LMFDB - Embedded newform 4003.2.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} +O(q^{10})$	\(q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} -4.32491 q^{10} +1.27907 q^{11} -13.7303 q^{12} +2.11227 q^{13} +4.97263 q^{14} -5.18877 q^{15} +7.19214 q^{16} -4.74604 q^{17} -16.1638 q^{18} +6.91804 q^{19} +7.62448 q^{20} +5.96586 q^{21} -3.25894 q^{22} -0.312750 q^{23} +19.4065 q^{24} -2.11866 q^{25} -5.38182 q^{26} -10.2220 q^{27} -8.76636 q^{28} +2.76156 q^{29} +13.2204 q^{30} +6.09804 q^{31} -5.62749 q^{32} -3.90987 q^{33} +12.0924 q^{34} -3.31286 q^{35} +28.4956 q^{36} -5.58541 q^{37} -17.6264 q^{38} -6.45678 q^{39} -10.7765 q^{40} -8.81948 q^{41} -15.2003 q^{42} +2.76370 q^{43} +5.74525 q^{44} +10.7687 q^{45} +0.796852 q^{46} +1.05384 q^{47} -21.9849 q^{48} -3.19099 q^{49} +5.39810 q^{50} +14.5077 q^{51} +9.48773 q^{52} -0.198763 q^{53} +26.0445 q^{54} +2.17117 q^{55} +12.3904 q^{56} -21.1471 q^{57} -7.03613 q^{58} -1.29207 q^{59} -23.3065 q^{60} +1.28912 q^{61} -15.5371 q^{62} -12.3814 q^{63} -0.0460754 q^{64} +3.58547 q^{65} +9.96191 q^{66} +4.45843 q^{67} -21.3179 q^{68} +0.956014 q^{69} +8.44079 q^{70} -3.26402 q^{71} -40.2758 q^{72} -3.95016 q^{73} +14.2310 q^{74} +6.47632 q^{75} +31.0739 q^{76} -2.49633 q^{77} +16.4511 q^{78} -14.7462 q^{79} +12.2083 q^{80} +12.2145 q^{81} +22.4710 q^{82} -10.7341 q^{83} +26.7970 q^{84} -8.05616 q^{85} -7.04160 q^{86} -8.44152 q^{87} -8.12037 q^{88} -5.43628 q^{89} -27.4373 q^{90} -4.12245 q^{91} -1.40479 q^{92} -18.6405 q^{93} -2.68508 q^{94} +11.7430 q^{95} +17.2021 q^{96} -8.36985 q^{97} +8.13028 q^{98} +8.11447 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54789	−1.80163	−0.900814	−	0.434206i	$-0.857029\pi$
$2$	−2.54789	−1.80163	−0.900814	+	0.434206i	$0.857029\pi$
$3$	−3.05680	−1.76484	−0.882422	−	0.470459i	$-0.844088\pi$
$3$	−3.05680	−1.76484	−0.882422	+	0.470459i	$0.844088\pi$
$4$	4.49172	2.24586
$5$	1.69745	0.759123	0.379562	−	0.925166i	$-0.376075\pi$
$5$	1.69745	0.759123	0.379562	+	0.925166i	$0.376075\pi$
$6$	7.78837	3.17959
$7$	−1.95167	−0.737661	−0.368831	−	0.929497i	$-0.620242\pi$
$7$	−1.95167	−0.737661	−0.368831	+	0.929497i	$0.620242\pi$
$8$	−6.34863	−2.24458
$9$	6.34402	2.11467
$10$	−4.32491	−1.36766
$11$	1.27907	0.385655	0.192828	−	0.981233i	$-0.438234\pi$
$11$	1.27907	0.385655	0.192828	+	0.981233i	$0.438234\pi$
$12$	−13.7303	−3.96359
$13$	2.11227	0.585838	0.292919	−	0.956137i	$-0.405373\pi$
$13$	2.11227	0.585838	0.292919	+	0.956137i	$0.405373\pi$
$14$	4.97263	1.32899
$15$	−5.18877	−1.33973
$16$	7.19214	1.79803
$17$	−4.74604	−1.15108	−0.575541	−	0.817773i	$-0.695209\pi$
$17$	−4.74604	−1.15108	−0.575541	+	0.817773i	$0.695209\pi$
$18$	−16.1638	−3.80985
$19$	6.91804	1.58711	0.793554	−	0.608500i	$-0.208229\pi$
$19$	6.91804	1.58711	0.793554	+	0.608500i	$0.208229\pi$
$20$	7.62448	1.70489
$21$	5.96586	1.30186
$22$	−3.25894	−0.694807
$23$	−0.312750	−0.0652129	−0.0326065	−	0.999468i	$-0.510381\pi$
$23$	−0.312750	−0.0652129	−0.0326065	+	0.999468i	$0.510381\pi$
$24$	19.4065	3.96133
$25$	−2.11866	−0.423732
$26$	−5.38182	−1.05546
$27$	−10.2220	−1.96722
$28$	−8.76636	−1.65669
$29$	2.76156	0.512808	0.256404	−	0.966570i	$-0.417462\pi$
$29$	2.76156	0.512808	0.256404	+	0.966570i	$0.417462\pi$
$30$	13.2204	2.41370
$31$	6.09804	1.09524	0.547621	−	0.836727i	$-0.315534\pi$
$31$	6.09804	1.09524	0.547621	+	0.836727i	$0.315534\pi$
$32$	−5.62749	−0.994809
$33$	−3.90987	−0.680621
$34$	12.0924	2.07382
$35$	−3.31286	−0.559976
$36$	28.4956	4.74926
$37$	−5.58541	−0.918235	−0.459118	−	0.888376i	$-0.651834\pi$
$37$	−5.58541	−0.918235	−0.459118	+	0.888376i	$0.651834\pi$
$38$	−17.6264	−2.85938
$39$	−6.45678	−1.03391
$40$	−10.7765	−1.70391
$41$	−8.81948	−1.37737	−0.688686	−	0.725060i	$-0.741812\pi$
$41$	−8.81948	−1.37737	−0.688686	+	0.725060i	$0.741812\pi$
$42$	−15.2003	−2.34546
$43$	2.76370	0.421460	0.210730	−	0.977544i	$-0.432416\pi$
$43$	2.76370	0.421460	0.210730	+	0.977544i	$0.432416\pi$
$44$	5.74525	0.866129
$45$	10.7687	1.60530
$46$	0.796852	0.117489
$47$	1.05384	0.153719	0.0768595	−	0.997042i	$-0.475511\pi$
$47$	1.05384	0.153719	0.0768595	+	0.997042i	$0.475511\pi$
$48$	−21.9849	−3.17325
$49$	−3.19099	−0.455856
$50$	5.39810	0.763407
$51$	14.5077	2.03148
$52$	9.48773	1.31571
$53$	−0.198763	−0.0273023	−0.0136511	−	0.999907i	$-0.504345\pi$
$53$	−0.198763	−0.0273023	−0.0136511	+	0.999907i	$0.504345\pi$
$54$	26.0445	3.54420
$55$	2.17117	0.292760
$56$	12.3904	1.65574
$57$	−21.1471	−2.80100
$58$	−7.03613	−0.923889
$59$	−1.29207	−0.168213	−0.0841064	−	0.996457i	$-0.526804\pi$
$59$	−1.29207	−0.168213	−0.0841064	+	0.996457i	$0.526804\pi$
$60$	−23.3065	−3.00886
$61$	1.28912	0.165055	0.0825274	−	0.996589i	$-0.473701\pi$
$61$	1.28912	0.165055	0.0825274	+	0.996589i	$0.473701\pi$
$62$	−15.5371	−1.97322
$63$	−12.3814	−1.55991
$64$	−0.0460754	−0.00575942
$65$	3.58547	0.444723
$66$	9.96191	1.22623
$67$	4.45843	0.544684	0.272342	−	0.962200i	$-0.412202\pi$
$67$	4.45843	0.544684	0.272342	+	0.962200i	$0.412202\pi$
$68$	−21.3179	−2.58517
$69$	0.956014	0.115091
$70$	8.44079	1.00887
$71$	−3.26402	−0.387367	−0.193684	−	0.981064i	$-0.562044\pi$
$71$	−3.26402	−0.387367	−0.193684	+	0.981064i	$0.562044\pi$
$72$	−40.2758	−4.74655
$73$	−3.95016	−0.462331	−0.231166	−	0.972914i	$-0.574254\pi$
$73$	−3.95016	−0.462331	−0.231166	+	0.972914i	$0.574254\pi$
$74$	14.2310	1.65432
$75$	6.47632	0.747821
$76$	31.0739	3.56442
$77$	−2.49633	−0.284483
$78$	16.4511	1.86273
