LMFDB - Embedded newform 8021.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56283 q^{2} -1.23829 q^{3} +4.56811 q^{4} +4.05265 q^{5} +3.17352 q^{6} +4.87248 q^{7} -6.58165 q^{8} -1.46665 q^{9} +O(q^{10})$	\(q-2.56283 q^{2} -1.23829 q^{3} +4.56811 q^{4} +4.05265 q^{5} +3.17352 q^{6} +4.87248 q^{7} -6.58165 q^{8} -1.46665 q^{9} -10.3863 q^{10} -3.99057 q^{11} -5.65663 q^{12} -1.00000 q^{13} -12.4874 q^{14} -5.01834 q^{15} +7.73144 q^{16} +5.49711 q^{17} +3.75878 q^{18} +1.70267 q^{19} +18.5130 q^{20} -6.03353 q^{21} +10.2272 q^{22} -9.30544 q^{23} +8.14996 q^{24} +11.4240 q^{25} +2.56283 q^{26} +5.53099 q^{27} +22.2581 q^{28} +4.11456 q^{29} +12.8612 q^{30} -1.19582 q^{31} -6.65109 q^{32} +4.94146 q^{33} -14.0882 q^{34} +19.7465 q^{35} -6.69982 q^{36} +10.4858 q^{37} -4.36365 q^{38} +1.23829 q^{39} -26.6731 q^{40} -8.69966 q^{41} +15.4629 q^{42} +1.57115 q^{43} -18.2294 q^{44} -5.94382 q^{45} +23.8483 q^{46} +10.3034 q^{47} -9.57373 q^{48} +16.7411 q^{49} -29.2778 q^{50} -6.80699 q^{51} -4.56811 q^{52} -13.2390 q^{53} -14.1750 q^{54} -16.1724 q^{55} -32.0690 q^{56} -2.10839 q^{57} -10.5449 q^{58} +5.59139 q^{59} -22.9244 q^{60} -2.10823 q^{61} +3.06469 q^{62} -7.14622 q^{63} +1.58276 q^{64} -4.05265 q^{65} -12.6641 q^{66} -6.21026 q^{67} +25.1114 q^{68} +11.5228 q^{69} -50.6070 q^{70} +6.07892 q^{71} +9.65296 q^{72} +11.9093 q^{73} -26.8734 q^{74} -14.1462 q^{75} +7.77798 q^{76} -19.4440 q^{77} -3.17352 q^{78} -1.84250 q^{79} +31.3328 q^{80} -2.44900 q^{81} +22.2958 q^{82} +9.60225 q^{83} -27.5618 q^{84} +22.2779 q^{85} -4.02660 q^{86} -5.09500 q^{87} +26.2645 q^{88} -15.8571 q^{89} +15.2330 q^{90} -4.87248 q^{91} -42.5083 q^{92} +1.48077 q^{93} -26.4059 q^{94} +6.90032 q^{95} +8.23595 q^{96} -17.9933 q^{97} -42.9047 q^{98} +5.85276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.56283	−1.81220	−0.906098	−	0.423067i	$-0.860953\pi$
$2$	−2.56283	−1.81220	−0.906098	+	0.423067i	$0.860953\pi$
$3$	−1.23829	−0.714925	−0.357462	−	0.933928i	$-0.616358\pi$
$3$	−1.23829	−0.714925	−0.357462	+	0.933928i	$0.616358\pi$
$4$	4.56811	2.28406
$5$	4.05265	1.81240	0.906201	−	0.422848i	$-0.138969\pi$
$5$	4.05265	1.81240	0.906201	+	0.422848i	$0.138969\pi$
$6$	3.17352	1.29558
$7$	4.87248	1.84163	0.920813	−	0.390004i	$-0.127526\pi$
$7$	4.87248	1.84163	0.920813	+	0.390004i	$0.127526\pi$
$8$	−6.58165	−2.32696
$9$	−1.46665	−0.488883
$10$	−10.3863	−3.28443
$11$	−3.99057	−1.20320	−0.601601	−	0.798797i	$-0.705470\pi$
$11$	−3.99057	−1.20320	−0.601601	+	0.798797i	$0.705470\pi$
$12$	−5.65663	−1.63293
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−12.4874	−3.33739
$15$	−5.01834	−1.29573
$16$	7.73144	1.93286
$17$	5.49711	1.33325	0.666623	−	0.745395i	$-0.267739\pi$
$17$	5.49711	1.33325	0.666623	+	0.745395i	$0.267739\pi$
$18$	3.75878	0.885952
$19$	1.70267	0.390619	0.195309	−	0.980742i	$-0.437429\pi$
$19$	1.70267	0.390619	0.195309	+	0.980742i	$0.437429\pi$
$20$	18.5130	4.13963
$21$	−6.03353	−1.31662
$22$	10.2272	2.18044
$23$	−9.30544	−1.94032	−0.970159	−	0.242470i	$-0.922043\pi$
$23$	−9.30544	−1.94032	−0.970159	+	0.242470i	$0.922043\pi$
$24$	8.14996	1.66360
$25$	11.4240	2.28480
$26$	2.56283	0.502613
$27$	5.53099	1.06444
$28$	22.2581	4.20638
$29$	4.11456	0.764054	0.382027	−	0.924151i	$-0.375226\pi$
$29$	4.11456	0.764054	0.382027	+	0.924151i	$0.375226\pi$
$30$	12.8612	2.34812
$31$	−1.19582	−0.214776	−0.107388	−	0.994217i	$-0.534249\pi$
$31$	−1.19582	−0.214776	−0.107388	+	0.994217i	$0.534249\pi$
$32$	−6.65109	−1.17576
$33$	4.94146	0.860199
$34$	−14.0882	−2.41610
$35$	19.7465	3.33777
$36$	−6.69982	−1.11664
$37$	10.4858	1.72386	0.861929	−	0.507029i	$-0.169256\pi$
$37$	10.4858	1.72386	0.861929	+	0.507029i	$0.169256\pi$
$38$	−4.36365	−0.707878
$39$	1.23829	0.198284
$40$	−26.6731	−4.21739
$41$	−8.69966	−1.35866	−0.679330	−	0.733833i	$-0.737729\pi$
$41$	−8.69966	−1.35866	−0.679330	+	0.733833i	$0.737729\pi$
$42$	15.4629	2.38598
$43$	1.57115	0.239599	0.119799	−	0.992798i	$-0.461775\pi$
$43$	1.57115	0.239599	0.119799	+	0.992798i	$0.461775\pi$
$44$	−18.2294	−2.74818
$45$	−5.94382	−0.886052
$46$	23.8483	3.51624
$47$	10.3034	1.50291	0.751454	−	0.659786i	$-0.229353\pi$
$47$	10.3034	1.50291	0.751454	+	0.659786i	$0.229353\pi$
$48$	−9.57373	−1.38185
$49$	16.7411	2.39159
$50$	−29.2778	−4.14051
$51$	−6.80699	−0.953170
$52$	−4.56811	−0.633483
$53$	−13.2390	−1.81852	−0.909260	−	0.416228i	$-0.863352\pi$
$53$	−13.2390	−1.81852	−0.909260	+	0.416228i	$0.863352\pi$
$54$	−14.1750	−1.92897
$55$	−16.1724	−2.18068
$56$	−32.0690	−4.28540
$57$	−2.10839	−0.279263
$58$	−10.5449	−1.38462
$59$	5.59139	0.727937	0.363969	−	0.931411i	$-0.381422\pi$
$59$	5.59139	0.727937	0.363969	+	0.931411i	$0.381422\pi$
$60$	−22.9244	−2.95952
$61$	−2.10823	−0.269932	−0.134966	−	0.990850i	$-0.543092\pi$
$61$	−2.10823	−0.269932	−0.134966	+	0.990850i	$0.543092\pi$
$62$	3.06469	0.389216
$63$	−7.14622	−0.900339
$64$	1.58276	0.197846
$65$	−4.05265	−0.502670
$66$	−12.6641	−1.55885
$67$	−6.21026	−0.758704	−0.379352	−	0.925252i	$-0.623853\pi$
$67$	−6.21026	−0.758704	−0.379352	+	0.925252i	$0.623853\pi$
$68$	25.1114	3.04521
$69$	11.5228	1.38718
$70$	−50.6070	−6.04869
$71$	6.07892	0.721435	0.360717	−	0.932675i	$-0.382532\pi$
$71$	6.07892	0.721435	0.360717	+	0.932675i	$0.382532\pi$
$72$	9.65296	1.13761
$73$	11.9093	1.39388	0.696939	−	0.717130i	$-0.254545\pi$
$73$	11.9093	1.39388	0.696939	+	0.717130i	$0.254545\pi$
$74$	−26.8734	−3.12397
$75$	−14.1462	−1.63346
