LMFDB - Embedded newform 8027.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74408 q^{2} +1.08258 q^{3} +5.52999 q^{4} +4.29779 q^{5} -2.97068 q^{6} +1.02479 q^{7} -9.68658 q^{8} -1.82803 q^{9} +O(q^{10})$	\(q-2.74408 q^{2} +1.08258 q^{3} +5.52999 q^{4} +4.29779 q^{5} -2.97068 q^{6} +1.02479 q^{7} -9.68658 q^{8} -1.82803 q^{9} -11.7935 q^{10} +0.412513 q^{11} +5.98663 q^{12} -3.44671 q^{13} -2.81212 q^{14} +4.65268 q^{15} +15.5208 q^{16} -0.0715217 q^{17} +5.01626 q^{18} +1.31456 q^{19} +23.7667 q^{20} +1.10942 q^{21} -1.13197 q^{22} -1.00000 q^{23} -10.4865 q^{24} +13.4710 q^{25} +9.45806 q^{26} -5.22671 q^{27} +5.66709 q^{28} +3.25477 q^{29} -12.7673 q^{30} -5.87497 q^{31} -23.2172 q^{32} +0.446576 q^{33} +0.196261 q^{34} +4.40434 q^{35} -10.1090 q^{36} -8.50838 q^{37} -3.60725 q^{38} -3.73133 q^{39} -41.6308 q^{40} -4.22079 q^{41} -3.04433 q^{42} -3.73835 q^{43} +2.28119 q^{44} -7.85648 q^{45} +2.74408 q^{46} -11.7534 q^{47} +16.8024 q^{48} -5.94980 q^{49} -36.9654 q^{50} -0.0774276 q^{51} -19.0603 q^{52} -9.88925 q^{53} +14.3425 q^{54} +1.77289 q^{55} -9.92674 q^{56} +1.42311 q^{57} -8.93135 q^{58} +1.06444 q^{59} +25.7293 q^{60} +14.8490 q^{61} +16.1214 q^{62} -1.87335 q^{63} +32.6683 q^{64} -14.8132 q^{65} -1.22544 q^{66} -13.5493 q^{67} -0.395514 q^{68} -1.08258 q^{69} -12.0859 q^{70} +6.75016 q^{71} +17.7074 q^{72} -4.34011 q^{73} +23.3477 q^{74} +14.5833 q^{75} +7.26948 q^{76} +0.422740 q^{77} +10.2391 q^{78} -5.84134 q^{79} +66.7050 q^{80} -0.174217 q^{81} +11.5822 q^{82} -15.0780 q^{83} +6.13506 q^{84} -0.307385 q^{85} +10.2583 q^{86} +3.52353 q^{87} -3.99584 q^{88} -12.8102 q^{89} +21.5588 q^{90} -3.53217 q^{91} -5.52999 q^{92} -6.36010 q^{93} +32.2523 q^{94} +5.64968 q^{95} -25.1344 q^{96} -12.2732 q^{97} +16.3267 q^{98} -0.754086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.74408	−1.94036	−0.970180	−	0.242387i	$-0.922070\pi$
$2$	−2.74408	−1.94036	−0.970180	+	0.242387i	$0.922070\pi$
$3$	1.08258	0.625025	0.312513	−	0.949914i	$-0.398829\pi$
$3$	1.08258	0.625025	0.312513	+	0.949914i	$0.398829\pi$
$4$	5.52999	2.76499
$5$	4.29779	1.92203	0.961014	−	0.276500i	$-0.0891745\pi$
$5$	4.29779	1.92203	0.961014	+	0.276500i	$0.0891745\pi$
$6$	−2.97068	−1.21277
$7$	1.02479	0.387335	0.193668	−	0.981067i	$-0.437962\pi$
$7$	1.02479	0.387335	0.193668	+	0.981067i	$0.437962\pi$
$8$	−9.68658	−3.42472
$9$	−1.82803	−0.609343
$10$	−11.7935	−3.72942
$11$	0.412513	0.124377	0.0621886	−	0.998064i	$-0.480192\pi$
$11$	0.412513	0.124377	0.0621886	+	0.998064i	$0.480192\pi$
$12$	5.98663	1.72819
$13$	−3.44671	−0.955946	−0.477973	−	0.878375i	$-0.658628\pi$
$13$	−3.44671	−0.955946	−0.477973	+	0.878375i	$0.658628\pi$
$14$	−2.81212	−0.751570
$15$	4.65268	1.20132
$16$	15.5208	3.88020
$17$	−0.0715217	−0.0173466	−0.00867328	−	0.999962i	$-0.502761\pi$
$17$	−0.0715217	−0.0173466	−0.00867328	+	0.999962i	$0.502761\pi$
$18$	5.01626	1.18234
$19$	1.31456	0.301580	0.150790	−	0.988566i	$-0.451818\pi$
$19$	1.31456	0.301580	0.150790	+	0.988566i	$0.451818\pi$
$20$	23.7667	5.31440
$21$	1.10942	0.242094
$22$	−1.13197	−0.241337
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−10.4865	−2.14054
$25$	13.4710	2.69419
$26$	9.45806	1.85488
$27$	−5.22671	−1.00588
$28$	5.66709	1.07098
$29$	3.25477	0.604395	0.302198	−	0.953245i	$-0.402280\pi$
$29$	3.25477	0.604395	0.302198	+	0.953245i	$0.402280\pi$
$30$	−12.7673	−2.33099
$31$	−5.87497	−1.05518	−0.527588	−	0.849500i	$-0.676904\pi$
$31$	−5.87497	−1.05518	−0.527588	+	0.849500i	$0.676904\pi$
$32$	−23.2172	−4.10426
$33$	0.446576	0.0777390
$34$	0.196261	0.0336586
$35$	4.40434	0.744469
$36$	−10.1090	−1.68483
$37$	−8.50838	−1.39877	−0.699385	−	0.714746i	$-0.746543\pi$
$37$	−8.50838	−1.39877	−0.699385	+	0.714746i	$0.746543\pi$
$38$	−3.60725	−0.585173
$39$	−3.73133	−0.597490
$40$	−41.6308	−6.58241
$41$	−4.22079	−0.659176	−0.329588	−	0.944125i	$-0.606910\pi$
$41$	−4.22079	−0.659176	−0.329588	+	0.944125i	$0.606910\pi$
$42$	−3.04433	−0.469750
$43$	−3.73835	−0.570092	−0.285046	−	0.958514i	$-0.592009\pi$
$43$	−3.73835	−0.570092	−0.285046	+	0.958514i	$0.592009\pi$
$44$	2.28119	0.343903
$45$	−7.85648	−1.17117
$46$	2.74408	0.404593
$47$	−11.7534	−1.71441	−0.857205	−	0.514976i	$-0.827801\pi$
$47$	−11.7534	−1.71441	−0.857205	+	0.514976i	$0.827801\pi$
$48$	16.8024	2.42522
$49$	−5.94980	−0.849971
$50$	−36.9654	−5.22770
$51$	−0.0774276	−0.0108420
$52$	−19.0603	−2.64319
$53$	−9.88925	−1.35839	−0.679197	−	0.733956i	$-0.737672\pi$
$53$	−9.88925	−1.35839	−0.679197	+	0.733956i	$0.737672\pi$
$54$	14.3425	1.95177
$55$	1.77289	0.239057
$56$	−9.92674	−1.32652
$57$	1.42311	0.188495
$58$	−8.93135	−1.17274
$59$	1.06444	0.138578	0.0692890	−	0.997597i	$-0.477927\pi$
$59$	1.06444	0.138578	0.0692890	+	0.997597i	$0.477927\pi$
$60$	25.7293	3.32163
$61$	14.8490	1.90122	0.950608	−	0.310395i	$-0.100461\pi$
$61$	14.8490	1.90122	0.950608	+	0.310395i	$0.100461\pi$
$62$	16.1214	2.04742
$63$	−1.87335	−0.236020
$64$	32.6683	4.08353
$65$	−14.8132	−1.83735
$66$	−1.22544	−0.150842
$67$	−13.5493	−1.65531	−0.827653	−	0.561240i	$-0.810324\pi$
$67$	−13.5493	−1.65531	−0.827653	+	0.561240i	$0.810324\pi$
$68$	−0.395514	−0.0479631
$69$	−1.08258	−0.130327
$70$	−12.0859	−1.44454
$71$	6.75016	0.801096	0.400548	−	0.916276i	$-0.368820\pi$
$71$	6.75016	0.801096	0.400548	+	0.916276i	$0.368820\pi$
$72$	17.7074	2.08683
$73$	−4.34011	−0.507972	−0.253986	−	0.967208i	$-0.581742\pi$
$73$	−4.34011	−0.507972	−0.253986	+	0.967208i	$0.581742\pi$
$74$	23.3477	2.71411
$75$	14.5833	1.68394