$79$	−14.7462	−1.65908	−0.829539	−	0.558449i	$-0.811397\pi$
$79$	−14.7462	−1.65908	−0.829539	+	0.558449i	$0.811397\pi$
$80$	12.2083	1.36493
$81$	12.2145	1.35717
$82$	22.4710	2.48151
$83$	−10.7341	−1.17822	−0.589110	−	0.808053i	$-0.700521\pi$
$83$	−10.7341	−1.17822	−0.589110	+	0.808053i	$0.700521\pi$
$84$	26.7970	2.92379
$85$	−8.05616	−0.873814
$86$	−7.04160	−0.759315
$87$	−8.44152	−0.905026
$88$	−8.12037	−0.865634
$89$	−5.43628	−0.576245	−0.288122	−	0.957594i	$-0.593031\pi$
$89$	−5.43628	−0.576245	−0.288122	+	0.957594i	$0.593031\pi$
$90$	−27.4373	−2.89215
$91$	−4.12245	−0.432150
$92$	−1.40479	−0.146459
$93$	−18.6405	−1.93293
$94$	−2.68508	−0.276945
$95$	11.7430	1.20481
$96$	17.2021	1.75568
$97$	−8.36985	−0.849830	−0.424915	−	0.905233i	$-0.639696\pi$
$97$	−8.36985	−0.849830	−0.424915	+	0.905233i	$0.639696\pi$
$98$	8.13028	0.821282
$99$	8.11447	0.815535
$100$	−9.51643	−0.951643
$101$	−12.6494	−1.25866	−0.629332	−	0.777137i	$-0.716671\pi$
$101$	−12.6494	−1.25866	−0.629332	+	0.777137i	$0.716671\pi$
$102$	−36.9639	−3.65997
$103$	−2.52520	−0.248815	−0.124408	−	0.992231i	$-0.539703\pi$
$103$	−2.52520	−0.248815	−0.124408	+	0.992231i	$0.539703\pi$
$104$	−13.4100	−1.31496
$105$	10.1268	0.988270
$106$	0.506427	0.0491885
$107$	5.53331	0.534925	0.267463	−	0.963568i	$-0.413815\pi$
$107$	5.53331	0.534925	0.267463	+	0.963568i	$0.413815\pi$
$108$	−45.9143	−4.41811
$109$	9.10785	0.872373	0.436187	−	0.899856i	$-0.356329\pi$
$109$	9.10785	0.872373	0.436187	+	0.899856i	$0.356329\pi$
$110$	−5.53188	−0.527444
$111$	17.0735	1.62054
$112$	−14.0367	−1.32634
$113$	12.4667	1.17277	0.586384	−	0.810033i	$-0.300551\pi$
$113$	12.4667	1.17277	0.586384	+	0.810033i	$0.300551\pi$
$114$	53.8803	5.04635
$115$	−0.530878	−0.0495046
$116$	12.4041	1.15170
$117$	13.4003	1.23886
$118$	3.29204	0.303057
$119$	9.26269	0.849109
$120$	32.9416	3.00714
$121$	−9.36397	−0.851270
$122$	−3.28453	−0.297367
$123$	26.9594	2.43085
$124$	27.3907	2.45976
$125$	−12.0836	−1.08079
$126$	31.5464	2.81038
$127$	18.0879	1.60504	0.802521	−	0.596625i	$-0.203492\pi$
$127$	18.0879	1.60504	0.802521	+	0.596625i	$0.203492\pi$
$128$	11.3724	1.00519
$129$	−8.44808	−0.743812
$130$	−9.13538	−0.801226
$131$	21.2647	1.85790	0.928952	−	0.370199i	$-0.120711\pi$
$131$	21.2647	1.85790	0.928952	+	0.370199i	$0.120711\pi$
$132$	−17.5621	−1.52858
$133$	−13.5017	−1.17075
$134$	−11.3596	−0.981318
$135$	−17.3513	−1.49336
$136$	30.1308	2.58370
$137$	6.22612	0.531934	0.265967	−	0.963982i	$-0.414309\pi$
$137$	6.22612	0.531934	0.265967	+	0.963982i	$0.414309\pi$
$138$	−2.43582	−0.207350
$139$	8.74712	0.741921	0.370961	−	0.928649i	$-0.379029\pi$
$139$	8.74712	0.741921	0.370961	+	0.928649i	$0.379029\pi$
$140$	−14.8805	−1.25763
$141$	−3.22139	−0.271290
$142$	8.31634	0.697892
$143$	2.70175	0.225932
$144$	45.6270	3.80225
$145$	4.68761	0.389284
$146$	10.0646	0.832948
$147$	9.75422	0.804514
$148$	−25.0881	−2.06223
$149$	3.31093	0.271242	0.135621	−	0.990761i	$-0.456697\pi$
$149$	3.31093	0.271242	0.135621	+	0.990761i	$0.456697\pi$
$150$	−16.5009	−1.34729
$151$	−8.30448	−0.675809	−0.337905	−	0.941180i	$-0.609718\pi$
$151$	−8.30448	−0.675809	−0.337905	+	0.941180i	$0.609718\pi$
$152$	−43.9201	−3.56239
$153$	−30.1089	−2.43416
$154$	6.36036	0.512533
$155$	10.3511	0.831423
$156$	−29.0021	−2.32203
$157$	22.8598	1.82441	0.912204	−	0.409737i	$-0.134379\pi$
$157$	22.8598	1.82441	0.912204	+	0.409737i	$0.134379\pi$
$158$	37.5717	2.98904
$159$	0.607580	0.0481842
$160$	−9.55239	−0.755182
$161$	0.610385	0.0481050
$162$	−31.1212	−2.44511
$163$	13.1912	1.03322	0.516609	−	0.856221i	$-0.327194\pi$
$163$	13.1912	1.03322	0.516609	+	0.856221i	$0.327194\pi$
$164$	−39.6147	−3.09339
$165$	−6.63682	−0.516676
$166$	27.3492	2.12271
$167$	3.38409	0.261869	0.130935	−	0.991391i	$-0.458202\pi$
$167$	3.38409	0.261869	0.130935	+	0.991391i	$0.458202\pi$
$168$	−37.8750	−2.92212
$169$	−8.53832	−0.656794
$170$	20.5262	1.57429
$171$	43.8882	3.35621
$172$	12.4138	0.946542
$173$	−1.31951	−0.100320	−0.0501601	−	0.998741i	$-0.515973\pi$
$173$	−1.31951	−0.100320	−0.0501601	+	0.998741i	$0.515973\pi$
$174$	21.5080	1.63052
$175$	4.13492	0.312571
$176$	9.19928	0.693422
$177$	3.94959	0.296869
$178$	13.8510	1.03818
$179$	6.00066	0.448510	0.224255	−	0.974530i	$-0.428005\pi$
$179$	6.00066	0.448510	0.224255	+	0.974530i	$0.428005\pi$
$180$	48.3698	3.60528
$181$	1.58330	0.117686	0.0588429	−	0.998267i	$-0.481259\pi$
$181$	1.58330	0.117686	0.0588429	+	0.998267i	$0.481259\pi$
$182$	10.5035	0.778574
$183$	−3.94058	−0.291296
$184$	1.98553	0.146376
$185$	−9.48095	−0.697054
$186$	47.4939	3.48242
$187$	−6.07053	−0.443921
$188$	4.73358	0.345232
$189$	19.9499	1.45114
$190$	−29.9199	−2.17062
$191$	−18.1483	−1.31317	−0.656583	−	0.754254i	$-0.727999\pi$
$191$	−18.1483	−1.31317	−0.656583	+	0.754254i	$0.727999\pi$
$192$	0.140843	0.0101645
$193$	20.5290	1.47771	0.738855	−	0.673865i	$-0.235367\pi$
$193$	20.5290	1.47771	0.738855	+	0.673865i	$0.235367\pi$
$194$	21.3254	1.53108
$195$	−10.9601	−0.784867
$196$	−14.3331	−1.02379
$197$	−8.67871	−0.618332	−0.309166	−	0.951008i	$-0.600050\pi$
$197$	−8.67871	−0.618332	−0.309166	+	0.951008i	$0.600050\pi$
$198$	−20.6747	−1.46929
$199$	20.9943	1.48825	0.744124	−	0.668042i	$-0.232867\pi$
$199$	20.9943	1.48825	0.744124	+	0.668042i	$0.232867\pi$
$200$	13.4506	0.951100
$201$	−13.6285	−0.961283
$202$	32.2293	2.26764
$203$	−5.38964	−0.378279
$204$	65.1645	4.56243
$205$	−14.9706	−1.04559
$206$	6.43392	0.448273
$207$	−1.98409	−0.137904