$76$	7.77798	0.892196
$77$	−19.4440	−2.21585
$78$	−3.17352	−0.359330
$79$	−1.84250	−0.207297	−0.103648	−	0.994614i	$-0.533052\pi$
$79$	−1.84250	−0.207297	−0.103648	+	0.994614i	$0.533052\pi$
$80$	31.3328	3.50312
$81$	−2.44900	−0.272111
$82$	22.2958	2.46216
$83$	9.60225	1.05398	0.526992	−	0.849870i	$-0.323320\pi$
$83$	9.60225	1.05398	0.526992	+	0.849870i	$0.323320\pi$
$84$	−27.5618	−3.00724
$85$	22.2779	2.41638
$86$	−4.02660	−0.434200
$87$	−5.09500	−0.546241
$88$	26.2645	2.79981
$89$	−15.8571	−1.68085	−0.840427	−	0.541925i	$-0.817695\pi$
$89$	−15.8571	−1.68085	−0.840427	+	0.541925i	$0.817695\pi$
$90$	15.2330	1.60570
$91$	−4.87248	−0.510775
$92$	−42.5083	−4.43180
$93$	1.48077	0.153549
$94$	−26.4059	−2.72356
$95$	6.90032	0.707958
$96$	8.23595	0.840579
$97$	−17.9933	−1.82694	−0.913472	−	0.406901i	$-0.866609\pi$
$97$	−17.9933	−1.82694	−0.913472	+	0.406901i	$0.866609\pi$
$98$	−42.9047	−4.33403
$99$	5.85276	0.588225
$100$	52.1861	5.21861
$101$	2.08172	0.207138	0.103569	−	0.994622i	$-0.466974\pi$
$101$	2.08172	0.207138	0.103569	+	0.994622i	$0.466974\pi$
$102$	17.4452	1.72733
$103$	14.5122	1.42992	0.714962	−	0.699163i	$-0.246444\pi$
$103$	14.5122	1.42992	0.714962	+	0.699163i	$0.246444\pi$
$104$	6.58165	0.645384
$105$	−24.4518	−2.38625
$106$	33.9294	3.29552
$107$	5.16202	0.499031	0.249516	−	0.968371i	$-0.419729\pi$
$107$	5.16202	0.499031	0.249516	+	0.968371i	$0.419729\pi$
$108$	25.2662	2.43124
$109$	−7.50427	−0.718779	−0.359389	−	0.933188i	$-0.617015\pi$
$109$	−7.50427	−0.718779	−0.359389	+	0.933188i	$0.617015\pi$
$110$	41.4471	3.95183
$111$	−12.9844	−1.23243
$112$	37.6713	3.55961
$113$	−2.89759	−0.272582	−0.136291	−	0.990669i	$-0.543518\pi$
$113$	−2.89759	−0.272582	−0.136291	+	0.990669i	$0.543518\pi$
$114$	5.40345	0.506080
$115$	−37.7117	−3.51664
$116$	18.7958	1.74514
$117$	1.46665	0.135592
$118$	−14.3298	−1.31917
$119$	26.7846	2.45534
$120$	33.0290	3.01512
$121$	4.92464	0.447694
$122$	5.40305	0.489169
$123$	10.7727	0.971339
$124$	−5.46265	−0.490560
$125$	26.0342	2.32857
$126$	18.3146	1.63159
$127$	16.8726	1.49720	0.748602	−	0.663020i	$-0.230725\pi$
$127$	16.8726	1.49720	0.748602	+	0.663020i	$0.230725\pi$
$128$	9.24583	0.817223
$129$	−1.94554	−0.171295
$130$	10.3863	0.910937
$131$	−2.95662	−0.258321	−0.129160	−	0.991624i	$-0.541228\pi$
$131$	−2.95662	−0.258321	−0.129160	+	0.991624i	$0.541228\pi$
$132$	22.5732	1.96474
$133$	8.29622	0.719374
$134$	15.9159	1.37492
$135$	22.4152	1.92919
$136$	−36.1801	−3.10241
$137$	−1.79015	−0.152943	−0.0764713	−	0.997072i	$-0.524365\pi$
$137$	−1.79015	−0.152943	−0.0764713	+	0.997072i	$0.524365\pi$
$138$	−29.5310	−2.51385
$139$	13.7280	1.16440	0.582198	−	0.813047i	$-0.302193\pi$
$139$	13.7280	1.16440	0.582198	+	0.813047i	$0.302193\pi$
$140$	90.2042	7.62365
$141$	−12.7586	−1.07447
$142$	−15.5792	−1.30738
$143$	3.99057	0.333708
$144$	−11.3393	−0.944942
$145$	16.6749	1.38477
$146$	−30.5215	−2.52598
$147$	−20.7303	−1.70980
$148$	47.9004	3.93739
$149$	−6.15405	−0.504160	−0.252080	−	0.967706i	$-0.581115\pi$
$149$	−6.15405	−0.504160	−0.252080	+	0.967706i	$0.581115\pi$
$150$	36.2543	2.96015
$151$	−5.08205	−0.413571	−0.206786	−	0.978386i	$-0.566300\pi$
$151$	−5.08205	−0.413571	−0.206786	+	0.978386i	$0.566300\pi$
$152$	−11.2064	−0.908956
$153$	−8.06233	−0.651801
$154$	49.8317	4.01555
$155$	−4.84625	−0.389260
$156$	5.65663	0.452893
$157$	5.28603	0.421871	0.210935	−	0.977500i	$-0.432349\pi$
$157$	5.28603	0.421871	0.210935	+	0.977500i	$0.432349\pi$
$158$	4.72201	0.375663
$159$	16.3937	1.30011
$160$	−26.9546	−2.13095
$161$	−45.3406	−3.57334
$162$	6.27637	0.493118
$163$	15.3659	1.20355	0.601773	−	0.798667i	$-0.294461\pi$
$163$	15.3659	1.20355	0.601773	+	0.798667i	$0.294461\pi$
$164$	−39.7411	−3.10325
$165$	20.0260	1.55903
$166$	−24.6090	−1.91003
$167$	10.0806	0.780064	0.390032	−	0.920801i	$-0.372464\pi$
$167$	10.0806	0.780064	0.390032	+	0.920801i	$0.372464\pi$
$168$	39.7106	3.06374
$169$	1.00000	0.0769231
$170$	−57.0945	−4.37895
$171$	−2.49722	−0.190967
$172$	7.17721	0.547257
$173$	−8.64466	−0.657241	−0.328621	−	0.944462i	$-0.606584\pi$
$173$	−8.64466	−0.657241	−0.328621	+	0.944462i	$0.606584\pi$
$174$	13.0576	0.989897
$175$	55.6633	4.20775
$176$	−30.8528	−2.32562
$177$	−6.92374	−0.520420
$178$	40.6392	3.04604
$179$	22.5170	1.68300	0.841498	−	0.540260i	$-0.181674\pi$
$179$	22.5170	1.68300	0.841498	+	0.540260i	$0.181674\pi$
$180$	−27.1520	−2.02379
$181$	−12.8110	−0.952233	−0.476117	−	0.879382i	$-0.657956\pi$
$181$	−12.8110	−0.952233	−0.476117	+	0.879382i	$0.657956\pi$
$182$	12.4874	0.925625
$183$	2.61059	0.192981
$184$	61.2451	4.51505
$185$	42.4954	3.12432
$186$	−3.79496	−0.278260
$187$	−21.9366	−1.60416
$188$	47.0672	3.43273
$189$	26.9496	1.96030
$190$	−17.6844	−1.28296
$191$	5.19661	0.376013	0.188007	−	0.982168i	$-0.439797\pi$
$191$	5.19661	0.376013	0.188007	+	0.982168i	$0.439797\pi$
$192$	−1.95991	−0.141445
$193$	−1.89499	−0.136404	−0.0682022	−	0.997672i	$-0.521726\pi$
$193$	−1.89499	−0.136404	−0.0682022	+	0.997672i	$0.521726\pi$
$194$	46.1139	3.31078
$195$	5.01834	0.359371
$196$	76.4753	5.46252
$197$	0.817311	0.0582310	0.0291155	−	0.999576i	$-0.490731\pi$
$197$	0.817311	0.0582310	0.0291155	+	0.999576i	$0.490731\pi$
$198$	−14.9997	−1.06598
$199$	6.49294	0.460272	0.230136	−	0.973158i	$-0.426083\pi$
$199$	6.49294	0.460272	0.230136	+	0.973158i	$0.426083\pi$
$200$	−75.1887	−5.31665
$201$	7.69008	0.542416
$202$	−5.33509	−0.375376
$203$	20.0481	1.40710
$204$	−31.0951	−2.17709
