LMFDB - Embedded newform 4021.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23064 q^{2} -3.03788 q^{3} +2.97574 q^{4} +2.24920 q^{5} +6.77641 q^{6} -3.34201 q^{7} -2.17651 q^{8} +6.22873 q^{9} +O(q^{10})$	\(q-2.23064 q^{2} -3.03788 q^{3} +2.97574 q^{4} +2.24920 q^{5} +6.77641 q^{6} -3.34201 q^{7} -2.17651 q^{8} +6.22873 q^{9} -5.01714 q^{10} -6.22124 q^{11} -9.03994 q^{12} -3.48745 q^{13} +7.45481 q^{14} -6.83280 q^{15} -1.09647 q^{16} +3.38316 q^{17} -13.8940 q^{18} -3.93987 q^{19} +6.69302 q^{20} +10.1526 q^{21} +13.8773 q^{22} +7.82970 q^{23} +6.61198 q^{24} +0.0588941 q^{25} +7.77922 q^{26} -9.80850 q^{27} -9.94494 q^{28} +6.51820 q^{29} +15.2415 q^{30} -6.09791 q^{31} +6.79884 q^{32} +18.8994 q^{33} -7.54660 q^{34} -7.51684 q^{35} +18.5351 q^{36} +1.57811 q^{37} +8.78840 q^{38} +10.5945 q^{39} -4.89541 q^{40} +4.63758 q^{41} -22.6468 q^{42} +4.51697 q^{43} -18.5128 q^{44} +14.0096 q^{45} -17.4652 q^{46} +2.88949 q^{47} +3.33094 q^{48} +4.16903 q^{49} -0.131371 q^{50} -10.2776 q^{51} -10.3777 q^{52} -8.89560 q^{53} +21.8792 q^{54} -13.9928 q^{55} +7.27392 q^{56} +11.9688 q^{57} -14.5397 q^{58} -14.7164 q^{59} -20.3326 q^{60} -10.9456 q^{61} +13.6022 q^{62} -20.8165 q^{63} -12.9728 q^{64} -7.84396 q^{65} -42.1577 q^{66} +12.3380 q^{67} +10.0674 q^{68} -23.7857 q^{69} +16.7673 q^{70} +9.26467 q^{71} -13.5569 q^{72} +6.95485 q^{73} -3.52020 q^{74} -0.178913 q^{75} -11.7240 q^{76} +20.7915 q^{77} -23.6324 q^{78} -1.18057 q^{79} -2.46617 q^{80} +11.1109 q^{81} -10.3448 q^{82} +15.0351 q^{83} +30.2116 q^{84} +7.60940 q^{85} -10.0757 q^{86} -19.8015 q^{87} +13.5406 q^{88} +13.1724 q^{89} -31.2504 q^{90} +11.6551 q^{91} +23.2991 q^{92} +18.5247 q^{93} -6.44541 q^{94} -8.86154 q^{95} -20.6541 q^{96} +2.87393 q^{97} -9.29959 q^{98} -38.7504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.23064	−1.57730	−0.788649	−	0.614844i	$-0.789219\pi$
$2$	−2.23064	−1.57730	−0.788649	+	0.614844i	$0.789219\pi$
$3$	−3.03788	−1.75392	−0.876961	−	0.480561i	$-0.840433\pi$
$3$	−3.03788	−1.75392	−0.876961	+	0.480561i	$0.840433\pi$
$4$	2.97574	1.48787
$5$	2.24920	1.00587	0.502936	−	0.864324i	$-0.332253\pi$
$5$	2.24920	1.00587	0.502936	+	0.864324i	$0.332253\pi$
$6$	6.77641	2.76646
$7$	−3.34201	−1.26316	−0.631581	−	0.775310i	$-0.717593\pi$
$7$	−3.34201	−1.26316	−0.631581	+	0.775310i	$0.717593\pi$
$8$	−2.17651	−0.769513
$9$	6.22873	2.07624
$10$	−5.01714	−1.58656
$11$	−6.22124	−1.87578	−0.937888	−	0.346939i	$-0.887221\pi$
$11$	−6.22124	−1.87578	−0.937888	+	0.346939i	$0.887221\pi$
$12$	−9.03994	−2.60960
$13$	−3.48745	−0.967244	−0.483622	−	0.875277i	$-0.660679\pi$
$13$	−3.48745	−0.967244	−0.483622	+	0.875277i	$0.660679\pi$
$14$	7.45481	1.99238
$15$	−6.83280	−1.76422
$16$	−1.09647	−0.274117
$17$	3.38316	0.820537	0.410268	−	0.911965i	$-0.365435\pi$
$17$	3.38316	0.820537	0.410268	+	0.911965i	$0.365435\pi$
$18$	−13.8940	−3.27485
$19$	−3.93987	−0.903867	−0.451934	−	0.892052i	$-0.649266\pi$
$19$	−3.93987	−0.903867	−0.451934	+	0.892052i	$0.649266\pi$
$20$	6.69302	1.49660
$21$	10.1526	2.21549
$22$	13.8773	2.95866
$23$	7.82970	1.63261	0.816303	−	0.577624i	$-0.196020\pi$
$23$	7.82970	1.63261	0.816303	+	0.577624i	$0.196020\pi$
$24$	6.61198	1.34967
$25$	0.0588941	0.0117788
$26$	7.77922	1.52563
$27$	−9.80850	−1.88765
$28$	−9.94494	−1.87942
$29$	6.51820	1.21040	0.605200	−	0.796074i	$-0.293093\pi$
$29$	6.51820	1.21040	0.605200	+	0.796074i	$0.293093\pi$
$30$	15.2415	2.78270
$31$	−6.09791	−1.09522	−0.547609	−	0.836734i	$-0.684462\pi$
$31$	−6.09791	−1.09522	−0.547609	+	0.836734i	$0.684462\pi$
$32$	6.79884	1.20188
$33$	18.8994	3.28996
$34$	−7.54660	−1.29423
$35$	−7.51684	−1.27058
$36$	18.5351	3.08918
$37$	1.57811	0.259440	0.129720	−	0.991551i	$-0.458592\pi$
$37$	1.57811	0.259440	0.129720	+	0.991551i	$0.458592\pi$
$38$	8.78840	1.42567
$39$	10.5945	1.69647
$40$	−4.89541	−0.774032
$41$	4.63758	0.724269	0.362134	−	0.932126i	$-0.382048\pi$
$41$	4.63758	0.724269	0.362134	+	0.932126i	$0.382048\pi$
$42$	−22.6468	−3.49448
$43$	4.51697	0.688832	0.344416	−	0.938817i	$-0.388077\pi$
$43$	4.51697	0.688832	0.344416	+	0.938817i	$0.388077\pi$
$44$	−18.5128	−2.79091
$45$	14.0096	2.08844
$46$	−17.4652	−2.57510
$47$	2.88949	0.421476	0.210738	−	0.977543i	$-0.432413\pi$
$47$	2.88949	0.421476	0.210738	+	0.977543i	$0.432413\pi$
$48$	3.33094	0.480780
$49$	4.16903	0.595576
$50$	−0.131371	−0.0185787
$51$	−10.2776	−1.43916
$52$	−10.3777	−1.43913
$53$	−8.89560	−1.22190	−0.610952	−	0.791668i	$-0.709213\pi$
$53$	−8.89560	−1.22190	−0.610952	+	0.791668i	$0.709213\pi$
$54$	21.8792	2.97738
$55$	−13.9928	−1.88679
$56$	7.27392	0.972019
$57$	11.9688	1.58531
$58$	−14.5397	−1.90916
$59$	−14.7164	−1.91591	−0.957954	−	0.286922i	$-0.907368\pi$
$59$	−14.7164	−1.91591	−0.957954	+	0.286922i	$0.907368\pi$
$60$	−20.3326	−2.62493
$61$	−10.9456	−1.40144	−0.700720	−	0.713437i	$-0.747138\pi$
$61$	−10.9456	−1.40144	−0.700720	+	0.713437i	$0.747138\pi$
$62$	13.6022	1.72748
$63$	−20.8165	−2.62263
$64$	−12.9728	−1.62160
$65$	−7.84396	−0.972924
$66$	−42.1577	−5.18925
$67$	12.3380	1.50733	0.753663	−	0.657261i	$-0.228285\pi$
$67$	12.3380	1.50733	0.753663	+	0.657261i	$0.228285\pi$
$68$	10.0674	1.22085
$69$	−23.7857	−2.86346
$70$	16.7673	2.00408
$71$	9.26467	1.09951	0.549757	−	0.835324i	$-0.314720\pi$
$71$	9.26467	1.09951	0.549757	+	0.835324i	$0.314720\pi$
$72$	−13.5569	−1.59770
$73$	6.95485	0.814004	0.407002	−	0.913427i	$-0.366574\pi$
$73$	6.95485	0.814004	0.407002	+	0.913427i	$0.366574\pi$
