LMFDB - Embedded newform 4010.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.18240 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.18240 q^{6} -2.63299 q^{7} +1.00000 q^{8} -1.60192 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.18240 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.18240 q^{6} -2.63299 q^{7} +1.00000 q^{8} -1.60192 q^{9} +1.00000 q^{10} -4.20254 q^{11} -1.18240 q^{12} +2.40716 q^{13} -2.63299 q^{14} -1.18240 q^{15} +1.00000 q^{16} +3.55792 q^{17} -1.60192 q^{18} -3.94123 q^{19} +1.00000 q^{20} +3.11325 q^{21} -4.20254 q^{22} +6.72994 q^{23} -1.18240 q^{24} +1.00000 q^{25} +2.40716 q^{26} +5.44133 q^{27} -2.63299 q^{28} +4.66799 q^{29} -1.18240 q^{30} -10.2504 q^{31} +1.00000 q^{32} +4.96909 q^{33} +3.55792 q^{34} -2.63299 q^{35} -1.60192 q^{36} -8.35458 q^{37} -3.94123 q^{38} -2.84624 q^{39} +1.00000 q^{40} +2.21091 q^{41} +3.11325 q^{42} +0.880466 q^{43} -4.20254 q^{44} -1.60192 q^{45} +6.72994 q^{46} +8.69379 q^{47} -1.18240 q^{48} -0.0673894 q^{49} +1.00000 q^{50} -4.20690 q^{51} +2.40716 q^{52} +10.1935 q^{53} +5.44133 q^{54} -4.20254 q^{55} -2.63299 q^{56} +4.66012 q^{57} +4.66799 q^{58} +13.8449 q^{59} -1.18240 q^{60} -4.31547 q^{61} -10.2504 q^{62} +4.21784 q^{63} +1.00000 q^{64} +2.40716 q^{65} +4.96909 q^{66} +3.17885 q^{67} +3.55792 q^{68} -7.95750 q^{69} -2.63299 q^{70} +8.33371 q^{71} -1.60192 q^{72} -3.76307 q^{73} -8.35458 q^{74} -1.18240 q^{75} -3.94123 q^{76} +11.0652 q^{77} -2.84624 q^{78} +1.62206 q^{79} +1.00000 q^{80} -1.62807 q^{81} +2.21091 q^{82} -2.28049 q^{83} +3.11325 q^{84} +3.55792 q^{85} +0.880466 q^{86} -5.51944 q^{87} -4.20254 q^{88} +14.5201 q^{89} -1.60192 q^{90} -6.33803 q^{91} +6.72994 q^{92} +12.1200 q^{93} +8.69379 q^{94} -3.94123 q^{95} -1.18240 q^{96} +18.1936 q^{97} -0.0673894 q^{98} +6.73214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.18240	−0.682661	−0.341330	−	0.939943i	$-0.610877\pi$
$3$	−1.18240	−0.682661	−0.341330	+	0.939943i	$0.610877\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.18240	−0.482714
$7$	−2.63299	−0.995175	−0.497587	−	0.867414i	$-0.665781\pi$
$7$	−2.63299	−0.995175	−0.497587	+	0.867414i	$0.665781\pi$
$8$	1.00000	0.353553
$9$	−1.60192	−0.533974
$10$	1.00000	0.316228
$11$	−4.20254	−1.26711	−0.633557	−	0.773696i	$-0.718406\pi$
$11$	−4.20254	−1.26711	−0.633557	+	0.773696i	$0.718406\pi$
$12$	−1.18240	−0.341330
$13$	2.40716	0.667627	0.333814	−	0.942639i	$-0.391664\pi$
$13$	2.40716	0.667627	0.333814	+	0.942639i	$0.391664\pi$
$14$	−2.63299	−0.703695
$15$	−1.18240	−0.305295
$16$	1.00000	0.250000
$17$	3.55792	0.862923	0.431462	−	0.902131i	$-0.357998\pi$
$17$	3.55792	0.862923	0.431462	+	0.902131i	$0.357998\pi$
$18$	−1.60192	−0.377577
$19$	−3.94123	−0.904179	−0.452090	−	0.891973i	$-0.649321\pi$
$19$	−3.94123	−0.904179	−0.452090	+	0.891973i	$0.649321\pi$
$20$	1.00000	0.223607
$21$	3.11325	0.679367
$22$	−4.20254	−0.895984
$23$	6.72994	1.40329	0.701645	−	0.712527i	$-0.252449\pi$
$23$	6.72994	1.40329	0.701645	+	0.712527i	$0.252449\pi$
$24$	−1.18240	−0.241357
$25$	1.00000	0.200000
$26$	2.40716	0.472084
$27$	5.44133	1.04718
$28$	−2.63299	−0.497587
$29$	4.66799	0.866823	0.433412	−	0.901196i	$-0.357310\pi$
$29$	4.66799	0.866823	0.433412	+	0.901196i	$0.357310\pi$
$30$	−1.18240	−0.215876
$31$	−10.2504	−1.84102	−0.920509	−	0.390722i	$-0.872225\pi$
$31$	−10.2504	−1.84102	−0.920509	+	0.390722i	$0.872225\pi$
$32$	1.00000	0.176777
$33$	4.96909	0.865008
$34$	3.55792	0.610179
$35$	−2.63299	−0.445056
$36$	−1.60192	−0.266987
$37$	−8.35458	−1.37348	−0.686742	−	0.726901i	$-0.740960\pi$
$37$	−8.35458	−1.37348	−0.686742	+	0.726901i	$0.740960\pi$
$38$	−3.94123	−0.639351
$39$	−2.84624	−0.455763
$40$	1.00000	0.158114
$41$	2.21091	0.345285	0.172643	−	0.984985i	$-0.444769\pi$
$41$	2.21091	0.345285	0.172643	+	0.984985i	$0.444769\pi$
$42$	3.11325	0.480385
$43$	0.880466	0.134270	0.0671349	−	0.997744i	$-0.478614\pi$
$43$	0.880466	0.134270	0.0671349	+	0.997744i	$0.478614\pi$
$44$	−4.20254	−0.633557
$45$	−1.60192	−0.238801
$46$	6.72994	0.992275
$47$	8.69379	1.26812	0.634060	−	0.773284i	$-0.281387\pi$
$47$	8.69379	1.26812	0.634060	+	0.773284i	$0.281387\pi$
$48$	−1.18240	−0.170665
$49$	−0.0673894	−0.00962706
$50$	1.00000	0.141421
$51$	−4.20690	−0.589084
$52$	2.40716	0.333814
$53$	10.1935	1.40019	0.700095	−	0.714050i	$-0.253141\pi$
$53$	10.1935	1.40019	0.700095	+	0.714050i	$0.253141\pi$
$54$	5.44133	0.740471
$55$	−4.20254	−0.566670
$56$	−2.63299	−0.351847
$57$	4.66012	0.617248
$58$	4.66799	0.612937
$59$	13.8449	1.80245	0.901227	−	0.433348i	$-0.142668\pi$
$59$	13.8449	1.80245	0.901227	+	0.433348i	$0.142668\pi$
$60$	−1.18240	−0.152648
$61$	−4.31547	−0.552540	−0.276270	−	0.961080i	$-0.589098\pi$
$61$	−4.31547	−0.552540	−0.276270	+	0.961080i	$0.589098\pi$
$62$	−10.2504	−1.30180
$63$	4.21784	0.531398
$64$	1.00000	0.125000
$65$	2.40716	0.298572
$66$	4.96909	0.611653
$67$	3.17885	0.388359	0.194179	−	0.980966i	$-0.437796\pi$
$67$	3.17885	0.388359	0.194179	+	0.980966i	$0.437796\pi$
$68$	3.55792	0.431462
$69$	−7.95750	−0.957970
$70$	−2.63299	−0.314702
$71$	8.33371	0.989029	0.494515	−	0.869169i	$-0.335346\pi$
$71$	8.33371	0.989029	0.494515	+	0.869169i	$0.335346\pi$
$72$	−1.60192	−0.188788
$73$	−3.76307	−0.440434	−0.220217	−	0.975451i	$-0.570676\pi$
$73$	−3.76307	−0.440434	−0.220217	+	0.975451i	$0.570676\pi$
$74$	−8.35458	−0.971200
$75$	−1.18240	−0.136532
$76$	−3.94123	−0.452090
$77$	11.0652	1.26100
$78$	−2.84624	−0.322273
$79$	1.62206	0.182496	0.0912481	−	0.995828i	$-0.470914\pi$
