LMFDB - Embedded newform 4007.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55145 q^{2} -0.786154 q^{3} +4.50991 q^{4} +3.16082 q^{5} +2.00584 q^{6} -3.53434 q^{7} -6.40393 q^{8} -2.38196 q^{9} +O(q^{10})$	\(q-2.55145 q^{2} -0.786154 q^{3} +4.50991 q^{4} +3.16082 q^{5} +2.00584 q^{6} -3.53434 q^{7} -6.40393 q^{8} -2.38196 q^{9} -8.06468 q^{10} -2.65345 q^{11} -3.54549 q^{12} -5.56342 q^{13} +9.01770 q^{14} -2.48489 q^{15} +7.31950 q^{16} +6.86387 q^{17} +6.07746 q^{18} -2.83267 q^{19} +14.2550 q^{20} +2.77854 q^{21} +6.77016 q^{22} -5.23765 q^{23} +5.03447 q^{24} +4.99076 q^{25} +14.1948 q^{26} +4.23105 q^{27} -15.9396 q^{28} -4.65163 q^{29} +6.34008 q^{30} -9.19866 q^{31} -5.86750 q^{32} +2.08602 q^{33} -17.5128 q^{34} -11.1714 q^{35} -10.7424 q^{36} -4.60653 q^{37} +7.22742 q^{38} +4.37371 q^{39} -20.2416 q^{40} +6.75656 q^{41} -7.08930 q^{42} -4.15206 q^{43} -11.9668 q^{44} -7.52895 q^{45} +13.3636 q^{46} +4.42979 q^{47} -5.75425 q^{48} +5.49156 q^{49} -12.7337 q^{50} -5.39606 q^{51} -25.0906 q^{52} +8.08584 q^{53} -10.7953 q^{54} -8.38708 q^{55} +22.6337 q^{56} +2.22691 q^{57} +11.8684 q^{58} -12.9765 q^{59} -11.2066 q^{60} -1.44137 q^{61} +23.4699 q^{62} +8.41866 q^{63} +0.331652 q^{64} -17.5850 q^{65} -5.32239 q^{66} -4.42265 q^{67} +30.9555 q^{68} +4.11760 q^{69} +28.5033 q^{70} -9.81626 q^{71} +15.2539 q^{72} +3.52549 q^{73} +11.7533 q^{74} -3.92351 q^{75} -12.7751 q^{76} +9.37821 q^{77} -11.1593 q^{78} +6.22198 q^{79} +23.1356 q^{80} +3.81963 q^{81} -17.2391 q^{82} -9.73280 q^{83} +12.5310 q^{84} +21.6954 q^{85} +10.5938 q^{86} +3.65690 q^{87} +16.9925 q^{88} -5.28644 q^{89} +19.2098 q^{90} +19.6630 q^{91} -23.6214 q^{92} +7.23156 q^{93} -11.3024 q^{94} -8.95355 q^{95} +4.61276 q^{96} +16.7863 q^{97} -14.0115 q^{98} +6.32043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.55145	−1.80415	−0.902075	−	0.431579i	$-0.857956\pi$
$2$	−2.55145	−1.80415	−0.902075	+	0.431579i	$0.857956\pi$
$3$	−0.786154	−0.453886	−0.226943	−	0.973908i	$-0.572873\pi$
$3$	−0.786154	−0.453886	−0.226943	+	0.973908i	$0.572873\pi$
$4$	4.50991	2.25496
$5$	3.16082	1.41356	0.706780	−	0.707433i	$-0.250147\pi$
$5$	3.16082	1.41356	0.706780	+	0.707433i	$0.250147\pi$
$6$	2.00584	0.818879
$7$	−3.53434	−1.33586	−0.667928	−	0.744226i	$-0.732818\pi$
$7$	−3.53434	−1.33586	−0.667928	+	0.744226i	$0.732818\pi$
$8$	−6.40393	−2.26413
$9$	−2.38196	−0.793987
$10$	−8.06468	−2.55027
$11$	−2.65345	−0.800046	−0.400023	−	0.916505i	$-0.630998\pi$
$11$	−2.65345	−0.800046	−0.400023	+	0.916505i	$0.630998\pi$
$12$	−3.54549	−1.02349
$13$	−5.56342	−1.54302	−0.771508	−	0.636219i	$-0.780497\pi$
$13$	−5.56342	−1.54302	−0.771508	+	0.636219i	$0.780497\pi$
$14$	9.01770	2.41008
$15$	−2.48489	−0.641596
$16$	7.31950	1.82987
$17$	6.86387	1.66473	0.832367	−	0.554225i	$-0.186985\pi$
$17$	6.86387	1.66473	0.832367	+	0.554225i	$0.186985\pi$
$18$	6.07746	1.43247
$19$	−2.83267	−0.649859	−0.324929	−	0.945738i	$-0.605341\pi$
$19$	−2.83267	−0.649859	−0.324929	+	0.945738i	$0.605341\pi$
$20$	14.2550	3.18752
$21$	2.77854	0.606326
$22$	6.77016	1.44340
$23$	−5.23765	−1.09213	−0.546063	−	0.837744i	$-0.683874\pi$
$23$	−5.23765	−1.09213	−0.546063	+	0.837744i	$0.683874\pi$
$24$	5.03447	1.02766
$25$	4.99076	0.998153
$26$	14.1948	2.78383
$27$	4.23105	0.814266
$28$	−15.9396	−3.01230
$29$	−4.65163	−0.863787	−0.431893	−	0.901925i	$-0.642154\pi$
$29$	−4.65163	−0.863787	−0.431893	+	0.901925i	$0.642154\pi$
$30$	6.34008	1.15753
$31$	−9.19866	−1.65213	−0.826064	−	0.563577i	$-0.809425\pi$
$31$	−9.19866	−1.65213	−0.826064	+	0.563577i	$0.809425\pi$
$32$	−5.86750	−1.03724
$33$	2.08602	0.363130
$34$	−17.5128	−3.00343
$35$	−11.1714	−1.88831
$36$	−10.7424	−1.79041
$37$	−4.60653	−0.757308	−0.378654	−	0.925538i	$-0.623613\pi$
$37$	−4.60653	−0.757308	−0.378654	+	0.925538i	$0.623613\pi$
$38$	7.22742	1.17244
$39$	4.37371	0.700354
$40$	−20.2416	−3.20049
$41$	6.75656	1.05520	0.527599	−	0.849494i	$-0.323092\pi$
$41$	6.75656	1.05520	0.527599	+	0.849494i	$0.323092\pi$
$42$	−7.08930	−1.09390
$43$	−4.15206	−0.633183	−0.316592	−	0.948562i	$-0.602538\pi$
$43$	−4.15206	−0.633183	−0.316592	+	0.948562i	$0.602538\pi$
$44$	−11.9668	−1.80407
$45$	−7.52895	−1.12235
$46$	13.3636	1.97036
$47$	4.42979	0.646151	0.323075	−	0.946373i	$-0.395283\pi$
$47$	4.42979	0.646151	0.323075	+	0.946373i	$0.395283\pi$
$48$	−5.75425	−0.830555
$49$	5.49156	0.784509
$50$	−12.7337	−1.80082
$51$	−5.39606	−0.755600
$52$	−25.0906	−3.47944
$53$	8.08584	1.11067	0.555337	−	0.831625i	$-0.312589\pi$
$53$	8.08584	1.11067	0.555337	+	0.831625i	$0.312589\pi$
$54$	−10.7953	−1.46906
$55$	−8.38708	−1.13091
$56$	22.6337	3.02455
$57$	2.22691	0.294962
$58$	11.8684	1.55840
$59$	−12.9765	−1.68940	−0.844698	−	0.535244i	$-0.820220\pi$
$59$	−12.9765	−1.68940	−0.844698	+	0.535244i	$0.820220\pi$
$60$	−11.2066	−1.44677
$61$	−1.44137	−0.184548	−0.0922740	−	0.995734i	$-0.529414\pi$
$61$	−1.44137	−0.184548	−0.0922740	+	0.995734i	$0.529414\pi$
$62$	23.4699	2.98069
$63$	8.41866	1.06065
$64$	0.331652	0.0414565
$65$	−17.5850	−2.18115
$66$	−5.32239	−0.655141
$67$	−4.42265	−0.540313	−0.270157	−	0.962816i	$-0.587075\pi$
$67$	−4.42265	−0.540313	−0.270157	+	0.962816i	$0.587075\pi$
$68$	30.9555	3.75390
$69$	4.11760	0.495701
$70$	28.5033	3.40680
$71$	−9.81626	−1.16498	−0.582488	−	0.812839i	$-0.697921\pi$
$71$	−9.81626	−1.16498	−0.582488	+	0.812839i	$0.697921\pi$
$72$	15.2539	1.79769
$73$	3.52549	0.412627	0.206314	−	0.978486i	$-0.433853\pi$
$73$	3.52549	0.412627	0.206314	+	0.978486i	$0.433853\pi$
