LMFDB - Embedded newform 8021.2.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.45553 q^{2} -0.403768 q^{3} +4.02965 q^{4} -2.39341 q^{5} +0.991465 q^{6} +2.40759 q^{7} -4.98387 q^{8} -2.83697 q^{9} +O(q^{10})$	\(q-2.45553 q^{2} -0.403768 q^{3} +4.02965 q^{4} -2.39341 q^{5} +0.991465 q^{6} +2.40759 q^{7} -4.98387 q^{8} -2.83697 q^{9} +5.87709 q^{10} -4.23177 q^{11} -1.62704 q^{12} -1.00000 q^{13} -5.91192 q^{14} +0.966380 q^{15} +4.17878 q^{16} -1.14503 q^{17} +6.96628 q^{18} +7.09149 q^{19} -9.64458 q^{20} -0.972107 q^{21} +10.3913 q^{22} +7.63884 q^{23} +2.01233 q^{24} +0.728389 q^{25} +2.45553 q^{26} +2.35678 q^{27} +9.70174 q^{28} -7.10929 q^{29} -2.37298 q^{30} -0.314912 q^{31} -0.293382 q^{32} +1.70865 q^{33} +2.81167 q^{34} -5.76234 q^{35} -11.4320 q^{36} +4.48001 q^{37} -17.4134 q^{38} +0.403768 q^{39} +11.9284 q^{40} -5.53667 q^{41} +2.38704 q^{42} +10.7028 q^{43} -17.0526 q^{44} +6.79002 q^{45} -18.7574 q^{46} +8.74317 q^{47} -1.68725 q^{48} -1.20351 q^{49} -1.78858 q^{50} +0.462328 q^{51} -4.02965 q^{52} +1.18170 q^{53} -5.78716 q^{54} +10.1284 q^{55} -11.9991 q^{56} -2.86331 q^{57} +17.4571 q^{58} -9.02602 q^{59} +3.89417 q^{60} +5.76384 q^{61} +0.773277 q^{62} -6.83026 q^{63} -7.63715 q^{64} +2.39341 q^{65} -4.19566 q^{66} -5.72303 q^{67} -4.61409 q^{68} -3.08431 q^{69} +14.1496 q^{70} +4.57099 q^{71} +14.1391 q^{72} -5.59868 q^{73} -11.0008 q^{74} -0.294100 q^{75} +28.5762 q^{76} -10.1884 q^{77} -0.991465 q^{78} -11.0874 q^{79} -10.0015 q^{80} +7.55932 q^{81} +13.5955 q^{82} -5.43149 q^{83} -3.91725 q^{84} +2.74053 q^{85} -26.2810 q^{86} +2.87050 q^{87} +21.0906 q^{88} -14.1393 q^{89} -16.6731 q^{90} -2.40759 q^{91} +30.7818 q^{92} +0.127151 q^{93} -21.4691 q^{94} -16.9728 q^{95} +0.118458 q^{96} -6.46546 q^{97} +2.95527 q^{98} +12.0054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45553	−1.73633	−0.868163	−	0.496280i	$-0.834699\pi$
$2$	−2.45553	−1.73633	−0.868163	+	0.496280i	$0.834699\pi$
$3$	−0.403768	−0.233115	−0.116558	−	0.993184i	$-0.537186\pi$
$3$	−0.403768	−0.233115	−0.116558	+	0.993184i	$0.537186\pi$
$4$	4.02965	2.01482
$5$	−2.39341	−1.07036	−0.535182	−	0.844737i	$-0.679757\pi$
$5$	−2.39341	−1.07036	−0.535182	+	0.844737i	$0.679757\pi$
$6$	0.991465	0.404764
$7$	2.40759	0.909983	0.454992	−	0.890496i	$-0.349642\pi$
$7$	2.40759	0.909983	0.454992	+	0.890496i	$0.349642\pi$
$8$	−4.98387	−1.76207
$9$	−2.83697	−0.945657
$10$	5.87709	1.85850
$11$	−4.23177	−1.27593	−0.637964	−	0.770066i	$-0.720223\pi$
$11$	−4.23177	−1.27593	−0.637964	+	0.770066i	$0.720223\pi$
$12$	−1.62704	−0.469687
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.91192	−1.58003
$15$	0.966380	0.249518
$16$	4.17878	1.04469
$17$	−1.14503	−0.277712	−0.138856	−	0.990313i	$-0.544342\pi$
$17$	−1.14503	−0.277712	−0.138856	+	0.990313i	$0.544342\pi$
$18$	6.96628	1.64197
$19$	7.09149	1.62690	0.813449	−	0.581636i	$-0.197587\pi$
$19$	7.09149	1.62690	0.813449	+	0.581636i	$0.197587\pi$
$20$	−9.64458	−2.15659
$21$	−0.972107	−0.212131
$22$	10.3913	2.21543
$23$	7.63884	1.59281	0.796404	−	0.604765i	$-0.206733\pi$
$23$	7.63884	1.59281	0.796404	+	0.604765i	$0.206733\pi$
$24$	2.01233	0.410765
$25$	0.728389	0.145678
$26$	2.45553	0.481570
$27$	2.35678	0.453563
$28$	9.70174	1.83346
$29$	−7.10929	−1.32016	−0.660081	−	0.751194i	$-0.729478\pi$
$29$	−7.10929	−1.32016	−0.660081	+	0.751194i	$0.729478\pi$
$30$	−2.37298	−0.433245
$31$	−0.314912	−0.0565598	−0.0282799	−	0.999600i	$-0.509003\pi$
$31$	−0.314912	−0.0565598	−0.0282799	+	0.999600i	$0.509003\pi$
$32$	−0.293382	−0.0518631
$33$	1.70865	0.297438
$34$	2.81167	0.482197
$35$	−5.76234	−0.974013
$36$	−11.4320	−1.90533
$37$	4.48001	0.736508	0.368254	−	0.929725i	$-0.379956\pi$
$37$	4.48001	0.736508	0.368254	+	0.929725i	$0.379956\pi$
$38$	−17.4134	−2.82483
$39$	0.403768	0.0646546
$40$	11.9284	1.88605
$41$	−5.53667	−0.864682	−0.432341	−	0.901710i	$-0.642312\pi$
$41$	−5.53667	−0.864682	−0.432341	+	0.901710i	$0.642312\pi$
$42$	2.38704	0.368328
$43$	10.7028	1.63216	0.816079	−	0.577940i	$-0.196143\pi$
$43$	10.7028	1.63216	0.816079	+	0.577940i	$0.196143\pi$
$44$	−17.0526	−2.57077
$45$	6.79002	1.01220
$46$	−18.7574	−2.76563
$47$	8.74317	1.27532	0.637661	−	0.770317i	$-0.279902\pi$
$47$	8.74317	1.27532	0.637661	+	0.770317i	$0.279902\pi$
$48$	−1.68725	−0.243534
$49$	−1.20351	−0.171931
$50$	−1.78858	−0.252944
$51$	0.462328	0.0647388
$52$	−4.02965	−0.558812
$53$	1.18170	0.162318	0.0811592	−	0.996701i	$-0.474138\pi$
$53$	1.18170	0.162318	0.0811592	+	0.996701i	$0.474138\pi$
$54$	−5.78716	−0.787532
$55$	10.1284	1.36571
$56$	−11.9991	−1.60345
$57$	−2.86331	−0.379255
$58$	17.4571	2.29223
$59$	−9.02602	−1.17509	−0.587544	−	0.809192i	$-0.699905\pi$
$59$	−9.02602	−1.17509	−0.587544	+	0.809192i	$0.699905\pi$
$60$	3.89417	0.502735
$61$	5.76384	0.737985	0.368992	−	0.929432i	$-0.379703\pi$
$61$	5.76384	0.737985	0.368992	+	0.929432i	$0.379703\pi$
$62$	0.773277	0.0982062
$63$	−6.83026	−0.860532
$64$	−7.63715	−0.954643
$65$	2.39341	0.296865
$66$	−4.19566	−0.516450
$67$	−5.72303	−0.699180	−0.349590	−	0.936903i	$-0.613679\pi$
$67$	−5.72303	−0.699180	−0.349590	+	0.936903i	$0.613679\pi$
$68$	−4.61409	−0.559540
$69$	−3.08431	−0.371308
$70$	14.1496	1.69120
$71$	4.57099	0.542477	0.271239	−	0.962512i	$-0.412567\pi$
$71$	4.57099	0.542477	0.271239	+	0.962512i	$0.412567\pi$
$72$	14.1391	1.66631
$73$	−5.59868	−0.655276	−0.327638	−	0.944803i	$-0.606253\pi$
$73$	−5.59868	−0.655276	−0.327638	+	0.944803i	$0.606253\pi$
$74$	−11.0008	−1.27882