$74$	−3.52020	−0.409215
$75$	−0.178913	−0.0206591
$76$	−11.7240	−1.34483
$77$	20.7915	2.36941
$78$	−23.6324	−2.67584
$79$	−1.18057	−0.132824	−0.0664120	−	0.997792i	$-0.521155\pi$
$79$	−1.18057	−0.132824	−0.0664120	+	0.997792i	$0.521155\pi$
$80$	−2.46617	−0.275727
$81$	11.1109	1.23454
$82$	−10.3448	−1.14239
$83$	15.0351	1.65031	0.825156	−	0.564905i	$-0.191087\pi$
$83$	15.0351	1.65031	0.825156	+	0.564905i	$0.191087\pi$
$84$	30.2116	3.29635
$85$	7.60940	0.825355
$86$	−10.0757	−1.08649
$87$	−19.8015	−2.12295
$88$	13.5406	1.44343
$89$	13.1724	1.39627	0.698137	−	0.715964i	$-0.254013\pi$
$89$	13.1724	1.39627	0.698137	+	0.715964i	$0.254013\pi$
$90$	−31.2504	−3.29408
$91$	11.6551	1.22178
$92$	23.2991	2.42910
$93$	18.5247	1.92093
$94$	−6.44541	−0.664793
$95$	−8.86154	−0.909175
$96$	−20.6541	−2.10800
$97$	2.87393	0.291804	0.145902	−	0.989299i	$-0.453392\pi$
$97$	2.87393	0.291804	0.145902	+	0.989299i	$0.453392\pi$
$98$	−9.29959	−0.939400
$99$	−38.7504	−3.89457
$100$	0.175253	0.0175253
$101$	−5.83154	−0.580260	−0.290130	−	0.956987i	$-0.593698\pi$
$101$	−5.83154	−0.580260	−0.290130	+	0.956987i	$0.593698\pi$
$102$	22.9257	2.26998
$103$	8.44649	0.832257	0.416128	−	0.909306i	$-0.363387\pi$
$103$	8.44649	0.832257	0.416128	+	0.909306i	$0.363387\pi$
$104$	7.59047	0.744307
$105$	22.8353	2.22850
$106$	19.8428	1.92731
$107$	−16.0823	−1.55473	−0.777366	−	0.629048i	$-0.783445\pi$
$107$	−16.0823	−1.55473	−0.777366	+	0.629048i	$0.783445\pi$
$108$	−29.1875	−2.80857
$109$	9.05662	0.867467	0.433733	−	0.901041i	$-0.357196\pi$
$109$	9.05662	0.867467	0.433733	+	0.901041i	$0.357196\pi$
$110$	31.2129	2.97603
$111$	−4.79412	−0.455038
$112$	3.66441	0.346254
$113$	1.08253	0.101836	0.0509178	−	0.998703i	$-0.483785\pi$
$113$	1.08253	0.101836	0.0509178	+	0.998703i	$0.483785\pi$
$114$	−26.6981	−2.50051
$115$	17.6106	1.64219
$116$	19.3964	1.80091
$117$	−21.7224	−2.00823
$118$	32.8269	3.02196
$119$	−11.3066	−1.03647
$120$	14.8717	1.35759
$121$	27.7039	2.51853
$122$	24.4156	2.21049
$123$	−14.0884	−1.27031
$124$	−18.1458	−1.62954
$125$	−11.1135	−0.994024
$126$	46.4340	4.13667
$127$	−2.82011	−0.250244	−0.125122	−	0.992141i	$-0.539932\pi$
$127$	−2.82011	−0.250244	−0.125122	+	0.992141i	$0.539932\pi$
$128$	15.3399	1.35587
$129$	−13.7220	−1.20816
$130$	17.4970	1.53459
$131$	10.6690	0.932154	0.466077	−	0.884744i	$-0.345667\pi$
$131$	10.6690	0.932154	0.466077	+	0.884744i	$0.345667\pi$
$132$	56.2396	4.89503
$133$	13.1671	1.14173
$134$	−27.5216	−2.37750
$135$	−22.0613	−1.89873
$136$	−7.36348	−0.631414
$137$	−22.5632	−1.92770	−0.963852	−	0.266439i	$-0.914153\pi$
$137$	−22.5632	−1.92770	−0.963852	+	0.266439i	$0.914153\pi$
$138$	53.0573	4.51653
$139$	1.05189	0.0892199	0.0446100	−	0.999004i	$-0.485795\pi$
$139$	1.05189	0.0892199	0.0446100	+	0.999004i	$0.485795\pi$
$140$	−22.3681	−1.89045
$141$	−8.77794	−0.739236
$142$	−20.6661	−1.73426
$143$	21.6963	1.81433
$144$	−6.82960	−0.569134
$145$	14.6607	1.21751
$146$	−15.5137	−1.28393
$147$	−12.6650	−1.04459
$148$	4.69605	0.386013
$149$	10.7092	0.877336	0.438668	−	0.898649i	$-0.355450\pi$
$149$	10.7092	0.877336	0.438668	+	0.898649i	$0.355450\pi$
$150$	0.399091	0.0325856
$151$	1.28966	0.104951	0.0524756	−	0.998622i	$-0.483289\pi$
$151$	1.28966	0.104951	0.0524756	+	0.998622i	$0.483289\pi$
$152$	8.57516	0.695537
$153$	21.0728	1.70363
$154$	−46.3782	−3.73726
$155$	−13.7154	−1.10165
$156$	31.5263	2.52412
$157$	4.43240	0.353744	0.176872	−	0.984234i	$-0.443402\pi$
$157$	4.43240	0.353744	0.176872	+	0.984234i	$0.443402\pi$
$158$	2.63341	0.209503
$159$	27.0238	2.14312
$160$	15.2919	1.20893
$161$	−26.1669	−2.06224
$162$	−24.7843	−1.94724
$163$	1.08681	0.0851258	0.0425629	−	0.999094i	$-0.486448\pi$
$163$	1.08681	0.0851258	0.0425629	+	0.999094i	$0.486448\pi$
$164$	13.8002	1.07762
$165$	42.5085	3.30928
$166$	−33.5377	−2.60303
$167$	19.1086	1.47867	0.739335	−	0.673338i	$-0.235140\pi$
$167$	19.1086	1.47867	0.739335	+	0.673338i	$0.235140\pi$
$168$	−22.0973	−1.70485
$169$	−0.837711	−0.0644393
$170$	−16.9738	−1.30183
$171$	−24.5404	−1.87665
$172$	13.4413	1.02489
$173$	7.42633	0.564613	0.282307	−	0.959324i	$-0.408900\pi$
$173$	7.42633	0.564613	0.282307	+	0.959324i	$0.408900\pi$
$174$	44.1700	3.34852
$175$	−0.196825	−0.0148786
$176$	6.82139	0.514182
$177$	44.7066	3.36035
$178$	−29.3829	−2.20234
$179$	−4.22898	−0.316089	−0.158045	−	0.987432i	$-0.550519\pi$
$179$	−4.22898	−0.316089	−0.158045	+	0.987432i	$0.550519\pi$
$180$	41.6890	3.10732
$181$	10.8206	0.804291	0.402146	−	0.915576i	$-0.368265\pi$
$181$	10.8206	0.804291	0.402146	+	0.915576i	$0.368265\pi$
$182$	−25.9982	−1.92712
$183$	33.2514	2.45802
$184$	−17.0414	−1.25631
$185$	3.54949	0.260964
$186$	−41.3220	−3.02987
$187$	−21.0475	−1.53914
$188$	8.59837	0.627100
$189$	32.7801	2.38440
$190$	19.7669	1.43404
$191$	−5.64874	−0.408728	−0.204364	−	0.978895i	$-0.565513\pi$
$191$	−5.64874	−0.408728	−0.204364	+	0.978895i	$0.565513\pi$
$192$	39.4099	2.84416
$193$	3.34304	0.240637	0.120318	−	0.992735i	$-0.461608\pi$
$193$	3.34304	0.240637	0.120318	+	0.992735i	$0.461608\pi$
$194$	−6.41070	−0.460262
$195$	23.8290	1.70643
$196$	12.4059	0.886138
$197$	−7.32050	−0.521564	−0.260782	−	0.965398i	$-0.583980\pi$
$197$	−7.32050	−0.521564	−0.260782	+	0.965398i	$0.583980\pi$
$198$	86.4381	6.14289
$199$	−18.4437	−1.30744	−0.653718	−	0.756738i	$-0.726792\pi$
$199$	−18.4437	−1.30744	−0.653718	+	0.756738i	$0.726792\pi$
$200$	−0.128184	−0.00906396
$201$	−37.4814	−2.64373
$202$	13.0080	0.915242
$203$	−21.7839	−1.52893
