LMFDB - Embedded newform 4003.2.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} +O(q^{10})$	\(q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} -7.64888 q^{10} -5.95997 q^{11} -9.45295 q^{12} -4.69577 q^{13} -2.75061 q^{14} -8.46560 q^{15} +1.79630 q^{16} +0.273086 q^{17} -9.15976 q^{18} +8.27742 q^{19} +11.6513 q^{20} -3.04431 q^{21} +14.1126 q^{22} +1.00000 q^{23} +9.97234 q^{24} +5.43438 q^{25} +11.1191 q^{26} -2.27558 q^{27} +4.18994 q^{28} -8.08895 q^{29} +20.0457 q^{30} +0.403546 q^{31} +3.35684 q^{32} +15.6195 q^{33} -0.646641 q^{34} +3.75230 q^{35} +13.9528 q^{36} +4.87945 q^{37} -19.6001 q^{38} +12.3064 q^{39} -12.2915 q^{40} +7.36311 q^{41} +7.20864 q^{42} -1.48896 q^{43} -21.4974 q^{44} +12.4955 q^{45} -2.36790 q^{46} -2.84372 q^{47} -4.70764 q^{48} -5.65064 q^{49} -12.8681 q^{50} -0.715688 q^{51} -16.9375 q^{52} -9.11543 q^{53} +5.38836 q^{54} -19.2521 q^{55} -4.42015 q^{56} -21.6930 q^{57} +19.1539 q^{58} +7.08591 q^{59} -30.5352 q^{60} +3.67954 q^{61} -0.955558 q^{62} +4.49350 q^{63} -11.5413 q^{64} -15.1684 q^{65} -36.9856 q^{66} +5.34809 q^{67} +0.985013 q^{68} -2.62074 q^{69} -8.88510 q^{70} +1.23645 q^{71} -14.7195 q^{72} -14.3861 q^{73} -11.5541 q^{74} -14.2421 q^{75} +29.8564 q^{76} -6.92323 q^{77} -29.1404 q^{78} +12.2858 q^{79} +5.80247 q^{80} -5.64117 q^{81} -17.4352 q^{82} +4.40796 q^{83} -10.9807 q^{84} +0.882130 q^{85} +3.52571 q^{86} +21.1991 q^{87} +22.6786 q^{88} +4.11367 q^{89} -29.5881 q^{90} -5.45471 q^{91} +3.60697 q^{92} -1.05759 q^{93} +6.73365 q^{94} +26.7380 q^{95} -8.79742 q^{96} +1.62836 q^{97} +13.3802 q^{98} -23.0549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.36790	−1.67436	−0.837181	−	0.546926i	$-0.815798\pi$
$2$	−2.36790	−1.67436	−0.837181	+	0.546926i	$0.815798\pi$
$3$	−2.62074	−1.51309	−0.756543	−	0.653943i	$-0.773113\pi$
$3$	−2.62074	−1.51309	−0.756543	+	0.653943i	$0.773113\pi$
$4$	3.60697	1.80349
$5$	3.23023	1.44460	0.722301	−	0.691578i	$-0.243084\pi$
$5$	3.23023	1.44460	0.722301	+	0.691578i	$0.243084\pi$
$6$	6.20567	2.53345
$7$	1.16162	0.439052	0.219526	−	0.975607i	$-0.429549\pi$
$7$	1.16162	0.439052	0.219526	+	0.975607i	$0.429549\pi$
$8$	−3.80516	−1.34533
$9$	3.86830	1.28943
$10$	−7.64888	−2.41879
$11$	−5.95997	−1.79700	−0.898499	−	0.438976i	$-0.855341\pi$
$11$	−5.95997	−1.79700	−0.898499	+	0.438976i	$0.855341\pi$
$12$	−9.45295	−2.72883
$13$	−4.69577	−1.30237	−0.651186	−	0.758918i	$-0.725728\pi$
$13$	−4.69577	−1.30237	−0.651186	+	0.758918i	$0.725728\pi$
$14$	−2.75061	−0.735131
$15$	−8.46560	−2.18581
$16$	1.79630	0.449075
$17$	0.273086	0.0662330	0.0331165	−	0.999451i	$-0.489457\pi$
$17$	0.273086	0.0662330	0.0331165	+	0.999451i	$0.489457\pi$
$18$	−9.15976	−2.15898
$19$	8.27742	1.89897	0.949485	−	0.313813i	$-0.101606\pi$
$19$	8.27742	1.89897	0.949485	+	0.313813i	$0.101606\pi$
$20$	11.6513	2.60532
$21$	−3.04431	−0.664323
$22$	14.1126	3.00882
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	9.97234	2.03559
$25$	5.43438	1.08688
$26$	11.1191	2.18064
$27$	−2.27558	−0.437936
$28$	4.18994	0.791823
$29$	−8.08895	−1.50208	−0.751040	−	0.660257i	$-0.770448\pi$
$29$	−8.08895	−1.50208	−0.751040	+	0.660257i	$0.770448\pi$
$30$	20.0457	3.65983
$31$	0.403546	0.0724790	0.0362395	−	0.999343i	$-0.488462\pi$
$31$	0.403546	0.0724790	0.0362395	+	0.999343i	$0.488462\pi$
$32$	3.35684	0.593411
$33$	15.6195	2.71901
$34$	−0.646641	−0.110898
$35$	3.75230	0.634255
$36$	13.9528	2.32547
$37$	4.87945	0.802176	0.401088	−	0.916040i	$-0.368632\pi$
$37$	4.87945	0.802176	0.401088	+	0.916040i	$0.368632\pi$
$38$	−19.6001	−3.17956
$39$	12.3064	1.97060
$40$	−12.2915	−1.94346
$41$	7.36311	1.14993	0.574963	−	0.818180i	$-0.305017\pi$
$41$	7.36311	1.14993	0.574963	+	0.818180i	$0.305017\pi$
$42$	7.20864	1.11232
$43$	−1.48896	−0.227064	−0.113532	−	0.993534i	$-0.536216\pi$
$43$	−1.48896	−0.227064	−0.113532	+	0.993534i	$0.536216\pi$
$44$	−21.4974	−3.24086
$45$	12.4955	1.86272
$46$	−2.36790	−0.349128
$47$	−2.84372	−0.414799	−0.207399	−	0.978256i	$-0.566500\pi$
$47$	−2.84372	−0.414799	−0.207399	+	0.978256i	$0.566500\pi$
$48$	−4.70764	−0.679490
$49$	−5.65064	−0.807234
$50$	−12.8681	−1.81982
$51$	−0.715688	−0.100216
$52$	−16.9375	−2.34881
$53$	−9.11543	−1.25210	−0.626050	−	0.779783i	$-0.715330\pi$
$53$	−9.11543	−1.25210	−0.626050	+	0.779783i	$0.715330\pi$
$54$	5.38836	0.733263
$55$	−19.2521	−2.59595
$56$	−4.42015	−0.590667
$57$	−21.6930	−2.87331
$58$	19.1539	2.51503
$59$	7.08591	0.922507	0.461254	−	0.887268i	$-0.347400\pi$
$59$	7.08591	0.922507	0.461254	+	0.887268i	$0.347400\pi$
$60$	−30.5352	−3.94208
$61$	3.67954	0.471116	0.235558	−	0.971860i	$-0.424308\pi$
$61$	3.67954	0.471116	0.235558	+	0.971860i	$0.424308\pi$
$62$	−0.955558	−0.121356
$63$	4.49350	0.566127
$64$	−11.5413	−1.44266
$65$	−15.1684	−1.88141
$66$	−36.9856	−4.55261
$67$	5.34809	0.653374	0.326687	−	0.945133i	$-0.394068\pi$
$67$	5.34809	0.653374	0.326687	+	0.945133i	$0.394068\pi$
$68$	0.985013	0.119450
$69$	−2.62074	−0.315500
$70$	−8.88510	−1.06197
$71$	1.23645	0.146740	0.0733701	−	0.997305i	$-0.476625\pi$
$71$	1.23645	0.146740	0.0733701	+	0.997305i	$0.476625\pi$
$72$	−14.7195	−1.73471
$73$	−14.3861	−1.68377	−0.841884	−	0.539658i	$-0.818553\pi$
$73$	−14.3861	−1.68377	−0.841884	+	0.539658i	$0.818553\pi$
$74$	−11.5541	−1.34313
$75$	−14.2421	−1.64454
$76$	29.8564	3.42476
$77$	−6.92323	−0.788975
$78$	−29.1404	−3.29950
$79$	12.2858	1.38226	0.691128	−	0.722732i	$-0.257114\pi$