$75$	−0.294100	−0.0339597
$76$	28.5762	3.27792
$77$	−10.1884	−1.16107
$78$	−0.991465	−0.112261
$79$	−11.0874	−1.24743	−0.623713	−	0.781653i	$-0.714377\pi$
$79$	−11.0874	−1.24743	−0.623713	+	0.781653i	$0.714377\pi$
$80$	−10.0015	−1.11820
$81$	7.55932	0.839925
$82$	13.5955	1.50137
$83$	−5.43149	−0.596183	−0.298091	−	0.954537i	$-0.596350\pi$
$83$	−5.43149	−0.596183	−0.298091	+	0.954537i	$0.596350\pi$
$84$	−3.91725	−0.427407
$85$	2.74053	0.297252
$86$	−26.2810	−2.83396
$87$	2.87050	0.307750
$88$	21.0906	2.24827
$89$	−14.1393	−1.49876	−0.749380	−	0.662140i	$-0.769649\pi$
$89$	−14.1393	−1.49876	−0.749380	+	0.662140i	$0.769649\pi$
$90$	−16.6731	−1.75750
$91$	−2.40759	−0.252384
$92$	30.7818	3.20923
$93$	0.127151	0.0131850
$94$	−21.4691	−2.21437
$95$	−16.9728	−1.74137
$96$	0.118458	0.0120901
$97$	−6.46546	−0.656468	−0.328234	−	0.944597i	$-0.606453\pi$
$97$	−6.46546	−0.656468	−0.328234	+	0.944597i	$0.606453\pi$
$98$	2.95527	0.298527
$99$	12.0054	1.20659
$100$	2.93515	0.293515
$101$	−12.6071	−1.25445	−0.627225	−	0.778838i	$-0.715809\pi$
$101$	−12.6071	−1.25445	−0.627225	+	0.778838i	$0.715809\pi$
$102$	−1.13526	−0.112408
$103$	−0.589224	−0.0580579	−0.0290290	−	0.999579i	$-0.509242\pi$
$103$	−0.589224	−0.0580579	−0.0290290	+	0.999579i	$0.509242\pi$
$104$	4.98387	0.488709
$105$	2.32665	0.227057
$106$	−2.90169	−0.281837
$107$	−19.5818	−1.89305	−0.946524	−	0.322633i	$-0.895432\pi$
$107$	−19.5818	−1.89305	−0.946524	+	0.322633i	$0.895432\pi$
$108$	9.49700	0.913849
$109$	0.912668	0.0874178	0.0437089	−	0.999044i	$-0.486083\pi$
$109$	0.912668	0.0874178	0.0437089	+	0.999044i	$0.486083\pi$
$110$	−24.8705	−2.37131
$111$	−1.80888	−0.171691
$112$	10.0608	0.950654
$113$	7.79524	0.733314	0.366657	−	0.930356i	$-0.380502\pi$
$113$	7.79524	0.733314	0.366657	+	0.930356i	$0.380502\pi$
$114$	7.03096	0.658510
$115$	−18.2828	−1.70488
$116$	−28.6480	−2.65990
$117$	2.83697	0.262278
$118$	22.1637	2.04033
$119$	−2.75677	−0.252713
$120$	−4.81631	−0.439667
$121$	6.90792	0.627993
$122$	−14.1533	−1.28138
$123$	2.23553	0.201571
$124$	−1.26898	−0.113958
$125$	10.2237	0.914435
$126$	16.7719	1.49416
$127$	−19.0972	−1.69461	−0.847303	−	0.531110i	$-0.821775\pi$
$127$	−19.0972	−1.69461	−0.847303	+	0.531110i	$0.821775\pi$
$128$	19.3400	1.70943
$129$	−4.32143	−0.380481
$130$	−5.87709	−0.515455
$131$	−4.86472	−0.425033	−0.212516	−	0.977158i	$-0.568166\pi$
$131$	−4.86472	−0.425033	−0.212516	+	0.977158i	$0.568166\pi$
$132$	6.88528	0.599286
$133$	17.0734	1.48045
$134$	14.0531	1.21400
$135$	−5.64073	−0.485477
$136$	5.70671	0.489346
$137$	17.4395	1.48995	0.744976	−	0.667091i	$-0.232461\pi$
$137$	17.4395	1.48995	0.744976	+	0.667091i	$0.232461\pi$
$138$	7.57364	0.644711
$139$	2.20410	0.186950	0.0934748	−	0.995622i	$-0.470203\pi$
$139$	2.20410	0.186950	0.0934748	+	0.995622i	$0.470203\pi$
$140$	−23.2202	−1.96247
$141$	−3.53021	−0.297297
$142$	−11.2242	−0.941917
$143$	4.23177	0.353879
$144$	−11.8551	−0.987923
$145$	17.0154	1.41305
$146$	13.7478	1.13777
$147$	0.485940	0.0400796
$148$	18.0529	1.48394
$149$	5.43417	0.445184	0.222592	−	0.974912i	$-0.428548\pi$
$149$	5.43417	0.445184	0.222592	+	0.974912i	$0.428548\pi$
$150$	0.722172	0.0589651
$151$	0.202150	0.0164508	0.00822538	−	0.999966i	$-0.497382\pi$
$151$	0.202150	0.0164508	0.00822538	+	0.999966i	$0.497382\pi$
$152$	−35.3431	−2.86670
$153$	3.24843	0.262620
$154$	25.0179	2.01600
$155$	0.753711	0.0605395
$156$	1.62704	0.130268
$157$	23.1063	1.84409	0.922043	−	0.387088i	$-0.126519\pi$
$157$	23.1063	1.84409	0.922043	+	0.387088i	$0.126519\pi$
$158$	27.2254	2.16594
$159$	−0.477130	−0.0378389
$160$	0.702181	0.0555123
$161$	18.3912	1.44943
$162$	−18.5622	−1.45838
$163$	−3.52793	−0.276329	−0.138165	−	0.990409i	$-0.544120\pi$
$163$	−3.52793	−0.276329	−0.138165	+	0.990409i	$0.544120\pi$
$164$	−22.3108	−1.74218
$165$	−4.08950	−0.318367
$166$	13.3372	1.03517
$167$	4.64087	0.359121	0.179561	−	0.983747i	$-0.442532\pi$
$167$	4.64087	0.359121	0.179561	+	0.983747i	$0.442532\pi$
$168$	4.84486	0.373789
$169$	1.00000	0.0769231
$170$	−6.72947	−0.516126
$171$	−20.1183	−1.53849
$172$	43.1284	3.28851
$173$	6.72223	0.511082	0.255541	−	0.966798i	$-0.417746\pi$
$173$	6.72223	0.511082	0.255541	+	0.966798i	$0.417746\pi$
$174$	−7.04862	−0.534354
$175$	1.75366	0.132564
$176$	−17.6836	−1.33295
$177$	3.64442	0.273931
$178$	34.7195	2.60234
$179$	−3.72726	−0.278588	−0.139294	−	0.990251i	$-0.544483\pi$
$179$	−3.72726	−0.278588	−0.139294	+	0.990251i	$0.544483\pi$
$180$	27.3614	2.03940
$181$	3.12794	0.232498	0.116249	−	0.993220i	$-0.462913\pi$
$181$	3.12794	0.232498	0.116249	+	0.993220i	$0.462913\pi$
$182$	5.91192	0.438221
$183$	−2.32725	−0.172036
$184$	−38.0710	−2.80663
$185$	−10.7225	−0.788332
$186$	−0.312224	−0.0228934
$187$	4.84553	0.354340
$188$	35.2319	2.56955
$189$	5.67416	0.412734
$190$	41.6773	3.02359
$191$	12.1726	0.880781	0.440391	−	0.897806i	$-0.354840\pi$
$191$	12.1726	0.880781	0.440391	+	0.897806i	$0.354840\pi$
$192$	3.08363	0.222542
$193$	−19.1176	−1.37612	−0.688058	−	0.725656i	$-0.741536\pi$
$193$	−19.1176	−1.37612	−0.688058	+	0.725656i	$0.741536\pi$
$194$	15.8761	1.13984
$195$	−0.966380	−0.0692039
$196$	−4.84974	−0.346410
$197$	23.5060	1.67474	0.837368	−	0.546639i	$-0.184093\pi$
$197$	23.5060	1.67474	0.837368	+	0.546639i	$0.184093\pi$
$198$	−29.4797	−2.09503
$199$	−4.87319	−0.345451	−0.172726	−	0.984970i	$-0.555257\pi$
$199$	−4.87319	−0.345451	−0.172726	+	0.984970i	$0.555257\pi$
$200$	−3.63020	−0.256694
$201$	2.31077	0.162989
$202$	30.9571	2.17813
$203$	−17.1163	−1.20133
