	0.0664017
$704$	35.7444	1.34717
$705$	26.4679	0.996839
$706$	−64.0182	−2.40936
$707$	−28.6096	−1.07597
$708$	39.9397	1.50103
$709$	−10.2121	−0.383523	−0.191761	−	0.981442i	$-0.561420\pi$
$709$	−10.2121	−0.383523	−0.191761	+	0.981442i	$0.561420\pi$
$710$	−1.51623	−0.0569033
$711$	2.03519	0.0763257
$712$	−57.8995	−2.16987
$713$	−27.7314	−1.03855
$714$	−14.9404	−0.559131
$715$	43.8738	1.64079
$716$	−25.1601	−0.940275
$717$	−16.6566	−0.622052
$718$	−46.3088	−1.72823
$719$	17.7922	0.663538	0.331769	−	0.943361i	$-0.392354\pi$
$719$	17.7922	0.663538	0.331769	+	0.943361i	$0.392354\pi$
$720$	25.4583	0.948775
$721$	−45.4938	−1.69428
$722$	15.1875	0.565219
$723$	−1.85856	−0.0691206
$724$	−5.42341	−0.201559
$725$	−106.321	−3.94866
$726$	22.1621	0.822514
$727$	17.3192	0.642333	0.321166	−	0.947023i	$-0.395925\pi$
$727$	17.3192	0.642333	0.321166	+	0.947023i	$0.395925\pi$
$728$	−45.6328	−1.69127
$729$	20.7684	0.769201
$730$	−125.972	−4.66244
$731$	−2.95005	−0.109111
$732$	−35.2119	−1.30147
$733$	−46.2614	−1.70870	−0.854351	−	0.519696i	$-0.826045\pi$
$733$	−46.2614	−1.70870	−0.854351	+	0.519696i	$0.826045\pi$
$734$	74.6131	2.75402
$735$	29.7156	1.09608
$736$	1.46261	0.0539127
$737$	−0.0923735	−0.00340262
$738$	25.8248	0.950626
$739$	−35.6200	−1.31030	−0.655151	−	0.755498i	$-0.727395\pi$
$739$	−35.6200	−1.31030	−0.655151	+	0.755498i	$0.727395\pi$
$740$	7.72724	0.284059
$741$	10.5980	0.389328
$742$	31.5836	1.15947
$743$	11.8628	0.435202	0.217601	−	0.976038i	$-0.430177\pi$
$743$	11.8628	0.435202	0.217601	+	0.976038i	$0.430177\pi$
$744$	−20.5352	−0.752857
$745$	−39.7453	−1.45615
$746$	36.4078	1.33298
$747$	−16.2034	−0.592851
$748$	24.8295	0.907856
$749$	47.2297	1.72574
$750$	−61.9067	−2.26051
$751$	−39.4769	−1.44053	−0.720267	−	0.693697i	$-0.755981\pi$
$751$	−39.4769	−1.44053	−0.720267	+	0.693697i	$0.755981\pi$
$752$	22.5303	0.821595
$753$	−15.8960	−0.579282
$754$	63.1556	2.29999
$755$	11.4345	0.416145
$756$	78.8955	2.86940
$757$	5.05330	0.183665	0.0918327	−	0.995774i	$-0.470728\pi$
$757$	5.05330	0.183665	0.0918327	+	0.995774i	$0.470728\pi$
$758$	72.5150	2.63386
$759$	37.9381	1.37707
$760$	−68.2921	−2.47721
$761$	2.73522	0.0991518	0.0495759	−	0.998770i	$-0.484213\pi$
$761$	2.73522	0.0991518	0.0495759	+	0.998770i	$0.484213\pi$
$762$	−2.80084	−0.101464
$763$	59.9164	2.16912
$764$	−87.4903	−3.16529
$765$	−9.42794	−0.340868
$766$	−54.4693	−1.96806
$767$	−22.2473	−0.803303
$768$	36.8021	1.32798
$769$	8.97463	0.323633	0.161817	−	0.986821i	$-0.448265\pi$
$769$	8.97463	0.323633	0.161817	+	0.986821i	$0.448265\pi$
$770$	−153.895	−5.54598