$205$	−35.2567	−2.46244
$206$	−37.1922	−2.59131
$207$	13.6478	0.948588
$208$	−7.73144	−0.536079
$209$	−6.79461	−0.469993
$210$	62.6659	4.32436
$211$	23.6744	1.62981	0.814905	−	0.579595i	$-0.196789\pi$
$211$	23.6744	1.62981	0.814905	+	0.579595i	$0.196789\pi$
$212$	−60.4774	−4.15361
$213$	−7.52744	−0.515771
$214$	−13.2294	−0.904342
$215$	6.36734	0.434249
$216$	−36.4030	−2.47691
$217$	−5.82662	−0.395537
$218$	19.2322	1.30257
$219$	−14.7471	−0.996518
$220$	−73.8773	−4.98081
$221$	−5.49711	−0.369776
$222$	33.2770	2.23340
$223$	−17.1908	−1.15118	−0.575592	−	0.817737i	$-0.695228\pi$
$223$	−17.1908	−1.15118	−0.575592	+	0.817737i	$0.695228\pi$
$224$	−32.4074	−2.16531
$225$	−16.7550	−1.11700
$226$	7.42604	0.493973
$227$	−15.7505	−1.04540	−0.522700	−	0.852517i	$-0.675075\pi$
$227$	−15.7505	−1.04540	−0.522700	+	0.852517i	$0.675075\pi$
$228$	−9.63136	−0.637853
$229$	−24.6928	−1.63175	−0.815873	−	0.578232i	$-0.803743\pi$
$229$	−24.6928	−1.63175	−0.815873	+	0.578232i	$0.803743\pi$
$230$	96.6488	6.37284
$231$	24.0772	1.58416
$232$	−27.0806	−1.77793
$233$	5.06884	0.332071	0.166036	−	0.986120i	$-0.446903\pi$
$233$	5.06884	0.332071	0.166036	+	0.986120i	$0.446903\pi$
$234$	−3.75878	−0.245719
$235$	41.7562	2.72387
$236$	25.5421	1.66265
$237$	2.28154	0.148202
$238$	−68.6444	−4.44956
$239$	−2.21186	−0.143073	−0.0715367	−	0.997438i	$-0.522790\pi$
$239$	−2.21186	−0.143073	−0.0715367	+	0.997438i	$0.522790\pi$
$240$	−38.7990	−2.50447
$241$	23.6190	1.52143	0.760717	−	0.649084i	$-0.224848\pi$
$241$	23.6190	1.52143	0.760717	+	0.649084i	$0.224848\pi$
$242$	−12.6210	−0.811310
$243$	−13.5604	−0.869900
$244$	−9.63065	−0.616539
$245$	67.8459	4.33452
$246$	−27.6086	−1.76026
$247$	−1.70267	−0.108338
$248$	7.87048	0.499776
$249$	−11.8903	−0.753519
$250$	−66.7214	−4.21983
$251$	−6.44338	−0.406703	−0.203351	−	0.979106i	$-0.565183\pi$
$251$	−6.44338	−0.406703	−0.203351	+	0.979106i	$0.565183\pi$
$252$	−32.6448	−2.05643
$253$	37.1340	2.33459
$254$	−43.2417	−2.71323
$255$	−27.5864	−1.72753
$256$	−26.8610	−1.67881
$257$	11.2092	0.699210	0.349605	−	0.936897i	$-0.386316\pi$
$257$	11.2092	0.699210	0.349605	+	0.936897i	$0.386316\pi$
$258$	4.98609	0.310420
$259$	51.0920	3.17470
$260$	−18.5130	−1.14813
$261$	−6.03461	−0.373533
$262$	7.57732	0.468128
$263$	14.8427	0.915241	0.457620	−	0.889148i	$-0.348702\pi$
$263$	14.8427	0.915241	0.457620	+	0.889148i	$0.348702\pi$
$264$	−32.5230	−2.00165
$265$	−53.6532	−3.29589
$266$	−21.2618	−1.30365
$267$	19.6357	1.20168
$268$	−28.3692	−1.73292
$269$	13.3097	0.811506	0.405753	−	0.913983i	$-0.367009\pi$
$269$	13.3097	0.811506	0.405753	+	0.913983i	$0.367009\pi$
$270$	−57.4464	−3.49607
$271$	4.02563	0.244540	0.122270	−	0.992497i	$-0.460983\pi$
$271$	4.02563	0.244540	0.122270	+	0.992497i	$0.460983\pi$
$272$	42.5006	2.57698
$273$	6.03353	0.365166
$274$	4.58785	0.277162
$275$	−45.5883	−2.74908
$276$	52.6374	3.16840
$277$	−7.07327	−0.424992	−0.212496	−	0.977162i	$-0.568159\pi$
$277$	−7.07327	−0.424992	−0.212496	+	0.977162i	$0.568159\pi$
$278$	−35.1827	−2.11012
$279$	1.75385	0.105000
$280$	−129.964	−7.76686
$281$	−18.7886	−1.12083	−0.560417	−	0.828211i	$-0.689359\pi$
$281$	−18.7886	−1.12083	−0.560417	+	0.828211i	$0.689359\pi$
$282$	32.6981	1.94714
$283$	−7.75523	−0.461000	−0.230500	−	0.973072i	$-0.574036\pi$
$283$	−7.75523	−0.461000	−0.230500	+	0.973072i	$0.574036\pi$
$284$	27.7692	1.64780
$285$	−8.54457	−0.506137
$286$	−10.2272	−0.604745
$287$	−42.3890	−2.50214
$288$	9.75482	0.574808
$289$	13.2182	0.777543
$290$	−42.7349	−2.50948
$291$	22.2809	1.30613
$292$	54.4030	3.18370
$293$	−9.97626	−0.582819	−0.291410	−	0.956598i	$-0.594124\pi$
$293$	−9.97626	−0.582819	−0.291410	+	0.956598i	$0.594124\pi$
$294$	53.1282	3.09850
$295$	22.6600	1.31931
$296$	−69.0140	−4.01136
$297$	−22.0718	−1.28073
$298$	15.7718	0.913637
$299$	9.30544	0.538147
$300$	−64.6213	−3.73092
$301$	7.65542	0.441251
$302$	13.0244	0.749473
$303$	−2.57776	−0.148088
$304$	13.1641	0.755011
$305$	−8.54394	−0.489224
$306$	20.6624	1.18119
$307$	1.34235	0.0766122	0.0383061	−	0.999266i	$-0.487804\pi$
$307$	1.34235	0.0766122	0.0383061	+	0.999266i	$0.487804\pi$
$308$	−88.8223	−5.06112
$309$	−17.9702	−1.02229
$310$	12.4201	0.705416
$311$	7.50700	0.425683	0.212842	−	0.977087i	$-0.431728\pi$
$311$	7.50700	0.425683	0.212842	+	0.977087i	$0.431728\pi$
$312$	−8.14996	−0.461401
$313$	−5.11958	−0.289376	−0.144688	−	0.989477i	$-0.546218\pi$
$313$	−5.11958	−0.289376	−0.144688	+	0.989477i	$0.546218\pi$
$314$	−13.5472	−0.764513
$315$	−28.9612	−1.63178
$316$	−8.41673	−0.473478
$317$	−10.6082	−0.595819	−0.297909	−	0.954594i	$-0.596289\pi$
$317$	−10.6082	−0.595819	−0.297909	+	0.954594i	$0.596289\pi$
$318$	−42.0143	−2.35605
$319$	−16.4194	−0.919311
$320$	6.41440	0.358576
$321$	−6.39205	−0.356770
$322$	116.200	6.47560
$323$	9.35976	0.520791
$324$	−11.1873	−0.621517
$325$	−11.4240	−0.633689
$326$	−39.3801	−2.18106
$327$	9.29243	0.513873
$328$	57.2581	3.16155
$329$	50.2032	2.76779
$330$	−51.3234	−2.82526
$331$	35.0442	1.92620	0.963102	−	0.269138i	$-0.0867387\pi$
$331$	35.0442	1.92620	0.963102	+	0.269138i	$0.0867387\pi$
$332$	43.8642	2.40736
$333$	−15.3790	−0.842765
$334$	−25.8350	−1.41363
$335$	−25.1680	−1.37508
$336$	−46.6479	−2.54485
$337$	15.6176	0.850747	0.425374	−	0.905018i	$-0.360143\pi$
$337$	15.6176	0.850747	0.425374	+	0.905018i	$0.360143\pi$
$338$	−2.56283	−0.139400
$339$	3.58804	0.194876
$340$	101.768	5.51914
$341$	4.77201	0.258419
$342$	6.39995	0.346069
$343$	47.4634	2.56278