$79$	1.62206	0.182496	0.0912481	+	0.995828i	$0.470914\pi$
$80$	1.00000	0.111803
$81$	−1.62807	−0.180897
$82$	2.21091	0.244154
$83$	−2.28049	−0.250317	−0.125158	−	0.992137i	$-0.539944\pi$
$83$	−2.28049	−0.250317	−0.125158	+	0.992137i	$0.539944\pi$
$84$	3.11325	0.339683
$85$	3.55792	0.385911
$86$	0.880466	0.0949431
$87$	−5.51944	−0.591746
$88$	−4.20254	−0.447992
$89$	14.5201	1.53913	0.769565	−	0.638569i	$-0.220473\pi$
$89$	14.5201	1.53913	0.769565	+	0.638569i	$0.220473\pi$
$90$	−1.60192	−0.168857
$91$	−6.33803	−0.664406
$92$	6.72994	0.701645
$93$	12.1200	1.25679
$94$	8.69379	0.896696
$95$	−3.94123	−0.404361
$96$	−1.18240	−0.120679
$97$	18.1936	1.84728	0.923642	−	0.383256i	$-0.125197\pi$
$97$	18.1936	1.84728	0.923642	+	0.383256i	$0.125197\pi$
$98$	−0.0673894	−0.00680736
$99$	6.73214	0.676606
$100$	1.00000	0.100000
$101$	12.7520	1.26887	0.634437	−	0.772975i	$-0.281232\pi$
$101$	12.7520	1.26887	0.634437	+	0.772975i	$0.281232\pi$
$102$	−4.20690	−0.416545
$103$	−3.78534	−0.372981	−0.186490	−	0.982457i	$-0.559711\pi$
$103$	−3.78534	−0.372981	−0.186490	+	0.982457i	$0.559711\pi$
$104$	2.40716	0.236042
$105$	3.11325	0.303822
$106$	10.1935	0.990083
$107$	−7.84118	−0.758036	−0.379018	−	0.925389i	$-0.623738\pi$
$107$	−7.84118	−0.758036	−0.379018	+	0.925389i	$0.623738\pi$
$108$	5.44133	0.523592
$109$	12.1919	1.16777	0.583884	−	0.811837i	$-0.301532\pi$
$109$	12.1919	1.16777	0.583884	+	0.811837i	$0.301532\pi$
$110$	−4.20254	−0.400696
$111$	9.87848	0.937624
$112$	−2.63299	−0.248794
$113$	−6.87104	−0.646373	−0.323186	−	0.946335i	$-0.604754\pi$
$113$	−6.87104	−0.646373	−0.323186	+	0.946335i	$0.604754\pi$
$114$	4.66012	0.436460
$115$	6.72994	0.627570
$116$	4.66799	0.433412
$117$	−3.85609	−0.356496
$118$	13.8449	1.27453
$119$	−9.36796	−0.858760
$120$	−1.18240	−0.107938
$121$	6.66133	0.605575
$122$	−4.31547	−0.390705
$123$	−2.61418	−0.235713
$124$	−10.2504	−0.920509
$125$	1.00000	0.0894427
$126$	4.21784	0.375755
$127$	−7.89749	−0.700789	−0.350395	−	0.936602i	$-0.613953\pi$
$127$	−7.89749	−0.700789	−0.350395	+	0.936602i	$0.613953\pi$
$128$	1.00000	0.0883883
$129$	−1.04107	−0.0916607
$130$	2.40716	0.211122
$131$	1.80764	0.157934	0.0789669	−	0.996877i	$-0.474838\pi$
$131$	1.80764	0.157934	0.0789669	+	0.996877i	$0.474838\pi$
$132$	4.96909	0.432504
$133$	10.3772	0.899816
$134$	3.17885	0.274611
$135$	5.44133	0.468315
$136$	3.55792	0.305089
$137$	19.6484	1.67867	0.839337	−	0.543612i	$-0.182944\pi$
$137$	19.6484	1.67867	0.839337	+	0.543612i	$0.182944\pi$
$138$	−7.95750	−0.677387
$139$	−16.9009	−1.43352	−0.716758	−	0.697322i	$-0.754375\pi$
$139$	−16.9009	−1.43352	−0.716758	+	0.697322i	$0.754375\pi$
$140$	−2.63299	−0.222528
$141$	−10.2796	−0.865696
$142$	8.33371	0.699349
$143$	−10.1162	−0.845959
$144$	−1.60192	−0.133494
$145$	4.66799	0.387655
$146$	−3.76307	−0.311434
$147$	0.0796815	0.00657202
$148$	−8.35458	−0.686742
$149$	17.3536	1.42166	0.710831	−	0.703363i	$-0.248319\pi$
$149$	17.3536	1.42166	0.710831	+	0.703363i	$0.248319\pi$
$150$	−1.18240	−0.0965428
$151$	−6.40420	−0.521166	−0.260583	−	0.965451i	$-0.583915\pi$
$151$	−6.40420	−0.521166	−0.260583	+	0.965451i	$0.583915\pi$
$152$	−3.94123	−0.319676
$153$	−5.69952	−0.460779
$154$	11.0652	0.891661
$155$	−10.2504	−0.823328
$156$	−2.84624	−0.227881
$157$	8.89730	0.710082	0.355041	−	0.934851i	$-0.384467\pi$
$157$	8.89730	0.710082	0.355041	+	0.934851i	$0.384467\pi$
$158$	1.62206	0.129044
$159$	−12.0529	−0.955854
$160$	1.00000	0.0790569
$161$	−17.7198	−1.39652
$162$	−1.62807	−0.127914
$163$	−4.73033	−0.370508	−0.185254	−	0.982691i	$-0.559311\pi$
$163$	−4.73033	−0.370508	−0.185254	+	0.982691i	$0.559311\pi$
$164$	2.21091	0.172643
$165$	4.96909	0.386843
$166$	−2.28049	−0.177001
$167$	−12.2448	−0.947528	−0.473764	−	0.880652i	$-0.657105\pi$
$167$	−12.2448	−0.947528	−0.473764	+	0.880652i	$0.657105\pi$
$168$	3.11325	0.240192
$169$	−7.20556	−0.554274
$170$	3.55792	0.272880
$171$	6.31354	0.482808
$172$	0.880466	0.0671349
$173$	−10.3881	−0.789792	−0.394896	−	0.918726i	$-0.629219\pi$
$173$	−10.3881	−0.789792	−0.394896	+	0.918726i	$0.629219\pi$
$174$	−5.51944	−0.418428
$175$	−2.63299	−0.199035
$176$	−4.20254	−0.316778
$177$	−16.3703	−1.23046
$178$	14.5201	1.08833
$179$	−11.8570	−0.886234	−0.443117	−	0.896464i	$-0.646127\pi$
$179$	−11.8570	−0.886234	−0.443117	+	0.896464i	$0.646127\pi$
$180$	−1.60192	−0.119400
$181$	8.91215	0.662435	0.331217	−	0.943554i	$-0.392541\pi$
$181$	8.91215	0.662435	0.331217	+	0.943554i	$0.392541\pi$
$182$	−6.33803	−0.469806
$183$	5.10263	0.377197
$184$	6.72994	0.496138
$185$	−8.35458	−0.614241
$186$	12.1200	0.888685
$187$	−14.9523	−1.09342
$188$	8.69379	0.634060
$189$	−14.3269	−1.04213
$190$	−3.94123	−0.285927
$191$	18.3485	1.32765	0.663825	−	0.747888i	$-0.268932\pi$
$191$	18.3485	1.32765	0.663825	+	0.747888i	$0.268932\pi$
$192$	−1.18240	−0.0853326
$193$	4.27460	0.307693	0.153846	−	0.988095i	$-0.450834\pi$
$193$	4.27460	0.307693	0.153846	+	0.988095i	$0.450834\pi$
$194$	18.1936	1.30623
$195$	−2.84624	−0.203823
$196$	−0.0673894	−0.00481353
$197$	9.03112	0.643440	0.321720	−	0.946835i	$-0.395739\pi$
$197$	9.03112	0.643440	0.321720	+	0.946835i	$0.395739\pi$
$198$	6.73214	0.478433
$199$	13.4278	0.951868	0.475934	−	0.879481i	$-0.342110\pi$
$199$	13.4278	0.951868	0.475934	+	0.879481i	$0.342110\pi$
$200$	1.00000	0.0707107
$201$	−3.75868	−0.265117
$202$	12.7520	0.897229
$203$	−12.2907	−0.862641
$204$	−4.20690	−0.294542
$205$	2.21091	0.154416
$206$	−3.78534	−0.263737
$207$	−10.7808	−0.749320
