LMFDB - Embedded newform 8021.2.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.33994 q^{2} -2.01648 q^{3} +3.47532 q^{4} +0.773021 q^{5} +4.71844 q^{6} -3.51939 q^{7} -3.45216 q^{8} +1.06619 q^{9} +O(q^{10})$	\(q-2.33994 q^{2} -2.01648 q^{3} +3.47532 q^{4} +0.773021 q^{5} +4.71844 q^{6} -3.51939 q^{7} -3.45216 q^{8} +1.06619 q^{9} -1.80882 q^{10} +4.07019 q^{11} -7.00791 q^{12} -1.00000 q^{13} +8.23517 q^{14} -1.55878 q^{15} +1.12720 q^{16} -0.0237100 q^{17} -2.49481 q^{18} -3.75986 q^{19} +2.68649 q^{20} +7.09679 q^{21} -9.52400 q^{22} +7.10815 q^{23} +6.96120 q^{24} -4.40244 q^{25} +2.33994 q^{26} +3.89949 q^{27} -12.2310 q^{28} +0.159300 q^{29} +3.64745 q^{30} +0.413557 q^{31} +4.26673 q^{32} -8.20745 q^{33} +0.0554801 q^{34} -2.72057 q^{35} +3.70534 q^{36} -1.36145 q^{37} +8.79784 q^{38} +2.01648 q^{39} -2.66859 q^{40} +10.8236 q^{41} -16.6061 q^{42} -10.0071 q^{43} +14.1452 q^{44} +0.824185 q^{45} -16.6327 q^{46} -0.619987 q^{47} -2.27298 q^{48} +5.38614 q^{49} +10.3014 q^{50} +0.0478108 q^{51} -3.47532 q^{52} -2.77125 q^{53} -9.12458 q^{54} +3.14634 q^{55} +12.1495 q^{56} +7.58167 q^{57} -0.372752 q^{58} -9.59792 q^{59} -5.41726 q^{60} +12.9828 q^{61} -0.967698 q^{62} -3.75233 q^{63} -12.2383 q^{64} -0.773021 q^{65} +19.2049 q^{66} -2.12362 q^{67} -0.0823999 q^{68} -14.3334 q^{69} +6.36596 q^{70} +15.4110 q^{71} -3.68064 q^{72} -7.68787 q^{73} +3.18571 q^{74} +8.87742 q^{75} -13.0667 q^{76} -14.3246 q^{77} -4.71844 q^{78} +5.47417 q^{79} +0.871350 q^{80} -11.0618 q^{81} -25.3265 q^{82} +8.64506 q^{83} +24.6636 q^{84} -0.0183284 q^{85} +23.4160 q^{86} -0.321225 q^{87} -14.0509 q^{88} -8.31238 q^{89} -1.92854 q^{90} +3.51939 q^{91} +24.7031 q^{92} -0.833929 q^{93} +1.45073 q^{94} -2.90645 q^{95} -8.60377 q^{96} -7.64103 q^{97} -12.6032 q^{98} +4.33958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.33994	−1.65459	−0.827294	−	0.561770i	$-0.810121\pi$
$2$	−2.33994	−1.65459	−0.827294	+	0.561770i	$0.810121\pi$
$3$	−2.01648	−1.16421	−0.582107	−	0.813112i	$-0.697772\pi$
$3$	−2.01648	−1.16421	−0.582107	+	0.813112i	$0.697772\pi$
$4$	3.47532	1.73766
$5$	0.773021	0.345706	0.172853	−	0.984948i	$-0.444702\pi$
$5$	0.773021	0.345706	0.172853	+	0.984948i	$0.444702\pi$
$6$	4.71844	1.92629
$7$	−3.51939	−1.33021	−0.665103	−	0.746752i	$-0.731612\pi$
$7$	−3.51939	−1.33021	−0.665103	+	0.746752i	$0.731612\pi$
$8$	−3.45216	−1.22052
$9$	1.06619	0.355396
$10$	−1.80882	−0.572000
$11$	4.07019	1.22721	0.613604	−	0.789614i	$-0.289719\pi$
$11$	4.07019	1.22721	0.613604	+	0.789614i	$0.289719\pi$
$12$	−7.00791	−2.02301
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	8.23517	2.20094
$15$	−1.55878	−0.402476
$16$	1.12720	0.281800
$17$	−0.0237100	−0.00575053	−0.00287527	−	0.999996i	$-0.500915\pi$
$17$	−0.0237100	−0.00575053	−0.00287527	+	0.999996i	$0.500915\pi$
$18$	−2.49481	−0.588033
$19$	−3.75986	−0.862570	−0.431285	−	0.902216i	$-0.641940\pi$
$19$	−3.75986	−0.862570	−0.431285	+	0.902216i	$0.641940\pi$
$20$	2.68649	0.600718
$21$	7.09679	1.54865
$22$	−9.52400	−2.03052
$23$	7.10815	1.48215	0.741076	−	0.671421i	$-0.234316\pi$
$23$	7.10815	1.48215	0.741076	+	0.671421i	$0.234316\pi$
$24$	6.96120	1.42095
$25$	−4.40244	−0.880488
$26$	2.33994	0.458900
$27$	3.89949	0.750458
$28$	−12.2310	−2.31145
$29$	0.159300	0.0295812	0.0147906	−	0.999891i	$-0.495292\pi$
$29$	0.159300	0.0295812	0.0147906	+	0.999891i	$0.495292\pi$
$30$	3.64745	0.665931
$31$	0.413557	0.0742770	0.0371385	−	0.999310i	$-0.488176\pi$
$31$	0.413557	0.0742770	0.0371385	+	0.999310i	$0.488176\pi$
$32$	4.26673	0.754259
$33$	−8.20745	−1.42873
$34$	0.0554801	0.00951475
$35$	−2.72057	−0.459860
$36$	3.70534	0.617557
$37$	−1.36145	−0.223821	−0.111911	−	0.993718i	$-0.535697\pi$
$37$	−1.36145	−0.223821	−0.111911	+	0.993718i	$0.535697\pi$
$38$	8.79784	1.42720
$39$	2.01648	0.322895
$40$	−2.66859	−0.421941
$41$	10.8236	1.69036	0.845180	−	0.534482i	$-0.179493\pi$
$41$	10.8236	1.69036	0.845180	+	0.534482i	$0.179493\pi$
$42$	−16.6061	−2.56237
$43$	−10.0071	−1.52607	−0.763034	−	0.646359i	$-0.776291\pi$
$43$	−10.0071	−1.52607	−0.763034	+	0.646359i	$0.776291\pi$
$44$	14.1452	2.13247
$45$	0.824185	0.122862
$46$	−16.6327	−2.45235
$47$	−0.619987	−0.0904345	−0.0452172	−	0.998977i	$-0.514398\pi$
$47$	−0.619987	−0.0904345	−0.0452172	+	0.998977i	$0.514398\pi$
$48$	−2.27298	−0.328076
$49$	5.38614	0.769449
$50$	10.3014	1.45684
$51$	0.0478108	0.00669485
$52$	−3.47532	−0.481940
$53$	−2.77125	−0.380661	−0.190330	−	0.981720i	$-0.560956\pi$
$53$	−2.77125	−0.380661	−0.190330	+	0.981720i	$0.560956\pi$
$54$	−9.12458	−1.24170
$55$	3.14634	0.424253
$56$	12.1495	1.62355
$57$	7.58167	1.00422
$58$	−0.372752	−0.0489447
$59$	−9.59792	−1.24954	−0.624771	−	0.780808i	$-0.714808\pi$
$59$	−9.59792	−1.24954	−0.624771	+	0.780808i	$0.714808\pi$
$60$	−5.41726	−0.699365
$61$	12.9828	1.66227	0.831136	−	0.556070i	$-0.187691\pi$
$61$	12.9828	1.66227	0.831136	+	0.556070i	$0.187691\pi$
$62$	−0.967698	−0.122898
$63$	−3.75233	−0.472750
$64$	−12.2383	−1.52979
$65$	−0.773021	−0.0958815
$66$	19.2049	2.36396
$67$	−2.12362	−0.259442	−0.129721	−	0.991551i	$-0.541408\pi$
$67$	−2.12362	−0.259442	−0.129721	+	0.991551i	$0.541408\pi$
$68$	−0.0823999	−0.00999246
$69$	−14.3334	−1.72554
$70$	6.36596	0.760878
$71$	15.4110	1.82895	0.914473	−	0.404647i	$-0.132605\pi$
$71$	15.4110	1.82895	0.914473	+	0.404647i	$0.132605\pi$
$72$	−3.68064	−0.433768
$73$	−7.68787	−0.899797	−0.449898	−	0.893080i	$-0.648540\pi$
$73$	−7.68787	−0.899797	−0.449898	+	0.893080i	$0.648540\pi$
$74$	3.18571	0.370332