$204$	1.86302	0.130437
$205$	13.2515	0.925524
$206$	1.44686	0.100807
$207$	−21.6712	−1.50625
$208$	−4.17878	−0.289746
$209$	−30.0096	−2.07581
$210$	−5.71316	−0.394245
$211$	−14.9739	−1.03085	−0.515424	−	0.856935i	$-0.672366\pi$
$211$	−14.9739	−1.03085	−0.515424	+	0.856935i	$0.672366\pi$
$212$	4.76182	0.327043
$213$	−1.84562	−0.126460
$214$	48.0839	3.28695
$215$	−25.6161	−1.74700
$216$	−11.7459	−0.799207
$217$	−0.758178	−0.0514685
$218$	−2.24109	−0.151786
$219$	2.26057	0.152755
$220$	40.8137	2.75166
$221$	1.14503	0.0770233
$222$	4.44177	0.298112
$223$	−15.9186	−1.06598	−0.532992	−	0.846120i	$-0.678933\pi$
$223$	−15.9186	−1.06598	−0.532992	+	0.846120i	$0.678933\pi$
$224$	−0.706343	−0.0471945
$225$	−2.06642	−0.137761
$226$	−19.1415	−1.27327
$227$	−21.5123	−1.42782	−0.713912	−	0.700235i	$-0.753078\pi$
$227$	−21.5123	−1.42782	−0.713912	+	0.700235i	$0.753078\pi$
$228$	−11.5381	−0.764133
$229$	10.8774	0.718799	0.359399	−	0.933184i	$-0.382982\pi$
$229$	10.8774	0.718799	0.359399	+	0.933184i	$0.382982\pi$
$230$	44.8941	2.96023
$231$	4.11374	0.270664
$232$	35.4318	2.32621
$233$	−9.71804	−0.636650	−0.318325	−	0.947982i	$-0.603120\pi$
$233$	−9.71804	−0.636650	−0.318325	+	0.947982i	$0.603120\pi$
$234$	−6.96628	−0.455400
$235$	−20.9259	−1.36506
$236$	−36.3717	−2.36760
$237$	4.47672	0.290794
$238$	6.76935	0.438792
$239$	17.7993	1.15134	0.575670	−	0.817682i	$-0.304741\pi$
$239$	17.7993	1.15134	0.575670	+	0.817682i	$0.304741\pi$
$240$	4.03828	0.260670
$241$	16.2090	1.04411	0.522055	−	0.852912i	$-0.325165\pi$
$241$	16.2090	1.04411	0.522055	+	0.852912i	$0.325165\pi$
$242$	−16.9626	−1.09040
$243$	−10.1226	−0.649362
$244$	23.2263	1.48691
$245$	2.88050	0.184028
$246$	−5.48941	−0.349992
$247$	−7.09149	−0.451221
$248$	1.56948	0.0996621
$249$	2.19306	0.138979
$250$	−25.1046	−1.58776
$251$	−15.5399	−0.980867	−0.490434	−	0.871479i	$-0.663162\pi$
$251$	−15.5399	−0.980867	−0.490434	+	0.871479i	$0.663162\pi$
$252$	−27.5236	−1.73382
$253$	−32.3258	−2.03231
$254$	46.8939	2.94239
$255$	−1.10654	−0.0692941
$256$	−32.2158	−2.01349
$257$	−19.3293	−1.20573	−0.602863	−	0.797845i	$-0.705974\pi$
$257$	−19.3293	−1.20573	−0.602863	+	0.797845i	$0.705974\pi$
$258$	10.6114	0.660639
$259$	10.7860	0.670210
$260$	9.64458	0.598132
$261$	20.1689	1.24842
$262$	11.9455	0.737995
$263$	3.96947	0.244768	0.122384	−	0.992483i	$-0.460946\pi$
$263$	3.96947	0.244768	0.122384	+	0.992483i	$0.460946\pi$
$264$	−8.51572	−0.524106
$265$	−2.82828	−0.173740
$266$	−41.9243	−2.57054
$267$	5.70898	0.349384
$268$	−23.0618	−1.40872
$269$	12.5168	0.763165	0.381583	−	0.924335i	$-0.375379\pi$
$269$	12.5168	0.763165	0.381583	+	0.924335i	$0.375379\pi$
$270$	13.8510	0.842945
$271$	26.4596	1.60731	0.803654	−	0.595097i	$-0.202886\pi$
$271$	26.4596	1.60731	0.803654	+	0.595097i	$0.202886\pi$
$272$	−4.78484	−0.290124
$273$	0.972107	0.0588346
$274$	−42.8232	−2.58704
$275$	−3.08238	−0.185874
$276$	−12.4287	−0.748120
$277$	19.0337	1.14362	0.571811	−	0.820385i	$-0.306241\pi$
$277$	19.0337	1.14362	0.571811	+	0.820385i	$0.306241\pi$
$278$	−5.41225	−0.324605
$279$	0.893396	0.0534862
$280$	28.7188	1.71627
$281$	13.9812	0.834047	0.417024	−	0.908896i	$-0.363073\pi$
$281$	13.9812	0.834047	0.417024	+	0.908896i	$0.363073\pi$
$282$	8.66855	0.516204
$283$	−6.69519	−0.397988	−0.198994	−	0.980001i	$-0.563767\pi$
$283$	−6.69519	−0.397988	−0.198994	+	0.980001i	$0.563767\pi$
$284$	18.4195	1.09300
$285$	6.85307	0.405941
$286$	−10.3913	−0.614449
$287$	−13.3300	−0.786846
$288$	0.832316	0.0490447
$289$	−15.6889	−0.922876
$290$	−41.7820	−2.45352
$291$	2.61054	0.153033
$292$	−22.5607	−1.32027
$293$	5.60294	0.327327	0.163664	−	0.986516i	$-0.447669\pi$
$293$	5.60294	0.327327	0.163664	+	0.986516i	$0.447669\pi$
$294$	−1.19324	−0.0695913
$295$	21.6029	1.25777
$296$	−22.3278	−1.29778
$297$	−9.97336	−0.578713
$298$	−13.3438	−0.772984
$299$	−7.63884	−0.441765
$300$	−1.18512	−0.0684229
$301$	25.7679	1.48524
$302$	−0.496387	−0.0285639
$303$	5.09032	0.292431
$304$	29.6337	1.69961
$305$	−13.7952	−0.789912
$306$	−7.97663	−0.455994
$307$	22.0305	1.25735	0.628673	−	0.777670i	$-0.283598\pi$
$307$	22.0305	1.25735	0.628673	+	0.777670i	$0.283598\pi$
$308$	−41.0556	−2.33936
$309$	0.237909	0.0135342
$310$	−1.85076	−0.105116
$311$	−25.1773	−1.42767	−0.713837	−	0.700311i	$-0.753044\pi$
$311$	−25.1773	−1.42767	−0.713837	+	0.700311i	$0.753044\pi$
$312$	−2.01233	−0.113926
$313$	13.7111	0.775000	0.387500	−	0.921870i	$-0.373339\pi$
$313$	13.7111	0.775000	0.387500	+	0.921870i	$0.373339\pi$
$314$	−56.7384	−3.20193
$315$	16.3476	0.921082
$316$	−44.6782	−2.51335
$317$	6.35784	0.357092	0.178546	−	0.983932i	$-0.442861\pi$
$317$	6.35784	0.357092	0.178546	+	0.983932i	$0.442861\pi$
$318$	1.17161	0.0657006
$319$	30.0849	1.68443
$320$	18.2788	1.02182
$321$	7.90651	0.441299
$322$	−45.1602	−2.51668
$323$	−8.11999	−0.451809
$324$	30.4614	1.69230
$325$	−0.728389	−0.0404037
$326$	8.66296	0.479797
$327$	−0.368506	−0.0203784
$328$	27.5940	1.52363
$329$	21.0500	1.16052
$330$	10.0419	0.552789
$331$	16.3584	0.899142	0.449571	−	0.893245i	$-0.351577\pi$
$331$	16.3584	0.899142	0.449571	+	0.893245i	$0.351577\pi$
$332$	−21.8870	−1.20120
$333$	−12.7096	−0.696484
$334$	−11.3958	−0.623551
$335$	13.6975	0.748376
$336$	−4.06222	−0.221612
$337$	−34.2099	−1.86353	−0.931765	−	0.363061i	$-0.881732\pi$
$337$	−34.2099	−1.86353	−0.931765	+	0.363061i	$0.881732\pi$
$338$	−2.45553	−0.133563
$339$	−3.14746	−0.170947
$340$	11.0434	0.598911
$341$	1.33264	0.0721662
$342$	49.4013	2.67132