$79$	12.2858	1.38226	0.691128	+	0.722732i	$0.257114\pi$
$80$	5.80247	0.648735
$81$	−5.64117	−0.626797
$82$	−17.4352	−1.92539
$83$	4.40796	0.483836	0.241918	−	0.970297i	$-0.422223\pi$
$83$	4.40796	0.483836	0.241918	+	0.970297i	$0.422223\pi$
$84$	−10.9807	−1.19810
$85$	0.882130	0.0956804
$86$	3.52571	0.380187
$87$	21.1991	2.27278
$88$	22.6786	2.41755
$89$	4.11367	0.436048	0.218024	−	0.975943i	$-0.430039\pi$
$89$	4.11367	0.436048	0.218024	+	0.975943i	$0.430039\pi$
$90$	−29.5881	−3.11886
$91$	−5.45471	−0.571809
$92$	3.60697	0.376053
$93$	−1.05759	−0.109667
$94$	6.73365	0.694523
$95$	26.7380	2.74326
$96$	−8.79742	−0.897883
$97$	1.62836	0.165335	0.0826673	−	0.996577i	$-0.473656\pi$
$97$	1.62836	0.165335	0.0826673	+	0.996577i	$0.473656\pi$
$98$	13.3802	1.35160
$99$	−23.0549	−2.31711
$100$	19.6017	1.96017
$101$	0.409125	0.0407095	0.0203547	−	0.999793i	$-0.493520\pi$
$101$	0.409125	0.0407095	0.0203547	+	0.999793i	$0.493520\pi$
$102$	1.69468	0.167798
$103$	15.9314	1.56977	0.784886	−	0.619640i	$-0.212721\pi$
$103$	15.9314	1.56977	0.784886	+	0.619640i	$0.212721\pi$
$104$	17.8681	1.75211
$105$	−9.83383	−0.959683
$106$	21.5845	2.09647
$107$	−9.82848	−0.950155	−0.475078	−	0.879944i	$-0.657580\pi$
$107$	−9.82848	−0.950155	−0.475078	+	0.879944i	$0.657580\pi$
$108$	−8.20796	−0.789812
$109$	−1.25265	−0.119982	−0.0599909	−	0.998199i	$-0.519107\pi$
$109$	−1.25265	−0.119982	−0.0599909	+	0.998199i	$0.519107\pi$
$110$	45.5870	4.34655
$111$	−12.7878	−1.21376
$112$	2.08662	0.197167
$113$	−9.36258	−0.880757	−0.440379	−	0.897812i	$-0.645156\pi$
$113$	−9.36258	−0.880757	−0.440379	+	0.897812i	$0.645156\pi$
$114$	51.3669	4.81095
$115$	3.23023	0.301220
$116$	−29.1766	−2.70898
$117$	−18.1646	−1.67932
$118$	−16.7788	−1.54461
$119$	0.317222	0.0290797
$120$	32.2129	2.94063
$121$	24.5212	2.22920
$122$	−8.71279	−0.788819
$123$	−19.2968	−1.73994
$124$	1.45558	0.130715
$125$	1.40316	0.125503
$126$	−10.6402	−0.947902
$127$	−15.4924	−1.37472	−0.687362	−	0.726315i	$-0.741231\pi$
$127$	−15.4924	−1.37472	−0.687362	+	0.726315i	$0.741231\pi$
$128$	20.6150	1.82212
$129$	3.90217	0.343567
$130$	35.9174	3.15016
$131$	−9.82582	−0.858486	−0.429243	−	0.903189i	$-0.641220\pi$
$131$	−9.82582	−0.858486	−0.429243	+	0.903189i	$0.641220\pi$
$132$	56.3392	4.90370
$133$	9.61523	0.833746
$134$	−12.6638	−1.09398
$135$	−7.35066	−0.632644
$136$	−1.03913	−0.0891050
$137$	−19.1051	−1.63226	−0.816129	−	0.577870i	$-0.803884\pi$
$137$	−19.1051	−1.63226	−0.816129	+	0.577870i	$0.803884\pi$
$138$	6.20567	0.528262
$139$	−8.54556	−0.724825	−0.362413	−	0.932018i	$-0.618047\pi$
$139$	−8.54556	−0.724825	−0.362413	+	0.932018i	$0.618047\pi$
$140$	13.5345	1.14387
$141$	7.45266	0.627627
$142$	−2.92781	−0.245696
$143$	27.9866	2.34036
$144$	6.94863	0.579052
$145$	−26.1292	−2.16991
$146$	34.0650	2.81924
$147$	14.8089	1.22141
$148$	17.6000	1.44671
$149$	11.5712	0.947952	0.473976	−	0.880538i	$-0.342818\pi$
$149$	11.5712	0.947952	0.473976	+	0.880538i	$0.342818\pi$
$150$	33.7240	2.75355
$151$	11.8956	0.968054	0.484027	−	0.875053i	$-0.339174\pi$
$151$	11.8956	0.968054	0.484027	+	0.875053i	$0.339174\pi$
$152$	−31.4969	−2.55473
$153$	1.05638	0.0854030
$154$	16.3935	1.32103
$155$	1.30355	0.104703
$156$	44.3889	3.55395
$157$	−24.7242	−1.97321	−0.986604	−	0.163131i	$-0.947841\pi$
$157$	−24.7242	−1.97321	−0.986604	+	0.163131i	$0.947841\pi$
$158$	−29.0915	−2.31440
$159$	23.8892	1.89454
$160$	10.8434	0.857243
$161$	1.16162	0.0915486
$162$	13.3578	1.04948
$163$	−1.11031	−0.0869662	−0.0434831	−	0.999054i	$-0.513845\pi$
$163$	−1.11031	−0.0869662	−0.0434831	+	0.999054i	$0.513845\pi$
$164$	26.5585	2.07387
$165$	50.4547	3.92789
$166$	−10.4376	−0.810117
$167$	−0.423596	−0.0327788	−0.0163894	−	0.999866i	$-0.505217\pi$
$167$	−0.423596	−0.0327788	−0.0163894	+	0.999866i	$0.505217\pi$
$168$	11.5841	0.893731
$169$	9.05025	0.696173
$170$	−2.08880	−0.160204
$171$	32.0195	2.44859
$172$	−5.37062	−0.409506
$173$	−1.60089	−0.121713	−0.0608565	−	0.998147i	$-0.519383\pi$
$173$	−1.60089	−0.121713	−0.0608565	+	0.998147i	$0.519383\pi$
$174$	−50.1974	−3.80545
$175$	6.31270	0.477195
$176$	−10.7059	−0.806987
$177$	−18.5704	−1.39583
$178$	−9.74077	−0.730101
$179$	11.1500	0.833388	0.416694	−	0.909047i	$-0.363189\pi$
$179$	11.1500	0.833388	0.416694	+	0.909047i	$0.363189\pi$
$180$	45.0709	3.35938
$181$	−2.23764	−0.166323	−0.0831613	−	0.996536i	$-0.526502\pi$
$181$	−2.23764	−0.166323	−0.0831613	+	0.996536i	$0.526502\pi$
$182$	12.9162	0.957414
$183$	−9.64312	−0.712840
$184$	−3.80515	−0.280520
$185$	15.7617	1.15883
$186$	2.50427	0.183622
$187$	−1.62758	−0.119021
$188$	−10.2572	−0.748084
$189$	−2.64337	−0.192277
$190$	−63.3129	−4.59320
$191$	10.0081	0.724158	0.362079	−	0.932147i	$-0.382067\pi$
$191$	10.0081	0.724158	0.362079	+	0.932147i	$0.382067\pi$
$192$	30.2467	2.18287
$193$	16.8540	1.21318	0.606589	−	0.795016i	$-0.292537\pi$
$193$	16.8540	1.21318	0.606589	+	0.795016i	$0.292537\pi$
$194$	−3.85580	−0.276830
$195$	39.7525	2.84674
$196$	−20.3817	−1.45583
$197$	−11.3691	−0.810012	−0.405006	−	0.914314i	$-0.632731\pi$
$197$	−11.3691	−0.810012	−0.405006	+	0.914314i	$0.632731\pi$
$198$	54.5918	3.87967
$199$	8.71490	0.617783	0.308892	−	0.951097i	$-0.400042\pi$
$199$	8.71490	0.617783	0.308892	+	0.951097i	$0.400042\pi$
$200$	−20.6787	−1.46220
$201$	−14.0160	−0.988611
$202$	−0.968770	−0.0681624
$203$	−9.39630	−0.659491
$204$	−2.58147	−0.180739
$205$	23.7846	1.66119
$206$	−37.7242	−2.62837
$207$	3.86830	0.268865
$208$	−8.43502	−0.584863