$74$	11.7533	1.36630
$75$	−3.92351	−0.453048
$76$	−12.7751	−1.46540
$77$	9.37821	1.06875
$78$	−11.1593	−1.26354
$79$	6.22198	0.700028	0.350014	−	0.936745i	$-0.386177\pi$
$79$	6.22198	0.700028	0.350014	+	0.936745i	$0.386177\pi$
$80$	23.1356	2.58664
$81$	3.81963	0.424403
$82$	−17.2391	−1.90374
$83$	−9.73280	−1.06831	−0.534157	−	0.845385i	$-0.679371\pi$
$83$	−9.73280	−1.06831	−0.534157	+	0.845385i	$0.679371\pi$
$84$	12.5310	1.36724
$85$	21.6954	2.35320
$86$	10.5938	1.14236
$87$	3.65690	0.392061
$88$	16.9925	1.81141
$89$	−5.28644	−0.560361	−0.280181	−	0.959947i	$-0.590394\pi$
$89$	−5.28644	−0.560361	−0.280181	+	0.959947i	$0.590394\pi$
$90$	19.2098	2.02489
$91$	19.6630	2.06125
$92$	−23.6214	−2.46270
$93$	7.23156	0.749878
$94$	−11.3024	−1.16575
$95$	−8.95355	−0.918615
$96$	4.61276	0.470788
$97$	16.7863	1.70439	0.852196	−	0.523222i	$-0.175270\pi$
$97$	16.7863	1.70439	0.852196	+	0.523222i	$0.175270\pi$
$98$	−14.0115	−1.41537
$99$	6.32043	0.635227
$100$	22.5079	2.25079
$101$	18.5361	1.84441	0.922204	−	0.386704i	$-0.126386\pi$
$101$	18.5361	1.84441	0.922204	+	0.386704i	$0.126386\pi$
$102$	13.7678	1.36322
$103$	13.0140	1.28231	0.641156	−	0.767411i	$-0.278455\pi$
$103$	13.0140	1.28231	0.641156	+	0.767411i	$0.278455\pi$
$104$	35.6278	3.49359
$105$	8.78244	0.857079
$106$	−20.6306	−2.00382
$107$	14.1471	1.36765	0.683824	−	0.729647i	$-0.260316\pi$
$107$	14.1471	1.36765	0.683824	+	0.729647i	$0.260316\pi$
$108$	19.0817	1.83614
$109$	3.57189	0.342125	0.171063	−	0.985260i	$-0.445280\pi$
$109$	3.57189	0.342125	0.171063	+	0.985260i	$0.445280\pi$
$110$	21.3992	2.04034
$111$	3.62144	0.343732
$112$	−25.8696	−2.44445
$113$	−3.66405	−0.344685	−0.172342	−	0.985037i	$-0.555134\pi$
$113$	−3.66405	−0.344685	−0.172342	+	0.985037i	$0.555134\pi$
$114$	−5.68187	−0.532156
$115$	−16.5553	−1.54379
$116$	−20.9785	−1.94780
$117$	13.2519	1.22514
$118$	33.1089	3.04792
$119$	−24.2593	−2.22384
$120$	15.9131	1.45266
$121$	−3.95918	−0.359926
$122$	3.67758	0.332952
$123$	−5.31170	−0.478940
$124$	−41.4852	−3.72548
$125$	−0.0291932	−0.00261112
$126$	−21.4798	−1.91358
$127$	20.4348	1.81330	0.906648	−	0.421887i	$-0.138632\pi$
$127$	20.4348	1.81330	0.906648	+	0.421887i	$0.138632\pi$
$128$	10.8888	0.962443
$129$	3.26416	0.287393
$130$	44.8672	3.93512
$131$	17.5924	1.53705	0.768526	−	0.639818i	$-0.220990\pi$
$131$	17.5924	1.53705	0.768526	+	0.639818i	$0.220990\pi$
$132$	9.40779	0.818843
$133$	10.0116	0.868117
$134$	11.2842	0.974806
$135$	13.3736	1.15101
$136$	−43.9557	−3.76917
$137$	−13.0544	−1.11531	−0.557655	−	0.830073i	$-0.688299\pi$
$137$	−13.0544	−1.11531	−0.557655	+	0.830073i	$0.688299\pi$
$138$	−10.5059	−0.894319
$139$	−11.7772	−0.998928	−0.499464	−	0.866335i	$-0.666470\pi$
$139$	−11.7772	−0.998928	−0.499464	+	0.866335i	$0.666470\pi$
$140$	−50.3821	−4.25806
$141$	−3.48249	−0.293279
$142$	25.0457	2.10179
$143$	14.7623	1.23448
$144$	−17.4348	−1.45290
$145$	−14.7030	−1.22101
$146$	−8.99512	−0.744441
$147$	−4.31721	−0.356078
$148$	−20.7750	−1.70770
$149$	−22.0498	−1.80639	−0.903195	−	0.429230i	$-0.858785\pi$
$149$	−22.0498	−1.80639	−0.903195	+	0.429230i	$0.858785\pi$
$150$	10.0107	0.817366
$151$	−15.8039	−1.28610	−0.643051	−	0.765823i	$-0.722332\pi$
$151$	−15.8039	−1.28610	−0.643051	+	0.765823i	$0.722332\pi$
$152$	18.1402	1.47137
$153$	−16.3495	−1.32178
$154$	−23.9281	−1.92818
$155$	−29.0753	−2.33538
$156$	19.7251	1.57927
$157$	−9.23167	−0.736768	−0.368384	−	0.929674i	$-0.620089\pi$
$157$	−9.23167	−0.736768	−0.368384	+	0.929674i	$0.620089\pi$
$158$	−15.8751	−1.26296
$159$	−6.35671	−0.504120
$160$	−18.5461	−1.46620
$161$	18.5116	1.45892
$162$	−9.74560	−0.765687
$163$	−9.96351	−0.780402	−0.390201	−	0.920730i	$-0.627595\pi$
$163$	−9.96351	−0.780402	−0.390201	+	0.920730i	$0.627595\pi$
$164$	30.4715	2.37943
$165$	6.59354	0.513306
$166$	24.8328	1.92740
$167$	7.09578	0.549088	0.274544	−	0.961575i	$-0.411473\pi$
$167$	7.09578	0.549088	0.274544	+	0.961575i	$0.411473\pi$
$168$	−17.7935	−1.37280
$169$	17.9517	1.38090
$170$	−55.3549	−4.24553
$171$	6.74731	0.515980
$172$	−18.7254	−1.42780
$173$	14.3674	1.09233	0.546167	−	0.837676i	$-0.316086\pi$
$173$	14.3674	1.09233	0.546167	+	0.837676i	$0.316086\pi$
$174$	−9.33041	−0.707337
$175$	−17.6391	−1.33339
$176$	−19.4219	−1.46398
$177$	10.2015	0.766793
$178$	13.4881	1.01098
$179$	4.85163	0.362628	0.181314	−	0.983425i	$-0.441965\pi$
$179$	4.85163	0.362628	0.181314	+	0.983425i	$0.441965\pi$
$180$	−33.9549	−2.53085
$181$	−9.45411	−0.702719	−0.351359	−	0.936241i	$-0.614280\pi$
$181$	−9.45411	−0.702719	−0.351359	+	0.936241i	$0.614280\pi$
$182$	−50.1693	−3.71880
$183$	1.13314	0.0837638
$184$	33.5415	2.47272
$185$	−14.5604	−1.07050
$186$	−18.4510	−1.35289
$187$	−18.2130	−1.33186
$188$	19.9780	1.45704
$189$	−14.9540	−1.08774
$190$	22.8446	1.65732
$191$	9.08750	0.657548	0.328774	−	0.944409i	$-0.393365\pi$
$191$	9.08750	0.657548	0.328774	+	0.944409i	$0.393365\pi$
$192$	−0.260730	−0.0188165
$193$	24.9594	1.79662	0.898308	−	0.439367i	$-0.144797\pi$
$193$	24.9594	1.79662	0.898308	+	0.439367i	$0.144797\pi$
$194$	−42.8295	−3.07498
$195$	13.8245	0.989992
$196$	24.7665	1.76903
$197$	−19.6408	−1.39935	−0.699675	−	0.714461i	$-0.746672\pi$
$197$	−19.6408	−1.39935	−0.699675	+	0.714461i	$0.746672\pi$
$198$	−16.1263	−1.14604
$199$	−7.53925	−0.534444	−0.267222	−	0.963635i	$-0.586106\pi$
$199$	−7.53925	−0.534444	−0.267222	+	0.963635i	$0.586106\pi$
$200$	−31.9605	−2.25995
$201$	3.47689	0.245241
$202$	−47.2939	−3.32759