$204$	−30.5835	−2.14128
$205$	10.4308	0.728522
$206$	−18.8410	−1.31272
$207$	48.7691	3.38969
$208$	3.82387	0.265138
$209$	24.5109	1.69545
$210$	−50.9372	−3.51500
$211$	−13.3947	−0.922130	−0.461065	−	0.887366i	$-0.652532\pi$
$211$	−13.3947	−0.922130	−0.461065	+	0.887366i	$0.652532\pi$
$212$	−26.4709	−1.81803
$213$	−28.1450	−1.92846
$214$	35.8737	2.45228
$215$	10.1596	0.692877
$216$	21.3483	1.45257
$217$	20.3793	1.38344
$218$	−20.2020	−1.36825
$219$	−21.1280	−1.42770
$220$	−41.6389	−2.80729
$221$	−11.7986	−0.793659
$222$	10.6939	0.717731
$223$	25.7360	1.72341	0.861706	−	0.507408i	$-0.169396\pi$
$223$	25.7360	1.72341	0.861706	+	0.507408i	$0.169396\pi$
$224$	−22.7218	−1.51816
$225$	0.366836	0.0244557
$226$	−2.41472	−0.160625
$227$	0.754576	0.0500830	0.0250415	−	0.999686i	$-0.492028\pi$
$227$	0.754576	0.0500830	0.0250415	+	0.999686i	$0.492028\pi$
$228$	35.6161	2.35874
$229$	7.11691	0.470299	0.235149	−	0.971959i	$-0.424442\pi$
$229$	7.11691	0.470299	0.235149	+	0.971959i	$0.424442\pi$
$230$	−39.2827	−2.59023
$231$	−63.1620	−4.15575
$232$	−14.1869	−0.931418
$233$	0.988894	0.0647846	0.0323923	−	0.999475i	$-0.489687\pi$
$233$	0.988894	0.0647846	0.0323923	+	0.999475i	$0.489687\pi$
$234$	48.4547	3.16758
$235$	6.49904	0.423951
$236$	−43.7920	−2.85062
$237$	3.58642	0.232963
$238$	25.2208	1.63482
$239$	7.68952	0.497394	0.248697	−	0.968581i	$-0.419998\pi$
$239$	7.68952	0.497394	0.248697	+	0.968581i	$0.419998\pi$
$240$	7.49195	0.483603
$241$	−20.1464	−1.29774	−0.648871	−	0.760898i	$-0.724759\pi$
$241$	−20.1464	−1.29774	−0.648871	+	0.760898i	$0.724759\pi$
$242$	−61.7972	−3.97248
$243$	−4.32805	−0.277644
$244$	−32.5712	−2.08516
$245$	9.37698	0.599073
$246$	31.4262	2.00366
$247$	13.7401	0.874260
$248$	13.2722	0.842784
$249$	−45.6747	−2.89452
$250$	24.7902	1.56787
$251$	−15.4925	−0.977879	−0.488940	−	0.872318i	$-0.662616\pi$
$251$	−15.4925	−0.977879	−0.488940	+	0.872318i	$0.662616\pi$
$252$	−61.9443	−3.90213
$253$	−48.7105	−3.06240
$254$	6.29064	0.394710
$255$	−23.1165	−1.44761
$256$	−8.27216	−0.517010
$257$	19.5521	1.21963	0.609814	−	0.792545i	$-0.291244\pi$
$257$	19.5521	1.21963	0.609814	+	0.792545i	$0.291244\pi$
$258$	30.6088	1.90562
$259$	−5.27407	−0.327715
$260$	−23.3416	−1.44758
$261$	40.6001	2.51308
$262$	−23.7986	−1.47028
$263$	−5.36389	−0.330752	−0.165376	−	0.986231i	$-0.552884\pi$
$263$	−5.36389	−0.330752	−0.165376	+	0.986231i	$0.552884\pi$
$264$	−41.1348	−2.53167
$265$	−20.0080	−1.22908
$266$	−29.3709	−1.80085
$267$	−40.0163	−2.44896
$268$	36.7146	2.24270
$269$	31.0657	1.89411	0.947056	−	0.321069i	$-0.104042\pi$
$269$	31.0657	1.89411	0.947056	+	0.321069i	$0.104042\pi$
$270$	49.2106	2.99486
$271$	15.0236	0.912616	0.456308	−	0.889822i	$-0.349171\pi$
$271$	15.0236	0.912616	0.456308	+	0.889822i	$0.349171\pi$
$272$	−3.70953	−0.224923
$273$	−35.4068	−2.14292
$274$	50.3303	3.04056
$275$	−0.366395	−0.0220944
$276$	−70.7800	−4.26045
$277$	−30.6157	−1.83952	−0.919760	−	0.392481i	$-0.871617\pi$
$277$	−30.6157	−1.83952	−0.919760	+	0.392481i	$0.871617\pi$
$278$	−2.34638	−0.140726
$279$	−37.9823	−2.27394
$280$	16.3605	0.977727
$281$	19.5115	1.16396	0.581978	−	0.813205i	$-0.302279\pi$
$281$	19.5115	1.16396	0.581978	+	0.813205i	$0.302279\pi$
$282$	19.5804	1.16600
$283$	12.6387	0.751293	0.375647	−	0.926763i	$-0.377421\pi$
$283$	12.6387	0.751293	0.375647	+	0.926763i	$0.377421\pi$
$284$	27.5692	1.63593
$285$	26.9203	1.59462
$286$	−48.3964	−2.86174
$287$	−15.4988	−0.914868
$288$	42.3482	2.49539
$289$	−5.55423	−0.326719
$290$	−32.7027	−1.92037
$291$	−8.73068	−0.511801
$292$	20.6958	1.21113
$293$	7.34132	0.428885	0.214442	−	0.976737i	$-0.431207\pi$
$293$	7.34132	0.428885	0.214442	+	0.976737i	$0.431207\pi$
$294$	28.2511	1.64764
$295$	−33.1000	−1.92716
$296$	−3.43478	−0.199643
$297$	61.0211	3.54080
$298$	−23.8884	−1.38382
$299$	−27.3057	−1.57913
$300$	−0.532399	−0.0307381
$301$	−15.0958	−0.870105
$302$	−2.87677	−0.165539
$303$	17.7155	1.01773
$304$	4.31994	0.247765
$305$	−24.6188	−1.40967
$306$	−47.0057	−2.68714
$307$	−6.83209	−0.389928	−0.194964	−	0.980810i	$-0.562459\pi$
$307$	−6.83209	−0.389928	−0.194964	+	0.980810i	$0.562459\pi$
$308$	61.8699	3.52536
$309$	−25.6594	−1.45971
$310$	30.5941	1.73763
$311$	−0.516618	−0.0292947	−0.0146473	−	0.999893i	$-0.504663\pi$
$311$	−0.516618	−0.0292947	−0.0146473	+	0.999893i	$0.504663\pi$
$312$	−23.0589	−1.30546
$313$	−9.24599	−0.522614	−0.261307	−	0.965256i	$-0.584154\pi$
$313$	−9.24599	−0.522614	−0.261307	+	0.965256i	$0.584154\pi$
$314$	−9.88707	−0.557960
$315$	−46.8204	−2.63803
$316$	−3.51305	−0.197625
$317$	−23.7022	−1.33125	−0.665624	−	0.746287i	$-0.731835\pi$
$317$	−23.7022	−1.33125	−0.665624	+	0.746287i	$0.731835\pi$
$318$	−60.2802	−3.38035
$319$	−40.5513	−2.27044
$320$	−29.1784	−1.63112
$321$	48.8561	2.72688
$322$	58.3689	3.25277
$323$	−13.3292	−0.741656
$324$	33.0630	1.83684
$325$	−0.205390	−0.0113930
$326$	−2.42428	−0.134269
$327$	−27.5130	−1.52147
$328$	−10.0937	−0.557334
$329$	−9.65671	−0.532392
$330$	−94.8210	−5.21972
$331$	−12.7294	−0.699671	−0.349835	−	0.936811i	$-0.613763\pi$
$331$	−12.7294	−0.699671	−0.349835	+	0.936811i	$0.613763\pi$
$332$	44.7403	2.45545
$333$	9.82964	0.538661
$334$	−42.6244	−2.33230
$335$	27.7506	1.51618
$336$	−11.1320	−0.607303
$337$	17.6609	0.962052	0.481026	−	0.876706i	$-0.340264\pi$
$337$	17.6609	0.962052	0.481026	+	0.876706i	$0.340264\pi$
$338$	1.86863	0.101640
$339$	−3.28859	−0.178612
$340$	22.6436	1.22802
$341$	37.9366	2.05438
$342$	54.7406	2.96003
$343$	9.46113	0.510853
