LMFDB - Embedded newform 8003.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47698 q^{2} +3.33984 q^{3} +4.13542 q^{4} -4.25899 q^{5} -8.27272 q^{6} +3.67754 q^{7} -5.28940 q^{8} +8.15455 q^{9} +O(q^{10})$	\(q-2.47698 q^{2} +3.33984 q^{3} +4.13542 q^{4} -4.25899 q^{5} -8.27272 q^{6} +3.67754 q^{7} -5.28940 q^{8} +8.15455 q^{9} +10.5494 q^{10} +5.06699 q^{11} +13.8117 q^{12} +5.67186 q^{13} -9.10919 q^{14} -14.2244 q^{15} +4.83089 q^{16} +1.81414 q^{17} -20.1987 q^{18} -3.82592 q^{19} -17.6127 q^{20} +12.2824 q^{21} -12.5508 q^{22} -1.03040 q^{23} -17.6658 q^{24} +13.1390 q^{25} -14.0491 q^{26} +17.2154 q^{27} +15.2082 q^{28} -4.85205 q^{29} +35.2335 q^{30} +3.01370 q^{31} -1.38721 q^{32} +16.9230 q^{33} -4.49359 q^{34} -15.6626 q^{35} +33.7226 q^{36} +10.1961 q^{37} +9.47671 q^{38} +18.9431 q^{39} +22.5275 q^{40} -3.08786 q^{41} -30.4233 q^{42} +2.59848 q^{43} +20.9542 q^{44} -34.7302 q^{45} +2.55229 q^{46} +6.13382 q^{47} +16.1344 q^{48} +6.52430 q^{49} -32.5450 q^{50} +6.05895 q^{51} +23.4555 q^{52} +1.00000 q^{53} -42.6422 q^{54} -21.5803 q^{55} -19.4520 q^{56} -12.7780 q^{57} +12.0184 q^{58} -0.760420 q^{59} -58.8238 q^{60} -10.6485 q^{61} -7.46488 q^{62} +29.9887 q^{63} -6.22570 q^{64} -24.1564 q^{65} -41.9178 q^{66} -1.42899 q^{67} +7.50225 q^{68} -3.44139 q^{69} +38.7960 q^{70} +14.0735 q^{71} -43.1327 q^{72} -4.28121 q^{73} -25.2556 q^{74} +43.8822 q^{75} -15.8218 q^{76} +18.6341 q^{77} -46.9217 q^{78} +4.21751 q^{79} -20.5747 q^{80} +33.0331 q^{81} +7.64857 q^{82} +0.501574 q^{83} +50.7930 q^{84} -7.72642 q^{85} -6.43638 q^{86} -16.2051 q^{87} -26.8014 q^{88} +0.641133 q^{89} +86.0259 q^{90} +20.8585 q^{91} -4.26116 q^{92} +10.0653 q^{93} -15.1933 q^{94} +16.2945 q^{95} -4.63305 q^{96} -4.30642 q^{97} -16.1606 q^{98} +41.3191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.47698	−1.75149	−0.875744	−	0.482775i	$-0.839629\pi$
$2$	−2.47698	−1.75149	−0.875744	+	0.482775i	$0.839629\pi$
$3$	3.33984	1.92826	0.964130	−	0.265431i	$-0.0855143\pi$
$3$	3.33984	1.92826	0.964130	+	0.265431i	$0.0855143\pi$
$4$	4.13542	2.06771
$5$	−4.25899	−1.90468	−0.952339	−	0.305040i	$-0.901330\pi$
$5$	−4.25899	−1.90468	−0.952339	+	0.305040i	$0.901330\pi$
$6$	−8.27272	−3.37732
$7$	3.67754	1.38998	0.694990	−	0.719020i	$-0.255409\pi$
$7$	3.67754	1.38998	0.694990	+	0.719020i	$0.255409\pi$
$8$	−5.28940	−1.87009
$9$	8.15455	2.71818
$10$	10.5494	3.33602
$11$	5.06699	1.52776	0.763878	−	0.645361i	$-0.223293\pi$
$11$	5.06699	1.52776	0.763878	+	0.645361i	$0.223293\pi$
$12$	13.8117	3.98709
$13$	5.67186	1.57309	0.786545	−	0.617533i	$-0.211868\pi$
$13$	5.67186	1.57309	0.786545	+	0.617533i	$0.211868\pi$
$14$	−9.10919	−2.43453
$15$	−14.2244	−3.67272
$16$	4.83089	1.20772
$17$	1.81414	0.439994	0.219997	−	0.975501i	$-0.429395\pi$
$17$	1.81414	0.439994	0.219997	+	0.975501i	$0.429395\pi$
$18$	−20.1987	−4.76087
$19$	−3.82592	−0.877725	−0.438863	−	0.898554i	$-0.644619\pi$
$19$	−3.82592	−0.877725	−0.438863	+	0.898554i	$0.644619\pi$
$20$	−17.6127	−3.93833
$21$	12.2824	2.68024
$22$	−12.5508	−2.67585
$23$	−1.03040	−0.214854	−0.107427	−	0.994213i	$-0.534261\pi$
$23$	−1.03040	−0.214854	−0.107427	+	0.994213i	$0.534261\pi$
$24$	−17.6658	−3.60601
$25$	13.1390	2.62780
$26$	−14.0491	−2.75525
$27$	17.2154	3.31311
$28$	15.2082	2.87408
$29$	−4.85205	−0.901003	−0.450501	−	0.892776i	$-0.648755\pi$
$29$	−4.85205	−0.901003	−0.450501	+	0.892776i	$0.648755\pi$
$30$	35.2335	6.43272
$31$	3.01370	0.541277	0.270638	−	0.962681i	$-0.412765\pi$
$31$	3.01370	0.541277	0.270638	+	0.962681i	$0.412765\pi$
$32$	−1.38721	−0.245226
$33$	16.9230	2.94591
$34$	−4.49359	−0.770645
$35$	−15.6626	−2.64746
$36$	33.7226	5.62043
$37$	10.1961	1.67623	0.838117	−	0.545491i	$-0.183657\pi$
$37$	10.1961	1.67623	0.838117	+	0.545491i	$0.183657\pi$
$38$	9.47671	1.53733
$39$	18.9431	3.03333
$40$	22.5275	3.56191
$41$	−3.08786	−0.482243	−0.241121	−	0.970495i	$-0.577515\pi$
$41$	−3.08786	−0.482243	−0.241121	+	0.970495i	$0.577515\pi$
$42$	−30.4233	−4.69441
$43$	2.59848	0.396264	0.198132	−	0.980175i	$-0.436512\pi$
$43$	2.59848	0.396264	0.198132	+	0.980175i	$0.436512\pi$
$44$	20.9542	3.15896
$45$	−34.7302	−5.17727
$46$	2.55229	0.376315
$47$	6.13382	0.894710	0.447355	−	0.894357i	$-0.352366\pi$
$47$	6.13382	0.894710	0.447355	+	0.894357i	$0.352366\pi$
$48$	16.1344	2.32880
$49$	6.52430	0.932043
$50$	−32.5450	−4.60256
$51$	6.05895	0.848423
$52$	23.4555	3.25270
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−42.6422	−5.80287
$55$	−21.5803	−2.90988
$56$	−19.4520	−2.59938
$57$	−12.7780	−1.69248
$58$	12.0184	1.57810
$59$	−0.760420	−0.0989983	−0.0494992	−	0.998774i	$-0.515763\pi$
$59$	−0.760420	−0.0989983	−0.0494992	+	0.998774i	$0.515763\pi$
$60$	−58.8238	−7.59412
$61$	−10.6485	−1.36340	−0.681701	−	0.731630i	$-0.738760\pi$
$61$	−10.6485	−1.36340	−0.681701	+	0.731630i	$0.738760\pi$
$62$	−7.46488	−0.948040
$63$	29.9887	3.77822
$64$	−6.22570	−0.778212
$65$	−24.1564	−2.99623
$66$	−41.9178	−5.15973
$67$	−1.42899	−0.174579	−0.0872894	−	0.996183i	$-0.527820\pi$
$67$	−1.42899	−0.174579	−0.0872894	+	0.996183i	$0.527820\pi$
$68$	7.50225	0.909781
$69$	−3.44139	−0.414295
$70$	38.7960	4.63700
$71$	14.0735	1.67021	0.835106	−	0.550089i	$-0.185406\pi$
$71$	14.0735	1.67021	0.835106	+	0.550089i	$0.185406\pi$
$72$	−43.1327	−5.08324
$73$	−4.28121	−0.501078	−0.250539	−	0.968107i	$-0.580608\pi$
$73$	−4.28121	−0.501078	−0.250539	+	0.968107i	$0.580608\pi$
$74$	−25.2556	−2.93590
$75$	43.8822	5.06708