$203$	16.4405	1.15389
$204$	−24.3358	−1.70384
$205$	21.3563	1.49159
$206$	−33.2047	−2.31348
$207$	12.4759	0.867134
$208$	−40.7215	−2.82353
$209$	7.51636	0.519917
$210$	−22.4080	−1.54630
$211$	−14.2150	−0.978602	−0.489301	−	0.872115i	$-0.662748\pi$
$211$	−14.2150	−0.978602	−0.489301	+	0.872115i	$0.662748\pi$
$212$	36.4664	2.50452
$213$	7.71709	0.528766
$214$	−36.0956	−2.46744
$215$	−13.1239	−0.895043
$216$	−27.0953	−1.84360
$217$	32.5112	2.20700
$218$	−9.11352	−0.617245
$219$	−2.77158	−0.187286
$220$	−37.8250	−2.55016
$221$	−38.1866	−2.56871
$222$	−9.23993	−0.620144
$223$	26.9952	1.80773	0.903867	−	0.427813i	$-0.140716\pi$
$223$	26.9952	1.80773	0.903867	+	0.427813i	$0.140716\pi$
$224$	20.7377	1.38560
$225$	−11.8878	−0.792521
$226$	9.34865	0.621863
$227$	−4.64651	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$227$	−4.64651	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$228$	10.0432	0.665127
$229$	−2.56576	−0.169550	−0.0847749	−	0.996400i	$-0.527017\pi$
$229$	−2.56576	−0.169550	−0.0847749	+	0.996400i	$0.527017\pi$
$230$	42.2400	2.78522
$231$	−7.37272	−0.485089
$232$	29.7887	1.95573
$233$	−4.00613	−0.262450	−0.131225	−	0.991353i	$-0.541891\pi$
$233$	−4.00613	−0.262450	−0.131225	+	0.991353i	$0.541891\pi$
$234$	−33.8115	−2.21033
$235$	14.0017	0.913373
$236$	−58.5229	−3.80951
$237$	−4.89144	−0.317733
$238$	61.8964	4.01215
$239$	2.41651	0.156311	0.0781556	−	0.996941i	$-0.475097\pi$
$239$	2.41651	0.156311	0.0781556	+	0.996941i	$0.475097\pi$
$240$	−18.1881	−1.17404
$241$	17.8903	1.15241	0.576207	−	0.817303i	$-0.304532\pi$
$241$	17.8903	1.15241	0.576207	+	0.817303i	$0.304532\pi$
$242$	10.1017	0.649360
$243$	−15.6960	−1.00690
$244$	−6.50044	−0.416148
$245$	17.3578	1.10895
$246$	13.5526	0.864079
$247$	15.7593	1.00274
$248$	58.9075	3.74063
$249$	7.65148	0.484893
$250$	0.0744851	0.00471085
$251$	8.38835	0.529468	0.264734	−	0.964321i	$-0.414716\pi$
$251$	8.38835	0.529468	0.264734	+	0.964321i	$0.414716\pi$
$252$	37.9675	2.39172
$253$	13.8979	0.873751
$254$	−52.1385	−3.27146
$255$	−17.0560	−1.06809
$256$	−28.4456	−1.77785
$257$	−0.564659	−0.0352224	−0.0176112	−	0.999845i	$-0.505606\pi$
$257$	−0.564659	−0.0352224	−0.0176112	+	0.999845i	$0.505606\pi$
$258$	−8.32835	−0.518500
$259$	16.2810	1.01165
$260$	−79.3067	−4.91839
$261$	11.0800	0.685836
$262$	−44.8861	−2.77307
$263$	3.07507	0.189617	0.0948085	−	0.995496i	$-0.469776\pi$
$263$	3.07507	0.189617	0.0948085	+	0.995496i	$0.469776\pi$
$264$	−13.3587	−0.822174
$265$	25.5578	1.57001
$266$	−25.5442	−1.56621
$267$	4.15595	0.254340
$268$	−19.9458	−1.21838
$269$	−1.80558	−0.110088	−0.0550439	−	0.998484i	$-0.517530\pi$
$269$	−1.80558	−0.110088	−0.0550439	+	0.998484i	$0.517530\pi$
$270$	−34.1221	−2.07660
$271$	27.0798	1.64498	0.822491	−	0.568779i	$-0.192584\pi$
$271$	27.0798	1.64498	0.822491	+	0.568779i	$0.192584\pi$
$272$	50.2401	3.04625
$273$	−15.4582	−0.935571
$274$	33.3076	2.01219
$275$	−13.2428	−0.798569
$276$	18.5700	1.11778
$277$	−10.2369	−0.615078	−0.307539	−	0.951535i	$-0.599505\pi$
$277$	−10.2369	−0.615078	−0.307539	+	0.951535i	$0.599505\pi$
$278$	30.0489	1.80222
$279$	21.9108	1.31177
$280$	71.5409	4.27538
$281$	6.54066	0.390183	0.195091	−	0.980785i	$-0.437500\pi$
$281$	6.54066	0.390183	0.195091	+	0.980785i	$0.437500\pi$
$282$	8.88542	0.529119
$283$	4.88018	0.290097	0.145048	−	0.989425i	$-0.453666\pi$
$283$	4.88018	0.290097	0.145048	+	0.989425i	$0.453666\pi$
$284$	−44.2705	−2.62697
$285$	7.03887	0.416947
$286$	−37.6653	−2.22720
$287$	−23.8800	−1.40959
$288$	13.9762	0.823553
$289$	30.1127	1.77134
$290$	37.5139	2.20289
$291$	−13.1966	−0.773600
$292$	15.8996	0.930457
$293$	−1.63206	−0.0953460	−0.0476730	−	0.998863i	$-0.515181\pi$
$293$	−1.63206	−0.0953460	−0.0476730	+	0.998863i	$0.515181\pi$
$294$	11.0152	0.642418
$295$	−41.0163	−2.38806
$296$	29.4999	1.71464
$297$	−11.2269	−0.651451
$298$	56.2591	3.25900
$299$	29.1393	1.68517
$300$	−17.6947	−1.02160
$301$	14.6748	0.845841
$302$	40.3229	2.32032
$303$	−14.5722	−0.837151
$304$	−20.7337	−1.18916
$305$	−4.55590	−0.260870
$306$	41.7149	2.38468
$307$	12.8017	0.730630	0.365315	−	0.930884i	$-0.380961\pi$
$307$	12.8017	0.730630	0.365315	+	0.930884i	$0.380961\pi$
$308$	42.2949	2.40998
$309$	−10.2310	−0.582023
$310$	74.1842	4.21338
$311$	10.2113	0.579027	0.289514	−	0.957174i	$-0.406506\pi$
$311$	10.2113	0.579027	0.289514	+	0.957174i	$0.406506\pi$
$312$	−28.0089	−1.58569
$313$	5.43015	0.306931	0.153465	−	0.988154i	$-0.450957\pi$
$313$	5.43015	0.306931	0.153465	+	0.988154i	$0.450957\pi$
$314$	23.5542	1.32924
$315$	26.6099	1.49930
$316$	28.0606	1.57853
$317$	5.65434	0.317580	0.158790	−	0.987312i	$-0.449241\pi$
$317$	5.65434	0.317580	0.158790	+	0.987312i	$0.449241\pi$
$318$	16.2189	0.909508
$319$	12.3429	0.691069
$320$	1.04829	0.0586013
$321$	−11.1218	−0.620756
$322$	−47.2316	−2.63211
$323$	−19.4431	−1.08184
$324$	17.2262	0.957011
$325$	−27.7657	−1.54017
$326$	25.4214	1.40796
$327$	−2.80806	−0.155286
$328$	−43.2685	−2.38911
$329$	−15.6564	−0.863164
$330$	−16.8231	−0.926081
$331$	10.4928	0.576739	0.288370	−	0.957519i	$-0.406887\pi$
$331$	10.4928	0.576739	0.288370	+	0.957519i	$0.406887\pi$
$332$	−43.8941	−2.40900
$333$	10.9726	0.601293
$334$	−18.1046	−0.990637
$335$	−13.9792	−0.763765
$336$	20.3375	1.10950
$337$	−16.5943	−0.903947	−0.451973	−	0.892031i	$-0.649280\pi$
$337$	−16.5943	−0.903947	−0.451973	+	0.892031i	$0.649280\pi$
$338$	−45.8029	−2.49135
$339$	2.88051	0.156448
$340$	97.8446	5.30637
$341$	24.4082	1.32178