$76$	7.26948	0.833867
$77$	0.422740	0.0481757
$78$	10.2391	1.15935
$79$	−5.84134	−0.657203	−0.328601	−	0.944469i	$-0.606577\pi$
$79$	−5.84134	−0.657203	−0.328601	+	0.944469i	$0.606577\pi$
$80$	66.7050	7.45785
$81$	−0.174217	−0.0193574
$82$	11.5822	1.27904
$83$	−15.0780	−1.65503	−0.827514	−	0.561445i	$-0.810246\pi$
$83$	−15.0780	−1.65503	−0.827514	+	0.561445i	$0.810246\pi$
$84$	6.13506	0.669390
$85$	−0.307385	−0.0333406
$86$	10.2583	1.10618
$87$	3.52353	0.377762
$88$	−3.99584	−0.425958
$89$	−12.8102	−1.35788	−0.678939	−	0.734195i	$-0.737560\pi$
$89$	−12.8102	−1.35788	−0.678939	+	0.734195i	$0.737560\pi$
$90$	21.5588	2.27250
$91$	−3.53217	−0.370272
$92$	−5.52999	−0.576541
$93$	−6.36010	−0.659512
$94$	32.2523	3.32657
$95$	5.64968	0.579645
$96$	−25.1344	−2.56526
$97$	−12.2732	−1.24615	−0.623077	−	0.782161i	$-0.714118\pi$
$97$	−12.2732	−1.24615	−0.623077	+	0.782161i	$0.714118\pi$
$98$	16.3267	1.64925
$99$	−0.754086	−0.0757885
$100$	74.4942	7.44942
$101$	12.2642	1.22033	0.610167	−	0.792273i	$-0.291102\pi$
$101$	12.2642	1.22033	0.610167	+	0.792273i	$0.291102\pi$
$102$	0.212468	0.0210375
$103$	15.5715	1.53431	0.767154	−	0.641463i	$-0.221672\pi$
$103$	15.5715	1.53431	0.767154	+	0.641463i	$0.221672\pi$
$104$	33.3869	3.27385
$105$	4.76803	0.465312
$106$	27.1369	2.63577
$107$	2.46460	0.238262	0.119131	−	0.992879i	$-0.461989\pi$
$107$	2.46460	0.238262	0.119131	+	0.992879i	$0.461989\pi$
$108$	−28.9036	−2.78125
$109$	−12.6075	−1.20758	−0.603791	−	0.797142i	$-0.706344\pi$
$109$	−12.6075	−1.20758	−0.603791	+	0.797142i	$0.706344\pi$
$110$	−4.86496	−0.463856
$111$	−9.21097	−0.874266
$112$	15.9056	1.50294
$113$	−7.34864	−0.691302	−0.345651	−	0.938363i	$-0.612342\pi$
$113$	−7.34864	−0.691302	−0.345651	+	0.938363i	$0.612342\pi$
$114$	−3.90512	−0.365748
$115$	−4.29779	−0.400771
$116$	17.9988	1.67115
$117$	6.30069	0.582499
$118$	−2.92091	−0.268891
$119$	−0.0732949	−0.00671894
$120$	−45.0685	−4.11418
$121$	−10.8298	−0.984530
$122$	−40.7468	−3.68904
$123$	−4.56932	−0.412002
$124$	−32.4885	−2.91756
$125$	36.4064	3.25628
$126$	5.14063	0.457964
$127$	3.10796	0.275787	0.137893	−	0.990447i	$-0.455967\pi$
$127$	3.10796	0.275787	0.137893	+	0.990447i	$0.455967\pi$
$128$	−43.2101	−3.81927
$129$	−4.04704	−0.356322
$130$	40.6487	3.56513
$131$	19.4833	1.70226	0.851132	−	0.524952i	$-0.175917\pi$
$131$	19.4833	1.70226	0.851132	+	0.524952i	$0.175917\pi$
$132$	2.46956	0.214948
$133$	1.34715	0.116813
$134$	37.1803	3.21189
$135$	−22.4633	−1.93333
$136$	0.692801	0.0594072
$137$	−13.3853	−1.14359	−0.571793	−	0.820398i	$-0.693752\pi$
$137$	−13.3853	−1.14359	−0.571793	+	0.820398i	$0.693752\pi$
$138$	2.97068	0.252881
$139$	3.91164	0.331781	0.165890	−	0.986144i	$-0.446950\pi$
$139$	3.91164	0.331781	0.165890	+	0.986144i	$0.446950\pi$
$140$	24.3560	2.05845
$141$	−12.7239	−1.07155
$142$	−18.5230	−1.55441
$143$	−1.42181	−0.118898
$144$	−28.3725	−2.36437
$145$	13.9883	1.16166
$146$	11.9096	0.985648
$147$	−6.44111	−0.531254
$148$	−47.0513	−3.86759
$149$	−11.8018	−0.966838	−0.483419	−	0.875389i	$-0.660605\pi$
$149$	−11.8018	−0.966838	−0.483419	+	0.875389i	$0.660605\pi$
$150$	−40.0179	−3.26744
$151$	−17.0316	−1.38601	−0.693007	−	0.720931i	$-0.743714\pi$
$151$	−17.0316	−1.38601	−0.693007	+	0.720931i	$0.743714\pi$
$152$	−12.7336	−1.03283
$153$	0.130744	0.0105700
$154$	−1.16003	−0.0934782
$155$	−25.2494	−2.02808
$156$	−20.6342	−1.65206
$157$	11.7841	0.940470	0.470235	−	0.882541i	$-0.344169\pi$
$157$	11.7841	0.940470	0.470235	+	0.882541i	$0.344169\pi$
$158$	16.0291	1.27521
$159$	−10.7059	−0.849030
$160$	−99.7825	−7.88850
$161$	−1.02479	−0.0807650
$162$	0.478065	0.0375604
$163$	−1.58664	−0.124275	−0.0621377	−	0.998068i	$-0.519792\pi$
$163$	−1.58664	−0.124275	−0.0621377	+	0.998068i	$0.519792\pi$
$164$	−23.3409	−1.82262
$165$	1.91929	0.149416
$166$	41.3753	3.21135
$167$	4.95996	0.383813	0.191907	−	0.981413i	$-0.438533\pi$
$167$	4.95996	0.383813	0.191907	+	0.981413i	$0.438533\pi$
$168$	−10.7464	−0.829106
$169$	−1.12018	−0.0861674
$170$	0.843489	0.0646927
$171$	−2.40305	−0.183766
$172$	−20.6730	−1.57630
$173$	−0.173427	−0.0131854	−0.00659270	−	0.999978i	$-0.502099\pi$
$173$	−0.173427	−0.0131854	−0.00659270	+	0.999978i	$0.502099\pi$
$174$	−9.66886	−0.732995
$175$	13.8049	1.04356
$176$	6.40253	0.482609
$177$	1.15234	0.0866148
$178$	35.1522	2.63477
$179$	13.1760	0.984818	0.492409	−	0.870364i	$-0.336116\pi$
$179$	13.1760	0.984818	0.492409	+	0.870364i	$0.336116\pi$
$180$	−43.4462	−3.23829
$181$	−2.97808	−0.221359	−0.110679	−	0.993856i	$-0.535303\pi$
$181$	−2.97808	−0.221359	−0.110679	+	0.993856i	$0.535303\pi$
$182$	9.69256	0.718460
$183$	16.0751	1.18831
$184$	9.68658	0.714104
$185$	−36.5672	−2.68847
$186$	17.4526	1.27969
$187$	−0.0295036	−0.00215752
$188$	−64.9962	−4.74033
$189$	−5.35629	−0.389613
$190$	−15.5032	−1.12472
$191$	−6.39942	−0.463046	−0.231523	−	0.972829i	$-0.574371\pi$
$191$	−6.39942	−0.463046	−0.231523	+	0.972829i	$0.574371\pi$
$192$	35.3659	2.55231
$193$	26.4838	1.90635	0.953174	−	0.302422i	$-0.0977953\pi$
$193$	26.4838	1.90635	0.953174	+	0.302422i	$0.0977953\pi$
$194$	33.6786	2.41799
$195$	−16.0364	−1.14839
$196$	−32.9023	−2.35017
$197$	15.0059	1.06913	0.534564	−	0.845128i	$-0.320476\pi$
$197$	15.0059	1.06913	0.534564	+	0.845128i	$0.320476\pi$
$198$	2.06927	0.147057
$199$	−20.1404	−1.42772	−0.713858	−	0.700291i	$-0.753054\pi$
$199$	−20.1404	−1.42772	−0.713858	+	0.700291i	$0.753054\pi$
$200$	−130.488	−9.22686
$201$	−14.6681	−1.03461
$202$	−33.6540	−2.36789
$203$	3.33546	0.234104