$76$	−15.8218	−1.81488
$77$	18.6341	2.12355
$78$	−46.9217	−5.31284
$79$	4.21751	0.474507	0.237253	−	0.971448i	$-0.423753\pi$
$79$	4.21751	0.474507	0.237253	+	0.971448i	$0.423753\pi$
$80$	−20.5747	−2.30032
$81$	33.0331	3.67034
$82$	7.64857	0.844643
$83$	0.501574	0.0550549	0.0275274	−	0.999621i	$-0.491237\pi$
$83$	0.501574	0.0550549	0.0275274	+	0.999621i	$0.491237\pi$
$84$	50.7930	5.54197
$85$	−7.72642	−0.838047
$86$	−6.43638	−0.694052
$87$	−16.2051	−1.73737
$88$	−26.8014	−2.85704
$89$	0.641133	0.0679600	0.0339800	−	0.999423i	$-0.489182\pi$
$89$	0.641133	0.0679600	0.0339800	+	0.999423i	$0.489182\pi$
$90$	86.0259	9.06793
$91$	20.8585	2.18656
$92$	−4.26116	−0.444257
$93$	10.0653	1.04372
$94$	−15.1933	−1.56707
$95$	16.2945	1.67178
$96$	−4.63305	−0.472859
$97$	−4.30642	−0.437251	−0.218625	−	0.975809i	$-0.570157\pi$
$97$	−4.30642	−0.437251	−0.218625	+	0.975809i	$0.570157\pi$
$98$	−16.1606	−1.63246
$99$	41.3191	4.15272
$100$	54.3354	5.43354
$101$	−1.79939	−0.179046	−0.0895229	−	0.995985i	$-0.528534\pi$
$101$	−1.79939	−0.179046	−0.0895229	+	0.995985i	$0.528534\pi$
$102$	−15.0079	−1.48600
$103$	6.20494	0.611391	0.305696	−	0.952129i	$-0.401111\pi$
$103$	6.20494	0.611391	0.305696	+	0.952129i	$0.401111\pi$
$104$	−30.0007	−2.94181
$105$	−52.3107	−5.10500
$106$	−2.47698	−0.240585
$107$	−16.3174	−1.57747	−0.788733	−	0.614736i	$-0.789263\pi$
$107$	−16.3174	−1.57747	−0.788733	+	0.614736i	$0.789263\pi$
$108$	71.1930	6.85055
$109$	17.1773	1.64529	0.822645	−	0.568555i	$-0.192498\pi$
$109$	17.1773	1.64529	0.822645	+	0.568555i	$0.192498\pi$
$110$	53.4539	5.09663
$111$	34.0535	3.23221
$112$	17.7658	1.67871
$113$	−20.0343	−1.88467	−0.942335	−	0.334670i	$-0.891375\pi$
$113$	−20.0343	−1.88467	−0.942335	+	0.334670i	$0.891375\pi$
$114$	31.6507	2.96436
$115$	4.38848	0.409228
$116$	−20.0653	−1.86301
$117$	46.2515	4.27595
$118$	1.88355	0.173394
$119$	6.67158	0.611583
$120$	75.2384	6.86829
$121$	14.6744	1.33404
$122$	26.3762	2.38798
$123$	−10.3130	−0.929889
$124$	12.4629	1.11920
$125$	−34.6640	−3.10044
$126$	−74.2814	−6.61751
$127$	−16.5121	−1.46522	−0.732608	−	0.680651i	$-0.761697\pi$
$127$	−16.5121	−1.46522	−0.732608	+	0.680651i	$0.761697\pi$
$128$	18.1953	1.60826
$129$	8.67851	0.764100
$130$	59.8349	5.24786
$131$	−2.86826	−0.250601	−0.125300	−	0.992119i	$-0.539989\pi$
$131$	−2.86826	−0.250601	−0.125300	+	0.992119i	$0.539989\pi$
$132$	69.9837	6.09130
$133$	−14.0700	−1.22002
$134$	3.53958	0.305773
$135$	−73.3203	−6.31040
$136$	−9.59573	−0.822827
$137$	−17.8195	−1.52243	−0.761213	−	0.648502i	$-0.775396\pi$
$137$	−17.8195	−1.52243	−0.761213	+	0.648502i	$0.775396\pi$
$138$	8.52425	0.725632
$139$	1.67633	0.142184	0.0710921	−	0.997470i	$-0.477352\pi$
$139$	1.67633	0.142184	0.0710921	+	0.997470i	$0.477352\pi$
$140$	−64.7715	−5.47419
$141$	20.4860	1.72523
$142$	−34.8597	−2.92536
$143$	28.7393	2.40330
$144$	39.3938	3.28281
$145$	20.6648	1.71612
$146$	10.6045	0.877632
$147$	21.7901	1.79722
$148$	42.1653	3.46597
$149$	−7.27059	−0.595630	−0.297815	−	0.954624i	$-0.596258\pi$
$149$	−7.27059	−0.595630	−0.297815	+	0.954624i	$0.596258\pi$
$150$	−108.695	−8.87494
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	20.2368	1.64142
$153$	14.7935	1.19599
$154$	−46.1562	−3.71937
$155$	−12.8353	−1.03096
$156$	78.3378	6.27205
$157$	−17.4520	−1.39282	−0.696411	−	0.717644i	$-0.745221\pi$
$157$	−17.4520	−1.39282	−0.696411	+	0.717644i	$0.745221\pi$
$158$	−10.4467	−0.831094
$159$	3.33984	0.264867
$160$	5.90810	0.467076
$161$	−3.78935	−0.298643
$162$	−81.8223	−6.42857
$163$	−1.15886	−0.0907688	−0.0453844	−	0.998970i	$-0.514451\pi$
$163$	−1.15886	−0.0907688	−0.0453844	+	0.998970i	$0.514451\pi$
$164$	−12.7696	−0.997139
$165$	−72.0748	−5.61101
$166$	−1.24239	−0.0964280
$167$	13.0179	1.00736	0.503678	−	0.863891i	$-0.331980\pi$
$167$	13.0179	1.00736	0.503678	+	0.863891i	$0.331980\pi$
$168$	−64.9666	−5.01228
$169$	19.1700	1.47461
$170$	19.1382	1.46783
$171$	−31.1986	−2.38582
$172$	10.7458	0.819361
$173$	10.4704	0.796050	0.398025	−	0.917375i	$-0.369696\pi$
$173$	10.4704	0.796050	0.398025	+	0.917375i	$0.369696\pi$
$174$	40.1397	3.04298
$175$	48.3192	3.65259
$176$	24.4781	1.84511
$177$	−2.53969	−0.190894
$178$	−1.58807	−0.119031
$179$	11.9116	0.890312	0.445156	−	0.895453i	$-0.353148\pi$
$179$	11.9116	0.890312	0.445156	+	0.895453i	$0.353148\pi$
$180$	−143.624	−10.7051
$181$	21.7693	1.61810	0.809049	−	0.587741i	$-0.199983\pi$
$181$	21.7693	1.61810	0.809049	+	0.587741i	$0.199983\pi$
$182$	−51.6660	−3.82974
$183$	−35.5644	−2.62899
$184$	5.45022	0.401796
$185$	−43.4252	−3.19269
$186$	−24.9315	−1.82807
$187$	9.19225	0.672204
$188$	25.3660	1.85000
$189$	63.3103	4.60515
$190$	−40.3612	−2.92811
$191$	0.735370	0.0532095	0.0266047	−	0.999646i	$-0.491530\pi$
$191$	0.735370	0.0532095	0.0266047	+	0.999646i	$0.491530\pi$
$192$	−20.7929	−1.50060
$193$	−18.2852	−1.31620	−0.658099	−	0.752932i	$-0.728639\pi$
$193$	−18.2852	−1.31620	−0.658099	+	0.752932i	$0.728639\pi$
$194$	10.6669	0.765840
$195$	−80.6786	−5.77751
$196$	26.9807	1.92720
$197$	−5.05507	−0.360159	−0.180079	−	0.983652i	$-0.557635\pi$
$197$	−5.05507	−0.360159	−0.180079	+	0.983652i	$0.557635\pi$
$198$	−102.346	−7.27345
$199$	−22.9390	−1.62610	−0.813052	−	0.582191i	$-0.802196\pi$
$199$	−22.9390	−1.62610	−0.813052	+	0.582191i	$0.802196\pi$
$200$	−69.4975	−4.91421
$201$	−4.77260	−0.336633
$202$	4.45705	0.313597
$203$	−17.8436	−1.25238
$204$	25.0563	1.75429
$205$	13.1512	0.918518
$206$	−15.3695	−1.07084
