LMFDB - Embedded newform 6002.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.09636 q^{3} +1.00000 q^{4} -1.63895 q^{5} +2.09636 q^{6} +0.351798 q^{7} -1.00000 q^{8} +1.39473 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.09636 q^{3} +1.00000 q^{4} -1.63895 q^{5} +2.09636 q^{6} +0.351798 q^{7} -1.00000 q^{8} +1.39473 q^{9} +1.63895 q^{10} -1.18042 q^{11} -2.09636 q^{12} -5.78326 q^{13} -0.351798 q^{14} +3.43584 q^{15} +1.00000 q^{16} -5.65862 q^{17} -1.39473 q^{18} +2.16697 q^{19} -1.63895 q^{20} -0.737496 q^{21} +1.18042 q^{22} +4.97255 q^{23} +2.09636 q^{24} -2.31383 q^{25} +5.78326 q^{26} +3.36522 q^{27} +0.351798 q^{28} +2.37332 q^{29} -3.43584 q^{30} +5.26239 q^{31} -1.00000 q^{32} +2.47459 q^{33} +5.65862 q^{34} -0.576581 q^{35} +1.39473 q^{36} -2.42401 q^{37} -2.16697 q^{38} +12.1238 q^{39} +1.63895 q^{40} -3.32712 q^{41} +0.737496 q^{42} +12.7055 q^{43} -1.18042 q^{44} -2.28590 q^{45} -4.97255 q^{46} +13.5997 q^{47} -2.09636 q^{48} -6.87624 q^{49} +2.31383 q^{50} +11.8625 q^{51} -5.78326 q^{52} -0.946318 q^{53} -3.36522 q^{54} +1.93466 q^{55} -0.351798 q^{56} -4.54276 q^{57} -2.37332 q^{58} -0.507851 q^{59} +3.43584 q^{60} +2.88543 q^{61} -5.26239 q^{62} +0.490665 q^{63} +1.00000 q^{64} +9.47849 q^{65} -2.47459 q^{66} -12.7577 q^{67} -5.65862 q^{68} -10.4243 q^{69} +0.576581 q^{70} -3.63583 q^{71} -1.39473 q^{72} +1.50855 q^{73} +2.42401 q^{74} +4.85063 q^{75} +2.16697 q^{76} -0.415271 q^{77} -12.1238 q^{78} -9.98672 q^{79} -1.63895 q^{80} -11.2389 q^{81} +3.32712 q^{82} +11.8071 q^{83} -0.737496 q^{84} +9.27421 q^{85} -12.7055 q^{86} -4.97533 q^{87} +1.18042 q^{88} +5.44617 q^{89} +2.28590 q^{90} -2.03454 q^{91} +4.97255 q^{92} -11.0319 q^{93} -13.5997 q^{94} -3.55157 q^{95} +2.09636 q^{96} -15.7399 q^{97} +6.87624 q^{98} -1.64638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.09636	−1.21034	−0.605168	−	0.796098i	$-0.706894\pi$
$3$	−2.09636	−1.21034	−0.605168	+	0.796098i	$0.706894\pi$
$4$	1.00000	0.500000
$5$	−1.63895	−0.732962	−0.366481	−	0.930426i	$-0.619438\pi$
$5$	−1.63895	−0.732962	−0.366481	+	0.930426i	$0.619438\pi$
$6$	2.09636	0.855836
$7$	0.351798	0.132967	0.0664836	−	0.997788i	$-0.478822\pi$
$7$	0.351798	0.132967	0.0664836	+	0.997788i	$0.478822\pi$
$8$	−1.00000	−0.353553
$9$	1.39473	0.464911
$10$	1.63895	0.518282
$11$	−1.18042	−0.355911	−0.177955	−	0.984039i	$-0.556948\pi$
$11$	−1.18042	−0.355911	−0.177955	+	0.984039i	$0.556948\pi$
$12$	−2.09636	−0.605168
$13$	−5.78326	−1.60399	−0.801994	−	0.597332i	$-0.796227\pi$
$13$	−5.78326	−1.60399	−0.801994	+	0.597332i	$0.796227\pi$
$14$	−0.351798	−0.0940220
$15$	3.43584	0.887130
$16$	1.00000	0.250000
$17$	−5.65862	−1.37242	−0.686208	−	0.727405i	$-0.740726\pi$
$17$	−5.65862	−1.37242	−0.686208	+	0.727405i	$0.740726\pi$
$18$	−1.39473	−0.328742
$19$	2.16697	0.497138	0.248569	−	0.968614i	$-0.420040\pi$
$19$	2.16697	0.497138	0.248569	+	0.968614i	$0.420040\pi$
$20$	−1.63895	−0.366481
$21$	−0.737496	−0.160935
$22$	1.18042	0.251667
$23$	4.97255	1.03685	0.518425	−	0.855123i	$-0.326519\pi$
$23$	4.97255	1.03685	0.518425	+	0.855123i	$0.326519\pi$
$24$	2.09636	0.427918
$25$	−2.31383	−0.462767
$26$	5.78326	1.13419
$27$	3.36522	0.647637
$28$	0.351798	0.0664836
$29$	2.37332	0.440714	0.220357	−	0.975419i	$-0.429278\pi$
$29$	2.37332	0.440714	0.220357	+	0.975419i	$0.429278\pi$
$30$	−3.43584	−0.627296
$31$	5.26239	0.945154	0.472577	−	0.881289i	$-0.343324\pi$
$31$	5.26239	0.945154	0.472577	+	0.881289i	$0.343324\pi$
$32$	−1.00000	−0.176777
$33$	2.47459	0.430772
$34$	5.65862	0.970445
$35$	−0.576581	−0.0974599
$36$	1.39473	0.232456
$37$	−2.42401	−0.398505	−0.199253	−	0.979948i	$-0.563851\pi$
$37$	−2.42401	−0.398505	−0.199253	+	0.979948i	$0.563851\pi$
$38$	−2.16697	−0.351529
$39$	12.1238	1.94136
$40$	1.63895	0.259141
$41$	−3.32712	−0.519609	−0.259804	−	0.965661i	$-0.583658\pi$
$41$	−3.32712	−0.519609	−0.259804	+	0.965661i	$0.583658\pi$
$42$	0.737496	0.113798
$43$	12.7055	1.93758	0.968788	−	0.247892i	$-0.0797378\pi$
$43$	12.7055	1.93758	0.968788	+	0.247892i	$0.0797378\pi$
$44$	−1.18042	−0.177955
$45$	−2.28590	−0.340763
$46$	−4.97255	−0.733163
$47$	13.5997	1.98372	0.991862	−	0.127321i	$-0.0406379\pi$
$47$	13.5997	1.98372	0.991862	+	0.127321i	$0.0406379\pi$
$48$	−2.09636	−0.302584
$49$	−6.87624	−0.982320
$50$	2.31383	0.327225
$51$	11.8625	1.66108
$52$	−5.78326	−0.801994
$53$	−0.946318	−0.129987	−0.0649934	−	0.997886i	$-0.520703\pi$
$53$	−0.946318	−0.129987	−0.0649934	+	0.997886i	$0.520703\pi$
$54$	−3.36522	−0.457948
$55$	1.93466	0.260869
$56$	−0.351798	−0.0470110
$57$	−4.54276	−0.601703
$58$	−2.37332	−0.311632
$59$	−0.507851	−0.0661166	−0.0330583	−	0.999453i	$-0.510525\pi$
$59$	−0.507851	−0.0661166	−0.0330583	+	0.999453i	$0.510525\pi$
$60$	3.43584	0.443565
$61$	2.88543	0.369441	0.184721	−	0.982791i	$-0.440862\pi$
$61$	2.88543	0.369441	0.184721	+	0.982791i	$0.440862\pi$
$62$	−5.26239	−0.668325
$63$	0.490665	0.0618180