$343$	−19.7507	−1.06644
$344$	−53.3413	−2.87597
$345$	7.38202	0.397434
$346$	−16.5067	−0.887404
$347$	28.1232	1.50973	0.754867	−	0.655878i	$-0.227701\pi$
$347$	28.1232	1.50973	0.754867	+	0.655878i	$0.227701\pi$
$348$	11.5671	0.620063
$349$	−24.5100	−1.31199	−0.655995	−	0.754766i	$-0.727751\pi$
$349$	−24.5100	−1.31199	−0.655995	+	0.754766i	$0.727751\pi$
$350$	−4.30618	−0.230175
$351$	−2.35678	−0.125796
$352$	1.24153	0.0661735
$353$	10.3281	0.549711	0.274856	−	0.961485i	$-0.411370\pi$
$353$	10.3281	0.549711	0.274856	+	0.961485i	$0.411370\pi$
$354$	−8.94899	−0.475633
$355$	−10.9402	−0.580648
$356$	−56.9764	−3.01974
$357$	1.11310	0.0589112
$358$	9.15241	0.483720
$359$	10.5285	0.555675	0.277837	−	0.960628i	$-0.410382\pi$
$359$	10.5285	0.555675	0.277837	+	0.960628i	$0.410382\pi$
$360$	−33.8406	−1.78356
$361$	31.2892	1.64680
$362$	−7.68077	−0.403692
$363$	−2.78919	−0.146395
$364$	−9.70174	−0.508509
$365$	13.3999	0.701384
$366$	5.71465	0.298710
$367$	6.74002	0.351826	0.175913	−	0.984406i	$-0.443712\pi$
$367$	6.74002	0.351826	0.175913	+	0.984406i	$0.443712\pi$
$368$	31.9210	1.66400
$369$	15.7074	0.817693
$370$	26.3294	1.36880
$371$	2.84504	0.147707
$372$	0.512375	0.0265654
$373$	−20.0751	−1.03945	−0.519723	−	0.854335i	$-0.673965\pi$
$373$	−20.0751	−1.03945	−0.519723	+	0.854335i	$0.673965\pi$
$374$	−11.8984	−0.615249
$375$	−4.12800	−0.213169
$376$	−43.5748	−2.24720
$377$	7.10929	0.366147
$378$	−13.9331	−0.716641
$379$	−0.279047	−0.0143337	−0.00716684	−	0.999974i	$-0.502281\pi$
$379$	−0.279047	−0.0143337	−0.00716684	+	0.999974i	$0.502281\pi$
$380$	−68.3945	−3.50856
$381$	7.71085	0.395039
$382$	−29.8903	−1.52932
$383$	−4.92801	−0.251810	−0.125905	−	0.992042i	$-0.540183\pi$
$383$	−4.92801	−0.251810	−0.125905	+	0.992042i	$0.540183\pi$
$384$	−7.80888	−0.398495
$385$	24.3849	1.24277
$386$	46.9439	2.38938
$387$	−30.3635	−1.54346
$388$	−26.0535	−1.32267
$389$	−27.3293	−1.38565	−0.692824	−	0.721107i	$-0.743634\pi$
$389$	−27.3293	−1.38565	−0.692824	+	0.721107i	$0.743634\pi$
$390$	2.37298	0.120160
$391$	−8.74673	−0.442341
$392$	5.99816	0.302953
$393$	1.96422	0.0990816
$394$	−57.7199	−2.90789
$395$	26.5366	1.33520
$396$	48.3777	2.43107
$397$	14.6039	0.732948	0.366474	−	0.930428i	$-0.380565\pi$
$397$	14.6039	0.732948	0.366474	+	0.930428i	$0.380565\pi$
$398$	11.9663	0.599816
$399$	−6.89368	−0.345116
$400$	3.04377	0.152189
$401$	−9.45439	−0.472130	−0.236065	−	0.971737i	$-0.575858\pi$
$401$	−9.45439	−0.472130	−0.236065	+	0.971737i	$0.575858\pi$
$402$	−5.67419	−0.283003
$403$	0.314912	0.0156869
$404$	−50.8020	−2.52750
$405$	−18.0925	−0.899025
$406$	42.0296	2.08589
$407$	−18.9584	−0.939732
$408$	−2.30418	−0.114074
$409$	17.8544	0.882844	0.441422	−	0.897300i	$-0.354474\pi$
$409$	17.8544	0.882844	0.441422	+	0.897300i	$0.354474\pi$
$410$	−32.5395	−1.60701
$411$	−7.04149	−0.347331
$412$	−2.37436	−0.116977
$413$	−21.7310	−1.06931
$414$	53.2143	2.61534
$415$	12.9997	0.638132
$416$	0.293382	0.0143842
$417$	−0.889945	−0.0435808
$418$	73.6896	3.60427
$419$	38.8002	1.89552	0.947758	−	0.318991i	$-0.103344\pi$
$419$	38.8002	1.89552	0.947758	+	0.318991i	$0.103344\pi$
$420$	9.37556	0.457481
$421$	−14.0749	−0.685968	−0.342984	−	0.939341i	$-0.611438\pi$
$421$	−14.0749	−0.685968	−0.342984	+	0.939341i	$0.611438\pi$
$422$	36.7690	1.78989
$423$	−24.8041	−1.20602
$424$	−5.88942	−0.286016
$425$	−0.834030	−0.0404564
$426$	4.53198	0.219575
$427$	13.8770	0.671554
$428$	−78.9080	−3.81416
$429$	−1.70865	−0.0824946
$430$	62.9012	3.03336
$431$	−4.92307	−0.237136	−0.118568	−	0.992946i	$-0.537830\pi$
$431$	−4.92307	−0.237136	−0.118568	+	0.992946i	$0.537830\pi$
$432$	9.84846	0.473834
$433$	−17.3077	−0.831753	−0.415876	−	0.909421i	$-0.636525\pi$
$433$	−17.3077	−0.831753	−0.415876	+	0.909421i	$0.636525\pi$
$434$	1.86173	0.0893660
$435$	−6.87028	−0.329405
$436$	3.67773	0.176132
$437$	54.1707	2.59134
$438$	−5.55090	−0.265232
$439$	−20.9324	−0.999047	−0.499523	−	0.866300i	$-0.666491\pi$
$439$	−20.9324	−0.999047	−0.499523	+	0.866300i	$0.666491\pi$
$440$	−50.4784	−2.40647
$441$	3.41433	0.162587
$442$	−2.81167	−0.133738
$443$	4.89449	0.232544	0.116272	−	0.993217i	$-0.462906\pi$
$443$	4.89449	0.232544	0.116272	+	0.993217i	$0.462906\pi$
$444$	−7.28916	−0.345928
$445$	33.8410	1.60422
$446$	39.0886	1.85090
$447$	−2.19414	−0.103779
$448$	−18.3871	−0.868709
$449$	−0.248055	−0.0117064	−0.00585322	−	0.999983i	$-0.501863\pi$
$449$	−0.248055	−0.0117064	−0.00585322	+	0.999983i	$0.501863\pi$
$450$	5.07416	0.239198
$451$	23.4299	1.10327
$452$	31.4121	1.47750
$453$	−0.0816218	−0.00383493
$454$	52.8243	2.47917
$455$	5.76234	0.270143
$456$	14.2704	0.668272
$457$	−22.9284	−1.07255	−0.536274	−	0.844044i	$-0.680169\pi$
$457$	−22.9284	−1.07255	−0.536274	+	0.844044i	$0.680169\pi$
$458$	−26.7098	−1.24807
$459$	−2.69859	−0.125960
$460$	−73.6734	−3.43504
$461$	−36.1939	−1.68572	−0.842860	−	0.538133i	$-0.819130\pi$
$461$	−36.1939	−1.68572	−0.842860	+	0.538133i	$0.819130\pi$
$462$	−10.1014	−0.469961
$463$	39.6044	1.84057	0.920287	−	0.391245i	$-0.127955\pi$
$463$	39.6044	1.84057	0.920287	+	0.391245i	$0.127955\pi$
$464$	−29.7082	−1.37917
$465$	−0.304324	−0.0141127
$466$	23.8630	1.10543
$467$	7.96310	0.368488	0.184244	−	0.982880i	$-0.441016\pi$
$467$	7.96310	0.368488	0.184244	+	0.982880i	$0.441016\pi$
$468$	11.4320	0.528444
$469$	−13.7787	−0.636242
$470$	51.3844	2.37018
$471$	−9.32959	−0.429885
$472$	44.9846	2.07058
$473$	−45.2917	−2.08252
$474$	−10.9927	−0.504913
$475$	5.16536	0.237003
$476$	−11.1088	−0.509172