$771$	12.4367	0.447896
$772$	25.2498	0.908759
$773$	34.2513	1.23193	0.615967	−	0.787772i	$-0.288766\pi$
$773$	34.2513	1.23193	0.615967	+	0.787772i	$0.288766\pi$
$774$	8.34856	0.300083
$775$	−38.7064	−1.39037
$776$	−18.3940	−0.660305
$777$	2.09263	0.0750727
$778$	48.5128	1.73927
$779$	−22.7057	−0.813516
$780$	46.5149	1.66550
$781$	0.682400	0.0244182
$782$	26.5728	0.950241
$783$	−54.3229	−1.94134
$784$	25.2949	0.903388
$785$	−44.4794	−1.58754
$786$	52.2417	1.86340
$787$	26.8581	0.957389	0.478694	−	0.877982i	$-0.341110\pi$
$787$	26.8581	0.957389	0.478694	+	0.877982i	$0.341110\pi$
$788$	−62.6399	−2.23145
$789$	8.61216	0.306601
$790$	−11.8000	−0.419827
$791$	60.9172	2.16597
$792$	−34.9580	−1.24218
$793$	19.6138	0.696507
$794$	−30.6651	−1.08826
$795$	−16.0167	−0.568053
$796$	28.5758	1.01284
$797$	−21.8180	−0.772834	−0.386417	−	0.922324i	$-0.626287\pi$
$797$	−21.8180	−0.772834	−0.386417	+	0.922324i	$0.626287\pi$
$798$	−37.1742	−1.31595
$799$	−8.34361	−0.295176
$800$	2.04146	0.0721763
$801$	−19.8885	−0.702724
$802$	69.3898	2.45024
$803$	56.6954	2.00074
$804$	−0.0979341	−0.00345387
$805$	−109.617	−3.86350
$806$	22.9919	0.809856
$807$	−9.68664	−0.340986
$808$	37.6801	1.32558
$809$	21.0055	0.738514	0.369257	−	0.929327i	$-0.379612\pi$
$809$	21.0055	0.738514	0.369257	+	0.929327i	$0.379612\pi$
$810$	−11.9917	−0.421346
$811$	24.2269	0.850722	0.425361	−	0.905024i	$-0.360147\pi$
$811$	24.2269	0.850722	0.425361	+	0.905024i	$0.360147\pi$
$812$	−147.440	−5.17414
$813$	−1.16197	−0.0407522
$814$	−5.22530	−0.183147
$815$	−1.05710	−0.0370286
$816$	6.44941	0.225774
$817$	−7.34021	−0.256801
$818$	80.1441	2.80217
$819$	−15.6749	−0.547724
$820$	−99.6557	−3.48013
$821$	−23.1127	−0.806639	−0.403320	−	0.915059i	$-0.632144\pi$
$821$	−23.1127	−0.806639	−0.403320	+	0.915059i	$0.632144\pi$
$822$	25.6600	0.894994
$823$	14.6899	0.512059	0.256030	−	0.966669i	$-0.417586\pi$
$823$	14.6899	0.512059	0.256030	+	0.966669i	$0.417586\pi$
$824$	59.9174	2.08732
$825$	52.9524	1.84357
$826$	78.0360	2.71522
$827$	−52.5408	−1.82702	−0.913511	−	0.406815i	$-0.866639\pi$
$827$	−52.5408	−1.82702	−0.913511	+	0.406815i	$0.866639\pi$
$828$	−50.0503	−1.73937
$829$	24.1312	0.838112	0.419056	−	0.907960i	$-0.362361\pi$
$829$	24.1312	0.838112	0.419056	+	0.907960i	$0.362361\pi$
$830$	93.9473	3.26096
$831$	−26.9601	−0.935236
$832$	−21.1090	−0.731821
$833$	−9.36741	−0.324561
$834$	−32.8606	−1.13787
$835$	−58.6480	−2.02960
$836$	61.7799	2.13670
$837$	−19.7763	−0.683571
$838$	92.3408	3.18986
$839$	43.4372	1.49962	0.749809	−	0.661654i	$-0.230145\pi$
$839$	43.4372	1.49962	0.749809	+	0.661654i	$0.230145\pi$