$204$	−0.428174	−0.0299782
$205$	−18.1400	−1.26696
$206$	−42.7295	−2.97711
$207$	1.82803	0.127057
$208$	−53.4957	−3.70926
$209$	0.542271	0.0375097
$210$	−13.0839	−0.902873
$211$	12.1324	0.835230	0.417615	−	0.908624i	$-0.362866\pi$
$211$	12.1324	0.835230	0.417615	+	0.908624i	$0.362866\pi$
$212$	−54.6874	−3.75595
$213$	7.30756	0.500705
$214$	−6.76307	−0.462314
$215$	−16.0666	−1.09573
$216$	50.6289	3.44486
$217$	−6.02063	−0.408707
$218$	34.5961	2.34314
$219$	−4.69850	−0.317495
$220$	9.80407	0.660990
$221$	0.246515	0.0165824
$222$	25.2757	1.69639
$223$	7.89368	0.528600	0.264300	−	0.964441i	$-0.414859\pi$
$223$	7.89368	0.528600	0.264300	+	0.964441i	$0.414859\pi$
$224$	−23.7928	−1.58972
$225$	−24.6253	−1.64169
$226$	20.1653	1.34137
$227$	4.14984	0.275434	0.137717	−	0.990472i	$-0.456024\pi$
$227$	4.14984	0.275434	0.137717	+	0.990472i	$0.456024\pi$
$228$	7.86976	0.521188
$229$	13.4732	0.890331	0.445165	−	0.895448i	$-0.353145\pi$
$229$	13.4732	0.890331	0.445165	+	0.895448i	$0.353145\pi$
$230$	11.7935	0.777639
$231$	0.457648	0.0301110
$232$	−31.5276	−2.06989
$233$	23.8912	1.56517	0.782584	−	0.622545i	$-0.213901\pi$
$233$	23.8912	1.56517	0.782584	+	0.622545i	$0.213901\pi$
$234$	−17.2896	−1.13026
$235$	−50.5136	−3.29514
$236$	5.88633	0.383168
$237$	−6.32370	−0.410768
$238$	0.201127	0.0130371
$239$	15.4884	1.00186	0.500931	−	0.865487i	$-0.332991\pi$
$239$	15.4884	1.00186	0.500931	+	0.865487i	$0.332991\pi$
$240$	72.2133	4.66135
$241$	−22.6314	−1.45782	−0.728909	−	0.684610i	$-0.759972\pi$
$241$	−22.6314	−1.45782	−0.728909	+	0.684610i	$0.759972\pi$
$242$	29.7180	1.91034
$243$	15.4915	0.993781
$244$	82.1146	5.25685
$245$	−25.5710	−1.63367
$246$	12.5386	0.799432
$247$	−4.53090	−0.288294
$248$	56.9084	3.61369
$249$	−16.3231	−1.03443
$250$	−99.9020	−6.31836
$251$	13.9559	0.880891	0.440445	−	0.897779i	$-0.354821\pi$
$251$	13.9559	0.880891	0.440445	+	0.897779i	$0.354821\pi$
$252$	−10.3596	−0.652595
$253$	−0.412513	−0.0259345
$254$	−8.52850	−0.535125
$255$	−0.332767	−0.0208387
$256$	53.2355	3.32722
$257$	−5.81639	−0.362816	−0.181408	−	0.983408i	$-0.558066\pi$
$257$	−5.81639	−0.362816	−0.181408	+	0.983408i	$0.558066\pi$
$258$	11.1054	0.691393
$259$	−8.71933	−0.541793
$260$	−81.9170	−5.08028
$261$	−5.94981	−0.368284
$262$	−53.4638	−3.30300
$263$	17.0060	1.04863	0.524316	−	0.851524i	$-0.324321\pi$
$263$	17.0060	1.04863	0.524316	+	0.851524i	$0.324321\pi$
$264$	−4.32580	−0.266234
$265$	−42.5019	−2.61087
$266$	−3.69669	−0.226658
$267$	−13.8680	−0.848708
$268$	−74.9273	−4.57691
$269$	5.82408	0.355100	0.177550	−	0.984112i	$-0.443183\pi$
$269$	5.82408	0.355100	0.177550	+	0.984112i	$0.443183\pi$
$270$	61.6411	3.75136
$271$	2.65208	0.161103	0.0805513	−	0.996750i	$-0.474332\pi$
$271$	2.65208	0.161103	0.0805513	+	0.996750i	$0.474332\pi$
$272$	−1.11007	−0.0673081
$273$	−3.82384	−0.231429
$274$	36.7305	2.21897
$275$	5.55694	0.335096
$276$	−5.98663	−0.360353
$277$	7.21255	0.433360	0.216680	−	0.976243i	$-0.430477\pi$
$277$	7.21255	0.433360	0.216680	+	0.976243i	$0.430477\pi$
$278$	−10.7339	−0.643774
$279$	10.7396	0.642965
$280$	−42.6630	−2.54960
$281$	−13.9617	−0.832884	−0.416442	−	0.909162i	$-0.636723\pi$
$281$	−13.9617	−0.832884	−0.416442	+	0.909162i	$0.636723\pi$
$282$	34.9155	2.07919
$283$	−17.0709	−1.01476	−0.507381	−	0.861722i	$-0.669386\pi$
$283$	−17.0709	−1.01476	−0.507381	+	0.861722i	$0.669386\pi$
$284$	37.3283	2.21503
$285$	6.11621	0.362293
$286$	3.90157	0.230705
$287$	−4.32543	−0.255322
$288$	42.4417	2.50090
$289$	−16.9949	−0.999699
$290$	−38.3850	−2.25405
$291$	−13.2867	−0.778878
$292$	−24.0008	−1.40454
$293$	−9.68544	−0.565829	−0.282915	−	0.959145i	$-0.591301\pi$
$293$	−9.68544	−0.565829	−0.282915	+	0.959145i	$0.591301\pi$
$294$	17.6749	1.03082
$295$	4.57473	0.266351
$296$	82.4171	4.79040
$297$	−2.15608	−0.125109
$298$	32.3850	1.87601
$299$	3.44671	0.199329
$300$	80.6457	4.65608
$301$	−3.83103	−0.220817
$302$	46.7362	2.68936
$303$	13.2769	0.762740
$304$	20.4030	1.17019
$305$	63.8177	3.65419
$306$	−0.358772	−0.0205096
$307$	10.7466	0.613341	0.306670	−	0.951816i	$-0.400785\pi$
$307$	10.7466	0.613341	0.306670	+	0.951816i	$0.400785\pi$
$308$	2.33775	0.133206
$309$	16.8574	0.958981
$310$	69.2863	3.93520
$311$	−21.2881	−1.20714	−0.603568	−	0.797312i	$-0.706255\pi$
$311$	−21.2881	−1.20714	−0.603568	+	0.797312i	$0.706255\pi$
$312$	36.1438	2.04624
$313$	−1.40921	−0.0796535	−0.0398268	−	0.999207i	$-0.512681\pi$
$313$	−1.40921	−0.0796535	−0.0398268	+	0.999207i	$0.512681\pi$
$314$	−32.3364	−1.82485
$315$	−8.05127	−0.453637
$316$	−32.3026	−1.81716
$317$	23.1007	1.29747	0.648733	−	0.761016i	$-0.275299\pi$
$317$	23.1007	1.29747	0.648733	+	0.761016i	$0.275299\pi$
$318$	29.3778	1.64742
$319$	1.34263	0.0751730
$320$	140.401	7.84867
$321$	2.66812	0.148920
$322$	2.81212	0.156713
$323$	−0.0940193	−0.00523137
$324$	−0.963417	−0.0535232
$325$	−46.4305	−2.57550
$326$	4.35388	0.241139
$327$	−13.6486	−0.754770
$328$	40.8850	2.25750
$329$	−12.0448	−0.664051
$330$	−5.26669	−0.289922
$331$	−10.6810	−0.587079	−0.293539	−	0.955947i	$-0.594833\pi$
$331$	−10.6810	−0.587079	−0.293539	+	0.955947i	$0.594833\pi$
$332$	−83.3813	−4.57614
$333$	15.5536	0.852331
$334$	−13.6105	−0.744736
$335$	−58.2318	−3.18154
$336$	17.2190	0.939375
$337$	−17.1780	−0.935744	−0.467872	−	0.883796i	$-0.654979\pi$
$337$	−17.1780	−0.935744	−0.467872	+	0.883796i	$0.654979\pi$
$338$	3.07385	0.167196
$339$	−7.95546	−0.432081
$340$	−1.69983	−0.0921865
$341$	−2.42350	−0.131240
$342$	6.59416	0.356571