$477$	−3.35244	−0.153498
$478$	−43.7067	−1.99910
$479$	−18.5862	−0.849226	−0.424613	−	0.905375i	$-0.639590\pi$
$479$	−18.5862	−0.849226	−0.424613	+	0.905375i	$0.639590\pi$
$480$	−0.283518	−0.0129408
$481$	−4.48001	−0.204271
$482$	−39.8017	−1.81292
$483$	−7.42576	−0.337884
$484$	27.8365	1.26529
$485$	15.4745	0.702659
$486$	24.8563	1.12750
$487$	24.5091	1.11061	0.555306	−	0.831646i	$-0.312601\pi$
$487$	24.5091	1.11061	0.555306	+	0.831646i	$0.312601\pi$
$488$	−28.7263	−1.30038
$489$	1.42447	0.0644166
$490$	−7.07316	−0.319533
$491$	−16.9718	−0.765927	−0.382964	−	0.923763i	$-0.625097\pi$
$491$	−16.9718	−0.765927	−0.382964	+	0.923763i	$0.625097\pi$
$492$	9.00839	0.406129
$493$	8.14038	0.366624
$494$	17.4134	0.783466
$495$	−28.7338	−1.29149
$496$	−1.31595	−0.0590877
$497$	11.0051	0.493645
$498$	−5.38513	−0.241313
$499$	33.2010	1.48628	0.743140	−	0.669136i	$-0.233336\pi$
$499$	33.2010	1.48628	0.743140	+	0.669136i	$0.233336\pi$
$500$	41.1979	1.84243
$501$	−1.87383	−0.0837167
$502$	38.1587	1.70310
$503$	20.7867	0.926834	0.463417	−	0.886140i	$-0.346623\pi$
$503$	20.7867	0.926834	0.463417	+	0.886140i	$0.346623\pi$
$504$	34.0412	1.51631
$505$	30.1738	1.34272
$506$	79.3772	3.52875
$507$	−0.403768	−0.0179319
$508$	−76.9552	−3.41433
$509$	21.2773	0.943100	0.471550	−	0.881839i	$-0.343695\pi$
$509$	21.2773	0.943100	0.471550	+	0.881839i	$0.343695\pi$
$510$	2.71714	0.120317
$511$	−13.4793	−0.596291
$512$	40.4270	1.78664
$513$	16.7131	0.737900
$514$	47.4637	2.09353
$515$	1.41025	0.0621431
$516$	−17.4139	−0.766603
$517$	−36.9991	−1.62722
$518$	−26.4854	−1.16370
$519$	−2.71422	−0.119141
$520$	−11.9284	−0.523096
$521$	−16.0862	−0.704749	−0.352374	−	0.935859i	$-0.614626\pi$
$521$	−16.0862	−0.704749	−0.352374	+	0.935859i	$0.614626\pi$
$522$	−49.5253	−2.16767
$523$	−2.71491	−0.118715	−0.0593574	−	0.998237i	$-0.518905\pi$
$523$	−2.71491	−0.118715	−0.0593574	+	0.998237i	$0.518905\pi$
$524$	−19.6031	−0.856366
$525$	−0.708072	−0.0309028
$526$	−9.74717	−0.424997
$527$	0.360585	0.0157073
$528$	7.14008	0.310732
$529$	35.3518	1.53704
$530$	6.94493	0.301668
$531$	25.6066	1.11123
$532$	68.7998	2.98285
$533$	5.53667	0.239820
$534$	−14.0186	−0.606645
$535$	46.8673	2.02625
$536$	28.5229	1.23200
$537$	1.50495	0.0649432
$538$	−30.7355	−1.32510
$539$	5.09300	0.219371
$540$	−22.7302	−0.978151
$541$	13.6330	0.586129	0.293064	−	0.956093i	$-0.405325\pi$
$541$	13.6330	0.586129	0.293064	+	0.956093i	$0.405325\pi$
$542$	−64.9725	−2.79081
$543$	−1.26296	−0.0541988
$544$	0.335932	0.0144030
$545$	−2.18439	−0.0935688
$546$	−2.38704	−0.102156
$547$	−10.2097	−0.436535	−0.218267	−	0.975889i	$-0.570040\pi$
$547$	−10.2097	−0.436535	−0.218267	+	0.975889i	$0.570040\pi$
$548$	70.2749	3.00199
$549$	−16.3519	−0.697880
$550$	7.56888	0.322738
$551$	−50.4155	−2.14777
$552$	15.3718	0.654269
$553$	−26.6938	−1.13514
$554$	−46.7378	−1.98570
$555$	4.32939	0.183772
$556$	8.88176	0.376671
$557$	41.6497	1.76475	0.882377	−	0.470543i	$-0.155942\pi$
$557$	41.6497	1.76475	0.882377	+	0.470543i	$0.155942\pi$
$558$	−2.19376	−0.0928694
$559$	−10.7028	−0.452679
$560$	−24.0795	−1.01755
$561$	−1.95647	−0.0826021
$562$	−34.3313	−1.44818
$563$	23.8102	1.00348	0.501740	−	0.865019i	$-0.332694\pi$
$563$	23.8102	1.00348	0.501740	+	0.865019i	$0.332694\pi$
$564$	−14.2255	−0.599002
$565$	−18.6572	−0.784913
$566$	16.4403	0.691036
$567$	18.1997	0.764318
$568$	−22.7813	−0.955881
$569$	19.8909	0.833871	0.416935	−	0.908936i	$-0.363104\pi$
$569$	19.8909	0.833871	0.416935	+	0.908936i	$0.363104\pi$
$570$	−16.8279	−0.704845
$571$	10.5123	0.439925	0.219963	−	0.975508i	$-0.429406\pi$
$571$	10.5123	0.439925	0.219963	+	0.975508i	$0.429406\pi$
$572$	17.0526	0.713004
$573$	−4.91492	−0.205324
$574$	32.7323	1.36622
$575$	5.56404	0.232037
$576$	21.6664	0.902765
$577$	−13.2938	−0.553428	−0.276714	−	0.960952i	$-0.589246\pi$
$577$	−13.2938	−0.553428	−0.276714	+	0.960952i	$0.589246\pi$
$578$	38.5246	1.60241
$579$	7.71907	0.320794
$580$	68.5662	2.84706
$581$	−13.0768	−0.542517
$582$	−6.41028	−0.265714
$583$	−5.00067	−0.207107
$584$	27.9031	1.15464
$585$	−6.79002	−0.280733
$586$	−13.7582	−0.568346
$587$	−28.8408	−1.19039	−0.595193	−	0.803583i	$-0.702924\pi$
$587$	−28.8408	−1.19039	−0.595193	+	0.803583i	$0.702924\pi$
$588$	1.95817	0.0807535
$589$	−2.23319	−0.0920171
$590$	−53.0467	−2.18390
$591$	−9.49098	−0.390407
$592$	18.7209	0.769426
$593$	3.73592	0.153416	0.0767079	−	0.997054i	$-0.475559\pi$
$593$	3.73592	0.153416	0.0767079	+	0.997054i	$0.475559\pi$
$594$	24.4899	1.00483
$595$	6.59807	0.270495
$596$	21.8978	0.896968
$597$	1.96764	0.0805300
$598$	18.7574	0.767048
$599$	13.8049	0.564051	0.282026	−	0.959407i	$-0.408994\pi$
$599$	13.8049	0.564051	0.282026	+	0.959407i	$0.408994\pi$
$600$	1.46576	0.0598393
$601$	−0.800403	−0.0326491	−0.0163246	−	0.999867i	$-0.505196\pi$
$601$	−0.800403	−0.0326491	−0.0163246	+	0.999867i	$0.505196\pi$
$602$	−63.2739	−2.57885
$603$	16.2361	0.661184
$604$	0.814595	0.0331454
$605$	−16.5334	−0.672180
$606$	−12.4995	−0.507756
$607$	1.23165	0.0499913	0.0249956	−	0.999688i	$-0.492043\pi$
$607$	1.23165	0.0499913	0.0249956	+	0.999688i	$0.492043\pi$
$608$	−2.08051	−0.0843759
$609$	6.91099	0.280047
$610$	33.8746	1.37154
$611$	−8.74317	−0.353711
$612$	13.0900	0.529133
$613$	45.1299	1.82278	0.911389	−	0.411546i	$-0.135011\pi$
$613$	45.1299	1.82278	0.911389	+	0.411546i	$0.135011\pi$
$614$	−54.0966	−2.18316
$615$	−5.35052	−0.215754
$616$	50.7776	2.04589
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−0.584195	−0.0234998