$344$	−10.3408	−0.557538
$345$	46.6979	2.51413
$346$	22.1548	1.19105
$347$	11.5249	0.618687	0.309344	−	0.950950i	$-0.399891\pi$
$347$	11.5249	0.618687	0.309344	+	0.950950i	$0.399891\pi$
$348$	−23.2745	−1.24765
$349$	23.9542	1.28224	0.641120	−	0.767440i	$-0.278470\pi$
$349$	23.9542	1.28224	0.641120	+	0.767440i	$0.278470\pi$
$350$	−142.656	−7.62527
$351$	−5.53099	−0.295222
$352$	26.5416	1.41467
$353$	12.1526	0.646815	0.323408	−	0.946260i	$-0.395172\pi$
$353$	12.1526	0.646815	0.323408	+	0.946260i	$0.395172\pi$
$354$	17.7444	0.943104
$355$	24.6357	1.30753
$356$	−72.4372	−3.83916
$357$	−33.1670	−1.75538
$358$	−57.7072	−3.04992
$359$	15.1453	0.799340	0.399670	−	0.916659i	$-0.369125\pi$
$359$	15.1453	0.799340	0.399670	+	0.916659i	$0.369125\pi$
$360$	39.1201	2.06181
$361$	−16.1009	−0.847417
$362$	32.8324	1.72563
$363$	−6.09811	−0.320068
$364$	−22.2581	−1.16664
$365$	48.2643	2.52627
$366$	−6.69052	−0.349719
$367$	−28.8675	−1.50687	−0.753437	−	0.657520i	$-0.771605\pi$
$367$	−28.8675	−1.50687	−0.753437	+	0.657520i	$0.771605\pi$
$368$	−71.9444	−3.75036
$369$	12.7593	0.664225
$370$	−108.909	−5.66189
$371$	−64.5070	−3.34904
$372$	6.76432	0.350714
$373$	14.7535	0.763905	0.381952	−	0.924182i	$-0.375252\pi$
$373$	14.7535	0.763905	0.381952	+	0.924182i	$0.375252\pi$
$374$	56.2199	2.90706
$375$	−32.2378	−1.66475
$376$	−67.8135	−3.49721
$377$	−4.11456	−0.211911
$378$	−69.0675	−3.55245
$379$	−38.1232	−1.95826	−0.979130	−	0.203237i	$-0.934854\pi$
$379$	−38.1232	−1.95826	−0.979130	+	0.203237i	$0.934854\pi$
$380$	31.5215	1.61702
$381$	−20.8931	−1.07039
$382$	−13.3180	−0.681410
$383$	10.7933	0.551513	0.275757	−	0.961227i	$-0.411072\pi$
$383$	10.7933	0.551513	0.275757	+	0.961227i	$0.411072\pi$
$384$	−11.4490	−0.584253
$385$	−78.7997	−4.01601
$386$	4.85655	0.247192
$387$	−2.30433	−0.117136
$388$	−82.1955	−4.17285
$389$	−15.1768	−0.769496	−0.384748	−	0.923022i	$-0.625712\pi$
$389$	−15.1768	−0.769496	−0.384748	+	0.923022i	$0.625712\pi$
$390$	−12.8612	−0.651251
$391$	−51.1530	−2.58692
$392$	−110.184	−5.56514
$393$	3.66114	0.184680
$394$	−2.09463	−0.105526
$395$	−7.46699	−0.375705
$396$	26.7361	1.34354
$397$	13.0531	0.655119	0.327559	−	0.944831i	$-0.393774\pi$
$397$	13.0531	0.655119	0.327559	+	0.944831i	$0.393774\pi$
$398$	−16.6403	−0.834104
$399$	−10.2731	−0.514298
$400$	88.3240	4.41620
$401$	1.55631	0.0777185	0.0388592	−	0.999245i	$-0.487628\pi$
$401$	1.55631	0.0777185	0.0388592	+	0.999245i	$0.487628\pi$
$402$	−19.7084	−0.982965
$403$	1.19582	0.0595681
$404$	9.50951	0.473116
$405$	−9.92494	−0.493174
$406$	−51.3800	−2.54995
$407$	−41.8444	−2.07415
$408$	44.8013	2.21799
$409$	15.7035	0.776489	0.388244	−	0.921556i	$-0.373082\pi$
$409$	15.7035	0.776489	0.388244	+	0.921556i	$0.373082\pi$
$410$	90.3571	4.46242
$411$	2.21671	0.109342
$412$	66.2932	3.26603
$413$	27.2440	1.34059
$414$	−34.9771	−1.71903
$415$	38.9146	1.91024
$416$	6.65109	0.326097
$417$	−16.9992	−0.832456
$418$	17.4135	0.851720
$419$	0.0486394	0.00237619	0.00118809	−	0.999999i	$-0.499622\pi$
$419$	0.0486394	0.00237619	0.00118809	+	0.999999i	$0.499622\pi$
$420$	−111.699	−5.45033
$421$	27.1658	1.32398	0.661989	−	0.749513i	$-0.269713\pi$
$421$	27.1658	1.32398	0.661989	+	0.749513i	$0.269713\pi$
$422$	−60.6734	−2.95354
$423$	−15.1115	−0.734746
$424$	87.1347	4.23163
$425$	62.7990	3.04620
$426$	19.2916	0.934679
$427$	−10.2723	−0.497113
$428$	23.5807	1.13982
$429$	−4.94146	−0.238576
$430$	−16.3184	−0.786945
$431$	−28.6233	−1.37874	−0.689369	−	0.724410i	$-0.742112\pi$
$431$	−28.6233	−1.37874	−0.689369	+	0.724410i	$0.742112\pi$
$432$	42.7625	2.05741
$433$	−4.08283	−0.196208	−0.0981041	−	0.995176i	$-0.531278\pi$
$433$	−4.08283	−0.196208	−0.0981041	+	0.995176i	$0.531278\pi$
$434$	14.9327	0.716791
$435$	−20.6483	−0.990009
$436$	−34.2804	−1.64173
$437$	−15.8441	−0.757925
$438$	37.7944	1.80589
$439$	−25.3654	−1.21062	−0.605312	−	0.795988i	$-0.706952\pi$
$439$	−25.3654	−1.21062	−0.605312	+	0.795988i	$0.706952\pi$
$440$	106.441	5.07438
$441$	−24.5533	−1.16921
$442$	14.0882	0.670106
$443$	1.70092	0.0808131	0.0404066	−	0.999183i	$-0.487135\pi$
$443$	1.70092	0.0808131	0.0404066	+	0.999183i	$0.487135\pi$
$444$	−59.3144	−2.81494
$445$	−64.2635	−3.04638
$446$	44.0572	2.08617
$447$	7.62048	0.360436
$448$	7.71200	0.364358
$449$	29.4736	1.39095	0.695474	−	0.718552i	$-0.255195\pi$
$449$	29.4736	1.39095	0.695474	+	0.718552i	$0.255195\pi$
$450$	42.9402	2.02422
$451$	34.7166	1.63474
$452$	−13.2365	−0.622593
$453$	6.29303	0.295672
$454$	40.3660	1.89447
$455$	−19.7465	−0.925730
$456$	13.8767	0.649835
$457$	−9.29246	−0.434683	−0.217341	−	0.976096i	$-0.569739\pi$
$457$	−9.29246	−0.434683	−0.217341	+	0.976096i	$0.569739\pi$
$458$	63.2835	2.95704
$459$	30.4045	1.41916
$460$	−172.271	−8.03220
$461$	−6.23044	−0.290180	−0.145090	−	0.989418i	$-0.546347\pi$
$461$	−6.23044	−0.290180	−0.145090	+	0.989418i	$0.546347\pi$
$462$	−61.7059	−2.87082
$463$	−4.86148	−0.225932	−0.112966	−	0.993599i	$-0.536035\pi$
$463$	−4.86148	−0.225932	−0.112966	+	0.993599i	$0.536035\pi$
$464$	31.8115	1.47681
$465$	6.00104	0.278292
$466$	−12.9906	−0.601778
$467$	4.30998	0.199442	0.0997210	−	0.995015i	$-0.468205\pi$
$467$	4.30998	0.199442	0.0997210	+	0.995015i	$0.468205\pi$
$468$	6.69982	0.309699
$469$	−30.2594	−1.39725
$470$	−107.014	−4.93619
$471$	−6.54561	−0.301606
$472$	−36.8006	−1.69388
$473$	−6.26980	−0.288286
$474$	−5.84719	−0.268571
$475$	19.4513	0.892486
$476$	122.355	5.60814
$477$	19.4170	0.889044