$209$	−49.3331	−3.41244
$210$	23.2856	1.60686
$211$	13.4361	0.924982	0.462491	−	0.886624i	$-0.346956\pi$
$211$	13.4361	0.924982	0.462491	+	0.886624i	$0.346956\pi$
$212$	−32.8791	−2.25815
$213$	−3.24043	−0.222031
$214$	23.2729	1.59090
$215$	−4.80967	−0.328017
$216$	8.65895	0.589167
$217$	0.468768	0.0318220
$218$	2.96615	0.200893
$219$	37.7023	2.54769
$220$	−69.4416	−4.68175
$221$	−1.28235	−0.0862601
$222$	30.2802	2.03228
$223$	−22.3198	−1.49464	−0.747321	−	0.664463i	$-0.768660\pi$
$223$	−22.3198	−1.49464	−0.747321	+	0.664463i	$0.768660\pi$
$224$	3.89938	0.260538
$225$	21.0218	1.40145
$226$	22.1697	1.47471
$227$	−22.2610	−1.47752	−0.738758	−	0.673971i	$-0.764587\pi$
$227$	−22.2610	−1.47752	−0.738758	+	0.673971i	$0.764587\pi$
$228$	−78.2460	−5.18197
$229$	5.15383	0.340574	0.170287	−	0.985394i	$-0.445530\pi$
$229$	5.15383	0.340574	0.170287	+	0.985394i	$0.445530\pi$
$230$	−7.64887	−0.504352
$231$	18.1440	1.19379
$232$	30.7797	2.02079
$233$	0.303341	0.0198725	0.00993627	−	0.999951i	$-0.496837\pi$
$233$	0.303341	0.0198725	0.00993627	+	0.999951i	$0.496837\pi$
$234$	43.0121	2.81179
$235$	−9.18586	−0.599220
$236$	25.5587	1.66373
$237$	−32.1978	−2.09147
$238$	−0.751152	−0.0486900
$239$	6.94556	0.449271	0.224636	−	0.974443i	$-0.427881\pi$
$239$	6.94556	0.449271	0.224636	+	0.974443i	$0.427881\pi$
$240$	−15.2068	−0.981593
$241$	−13.1719	−0.848477	−0.424238	−	0.905551i	$-0.639458\pi$
$241$	−13.1719	−0.848477	−0.424238	+	0.905551i	$0.639458\pi$
$242$	−58.0639	−3.73249
$243$	21.6108	1.38633
$244$	13.2720	0.849652
$245$	−18.2529	−1.16613
$246$	45.6931	2.91328
$247$	−38.8688	−2.47317
$248$	−1.53555	−0.0975078
$249$	−11.5521	−0.732086
$250$	−3.32255	−0.210137
$251$	10.1886	0.643099	0.321550	−	0.946893i	$-0.395796\pi$
$251$	10.1886	0.643099	0.321550	+	0.946893i	$0.395796\pi$
$252$	16.2079	1.02100
$253$	−5.95996	−0.374700
$254$	36.6844	2.30179
$255$	−2.31184	−0.144773
$256$	−25.7317	−1.60823
$257$	−5.09460	−0.317792	−0.158896	−	0.987295i	$-0.550794\pi$
$257$	−5.09460	−0.317792	−0.158896	+	0.987295i	$0.550794\pi$
$258$	−9.23997	−0.575256
$259$	5.66807	0.352197
$260$	−54.7120	−3.39310
$261$	−31.2905	−1.93683
$262$	23.2666	1.43742
$263$	8.99407	0.554598	0.277299	−	0.960784i	$-0.410561\pi$
$263$	8.99407	0.554598	0.277299	+	0.960784i	$0.410561\pi$
$264$	−59.4348	−3.65796
$265$	−29.4449	−1.80879
$266$	−22.7679	−1.39599
$267$	−10.7809	−0.659778
$268$	19.2904	1.17835
$269$	−18.9194	−1.15353	−0.576767	−	0.816908i	$-0.695686\pi$
$269$	−18.9194	−1.15353	−0.576767	+	0.816908i	$0.695686\pi$
$270$	17.4057	1.05927
$271$	−10.3231	−0.627084	−0.313542	−	0.949574i	$-0.601516\pi$
$271$	−10.3231	−0.627084	−0.313542	+	0.949574i	$0.601516\pi$
$272$	0.490544	0.0297436
$273$	14.2954	0.865196
$274$	45.2390	2.73299
$275$	−32.3887	−1.95311
$276$	−9.45295	−0.569000
$277$	23.3823	1.40491	0.702454	−	0.711730i	$-0.252088\pi$
$277$	23.3823	1.40491	0.702454	+	0.711730i	$0.252088\pi$
$278$	20.2351	1.21362
$279$	1.56104	0.0934567
$280$	−14.2781	−0.853280
$281$	−9.32947	−0.556550	−0.278275	−	0.960501i	$-0.589763\pi$
$281$	−9.32947	−0.556550	−0.278275	+	0.960501i	$0.589763\pi$
$282$	−17.6472	−1.05087
$283$	9.07449	0.539422	0.269711	−	0.962941i	$-0.413072\pi$
$283$	9.07449	0.539422	0.269711	+	0.962941i	$0.413072\pi$
$284$	4.45986	0.264644
$285$	−70.0733	−4.15079
$286$	−66.2697	−3.91861
$287$	8.55315	0.504877
$288$	12.9853	0.765164
$289$	−16.9254	−0.995613
$290$	61.8714	3.63321
$291$	−4.26751	−0.250166
$292$	−51.8903	−3.03665
$293$	−0.732174	−0.0427740	−0.0213870	−	0.999771i	$-0.506808\pi$
$293$	−0.732174	−0.0427740	−0.0213870	+	0.999771i	$0.506808\pi$
$294$	−35.0660	−2.04509
$295$	22.8891	1.33266
$296$	−18.5670	−1.07919
$297$	13.5624	0.786970
$298$	−27.3996	−1.58721
$299$	−4.69577	−0.271563
$300$	−51.3710	−2.96590
$301$	−1.72960	−0.0996927
$302$	−28.1677	−1.62087
$303$	−1.07221	−0.0615970
$304$	14.8687	0.852780
$305$	11.8857	0.680576
$306$	−2.50140	−0.142996
$307$	−8.27546	−0.472306	−0.236153	−	0.971716i	$-0.575887\pi$
$307$	−8.27546	−0.472306	−0.236153	+	0.971716i	$0.575887\pi$
$308$	−24.9719	−1.42290
$309$	−41.7522	−2.37520
$310$	−3.08667	−0.175311
$311$	−13.1401	−0.745106	−0.372553	−	0.928011i	$-0.621518\pi$
$311$	−13.1401	−0.745106	−0.372553	+	0.928011i	$0.621518\pi$
$312$	−46.8278	−2.65110
$313$	12.0949	0.683644	0.341822	−	0.939765i	$-0.388956\pi$
$313$	12.0949	0.683644	0.341822	+	0.939765i	$0.388956\pi$
$314$	58.5446	3.30386
$315$	14.5150	0.817829
$316$	44.3144	2.49288
$317$	−8.29138	−0.465690	−0.232845	−	0.972514i	$-0.574803\pi$
$317$	−8.29138	−0.465690	−0.232845	+	0.972514i	$0.574803\pi$
$318$	−56.5674	−3.17214
$319$	48.2099	2.69923
$320$	−37.2810	−2.08407
$321$	25.7579	1.43767
$322$	−2.75061	−0.153285
$323$	2.26045	0.125775
$324$	−20.3475	−1.13042
$325$	−25.5186	−1.41552
$326$	2.62911	0.145613
$327$	3.28286	0.181543
$328$	−28.0178	−1.54702
$329$	−3.30332	−0.182118
$330$	−119.472	−6.57671
$331$	−4.88230	−0.268356	−0.134178	−	0.990957i	$-0.542839\pi$
$331$	−4.88230	−0.268356	−0.134178	+	0.990957i	$0.542839\pi$
$332$	15.8994	0.872592
$333$	18.8751	1.03435
$334$	1.00303	0.0548836
$335$	17.2756	0.943865
$336$	−5.46850	−0.298331
$337$	16.9669	0.924244	0.462122	−	0.886816i	$-0.347088\pi$
$337$	16.9669	0.924244	0.462122	+	0.886816i	$0.347088\pi$
$338$	−21.4301	−1.16565
$339$	24.5369	1.33266
$340$	3.18182	0.172558
$341$	−2.40512	−0.130245
$342$	−75.8191	−4.09983
$343$	−14.6953	−0.793469
$344$	5.66571	0.305475
$345$	−8.46560	−0.455773