$75$	8.87742	1.02508
$76$	−13.0667	−1.49885
$77$	−14.3246	−1.63244
$78$	−4.71844	−0.534258
$79$	5.47417	0.615892	0.307946	−	0.951404i	$-0.400358\pi$
$79$	5.47417	0.615892	0.307946	+	0.951404i	$0.400358\pi$
$80$	0.871350	0.0974199
$81$	−11.0618	−1.22909
$82$	−25.3265	−2.79685
$83$	8.64506	0.948919	0.474460	−	0.880277i	$-0.342644\pi$
$83$	8.64506	0.948919	0.474460	+	0.880277i	$0.342644\pi$
$84$	24.6636	2.69102
$85$	−0.0183284	−0.00198799
$86$	23.4160	2.52501
$87$	−0.321225	−0.0344389
$88$	−14.0509	−1.49783
$89$	−8.31238	−0.881110	−0.440555	−	0.897726i	$-0.645218\pi$
$89$	−8.31238	−0.881110	−0.440555	+	0.897726i	$0.645218\pi$
$90$	−1.92854	−0.203286
$91$	3.51939	0.368933
$92$	24.7031	2.57548
$93$	−0.833929	−0.0864744
$94$	1.45073	0.149632
$95$	−2.90645	−0.298195
$96$	−8.60377	−0.878119
$97$	−7.64103	−0.775829	−0.387915	−	0.921695i	$-0.626804\pi$
$97$	−7.64103	−0.775829	−0.387915	+	0.921695i	$0.626804\pi$
$98$	−12.6032	−1.27312
$99$	4.33958	0.436144
$100$	−15.2999	−1.52999
$101$	18.3082	1.82173	0.910865	−	0.412704i	$-0.135416\pi$
$101$	18.3082	1.82173	0.910865	+	0.412704i	$0.135416\pi$
$102$	−0.111874	−0.0110772
$103$	−3.77079	−0.371547	−0.185774	−	0.982593i	$-0.559479\pi$
$103$	−3.77079	−0.371547	−0.185774	+	0.982593i	$0.559479\pi$
$104$	3.45216	0.338512
$105$	5.48597	0.535375
$106$	6.48456	0.629837
$107$	1.29100	0.124806	0.0624028	−	0.998051i	$-0.480124\pi$
$107$	1.29100	0.124806	0.0624028	+	0.998051i	$0.480124\pi$
$108$	13.5520	1.30404
$109$	−12.4373	−1.19128	−0.595640	−	0.803252i	$-0.703101\pi$
$109$	−12.4373	−1.19128	−0.595640	+	0.803252i	$0.703101\pi$
$110$	−7.36225	−0.701963
$111$	2.74534	0.260576
$112$	−3.96706	−0.374852
$113$	1.67741	0.157798	0.0788990	−	0.996883i	$-0.474860\pi$
$113$	1.67741	0.157798	0.0788990	+	0.996883i	$0.474860\pi$
$114$	−17.7406	−1.66156
$115$	5.49475	0.512389
$116$	0.553617	0.0514021
$117$	−1.06619	−0.0985690
$118$	22.4586	2.06748
$119$	0.0834450	0.00764939
$120$	5.38115	0.491230
$121$	5.56643	0.506039
$122$	−30.3789	−2.75037
$123$	−21.8255	−1.96794
$124$	1.43724	0.129068
$125$	−7.26828	−0.650095
$126$	8.78023	0.782205
$127$	−8.00984	−0.710759	−0.355379	−	0.934722i	$-0.615648\pi$
$127$	−8.00984	−0.710759	−0.355379	+	0.934722i	$0.615648\pi$
$128$	20.1034	1.77691
$129$	20.1791	1.77667
$130$	1.80882	0.158644
$131$	−8.34222	−0.728863	−0.364432	−	0.931230i	$-0.618737\pi$
$131$	−8.34222	−0.728863	−0.364432	+	0.931230i	$0.618737\pi$
$132$	−28.5235	−2.48265
$133$	13.2324	1.14740
$134$	4.96914	0.429269
$135$	3.01439	0.259437
$136$	0.0818508	0.00701864
$137$	−3.67926	−0.314340	−0.157170	−	0.987572i	$-0.550237\pi$
$137$	−3.67926	−0.314340	−0.157170	+	0.987572i	$0.550237\pi$
$138$	33.5394	2.85506
$139$	−2.19813	−0.186443	−0.0932215	−	0.995645i	$-0.529716\pi$
$139$	−2.19813	−0.186443	−0.0932215	+	0.995645i	$0.529716\pi$
$140$	−9.45484	−0.799080
$141$	1.25019	0.105285
$142$	−36.0608	−3.02615
$143$	−4.07019	−0.340366
$144$	1.20181	0.100151
$145$	0.123142	0.0102264
$146$	17.9891	1.48879
$147$	−10.8610	−0.895803
$148$	−4.73148	−0.388925
$149$	20.5040	1.67975	0.839876	−	0.542778i	$-0.182627\pi$
$149$	20.5040	1.67975	0.839876	+	0.542778i	$0.182627\pi$
$150$	−20.7726	−1.69608
$151$	4.56521	0.371512	0.185756	−	0.982596i	$-0.440527\pi$
$151$	4.56521	0.371512	0.185756	+	0.982596i	$0.440527\pi$
$152$	12.9796	1.05279
$153$	−0.0252793	−0.00204371
$154$	33.5187	2.70101
$155$	0.319688	0.0256780
$156$	7.00791	0.561082
$157$	−13.7044	−1.09373	−0.546864	−	0.837222i	$-0.684178\pi$
$157$	−13.7044	−1.09373	−0.546864	+	0.837222i	$0.684178\pi$
$158$	−12.8092	−1.01905
$159$	5.58817	0.443171
$160$	3.29827	0.260751
$161$	−25.0164	−1.97157
$162$	25.8840	2.03364
$163$	20.6675	1.61880	0.809401	−	0.587256i	$-0.199792\pi$
$163$	20.6675	1.61880	0.809401	+	0.587256i	$0.199792\pi$
$164$	37.6154	2.93727
$165$	−6.34453	−0.493921
$166$	−20.2289	−1.57007
$167$	−23.4920	−1.81787	−0.908933	−	0.416942i	$-0.863102\pi$
$167$	−23.4920	−1.81787	−0.908933	+	0.416942i	$0.863102\pi$
$168$	−24.4992	−1.89016
$169$	1.00000	0.0769231
$170$	0.0428873	0.00328930
$171$	−4.00871	−0.306554
$172$	−34.7778	−2.65178
$173$	−5.45235	−0.414535	−0.207267	−	0.978284i	$-0.566457\pi$
$173$	−5.45235	−0.414535	−0.207267	+	0.978284i	$0.566457\pi$
$174$	0.751646	0.0569822
$175$	15.4939	1.17123
$176$	4.58792	0.345827
$177$	19.3540	1.45474
$178$	19.4505	1.45787
$179$	8.21099	0.613718	0.306859	−	0.951755i	$-0.400722\pi$
$179$	8.21099	0.613718	0.306859	+	0.951755i	$0.400722\pi$
$180$	2.86431	0.213493
$181$	18.5214	1.37668	0.688342	−	0.725386i	$-0.258339\pi$
$181$	18.5214	1.37668	0.688342	+	0.725386i	$0.258339\pi$
$182$	−8.23517	−0.610432
$183$	−26.1795	−1.93524
$184$	−24.5385	−1.80900
$185$	−1.05243	−0.0773763
$186$	1.95134	0.143079
$187$	−0.0965043	−0.00705710
$188$	−2.15465	−0.157144
$189$	−13.7239	−0.998264
$190$	6.80091	0.493390
$191$	−2.91116	−0.210644	−0.105322	−	0.994438i	$-0.533587\pi$
$191$	−2.91116	−0.210644	−0.105322	+	0.994438i	$0.533587\pi$
$192$	24.6783	1.78100
$193$	3.73099	0.268562	0.134281	−	0.990943i	$-0.457127\pi$
$193$	3.73099	0.268562	0.134281	+	0.990943i	$0.457127\pi$
$194$	17.8796	1.28368
$195$	1.55878	0.111627
$196$	18.7186	1.33704
$197$	14.9934	1.06823	0.534116	−	0.845411i	$-0.320644\pi$
$197$	14.9934	1.06823	0.534116	+	0.845411i	$0.320644\pi$
$198$	−10.1544	−0.721639
$199$	7.98264	0.565874	0.282937	−	0.959138i	$-0.408691\pi$
$199$	7.98264	0.565874	0.282937	+	0.959138i	$0.408691\pi$
$200$	15.1979	1.07465
$201$	4.28224	0.302046
$202$	−42.8400	−3.01421
$203$	−0.560639	−0.0393491