$342$	−17.2154	−0.930905
$343$	5.33133	0.287865
$344$	26.5895	1.43361
$345$	13.0150	0.700703
$346$	−36.6578	−1.97074
$347$	−26.2533	−1.40935	−0.704676	−	0.709529i	$-0.748908\pi$
$347$	−26.2533	−1.40935	−0.704676	+	0.709529i	$0.748908\pi$
$348$	16.4923	0.884080
$349$	3.74426	0.200426	0.100213	−	0.994966i	$-0.468048\pi$
$349$	3.74426	0.200426	0.100213	+	0.994966i	$0.468048\pi$
$350$	45.0052	2.40563
$351$	−23.5391	−1.25643
$352$	15.5691	0.829838
$353$	−9.78143	−0.520613	−0.260306	−	0.965526i	$-0.583824\pi$
$353$	−9.78143	−0.520613	−0.260306	+	0.965526i	$0.583824\pi$
$354$	−26.0287	−1.38341
$355$	−31.0274	−1.64676
$356$	−23.8414	−1.26359
$357$	19.0715	1.00937
$358$	−12.3787	−0.654235
$359$	9.50178	0.501485	0.250742	−	0.968054i	$-0.419325\pi$
$359$	9.50178	0.501485	0.250742	+	0.968054i	$0.419325\pi$
$360$	48.2148	2.54114
$361$	−10.9760	−0.577683
$362$	24.1217	1.26781
$363$	3.11253	0.163365
$364$	88.6786	4.64802
$365$	11.1434	0.583273
$366$	−2.89114	−0.151123
$367$	−4.65779	−0.243135	−0.121567	−	0.992583i	$-0.538792\pi$
$367$	−4.65779	−0.243135	−0.121567	+	0.992583i	$0.538792\pi$
$368$	−38.3370	−1.99845
$369$	−16.0939	−0.837814
$370$	37.1501	1.93134
$371$	−28.5781	−1.48370
$372$	32.6137	1.69094
$373$	−7.27965	−0.376926	−0.188463	−	0.982080i	$-0.560351\pi$
$373$	−7.27965	−0.376926	−0.188463	+	0.982080i	$0.560351\pi$
$374$	46.4695	2.40288
$375$	0.0229503	0.00118515
$376$	−28.3680	−1.46297
$377$	25.8790	1.33284
$378$	38.1544	1.96245
$379$	16.4188	0.843379	0.421689	−	0.906740i	$-0.361437\pi$
$379$	16.4188	0.843379	0.421689	+	0.906740i	$0.361437\pi$
$380$	−40.3797	−2.07144
$381$	−16.0649	−0.823030
$382$	−23.1863	−1.18632
$383$	−28.5993	−1.46135	−0.730677	−	0.682723i	$-0.760795\pi$
$383$	−28.5993	−1.46135	−0.730677	+	0.682723i	$0.760795\pi$
$384$	−8.56027	−0.436840
$385$	29.6428	1.51074
$386$	−63.6827	−3.24136
$387$	9.89005	0.502739
$388$	75.7049	3.84333
$389$	31.9423	1.61954	0.809770	−	0.586747i	$-0.199592\pi$
$389$	31.9423	1.61954	0.809770	+	0.586747i	$0.199592\pi$
$390$	−35.2725	−1.78609
$391$	−35.9506	−1.81810
$392$	−35.1676	−1.77623
$393$	−13.8303	−0.697647
$394$	50.1126	2.52464
$395$	19.6666	0.989532
$396$	28.5046	1.43241
$397$	−35.1190	−1.76257	−0.881286	−	0.472584i	$-0.843321\pi$
$397$	−35.1190	−1.76257	−0.881286	+	0.472584i	$0.843321\pi$
$398$	19.2361	0.964216
$399$	−7.87067	−0.394027
$400$	36.5299	1.82649
$401$	22.0476	1.10100	0.550502	−	0.834834i	$-0.314436\pi$
$401$	22.0476	1.10100	0.550502	+	0.834834i	$0.314436\pi$
$402$	−8.87112	−0.442451
$403$	51.1760	2.54926
$404$	83.5961	4.15906
$405$	12.0731	0.599919
$406$	−41.9471	−2.08180
$407$	12.2232	0.605882
$408$	34.5560	1.71078
$409$	−29.2241	−1.44504	−0.722519	−	0.691351i	$-0.757016\pi$
$409$	−29.2241	−1.44504	−0.722519	+	0.691351i	$0.757016\pi$
$410$	−54.4895	−2.69104
$411$	10.2627	0.506224
$412$	58.6922	2.89156
$413$	45.8633	2.25679
$414$	−31.8316	−1.56444
$415$	−30.7636	−1.51013
$416$	32.6434	1.60047
$417$	9.25868	0.453400
$418$	−19.1776	−0.938009
$419$	−25.8468	−1.26270	−0.631349	−	0.775499i	$-0.717499\pi$
$419$	−25.8468	−1.26270	−0.631349	+	0.775499i	$0.717499\pi$
$420$	39.6081	1.93268
$421$	−19.1652	−0.934057	−0.467029	−	0.884242i	$-0.654675\pi$
$421$	−19.1652	−0.934057	−0.467029	+	0.884242i	$0.654675\pi$
$422$	36.2689	1.76554
$423$	−10.5516	−0.513035
$424$	−51.7811	−2.51471
$425$	34.2560	1.66166
$426$	−19.6898	−0.953974
$427$	5.09428	0.246530
$428$	63.8020	3.08399
$429$	−11.6054	−0.560316
$430$	33.4850	1.61479
$431$	39.7212	1.91330	0.956651	−	0.291237i	$-0.0940667\pi$
$431$	39.7212	1.91330	0.956651	+	0.291237i	$0.0940667\pi$
$432$	30.9692	1.49000
$433$	16.8111	0.807889	0.403945	−	0.914783i	$-0.367639\pi$
$433$	16.8111	0.807889	0.403945	+	0.914783i	$0.367639\pi$
$434$	−82.9508	−3.98176
$435$	11.5588	0.554202
$436$	16.1089	0.771478
$437$	14.8365	0.709728
$438$	7.07155	0.337892
$439$	32.2751	1.54041	0.770204	−	0.637798i	$-0.220155\pi$
$439$	32.2751	1.54041	0.770204	+	0.637798i	$0.220155\pi$
$440$	53.7103	2.56054
$441$	−13.0807	−0.622890
$442$	97.4314	4.63434
$443$	−7.24541	−0.344240	−0.172120	−	0.985076i	$-0.555062\pi$
$443$	−7.24541	−0.344240	−0.172120	+	0.985076i	$0.555062\pi$
$444$	16.3324	0.775100
$445$	−16.7095	−0.792104
$446$	−68.8771	−3.26142
$447$	17.3345	0.819896
$448$	−1.17217	−0.0553799
$449$	−26.8196	−1.26570	−0.632848	−	0.774276i	$-0.718114\pi$
$449$	−26.8196	−1.26570	−0.632848	+	0.774276i	$0.718114\pi$
$450$	30.3312	1.42983
$451$	−17.9282	−0.844207
$452$	−16.5245	−0.777249
$453$	12.4243	0.583744
$454$	11.8554	0.556399
$455$	62.1513	2.91370
$456$	−14.2610	−0.667833
$457$	32.0591	1.49966	0.749832	−	0.661629i	$-0.230134\pi$
$457$	32.0591	1.49966	0.749832	+	0.661629i	$0.230134\pi$
$458$	6.54640	0.305893
$459$	29.0414	1.35554
$460$	−74.6628	−3.48117
$461$	−11.6128	−0.540862	−0.270431	−	0.962739i	$-0.587166\pi$
$461$	−11.6128	−0.540862	−0.270431	+	0.962739i	$0.587166\pi$
$462$	18.8111	0.875174
$463$	0.494560	0.0229842	0.0114921	−	0.999934i	$-0.496342\pi$
$463$	0.494560	0.0229842	0.0114921	+	0.999934i	$0.496342\pi$
$464$	−34.0476	−1.58062
$465$	22.8576	1.06000
$466$	10.2215	0.473500
$467$	38.6438	1.78822	0.894110	−	0.447848i	$-0.147809\pi$
$467$	38.6438	1.78822	0.894110	+	0.447848i	$0.147809\pi$
$468$	59.7648	2.76263
$469$	15.6312	0.721780
$470$	−35.7248	−1.64786
$471$	7.25752	0.334409
$472$	83.1005	3.82501
$473$	11.0173	0.506576
$474$	12.4803	0.573238
$475$	−14.1372	−0.648659
$476$	−109.407	−5.01467
$477$	−19.2602	−0.881862
$478$	−6.16562	−0.282009