$208$	15.1917	1.05336
$209$	8.84869	0.612077
$210$	−25.8018	−1.78049
$211$	−18.3322	−1.26204	−0.631021	−	0.775766i	$-0.717364\pi$
$211$	−18.3322	−1.26204	−0.631021	+	0.775766i	$0.717364\pi$
$212$	−0.892790	−0.0613171
$213$	9.97744	0.683643
$214$	−14.0982	−0.963736
$215$	4.69125	0.319940
$216$	64.8956	4.41559
$217$	−11.9014	−0.807917
$218$	−23.2058	−1.57169
$219$	12.0748	0.815942
$220$	9.75228	0.657499
$221$	−10.0249	−0.674348
$222$	−43.5012	−2.91961
$223$	−14.7292	−0.986339	−0.493170	−	0.869933i	$-0.664162\pi$
$223$	−14.7292	−0.986339	−0.493170	+	0.869933i	$0.664162\pi$
$224$	10.9830	0.733832
$225$	−13.4408	−0.896054
$226$	−31.7637	−2.11289
$227$	−8.39648	−0.557294	−0.278647	−	0.960394i	$-0.589886\pi$
$227$	−8.39648	−0.557294	−0.278647	+	0.960394i	$0.589886\pi$
$228$	−94.9867	−6.29065
$229$	20.6880	1.36710	0.683550	−	0.729904i	$-0.260435\pi$
$229$	20.6880	1.36710	0.683550	+	0.729904i	$0.260435\pi$
$230$	1.35262	0.0891889
$231$	7.63077	0.502068
$232$	−17.5321	−1.15104
$233$	−22.1788	−1.45298	−0.726492	−	0.687175i	$-0.758851\pi$
$233$	−22.1788	−1.45298	−0.726492	+	0.687175i	$0.758851\pi$
$234$	−34.1424	−2.23196
$235$	1.78885	0.116692
$236$	−5.80361	−0.377783
$237$	45.0762	2.92801
$238$	−23.6003	−1.52978
$239$	2.61708	0.169285	0.0846425	−	0.996411i	$-0.473025\pi$
$239$	2.61708	0.169285	0.0846425	+	0.996411i	$0.473025\pi$
$240$	−37.3183	−2.40889
$241$	3.88922	0.250527	0.125263	−	0.992124i	$-0.460022\pi$
$241$	3.88922	0.250527	0.125263	+	0.992124i	$0.460022\pi$
$242$	23.8583	1.53367
$243$	−6.67131	−0.427965
$244$	5.79037	0.370690
$245$	−5.41655	−0.346051
$246$	−68.6894	−4.37948
$247$	14.6128	0.929788
$248$	−38.7142	−2.45836
$249$	32.8119	2.07937
$250$	30.7876	1.94718
$251$	−15.8612	−1.00115	−0.500576	−	0.865693i	$-0.666878\pi$
$251$	−15.8612	−1.00115	−0.500576	+	0.865693i	$0.666878\pi$
$252$	−55.6139	−3.50335
$253$	−0.400031	−0.0251497
$254$	−46.0859	−2.89169
$255$	24.6261	1.54214
$256$	−28.8834	−1.80521
$257$	−13.8317	−0.862797	−0.431398	−	0.902162i	$-0.641980\pi$
$257$	−13.8317	−0.862797	−0.431398	+	0.902162i	$0.641980\pi$
$258$	21.5247	1.34007
$259$	10.9009	0.677347
$260$	16.1050	0.998787
$261$	17.5194	1.08442
$262$	−54.1800	−3.34725
$263$	−27.6002	−1.70190	−0.850949	−	0.525248i	$-0.823973\pi$
$263$	−27.6002	−1.70190	−0.850949	+	0.525248i	$0.823973\pi$
$264$	24.8223	1.52771
$265$	−0.337391	−0.0207258
$266$	34.4008	2.10925
$267$	16.6176	1.01698
$268$	20.0261	1.22329
$269$	−1.80058	−0.109783	−0.0548915	−	0.998492i	$-0.517481\pi$
$269$	−1.80058	−0.109783	−0.0548915	+	0.998492i	$0.517481\pi$
$270$	44.2092	2.69049
$271$	−6.62851	−0.402653	−0.201327	−	0.979524i	$-0.564525\pi$
$271$	−6.62851	−0.402653	−0.201327	+	0.979524i	$0.564525\pi$
$272$	−34.1341	−2.06969
$273$	12.6015	0.762677
$274$	−15.8635	−0.958346
$275$	−2.70992	−0.163415
$276$	4.29415	0.258478
$277$	−15.9509	−0.958397	−0.479199	−	0.877706i	$-0.659073\pi$
$277$	−15.9509	−0.958397	−0.479199	+	0.877706i	$0.659073\pi$
$278$	−22.2867	−1.33667
$279$	38.6861	2.31608
$280$	21.0321	1.25691
$281$	−15.0481	−0.897695	−0.448848	−	0.893608i	$-0.648165\pi$
$281$	−15.0481	−0.897695	−0.448848	+	0.893608i	$0.648165\pi$
$282$	8.20774	0.488764
$283$	21.5951	1.28370	0.641849	−	0.766831i	$-0.278168\pi$
$283$	21.5951	1.28370	0.641849	+	0.766831i	$0.278168\pi$
$284$	−14.6611	−0.869974
$285$	−35.8961	−2.12630
$286$	−6.88375	−0.407045
$287$	17.2127	1.01603
$288$	−35.7009	−2.10369
$289$	5.52486	0.324992
$290$	−11.9435	−0.701346
$291$	25.5850	1.49982
$292$	−17.7430	−1.03833
$293$	17.2953	1.01040	0.505202	−	0.863001i	$-0.331418\pi$
$293$	17.2953	1.01040	0.505202	+	0.863001i	$0.331418\pi$
$294$	−24.8526	−1.44943
$295$	−2.19322	−0.127694
$296$	35.4597	2.06105
$297$	−13.0747	−0.758670
$298$	−8.43586	−0.488676
$299$	−0.660613	−0.0382042
$300$	29.0898	1.67950
$301$	−5.39383	−0.310895
$302$	21.1589	1.21756
$303$	38.6667	2.22134
$304$	49.7555	2.85367
$305$	2.18822	0.125297
$306$	76.7141	4.38546
$307$	8.47402	0.483638	0.241819	−	0.970321i	$-0.422256\pi$
$307$	8.47402	0.483638	0.241819	+	0.970321i	$0.422256\pi$
$308$	−11.2128	−0.638910
$309$	7.71903	0.439120
$310$	−26.3735	−1.49791
$311$	−26.9798	−1.52988	−0.764941	−	0.644100i	$-0.777232\pi$
$311$	−26.9798	−1.52988	−0.764941	+	0.644100i	$0.777232\pi$
$312$	40.9917	2.32070
$313$	−6.65398	−0.376105	−0.188053	−	0.982159i	$-0.560218\pi$
$313$	−6.65398	−0.376105	−0.188053	+	0.982159i	$0.560218\pi$
$314$	−58.2441	−3.28690
$315$	−21.0168	−1.18417
$316$	−66.2359	−3.72606
$317$	1.90143	0.106795	0.0533974	−	0.998573i	$-0.482995\pi$
$317$	1.90143	0.106795	0.0533974	+	0.998573i	$0.482995\pi$
$318$	−1.54804	−0.0868100
$319$	3.53224	0.197767
$320$	−0.0782107	−0.00437211
$321$	−16.9142	−0.944059
$322$	−1.55519	−0.0866674
$323$	−32.8333	−1.82689
$324$	54.8642	3.04801
$325$	−4.47518	−0.248238
$326$	−33.6098	−1.86147
$327$	−27.8408	−1.53960
$328$	55.9916	3.09162
$329$	−2.05676	−0.113393
$330$	16.9099	0.930857
$331$	16.8542	0.926390	0.463195	−	0.886256i	$-0.346703\pi$
$331$	16.8542	0.926390	0.463195	+	0.886256i	$0.346703\pi$
$332$	−48.2146	−2.64612
$333$	−35.4339	−1.94177
$334$	−8.62229	−0.471791
$335$	7.56797	0.413483
$336$	42.9073	2.34078
$337$	−13.7120	−0.746942	−0.373471	−	0.927642i	$-0.621832\pi$
$337$	−13.7120	−0.746942	−0.373471	+	0.927642i	$0.621832\pi$
$338$	21.7547	1.18330
$339$	−38.1082	−2.06975
$340$	−36.1861	−1.96246
$341$	7.79985	0.422386
$342$	−111.822	−6.04664
$343$	19.8894	1.07393
$344$	−17.5457	−0.946001