$64$	1.00000	0.125000
$65$	9.47849	1.17566
$66$	−2.47459	−0.304601
$67$	−12.7577	−1.55860	−0.779300	−	0.626652i	$-0.784425\pi$
$67$	−12.7577	−1.55860	−0.779300	+	0.626652i	$0.784425\pi$
$68$	−5.65862	−0.686208
$69$	−10.4243	−1.25494
$70$	0.576581	0.0689146
$71$	−3.63583	−0.431494	−0.215747	−	0.976449i	$-0.569219\pi$
$71$	−3.63583	−0.431494	−0.215747	+	0.976449i	$0.569219\pi$
$72$	−1.39473	−0.164371
$73$	1.50855	0.176563	0.0882813	−	0.996096i	$-0.471863\pi$
$73$	1.50855	0.176563	0.0882813	+	0.996096i	$0.471863\pi$
$74$	2.42401	0.281786
$75$	4.85063	0.560103
$76$	2.16697	0.248569
$77$	−0.415271	−0.0473245
$78$	−12.1238	−1.37275
$79$	−9.98672	−1.12359	−0.561797	−	0.827275i	$-0.689890\pi$
$79$	−9.98672	−1.12359	−0.561797	+	0.827275i	$0.689890\pi$
$80$	−1.63895	−0.183241
$81$	−11.2389	−1.24877
$82$	3.32712	0.367419
$83$	11.8071	1.29600	0.647998	−	0.761642i	$-0.275606\pi$
$83$	11.8071	1.29600	0.647998	+	0.761642i	$0.275606\pi$
$84$	−0.737496	−0.0804675
$85$	9.27421	1.00593
$86$	−12.7055	−1.37007
$87$	−4.97533	−0.533412
$88$	1.18042	0.125834
$89$	5.44617	0.577293	0.288646	−	0.957436i	$-0.406795\pi$
$89$	5.44617	0.577293	0.288646	+	0.957436i	$0.406795\pi$
$90$	2.28590	0.240955
$91$	−2.03454	−0.213278
$92$	4.97255	0.518425
$93$	−11.0319	−1.14395
$94$	−13.5997	−1.40270
$95$	−3.55157	−0.364383
$96$	2.09636	0.213959
$97$	−15.7399	−1.59815	−0.799073	−	0.601234i	$-0.794676\pi$
$97$	−15.7399	−1.59815	−0.799073	+	0.601234i	$0.794676\pi$
$98$	6.87624	0.694605
$99$	−1.64638	−0.165467
$100$	−2.31383	−0.231383
$101$	6.39617	0.636443	0.318222	−	0.948016i	$-0.396914\pi$
$101$	6.39617	0.636443	0.318222	+	0.948016i	$0.396914\pi$
$102$	−11.8625	−1.17456
$103$	10.2622	1.01116	0.505581	−	0.862779i	$-0.331278\pi$
$103$	10.2622	1.01116	0.505581	+	0.862779i	$0.331278\pi$
$104$	5.78326	0.567095
$105$	1.20872	0.117959
$106$	0.946318	0.0919146
$107$	−3.10744	−0.300407	−0.150204	−	0.988655i	$-0.547993\pi$
$107$	−3.10744	−0.300407	−0.150204	+	0.988655i	$0.547993\pi$
$108$	3.36522	0.323818
$109$	15.1872	1.45467	0.727333	−	0.686284i	$-0.240759\pi$
$109$	15.1872	1.45467	0.727333	+	0.686284i	$0.240759\pi$
$110$	−1.93466	−0.184462
$111$	5.08161	0.482325
$112$	0.351798	0.0332418
$113$	18.6162	1.75127	0.875634	−	0.482975i	$-0.160444\pi$
$113$	18.6162	1.75127	0.875634	+	0.482975i	$0.160444\pi$
$114$	4.54276	0.425468
$115$	−8.14978	−0.759971
$116$	2.37332	0.220357
$117$	−8.06611	−0.745712
$118$	0.507851	0.0467515
$119$	−1.99069	−0.182486
$120$	−3.43584	−0.313648
$121$	−9.60660	−0.873327
$122$	−2.88543	−0.261234
$123$	6.97484	0.628901
$124$	5.26239	0.472577
$125$	11.9870	1.07215
$126$	−0.490665	−0.0437119
$127$	−14.0234	−1.24438	−0.622189	−	0.782867i	$-0.713757\pi$
$127$	−14.0234	−1.24438	−0.622189	+	0.782867i	$0.713757\pi$
$128$	−1.00000	−0.0883883
$129$	−26.6354	−2.34512
$130$	−9.47849	−0.831319
$131$	11.3702	0.993421	0.496711	−	0.867916i	$-0.334541\pi$
$131$	11.3702	0.993421	0.496711	+	0.867916i	$0.334541\pi$
$132$	2.47459	0.215386
$133$	0.762337	0.0661030
$134$	12.7577	1.10210
$135$	−5.51543	−0.474693
$136$	5.65862	0.485222
$137$	6.58198	0.562337	0.281168	−	0.959658i	$-0.409278\pi$
$137$	6.58198	0.562337	0.281168	+	0.959658i	$0.409278\pi$
$138$	10.4243	0.887373
$139$	16.7400	1.41986	0.709932	−	0.704270i	$-0.248726\pi$
$139$	16.7400	1.41986	0.709932	+	0.704270i	$0.248726\pi$
$140$	−0.576581	−0.0487300
$141$	−28.5099	−2.40097
$142$	3.63583	0.305112
$143$	6.82669	0.570877
$144$	1.39473	0.116228
$145$	−3.88975	−0.323027
$146$	−1.50855	−0.124849
$147$	14.4151	1.18894
$148$	−2.42401	−0.199253
$149$	11.5959	0.949974	0.474987	−	0.879993i	$-0.342453\pi$
$149$	11.5959	0.949974	0.474987	+	0.879993i	$0.342453\pi$
$150$	−4.85063	−0.396052
$151$	3.71912	0.302658	0.151329	−	0.988483i	$-0.451645\pi$
$151$	3.71912	0.302658	0.151329	+	0.988483i	$0.451645\pi$
$152$	−2.16697	−0.175765
$153$	−7.89227	−0.638052
$154$	0.415271	0.0334635
$155$	−8.62482	−0.692762
$156$	12.1238	0.970681
$157$	−7.24700	−0.578374	−0.289187	−	0.957273i	$-0.593385\pi$
$157$	−7.24700	−0.578374	−0.289187	+	0.957273i	$0.593385\pi$
$158$	9.98672	0.794501
$159$	1.98383	0.157328
$160$	1.63895	0.129571
$161$	1.74934	0.137867
$162$	11.2389	0.883013
$163$	−13.0583	−1.02281	−0.511404	−	0.859341i	$-0.670874\pi$
$163$	−13.0583	−1.02281	−0.511404	+	0.859341i	$0.670874\pi$
$164$	−3.32712	−0.259804
$165$	−4.05574	−0.315739
$166$	−11.8071	−0.916408
$167$	1.37630	0.106501	0.0532505	−	0.998581i	$-0.483042\pi$
$167$	1.37630	0.106501	0.0532505	+	0.998581i	$0.483042\pi$
$168$	0.737496	0.0568991
$169$	20.4461	1.57278
$170$	−9.27421	−0.711299
$171$	3.02235	0.231125
$172$	12.7055	0.968788
$173$	−21.9487	−1.66873	−0.834364	−	0.551214i	$-0.814165\pi$
$173$	−21.9487	−1.66873	−0.834364	+	0.551214i	$0.814165\pi$
$174$	4.97533	0.377179
$175$	−0.814002	−0.0615328
$176$	−1.18042	−0.0889777
$177$	1.06464	0.0800233
$178$	−5.44617	−0.408208
$179$	−11.7423	−0.877661	−0.438830	−	0.898570i	$-0.644607\pi$