$208$	2.40716	0.166907
$209$	16.5632	1.14570
$210$	3.11325	0.214835
$211$	12.3616	0.851010	0.425505	−	0.904956i	$-0.360097\pi$
$211$	12.3616	0.851010	0.425505	+	0.904956i	$0.360097\pi$
$212$	10.1935	0.700095
$213$	−9.85380	−0.675171
$214$	−7.84118	−0.536012
$215$	0.880466	0.0600473
$216$	5.44133	0.370235
$217$	26.9890	1.83213
$218$	12.1919	0.825737
$219$	4.44946	0.300667
$220$	−4.20254	−0.283335
$221$	8.56451	0.576111
$222$	9.87848	0.663000
$223$	17.7961	1.19171	0.595857	−	0.803091i	$-0.296813\pi$
$223$	17.7961	1.19171	0.595857	+	0.803091i	$0.296813\pi$
$224$	−2.63299	−0.175924
$225$	−1.60192	−0.106795
$226$	−6.87104	−0.457055
$227$	−15.7330	−1.04424	−0.522118	−	0.852873i	$-0.674858\pi$
$227$	−15.7330	−1.04424	−0.522118	+	0.852873i	$0.674858\pi$
$228$	4.66012	0.308624
$229$	−22.4376	−1.48272	−0.741359	−	0.671109i	$-0.765818\pi$
$229$	−22.4376	−1.48272	−0.741359	+	0.671109i	$0.765818\pi$
$230$	6.72994	0.443759
$231$	−13.0836	−0.860835
$232$	4.66799	0.306468
$233$	−17.4192	−1.14117	−0.570586	−	0.821238i	$-0.693284\pi$
$233$	−17.4192	−1.14117	−0.570586	+	0.821238i	$0.693284\pi$
$234$	−3.85609	−0.252081
$235$	8.69379	0.567121
$236$	13.8449	0.901227
$237$	−1.91793	−0.124583
$238$	−9.36796	−0.607235
$239$	5.75105	0.372004	0.186002	−	0.982549i	$-0.440447\pi$
$239$	5.75105	0.372004	0.186002	+	0.982549i	$0.440447\pi$
$240$	−1.18240	−0.0763238
$241$	16.7554	1.07931	0.539656	−	0.841886i	$-0.318554\pi$
$241$	16.7554	1.07931	0.539656	+	0.841886i	$0.318554\pi$
$242$	6.66133	0.428206
$243$	−14.3989	−0.923693
$244$	−4.31547	−0.276270
$245$	−0.0673894	−0.00430535
$246$	−2.61418	−0.166674
$247$	−9.48718	−0.603655
$248$	−10.2504	−0.650898
$249$	2.69646	0.170881
$250$	1.00000	0.0632456
$251$	14.7413	0.930465	0.465233	−	0.885188i	$-0.345971\pi$
$251$	14.7413	0.930465	0.465233	+	0.885188i	$0.345971\pi$
$252$	4.21784	0.265699
$253$	−28.2828	−1.77813
$254$	−7.89749	−0.495533
$255$	−4.20690	−0.263446
$256$	1.00000	0.0625000
$257$	21.6831	1.35256	0.676278	−	0.736646i	$-0.263592\pi$
$257$	21.6831	1.35256	0.676278	+	0.736646i	$0.263592\pi$
$258$	−1.04107	−0.0648139
$259$	21.9975	1.36686
$260$	2.40716	0.149286
$261$	−7.47775	−0.462861
$262$	1.80764	0.111676
$263$	−9.48361	−0.584785	−0.292392	−	0.956298i	$-0.594451\pi$
$263$	−9.48361	−0.584785	−0.292392	+	0.956298i	$0.594451\pi$
$264$	4.96909	0.305827
$265$	10.1935	0.626184
$266$	10.3772	0.636266
$267$	−17.1686	−1.05070
$268$	3.17885	0.194179
$269$	−19.0776	−1.16318	−0.581591	−	0.813481i	$-0.697570\pi$
$269$	−19.0776	−1.16318	−0.581591	+	0.813481i	$0.697570\pi$
$270$	5.44133	0.331149
$271$	11.0473	0.671078	0.335539	−	0.942026i	$-0.391081\pi$
$271$	11.0473	0.671078	0.335539	+	0.942026i	$0.391081\pi$
$272$	3.55792	0.215731
$273$	7.49410	0.453564
$274$	19.6484	1.18700
$275$	−4.20254	−0.253423
$276$	−7.95750	−0.478985
$277$	−4.32615	−0.259933	−0.129967	−	0.991518i	$-0.541487\pi$
$277$	−4.32615	−0.259933	−0.129967	+	0.991518i	$0.541487\pi$
$278$	−16.9009	−1.01365
$279$	16.4203	0.983056
$280$	−2.63299	−0.157351
$281$	11.7578	0.701413	0.350707	−	0.936485i	$-0.385941\pi$
$281$	11.7578	0.701413	0.350707	+	0.936485i	$0.385941\pi$
$282$	−10.2796	−0.612139
$283$	8.23181	0.489330	0.244665	−	0.969608i	$-0.421322\pi$
$283$	8.23181	0.489330	0.244665	+	0.969608i	$0.421322\pi$
$284$	8.33371	0.494515
$285$	4.66012	0.276042
$286$	−10.1162	−0.598183
$287$	−5.82128	−0.343619
$288$	−1.60192	−0.0943942
$289$	−4.34118	−0.255363
$290$	4.66799	0.274114
$291$	−21.5122	−1.26107
$292$	−3.76307	−0.220217
$293$	−13.2637	−0.774874	−0.387437	−	0.921896i	$-0.626640\pi$
$293$	−13.2637	−0.774874	−0.387437	+	0.921896i	$0.626640\pi$
$294$	0.0796815	0.00464712
$295$	13.8449	0.806082
$296$	−8.35458	−0.485600
$297$	−22.8674	−1.32690
$298$	17.3536	1.00527
$299$	16.2001	0.936874
$300$	−1.18240	−0.0682661
$301$	−2.31825	−0.133622
$302$	−6.40420	−0.368520
$303$	−15.0780	−0.866210
$304$	−3.94123	−0.226045
$305$	−4.31547	−0.247103
$306$	−5.69952	−0.325820
$307$	29.8505	1.70366	0.851830	−	0.523819i	$-0.175493\pi$
$307$	29.8505	1.70366	0.851830	+	0.523819i	$0.175493\pi$
$308$	11.0652	0.630499
$309$	4.47580	0.254619
$310$	−10.2504	−0.582181
$311$	14.1156	0.800425	0.400212	−	0.916422i	$-0.368936\pi$
$311$	14.1156	0.800425	0.400212	+	0.916422i	$0.368936\pi$
$312$	−2.84624	−0.161137
$313$	−0.332159	−0.0187747	−0.00938736	−	0.999956i	$-0.502988\pi$
$313$	−0.332159	−0.0187747	−0.00938736	+	0.999956i	$0.502988\pi$
$314$	8.89730	0.502104
$315$	4.21784	0.237648
$316$	1.62206	0.0912481
$317$	10.5783	0.594139	0.297069	−	0.954856i	$-0.403991\pi$
$317$	10.5783	0.594139	0.297069	+	0.954856i	$0.403991\pi$
$318$	−12.0529	−0.675891
$319$	−19.6174	−1.09836
$320$	1.00000	0.0559017
$321$	9.27144	0.517481
$322$	−17.7198	−0.987487
$323$	−14.0226	−0.780237
$324$	−1.62807	−0.0904486
$325$	2.40716	0.133525
$326$	−4.73033	−0.261988
$327$	−14.4157	−0.797189
$328$	2.21091	0.122077
$329$	−22.8906	−1.26200
$330$	4.96909	0.273540
$331$	11.4243	0.627934	0.313967	−	0.949434i	$-0.398342\pi$
$331$	11.4243	0.627934	0.313967	+	0.949434i	$0.398342\pi$
$332$	−2.28049	−0.125158
$333$	13.3834	0.733405
$334$	−12.2448	−0.670004
$335$	3.17885	0.173679
$336$	3.11325	0.169842
$337$	−11.6337	−0.633730	−0.316865	−	0.948471i	$-0.602630\pi$
$337$	−11.6337	−0.633730	−0.316865	+	0.948471i	$0.602630\pi$
$338$	−7.20556	−0.391931
$339$	8.12434	0.441253
$340$	3.55792	0.192956
$341$	43.0775	2.33278
$342$	6.31354	0.341397
$343$	18.6083	1.00476
$344$	0.880466	0.0474716
$345$	−7.95750	−0.428417
$346$	−10.3881	−0.558467