$478$	5.66863	0.259277
$479$	39.6327	1.81086	0.905432	−	0.424491i	$-0.139547\pi$
$479$	39.6327	1.81086	0.905432	+	0.424491i	$0.139547\pi$
$480$	33.3775	1.52347
$481$	−10.4858	−0.478112
$482$	−60.5316	−2.75714
$483$	56.1446	2.55467
$484$	22.4963	1.02256
$485$	−72.9207	−3.31116
$486$	34.7531	1.57643
$487$	−14.3596	−0.650697	−0.325348	−	0.945594i	$-0.605482\pi$
$487$	−14.3596	−0.650697	−0.325348	+	0.945594i	$0.605482\pi$
$488$	13.8756	0.628121
$489$	−19.0273	−0.860445
$490$	−173.878	−7.85500
$491$	22.4325	1.01236	0.506182	−	0.862427i	$-0.331056\pi$
$491$	22.4325	1.01236	0.506182	+	0.862427i	$0.331056\pi$
$492$	49.2108	2.21859
$493$	22.6182	1.01867
$494$	4.36365	0.196330
$495$	23.7192	1.06610
$496$	−9.24542	−0.415132
$497$	29.6194	1.32861
$498$	30.4729	1.36553
$499$	32.0426	1.43443	0.717213	−	0.696854i	$-0.245418\pi$
$499$	32.0426	1.43443	0.717213	+	0.696854i	$0.245418\pi$
$500$	118.927	5.31859
$501$	−12.4827	−0.557687
$502$	16.5133	0.737025
$503$	−26.8454	−1.19698	−0.598489	−	0.801131i	$-0.704232\pi$
$503$	−26.8454	−1.19698	−0.598489	+	0.801131i	$0.704232\pi$
$504$	47.0339	2.09506
$505$	8.43647	0.375418
$506$	−95.1682	−4.23074
$507$	−1.23829	−0.0549942
$508$	77.0761	3.41970
$509$	−8.77411	−0.388906	−0.194453	−	0.980912i	$-0.562293\pi$
$509$	−8.77411	−0.388906	−0.194453	+	0.980912i	$0.562293\pi$
$510$	70.6993	3.13062
$511$	58.0279	2.56700
$512$	50.3487	2.22512
$513$	9.41743	0.415790
$514$	−28.7273	−1.26711
$515$	58.8127	2.59160
$516$	−8.88744	−0.391248
$517$	−41.1165	−1.80830
$518$	−130.940	−5.75318
$519$	10.7046	0.469878
$520$	26.6731	1.16969
$521$	9.56273	0.418951	0.209475	−	0.977814i	$-0.432824\pi$
$521$	9.56273	0.418951	0.209475	+	0.977814i	$0.432824\pi$
$522$	15.4657	0.676915
$523$	4.51712	0.197520	0.0987599	−	0.995111i	$-0.468512\pi$
$523$	4.51712	0.197520	0.0987599	+	0.995111i	$0.468512\pi$
$524$	−13.5062	−0.590020
$525$	−68.9270	−3.00822
$526$	−38.0394	−1.65860
$527$	−6.57356	−0.286349
$528$	38.2046	1.66264
$529$	63.5912	2.76483
$530$	137.504	5.97280
$531$	−8.20060	−0.355876
$532$	37.8981	1.64309
$533$	8.69966	0.376824
$534$	−50.3229	−2.17769
$535$	20.9199	0.904445
$536$	40.8738	1.76548
$537$	−27.8824	−1.20322
$538$	−34.1105	−1.47061
$539$	−66.8065	−2.87756
$540$	102.395	4.40638
$541$	12.6459	0.543688	0.271844	−	0.962341i	$-0.412366\pi$
$541$	12.6459	0.543688	0.271844	+	0.962341i	$0.412366\pi$
$542$	−10.3170	−0.443154
$543$	15.8637	0.680775
$544$	−36.5618	−1.56757
$545$	−30.4122	−1.30272
$546$	−15.4629	−0.661752
$547$	14.7939	0.632542	0.316271	−	0.948669i	$-0.397569\pi$
$547$	14.7939	0.632542	0.316271	+	0.948669i	$0.397569\pi$
$548$	−8.17759	−0.349329
$549$	3.09204	0.131965
$550$	116.835	4.98186
$551$	7.00573	0.298454
$552$	−75.8390	−3.22792
$553$	−8.97753	−0.381763
$554$	18.1276	0.770169
$555$	−52.6214	−2.23366
$556$	62.7112	2.65955
$557$	−40.5438	−1.71790	−0.858948	−	0.512063i	$-0.828882\pi$
$557$	−40.5438	−1.71790	−0.858948	+	0.512063i	$0.828882\pi$
$558$	−4.49482	−0.190281
$559$	−1.57115	−0.0664527
$560$	152.669	6.45143
$561$	27.1638	1.14686
$562$	48.1520	2.03117
$563$	−10.3730	−0.437171	−0.218585	−	0.975818i	$-0.570144\pi$
$563$	−10.3730	−0.437171	−0.218585	+	0.975818i	$0.570144\pi$
$564$	−58.2826	−2.45414
$565$	−11.7429	−0.494028
$566$	19.8754	0.835423
$567$	−11.9327	−0.501126
$568$	−40.0093	−1.67875
$569$	11.6891	0.490033	0.245017	−	0.969519i	$-0.421207\pi$
$569$	11.6891	0.490033	0.245017	+	0.969519i	$0.421207\pi$
$570$	21.8983	0.917219
$571$	25.8972	1.08376	0.541882	−	0.840454i	$-0.317712\pi$
$571$	25.8972	1.08376	0.541882	+	0.840454i	$0.317712\pi$
$572$	18.2294	0.762208
$573$	−6.43488	−0.268821
$574$	108.636	4.53437
$575$	−106.305	−4.43324
$576$	−2.32136	−0.0967233
$577$	4.12170	0.171589	0.0857944	−	0.996313i	$-0.472657\pi$
$577$	4.12170	0.171589	0.0857944	+	0.996313i	$0.472657\pi$
$578$	−33.8761	−1.40906
$579$	2.34654	0.0975189
$580$	76.1728	3.16290
$581$	46.7868	1.94104
$582$	−57.1021	−2.36696
$583$	52.8313	2.18805
$584$	−78.3828	−3.24350
$585$	5.94382	0.245747
$586$	25.5675	1.05618
$587$	−33.2141	−1.37089	−0.685446	−	0.728123i	$-0.740393\pi$
$587$	−33.2141	−1.37089	−0.685446	+	0.728123i	$0.740393\pi$
$588$	−94.6983	−3.90529
$589$	−2.03609	−0.0838955
$590$	−58.0737	−2.39086
$591$	−1.01206	−0.0416308
$592$	81.0705	3.33198
$593$	24.7751	1.01739	0.508696	−	0.860946i	$-0.330128\pi$
$593$	24.7751	1.01739	0.508696	+	0.860946i	$0.330128\pi$
$594$	56.5663	2.32094
$595$	108.549	4.45006
$596$	−28.1124	−1.15153
$597$	−8.04012	−0.329060
$598$	−23.8483	−0.975229
$599$	34.8681	1.42467	0.712337	−	0.701838i	$-0.247637\pi$
$599$	34.8681	1.42467	0.712337	+	0.701838i	$0.247637\pi$
$600$	93.1052	3.80100
$601$	29.9899	1.22332	0.611658	−	0.791122i	$-0.290503\pi$
$601$	29.9899	1.22332	0.611658	+	0.791122i	$0.290503\pi$
$602$	−19.6196	−0.799634
$603$	9.10827	0.370918
$604$	−23.2154	−0.944621
$605$	19.9579	0.811402
$606$	6.60637	0.268365
$607$	−0.933002	−0.0378694	−0.0189347	−	0.999821i	$-0.506027\pi$
$607$	−0.933002	−0.0378694	−0.0189347	+	0.999821i	$0.506027\pi$
$608$	−11.3246	−0.459273
$609$	−24.8253	−1.00597
$610$	21.8967	0.886571
$611$	−10.3034	−0.416832
$612$	−36.8296	−1.48875
$613$	−38.3747	−1.54994	−0.774969	−	0.631999i	$-0.782234\pi$
$613$	−38.3747	−1.54994	−0.774969	+	0.631999i	$0.782234\pi$
$614$	−3.44023	−0.138836
$615$	43.6579	1.76046
$616$	127.973	5.15620
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	46.0546	1.85259
$619$	23.7983	0.956534	0.478267	−	0.878214i	$-0.341265\pi$