$179$	−11.7423	−0.877661	−0.438830	+	0.898570i	$0.644607\pi$
$180$	−2.28590	−0.170381
$181$	16.3001	1.21157	0.605787	−	0.795627i	$-0.292858\pi$
$181$	16.3001	1.21157	0.605787	+	0.795627i	$0.292858\pi$
$182$	2.03454	0.150810
$183$	−6.04890	−0.447148
$184$	−4.97255	−0.366582
$185$	3.97284	0.292089
$186$	11.0319	0.808897
$187$	6.67956	0.488458
$188$	13.5997	0.991862
$189$	1.18388	0.0861144
$190$	3.55157	0.257658
$191$	11.8111	0.854622	0.427311	−	0.904105i	$-0.359461\pi$
$191$	11.8111	0.854622	0.427311	+	0.904105i	$0.359461\pi$
$192$	−2.09636	−0.151292
$193$	−19.2132	−1.38300	−0.691498	−	0.722378i	$-0.743049\pi$
$193$	−19.2132	−1.38300	−0.691498	+	0.722378i	$0.743049\pi$
$194$	15.7399	1.13006
$195$	−19.8704	−1.42295
$196$	−6.87624	−0.491160
$197$	−17.6068	−1.25443	−0.627217	−	0.778845i	$-0.715806\pi$
$197$	−17.6068	−1.25443	−0.627217	+	0.778845i	$0.715806\pi$
$198$	1.64638	0.117003
$199$	5.33798	0.378400	0.189200	−	0.981939i	$-0.439411\pi$
$199$	5.33798	0.378400	0.189200	+	0.981939i	$0.439411\pi$
$200$	2.31383	0.163613
$201$	26.7447	1.88643
$202$	−6.39617	−0.450033
$203$	0.834929	0.0586005
$204$	11.8625	0.830542
$205$	5.45299	0.380853
$206$	−10.2622	−0.714999
$207$	6.93539	0.482043
$208$	−5.78326	−0.400997
$209$	−2.55794	−0.176937
$210$	−1.20872	−0.0834097
$211$	8.97830	0.618091	0.309046	−	0.951047i	$-0.399990\pi$
$211$	8.97830	0.618091	0.309046	+	0.951047i	$0.399990\pi$
$212$	−0.946318	−0.0649934
$213$	7.62203	0.522253
$214$	3.10744	0.212420
$215$	−20.8238	−1.42017
$216$	−3.36522	−0.228974
$217$	1.85130	0.125674
$218$	−15.1872	−1.02860
$219$	−3.16247	−0.213700
$220$	1.93466	0.130435
$221$	32.7252	2.20134
$222$	−5.08161	−0.341055
$223$	−13.5718	−0.908837	−0.454418	−	0.890788i	$-0.650153\pi$
$223$	−13.5718	−0.908837	−0.454418	+	0.890788i	$0.650153\pi$
$224$	−0.351798	−0.0235055
$225$	−3.22718	−0.215145
$226$	−18.6162	−1.23833
$227$	3.69061	0.244955	0.122477	−	0.992471i	$-0.460916\pi$
$227$	3.69061	0.244955	0.122477	+	0.992471i	$0.460916\pi$
$228$	−4.54276	−0.300852
$229$	26.7085	1.76495	0.882475	−	0.470359i	$-0.155876\pi$
$229$	26.7085	1.76495	0.882475	+	0.470359i	$0.155876\pi$
$230$	8.14978	0.537381
$231$	0.870558	0.0572785
$232$	−2.37332	−0.155816
$233$	3.39484	0.222403	0.111202	−	0.993798i	$-0.464530\pi$
$233$	3.39484	0.222403	0.111202	+	0.993798i	$0.464530\pi$
$234$	8.06611	0.527298
$235$	−22.2893	−1.45399
$236$	−0.507851	−0.0330583
$237$	20.9358	1.35993
$238$	1.99069	0.129037
$239$	20.8642	1.34959	0.674796	−	0.738004i	$-0.264232\pi$
$239$	20.8642	1.34959	0.674796	+	0.738004i	$0.264232\pi$
$240$	3.43584	0.221782
$241$	−11.7101	−0.754312	−0.377156	−	0.926150i	$-0.623098\pi$
$241$	−11.7101	−0.754312	−0.377156	+	0.926150i	$0.623098\pi$
$242$	9.60660	0.617536
$243$	13.4652	0.863792
$244$	2.88543	0.184721
$245$	11.2698	0.720003
$246$	−6.97484	−0.444700
$247$	−12.5322	−0.797402
$248$	−5.26239	−0.334162
$249$	−24.7519	−1.56859
$250$	−11.9870	−0.758126
$251$	−3.26553	−0.206119	−0.103059	−	0.994675i	$-0.532863\pi$
$251$	−3.26553	−0.206119	−0.103059	+	0.994675i	$0.532863\pi$
$252$	0.490665	0.0309090
$253$	−5.86972	−0.369026
$254$	14.0234	0.879908
$255$	−19.4421	−1.21751
$256$	1.00000	0.0625000
$257$	−3.97024	−0.247657	−0.123828	−	0.992304i	$-0.539517\pi$
$257$	−3.97024	−0.247657	−0.123828	+	0.992304i	$0.539517\pi$
$258$	26.6354	1.65825
$259$	−0.852763	−0.0529881
$260$	9.47849	0.587831
$261$	3.31015	0.204893
$262$	−11.3702	−0.702455
$263$	−9.38158	−0.578493	−0.289247	−	0.957255i	$-0.593405\pi$
$263$	−9.38158	−0.578493	−0.289247	+	0.957255i	$0.593405\pi$
$264$	−2.47459	−0.152301
$265$	1.55097	0.0952754
$266$	−0.762337	−0.0467419
$267$	−11.4171	−0.698718
$268$	−12.7577	−0.779300
$269$	−4.67569	−0.285082	−0.142541	−	0.989789i	$-0.545527\pi$
$269$	−4.67569	−0.285082	−0.142541	+	0.989789i	$0.545527\pi$
$270$	5.51543	0.335659
$271$	−15.6949	−0.953394	−0.476697	−	0.879068i	$-0.658166\pi$
$271$	−15.6949	−0.953394	−0.476697	+	0.879068i	$0.658166\pi$
$272$	−5.65862	−0.343104
$273$	4.26513	0.258138
$274$	−6.58198	−0.397632
$275$	2.73130	0.164704
$276$	−10.4243	−0.627468
$277$	27.5760	1.65688	0.828441	−	0.560076i	$-0.189228\pi$
$277$	27.5760	1.65688	0.828441	+	0.560076i	$0.189228\pi$
$278$	−16.7400	−1.00400
$279$	7.33964	0.439413
$280$	0.576581	0.0344573
$281$	5.25916	0.313735	0.156868	−	0.987620i	$-0.449860\pi$
$281$	5.25916	0.313735	0.156868	+	0.987620i	$0.449860\pi$
$282$	28.5099	1.69774
$283$	−32.4183	−1.92707	−0.963534	−	0.267585i	$-0.913774\pi$
$283$	−32.4183	−1.92707	−0.963534	+	0.267585i	$0.913774\pi$
$284$	−3.63583	−0.215747
$285$	7.44537	0.441026
$286$	−6.82669	−0.403671
$287$	−1.17047	−0.0690909
$288$	−1.39473	−0.0821855
$289$	15.0199	0.883526
$290$	3.88975	0.228414
$291$	32.9966	1.93429
$292$	1.50855	0.0882813
$293$	−4.68375	−0.273628	−0.136814	−	0.990597i	$-0.543686\pi$
$293$	−4.68375	−0.273628	−0.136814	+	0.990597i	$0.543686\pi$
$294$	−14.4151	−0.840705