$344$	−9.83124	−0.530065
$345$	−53.4988	−2.88028
$346$	−16.5654	−0.890563
$347$	−5.21079	−0.279730	−0.139865	−	0.990171i	$-0.544667\pi$
$347$	−5.21079	−0.279730	−0.139865	+	0.990171i	$0.544667\pi$
$348$	−58.9241	−3.15866
$349$	−4.31300	−0.230870	−0.115435	−	0.993315i	$-0.536826\pi$
$349$	−4.31300	−0.230870	−0.115435	+	0.993315i	$0.536826\pi$
$350$	0.439044	0.0234679
$351$	34.2066	1.82581
$352$	−42.2973	−2.25445
$353$	8.18716	0.435759	0.217879	−	0.975976i	$-0.430086\pi$
$353$	8.18716	0.435759	0.217879	+	0.975976i	$0.430086\pi$
$354$	−99.7241	−5.30028
$355$	20.8381	1.10597
$356$	39.1976	2.07747
$357$	34.3480	1.81789
$358$	9.43332	0.498566
$359$	−29.1309	−1.53747	−0.768735	−	0.639567i	$-0.779114\pi$
$359$	−29.1309	−1.53747	−0.768735	+	0.639567i	$0.779114\pi$
$360$	−30.4922	−1.60708
$361$	−3.47746	−0.183024
$362$	−24.1369	−1.26861
$363$	−84.1611	−4.41731
$364$	34.6825	1.81785
$365$	15.6428	0.818784
$366$	−74.1718	−3.87702
$367$	−20.5206	−1.07117	−0.535584	−	0.844482i	$-0.679909\pi$
$367$	−20.5206	−1.07117	−0.535584	+	0.844482i	$0.679909\pi$
$368$	−8.58502	−0.447525
$369$	28.8862	1.50376
$370$	−7.91762	−0.411618
$371$	29.7292	1.54346
$372$	55.1248	2.85809
$373$	−16.7968	−0.869704	−0.434852	−	0.900502i	$-0.643199\pi$
$373$	−16.7968	−0.869704	−0.434852	+	0.900502i	$0.643199\pi$
$374$	46.9492	2.42769
$375$	33.7616	1.74344
$376$	−6.28901	−0.324331
$377$	−22.7319	−1.17075
$378$	−73.1205	−3.76091
$379$	−9.59442	−0.492832	−0.246416	−	0.969164i	$-0.579253\pi$
$379$	−9.59442	−0.492832	−0.246416	+	0.969164i	$0.579253\pi$
$380$	−26.3696	−1.35273
$381$	8.56717	0.438909
$382$	12.6003	0.644686
$383$	−4.21799	−0.215529	−0.107765	−	0.994176i	$-0.534369\pi$
$383$	−4.21799	−0.215529	−0.107765	+	0.994176i	$0.534369\pi$
$384$	−46.6009	−2.37809
$385$	46.7641	2.38332
$386$	−7.45710	−0.379556
$387$	28.1350	1.43018
$388$	8.55207	0.434166
$389$	−26.3152	−1.33423	−0.667117	−	0.744953i	$-0.732472\pi$
$389$	−26.3152	−1.33423	−0.667117	+	0.744953i	$0.732472\pi$
$390$	−53.1539	−2.69155
$391$	26.4891	1.33961
$392$	−9.07394	−0.458303
$393$	−32.4111	−1.63493
$394$	16.3294	0.822662
$395$	−2.65533	−0.133604
$396$	−115.311	−5.79460
$397$	−1.18541	−0.0594941	−0.0297470	−	0.999557i	$-0.509470\pi$
$397$	−1.18541	−0.0594941	−0.0297470	+	0.999557i	$0.509470\pi$
$398$	41.1411	2.06222
$399$	−40.0000	−2.00251
$400$	−0.0645755	−0.00322878
$401$	−25.8813	−1.29245	−0.646226	−	0.763146i	$-0.723654\pi$
$401$	−25.8813	−1.29245	−0.646226	+	0.763146i	$0.723654\pi$
$402$	83.6073	4.16995
$403$	21.2662	1.05934
$404$	−17.3531	−0.863350
$405$	24.9906	1.24179
$406$	48.5919	2.41158
$407$	−9.81783	−0.486652
$408$	22.3694	1.10745
$409$	24.7032	1.22149	0.610747	−	0.791826i	$-0.290869\pi$
$409$	24.7032	1.22149	0.610747	+	0.791826i	$0.290869\pi$
$410$	−23.2674	−1.14910
$411$	68.5443	3.38104
$412$	25.1345	1.23829
$413$	49.1823	2.42010
$414$	−108.786	−5.34654
$415$	33.8168	1.66000
$416$	−23.7106	−1.16251
$417$	−3.19551	−0.156485
$418$	−54.6748	−2.67423
$419$	15.8911	0.776330	0.388165	−	0.921590i	$-0.373109\pi$
$419$	15.8911	0.776330	0.388165	+	0.921590i	$0.373109\pi$
$420$	67.9518	3.31571
$421$	24.4041	1.18938	0.594692	−	0.803953i	$-0.297274\pi$
$421$	24.4041	1.18938	0.594692	+	0.803953i	$0.297274\pi$
$422$	29.8787	1.45447
$423$	17.9979	0.875086
$424$	19.3614	0.940271
$425$	0.199248	0.00966496
$426$	62.7812	3.04176
$427$	36.5803	1.77024
$428$	−47.8566	−2.31324
$429$	−65.9107	−3.18220
$430$	−22.6623	−1.09287
$431$	−1.69994	−0.0818833	−0.0409416	−	0.999162i	$-0.513036\pi$
$431$	−1.69994	−0.0818833	−0.0409416	+	0.999162i	$0.513036\pi$
$432$	10.7547	0.517436
$433$	−4.30105	−0.206695	−0.103348	−	0.994645i	$-0.532955\pi$
$433$	−4.30105	−0.206695	−0.103348	+	0.994645i	$0.532955\pi$
$434$	−45.4588	−2.18209
$435$	−44.5376	−2.13541
$436$	26.9501	1.29068
$437$	−30.8480	−1.47566
$438$	47.1289	2.25191
$439$	−21.5339	−1.02775	−0.513877	−	0.857864i	$-0.671791\pi$
$439$	−21.5339	−1.02775	−0.513877	+	0.857864i	$0.671791\pi$
$440$	30.4555	1.45191
$441$	25.9678	1.23656
$442$	26.3184	1.25184
$443$	26.1051	1.24029	0.620145	−	0.784488i	$-0.287074\pi$
$443$	26.1051	1.24029	0.620145	+	0.784488i	$0.287074\pi$
$444$	−14.2660	−0.677037
$445$	29.6274	1.40447
$446$	−57.4077	−2.71833
$447$	−32.5334	−1.53878
$448$	43.3552	2.04834
$449$	−1.95397	−0.0922136	−0.0461068	−	0.998937i	$-0.514681\pi$
$449$	−1.95397	−0.0922136	−0.0461068	+	0.998937i	$0.514681\pi$
$450$	−0.818277	−0.0385739
$451$	−28.8515	−1.35857
$452$	3.22131	0.151518
$453$	−3.91784	−0.184076
$454$	−1.68318	−0.0789957
$455$	26.2146	1.22896
$456$	−26.0503	−1.21992
$457$	−14.4095	−0.674047	−0.337023	−	0.941496i	$-0.609420\pi$
$457$	−14.4095	−0.674047	−0.337023	+	0.941496i	$0.609420\pi$
$458$	−15.8752	−0.741801
$459$	−33.1837	−1.54888
$460$	52.4044	2.44337
$461$	−21.9712	−1.02330	−0.511650	−	0.859194i	$-0.670966\pi$
$461$	−21.9712	−1.02330	−0.511650	+	0.859194i	$0.670966\pi$
$462$	140.891	6.55486
$463$	38.2997	1.77994	0.889970	−	0.456020i	$-0.150725\pi$
$463$	38.2997	1.77994	0.889970	+	0.456020i	$0.150725\pi$
$464$	−7.14700	−0.331791
$465$	41.6658	1.93221
$466$	−2.20586	−0.102185
$467$	−18.5430	−0.858066	−0.429033	−	0.903289i	$-0.641146\pi$
$467$	−18.5430	−0.858066	−0.429033	+	0.903289i	$0.641146\pi$
$468$	−64.6400	−2.98799
$469$	−41.2337	−1.90400
$470$	−14.4970	−0.668697
$471$	−13.4651	−0.620439
$472$	32.0303	1.47432
$473$	−28.1012	−1.29209
$474$	−8.00000	−0.367452
$475$	−0.232035	−0.0106465
$476$	−33.6453	−1.54213
$477$	−55.4083	−2.53697