$347$	−21.8497	−1.17295	−0.586476	−	0.809967i	$-0.699485\pi$
$347$	−21.8497	−1.17295	−0.586476	+	0.809967i	$0.699485\pi$
$348$	−5.51944	−0.295873
$349$	20.1748	1.07993	0.539966	−	0.841687i	$-0.318437\pi$
$349$	20.1748	1.07993	0.539966	+	0.841687i	$0.318437\pi$
$350$	−2.63299	−0.140739
$351$	13.0982	0.699129
$352$	−4.20254	−0.223996
$353$	−19.5038	−1.03808	−0.519041	−	0.854749i	$-0.673711\pi$
$353$	−19.5038	−1.03808	−0.519041	+	0.854749i	$0.673711\pi$
$354$	−16.3703	−0.870070
$355$	8.33371	0.442307
$356$	14.5201	0.769565
$357$	11.0767	0.586241
$358$	−11.8570	−0.626662
$359$	−6.65083	−0.351017	−0.175509	−	0.984478i	$-0.556157\pi$
$359$	−6.65083	−0.351017	−0.175509	+	0.984478i	$0.556157\pi$
$360$	−1.60192	−0.0844287
$361$	−3.46674	−0.182460
$362$	8.91215	0.468412
$363$	−7.87638	−0.413403
$364$	−6.33803	−0.332203
$365$	−3.76307	−0.196968
$366$	5.10263	0.266719
$367$	−14.1221	−0.737165	−0.368583	−	0.929595i	$-0.620157\pi$
$367$	−14.1221	−0.737165	−0.368583	+	0.929595i	$0.620157\pi$
$368$	6.72994	0.350822
$369$	−3.54170	−0.184374
$370$	−8.35458	−0.434334
$371$	−26.8394	−1.39343
$372$	12.1200	0.628395
$373$	−26.2891	−1.36120	−0.680600	−	0.732655i	$-0.738281\pi$
$373$	−26.2891	−1.36120	−0.680600	+	0.732655i	$0.738281\pi$
$374$	−14.9523	−0.773166
$375$	−1.18240	−0.0610590
$376$	8.69379	0.448348
$377$	11.2366	0.578715
$378$	−14.3269	−0.736898
$379$	10.8505	0.557351	0.278675	−	0.960385i	$-0.410105\pi$
$379$	10.8505	0.557351	0.278675	+	0.960385i	$0.410105\pi$
$380$	−3.94123	−0.202181
$381$	9.33802	0.478401
$382$	18.3485	0.938790
$383$	−12.5500	−0.641277	−0.320639	−	0.947202i	$-0.603897\pi$
$383$	−12.5500	−0.641277	−0.320639	+	0.947202i	$0.603897\pi$
$384$	−1.18240	−0.0603393
$385$	11.0652	0.563936
$386$	4.27460	0.217571
$387$	−1.41044	−0.0716966
$388$	18.1936	0.923642
$389$	−12.0320	−0.610048	−0.305024	−	0.952345i	$-0.598665\pi$
$389$	−12.0320	−0.610048	−0.305024	+	0.952345i	$0.598665\pi$
$390$	−2.84624	−0.144125
$391$	23.9446	1.21093
$392$	−0.0673894	−0.00340368
$393$	−2.13735	−0.107815
$394$	9.03112	0.454981
$395$	1.62206	0.0816148
$396$	6.73214	0.338303
$397$	37.0121	1.85758	0.928792	−	0.370602i	$-0.120848\pi$
$397$	37.0121	1.85758	0.928792	+	0.370602i	$0.120848\pi$
$398$	13.4278	0.673072
$399$	−12.2700	−0.614269
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−3.75868	−0.187466
$403$	−24.6743	−1.22911
$404$	12.7520	0.634437
$405$	−1.62807	−0.0808997
$406$	−12.2907	−0.609979
$407$	35.1104	1.74036
$408$	−4.20690	−0.208273
$409$	10.7875	0.533410	0.266705	−	0.963778i	$-0.414065\pi$
$409$	10.7875	0.533410	0.266705	+	0.963778i	$0.414065\pi$
$410$	2.21091	0.109189
$411$	−23.2323	−1.14596
$412$	−3.78534	−0.186490
$413$	−36.4534	−1.79376
$414$	−10.7808	−0.529849
$415$	−2.28049	−0.111945
$416$	2.40716	0.118021
$417$	19.9837	0.978605
$418$	16.5632	0.810130
$419$	9.74173	0.475915	0.237957	−	0.971276i	$-0.423522\pi$
$419$	9.74173	0.475915	0.237957	+	0.971276i	$0.423522\pi$
$420$	3.11325	0.151911
$421$	−31.9447	−1.55689	−0.778444	−	0.627714i	$-0.783991\pi$
$421$	−31.9447	−1.55689	−0.778444	+	0.627714i	$0.783991\pi$
$422$	12.3616	0.601755
$423$	−13.9268	−0.677144
$424$	10.1935	0.495042
$425$	3.55792	0.172585
$426$	−9.85380	−0.477418
$427$	11.3626	0.549874
$428$	−7.84118	−0.379018
$429$	11.9614	0.577503
$430$	0.880466	0.0424598
$431$	4.76676	0.229607	0.114803	−	0.993388i	$-0.463376\pi$
$431$	4.76676	0.229607	0.114803	+	0.993388i	$0.463376\pi$
$432$	5.44133	0.261796
$433$	23.3231	1.12084	0.560419	−	0.828210i	$-0.310640\pi$
$433$	23.3231	1.12084	0.560419	+	0.828210i	$0.310640\pi$
$434$	26.9890	1.29551
$435$	−5.51944	−0.264637
$436$	12.1919	0.583884
$437$	−26.5242	−1.26882
$438$	4.44946	0.212603
$439$	−29.7324	−1.41905	−0.709524	−	0.704681i	$-0.751090\pi$
$439$	−29.7324	−1.41905	−0.709524	+	0.704681i	$0.751090\pi$
$440$	−4.20254	−0.200348
$441$	0.107953	0.00514060
$442$	8.56451	0.407372
$443$	2.58668	0.122897	0.0614483	−	0.998110i	$-0.480428\pi$
$443$	2.58668	0.122897	0.0614483	+	0.998110i	$0.480428\pi$
$444$	9.87848	0.468812
$445$	14.5201	0.688320
$446$	17.7961	0.842668
$447$	−20.5189	−0.970513
$448$	−2.63299	−0.124397
$449$	19.5428	0.922283	0.461142	−	0.887327i	$-0.347440\pi$
$449$	19.5428	0.922283	0.461142	+	0.887327i	$0.347440\pi$
$450$	−1.60192	−0.0755154
$451$	−9.29142	−0.437516
$452$	−6.87104	−0.323186
$453$	7.57235	0.355780
$454$	−15.7330	−0.738386
$455$	−6.33803	−0.297131
$456$	4.66012	0.218230
$457$	23.8835	1.11722	0.558612	−	0.829429i	$-0.311334\pi$
$457$	23.8835	1.11722	0.558612	+	0.829429i	$0.311334\pi$
$458$	−22.4376	−1.04844
$459$	19.3598	0.903640
$460$	6.72994	0.313785
$461$	−9.49620	−0.442282	−0.221141	−	0.975242i	$-0.570978\pi$
$461$	−9.49620	−0.442282	−0.221141	+	0.975242i	$0.570978\pi$
$462$	−13.0836	−0.608702
$463$	−23.1931	−1.07788	−0.538938	−	0.842345i	$-0.681174\pi$
$463$	−23.1931	−1.07788	−0.538938	+	0.842345i	$0.681174\pi$
$464$	4.66799	0.216706
$465$	12.1200	0.562054
$466$	−17.4192	−0.806930
$467$	15.7165	0.727273	0.363636	−	0.931541i	$-0.381535\pi$
$467$	15.7165	0.727273	0.363636	+	0.931541i	$0.381535\pi$
$468$	−3.85609	−0.178248
$469$	−8.36987	−0.386485
$470$	8.69379	0.401015
$471$	−10.5202	−0.484745
$472$	13.8449	0.637264
$473$	−3.70019	−0.170135
$474$	−1.91793	−0.0880935
$475$	−3.94123	−0.180836
$476$	−9.36796	−0.429380
$477$	−16.3293	−0.747665
$478$	5.75105	0.263047
$479$	−8.39491	−0.383573	−0.191787	−	0.981437i	$-0.561428\pi$
$479$	−8.39491	−0.383573	−0.191787	+	0.981437i	$0.561428\pi$
$480$	−1.18240	−0.0539691
