LMFDB - Embedded newform 4003.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} +O(q^{10})$	\(q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} -5.72129 q^{10} +3.01593 q^{11} +8.81594 q^{12} +2.19057 q^{13} +7.20742 q^{14} +3.01942 q^{15} +19.3194 q^{16} -4.87502 q^{17} +2.22745 q^{18} +3.05249 q^{19} +12.0498 q^{20} -3.80372 q^{21} -8.49373 q^{22} -2.52458 q^{23} -16.4565 q^{24} -0.872998 q^{25} -6.16927 q^{26} -5.63443 q^{27} -15.1798 q^{28} +4.33871 q^{29} -8.50355 q^{30} -7.97929 q^{31} -32.2647 q^{32} +4.48257 q^{33} +13.7294 q^{34} -5.19901 q^{35} -4.69131 q^{36} -4.37466 q^{37} -8.59668 q^{38} +3.25584 q^{39} -22.4931 q^{40} +7.43043 q^{41} +10.7124 q^{42} +3.81685 q^{43} +17.8889 q^{44} -1.60675 q^{45} +7.10995 q^{46} -11.2833 q^{47} +28.7144 q^{48} -0.450529 q^{49} +2.45861 q^{50} -7.24573 q^{51} +12.9933 q^{52} -2.47557 q^{53} +15.8682 q^{54} +6.12687 q^{55} +28.3358 q^{56} +4.53691 q^{57} -12.2191 q^{58} -13.3144 q^{59} +17.9096 q^{60} -9.04921 q^{61} +22.4720 q^{62} +2.02411 q^{63} +52.2278 q^{64} +4.45015 q^{65} -12.6242 q^{66} +3.65186 q^{67} -28.9160 q^{68} -3.75228 q^{69} +14.6419 q^{70} -1.86745 q^{71} +8.75716 q^{72} +13.5051 q^{73} +12.3203 q^{74} -1.29754 q^{75} +18.1057 q^{76} -7.71835 q^{77} -9.16938 q^{78} +13.6991 q^{79} +39.2474 q^{80} -6.00169 q^{81} -20.9262 q^{82} +2.47599 q^{83} -22.5617 q^{84} -9.90361 q^{85} -10.7493 q^{86} +6.44862 q^{87} -33.3929 q^{88} +1.92010 q^{89} +4.52507 q^{90} -5.60609 q^{91} -14.9745 q^{92} -11.8596 q^{93} +31.7770 q^{94} +6.20114 q^{95} -47.9550 q^{96} -16.5638 q^{97} +1.26882 q^{98} -2.38535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.81629	−1.99142	−0.995708	−	0.0925529i	$-0.970497\pi$
$2$	−2.81629	−1.99142	−0.995708	+	0.0925529i	$0.970497\pi$
$3$	1.48630	0.858115	0.429057	−	0.903277i	$-0.358846\pi$
$3$	1.48630	0.858115	0.429057	+	0.903277i	$0.358846\pi$
$4$	5.93147	2.96574
$5$	2.03150	0.908515	0.454258	−	0.890870i	$-0.349905\pi$
$5$	2.03150	0.908515	0.454258	+	0.890870i	$0.349905\pi$
$6$	−4.18584	−1.70886
$7$	−2.55919	−0.967284	−0.483642	−	0.875266i	$-0.660686\pi$
$7$	−2.55919	−0.967284	−0.483642	+	0.875266i	$0.660686\pi$
$8$	−11.0722	−3.91460
$9$	−0.790918	−0.263639
$10$	−5.72129	−1.80923
$11$	3.01593	0.909338	0.454669	−	0.890661i	$-0.349758\pi$
$11$	3.01593	0.909338	0.454669	+	0.890661i	$0.349758\pi$
$12$	8.81594	2.54494
$13$	2.19057	0.607555	0.303777	−	0.952743i	$-0.401752\pi$
$13$	2.19057	0.607555	0.303777	+	0.952743i	$0.401752\pi$
$14$	7.20742	1.92626
$15$	3.01942	0.779610
$16$	19.3194	4.82985
$17$	−4.87502	−1.18237	−0.591183	−	0.806538i	$-0.701339\pi$
$17$	−4.87502	−1.18237	−0.591183	+	0.806538i	$0.701339\pi$
$18$	2.22745	0.525015
$19$	3.05249	0.700289	0.350144	−	0.936696i	$-0.386132\pi$
$19$	3.05249	0.700289	0.350144	+	0.936696i	$0.386132\pi$
$20$	12.0498	2.69442
$21$	−3.80372	−0.830041
$22$	−8.49373	−1.81087
$23$	−2.52458	−0.526412	−0.263206	−	0.964740i	$-0.584780\pi$
$23$	−2.52458	−0.526412	−0.263206	+	0.964740i	$0.584780\pi$
$24$	−16.4565	−3.35917
$25$	−0.872998	−0.174600
$26$	−6.16927	−1.20989
$27$	−5.63443	−1.08435
$28$	−15.1798	−2.86871
$29$	4.33871	0.805678	0.402839	−	0.915271i	$-0.368023\pi$
$29$	4.33871	0.805678	0.402839	+	0.915271i	$0.368023\pi$
$30$	−8.50355	−1.55253
$31$	−7.97929	−1.43312	−0.716562	−	0.697524i	$-0.754285\pi$
$31$	−7.97929	−1.43312	−0.716562	+	0.697524i	$0.754285\pi$
$32$	−32.2647	−5.70365
$33$	4.48257	0.780316
$34$	13.7294	2.35458
$35$	−5.19901	−0.878793
$36$	−4.69131	−0.781885
$37$	−4.37466	−0.719190	−0.359595	−	0.933108i	$-0.617085\pi$
$37$	−4.37466	−0.719190	−0.359595	+	0.933108i	$0.617085\pi$
$38$	−8.59668	−1.39457
$39$	3.25584	0.521352
$40$	−22.4931	−3.55647
$41$	7.43043	1.16044	0.580219	−	0.814460i	$-0.302967\pi$
$41$	7.43043	1.16044	0.580219	+	0.814460i	$0.302967\pi$
$42$	10.7124	1.65296
$43$	3.81685	0.582064	0.291032	−	0.956713i	$-0.406001\pi$
$43$	3.81685	0.582064	0.291032	+	0.956713i	$0.406001\pi$
$44$	17.8889	2.69686
$45$	−1.60675	−0.239520
$46$	7.10995	1.04831
$47$	−11.2833	−1.64584	−0.822918	−	0.568160i	$-0.807656\pi$
$47$	−11.2833	−1.64584	−0.822918	+	0.568160i	$0.807656\pi$
$48$	28.7144	4.14457
$49$	−0.450529	−0.0643612
$50$	2.45861	0.347700
$51$	−7.24573	−1.01461
$52$	12.9933	1.80185
$53$	−2.47557	−0.340045	−0.170023	−	0.985440i	$-0.554384\pi$
$53$	−2.47557	−0.340045	−0.170023	+	0.985440i	$0.554384\pi$
$54$	15.8682	2.15939
$55$	6.12687	0.826147
$56$	28.3358	3.78653
$57$	4.53691	0.600928
$58$	−12.2191	−1.60444
$59$	−13.3144	−1.73339	−0.866694	−	0.498841i	$-0.833759\pi$
$59$	−13.3144	−1.73339	−0.866694	+	0.498841i	$0.833759\pi$
$60$	17.9096	2.31212
$61$	−9.04921	−1.15863	−0.579316	−	0.815103i	$-0.696680\pi$
$61$	−9.04921	−1.15863	−0.579316	+	0.815103i	$0.696680\pi$
$62$	22.4720	2.85394
$63$	2.02411	0.255014
$64$	52.2278	6.52848
$65$	4.45015	0.551973
$66$	−12.6242	−1.55393
$67$	3.65186	0.446146	0.223073	−	0.974802i	$-0.428391\pi$
$67$	3.65186	0.446146	0.223073	+	0.974802i	$0.428391\pi$
$68$	−28.9160	−3.50658
$69$	−3.75228	−0.451722
$70$	14.6419	1.75004
$71$	−1.86745	−0.221626	−0.110813	−	0.993841i	$-0.535345\pi$
$71$	−1.86745	−0.221626	−0.110813	+	0.993841i	$0.535345\pi$
$72$	8.75716	1.03204
$73$	13.5051	1.58065	0.790325	−	0.612687i	$-0.209912\pi$
$73$	13.5051	1.58065	0.790325	+	0.612687i	$0.209912\pi$
$74$	12.3203	1.43221
$75$	−1.29754	−0.149827
$76$	18.1057	2.07687
$77$	−7.71835	−0.879588
$78$	−9.16938	−1.03823