$343$	−13.2709	−0.716559
$344$	36.2118	1.95241
$345$	−4.65268	−0.250492
$346$	0.475898	0.0255844
$347$	13.3263	0.715391	0.357695	−	0.933838i	$-0.383563\pi$
$347$	13.3263	0.715391	0.357695	+	0.933838i	$0.383563\pi$
$348$	19.4851	1.04451
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−37.8819	−2.02487
$351$	18.0150	0.961567
$352$	−9.57739	−0.510476
$353$	5.32222	0.283273	0.141637	−	0.989919i	$-0.454764\pi$
$353$	5.32222	0.283273	0.141637	+	0.989919i	$0.454764\pi$
$354$	−3.16210	−0.168064
$355$	29.0107	1.53973
$356$	−70.8402	−3.75452
$357$	−0.0793473	−0.00419950
$358$	−36.1559	−1.91090
$359$	14.9227	0.787588	0.393794	−	0.919199i	$-0.371162\pi$
$359$	14.9227	0.787588	0.393794	+	0.919199i	$0.371162\pi$
$360$	76.1024	4.01095
$361$	−17.2719	−0.909050
$362$	8.17208	0.429515
$363$	−11.7241	−0.615356
$364$	−19.5328	−1.02380
$365$	−18.6529	−0.976336
$366$	−44.1115	−2.30574
$367$	33.5054	1.74897	0.874485	−	0.485053i	$-0.161200\pi$
$367$	33.5054	1.74897	0.874485	+	0.485053i	$0.161200\pi$
$368$	−15.5208	−0.809077
$369$	7.71573	0.401665
$370$	100.343	5.21660
$371$	−10.1344	−0.526154
$372$	−35.1713	−1.82355
$373$	−6.77395	−0.350742	−0.175371	−	0.984502i	$-0.556112\pi$
$373$	−6.77395	−0.350742	−0.175371	+	0.984502i	$0.556112\pi$
$374$	0.0809604	0.00418636
$375$	39.4126	2.03526
$376$	113.850	5.87138
$377$	−11.2182	−0.577769
$378$	14.6981	0.755989
$379$	4.28384	0.220046	0.110023	−	0.993929i	$-0.464908\pi$
$379$	4.28384	0.220046	0.110023	+	0.993929i	$0.464908\pi$
$380$	31.2427	1.60271
$381$	3.36460	0.172374
$382$	17.5605	0.898475
$383$	−33.5268	−1.71314	−0.856571	−	0.516029i	$-0.827410\pi$
$383$	−33.5268	−1.71314	−0.856571	+	0.516029i	$0.827410\pi$
$384$	−46.7782	−2.38714
$385$	1.81685	0.0925951
$386$	−72.6738	−3.69900
$387$	6.83381	0.347382
$388$	−67.8706	−3.44561
$389$	30.5098	1.54691	0.773455	−	0.633852i	$-0.218527\pi$
$389$	30.5098	1.54691	0.773455	+	0.633852i	$0.218527\pi$
$390$	44.0053	2.22830
$391$	0.0715217	0.00361701
$392$	57.6332	2.91092
$393$	21.0921	1.06396
$394$	−41.1775	−2.07449
$395$	−25.1048	−1.26316
$396$	−4.17009	−0.209555
$397$	−36.6532	−1.83957	−0.919785	−	0.392423i	$-0.871637\pi$
$397$	−36.6532	−1.83957	−0.919785	+	0.392423i	$0.871637\pi$
$398$	55.2669	2.77028
$399$	1.45839	0.0730108
$400$	209.080	10.4540
$401$	−2.29459	−0.114586	−0.0572932	−	0.998357i	$-0.518247\pi$
$401$	−2.29459	−0.114586	−0.0572932	+	0.998357i	$0.518247\pi$
$402$	40.2505	2.00751
$403$	20.2493	1.00869
$404$	67.8209	3.37422
$405$	−0.748746	−0.0372055
$406$	−9.15279	−0.454245
$407$	−3.50982	−0.173975
$408$	0.750009	0.0371310
$409$	−4.75661	−0.235199	−0.117600	−	0.993061i	$-0.537520\pi$
$409$	−4.75661	−0.235199	−0.117600	+	0.993061i	$0.537520\pi$
$410$	49.7778	2.45835
$411$	−14.4906	−0.714771
$412$	86.1103	4.24235
$413$	1.09083	0.0536762
$414$	−5.01626	−0.246536
$415$	−64.8021	−3.18101
$416$	80.0230	3.92345
$417$	4.23465	0.207372
$418$	−1.48804	−0.0727823
$419$	−15.3604	−0.750402	−0.375201	−	0.926943i	$-0.622426\pi$
$419$	−15.3604	−0.750402	−0.375201	+	0.926943i	$0.622426\pi$
$420$	26.3672	1.28659
$421$	−0.419289	−0.0204349	−0.0102175	−	0.999948i	$-0.503252\pi$
$421$	−0.419289	−0.0204349	−0.0102175	+	0.999948i	$0.503252\pi$
$422$	−33.2924	−1.62065
$423$	21.4856	1.04466
$424$	95.7930	4.65212
$425$	−0.963466	−0.0467350
$426$	−20.0525	−0.971548
$427$	15.2171	0.736408
$428$	13.6292	0.658793
$429$	−1.53922	−0.0743142
$430$	44.0881	2.12612
$431$	22.9802	1.10692	0.553458	−	0.832877i	$-0.313308\pi$
$431$	22.9802	1.10692	0.553458	+	0.832877i	$0.313308\pi$
$432$	−81.1227	−3.90302
$433$	21.6085	1.03844	0.519219	−	0.854642i	$-0.326223\pi$
$433$	21.6085	1.03844	0.519219	+	0.854642i	$0.326223\pi$
$434$	16.5211	0.793038
$435$	15.1434	0.726070
$436$	−69.7195	−3.33896
$437$	−1.31456	−0.0628837
$438$	12.8931	0.616055
$439$	−0.855417	−0.0408268	−0.0204134	−	0.999792i	$-0.506498\pi$
$439$	−0.855417	−0.0408268	−0.0204134	+	0.999792i	$0.506498\pi$
$440$	−17.1733	−0.818703
$441$	10.8764	0.517924
$442$	−0.676457	−0.0321758
$443$	−16.7723	−0.796878	−0.398439	−	0.917195i	$-0.630448\pi$
$443$	−16.7723	−0.796878	−0.398439	+	0.917195i	$0.630448\pi$
$444$	−50.9365	−2.41734
$445$	−55.0555	−2.60988
$446$	−21.6609	−1.02567
$447$	−12.7763	−0.604298
$448$	33.4782	1.58170
$449$	28.2255	1.33205	0.666023	−	0.745931i	$-0.267995\pi$
$449$	28.2255	1.33205	0.666023	+	0.745931i	$0.267995\pi$
$450$	67.5739	3.18546
$451$	−1.74113	−0.0819866
$452$	−40.6379	−1.91145
$453$	−18.4380	−0.866293
$454$	−11.3875	−0.534442
$455$	−15.1805	−0.711672
$456$	−13.7850	−0.645543
$457$	−0.734756	−0.0343704	−0.0171852	−	0.999852i	$-0.505470\pi$
$457$	−0.734756	−0.0343704	−0.0171852	+	0.999852i	$0.505470\pi$
$458$	−36.9714	−1.72756
$459$	0.373823	0.0174486
$460$	−23.7667	−1.10813
$461$	6.50897	0.303153	0.151576	−	0.988446i	$-0.451565\pi$
$461$	6.50897	0.303153	0.151576	+	0.988446i	$0.451565\pi$
$462$	−1.25582	−0.0584263
$463$	32.7625	1.52260	0.761300	−	0.648399i	$-0.224561\pi$
$463$	32.7625	1.52260	0.761300	+	0.648399i	$0.224561\pi$
$464$	50.5166	2.34517
$465$	−27.3344	−1.26760
$466$	−65.5596	−3.03699
$467$	15.6086	0.722282	0.361141	−	0.932511i	$-0.382387\pi$
$467$	15.6086	0.722282	0.361141	+	0.932511i	$0.382387\pi$
$468$	34.8428	1.61061
$469$	−13.8852	−0.641159
$470$	138.613	6.39376
$471$	12.7571	0.587817
$472$	−10.3108	−0.474592
$473$	−1.54212	−0.0709066
$474$	17.3527	0.797038
$475$	17.7083	0.812514
$476$	−0.405320	−0.0185778
$477$	18.0778	0.827728
$478$	−42.5014	−1.94397
$479$	−34.6890	−1.58498	−0.792491	−	0.609884i	$-0.791216\pi$