$204$	0.166158	0.0116334
$205$	8.36686	0.584367
$206$	8.82343	0.614757
$207$	7.57862	0.526751
$208$	−1.12720	−0.0781573
$209$	−15.3033	−1.05855
$210$	−12.8368	−0.885825
$211$	−15.2450	−1.04951	−0.524754	−	0.851254i	$-0.675843\pi$
$211$	−15.2450	−1.04951	−0.524754	+	0.851254i	$0.675843\pi$
$212$	−9.63099	−0.661459
$213$	−31.0759	−2.12929
$214$	−3.02086	−0.206502
$215$	−7.73569	−0.527570
$216$	−13.4617	−0.915950
$217$	−1.45547	−0.0988038
$218$	29.1026	1.97108
$219$	15.5024	1.04756
$220$	10.9345	0.737207
$221$	0.0237100	0.00159491
$222$	−6.42393	−0.431146
$223$	6.21832	0.416410	0.208205	−	0.978085i	$-0.433238\pi$
$223$	6.21832	0.416410	0.208205	+	0.978085i	$0.433238\pi$
$224$	−15.0163	−1.00332
$225$	−4.69382	−0.312921
$226$	−3.92505	−0.261090
$227$	−4.63500	−0.307636	−0.153818	−	0.988099i	$-0.549157\pi$
$227$	−4.63500	−0.307636	−0.153818	+	0.988099i	$0.549157\pi$
$228$	26.3487	1.74499
$229$	−19.2419	−1.27154	−0.635770	−	0.771879i	$-0.719317\pi$
$229$	−19.2419	−1.27154	−0.635770	+	0.771879i	$0.719317\pi$
$230$	−12.8574	−0.847792
$231$	28.8853	1.90051
$232$	−0.549928	−0.0361045
$233$	6.58646	0.431494	0.215747	−	0.976449i	$-0.430781\pi$
$233$	6.58646	0.431494	0.215747	+	0.976449i	$0.430781\pi$
$234$	2.49481	0.163091
$235$	−0.479263	−0.0312637
$236$	−33.3558	−2.17128
$237$	−11.0385	−0.717030
$238$	−0.195256	−0.0126566
$239$	13.3702	0.864844	0.432422	−	0.901671i	$-0.357659\pi$
$239$	13.3702	0.864844	0.432422	+	0.901671i	$0.357659\pi$
$240$	−1.75706	−0.113418
$241$	−10.2864	−0.662607	−0.331303	−	0.943524i	$-0.607488\pi$
$241$	−10.2864	−0.662607	−0.331303	+	0.943524i	$0.607488\pi$
$242$	−13.0251	−0.837286
$243$	10.6074	0.680466
$244$	45.1192	2.88846
$245$	4.16360	0.266003
$246$	51.0704	3.25613
$247$	3.75986	0.239234
$248$	−1.42766	−0.0906567
$249$	−17.4326	−1.10475
$250$	17.0073	1.07564
$251$	4.28823	0.270671	0.135335	−	0.990800i	$-0.456789\pi$
$251$	4.28823	0.270671	0.135335	+	0.990800i	$0.456789\pi$
$252$	−13.0406	−0.821478
$253$	28.9315	1.81891
$254$	18.7426	1.17601
$255$	0.0369588	0.00231445
$256$	−22.5642	−1.41026
$257$	−16.5370	−1.03155	−0.515774	−	0.856725i	$-0.672496\pi$
$257$	−16.5370	−1.03155	−0.515774	+	0.856725i	$0.672496\pi$
$258$	−47.2179	−2.93966
$259$	4.79149	0.297728
$260$	−2.68649	−0.166609
$261$	0.169843	0.0105130
$262$	19.5203	1.20597
$263$	19.6511	1.21174	0.605868	−	0.795565i	$-0.292826\pi$
$263$	19.6511	1.21174	0.605868	+	0.795565i	$0.292826\pi$
$264$	28.3334	1.74380
$265$	−2.14224	−0.131597
$266$	−30.9631	−1.89847
$267$	16.7617	1.02580
$268$	−7.38026	−0.450821
$269$	8.96686	0.546719	0.273359	−	0.961912i	$-0.411865\pi$
$269$	8.96686	0.546719	0.273359	+	0.961912i	$0.411865\pi$
$270$	−7.05349	−0.429262
$271$	−7.86091	−0.477516	−0.238758	−	0.971079i	$-0.576740\pi$
$271$	−7.86091	−0.477516	−0.238758	+	0.971079i	$0.576740\pi$
$272$	−0.0267260	−0.00162050
$273$	−7.09679	−0.429517
$274$	8.60924	0.520103
$275$	−17.9188	−1.08054
$276$	−49.8133	−2.99841
$277$	−14.0092	−0.841732	−0.420866	−	0.907123i	$-0.638274\pi$
$277$	−14.0092	−0.841732	−0.420866	+	0.907123i	$0.638274\pi$
$278$	5.14349	0.308486
$279$	0.440929	0.0263977
$280$	9.39182	0.561269
$281$	−28.7490	−1.71502	−0.857509	−	0.514468i	$-0.827989\pi$
$281$	−28.7490	−1.71502	−0.857509	+	0.514468i	$0.827989\pi$
$282$	−2.92537	−0.174203
$283$	−21.4797	−1.27683	−0.638417	−	0.769691i	$-0.720410\pi$
$283$	−21.4797	−1.27683	−0.638417	+	0.769691i	$0.720410\pi$
$284$	53.5580	3.17809
$285$	5.86079	0.347163
$286$	9.52400	0.563166
$287$	−38.0925	−2.24853
$288$	4.54913	0.268060
$289$	−16.9994	−0.999967
$290$	−0.288145	−0.0169205
$291$	15.4080	0.903232
$292$	−26.7178	−1.56354
$293$	−11.3096	−0.660715	−0.330358	−	0.943856i	$-0.607169\pi$
$293$	−11.3096	−0.660715	−0.330358	+	0.943856i	$0.607169\pi$
$294$	25.4142	1.48218
$295$	−7.41939	−0.431974
$296$	4.69994	0.273179
$297$	15.8717	0.920968
$298$	−47.9781	−2.77930
$299$	−7.10815	−0.411075
$300$	30.8519	1.78123
$301$	35.2189	2.02998
$302$	−10.6823	−0.614698
$303$	−36.9180	−2.12089
$304$	−4.23811	−0.243072
$305$	10.0359	0.574657
$306$	0.0591521	0.00338150
$307$	9.19045	0.524527	0.262263	−	0.964996i	$-0.415531\pi$
$307$	9.19045	0.524527	0.262263	+	0.964996i	$0.415531\pi$
$308$	−49.7825	−2.83662
$309$	7.60372	0.432561
$310$	−0.748051	−0.0424865
$311$	−17.5496	−0.995147	−0.497573	−	0.867422i	$-0.665775\pi$
$311$	−17.5496	−0.995147	−0.497573	+	0.867422i	$0.665775\pi$
$312$	−6.96120	−0.394100
$313$	−16.5509	−0.935513	−0.467757	−	0.883857i	$-0.654938\pi$
$313$	−16.5509	−0.935513	−0.467757	+	0.883857i	$0.654938\pi$
$314$	32.0674	1.80967
$315$	−2.90063	−0.163432
$316$	19.0245	1.07021
$317$	1.11964	0.0628850	0.0314425	−	0.999506i	$-0.489990\pi$
$317$	1.11964	0.0628850	0.0314425	+	0.999506i	$0.489990\pi$
$318$	−13.0760	−0.733265
$319$	0.648380	0.0363023
$320$	−9.46046	−0.528856
$321$	−2.60327	−0.145300
$322$	58.5369	3.26213
$323$	0.0891463	0.00496023
$324$	−38.4433	−2.13574
$325$	4.40244	0.244203
$326$	−48.3607	−2.67845
$327$	25.0796	1.38691
$328$	−37.3647	−2.06312
$329$	2.18198	0.120296
$330$	14.8458	0.817236
$331$	19.1692	1.05363	0.526816	−	0.849979i	$-0.323386\pi$
$331$	19.1692	1.05363	0.526816	+	0.849979i	$0.323386\pi$
$332$	30.0443	1.64890
$333$	−1.45156	−0.0795451
$334$	54.9699	3.00782
$335$	−1.64160	−0.0896904
$336$	7.99950	0.436408
$337$	−15.6257	−0.851186	−0.425593	−	0.904915i	$-0.639934\pi$
$337$	−15.6257	−0.851186	−0.425593	+	0.904915i	$0.639934\pi$
$338$	−2.33994	−0.127276
$339$	−3.38247	−0.183711
$340$	−0.0636969	−0.00345445
$341$	1.68325	0.0911534