$346$	3.79074	0.203792
$347$	−32.7364	−1.75738	−0.878690	−	0.477392i	$-0.841582\pi$
$347$	−32.7364	−1.75738	−0.878690	+	0.477392i	$0.841582\pi$
$348$	76.4644	4.09892
$349$	−19.7796	−1.05878	−0.529389	−	0.848379i	$-0.677579\pi$
$349$	−19.7796	−1.05878	−0.529389	+	0.848379i	$0.677579\pi$
$350$	−14.9479	−0.798997
$351$	10.6856	0.570356
$352$	−20.0067	−1.06636
$353$	−20.9130	−1.11309	−0.556543	−	0.830819i	$-0.687873\pi$
$353$	−20.9130	−1.11309	−0.556543	+	0.830819i	$0.687873\pi$
$354$	43.9728	2.33713
$355$	3.99403	0.211981
$356$	14.8379	0.786406
$357$	−0.831358	−0.0440002
$358$	−26.4021	−1.39539
$359$	1.15416	0.0609142	0.0304571	−	0.999536i	$-0.490304\pi$
$359$	1.15416	0.0609142	0.0304571	+	0.999536i	$0.490304\pi$
$360$	−47.5473	−2.50596
$361$	49.5156	2.60609
$362$	5.29852	0.278484
$363$	−64.2638	−3.37297
$364$	−19.6750	−1.03125
$365$	−46.4705	−2.43238
$366$	22.8340	1.19355
$367$	−13.3643	−0.697610	−0.348805	−	0.937195i	$-0.613412\pi$
$367$	−13.3643	−0.697610	−0.348805	+	0.937195i	$0.613412\pi$
$368$	1.79630	0.0936387
$369$	28.4827	1.48275
$370$	−37.3223	−1.94029
$371$	−10.5887	−0.549737
$372$	−3.81470	−0.197783
$373$	6.30895	0.326665	0.163332	−	0.986571i	$-0.447776\pi$
$373$	6.30895	0.326665	0.163332	+	0.986571i	$0.447776\pi$
$374$	3.85396	0.199283
$375$	−3.67732	−0.189896
$376$	10.8208	0.558040
$377$	37.9838	1.95627
$378$	6.25924	0.321941
$379$	−5.67432	−0.291470	−0.145735	−	0.989324i	$-0.546555\pi$
$379$	−5.67432	−0.291470	−0.145735	+	0.989324i	$0.546555\pi$
$380$	96.4431	4.94742
$381$	40.6015	2.08008
$382$	−23.6981	−1.21250
$383$	−34.4123	−1.75839	−0.879193	−	0.476466i	$-0.841917\pi$
$383$	−34.4123	−1.75839	−0.879193	+	0.476466i	$0.841917\pi$
$384$	−54.0265	−2.75703
$385$	−22.3636	−1.13975
$386$	−39.9087	−2.03130
$387$	−5.75973	−0.292783
$388$	5.87344	0.298179
$389$	24.7281	1.25376	0.626881	−	0.779115i	$-0.284331\pi$
$389$	24.7281	1.25376	0.626881	+	0.779115i	$0.284331\pi$
$390$	−94.1302	−4.76647
$391$	0.273086	0.0138105
$392$	21.5015	1.08599
$393$	25.7509	1.29896
$394$	26.9209	1.35625
$395$	39.6858	1.99681
$396$	−83.1584	−4.17887
$397$	0.200175	0.0100465	0.00502325	−	0.999987i	$-0.498401\pi$
$397$	0.200175	0.0100465	0.00502325	+	0.999987i	$0.498401\pi$
$398$	−20.6361	−1.03439
$399$	−25.1990	−1.26153
$400$	9.76179	0.488090
$401$	20.6837	1.03290	0.516448	−	0.856319i	$-0.327254\pi$
$401$	20.6837	1.03290	0.516448	+	0.856319i	$0.327254\pi$
$402$	33.1885	1.65529
$403$	−1.89496	−0.0943946
$404$	1.47570	0.0734190
$405$	−18.2223	−0.905472
$406$	22.2495	1.10423
$407$	−29.0813	−1.44151
$408$	2.72330	0.134824
$409$	20.0039	0.989130	0.494565	−	0.869141i	$-0.335327\pi$
$409$	20.0039	0.989130	0.494565	+	0.869141i	$0.335327\pi$
$410$	−56.3195	−2.78142
$411$	50.0696	2.46975
$412$	57.4643	2.83106
$413$	8.23115	0.405028
$414$	−9.15975	−0.450177
$415$	14.2387	0.698951
$416$	−15.7630	−0.772842
$417$	22.3957	1.09672
$418$	116.816	5.71366
$419$	23.3874	1.14255	0.571274	−	0.820759i	$-0.306449\pi$
$419$	23.3874	1.14255	0.571274	+	0.820759i	$0.306449\pi$
$420$	−35.4703	−1.73078
$421$	−29.1388	−1.42014	−0.710070	−	0.704131i	$-0.751337\pi$
$421$	−29.1388	−1.42014	−0.710070	+	0.704131i	$0.751337\pi$
$422$	−31.8155	−1.54875
$423$	−11.0003	−0.534855
$424$	34.6856	1.68448
$425$	1.48405	0.0719872
$426$	7.67303	0.371759
$427$	4.27423	0.206844
$428$	−35.4511	−1.71359
$429$	−73.3458	−3.54117
$430$	11.3888	0.549219
$431$	−26.1859	−1.26133	−0.630665	−	0.776055i	$-0.717218\pi$
$431$	−26.1859	−1.26133	−0.630665	+	0.776055i	$0.717218\pi$
$432$	−4.08763	−0.196666
$433$	15.5373	0.746675	0.373337	−	0.927696i	$-0.378213\pi$
$433$	15.5373	0.746675	0.373337	+	0.927696i	$0.378213\pi$
$434$	−1.11000	−0.0532816
$435$	68.4778	3.28326
$436$	−4.51826	−0.216385
$437$	8.27741	0.395962
$438$	−89.2755	−4.26575
$439$	18.6711	0.891122	0.445561	−	0.895252i	$-0.353004\pi$
$439$	18.6711	0.891122	0.445561	+	0.895252i	$0.353004\pi$
$440$	73.2571	3.49239
$441$	−21.8583	−1.04087
$442$	3.03648	0.144431
$443$	37.3852	1.77622	0.888112	−	0.459627i	$-0.152017\pi$
$443$	37.3852	1.77622	0.888112	+	0.459627i	$0.152017\pi$
$444$	−46.1251	−2.18900
$445$	13.2881	0.629916
$446$	52.8511	2.50257
$447$	−30.3252	−1.43433
$448$	−13.4066	−0.633402
$449$	23.9745	1.13143	0.565714	−	0.824602i	$-0.308601\pi$
$449$	23.9745	1.13143	0.565714	+	0.824602i	$0.308601\pi$
$450$	−49.7776	−2.34654
$451$	−43.8839	−2.06641
$452$	−33.7705	−1.58843
$453$	−31.1754	−1.46475
$454$	52.7120	2.47390
$455$	−17.6200	−0.826036
$456$	82.5452	3.86553
$457$	29.2875	1.37001	0.685006	−	0.728537i	$-0.259800\pi$
$457$	29.2875	1.37001	0.685006	+	0.728537i	$0.259800\pi$
$458$	−12.2038	−0.570245
$459$	−0.621429	−0.0290058
$460$	11.6513	0.543247
$461$	−23.4979	−1.09440	−0.547202	−	0.837000i	$-0.684307\pi$
$461$	−23.4979	−1.09440	−0.547202	+	0.837000i	$0.684307\pi$
$462$	−42.9633	−1.99883
$463$	−0.980451	−0.0455654	−0.0227827	−	0.999740i	$-0.507253\pi$
$463$	−0.980451	−0.0455654	−0.0227827	+	0.999740i	$0.507253\pi$
$464$	−14.5302	−0.674547
$465$	−3.41626	−0.158425
$466$	−0.718283	−0.0332738
$467$	−16.5640	−0.766492	−0.383246	−	0.923646i	$-0.625194\pi$
$467$	−16.5640	−0.766492	−0.383246	+	0.923646i	$0.625194\pi$
$468$	−65.5193	−3.02863
$469$	6.21246	0.286865
$470$	21.7512	1.00331
$471$	64.7959	2.98564
$472$	−26.9630	−1.24107
$473$	8.87413	0.408033
$474$	76.2414	3.50188
$475$	44.9827	2.06395
$476$	1.14421	0.0524449
$477$	−35.2612	−1.61450
$478$	−16.4464	−0.752242