$479$	−34.6890	−1.58498	−0.792491	+	0.609884i	$0.791216\pi$
$480$	−108.022	−4.93051
$481$	29.3259	1.33715
$482$	62.1025	2.82869
$483$	−1.10942	−0.0504802
$484$	−59.8889	−2.72222
$485$	−52.7475	−2.39514
$486$	−42.5100	−1.92829
$487$	−25.9622	−1.17646	−0.588229	−	0.808694i	$-0.700175\pi$
$487$	−25.9622	−1.17646	−0.588229	+	0.808694i	$0.700175\pi$
$488$	−143.836	−6.51114
$489$	−1.71766	−0.0776753
$490$	70.1688	3.16990
$491$	27.5592	1.24373	0.621864	−	0.783125i	$-0.286376\pi$
$491$	27.5592	1.24373	0.621864	+	0.783125i	$0.286376\pi$
$492$	−25.2683	−1.13918
$493$	−0.232786	−0.0104842
$494$	12.4332	0.559394
$495$	−3.24090	−0.145668
$496$	−91.1842	−4.09429
$497$	6.91751	0.310293
$498$	44.7919	2.00718
$499$	30.1021	1.34755	0.673777	−	0.738935i	$-0.264671\pi$
$499$	30.1021	1.34755	0.673777	+	0.738935i	$0.264671\pi$
$500$	201.327	9.00360
$501$	5.36953	0.239893
$502$	−38.2962	−1.70924
$503$	19.4059	0.865268	0.432634	−	0.901570i	$-0.357584\pi$
$503$	19.4059	0.865268	0.432634	+	0.901570i	$0.357584\pi$
$504$	18.1464	0.808304
$505$	52.7089	2.34552
$506$	1.13197	0.0503222
$507$	−1.21267	−0.0538568
$508$	17.1870	0.762549
$509$	25.8902	1.14756	0.573781	−	0.819009i	$-0.305476\pi$
$509$	25.8902	1.14756	0.573781	+	0.819009i	$0.305476\pi$
$510$	0.913141	0.0404346
$511$	−4.44772	−0.196755
$512$	−59.6624	−2.63673
$513$	−6.87080	−0.303353
$514$	15.9607	0.703994
$515$	66.9231	2.94898
$516$	−22.3801	−0.985229
$517$	−4.84843	−0.213234
$518$	23.9266	1.05127
$519$	−0.187748	−0.00824121
$520$	143.490	6.29243
$521$	−26.6991	−1.16971	−0.584854	−	0.811139i	$-0.698848\pi$
$521$	−26.6991	−1.16971	−0.584854	+	0.811139i	$0.698848\pi$
$522$	16.3268	0.714604
$523$	6.06322	0.265126	0.132563	−	0.991175i	$-0.457679\pi$
$523$	6.06322	0.265126	0.132563	+	0.991175i	$0.457679\pi$
$524$	107.742	4.70675
$525$	14.9449	0.652249
$526$	−46.6658	−2.03472
$527$	0.420188	0.0183037
$528$	6.93122	0.301643
$529$	1.00000	0.0434783
$530$	116.629	5.06603
$531$	−1.94583	−0.0844416
$532$	7.44971	0.322986
$533$	14.5478	0.630137
$534$	38.0549	1.64680
$535$	10.5923	0.457946
$536$	131.246	5.66897
$537$	14.2640	0.615536
$538$	−15.9817	−0.689022
$539$	−2.45437	−0.105717
$540$	−124.222	−5.34565
$541$	9.32519	0.400921	0.200461	−	0.979702i	$-0.435756\pi$
$541$	9.32519	0.400921	0.200461	+	0.979702i	$0.435756\pi$
$542$	−7.27754	−0.312597
$543$	−3.22399	−0.138355
$544$	1.66053	0.0711947
$545$	−54.1845	−2.32101
$546$	10.4929	0.449056
$547$	−24.0579	−1.02864	−0.514321	−	0.857598i	$-0.671956\pi$
$547$	−24.0579	−1.02864	−0.514321	+	0.857598i	$0.671956\pi$
$548$	−74.0208	−3.16201
$549$	−27.1444	−1.15849
$550$	−15.2487	−0.650207
$551$	4.27857	0.182273
$552$	10.4865	0.446333
$553$	−5.98617	−0.254558
$554$	−19.7918	−0.840874
$555$	−39.5868	−1.68036
$556$	21.6313	0.917373
$557$	21.0836	0.893340	0.446670	−	0.894699i	$-0.352610\pi$
$557$	21.0836	0.893340	0.446670	+	0.894699i	$0.352610\pi$
$558$	−29.4704	−1.24758
$559$	12.8850	0.544978
$560$	68.3589	2.88869
$561$	−0.0319399	−0.00134850
$562$	38.3120	1.61609
$563$	10.1202	0.426517	0.213259	−	0.976996i	$-0.431592\pi$
$563$	10.1202	0.426517	0.213259	+	0.976996i	$0.431592\pi$
$564$	−70.3633	−2.96283
$565$	−31.5829	−1.32870
$566$	46.8441	1.96900
$567$	−0.178536	−0.00749781
$568$	−65.3859	−2.74353
$569$	−7.44097	−0.311942	−0.155971	−	0.987762i	$-0.549851\pi$
$569$	−7.44097	−0.311942	−0.155971	+	0.987762i	$0.549851\pi$
$570$	−16.7834	−0.702978
$571$	2.20014	0.0920731	0.0460365	−	0.998940i	$-0.485341\pi$
$571$	2.20014	0.0920731	0.0460365	+	0.998940i	$0.485341\pi$
$572$	−7.86261	−0.328752
$573$	−6.92785	−0.289415
$574$	11.8693	0.495417
$575$	−13.4710	−0.561778
$576$	−59.7186	−2.48827
$577$	15.7345	0.655036	0.327518	−	0.944845i	$-0.393788\pi$
$577$	15.7345	0.655036	0.327518	+	0.944845i	$0.393788\pi$
$578$	46.6354	1.93978
$579$	28.6708	1.19152
$580$	77.3551	3.21200
$581$	−15.4519	−0.641051
$582$	36.4597	1.51130
$583$	−4.07944	−0.168953
$584$	42.0409	1.73966
$585$	27.0790	1.11958
$586$	26.5776	1.09791
$587$	42.2792	1.74505	0.872524	−	0.488571i	$-0.162481\pi$
$587$	42.2792	1.74505	0.872524	+	0.488571i	$0.162481\pi$
$588$	−35.6193	−1.46891
$589$	−7.72298	−0.318220
$590$	−12.5534	−0.516817
$591$	16.2451	0.668232
$592$	−132.057	−5.42750
$593$	−22.8543	−0.938512	−0.469256	−	0.883062i	$-0.655478\pi$
$593$	−22.8543	−0.938512	−0.469256	+	0.883062i	$0.655478\pi$
$594$	5.91647	0.242756
$595$	−0.315006	−0.0129140
$596$	−65.2636	−2.67330
$597$	−21.8035	−0.892359
$598$	−9.45806	−0.386769
$599$	8.39772	0.343121	0.171561	−	0.985174i	$-0.445119\pi$
$599$	8.39772	0.343121	0.171561	+	0.985174i	$0.445119\pi$
$600$	−141.263	−5.76702
$601$	33.7969	1.37860	0.689302	−	0.724474i	$-0.257917\pi$
$601$	33.7969	1.37860	0.689302	+	0.724474i	$0.257917\pi$
$602$	10.5127	0.428464
$603$	24.7685	1.00865
$604$	−94.1846	−3.83232
$605$	−46.5443	−1.89229
$606$	−36.4330	−1.47999
$607$	−18.5094	−0.751272	−0.375636	−	0.926767i	$-0.622576\pi$
$607$	−18.5094	−0.751272	−0.375636	+	0.926767i	$0.622576\pi$
$608$	−30.5203	−1.23776
$609$	3.61089	0.146321
$610$	−175.121	−7.09044
$611$	40.5106	1.63888
$612$	0.723012	0.0292260
$613$	−41.6582	−1.68256	−0.841279	−	0.540602i	$-0.818197\pi$
$613$	−41.6582	−1.68256	−0.841279	+	0.540602i	$0.818197\pi$
$614$	−29.4896	−1.19010
$615$	−19.6380	−0.791879
$616$	−4.09491	−0.164989
$617$	−10.4087	−0.419037	−0.209519	−	0.977805i	$-0.567190\pi$
$617$	−10.4087	−0.419037	−0.209519	+	0.977805i	$0.567190\pi$
$618$	−46.2580	−1.86077
$619$	−4.17719	−0.167895	−0.0839476	−	0.996470i	$-0.526753\pi$