$207$	−8.40249	−0.584013
$208$	27.4001	1.89986
$209$	−19.3859	−1.34095
$210$	129.572	8.94135
$211$	−14.2825	−0.983251	−0.491625	−	0.870807i	$-0.663597\pi$
$211$	−14.2825	−0.983251	−0.491625	+	0.870807i	$0.663597\pi$
$212$	4.13542	0.284022
$213$	47.0031	3.22060
$214$	40.4179	2.76291
$215$	−11.0669	−0.754756
$216$	−91.0592	−6.19580
$217$	11.0830	0.752364
$218$	−42.5479	−2.88171
$219$	−14.2986	−0.966208
$220$	−89.2436	−6.01681
$221$	10.2896	0.692150
$222$	−84.3498	−5.66119
$223$	−25.0957	−1.68053	−0.840267	−	0.542173i	$-0.817602\pi$
$223$	−25.0957	−1.68053	−0.840267	+	0.542173i	$0.817602\pi$
$224$	−5.10151	−0.340859
$225$	107.143	7.14285
$226$	49.6246	3.30098
$227$	−9.33286	−0.619443	−0.309722	−	0.950827i	$-0.600236\pi$
$227$	−9.33286	−0.619443	−0.309722	+	0.950827i	$0.600236\pi$
$228$	−52.8423	−3.49957
$229$	24.8197	1.64013	0.820065	−	0.572271i	$-0.193937\pi$
$229$	24.8197	1.64013	0.820065	+	0.572271i	$0.193937\pi$
$230$	−10.8702	−0.716759
$231$	62.2349	4.09475
$232$	25.6644	1.68495
$233$	−9.72240	−0.636936	−0.318468	−	0.947934i	$-0.603168\pi$
$233$	−9.72240	−0.636936	−0.318468	+	0.947934i	$0.603168\pi$
$234$	−114.564	−7.48928
$235$	−26.1239	−1.70413
$236$	−3.14466	−0.204700
$237$	14.0858	0.914973
$238$	−16.5254	−1.07118
$239$	−0.809275	−0.0523477	−0.0261738	−	0.999657i	$-0.508332\pi$
$239$	−0.809275	−0.0523477	−0.0261738	+	0.999657i	$0.508332\pi$
$240$	−68.7163	−4.43562
$241$	6.39407	0.411879	0.205939	−	0.978565i	$-0.433975\pi$
$241$	6.39407	0.411879	0.205939	+	0.978565i	$0.433975\pi$
$242$	−36.3483	−2.33655
$243$	58.6792	3.76427
$244$	−44.0361	−2.81913
$245$	−27.7869	−1.77524
$246$	25.5450	1.62869
$247$	−21.7000	−1.38074
$248$	−15.9407	−1.01223
$249$	1.67518	0.106160
$250$	85.8619	5.43038
$251$	−21.3294	−1.34630	−0.673150	−	0.739506i	$-0.735059\pi$
$251$	−21.3294	−1.34630	−0.673150	+	0.739506i	$0.735059\pi$
$252$	124.016	7.81227
$253$	−5.22105	−0.328245
$254$	40.9002	2.56631
$255$	−25.8050	−1.61597
$256$	−32.6181	−2.03863
$257$	−25.4932	−1.59022	−0.795110	−	0.606465i	$-0.792587\pi$
$257$	−25.4932	−1.59022	−0.795110	+	0.606465i	$0.792587\pi$
$258$	−21.4965	−1.33831
$259$	37.4967	2.32993
$260$	−99.8969	−6.19534
$261$	−39.5663	−2.44909
$262$	7.10462	0.438925
$263$	−4.94808	−0.305112	−0.152556	−	0.988295i	$-0.548750\pi$
$263$	−4.94808	−0.305112	−0.152556	+	0.988295i	$0.548750\pi$
$264$	−89.5124	−5.50911
$265$	−4.25899	−0.261628
$266$	34.8510	2.13685
$267$	2.14128	0.131044
$268$	−5.90948	−0.360979
$269$	5.80121	0.353706	0.176853	−	0.984237i	$-0.443408\pi$
$269$	5.80121	0.353706	0.176853	+	0.984237i	$0.443408\pi$
$270$	181.613	11.0526
$271$	−19.5345	−1.18663	−0.593317	−	0.804969i	$-0.702182\pi$
$271$	−19.5345	−1.18663	−0.593317	+	0.804969i	$0.702182\pi$
$272$	8.76392	0.531391
$273$	69.6641	4.21626
$274$	44.1386	2.66651
$275$	66.5753	4.01464
$276$	−14.2316	−0.856642
$277$	−21.3580	−1.28328	−0.641638	−	0.767008i	$-0.721745\pi$
$277$	−21.3580	−1.28328	−0.641638	+	0.767008i	$0.721745\pi$
$278$	−4.15223	−0.249034
$279$	24.5754	1.47129
$280$	82.8458	4.95099
$281$	19.4050	1.15760	0.578801	−	0.815469i	$-0.303521\pi$
$281$	19.4050	1.15760	0.578801	+	0.815469i	$0.303521\pi$
$282$	−50.7434	−3.02172
$283$	−14.6766	−0.872436	−0.436218	−	0.899841i	$-0.643682\pi$
$283$	−14.6766	−0.872436	−0.436218	+	0.899841i	$0.643682\pi$
$284$	58.1997	3.45352
$285$	54.4212	3.22364
$286$	−71.1866	−4.20935
$287$	−11.3557	−0.670308
$288$	−11.3121	−0.666569
$289$	−13.7089	−0.806405
$290$	−51.1864	−3.00577
$291$	−14.3828	−0.843133
$292$	−17.7046	−1.03608
$293$	−23.7041	−1.38481	−0.692404	−	0.721510i	$-0.743448\pi$
$293$	−23.7041	−1.38481	−0.692404	+	0.721510i	$0.743448\pi$
$294$	−53.9737	−3.14781
$295$	3.23862	0.188560
$296$	−53.9314	−3.13470
$297$	87.2304	5.06162
$298$	18.0091	1.04324
$299$	−5.84431	−0.337985
$300$	181.472	10.4773
$301$	9.55601	0.550799
$302$	2.47698	0.142534
$303$	−6.00967	−0.345247
$304$	−18.4826	−1.06005
$305$	45.3519	2.59684
$306$	−36.6432	−2.09475
$307$	−3.72140	−0.212392	−0.106196	−	0.994345i	$-0.533867\pi$
$307$	−3.72140	−0.212392	−0.106196	+	0.994345i	$0.533867\pi$
$308$	77.0598	4.39089
$309$	20.7235	1.17892
$310$	31.7928	1.80571
$311$	11.5548	0.655214	0.327607	−	0.944814i	$-0.393758\pi$
$311$	11.5548	0.655214	0.327607	+	0.944814i	$0.393758\pi$
$312$	−100.198	−5.67258
$313$	31.1724	1.76197	0.880984	−	0.473146i	$-0.156882\pi$
$313$	31.1724	1.76197	0.880984	+	0.473146i	$0.156882\pi$
$314$	43.2282	2.43951
$315$	−127.722	−7.19630
$316$	17.4412	0.981144
$317$	17.4440	0.979754	0.489877	−	0.871792i	$-0.337042\pi$
$317$	17.4440	0.979754	0.489877	+	0.871792i	$0.337042\pi$
$318$	−8.27272	−0.463911
$319$	−24.5853	−1.37651
$320$	26.5152	1.48224
$321$	−54.4977	−3.04176
$322$	9.38615	0.523070
$323$	−6.94076	−0.386194
$324$	136.606	7.58922
$325$	74.5226	4.13377
$326$	2.87047	0.158981
$327$	57.3696	3.17255
$328$	16.3329	0.901836
$329$	22.5574	1.24363
$330$	178.528	9.82763
$331$	−23.8470	−1.31075	−0.655375	−	0.755304i	$-0.727489\pi$
$331$	−23.8470	−1.31075	−0.655375	+	0.755304i	$0.727489\pi$
$332$	2.07422	0.113838
$333$	83.1449	4.55631
$334$	−32.2451	−1.76437
$335$	6.08605	0.332516
$336$	59.3350	3.23699
$337$	15.6445	0.852212	0.426106	−	0.904673i	$-0.359885\pi$
$337$	15.6445	0.852212	0.426106	+	0.904673i	$0.359885\pi$
$338$	−47.4836	−2.58277
$339$	−66.9115	−3.63413
$340$	−31.9520	−1.73284
$341$	15.2704	0.826939
$342$	77.2784	4.17874
$343$	−1.74941	−0.0944593
$344$	−13.7444	−0.741048
$345$	14.6568	0.789098