$342$	9.38014	0.507220
$343$	5.67981	0.306681
$344$	34.5460	1.86260
$345$	−11.0801	−0.596530
$346$	12.7582	0.685884
$347$	2.41576	0.129685	0.0648423	−	0.997896i	$-0.479346\pi$
$347$	2.41576	0.129685	0.0648423	+	0.997896i	$0.479346\pi$
$348$	−1.11636	−0.0598431
$349$	−8.12688	−0.435022	−0.217511	−	0.976058i	$-0.569794\pi$
$349$	−8.12688	−0.435022	−0.217511	+	0.976058i	$0.569794\pi$
$350$	−36.2548	−1.93790
$351$	−3.89949	−0.208140
$352$	17.3664	0.925632
$353$	−19.1839	−1.02106	−0.510529	−	0.859861i	$-0.670550\pi$
$353$	−19.1839	−1.02106	−0.510529	+	0.859861i	$0.670550\pi$
$354$	−45.2872	−2.40699
$355$	11.9130	0.632277
$356$	−28.8881	−1.53107
$357$	−0.168265	−0.00890553
$358$	−19.2132	−1.01545
$359$	−6.65803	−0.351397	−0.175699	−	0.984444i	$-0.556218\pi$
$359$	−6.65803	−0.351397	−0.175699	+	0.984444i	$0.556218\pi$
$360$	−2.84522	−0.149956
$361$	−4.86349	−0.255973
$362$	−43.3390	−2.27784
$363$	−11.2246	−0.589138
$364$	12.2310	0.641080
$365$	−5.94288	−0.311065
$366$	61.2583	3.20202
$367$	21.2132	1.10732	0.553661	−	0.832742i	$-0.313230\pi$
$367$	21.2132	1.10732	0.553661	+	0.832742i	$0.313230\pi$
$368$	8.01231	0.417671
$369$	11.5400	0.600746
$370$	2.46262	0.128026
$371$	9.75313	0.506357
$372$	−2.89817	−0.150263
$373$	−29.3856	−1.52153	−0.760764	−	0.649029i	$-0.775175\pi$
$373$	−29.3856	−1.52153	−0.760764	+	0.649029i	$0.775175\pi$
$374$	0.225814	0.0116766
$375$	14.6563	0.756850
$376$	2.14029	0.110377
$377$	−0.159300	−0.00820436
$378$	32.1130	1.65171
$379$	−15.1441	−0.777901	−0.388951	−	0.921259i	$-0.627162\pi$
$379$	−15.1441	−0.777901	−0.388951	+	0.921259i	$0.627162\pi$
$380$	−10.1008	−0.518162
$381$	16.1517	0.827476
$382$	6.81194	0.348529
$383$	0.0675896	0.00345367	0.00172683	−	0.999999i	$-0.499450\pi$
$383$	0.0675896	0.00345367	0.00172683	+	0.999999i	$0.499450\pi$
$384$	−40.5381	−2.06870
$385$	−11.0732	−0.564344
$386$	−8.73028	−0.444360
$387$	−10.6694	−0.542358
$388$	−26.5550	−1.34813
$389$	−37.3653	−1.89450	−0.947248	−	0.320501i	$-0.896149\pi$
$389$	−37.3653	−1.89450	−0.947248	+	0.320501i	$0.896149\pi$
$390$	−3.64745	−0.184696
$391$	−0.168535	−0.00852316
$392$	−18.5938	−0.939129
$393$	16.8219	0.848553
$394$	−35.0836	−1.76748
$395$	4.23165	0.212917
$396$	15.0814	0.757870
$397$	28.2872	1.41970	0.709848	−	0.704355i	$-0.248764\pi$
$397$	28.2872	1.41970	0.709848	+	0.704355i	$0.248764\pi$
$398$	−18.6789	−0.936288
$399$	−26.6829	−1.33582
$400$	−4.96243	−0.248121
$401$	34.8377	1.73971	0.869857	−	0.493304i	$-0.164211\pi$
$401$	34.8377	1.73971	0.869857	+	0.493304i	$0.164211\pi$
$402$	−10.0202	−0.499761
$403$	−0.413557	−0.0206007
$404$	63.6267	3.16555
$405$	−8.55101	−0.424903
$406$	1.31186	0.0651066
$407$	−5.54136	−0.274675
$408$	−0.165050	−0.00817121
$409$	20.9664	1.03672	0.518361	−	0.855162i	$-0.326542\pi$
$409$	20.9664	1.03672	0.518361	+	0.855162i	$0.326542\pi$
$410$	−19.5779	−0.966886
$411$	7.41915	0.365959
$412$	−13.1047	−0.645622
$413$	33.7789	1.66215
$414$	−17.7335	−0.871555
$415$	6.68282	0.328047
$416$	−4.26673	−0.209194
$417$	4.43248	0.217060
$418$	35.8088	1.75147
$419$	−31.4098	−1.53447	−0.767235	−	0.641366i	$-0.778368\pi$
$419$	−31.4098	−1.53447	−0.767235	+	0.641366i	$0.778368\pi$
$420$	19.0655	0.930300
$421$	−9.38507	−0.457400	−0.228700	−	0.973497i	$-0.573448\pi$
$421$	−9.38507	−0.457400	−0.228700	+	0.973497i	$0.573448\pi$
$422$	35.6723	1.73650
$423$	−0.661023	−0.0321400
$424$	9.56680	0.464605
$425$	0.104382	0.00506327
$426$	72.7157	3.52309
$427$	−45.6914	−2.21116
$428$	4.48663	0.216869
$429$	8.20745	0.396259
$430$	18.1011	0.872911
$431$	21.7609	1.04819	0.524093	−	0.851661i	$-0.324404\pi$
$431$	21.7609	1.04819	0.524093	+	0.851661i	$0.324404\pi$
$432$	4.39551	0.211479
$433$	−17.4104	−0.836690	−0.418345	−	0.908288i	$-0.637390\pi$
$433$	−17.4104	−0.836690	−0.418345	+	0.908288i	$0.637390\pi$
$434$	3.40571	0.163479
$435$	−0.248313	−0.0119057
$436$	−43.2237	−2.07004
$437$	−26.7256	−1.27846
$438$	−36.2747	−1.73327
$439$	26.8936	1.28356	0.641781	−	0.766888i	$-0.278196\pi$
$439$	26.8936	1.28356	0.641781	+	0.766888i	$0.278196\pi$
$440$	−10.8617	−0.517809
$441$	5.74263	0.273459
$442$	−0.0554801	−0.00263892
$443$	29.4850	1.40087	0.700437	−	0.713715i	$-0.252989\pi$
$443$	29.4850	1.40087	0.700437	+	0.713715i	$0.252989\pi$
$444$	9.54092	0.452792
$445$	−6.42564	−0.304605
$446$	−14.5505	−0.688986
$447$	−41.3459	−1.95559
$448$	43.0714	2.03493
$449$	−14.7078	−0.694105	−0.347053	−	0.937846i	$-0.612817\pi$
$449$	−14.7078	−0.694105	−0.347053	+	0.937846i	$0.612817\pi$
$450$	10.9833	0.517756
$451$	44.0540	2.07442
$452$	5.82955	0.274199
$453$	−9.20565	−0.432519
$454$	10.8456	0.509011
$455$	2.72057	0.127542
$456$	−26.1731	−1.22567
$457$	−4.81075	−0.225037	−0.112519	−	0.993650i	$-0.535892\pi$
$457$	−4.81075	−0.225037	−0.112519	+	0.993650i	$0.535892\pi$
$458$	45.0249	2.10387
$459$	−0.0924571	−0.00431553
$460$	19.0960	0.890357
$461$	−30.4685	−1.41906	−0.709530	−	0.704675i	$-0.751093\pi$
$461$	−30.4685	−1.41906	−0.709530	+	0.704675i	$0.751093\pi$
$462$	−67.5898	−3.14456
$463$	−12.8273	−0.596134	−0.298067	−	0.954545i	$-0.596342\pi$
$463$	−12.8273	−0.596134	−0.298067	+	0.954545i	$0.596342\pi$
$464$	0.179563	0.00833599
$465$	−0.644645	−0.0298947
$466$	−15.4119	−0.713944
$467$	13.5838	0.628583	0.314291	−	0.949327i	$-0.398233\pi$
$467$	13.5838	0.628583	0.314291	+	0.949327i	$0.398233\pi$
$468$	−3.70534	−0.171279
$469$	7.47386	0.345111
$470$	1.12145	0.0517285
$471$	27.6346	1.27333
$472$	33.1335	1.52509
$473$	−40.7307	−1.87280
$474$	25.8295	1.18639
$475$	16.5525	0.759482
$476$	0.289998	0.0132920