$79$	13.6991	1.54127	0.770633	−	0.637279i	$-0.219940\pi$
$79$	13.6991	1.54127	0.770633	+	0.637279i	$0.219940\pi$
$80$	39.2474	4.38800
$81$	−6.00169	−0.666855
$82$	−20.9262	−2.31091
$83$	2.47599	0.271775	0.135888	−	0.990724i	$-0.456611\pi$
$83$	2.47599	0.271775	0.135888	+	0.990724i	$0.456611\pi$
$84$	−22.5617	−2.46168
$85$	−9.90361	−1.07420
$86$	−10.7493	−1.15913
$87$	6.44862	0.691364
$88$	−33.3929	−3.55969
$89$	1.92010	0.203530	0.101765	−	0.994808i	$-0.467551\pi$
$89$	1.92010	0.203530	0.101765	+	0.994808i	$0.467551\pi$
$90$	4.52507	0.476985
$91$	−5.60609	−0.587678
$92$	−14.9745	−1.56120
$93$	−11.8596	−1.22978
$94$	31.7770	3.27755
$95$	6.20114	0.636223
$96$	−47.9550	−4.89438
$97$	−16.5638	−1.68180	−0.840899	−	0.541192i	$-0.817973\pi$
$97$	−16.5638	−1.68180	−0.840899	+	0.541192i	$0.817973\pi$
$98$	1.26882	0.128170
$99$	−2.38535	−0.239737
$100$	−5.17816	−0.517816
$101$	−17.9038	−1.78149	−0.890746	−	0.454502i	$-0.849817\pi$
$101$	−17.9038	−1.78149	−0.890746	+	0.454502i	$0.849817\pi$
$102$	20.4061	2.02050
$103$	13.8252	1.36224	0.681119	−	0.732173i	$-0.261494\pi$
$103$	13.8252	1.36224	0.681119	+	0.732173i	$0.261494\pi$
$104$	−24.2543	−2.37833
$105$	−7.72727	−0.754105
$106$	6.97191	0.677172
$107$	−7.33026	−0.708643	−0.354322	−	0.935124i	$-0.615288\pi$
$107$	−7.33026	−0.708643	−0.354322	+	0.935124i	$0.615288\pi$
$108$	−33.4205	−3.21589
$109$	1.38714	0.132864	0.0664318	−	0.997791i	$-0.478839\pi$
$109$	1.38714	0.132864	0.0664318	+	0.997791i	$0.478839\pi$
$110$	−17.2550	−1.64520
$111$	−6.50205	−0.617147
$112$	−49.4421	−4.67184
$113$	−14.5427	−1.36806	−0.684030	−	0.729454i	$-0.739774\pi$
$113$	−14.5427	−1.36806	−0.684030	+	0.729454i	$0.739774\pi$
$114$	−12.7772	−1.19670
$115$	−5.12870	−0.478254
$116$	25.7349	2.38943
$117$	−1.73256	−0.160175
$118$	37.4972	3.45189
$119$	12.4761	1.14368
$120$	−33.4315	−3.05186
$121$	−1.90416	−0.173105
$122$	25.4852	2.30732
$123$	11.0438	0.995789
$124$	−47.3289	−4.25026
$125$	−11.9310	−1.06714
$126$	−5.70048	−0.507839
$127$	−16.6270	−1.47541	−0.737706	−	0.675122i	$-0.764091\pi$
$127$	−16.6270	−1.47541	−0.737706	+	0.675122i	$0.764091\pi$
$128$	−82.5592	−7.29727
$129$	5.67297	0.499477
$130$	−12.5329	−1.09921
$131$	12.2836	1.07322	0.536612	−	0.843829i	$-0.319704\pi$
$131$	12.2836	1.07322	0.536612	+	0.843829i	$0.319704\pi$
$132$	26.5883	2.31421
$133$	−7.81191	−0.677378
$134$	−10.2847	−0.888461
$135$	−11.4464	−0.985146
$136$	53.9769	4.62848
$137$	9.56305	0.817027	0.408513	−	0.912752i	$-0.366047\pi$
$137$	9.56305	0.817027	0.408513	+	0.912752i	$0.366047\pi$
$138$	10.5675	0.899566
$139$	−17.0687	−1.44775	−0.723874	−	0.689932i	$-0.757640\pi$
$139$	−17.0687	−1.44775	−0.723874	+	0.689932i	$0.757640\pi$
$140$	−30.8378	−2.60627
$141$	−16.7703	−1.41232
$142$	5.25929	0.441349
$143$	6.60661	0.552472
$144$	−15.2801	−1.27334
$145$	8.81410	0.731971
$146$	−38.0342	−3.14773
$147$	−0.669620	−0.0552293
$148$	−25.9482	−2.13293
$149$	9.81087	0.803737	0.401869	−	0.915697i	$-0.368361\pi$
$149$	9.81087	0.803737	0.401869	+	0.915697i	$0.368361\pi$
$150$	3.65423	0.298367
$151$	18.9683	1.54362	0.771810	−	0.635853i	$-0.219352\pi$
$151$	18.9683	1.54362	0.771810	+	0.635853i	$0.219352\pi$
$152$	−33.7976	−2.74135
$153$	3.85574	0.311718
$154$	21.7371	1.75163
$155$	−16.2100	−1.30201
$156$	19.3119	1.54619
$157$	0.172985	0.0138057	0.00690284	−	0.999976i	$-0.497803\pi$
$157$	0.172985	0.0138057	0.00690284	+	0.999976i	$0.497803\pi$
$158$	−38.5805	−3.06930
$159$	−3.67943	−0.291798
$160$	−65.5458	−5.18185
$161$	6.46090	0.509190
$162$	16.9025	1.32799
$163$	8.36622	0.655293	0.327646	−	0.944800i	$-0.393745\pi$
$163$	8.36622	0.655293	0.327646	+	0.944800i	$0.393745\pi$
$164$	44.0734	3.44155
$165$	9.10636	0.708929
$166$	−6.97310	−0.541217
$167$	0.190375	0.0147317	0.00736585	−	0.999973i	$-0.497655\pi$
$167$	0.190375	0.0147317	0.00736585	+	0.999973i	$0.497655\pi$
$168$	42.1154	3.24927
$169$	−8.20140	−0.630877
$170$	27.8914	2.13917
$171$	−2.41427	−0.184624
$172$	22.6395	1.72625
$173$	−20.6229	−1.56793	−0.783965	−	0.620805i	$-0.786806\pi$
$173$	−20.6229	−1.56793	−0.783965	+	0.620805i	$0.786806\pi$
$174$	−18.1612	−1.37679
$175$	2.23417	0.168888
$176$	58.2660	4.39197
$177$	−19.7892	−1.48744
$178$	−5.40754	−0.405312
$179$	−1.27139	−0.0950281	−0.0475140	−	0.998871i	$-0.515130\pi$
$179$	−1.27139	−0.0950281	−0.0475140	+	0.998871i	$0.515130\pi$
$180$	−9.53040	−0.710354
$181$	3.27974	0.243782	0.121891	−	0.992544i	$-0.461104\pi$
$181$	3.27974	0.243782	0.121891	+	0.992544i	$0.461104\pi$
$182$	15.7884	1.17031
$183$	−13.4498	−0.994240
$184$	27.9526	2.06069
$185$	−8.88714	−0.653395
$186$	33.4001	2.44901
$187$	−14.7027	−1.07517
$188$	−66.9265	−4.88112
$189$	14.4196	1.04887
$190$	−17.4642	−1.26698
$191$	9.90175	0.716466	0.358233	−	0.933632i	$-0.383379\pi$
$191$	9.90175	0.716466	0.358233	+	0.933632i	$0.383379\pi$
$192$	77.6261	5.60218
$193$	−0.457067	−0.0329004	−0.0164502	−	0.999865i	$-0.505236\pi$
$193$	−0.457067	−0.0329004	−0.0164502	+	0.999865i	$0.505236\pi$
$194$	46.6484	3.34916
$195$	6.61425	0.473656
$196$	−2.67230	−0.190878
$197$	−3.46518	−0.246884	−0.123442	−	0.992352i	$-0.539393\pi$
$197$	−3.46518	−0.246884	−0.123442	+	0.992352i	$0.539393\pi$
$198$	6.71784	0.477416
$199$	10.1540	0.719795	0.359898	−	0.932992i	$-0.382812\pi$
$199$	10.1540	0.719795	0.359898	+	0.932992i	$0.382812\pi$
$200$	9.66597	0.683487
$201$	5.42775	0.382844
$202$	50.4221	3.54769
$203$	−11.1036	−0.779320
$204$	−42.9778	−3.00905
$205$	15.0949	1.05428
$206$	−38.9357	−2.71278