$619$	23.7983	0.956534	0.478267	+	0.878214i	$0.341265\pi$
$620$	−22.1382	−0.889093
$621$	−51.4683	−2.06535
$622$	−19.2392	−0.771421
$623$	−77.2637	−3.09550
$624$	9.57373	0.383256
$625$	48.3878	1.93551
$626$	13.1206	0.524406
$627$	8.41367	0.336010
$628$	24.1472	0.963577
$629$	57.6417	2.29833
$630$	74.2226	2.95710
$631$	−22.4656	−0.894339	−0.447170	−	0.894449i	$-0.647568\pi$
$631$	−22.4656	−0.894339	−0.447170	+	0.894449i	$0.647568\pi$
$632$	12.1267	0.482372
$633$	−29.3156	−1.16519
$634$	27.1872	1.07974
$635$	68.3789	2.71354
$636$	74.8883	2.96951
$637$	−16.7411	−0.663307
$638$	42.0803	1.66597
$639$	−8.91563	−0.352697
$640$	37.4701	1.48114
$641$	26.2454	1.03663	0.518315	−	0.855190i	$-0.326560\pi$
$641$	26.2454	1.03663	0.518315	+	0.855190i	$0.326560\pi$
$642$	16.3818	0.646537
$643$	45.3732	1.78934	0.894672	−	0.446724i	$-0.147409\pi$
$643$	45.3732	1.78934	0.894672	+	0.446724i	$0.147409\pi$
$644$	−207.121	−8.16171
$645$	−7.88459	−0.310455
$646$	−23.9875	−0.943775
$647$	17.6110	0.692360	0.346180	−	0.938168i	$-0.387479\pi$
$647$	17.6110	0.692360	0.346180	+	0.938168i	$0.387479\pi$
$648$	16.1184	0.633192
$649$	−22.3128	−0.875855
$650$	29.2778	1.14837
$651$	7.21502	0.282779
$652$	70.1930	2.74897
$653$	−19.5522	−0.765135	−0.382568	−	0.923928i	$-0.624960\pi$
$653$	−19.5522	−0.765135	−0.382568	+	0.923928i	$0.624960\pi$
$654$	−23.8150	−0.931238
$655$	−11.9822	−0.468181
$656$	−67.2609	−2.62610
$657$	−17.4668	−0.681443
$658$	−128.663	−5.01579
$659$	−25.1736	−0.980624	−0.490312	−	0.871547i	$-0.663117\pi$
$659$	−25.1736	−0.980624	−0.490312	+	0.871547i	$0.663117\pi$
$660$	91.4812	3.56090
$661$	23.0217	0.895441	0.447720	−	0.894174i	$-0.352236\pi$
$661$	23.0217	0.895441	0.447720	+	0.894174i	$0.352236\pi$
$662$	−89.8124	−3.49066
$663$	6.80699	0.264362
$664$	−63.1987	−2.45258
$665$	33.6217	1.30379
$666$	39.4138	1.52726
$667$	−38.2878	−1.48251
$668$	46.0495	1.78171
$669$	21.2872	0.823009
$670$	64.5015	2.49191
$671$	8.41305	0.324782
$672$	40.1296	1.54803
$673$	3.79538	0.146301	0.0731507	−	0.997321i	$-0.476695\pi$
$673$	3.79538	0.146301	0.0731507	+	0.997321i	$0.476695\pi$
$674$	−40.0254	−1.54172
$675$	63.1860	2.43203
$676$	4.56811	0.175697
$677$	13.7667	0.529099	0.264549	−	0.964372i	$-0.414777\pi$
$677$	13.7667	0.529099	0.264549	+	0.964372i	$0.414777\pi$
$678$	−9.19556	−0.353153
$679$	−87.6721	−3.36455
$680$	−146.625	−5.62282
$681$	19.5037	0.747382
$682$	−12.2299	−0.468306
$683$	10.8975	0.416983	0.208491	−	0.978024i	$-0.433145\pi$
$683$	10.8975	0.416983	0.208491	+	0.978024i	$0.433145\pi$
$684$	−11.4076	−0.436179
$685$	−7.25484	−0.277193
$686$	−121.641	−4.64427
$687$	30.5767	1.16657
$688$	12.1473	0.463111
$689$	13.2390	0.504367
$690$	−119.679	−4.55610
$691$	−9.56697	−0.363945	−0.181972	−	0.983304i	$-0.558248\pi$
$691$	−9.56697	−0.363945	−0.181972	+	0.983304i	$0.558248\pi$
$692$	−39.4898	−1.50118
$693$	28.5175	1.08329
$694$	−29.5363	−1.12118
$695$	55.6349	2.11035
$696$	33.5335	1.27108
$697$	−47.8230	−1.81143
$698$	−61.3907	−2.32367
$699$	−6.27668	−0.237406
$700$	254.276	9.61073
$701$	−7.67750	−0.289975	−0.144988	−	0.989433i	$-0.546314\pi$
$701$	−7.67750	−0.289975	−0.144988	+	0.989433i	$0.546314\pi$
$702$	14.1750	0.535001
$703$	17.8539	0.673371
$704$	−6.31613	−0.238048
$705$	−51.7061	−1.94736
$706$	−31.1450	−1.17216
$707$	10.1431	0.381472
$708$	−31.6284	−1.18867
$709$	−39.1930	−1.47192	−0.735961	−	0.677024i	$-0.763269\pi$
$709$	−39.1930	−1.47192	−0.735961	+	0.677024i	$0.763269\pi$
$710$	−63.1373	−2.36950
$711$	2.70229	0.101344
$712$	104.366	3.91129
$713$	11.1276	0.416734
$714$	85.0014	3.18110
$715$	16.1724	0.604813
$716$	102.860	3.84406
$717$	2.73891	0.102287
$718$	−38.8149	−1.44856
$719$	−28.2333	−1.05292	−0.526462	−	0.850199i	$-0.676482\pi$
$719$	−28.2333	−1.05292	−0.526462	+	0.850199i	$0.676482\pi$
$720$	−45.9543	−1.71261
$721$	70.7102	2.63339
$722$	41.2640	1.53569
$723$	−29.2471	−1.08771
$724$	−58.5221	−2.17496
$725$	47.0047	1.74571
$726$	15.6284	0.580026
$727$	28.8804	1.07111	0.535557	−	0.844499i	$-0.320102\pi$
$727$	28.8804	1.07111	0.535557	+	0.844499i	$0.320102\pi$
$728$	32.0690	1.18856
$729$	24.1386	0.894024
$730$	−123.693	−4.57809
$731$	8.63681	0.319444
$732$	11.9255	0.440779
$733$	50.9456	1.88172	0.940860	−	0.338795i	$-0.110019\pi$
$733$	50.9456	1.88172	0.940860	+	0.338795i	$0.110019\pi$
$734$	73.9827	2.73075
$735$	−84.0126	−3.09885
$736$	61.8913	2.28135
$737$	24.7825	0.912874
$738$	−32.7001	−1.20371
$739$	6.06544	0.223121	0.111560	−	0.993758i	$-0.464415\pi$
$739$	6.06544	0.223121	0.111560	+	0.993758i	$0.464415\pi$
$740$	194.124	7.13613
$741$	2.10839	0.0774536
$742$	165.321	6.06911
$743$	−10.8732	−0.398898	−0.199449	−	0.979908i	$-0.563915\pi$
$743$	−10.8732	−0.398898	−0.199449	+	0.979908i	$0.563915\pi$
$744$	−9.74590	−0.357302
$745$	−24.9402	−0.913740
$746$	−37.8106	−1.38435
$747$	−14.0831	−0.515275
$748$	−100.209	−3.66400
$749$	25.1518	0.919029
$750$	82.6202	3.01686
$751$	−11.2545	−0.410683	−0.205342	−	0.978690i	$-0.565831\pi$
$751$	−11.2545	−0.410683	−0.205342	+	0.978690i	$0.565831\pi$
$752$	79.6602	2.90491
$753$	7.97875	0.290762
$754$	10.5449	0.384024
$755$	−20.5958	−0.749557
$756$	123.109	4.47743
$757$	−13.5384	−0.492061	−0.246030	−	0.969262i	$-0.579126\pi$
$757$	−13.5384	−0.492061	−0.246030	+	0.969262i	$0.579126\pi$
$758$	97.7035	3.54875
$759$	−45.9825	−1.66906
$760$	−45.4155	−1.64739
$761$	4.78768	0.173553	0.0867766	−	0.996228i	$-0.472343\pi$
$761$	4.78768	0.173553	0.0867766	+	0.996228i	$0.472343\pi$