$619$	15.9094	0.639454	0.319727	−	0.947510i	$-0.396409\pi$
$619$	15.9094	0.639454	0.319727	+	0.947510i	$0.396409\pi$
$620$	3.03719	0.121977
$621$	18.0031	0.722438
$622$	61.8238	2.47891
$623$	−34.0416	−1.36385
$624$	1.68725	0.0675443
$625$	−28.1114	−1.12446
$626$	−33.6682	−1.34565
$627$	12.1169	0.483902
$628$	93.1104	3.71551
$629$	−5.12976	−0.204537
$630$	−40.1421	−1.59930
$631$	−21.8244	−0.868818	−0.434409	−	0.900716i	$-0.643043\pi$
$631$	−21.8244	−0.868818	−0.434409	+	0.900716i	$0.643043\pi$
$632$	55.2581	2.19805
$633$	6.04599	0.240306
$634$	−15.6119	−0.620027
$635$	45.7074	1.81384
$636$	−1.92267	−0.0762387
$637$	1.20351	0.0476849
$638$	−73.8746	−2.92472
$639$	−12.9678	−0.512998
$640$	−46.2885	−1.82972
$641$	30.9283	1.22159	0.610797	−	0.791787i	$-0.290849\pi$
$641$	30.9283	1.22159	0.610797	+	0.791787i	$0.290849\pi$
$642$	−19.4147	−0.766238
$643$	41.9611	1.65478	0.827392	−	0.561624i	$-0.189823\pi$
$643$	41.9611	1.65478	0.827392	+	0.561624i	$0.189823\pi$
$644$	74.1100	2.92034
$645$	10.3429	0.407253
$646$	19.9389	0.784486
$647$	23.4538	0.922063	0.461031	−	0.887384i	$-0.347480\pi$
$647$	23.4538	0.922063	0.461031	+	0.887384i	$0.347480\pi$
$648$	−37.6747	−1.48000
$649$	38.1961	1.49933
$650$	1.78858	0.0701540
$651$	0.306128	0.0119981
$652$	−14.2163	−0.556755
$653$	−7.95515	−0.311309	−0.155655	−	0.987812i	$-0.549749\pi$
$653$	−7.95515	−0.311309	−0.155655	+	0.987812i	$0.549749\pi$
$654$	0.904879	0.0353836
$655$	11.6432	0.454939
$656$	−23.1365	−0.903328
$657$	15.8833	0.619667
$658$	−51.6889	−2.01504
$659$	−22.4890	−0.876047	−0.438023	−	0.898964i	$-0.644321\pi$
$659$	−22.4890	−0.876047	−0.438023	+	0.898964i	$0.644321\pi$
$660$	−16.4793	−0.641454
$661$	40.2155	1.56420	0.782102	−	0.623151i	$-0.214148\pi$
$661$	40.2155	1.56420	0.782102	+	0.623151i	$0.214148\pi$
$662$	−40.1687	−1.56120
$663$	−0.462328	−0.0179553
$664$	27.0698	1.05051
$665$	−40.8635	−1.58462
$666$	31.2090	1.20932
$667$	−54.3067	−2.10276
$668$	18.7011	0.723566
$669$	6.42740	0.248497
$670$	−33.6348	−1.29942
$671$	−24.3913	−0.941615
$672$	0.285198	0.0110018
$673$	−30.5426	−1.17733	−0.588664	−	0.808377i	$-0.700346\pi$
$673$	−30.5426	−1.17733	−0.588664	+	0.808377i	$0.700346\pi$
$674$	84.0035	3.23569
$675$	1.71665	0.0660740
$676$	4.02965	0.154987
$677$	−33.4114	−1.28410	−0.642052	−	0.766661i	$-0.721917\pi$
$677$	−33.4114	−1.28410	−0.642052	+	0.766661i	$0.721917\pi$
$678$	7.72871	0.296819
$679$	−15.5662	−0.597374
$680$	−13.6585	−0.523778
$681$	8.68599	0.332848
$682$	−3.27233	−0.125304
$683$	−36.5640	−1.39908	−0.699541	−	0.714593i	$-0.746612\pi$
$683$	−36.5640	−1.39908	−0.699541	+	0.714593i	$0.746612\pi$
$684$	−81.0699	−3.09979
$685$	−41.7397	−1.59479
$686$	48.4985	1.85168
$687$	−4.39194	−0.167563
$688$	44.7245	1.70511
$689$	−1.18170	−0.0450190
$690$	−18.1268	−0.690075
$691$	−15.3845	−0.585254	−0.292627	−	0.956227i	$-0.594529\pi$
$691$	−15.3845	−0.585254	−0.292627	+	0.956227i	$0.594529\pi$
$692$	27.0882	1.02974
$693$	28.9041	1.09798
$694$	−69.0576	−2.62139
$695$	−5.27531	−0.200104
$696$	−14.3062	−0.542276
$697$	6.33967	0.240132
$698$	60.1851	2.27804
$699$	3.92383	0.148413
$700$	7.06664	0.267094
$701$	13.8074	0.521497	0.260748	−	0.965407i	$-0.416031\pi$
$701$	13.8074	0.521497	0.260748	+	0.965407i	$0.416031\pi$
$702$	5.78716	0.218422
$703$	31.7699	1.19822
$704$	32.3187	1.21806
$705$	8.44922	0.318216
$706$	−25.3611	−0.954478
$707$	−30.3526	−1.14153
$708$	14.6857	0.551923
$709$	20.3177	0.763049	0.381525	−	0.924359i	$-0.375399\pi$
$709$	20.3177	0.763049	0.381525	+	0.924359i	$0.375399\pi$
$710$	26.8641	1.00819
$711$	31.4546	1.17964
$712$	70.4684	2.64092
$713$	−2.40556	−0.0900889
$714$	−2.73324	−0.102289
$715$	−10.1284	−0.378779
$716$	−15.0195	−0.561307
$717$	−7.18677	−0.268395
$718$	−25.8532	−0.964832
$719$	43.2167	1.61171	0.805855	−	0.592113i	$-0.201706\pi$
$719$	43.2167	1.61171	0.805855	+	0.592113i	$0.201706\pi$
$720$	28.3740	1.05744
$721$	−1.41861	−0.0528317
$722$	−76.8317	−2.85938
$723$	−6.54465	−0.243398
$724$	12.6045	0.468443
$725$	−5.17833	−0.192318
$726$	6.84896	0.254189
$727$	−37.9514	−1.40754	−0.703769	−	0.710429i	$-0.748501\pi$
$727$	−37.9514	−1.40754	−0.703769	+	0.710429i	$0.748501\pi$
$728$	11.9991	0.444717
$729$	−18.5908	−0.688549
$730$	−32.9040	−1.21783
$731$	−12.2550	−0.453269
$732$	−9.37802	−0.346621
$733$	1.31164	0.0484467	0.0242233	−	0.999707i	$-0.492289\pi$
$733$	1.31164	0.0484467	0.0242233	+	0.999707i	$0.492289\pi$
$734$	−16.5504	−0.610885
$735$	−1.16305	−0.0428998
$736$	−2.24110	−0.0826079
$737$	24.2186	0.892103
$738$	−38.5700	−1.41978
$739$	9.08880	0.334337	0.167169	−	0.985928i	$-0.446538\pi$
$739$	9.08880	0.334337	0.167169	+	0.985928i	$0.446538\pi$
$740$	−43.2078	−1.58835
$741$	2.86331	0.105186
$742$	−6.98609	−0.256467
$743$	51.4375	1.88706	0.943529	−	0.331291i	$-0.107484\pi$
$743$	51.4375	1.88706	0.943529	+	0.331291i	$0.107484\pi$
$744$	−0.633705	−0.0232328
$745$	−13.0062	−0.476509
$746$	49.2950	1.80482
$747$	15.4090	0.563785
$748$	19.5258	0.713933
$749$	−47.1450	−1.72264
$750$	10.1364	0.370130
$751$	−24.5759	−0.896788	−0.448394	−	0.893836i	$-0.648004\pi$
$751$	−24.5759	−0.896788	−0.448394	+	0.893836i	$0.648004\pi$
$752$	36.5357	1.33232
$753$	6.27449	0.228655
$754$	−17.4571	−0.635751
$755$	−0.483828	−0.0176083
$756$	22.8649	0.831587
$757$	−16.6562	−0.605379	−0.302690	−	0.953089i	$-0.597885\pi$
$757$	−16.6562	−0.605379	−0.302690	+	0.953089i	$0.597885\pi$
$758$	0.685209	0.0248879
$759$	13.0521	0.473762
$760$	84.5903	3.06841
$761$	−18.3110	−0.663774	−0.331887	−	0.943319i	$-0.607685\pi$