$840$	−81.1719	−2.80070
$841$	72.5188	2.50065
$842$	−48.0285	−1.65517
$843$	−3.10916	−0.107085
$844$	66.8908	2.30248
$845$	25.3575	0.872323
$846$	23.6122	0.811805
$847$	28.8196	0.990253
$848$	−13.6339	−0.468190
$849$	18.4981	0.634854
$850$	37.0892	1.27215
$851$	−3.72192	−0.127586
$852$	0.723479	0.0247860
$853$	−30.1252	−1.03147	−0.515733	−	0.856749i	$-0.672480\pi$
$853$	−30.1252	−1.03147	−0.515733	+	0.856749i	$0.672480\pi$
$854$	−68.7986	−2.35424
$855$	−23.4583	−0.802257
$856$	−62.2037	−2.12608
$857$	−26.7327	−0.913171	−0.456586	−	0.889679i	$-0.650928\pi$
$857$	−26.7327	−0.913171	−0.456586	+	0.889679i	$0.650928\pi$
$858$	−31.4542	−1.07383
$859$	54.2227	1.85006	0.925028	−	0.379900i	$-0.124042\pi$
$859$	54.2227	1.85006	0.925028	+	0.379900i	$0.124042\pi$
$860$	−32.2163	−1.09857
$861$	−26.9880	−0.919747
$862$	45.0429	1.53417
$863$	5.88736	0.200408	0.100204	−	0.994967i	$-0.468050\pi$
$863$	5.88736	0.200408	0.100204	+	0.994967i	$0.468050\pi$
$864$	1.04305	0.0354851
$865$	73.9734	2.51517
$866$	−17.2120	−0.584889
$867$	17.2662	0.586390
$868$	−53.6759	−1.82188
$869$	5.31076	0.180155
$870$	112.341	3.80873
$871$	0.0545514	0.00184841
$872$	−78.9127	−2.67232
$873$	−6.31833	−0.213843
$874$	66.1176	2.23646
$875$	−80.5034	−2.72151
$876$	60.1082	2.03087
$877$	30.6843	1.03613	0.518067	−	0.855340i	$-0.326652\pi$
$877$	30.6843	1.03613	0.518067	+	0.855340i	$0.326652\pi$
$878$	19.5984	0.661415
$879$	−23.8495	−0.804423
$880$	66.4325	2.23944
$881$	29.4768	0.993100	0.496550	−	0.868008i	$-0.334600\pi$
$881$	29.4768	0.993100	0.496550	+	0.868008i	$0.334600\pi$
$882$	26.5095	0.892623
$883$	48.1323	1.61978	0.809890	−	0.586582i	$-0.199527\pi$
$883$	48.1323	1.61978	0.809890	+	0.586582i	$0.199527\pi$
$884$	−14.6631	−0.493174
$885$	−39.5736	−1.33025
$886$	7.76177	0.260762
$887$	−46.5561	−1.56320	−0.781601	−	0.623778i	$-0.785597\pi$
$887$	−46.5561	−1.56320	−0.781601	+	0.623778i	$0.785597\pi$
$888$	−2.75609	−0.0924883
$889$	−3.64221	−0.122156
$890$	115.313	3.86531
$891$	5.39702	0.180807
$892$	64.2430	2.15101
$893$	−20.7603	−0.694717
$894$	28.4943	0.952993
$895$	24.9294	0.833298
$896$	72.6205	2.42608
$897$	−22.4045	−0.748063
$898$	84.0967	2.80634
$899$	36.9581	1.23262
$900$	−69.8581	−2.32860
$901$	5.04902	0.168207
$902$	67.3890	2.24381
$903$	−8.72457	−0.290335
$904$	−80.2307	−2.66843
$905$	5.37369	0.178628
$906$	−8.19768	−0.272350
$907$	48.3460	1.60530	0.802651	−	0.596450i	$-0.203422\pi$
$907$	48.3460	1.60530	0.802651	+	0.596450i	$0.203422\pi$
$908$	−33.3088	−1.10539
$909$	12.9431	0.429296
$910$	90.8829	3.01274
$911$	9.76175	0.323421	0.161711	−	0.986838i	$-0.448299\pi$