$762$	53.5456	1.93975
$763$	−36.5644	−1.32372
$764$	23.7387	0.858836
$765$	−32.6738	−1.18132
$766$	−27.6615	−0.999451
$767$	−5.59139	−0.201893
$768$	33.2616	1.20023
$769$	27.1314	0.978384	0.489192	−	0.872176i	$-0.337292\pi$
$769$	27.1314	0.978384	0.489192	+	0.872176i	$0.337292\pi$
$770$	201.951	7.27779
$771$	−13.8802	−0.499882
$772$	−8.65654	−0.311556
$773$	−33.8242	−1.21657	−0.608285	−	0.793718i	$-0.708142\pi$
$773$	−33.8242	−1.21657	−0.608285	+	0.793718i	$0.708142\pi$
$774$	5.90561	0.212273
$775$	−13.6611	−0.490720
$776$	118.426	4.25123
$777$	−63.2665	−2.26967
$778$	38.8957	1.39448
$779$	−14.8126	−0.530718
$780$	22.9244	0.820824
$781$	−24.2583	−0.868031
$782$	131.097	4.68801
$783$	22.7576	0.813289
$784$	129.433	4.62260
$785$	21.4224	0.764599
$786$	−9.38289	−0.334677
$787$	−23.8773	−0.851133	−0.425567	−	0.904927i	$-0.639925\pi$
$787$	−23.8773	−0.851133	−0.425567	+	0.904927i	$0.639925\pi$
$788$	3.73357	0.133003
$789$	−18.3795	−0.654328
$790$	19.1367	0.680852
$791$	−14.1185	−0.501995
$792$	−38.5208	−1.36878
$793$	2.10823	0.0748655
$794$	−33.4530	−1.18720
$795$	66.4380	2.35631
$796$	29.6605	1.05129
$797$	−20.0078	−0.708714	−0.354357	−	0.935110i	$-0.615300\pi$
$797$	−20.0078	−0.708714	−0.354357	+	0.935110i	$0.615300\pi$
$798$	26.3282	0.932009
$799$	56.6390	2.00374
$800$	−75.9821	−2.68637
$801$	23.2568	0.821740
$802$	−3.98857	−0.140841
$803$	−47.5249	−1.67712
$804$	35.1292	1.23891
$805$	−183.750	−6.47633
$806$	−3.06469	−0.107949
$807$	−16.4812	−0.580166
$808$	−13.7011	−0.482004
$809$	16.1168	0.566637	0.283319	−	0.959026i	$-0.408565\pi$
$809$	16.1168	0.566637	0.283319	+	0.959026i	$0.408565\pi$
$810$	25.4360	0.893728
$811$	8.99561	0.315879	0.157939	−	0.987449i	$-0.449515\pi$
$811$	8.99561	0.315879	0.157939	+	0.987449i	$0.449515\pi$
$812$	91.5821	3.21390
$813$	−4.98488	−0.174827
$814$	107.240	3.75877
$815$	62.2725	2.18131
$816$	−52.6279	−1.84234
$817$	2.67515	0.0935917
$818$	−40.2455	−1.40715
$819$	7.14622	0.249709
$820$	−161.057	−5.62434
$821$	−53.1838	−1.85613	−0.928063	−	0.372422i	$-0.878527\pi$
$821$	−53.1838	−1.85613	−0.928063	+	0.372422i	$0.878527\pi$
$822$	−5.68106	−0.198150
$823$	2.24202	0.0781520	0.0390760	−	0.999236i	$-0.487559\pi$
$823$	2.24202	0.0781520	0.0390760	+	0.999236i	$0.487559\pi$
$824$	−95.5139	−3.32738
$825$	56.4513	1.96538
$826$	−69.8217	−2.42941
$827$	−15.1003	−0.525090	−0.262545	−	0.964920i	$-0.584562\pi$
$827$	−15.1003	−0.525090	−0.262545	+	0.964920i	$0.584562\pi$
$828$	62.3447	2.16663
$829$	8.02760	0.278810	0.139405	−	0.990235i	$-0.455481\pi$
$829$	8.02760	0.278810	0.139405	+	0.990235i	$0.455481\pi$
$830$	−99.7316	−3.46174
$831$	8.75873	0.303837
$832$	−1.58276	−0.0548725
$833$	92.0277	3.18857
$834$	43.5662	1.50857
$835$	40.8534	1.41379
$836$	−31.0386	−1.07349
$837$	−6.61407	−0.228616
$838$	−0.124655	−0.00430612
$839$	−8.91950	−0.307936	−0.153968	−	0.988076i	$-0.549205\pi$
$839$	−8.91950	−0.307936	−0.153968	+	0.988076i	$0.549205\pi$
$840$	160.933	5.55272
$841$	−12.0704	−0.416221
$842$	−69.6213	−2.39931
$843$	23.2657	0.801312
$844$	108.147	3.72258
$845$	4.05265	0.139416
$846$	38.7282	1.33150
$847$	23.9952	0.824486
$848$	−102.357	−3.51495
$849$	9.60319	0.329580
$850$	−160.943	−5.52031
$851$	−97.5751	−3.34483
$852$	−34.3862	−1.17805
$853$	−31.8637	−1.09099	−0.545496	−	0.838113i	$-0.683659\pi$
$853$	−31.8637	−1.09099	−0.545496	+	0.838113i	$0.683659\pi$
$854$	26.3263	0.900866
$855$	−10.1203	−0.346109
$856$	−33.9746	−1.16123
$857$	−35.2909	−1.20551	−0.602757	−	0.797925i	$-0.705931\pi$
$857$	−35.2909	−1.20551	−0.602757	+	0.797925i	$0.705931\pi$
$858$	12.6641	0.432347
$859$	6.83741	0.233289	0.116645	−	0.993174i	$-0.462786\pi$
$859$	6.83741	0.233289	0.116645	+	0.993174i	$0.462786\pi$
$860$	29.0867	0.991850
$861$	52.4897	1.78884
$862$	73.3569	2.49854
$863$	−22.2694	−0.758058	−0.379029	−	0.925385i	$-0.623742\pi$
$863$	−22.2694	−0.758058	−0.379029	+	0.925385i	$0.623742\pi$
$864$	−36.7871	−1.25152
$865$	−35.0338	−1.19119
$866$	10.4636	0.355568
$867$	−16.3680	−0.555885
$868$	−26.6167	−0.903429
$869$	7.35260	0.249420
$870$	52.9181	1.79409
$871$	6.21026	0.210427
$872$	49.3905	1.67257
$873$	26.3899	0.893162
$874$	40.6057	1.37351
$875$	126.851	4.28836
$876$	−67.3665	−2.27610
$877$	−25.1074	−0.847817	−0.423908	−	0.905705i	$-0.639342\pi$
$877$	−25.1074	−0.847817	−0.423908	+	0.905705i	$0.639342\pi$
$878$	65.0073	2.19389
$879$	12.3535	0.416672
$880$	−125.036	−4.21496
$881$	6.03299	0.203257	0.101628	−	0.994822i	$-0.467595\pi$
$881$	6.03299	0.203257	0.101628	+	0.994822i	$0.467595\pi$
$882$	62.9261	2.11883
$883$	13.8707	0.466786	0.233393	−	0.972383i	$-0.425017\pi$
$883$	13.8707	0.466786	0.233393	+	0.972383i	$0.425017\pi$
$884$	−25.1114	−0.844589
$885$	−28.0595	−0.943210
$886$	−4.35917	−0.146449
$887$	37.8631	1.27132	0.635659	−	0.771970i	$-0.280728\pi$
$887$	37.8631	1.27132	0.635659	+	0.771970i	$0.280728\pi$
$888$	85.4590	2.86782
$889$	82.2117	2.75729
$890$	164.697	5.52064
$891$	9.77289	0.327404
$892$	−78.5297	−2.62937
$893$	17.5433	0.587064
$894$	−19.5300	−0.653181
$895$	91.2534	3.05026
$896$	45.0501	1.50502
$897$	−11.5228	−0.384735
$898$	−75.5360	−2.52067
$899$	−4.92028	−0.164100
$900$	−76.5387	−2.55129
$901$	−72.7764	−2.42453
$902$	−88.9729	−2.96247
$903$	−9.47960	−0.315461
$904$	19.0709	0.634289
$905$	−51.9185	−1.72583
$906$	−16.1280	−0.535816
$907$	−23.7394	−0.788253	−0.394126	−	0.919056i	$-0.628953\pi$
$907$	−23.7394	−0.788253	−0.394126	+	0.919056i	$0.628953\pi$
$908$	−71.9503	−2.38775