$346$	−25.9350	−1.39427
$347$	13.4730	0.723267	0.361633	−	0.932320i	$-0.382219\pi$
$347$	13.4730	0.723267	0.361633	+	0.932320i	$0.382219\pi$
$348$	−67.0149	−3.59238
$349$	−2.28436	−0.122279	−0.0611395	−	0.998129i	$-0.519473\pi$
$349$	−2.28436	−0.122279	−0.0611395	+	0.998129i	$0.519473\pi$
$350$	−119.686	−6.39747
$351$	97.6433	5.21181
$352$	−7.02897	−0.374645
$353$	−4.28704	−0.228176	−0.114088	−	0.993471i	$-0.536395\pi$
$353$	−4.28704	−0.228176	−0.114088	+	0.993471i	$0.536395\pi$
$354$	6.29075	0.334349
$355$	−59.9387	−3.18122
$356$	2.65136	0.140522
$357$	22.2820	1.17929
$358$	−29.5047	−1.55937
$359$	13.2964	0.701758	0.350879	−	0.936421i	$-0.385883\pi$
$359$	13.2964	0.701758	0.350879	+	0.936421i	$0.385883\pi$
$360$	183.702	9.68194
$361$	−4.36237	−0.229598
$362$	−53.9220	−2.83408
$363$	49.0103	2.57237
$364$	86.2587	4.52118
$365$	18.2336	0.954392
$366$	88.0922	4.60465
$367$	33.5342	1.75047	0.875235	−	0.483698i	$-0.160707\pi$
$367$	33.5342	1.75047	0.875235	+	0.483698i	$0.160707\pi$
$368$	−4.97777	−0.259484
$369$	−25.1801	−1.31083
$370$	107.563	5.59195
$371$	3.67754	0.190928
$372$	41.6243	2.15812
$373$	−6.64895	−0.344270	−0.172135	−	0.985073i	$-0.555066\pi$
$373$	−6.64895	−0.344270	−0.172135	+	0.985073i	$0.555066\pi$
$374$	−22.7690	−1.17736
$375$	−115.772	−5.97845
$376$	−32.4442	−1.67318
$377$	−27.5201	−1.41736
$378$	−156.818	−8.06587
$379$	−0.520823	−0.0267529	−0.0133765	−	0.999911i	$-0.504258\pi$
$379$	−0.520823	−0.0267529	−0.0133765	+	0.999911i	$0.504258\pi$
$380$	67.3849	3.45677
$381$	−55.1480	−2.82532
$382$	−1.82150	−0.0931958
$383$	10.5187	0.537479	0.268739	−	0.963213i	$-0.413393\pi$
$383$	10.5187	0.537479	0.268739	+	0.963213i	$0.413393\pi$
$384$	60.7696	3.10113
$385$	−79.3624	−4.04468
$386$	45.2920	2.30530
$387$	21.1894	1.07712
$388$	−17.8089	−0.904109
$389$	−11.6602	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$389$	−11.6602	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$390$	199.839	10.1192
$391$	−1.86930	−0.0945346
$392$	−34.5096	−1.74300
$393$	−9.57954	−0.483224
$394$	12.5213	0.630814
$395$	−17.9623	−0.903783
$396$	170.872	8.58664
$397$	26.6430	1.33717	0.668586	−	0.743635i	$-0.266900\pi$
$397$	26.6430	1.33717	0.668586	+	0.743635i	$0.266900\pi$
$398$	56.8195	2.84810
$399$	−46.9915	−2.35252
$400$	63.4731	3.17365
$401$	−23.6573	−1.18139	−0.590695	−	0.806895i	$-0.701146\pi$
$401$	−23.6573	−1.18139	−0.590695	+	0.806895i	$0.701146\pi$
$402$	11.8216	0.589609
$403$	17.0933	0.851477
$404$	−7.44123	−0.370215
$405$	−140.688	−6.99083
$406$	44.1982	2.19352
$407$	51.6637	2.56088
$408$	−32.0482	−1.58662
$409$	−2.49228	−0.123235	−0.0616177	−	0.998100i	$-0.519626\pi$
$409$	−2.49228	−0.123235	−0.0616177	+	0.998100i	$0.519626\pi$
$410$	−32.5752	−1.60877
$411$	−59.5145	−2.93563
$412$	25.6601	1.26418
$413$	−2.79648	−0.137606
$414$	20.8128	1.02289
$415$	−2.13620	−0.104862
$416$	−7.86804	−0.385762
$417$	5.59867	0.274168
$418$	48.0185	2.34866
$419$	8.92565	0.436046	0.218023	−	0.975944i	$-0.430039\pi$
$419$	8.92565	0.436046	0.218023	+	0.975944i	$0.430039\pi$
$420$	−216.327	−10.5557
$421$	−34.6264	−1.68759	−0.843793	−	0.536668i	$-0.819683\pi$
$421$	−34.6264	−1.68759	−0.843793	+	0.536668i	$0.819683\pi$
$422$	35.3776	1.72215
$423$	50.0186	2.43199
$424$	−5.28940	−0.256876
$425$	23.8360	1.15622
$426$	−116.426	−5.64085
$427$	−39.1603	−1.89510
$428$	−67.4795	−3.26175
$429$	95.9846	4.63418
$430$	27.4125	1.32195
$431$	10.4839	0.504990	0.252495	−	0.967598i	$-0.418749\pi$
$431$	10.4839	0.504990	0.252495	+	0.967598i	$0.418749\pi$
$432$	83.1657	4.00131
$433$	−13.4972	−0.648636	−0.324318	−	0.945948i	$-0.605135\pi$
$433$	−13.4972	−0.648636	−0.324318	+	0.945948i	$0.605135\pi$
$434$	−27.4524	−1.31776
$435$	69.0173	3.30913
$436$	71.0356	3.40199
$437$	3.94224	0.188583
$438$	35.4173	1.69230
$439$	−5.01845	−0.239518	−0.119759	−	0.992803i	$-0.538212\pi$
$439$	−5.01845	−0.239518	−0.119759	+	0.992803i	$0.538212\pi$
$440$	114.147	5.44174
$441$	53.2028	2.53346
$442$	−25.4870	−1.21229
$443$	−0.551182	−0.0261874	−0.0130937	−	0.999914i	$-0.504168\pi$
$443$	−0.551182	−0.0261874	−0.0130937	+	0.999914i	$0.504168\pi$
$444$	140.826	6.68329
$445$	−2.73058	−0.129442
$446$	62.1616	2.94343
$447$	−24.2826	−1.14853
$448$	−22.8952	−1.08170
$449$	−19.8262	−0.935655	−0.467828	−	0.883820i	$-0.654963\pi$
$449$	−19.8262	−0.935655	−0.467828	+	0.883820i	$0.654963\pi$
$450$	−265.390	−12.5106
$451$	−15.6462	−0.736749
$452$	−82.8504	−3.89696
$453$	−3.33984	−0.156920
$454$	23.1173	1.08495
$455$	−88.8361	−4.16470
$456$	67.5878	3.16509
$457$	13.4033	0.626978	0.313489	−	0.949592i	$-0.398502\pi$
$457$	13.4033	0.626978	0.313489	+	0.949592i	$0.398502\pi$
$458$	−61.4778	−2.87267
$459$	31.2312	1.45775
$460$	18.1482	0.846166
$461$	3.59701	0.167529	0.0837647	−	0.996486i	$-0.473306\pi$
$461$	3.59701	0.167529	0.0837647	+	0.996486i	$0.473306\pi$
$462$	−154.155	−7.17192
$463$	14.4162	0.669978	0.334989	−	0.942222i	$-0.391267\pi$
$463$	14.4162	0.669978	0.334989	+	0.942222i	$0.391267\pi$
$464$	−23.4397	−1.08816
$465$	−42.8680	−1.98796
$466$	24.0822	1.11559
$467$	−24.7027	−1.14311	−0.571553	−	0.820565i	$-0.693659\pi$
$467$	−24.7027	−1.14311	−0.571553	+	0.820565i	$0.693659\pi$
$468$	191.269	8.84143
$469$	−5.25516	−0.242661
$470$	64.7083	2.98477
$471$	−58.2869	−2.68572
$472$	4.02217	0.185135
$473$	13.1665	0.605395
$474$	−34.8903	−1.60256
$475$	−50.2687	−2.30649
$476$	27.5898	1.26458
$477$	8.15455	0.373371
$478$	2.00456	0.0916863