$479$	−28.6717	−1.31005	−0.655023	−	0.755609i	$-0.727341\pi$
$479$	−28.6717	−1.31005	−0.655023	+	0.755609i	$0.727341\pi$
$480$	14.5801	0.665487
$481$	25.6281	1.16854
$482$	−45.6462	−2.07913
$483$	−14.5530	−0.662185
$484$	−17.8556	−0.811617
$485$	53.0585	2.40926
$486$	40.0475	1.81659
$487$	2.32337	0.105282	0.0526410	−	0.998614i	$-0.483236\pi$
$487$	2.32337	0.105282	0.0526410	+	0.998614i	$0.483236\pi$
$488$	9.23041	0.417841
$489$	7.83285	0.354214
$490$	−44.2877	−2.00071
$491$	−8.65794	−0.390727	−0.195364	−	0.980731i	$-0.562589\pi$
$491$	−8.65794	−0.390727	−0.195364	+	0.980731i	$0.562589\pi$
$492$	−23.9553	−1.07999
$493$	−31.9282	−1.43797
$494$	−40.2092	−1.80910
$495$	19.9777	0.897931
$496$	−67.3295	−3.02319
$497$	34.6940	1.55624
$498$	−19.5224	−0.874820
$499$	−36.7323	−1.64436	−0.822182	−	0.569224i	$-0.807244\pi$
$499$	−36.7323	−1.64436	−0.822182	+	0.569224i	$0.807244\pi$
$500$	−0.131659	−0.00588796
$501$	−5.57838	−0.249224
$502$	−21.4025	−0.955240
$503$	−9.90086	−0.441458	−0.220729	−	0.975335i	$-0.570844\pi$
$503$	−9.90086	−0.441458	−0.220729	+	0.975335i	$0.570844\pi$
$504$	−53.9125	−2.40145
$505$	58.5891	2.60718
$506$	−35.4598	−1.57638
$507$	−14.1128	−0.626771
$508$	92.1593	4.08891
$509$	−7.99336	−0.354299	−0.177150	−	0.984184i	$-0.556688\pi$
$509$	−7.99336	−0.354299	−0.177150	+	0.984184i	$0.556688\pi$
$510$	43.5175	1.92699
$511$	−12.4603	−0.551210
$512$	50.7999	2.24506
$513$	−11.9852	−0.529158
$514$	1.44070	0.0635465
$515$	41.1350	1.81262
$516$	14.7211	0.648059
$517$	−11.7542	−0.516951
$518$	−41.5403	−1.82518
$519$	−11.2950	−0.495796
$520$	112.613	4.93840
$521$	14.6113	0.640133	0.320066	−	0.947395i	$-0.396295\pi$
$521$	14.6113	0.640133	0.320066	+	0.947395i	$0.396295\pi$
$522$	−28.2701	−1.23735
$523$	−6.49644	−0.284070	−0.142035	−	0.989862i	$-0.545364\pi$
$523$	−6.49644	−0.284070	−0.142035	+	0.989862i	$0.545364\pi$
$524$	79.3401	3.46599
$525$	13.8670	0.605206
$526$	−7.84590	−0.342098
$527$	−63.1384	−2.75035
$528$	15.2686	0.664482
$529$	4.43299	0.192739
$530$	−65.2097	−2.83253
$531$	30.9095	1.34136
$532$	45.1515	1.95757
$533$	−37.5896	−1.62819
$534$	−10.6037	−0.458868
$535$	44.7163	1.93325
$536$	28.3224	1.22334
$537$	−3.81413	−0.164592
$538$	4.60684	0.198615
$539$	−14.5716	−0.627644
$540$	60.3137	2.59549
$541$	−42.1952	−1.81412	−0.907058	−	0.421007i	$-0.861677\pi$
$541$	−42.1952	−1.81412	−0.907058	+	0.421007i	$0.861677\pi$
$542$	−69.0929	−2.96779
$543$	7.43239	0.318954
$544$	−40.2738	−1.72672
$545$	11.2901	0.483615
$546$	39.4408	1.68791
$547$	32.8995	1.40668	0.703341	−	0.710853i	$-0.251691\pi$
$547$	32.8995	1.40668	0.703341	+	0.710853i	$0.251691\pi$
$548$	−58.8741	−2.51498
$549$	3.43328	0.146529
$550$	33.7883	1.44074
$551$	13.1765	0.561339
$552$	−26.3688	−1.12233
$553$	−21.9906	−0.935136
$554$	26.1191	1.10969
$555$	11.4467	0.485886
$556$	−53.1141	−2.25254
$557$	33.0218	1.39918	0.699589	−	0.714546i	$-0.253367\pi$
$557$	33.0218	1.39918	0.699589	+	0.714546i	$0.253367\pi$
$558$	−55.9045	−2.36663
$559$	23.0997	0.977012
$560$	−81.7691	−3.45537
$561$	14.3182	0.604515
$562$	−16.6882	−0.703948
$563$	22.0969	0.931272	0.465636	−	0.884976i	$-0.345826\pi$
$563$	22.0969	0.931272	0.465636	+	0.884976i	$0.345826\pi$
$564$	−15.7057	−0.661331
$565$	−11.5814	−0.487233
$566$	−12.4516	−0.523378
$567$	−13.4999	−0.566941
$568$	62.8626	2.63766
$569$	16.2844	0.682679	0.341340	−	0.939940i	$-0.389119\pi$
$569$	16.2844	0.682679	0.341340	+	0.939940i	$0.389119\pi$
$570$	−17.9593	−0.752234
$571$	9.63072	0.403033	0.201517	−	0.979485i	$-0.435413\pi$
$571$	9.63072	0.403033	0.201517	+	0.979485i	$0.435413\pi$
$572$	66.5767	2.78371
$573$	−7.14417	−0.298452
$574$	60.9287	2.54311
$575$	−26.1399	−1.09011
$576$	−0.789982	−0.0329159
$577$	20.8869	0.869532	0.434766	−	0.900543i	$-0.356831\pi$
$577$	20.8869	0.869532	0.434766	+	0.900543i	$0.356831\pi$
$578$	−76.8313	−3.19576
$579$	−19.6219	−0.815459
$580$	−66.3091	−2.75334
$581$	34.3990	1.42711
$582$	33.6706	1.39569
$583$	−21.4554	−0.888591
$584$	−22.5770	−0.934242
$585$	41.8867	1.73180
$586$	4.16413	0.172019
$587$	−19.4934	−0.804580	−0.402290	−	0.915512i	$-0.631786\pi$
$587$	−19.4934	−0.804580	−0.402290	+	0.915512i	$0.631786\pi$
$588$	−19.4703	−0.802940
$589$	26.0568	1.07365
$590$	104.651	4.30842
$591$	15.4407	0.635146
$592$	−33.7175	−1.38578
$593$	−14.9393	−0.613482	−0.306741	−	0.951793i	$-0.599239\pi$
$593$	−14.9393	−0.613482	−0.306741	+	0.951793i	$0.599239\pi$
$594$	28.6449	1.17531
$595$	−76.6791	−3.14354
$596$	−99.4427	−4.07333
$597$	5.92701	0.242577
$598$	−74.3475	−3.04030
$599$	−40.1787	−1.64166	−0.820829	−	0.571174i	$-0.806488\pi$
$599$	−40.1787	−1.64166	−0.820829	+	0.571174i	$0.806488\pi$
$600$	25.1259	1.02576
$601$	38.8101	1.58310	0.791549	−	0.611106i	$-0.209275\pi$
$601$	38.8101	1.58310	0.791549	+	0.611106i	$0.209275\pi$
$602$	−37.4420	−1.52602
$603$	10.5346	0.429002
$604$	−71.2742	−2.90010
$605$	−12.5143	−0.508777
$606$	37.1803	1.51035
$607$	6.72589	0.272995	0.136498	−	0.990640i	$-0.456415\pi$
$607$	6.72589	0.272995	0.136498	+	0.990640i	$0.456415\pi$
$608$	16.6207	0.674058
$609$	−12.9247	−0.523736
$610$	11.6242	0.470648
$611$	−24.6448	−0.997021
$612$	−73.7348	−2.98055
$613$	−30.6440	−1.23770	−0.618850	−	0.785509i	$-0.712401\pi$
$613$	−30.6440	−1.23770	−0.618850	+	0.785509i	$0.712401\pi$
$614$	−32.6629	−1.31817
$615$	−16.7893	−0.677010
$616$	−60.0574	−2.41978
$617$	34.6042	1.39311	0.696556	−	0.717502i	$-0.254715\pi$
$617$	34.6042	1.39311	0.696556	+	0.717502i	$0.254715\pi$
$618$	26.1040	1.05006