$761$	−18.3110	−0.663774	−0.331887	+	0.943319i	$0.607685\pi$
$762$	−18.9342	−0.685915
$763$	2.19733	0.0795487
$764$	49.0515	1.77462
$765$	−7.77481	−0.281099
$766$	12.1009	0.437224
$767$	9.02602	0.325911
$768$	13.0077	0.469375
$769$	43.3982	1.56498	0.782489	−	0.622665i	$-0.213950\pi$
$769$	43.3982	1.56498	0.782489	+	0.622665i	$0.213950\pi$
$770$	−59.8780	−2.15785
$771$	7.80453	0.281073
$772$	−77.0372	−2.77263
$773$	42.5648	1.53095	0.765475	−	0.643465i	$-0.222504\pi$
$773$	42.5648	1.53095	0.765475	+	0.643465i	$0.222504\pi$
$774$	74.5585	2.67995
$775$	−0.229378	−0.00823951
$776$	32.2230	1.15674
$777$	−4.35504	−0.156236
$778$	67.1079	2.40594
$779$	−39.2632	−1.40675
$780$	−3.89417	−0.139434
$781$	−19.3434	−0.692162
$782$	21.4779	0.768048
$783$	−16.7550	−0.598776
$784$	−5.02921	−0.179615
$785$	−55.3028	−1.97384
$786$	−4.82320	−0.172038
$787$	−10.0284	−0.357472	−0.178736	−	0.983897i	$-0.557201\pi$
$787$	−10.0284	−0.357472	−0.178736	+	0.983897i	$0.557201\pi$
$788$	94.7211	3.37430
$789$	−1.60274	−0.0570591
$790$	−65.1615	−2.31834
$791$	18.7677	0.667304
$792$	−59.8335	−2.12609
$793$	−5.76384	−0.204680
$794$	−35.8603	−1.27264
$795$	1.14197	0.0405014
$796$	−19.6372	−0.696024
$797$	−4.15142	−0.147051	−0.0735255	−	0.997293i	$-0.523425\pi$
$797$	−4.15142	−0.147051	−0.0735255	+	0.997293i	$0.523425\pi$
$798$	16.9277	0.599233
$799$	−10.0112	−0.354172
$800$	−0.213696	−0.00755529
$801$	40.1127	1.41731
$802$	23.2156	0.819771
$803$	23.6924	0.836086
$804$	9.31161	0.328395
$805$	−44.0175	−1.55141
$806$	−0.773277	−0.0272375
$807$	−5.05390	−0.177906
$808$	62.8320	2.21042
$809$	−8.39093	−0.295009	−0.147505	−	0.989061i	$-0.547124\pi$
$809$	−8.39093	−0.295009	−0.147505	+	0.989061i	$0.547124\pi$
$810$	44.4268	1.56100
$811$	41.3011	1.45028	0.725139	−	0.688603i	$-0.241775\pi$
$811$	41.3011	1.45028	0.725139	+	0.688603i	$0.241775\pi$
$812$	−68.9725	−2.42046
$813$	−10.6835	−0.374688
$814$	46.5529	1.63168
$815$	8.44378	0.295773
$816$	1.93196	0.0676323
$817$	75.8986	2.65536
$818$	−43.8421	−1.53290
$819$	6.83026	0.238669
$820$	53.3988	1.86477
$821$	49.8322	1.73916	0.869579	−	0.493795i	$-0.164391\pi$
$821$	49.8322	1.73916	0.869579	+	0.493795i	$0.164391\pi$
$822$	17.2906	0.603079
$823$	44.1764	1.53989	0.769946	−	0.638109i	$-0.220283\pi$
$823$	44.1764	1.53989	0.769946	+	0.638109i	$0.220283\pi$
$824$	2.93662	0.102302
$825$	1.24456	0.0433302
$826$	53.3611	1.85667
$827$	−0.332211	−0.0115521	−0.00577605	−	0.999983i	$-0.501839\pi$
$827$	−0.332211	−0.0115521	−0.00577605	+	0.999983i	$0.501839\pi$
$828$	−87.3272	−3.03483
$829$	−4.61356	−0.160235	−0.0801177	−	0.996785i	$-0.525530\pi$
$829$	−4.61356	−0.160235	−0.0801177	+	0.996785i	$0.525530\pi$
$830$	−31.9213	−1.10801
$831$	−7.68518	−0.266596
$832$	7.63715	0.264770
$833$	1.37806	0.0477471
$834$	2.18529	0.0756704
$835$	−11.1075	−0.384390
$836$	−120.928	−4.18239
$837$	−0.742178	−0.0256534
$838$	−95.2753	−3.29123
$839$	−35.9053	−1.23959	−0.619794	−	0.784765i	$-0.712784\pi$
$839$	−35.9053	−1.23959	−0.619794	+	0.784765i	$0.712784\pi$
$840$	−11.5957	−0.400090
$841$	21.5421	0.742829
$842$	34.5614	1.19106
$843$	−5.64515	−0.194429
$844$	−60.3397	−2.07698
$845$	−2.39341	−0.0823356
$846$	60.9074	2.09404
$847$	16.6314	0.571463
$848$	4.93804	0.169573
$849$	2.70330	0.0927771
$850$	2.04799	0.0702454
$851$	34.2220	1.17312
$852$	−7.43720	−0.254794
$853$	10.1492	0.347502	0.173751	−	0.984790i	$-0.444411\pi$
$853$	10.1492	0.347502	0.173751	+	0.984790i	$0.444411\pi$
$854$	−34.0754	−1.16604
$855$	48.1514	1.64674
$856$	97.5935	3.33568
$857$	36.0231	1.23052	0.615262	−	0.788322i	$-0.289050\pi$
$857$	36.0231	1.23052	0.615262	+	0.788322i	$0.289050\pi$
$858$	4.19566	0.143237
$859$	−10.5117	−0.358655	−0.179327	−	0.983789i	$-0.557392\pi$
$859$	−10.5117	−0.358655	−0.179327	+	0.983789i	$0.557392\pi$
$860$	−103.224	−3.51990
$861$	5.38223	0.183426
$862$	12.0888	0.411745
$863$	20.4104	0.694777	0.347389	−	0.937721i	$-0.387068\pi$
$863$	20.4104	0.694777	0.347389	+	0.937721i	$0.387068\pi$
$864$	−0.691436	−0.0235231
$865$	−16.0890	−0.547043
$866$	42.4995	1.44419
$867$	6.33467	0.215137
$868$	−3.05519	−0.103700
$869$	46.9193	1.59163
$870$	16.8702	0.571953
$871$	5.72303	0.193918
$872$	−4.54863	−0.154036
$873$	18.3423	0.620793
$874$	−133.018	−4.49940
$875$	24.6145	0.832121
$876$	9.10929	0.307775
$877$	40.6149	1.37147	0.685734	−	0.727852i	$-0.259481\pi$
$877$	40.6149	1.37147	0.685734	+	0.727852i	$0.259481\pi$
$878$	51.4001	1.73467
$879$	−2.26228	−0.0763050
$880$	42.3241	1.42675
$881$	8.58271	0.289159	0.144579	−	0.989493i	$-0.453817\pi$
$881$	8.58271	0.289159	0.144579	+	0.989493i	$0.453817\pi$
$882$	−8.38401	−0.282304
$883$	26.1720	0.880757	0.440379	−	0.897812i	$-0.354844\pi$
$883$	26.1720	0.880757	0.440379	+	0.897812i	$0.354844\pi$
$884$	4.61409	0.155188
$885$	−8.72256	−0.293206
$886$	−12.0186	−0.403773
$887$	−2.15068	−0.0722128	−0.0361064	−	0.999348i	$-0.511496\pi$
$887$	−2.15068	−0.0722128	−0.0361064	+	0.999348i	$0.511496\pi$
$888$	9.01524	0.302532
$889$	−45.9783	−1.54206
$890$	−83.0978	−2.78545
$891$	−31.9894	−1.07168
$892$	−64.1462	−2.14777
$893$	62.0021	2.07482
$894$	5.38779	0.180195
$895$	8.92084	0.298191
$896$	46.5629	1.55556
$897$	3.08431	0.102982
$898$	0.609108	0.0203262
$899$	2.23880	0.0746681
$900$	−8.32694	−0.277565
$901$	−1.35308	−0.0450777
$902$	−57.5330	−1.91564
$903$	−10.4042	−0.346231
$904$	−38.8505	−1.29215
$905$	−7.48643	−0.248857
$906$	0.200425	0.00665868
$907$	2.45325	0.0814589	0.0407294	−	0.999170i	$-0.487032\pi$