$619$	−4.17719	−0.167895	−0.0839476	+	0.996470i	$0.526753\pi$
$620$	−139.629	−5.60762
$621$	5.22671	0.209741
$622$	58.4162	2.34228
$623$	−13.1278	−0.525954
$624$	−57.9132	−2.31838
$625$	89.1119	3.56448
$626$	3.86700	0.154556
$627$	0.587050	0.0234445
$628$	65.1657	2.60039
$629$	0.608534	0.0242638
$630$	22.0933	0.880220
$631$	−34.0266	−1.35458	−0.677288	−	0.735718i	$-0.736845\pi$
$631$	−34.0266	−1.35458	−0.677288	+	0.735718i	$0.736845\pi$
$632$	56.5826	2.25074
$633$	13.1343	0.522040
$634$	−63.3903	−2.51755
$635$	13.3573	0.530070
$636$	−59.2033	−2.34756
$637$	20.5072	0.812527
$638$	−3.68430	−0.145863
$639$	−12.3395	−0.488143
$640$	−185.708	−7.34074
$641$	13.5555	0.535410	0.267705	−	0.963501i	$-0.413735\pi$
$641$	13.5555	0.535410	0.267705	+	0.963501i	$0.413735\pi$
$642$	−7.32154	−0.288958
$643$	−42.6654	−1.68256	−0.841280	−	0.540599i	$-0.818198\pi$
$643$	−42.6654	−1.68256	−0.841280	+	0.540599i	$0.818198\pi$
$644$	−5.66709	−0.223315
$645$	−17.3933	−0.684861
$646$	0.257997	0.0101507
$647$	−44.7681	−1.76002	−0.880008	−	0.474959i	$-0.842463\pi$
$647$	−44.7681	−1.76002	−0.880008	+	0.474959i	$0.842463\pi$
$648$	1.68756	0.0662938
$649$	0.439095	0.0172360
$650$	127.409	4.99740
$651$	−6.51779	−0.255452
$652$	−8.77411	−0.343621
$653$	33.2256	1.30022	0.650109	−	0.759841i	$-0.274723\pi$
$653$	33.2256	1.30022	0.650109	+	0.759841i	$0.274723\pi$
$654$	37.4529	1.46452
$655$	83.7350	3.27180
$656$	−65.5100	−2.55774
$657$	7.93386	0.309529
$658$	33.0519	1.28850
$659$	−19.5485	−0.761500	−0.380750	−	0.924678i	$-0.624334\pi$
$659$	−19.5485	−0.761500	−0.380750	+	0.924678i	$0.624334\pi$
$660$	10.6136	0.413136
$661$	44.6839	1.73800	0.869002	−	0.494808i	$-0.164762\pi$
$661$	44.6839	1.73800	0.869002	+	0.494808i	$0.164762\pi$
$662$	29.3094	1.13914
$663$	0.266871	0.0103644
$664$	146.055	5.66801
$665$	5.78975	0.224517
$666$	−42.6803	−1.65383
$667$	−3.25477	−0.126025
$668$	27.4285	1.06124
$669$	8.54551	0.330388
$670$	159.793	6.17334
$671$	6.12539	0.236468
$672$	−25.7575	−0.993618
$673$	−15.1182	−0.582765	−0.291383	−	0.956607i	$-0.594115\pi$
$673$	−15.1182	−0.582765	−0.291383	+	0.956607i	$0.594115\pi$
$674$	47.1378	1.81568
$675$	−70.4088	−2.71003
$676$	−6.19456	−0.238252
$677$	0.483283	0.0185741	0.00928704	−	0.999957i	$-0.497044\pi$
$677$	0.483283	0.0185741	0.00928704	+	0.999957i	$0.497044\pi$
$678$	21.8304	0.838393
$679$	−12.5775	−0.482679
$680$	2.97751	0.114182
$681$	4.49251	0.172153
$682$	6.65029	0.254653
$683$	−22.5840	−0.864152	−0.432076	−	0.901837i	$-0.642219\pi$
$683$	−22.5840	−0.864152	−0.432076	+	0.901837i	$0.642219\pi$
$684$	−13.2888	−0.508111
$685$	−57.5273	−2.19801
$686$	36.4163	1.39038
$687$	14.5857	0.556479
$688$	−58.0221	−2.21207
$689$	34.0854	1.29855
$690$	12.7673	0.486044
$691$	−49.8374	−1.89590	−0.947951	−	0.318415i	$-0.896850\pi$
$691$	−49.8374	−1.89590	−0.947951	+	0.318415i	$0.896850\pi$
$692$	−0.959049	−0.0364576
$693$	−0.772782	−0.0293556
$694$	−36.5683	−1.38812
$695$	16.8114	0.637692
$696$	−34.1310	−1.29373
$697$	0.301878	0.0114344
$698$	2.74408	0.103865
$699$	25.8641	0.978269
$700$	76.3412	2.88543
$701$	−16.8061	−0.634758	−0.317379	−	0.948299i	$-0.602803\pi$
$701$	−16.8061	−0.634758	−0.317379	+	0.948299i	$0.602803\pi$
$702$	−49.4345	−1.86579
$703$	−11.1847	−0.421841
$704$	13.4761	0.507899
$705$	−54.6848	−2.05955
$706$	−14.6046	−0.549652
$707$	12.5683	0.472678
$708$	6.37240	0.239489
$709$	13.5735	0.509765	0.254883	−	0.966972i	$-0.417963\pi$
$709$	13.5735	0.509765	0.254883	+	0.966972i	$0.417963\pi$
$710$	−79.6078	−2.98763
$711$	10.6782	0.400462
$712$	124.087	4.65036
$713$	5.87497	0.220019
$714$	0.217736	0.00814855
$715$	−6.11065	−0.228525
$716$	72.8629	2.72302
$717$	16.7674	0.626189
$718$	−40.9490	−1.52820
$719$	−9.62768	−0.359052	−0.179526	−	0.983753i	$-0.557456\pi$
$719$	−9.62768	−0.359052	−0.179526	+	0.983753i	$0.557456\pi$
$720$	−121.939	−4.54439
$721$	15.9576	0.594292
$722$	47.3956	1.76388
$723$	−24.5002	−0.911173
$724$	−16.4687	−0.612055
$725$	43.8448	1.62836
$726$	32.1719	1.19401
$727$	5.76941	0.213976	0.106988	−	0.994260i	$-0.465879\pi$
$727$	5.76941	0.213976	0.106988	+	0.994260i	$0.465879\pi$
$728$	34.2146	1.26808
$729$	17.2934	0.640496
$730$	51.1850	1.89444
$731$	0.267373	0.00988914
$732$	88.8953	3.28566
$733$	1.38520	0.0511636	0.0255818	−	0.999673i	$-0.491856\pi$
$733$	1.38520	0.0511636	0.0255818	+	0.999673i	$0.491856\pi$
$734$	−91.9417	−3.39363
$735$	−27.6825	−1.02108
$736$	23.2172	0.855797
$737$	−5.58925	−0.205883
$738$	−21.1726	−0.779374
$739$	25.1409	0.924822	0.462411	−	0.886666i	$-0.346985\pi$
$739$	25.1409	0.924822	0.462411	+	0.886666i	$0.346985\pi$
$740$	−202.216	−7.43361
$741$	−4.90504	−0.180191
$742$	27.8097	1.02093
$743$	−24.7587	−0.908308	−0.454154	−	0.890923i	$-0.650058\pi$
$743$	−24.7587	−0.908308	−0.454154	+	0.890923i	$0.650058\pi$
$744$	61.6076	2.25865
$745$	−50.7214	−1.85829
$746$	18.5883	0.680565
$747$	27.5631	1.00848
$748$	−0.163155	−0.00596553
$749$	2.52571	0.0922873
$750$	−108.152	−3.94913
$751$	−15.8828	−0.579573	−0.289786	−	0.957091i	$-0.593584\pi$
$751$	−15.8828	−0.579573	−0.289786	+	0.957091i	$0.593584\pi$
$752$	−182.422	−6.65225
$753$	15.1084	0.550579
$754$	30.7838	1.12108
$755$	−73.1982	−2.66396
$756$	−29.6202	−1.07728
$757$	−22.6439	−0.823006	−0.411503	−	0.911408i	$-0.634996\pi$
$757$	−22.6439	−0.823006	−0.411503	+	0.911408i	$0.634996\pi$
$758$	−11.7552	−0.426969
$759$	−0.446576	−0.0162097
$760$	−54.7261	−1.98512
$761$	26.8467	0.973193	0.486597	−	0.873627i	$-0.338238\pi$