$295$	0.832344	0.0484610
$296$	2.42401	0.140893
$297$	−3.97238	−0.230501
$298$	−11.5959	−0.671733
$299$	−28.7576	−1.66309
$300$	4.85063	0.280051
$301$	4.46978	0.257634
$302$	−3.71912	−0.214011
$303$	−13.4087	−0.770310
$304$	2.16697	0.124284
$305$	−4.72908	−0.270786
$306$	7.89227	0.451171
$307$	−5.80406	−0.331255	−0.165628	−	0.986188i	$-0.552965\pi$
$307$	−5.80406	−0.331255	−0.165628	+	0.986188i	$0.552965\pi$
$308$	−0.415271	−0.0236622
$309$	−21.5132	−1.22384
$310$	8.62482	0.489857
$311$	−9.09059	−0.515480	−0.257740	−	0.966214i	$-0.582978\pi$
$311$	−9.09059	−0.515480	−0.257740	+	0.966214i	$0.582978\pi$
$312$	−12.1238	−0.686375
$313$	1.72354	0.0974202	0.0487101	−	0.998813i	$-0.484489\pi$
$313$	1.72354	0.0974202	0.0487101	+	0.998813i	$0.484489\pi$
$314$	7.24700	0.408972
$315$	−0.804177	−0.0453102
$316$	−9.98672	−0.561797
$317$	−16.0419	−0.901002	−0.450501	−	0.892776i	$-0.648755\pi$
$317$	−16.0419	−0.901002	−0.450501	+	0.892776i	$0.648755\pi$
$318$	−1.98383	−0.111247
$319$	−2.80152	−0.156855
$320$	−1.63895	−0.0916203
$321$	6.51431	0.363594
$322$	−1.74934	−0.0974866
$323$	−12.2621	−0.682280
$324$	−11.2389	−0.624384
$325$	13.3815	0.742272
$326$	13.0583	0.723234
$327$	−31.8378	−1.76063
$328$	3.32712	0.183709
$329$	4.78436	0.263770
$330$	4.05574	0.223261
$331$	7.26817	0.399495	0.199747	−	0.979847i	$-0.435988\pi$
$331$	7.26817	0.399495	0.199747	+	0.979847i	$0.435988\pi$
$332$	11.8071	0.647998
$333$	−3.38085	−0.185270
$334$	−1.37630	−0.0753075
$335$	20.9092	1.14239
$336$	−0.737496	−0.0402337
$337$	18.8652	1.02766	0.513828	−	0.857894i	$-0.328227\pi$
$337$	18.8652	1.02766	0.513828	+	0.857894i	$0.328227\pi$
$338$	−20.4461	−1.11212
$339$	−39.0264	−2.11962
$340$	9.27421	0.502964
$341$	−6.21185	−0.336391
$342$	−3.02235	−0.163430
$343$	−4.88164	−0.263584
$344$	−12.7055	−0.685036
$345$	17.0849	0.919820
$346$	21.9487	1.17997
$347$	−12.4793	−0.669922	−0.334961	−	0.942232i	$-0.608723\pi$
$347$	−12.4793	−0.669922	−0.334961	+	0.942232i	$0.608723\pi$
$348$	−4.97533	−0.266706
$349$	24.7433	1.32448	0.662238	−	0.749293i	$-0.269607\pi$
$349$	24.7433	1.32448	0.662238	+	0.749293i	$0.269607\pi$
$350$	0.814002	0.0435102
$351$	−19.4619	−1.03880
$352$	1.18042	0.0629168
$353$	−20.1450	−1.07221	−0.536105	−	0.844151i	$-0.680105\pi$
$353$	−20.1450	−1.07221	−0.536105	+	0.844151i	$0.680105\pi$
$354$	−1.06464	−0.0565850
$355$	5.95896	0.316269
$356$	5.44617	0.288646
$357$	4.17321	0.220870
$358$	11.7423	0.620600
$359$	−6.67578	−0.352334	−0.176167	−	0.984360i	$-0.556370\pi$
$359$	−6.67578	−0.352334	−0.176167	+	0.984360i	$0.556370\pi$
$360$	2.28590	0.120478
$361$	−14.3042	−0.752854
$362$	−16.3001	−0.856712
$363$	20.1389	1.05702
$364$	−2.03454	−0.106639
$365$	−2.47244	−0.129414
$366$	6.04890	0.316181
$367$	−24.0872	−1.25734	−0.628672	−	0.777671i	$-0.716401\pi$
$367$	−24.0872	−1.25734	−0.628672	+	0.777671i	$0.716401\pi$
$368$	4.97255	0.259212
$369$	−4.64045	−0.241572
$370$	−3.97284	−0.206538
$371$	−0.332913	−0.0172840
$372$	−11.0319	−0.571976
$373$	−28.5444	−1.47797	−0.738986	−	0.673720i	$-0.764695\pi$
$373$	−28.5444	−1.47797	−0.738986	+	0.673720i	$0.764695\pi$
$374$	−6.67956	−0.345392
$375$	−25.1292	−1.29766
$376$	−13.5997	−0.701352
$377$	−13.7255	−0.706900
$378$	−1.18388	−0.0608921
$379$	−15.7164	−0.807296	−0.403648	−	0.914914i	$-0.632258\pi$
$379$	−15.7164	−0.807296	−0.403648	+	0.914914i	$0.632258\pi$
$380$	−3.55157	−0.182191
$381$	29.3982	1.50612
$382$	−11.8111	−0.604309
$383$	−5.61674	−0.287002	−0.143501	−	0.989650i	$-0.545836\pi$
$383$	−5.61674	−0.287002	−0.143501	+	0.989650i	$0.545836\pi$
$384$	2.09636	0.106980
$385$	0.680609	0.0346871
$386$	19.2132	0.977926
$387$	17.7208	0.900801
$388$	−15.7399	−0.799073
$389$	0.210807	0.0106884	0.00534418	−	0.999986i	$-0.498299\pi$
$389$	0.210807	0.0106884	0.00534418	+	0.999986i	$0.498299\pi$
$390$	19.8704	1.00617
$391$	−28.1378	−1.42299
$392$	6.87624	0.347302
$393$	−23.8361	−1.20237
$394$	17.6068	0.887018
$395$	16.3678	0.823552
$396$	−1.64638	−0.0827335
$397$	−8.63726	−0.433491	−0.216746	−	0.976228i	$-0.569544\pi$
$397$	−8.63726	−0.433491	−0.216746	+	0.976228i	$0.569544\pi$
$398$	−5.33798	−0.267569
$399$	−1.59813	−0.0800068
$400$	−2.31383	−0.115692
$401$	8.52496	0.425716	0.212858	−	0.977083i	$-0.431723\pi$
$401$	8.52496	0.425716	0.212858	+	0.977083i	$0.431723\pi$
$402$	−26.7447	−1.33391
$403$	−30.4338	−1.51601
$404$	6.39617	0.318222
$405$	18.4201	0.915300
$406$	−0.834929	−0.0414368
$407$	2.86136	0.141832
$408$	−11.8625	−0.587282
$409$	−32.9748	−1.63050	−0.815248	−	0.579112i	$-0.803400\pi$
$409$	−32.9748	−1.63050	−0.815248	+	0.579112i	$0.803400\pi$
$410$	−5.45299	−0.269304
$411$	−13.7982	−0.680616
$412$	10.2622	0.505581
$413$	−0.178661	−0.00879134
$414$	−6.93539	−0.340856
$415$	−19.3513	−0.949916
$416$	5.78326	0.283548
$417$	−35.0930	−1.71851
$418$	2.55794	0.125113
$419$	12.8564	0.628077	0.314038	−	0.949410i	$-0.398318\pi$
$419$	12.8564	0.628077	0.314038	+	0.949410i	$0.398318\pi$