$619$	29.5011	1.18575	0.592874	−	0.805295i	$-0.297993\pi$
$619$	29.5011	1.18575	0.592874	+	0.805295i	$0.297993\pi$
$620$	−131.127	−5.26619
$621$	−22.1608	−0.889281
$622$	−26.0535	−1.04465
$623$	18.6841	0.748561
$624$	32.0133	1.28156
$625$	−25.0461	−1.00184
$626$	−13.8548	−0.553749
$627$	−5.90901	−0.235983
$628$	−41.6340	−1.66138
$629$	−31.6186	−1.26072
$630$	−67.8938	−2.70495
$631$	6.02547	0.239870	0.119935	−	0.992782i	$-0.461731\pi$
$631$	6.02547	0.239870	0.119935	+	0.992782i	$0.461731\pi$
$632$	−39.8451	−1.58495
$633$	11.1752	0.444174
$634$	−14.4268	−0.572961
$635$	64.5907	2.56320
$636$	−28.6682	−1.13677
$637$	−30.5519	−1.21051
$638$	−31.4923	−1.24679
$639$	23.3820	0.924976
$640$	34.4175	1.36047
$641$	−13.3080	−0.525636	−0.262818	−	0.964845i	$-0.584652\pi$
$641$	−13.3080	−0.525636	−0.262818	+	0.964845i	$0.584652\pi$
$642$	28.3767	1.11994
$643$	43.7669	1.72600	0.863000	−	0.505204i	$-0.168583\pi$
$643$	43.7669	1.72600	0.863000	+	0.505204i	$0.168583\pi$
$644$	83.4859	3.28981
$645$	10.3174	0.406247
$646$	49.6081	1.95181
$647$	−33.6156	−1.32156	−0.660782	−	0.750577i	$-0.729775\pi$
$647$	−33.6156	−1.32156	−0.660782	+	0.750577i	$0.729775\pi$
$648$	−24.4606	−0.960904
$649$	34.4325	1.35159
$650$	70.8430	2.77869
$651$	−25.5588	−1.00173
$652$	−44.9346	−1.75977
$653$	−33.0857	−1.29474	−0.647372	−	0.762174i	$-0.724132\pi$
$653$	−33.0857	−1.29474	−0.647372	+	0.762174i	$0.724132\pi$
$654$	7.16463	0.280159
$655$	55.6063	2.17272
$656$	49.4546	1.93088
$657$	−8.39758	−0.327621
$658$	39.9465	1.55728
$659$	−30.7643	−1.19841	−0.599203	−	0.800597i	$-0.704516\pi$
$659$	−30.7643	−1.19841	−0.599203	+	0.800597i	$0.704516\pi$
$660$	29.7363	1.15748
$661$	−17.0265	−0.662254	−0.331127	−	0.943586i	$-0.607429\pi$
$661$	−17.0265	−0.662254	−0.331127	+	0.943586i	$0.607429\pi$
$662$	−26.7720	−1.04052
$663$	30.0206	1.16590
$664$	62.3282	2.41880
$665$	31.6449	1.22714
$666$	−27.9960	−1.08482
$667$	24.3636	0.943364
$668$	32.0014	1.23817
$669$	−21.2224	−0.820506
$670$	35.6673	1.37795
$671$	3.82460	0.147647
$672$	−16.3031	−0.628904
$673$	41.5037	1.59985	0.799926	−	0.600099i	$-0.204872\pi$
$673$	41.5037	1.59985	0.799926	+	0.600099i	$0.204872\pi$
$674$	42.3395	1.63086
$675$	21.1162	0.812762
$676$	80.9606	3.11387
$677$	25.8786	0.994596	0.497298	−	0.867580i	$-0.334326\pi$
$677$	25.8786	0.994596	0.497298	+	0.867580i	$0.334326\pi$
$678$	−7.34948	−0.282255
$679$	−59.3286	−2.27682
$680$	−138.936	−5.32796
$681$	3.65287	0.139978
$682$	−62.2764	−2.38469
$683$	−2.79258	−0.106855	−0.0534276	−	0.998572i	$-0.517015\pi$
$683$	−2.79258	−0.106855	−0.0534276	+	0.998572i	$0.517015\pi$
$684$	30.4298	1.16351
$685$	−41.2625	−1.57656
$686$	−13.6026	−0.519351
$687$	2.01708	0.0769564
$688$	−30.3910	−1.15865
$689$	−44.9849	−1.71379
$690$	−33.2071	−1.26417
$691$	14.8748	0.565865	0.282933	−	0.959140i	$-0.408693\pi$
$691$	14.8748	0.565865	0.282933	+	0.959140i	$0.408693\pi$
$692$	64.7958	2.46317
$693$	−22.3385	−0.848571
$694$	66.9841	2.54268
$695$	−37.2255	−1.41205
$696$	−23.4185	−0.887677
$697$	46.3762	1.75662
$698$	−9.55331	−0.361598
$699$	3.14944	0.119123
$700$	−79.5506	−3.00673
$701$	−28.6137	−1.08072	−0.540362	−	0.841432i	$-0.681713\pi$
$701$	−28.6137	−1.08072	−0.540362	+	0.841432i	$0.681713\pi$
$702$	60.0590	2.26678
$703$	13.0488	0.492144
$704$	−0.880023	−0.0331671
$705$	−11.0075	−0.414567
$706$	24.9569	0.939263
$707$	−65.5128	−2.46386
$708$	46.0080	1.72909
$709$	−23.4967	−0.882436	−0.441218	−	0.897400i	$-0.645453\pi$
$709$	−23.4967	−0.882436	−0.441218	+	0.897400i	$0.645453\pi$
$710$	79.1650	2.97101
$711$	−14.8205	−0.555813
$712$	33.8540	1.26873
$713$	48.1794	1.80433
$714$	−48.6601	−1.82106
$715$	46.6609	1.74502
$716$	21.8804	0.817710
$717$	−1.89975	−0.0709475
$718$	−24.2434	−0.904754
$719$	22.4229	0.836233	0.418117	−	0.908393i	$-0.362690\pi$
$719$	22.4229	0.836233	0.418117	+	0.908393i	$0.362690\pi$
$720$	−55.1081	−2.05376
$721$	−45.9960	−1.71298
$722$	28.0047	1.04223
$723$	−14.0645	−0.523065
$724$	−42.6372	−1.58460
$725$	−23.2152	−0.862191
$726$	−7.94147	−0.294736
$727$	22.6474	0.839946	0.419973	−	0.907537i	$-0.362040\pi$
$727$	22.6474	0.839946	0.419973	+	0.907537i	$0.362040\pi$
$728$	−125.921	−4.66693
$729$	0.880565	0.0326135
$730$	−28.4319	−1.05231
$731$	−28.4992	−1.05408
$732$	5.11035	0.188884
$733$	7.48041	0.276295	0.138148	−	0.990412i	$-0.455885\pi$
$733$	7.48041	0.276295	0.138148	+	0.990412i	$0.455885\pi$
$734$	11.8841	0.438651
$735$	−13.6459	−0.503337
$736$	30.7319	1.13279
$737$	11.7353	0.432276
$738$	41.0628	1.51154
$739$	22.6756	0.834134	0.417067	−	0.908876i	$-0.363058\pi$
$739$	22.6756	0.834134	0.417067	+	0.908876i	$0.363058\pi$
$740$	−65.6661	−2.41393
$741$	−12.3893	−0.455131
$742$	72.9157	2.67682
$743$	−29.6865	−1.08909	−0.544545	−	0.838731i	$-0.683298\pi$
$743$	−29.6865	−1.08909	−0.544545	+	0.838731i	$0.683298\pi$
$744$	−46.3104	−1.69782
$745$	−69.6954	−2.55344
$746$	18.5737	0.680031
$747$	23.1832	0.848228
$748$	−82.1389	−3.00330
$749$	−50.0005	−1.82698
$750$	−0.0585567	−0.00213819
$751$	2.46661	0.0900079	0.0450040	−	0.998987i	$-0.485670\pi$
$751$	2.46661	0.0900079	0.0450040	+	0.998987i	$0.485670\pi$
$752$	32.4238	1.18237
$753$	−6.59454	−0.240318
$754$	−66.0291	−2.40464
$755$	−49.9532	−1.81798
$756$	−67.4411	−2.45281
$757$	−9.18093	−0.333686	−0.166843	−	0.985983i	$-0.553357\pi$
$757$	−9.18093	−0.333686	−0.166843	+	0.985983i	$0.553357\pi$
$758$	−41.8919	−1.52158
$759$	−10.9259	−0.396584
$760$	57.3379	2.07986
$761$	15.8543	0.574717	0.287359	−	0.957823i	$-0.407223\pi$