$477$	−2.95467	−0.135285
$478$	−31.2854	−1.43096
$479$	8.23932	0.376464	0.188232	−	0.982125i	$-0.439724\pi$
$479$	8.23932	0.376464	0.188232	+	0.982125i	$0.439724\pi$
$480$	−6.65090	−0.303571
$481$	1.36145	0.0620768
$482$	24.0696	1.09634
$483$	50.4451	2.29533
$484$	19.3451	0.879324
$485$	−5.90668	−0.268209
$486$	−24.8207	−1.12589
$487$	34.0602	1.54342	0.771708	−	0.635977i	$-0.219403\pi$
$487$	34.0602	1.54342	0.771708	+	0.635977i	$0.219403\pi$
$488$	−44.8185	−2.02884
$489$	−41.6755	−1.88463
$490$	−9.74258	−0.440125
$491$	3.80753	0.171832	0.0859158	−	0.996302i	$-0.472618\pi$
$491$	3.80753	0.171832	0.0859158	+	0.996302i	$0.472618\pi$
$492$	−75.8506	−3.41961
$493$	−0.00377700	−0.000170108 0
$494$	−8.79784	−0.395833
$495$	3.35459	0.150778
$496$	0.466162	0.0209313
$497$	−54.2373	−2.43288
$498$	40.7912	1.82790
$499$	−10.6181	−0.475331	−0.237666	−	0.971347i	$-0.576382\pi$
$499$	−10.6181	−0.475331	−0.237666	+	0.971347i	$0.576382\pi$
$500$	−25.2596	−1.12964
$501$	47.3711	2.11639
$502$	−10.0342	−0.447848
$503$	−12.9522	−0.577511	−0.288756	−	0.957403i	$-0.593242\pi$
$503$	−12.9522	−0.577511	−0.288756	+	0.957403i	$0.593242\pi$
$504$	12.9536	0.577001
$505$	14.1526	0.629782
$506$	−67.6980	−3.00954
$507$	−2.01648	−0.0895550
$508$	−27.8368	−1.23506
$509$	4.04132	0.179128	0.0895641	−	0.995981i	$-0.471453\pi$
$509$	4.04132	0.179128	0.0895641	+	0.995981i	$0.471453\pi$
$510$	−0.0864813	−0.00382946
$511$	27.0566	1.19692
$512$	12.5920	0.556493
$513$	−14.6615	−0.647322
$514$	38.6955	1.70679
$515$	−2.91490	−0.128446
$516$	70.1288	3.08725
$517$	−2.52347	−0.110982
$518$	−11.2118	−0.492618
$519$	10.9946	0.482607
$520$	2.66859	0.117025
$521$	25.0922	1.09931	0.549654	−	0.835392i	$-0.314759\pi$
$521$	25.0922	1.09931	0.549654	+	0.835392i	$0.314759\pi$
$522$	−0.397423	−0.0173947
$523$	18.1547	0.793848	0.396924	−	0.917851i	$-0.370078\pi$
$523$	18.1547	0.793848	0.396924	+	0.917851i	$0.370078\pi$
$524$	−28.9919	−1.26652
$525$	−31.2432	−1.36356
$526$	−45.9823	−2.00492
$527$	−0.00980545	−0.000427132 0
$528$	−9.25144	−0.402617
$529$	27.5259	1.19678
$530$	5.01271	0.217738
$531$	−10.2332	−0.444082
$532$	45.9869	1.99378
$533$	−10.8236	−0.468821
$534$	−39.2214	−1.69728
$535$	0.997969	0.0431460
$536$	7.33107	0.316654
$537$	−16.5573	−0.714500
$538$	−20.9819	−0.904594
$539$	21.9226	0.944274
$540$	10.4760	0.450814
$541$	−40.2434	−1.73020	−0.865100	−	0.501599i	$-0.832745\pi$
$541$	−40.2434	−1.73020	−0.865100	+	0.501599i	$0.832745\pi$
$542$	18.3941	0.790093
$543$	−37.3480	−1.60276
$544$	−0.101164	−0.00433739
$545$	−9.61432	−0.411832
$546$	16.6061	0.710673
$547$	−28.6181	−1.22362	−0.611810	−	0.791004i	$-0.709558\pi$
$547$	−28.6181	−1.22362	−0.611810	+	0.791004i	$0.709558\pi$
$548$	−12.7866	−0.546216
$549$	13.8420	0.590764
$550$	41.9288	1.78785
$551$	−0.598944	−0.0255159
$552$	49.4813	2.10606
$553$	−19.2658	−0.819263
$554$	32.7807	1.39272
$555$	2.12220	0.0900826
$556$	−7.63920	−0.323974
$557$	32.7536	1.38782	0.693908	−	0.720064i	$-0.255888\pi$
$557$	32.7536	1.38782	0.693908	+	0.720064i	$0.255888\pi$
$558$	−1.03175	−0.0436774
$559$	10.0071	0.423255
$560$	−3.06662	−0.129589
$561$	0.194599	0.00821597
$562$	67.2708	2.83765
$563$	7.93524	0.334431	0.167215	−	0.985920i	$-0.446522\pi$
$563$	7.93524	0.334431	0.167215	+	0.985920i	$0.446522\pi$
$564$	4.34481	0.182950
$565$	1.29668	0.0545516
$566$	50.2611	2.11263
$567$	38.9309	1.63494
$568$	−53.2011	−2.23227
$569$	5.91681	0.248045	0.124023	−	0.992279i	$-0.460420\pi$
$569$	5.91681	0.248045	0.124023	+	0.992279i	$0.460420\pi$
$570$	−13.7139	−0.574412
$571$	−0.730428	−0.0305674	−0.0152837	−	0.999883i	$-0.504865\pi$
$571$	−0.730428	−0.0305674	−0.0152837	+	0.999883i	$0.504865\pi$
$572$	−14.1452	−0.591440
$573$	5.87029	0.245235
$574$	89.1341	3.72038
$575$	−31.2932	−1.30502
$576$	−13.0483	−0.543680
$577$	−8.99377	−0.374416	−0.187208	−	0.982320i	$-0.559944\pi$
$577$	−8.99377	−0.374416	−0.187208	+	0.982320i	$0.559944\pi$
$578$	39.7777	1.65453
$579$	−7.52346	−0.312664
$580$	0.427958	0.0177700
$581$	−30.4254	−1.26226
$582$	−36.0537	−1.49448
$583$	−11.2795	−0.467150
$584$	26.5397	1.09822
$585$	−0.824185	−0.0340759
$586$	26.4638	1.09321
$587$	24.0370	0.992115	0.496057	−	0.868290i	$-0.334781\pi$
$587$	24.0370	0.992115	0.496057	+	0.868290i	$0.334781\pi$
$588$	−37.7456	−1.55660
$589$	−1.55491	−0.0640691
$590$	17.3609	0.714738
$591$	−30.2338	−1.24365
$592$	−1.53463	−0.0630728
$593$	16.6478	0.683645	0.341823	−	0.939765i	$-0.388956\pi$
$593$	16.6478	0.683645	0.341823	+	0.939765i	$0.388956\pi$
$594$	−37.1388	−1.52382
$595$	0.0645048	0.00264444
$596$	71.2579	2.91884
$597$	−16.0968	−0.658799
$598$	16.6327	0.680160
$599$	10.9871	0.448921	0.224461	−	0.974483i	$-0.427938\pi$
$599$	10.9871	0.448921	0.224461	+	0.974483i	$0.427938\pi$
$600$	−30.6462	−1.25113
$601$	16.0396	0.654270	0.327135	−	0.944978i	$-0.393917\pi$
$601$	16.0396	0.654270	0.327135	+	0.944978i	$0.393917\pi$
$602$	−82.4101	−3.35879
$603$	−2.26418	−0.0922044
$604$	15.8656	0.645561
$605$	4.30297	0.174941
$606$	86.3860	3.50919
$607$	−24.8046	−1.00679	−0.503394	−	0.864057i	$-0.667916\pi$
$607$	−24.8046	−1.00679	−0.503394	+	0.864057i	$0.667916\pi$
$608$	−16.0423	−0.650601
$609$	1.13052	0.0458108
$610$	−23.4835	−0.950819
$611$	0.619987	0.0250820
$612$	−0.0878538	−0.00355128
$613$	−15.9599	−0.644615	−0.322308	−	0.946635i	$-0.604459\pi$
$613$	−15.9599	−0.644615	−0.322308	+	0.946635i	$0.604459\pi$
$614$	−21.5051	−0.867875
$615$	−16.8716	−0.680328
$616$	49.4508	1.99243
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−17.7923	−0.715709