$479$	23.2008	1.06007	0.530036	−	0.847975i	$-0.322178\pi$
$479$	23.2008	1.06007	0.530036	+	0.847975i	$0.322178\pi$
$480$	19.7321	0.900645
$481$	57.8310	2.63687
$482$	−15.8380	−0.721401
$483$	−12.6558	−0.575861
$484$	60.6850	2.75841
$485$	18.3410	0.832822
$486$	−145.347	−6.59308
$487$	−27.7729	−1.25851	−0.629256	−	0.777198i	$-0.716640\pi$
$487$	−27.7729	−1.25851	−0.629256	+	0.777198i	$0.716640\pi$
$488$	56.3243	2.54968
$489$	−3.87041	−0.175026
$490$	68.8276	3.10932
$491$	−2.06017	−0.0929743	−0.0464871	−	0.998919i	$-0.514803\pi$
$491$	−2.06017	−0.0929743	−0.0464871	+	0.998919i	$0.514803\pi$
$492$	−42.6485	−1.92274
$493$	−8.80231	−0.396436
$494$	53.7506	2.41835
$495$	−175.978	−7.90961
$496$	14.5589	0.653712
$497$	51.7557	2.32156
$498$	−4.14938	−0.185938
$499$	26.6202	1.19168	0.595842	−	0.803102i	$-0.296819\pi$
$499$	26.6202	1.19168	0.595842	+	0.803102i	$0.296819\pi$
$500$	−143.350	−6.41082
$501$	43.4778	1.94245
$502$	52.8325	2.35803
$503$	−1.54963	−0.0690948	−0.0345474	−	0.999403i	$-0.510999\pi$
$503$	−1.54963	−0.0690948	−0.0345474	+	0.999403i	$0.510999\pi$
$504$	−158.622	−7.06560
$505$	7.66358	0.341025
$506$	12.9324	0.574917
$507$	64.0247	2.84343
$508$	−68.2847	−3.02965
$509$	25.6589	1.13731	0.568656	−	0.822575i	$-0.307464\pi$
$509$	25.6589	1.13731	0.568656	+	0.822575i	$0.307464\pi$
$510$	63.9185	2.83036
$511$	−15.7443	−0.696488
$512$	44.4036	1.96238
$513$	−65.8647	−2.90800
$514$	63.1461	2.78525
$515$	−26.4268	−1.16450
$516$	35.8893	1.57994
$517$	31.0800	1.36690
$518$	−92.8785	−4.08085
$519$	34.9695	1.53499
$520$	127.773	5.60321
$521$	−7.27996	−0.318941	−0.159470	−	0.987203i	$-0.550979\pi$
$521$	−7.27996	−0.318941	−0.159470	+	0.987203i	$0.550979\pi$
$522$	98.0049	4.28956
$523$	21.0208	0.919174	0.459587	−	0.888133i	$-0.347997\pi$
$523$	21.0208	0.919174	0.459587	+	0.888133i	$0.347997\pi$
$524$	−11.8615	−0.518171
$525$	161.379	7.04314
$526$	12.2563	0.534400
$527$	5.46728	0.238159
$528$	81.7530	3.55784
$529$	−21.9383	−0.953838
$530$	10.5494	0.458238
$531$	−6.20089	−0.269096
$532$	−58.1853	−2.52265
$533$	−17.5139	−0.758611
$534$	−5.30392	−0.229523
$535$	69.4958	3.00457
$536$	7.55850	0.326477
$537$	39.7827	1.71675
$538$	−14.3695	−0.619512
$539$	33.0586	1.42393
$540$	−303.210	−13.0481
$541$	−21.1400	−0.908880	−0.454440	−	0.890777i	$-0.650161\pi$
$541$	−21.1400	−0.908880	−0.454440	+	0.890777i	$0.650161\pi$
$542$	48.3865	2.07838
$543$	72.7060	3.12011
$544$	−2.51659	−0.107898
$545$	−73.1581	−3.13375
$546$	−172.556	−7.38473
$547$	17.5316	0.749599	0.374799	−	0.927106i	$-0.377712\pi$
$547$	17.5316	0.749599	0.374799	+	0.927106i	$0.377712\pi$
$548$	−73.6914	−3.14794
$549$	−86.8339	−3.70598
$550$	−164.906	−7.03160
$551$	18.5635	0.790833
$552$	18.2029	0.774767
$553$	15.5101	0.659555
$554$	52.9032	2.24764
$555$	−145.033	−6.15633
$556$	6.93232	0.293996
$557$	32.4728	1.37592	0.687959	−	0.725750i	$-0.258507\pi$
$557$	32.4728	1.37592	0.687959	+	0.725750i	$0.258507\pi$
$558$	−60.8727	−2.57695
$559$	14.7382	0.623359
$560$	−75.6643	−3.19740
$561$	30.7007	1.29618
$562$	−48.0657	−2.02753
$563$	5.86055	0.246993	0.123496	−	0.992345i	$-0.460589\pi$
$563$	5.86055	0.246993	0.123496	+	0.992345i	$0.460589\pi$
$564$	84.7183	3.56728
$565$	85.3260	3.58969
$566$	36.3537	1.52806
$567$	121.481	5.10170
$568$	−74.4402	−3.12344
$569$	−16.7995	−0.704273	−0.352136	−	0.935949i	$-0.614545\pi$
$569$	−16.7995	−0.704273	−0.352136	+	0.935949i	$0.614545\pi$
$570$	−134.800	−5.64616
$571$	23.1903	0.970483	0.485241	−	0.874380i	$-0.338732\pi$
$571$	23.1903	0.970483	0.485241	+	0.874380i	$0.338732\pi$
$572$	118.849	4.96933
$573$	2.45602	0.102602
$574$	28.1279	1.17404
$575$	−13.5385	−0.564594
$576$	−50.7678	−2.11532
$577$	−30.3808	−1.26477	−0.632385	−	0.774655i	$-0.717924\pi$
$577$	−30.3808	−1.26477	−0.632385	+	0.774655i	$0.717924\pi$
$578$	33.9566	1.41241
$579$	−61.0697	−2.53797
$580$	85.4579	3.54844
$581$	1.84456	0.0765251
$582$	35.6258	1.47674
$583$	5.06699	0.209853
$584$	22.6450	0.937059
$585$	−196.985	−8.14431
$586$	58.7146	2.42548
$587$	9.42372	0.388959	0.194479	−	0.980907i	$-0.437698\pi$
$587$	9.42372	0.388959	0.194479	+	0.980907i	$0.437698\pi$
$588$	90.1115	3.71613
$589$	−11.5302	−0.475092
$590$	−8.02200	−0.330261
$591$	−16.8831	−0.694479
$592$	49.2564	2.02443
$593$	2.76119	0.113388	0.0566942	−	0.998392i	$-0.481944\pi$
$593$	2.76119	0.113388	0.0566942	+	0.998392i	$0.481944\pi$
$594$	−216.068	−8.86537
$595$	−28.4142	−1.16487
$596$	−30.0670	−1.23159
$597$	−76.6127	−3.13555
$598$	14.4762	0.591977
$599$	−44.1434	−1.80365	−0.901826	−	0.432099i	$-0.857773\pi$
$599$	−44.1434	−1.80365	−0.901826	+	0.432099i	$0.857773\pi$
$600$	−232.111	−9.47588
$601$	5.61418	0.229007	0.114504	−	0.993423i	$-0.463472\pi$
$601$	5.61418	0.229007	0.114504	+	0.993423i	$0.463472\pi$
$602$	−23.6700	−0.964719
$603$	−11.6528	−0.474537
$604$	−4.13542	−0.168268
$605$	−62.4983	−2.54092
$606$	14.8858	0.604696
$607$	−19.6623	−0.798068	−0.399034	−	0.916936i	$-0.630654\pi$
$607$	−19.6623	−0.798068	−0.399034	+	0.916936i	$0.630654\pi$
$608$	5.30734	0.215241
$609$	−59.5948	−2.41490
$610$	−112.336	−4.54834
$611$	34.7901	1.40746
$612$	61.1775	2.47295
$613$	−40.8268	−1.64898	−0.824489	−	0.565877i	$-0.808538\pi$
$613$	−40.8268	−1.64898	−0.824489	+	0.565877i	$0.808538\pi$
$614$	9.21784	0.372002
$615$	43.9229	1.77114
$616$	−98.5631	−3.97122
$617$	28.6299	1.15260	0.576298	−	0.817240i	$-0.304497\pi$
$617$	28.6299	1.15260	0.576298	+	0.817240i	$0.304497\pi$
$618$	−51.3318	−2.06487