$345$	1.62279	0.0873679
$346$	3.36195	0.180739
$347$	2.62664	0.141006	0.0705028	−	0.997512i	$-0.477540\pi$
$347$	2.62664	0.141006	0.0705028	+	0.997512i	$0.477540\pi$
$348$	−37.9170	−2.03256
$349$	18.1831	0.973319	0.486659	−	0.873592i	$-0.338215\pi$
$349$	18.1831	0.973319	0.486659	+	0.873592i	$0.338215\pi$
$350$	−10.5353	−0.563136
$351$	−21.5916	−1.15247
$352$	−7.19798	−0.383653
$353$	−29.0730	−1.54740	−0.773699	−	0.633553i	$-0.781596\pi$
$353$	−29.0730	−1.54740	−0.773699	+	0.633553i	$0.781596\pi$
$354$	−10.0631	−0.534848
$355$	−5.54051	−0.294060
$356$	−24.4183	−1.29417
$357$	−28.3142	−1.49854
$358$	−15.2890	−0.808049
$359$	−20.1578	−1.06389	−0.531945	−	0.846779i	$-0.678539\pi$
$359$	−20.1578	−1.06389	−0.531945	+	0.846779i	$0.678539\pi$
$360$	−68.3662	−3.60322
$361$	28.8593	1.51891
$362$	−4.03407	−0.212026
$363$	28.6238	1.50236
$364$	−18.5169	−0.970550
$365$	−6.70520	−0.350966
$366$	10.0401	0.524807
$367$	9.34111	0.487602	0.243801	−	0.969825i	$-0.421606\pi$
$367$	9.34111	0.487602	0.243801	+	0.969825i	$0.421606\pi$
$368$	−2.24934	−0.117255
$369$	−55.9509	−2.91269
$370$	24.1564	1.25583
$371$	0.387920	0.0201398
$372$	−83.7279	−4.34109
$373$	15.1424	0.784043	0.392022	−	0.919956i	$-0.371776\pi$
$373$	15.1424	0.784043	0.392022	+	0.919956i	$0.371776\pi$
$374$	15.4670	0.799781
$375$	36.9371	1.90742
$376$	−6.69047	−0.345035
$377$	5.83315	0.300423
$378$	−50.8301	−2.61442
$379$	−6.39086	−0.328277	−0.164138	−	0.986437i	$-0.552484\pi$
$379$	−6.39086	−0.328277	−0.164138	+	0.986437i	$0.552484\pi$
$380$	52.7465	2.70584
$381$	−55.2910	−2.83265
$382$	46.2398	2.36584
$383$	0.122038	0.00623583	0.00311791	−	0.999995i	$-0.499008\pi$
$383$	0.122038	0.00623583	0.00311791	+	0.999995i	$0.499008\pi$
$384$	−34.7630	−1.77399
$385$	−4.23740	−0.215958
$386$	−52.3055	−2.66228
$387$	17.5330	0.891251
$388$	−37.5951	−1.90860
$389$	6.44018	0.326530	0.163265	−	0.986582i	$-0.447797\pi$
$389$	6.44018	0.326530	0.163265	+	0.986582i	$0.447797\pi$
$390$	27.9250	1.41404
$391$	1.48432	0.0750655
$392$	20.2584	1.02320
$393$	−65.0019	−3.27891
$394$	22.1124	1.11400
$395$	−25.0310	−1.25944
$396$	36.4480	1.83158
$397$	−21.3887	−1.07347	−0.536735	−	0.843751i	$-0.680342\pi$
$397$	−21.3887	−1.07347	−0.536735	+	0.843751i	$0.680342\pi$
$398$	−53.4911	−2.68127
$399$	41.2720	2.06619
$400$	−15.2377	−0.761885
$401$	−1.20640	−0.0602445	−0.0301223	−	0.999546i	$-0.509590\pi$
$401$	−1.20640	−0.0602445	−0.0301223	+	0.999546i	$0.509590\pi$
$402$	34.7239	1.73187
$403$	12.8807	0.641634
$404$	−56.8177	−2.82678
$405$	20.7335	1.03026
$406$	13.7322	0.681517
$407$	−7.14415	−0.354122
$408$	−92.1039	−4.55982
$409$	28.2505	1.39690	0.698449	−	0.715660i	$-0.253874\pi$
$409$	28.2505	1.39690	0.698449	+	0.715660i	$0.253874\pi$
$410$	38.1435	1.88377
$411$	−19.0320	−0.938779
$412$	−11.3425	−0.558805
$413$	2.52169	0.124084
$414$	5.05524	0.248452
$415$	−18.2206	−0.894414
$416$	−11.8868	−0.582797
$417$	−26.7382	−1.30937
$418$	−22.5454	−1.10273
$419$	2.55944	0.125037	0.0625184	−	0.998044i	$-0.480087\pi$
$419$	2.55944	0.125037	0.0625184	+	0.998044i	$0.480087\pi$
$420$	45.4866	2.21952
$421$	−31.2538	−1.52322	−0.761608	−	0.648038i	$-0.775590\pi$
$421$	−31.2538	−1.52322	−0.761608	+	0.648038i	$0.775590\pi$
$422$	46.7084	2.27373
$423$	6.68561	0.325065
$424$	1.26188	0.0612821
$425$	10.0552	0.487751
$426$	−25.4214	−1.23167
$427$	−2.51593	−0.121755
$428$	24.8541	1.20137
$429$	−8.25870	−0.398734
$430$	−11.9528	−0.576413
$431$	18.4718	0.889757	0.444878	−	0.895591i	$-0.353247\pi$
$431$	18.4718	0.889757	0.444878	+	0.895591i	$0.353247\pi$
$432$	−73.5179	−3.53713
$433$	16.6879	0.801970	0.400985	−	0.916085i	$-0.368668\pi$
$433$	16.6879	0.801970	0.400985	+	0.916085i	$0.368668\pi$
$434$	30.3233	1.45557
$435$	−14.3291	−0.687026
$436$	40.9099	1.95923
$437$	−2.16362	−0.103500
$438$	−30.7653	−1.47002
$439$	5.43370	0.259336	0.129668	−	0.991557i	$-0.458609\pi$
$439$	5.43370	0.259336	0.129668	+	0.991557i	$0.458609\pi$
$440$	−13.7839	−0.657123
$441$	−20.2437	−0.963986
$442$	25.5423	1.21492
$443$	20.2292	0.961117	0.480559	−	0.876963i	$-0.340434\pi$
$443$	20.2292	0.961117	0.480559	+	0.876963i	$0.340434\pi$
$444$	76.6893	3.63951
$445$	−9.22782	−0.437441
$446$	37.5283	1.77702
$447$	−10.1208	−0.478699
$448$	0.0899239	0.00424850
$449$	−32.5339	−1.53537	−0.767684	−	0.640828i	$-0.778591\pi$
$449$	−32.5339	−1.53537	−0.767684	+	0.640828i	$0.778591\pi$
$450$	34.2457	1.61436
$451$	−11.2808	−0.531191
$452$	55.9969	2.63387
$453$	25.3851	1.19270
$454$	21.3933	1.00404
$455$	−6.99766	−0.328055
$456$	134.255	6.28706
$457$	−8.38603	−0.392282	−0.196141	−	0.980576i	$-0.562841\pi$
$457$	−8.38603	−0.392282	−0.196141	+	0.980576i	$0.562841\pi$
$458$	−52.7106	−2.46300
$459$	48.5139	2.26444
$460$	−2.38456	−0.111181
$461$	−28.8811	−1.34513	−0.672563	−	0.740040i	$-0.734807\pi$
$461$	−28.8811	−1.34513	−0.672563	+	0.740040i	$0.734807\pi$
$462$	−19.4423	−0.904540
$463$	−9.29190	−0.431831	−0.215916	−	0.976412i	$-0.569274\pi$
$463$	−9.29190	−0.431831	−0.215916	+	0.976412i	$0.569274\pi$
$464$	19.8615	0.922046
$465$	−31.6413	−1.46733
$466$	56.5092	2.61774
$467$	−1.33238	−0.0616553	−0.0308276	−	0.999525i	$-0.509814\pi$
$467$	−1.33238	−0.0616553	−0.0308276	+	0.999525i	$0.509814\pi$
$468$	60.1903	2.78230
$469$	−8.70138	−0.401793
$470$	−4.55779	−0.210235
$471$	−69.8777	−3.21979
$472$	8.20286	0.377567
$473$	3.53498	0.162539
$474$	−114.849	−5.27519
$475$	−14.6570	−0.672508
$476$	41.6054	1.90698
$477$	−1.26096	−0.0577353