$909$	−3.05314	−0.101266
$910$	50.6070	1.67760
$911$	−48.7818	−1.61621	−0.808106	−	0.589037i	$-0.799507\pi$
$911$	−48.7818	−1.61621	−0.808106	+	0.589037i	$0.799507\pi$
$912$	−16.3009	−0.539776
$913$	−38.3185	−1.26816
$914$	23.8150	0.787731
$915$	10.5798	0.349759
$916$	−112.799	−3.72700
$917$	−14.4061	−0.475731
$918$	−77.9215	−2.57179
$919$	6.39041	0.210800	0.105400	−	0.994430i	$-0.466388\pi$
$919$	6.39041	0.210800	0.105400	+	0.994430i	$0.466388\pi$
$920$	248.205	8.18309
$921$	−1.66222	−0.0547720
$922$	15.9676	0.525864
$923$	−6.07892	−0.200090
$924$	109.987	3.61832
$925$	119.790	3.93867
$926$	12.4592	0.409433
$927$	−21.2842	−0.699066
$928$	−27.3663	−0.898343
$929$	6.75669	0.221680	0.110840	−	0.993838i	$-0.464646\pi$
$929$	6.75669	0.221680	0.110840	+	0.993838i	$0.464646\pi$
$930$	−15.3797	−0.504319
$931$	28.5045	0.934199
$932$	23.1551	0.758469
$933$	−9.29581	−0.304331
$934$	−11.0458	−0.361428
$935$	−88.9014	−2.90739
$936$	−9.65296	−0.315517
$937$	−17.9366	−0.585962	−0.292981	−	0.956118i	$-0.594647\pi$
$937$	−17.9366	−0.585962	−0.292981	+	0.956118i	$0.594647\pi$
$938$	77.5498	2.53209
$939$	6.33950	0.206882
$940$	190.747	6.22148
$941$	−25.6770	−0.837046	−0.418523	−	0.908206i	$-0.637452\pi$
$941$	−25.6770	−0.837046	−0.418523	+	0.908206i	$0.637452\pi$
$942$	16.7753	0.546569
$943$	80.9542	2.63623
$944$	43.2295	1.40700
$945$	109.218	3.55285
$946$	16.0684	0.522430
$947$	−35.5350	−1.15473	−0.577366	−	0.816486i	$-0.695919\pi$
$947$	−35.5350	−1.15473	−0.577366	+	0.816486i	$0.695919\pi$
$948$	10.4223	0.338501
$949$	−11.9093	−0.386592
$950$	−49.8504	−1.61736
$951$	13.1360	0.425965
$952$	−176.287	−5.71349
$953$	−8.98819	−0.291156	−0.145578	−	0.989347i	$-0.546504\pi$
$953$	−8.98819	−0.291156	−0.145578	+	0.989347i	$0.546504\pi$
$954$	−49.7625	−1.61112
$955$	21.0600	0.681487
$956$	−10.1040	−0.326788
$957$	20.3319	0.657238
$958$	−101.572	−3.28164
$959$	−8.72246	−0.281663
$960$	−7.94285	−0.256355
$961$	−29.5700	−0.953871
$962$	26.8734	0.866433
$963$	−7.57086	−0.243968
$964$	107.894	3.47504
$965$	−7.67974	−0.247220
$966$	−143.889	−4.62956
$967$	−43.9132	−1.41215	−0.706076	−	0.708136i	$-0.749537\pi$
$967$	−43.9132	−1.41215	−0.706076	+	0.708136i	$0.749537\pi$
$968$	−32.4122	−1.04177
$969$	−11.5901	−0.372326
$970$	186.884	6.00047
$971$	13.8000	0.442862	0.221431	−	0.975176i	$-0.428927\pi$
$971$	13.8000	0.442862	0.221431	+	0.975176i	$0.428927\pi$
$972$	−61.9455	−1.98690
$973$	66.8896	2.14438
$974$	36.8013	1.17919
$975$	14.1462	0.453040
$976$	−16.2997	−0.521740
$977$	−28.1168	−0.899536	−0.449768	−	0.893145i	$-0.648493\pi$
$977$	−28.1168	−0.899536	−0.449768	+	0.893145i	$0.648493\pi$
$978$	48.7639	1.55930
$979$	63.2790	2.02241
$980$	309.928	9.90028
$981$	11.0061	0.351399
$982$	−57.4907	−1.83460
$983$	7.14558	0.227909	0.113954	−	0.993486i	$-0.463648\pi$
$983$	7.14558	0.227909	0.113954	+	0.993486i	$0.463648\pi$
$984$	−70.9019	−2.26027
$985$	3.31228	0.105538
$986$	−57.9666	−1.84603
$987$	−62.1659	−1.97876
$988$	−7.77798	−0.247451
$989$	−14.6203	−0.464898
$990$	−60.7884	−1.93198
$991$	−36.0349	−1.14469	−0.572343	−	0.820014i	$-0.693966\pi$
$991$	−36.0349	−1.14469	−0.572343	+	0.820014i	$0.693966\pi$
$992$	7.95352	0.252525
$993$	−43.3947	−1.37709
$994$	−75.9097	−2.40771
$995$	26.3136	0.834198
$996$	−54.3164	−1.72108
$997$	−1.60687	−0.0508901	−0.0254451	−	0.999676i	$-0.508100\pi$
$997$	−1.60687	−0.0508901	−0.0254451	+	0.999676i	$0.508100\pi$
$998$	−82.1199	−2.59946
$999$	57.9969	1.83494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.9	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.9	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56283 q^{2} -1.23829 q^{3} +4.56811 q^{4} +4.05265 q^{5} +3.17352 q^{6} +4.87248 q^{7} -6.58165 q^{8} -1.46665 q^{9} +O(q^{10})\)	\(q-2.56283 q^{2} -1.23829 q^{3} +4.56811 q^{4} +4.05265 q^{5} +3.17352 q^{6} +4.87248 q^{7} -6.58165 q^{8} -1.46665 q^{9} -10.3863 q^{10} -3.99057 q^{11} -5.65663 q^{12} -1.00000 q^{13} -12.4874 q^{14} -5.01834 q^{15} +7.73144 q^{16} +5.49711 q^{17} +3.75878 q^{18} +1.70267 q^{19} +18.5130 q^{20} -6.03353 q^{21} +10.2272 q^{22} -9.30544 q^{23} +8.14996 q^{24} +11.4240 q^{25} +2.56283 q^{26} +5.53099 q^{27} +22.2581 q^{28} +4.11456 q^{29} +12.8612 q^{30} -1.19582 q^{31} -6.65109 q^{32} +4.94146 q^{33} -14.0882 q^{34} +19.7465 q^{35} -6.69982 q^{36} +10.4858 q^{37} -4.36365 q^{38} +1.23829 q^{39} -26.6731 q^{40} -8.69966 q^{41} +15.4629 q^{42} +1.57115 q^{43} -18.2294 q^{44} -5.94382 q^{45} +23.8483 q^{46} +10.3034 q^{47} -9.57373 q^{48} +16.7411 q^{49} -29.2778 q^{50} -6.80699 q^{51} -4.56811 q^{52} -13.2390 q^{53} -14.1750 q^{54} -16.1724 q^{55} -32.0690 q^{56} -2.10839 q^{57} -10.5449 q^{58} +5.59139 q^{59} -22.9244 q^{60} -2.10823 q^{61} +3.06469 q^{62} -7.14622 q^{63} +1.58276 q^{64} -4.05265 q^{65} -12.6641 q^{66} -6.21026 q^{67} +25.1114 q^{68} +11.5228 q^{69} -50.6070 q^{70} +6.07892 q^{71} +9.65296 q^{72} +11.9093 q^{73} -26.8734 q^{74} -14.1462 q^{75} +7.77798 q^{76} -19.4440 q^{77} -3.17352 q^{78} -1.84250 q^{79} +31.3328 q^{80} -2.44900 q^{81} +22.2958 q^{82} +9.60225 q^{83} -27.5618 q^{84} +22.2779 q^{85} -4.02660 q^{86} -5.09500 q^{87} +26.2645 q^{88} -15.8571 q^{89} +15.2330 q^{90} -4.87248 q^{91} -42.5083 q^{92} +1.48077 q^{93} -26.4059 q^{94} +6.90032 q^{95} +8.23595 q^{96} -17.9933 q^{97} -42.9047 q^{98} +5.85276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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