$478$	−17.1525	−0.784538
$479$	−5.73607	−0.262088	−0.131044	−	0.991377i	$-0.541833\pi$
$479$	−5.73607	−0.262088	−0.131044	+	0.991377i	$0.541833\pi$
$480$	−46.4551	−2.12038
$481$	−5.50359	−0.250942
$482$	44.9393	2.04693
$483$	79.4921	3.61702
$484$	82.4394	3.74724
$485$	6.46405	0.293517
$486$	9.65430	0.437928
$487$	−11.5934	−0.525347	−0.262674	−	0.964885i	$-0.584604\pi$
$487$	−11.5934	−0.525347	−0.262674	+	0.964885i	$0.584604\pi$
$488$	23.8232	1.07843
$489$	−3.30161	−0.149304
$490$	−20.9166	−0.944917
$491$	3.76763	0.170031	0.0850153	−	0.996380i	$-0.472906\pi$
$491$	3.76763	0.170031	0.0850153	+	0.996380i	$0.472906\pi$
$492$	−41.9234	−1.89005
$493$	22.0521	0.993177
$494$	−30.6491	−1.37897
$495$	−87.1574	−3.91744
$496$	6.68617	0.300218
$497$	−30.9626	−1.38886
$498$	101.884	4.56552
$499$	1.88767	0.0845038	0.0422519	−	0.999107i	$-0.486547\pi$
$499$	1.88767	0.0845038	0.0422519	+	0.999107i	$0.486547\pi$
$500$	−33.0709	−1.47898
$501$	−58.0498	−2.59347
$502$	34.5582	1.54241
$503$	−7.29039	−0.325062	−0.162531	−	0.986703i	$-0.551966\pi$
$503$	−7.29039	−0.325062	−0.162531	+	0.986703i	$0.551966\pi$
$504$	45.3073	2.01815
$505$	−13.1163	−0.583667
$506$	108.655	4.83032
$507$	2.54487	0.113022
$508$	−8.39191	−0.372331
$509$	−35.9919	−1.59531	−0.797655	−	0.603113i	$-0.793927\pi$
$509$	−35.9919	−1.59531	−0.797655	+	0.603113i	$0.793927\pi$
$510$	51.5644	2.28331
$511$	−23.2432	−1.02822
$512$	−12.2277	−0.540392
$513$	38.6442	1.70618
$514$	−43.6137	−1.92372
$515$	18.9978	0.837144
$516$	−40.8331	−1.79758
$517$	−17.9762	−0.790594
$518$	11.7645	0.516904
$519$	−22.5603	−0.990287
$520$	17.0725	0.748677
$521$	−7.77349	−0.340563	−0.170281	−	0.985395i	$-0.554468\pi$
$521$	−7.77349	−0.340563	−0.170281	+	0.985395i	$0.554468\pi$
$522$	−90.5640	−3.96388
$523$	9.46633	0.413934	0.206967	−	0.978348i	$-0.433641\pi$
$523$	9.46633	0.413934	0.206967	+	0.978348i	$0.433641\pi$
$524$	31.7481	1.38692
$525$	0.597931	0.0260958
$526$	11.9649	0.521694
$527$	−20.6302	−0.898666
$528$	−20.7226	−0.901835
$529$	38.3042	1.66540
$530$	44.6305	1.93862
$531$	−91.6643	−3.97789
$532$	39.1817	1.69874
$533$	−16.1733	−0.700544
$534$	89.2617	3.86273
$535$	−36.1722	−1.56386
$536$	−26.8538	−1.15991
$537$	12.8472	0.554396
$538$	−69.2963	−2.98758
$539$	−25.9366	−1.11717
$540$	−65.6485	−2.82506
$541$	−26.1859	−1.12582	−0.562911	−	0.826518i	$-0.690318\pi$
$541$	−26.1859	−1.12582	−0.562911	+	0.826518i	$0.690318\pi$
$542$	−33.5121	−1.43947
$543$	−32.8718	−1.41066
$544$	23.0016	0.986184
$545$	20.3701	0.872561
$546$	78.9796	3.38002
$547$	−8.77821	−0.375329	−0.187664	−	0.982233i	$-0.560092\pi$
$547$	−8.77821	−0.375329	−0.187664	+	0.982233i	$0.560092\pi$
$548$	−67.1421	−2.86817
$549$	−68.1771	−2.90973
$550$	0.817293	0.0348495
$551$	−25.6808	−1.09404
$552$	51.7699	2.20347
$553$	3.94546	0.167778
$554$	68.2925	2.90147
$555$	−10.7829	−0.457710
$556$	3.13014	0.132747
$557$	−18.7104	−0.792786	−0.396393	−	0.918081i	$-0.629738\pi$
$557$	−18.7104	−0.792786	−0.396393	+	0.918081i	$0.629738\pi$
$558$	84.7246	3.58668
$559$	−15.7527	−0.666268
$560$	8.24198	0.348287
$561$	63.9397	2.69954
$562$	−43.5230	−1.83590
$563$	−35.5599	−1.49867	−0.749336	−	0.662190i	$-0.769627\pi$
$563$	−35.5599	−1.49867	−0.749336	+	0.662190i	$0.769627\pi$
$564$	−26.1208	−1.09989
$565$	2.43482	0.102434
$566$	−28.1924	−1.18501
$567$	−37.1327	−1.55943
$568$	−20.1647	−0.846091
$569$	−2.78424	−0.116722	−0.0583608	−	0.998296i	$-0.518587\pi$
$569$	−2.78424	−0.116722	−0.0583608	+	0.998296i	$0.518587\pi$
$570$	−60.0494	−2.51519
$571$	−1.30110	−0.0544494	−0.0272247	−	0.999629i	$-0.508667\pi$
$571$	−1.30110	−0.0544494	−0.0272247	+	0.999629i	$0.508667\pi$
$572$	64.5623	2.69949
$573$	17.1602	0.716878
$574$	34.5723	1.44302
$575$	0.461124	0.0192302
$576$	−80.8041	−3.36684
$577$	−41.7284	−1.73718	−0.868589	−	0.495534i	$-0.834972\pi$
$577$	−41.7284	−1.73718	−0.868589	+	0.495534i	$0.834972\pi$
$578$	12.3895	0.515334
$579$	−10.1558	−0.422059
$580$	43.6264	1.81149
$581$	−50.2473	−2.08461
$582$	19.4750	0.807263
$583$	55.3417	2.29202
$584$	−15.1373	−0.626386
$585$	−48.8579	−2.02003
$586$	−16.3758	−0.676479
$587$	8.33272	0.343928	0.171964	−	0.985103i	$-0.444989\pi$
$587$	8.33272	0.343928	0.171964	+	0.985103i	$0.444989\pi$
$588$	−37.6878	−1.55422
$589$	24.0250	0.989931
$590$	73.8341	3.03970
$591$	22.2388	0.914783
$592$	−1.73035	−0.0711170
$593$	−20.0467	−0.823217	−0.411609	−	0.911361i	$-0.635033\pi$
$593$	−20.0467	−0.823217	−0.411609	+	0.911361i	$0.635033\pi$
$594$	−136.116	−5.58490
$595$	−25.4307	−1.04256
$596$	31.8679	1.30536
$597$	56.0297	2.29314
$598$	60.9090	2.49075
$599$	−12.2129	−0.499007	−0.249504	−	0.968374i	$-0.580267\pi$
$599$	−12.2129	−0.499007	−0.249504	+	0.968374i	$0.580267\pi$
$600$	0.389407	0.0158975
$601$	−21.6782	−0.884272	−0.442136	−	0.896948i	$-0.645779\pi$
$601$	−21.6782	−0.884272	−0.442136	+	0.896948i	$0.645779\pi$
$602$	33.6732	1.37242
$603$	76.8500	3.12958
$604$	3.83769	0.156153
$605$	62.3115	2.53332
$606$	−39.5169	−1.60526
$607$	2.76489	0.112223	0.0561117	−	0.998424i	$-0.482130\pi$
$607$	2.76489	0.112223	0.0561117	+	0.998424i	$0.482130\pi$
$608$	−26.7865	−1.08634
$609$	66.1769	2.68162
$610$	54.9156	2.22347
$611$	−10.0770	−0.407670
$612$	62.7070	2.53478
$613$	−23.1956	−0.936861	−0.468430	−	0.883500i	$-0.655180\pi$
$613$	−23.1956	−0.936861	−0.468430	+	0.883500i	$0.655180\pi$
$614$	15.2399	0.615033
$615$	−31.6877	−1.27777
$616$	−45.2528	−1.82329
$617$	33.9326	1.36607	0.683037	−	0.730384i	$-0.260659\pi$