$207$	1.99674	0.138783
$208$	42.3205	2.93440
$209$	9.20610	0.636799
$210$	21.7622	1.50174
$211$	13.6537	0.939959	0.469979	−	0.882677i	$-0.344261\pi$
$211$	13.6537	0.939959	0.469979	+	0.882677i	$0.344261\pi$
$212$	−14.6838	−1.00848
$213$	−2.77559	−0.190181
$214$	20.6441	1.41120
$215$	7.75393	0.528814
$216$	62.3853	4.24478
$217$	20.4206	1.38624
$218$	−3.90658	−0.264587
$219$	20.0726	1.35638
$220$	36.3414	2.45013
$221$	−10.6791	−0.718352
$222$	18.3116	1.22900
$223$	−3.28824	−0.220197	−0.110098	−	0.993921i	$-0.535117\pi$
$223$	−3.28824	−0.220197	−0.110098	+	0.993921i	$0.535117\pi$
$224$	82.5716	5.51705
$225$	0.690470	0.0460313
$226$	40.9563	2.72437
$227$	−28.2516	−1.87512	−0.937562	−	0.347819i	$-0.886922\pi$
$227$	−28.2516	−1.87512	−0.937562	+	0.347819i	$0.886922\pi$
$228$	26.9105	1.78219
$229$	−13.8737	−0.916803	−0.458401	−	0.888745i	$-0.651578\pi$
$229$	−13.8737	−0.916803	−0.458401	+	0.888745i	$0.651578\pi$
$230$	14.4439	0.952402
$231$	−11.4718	−0.754787
$232$	−48.0389	−3.15391
$233$	8.45035	0.553601	0.276800	−	0.960927i	$-0.410726\pi$
$233$	8.45035	0.553601	0.276800	+	0.960927i	$0.410726\pi$
$234$	4.87939	0.318976
$235$	−22.9220	−1.49527
$236$	−78.9740	−5.14077
$237$	20.3609	1.32258
$238$	−35.1363	−2.27755
$239$	−13.7979	−0.892509	−0.446254	−	0.894906i	$-0.647242\pi$
$239$	−13.7979	−0.892509	−0.446254	+	0.894906i	$0.647242\pi$
$240$	58.3334	3.76540
$241$	20.4498	1.31729	0.658644	−	0.752455i	$-0.271130\pi$
$241$	20.4498	1.31729	0.658644	+	0.752455i	$0.271130\pi$
$242$	5.36265	0.344724
$243$	7.98299	0.512109
$244$	−53.6751	−3.43620
$245$	−0.915250	−0.0584732
$246$	−31.1026	−1.98303
$247$	6.68669	0.425464
$248$	88.3479	5.61010
$249$	3.68006	0.233214
$250$	33.6011	2.12512
$251$	15.8650	1.00139	0.500696	−	0.865623i	$-0.333077\pi$
$251$	15.8650	1.00139	0.500696	+	0.865623i	$0.333077\pi$
$252$	12.0060	0.756305
$253$	−7.61397	−0.478686
$254$	46.8265	2.93816
$255$	−14.7197	−0.921784
$256$	128.055	8.00341
$257$	−14.0306	−0.875202	−0.437601	−	0.899169i	$-0.644172\pi$
$257$	−14.0306	−0.875202	−0.437601	+	0.899169i	$0.644172\pi$
$258$	−15.9767	−0.994667
$259$	11.1956	0.695661
$260$	26.3959	1.63701
$261$	−3.43156	−0.212409
$262$	−34.5942	−2.13724
$263$	−11.3597	−0.700468	−0.350234	−	0.936662i	$-0.613898\pi$
$263$	−11.3597	−0.700468	−0.350234	+	0.936662i	$0.613898\pi$
$264$	−49.6317	−3.05462
$265$	−5.02912	−0.308937
$266$	22.0006	1.34894
$267$	2.85384	0.174652
$268$	21.6609	1.32315
$269$	−4.45571	−0.271670	−0.135835	−	0.990731i	$-0.543372\pi$
$269$	−4.45571	−0.271670	−0.135835	+	0.990731i	$0.543372\pi$
$270$	32.2363	1.96184
$271$	−18.6220	−1.13120	−0.565602	−	0.824678i	$-0.691356\pi$
$271$	−18.6220	−1.13120	−0.565602	+	0.824678i	$0.691356\pi$
$272$	−94.1825	−5.71065
$273$	−8.33232	−0.504295
$274$	−26.9323	−1.62704
$275$	−2.63290	−0.158770
$276$	−22.2566	−1.33969
$277$	−13.2756	−0.797651	−0.398825	−	0.917027i	$-0.630582\pi$
$277$	−13.2756	−0.797651	−0.398825	+	0.917027i	$0.630582\pi$
$278$	48.0704	2.88307
$279$	6.31097	0.377828
$280$	57.5642	3.44012
$281$	−20.5189	−1.22406	−0.612029	−	0.790836i	$-0.709646\pi$
$281$	−20.5189	−1.22406	−0.612029	+	0.790836i	$0.709646\pi$
$282$	47.2301	2.81251
$283$	25.3166	1.50492	0.752459	−	0.658640i	$-0.228868\pi$
$283$	25.3166	1.50492	0.752459	+	0.658640i	$0.228868\pi$
$284$	−11.0768	−0.657284
$285$	9.21674	0.545952
$286$	−18.6061	−1.10020
$287$	−19.0159	−1.12247
$288$	25.5187	1.50371
$289$	6.76580	0.397988
$290$	−24.8230	−1.45766
$291$	−24.6187	−1.44318
$292$	80.1050	4.68779
$293$	21.0101	1.22743	0.613713	−	0.789530i	$-0.289675\pi$
$293$	21.0101	1.22743	0.613713	+	0.789530i	$0.289675\pi$
$294$	1.88584	0.109985
$295$	−27.0482	−1.57481
$296$	48.4369	2.81534
$297$	−16.9931	−0.986038
$298$	−27.6302	−1.60058
$299$	−5.53028	−0.319824
$300$	−7.69630	−0.444346
$301$	−9.76805	−0.563021
$302$	−53.4202	−3.07399
$303$	−26.6103	−1.52872
$304$	58.9723	3.38229
$305$	−18.3835	−1.05264
$306$	−10.8589	−0.620760
$307$	9.65309	0.550931	0.275466	−	0.961311i	$-0.411168\pi$
$307$	9.65309	0.550931	0.275466	+	0.961311i	$0.411168\pi$
$308$	−45.7812	−2.60863
$309$	20.5484	1.16896
$310$	45.6519	2.59285
$311$	−15.8888	−0.900973	−0.450486	−	0.892783i	$-0.648749\pi$
$311$	−15.8888	−0.900973	−0.450486	+	0.892783i	$0.648749\pi$
$312$	−36.0492	−2.04088
$313$	16.1994	0.915645	0.457823	−	0.889044i	$-0.348629\pi$
$313$	16.1994	0.915645	0.457823	+	0.889044i	$0.348629\pi$
$314$	−0.487175	−0.0274929
$315$	4.11199	0.231684
$316$	81.2557	4.57099
$317$	3.60294	0.202361	0.101181	−	0.994868i	$-0.467738\pi$
$317$	3.60294	0.202361	0.101181	+	0.994868i	$0.467738\pi$
$318$	10.3623	0.581091
$319$	13.0853	0.732634
$320$	106.101	5.93122
$321$	−10.8950	−0.608097
$322$	−18.1957	−1.01401
$323$	−14.8809	−0.827997
$324$	−35.5989	−1.97772
$325$	−1.91236	−0.106079
$326$	−23.5617	−1.30496
$327$	2.06170	0.114012
$328$	−82.2708	−4.54265
$329$	28.8761	1.59199
$330$	−25.6461	−1.41177
$331$	−33.9941	−1.86848	−0.934241	−	0.356642i	$-0.883922\pi$
$331$	−33.9941	−1.86848	−0.934241	+	0.356642i	$0.883922\pi$
$332$	14.6863	0.806013
$333$	3.46000	0.189607
$334$	−0.536152	−0.0293369
$335$	7.41876	0.405330
$336$	−73.4857	−4.00897
$337$	6.78669	0.369695	0.184847	−	0.982767i	$-0.440821\pi$
$337$	6.78669	0.369695	0.184847	+	0.982767i	$0.440821\pi$
$338$	23.0975	1.25634
$339$	−21.6147	−1.17395
$340$	−58.7430	−3.18579
$341$	−24.0650	−1.30319
$342$	6.79927	0.367662
$343$	19.0673	1.02954
$344$	−42.2607	−2.27855