$479$	−7.45352	−0.340560	−0.170280	−	0.985396i	$-0.554467\pi$
$479$	−7.45352	−0.340560	−0.170280	+	0.985396i	$0.554467\pi$
$480$	−28.4177	−1.29708
$481$	−22.9128	−1.04473
$482$	31.1898	1.42066
$483$	−3.04431	−0.138521
$484$	88.4473	4.02033
$485$	5.25997	0.238843
$486$	−51.1723	−2.32122
$487$	30.8128	1.39626	0.698130	−	0.715971i	$-0.254016\pi$
$487$	30.8128	1.39626	0.698130	+	0.715971i	$0.254016\pi$
$488$	−14.0012	−0.633805
$489$	2.90984	0.131587
$490$	43.2210	1.95253
$491$	−19.7841	−0.892843	−0.446421	−	0.894823i	$-0.647302\pi$
$491$	−19.7841	−0.892843	−0.446421	+	0.894823i	$0.647302\pi$
$492$	−69.6031	−3.13795
$493$	−2.20898	−0.0994873
$494$	92.0377	4.14097
$495$	−74.4727	−3.34730
$496$	0.724890	0.0325485
$497$	1.43629	0.0644265
$498$	27.3543	1.22578
$499$	−34.9866	−1.56622	−0.783108	−	0.621885i	$-0.786367\pi$
$499$	−34.9866	−1.56622	−0.783108	+	0.621885i	$0.786367\pi$
$500$	5.06116	0.226342
$501$	1.11014	0.0495972
$502$	−24.1256	−1.07678
$503$	−14.9569	−0.666896	−0.333448	−	0.942769i	$-0.608212\pi$
$503$	−14.9569	−0.666896	−0.333448	+	0.942769i	$0.608212\pi$
$504$	−17.0985	−0.761626
$505$	1.32157	0.0588090
$506$	14.1126	0.627383
$507$	−23.7184	−1.05337
$508$	−55.8805	−2.47930
$509$	−35.2583	−1.56280	−0.781399	−	0.624031i	$-0.785494\pi$
$509$	−35.2583	−1.56280	−0.781399	+	0.624031i	$0.785494\pi$
$510$	5.47421	0.242402
$511$	−16.7112	−0.739261
$512$	19.7003	0.870639
$513$	−18.8359	−0.831627
$514$	12.0635	0.532099
$515$	51.4622	2.26770
$516$	14.0750	0.619619
$517$	16.9485	0.745393
$518$	−13.4214	−0.589704
$519$	4.19551	0.184162
$520$	57.7182	2.53111
$521$	−25.2947	−1.10818	−0.554091	−	0.832456i	$-0.686934\pi$
$521$	−25.2947	−1.10818	−0.554091	+	0.832456i	$0.686934\pi$
$522$	74.0928	3.24295
$523$	−7.08519	−0.309814	−0.154907	−	0.987929i	$-0.549508\pi$
$523$	−7.08519	−0.309814	−0.154907	+	0.987929i	$0.549508\pi$
$524$	−35.4414	−1.54827
$525$	−16.5440	−0.722038
$526$	−21.2971	−0.928598
$527$	0.110203	0.00480050
$528$	28.0574	1.22104
$529$	−22.0000	−0.956522
$530$	69.7228	3.02857
$531$	27.4104	1.18951
$532$	34.6818	1.50365
$533$	−34.5755	−1.49763
$534$	25.5281	1.10471
$535$	−31.7483	−1.37260
$536$	−20.3503	−0.879000
$537$	−29.2212	−1.26099
$538$	44.7993	1.93143
$539$	33.6776	1.45060
$540$	−26.5136	−1.14096
$541$	42.4556	1.82531	0.912655	−	0.408731i	$-0.134029\pi$
$541$	42.4556	1.82531	0.912655	+	0.408731i	$0.134029\pi$
$542$	24.4441	1.04996
$543$	5.86428	0.251660
$544$	0.916706	0.0393034
$545$	−4.04633	−0.173326
$546$	−33.8501	−1.44865
$547$	−26.1683	−1.11887	−0.559437	−	0.828873i	$-0.688983\pi$
$547$	−26.1683	−1.11887	−0.559437	+	0.828873i	$0.688983\pi$
$548$	−68.9115	−2.94375
$549$	14.2335	0.607473
$550$	76.6935	3.27022
$551$	−66.9556	−2.85240
$552$	9.97233	0.424451
$553$	14.2714	0.606882
$554$	−55.3671	−2.35232
$555$	−41.3075	−1.75340
$556$	−30.8236	−1.30721
$557$	−32.1710	−1.36313	−0.681565	−	0.731757i	$-0.738700\pi$
$557$	−32.1710	−1.36313	−0.681565	+	0.731757i	$0.738700\pi$
$558$	−3.69638	−0.156480
$559$	6.99180	0.295721
$560$	6.74027	0.284828
$561$	4.26548	0.180089
$562$	22.0913	0.931865
$563$	1.40481	0.0592055	0.0296027	−	0.999562i	$-0.490576\pi$
$563$	1.40481	0.0592055	0.0296027	+	0.999562i	$0.490576\pi$
$564$	26.8815	1.13192
$565$	−30.2433	−1.27234
$566$	−21.4875	−0.903188
$567$	−6.55291	−0.275196
$568$	−4.70490	−0.197413
$569$	−18.5474	−0.777546	−0.388773	−	0.921334i	$-0.627101\pi$
$569$	−18.5474	−0.777546	−0.388773	+	0.921334i	$0.627101\pi$
$570$	165.927	6.94992
$571$	−20.3961	−0.853551	−0.426775	−	0.904358i	$-0.640350\pi$
$571$	−20.3961	−0.853551	−0.426775	+	0.904358i	$0.640350\pi$
$572$	100.947	4.22080
$573$	−26.2286	−1.09571
$574$	−20.2530	−0.845346
$575$	5.43438	0.226629
$576$	−44.6451	−1.86021
$577$	−22.7231	−0.945974	−0.472987	−	0.881069i	$-0.656824\pi$
$577$	−22.7231	−0.945974	−0.472987	+	0.881069i	$0.656824\pi$
$578$	40.0778	1.66702
$579$	−44.1700	−1.83564
$580$	−94.2472	−3.91340
$581$	5.12038	0.212429
$582$	10.1051	0.418868
$583$	54.3277	2.25002
$584$	54.7414	2.26522
$585$	−58.6759	−2.42595
$586$	1.73372	0.0716192
$587$	−45.5761	−1.88113	−0.940564	−	0.339615i	$-0.889703\pi$
$587$	−45.5761	−1.88113	−0.940564	+	0.339615i	$0.889703\pi$
$588$	53.4152	2.20280
$589$	3.34032	0.137635
$590$	−54.1993	−2.23135
$591$	29.7954	1.22562
$592$	8.76495	0.360237
$593$	−22.0569	−0.905767	−0.452884	−	0.891570i	$-0.649605\pi$
$593$	−22.0569	−0.905767	−0.452884	+	0.891570i	$0.649605\pi$
$594$	−32.1145	−1.31767
$595$	1.02470	0.0420086
$596$	41.7371	1.70962
$597$	−22.8395	−0.934760
$598$	11.1191	0.454695
$599$	−6.86560	−0.280521	−0.140260	−	0.990115i	$-0.544794\pi$
$599$	−6.86560	−0.280521	−0.140260	+	0.990115i	$0.544794\pi$
$600$	54.1935	2.21244
$601$	42.3508	1.72752	0.863762	−	0.503900i	$-0.168102\pi$
$601$	42.3508	1.72752	0.863762	+	0.503900i	$0.168102\pi$
$602$	4.09554	0.166922
$603$	20.6880	0.842481
$604$	42.9073	1.74587
$605$	79.2091	3.22031
$606$	2.53890	0.103136
$607$	36.4480	1.47938	0.739689	−	0.672949i	$-0.234972\pi$
$607$	36.4480	1.47938	0.739689	+	0.672949i	$0.234972\pi$
$608$	27.7860	1.12687
$609$	24.6253	0.997867
$610$	−28.1443	−1.13953
$611$	13.3534	0.540223
$612$	3.81032	0.154023
$613$	−33.1476	−1.33882	−0.669409	−	0.742895i	$-0.733452\pi$
$613$	−33.1476	−1.33882	−0.669409	+	0.742895i	$0.733452\pi$
$614$	19.5955	0.790810
$615$	−62.3332	−2.51352
$616$	26.3439	1.06143
$617$	−15.7496	−0.634057	−0.317028	−	0.948416i	$-0.602685\pi$
$617$	−15.7496	−0.634057	−0.317028	+	0.948416i	$0.602685\pi$