$481$	−20.1108	−0.916975
$482$	16.7554	0.763189
$483$	20.9520	0.953348
$484$	6.66133	0.302788
$485$	18.1936	0.826131
$486$	−14.3989	−0.653149
$487$	−21.6381	−0.980516	−0.490258	−	0.871577i	$-0.663097\pi$
$487$	−21.6381	−0.980516	−0.490258	+	0.871577i	$0.663097\pi$
$488$	−4.31547	−0.195352
$489$	5.59315	0.252931
$490$	−0.0673894	−0.00304434
$491$	9.47304	0.427512	0.213756	−	0.976887i	$-0.431430\pi$
$491$	9.47304	0.427512	0.213756	+	0.976887i	$0.431430\pi$
$492$	−2.61418	−0.117856
$493$	16.6083	0.748002
$494$	−9.48718	−0.426848
$495$	6.73214	0.302587
$496$	−10.2504	−0.460254
$497$	−21.9425	−0.984257
$498$	2.69646	0.120831
$499$	26.9868	1.20810	0.604048	−	0.796948i	$-0.293553\pi$
$499$	26.9868	1.20810	0.604048	+	0.796948i	$0.293553\pi$
$500$	1.00000	0.0447214
$501$	14.4782	0.646840
$502$	14.7413	0.657938
$503$	−23.4870	−1.04723	−0.523617	−	0.851954i	$-0.675418\pi$
$503$	−23.4870	−1.04723	−0.523617	+	0.851954i	$0.675418\pi$
$504$	4.21784	0.187877
$505$	12.7520	0.567457
$506$	−28.2828	−1.25732
$507$	8.51988	0.378381
$508$	−7.89749	−0.350395
$509$	−3.96687	−0.175829	−0.0879143	−	0.996128i	$-0.528020\pi$
$509$	−3.96687	−0.175829	−0.0879143	+	0.996128i	$0.528020\pi$
$510$	−4.20690	−0.186285
$511$	9.90810	0.438308
$512$	1.00000	0.0441942
$513$	−21.4455	−0.946842
$514$	21.6831	0.956402
$515$	−3.78534	−0.166802
$516$	−1.04107	−0.0458304
$517$	−36.5360	−1.60685
$518$	21.9975	0.966514
$519$	12.2829	0.539160
$520$	2.40716	0.105561
$521$	5.68151	0.248911	0.124456	−	0.992225i	$-0.460282\pi$
$521$	5.68151	0.248911	0.124456	+	0.992225i	$0.460282\pi$
$522$	−7.47775	−0.327292
$523$	−34.7175	−1.51809	−0.759046	−	0.651037i	$-0.774334\pi$
$523$	−34.7175	−1.51809	−0.759046	+	0.651037i	$0.774334\pi$
$524$	1.80764	0.0789669
$525$	3.11325	0.135873
$526$	−9.48361	−0.413505
$527$	−36.4700	−1.58866
$528$	4.96909	0.216252
$529$	22.2921	0.969221
$530$	10.1935	0.442779
$531$	−22.1785	−0.962464
$532$	10.3772	0.449908
$533$	5.32201	0.230522
$534$	−17.1686	−0.742960
$535$	−7.84118	−0.339004
$536$	3.17885	0.137306
$537$	14.0198	0.604997
$538$	−19.0776	−0.822494
$539$	0.283207	0.0121986
$540$	5.44133	0.234157
$541$	−28.8531	−1.24049	−0.620246	−	0.784407i	$-0.712967\pi$
$541$	−28.8531	−1.24049	−0.620246	+	0.784407i	$0.712967\pi$
$542$	11.0473	0.474524
$543$	−10.5377	−0.452218
$544$	3.55792	0.152545
$545$	12.1919	0.522242
$546$	7.49410	0.320718
$547$	19.1781	0.819995	0.409997	−	0.912087i	$-0.365530\pi$
$547$	19.1781	0.819995	0.409997	+	0.912087i	$0.365530\pi$
$548$	19.6484	0.839337
$549$	6.91306	0.295042
$550$	−4.20254	−0.179197
$551$	−18.3976	−0.783764
$552$	−7.95750	−0.338694
$553$	−4.27087	−0.181616
$554$	−4.32615	−0.183801
$555$	9.87848	0.419318
$556$	−16.9009	−0.716758
$557$	−13.4446	−0.569666	−0.284833	−	0.958577i	$-0.591938\pi$
$557$	−13.4446	−0.569666	−0.284833	+	0.958577i	$0.591938\pi$
$558$	16.4203	0.695126
$559$	2.11943	0.0896422
$560$	−2.63299	−0.111264
$561$	17.6797	0.746436
$562$	11.7578	0.495974
$563$	−28.5338	−1.20256	−0.601279	−	0.799039i	$-0.705342\pi$
$563$	−28.5338	−1.20256	−0.601279	+	0.799039i	$0.705342\pi$
$564$	−10.2796	−0.432848
$565$	−6.87104	−0.289067
$566$	8.23181	0.346009
$567$	4.28670	0.180024
$568$	8.33371	0.349675
$569$	−13.1220	−0.550102	−0.275051	−	0.961430i	$-0.588695\pi$
$569$	−13.1220	−0.550102	−0.275051	+	0.961430i	$0.588695\pi$
$570$	4.66012	0.195191
$571$	15.5531	0.650876	0.325438	−	0.945563i	$-0.394488\pi$
$571$	15.5531	0.650876	0.325438	+	0.945563i	$0.394488\pi$
$572$	−10.1162	−0.422980
$573$	−21.6953	−0.906334
$574$	−5.82128	−0.242976
$575$	6.72994	0.280658
$576$	−1.60192	−0.0667468
$577$	−23.0810	−0.960875	−0.480437	−	0.877029i	$-0.659522\pi$
$577$	−23.0810	−0.960875	−0.480437	+	0.877029i	$0.659522\pi$
$578$	−4.34118	−0.180569
$579$	−5.05430	−0.210050
$580$	4.66799	0.193828
$581$	6.00451	0.249109
$582$	−21.5122	−0.891710
$583$	−42.8387	−1.77420
$584$	−3.76307	−0.155717
$585$	−3.85609	−0.159430
$586$	−13.2637	−0.547919
$587$	28.7508	1.18667	0.593336	−	0.804955i	$-0.297811\pi$
$587$	28.7508	1.18667	0.593336	+	0.804955i	$0.297811\pi$
$588$	0.0796815	0.00328601
$589$	40.3990	1.66461
$590$	13.8449	0.569986
$591$	−10.6784	−0.439252
$592$	−8.35458	−0.343371
$593$	−38.1361	−1.56606	−0.783030	−	0.621984i	$-0.786327\pi$
$593$	−38.1361	−1.56606	−0.783030	+	0.621984i	$0.786327\pi$
$594$	−22.8674	−0.938260
$595$	−9.36796	−0.384049
$596$	17.3536	0.710831
$597$	−15.8770	−0.649803
$598$	16.2001	0.662470
$599$	26.8845	1.09847	0.549236	−	0.835667i	$-0.314919\pi$
$599$	26.8845	1.09847	0.549236	+	0.835667i	$0.314919\pi$
$600$	−1.18240	−0.0482714
$601$	−38.6447	−1.57635	−0.788176	−	0.615450i	$-0.788974\pi$
$601$	−38.6447	−1.57635	−0.788176	+	0.615450i	$0.788974\pi$
$602$	−2.31825	−0.0944850
$603$	−5.09228	−0.207374
$604$	−6.40420	−0.260583
$605$	6.66133	0.270822
$606$	−15.0780	−0.612503
$607$	−2.30718	−0.0936456	−0.0468228	−	0.998903i	$-0.514910\pi$
$607$	−2.30718	−0.0936456	−0.0468228	+	0.998903i	$0.514910\pi$
$608$	−3.94123	−0.159838
$609$	14.5326	0.588891
$610$	−4.31547	−0.174728
$611$	20.9274	0.846632
$612$	−5.69952	−0.230389
$613$	18.1668	0.733749	0.366875	−	0.930270i	$-0.380428\pi$
$613$	18.1668	0.733749	0.366875	+	0.930270i	$0.380428\pi$
$614$	29.8505	1.20467
$615$	−2.61418	−0.105414
$616$	11.0652	0.445830
$617$	45.1900	1.81928	0.909640	−	0.415397i	$-0.136357\pi$
$617$	45.1900	1.81928	0.909640	+	0.415397i	$0.136357\pi$
$618$	4.47580	0.180043
$619$	38.8093	1.55988	0.779938	−	0.625856i	$-0.215250\pi$
$619$	38.8093	1.55988	0.779938	+	0.625856i	$0.215250\pi$