$478$	−6.66803	−0.304988
$479$	21.5871	0.986340	0.493170	−	0.869933i	$-0.335838\pi$
$479$	21.5871	0.986340	0.493170	+	0.869933i	$0.335838\pi$
$480$	29.1997	1.33278
$481$	−11.7979	−0.537937
$482$	−9.90930	−0.451356
$483$	−1.86582	−0.0848979
$484$	−42.0604	−1.91183
$485$	−14.2074	−0.645126
$486$	16.9977	0.771033
$487$	17.4192	0.789340	0.394670	−	0.918823i	$-0.370859\pi$
$487$	17.4192	0.789340	0.394670	+	0.918823i	$0.370859\pi$
$488$	−8.18414	−0.370479
$489$	−40.3230	−1.82347
$490$	13.8008	0.623455
$491$	−1.85911	−0.0839006	−0.0419503	−	0.999120i	$-0.513357\pi$
$491$	−1.85911	−0.0839006	−0.0419503	+	0.999120i	$0.513357\pi$
$492$	121.094	5.45934
$493$	−13.1064	−0.590284
$494$	−37.2317	−1.67513
$495$	13.7739	0.619091
$496$	43.8580	1.96928
$497$	6.37028	0.285746
$498$	−83.6011	−3.74626
$499$	−29.4259	−1.31728	−0.658641	−	0.752457i	$-0.728869\pi$
$499$	−29.4259	−1.31728	−0.658641	+	0.752457i	$0.728869\pi$
$500$	−54.2761	−2.42730
$501$	−10.3445	−0.462158
$502$	40.4126	1.80370
$503$	1.79364	0.0799743	0.0399872	−	0.999200i	$-0.487268\pi$
$503$	1.79364	0.0799743	0.0399872	+	0.999200i	$0.487268\pi$
$504$	78.6050	3.50135
$505$	−21.4718	−0.955481
$506$	1.01923	0.0453104
$507$	26.0999	1.15914
$508$	81.2458	3.60470
$509$	−38.0802	−1.68787	−0.843937	−	0.536442i	$-0.819768\pi$
$509$	−38.0802	−1.68787	−0.843937	+	0.536442i	$0.819768\pi$
$510$	−62.7444	−2.77837
$511$	7.70940	0.341044
$512$	50.8468	2.24713
$513$	−70.7161	−3.12219
$514$	35.2416	1.55444
$515$	−4.28640	−0.188882
$516$	−37.9464	−1.67050
$517$	1.34795	0.0592826
$518$	−27.7742	−1.22033
$519$	4.03346	0.177049
$520$	−22.7628	−0.998217
$521$	−14.8236	−0.649433	−0.324717	−	0.945811i	$-0.605269\pi$
$521$	−14.8236	−0.649433	−0.324717	+	0.945811i	$0.605269\pi$
$522$	−44.6373	−1.95372
$523$	−0.830678	−0.0363230	−0.0181615	−	0.999835i	$-0.505781\pi$
$523$	−0.830678	−0.0363230	−0.0181615	+	0.999835i	$0.505781\pi$
$524$	95.5151	4.17260
$525$	−12.6396	−0.551638
$526$	70.3220	3.06619
$527$	−28.9415	−1.26071
$528$	−28.1203	−1.22378
$529$	−22.9022	−0.995747
$530$	0.859634	0.0373401
$531$	−8.19690	−0.355715
$532$	−60.6460	−2.62934
$533$	−18.6291	−0.806917
$534$	−42.3398	−1.83222
$535$	9.39252	0.406074
$536$	−28.3049	−1.22259
$537$	−18.3428	−0.791551
$538$	4.58766	0.197788
$539$	−4.08151	−0.175803
$540$	−77.9373	−3.35389
$541$	7.05717	0.303411	0.151706	−	0.988426i	$-0.451523\pi$
$541$	7.05717	0.303411	0.151706	+	0.988426i	$0.451523\pi$
$542$	16.8887	0.725431
$543$	−4.83983	−0.207697
$544$	26.7083	1.14511
$545$	15.4601	0.662239
$546$	−32.1072	−1.37406
$547$	−37.1334	−1.58771	−0.793854	−	0.608109i	$-0.791928\pi$
$547$	−37.1334	−1.58771	−0.793854	+	0.608109i	$0.791928\pi$
$548$	27.9660	1.19465
$549$	8.17820	0.349037
$550$	6.90458	0.294412
$551$	19.1046	0.813881
$552$	−6.06938	−0.258330
$553$	28.7797	1.22384
$554$	40.6411	1.72668
$555$	28.9814	1.23019
$556$	39.2897	1.66625
$557$	33.0107	1.39871	0.699355	−	0.714775i	$-0.253471\pi$
$557$	33.0107	1.39871	0.699355	+	0.714775i	$0.253471\pi$
$558$	−98.5678	−4.17271
$559$	5.83768	0.246908
$560$	−23.8266	−1.00686
$561$	18.5564	0.783452
$562$	38.3409	1.61731
$563$	−0.884460	−0.0372755	−0.0186378	−	0.999826i	$-0.505933\pi$
$563$	−0.884460	−0.0372755	−0.0186378	+	0.999826i	$0.505933\pi$
$564$	−14.4696	−0.609280
$565$	21.1616	0.890275
$566$	−55.0220	−2.31275
$567$	−23.8387	−1.00113
$568$	20.7220	0.869477
$569$	−5.12423	−0.214819	−0.107410	−	0.994215i	$-0.534256\pi$
$569$	−5.12423	−0.214819	−0.107410	+	0.994215i	$0.534256\pi$
$570$	91.4592	3.83080
$571$	−0.674828	−0.0282407	−0.0141203	−	0.999900i	$-0.504495\pi$
$571$	−0.674828	−0.0282407	−0.0141203	+	0.999900i	$0.504495\pi$
$572$	12.1355	0.507411
$573$	55.4757	2.31753
$574$	−43.8560	−1.83051
$575$	0.662611	0.0276328
$576$	−0.292303	−0.0121793
$577$	−18.0723	−0.752362	−0.376181	−	0.926546i	$-0.622763\pi$
$577$	−18.0723	−0.752362	−0.376181	+	0.926546i	$0.622763\pi$
$578$	−14.0767	−0.585514
$579$	−62.7530	−2.60793
$580$	21.0554	0.874279
$581$	20.9494	0.869127
$582$	−65.1876	−2.70211
$583$	−0.254233	−0.0105293
$584$	25.0781	1.03774
$585$	22.7463	0.940444
$586$	−44.0665	−1.82037
$587$	−38.8470	−1.60339	−0.801693	−	0.597736i	$-0.796067\pi$
$587$	−38.8470	−1.60339	−0.801693	+	0.597736i	$0.796067\pi$
$588$	43.8132	1.80683
$589$	42.1865	1.73827
$590$	5.58808	0.230057
$591$	26.5291	1.09126
$592$	−40.1710	−1.65102
$593$	−28.1628	−1.15651	−0.578253	−	0.815858i	$-0.696265\pi$
$593$	−28.1628	−1.15651	−0.578253	+	0.815858i	$0.696265\pi$
$594$	33.3128	1.36684
$595$	15.7230	0.644579
$596$	14.8718	0.609171
$597$	−64.1754	−2.62652
$598$	1.68317	0.0688298
$599$	8.01136	0.327335	0.163668	−	0.986516i	$-0.447668\pi$
$599$	8.01136	0.327335	0.163668	+	0.986516i	$0.447668\pi$
$600$	−41.1157	−1.67854
$601$	−31.6868	−1.29253	−0.646265	−	0.763113i	$-0.723670\pi$
$601$	−31.6868	−1.29253	−0.646265	+	0.763113i	$0.723670\pi$
$602$	13.7429	0.560117
$603$	28.2844	1.15183
$604$	−37.3014	−1.51777
$605$	−15.8949	−0.646219
$606$	−98.5184	−4.00204
$607$	−1.05334	−0.0427538	−0.0213769	−	0.999771i	$-0.506805\pi$
$607$	−1.05334	−0.0427538	−0.0213769	+	0.999771i	$0.506805\pi$
$608$	−38.9312	−1.57887
$609$	16.4750	0.667603
$610$	−5.57533	−0.225739
$611$	2.22600	0.0900545
$612$	−135.241	−5.46679
$613$	−18.1006	−0.731075	−0.365538	−	0.930797i	$-0.619115\pi$
$613$	−18.1006	−0.731075	−0.365538	+	0.930797i	$0.619115\pi$
$614$	−21.5908	−0.871335
$615$	45.7622	1.84531
$616$	15.8483	0.638545
$617$	4.02776	0.162152	0.0810758	−	0.996708i	$-0.474164\pi$