$619$	−25.9720	−1.04390	−0.521951	−	0.852975i	$-0.674796\pi$
$619$	−25.9720	−1.04390	−0.521951	+	0.852975i	$0.674796\pi$
$620$	−53.0795	−2.13173
$621$	−17.7388	−0.711835
$622$	−28.6211	−1.14760
$623$	2.35779	0.0944630
$624$	91.5121	3.66342
$625$	81.9384	3.27754
$626$	−77.2134	−3.08607
$627$	−64.7459	−2.58570
$628$	−72.1714	−2.87995
$629$	18.4972	0.737533
$630$	316.364	12.6042
$631$	21.5365	0.857353	0.428676	−	0.903458i	$-0.358980\pi$
$631$	21.5365	0.857353	0.428676	+	0.903458i	$0.358980\pi$
$632$	−22.3081	−0.887369
$633$	−47.7014	−1.89596
$634$	−43.2085	−1.71603
$635$	70.3251	2.79077
$636$	13.8117	0.547668
$637$	37.0049	1.46619
$638$	60.8973	2.41095
$639$	114.763	4.53995
$640$	−77.4938	−3.06321
$641$	23.9162	0.944635	0.472317	−	0.881429i	$-0.343418\pi$
$641$	23.9162	0.944635	0.472317	+	0.881429i	$0.343418\pi$
$642$	134.990	5.32762
$643$	−12.2402	−0.482707	−0.241353	−	0.970437i	$-0.577591\pi$
$643$	−12.2402	−0.482707	−0.241353	+	0.970437i	$0.577591\pi$
$644$	−15.6706	−0.617508
$645$	−36.9617	−1.45537
$646$	17.1921	0.676414
$647$	−9.79158	−0.384947	−0.192473	−	0.981302i	$-0.561651\pi$
$647$	−9.79158	−0.384947	−0.192473	+	0.981302i	$0.561651\pi$
$648$	−174.725	−6.86386
$649$	−3.85305	−0.151245
$650$	−184.591	−7.24025
$651$	37.0155	1.45075
$652$	−4.79237	−0.187684
$653$	22.7892	0.891810	0.445905	−	0.895080i	$-0.352882\pi$
$653$	22.7892	0.891810	0.445905	+	0.895080i	$0.352882\pi$
$654$	−142.103	−5.55668
$655$	12.2159	0.477314
$656$	−14.9171	−0.582415
$657$	−34.9114	−1.36202
$658$	−55.8741	−2.17820
$659$	−12.1921	−0.474937	−0.237468	−	0.971395i	$-0.576318\pi$
$659$	−12.1921	−0.474937	−0.237468	+	0.971395i	$0.576318\pi$
$660$	−298.060	−11.6020
$661$	39.9163	1.55256	0.776281	−	0.630387i	$-0.217104\pi$
$661$	39.9163	1.55256	0.776281	+	0.630387i	$0.217104\pi$
$662$	59.0685	2.29576
$663$	34.3655	1.33465
$664$	−2.65303	−0.102957
$665$	59.9238	2.32375
$666$	−205.948	−7.98033
$667$	4.99957	0.193584
$668$	53.8346	2.08292
$669$	−83.8158	−3.24050
$670$	−15.0750	−0.582399
$671$	−53.9560	−2.08295
$672$	−17.0382	−0.657264
$673$	40.8800	1.57581	0.787905	−	0.615797i	$-0.211166\pi$
$673$	40.8800	1.57581	0.787905	+	0.615797i	$0.211166\pi$
$674$	−38.7512	−1.49264
$675$	226.193	8.70619
$676$	79.2759	3.04907
$677$	22.5493	0.866639	0.433320	−	0.901240i	$-0.357342\pi$
$677$	22.5493	0.866639	0.433320	+	0.901240i	$0.357342\pi$
$678$	165.738	6.36515
$679$	−15.8370	−0.607770
$680$	40.8681	1.56722
$681$	−31.1703	−1.19445
$682$	−37.8245	−1.44837
$683$	32.5639	1.24602	0.623011	−	0.782213i	$-0.285909\pi$
$683$	32.5639	1.24602	0.623011	+	0.782213i	$0.285909\pi$
$684$	−129.020	−4.93319
$685$	75.8933	2.89973
$686$	4.33325	0.165444
$687$	82.8938	3.16260
$688$	12.5530	0.478577
$689$	5.67186	0.216081
$690$	−36.3047	−1.38210
$691$	46.9169	1.78480	0.892401	−	0.451244i	$-0.149020\pi$
$691$	46.9169	1.78480	0.892401	+	0.451244i	$0.149020\pi$
$692$	43.2996	1.64600
$693$	151.953	5.77220
$694$	−33.3723	−1.26679
$695$	−7.13946	−0.270815
$696$	85.7152	3.24903
$697$	−5.60182	−0.212184
$698$	5.65831	0.214170
$699$	−32.4713	−1.22818
$700$	199.820	7.55250
$701$	6.50048	0.245520	0.122760	−	0.992436i	$-0.460825\pi$
$701$	6.50048	0.245520	0.122760	+	0.992436i	$0.460825\pi$
$702$	−241.860	−9.12843
$703$	−39.0095	−1.47127
$704$	−31.5456	−1.18892
$705$	−87.2497	−3.28601
$706$	10.6189	0.399648
$707$	−6.61732	−0.248870
$708$	−10.5027	−0.394715
$709$	29.4142	1.10467	0.552336	−	0.833622i	$-0.313737\pi$
$709$	29.4142	1.10467	0.552336	+	0.833622i	$0.313737\pi$
$710$	148.467	5.57187
$711$	34.3919	1.28980
$712$	−3.39121	−0.127091
$713$	−3.10533	−0.116296
$714$	−55.1921	−2.06551
$715$	−122.400	−4.57751
$716$	49.2594	1.84091
$717$	−2.70285	−0.100940
$718$	−32.9349	−1.22912
$719$	8.03290	0.299577	0.149788	−	0.988718i	$-0.452141\pi$
$719$	8.03290	0.299577	0.149788	+	0.988718i	$0.452141\pi$
$720$	−167.778	−6.25270
$721$	22.8189	0.849821
$722$	10.8055	0.402139
$723$	21.3552	0.794209
$724$	90.0252	3.34576
$725$	−63.7511	−2.36766
$726$	−121.397	−4.50548
$727$	7.37245	0.273429	0.136714	−	0.990611i	$-0.456346\pi$
$727$	7.37245	0.273429	0.136714	+	0.990611i	$0.456346\pi$
$728$	−110.329	−4.08906
$729$	96.8799	3.58815
$730$	−45.1643	−1.67161
$731$	4.71401	0.174354
$732$	−147.074	−5.43601
$733$	0.321535	0.0118762	0.00593809	−	0.999982i	$-0.498110\pi$
$733$	0.321535	0.0118762	0.00593809	+	0.999982i	$0.498110\pi$
$734$	−83.0635	−3.06593
$735$	−92.8040	−3.42313
$736$	1.42938	0.0526878
$737$	−7.24068	−0.266714
$738$	62.3707	2.29590
$739$	−32.7289	−1.20395	−0.601976	−	0.798514i	$-0.705620\pi$
$739$	−32.7289	−1.20395	−0.601976	+	0.798514i	$0.705620\pi$
$740$	−179.582	−6.60156
$741$	−72.4748	−2.66243
$742$	−9.10919	−0.334409
$743$	14.2001	0.520952	0.260476	−	0.965480i	$-0.416120\pi$
$743$	14.2001	0.520952	0.260476	+	0.965480i	$0.416120\pi$
$744$	−53.2394	−1.95185
$745$	30.9654	1.13448
$746$	16.4693	0.602984
$747$	4.09011	0.149649
$748$	38.0139	1.38992
$749$	−60.0080	−2.19265
$750$	286.765	10.4712
$751$	−4.20061	−0.153282	−0.0766412	−	0.997059i	$-0.524420\pi$
$751$	−4.20061	−0.153282	−0.0766412	+	0.997059i	$0.524420\pi$
$752$	29.6318	1.08056
$753$	−71.2368	−2.59601
$754$	68.1668	2.48249
$755$	4.25899	0.155001
$756$	261.815	9.52213
$757$	−25.6597	−0.932616	−0.466308	−	0.884622i	$-0.654416\pi$
$757$	−25.6597	−0.932616	−0.466308	+	0.884622i	$0.654416\pi$
$758$	1.29007	0.0468574
$759$	−17.4375	−0.632941
$760$	−86.1884	−3.12638
$761$	33.5760	1.21713	0.608564	−	0.793505i	$-0.291746\pi$