$420$	1.20872	0.0589796
$421$	4.93369	0.240453	0.120227	−	0.992746i	$-0.461638\pi$
$421$	4.93369	0.240453	0.120227	+	0.992746i	$0.461638\pi$
$422$	−8.97830	−0.437057
$423$	18.9680	0.922256
$424$	0.946318	0.0459573
$425$	13.0931	0.635108
$426$	−7.62203	−0.369288
$427$	1.01509	0.0491236
$428$	−3.10744	−0.150204
$429$	−14.3112	−0.690952
$430$	20.8238	1.00421
$431$	11.5436	0.556036	0.278018	−	0.960576i	$-0.410322\pi$
$431$	11.5436	0.556036	0.278018	+	0.960576i	$0.410322\pi$
$432$	3.36522	0.161909
$433$	−31.8626	−1.53122	−0.765609	−	0.643306i	$-0.777562\pi$
$433$	−31.8626	−1.53122	−0.765609	+	0.643306i	$0.777562\pi$
$434$	−1.85130	−0.0888653
$435$	8.15434	0.390970
$436$	15.1872	0.727333
$437$	10.7754	0.515457
$438$	3.16247	0.151109
$439$	5.74951	0.274409	0.137205	−	0.990543i	$-0.456188\pi$
$439$	5.74951	0.274409	0.137205	+	0.990543i	$0.456188\pi$
$440$	−1.93466	−0.0922312
$441$	−9.59053	−0.456692
$442$	−32.7252	−1.55658
$443$	−23.3036	−1.10719	−0.553594	−	0.832787i	$-0.686744\pi$
$443$	−23.3036	−1.10719	−0.553594	+	0.832787i	$0.686744\pi$
$444$	5.08161	0.241162
$445$	−8.92602	−0.423134
$446$	13.5718	0.642645
$447$	−24.3092	−1.14979
$448$	0.351798	0.0166209
$449$	−16.6340	−0.785005	−0.392503	−	0.919751i	$-0.628391\pi$
$449$	−16.6340	−0.785005	−0.392503	+	0.919751i	$0.628391\pi$
$450$	3.22718	0.152131
$451$	3.92741	0.184934
$452$	18.6162	0.875634
$453$	−7.79662	−0.366317
$454$	−3.69061	−0.173209
$455$	3.33452	0.156325
$456$	4.54276	0.212734
$457$	−0.671173	−0.0313962	−0.0156981	−	0.999877i	$-0.504997\pi$
$457$	−0.671173	−0.0313962	−0.0156981	+	0.999877i	$0.504997\pi$
$458$	−26.7085	−1.24801
$459$	−19.0425	−0.888827
$460$	−8.14978	−0.379986
$461$	9.29091	0.432721	0.216360	−	0.976314i	$-0.430581\pi$
$461$	9.29091	0.432721	0.216360	+	0.976314i	$0.430581\pi$
$462$	−0.870558	−0.0405020
$463$	−7.41188	−0.344459	−0.172230	−	0.985057i	$-0.555097\pi$
$463$	−7.41188	−0.344459	−0.172230	+	0.985057i	$0.555097\pi$
$464$	2.37332	0.110178
$465$	18.0807	0.838474
$466$	−3.39484	−0.157263
$467$	9.18352	0.424962	0.212481	−	0.977165i	$-0.431846\pi$
$467$	9.18352	0.424962	0.212481	+	0.977165i	$0.431846\pi$
$468$	−8.06611	−0.372856
$469$	−4.48813	−0.207243
$470$	22.2893	1.02813
$471$	15.1923	0.700026
$472$	0.507851	0.0233757
$473$	−14.9979	−0.689604
$474$	−20.9358	−0.961613
$475$	−5.01401	−0.230059
$476$	−1.99069	−0.0912432
$477$	−1.31986	−0.0604324
$478$	−20.8642	−0.954306
$479$	22.5962	1.03245	0.516224	−	0.856454i	$-0.327337\pi$
$479$	22.5962	1.03245	0.516224	+	0.856454i	$0.327337\pi$
$480$	−3.43584	−0.156824
$481$	14.0187	0.639197
$482$	11.7101	0.533379
$483$	−3.66724	−0.166865
$484$	−9.60660	−0.436664
$485$	25.7970	1.17138
$486$	−13.4652	−0.610793
$487$	2.49179	0.112914	0.0564569	−	0.998405i	$-0.482020\pi$
$487$	2.49179	0.112914	0.0564569	+	0.998405i	$0.482020\pi$
$488$	−2.88543	−0.130617
$489$	27.3750	1.23794
$490$	−11.2698	−0.509119
$491$	−7.12504	−0.321549	−0.160774	−	0.986991i	$-0.551399\pi$
$491$	−7.12504	−0.321549	−0.160774	+	0.986991i	$0.551399\pi$
$492$	6.97484	0.314450
$493$	−13.4297	−0.604843
$494$	12.5322	0.563849
$495$	2.69833	0.121281
$496$	5.26239	0.236288
$497$	−1.27908	−0.0573746
$498$	24.7519	1.10916
$499$	6.77556	0.303316	0.151658	−	0.988433i	$-0.451539\pi$
$499$	6.77556	0.303316	0.151658	+	0.988433i	$0.451539\pi$
$500$	11.9870	0.536076
$501$	−2.88521	−0.128902
$502$	3.26553	0.145748
$503$	−3.33860	−0.148861	−0.0744304	−	0.997226i	$-0.523714\pi$
$503$	−3.33860	−0.148861	−0.0744304	+	0.997226i	$0.523714\pi$
$504$	−0.490665	−0.0218560
$505$	−10.4830	−0.466489
$506$	5.86972	0.260941
$507$	−42.8624	−1.90359
$508$	−14.0234	−0.622189
$509$	17.6637	0.782931	0.391466	−	0.920193i	$-0.371968\pi$
$509$	17.6637	0.782931	0.391466	+	0.920193i	$0.371968\pi$
$510$	19.4421	0.860911
$511$	0.530705	0.0234770
$512$	−1.00000	−0.0441942
$513$	7.29233	0.321964
$514$	3.97024	0.175120
$515$	−16.8192	−0.741143
$516$	−26.6354	−1.17256
$517$	−16.0534	−0.706029
$518$	0.852763	0.0374682
$519$	46.0124	2.01972
$520$	−9.47849	−0.415659
$521$	−5.66668	−0.248262	−0.124131	−	0.992266i	$-0.539614\pi$
$521$	−5.66668	−0.248262	−0.124131	+	0.992266i	$0.539614\pi$
$522$	−3.31015	−0.144881
$523$	30.9761	1.35449	0.677245	−	0.735758i	$-0.263174\pi$
$523$	30.9761	1.35449	0.677245	+	0.735758i	$0.263174\pi$
$524$	11.3702	0.496711
$525$	1.70644	0.0744753
$526$	9.38158	0.409056
$527$	−29.7779	−1.29714
$528$	2.47459	0.107693
$529$	1.72629	0.0750560
$530$	−1.55097	−0.0673699
$531$	−0.708318	−0.0307384
$532$	0.762337	0.0330515
$533$	19.2416	0.833446
$534$	11.4171	0.494068
$535$	5.09294	0.220187
$536$	12.7577	0.551048
$537$	24.6161	1.06226
$538$	4.67569	0.201583
$539$	8.11687	0.349618
$540$	−5.51543	−0.237347
$541$	−22.1325	−0.951551	−0.475775	−	0.879567i	$-0.657833\pi$
$541$	−22.1325	−0.951551	−0.475775	+	0.879567i	$0.657833\pi$
$542$	15.6949	0.674152
$543$	−34.1708	−1.46641
$544$	5.65862	0.242611
$545$	−24.8911	−1.06622