$617$	4.02776	0.162152	0.0810758	+	0.996708i	$0.474164\pi$
$618$	−19.6672	−0.791131
$619$	−25.7600	−1.03538	−0.517690	−	0.855568i	$-0.673208\pi$
$619$	−25.7600	−1.03538	−0.517690	+	0.855568i	$0.673208\pi$
$620$	46.4944	1.86726
$621$	3.19693	0.128288
$622$	68.7414	2.75628
$623$	10.6098	0.425073
$624$	−46.4381	−1.85901
$625$	−9.91798	−0.396719
$626$	16.9536	0.677601
$627$	−27.0487	−1.08022
$628$	102.680	4.09737
$629$	26.5085	1.05696
$630$	53.5485	2.13342
$631$	5.70380	0.227065	0.113532	−	0.993534i	$-0.463783\pi$
$631$	5.70380	0.227065	0.113532	+	0.993534i	$0.463783\pi$
$632$	93.6182	3.72393
$633$	56.0379	2.22731
$634$	−4.84462	−0.192404
$635$	30.7033	1.21842
$636$	2.72908	0.108215
$637$	−6.74023	−0.267058
$638$	−8.99973	−0.356303
$639$	−20.7070	−0.819155
$640$	19.3040	0.763059
$641$	13.3053	0.525526	0.262763	−	0.964860i	$-0.415366\pi$
$641$	13.3053	0.525526	0.262763	+	0.964860i	$0.415366\pi$
$642$	43.0955	1.70084
$643$	−6.25771	−0.246780	−0.123390	−	0.992358i	$-0.539377\pi$
$643$	−6.25771	−0.246780	−0.123390	+	0.992358i	$0.539377\pi$
$644$	2.74168	0.108037
$645$	−14.3402	−0.564645
$646$	83.6554	3.29138
$647$	−13.2687	−0.521646	−0.260823	−	0.965387i	$-0.583994\pi$
$647$	−13.2687	−0.521646	−0.260823	+	0.965387i	$0.583994\pi$
$648$	−77.5453	−3.04627
$649$	−1.65265	−0.0648722
$650$	11.4023	0.447233
$651$	36.3801	1.42585
$652$	59.2514	2.32047
$653$	−35.0646	−1.37218	−0.686091	−	0.727516i	$-0.740675\pi$
$653$	−35.0646	−1.37218	−0.686091	+	0.727516i	$0.740675\pi$
$654$	70.9353	2.77379
$655$	36.0958	1.41038
$656$	−63.4309	−2.47656
$657$	−25.0599	−0.977679
$658$	5.24038	0.204291
$659$	−17.9489	−0.699192	−0.349596	−	0.936901i	$-0.613681\pi$
$659$	−17.9489	−0.699192	−0.349596	+	0.936901i	$0.613681\pi$
$660$	−29.8108	−1.16038
$661$	31.8572	1.23910	0.619551	−	0.784956i	$-0.287315\pi$
$661$	31.8572	1.23910	0.619551	+	0.784956i	$0.287315\pi$
$662$	−42.9425	−1.66901
$663$	30.6441	1.19012
$664$	68.1468	2.64461
$665$	−22.9185	−0.888742
$666$	90.2816	3.49834
$667$	−0.863677	−0.0334417
$668$	15.2004	0.588122
$669$	45.0242	1.74073
$670$	−19.2823	−0.744942
$671$	1.64888	0.0636543
$672$	−33.5728	−1.29510
$673$	−25.1467	−0.969334	−0.484667	−	0.874699i	$-0.661059\pi$
$673$	−25.1467	−0.969334	−0.484667	+	0.874699i	$0.661059\pi$
$674$	34.9367	1.34571
$675$	21.6569	0.833575
$676$	−38.3518	−1.47507
$677$	29.6637	1.14007	0.570035	−	0.821621i	$-0.306930\pi$
$677$	29.6637	1.14007	0.570035	+	0.821621i	$0.306930\pi$
$678$	97.0952	3.72892
$679$	16.3352	0.626887
$680$	51.1456	1.96134
$681$	25.6664	0.983537
$682$	−19.8731	−0.760982
$683$	13.3108	0.509325	0.254662	−	0.967030i	$-0.418036\pi$
$683$	13.3108	0.509325	0.254662	+	0.967030i	$0.418036\pi$
$684$	197.134	7.53759
$685$	10.5685	0.403803
$686$	−50.6760	−1.93482
$687$	−63.2389	−2.41272
$688$	19.8769	0.757800
$689$	−0.419842	−0.0159947
$690$	−4.13468	−0.157404
$691$	22.1038	0.840867	0.420433	−	0.907323i	$-0.361878\pi$
$691$	22.1038	0.840867	0.420433	+	0.907323i	$0.361878\pi$
$692$	−5.92685	−0.225305
$693$	−15.8368	−0.601588
$694$	−6.69239	−0.254040
$695$	14.8478	0.563210
$696$	53.5921	2.03140
$697$	41.8576	1.58547
$698$	−46.3285	−1.75356
$699$	67.7963	2.56429
$700$	18.5729	0.701991
$701$	33.2557	1.25605	0.628026	−	0.778192i	$-0.283863\pi$
$701$	33.2557	1.25605	0.628026	+	0.778192i	$0.283863\pi$
$702$	55.0129	2.07633
$703$	−38.6401	−1.45734
$704$	−0.0589339	−0.00222115
$705$	−5.46815	−0.205943
$706$	74.0746	2.78784
$707$	24.6875	0.928467
$708$	17.7405	0.666727
$709$	−21.4090	−0.804033	−0.402016	−	0.915633i	$-0.631690\pi$
$709$	−21.4090	−0.804033	−0.402016	+	0.915633i	$0.631690\pi$
$710$	14.1166	0.529786
$711$	−93.5502	−3.50841
$712$	34.5129	1.29343
$713$	−1.90716	−0.0714239
$714$	72.1413	2.69982
$715$	4.58609	0.171510
$716$	26.9533	1.00729
$717$	−7.99989	−0.298761
$718$	51.3598	1.91673
$719$	−34.4595	−1.28512	−0.642561	−	0.766234i	$-0.722128\pi$
$719$	−34.4595	−1.28512	−0.642561	+	0.766234i	$0.722128\pi$
$720$	77.4497	2.88638
$721$	4.92835	0.183541
$722$	−73.5302	−2.73651
$723$	−11.8886	−0.442141
$724$	7.11175	0.264306
$725$	−5.85080	−0.217293
$726$	−72.9301	−2.70669
$727$	0.0869977	0.00322657	0.00161328	−	0.999999i	$-0.499486\pi$
$727$	0.0869977	0.00322657	0.00161328	+	0.999999i	$0.499486\pi$
$728$	26.1719	0.969995
$729$	−16.2507	−0.601876
$730$	17.0841	0.632310
$731$	−13.1166	−0.485136
$732$	−17.7000	−0.654211
$733$	−30.1407	−1.11327	−0.556636	−	0.830757i	$-0.687908\pi$
$733$	−30.1407	−1.11327	−0.556636	+	0.830757i	$0.687908\pi$
$734$	−23.8001	−0.878477
$735$	16.5573	0.610725
$736$	1.76000	0.0648744
$737$	5.70267	0.210060
$738$	142.557	5.24758
$739$	−12.4239	−0.457021	−0.228510	−	0.973541i	$-0.573385\pi$
$739$	−12.4239	−0.457021	−0.228510	+	0.973541i	$0.573385\pi$
$740$	−42.5858	−1.56549
$741$	−44.6683	−1.64093
$742$	−0.988377	−0.0362845
$743$	−36.1729	−1.32705	−0.663527	−	0.748152i	$-0.730941\pi$
$743$	−36.1729	−1.32705	−0.663527	+	0.748152i	$0.730941\pi$
$744$	118.342	4.33861
$745$	5.62013	0.205906
$746$	−38.5811	−1.41255
$747$	−68.0972	−2.49155
$748$	−27.2672	−0.996986
$749$	−10.7992	−0.394594
$750$	−94.1114	−3.43646
$751$	34.6758	1.26534	0.632670	−	0.774422i	$-0.281959\pi$
$751$	34.6758	1.26534	0.632670	+	0.774422i	$0.281959\pi$
$752$	7.57940	0.276392
$753$	48.4846	1.76688
$754$	−14.8622	−0.541249
$755$	−14.0965	−0.513023
$756$	89.6096	3.25907
$757$	7.74052	0.281334	0.140667	−	0.990057i	$-0.455075\pi$
$757$	7.74052	0.281334	0.140667	+	0.990057i	$0.455075\pi$