$345$	−7.62278	−0.410396
$346$	58.0800	3.12240
$347$	−23.3272	−1.25227	−0.626134	−	0.779716i	$-0.715364\pi$
$347$	−23.3272	−1.25227	−0.626134	+	0.779716i	$0.715364\pi$
$348$	38.2498	2.05040
$349$	−4.89243	−0.261886	−0.130943	−	0.991390i	$-0.541800\pi$
$349$	−4.89243	−0.261886	−0.130943	+	0.991390i	$0.541800\pi$
$350$	−6.29207	−0.336325
$351$	−12.3426	−0.658800
$352$	−97.3081	−5.18654
$353$	8.81005	0.468911	0.234456	−	0.972127i	$-0.424669\pi$
$353$	8.81005	0.468911	0.234456	+	0.972127i	$0.424669\pi$
$354$	55.7320	2.96212
$355$	−3.79374	−0.201351
$356$	11.3890	0.603616
$357$	18.5432	0.981412
$358$	3.58060	0.189240
$359$	−20.2522	−1.06887	−0.534435	−	0.845209i	$-0.679476\pi$
$359$	−20.2522	−1.06887	−0.534435	+	0.845209i	$0.679476\pi$
$360$	17.7902	0.937626
$361$	−9.68231	−0.509595
$362$	−9.23670	−0.485470
$363$	−2.83014	−0.148544
$364$	−33.2524	−1.74290
$365$	27.4356	1.43605
$366$	37.8786	1.97994
$367$	−18.8012	−0.981413	−0.490707	−	0.871325i	$-0.663261\pi$
$367$	−18.8012	−0.981413	−0.490707	+	0.871325i	$0.663261\pi$
$368$	−48.7735	−2.54249
$369$	−5.87686	−0.305937
$370$	25.0287	1.30118
$371$	6.33546	0.328921
$372$	−70.3449	−3.64721
$373$	10.4843	0.542857	0.271428	−	0.962459i	$-0.412504\pi$
$373$	10.4843	0.542857	0.271428	+	0.962459i	$0.412504\pi$
$374$	41.4071	2.14111
$375$	−17.7330	−0.915730
$376$	124.930	6.44279
$377$	9.50425	0.489494
$378$	−40.6098	−2.08874
$379$	−0.572538	−0.0294093	−0.0147047	−	0.999892i	$-0.504681\pi$
$379$	−0.572538	−0.0294093	−0.0147047	+	0.999892i	$0.504681\pi$
$380$	36.7819	1.88687
$381$	−24.7127	−1.26607
$382$	−27.8862	−1.42678
$383$	7.59912	0.388297	0.194148	−	0.980972i	$-0.437806\pi$
$383$	7.59912	0.388297	0.194148	+	0.980972i	$0.437806\pi$
$384$	−122.708	−6.26189
$385$	−15.6799	−0.799119
$386$	1.28723	0.0655183
$387$	−3.01881	−0.153455
$388$	−98.2477	−4.98777
$389$	−16.6276	−0.843051	−0.421525	−	0.906817i	$-0.638505\pi$
$389$	−16.6276	−0.843051	−0.421525	+	0.906817i	$0.638505\pi$
$390$	−18.6276	−0.943246
$391$	12.3074	0.622412
$392$	4.98832	0.251948
$393$	18.2571	0.920950
$394$	9.75895	0.491649
$395$	27.8297	1.40026
$396$	−14.1487	−0.710997
$397$	−24.2546	−1.21730	−0.608651	−	0.793438i	$-0.708289\pi$
$397$	−24.2546	−1.21730	−0.608651	+	0.793438i	$0.708289\pi$
$398$	−28.5965	−1.43341
$399$	−11.6108	−0.581268
$400$	−16.8658	−0.843291
$401$	−9.21474	−0.460162	−0.230081	−	0.973171i	$-0.573899\pi$
$401$	−9.21474	−0.460162	−0.230081	+	0.973171i	$0.573899\pi$
$402$	−15.2861	−0.762402
$403$	−17.4792	−0.870701
$404$	−106.196	−5.28343
$405$	−12.1925	−0.605848
$406$	31.2709	1.55195
$407$	−13.1937	−0.653986
$408$	80.2258	3.97177
$409$	32.1400	1.58922	0.794610	−	0.607120i	$-0.207675\pi$
$409$	32.1400	1.58922	0.794610	+	0.607120i	$0.207675\pi$
$410$	−42.5117	−2.09950
$411$	14.2135	0.701102
$412$	82.0038	4.04004
$413$	34.0741	1.67668
$414$	−5.62339	−0.276375
$415$	5.02998	0.246912
$416$	−70.6781	−3.46528
$417$	−25.3692	−1.24233
$418$	−25.9270	−1.26813
$419$	−28.2051	−1.37791	−0.688954	−	0.724805i	$-0.741930\pi$
$419$	−28.2051	−1.37791	−0.688954	+	0.724805i	$0.741930\pi$
$420$	−45.8341	−2.23648
$421$	22.8254	1.11244	0.556222	−	0.831034i	$-0.312250\pi$
$421$	22.8254	1.11244	0.556222	+	0.831034i	$0.312250\pi$
$422$	−38.4527	−1.87185
$423$	8.92416	0.433907
$424$	27.4099	1.33114
$425$	4.25588	0.206441
$426$	7.81687	0.378728
$427$	23.1587	1.12073
$428$	−43.4792	−2.10165
$429$	9.81939	0.474085
$430$	−21.8373	−1.05309
$431$	−17.6511	−0.850221	−0.425111	−	0.905141i	$-0.639765\pi$
$431$	−17.6511	−0.850221	−0.425111	+	0.905141i	$0.639765\pi$
$432$	−108.854	−5.23724
$433$	26.9746	1.29632	0.648158	−	0.761506i	$-0.275540\pi$
$433$	26.9746	1.29632	0.648158	+	0.761506i	$0.275540\pi$
$434$	−57.5101	−2.76057
$435$	13.1004	0.628115
$436$	8.22777	0.394039
$437$	−7.70626	−0.368641
$438$	−56.5301	−2.70112
$439$	−35.0299	−1.67188	−0.835942	−	0.548817i	$-0.815078\pi$
$439$	−35.0299	−1.67188	−0.835942	+	0.548817i	$0.815078\pi$
$440$	−67.8377	−3.23403
$441$	0.356331	0.0169682
$442$	30.0753	1.43054
$443$	26.8827	1.27724	0.638618	−	0.769524i	$-0.279507\pi$
$443$	26.8827	1.27724	0.638618	+	0.769524i	$0.279507\pi$
$444$	−38.5667	−1.83030
$445$	3.90068	0.184910
$446$	9.26063	0.438503
$447$	14.5819	0.689699
$448$	−133.661	−6.31490
$449$	23.2977	1.09949	0.549744	−	0.835333i	$-0.314725\pi$
$449$	23.2977	1.09949	0.549744	+	0.835333i	$0.314725\pi$
$450$	−1.94456	−0.0916675
$451$	22.4097	1.05523
$452$	−86.2594	−4.05730
$453$	28.1926	1.32460
$454$	79.5645	3.73415
$455$	−11.3888	−0.533915
$456$	−50.2333	−2.35239
$457$	−0.147124	−0.00688218	−0.00344109	−	0.999994i	$-0.501095\pi$
$457$	−0.147124	−0.00688218	−0.00344109	+	0.999994i	$0.501095\pi$
$458$	39.0725	1.82574
$459$	27.4680	1.28209
$460$	−30.4207	−1.41837
$461$	10.0003	0.465762	0.232881	−	0.972505i	$-0.425185\pi$
$461$	10.0003	0.465762	0.232881	+	0.972505i	$0.425185\pi$
$462$	32.3078	1.50309
$463$	11.8656	0.551442	0.275721	−	0.961238i	$-0.411083\pi$
$463$	11.8656	0.551442	0.275721	+	0.961238i	$0.411083\pi$
$464$	83.8214	3.89131
$465$	−24.0928	−1.11728
$466$	−23.7986	−1.10245
$467$	34.2298	1.58396	0.791982	−	0.610544i	$-0.209049\pi$
$467$	34.2298	1.58396	0.791982	+	0.610544i	$0.209049\pi$
$468$	−10.2766	−0.475038
$469$	−9.34581	−0.431550
$470$	64.5550	2.97770
$471$	0.257107	0.0118469
$472$	147.419	6.78551
$473$	11.5114	0.529293
$474$	−57.3422	−2.63381
$475$	−2.66482	−0.122270
$476$	74.0017	3.39186
$477$	1.95797	0.0896493
$478$	38.8587	1.77736