$617$	33.9326	1.36607	0.683037	+	0.730384i	$0.260659\pi$
$618$	57.2368	2.30240
$619$	41.2054	1.65618	0.828091	−	0.560593i	$-0.189427\pi$
$619$	41.2054	1.65618	0.828091	+	0.560593i	$0.189427\pi$
$620$	−40.8135	−1.63911
$621$	−76.7976	−3.08178
$622$	1.15239	0.0462065
$623$	−44.0224	−1.76372
$624$	−11.6165	−0.465031
$625$	−25.2910	−1.01164
$626$	20.6244	0.824318
$627$	−74.4611	−2.97369
$628$	13.1896	0.526324
$629$	5.33901	0.212880
$630$	104.439	4.16096
$631$	42.2057	1.68018	0.840091	−	0.542446i	$-0.182502\pi$
$631$	42.2057	1.68018	0.840091	+	0.542446i	$0.182502\pi$
$632$	2.56951	0.102210
$633$	40.6916	1.61734
$634$	52.8710	2.09977
$635$	−6.34299	−0.251714
$636$	80.4156	3.18869
$637$	−14.5393	−0.576067
$638$	90.4552	3.58116
$639$	57.7071	2.28286
$640$	34.5025	1.36383
$641$	−34.6011	−1.36666	−0.683330	−	0.730110i	$-0.739469\pi$
$641$	−34.6011	−1.36666	−0.683330	+	0.730110i	$0.739469\pi$
$642$	−108.980	−4.30110
$643$	−49.9586	−1.97018	−0.985088	−	0.172050i	$-0.944961\pi$
$643$	−49.9586	−1.97018	−0.985088	+	0.172050i	$0.944961\pi$
$644$	−77.8659	−3.06835
$645$	−30.8636	−1.21525
$646$	29.7326	1.16981
$647$	40.9311	1.60917	0.804584	−	0.593839i	$-0.202388\pi$
$647$	40.9311	1.60917	0.804584	+	0.593839i	$0.202388\pi$
$648$	−24.1830	−0.949996
$649$	91.5541	3.59381
$650$	0.458151	0.0179701
$651$	−61.9099	−2.42644
$652$	3.23407	0.126656
$653$	−20.0698	−0.785394	−0.392697	−	0.919668i	$-0.628458\pi$
$653$	−20.0698	−0.785394	−0.392697	+	0.919668i	$0.628458\pi$
$654$	61.3714	2.39981
$655$	23.9967	0.937628
$656$	−5.08496	−0.198534
$657$	43.3199	1.69007
$658$	21.5406	0.839741
$659$	−24.5763	−0.957356	−0.478678	−	0.877991i	$-0.658884\pi$
$659$	−24.5763	−0.957356	−0.478678	+	0.877991i	$0.658884\pi$
$660$	126.494	4.92378
$661$	20.9537	0.815004	0.407502	−	0.913204i	$-0.366400\pi$
$661$	20.9537	0.815004	0.407502	+	0.913204i	$0.366400\pi$
$662$	28.3947	1.10359
$663$	35.8427	1.39202
$664$	−32.7240	−1.26994
$665$	29.6154	1.14843
$666$	−21.9264	−0.849629
$667$	51.0356	1.97610
$668$	56.8622	2.20007
$669$	−78.1830	−3.02273
$670$	−61.9015	−2.39146
$671$	68.0952	2.62879
$672$	69.0262	2.66274
$673$	43.1704	1.66410	0.832048	−	0.554704i	$-0.187169\pi$
$673$	43.1704	1.66410	0.832048	+	0.554704i	$0.187169\pi$
$674$	−39.3951	−1.51744
$675$	−0.577663	−0.0222343
$676$	−2.49281	−0.0958772
$677$	32.8611	1.26296	0.631478	−	0.775394i	$-0.282449\pi$
$677$	32.8611	1.26296	0.631478	+	0.775394i	$0.282449\pi$
$678$	7.33564	0.281724
$679$	−9.60472	−0.368595
$680$	−16.5619	−0.635121
$681$	−2.29231	−0.0878416
$682$	−84.6228	−3.24037
$683$	27.3442	1.04630	0.523148	−	0.852242i	$-0.324758\pi$
$683$	27.3442	1.04630	0.523148	+	0.852242i	$0.324758\pi$
$684$	−73.0256	−2.79220
$685$	−50.7491	−1.93902
$686$	−21.1043	−0.805767
$687$	−21.6203	−0.824867
$688$	−4.95272	−0.188821
$689$	31.0229	1.18188
$690$	119.336	4.54306
$691$	−7.59470	−0.288916	−0.144458	−	0.989511i	$-0.546144\pi$
$691$	−7.59470	−0.288916	−0.144458	+	0.989511i	$0.546144\pi$
$692$	22.0988	0.840070
$693$	129.504	4.91946
$694$	11.6234	0.441217
$695$	2.36590	0.0897438
$696$	43.0982	1.63363
$697$	15.6897	0.594289
$698$	9.62074	0.364150
$699$	−3.00414	−0.113627
$700$	−0.585699	−0.0221373
$701$	35.9724	1.35866	0.679330	−	0.733833i	$-0.262271\pi$
$701$	35.9724	1.35866	0.679330	+	0.733833i	$0.262271\pi$
$702$	−76.3025	−2.87985
$703$	−6.21756	−0.234500
$704$	80.7070	3.04176
$705$	−19.7433	−0.743577
$706$	−18.2626	−0.687321
$707$	19.4891	0.732961
$708$	133.035	4.99976
$709$	1.92659	0.0723545	0.0361772	−	0.999345i	$-0.488482\pi$
$709$	1.92659	0.0723545	0.0361772	+	0.999345i	$0.488482\pi$
$710$	−46.4822	−1.74445
$711$	−7.35342	−0.275775
$712$	−28.6699	−1.07445
$713$	−47.7449	−1.78806
$714$	−76.6178	−2.86735
$715$	48.7992	1.82499
$716$	−12.5843	−0.470299
$717$	−23.3599	−0.872390
$718$	64.9804	2.42505
$719$	23.9245	0.892234	0.446117	−	0.894975i	$-0.352807\pi$
$719$	23.9245	0.892234	0.446117	+	0.894975i	$0.352807\pi$
$720$	−15.3611	−0.572476
$721$	−28.2282	−1.05127
$722$	7.75695	0.288684
$723$	61.2024	2.27614
$724$	32.1993	1.19668
$725$	0.383884	0.0142571
$726$	187.733	6.96741
$727$	−23.8601	−0.884924	−0.442462	−	0.896787i	$-0.645895\pi$
$727$	−23.8601	−0.884924	−0.442462	+	0.896787i	$0.645895\pi$
$728$	−25.3674	−0.940179
$729$	−20.1845	−0.747576
$730$	−34.8935	−1.29147
$731$	15.2816	0.565212
$732$	98.9474	3.65720
$733$	29.4938	1.08938	0.544688	−	0.838639i	$-0.316648\pi$
$733$	29.4938	1.08938	0.544688	+	0.838639i	$0.316648\pi$
$734$	45.7741	1.68955
$735$	−28.4862	−1.05073
$736$	53.2329	1.96219
$737$	−76.7577	−2.82741
$738$	−64.4347	−2.37187
$739$	−46.3221	−1.70398	−0.851992	−	0.523555i	$-0.824606\pi$
$739$	−46.3221	−1.70398	−0.851992	+	0.523555i	$0.824606\pi$
$740$	10.5623	0.388280
$741$	−41.7407	−1.53338
$742$	−66.3149	−2.43450
$743$	−29.4358	−1.07990	−0.539948	−	0.841698i	$-0.681556\pi$
$743$	−29.4358	−1.07990	−0.539948	+	0.841698i	$0.681556\pi$
$744$	−40.3193	−1.47818
$745$	24.0872	0.882488
$746$	37.4675	1.37178
$747$	93.6493	3.42645
$748$	−62.6317	−2.29004
$749$	53.7471	1.96388
$750$	−75.3098	−2.74993
$751$	−29.9554	−1.09309	−0.546544	−	0.837430i	$-0.684057\pi$
$751$	−29.9554	−1.09309	−0.546544	+	0.837430i	$0.684057\pi$
$752$	−3.16824	−0.115534
$753$	47.0645	1.71512
$754$	50.7065	1.84662
$755$	2.90071	0.105567
$756$	97.5449	3.54767
$757$	−42.1430	−1.53171	−0.765857	−	0.643010i	$-0.777685\pi$
$757$	−42.1430	−1.53171	−0.765857	+	0.643010i	$0.777685\pi$
$758$	21.4017	0.777343
$759$	147.977	5.37121
$760$	19.2872	0.699622