$761$	15.8543	0.574717	0.287359	+	0.957823i	$0.407223\pi$
$762$	40.9889	1.48487
$763$	−12.6243	−0.457030
$764$	40.9838	1.48274
$765$	−51.6777	−1.86841
$766$	72.9697	2.63650
$767$	72.1937	2.60676
$768$	22.3626	0.806941
$769$	7.81095	0.281670	0.140835	−	0.990033i	$-0.455021\pi$
$769$	7.81095	0.281670	0.140835	+	0.990033i	$0.455021\pi$
$770$	−75.6322	−2.72560
$771$	0.443909	0.0159870
$772$	112.565	4.05129
$773$	48.6830	1.75101	0.875503	−	0.483213i	$-0.160530\pi$
$773$	48.6830	1.75101	0.875503	+	0.483213i	$0.160530\pi$
$774$	−25.2340	−0.907017
$775$	−45.9083	−1.64908
$776$	−107.498	−3.85897
$777$	−12.7994	−0.459176
$778$	−81.4994	−2.92189
$779$	−19.1391	−0.685730
$780$	62.3473	2.23239
$781$	26.0470	0.932035
$782$	91.7262	3.28012
$783$	−19.6813	−0.703352
$784$	40.1955	1.43555
$785$	−29.1796	−1.04147
$786$	35.2874	1.25866
$787$	12.0156	0.428310	0.214155	−	0.976800i	$-0.431300\pi$
$787$	12.0156	0.428310	0.214155	+	0.976800i	$0.431300\pi$
$788$	−88.5784	−3.15548
$789$	−2.41748	−0.0860646
$790$	−50.1783	−1.78526
$791$	12.9500	0.460449
$792$	−40.4756	−1.43824
$793$	8.01893	0.284761
$794$	89.6045	3.17994
$795$	−20.0924	−0.712604
$796$	−34.0014	−1.20515
$797$	5.82491	0.206329	0.103164	−	0.994664i	$-0.467103\pi$
$797$	5.82491	0.206329	0.103164	+	0.994664i	$0.467103\pi$
$798$	20.0817	0.710883
$799$	30.4055	1.07567
$800$	−29.2833	−1.03532
$801$	12.5921	0.444920
$802$	−56.2534	−1.98638
$803$	−9.35472	−0.330121
$804$	15.6805	0.553007
$805$	58.5119	2.06227
$806$	−130.573	−4.59925
$807$	1.41946	0.0499674
$808$	−118.704	−4.17598
$809$	32.7147	1.15019	0.575094	−	0.818087i	$-0.304965\pi$
$809$	32.7147	1.15019	0.575094	+	0.818087i	$0.304965\pi$
$810$	−30.8041	−1.08234
$811$	−16.0069	−0.562080	−0.281040	−	0.959696i	$-0.590679\pi$
$811$	−16.0069	−0.562080	−0.281040	+	0.959696i	$0.590679\pi$
$812$	74.1450	2.60198
$813$	−21.2889	−0.746634
$814$	−31.1869	−1.09310
$815$	−31.4928	−1.10315
$816$	−39.4964	−1.38265
$817$	11.7614	0.411480
$818$	74.5639	2.60707
$819$	−46.8366	−1.63660
$820$	96.3149	3.36346
$821$	38.4264	1.34109	0.670545	−	0.741869i	$-0.266060\pi$
$821$	38.4264	1.34109	0.670545	+	0.741869i	$0.266060\pi$
$822$	−26.1849	−0.913304
$823$	−20.3242	−0.708456	−0.354228	−	0.935159i	$-0.615256\pi$
$823$	−20.3242	−0.708456	−0.354228	+	0.935159i	$0.615256\pi$
$824$	−83.3410	−2.90332
$825$	10.4109	0.362459
$826$	−117.018	−4.07158
$827$	47.7091	1.65901	0.829504	−	0.558501i	$-0.188623\pi$
$827$	47.7091	1.65901	0.829504	+	0.558501i	$0.188623\pi$
$828$	56.2652	1.95535
$829$	49.1008	1.70534	0.852671	−	0.522449i	$-0.174981\pi$
$829$	49.1008	1.70534	0.852671	+	0.522449i	$0.174981\pi$
$830$	78.4919	2.72449
$831$	8.04781	0.279175
$832$	−1.84512	−0.0639681
$833$	37.6934	1.30600
$834$	−23.6231	−0.818001
$835$	22.4285	0.776169
$836$	33.8981	1.17239
$837$	−38.9200	−1.34527
$838$	65.9469	2.27810
$839$	−27.5354	−0.950626	−0.475313	−	0.879817i	$-0.657665\pi$
$839$	−27.5354	−0.950626	−0.475313	+	0.879817i	$0.657665\pi$
$840$	−56.2421	−1.94054
$841$	−7.36231	−0.253873
$842$	48.8992	1.68518
$843$	−5.14196	−0.177099
$844$	−64.1085	−2.20671
$845$	56.7420	1.95198
$846$	26.9219	0.925593
$847$	13.9931	0.480809
$848$	59.1842	2.03240
$849$	−3.83658	−0.131671
$850$	−87.4025	−2.99788
$851$	24.1274	0.827076
$852$	34.8034	1.19235
$853$	22.4324	0.768070	0.384035	−	0.923319i	$-0.374534\pi$
$853$	22.4324	0.768070	0.384035	+	0.923319i	$0.374534\pi$
$854$	−12.9978	−0.444776
$855$	21.3270	0.729368
$856$	−90.5967	−3.09653
$857$	24.9326	0.851681	0.425840	−	0.904798i	$-0.359979\pi$
$857$	24.9326	0.851681	0.425840	+	0.904798i	$0.359979\pi$
$858$	29.6107	1.01089
$859$	15.7501	0.537385	0.268693	−	0.963226i	$-0.413408\pi$
$859$	15.7501	0.537385	0.268693	+	0.963226i	$0.413408\pi$
$860$	−59.1877	−2.01828
$861$	18.7734	0.639794
$862$	−101.347	−3.45188
$863$	57.4253	1.95478	0.977391	−	0.211441i	$-0.0678157\pi$
$863$	57.4253	1.95478	0.977391	+	0.211441i	$0.0678157\pi$
$864$	−24.8257	−0.844587
$865$	45.4128	1.54408
$866$	−42.8927	−1.45755
$867$	−23.6733	−0.803986
$868$	146.623	4.97670
$869$	−16.5097	−0.560055
$870$	−29.4917	−0.999863
$871$	24.6051	0.833712
$872$	−22.8741	−0.774616
$873$	−39.9844	−1.35327
$874$	−37.8547	−1.28046
$875$	0.103179	0.00348808
$876$	−12.4996	−0.422321
$877$	23.3093	0.787099	0.393550	−	0.919303i	$-0.371247\pi$
$877$	23.3093	0.787099	0.393550	+	0.919303i	$0.371247\pi$
$878$	−82.3484	−2.77913
$879$	1.28305	0.0432763
$880$	−61.3892	−2.06943
$881$	37.8457	1.27506	0.637528	−	0.770428i	$-0.279957\pi$
$881$	37.8457	1.27506	0.637528	+	0.770428i	$0.279957\pi$
$882$	33.3748	1.12379
$883$	−9.65821	−0.325025	−0.162512	−	0.986707i	$-0.551960\pi$
$883$	−9.65821	−0.325025	−0.162512	+	0.986707i	$0.551960\pi$
$884$	−172.218	−5.79233
$885$	32.2451	1.08391
$886$	18.4863	0.621061
$887$	−39.4151	−1.32343	−0.661715	−	0.749755i	$-0.730171\pi$
$887$	−39.4151	−1.32343	−0.661715	+	0.749755i	$0.730171\pi$
$888$	−23.1914	−0.778254
$889$	−72.2236	−2.42230
$890$	42.6334	1.42908
$891$	−10.1352	−0.339542
$892$	121.746	4.07636
$893$	−12.5481	−0.419907
$894$	−44.2283	−1.47922
$895$	15.3351	0.512596
$896$	−38.4847	−1.28568
$897$	−22.9080	−0.764875
$898$	68.4290	2.28351
$899$	42.7888	1.42709
$900$	−53.6130	−1.78710
$901$	55.5001	1.84898
$902$	45.7430	1.52308
$903$	−11.5366	−0.383916
$904$	23.4643	0.780411
$905$	−29.8827	−0.993335
$906$	−31.7000	−1.05316
$907$	−1.40160	−0.0465393	−0.0232697	−	0.999729i	$-0.507408\pi$
$907$	−1.40160	−0.0465393	−0.0232697	+	0.999729i	$0.507408\pi$