$479$	−12.6273	−0.576957	−0.288479	−	0.957486i	$-0.593149\pi$
$479$	−12.6273	−0.576957	−0.288479	+	0.957486i	$0.593149\pi$
$480$	−97.4206	−4.44662
$481$	−9.58300	−0.436947
$482$	−57.5925	−2.62327
$483$	9.60282	0.436944
$484$	−11.2945	−0.513384
$485$	−33.6494	−1.52794
$486$	−22.4824	−1.01982
$487$	21.4702	0.972910	0.486455	−	0.873706i	$-0.338290\pi$
$487$	21.4702	0.972910	0.486455	+	0.873706i	$0.338290\pi$
$488$	100.194	4.53558
$489$	12.4347	0.562316
$490$	2.57761	0.116444
$491$	−23.4050	−1.05625	−0.528127	−	0.849166i	$-0.677105\pi$
$491$	−23.4050	−1.05625	−0.528127	+	0.849166i	$0.677105\pi$
$492$	65.5062	2.95325
$493$	−21.1513	−0.952606
$494$	−18.8316	−0.847275
$495$	−4.84585	−0.217805
$496$	−154.155	−6.92177
$497$	4.77918	0.214375
$498$	−10.3641	−0.464427
$499$	3.02449	0.135395	0.0676975	−	0.997706i	$-0.478435\pi$
$499$	3.02449	0.135395	0.0676975	+	0.997706i	$0.478435\pi$
$500$	−70.7684	−3.16486
$501$	0.282955	0.0126415
$502$	−44.6805	−1.99419
$503$	8.71329	0.388506	0.194253	−	0.980951i	$-0.437772\pi$
$503$	8.71329	0.388506	0.194253	+	0.980951i	$0.437772\pi$
$504$	−22.4113	−0.998278
$505$	−36.3715	−1.61851
$506$	21.4431	0.953264
$507$	−12.1897	−0.541365
$508$	−98.6228	−4.37568
$509$	13.2435	0.587006	0.293503	−	0.955958i	$-0.405179\pi$
$509$	13.2435	0.587006	0.293503	+	0.955958i	$0.405179\pi$
$510$	41.4549	1.83566
$511$	−34.5621	−1.52894
$512$	−195.520	−8.64085
$513$	−17.1990	−0.759356
$514$	39.5141	1.74289
$515$	28.0859	1.23761
$516$	33.6491	1.48132
$517$	−34.0296	−1.49662
$518$	−31.5300	−1.38535
$519$	−30.6518	−1.34546
$520$	−49.2727	−2.16075
$521$	15.0482	0.659275	0.329637	−	0.944108i	$-0.393074\pi$
$521$	15.0482	0.659275	0.329637	+	0.944108i	$0.393074\pi$
$522$	9.66427	0.422994
$523$	−33.0303	−1.44431	−0.722157	−	0.691730i	$-0.756849\pi$
$523$	−33.0303	−1.44431	−0.722157	+	0.691730i	$0.756849\pi$
$524$	72.8599	3.18290
$525$	3.32065	0.144925
$526$	31.9921	1.39492
$527$	38.8992	1.69448
$528$	86.6007	3.76881
$529$	−16.6265	−0.722890
$530$	14.1635	0.615221
$531$	10.5306	0.456989
$532$	−46.3361	−2.00893
$533$	16.2769	0.705030
$534$	−8.03722	−0.347805
$535$	−14.8914	−0.643813
$536$	−40.4339	−1.74648
$537$	−1.88966	−0.0815450
$538$	12.5486	0.541007
$539$	−1.35876	−0.0585261
$540$	−67.8938	−2.92168
$541$	25.9573	1.11599	0.557996	−	0.829844i	$-0.311571\pi$
$541$	25.9573	1.11599	0.557996	+	0.829844i	$0.311571\pi$
$542$	52.4448	2.25270
$543$	4.87468	0.209192
$544$	157.291	6.74380
$545$	2.81797	0.120709
$546$	23.4662	1.00426
$547$	21.0968	0.902036	0.451018	−	0.892515i	$-0.351061\pi$
$547$	21.0968	0.902036	0.451018	+	0.892515i	$0.351061\pi$
$548$	56.7230	2.42308
$549$	7.15719	0.305461
$550$	7.41501	0.316177
$551$	13.2439	0.564208
$552$	41.5459	1.76831
$553$	−35.0586	−1.49084
$554$	37.3878	1.58845
$555$	−13.2089	−0.560688
$556$	−101.243	−4.29364
$557$	−4.73538	−0.200645	−0.100322	−	0.994955i	$-0.531987\pi$
$557$	−4.73538	−0.200645	−0.100322	+	0.994955i	$0.531987\pi$
$558$	−17.7735	−0.752412
$559$	8.36107	0.353636
$560$	−100.442	−4.24444
$561$	−21.8526	−0.922619
$562$	57.7872	2.43761
$563$	−13.6152	−0.573812	−0.286906	−	0.957959i	$-0.592627\pi$
$563$	−13.6152	−0.573812	−0.286906	+	0.957959i	$0.592627\pi$
$564$	−99.4727	−4.18856
$565$	−29.5435	−1.24290
$566$	−71.2989	−2.99692
$567$	15.3595	0.645038
$568$	20.6767	0.867577
$569$	−28.9909	−1.21536	−0.607681	−	0.794181i	$-0.707900\pi$
$569$	−28.9909	−1.21536	−0.607681	+	0.794181i	$0.707900\pi$
$570$	−25.9570	−1.08722
$571$	14.1605	0.592599	0.296299	−	0.955095i	$-0.404247\pi$
$571$	14.1605	0.592599	0.296299	+	0.955095i	$0.404247\pi$
$572$	39.1869	1.63849
$573$	14.7170	0.614810
$574$	53.5542	2.23531
$575$	2.20396	0.0919114
$576$	−41.3079	−1.72116
$577$	−34.1981	−1.42369	−0.711843	−	0.702339i	$-0.752139\pi$
$577$	−34.1981	−1.42369	−0.711843	+	0.702339i	$0.752139\pi$
$578$	−19.0544	−0.792560
$579$	−0.679337	−0.0282323
$580$	52.2806	2.17083
$581$	−6.33654	−0.262884
$582$	69.3334	2.87396
$583$	−7.46614	−0.309216
$584$	−149.530	−6.18761
$585$	−3.51970	−0.145522
$586$	−59.1706	−2.44431
$587$	36.8976	1.52293	0.761463	−	0.648208i	$-0.224481\pi$
$587$	36.8976	1.52293	0.761463	+	0.648208i	$0.224481\pi$
$588$	−3.97183	−0.163796
$589$	−24.3567	−1.00360
$590$	76.1756	3.13610
$591$	−5.15029	−0.211855
$592$	−84.5159	−3.47358
$593$	8.08364	0.331955	0.165978	−	0.986130i	$-0.446922\pi$
$593$	8.08364	0.331955	0.165978	+	0.986130i	$0.446922\pi$
$594$	47.8574	1.96361
$595$	25.3453	1.03905
$596$	58.1929	2.38367
$597$	15.0918	0.617667
$598$	15.5748	0.636903
$599$	−13.5911	−0.555316	−0.277658	−	0.960680i	$-0.589558\pi$
$599$	−13.5911	−0.555316	−0.277658	+	0.960680i	$0.589558\pi$
$600$	14.3665	0.586510
$601$	−1.41714	−0.0578062	−0.0289031	−	0.999582i	$-0.509201\pi$
$601$	−1.41714	−0.0578062	−0.0289031	+	0.999582i	$0.509201\pi$
$602$	27.5096	1.12121
$603$	−2.88832	−0.117622
$604$	112.510	4.57797
$605$	−3.86830	−0.157269
$606$	74.9423	3.04432
$607$	−2.38137	−0.0966567	−0.0483284	−	0.998832i	$-0.515389\pi$
$607$	−2.38137	−0.0966567	−0.0483284	+	0.998832i	$0.515389\pi$
$608$	−98.4876	−3.99420
$609$	−16.5033	−0.668746
$610$	51.7732	2.09624
$611$	−24.7168	−0.999936
$612$	22.8702	0.924473
$613$	16.7338	0.675871	0.337936	−	0.941169i	$-0.390271\pi$
$613$	16.7338	0.675871	0.337936	+	0.941169i	$0.390271\pi$
$614$	−27.1859	−1.09713
$615$	22.4356	0.904690
$616$	85.4588	3.44323
$617$	18.4652	0.743381	0.371690	−	0.928357i	$-0.378778\pi$
$617$	18.4652	0.743381	0.371690	+	0.928357i	$0.378778\pi$