$620$	−10.2504	−0.411664
$621$	36.6198	1.46950
$622$	14.1156	0.565986
$623$	−38.2313	−1.53170
$624$	−2.84624	−0.113941
$625$	1.00000	0.0400000
$626$	−0.332159	−0.0132757
$627$	−19.5843	−0.782123
$628$	8.89730	0.355041
$629$	−29.7250	−1.18521
$630$	4.21784	0.168043
$631$	−24.7444	−0.985058	−0.492529	−	0.870296i	$-0.663927\pi$
$631$	−24.7444	−0.985058	−0.492529	+	0.870296i	$0.663927\pi$
$632$	1.62206	0.0645222
$633$	−14.6164	−0.580951
$634$	10.5783	0.420119
$635$	−7.89749	−0.313402
$636$	−12.0529	−0.477927
$637$	−0.162217	−0.00642729
$638$	−19.6174	−0.776660
$639$	−13.3500	−0.528116
$640$	1.00000	0.0395285
$641$	−8.90065	−0.351555	−0.175777	−	0.984430i	$-0.556244\pi$
$641$	−8.90065	−0.351555	−0.175777	+	0.984430i	$0.556244\pi$
$642$	9.27144	0.365914
$643$	−43.0936	−1.69944	−0.849722	−	0.527231i	$-0.823230\pi$
$643$	−43.0936	−1.69944	−0.849722	+	0.527231i	$0.823230\pi$
$644$	−17.7198	−0.698259
$645$	−1.04107	−0.0409919
$646$	−14.0226	−0.551711
$647$	34.0553	1.33885	0.669427	−	0.742878i	$-0.266540\pi$
$647$	34.0553	1.33885	0.669427	+	0.742878i	$0.266540\pi$
$648$	−1.62807	−0.0639568
$649$	−58.1838	−2.28391
$650$	2.40716	0.0944167
$651$	−31.9119	−1.25073
$652$	−4.73033	−0.185254
$653$	30.5247	1.19452	0.597262	−	0.802046i	$-0.296255\pi$
$653$	30.5247	1.19452	0.597262	+	0.802046i	$0.296255\pi$
$654$	−14.4157	−0.563698
$655$	1.80764	0.0706302
$656$	2.21091	0.0863214
$657$	6.02814	0.235180
$658$	−22.8906	−0.892370
$659$	1.04605	0.0407484	0.0203742	−	0.999792i	$-0.493514\pi$
$659$	1.04605	0.0407484	0.0203742	+	0.999792i	$0.493514\pi$
$660$	4.96909	0.193422
$661$	−33.4476	−1.30096	−0.650480	−	0.759523i	$-0.725432\pi$
$661$	−33.4476	−1.30096	−0.650480	+	0.759523i	$0.725432\pi$
$662$	11.4243	0.444016
$663$	−10.1267	−0.393288
$664$	−2.28049	−0.0885003
$665$	10.3772	0.402410
$666$	13.3834	0.518596
$667$	31.4153	1.21640
$668$	−12.2448	−0.473764
$669$	−21.0421	−0.813536
$670$	3.17885	0.122810
$671$	18.1359	0.700131
$672$	3.11325	0.120096
$673$	19.2485	0.741975	0.370987	−	0.928638i	$-0.379019\pi$
$673$	19.2485	0.741975	0.370987	+	0.928638i	$0.379019\pi$
$674$	−11.6337	−0.448115
$675$	5.44133	0.209437
$676$	−7.20556	−0.277137
$677$	27.9365	1.07369	0.536844	−	0.843682i	$-0.319617\pi$
$677$	27.9365	1.07369	0.536844	+	0.843682i	$0.319617\pi$
$678$	8.12434	0.312013
$679$	−47.9036	−1.83837
$680$	3.55792	0.136440
$681$	18.6027	0.712859
$682$	43.0775	1.64952
$683$	32.4843	1.24298	0.621489	−	0.783423i	$-0.286528\pi$
$683$	32.4843	1.24298	0.621489	+	0.783423i	$0.286528\pi$
$684$	6.31354	0.241404
$685$	19.6484	0.750726
$686$	18.6083	0.710469
$687$	26.5303	1.01219
$688$	0.880466	0.0335675
$689$	24.5375	0.934804
$690$	−7.95750	−0.302937
$691$	15.1669	0.576974	0.288487	−	0.957484i	$-0.406848\pi$
$691$	15.1669	0.576974	0.288487	+	0.957484i	$0.406848\pi$
$692$	−10.3881	−0.394896
$693$	−17.7256	−0.673341
$694$	−21.8497	−0.829402
$695$	−16.9009	−0.641088
$696$	−5.51944	−0.209214
$697$	7.86623	0.297955
$698$	20.1748	0.763627
$699$	20.5965	0.779033
$700$	−2.63299	−0.0995175
$701$	6.60370	0.249418	0.124709	−	0.992193i	$-0.460200\pi$
$701$	6.60370	0.249418	0.124709	+	0.992193i	$0.460200\pi$
$702$	13.0982	0.494359
$703$	32.9273	1.24188
$704$	−4.20254	−0.158389
$705$	−10.2796	−0.387151
$706$	−19.5038	−0.734035
$707$	−33.5759	−1.26275
$708$	−16.3703	−0.615232
$709$	−39.1024	−1.46852	−0.734260	−	0.678868i	$-0.762471\pi$
$709$	−39.1024	−1.46852	−0.734260	+	0.678868i	$0.762471\pi$
$710$	8.33371	0.312758
$711$	−2.59842	−0.0974483
$712$	14.5201	0.544165
$713$	−68.9842	−2.58348
$714$	11.0767	0.414535
$715$	−10.1162	−0.378324
$716$	−11.8570	−0.443117
$717$	−6.80006	−0.253953
$718$	−6.65083	−0.248207
$719$	−36.7878	−1.37195	−0.685977	−	0.727623i	$-0.740625\pi$
$719$	−36.7878	−1.37195	−0.685977	+	0.727623i	$0.740625\pi$
$720$	−1.60192	−0.0597001
$721$	9.96674	0.371181
$722$	−3.46674	−0.129019
$723$	−19.8117	−0.736804
$724$	8.91215	0.331217
$725$	4.66799	0.173365
$726$	−7.87638	−0.292320
$727$	9.24472	0.342868	0.171434	−	0.985196i	$-0.445160\pi$
$727$	9.24472	0.342868	0.171434	+	0.985196i	$0.445160\pi$
$728$	−6.33803	−0.234903
$729$	21.9096	0.811466
$730$	−3.76307	−0.139277
$731$	3.13263	0.115865
$732$	5.10263	0.188599
$733$	−6.82845	−0.252214	−0.126107	−	0.992017i	$-0.540248\pi$
$733$	−6.82845	−0.252214	−0.126107	+	0.992017i	$0.540248\pi$
$734$	−14.1221	−0.521255
$735$	0.0796815	0.00293909
$736$	6.72994	0.248069
$737$	−13.3592	−0.492094
$738$	−3.54170	−0.130372
$739$	−4.13084	−0.151956	−0.0759778	−	0.997110i	$-0.524208\pi$
$739$	−4.13084	−0.151956	−0.0759778	+	0.997110i	$0.524208\pi$
$740$	−8.35458	−0.307120
$741$	11.2177	0.412091
$742$	−26.8394	−0.985306
$743$	41.8585	1.53564	0.767820	−	0.640665i	$-0.221341\pi$
$743$	41.8585	1.53564	0.767820	+	0.640665i	$0.221341\pi$
$744$	12.1200	0.444343
$745$	17.3536	0.635787
$746$	−26.2891	−0.962513
$747$	3.65318	0.133663
$748$	−14.9523	−0.546711
$749$	20.6457	0.754378
$750$	−1.18240	−0.0431753
$751$	−20.3253	−0.741682	−0.370841	−	0.928696i	$-0.620930\pi$
$751$	−20.3253	−0.741682	−0.370841	+	0.928696i	$0.620930\pi$
$752$	8.69379	0.317030
$753$	−17.4302	−0.635192
$754$	11.2366	0.409213
$755$	−6.40420	−0.233073
$756$	−14.3269	−0.521066
$757$	1.60576	0.0583625	0.0291813	−	0.999574i	$-0.490710\pi$
$757$	1.60576	0.0583625	0.0291813	+	0.999574i	$0.490710\pi$
$758$	10.8505	0.394106
$759$	33.4417	1.21386
$760$	−3.94123	−0.142963
$761$	5.12103	0.185637	0.0928187	−	0.995683i	$-0.470412\pi$
$761$	5.12103	0.185637	0.0928187	+	0.995683i	$0.470412\pi$