$761$	33.5760	1.21713	0.608564	+	0.793505i	$0.291746\pi$
$762$	136.600	4.94851
$763$	63.1703	2.28692
$764$	3.04107	0.110022
$765$	−63.0055	−2.27797
$766$	−26.0545	−0.941388
$767$	−4.31300	−0.155733
$768$	−108.939	−3.93101
$769$	23.5681	0.849888	0.424944	−	0.905220i	$-0.360294\pi$
$769$	23.5681	0.849888	0.424944	+	0.905220i	$0.360294\pi$
$770$	196.579	7.08421
$771$	−85.1432	−3.06636
$772$	−75.6171	−2.72152
$773$	21.3047	0.766279	0.383139	−	0.923691i	$-0.374843\pi$
$773$	21.3047	0.766279	0.383139	+	0.923691i	$0.374843\pi$
$774$	−52.4858	−1.88656
$775$	39.5970	1.42237
$776$	22.7784	0.817697
$777$	125.233	4.49271
$778$	28.8822	1.03548
$779$	11.8139	0.423277
$780$	−333.640	−11.9462
$781$	71.3101	2.55168
$782$	4.63022	0.165576
$783$	−83.5300	−2.98512
$784$	31.5182	1.12565
$785$	74.3279	2.65288
$786$	23.7283	0.846361
$787$	39.8017	1.41878	0.709388	−	0.704818i	$-0.248971\pi$
$787$	39.8017	1.41878	0.709388	+	0.704818i	$0.248971\pi$
$788$	−20.9048	−0.744704
$789$	−16.5258	−0.588335
$790$	44.4923	1.58297
$791$	−73.6770	−2.61965
$792$	−218.553	−7.76595
$793$	−60.3969	−2.14476
$794$	−65.9941	−2.34204
$795$	−14.2244	−0.504486
$796$	−94.8626	−3.36232
$797$	−8.14988	−0.288683	−0.144342	−	0.989528i	$-0.546106\pi$
$797$	−8.14988	−0.288683	−0.144342	+	0.989528i	$0.546106\pi$
$798$	116.397	4.12040
$799$	11.1276	0.393667
$800$	−18.2265	−0.644405
$801$	5.22816	0.184728
$802$	58.5987	2.06919
$803$	−21.6929	−0.765525
$804$	−19.7367	−0.696061
$805$	16.1388	0.568819
$806$	−42.3397	−1.49135
$807$	19.3751	0.682037
$808$	9.51769	0.334831
$809$	27.0661	0.951592	0.475796	−	0.879556i	$-0.342160\pi$
$809$	27.0661	0.951592	0.475796	+	0.879556i	$0.342160\pi$
$810$	348.480	12.2444
$811$	−3.85277	−0.135289	−0.0676445	−	0.997709i	$-0.521548\pi$
$811$	−3.85277	−0.135289	−0.0676445	+	0.997709i	$0.521548\pi$
$812$	−73.7909	−2.58955
$813$	−65.2420	−2.28814
$814$	−127.970	−4.48535
$815$	4.93557	0.172885
$816$	29.2701	1.02466
$817$	−9.94156	−0.347811
$818$	6.17333	0.215845
$819$	170.092	5.94348
$820$	54.3857	1.89923
$821$	46.6944	1.62965	0.814824	−	0.579709i	$-0.196834\pi$
$821$	46.6944	1.62965	0.814824	+	0.579709i	$0.196834\pi$
$822$	147.416	5.14173
$823$	32.6915	1.13955	0.569776	−	0.821800i	$-0.307030\pi$
$823$	32.6915	1.13955	0.569776	+	0.821800i	$0.307030\pi$
$824$	−32.8204	−1.14335
$825$	222.351	7.74127
$826$	6.92681	0.241015
$827$	−41.8078	−1.45380	−0.726899	−	0.686744i	$-0.759039\pi$
$827$	−41.8078	−1.45380	−0.726899	+	0.686744i	$0.759039\pi$
$828$	−34.7479	−1.20757
$829$	−47.1004	−1.63587	−0.817933	−	0.575314i	$-0.804880\pi$
$829$	−47.1004	−1.63587	−0.817933	+	0.575314i	$0.804880\pi$
$830$	5.29132	0.183664
$831$	−71.3323	−2.47449
$832$	−35.3113	−1.22420
$833$	11.8360	0.410093
$834$	−13.8678	−0.480202
$835$	−55.4432	−1.91869
$836$	−80.1689	−2.77270
$837$	51.8821	1.79331
$838$	−22.1086	−0.763730
$839$	15.4450	0.533222	0.266611	−	0.963804i	$-0.414096\pi$
$839$	15.4450	0.533222	0.266611	+	0.963804i	$0.414096\pi$
$840$	276.692	9.54679
$841$	−5.45762	−0.188194
$842$	85.7688	2.95579
$843$	64.8095	2.23216
$844$	−59.0644	−2.03308
$845$	−81.6447	−2.80866
$846$	−123.895	−4.25960
$847$	53.9658	1.85429
$848$	4.83089	0.165893
$849$	−49.0177	−1.68228
$850$	−59.0413	−2.02510
$851$	−10.5061	−0.360146
$852$	194.378	6.65928
$853$	43.1807	1.47848	0.739239	−	0.673443i	$-0.235185\pi$
$853$	43.1807	1.47848	0.739239	+	0.673443i	$0.235185\pi$
$854$	96.9994	3.31925
$855$	132.875	4.54422
$856$	86.3095	2.95000
$857$	−27.4653	−0.938198	−0.469099	−	0.883146i	$-0.655421\pi$
$857$	−27.4653	−0.938198	−0.469099	+	0.883146i	$0.655421\pi$
$858$	−237.752	−8.11672
$859$	−28.9061	−0.986263	−0.493132	−	0.869955i	$-0.664148\pi$
$859$	−28.9061	−0.986263	−0.493132	+	0.869955i	$0.664148\pi$
$860$	−45.7663	−1.56062
$861$	−37.9264	−1.29253
$862$	−25.9683	−0.884484
$863$	−7.10670	−0.241915	−0.120957	−	0.992658i	$-0.538596\pi$
$863$	−7.10670	−0.241915	−0.120957	+	0.992658i	$0.538596\pi$
$864$	−23.8813	−0.812459
$865$	−44.5933	−1.51622
$866$	33.4324	1.13608
$867$	−45.7855	−1.55496
$868$	45.8329	1.55567
$869$	21.3701	0.724931
$870$	−170.954	−5.79590
$871$	−8.10502	−0.274628
$872$	−90.8578	−3.07683
$873$	−35.1169	−1.18853
$874$	−9.76485	−0.330301
$875$	−127.478	−4.30955
$876$	−59.1307	−1.99784
$877$	35.4880	1.19835	0.599173	−	0.800620i	$-0.295496\pi$
$877$	35.4880	1.19835	0.599173	+	0.800620i	$0.295496\pi$
$878$	12.4306	0.419512
$879$	−79.1680	−2.67027
$880$	−104.252	−3.51433
$881$	−29.9141	−1.00783	−0.503915	−	0.863753i	$-0.668108\pi$
$881$	−29.9141	−1.00783	−0.503915	+	0.863753i	$0.668108\pi$
$882$	−131.782	−4.43733
$883$	21.6226	0.727659	0.363829	−	0.931466i	$-0.381469\pi$
$883$	21.6226	0.727659	0.363829	+	0.931466i	$0.381469\pi$
$884$	42.5517	1.43117
$885$	10.8165	0.363593
$886$	1.36527	0.0458670
$887$	0.553736	0.0185926	0.00929632	−	0.999957i	$-0.497041\pi$
$887$	0.553736	0.0185926	0.00929632	+	0.999957i	$0.497041\pi$
$888$	−180.123	−6.04452
$889$	−60.7241	−2.03662
$890$	6.76359	0.226716
$891$	167.379	5.60739
$892$	−103.781	−3.47486
$893$	−23.4675	−0.785309
$894$	60.1476	2.01164
$895$	−50.7312	−1.69576
$896$	66.9141	2.23544
$897$	−19.5191	−0.651723
$898$	49.1090	1.63879
$899$	−14.6226	−0.487692
$900$	443.081	14.7694
$901$	1.81414	0.0604378
$902$	38.7552	1.29041
$903$	31.9156	1.06208
$904$	105.970	3.52450
$905$	−92.7152	−3.08196
$906$	8.27272	0.274843
$907$	22.4481	0.745378	0.372689	−	0.927956i	$-0.378436\pi$
$907$	22.4481	0.745378	0.372689	+	0.927956i	$0.378436\pi$