$619$	−18.5654	−0.746207	−0.373103	−	0.927790i	$-0.621706\pi$
$619$	−18.5654	−0.746207	−0.373103	+	0.927790i	$0.621706\pi$
$620$	1.11102	0.0446196
$621$	27.7182	1.11229
$622$	41.0650	1.64656
$623$	29.2545	1.17206
$624$	2.27298	0.0909918
$625$	16.3937	0.655746
$626$	38.7282	1.54789
$627$	30.8588	1.23238
$628$	−47.6270	−1.90053
$629$	0.0322801	0.00128709
$630$	6.78731	0.270413
$631$	29.0738	1.15741	0.578704	−	0.815537i	$-0.303559\pi$
$631$	29.0738	1.15741	0.578704	+	0.815537i	$0.303559\pi$
$632$	−18.8977	−0.751709
$633$	30.7412	1.22185
$634$	−2.61988	−0.104049
$635$	−6.19178	−0.245713
$636$	19.4207	0.770080
$637$	−5.38614	−0.213407
$638$	−1.51717	−0.0600654
$639$	16.4310	0.650000
$640$	15.5404	0.614287
$641$	19.8464	0.783884	0.391942	−	0.919990i	$-0.371803\pi$
$641$	19.8464	0.783884	0.391942	+	0.919990i	$0.371803\pi$
$642$	6.09150	0.240412
$643$	28.8681	1.13845	0.569224	−	0.822182i	$-0.307244\pi$
$643$	28.8681	1.13845	0.569224	+	0.822182i	$0.307244\pi$
$644$	−86.9400	−3.42591
$645$	15.5989	0.614205
$646$	−0.208597	−0.00820714
$647$	2.20922	0.0868533	0.0434266	−	0.999057i	$-0.486173\pi$
$647$	2.20922	0.0868533	0.0434266	+	0.999057i	$0.486173\pi$
$648$	38.1871	1.50013
$649$	−39.0653	−1.53345
$650$	−10.3014	−0.404056
$651$	2.93493	0.115029
$652$	71.8261	2.81293
$653$	−9.40549	−0.368065	−0.184033	−	0.982920i	$-0.558915\pi$
$653$	−9.40549	−0.368065	−0.184033	+	0.982920i	$0.558915\pi$
$654$	−58.6848	−2.29476
$655$	−6.44871	−0.251972
$656$	12.2003	0.476343
$657$	−8.19670	−0.319784
$658$	−5.10570	−0.199041
$659$	2.84316	0.110754	0.0553769	−	0.998466i	$-0.482364\pi$
$659$	2.84316	0.110754	0.0553769	+	0.998466i	$0.482364\pi$
$660$	−22.0493	−0.858267
$661$	45.5170	1.77041	0.885203	−	0.465204i	$-0.154019\pi$
$661$	45.5170	1.77041	0.885203	+	0.465204i	$0.154019\pi$
$662$	−44.8547	−1.74333
$663$	−0.0478108	−0.00185682
$664$	−29.8441	−1.15818
$665$	10.2289	0.396661
$666$	3.39657	0.131614
$667$	1.13233	0.0438439
$668$	−81.6422	−3.15883
$669$	−12.5391	−0.484790
$670$	3.84125	0.148401
$671$	52.8423	2.03995
$672$	30.2801	1.16808
$673$	5.45621	0.210321	0.105161	−	0.994455i	$-0.466464\pi$
$673$	5.45621	0.210321	0.105161	+	0.994455i	$0.466464\pi$
$674$	36.5632	1.40836
$675$	−17.1673	−0.660769
$676$	3.47532	0.133666
$677$	40.3852	1.55213	0.776065	−	0.630652i	$-0.217213\pi$
$677$	40.3852	1.55213	0.776065	+	0.630652i	$0.217213\pi$
$678$	7.91478	0.303965
$679$	26.8918	1.03201
$680$	0.0632724	0.00242638
$681$	9.34639	0.358154
$682$	−3.93871	−0.150821
$683$	2.67193	0.102238	0.0511192	−	0.998693i	$-0.483721\pi$
$683$	2.67193	0.102238	0.0511192	+	0.998693i	$0.483721\pi$
$684$	−13.9315	−0.532686
$685$	−2.84414	−0.108669
$686$	−13.2904	−0.507430
$687$	38.8009	1.48035
$688$	−11.2800	−0.430046
$689$	2.77125	0.105576
$690$	25.9267	0.987011
$691$	−21.1726	−0.805445	−0.402722	−	0.915322i	$-0.631936\pi$
$691$	−21.1726	−0.805445	−0.402722	+	0.915322i	$0.631936\pi$
$692$	−18.9487	−0.720320
$693$	−15.2727	−0.580162
$694$	−5.65272	−0.214574
$695$	−1.69920	−0.0644544
$696$	1.10892	0.0420334
$697$	−0.256628	−0.00972046
$698$	19.0164	0.719782
$699$	−13.2815	−0.502351
$700$	53.8463	2.03520
$701$	37.2130	1.40552	0.702758	−	0.711429i	$-0.251951\pi$
$701$	37.2130	1.40552	0.702758	+	0.711429i	$0.251951\pi$
$702$	9.12458	0.344385
$703$	5.11886	0.193061
$704$	−49.8122	−1.87737
$705$	0.966425	0.0363977
$706$	44.8893	1.68943
$707$	−64.4337	−2.42328
$708$	67.2613	2.52783
$709$	45.1077	1.69406	0.847028	−	0.531548i	$-0.178389\pi$
$709$	45.1077	1.69406	0.847028	+	0.531548i	$0.178389\pi$
$710$	−27.8757	−1.04616
$711$	5.83648	0.218885
$712$	28.6956	1.07541
$713$	2.93963	0.110090
$714$	0.393730	0.0147350
$715$	−3.14634	−0.117667
$716$	28.5358	1.06643
$717$	−26.9607	−1.00686
$718$	15.5794	0.581418
$719$	−11.9782	−0.446712	−0.223356	−	0.974737i	$-0.571701\pi$
$719$	−11.9782	−0.446712	−0.223356	+	0.974737i	$0.571701\pi$
$720$	0.929022	0.0346226
$721$	13.2709	0.494234
$722$	11.3803	0.423530
$723$	20.7424	0.771417
$724$	64.3677	2.39221
$725$	−0.701308	−0.0260459
$726$	26.2649	0.974781
$727$	−5.37189	−0.199232	−0.0996162	−	0.995026i	$-0.531762\pi$
$727$	−5.37189	−0.199232	−0.0996162	+	0.995026i	$0.531762\pi$
$728$	−12.1495	−0.450290
$729$	11.7958	0.436881
$730$	13.9060	0.514684
$731$	0.237269	0.00877570
$732$	−90.9819	−3.36279
$733$	50.1401	1.85197	0.925983	−	0.377565i	$-0.123239\pi$
$733$	50.1401	1.85197	0.925983	+	0.377565i	$0.123239\pi$
$734$	−49.6377	−1.83216
$735$	−8.39581	−0.309684
$736$	30.3286	1.11793
$737$	−8.64353	−0.318389
$738$	−27.0028	−0.993987
$739$	40.8808	1.50383	0.751913	−	0.659263i	$-0.229131\pi$
$739$	40.8808	1.50383	0.751913	+	0.659263i	$0.229131\pi$
$740$	−3.65753	−0.134454
$741$	−7.58167	−0.278520
$742$	−22.8217	−0.837813
$743$	−6.26865	−0.229974	−0.114987	−	0.993367i	$-0.536683\pi$
$743$	−6.26865	−0.229974	−0.114987	+	0.993367i	$0.536683\pi$
$744$	2.87885	0.105544
$745$	15.8500	0.580700
$746$	68.7605	2.51750
$747$	9.21725	0.337242
$748$	−0.335383	−0.0122628
$749$	−4.54353	−0.166017
$750$	−34.2950	−1.25227
$751$	17.9113	0.653593	0.326796	−	0.945095i	$-0.394031\pi$
$751$	17.9113	0.653593	0.326796	+	0.945095i	$0.394031\pi$
$752$	−0.698850	−0.0254844
$753$	−8.64713	−0.315119
$754$	0.372752	0.0135748
$755$	3.52901	0.128434
$756$	−47.6948	−1.73464
$757$	37.1748	1.35114	0.675570	−	0.737296i	$-0.263898\pi$
$757$	37.1748	1.35114	0.675570	+	0.737296i	$0.263898\pi$
$758$	35.4363	1.28711
$759$	−58.3398	−2.11760
$760$	10.0335	0.363954
$761$	22.7538	0.824825	0.412413	−	0.910997i	$-0.364686\pi$