$761$	−33.6605	−1.22019	−0.610097	−	0.792327i	$-0.708869\pi$
$761$	−33.6605	−1.22019	−0.610097	+	0.792327i	$0.708869\pi$
$762$	−19.1102	−0.692291
$763$	−30.2673	−1.09575
$764$	−16.8091	−0.608134
$765$	47.3969	1.71364
$766$	9.40880	0.339954
$767$	51.3226	1.85315
$768$	25.1298	0.906795
$769$	50.2111	1.81066	0.905330	−	0.424709i	$-0.139624\pi$
$769$	50.2111	1.81066	0.905330	+	0.424709i	$0.139624\pi$
$770$	−104.314	−3.75920
$771$	−59.3970	−2.13913
$772$	9.94799	0.358036
$773$	−27.4030	−0.985616	−0.492808	−	0.870138i	$-0.664029\pi$
$773$	−27.4030	−0.985616	−0.492808	+	0.870138i	$0.664029\pi$
$774$	−62.7589	−2.25582
$775$	−0.359131	−0.0129004
$776$	−6.25515	−0.224547
$777$	16.0220	0.574786
$778$	58.6997	2.10449
$779$	−18.2714	−0.654643
$780$	70.9089	2.53895
$781$	−57.6378	−2.06244
$782$	−59.0876	−2.11297
$783$	−63.9338	−2.28481
$784$	−4.57121	−0.163257
$785$	9.96935	0.355821
$786$	72.2975	2.57877
$787$	−33.4663	−1.19295	−0.596473	−	0.802633i	$-0.703432\pi$
$787$	−33.4663	−1.19295	−0.596473	+	0.802633i	$0.703432\pi$
$788$	−21.7839	−0.776018
$789$	16.2949	0.580113
$790$	5.92307	0.210733
$791$	−3.61782	−0.128635
$792$	84.3408	2.99692
$793$	38.1722	1.35553
$794$	2.64422	0.0938399
$795$	60.7818	2.15571
$796$	−54.8834	−1.94529
$797$	−36.5540	−1.29481	−0.647405	−	0.762146i	$-0.724146\pi$
$797$	−36.5540	−1.29481	−0.647405	+	0.762146i	$0.724146\pi$
$798$	89.2255	3.15855
$799$	9.77562	0.345836
$800$	0.400412	0.0141567
$801$	82.0474	2.89900
$802$	57.7318	2.03858
$803$	−43.2678	−1.52689
$804$	−111.535	−3.93352
$805$	−58.8546	−2.07435
$806$	−47.4370	−1.67090
$807$	−94.3741	−3.32212
$808$	12.6924	0.446517
$809$	−18.2619	−0.642056	−0.321028	−	0.947070i	$-0.604028\pi$
$809$	−18.2619	−0.642056	−0.321028	+	0.947070i	$0.604028\pi$
$810$	−55.7449	−1.95868
$811$	41.3542	1.45214	0.726071	−	0.687620i	$-0.241345\pi$
$811$	41.3542	1.45214	0.726071	+	0.687620i	$0.241345\pi$
$812$	−64.8231	−2.27484
$813$	−45.6398	−1.60066
$814$	21.9000	0.767595
$815$	2.44446	0.0856256
$816$	11.2691	0.394498
$817$	−17.7963	−0.622612
$818$	−55.1038	−1.92666
$819$	72.5964	2.53672
$820$	31.0394	1.08394
$821$	10.2378	0.357301	0.178650	−	0.983913i	$-0.442827\pi$
$821$	10.2378	0.357301	0.178650	+	0.983913i	$0.442827\pi$
$822$	−152.897	−5.33291
$823$	−42.8905	−1.49507	−0.747535	−	0.664222i	$-0.768763\pi$
$823$	−42.8905	−1.49507	−0.747535	+	0.664222i	$0.768763\pi$
$824$	−18.3839	−0.640432
$825$	1.11306	0.0387519
$826$	−109.708	−3.81722
$827$	13.5089	0.469751	0.234876	−	0.972025i	$-0.424532\pi$
$827$	13.5089	0.469751	0.234876	+	0.972025i	$0.424532\pi$
$828$	145.124	5.04340
$829$	20.5840	0.714911	0.357456	−	0.933930i	$-0.383644\pi$
$829$	20.5840	0.714911	0.357456	+	0.933930i	$0.383644\pi$
$830$	−75.4330	−2.61832
$831$	93.0070	3.22638
$832$	45.2420	1.56848
$833$	14.1045	0.488692
$834$	7.12802	0.246823
$835$	42.9791	1.48735
$836$	72.9378	2.52261
$837$	59.8114	2.06738
$838$	−35.4472	−1.22450
$839$	−36.6110	−1.26395	−0.631976	−	0.774988i	$-0.717756\pi$
$839$	−36.6110	−1.26395	−0.631976	+	0.774988i	$0.717756\pi$
$840$	−49.7013	−1.71486
$841$	13.4869	0.465067
$842$	−54.4367	−1.87601
$843$	−59.2735	−2.04149
$844$	−39.8591	−1.37201
$845$	−1.88418	−0.0648177
$846$	−40.1467	−1.38027
$847$	−92.5866	−3.18131
$848$	9.75374	0.334945
$849$	−38.3949	−1.31771
$850$	−0.444450	−0.0152445
$851$	12.3562	0.423564
$852$	−83.7520	−2.86930
$853$	−23.4713	−0.803642	−0.401821	−	0.915718i	$-0.631623\pi$
$853$	−23.4713	−0.803642	−0.401821	+	0.915718i	$0.631623\pi$
$854$	−81.5973	−2.79220
$855$	−55.1961	−1.88767
$856$	35.0033	1.19639
$857$	6.24837	0.213440	0.106720	−	0.994289i	$-0.465965\pi$
$857$	6.24837	0.213440	0.106720	+	0.994289i	$0.465965\pi$
$858$	147.023	5.01927
$859$	43.4364	1.48203	0.741015	−	0.671488i	$-0.234345\pi$
$859$	43.4364	1.48203	0.741015	+	0.671488i	$0.234345\pi$
$860$	30.2322	1.03091
$861$	47.0837	1.60461
$862$	3.79195	0.129154
$863$	40.3014	1.37187	0.685937	−	0.727661i	$-0.259392\pi$
$863$	40.3014	1.37187	0.685937	+	0.727661i	$0.259392\pi$
$864$	−66.6865	−2.26872
$865$	16.7033	0.567929
$866$	9.59407	0.326020
$867$	16.8731	0.573040
$868$	60.6434	2.05837
$869$	7.34459	0.249148
$870$	99.3471	3.36818
$871$	−43.0281	−1.45795
$872$	−19.7118	−0.667527
$873$	17.9010	0.605856
$874$	68.8106	2.32755
$875$	37.1415	1.25561
$876$	−62.8714	−2.12423
$877$	31.0082	1.04707	0.523536	−	0.852003i	$-0.324612\pi$
$877$	31.0082	1.04707	0.523536	+	0.852003i	$0.324612\pi$
$878$	48.0342	1.62108
$879$	−22.3021	−0.752230
$880$	15.3427	0.517201
$881$	19.3996	0.653590	0.326795	−	0.945095i	$-0.394031\pi$
$881$	19.3996	0.653590	0.326795	+	0.945095i	$0.394031\pi$
$882$	−57.9246	−1.95042
$883$	−37.7031	−1.26881	−0.634406	−	0.773000i	$-0.718755\pi$
$883$	−37.7031	−1.26881	−0.634406	+	0.773000i	$0.718755\pi$
$884$	−35.1095	−1.18086
$885$	100.554	3.38009
$886$	−58.2309	−1.95631
$887$	−18.9330	−0.635707	−0.317854	−	0.948140i	$-0.602962\pi$
$887$	−18.9330	−0.635707	−0.317854	+	0.948140i	$0.602962\pi$
$888$	10.4345	0.350158
$889$	9.42484	0.316099
$890$	−66.0879	−2.21527
$891$	−69.1235	−2.31572
$892$	76.5836	2.56421
$893$	−11.3842	−0.380958
$894$	72.5703	2.42711
$895$	−9.51182	−0.317945
$896$	−51.2662	−1.71268
$897$	82.9514	2.76967
$898$	4.35860	0.145448
$899$	−39.7474	−1.32565
$900$	1.09161	0.0363869
$901$	−30.0952	−1.00262
$902$	64.3572	2.14286
$903$	45.8592	1.52610
$904$	−2.35613	−0.0783638
$905$	24.3377	0.809014
$906$	8.73927	0.290343
$907$	−38.9416	−1.29303	−0.646517	−	0.762900i	$-0.723775\pi$