$618$	98.8653	3.97695
$619$	23.6842	0.951946	0.475973	−	0.879460i	$-0.342096\pi$
$619$	23.6842	0.951946	0.475973	+	0.879460i	$0.342096\pi$
$620$	4.70185	0.188831
$621$	−2.27558	−0.0913160
$622$	31.1145	1.24758
$623$	4.77852	0.191447
$624$	22.1060	0.884949
$625$	−22.6394	−0.905576
$626$	−28.6396	−1.14467
$627$	129.289	5.16332
$628$	−89.1796	−3.55865
$629$	1.33251	0.0531305
$630$	−34.3702	−1.36934
$631$	−21.7893	−0.867418	−0.433709	−	0.901053i	$-0.642795\pi$
$631$	−21.7893	−0.867418	−0.433709	+	0.901053i	$0.642795\pi$
$632$	−46.7492	−1.85959
$633$	−35.2127	−1.39958
$634$	19.6332	0.779733
$635$	−50.0439	−1.98593
$636$	86.1677	3.41677
$637$	26.5341	1.05132
$638$	−114.156	−4.51949
$639$	4.78297	0.189211
$640$	66.5911	2.63224
$641$	−31.9045	−1.26015	−0.630075	−	0.776534i	$-0.716976\pi$
$641$	−31.9045	−1.26015	−0.630075	+	0.776534i	$0.716976\pi$
$642$	−60.9923	−2.40717
$643$	7.18518	0.283356	0.141678	−	0.989913i	$-0.454750\pi$
$643$	7.18518	0.283356	0.141678	+	0.989913i	$0.454750\pi$
$644$	4.18993	0.165107
$645$	12.6049	0.496318
$646$	−5.35252	−0.210592
$647$	−1.64595	−0.0647088	−0.0323544	−	0.999476i	$-0.510301\pi$
$647$	−1.64595	−0.0647088	−0.0323544	+	0.999476i	$0.510301\pi$
$648$	21.4655	0.843246
$649$	−42.2318	−1.65774
$650$	60.4256	2.37009
$651$	−1.22852	−0.0481495
$652$	−4.00486	−0.156842
$653$	−6.79202	−0.265792	−0.132896	−	0.991130i	$-0.542428\pi$
$653$	−6.79202	−0.265792	−0.132896	+	0.991130i	$0.542428\pi$
$654$	−7.77351	−0.303968
$655$	−31.7396	−1.24017
$656$	13.2264	0.516403
$657$	−55.6498	−2.17111
$658$	7.82196	0.304932
$659$	−31.3243	−1.22022	−0.610111	−	0.792316i	$-0.708875\pi$
$659$	−31.3243	−1.22022	−0.610111	+	0.792316i	$0.708875\pi$
$660$	181.989	7.08390
$661$	−35.3664	−1.37559	−0.687796	−	0.725904i	$-0.741422\pi$
$661$	−35.3664	−1.37559	−0.687796	+	0.725904i	$0.741422\pi$
$662$	11.5608	0.449324
$663$	3.36071	0.130519
$664$	−16.7730	−0.650917
$665$	31.0594	1.20443
$666$	−44.6945	−1.73188
$667$	−8.08895	−0.313205
$668$	−1.52790	−0.0591162
$669$	58.4944	2.26152
$670$	−40.9069	−1.58037
$671$	−21.9299	−0.846595
$672$	−10.2193	−0.394217
$673$	−2.89140	−0.111455	−0.0557276	−	0.998446i	$-0.517748\pi$
$673$	−2.89140	−0.111455	−0.0557276	+	0.998446i	$0.517748\pi$
$674$	−40.1759	−1.54752
$675$	−12.3664	−0.475983
$676$	32.6440	1.25554
$677$	44.9906	1.72913	0.864565	−	0.502522i	$-0.167594\pi$
$677$	44.9906	1.72913	0.864565	+	0.502522i	$0.167594\pi$
$678$	−58.1011	−2.23136
$679$	1.89154	0.0725905
$680$	−3.35664	−0.128721
$681$	58.3404	2.23561
$682$	5.69509	0.218076
$683$	−15.4299	−0.590409	−0.295204	−	0.955434i	$-0.595388\pi$
$683$	−15.4299	−0.590409	−0.295204	+	0.955434i	$0.595388\pi$
$684$	115.493	4.41600
$685$	−61.7138	−2.35796
$686$	34.7969	1.32855
$687$	−13.5069	−0.515319
$688$	−2.67461	−0.101969
$689$	42.8040	1.63070
$690$	20.0457	0.763128
$691$	−40.4436	−1.53855	−0.769274	−	0.638920i	$-0.779382\pi$
$691$	−40.4436	−1.53855	−0.769274	+	0.638920i	$0.779382\pi$
$692$	−5.77435	−0.219508
$693$	−26.7811	−1.01733
$694$	77.5166	2.94249
$695$	−27.6041	−1.04708
$696$	−80.6657	−3.05763
$697$	2.01076	0.0761630
$698$	46.8362	1.77278
$699$	−0.794980	−0.0300689
$700$	22.7697	0.860615
$701$	−46.0718	−1.74011	−0.870055	−	0.492955i	$-0.835917\pi$
$701$	−46.0718	−1.74011	−0.870055	+	0.492955i	$0.835917\pi$
$702$	−25.3025	−0.954982
$703$	40.3892	1.52331
$704$	68.7856	2.59246
$705$	24.0738	0.906671
$706$	49.5200	1.86371
$707$	0.475249	0.0178736
$708$	−66.9828	−2.51737
$709$	−52.1758	−1.95950	−0.979752	−	0.200214i	$-0.935836\pi$
$709$	−52.1758	−1.95950	−0.979752	+	0.200214i	$0.935836\pi$
$710$	−9.45748	−0.354933
$711$	47.5250	1.78233
$712$	−15.6531	−0.586626
$713$	0.403546	0.0151129
$714$	1.96858	0.0736722
$715$	90.4032	3.38089
$716$	40.2176	1.50300
$717$	−18.2025	−0.679786
$718$	−2.73294	−0.101992
$719$	−34.8949	−1.30136	−0.650680	−	0.759352i	$-0.725516\pi$
$719$	−34.8949	−1.30136	−0.650680	+	0.759352i	$0.725516\pi$
$720$	22.4457	0.836500
$721$	18.5063	0.689211
$722$	−117.248	−4.36353
$723$	34.5202	1.28382
$724$	−8.07111	−0.299960
$725$	−43.9585	−1.63258
$726$	152.170	5.64758
$727$	43.8113	1.62487	0.812436	−	0.583051i	$-0.198141\pi$
$727$	43.8113	1.62487	0.812436	+	0.583051i	$0.198141\pi$
$728$	20.7560	0.769269
$729$	−39.7129	−1.47085
$730$	110.038	4.07268
$731$	−0.406613	−0.0150391
$732$	−34.7825	−1.28560
$733$	−40.3876	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$733$	−40.3876	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$734$	31.6454	1.16805
$735$	47.8360	1.76446
$736$	3.35684	0.123735
$737$	−31.8745	−1.17411
$738$	−67.4443	−2.48266
$739$	11.0165	0.405250	0.202625	−	0.979256i	$-0.435053\pi$
$739$	11.0165	0.405250	0.202625	+	0.979256i	$0.435053\pi$
$740$	56.8521	2.08993
$741$	101.865	3.74211
$742$	25.0730	0.920458
$743$	−33.8313	−1.24115	−0.620575	−	0.784147i	$-0.713101\pi$
$743$	−33.8313	−1.24115	−0.620575	+	0.784147i	$0.713101\pi$
$744$	4.02430	0.147538
$745$	37.3777	1.36941
$746$	−14.9390	−0.546955
$747$	17.0513	0.623874
$748$	−5.87064	−0.214652
$749$	−11.4170	−0.417167
$750$	8.70755	0.317955
$751$	11.6347	0.424558	0.212279	−	0.977209i	$-0.431912\pi$
$751$	11.6347	0.424558	0.212279	+	0.977209i	$0.431912\pi$
$752$	−5.10817	−0.186276
$753$	−26.7017	−0.973065
$754$	−89.9421	−3.27550
$755$	38.4257	1.39845
$756$	−9.53455	−0.346768
$757$	19.0459	0.692236	0.346118	−	0.938191i	$-0.387500\pi$
$757$	19.0459	0.692236	0.346118	+	0.938191i	$0.387500\pi$
$758$	13.4363	0.488027