$911$	9.76175	0.323421	0.161711	+	0.986838i	$0.448299\pi$
$912$	16.0472	0.531376
$913$	−42.2822	−1.39934
$914$	1.06358	0.0351801
$915$	34.8891	1.15340
$916$	4.80781	0.158855
$917$	67.9350	2.24341
$918$	18.9501	0.625445
$919$	−0.514857	−0.0169836	−0.00849179	−	0.999964i	$-0.502703\pi$
$919$	−0.514857	−0.0169836	−0.00849179	+	0.999964i	$0.502703\pi$
$920$	144.371	4.75977
$921$	18.8289	0.620435
$922$	−17.9730	−0.591910
$923$	−0.402994	−0.0132647
$924$	73.4316	2.41572
$925$	−5.19490	−0.170807
$926$	30.7277	1.00977
$927$	20.5816	0.675989
$928$	−1.94925	−0.0639872
$929$	−12.8592	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$929$	−12.8592	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$930$	40.8981	1.34110
$931$	−23.3077	−0.763879
$932$	−83.2732	−2.72770
$933$	27.5284	0.901238
$934$	95.1443	3.11322
$935$	−24.6019	−0.804567
$936$	20.6445	0.674788
$937$	21.1431	0.690714	0.345357	−	0.938471i	$-0.387758\pi$
$937$	21.1431	0.690714	0.345357	+	0.938471i	$0.387758\pi$
$938$	−0.191348	−0.00624773
$939$	−7.61287	−0.248437
$940$	−91.1174	−2.97192
$941$	12.8423	0.418647	0.209323	−	0.977846i	$-0.432874\pi$
$941$	12.8423	0.418647	0.209323	+	0.977846i	$0.432874\pi$
$942$	31.8884	1.03898
$943$	48.0004	1.56311
$944$	−33.6862	−1.09639
$945$	−78.1723	−2.54294
$946$	21.7853	0.708300
$947$	−14.1061	−0.458388	−0.229194	−	0.973381i	$-0.573609\pi$
$947$	−14.1061	−0.458388	−0.229194	+	0.973381i	$0.573609\pi$
$948$	5.63045	0.182869
$949$	−33.4816	−1.08686
$950$	92.2841	2.99409
$951$	−3.35678	−0.108851
$952$	25.5882	0.829318
$953$	−49.9114	−1.61679	−0.808395	−	0.588640i	$-0.799663\pi$
$953$	−49.9114	−1.61679	−0.808395	+	0.588640i	$0.799663\pi$
$954$	−14.2886	−0.462611
$955$	86.6883	2.80517
$956$	57.3413	1.85455
$957$	−50.5607	−1.63440
$958$	60.5875	1.95749
$959$	33.3682	1.07751
$960$	−37.5487	−1.21188
$961$	−17.5453	−0.565978
$962$	3.08582	0.0994907
$963$	−21.3670	−0.688541
$964$	6.39821	0.206072
$965$	−25.0183	−0.805368
$966$	78.5873	2.52850
$967$	50.4565	1.62257	0.811286	−	0.584649i	$-0.198768\pi$
$967$	50.4565	1.62257	0.811286	+	0.584649i	$0.198768\pi$
$968$	−37.9567	−1.21998
$969$	−5.94274	−0.190908
$970$	36.6337	1.17624
$971$	−33.0044	−1.05916	−0.529581	−	0.848259i	$-0.677651\pi$
$971$	−33.0044	−1.05916	−0.529581	+	0.848259i	$0.677651\pi$
$972$	−58.6546	−1.88135
$973$	−42.7319	−1.36992
$974$	5.23444	0.167722
$975$	−31.2712	−1.00148
$976$	29.6987	0.950632
$977$	−32.3762	−1.03581	−0.517903	−	0.855440i	$-0.673287\pi$
$977$	−32.3762	−1.03581	−0.517903	+	0.855440i	$0.673287\pi$
$978$	0.757859	0.0242337