$908$	−38.5953	−1.28083
$909$	−14.6732	−0.486680
$910$	220.045	7.29442
$911$	−12.2994	−0.407496	−0.203748	−	0.979023i	$-0.565312\pi$
$911$	−12.2994	−0.407496	−0.203748	+	0.979023i	$0.565312\pi$
$912$	−61.7289	−2.04405
$913$	2.54147	0.0841104
$914$	−33.1996	−1.09815
$915$	151.468	5.00739
$916$	102.640	3.39132
$917$	−10.5481	−0.348330
$918$	−77.3590	−2.55323
$919$	−9.29356	−0.306566	−0.153283	−	0.988182i	$-0.548985\pi$
$919$	−9.29356	−0.306566	−0.153283	+	0.988182i	$0.548985\pi$
$920$	−23.2125	−0.765292
$921$	−12.4289	−0.409546
$922$	−8.90972	−0.293426
$923$	79.8226	2.62739
$924$	257.368	8.46678
$925$	133.967	4.40481
$926$	−35.7086	−1.17346
$927$	50.5985	1.66187
$928$	6.73079	0.220949
$929$	−1.24007	−0.0406855	−0.0203428	−	0.999793i	$-0.506476\pi$
$929$	−1.24007	−0.0406855	−0.0203428	+	0.999793i	$0.506476\pi$
$930$	106.183	3.48188
$931$	−24.9614	−0.818077
$932$	−40.2063	−1.31700
$933$	38.5913	1.26342
$934$	61.1881	2.00214
$935$	−39.1497	−1.28033
$936$	−244.643	−7.99639
$937$	19.8684	0.649071	0.324536	−	0.945873i	$-0.394792\pi$
$937$	19.8684	0.649071	0.324536	+	0.945873i	$0.394792\pi$
$938$	13.0169	0.425018
$939$	104.111	3.39753
$940$	−108.033	−3.52366
$941$	4.17502	0.136102	0.0680509	−	0.997682i	$-0.478322\pi$
$941$	4.17502	0.136102	0.0680509	+	0.997682i	$0.478322\pi$
$942$	144.376	4.70401
$943$	3.18175	0.103612
$944$	−3.67351	−0.119562
$945$	−269.638	−8.77133
$946$	−32.6131	−1.06034
$947$	35.8356	1.16450	0.582251	−	0.813009i	$-0.302172\pi$
$947$	35.8356	1.16450	0.582251	+	0.813009i	$0.302172\pi$
$948$	58.2509	1.89190
$949$	−24.2824	−0.788240
$950$	124.515	4.03979
$951$	58.2603	1.88922
$952$	−35.2887	−1.14371
$953$	−58.2960	−1.88839	−0.944196	−	0.329383i	$-0.893159\pi$
$953$	−58.2960	−1.88839	−0.944196	+	0.329383i	$0.893159\pi$
$954$	−20.1987	−0.653956
$955$	−3.13193	−0.101347
$956$	−3.34670	−0.108240
$957$	−82.1111	−2.65427
$958$	−57.4679	−1.85670
$959$	−65.5321	−2.11614
$960$	88.5566	2.85815
$961$	−21.9176	−0.707019
$962$	−143.246	−4.61844
$963$	−133.061	−4.28784
$964$	26.4422	0.851646
$965$	77.8765	2.50693
$966$	31.3483	1.00861
$967$	19.1299	0.615177	0.307589	−	0.951519i	$-0.400478\pi$
$967$	19.1299	0.615177	0.307589	+	0.951519i	$0.400478\pi$
$968$	−77.6190	−2.49477
$969$	−23.1810	−0.744682
$970$	−45.4303	−1.45868
$971$	21.8840	0.702291	0.351146	−	0.936321i	$-0.385792\pi$
$971$	21.8840	0.702291	0.351146	+	0.936321i	$0.385792\pi$
$972$	242.663	7.78343
$973$	6.16476	0.197633
$974$	68.7930	2.20427
$975$	248.894	7.97098
$976$	−51.4418	−1.64661
$977$	−43.9680	−1.40666	−0.703331	−	0.710862i	$-0.748305\pi$
$977$	−43.9680	−1.40666	−0.703331	+	0.710862i	$0.748305\pi$
$978$	9.58692	0.306556
$979$	3.24862	0.103826
$980$	−114.911	−3.67069
$981$	140.073	4.47220
$982$	5.10300	0.162843
$983$	−29.0066	−0.925165	−0.462583	−	0.886576i	$-0.653077\pi$
$983$	−29.0066	−0.925165	−0.462583	+	0.886576i	$0.653077\pi$
$984$	54.5495	1.73897
$985$	21.5295	0.685986
$986$	21.8031	0.694353
$987$	75.3381	2.39804
$988$	−89.7389	−2.85498
$989$	−2.67748	−0.0851390
$990$	435.893	13.8536
$991$	6.59738	0.209573	0.104786	−	0.994495i	$-0.466584\pi$
$991$	6.59738	0.209573	0.104786	+	0.994495i	$0.466584\pi$
$992$	−4.18063	−0.132735
$993$	−79.6453	−2.52747
$994$	−128.198	−4.06619
$995$	97.6971	3.09721
$996$	6.92757	0.219509
$997$	−8.69284	−0.275305	−0.137652	−	0.990481i	$-0.543956\pi$
$997$	−8.69284	−0.275305	−0.137652	+	0.990481i	$0.543956\pi$
$998$	−65.9376	−2.08722
$999$	175.531	5.55354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.17	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.17	✓	179	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47698 q^{2} +3.33984 q^{3} +4.13542 q^{4} -4.25899 q^{5} -8.27272 q^{6} +3.67754 q^{7} -5.28940 q^{8} +8.15455 q^{9} +O(q^{10})\)	\(q-2.47698 q^{2} +3.33984 q^{3} +4.13542 q^{4} -4.25899 q^{5} -8.27272 q^{6} +3.67754 q^{7} -5.28940 q^{8} +8.15455 q^{9} +10.5494 q^{10} +5.06699 q^{11} +13.8117 q^{12} +5.67186 q^{13} -9.10919 q^{14} -14.2244 q^{15} +4.83089 q^{16} +1.81414 q^{17} -20.1987 q^{18} -3.82592 q^{19} -17.6127 q^{20} +12.2824 q^{21} -12.5508 q^{22} -1.03040 q^{23} -17.6658 q^{24} +13.1390 q^{25} -14.0491 q^{26} +17.2154 q^{27} +15.2082 q^{28} -4.85205 q^{29} +35.2335 q^{30} +3.01370 q^{31} -1.38721 q^{32} +16.9230 q^{33} -4.49359 q^{34} -15.6626 q^{35} +33.7226 q^{36} +10.1961 q^{37} +9.47671 q^{38} +18.9431 q^{39} +22.5275 q^{40} -3.08786 q^{41} -30.4233 q^{42} +2.59848 q^{43} +20.9542 q^{44} -34.7302 q^{45} +2.55229 q^{46} +6.13382 q^{47} +16.1344 q^{48} +6.52430 q^{49} -32.5450 q^{50} +6.05895 q^{51} +23.4555 q^{52} +1.00000 q^{53} -42.6422 q^{54} -21.5803 q^{55} -19.4520 q^{56} -12.7780 q^{57} +12.0184 q^{58} -0.760420 q^{59} -58.8238 q^{60} -10.6485 q^{61} -7.46488 q^{62} +29.9887 q^{63} -6.22570 q^{64} -24.1564 q^{65} -41.9178 q^{66} -1.42899 q^{67} +7.50225 q^{68} -3.44139 q^{69} +38.7960 q^{70} +14.0735 q^{71} -43.1327 q^{72} -4.28121 q^{73} -25.2556 q^{74} +43.8822 q^{75} -15.8218 q^{76} +18.6341 q^{77} -46.9217 q^{78} +4.21751 q^{79} -20.5747 q^{80} +33.0331 q^{81} +7.64857 q^{82} +0.501574 q^{83} +50.7930 q^{84} -7.72642 q^{85} -6.43638 q^{86} -16.2051 q^{87} -26.8014 q^{88} +0.641133 q^{89} +86.0259 q^{90} +20.8585 q^{91} -4.26116 q^{92} +10.0653 q^{93} -15.1933 q^{94} +16.2945 q^{95} -4.63305 q^{96} -4.30642 q^{97} -16.1606 q^{98} +41.3191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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