$907$	−38.9416	−1.29303	−0.646517	+	0.762900i	$0.723775\pi$
$908$	2.24542	0.0745168
$909$	−36.3231	−1.20476
$910$	−58.4752	−1.93843
$911$	−19.4641	−0.644876	−0.322438	−	0.946591i	$-0.604502\pi$
$911$	−19.4641	−0.644876	−0.322438	+	0.946591i	$0.604502\pi$
$912$	−13.1235	−0.434561
$913$	−93.5367	−3.09561
$914$	32.1423	1.06317
$915$	74.7890	2.47245
$916$	21.1780	0.699742
$917$	−35.6559	−1.17746
$918$	74.0208	2.44305
$919$	7.39793	0.244035	0.122018	−	0.992528i	$-0.461064\pi$
$919$	7.39793	0.244035	0.122018	+	0.992528i	$0.461064\pi$
$920$	−38.3296	−1.26369
$921$	20.7551	0.683904
$922$	49.0097	1.61405
$923$	−32.3101	−1.06350
$924$	−187.953	−6.18321
$925$	0.0929416	0.00305590
$926$	−85.4327	−2.80749
$927$	52.6109	1.72797
$928$	44.3162	1.45475
$929$	−51.8458	−1.70101	−0.850503	−	0.525970i	$-0.823703\pi$
$929$	−51.8458	−1.70101	−0.850503	+	0.525970i	$0.823703\pi$
$930$	−92.9413	−3.04767
$931$	−16.4254	−0.538321
$932$	2.94269	0.0963909
$933$	1.56942	0.0513806
$934$	41.3626	1.35342
$935$	−47.3399	−1.54818
$936$	47.2790	1.54536
$937$	−37.1131	−1.21243	−0.606216	−	0.795300i	$-0.707313\pi$
$937$	−37.1131	−1.21243	−0.606216	+	0.795300i	$0.707313\pi$
$938$	91.9774	3.00317
$939$	28.0882	0.916625
$940$	19.3394	0.630783
$941$	32.1935	1.04948	0.524739	−	0.851263i	$-0.324163\pi$
$941$	32.1935	1.04948	0.524739	+	0.851263i	$0.324163\pi$
$942$	30.0357	0.978618
$943$	36.3109	1.18244
$944$	16.1360	0.525183
$945$	73.7290	2.39840
$946$	62.6835	2.03802
$947$	55.6413	1.80810	0.904049	−	0.427429i	$-0.140581\pi$
$947$	55.6413	1.80810	0.904049	+	0.427429i	$0.140581\pi$
$948$	10.6722	0.346618
$949$	−24.2547	−0.787340
$950$	0.517586	0.0167927
$951$	72.0045	2.33491
$952$	24.6088	0.797577
$953$	−7.95041	−0.257539	−0.128769	−	0.991675i	$-0.541103\pi$
$953$	−7.95041	−0.257539	−0.128769	+	0.991675i	$0.541103\pi$
$954$	123.596	4.00156
$955$	−12.7051	−0.411128
$956$	22.8820	0.740056
$957$	123.190	3.98217
$958$	12.7951	0.413390
$959$	75.4064	2.43500
$960$	88.6406	2.86086
$961$	6.18457	0.199502
$962$	12.2765	0.395810
$963$	−100.172	−3.22800
$964$	−59.9503	−1.93087
$965$	7.51915	0.242050
$966$	−177.318	−5.70511
$967$	14.3116	0.460230	0.230115	−	0.973163i	$-0.426090\pi$
$967$	14.3116	0.460230	0.230115	+	0.973163i	$0.426090\pi$
$968$	−60.2978	−1.93804
$969$	40.4925	1.30081
$970$	−14.4189	−0.462964
$971$	−29.9318	−0.960557	−0.480278	−	0.877116i	$-0.659464\pi$
$971$	−29.9318	−0.960557	−0.480278	+	0.877116i	$0.659464\pi$
$972$	−12.8791	−0.413098
$973$	−3.51542	−0.112699
$974$	25.8607	0.828629
$975$	0.623951	0.0199824
$976$	12.0015	0.384158
$977$	−30.0999	−0.962980	−0.481490	−	0.876451i	$-0.659904\pi$
$977$	−30.0999	−0.962980	−0.481490	+	0.876451i	$0.659904\pi$
$978$	7.36469	0.235497
$979$	−81.9488	−2.61910
$980$	27.9034	0.891342
$981$	56.4112	1.80107
$982$	−8.40421	−0.268189
$983$	26.6140	0.848856	0.424428	−	0.905462i	$-0.360475\pi$
$983$	26.6140	0.848856	0.424428	+	0.905462i	$0.360475\pi$
$984$	30.6636	0.977520
$985$	−16.4653	−0.524627
$986$	−49.1902	−1.56654
$987$	29.3360	0.933774
$988$	40.8868	1.30078
$989$	35.3665	1.12459
$990$	194.416	6.17896
$991$	−43.7468	−1.38966	−0.694831	−	0.719173i	$-0.744521\pi$
$991$	−43.7468	−1.38966	−0.694831	+	0.719173i	$0.744521\pi$
$992$	−41.4588	−1.31632
$993$	38.6704	1.22717
$994$	69.0664	2.19065
$995$	−41.4834	−1.31511
$996$	−135.916	−4.30666
$997$	−10.4070	−0.329592	−0.164796	−	0.986328i	$-0.552697\pi$
$997$	−10.4070	−0.329592	−0.164796	+	0.986328i	$0.552697\pi$
$998$	−4.21071	−0.133288
$999$	−15.4789	−0.489732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.20	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.20	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23064 q^{2} -3.03788 q^{3} +2.97574 q^{4} +2.24920 q^{5} +6.77641 q^{6} -3.34201 q^{7} -2.17651 q^{8} +6.22873 q^{9} +O(q^{10})\)	\(q-2.23064 q^{2} -3.03788 q^{3} +2.97574 q^{4} +2.24920 q^{5} +6.77641 q^{6} -3.34201 q^{7} -2.17651 q^{8} +6.22873 q^{9} -5.01714 q^{10} -6.22124 q^{11} -9.03994 q^{12} -3.48745 q^{13} +7.45481 q^{14} -6.83280 q^{15} -1.09647 q^{16} +3.38316 q^{17} -13.8940 q^{18} -3.93987 q^{19} +6.69302 q^{20} +10.1526 q^{21} +13.8773 q^{22} +7.82970 q^{23} +6.61198 q^{24} +0.0588941 q^{25} +7.77922 q^{26} -9.80850 q^{27} -9.94494 q^{28} +6.51820 q^{29} +15.2415 q^{30} -6.09791 q^{31} +6.79884 q^{32} +18.8994 q^{33} -7.54660 q^{34} -7.51684 q^{35} +18.5351 q^{36} +1.57811 q^{37} +8.78840 q^{38} +10.5945 q^{39} -4.89541 q^{40} +4.63758 q^{41} -22.6468 q^{42} +4.51697 q^{43} -18.5128 q^{44} +14.0096 q^{45} -17.4652 q^{46} +2.88949 q^{47} +3.33094 q^{48} +4.16903 q^{49} -0.131371 q^{50} -10.2776 q^{51} -10.3777 q^{52} -8.89560 q^{53} +21.8792 q^{54} -13.9928 q^{55} +7.27392 q^{56} +11.9688 q^{57} -14.5397 q^{58} -14.7164 q^{59} -20.3326 q^{60} -10.9456 q^{61} +13.6022 q^{62} -20.8165 q^{63} -12.9728 q^{64} -7.84396 q^{65} -42.1577 q^{66} +12.3380 q^{67} +10.0674 q^{68} -23.7857 q^{69} +16.7673 q^{70} +9.26467 q^{71} -13.5569 q^{72} +6.95485 q^{73} -3.52020 q^{74} -0.178913 q^{75} -11.7240 q^{76} +20.7915 q^{77} -23.6324 q^{78} -1.18057 q^{79} -2.46617 q^{80} +11.1109 q^{81} -10.3448 q^{82} +15.0351 q^{83} +30.2116 q^{84} +7.60940 q^{85} -10.0757 q^{86} -19.8015 q^{87} +13.5406 q^{88} +13.1724 q^{89} -31.2504 q^{90} +11.6551 q^{91} +23.2991 q^{92} +18.5247 q^{93} -6.44541 q^{94} -8.86154 q^{95} -20.6541 q^{96} +2.87393 q^{97} -9.29959 q^{98} -38.7504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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