$546$	−4.26513	−0.182531
$547$	6.17834	0.264167	0.132083	−	0.991239i	$-0.457833\pi$
$547$	6.17834	0.264167	0.132083	+	0.991239i	$0.457833\pi$
$548$	6.58198	0.281168
$549$	4.02441	0.171757
$550$	−2.73130	−0.116463
$551$	5.14291	0.219095
$552$	10.4243	0.443687
$553$	−3.51331	−0.149401
$554$	−27.5760	−1.17159
$555$	−8.32851	−0.353526
$556$	16.7400	0.709932
$557$	−24.5230	−1.03907	−0.519536	−	0.854449i	$-0.673895\pi$
$557$	−24.5230	−1.03907	−0.519536	+	0.854449i	$0.673895\pi$
$558$	−7.33964	−0.310712
$559$	−73.4794	−3.10785
$560$	−0.576581	−0.0243650
$561$	−14.0028	−0.591198
$562$	−5.25916	−0.221844
$563$	12.6034	0.531169	0.265584	−	0.964088i	$-0.414435\pi$
$563$	12.6034	0.531169	0.265584	+	0.964088i	$0.414435\pi$
$564$	−28.5099	−1.20049
$565$	−30.5111	−1.28361
$566$	32.4183	1.36264
$567$	−3.95383	−0.166045
$568$	3.63583	0.152556
$569$	−23.7733	−0.996627	−0.498313	−	0.866997i	$-0.666047\pi$
$569$	−23.7733	−0.996627	−0.498313	+	0.866997i	$0.666047\pi$
$570$	−7.44537	−0.311852
$571$	7.40722	0.309983	0.154991	−	0.987916i	$-0.450465\pi$
$571$	7.40722	0.309983	0.154991	+	0.987916i	$0.450465\pi$
$572$	6.82669	0.285438
$573$	−24.7604	−1.03438
$574$	1.17047	0.0488546
$575$	−11.5057	−0.479819
$576$	1.39473	0.0581139
$577$	−17.1347	−0.713327	−0.356664	−	0.934233i	$-0.616086\pi$
$577$	−17.1347	−0.713327	−0.356664	+	0.934233i	$0.616086\pi$
$578$	−15.0199	−0.624747
$579$	40.2778	1.67389
$580$	−3.88975	−0.161513
$581$	4.15371	0.172325
$582$	−32.9966	−1.36775
$583$	1.11706	0.0462637
$584$	−1.50855	−0.0624243
$585$	13.2200	0.546579
$586$	4.68375	0.193484
$587$	37.5896	1.55149	0.775744	−	0.631047i	$-0.217375\pi$
$587$	37.5896	1.55149	0.775744	+	0.631047i	$0.217375\pi$
$588$	14.4151	0.594468
$589$	11.4035	0.469871
$590$	−0.832344	−0.0342671
$591$	36.9102	1.51828
$592$	−2.42401	−0.0996263
$593$	−8.18416	−0.336083	−0.168042	−	0.985780i	$-0.553744\pi$
$593$	−8.18416	−0.336083	−0.168042	+	0.985780i	$0.553744\pi$
$594$	3.97238	0.162989
$595$	3.26265	0.133756
$596$	11.5959	0.474987
$597$	−11.1903	−0.457990
$598$	28.7576	1.17598
$599$	−4.68968	−0.191615	−0.0958076	−	0.995400i	$-0.530543\pi$
$599$	−4.68968	−0.191615	−0.0958076	+	0.995400i	$0.530543\pi$
$600$	−4.85063	−0.198026
$601$	−8.74861	−0.356863	−0.178432	−	0.983952i	$-0.557102\pi$
$601$	−8.74861	−0.356863	−0.178432	+	0.983952i	$0.557102\pi$
$602$	−4.46978	−0.182175
$603$	−17.7936	−0.724611
$604$	3.71912	0.151329
$605$	15.7448	0.640116
$606$	13.4087	0.544691
$607$	−19.5784	−0.794663	−0.397332	−	0.917675i	$-0.630064\pi$
$607$	−19.5784	−0.794663	−0.397332	+	0.917675i	$0.630064\pi$
$608$	−2.16697	−0.0878823
$609$	−1.75031	−0.0709262
$610$	4.72908	0.191475
$611$	−78.6507	−3.18187
$612$	−7.89227	−0.319026
$613$	0.107812	0.00435448	0.00217724	−	0.999998i	$-0.499307\pi$
$613$	0.107812	0.00435448	0.00217724	+	0.999998i	$0.499307\pi$
$614$	5.80406	0.234233
$615$	−11.4314	−0.460960
$616$	0.415271	0.0167317
$617$	−22.1242	−0.890686	−0.445343	−	0.895360i	$-0.646918\pi$
$617$	−22.1242	−0.890686	−0.445343	+	0.895360i	$0.646918\pi$
$618$	21.5132	0.865389
$619$	25.2216	1.01374	0.506870	−	0.862022i	$-0.330802\pi$
$619$	25.2216	1.01374	0.506870	+	0.862022i	$0.330802\pi$
$620$	−8.62482	−0.346381
$621$	16.7337	0.671501
$622$	9.09059	0.364500
$623$	1.91595	0.0767610
$624$	12.1238	0.485341
$625$	−8.07701	−0.323081
$626$	−1.72354	−0.0688865
$627$	5.36238	0.214153
$628$	−7.24700	−0.289187
$629$	13.7166	0.546915
$630$	0.804177	0.0320392
$631$	17.5667	0.699321	0.349660	−	0.936877i	$-0.386297\pi$
$631$	17.5667	0.699321	0.349660	+	0.936877i	$0.386297\pi$
$632$	9.98672	0.397251
$633$	−18.8218	−0.748098
$634$	16.0419	0.637104
$635$	22.9837	0.912082
$636$	1.98383	0.0786638
$637$	39.7671	1.57563
$638$	2.80152	0.110913
$639$	−5.07102	−0.200607
$640$	1.63895	0.0647853
$641$	−21.5669	−0.851843	−0.425921	−	0.904760i	$-0.640050\pi$
$641$	−21.5669	−0.851843	−0.425921	+	0.904760i	$0.640050\pi$
$642$	−6.51431	−0.257099
$643$	23.8596	0.940931	0.470465	−	0.882418i	$-0.344086\pi$
$643$	23.8596	0.940931	0.470465	+	0.882418i	$0.344086\pi$
$644$	1.74934	0.0689335
$645$	43.6542	1.71888
$646$	12.2621	0.482445
$647$	37.8162	1.48671	0.743354	−	0.668898i	$-0.233234\pi$
$647$	37.8162	1.48671	0.743354	+	0.668898i	$0.233234\pi$
$648$	11.2389	0.441506
$649$	0.599479	0.0235316
$650$	−13.3815	−0.524865
$651$	−3.88100	−0.152108
$652$	−13.0583	−0.511404
$653$	42.4552	1.66140	0.830700	−	0.556720i	$-0.187940\pi$
$653$	42.4552	1.66140	0.830700	+	0.556720i	$0.187940\pi$
$654$	31.8378	1.24496
$655$	−18.6353	−0.728140
$656$	−3.32712	−0.129902
$657$	2.10403	0.0820859
$658$	−4.78436	−0.186514
$659$	−19.6938	−0.767162	−0.383581	−	0.923507i	$-0.625309\pi$
$659$	−19.6938	−0.767162	−0.383581	+	0.923507i	$0.625309\pi$
$660$	−4.05574	−0.157870
$661$	13.8616	0.539153	0.269576	−	0.962979i	$-0.413116\pi$
$661$	13.8616	0.539153	0.269576	+	0.962979i	$0.413116\pi$
$662$	−7.26817	−0.282485
$663$	−68.6040	−2.66436