$761$	22.7538	0.824825	0.412413	+	0.910997i	$0.364686\pi$
$762$	−37.7940	−1.36913
$763$	43.7719	1.58465
$764$	−10.1172	−0.366028
$765$	−0.0195415	−0.000706523 0
$766$	−0.158156	−0.00571439
$767$	9.59792	0.346561
$768$	45.5002	1.64185
$769$	32.6171	1.17620	0.588101	−	0.808788i	$-0.299876\pi$
$769$	32.6171	1.17620	0.588101	+	0.808788i	$0.299876\pi$
$770$	25.9107	0.933756
$771$	33.3465	1.20094
$772$	12.9664	0.466670
$773$	−39.4673	−1.41954	−0.709770	−	0.704433i	$-0.751201\pi$
$773$	−39.4673	−1.41954	−0.709770	+	0.704433i	$0.751201\pi$
$774$	24.9658	0.897378
$775$	−1.82066	−0.0654000
$776$	26.3780	0.946916
$777$	−9.66193	−0.346620
$778$	87.4326	3.13461
$779$	−40.6951	−1.45805
$780$	5.41726	0.193969
$781$	62.7256	2.24450
$782$	0.394361	0.0141023
$783$	0.621188	0.0221995
$784$	6.07126	0.216831
$785$	−10.5938	−0.378108
$786$	−39.3623	−1.40401
$787$	8.42976	0.300488	0.150244	−	0.988649i	$-0.451994\pi$
$787$	8.42976	0.300488	0.150244	+	0.988649i	$0.451994\pi$
$788$	52.1067	1.85622
$789$	−39.6260	−1.41072
$790$	−9.90180	−0.352290
$791$	−5.90348	−0.209904
$792$	−14.9809	−0.532324
$793$	−12.9828	−0.461031
$794$	−66.1904	−2.34901
$795$	4.31978	0.153207
$796$	27.7422	0.983297
$797$	−18.0917	−0.640842	−0.320421	−	0.947275i	$-0.603824\pi$
$797$	−18.0917	−0.640842	−0.320421	+	0.947275i	$0.603824\pi$
$798$	62.4364	2.21022
$799$	0.0146999	0.000520046 0
$800$	−18.7840	−0.664115
$801$	−8.86255	−0.313143
$802$	−81.5182	−2.87851
$803$	−31.2911	−1.10424
$804$	14.8821	0.524852
$805$	−19.3382	−0.681582
$806$	0.967698	0.0340857
$807$	−18.0815	−0.636498
$808$	−63.2026	−2.22346
$809$	−21.7542	−0.764837	−0.382419	−	0.923989i	$-0.624909\pi$
$809$	−21.7542	−0.764837	−0.382419	+	0.923989i	$0.624909\pi$
$810$	20.0089	0.703039
$811$	−14.8750	−0.522332	−0.261166	−	0.965294i	$-0.584107\pi$
$811$	−14.8750	−0.522332	−0.261166	+	0.965294i	$0.584107\pi$
$812$	−1.94840	−0.0683754
$813$	15.8514	0.555932
$814$	12.9665	0.454474
$815$	15.9764	0.559629
$816$	0.0538923	0.00188661
$817$	37.6252	1.31634
$818$	−49.0601	−1.71535
$819$	3.75233	0.131117
$820$	29.0775	1.01543
$821$	11.3798	0.397159	0.198580	−	0.980085i	$-0.436367\pi$
$821$	11.3798	0.397159	0.198580	+	0.980085i	$0.436367\pi$
$822$	−17.3604	−0.605512
$823$	−18.4850	−0.644345	−0.322173	−	0.946681i	$-0.604413\pi$
$823$	−18.4850	−0.644345	−0.322173	+	0.946681i	$0.604413\pi$
$824$	13.0174	0.453481
$825$	36.1328	1.25798
$826$	−79.0405	−2.75017
$827$	−36.9422	−1.28460	−0.642302	−	0.766451i	$-0.722021\pi$
$827$	−36.9422	−1.28460	−0.642302	+	0.766451i	$0.722021\pi$
$828$	26.3381	0.915313
$829$	47.0623	1.63454	0.817270	−	0.576254i	$-0.195486\pi$
$829$	47.0623	1.63454	0.817270	+	0.576254i	$0.195486\pi$
$830$	−15.6374	−0.542782
$831$	28.2493	0.979956
$832$	12.2383	0.424286
$833$	−0.127706	−0.00442474
$834$	−10.3717	−0.359144
$835$	−18.1598	−0.628447
$836$	−53.1839	−1.83940
$837$	1.61266	0.0557418
$838$	73.4971	2.53892
$839$	42.2535	1.45875	0.729376	−	0.684113i	$-0.239811\pi$
$839$	42.2535	1.45875	0.729376	+	0.684113i	$0.239811\pi$
$840$	−18.9384	−0.653437
$841$	−28.9746	−0.999125
$842$	21.9605	0.756809
$843$	57.9717	1.99665
$844$	−52.9811	−1.82369
$845$	0.773021	0.0265927
$846$	1.54675	0.0531785
$847$	−19.5905	−0.673137
$848$	−3.12376	−0.107270
$849$	43.3133	1.48651
$850$	−0.244248	−0.00837762
$851$	−9.67741	−0.331737
$852$	−107.999	−3.69997
$853$	−41.1621	−1.40936	−0.704681	−	0.709524i	$-0.748910\pi$
$853$	−41.1621	−1.40936	−0.704681	+	0.709524i	$0.748910\pi$
$854$	106.915	3.65856
$855$	−3.09882	−0.105977
$856$	−4.45673	−0.152328
$857$	33.3084	1.13779	0.568896	−	0.822409i	$-0.307371\pi$
$857$	33.3084	1.13779	0.568896	+	0.822409i	$0.307371\pi$
$858$	−19.2049	−0.655646
$859$	31.2782	1.06720	0.533600	−	0.845737i	$-0.320839\pi$
$859$	31.2782	1.06720	0.533600	+	0.845737i	$0.320839\pi$
$860$	−26.8840	−0.916737
$861$	76.8126	2.61777
$862$	−50.9192	−1.73432
$863$	−5.20624	−0.177222	−0.0886112	−	0.996066i	$-0.528243\pi$
$863$	−5.20624	−0.177222	−0.0886112	+	0.996066i	$0.528243\pi$
$864$	16.6381	0.566039
$865$	−4.21478	−0.143307
$866$	40.7393	1.38438
$867$	34.2790	1.16418
$868$	−5.05822	−0.171687
$869$	22.2809	0.755827
$870$	0.581039	0.0196991
$871$	2.12362	0.0719561
$872$	42.9356	1.45398
$873$	−8.14677	−0.275726
$874$	62.5364	2.11532
$875$	25.5800	0.864761
$876$	53.8758	1.82030
$877$	−8.33278	−0.281378	−0.140689	−	0.990054i	$-0.544932\pi$
$877$	−8.33278	−0.281378	−0.140689	+	0.990054i	$0.544932\pi$
$878$	−62.9294	−2.12376
$879$	22.8056	0.769214
$880$	3.54656	0.119554
$881$	27.5518	0.928244	0.464122	−	0.885771i	$-0.346370\pi$
$881$	27.5518	0.928244	0.464122	+	0.885771i	$0.346370\pi$
$882$	−13.4374	−0.452461
$883$	−6.61477	−0.222605	−0.111302	−	0.993787i	$-0.535502\pi$
$883$	−6.61477	−0.222605	−0.111302	+	0.993787i	$0.535502\pi$
$884$	0.0823999	0.00277141
$885$	14.9611	0.502910
$886$	−68.9930	−2.31787
$887$	44.3245	1.48827	0.744136	−	0.668029i	$-0.232862\pi$
$887$	44.3245	1.48827	0.744136	+	0.668029i	$0.232862\pi$
$888$	−9.47733	−0.318039
$889$	28.1898	0.945456
$890$	15.0356	0.503995
$891$	−45.0236	−1.50835
$892$	21.6107	0.723578
$893$	2.33106	0.0780061
$894$	96.7468	3.23570
$895$	6.34727	0.212166
$896$	−70.7518	−2.36365
$897$	14.3334	0.478580
$898$	34.4154	1.14846
$899$	0.0658795	0.00219721
$900$	−16.3125	−0.543751
$901$	0.0657065	0.00218900
$902$	−103.084	−3.43231
$903$	−71.0182	−2.36334
$904$	−5.79070	−0.192596
$905$	14.3174	0.475928
$906$	21.5407	0.715641
$907$	31.0948	1.03248	0.516242	−	0.856443i	$-0.327330\pi$