$762$	9.33802	0.338281
$763$	−32.1010	−1.16213
$764$	18.3485	0.663825
$765$	−5.69952	−0.206067
$766$	−12.5500	−0.453451
$767$	33.3270	1.20337
$768$	−1.18240	−0.0426663
$769$	−24.7309	−0.891819	−0.445909	−	0.895078i	$-0.647120\pi$
$769$	−24.7309	−0.891819	−0.445909	+	0.895078i	$0.647120\pi$
$770$	11.0652	0.398763
$771$	−25.6382	−0.923337
$772$	4.27460	0.153846
$773$	−23.4347	−0.842888	−0.421444	−	0.906854i	$-0.638477\pi$
$773$	−23.4347	−0.842888	−0.421444	+	0.906854i	$0.638477\pi$
$774$	−1.41044	−0.0506972
$775$	−10.2504	−0.368204
$776$	18.1936	0.653114
$777$	−26.0099	−0.933100
$778$	−12.0320	−0.431369
$779$	−8.71368	−0.312200
$780$	−2.84624	−0.101912
$781$	−35.0227	−1.25321
$782$	23.9446	0.856258
$783$	25.4000	0.907724
$784$	−0.0673894	−0.00240676
$785$	8.89730	0.317558
$786$	−2.13735	−0.0762369
$787$	−52.1691	−1.85963	−0.929814	−	0.368029i	$-0.880033\pi$
$787$	−52.1691	−1.85963	−0.929814	+	0.368029i	$0.880033\pi$
$788$	9.03112	0.321720
$789$	11.2135	0.399210
$790$	1.62206	0.0577104
$791$	18.0913	0.643254
$792$	6.73214	0.239216
$793$	−10.3881	−0.368891
$794$	37.0121	1.31351
$795$	−12.0529	−0.427471
$796$	13.4278	0.475934
$797$	23.7443	0.841067	0.420533	−	0.907277i	$-0.361843\pi$
$797$	23.7443	0.841067	0.420533	+	0.907277i	$0.361843\pi$
$798$	−12.2700	−0.434354
$799$	30.9319	1.09429
$800$	1.00000	0.0353553
$801$	−23.2601	−0.821856
$802$	1.00000	0.0353112
$803$	15.8144	0.558079
$804$	−3.75868	−0.132559
$805$	−17.7198	−0.624542
$806$	−24.6743	−0.869114
$807$	22.5574	0.794059
$808$	12.7520	0.448614
$809$	24.1582	0.849358	0.424679	−	0.905344i	$-0.360387\pi$
$809$	24.1582	0.849358	0.424679	+	0.905344i	$0.360387\pi$
$810$	−1.62807	−0.0572047
$811$	−32.6393	−1.14612	−0.573060	−	0.819514i	$-0.694244\pi$
$811$	−32.6393	−1.14612	−0.573060	+	0.819514i	$0.694244\pi$
$812$	−12.2907	−0.431320
$813$	−13.0624	−0.458119
$814$	35.1104	1.23062
$815$	−4.73033	−0.165696
$816$	−4.20690	−0.147271
$817$	−3.47012	−0.121404
$818$	10.7875	0.377178
$819$	10.1530	0.354776
$820$	2.21091	0.0772082
$821$	−10.7472	−0.375078	−0.187539	−	0.982257i	$-0.560051\pi$
$821$	−10.7472	−0.375078	−0.187539	+	0.982257i	$0.560051\pi$
$822$	−23.2323	−0.810319
$823$	−3.90458	−0.136105	−0.0680526	−	0.997682i	$-0.521679\pi$
$823$	−3.90458	−0.136105	−0.0680526	+	0.997682i	$0.521679\pi$
$824$	−3.78534	−0.131869
$825$	4.96909	0.173002
$826$	−36.4534	−1.26838
$827$	20.1950	0.702249	0.351125	−	0.936329i	$-0.385799\pi$
$827$	20.1950	0.702249	0.351125	+	0.936329i	$0.385799\pi$
$828$	−10.7808	−0.374660
$829$	−12.7290	−0.442095	−0.221048	−	0.975263i	$-0.570948\pi$
$829$	−12.7290	−0.442095	−0.221048	+	0.975263i	$0.570948\pi$
$830$	−2.28049	−0.0791571
$831$	5.11526	0.177446
$832$	2.40716	0.0834534
$833$	−0.239766	−0.00830741
$834$	19.9837	0.691978
$835$	−12.2448	−0.423748
$836$	16.5632	0.572849
$837$	−55.7755	−1.92788
$838$	9.74173	0.336523
$839$	9.31541	0.321604	0.160802	−	0.986987i	$-0.448592\pi$
$839$	9.31541	0.321604	0.160802	+	0.986987i	$0.448592\pi$
$840$	3.11325	0.107417
$841$	−7.20990	−0.248617
$842$	−31.9447	−1.10089
$843$	−13.9025	−0.478827
$844$	12.3616	0.425505
$845$	−7.20556	−0.247879
$846$	−13.9268	−0.478813
$847$	−17.5392	−0.602653
$848$	10.1935	0.350047
$849$	−9.73331	−0.334046
$850$	3.55792	0.122036
$851$	−56.2258	−1.92740
$852$	−9.85380	−0.337586
$853$	−3.18344	−0.108999	−0.0544994	−	0.998514i	$-0.517356\pi$
$853$	−3.18344	−0.108999	−0.0544994	+	0.998514i	$0.517356\pi$
$854$	11.3626	0.388820
$855$	6.31354	0.215919
$856$	−7.84118	−0.268006
$857$	44.9693	1.53612	0.768062	−	0.640376i	$-0.221221\pi$
$857$	44.9693	1.53612	0.768062	+	0.640376i	$0.221221\pi$
$858$	11.9614	0.408356
$859$	14.4647	0.493530	0.246765	−	0.969075i	$-0.420632\pi$
$859$	14.4647	0.493530	0.246765	+	0.969075i	$0.420632\pi$
$860$	0.880466	0.0300236
$861$	6.88310	0.234575
$862$	4.76676	0.162357
$863$	−11.4611	−0.390140	−0.195070	−	0.980789i	$-0.562493\pi$
$863$	−11.4611	−0.390140	−0.195070	+	0.980789i	$0.562493\pi$
$864$	5.44133	0.185118
$865$	−10.3881	−0.353206
$866$	23.3231	0.792551
$867$	5.13302	0.174327
$868$	26.9890	0.916067
$869$	−6.81678	−0.231243
$870$	−5.51944	−0.187127
$871$	7.65202	0.259279
$872$	12.1919	0.412868
$873$	−29.1448	−0.986402
$874$	−26.5242	−0.897195
$875$	−2.63299	−0.0890111
$876$	4.44946	0.150333
$877$	−10.7584	−0.363285	−0.181642	−	0.983365i	$-0.558141\pi$
$877$	−10.7584	−0.363285	−0.181642	+	0.983365i	$0.558141\pi$
$878$	−29.7324	−1.00342
$879$	15.6830	0.528976
$880$	−4.20254	−0.141668
$881$	31.0625	1.04652	0.523261	−	0.852173i	$-0.324715\pi$
$881$	31.0625	1.04652	0.523261	+	0.852173i	$0.324715\pi$
$882$	0.107953	0.00363495
$883$	35.8936	1.20791	0.603957	−	0.797017i	$-0.293590\pi$
$883$	35.8936	1.20791	0.603957	+	0.797017i	$0.293590\pi$
$884$	8.56451	0.288056
$885$	−16.3703	−0.550280
$886$	2.58668	0.0869011
$887$	−28.0289	−0.941119	−0.470559	−	0.882368i	$-0.655948\pi$
$887$	−28.0289	−0.941119	−0.470559	+	0.882368i	$0.655948\pi$
$888$	9.87848	0.331500
$889$	20.7940	0.697408
$890$	14.5201	0.486716
$891$	6.84205	0.229217
$892$	17.7961	0.595857
$893$	−34.2642	−1.14661
$894$	−20.5189	−0.686256
$895$	−11.8570	−0.396336
$896$	−2.63299	−0.0879619
$897$	−19.1550	−0.639567
$898$	19.5428	0.652153
$899$	−47.8485	−1.59584
$900$	−1.60192	−0.0533974
$901$	36.2678	1.20826
$902$	−9.29142	−0.309370
$903$	2.74111	0.0912185
$904$	−6.87104	−0.228527
$905$	8.91215	0.296250
$906$	7.57235	0.251574
$907$	−25.2159	−0.837279	−0.418639	−	0.908153i	$-0.637493\pi$
$907$	−25.2159	−0.837279	−0.418639	+	0.908153i	$0.637493\pi$