$618$	−57.8701	−2.32788
$619$	32.7168	1.31500	0.657500	−	0.753455i	$-0.271614\pi$
$619$	32.7168	1.31500	0.657500	+	0.753455i	$0.271614\pi$
$620$	−96.1489	−3.86143
$621$	14.2246	0.570814
$622$	44.7475	1.79421
$623$	−4.91390	−0.196871
$624$	62.9009	2.51805
$625$	−19.8729	−0.794915
$626$	−45.6222	−1.82343
$627$	13.6830	0.546447
$628$	1.02605	0.0409440
$629$	21.3266	0.850345
$630$	−11.5805	−0.461380
$631$	−9.98542	−0.397513	−0.198757	−	0.980049i	$-0.563690\pi$
$631$	−9.98542	−0.397513	−0.198757	+	0.980049i	$0.563690\pi$
$632$	−151.678	−6.03344
$633$	20.2935	0.806592
$634$	−10.1469	−0.402986
$635$	−33.7779	−1.34043
$636$	−21.8244	−0.865396
$637$	−0.986915	−0.0391030
$638$	−36.8518	−1.45898
$639$	1.47700	0.0584293
$640$	−167.719	−6.62968
$641$	−43.1288	−1.70349	−0.851743	−	0.523959i	$-0.824454\pi$
$641$	−43.1288	−1.70349	−0.851743	+	0.523959i	$0.824454\pi$
$642$	30.6833	1.21097
$643$	14.5594	0.574165	0.287082	−	0.957906i	$-0.407315\pi$
$643$	14.5594	0.574165	0.287082	+	0.957906i	$0.407315\pi$
$644$	38.3226	1.51012
$645$	11.5247	0.453783
$646$	41.9090	1.64889
$647$	6.24930	0.245685	0.122843	−	0.992426i	$-0.460799\pi$
$647$	6.24930	0.245685	0.122843	+	0.992426i	$0.460799\pi$
$648$	66.4517	2.61047
$649$	−40.1553	−1.57623
$650$	5.38576	0.211247
$651$	30.3510	1.18955
$652$	49.6240	1.94343
$653$	−15.2811	−0.597997	−0.298999	−	0.954254i	$-0.596653\pi$
$653$	−15.2811	−0.597997	−0.298999	+	0.954254i	$0.596653\pi$
$654$	−5.80634	−0.227046
$655$	24.9542	0.975041
$656$	143.552	5.60475
$657$	−10.6814	−0.416722
$658$	−81.3234	−3.17032
$659$	17.6474	0.687446	0.343723	−	0.939071i	$-0.388312\pi$
$659$	17.6474	0.687446	0.343723	+	0.939071i	$0.388312\pi$
$660$	54.0141	2.10250
$661$	23.7077	0.922124	0.461062	−	0.887368i	$-0.347469\pi$
$661$	23.7077	0.922124	0.461062	+	0.887368i	$0.347469\pi$
$662$	95.7370	3.72092
$663$	−15.8723	−0.616428
$664$	−27.4145	−1.06389
$665$	−15.8699	−0.615409
$666$	−9.74435	−0.377586
$667$	−10.9534	−0.424119
$668$	1.12921	0.0436903
$669$	−4.88730	−0.188954
$670$	−20.8934	−0.807181
$671$	−27.2918	−1.05359
$672$	122.726	4.73426
$673$	−34.9503	−1.34724	−0.673618	−	0.739080i	$-0.735260\pi$
$673$	−34.9503	−1.34724	−0.673618	+	0.739080i	$0.735260\pi$
$674$	−19.1133	−0.736216
$675$	4.91885	0.189327
$676$	−48.6464	−1.87102
$677$	−8.41778	−0.323522	−0.161761	−	0.986830i	$-0.551717\pi$
$677$	−8.41778	−0.323522	−0.161761	+	0.986830i	$0.551717\pi$
$678$	60.8733	2.33783
$679$	42.3900	1.62678
$680$	109.654	4.20505
$681$	−41.9903	−1.60907
$682$	67.7739	2.59520
$683$	−3.03009	−0.115943	−0.0579716	−	0.998318i	$-0.518463\pi$
$683$	−3.03009	−0.115943	−0.0579716	+	0.998318i	$0.518463\pi$
$684$	−14.3202	−0.547545
$685$	19.4274	0.742281
$686$	−53.6991	−2.05024
$687$	−20.6205	−0.786722
$688$	73.7393	2.81128
$689$	−5.42290	−0.206596
$690$	21.4679	0.817270
$691$	8.46062	0.321857	0.160929	−	0.986966i	$-0.448551\pi$
$691$	8.46062	0.321857	0.160929	+	0.986966i	$0.448551\pi$
$692$	−122.324	−4.65007
$693$	6.10458	0.231894
$694$	65.6960	2.49378
$695$	−34.6751	−1.31530
$696$	−71.4001	−2.70641
$697$	−36.2235	−1.37206
$698$	13.7785	0.521523
$699$	12.5597	0.475053
$700$	13.2519	0.500876
$701$	−7.40067	−0.279520	−0.139760	−	0.990185i	$-0.544633\pi$
$701$	−7.40067	−0.279520	−0.139760	+	0.990185i	$0.544633\pi$
$702$	34.7604	1.31195
$703$	−13.3536	−0.503641
$704$	157.516	5.93659
$705$	−34.0690	−1.28311
$706$	−24.8116	−0.933797
$707$	45.8192	1.72321
$708$	−117.379	−4.41137
$709$	9.96829	0.374367	0.187184	−	0.982325i	$-0.440064\pi$
$709$	9.96829	0.374367	0.187184	+	0.982325i	$0.440064\pi$
$710$	10.6843	0.400973
$711$	−10.8348	−0.406338
$712$	−21.2596	−0.796737
$713$	20.1444	0.754414
$714$	−52.2230	−1.95440
$715$	13.4213	0.501930
$716$	−7.54121	−0.281828
$717$	−20.5077	−0.765875
$718$	57.0360	2.12857
$719$	−38.8099	−1.44736	−0.723682	−	0.690133i	$-0.757552\pi$
$719$	−38.8099	−1.44736	−0.723682	+	0.690133i	$0.757552\pi$
$720$	−31.0415	−1.15685
$721$	−35.3814	−1.31767
$722$	27.2682	1.01482
$723$	30.3945	1.13038
$724$	19.4537	0.722992
$725$	−3.78769	−0.140671
$726$	7.97050	0.295813
$727$	−21.7244	−0.805713	−0.402857	−	0.915263i	$-0.631983\pi$
$727$	−21.7244	−0.805713	−0.402857	+	0.915263i	$0.631983\pi$
$728$	62.0715	2.30052
$729$	29.8702	1.10630
$730$	−77.2666	−2.85976
$731$	−18.6072	−0.688212
$732$	−79.7773	−2.94865
$733$	29.5562	1.09168	0.545842	−	0.837888i	$-0.316210\pi$
$733$	29.5562	1.09168	0.545842	+	0.837888i	$0.316210\pi$
$734$	52.9495	1.95440
$735$	−1.36033	−0.0501767
$736$	81.4550	3.00247
$737$	11.0138	0.405697
$738$	16.5509	0.609248
$739$	−2.28027	−0.0838809	−0.0419405	−	0.999120i	$-0.513354\pi$
$739$	−2.28027	−0.0838809	−0.0419405	+	0.999120i	$0.513354\pi$
$740$	−52.7138	−1.93780
$741$	9.93841	0.365097
$742$	−17.8425	−0.655018
$743$	44.6865	1.63939	0.819694	−	0.572801i	$-0.194143\pi$
$743$	44.6865	1.63939	0.819694	+	0.572801i	$0.194143\pi$
$744$	131.311	4.81411
$745$	19.9308	0.730208
$746$	−29.5268	−1.08105
$747$	−1.95830	−0.0716506
$748$	−87.2088	−3.18867
$749$	18.7596	0.685459
$750$	49.9413	1.82360
$751$	35.6545	1.30105	0.650526	−	0.759484i	$-0.274549\pi$
$751$	35.6545	1.30105	0.650526	+	0.759484i	$0.274549\pi$
$752$	−217.987	−7.94915
$753$	23.5802	0.859309
$754$	−26.7667	−0.974785
$755$	38.5342	1.40240
$756$	85.5295	3.11068
$757$	−3.73627	−0.135797	−0.0678986	−	0.997692i	$-0.521629\pi$
$757$	−3.73627	−0.135797	−0.0678986	+	0.997692i	$0.521629\pi$
$758$	1.61243	0.0585662