$761$	26.8467	0.973193	0.486597	+	0.873627i	$0.338238\pi$
$762$	−9.23274	−0.334467
$763$	−12.9201	−0.467739
$764$	−35.3887	−1.28032
$765$	0.561909	0.0203159
$766$	92.0004	3.32411
$767$	−3.66881	−0.132473
$768$	57.6314	2.07959
$769$	−22.9419	−0.827307	−0.413653	−	0.910434i	$-0.635747\pi$
$769$	−22.9419	−0.827307	−0.413653	+	0.910434i	$0.635747\pi$
$770$	−4.98558	−0.179668
$771$	−6.29668	−0.226769
$772$	146.455	5.27104
$773$	16.9885	0.611035	0.305518	−	0.952186i	$-0.401170\pi$
$773$	16.9885	0.611035	0.305518	+	0.952186i	$0.401170\pi$
$774$	−18.7525	−0.674046
$775$	−79.1415	−2.84285
$776$	118.885	4.26773
$777$	−9.43933	−0.338634
$778$	−83.7215	−3.00156
$779$	−5.54846	−0.198794
$780$	−88.6813	−3.17530
$781$	2.78453	0.0996382
$782$	−0.196261	−0.00701829
$783$	−17.0117	−0.607949
$784$	−92.3456	−3.29806
$785$	50.6453	1.80761
$786$	−57.8786	−2.06446
$787$	−43.1883	−1.53950	−0.769749	−	0.638347i	$-0.779618\pi$
$787$	−43.1883	−1.53950	−0.769749	+	0.638347i	$0.779618\pi$
$788$	82.9826	2.95613
$789$	18.4102	0.655422
$790$	68.8898	2.45099
$791$	−7.53084	−0.267766
$792$	7.30451	0.259555
$793$	−51.1801	−1.81746
$794$	100.579	3.56943
$795$	−46.0115	−1.63186
$796$	−111.376	−3.94763
$797$	34.0261	1.20527	0.602634	−	0.798018i	$-0.294118\pi$
$797$	34.0261	1.20527	0.602634	+	0.798018i	$0.294118\pi$
$798$	−4.00194	−0.141667
$799$	0.840623	0.0297391
$800$	−312.758	−11.0577
$801$	23.4174	0.827414
$802$	6.29654	0.222339
$803$	−1.79035	−0.0631802
$804$	−81.1144	−2.86069
$805$	−4.40434	−0.155233
$806$	−55.5659	−1.95722
$807$	6.30500	0.221947
$808$	−118.798	−4.17931
$809$	2.68027	0.0942333	0.0471167	−	0.998889i	$-0.484997\pi$
$809$	2.68027	0.0942333	0.0471167	+	0.998889i	$0.484997\pi$
$810$	2.05462	0.0721920
$811$	39.7688	1.39647	0.698237	−	0.715867i	$-0.253968\pi$
$811$	39.7688	1.39647	0.698237	+	0.715867i	$0.253968\pi$
$812$	18.4451	0.647295
$813$	2.87108	0.100693
$814$	9.63123	0.337574
$815$	−6.81905	−0.238861
$816$	−1.20174	−0.0420693
$817$	−4.91427	−0.171928
$818$	13.0525	0.456371
$819$	6.45691	0.225623
$820$	−100.314	−3.50312
$821$	−19.5628	−0.682748	−0.341374	−	0.939928i	$-0.610892\pi$
$821$	−19.5628	−0.682748	−0.341374	+	0.939928i	$0.610892\pi$
$822$	39.7635	1.38691
$823$	24.6607	0.859618	0.429809	−	0.902920i	$-0.358581\pi$
$823$	24.6607	0.859618	0.429809	+	0.902920i	$0.358581\pi$
$824$	−150.835	−5.25458
$825$	6.01581	0.209444
$826$	−2.99332	−0.104151
$827$	−1.02789	−0.0357431	−0.0178716	−	0.999840i	$-0.505689\pi$
$827$	−1.02789	−0.0357431	−0.0178716	+	0.999840i	$0.505689\pi$
$828$	10.1090	0.351312
$829$	−24.5332	−0.852075	−0.426037	−	0.904706i	$-0.640091\pi$
$829$	−24.5332	−0.852075	−0.426037	+	0.904706i	$0.640091\pi$
$830$	177.822	6.17230
$831$	7.80813	0.270861
$832$	−112.598	−3.90364
$833$	0.425540	0.0147441
$834$	−11.6202	−0.402375
$835$	21.3169	0.737700
$836$	2.99875	0.103714
$837$	30.7068	1.06138
$838$	42.1501	1.45605
$839$	22.1418	0.764421	0.382210	−	0.924075i	$-0.375163\pi$
$839$	22.1418	0.764421	0.382210	+	0.924075i	$0.375163\pi$
$840$	−46.1859	−1.59357
$841$	−18.4065	−0.634707
$842$	1.15056	0.0396511
$843$	−15.1146	−0.520574
$844$	67.0921	2.30941
$845$	−4.81427	−0.165616
$846$	−58.9582	−2.02702
$847$	−11.0983	−0.381343
$848$	−153.489	−5.27084
$849$	−18.4806	−0.634252
$850$	2.64383	0.0906826
$851$	8.50838	0.291664
$852$	40.4107	1.38445
$853$	−45.1938	−1.54741	−0.773704	−	0.633547i	$-0.781598\pi$
$853$	−45.1938	−1.54741	−0.773704	+	0.633547i	$0.781598\pi$
$854$	−41.7570	−1.42890
$855$	−10.3278	−0.353203
$856$	−23.8736	−0.815982
$857$	25.8006	0.881332	0.440666	−	0.897671i	$-0.354742\pi$
$857$	25.8006	0.881332	0.440666	+	0.897671i	$0.354742\pi$
$858$	4.22375	0.144196
$859$	−52.5787	−1.79396	−0.896981	−	0.442069i	$-0.854245\pi$
$859$	−52.5787	−1.79396	−0.896981	+	0.442069i	$0.854245\pi$
$860$	−88.8482	−3.02970
$861$	−4.68261	−0.159583
$862$	−63.0595	−2.14782
$863$	1.29456	0.0440672	0.0220336	−	0.999757i	$-0.492986\pi$
$863$	1.29456	0.0440672	0.0220336	+	0.999757i	$0.492986\pi$
$864$	121.349	4.12839
$865$	−0.745352	−0.0253427
$866$	−59.2954	−2.01494
$867$	−18.3982	−0.624837
$868$	−33.2940	−1.13007
$869$	−2.40963	−0.0817411
$870$	−41.5547	−1.40884
$871$	46.7004	1.58238
$872$	122.124	4.13564
$873$	22.4358	0.759335
$874$	3.60725	0.122017
$875$	37.3090	1.26127
$876$	−25.9827	−0.877873
$877$	−20.8473	−0.703962	−0.351981	−	0.936007i	$-0.614492\pi$
$877$	−20.8473	−0.703962	−0.351981	+	0.936007i	$0.614492\pi$
$878$	2.34733	0.0792187
$879$	−10.4852	−0.353658
$880$	27.5167	0.927587
$881$	−43.5338	−1.46669	−0.733345	−	0.679857i	$-0.762042\pi$
$881$	−43.5338	−1.46669	−0.733345	+	0.679857i	$0.762042\pi$
$882$	−29.8458	−1.00496
$883$	8.49008	0.285714	0.142857	−	0.989743i	$-0.454371\pi$
$883$	8.49008	0.285714	0.142857	+	0.989743i	$0.454371\pi$
$884$	1.36322	0.0458502
$885$	4.95249	0.166476
$886$	46.0247	1.54623
$887$	16.8629	0.566200	0.283100	−	0.959090i	$-0.408637\pi$
$887$	16.8629	0.566200	0.283100	+	0.959090i	$0.408637\pi$
$888$	89.2228	2.99412
$889$	3.18501	0.106822
$890$	151.077	5.06410
$891$	−0.0718667	−0.00240762
$892$	43.6520	1.46158
$893$	−15.4505	−0.517031
$894$	35.0592	1.17256
$895$	56.6275	1.89285
$896$	−44.2814	−1.47934
$897$	3.73133	0.124585
$898$	−77.4532	−2.58465
$899$	−19.1217	−0.637743
$900$	−136.178	−4.53926
$901$	0.707296	0.0235634
$902$	4.77780	0.159083
$903$	−4.14738	−0.138016
$904$	71.1832	2.36752
$905$	−12.7991	−0.425457
$906$	50.5954	1.68092
$907$	16.7024	0.554593	0.277296	−	0.960784i	$-0.410562\pi$
$907$	16.7024	0.554593	0.277296	+	0.960784i	$0.410562\pi$