$907$	2.45325	0.0814589	0.0407294	+	0.999170i	$0.487032\pi$
$908$	−86.6872	−2.87682
$909$	35.7659	1.18628
$910$	−14.1496	−0.469055
$911$	−44.3650	−1.46988	−0.734939	−	0.678134i	$-0.762789\pi$
$911$	−44.3650	−1.46988	−0.734939	+	0.678134i	$0.762789\pi$
$912$	−11.9651	−0.396206
$913$	22.9848	0.760687
$914$	56.3016	1.86229
$915$	5.57006	0.184141
$916$	43.8321	1.44825
$917$	−11.7122	−0.386772
$918$	6.62649	0.218707
$919$	17.8811	0.589842	0.294921	−	0.955522i	$-0.404707\pi$
$919$	17.8811	0.589842	0.294921	+	0.955522i	$0.404707\pi$
$920$	91.1193	3.00412
$921$	−8.89520	−0.293107
$922$	88.8755	2.92696
$923$	−4.57099	−0.150456
$924$	16.5769	0.545341
$925$	3.26319	0.107293
$926$	−97.2500	−3.19583
$927$	1.67161	0.0549029
$928$	2.08574	0.0684677
$929$	46.8382	1.53671	0.768356	−	0.640023i	$-0.221075\pi$
$929$	46.8382	1.53671	0.768356	+	0.640023i	$0.221075\pi$
$930$	0.747279	0.0245042
$931$	−8.53470	−0.279714
$932$	−39.1603	−1.28274
$933$	10.1658	0.332813
$934$	−19.5537	−0.639816
$935$	−11.5973	−0.379272
$936$	−14.1391	−0.462151
$937$	−21.8014	−0.712219	−0.356110	−	0.934444i	$-0.615897\pi$
$937$	−21.8014	−0.712219	−0.356110	+	0.934444i	$0.615897\pi$
$938$	33.8341	1.10472
$939$	−5.53612	−0.180664
$940$	−84.3242	−2.75035
$941$	46.3847	1.51210	0.756050	−	0.654514i	$-0.227127\pi$
$941$	46.3847	1.51210	0.756050	+	0.654514i	$0.227127\pi$
$942$	22.9091	0.746420
$943$	−42.2937	−1.37727
$944$	−37.7177	−1.22761
$945$	−13.5806	−0.441776
$946$	111.215	3.61592
$947$	32.6098	1.05968	0.529838	−	0.848099i	$-0.322253\pi$
$947$	32.6098	1.05968	0.529838	+	0.848099i	$0.322253\pi$
$948$	18.0396	0.585900
$949$	5.59868	0.181741
$950$	−12.6837	−0.411514
$951$	−2.56709	−0.0832436
$952$	13.7394	0.445297
$953$	11.9928	0.388485	0.194243	−	0.980954i	$-0.437775\pi$
$953$	11.9928	0.388485	0.194243	+	0.980954i	$0.437775\pi$
$954$	8.23202	0.266522
$955$	−29.1341	−0.942756
$956$	71.7248	2.31975
$957$	−12.1473	−0.392667
$958$	45.6391	1.47453
$959$	41.9870	1.35583
$960$	−7.38038	−0.238201
$961$	−30.9008	−0.996801
$962$	11.0008	0.354680
$963$	55.5531	1.79017
$964$	65.3164	2.10370
$965$	45.7562	1.47294
$966$	18.2342	0.586676
$967$	24.5220	0.788574	0.394287	−	0.918987i	$-0.370992\pi$
$967$	24.5220	0.788574	0.394287	+	0.918987i	$0.370992\pi$
$968$	−34.4282	−1.10656
$969$	3.27859	0.105324
$970$	−37.9981	−1.22004
$971$	36.0103	1.15563	0.577813	−	0.816169i	$-0.303906\pi$
$971$	36.0103	1.15563	0.577813	+	0.816169i	$0.303906\pi$
$972$	−40.7903	−1.30835
$973$	5.30657	0.170121
$974$	−60.1829	−1.92838
$975$	0.294100	0.00941873
$976$	24.0858	0.770968
$977$	−38.5172	−1.23228	−0.616138	−	0.787638i	$-0.711304\pi$
$977$	−38.5172	−1.23228	−0.616138	+	0.787638i	$0.711304\pi$
$978$	−3.49782	−0.111848
$979$	59.8343	1.91231
$980$	11.6074	0.370784
$981$	−2.58921	−0.0826673
$982$	41.6749	1.32990
$983$	37.3994	1.19285	0.596427	−	0.802667i	$-0.296586\pi$
$983$	37.3994	1.19285	0.596427	+	0.802667i	$0.296586\pi$
$984$	−11.1416	−0.355181
$985$	−56.2595	−1.79258
$986$	−19.9890	−0.636579
$987$	−8.49929	−0.270535
$988$	−28.5762	−0.909130
$989$	81.7567	2.59971
$990$	70.5570	2.24245
$991$	8.42885	0.267751	0.133876	−	0.990998i	$-0.457258\pi$
$991$	8.42885	0.267751	0.133876	+	0.990998i	$0.457258\pi$
$992$	0.0923893	0.00293336
$993$	−6.60501	−0.209604
$994$	−27.0233	−0.857129
$995$	11.6635	0.369758
$996$	8.83726	0.280019
$997$	4.46918	0.141540	0.0707702	−	0.997493i	$-0.477454\pi$
$997$	4.46918	0.141540	0.0707702	+	0.997493i	$0.477454\pi$
$998$	−81.5261	−2.58066
$999$	10.5584	0.334053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.15	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.45553 q^{2} -0.403768 q^{3} +4.02965 q^{4} -2.39341 q^{5} +0.991465 q^{6} +2.40759 q^{7} -4.98387 q^{8} -2.83697 q^{9} +O(q^{10})\)	\(q-2.45553 q^{2} -0.403768 q^{3} +4.02965 q^{4} -2.39341 q^{5} +0.991465 q^{6} +2.40759 q^{7} -4.98387 q^{8} -2.83697 q^{9} +5.87709 q^{10} -4.23177 q^{11} -1.62704 q^{12} -1.00000 q^{13} -5.91192 q^{14} +0.966380 q^{15} +4.17878 q^{16} -1.14503 q^{17} +6.96628 q^{18} +7.09149 q^{19} -9.64458 q^{20} -0.972107 q^{21} +10.3913 q^{22} +7.63884 q^{23} +2.01233 q^{24} +0.728389 q^{25} +2.45553 q^{26} +2.35678 q^{27} +9.70174 q^{28} -7.10929 q^{29} -2.37298 q^{30} -0.314912 q^{31} -0.293382 q^{32} +1.70865 q^{33} +2.81167 q^{34} -5.76234 q^{35} -11.4320 q^{36} +4.48001 q^{37} -17.4134 q^{38} +0.403768 q^{39} +11.9284 q^{40} -5.53667 q^{41} +2.38704 q^{42} +10.7028 q^{43} -17.0526 q^{44} +6.79002 q^{45} -18.7574 q^{46} +8.74317 q^{47} -1.68725 q^{48} -1.20351 q^{49} -1.78858 q^{50} +0.462328 q^{51} -4.02965 q^{52} +1.18170 q^{53} -5.78716 q^{54} +10.1284 q^{55} -11.9991 q^{56} -2.86331 q^{57} +17.4571 q^{58} -9.02602 q^{59} +3.89417 q^{60} +5.76384 q^{61} +0.773277 q^{62} -6.83026 q^{63} -7.63715 q^{64} +2.39341 q^{65} -4.19566 q^{66} -5.72303 q^{67} -4.61409 q^{68} -3.08431 q^{69} +14.1496 q^{70} +4.57099 q^{71} +14.1391 q^{72} -5.59868 q^{73} -11.0008 q^{74} -0.294100 q^{75} +28.5762 q^{76} -10.1884 q^{77} -0.991465 q^{78} -11.0874 q^{79} -10.0015 q^{80} +7.55932 q^{81} +13.5955 q^{82} -5.43149 q^{83} -3.91725 q^{84} +2.74053 q^{85} -26.2810 q^{86} +2.87050 q^{87} +21.0906 q^{88} -14.1393 q^{89} -16.6731 q^{90} -2.40759 q^{91} +30.7818 q^{92} +0.127151 q^{93} -21.4691 q^{94} -16.9728 q^{95} +0.118458 q^{96} -6.46546 q^{97} +2.95527 q^{98} +12.0054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 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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