$759$	15.6195	0.566953
$760$	−101.742	−3.69057
$761$	32.4268	1.17547	0.587736	−	0.809053i	$-0.300019\pi$
$761$	32.4268	1.17547	0.587736	+	0.809053i	$0.300019\pi$
$762$	−96.1405	−3.48280
$763$	−1.45510	−0.0526782
$764$	36.0988	1.30601
$765$	3.41234	0.123373
$766$	81.4850	2.94417
$767$	−33.2738	−1.20145
$768$	67.4362	2.43340
$769$	32.9396	1.18783	0.593917	−	0.804526i	$-0.297581\pi$
$769$	32.9396	1.18783	0.593917	+	0.804526i	$0.297581\pi$
$770$	52.9549	1.90836
$771$	13.3516	0.480847
$772$	60.7919	2.18795
$773$	17.1105	0.615424	0.307712	−	0.951480i	$-0.400437\pi$
$773$	17.1105	0.615424	0.307712	+	0.951480i	$0.400437\pi$
$774$	13.6385	0.490225
$775$	2.19302	0.0787757
$776$	−6.19615	−0.222429
$777$	−14.8546	−0.532904
$778$	−58.5537	−2.09925
$779$	60.9476	2.18367
$780$	143.386	5.13405
$781$	−7.36923	−0.263692
$782$	−0.646641	−0.0231238
$783$	18.4071	0.657815
$784$	−10.1502	−0.362509
$785$	−79.8650	−2.85050
$786$	−60.9758	−2.17493
$787$	−12.5717	−0.448134	−0.224067	−	0.974574i	$-0.571933\pi$
$787$	−12.5717	−0.448134	−0.224067	+	0.974574i	$0.571933\pi$
$788$	−41.0079	−1.46085
$789$	−23.5711	−0.839155
$790$	−93.9723	−3.34338
$791$	−10.8758	−0.386698
$792$	87.7275	3.11726
$793$	−17.2783	−0.613569
$794$	−0.473995	−0.0168215
$795$	77.1676	2.73685
$796$	31.4344	1.11416
$797$	−27.2521	−0.965319	−0.482660	−	0.875808i	$-0.660329\pi$
$797$	−27.2521	−0.965319	−0.482660	+	0.875808i	$0.660329\pi$
$798$	59.6689	2.11226
$799$	−0.776579	−0.0274734
$800$	18.2424	0.644965
$801$	15.9129	0.562254
$802$	−48.9771	−1.72944
$803$	85.7408	3.02573
$804$	−50.5552	−1.78295
$805$	3.75230	0.132251
$806$	4.48708	0.158051
$807$	49.5828	1.74540
$808$	−1.55679	−0.0547675
$809$	−47.4499	−1.66825	−0.834124	−	0.551577i	$-0.814026\pi$
$809$	−47.4499	−1.66825	−0.834124	+	0.551577i	$0.814026\pi$
$810$	43.1486	1.51609
$811$	26.7380	0.938897	0.469449	−	0.882960i	$-0.344453\pi$
$811$	26.7380	0.938897	0.469449	+	0.882960i	$0.344453\pi$
$812$	−33.8922	−1.18938
$813$	27.0542	0.948832
$814$	68.8618	2.41361
$815$	−3.58656	−0.125632
$816$	−1.28559	−0.0450047
$817$	−12.3247	−0.431187
$818$	−47.3674	−1.65616
$819$	−21.1004	−0.737309
$820$	85.7902	2.99592
$821$	−18.1586	−0.633739	−0.316870	−	0.948469i	$-0.602632\pi$
$821$	−18.1586	−0.633739	−0.316870	+	0.948469i	$0.602632\pi$
$822$	−118.560	−4.13525
$823$	31.4304	1.09560	0.547798	−	0.836611i	$-0.315466\pi$
$823$	31.4304	1.09560	0.547798	+	0.836611i	$0.315466\pi$
$824$	−60.6216	−2.11185
$825$	84.8826	2.95523
$826$	−19.4906	−0.678164
$827$	34.4447	1.19776	0.598879	−	0.800839i	$-0.295613\pi$
$827$	34.4447	1.19776	0.598879	+	0.800839i	$0.295613\pi$
$828$	13.9528	0.484894
$829$	7.54813	0.262157	0.131079	−	0.991372i	$-0.458156\pi$
$829$	7.54813	0.262157	0.131079	+	0.991372i	$0.458156\pi$
$830$	−33.7159	−1.17030
$831$	−61.2791	−2.12575
$832$	54.1952	1.87888
$833$	−1.54311	−0.0534655
$834$	−53.0309	−1.83631
$835$	−1.36831	−0.0473524
$836$	−177.943	−6.15429
$837$	−0.918302	−0.0317412
$838$	−55.3791	−1.91304
$839$	−30.6368	−1.05770	−0.528849	−	0.848716i	$-0.677376\pi$
$839$	−30.6368	−1.05770	−0.528849	+	0.848716i	$0.677376\pi$
$840$	37.4192	1.29109
$841$	36.4311	1.25624
$842$	68.9980	2.37783
$843$	24.4502	0.842108
$844$	48.4638	1.66819
$845$	29.2344	1.00569
$846$	26.0478	0.895541
$847$	28.4843	0.978734
$848$	−16.3741	−0.562288
$849$	−23.7819	−0.816193
$850$	−3.51410	−0.120533
$851$	4.87944	0.167265
$852$	−11.6881	−0.400429
$853$	−26.6251	−0.911625	−0.455813	−	0.890076i	$-0.650651\pi$
$853$	−26.6251	−0.911625	−0.455813	+	0.890076i	$0.650651\pi$
$854$	−10.1210	−0.346332
$855$	103.430	3.53724
$856$	37.3989	1.27827
$857$	2.67059	0.0912255	0.0456128	−	0.998959i	$-0.485476\pi$
$857$	2.67059	0.0912255	0.0456128	+	0.998959i	$0.485476\pi$
$858$	173.676	5.92919
$859$	−55.1713	−1.88242	−0.941210	−	0.337823i	$-0.890310\pi$
$859$	−55.1713	−1.88242	−0.941210	+	0.337823i	$0.890310\pi$
$860$	−17.3483	−0.591574
$861$	−22.4156	−0.763922
$862$	62.0057	2.11192
$863$	33.3886	1.13656	0.568281	−	0.822835i	$-0.307609\pi$
$863$	33.3886	1.13656	0.568281	+	0.822835i	$0.307609\pi$
$864$	−7.63877	−0.259876
$865$	−5.17123	−0.175827
$866$	−36.7908	−1.25020
$867$	44.3572	1.50645
$868$	1.69083	0.0573906
$869$	−73.2227	−2.48391
$870$	−162.149	−5.49737
$871$	−25.1134	−0.850935
$872$	4.76651	0.161414
$873$	6.29897	0.213188
$874$	−19.6001	−0.662984
$875$	1.62994	0.0551021
$876$	135.991	4.59472
$877$	−31.1685	−1.05249	−0.526243	−	0.850334i	$-0.676400\pi$
$877$	−31.1685	−1.05249	−0.526243	+	0.850334i	$0.676400\pi$
$878$	−44.2113	−1.49206
$879$	1.91884	0.0647208
$880$	−34.5825	−1.16578
$881$	0.0372684	0.00125560	0.000627802	−	1.00000i	$-0.499800\pi$
$881$	0.0372684	0.00125560	0.000627802		1.00000i	$0.499800\pi$
$882$	51.7584	1.74280
$883$	−32.3896	−1.09000	−0.544998	−	0.838437i	$-0.683470\pi$
$883$	−32.3896	−1.09000	−0.544998	+	0.838437i	$0.683470\pi$
$884$	−4.62539	−0.155569
$885$	−59.9865	−2.01643
$886$	−88.5246	−2.97404
$887$	−56.6582	−1.90240	−0.951198	−	0.308581i	$-0.900146\pi$
$887$	−56.6582	−1.90240	−0.951198	+	0.308581i	$0.900146\pi$
$888$	48.6595	1.63290
$889$	−17.9963	−0.603575
$890$	−31.4649	−1.05471
$891$	33.6212	1.12635
$892$	−80.5068	−2.69557
$893$	−23.5386	−0.787691
$894$	71.8073	2.40159
$895$	36.0170	1.20391
$896$	23.9468	0.800006
$897$	12.3064	0.410899
$898$	−56.7694	−1.89442
$899$	−3.26426	−0.108869
$900$	75.8251	2.52750
$901$	−2.48930	−0.0829304
$902$	103.913	3.45992
$903$	4.53285	0.150844
$904$	35.6261	1.18490