$759$	−11.3166	−0.410768
$760$	−68.6599	−2.49056
$761$	−43.5350	−1.57814	−0.789072	−	0.614301i	$-0.789438\pi$
$761$	−43.5350	−1.57814	−0.789072	+	0.614301i	$0.789438\pi$
$762$	69.5982	2.52128
$763$	−3.54995	−0.128517
$764$	58.7320	2.12485
$765$	7.83294	0.283201
$766$	−21.4013	−0.773260
$767$	−29.1661	−1.05313
$768$	190.327	6.86785
$769$	−12.2394	−0.441363	−0.220682	−	0.975346i	$-0.570828\pi$
$769$	−12.2394	−0.441363	−0.220682	+	0.975346i	$0.570828\pi$
$770$	44.1590	1.59138
$771$	−20.8536	−0.751024
$772$	−2.71108	−0.0975738
$773$	−10.7652	−0.387199	−0.193600	−	0.981081i	$-0.562016\pi$
$773$	−10.7652	−0.387199	−0.193600	+	0.981081i	$0.562016\pi$
$774$	8.50184	0.305593
$775$	6.96591	0.250223
$776$	183.397	6.58356
$777$	16.6400	0.596957
$778$	46.8280	1.67886
$779$	22.6813	0.812642
$780$	39.2322	1.40474
$781$	−5.63211	−0.201533
$782$	−34.6612	−1.23948
$783$	−24.4462	−0.873635
$784$	−8.70395	−0.310855
$785$	0.351419	0.0125427
$786$	−51.4173	−1.83399
$787$	2.45808	0.0876212	0.0438106	−	0.999040i	$-0.486050\pi$
$787$	2.45808	0.0876212	0.0438106	+	0.999040i	$0.486050\pi$
$788$	−20.5536	−0.732193
$789$	−16.8839	−0.601082
$790$	−78.3764	−2.78851
$791$	37.2175	1.32330
$792$	26.4110	0.938474
$793$	−19.8229	−0.703933
$794$	68.3078	2.42415
$795$	−7.47477	−0.265103
$796$	60.2279	2.13472
$797$	−20.9977	−0.743777	−0.371888	−	0.928277i	$-0.621290\pi$
$797$	−20.9977	−0.743777	−0.371888	+	0.928277i	$0.621290\pi$
$798$	32.6994	1.15755
$799$	55.0062	1.94598
$800$	28.1670	0.995855
$801$	−1.51864	−0.0536585
$802$	25.9514	0.916374
$803$	40.7304	1.43735
$804$	32.1946	1.13541
$805$	13.1253	0.462607
$806$	49.2264	1.73393
$807$	−6.62252	−0.233124
$808$	198.233	6.97382
$809$	−28.8485	−1.01426	−0.507129	−	0.861870i	$-0.669293\pi$
$809$	−28.8485	−1.01426	−0.507129	+	0.861870i	$0.669293\pi$
$810$	34.3375	1.20650
$811$	24.4558	0.858759	0.429380	−	0.903124i	$-0.358732\pi$
$811$	24.4558	0.858759	0.429380	+	0.903124i	$0.358732\pi$
$812$	−65.8607	−2.31126
$813$	−27.6778	−0.970703
$814$	37.1572	1.30236
$815$	16.9960	0.595344
$816$	−139.983	−4.90039
$817$	11.6509	0.407613
$818$	−90.5155	−3.16480
$819$	4.43396	0.154935
$820$	89.5352	3.12670
$821$	−26.2930	−0.917633	−0.458816	−	0.888531i	$-0.651726\pi$
$821$	−26.2930	−0.917633	−0.458816	+	0.888531i	$0.651726\pi$
$822$	−40.0294	−1.39619
$823$	−32.8048	−1.14350	−0.571752	−	0.820427i	$-0.693736\pi$
$823$	−32.8048	−1.14350	−0.571752	+	0.820427i	$0.693736\pi$
$824$	−153.075	−5.33261
$825$	−3.91328	−0.136243
$826$	−95.9625	−3.33896
$827$	−39.4766	−1.37273	−0.686367	−	0.727255i	$-0.740796\pi$
$827$	−39.4766	−1.37273	−0.686367	+	0.727255i	$0.740796\pi$
$828$	11.8436	0.411594
$829$	−23.7462	−0.824740	−0.412370	−	0.911017i	$-0.635299\pi$
$829$	−23.7462	−0.824740	−0.412370	+	0.911017i	$0.635299\pi$
$830$	−14.1659	−0.491704
$831$	−19.7314	−0.684476
$832$	114.409	3.96641
$833$	2.19634	0.0760985
$834$	71.4469	2.47400
$835$	0.386748	0.0133840
$836$	54.6057	1.88858
$837$	44.9588	1.55400
$838$	79.4336	2.74399
$839$	30.7385	1.06121	0.530606	−	0.847619i	$-0.321964\pi$
$839$	30.7385	1.06121	0.530606	+	0.847619i	$0.321964\pi$
$840$	85.5576	2.95202
$841$	−10.1756	−0.350882
$842$	−64.2830	−2.21534
$843$	−30.4973	−1.05038
$844$	80.9865	2.78767
$845$	−16.6612	−0.573162
$846$	−25.1330	−0.864090
$847$	4.87311	0.167442
$848$	−47.8265	−1.64237
$849$	37.6281	1.29139
$850$	−11.9858	−0.411109
$851$	11.0442	0.378590
$852$	−16.4634	−0.564025
$853$	−18.1625	−0.621871	−0.310935	−	0.950431i	$-0.600642\pi$
$853$	−18.1625	−0.621871	−0.310935	+	0.950431i	$0.600642\pi$
$854$	−65.2215	−2.23183
$855$	−4.90459	−0.167733
$856$	81.1618	2.77405
$857$	54.5035	1.86180	0.930902	−	0.365268i	$-0.119023\pi$
$857$	54.5035	1.86180	0.930902	+	0.365268i	$0.119023\pi$
$858$	−27.6542	−0.944099
$859$	13.8291	0.471841	0.235921	−	0.971772i	$-0.424189\pi$
$859$	13.8291	0.471841	0.235921	+	0.971772i	$0.424189\pi$
$860$	45.9922	1.56832
$861$	−28.2633	−0.963211
$862$	49.7104	1.69314
$863$	−32.9793	−1.12263	−0.561315	−	0.827602i	$-0.689704\pi$
$863$	−32.9793	−1.12263	−0.561315	+	0.827602i	$0.689704\pi$
$864$	181.793	6.18474
$865$	−41.8955	−1.42449
$866$	−75.9681	−2.58150
$867$	10.0560	0.341520
$868$	121.124	4.11121
$869$	41.3155	1.40153
$870$	−36.8944	−1.25084
$871$	7.99965	0.271058
$872$	−15.3586	−0.520108
$873$	13.1006	0.443388
$874$	21.7031	0.734117
$875$	30.5338	1.03223
$876$	119.060	4.02266
$877$	−36.8505	−1.24435	−0.622176	−	0.782877i	$-0.713751\pi$
$877$	−36.8505	−1.24435	−0.622176	+	0.782877i	$0.713751\pi$
$878$	98.6542	3.32942
$879$	31.2273	1.05327
$880$	118.368	3.99017
$881$	−19.4408	−0.654976	−0.327488	−	0.944855i	$-0.606202\pi$
$881$	−19.4408	−0.654976	−0.327488	+	0.944855i	$0.606202\pi$
$882$	−1.00353	−0.0337906
$883$	−44.2554	−1.48931	−0.744656	−	0.667448i	$-0.767386\pi$
$883$	−44.2554	−1.48931	−0.744656	+	0.667448i	$0.767386\pi$
$884$	−63.3426	−2.13044
$885$	−40.2017	−1.35137
$886$	−75.7094	−2.54351
$887$	37.0797	1.24501	0.622507	−	0.782614i	$-0.286114\pi$
$887$	37.0797	1.24501	0.622507	+	0.782614i	$0.286114\pi$
$888$	71.9917	2.41588
$889$	42.5518	1.42714
$890$	−10.9854	−0.368233
$891$	−18.1007	−0.606396
$892$	−19.5041	−0.653046
$893$	−34.4421	−1.15256
$894$	−41.0667	−1.37348
$895$	−2.58283	−0.0863345
$896$	211.285	7.05853
$897$	−8.21964	−0.274446
$898$	−65.6131	−2.18954
$899$	−34.6198	−1.15464
$900$	4.09550	0.136517
$901$	12.0684	0.402058
$902$	−63.1121	−2.10140
$903$	−14.5182	−0.483137
$904$	161.019	5.35540