$908$	−15.7330	−0.522118
$909$	−20.4278	−0.677546
$910$	−6.33803	−0.210104
$911$	−42.8044	−1.41817	−0.709087	−	0.705121i	$-0.750893\pi$
$911$	−42.8044	−1.41817	−0.709087	+	0.705121i	$0.750893\pi$
$912$	4.66012	0.154312
$913$	9.58386	0.317180
$914$	23.8835	0.789997
$915$	5.10263	0.168688
$916$	−22.4376	−0.741359
$917$	−4.75948	−0.157172
$918$	19.3598	0.638970
$919$	4.90485	0.161796	0.0808980	−	0.996722i	$-0.474221\pi$
$919$	4.90485	0.161796	0.0808980	+	0.996722i	$0.474221\pi$
$920$	6.72994	0.221880
$921$	−35.2953	−1.16302
$922$	−9.49620	−0.312741
$923$	20.0606	0.660303
$924$	−13.0836	−0.430417
$925$	−8.35458	−0.274697
$926$	−23.1931	−0.762174
$927$	6.06382	0.199162
$928$	4.66799	0.153234
$929$	−25.2402	−0.828106	−0.414053	−	0.910253i	$-0.635887\pi$
$929$	−25.2402	−0.828106	−0.414053	+	0.910253i	$0.635887\pi$
$930$	12.1200	0.397432
$931$	0.265597	0.00870459
$932$	−17.4192	−0.570586
$933$	−16.6904	−0.546419
$934$	15.7165	0.514260
$935$	−14.9523	−0.488993
$936$	−3.85609	−0.126040
$937$	−9.47052	−0.309389	−0.154694	−	0.987962i	$-0.549439\pi$
$937$	−9.47052	−0.309389	−0.154694	+	0.987962i	$0.549439\pi$
$938$	−8.36987	−0.273286
$939$	0.392746	0.0128168
$940$	8.69379	0.283560
$941$	51.9037	1.69201	0.846006	−	0.533174i	$-0.179001\pi$
$941$	51.9037	1.69201	0.846006	+	0.533174i	$0.179001\pi$
$942$	−10.5202	−0.342766
$943$	14.8793	0.484535
$944$	13.8449	0.450613
$945$	−14.3269	−0.466055
$946$	−3.70019	−0.120304
$947$	−47.8597	−1.55523	−0.777615	−	0.628741i	$-0.783571\pi$
$947$	−47.8597	−1.55523	−0.777615	+	0.628741i	$0.783571\pi$
$948$	−1.91793	−0.0622915
$949$	−9.05832	−0.294045
$950$	−3.94123	−0.127870
$951$	−12.5079	−0.405595
$952$	−9.36796	−0.303617
$953$	46.2285	1.49749	0.748743	−	0.662860i	$-0.230658\pi$
$953$	46.2285	1.49749	0.748743	+	0.662860i	$0.230658\pi$
$954$	−16.3293	−0.528679
$955$	18.3485	0.593743
$956$	5.75105	0.186002
$957$	23.1957	0.749809
$958$	−8.39491	−0.271227
$959$	−51.7339	−1.67057
$960$	−1.18240	−0.0381619
$961$	74.0697	2.38935
$962$	−20.1108	−0.648399
$963$	12.5610	0.404772
$964$	16.7554	0.539656
$965$	4.27460	0.137604
$966$	20.9520	0.674119
$967$	48.1468	1.54830	0.774149	−	0.633004i	$-0.218178\pi$
$967$	48.1468	1.54830	0.774149	+	0.633004i	$0.218178\pi$
$968$	6.66133	0.214103
$969$	16.5803	0.532637
$970$	18.1936	0.584163
$971$	1.93485	0.0620923	0.0310461	−	0.999518i	$-0.490116\pi$
$971$	1.93485	0.0620923	0.0310461	+	0.999518i	$0.490116\pi$
$972$	−14.3989	−0.461846
$973$	44.4998	1.42660
$974$	−21.6381	−0.693330
$975$	−2.84624	−0.0911526
$976$	−4.31547	−0.138135
$977$	−11.0557	−0.353704	−0.176852	−	0.984237i	$-0.556591\pi$
$977$	−11.0557	−0.353704	−0.176852	+	0.984237i	$0.556591\pi$
$978$	5.59315	0.178849
$979$	−61.0214	−1.95025
$980$	−0.0673894	−0.00215268
$981$	−19.5304	−0.623558
$982$	9.47304	0.302297
$983$	−14.2149	−0.453383	−0.226692	−	0.973967i	$-0.572791\pi$
$983$	−14.2149	−0.453383	−0.226692	+	0.973967i	$0.572791\pi$
$984$	−2.61418	−0.0833371
$985$	9.03112	0.287755
$986$	16.6083	0.528917
$987$	27.0660	0.861519
$988$	−9.48718	−0.301827
$989$	5.92548	0.188419
$990$	6.73214	0.213962
$991$	−9.12700	−0.289929	−0.144964	−	0.989437i	$-0.546307\pi$
$991$	−9.12700	−0.289929	−0.144964	+	0.989437i	$0.546307\pi$
$992$	−10.2504	−0.325449
$993$	−13.5081	−0.428666
$994$	−21.9425	−0.695975
$995$	13.4278	0.425688
$996$	2.69646	0.0854407
$997$	−47.4372	−1.50235	−0.751175	−	0.660103i	$-0.770513\pi$
$997$	−47.4372	−1.50235	−0.751175	+	0.660103i	$0.770513\pi$
$998$	26.9868	0.854253
$999$	−45.4600	−1.43829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.9	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.18240 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.18240 q^{6} -2.63299 q^{7} +1.00000 q^{8} -1.60192 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.18240 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.18240 q^{6} -2.63299 q^{7} +1.00000 q^{8} -1.60192 q^{9} +1.00000 q^{10} -4.20254 q^{11} -1.18240 q^{12} +2.40716 q^{13} -2.63299 q^{14} -1.18240 q^{15} +1.00000 q^{16} +3.55792 q^{17} -1.60192 q^{18} -3.94123 q^{19} +1.00000 q^{20} +3.11325 q^{21} -4.20254 q^{22} +6.72994 q^{23} -1.18240 q^{24} +1.00000 q^{25} +2.40716 q^{26} +5.44133 q^{27} -2.63299 q^{28} +4.66799 q^{29} -1.18240 q^{30} -10.2504 q^{31} +1.00000 q^{32} +4.96909 q^{33} +3.55792 q^{34} -2.63299 q^{35} -1.60192 q^{36} -8.35458 q^{37} -3.94123 q^{38} -2.84624 q^{39} +1.00000 q^{40} +2.21091 q^{41} +3.11325 q^{42} +0.880466 q^{43} -4.20254 q^{44} -1.60192 q^{45} +6.72994 q^{46} +8.69379 q^{47} -1.18240 q^{48} -0.0673894 q^{49} +1.00000 q^{50} -4.20690 q^{51} +2.40716 q^{52} +10.1935 q^{53} +5.44133 q^{54} -4.20254 q^{55} -2.63299 q^{56} +4.66012 q^{57} +4.66799 q^{58} +13.8449 q^{59} -1.18240 q^{60} -4.31547 q^{61} -10.2504 q^{62} +4.21784 q^{63} +1.00000 q^{64} +2.40716 q^{65} +4.96909 q^{66} +3.17885 q^{67} +3.55792 q^{68} -7.95750 q^{69} -2.63299 q^{70} +8.33371 q^{71} -1.60192 q^{72} -3.76307 q^{73} -8.35458 q^{74} -1.18240 q^{75} -3.94123 q^{76} +11.0652 q^{77} -2.84624 q^{78} +1.62206 q^{79} +1.00000 q^{80} -1.62807 q^{81} +2.21091 q^{82} -2.28049 q^{83} +3.11325 q^{84} +3.55792 q^{85} +0.880466 q^{86} -5.51944 q^{87} -4.20254 q^{88} +14.5201 q^{89} -1.60192 q^{90} -6.33803 q^{91} +6.72994 q^{92} +12.1200 q^{93} +8.69379 q^{94} -3.94123 q^{95} -1.18240 q^{96} +18.1936 q^{97} -0.0673894 q^{98} +6.73214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

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