$908$	−20.9554	−0.695428
$909$	−44.1522	−1.46444
$910$	−158.576	−5.25674
$911$	−37.0821	−1.22859	−0.614293	−	0.789078i	$-0.710559\pi$
$911$	−37.0821	−1.22859	−0.614293	+	0.789078i	$0.710559\pi$
$912$	16.2999	0.539743
$913$	25.8255	0.854701
$914$	−81.7974	−2.70562
$915$	3.58164	0.118405
$916$	−11.5713	−0.382328
$917$	−62.1774	−2.05328
$918$	−74.0978	−2.44559
$919$	−29.1651	−0.962068	−0.481034	−	0.876702i	$-0.659739\pi$
$919$	−29.1651	−0.962068	−0.481034	+	0.876702i	$0.659739\pi$
$920$	106.019	3.49533
$921$	−10.0641	−0.331623
$922$	29.6295	0.975797
$923$	54.6120	1.79758
$924$	−33.2503	−1.09386
$925$	−22.9901	−0.755909
$926$	−1.26185	−0.0414669
$927$	−30.9989	−1.01814
$928$	27.2934	0.895951
$929$	32.2894	1.05938	0.529691	−	0.848191i	$-0.322308\pi$
$929$	32.2894	1.05938	0.529691	+	0.848191i	$0.322308\pi$
$930$	−58.3202	−1.91239
$931$	−15.5558	−0.509820
$932$	−18.0673	−0.591814
$933$	−8.02762	−0.262812
$934$	−98.5977	−3.22622
$935$	−57.5679	−1.88267
$936$	−84.8640	−2.77387
$937$	4.45145	0.145422	0.0727112	−	0.997353i	$-0.476835\pi$
$937$	4.45145	0.145422	0.0727112	+	0.997353i	$0.476835\pi$
$938$	−39.8822	−1.30220
$939$	−4.26894	−0.139312
$940$	63.1467	2.05962
$941$	9.70654	0.316424	0.158212	−	0.987405i	$-0.449427\pi$
$941$	9.70654	0.316424	0.158212	+	0.987405i	$0.449427\pi$
$942$	−18.5172	−0.603323
$943$	−35.3885	−1.15241
$944$	−94.9814	−3.09138
$945$	−47.2668	−1.53759
$946$	−28.1101	−0.913939
$947$	14.0305	0.455929	0.227965	−	0.973669i	$-0.426793\pi$
$947$	14.0305	0.455929	0.227965	+	0.973669i	$0.426793\pi$
$948$	−22.0600	−0.716474
$949$	−19.6138	−0.636690
$950$	36.0704	1.17028
$951$	−4.44518	−0.144145
$952$	155.355	5.03507
$953$	−38.0163	−1.23147	−0.615735	−	0.787953i	$-0.711141\pi$
$953$	−38.0163	−1.23147	−0.615735	+	0.787953i	$0.711141\pi$
$954$	49.1414	1.59101
$955$	28.7239	0.929484
$956$	10.8983	0.352475
$957$	−9.70342	−0.313667
$958$	73.1546	2.36352
$959$	46.1386	1.48989
$960$	−0.824118	−0.0265983
$961$	53.6153	1.72953
$962$	−65.3888	−2.10822
$963$	−33.6978	−1.08589
$964$	80.6837	2.59865
$965$	78.8920	2.53962
$966$	37.1313	1.19468
$967$	−12.6036	−0.405305	−0.202653	−	0.979251i	$-0.564956\pi$
$967$	−12.6036	−0.405305	−0.202653	+	0.979251i	$0.564956\pi$
$968$	25.3543	0.814919
$969$	15.2853	0.491033
$970$	−135.376	−4.34667
$971$	−16.8926	−0.542108	−0.271054	−	0.962564i	$-0.587372\pi$
$971$	−16.8926	−0.542108	−0.271054	+	0.962564i	$0.587372\pi$
$972$	−70.7875	−2.27051
$973$	41.6246	1.33442
$974$	−5.92797	−0.189944
$975$	21.8281	0.699060
$976$	−10.5501	−0.337700
$977$	17.6812	0.565672	0.282836	−	0.959168i	$-0.408725\pi$
$977$	17.6812	0.565672	0.282836	+	0.959168i	$0.408725\pi$
$978$	−19.9852	−0.639055
$979$	14.0273	0.448315
$980$	78.2823	2.50064
$981$	−8.50811	−0.271643
$982$	22.0903	0.704931
$983$	−25.9834	−0.828741	−0.414371	−	0.910108i	$-0.635998\pi$
$983$	−25.9834	−0.828741	−0.414371	+	0.910108i	$0.635998\pi$
$984$	34.0157	1.08438
$985$	−62.0810	−1.97807
$986$	81.4634	2.59432
$987$	12.3083	0.391778
$988$	71.0733	2.26114
$989$	21.7470	0.691516
$990$	−50.9722	−1.62000
$991$	16.8308	0.534648	0.267324	−	0.963607i	$-0.413861\pi$
$991$	16.8308	0.534648	0.267324	+	0.963607i	$0.413861\pi$
$992$	53.9731	1.71365
$993$	−8.24900	−0.261774
$994$	−88.5201	−2.80769
$995$	−23.8302	−0.755468
$996$	34.5075	1.09341
$997$	−24.8267	−0.786270	−0.393135	−	0.919481i	$-0.628610\pi$
$997$	−24.8267	−0.786270	−0.393135	+	0.919481i	$0.628610\pi$
$998$	93.7208	2.96668
$999$	−19.4904	−0.616650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.13	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.13	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55145 q^{2} -0.786154 q^{3} +4.50991 q^{4} +3.16082 q^{5} +2.00584 q^{6} -3.53434 q^{7} -6.40393 q^{8} -2.38196 q^{9} +O(q^{10})\)	\(q-2.55145 q^{2} -0.786154 q^{3} +4.50991 q^{4} +3.16082 q^{5} +2.00584 q^{6} -3.53434 q^{7} -6.40393 q^{8} -2.38196 q^{9} -8.06468 q^{10} -2.65345 q^{11} -3.54549 q^{12} -5.56342 q^{13} +9.01770 q^{14} -2.48489 q^{15} +7.31950 q^{16} +6.86387 q^{17} +6.07746 q^{18} -2.83267 q^{19} +14.2550 q^{20} +2.77854 q^{21} +6.77016 q^{22} -5.23765 q^{23} +5.03447 q^{24} +4.99076 q^{25} +14.1948 q^{26} +4.23105 q^{27} -15.9396 q^{28} -4.65163 q^{29} +6.34008 q^{30} -9.19866 q^{31} -5.86750 q^{32} +2.08602 q^{33} -17.5128 q^{34} -11.1714 q^{35} -10.7424 q^{36} -4.60653 q^{37} +7.22742 q^{38} +4.37371 q^{39} -20.2416 q^{40} +6.75656 q^{41} -7.08930 q^{42} -4.15206 q^{43} -11.9668 q^{44} -7.52895 q^{45} +13.3636 q^{46} +4.42979 q^{47} -5.75425 q^{48} +5.49156 q^{49} -12.7337 q^{50} -5.39606 q^{51} -25.0906 q^{52} +8.08584 q^{53} -10.7953 q^{54} -8.38708 q^{55} +22.6337 q^{56} +2.22691 q^{57} +11.8684 q^{58} -12.9765 q^{59} -11.2066 q^{60} -1.44137 q^{61} +23.4699 q^{62} +8.41866 q^{63} +0.331652 q^{64} -17.5850 q^{65} -5.32239 q^{66} -4.42265 q^{67} +30.9555 q^{68} +4.11760 q^{69} +28.5033 q^{70} -9.81626 q^{71} +15.2539 q^{72} +3.52549 q^{73} +11.7533 q^{74} -3.92351 q^{75} -12.7751 q^{76} +9.37821 q^{77} -11.1593 q^{78} +6.22198 q^{79} +23.1356 q^{80} +3.81963 q^{81} -17.2391 q^{82} -9.73280 q^{83} +12.5310 q^{84} +21.6954 q^{85} +10.5938 q^{86} +3.65690 q^{87} +16.9925 q^{88} -5.28644 q^{89} +19.2098 q^{90} +19.6630 q^{91} -23.6214 q^{92} +7.23156 q^{93} -11.3024 q^{94} -8.95355 q^{95} +4.61276 q^{96} +16.7863 q^{97} -14.0115 q^{98} +6.32043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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