$979$	−51.8982	−1.65867
$980$	−102.298	−3.26779
$981$	−27.1065	−0.865444
$982$	83.1521	2.65349
$983$	−43.0429	−1.37286	−0.686428	−	0.727198i	$-0.740822\pi$
$983$	−43.0429	−1.37286	−0.686428	+	0.727198i	$0.740822\pi$
$984$	35.5444	1.13311
$985$	62.0656	1.97758
$986$	−35.4139	−1.12781
$987$	−24.6757	−0.785435
$988$	−36.4843	−1.16072
$989$	15.5174	0.493424
$990$	69.6227	2.21275
$991$	−53.0669	−1.68573	−0.842863	−	0.538129i	$-0.819131\pi$
$991$	−53.0669	−1.68573	−0.842863	+	0.538129i	$0.819131\pi$
$992$	−0.709628	−0.0225307
$993$	27.2352	0.864283
$994$	1.41356	0.0448356
$995$	−28.3138	−0.897608
$996$	−44.8274	−1.42041
$997$	−11.8393	−0.374954	−0.187477	−	0.982269i	$-0.560031\pi$
$997$	−11.8393	−0.374954	−0.187477	+	0.982269i	$0.560031\pi$
$998$	56.4878	1.78809
$999$	−2.65424	−0.0839765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.14	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.14	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +O(q^{10})\)	\(q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +9.64388 q^{10} -4.34035 q^{11} -4.60163 q^{12} +2.56321 q^{13} -8.99086 q^{14} +4.55944 q^{15} +3.88114 q^{16} -1.43730 q^{17} +4.06751 q^{18} -3.57623 q^{19} -15.6962 q^{20} -4.25071 q^{21} +10.6140 q^{22} +7.56025 q^{23} +5.59838 q^{24} +10.5523 q^{25} -6.26814 q^{26} +5.39150 q^{27} +14.6333 q^{28} -10.0757 q^{29} -11.1498 q^{30} -3.66806 q^{31} +0.193461 q^{32} +5.01811 q^{33} +3.51480 q^{34} -14.4992 q^{35} -6.62019 q^{36} -0.492301 q^{37} +8.74543 q^{38} -2.96346 q^{39} +19.0961 q^{40} +6.34905 q^{41} +10.3948 q^{42} +2.05250 q^{43} -17.2751 q^{44} +6.55950 q^{45} -18.4880 q^{46} +5.80507 q^{47} -4.48718 q^{48} +6.51738 q^{49} -25.8048 q^{50} +1.66173 q^{51} +10.2019 q^{52} -3.51286 q^{53} -13.1845 q^{54} +17.1168 q^{55} -17.8030 q^{56} +4.13467 q^{57} +24.6393 q^{58} -8.67947 q^{59} +18.1471 q^{60} +7.65206 q^{61} +8.96998 q^{62} -6.11533 q^{63} -8.23537 q^{64} -10.1084 q^{65} -12.2714 q^{66} +0.0212825 q^{67} -5.72061 q^{68} -8.74079 q^{69} +35.4567 q^{70} -0.157222 q^{71} +8.05418 q^{72} -13.0624 q^{73} +1.20389 q^{74} -12.2000 q^{75} -14.2339 q^{76} -15.9577 q^{77} +7.24692 q^{78} -1.22358 q^{79} -15.3058 q^{80} -1.24345 q^{81} -15.5262 q^{82} +9.74164 q^{83} -16.9183 q^{84} +5.66817 q^{85} -5.01924 q^{86} +11.6490 q^{87} +21.0171 q^{88} +11.9571 q^{89} -16.0408 q^{90} +9.42389 q^{91} +30.0907 q^{92} +4.24084 q^{93} -14.1959 q^{94} +14.1034 q^{95} -0.223671 q^{96} +3.79864 q^{97} -15.9378 q^{98} +7.21936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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