$905$	−7.22809	−0.240270
$906$	73.8204	2.45252
$907$	−10.4365	−0.346538	−0.173269	−	0.984875i	$-0.555433\pi$
$907$	−10.4365	−0.346538	−0.173269	+	0.984875i	$0.555433\pi$
$908$	−80.2949	−2.66468
$909$	1.58262	0.0524921
$910$	41.7224	1.38308
$911$	38.8754	1.28800	0.643999	−	0.765026i	$-0.277274\pi$
$911$	38.8754	1.28800	0.643999	+	0.765026i	$0.277274\pi$
$912$	−38.9671	−1.29033
$913$	−26.2713	−0.869452
$914$	−69.3500	−2.29390
$915$	−31.1495	−1.02977
$916$	18.5897	0.614221
$917$	−11.4139	−0.376920
$918$	1.47149	0.0485663
$919$	18.5725	0.612649	0.306325	−	0.951927i	$-0.400901\pi$
$919$	18.5725	0.612649	0.306325	+	0.951927i	$0.400901\pi$
$920$	−12.2915	−0.405240
$921$	21.6879	0.714639
$922$	55.6407	1.83243
$923$	−5.80610	−0.191110
$924$	65.4449	2.15298
$925$	26.5168	0.871866
$926$	2.32161	0.0762930
$927$	61.6276	2.02412
$928$	−27.1533	−0.891351
$929$	2.69095	0.0882872	0.0441436	−	0.999025i	$-0.485944\pi$
$929$	2.69095	0.0882872	0.0441436	+	0.999025i	$0.485944\pi$
$930$	8.08938	0.265261
$931$	−46.7727	−1.53291
$932$	1.09414	0.0358399
$933$	34.4368	1.12741
$934$	39.2220	1.28338
$935$	−5.25746	−0.171937
$936$	69.1192	2.25923
$937$	49.5245	1.61790	0.808948	−	0.587881i	$-0.200038\pi$
$937$	49.5245	1.61790	0.808948	+	0.587881i	$0.200038\pi$
$938$	−14.7105	−0.480315
$939$	−31.6976	−1.03441
$940$	−33.1331	−1.08068
$941$	12.4547	0.406010	0.203005	−	0.979178i	$-0.434929\pi$
$941$	12.4547	0.406010	0.203005	+	0.979178i	$0.434929\pi$
$942$	−153.430	−4.99903
$943$	7.36311	0.239776
$944$	12.7284	0.414275
$945$	−8.53868	−0.277763
$946$	−21.0131	−0.683195
$947$	−34.1295	−1.10906	−0.554530	−	0.832164i	$-0.687102\pi$
$947$	−34.1295	−1.10906	−0.554530	+	0.832164i	$0.687102\pi$
$948$	−116.137	−3.77194
$949$	67.5539	2.19289
$950$	−106.515	−3.45579
$951$	21.7296	0.704630
$952$	−1.20708	−0.0391217
$953$	−7.39659	−0.239599	−0.119800	−	0.992798i	$-0.538225\pi$
$953$	−7.39659	−0.239599	−0.119800	+	0.992798i	$0.538225\pi$
$954$	83.4951	2.70326
$955$	32.3283	1.04612
$956$	25.0524	0.810254
$957$	−126.346	−4.08418
$958$	17.6492	0.570221
$959$	−22.1929	−0.716646
$960$	97.7039	3.15338
$961$	−30.8372	−0.994747
$962$	54.2552	1.74926
$963$	−38.0195	−1.22516
$964$	−47.5107	−1.53022
$965$	54.4423	1.75256
$966$	7.20864	0.231934
$967$	−14.9572	−0.480991	−0.240495	−	0.970650i	$-0.577310\pi$
$967$	−14.9572	−0.480991	−0.240495	+	0.970650i	$0.577310\pi$
$968$	−93.3070	−2.99900
$969$	−5.92405	−0.190308
$970$	−12.4551	−0.399909
$971$	54.4507	1.74741	0.873703	−	0.486459i	$-0.161712\pi$
$971$	54.4507	1.74741	0.873703	+	0.486459i	$0.161712\pi$
$972$	77.9496	2.50023
$973$	−9.92671	−0.318236
$974$	−72.9617	−2.33784
$975$	66.8777	2.14180
$976$	6.60956	0.211567
$977$	−18.4733	−0.591012	−0.295506	−	0.955341i	$-0.595488\pi$
$977$	−18.4733	−0.591012	−0.295506	+	0.955341i	$0.595488\pi$
$978$	−6.89022	−0.220325
$979$	−24.5173	−0.783577
$980$	−65.8375	−2.10310
$981$	−4.84561	−0.154708
$982$	46.8468	1.49494
$983$	10.9429	0.349025	0.174513	−	0.984655i	$-0.444165\pi$
$983$	10.9429	0.349025	0.174513	+	0.984655i	$0.444165\pi$
$984$	73.4275	2.34078
$985$	−36.7247	−1.17015
$986$	5.23065	0.166578
$987$	8.65717	0.275561
$988$	−140.199	−4.46032
$989$	−1.48896	−0.0473460
$990$	176.344	5.60459
$991$	7.24628	0.230186	0.115093	−	0.993355i	$-0.463283\pi$
$991$	7.24628	0.230186	0.115093	+	0.993355i	$0.463283\pi$
$992$	1.35464	0.0430098
$993$	12.7953	0.406046
$994$	−3.40100	−0.107873
$995$	28.1511	0.892451
$996$	−41.6682	−1.32031
$997$	−11.4549	−0.362781	−0.181390	−	0.983411i	$-0.558060\pi$
$997$	−11.4549	−0.362781	−0.181390	+	0.983411i	$0.558060\pi$
$998$	82.8450	2.62241
$999$	−11.1036	−0.351302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.19	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} +O(q^{10})\)	\(q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} -7.64888 q^{10} -5.95997 q^{11} -9.45295 q^{12} -4.69577 q^{13} -2.75061 q^{14} -8.46560 q^{15} +1.79630 q^{16} +0.273086 q^{17} -9.15976 q^{18} +8.27742 q^{19} +11.6513 q^{20} -3.04431 q^{21} +14.1126 q^{22} +1.00000 q^{23} +9.97234 q^{24} +5.43438 q^{25} +11.1191 q^{26} -2.27558 q^{27} +4.18994 q^{28} -8.08895 q^{29} +20.0457 q^{30} +0.403546 q^{31} +3.35684 q^{32} +15.6195 q^{33} -0.646641 q^{34} +3.75230 q^{35} +13.9528 q^{36} +4.87945 q^{37} -19.6001 q^{38} +12.3064 q^{39} -12.2915 q^{40} +7.36311 q^{41} +7.20864 q^{42} -1.48896 q^{43} -21.4974 q^{44} +12.4955 q^{45} -2.36790 q^{46} -2.84372 q^{47} -4.70764 q^{48} -5.65064 q^{49} -12.8681 q^{50} -0.715688 q^{51} -16.9375 q^{52} -9.11543 q^{53} +5.38836 q^{54} -19.2521 q^{55} -4.42015 q^{56} -21.6930 q^{57} +19.1539 q^{58} +7.08591 q^{59} -30.5352 q^{60} +3.67954 q^{61} -0.955558 q^{62} +4.49350 q^{63} -11.5413 q^{64} -15.1684 q^{65} -36.9856 q^{66} +5.34809 q^{67} +0.985013 q^{68} -2.62074 q^{69} -8.88510 q^{70} +1.23645 q^{71} -14.7195 q^{72} -14.3861 q^{73} -11.5541 q^{74} -14.2421 q^{75} +29.8564 q^{76} -6.92323 q^{77} -29.1404 q^{78} +12.2858 q^{79} +5.80247 q^{80} -5.64117 q^{81} -17.4352 q^{82} +4.40796 q^{83} -10.9807 q^{84} +0.882130 q^{85} +3.52571 q^{86} +21.1991 q^{87} +22.6786 q^{88} +4.11367 q^{89} -29.5881 q^{90} -5.45471 q^{91} +3.60697 q^{92} -1.05759 q^{93} +6.73365 q^{94} +26.7380 q^{95} -8.79742 q^{96} +1.62836 q^{97} +13.3802 q^{98} -23.0549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 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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