$664$	−11.8071	−0.458204
$665$	−1.24943	−0.0484510
$666$	3.38085	0.131005
$667$	11.8014	0.456954
$668$	1.37630	0.0532505
$669$	28.4515	1.10000
$670$	−20.9092	−0.807795
$671$	−3.40603	−0.131488
$672$	0.737496	0.0284495
$673$	−11.9973	−0.462463	−0.231231	−	0.972899i	$-0.574275\pi$
$673$	−11.9973	−0.462463	−0.231231	+	0.972899i	$0.574275\pi$
$674$	−18.8652	−0.726662
$675$	−7.78655	−0.299705
$676$	20.4461	0.786388
$677$	17.9538	0.690019	0.345010	−	0.938599i	$-0.387876\pi$
$677$	17.9538	0.690019	0.345010	+	0.938599i	$0.387876\pi$
$678$	39.0264	1.49880
$679$	−5.53727	−0.212501
$680$	−9.27421	−0.355650
$681$	−7.73686	−0.296477
$682$	6.21185	0.237864
$683$	9.73211	0.372389	0.186194	−	0.982513i	$-0.440385\pi$
$683$	9.73211	0.372389	0.186194	+	0.982513i	$0.440385\pi$
$684$	3.02235	0.115562
$685$	−10.7876	−0.412171
$686$	4.88164	0.186382
$687$	−55.9908	−2.13618
$688$	12.7055	0.484394
$689$	5.47281	0.208497
$690$	−17.0849	−0.650411
$691$	−12.1691	−0.462934	−0.231467	−	0.972843i	$-0.574353\pi$
$691$	−12.1691	−0.462934	−0.231467	+	0.972843i	$0.574353\pi$
$692$	−21.9487	−0.834364
$693$	−0.579192	−0.0220017
$694$	12.4793	0.473706
$695$	−27.4360	−1.04071
$696$	4.97533	0.188589
$697$	18.8269	0.713119
$698$	−24.7433	−0.936546
$699$	−7.11681	−0.269183
$700$	−0.814002	−0.0307664
$701$	−33.6376	−1.27047	−0.635237	−	0.772317i	$-0.719098\pi$
$701$	−33.6376	−1.27047	−0.635237	+	0.772317i	$0.719098\pi$
$702$	19.4619	0.734543
$703$	−5.25277	−0.198112
$704$	−1.18042	−0.0444889
$705$	46.7265	1.75982
$706$	20.1450	0.758167
$707$	2.25016	0.0846261
$708$	1.06464	0.0400116
$709$	−14.7619	−0.554393	−0.277197	−	0.960813i	$-0.589405\pi$
$709$	−14.7619	−0.554393	−0.277197	+	0.960813i	$0.589405\pi$
$710$	−5.95896	−0.223636
$711$	−13.9288	−0.522372
$712$	−5.44617	−0.204104
$713$	26.1675	0.979982
$714$	−4.17321	−0.156178
$715$	−11.1886	−0.418431
$716$	−11.7423	−0.438830
$717$	−43.7389	−1.63346
$718$	6.67578	0.249138
$719$	19.8532	0.740401	0.370201	−	0.928952i	$-0.379289\pi$
$719$	19.8532	0.740401	0.370201	+	0.928952i	$0.379289\pi$
$720$	−2.28590	−0.0851906
$721$	3.61021	0.134451
$722$	14.3042	0.532348
$723$	24.5486	0.912971
$724$	16.3001	0.605787
$725$	−5.49146	−0.203948
$726$	−20.1389	−0.747425
$727$	4.50487	0.167077	0.0835383	−	0.996505i	$-0.473378\pi$
$727$	4.50487	0.167077	0.0835383	+	0.996505i	$0.473378\pi$
$728$	2.03454	0.0754051
$729$	5.48884	0.203290
$730$	2.47244	0.0915093
$731$	−71.8957	−2.65916
$732$	−6.04890	−0.223574
$733$	4.50887	0.166539	0.0832695	−	0.996527i	$-0.473464\pi$
$733$	4.50887	0.166539	0.0832695	+	0.996527i	$0.473464\pi$
$734$	24.0872	0.889076
$735$	−23.6256	−0.871445
$736$	−4.97255	−0.183291
$737$	15.0595	0.554722
$738$	4.64045	0.170817
$739$	−0.193535	−0.00711930	−0.00355965	−	0.999994i	$-0.501133\pi$
$739$	−0.193535	−0.00711930	−0.00355965	+	0.999994i	$0.501133\pi$
$740$	3.97284	0.146045
$741$	26.2720	0.965124
$742$	0.332913	0.0122216
$743$	−15.8009	−0.579677	−0.289839	−	0.957076i	$-0.593602\pi$
$743$	−15.8009	−0.579677	−0.289839	+	0.957076i	$0.593602\pi$
$744$	11.0319	0.404448
$745$	−19.0051	−0.696295
$746$	28.5444	1.04508
$747$	16.4678	0.602524
$748$	6.67956	0.244229
$749$	−1.09319	−0.0399443
$750$	25.1292	0.917587
$751$	−25.2326	−0.920750	−0.460375	−	0.887724i	$-0.652285\pi$
$751$	−25.2326	−0.920750	−0.460375	+	0.887724i	$0.652285\pi$
$752$	13.5997	0.495931
$753$	6.84574	0.249473
$754$	13.7255	0.499853
$755$	−6.09546	−0.221836
$756$	1.18388	0.0430572
$757$	−46.6580	−1.69581	−0.847907	−	0.530145i	$-0.822137\pi$
$757$	−46.6580	−1.69581	−0.847907	+	0.530145i	$0.822137\pi$
$758$	15.7164	0.570844
$759$	12.3051	0.446645
$760$	3.55157	0.128829
$761$	12.4573	0.451575	0.225788	−	0.974177i	$-0.427504\pi$
$761$	12.4573	0.451575	0.225788	+	0.974177i	$0.427504\pi$
$762$	−29.3982	−1.06498
$763$	5.34282	0.193423
$764$	11.8111	0.427311
$765$	12.9351	0.467668
$766$	5.61674	0.202941
$767$	2.93704	0.106050
$768$	−2.09636	−0.0756460
$769$	−43.3761	−1.56418	−0.782091	−	0.623164i	$-0.785847\pi$
$769$	−43.3761	−1.56418	−0.782091	+	0.623164i	$0.785847\pi$
$770$	−0.680609	−0.0245275
$771$	8.32306	0.299748
$772$	−19.2132	−0.691498
$773$	−31.8881	−1.14693	−0.573467	−	0.819229i	$-0.694402\pi$
$773$	−31.8881	−1.14693	−0.573467	+	0.819229i	$0.694402\pi$
$774$	−17.7208	−0.636963
$775$	−12.1763	−0.437386
$776$	15.7399	0.565030
$777$	1.78770	0.0641334
$778$	−0.210807	−0.00755781
$779$	−7.20977	−0.258317
$780$	−19.8704	−0.711473
$781$	4.29182	0.153573
$782$	28.1378	1.00620
$783$	7.98673	0.285422
$784$	−6.87624	−0.245580
$785$	11.8775	0.423926
$786$	23.8361	0.850206
$787$	−14.1830	−0.505569	−0.252784	−	0.967523i	$-0.581346\pi$
$787$	−14.1830	−0.505569	−0.252784	+	0.967523i	$0.581346\pi$
$788$	−17.6068	−0.627217
$789$	19.6672	0.700171
$790$	−16.3678	−0.582339
$791$	6.54916	0.232861
$792$	1.64638	0.0585014
$793$	−16.6872	−0.592579
$794$	8.63726	0.306525
$795$	−3.25140	−0.115315
$796$	5.33798	0.189200