$758$	16.2832	0.591432
$759$	1.22281	0.0443853
$760$	−74.5522	−2.70429
$761$	−48.6175	−1.76238	−0.881191	−	0.472760i	$-0.843258\pi$
$761$	−48.6175	−1.76238	−0.881191	+	0.472760i	$0.843258\pi$
$762$	140.875	5.10337
$763$	−17.7755	−0.643516
$764$	−81.5172	−2.94919
$765$	−51.1084	−1.84783
$766$	−0.310938	−0.0112346
$767$	−2.72919	−0.0985455
$768$	88.2906	3.18591
$769$	0.979541	0.0353231	0.0176616	−	0.999844i	$-0.494378\pi$
$769$	0.979541	0.0353231	0.0176616	+	0.999844i	$0.494378\pi$
$770$	10.7964	0.389075
$771$	42.2807	1.52270
$772$	92.2106	3.31873
$773$	1.19604	0.0430186	0.0215093	−	0.999769i	$-0.493153\pi$
$773$	1.19604	0.0430186	0.0215093	+	0.999769i	$0.493153\pi$
$774$	−44.6720	−1.60570
$775$	−12.9197	−0.464089
$776$	53.1371	1.90751
$777$	−33.3217	−1.19541
$778$	−16.4088	−0.588286
$779$	−61.0135	−2.18604
$780$	−49.2296	−1.76270
$781$	−4.17492	−0.149390
$782$	−3.78189	−0.135240
$783$	−28.2286	−1.00881
$784$	−22.9500	−0.819644
$785$	38.8033	1.38495
$786$	165.617	5.90738
$787$	−22.6952	−0.808997	−0.404499	−	0.914539i	$-0.632554\pi$
$787$	−22.6952	−0.808997	−0.404499	+	0.914539i	$0.632554\pi$
$788$	−38.9824	−1.38869
$789$	84.3681	3.00358
$790$	63.7761	2.26905
$791$	−24.3308	−0.865105
$792$	−51.5158	−1.83053
$793$	2.72297	0.0966954
$794$	54.4960	1.93399
$795$	1.03134	0.0365778
$796$	94.3007	3.34240
$797$	31.4101	1.11260	0.556301	−	0.830981i	$-0.312220\pi$
$797$	31.4101	1.11260	0.556301	+	0.830981i	$0.312220\pi$
$798$	−105.156	−3.72250
$799$	−5.00159	−0.176943
$800$	11.9227	0.421532
$801$	−34.4879	−1.21857
$802$	3.07376	0.108538
$803$	−5.05255	−0.178300
$804$	−61.2156	−2.15891
$805$	1.03610	0.0365177
$806$	−32.8186	−1.15599
$807$	5.50400	0.193750
$808$	80.3064	2.82517
$809$	19.1638	0.673764	0.336882	−	0.941547i	$-0.390628\pi$
$809$	19.1638	0.673764	0.336882	+	0.941547i	$0.390628\pi$
$810$	−52.8266	−1.85614
$811$	39.6043	1.39070	0.695348	−	0.718673i	$-0.255250\pi$
$811$	39.6043	1.39070	0.695348	+	0.718673i	$0.255250\pi$
$812$	−24.2088	−0.849562
$813$	20.2620	0.710620
$814$	18.2025	0.637997
$815$	22.3915	0.784340
$816$	104.341	3.65267
$817$	19.1194	0.668903
$818$	−71.9791	−2.51669
$819$	−26.1529	−0.913856
$820$	−67.2440	−2.34826
$821$	36.9958	1.29116	0.645582	−	0.763691i	$-0.276615\pi$
$821$	36.9958	1.29116	0.645582	+	0.763691i	$0.276615\pi$
$822$	48.4914	1.69133
$823$	20.1681	0.703016	0.351508	−	0.936185i	$-0.385669\pi$
$823$	20.1681	0.703016	0.351508	+	0.936185i	$0.385669\pi$
$824$	16.0316	0.558486
$825$	8.28369	0.288401
$826$	−6.42497	−0.223553
$827$	39.7977	1.38390	0.691951	−	0.721945i	$-0.256751\pi$
$827$	39.7977	1.38390	0.691951	+	0.721945i	$0.256751\pi$
$828$	−8.91199	−0.309713
$829$	13.1943	0.458256	0.229128	−	0.973396i	$-0.426412\pi$
$829$	13.1943	0.458256	0.229128	+	0.973396i	$0.426412\pi$
$830$	46.4240	1.61140
$831$	48.7587	1.69142
$832$	−0.0973236	−0.00337409
$833$	15.1446	0.524728
$834$	68.1259	2.35901
$835$	5.74434	0.198791
$836$	39.7459	1.37464
$837$	−62.3341	−2.15458
$838$	−6.52116	−0.225270
$839$	34.5099	1.19141	0.595707	−	0.803202i	$-0.296872\pi$
$839$	34.5099	1.19141	0.595707	+	0.803202i	$0.296872\pi$
$840$	−64.2910	−2.21825
$841$	−21.3738	−0.737028
$842$	79.6310	2.74427
$843$	45.9991	1.58429
$844$	−82.3433	−2.83437
$845$	−14.4934	−0.498587
$846$	−17.0342	−0.585647
$847$	18.2754	0.627949
$848$	−1.42953	−0.0490904
$849$	−66.0120	−2.26553
$850$	−25.6196	−0.878745
$851$	1.74684	0.0598808
$852$	44.8159	1.53537
$853$	−19.8552	−0.679828	−0.339914	−	0.940456i	$-0.610398\pi$
$853$	−19.8552	−0.679828	−0.339914	+	0.940456i	$0.610398\pi$
$854$	6.41031	0.219356
$855$	74.4980	2.54778
$856$	−35.1289	−1.20068
$857$	−30.3386	−1.03635	−0.518173	−	0.855276i	$-0.673388\pi$
$857$	−30.3386	−1.03635	−0.518173	+	0.855276i	$0.673388\pi$
$858$	21.0422	0.718370
$859$	−30.2650	−1.03263	−0.516315	−	0.856399i	$-0.672696\pi$
$859$	−30.2650	−1.03263	−0.516315	+	0.856399i	$0.672696\pi$
$860$	21.0718	0.718542
$861$	−52.6158	−1.79314
$862$	−47.0641	−1.60301
$863$	−47.6875	−1.62330	−0.811651	−	0.584143i	$-0.801431\pi$
$863$	−47.6875	−1.62330	−0.811651	+	0.584143i	$0.801431\pi$
$864$	57.5241	1.95701
$865$	−2.23980	−0.0761553
$866$	−42.5189	−1.44485
$867$	−16.8884	−0.573559
$868$	−53.4576	−1.81447
$869$	−18.8615	−0.639832
$870$	36.5088	1.23777
$871$	9.41741	0.319097
$872$	−57.8223	−1.95811
$873$	−53.0985	−1.79711
$874$	5.51265	0.186468
$875$	23.5831	0.797255
$876$	54.2368	1.83249
$877$	18.0714	0.610229	0.305115	−	0.952316i	$-0.401305\pi$
$877$	18.0714	0.610229	0.305115	+	0.952316i	$0.401305\pi$
$878$	−13.8444	−0.467227
$879$	−52.8683	−1.78320
$880$	15.6153	0.526392
$881$	16.2125	0.546213	0.273107	−	0.961984i	$-0.411949\pi$
$881$	16.2125	0.546213	0.273107	+	0.961984i	$0.411949\pi$
$882$	51.5786	1.73674
$883$	37.3852	1.25811	0.629056	−	0.777360i	$-0.283442\pi$
$883$	37.3852	1.25811	0.629056	+	0.777360i	$0.283442\pi$
$884$	−45.0291	−1.51449
$885$	6.70423	0.225360
$886$	−51.5417	−1.73158
$887$	4.92612	0.165403	0.0827014	−	0.996574i	$-0.473645\pi$
$887$	4.92612	0.165403	0.0827014	+	0.996574i	$0.473645\pi$
$888$	−108.393	−3.63743
$889$	−35.3016	−1.18398
$890$	23.5114	0.788105
$891$	15.6233	0.523399
$892$	−66.1594	−2.21518
$893$	7.29054	0.243969
$894$	25.7867	0.862437
$895$	10.1858	0.340475
$896$	−22.1951	−0.741486
$897$	2.01936	0.0674245
$898$	82.8926	2.76616
$899$	16.8401	0.561648
$900$	−60.3724	−2.01241
$901$	0.943338	0.0314272
$902$	28.7421	0.957008
$903$	16.4878	0.548681
$904$	−79.1464	−2.63237