$905$	6.66281	0.221479
$906$	−79.3984	−2.63784
$907$	−19.0950	−0.634039	−0.317020	−	0.948419i	$-0.602682\pi$
$907$	−19.0950	−0.634039	−0.317020	+	0.948419i	$0.602682\pi$
$908$	−167.573	−5.56112
$909$	14.1604	0.469671
$910$	32.0741	1.06325
$911$	16.4271	0.544256	0.272128	−	0.962261i	$-0.412273\pi$
$911$	16.4271	0.544256	0.272128	+	0.962261i	$0.412273\pi$
$912$	87.6504	2.90239
$913$	7.46742	0.247135
$914$	0.414344	0.0137053
$915$	−27.3234	−0.903282
$916$	−82.2917	−2.71900
$917$	−31.4362	−1.03811
$918$	−77.3577	−2.55318
$919$	47.1222	1.55442	0.777209	−	0.629242i	$-0.216635\pi$
$919$	47.1222	1.55442	0.777209	+	0.629242i	$0.216635\pi$
$920$	56.7857	1.87217
$921$	14.3474	0.472762
$922$	−28.1638	−0.927526
$923$	−4.09079	−0.134650
$924$	−68.0445	−2.23850
$925$	3.81907	0.125570
$926$	−33.4170	−1.09815
$927$	−10.9346	−0.359140
$928$	−139.987	−4.59531
$929$	52.3918	1.71892	0.859460	−	0.511203i	$-0.170800\pi$
$929$	52.3918	1.71892	0.859460	+	0.511203i	$0.170800\pi$
$930$	67.8523	2.22496
$931$	−1.37523	−0.0450715
$932$	50.1230	1.64183
$933$	−23.6155	−0.773138
$934$	−96.4008	−3.15433
$935$	−29.8686	−0.976808
$936$	19.1832	0.627022
$937$	−15.8871	−0.519008	−0.259504	−	0.965742i	$-0.583559\pi$
$937$	−15.8871	−0.519008	−0.259504	+	0.965742i	$0.583559\pi$
$938$	26.3205	0.859395
$939$	24.0772	0.785729
$940$	−135.961	−4.43457
$941$	−52.4610	−1.71018	−0.855090	−	0.518480i	$-0.826498\pi$
$941$	−52.4610	−1.71018	−0.855090	+	0.518480i	$0.826498\pi$
$942$	−0.724087	−0.0235920
$943$	−18.7587	−0.610869
$944$	−257.226	−8.37201
$945$	29.2935	0.952917
$946$	−32.4193	−1.05404
$947$	−34.4633	−1.11991	−0.559954	−	0.828524i	$-0.689181\pi$
$947$	−34.4633	−1.11991	−0.559954	+	0.828524i	$0.689181\pi$
$948$	120.770	3.92243
$949$	29.5838	0.960332
$950$	7.50489	0.243491
$951$	5.35505	0.173649
$952$	−138.137	−4.47706
$953$	−57.4001	−1.85937	−0.929685	−	0.368354i	$-0.879921\pi$
$953$	−57.4001	−1.85937	−0.929685	+	0.368354i	$0.879921\pi$
$954$	−5.51421	−0.178529
$955$	20.1154	0.650920
$956$	−81.8416	−2.64695
$957$	19.4486	0.628684
$958$	35.5622	1.14896
$959$	−24.4737	−0.790297
$960$	157.698	5.08967
$961$	32.6691	1.05384
$962$	26.9885	0.870144
$963$	5.79764	0.186826
$964$	121.298	3.90673
$965$	−0.928532	−0.0298905
$966$	−27.0443	−0.870136
$967$	8.50962	0.273651	0.136825	−	0.990595i	$-0.456310\pi$
$967$	8.50962	0.273651	0.136825	+	0.990595i	$0.456310\pi$
$968$	21.0831	0.677637
$969$	−22.1175	−0.710517
$970$	94.7663	3.04276
$971$	10.2124	0.327733	0.163866	−	0.986483i	$-0.447603\pi$
$971$	10.2124	0.327733	0.163866	+	0.986483i	$0.447603\pi$
$972$	47.3509	1.51878
$973$	43.6821	1.40038
$974$	−60.4664	−1.93747
$975$	−2.84234	−0.0910278
$976$	−174.825	−5.59603
$977$	−3.01790	−0.0965513	−0.0482756	−	0.998834i	$-0.515373\pi$
$977$	−3.01790	−0.0965513	−0.0482756	+	0.998834i	$0.515373\pi$
$978$	−35.0197	−1.11981
$979$	5.79088	0.185077
$980$	−5.42878	−0.173416
$981$	−1.09711	−0.0350281
$982$	65.9152	2.10344
$983$	4.84215	0.154441	0.0772203	−	0.997014i	$-0.475396\pi$
$983$	4.84215	0.154441	0.0772203	+	0.997014i	$0.475396\pi$
$984$	−122.279	−3.89811
$985$	−7.03953	−0.224298
$986$	59.5681	1.89704
$987$	42.9185	1.36611
$988$	39.6619	1.26181
$989$	−9.63595	−0.306405
$990$	13.6473	0.433740
$991$	3.86210	0.122683	0.0613417	−	0.998117i	$-0.480462\pi$
$991$	3.86210	0.122683	0.0613417	+	0.998117i	$0.480462\pi$
$992$	257.450	8.17403
$993$	−50.5253	−1.60337
$994$	−13.4595	−0.426910
$995$	20.6278	0.653945
$996$	21.8282	0.691652
$997$	−29.0506	−0.920040	−0.460020	−	0.887909i	$-0.652158\pi$
$997$	−29.0506	−0.920040	−0.460020	+	0.887909i	$0.652158\pi$
$998$	−8.51784	−0.269628
$999$	24.6487	0.779852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.1	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.1	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} +O(q^{10})\)	\(q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} -5.72129 q^{10} +3.01593 q^{11} +8.81594 q^{12} +2.19057 q^{13} +7.20742 q^{14} +3.01942 q^{15} +19.3194 q^{16} -4.87502 q^{17} +2.22745 q^{18} +3.05249 q^{19} +12.0498 q^{20} -3.80372 q^{21} -8.49373 q^{22} -2.52458 q^{23} -16.4565 q^{24} -0.872998 q^{25} -6.16927 q^{26} -5.63443 q^{27} -15.1798 q^{28} +4.33871 q^{29} -8.50355 q^{30} -7.97929 q^{31} -32.2647 q^{32} +4.48257 q^{33} +13.7294 q^{34} -5.19901 q^{35} -4.69131 q^{36} -4.37466 q^{37} -8.59668 q^{38} +3.25584 q^{39} -22.4931 q^{40} +7.43043 q^{41} +10.7124 q^{42} +3.81685 q^{43} +17.8889 q^{44} -1.60675 q^{45} +7.10995 q^{46} -11.2833 q^{47} +28.7144 q^{48} -0.450529 q^{49} +2.45861 q^{50} -7.24573 q^{51} +12.9933 q^{52} -2.47557 q^{53} +15.8682 q^{54} +6.12687 q^{55} +28.3358 q^{56} +4.53691 q^{57} -12.2191 q^{58} -13.3144 q^{59} +17.9096 q^{60} -9.04921 q^{61} +22.4720 q^{62} +2.02411 q^{63} +52.2278 q^{64} +4.45015 q^{65} -12.6242 q^{66} +3.65186 q^{67} -28.9160 q^{68} -3.75228 q^{69} +14.6419 q^{70} -1.86745 q^{71} +8.75716 q^{72} +13.5051 q^{73} +12.3203 q^{74} -1.29754 q^{75} +18.1057 q^{76} -7.71835 q^{77} -9.16938 q^{78} +13.6991 q^{79} +39.2474 q^{80} -6.00169 q^{81} -20.9262 q^{82} +2.47599 q^{83} -22.5617 q^{84} -9.90361 q^{85} -10.7493 q^{86} +6.44862 q^{87} -33.3929 q^{88} +1.92010 q^{89} +4.52507 q^{90} -5.60609 q^{91} -14.9745 q^{92} -11.8596 q^{93} +31.7770 q^{94} +6.20114 q^{95} -47.9550 q^{96} -16.5638 q^{97} +1.26882 q^{98} -2.38535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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