$907$	31.0948	1.03248	0.516242	+	0.856443i	$0.327330\pi$
$908$	−16.1081	−0.534567
$909$	19.5199	0.647435
$910$	−6.36596	−0.211030
$911$	14.9086	0.493944	0.246972	−	0.969023i	$-0.420564\pi$
$911$	14.9086	0.493944	0.246972	+	0.969023i	$0.420564\pi$
$912$	8.54606	0.282988
$913$	35.1870	1.16452
$914$	11.2569	0.372344
$915$	−20.2373	−0.669024
$916$	−66.8717	−2.20950
$917$	29.3596	0.969539
$918$	0.216344	0.00714042
$919$	25.9652	0.856514	0.428257	−	0.903657i	$-0.359128\pi$
$919$	25.9652	0.856514	0.428257	+	0.903657i	$0.359128\pi$
$920$	−18.9687	−0.625381
$921$	−18.5324	−0.610662
$922$	71.2945	2.34796
$923$	−15.4110	−0.507258
$924$	100.385	3.30244
$925$	5.99371	0.197072
$926$	30.0150	0.986355
$927$	−4.02037	−0.132046
$928$	0.679689	0.0223119
$929$	60.4094	1.98197	0.990984	−	0.133982i	$-0.0427764\pi$
$929$	60.4094	1.98197	0.990984	+	0.133982i	$0.0427764\pi$
$930$	1.50843	0.0494634
$931$	−20.2511	−0.663703
$932$	22.8901	0.749789
$933$	35.3884	1.15856
$934$	−31.7852	−1.04004
$935$	−0.0745999	−0.00243968
$936$	3.68064	0.120306
$937$	−57.6164	−1.88225	−0.941123	−	0.338065i	$-0.890228\pi$
$937$	−57.6164	−1.88225	−0.941123	+	0.338065i	$0.890228\pi$
$938$	−17.4884	−0.571016
$939$	33.3746	1.08914
$940$	−1.66559	−0.0543257
$941$	42.6376	1.38995	0.694973	−	0.719036i	$-0.255416\pi$
$941$	42.6376	1.38995	0.694973	+	0.719036i	$0.255416\pi$
$942$	−64.6632	−2.10684
$943$	76.9357	2.50537
$944$	−10.8188	−0.352121
$945$	−10.6088	−0.345105
$946$	95.3075	3.09871
$947$	−2.96295	−0.0962829	−0.0481414	−	0.998841i	$-0.515330\pi$
$947$	−2.96295	−0.0962829	−0.0481414	+	0.998841i	$0.515330\pi$
$948$	−38.3624	−1.24595
$949$	7.68787	0.249559
$950$	−38.7319	−1.25663
$951$	−2.25772	−0.0732117
$952$	−0.288065	−0.00933625
$953$	31.9762	1.03581	0.517905	−	0.855438i	$-0.326712\pi$
$953$	31.9762	1.03581	0.517905	+	0.855438i	$0.326712\pi$
$954$	6.91376	0.223841
$955$	−2.25039	−0.0728209
$956$	46.4656	1.50280
$957$	−1.30744	−0.0422637
$958$	−19.2795	−0.622893
$959$	12.9488	0.418137
$960$	19.0768	0.615702
$961$	−30.8290	−0.994483
$962$	−3.18571	−0.102712
$963$	1.37645	0.0443553
$964$	−35.7486	−1.15138
$965$	2.88413	0.0928435
$966$	−118.038	−3.79782
$967$	38.3156	1.23215	0.616073	−	0.787689i	$-0.288723\pi$
$967$	38.3156	1.23215	0.616073	+	0.787689i	$0.288723\pi$
$968$	−19.2162	−0.617632
$969$	−0.179762	−0.00577478
$970$	13.8213	0.443774
$971$	17.8864	0.574002	0.287001	−	0.957930i	$-0.407342\pi$
$971$	17.8864	0.574002	0.287001	+	0.957930i	$0.407342\pi$
$972$	36.8642	1.18242
$973$	7.73609	0.248008
$974$	−79.6989	−2.55372
$975$	−8.87742	−0.284305
$976$	14.6342	0.468428
$977$	57.1485	1.82834	0.914171	−	0.405328i	$-0.132843\pi$
$977$	57.1485	1.82834	0.914171	+	0.405328i	$0.132843\pi$
$978$	97.5183	3.11829
$979$	−33.8329	−1.08131
$980$	14.4698	0.462222
$981$	−13.2605	−0.423376
$982$	−8.90940	−0.284310
$983$	18.4399	0.588143	0.294071	−	0.955783i	$-0.404990\pi$
$983$	18.4399	0.588143	0.294071	+	0.955783i	$0.404990\pi$
$984$	75.3451	2.40191
$985$	11.5902	0.369294
$986$	0.00883796	0.000281458 0
$987$	−4.39992	−0.140051
$988$	13.0667	0.415707
$989$	−71.1320	−2.26186
$990$	−7.84954	−0.249475
$991$	60.8991	1.93453	0.967263	−	0.253778i	$-0.0816731\pi$
$991$	60.8991	1.93453	0.967263	+	0.253778i	$0.0816731\pi$
$992$	1.76454	0.0560241
$993$	−38.6542	−1.22665
$994$	126.912	4.02541
$995$	6.17075	0.195626
$996$	−60.5838	−1.91967
$997$	−5.98156	−0.189438	−0.0947189	−	0.995504i	$-0.530195\pi$
$997$	−5.98156	−0.189438	−0.0947189	+	0.995504i	$0.530195\pi$
$998$	24.8457	0.786477
$999$	−5.30897	−0.167968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.19	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.33994 q^{2} -2.01648 q^{3} +3.47532 q^{4} +0.773021 q^{5} +4.71844 q^{6} -3.51939 q^{7} -3.45216 q^{8} +1.06619 q^{9} +O(q^{10})\)	\(q-2.33994 q^{2} -2.01648 q^{3} +3.47532 q^{4} +0.773021 q^{5} +4.71844 q^{6} -3.51939 q^{7} -3.45216 q^{8} +1.06619 q^{9} -1.80882 q^{10} +4.07019 q^{11} -7.00791 q^{12} -1.00000 q^{13} +8.23517 q^{14} -1.55878 q^{15} +1.12720 q^{16} -0.0237100 q^{17} -2.49481 q^{18} -3.75986 q^{19} +2.68649 q^{20} +7.09679 q^{21} -9.52400 q^{22} +7.10815 q^{23} +6.96120 q^{24} -4.40244 q^{25} +2.33994 q^{26} +3.89949 q^{27} -12.2310 q^{28} +0.159300 q^{29} +3.64745 q^{30} +0.413557 q^{31} +4.26673 q^{32} -8.20745 q^{33} +0.0554801 q^{34} -2.72057 q^{35} +3.70534 q^{36} -1.36145 q^{37} +8.79784 q^{38} +2.01648 q^{39} -2.66859 q^{40} +10.8236 q^{41} -16.6061 q^{42} -10.0071 q^{43} +14.1452 q^{44} +0.824185 q^{45} -16.6327 q^{46} -0.619987 q^{47} -2.27298 q^{48} +5.38614 q^{49} +10.3014 q^{50} +0.0478108 q^{51} -3.47532 q^{52} -2.77125 q^{53} -9.12458 q^{54} +3.14634 q^{55} +12.1495 q^{56} +7.58167 q^{57} -0.372752 q^{58} -9.59792 q^{59} -5.41726 q^{60} +12.9828 q^{61} -0.967698 q^{62} -3.75233 q^{63} -12.2383 q^{64} -0.773021 q^{65} +19.2049 q^{66} -2.12362 q^{67} -0.0823999 q^{68} -14.3334 q^{69} +6.36596 q^{70} +15.4110 q^{71} -3.68064 q^{72} -7.68787 q^{73} +3.18571 q^{74} +8.87742 q^{75} -13.0667 q^{76} -14.3246 q^{77} -4.71844 q^{78} +5.47417 q^{79} +0.871350 q^{80} -11.0618 q^{81} -25.3265 q^{82} +8.64506 q^{83} +24.6636 q^{84} -0.0183284 q^{85} +23.4160 q^{86} -0.321225 q^{87} -14.0509 q^{88} -8.31238 q^{89} -1.92854 q^{90} +3.51939 q^{91} +24.7031 q^{92} -0.833929 q^{93} +1.45073 q^{94} -2.90645 q^{95} -8.60377 q^{96} -7.64103 q^{97} -12.6032 q^{98} +4.33958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 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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