$908$	22.9485	0.761574
$909$	−22.4193	−0.743602
$910$	41.6565	1.38090
$911$	−9.18788	−0.304408	−0.152204	−	0.988349i	$-0.548637\pi$
$911$	−9.18788	−0.304408	−0.152204	+	0.988349i	$0.548637\pi$
$912$	22.0877	0.731398
$913$	−6.21988	−0.205848
$914$	2.01623	0.0666910
$915$	69.0874	2.28396
$916$	74.5064	2.46176
$917$	19.9663	0.659347
$918$	−1.02580	−0.0338565
$919$	−21.2029	−0.699419	−0.349709	−	0.936858i	$-0.613720\pi$
$919$	−21.2029	−0.699419	−0.349709	+	0.936858i	$0.613720\pi$
$920$	41.6308	1.37253
$921$	11.6340	0.383354
$922$	−17.8611	−0.588225
$923$	−23.2658	−0.765805
$924$	2.53079	0.0832569
$925$	−114.616	−3.76855
$926$	−89.9029	−2.95439
$927$	−28.4652	−0.934920
$928$	−75.5665	−2.48059
$929$	50.0462	1.64196	0.820980	−	0.570956i	$-0.193427\pi$
$929$	50.0462	1.64196	0.820980	+	0.570956i	$0.193427\pi$
$930$	75.0077	2.45960
$931$	−7.82135	−0.256334
$932$	132.118	4.32768
$933$	−23.0459	−0.754490
$934$	−42.8314	−1.40149
$935$	−0.126800	−0.00414681
$936$	−61.0322	−1.99490
$937$	−24.6960	−0.806783	−0.403392	−	0.915027i	$-0.632169\pi$
$937$	−24.6960	−0.806783	−0.403392	+	0.915027i	$0.632169\pi$
$938$	38.1021	1.24408
$939$	−1.52558	−0.0497855
$940$	−279.340	−9.11105
$941$	55.0132	1.79338	0.896690	−	0.442658i	$-0.145965\pi$
$941$	55.0132	1.79338	0.896690	+	0.442658i	$0.145965\pi$
$942$	−35.0066	−1.14058
$943$	4.22079	0.137448
$944$	16.5209	0.537711
$945$	−23.0202	−0.748847
$946$	4.23169	0.137584
$947$	−35.4268	−1.15122	−0.575608	−	0.817725i	$-0.695235\pi$
$947$	−35.4268	−1.15122	−0.575608	+	0.817725i	$0.695235\pi$
$948$	−34.9700	−1.13577
$949$	14.9591	0.485594
$950$	−48.5931	−1.57657
$951$	25.0083	0.810949
$952$	0.709977	0.0230105
$953$	−8.46803	−0.274307	−0.137153	−	0.990550i	$-0.543795\pi$
$953$	−8.46803	−0.274307	−0.137153	+	0.990550i	$0.543795\pi$
$954$	−49.6071	−1.60609
$955$	−27.5033	−0.889987
$956$	85.6507	2.77014
$957$	1.45350	0.0469851
$958$	95.1895	3.07543
$959$	−13.7172	−0.442952
$960$	151.995	4.90562
$961$	3.51530	0.113397
$962$	−80.4728	−2.59455
$963$	−4.50537	−0.145183
$964$	−125.152	−4.03086
$965$	113.822	3.66405
$966$	3.04433	0.0979497
$967$	−40.2692	−1.29497	−0.647485	−	0.762078i	$-0.724179\pi$
$967$	−40.2692	−1.29497	−0.647485	+	0.762078i	$0.724179\pi$
$968$	104.904	3.37174
$969$	−0.101783	−0.00326974
$970$	144.744	4.64744
$971$	44.9410	1.44222	0.721112	−	0.692818i	$-0.243631\pi$
$971$	44.9410	1.44222	0.721112	+	0.692818i	$0.243631\pi$
$972$	85.6679	2.74780
$973$	4.00862	0.128511
$974$	71.2423	2.28275
$975$	−50.2645	−1.60975
$976$	230.468	7.37709
$977$	−29.2491	−0.935762	−0.467881	−	0.883792i	$-0.654982\pi$
$977$	−29.2491	−0.935762	−0.467881	+	0.883792i	$0.654982\pi$
$978$	4.71340	0.150718
$979$	−5.28437	−0.168889
$980$	−141.407	−4.51708
$981$	23.0469	0.735832
$982$	−75.6247	−2.41328
$983$	−5.57283	−0.177746	−0.0888728	−	0.996043i	$-0.528326\pi$
$983$	−5.57283	−0.177746	−0.0888728	+	0.996043i	$0.528326\pi$
$984$	44.2611	1.41099
$985$	64.4922	2.05489
$986$	0.638785	0.0203431
$987$	−13.0394	−0.415049
$988$	−25.0558	−0.797131
$989$	3.73835	0.118872
$990$	8.89329	0.282647
$991$	17.9078	0.568860	0.284430	−	0.958697i	$-0.408196\pi$
$991$	17.9078	0.568860	0.284430	+	0.958697i	$0.408196\pi$
$992$	136.400	4.33071
$993$	−11.5629	−0.366939
$994$	−18.9822	−0.602080
$995$	−86.5592	−2.74411
$996$	−90.2666	−2.86021
$997$	34.9697	1.10750	0.553751	−	0.832682i	$-0.313196\pi$
$997$	34.9697	1.10750	0.553751	+	0.832682i	$0.313196\pi$
$998$	−82.6026	−2.61474
$999$	44.4708	1.40699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.3	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.3	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74408 q^{2} +1.08258 q^{3} +5.52999 q^{4} +4.29779 q^{5} -2.97068 q^{6} +1.02479 q^{7} -9.68658 q^{8} -1.82803 q^{9} +O(q^{10})\)	\(q-2.74408 q^{2} +1.08258 q^{3} +5.52999 q^{4} +4.29779 q^{5} -2.97068 q^{6} +1.02479 q^{7} -9.68658 q^{8} -1.82803 q^{9} -11.7935 q^{10} +0.412513 q^{11} +5.98663 q^{12} -3.44671 q^{13} -2.81212 q^{14} +4.65268 q^{15} +15.5208 q^{16} -0.0715217 q^{17} +5.01626 q^{18} +1.31456 q^{19} +23.7667 q^{20} +1.10942 q^{21} -1.13197 q^{22} -1.00000 q^{23} -10.4865 q^{24} +13.4710 q^{25} +9.45806 q^{26} -5.22671 q^{27} +5.66709 q^{28} +3.25477 q^{29} -12.7673 q^{30} -5.87497 q^{31} -23.2172 q^{32} +0.446576 q^{33} +0.196261 q^{34} +4.40434 q^{35} -10.1090 q^{36} -8.50838 q^{37} -3.60725 q^{38} -3.73133 q^{39} -41.6308 q^{40} -4.22079 q^{41} -3.04433 q^{42} -3.73835 q^{43} +2.28119 q^{44} -7.85648 q^{45} +2.74408 q^{46} -11.7534 q^{47} +16.8024 q^{48} -5.94980 q^{49} -36.9654 q^{50} -0.0774276 q^{51} -19.0603 q^{52} -9.88925 q^{53} +14.3425 q^{54} +1.77289 q^{55} -9.92674 q^{56} +1.42311 q^{57} -8.93135 q^{58} +1.06444 q^{59} +25.7293 q^{60} +14.8490 q^{61} +16.1214 q^{62} -1.87335 q^{63} +32.6683 q^{64} -14.8132 q^{65} -1.22544 q^{66} -13.5493 q^{67} -0.395514 q^{68} -1.08258 q^{69} -12.0859 q^{70} +6.75016 q^{71} +17.7074 q^{72} -4.34011 q^{73} +23.3477 q^{74} +14.5833 q^{75} +7.26948 q^{76} +0.422740 q^{77} +10.2391 q^{78} -5.84134 q^{79} +66.7050 q^{80} -0.174217 q^{81} +11.5822 q^{82} -15.0780 q^{83} +6.13506 q^{84} -0.307385 q^{85} +10.2583 q^{86} +3.52353 q^{87} -3.99584 q^{88} -12.8102 q^{89} +21.5588 q^{90} -3.53217 q^{91} -5.52999 q^{92} -6.36010 q^{93} +32.2523 q^{94} +5.64968 q^{95} -25.1344 q^{96} -12.2732 q^{97} +16.3267 q^{98} -0.754086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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