$905$	2.68758	0.0893380
$906$	−64.6784	−2.14880
$907$	28.4442	0.944474	0.472237	−	0.881472i	$-0.343447\pi$
$907$	28.4442	0.944474	0.472237	+	0.881472i	$0.343447\pi$
$908$	−37.7147	−1.25161
$909$	−80.2481	−2.66166
$910$	17.8292	0.591033
$911$	−8.58577	−0.284459	−0.142230	−	0.989834i	$-0.545427\pi$
$911$	−8.58577	−0.284459	−0.142230	+	0.989834i	$0.545427\pi$
$912$	−152.093	−5.03629
$913$	−13.7297	−0.454387
$914$	21.3667	0.706746
$915$	−6.68894	−0.221130
$916$	92.9246	3.07032
$917$	−41.5016	−1.37050
$918$	−123.608	−4.07967
$919$	23.6006	0.778513	0.389257	−	0.921129i	$-0.372732\pi$
$919$	23.6006	0.778513	0.389257	+	0.921129i	$0.372732\pi$
$920$	3.37035	0.111117
$921$	−25.9034	−0.853545
$922$	73.5857	2.42342
$923$	−6.89448	−0.226935
$924$	34.2753	1.12758
$925$	11.8336	0.389086
$926$	23.6747	0.777999
$927$	−16.0199	−0.526163
$928$	−15.5406	−0.510146
$929$	28.0146	0.919128	0.459564	−	0.888145i	$-0.348006\pi$
$929$	28.0146	0.919128	0.459564	+	0.888145i	$0.348006\pi$
$930$	80.6185	2.64358
$931$	−22.0754	−0.723492
$932$	−99.6213	−3.26320
$933$	82.4717	2.70000
$934$	3.39476	0.111080
$935$	−10.3044	−0.336991
$936$	−85.0734	−2.78071
$937$	−34.4427	−1.12520	−0.562598	−	0.826731i	$-0.690198\pi$
$937$	−34.4427	−1.12520	−0.562598	+	0.826731i	$0.690198\pi$
$938$	22.1701	0.723881
$939$	20.3399	0.663767
$940$	8.03502	0.262074
$941$	−9.61440	−0.313420	−0.156710	−	0.987645i	$-0.550089\pi$
$941$	−9.61440	−0.313420	−0.156710	+	0.987645i	$0.550089\pi$
$942$	178.040	5.80087
$943$	2.75829	0.0898224
$944$	−9.29272	−0.302452
$945$	33.8640	1.10160
$946$	−9.00672	−0.292834
$947$	−31.7865	−1.03292	−0.516461	−	0.856310i	$-0.672751\pi$
$947$	−31.7865	−1.03292	−0.516461	+	0.856310i	$0.672751\pi$
$948$	202.470	6.57591
$949$	−8.34380	−0.270851
$950$	37.3443	1.21161
$951$	−5.81228	−0.188476
$952$	−58.8054	−1.90589
$953$	48.9178	1.58460	0.792302	−	0.610129i	$-0.208882\pi$
$953$	48.9178	1.58460	0.792302	+	0.610129i	$0.208882\pi$
$954$	3.21278	0.104018
$955$	−30.8059	−0.996855
$956$	11.7552	0.380191
$957$	−10.7973	−0.349028
$958$	−55.0015	−1.77702
$959$	−12.1513	−0.392387
$960$	0.239074	0.00771609
$961$	6.18614	0.199553
$962$	30.0597	0.969163
$963$	35.1034	1.13119
$964$	17.4693	0.562649
$965$	34.8470	1.12176
$966$	4.75390	0.152954
$967$	−35.3648	−1.13725	−0.568627	−	0.822595i	$-0.692525\pi$
$967$	−35.3648	−1.13725	−0.568627	+	0.822595i	$0.692525\pi$
$968$	59.4484	1.91074
$969$	100.365	3.22418
$970$	36.1989	1.16228
$971$	27.7055	0.889113	0.444556	−	0.895751i	$-0.353361\pi$
$971$	27.7055	0.889113	0.444556	+	0.895751i	$0.353361\pi$
$972$	−29.9657	−0.961150
$973$	−17.0715	−0.547286
$974$	−44.3822	−1.42210
$975$	13.6797	0.438102
$976$	9.27153	0.296774
$977$	25.9738	0.830974	0.415487	−	0.909599i	$-0.363611\pi$
$977$	25.9738	0.830974	0.415487	+	0.909599i	$0.363611\pi$
$978$	102.738	3.28521
$979$	−6.95341	−0.222232
$980$	−24.3297	−0.777182
$981$	57.7803	1.84478
$982$	4.73681	0.151158
$983$	−1.36130	−0.0434187	−0.0217094	−	0.999764i	$-0.506911\pi$
$983$	−1.36130	−0.0434187	−0.0217094	+	0.999764i	$0.506911\pi$
$984$	−171.155	−5.45623
$985$	−14.7317	−0.469391
$986$	33.3937	1.06347
$987$	6.28709	0.200120
$988$	65.6365	2.08818
$989$	−0.864348	−0.0274847
$990$	−35.0944	−1.11537
$991$	−7.15478	−0.227279	−0.113639	−	0.993522i	$-0.536251\pi$
$991$	−7.15478	−0.227279	−0.113639	+	0.993522i	$0.536251\pi$
$992$	−34.3167	−1.08956
$993$	−51.5198	−1.63493
$994$	−16.2307	−0.514808
$995$	35.6368	1.12976
$996$	147.382	4.66998
$997$	−41.9249	−1.32777	−0.663887	−	0.747833i	$-0.731094\pi$
$997$	−41.9249	−1.32777	−0.663887	+	0.747833i	$0.731094\pi$
$998$	74.9738	2.37325
$999$	57.0939	1.80637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.12	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} +O(q^{10})\)	\(q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} -4.32491 q^{10} +1.27907 q^{11} -13.7303 q^{12} +2.11227 q^{13} +4.97263 q^{14} -5.18877 q^{15} +7.19214 q^{16} -4.74604 q^{17} -16.1638 q^{18} +6.91804 q^{19} +7.62448 q^{20} +5.96586 q^{21} -3.25894 q^{22} -0.312750 q^{23} +19.4065 q^{24} -2.11866 q^{25} -5.38182 q^{26} -10.2220 q^{27} -8.76636 q^{28} +2.76156 q^{29} +13.2204 q^{30} +6.09804 q^{31} -5.62749 q^{32} -3.90987 q^{33} +12.0924 q^{34} -3.31286 q^{35} +28.4956 q^{36} -5.58541 q^{37} -17.6264 q^{38} -6.45678 q^{39} -10.7765 q^{40} -8.81948 q^{41} -15.2003 q^{42} +2.76370 q^{43} +5.74525 q^{44} +10.7687 q^{45} +0.796852 q^{46} +1.05384 q^{47} -21.9849 q^{48} -3.19099 q^{49} +5.39810 q^{50} +14.5077 q^{51} +9.48773 q^{52} -0.198763 q^{53} +26.0445 q^{54} +2.17117 q^{55} +12.3904 q^{56} -21.1471 q^{57} -7.03613 q^{58} -1.29207 q^{59} -23.3065 q^{60} +1.28912 q^{61} -15.5371 q^{62} -12.3814 q^{63} -0.0460754 q^{64} +3.58547 q^{65} +9.96191 q^{66} +4.45843 q^{67} -21.3179 q^{68} +0.956014 q^{69} +8.44079 q^{70} -3.26402 q^{71} -40.2758 q^{72} -3.95016 q^{73} +14.2310 q^{74} +6.47632 q^{75} +31.0739 q^{76} -2.49633 q^{77} +16.4511 q^{78} -14.7462 q^{79} +12.2083 q^{80} +12.2145 q^{81} +22.4710 q^{82} -10.7341 q^{83} +26.7970 q^{84} -8.05616 q^{85} -7.04160 q^{86} -8.44152 q^{87} -8.12037 q^{88} -5.43628 q^{89} -27.4373 q^{90} -4.12245 q^{91} -1.40479 q^{92} -18.6405 q^{93} -2.68508 q^{94} +11.7430 q^{95} +17.2021 q^{96} -8.36985 q^{97} +8.13028 q^{98} +8.11447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 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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