$797$	23.8390	0.844422	0.422211	−	0.906498i	$-0.361254\pi$
$797$	23.8390	0.844422	0.422211	+	0.906498i	$0.361254\pi$
$798$	1.59813	0.0565733
$799$	−76.9556	−2.72249
$800$	2.31383	0.0818063
$801$	7.59596	0.268390
$802$	−8.52496	−0.301027
$803$	−1.78073	−0.0628405
$804$	26.7447	0.943214
$805$	−2.86708	−0.101051
$806$	30.4338	1.07198
$807$	9.80194	0.345045
$808$	−6.39617	−0.225017
$809$	−33.0898	−1.16337	−0.581687	−	0.813413i	$-0.697607\pi$
$809$	−33.0898	−1.16337	−0.581687	+	0.813413i	$0.697607\pi$
$810$	−18.4201	−0.647215
$811$	−5.98891	−0.210299	−0.105150	−	0.994456i	$-0.533532\pi$
$811$	−5.98891	−0.210299	−0.105150	+	0.994456i	$0.533532\pi$
$812$	0.834929	0.0293002
$813$	32.9021	1.15393
$814$	−2.86136	−0.100291
$815$	21.4020	0.749679
$816$	11.8625	0.415271
$817$	27.5325	0.963241
$818$	32.9748	1.15294
$819$	−2.83764	−0.0991553
$820$	5.45299	0.190427
$821$	−4.96783	−0.173378	−0.0866892	−	0.996235i	$-0.527629\pi$
$821$	−4.96783	−0.173378	−0.0866892	+	0.996235i	$0.527629\pi$
$822$	13.7982	0.481268
$823$	2.51751	0.0877547	0.0438774	−	0.999037i	$-0.486029\pi$
$823$	2.51751	0.0877547	0.0438774	+	0.999037i	$0.486029\pi$
$824$	−10.2622	−0.357500
$825$	−5.72580	−0.199347
$826$	0.178661	0.00621642
$827$	10.2749	0.357292	0.178646	−	0.983913i	$-0.442828\pi$
$827$	10.2749	0.357292	0.178646	+	0.983913i	$0.442828\pi$
$828$	6.93539	0.241022
$829$	20.2027	0.701670	0.350835	−	0.936437i	$-0.385898\pi$
$829$	20.2027	0.701670	0.350835	+	0.936437i	$0.385898\pi$
$830$	19.3513	0.671692
$831$	−57.8093	−2.00538
$832$	−5.78326	−0.200498
$833$	38.9100	1.34815
$834$	35.0930	1.21517
$835$	−2.25568	−0.0780612
$836$	−2.55794	−0.0884683
$837$	17.7091	0.612116
$838$	−12.8564	−0.444117
$839$	21.4581	0.740815	0.370408	−	0.928869i	$-0.379218\pi$
$839$	21.4581	0.740815	0.370408	+	0.928869i	$0.379218\pi$
$840$	−1.20872	−0.0417049
$841$	−23.3674	−0.805771
$842$	−4.93369	−0.170026
$843$	−11.0251	−0.379725
$844$	8.97830	0.309046
$845$	−33.5102	−1.15279
$846$	−18.9680	−0.652133
$847$	−3.37958	−0.116124
$848$	−0.946318	−0.0324967
$849$	67.9605	2.33240
$850$	−13.0931	−0.449089
$851$	−12.0535	−0.413190
$852$	7.62203	0.261126
$853$	−39.4739	−1.35156	−0.675780	−	0.737103i	$-0.736193\pi$
$853$	−39.4739	−1.35156	−0.675780	+	0.737103i	$0.736193\pi$
$854$	−1.01509	−0.0347356
$855$	−4.95349	−0.169406
$856$	3.10744	0.106210
$857$	48.9342	1.67156	0.835779	−	0.549065i	$-0.185016\pi$
$857$	48.9342	1.67156	0.835779	+	0.549065i	$0.185016\pi$
$858$	14.3112	0.488577
$859$	57.5739	1.96440	0.982199	−	0.187846i	$-0.0601504\pi$
$859$	57.5739	1.96440	0.982199	+	0.187846i	$0.0601504\pi$
$860$	−20.8238	−0.710085
$861$	2.45374	0.0836232
$862$	−11.5436	−0.393177
$863$	24.2570	0.825720	0.412860	−	0.910795i	$-0.364530\pi$
$863$	24.2570	0.825720	0.412860	+	0.910795i	$0.364530\pi$
$864$	−3.36522	−0.114487
$865$	35.9729	1.22311
$866$	31.8626	1.08273
$867$	−31.4872	−1.06936
$868$	1.85130	0.0628372
$869$	11.7886	0.399899
$870$	−8.15434	−0.276458
$871$	73.7810	2.49997
$872$	−15.1872	−0.514302
$873$	−21.9530	−0.742997
$874$	−10.7754	−0.364483
$875$	4.21701	0.142561
$876$	−3.16247	−0.106850
$877$	−54.3264	−1.83447	−0.917236	−	0.398344i	$-0.869585\pi$
$877$	−54.3264	−1.83447	−0.917236	+	0.398344i	$0.869585\pi$
$878$	−5.74951	−0.194037
$879$	9.81885	0.331181
$880$	1.93466	0.0652173
$881$	23.0984	0.778205	0.389102	−	0.921195i	$-0.372785\pi$
$881$	23.0984	0.778205	0.389102	+	0.921195i	$0.372785\pi$
$882$	9.59053	0.322930
$883$	−28.4166	−0.956295	−0.478147	−	0.878280i	$-0.658692\pi$
$883$	−28.4166	−0.956295	−0.478147	+	0.878280i	$0.658692\pi$
$884$	32.7252	1.10067
$885$	−1.74490	−0.0586540
$886$	23.3036	0.782900
$887$	23.7497	0.797438	0.398719	−	0.917073i	$-0.369455\pi$
$887$	23.7497	0.797438	0.398719	+	0.917073i	$0.369455\pi$
$888$	−5.08161	−0.170528
$889$	−4.93342	−0.165462
$890$	8.92602	0.299201
$891$	13.2667	0.444450
$892$	−13.5718	−0.454418
$893$	29.4702	0.986183
$894$	24.3092	0.813022
$895$	19.2451	0.643292
$896$	−0.351798	−0.0117528
$897$	60.2863	2.01290
$898$	16.6340	0.555083
$899$	12.4893	0.416542
$900$	−3.22718	−0.107573
$901$	5.35485	0.178396
$902$	−3.92741	−0.130768
$903$	−9.37028	−0.311824
$904$	−18.6162	−0.619167
$905$	−26.7150	−0.888038
$906$	7.79662	0.259025
$907$	20.9260	0.694837	0.347418	−	0.937710i	$-0.387058\pi$
$907$	20.9260	0.694837	0.347418	+	0.937710i	$0.387058\pi$
$908$	3.69061	0.122477
$909$	8.92096	0.295890
$910$	−3.33452	−0.110538
$911$	−1.80032	−0.0596472	−0.0298236	−	0.999555i	$-0.509495\pi$
$911$	−1.80032	−0.0596472	−0.0298236	+	0.999555i	$0.509495\pi$
$912$	−4.54276	−0.150426
$913$	−13.9374	−0.461259
$914$	0.671173	0.0222004
$915$	9.91387	0.327742
$916$	26.7085	0.882475
$917$	4.00002	0.132092
$918$	19.0425	0.628495
$919$	−55.4142	−1.82795	−0.913973	−	0.405775i	$-0.867002\pi$
$919$	−55.4142	−1.82795	−0.913973	+	0.405775i	$0.867002\pi$
$920$	8.14978	0.268690
$921$	12.1674	0.400930
$922$	−9.29091	−0.305980
$923$	21.0270	0.692111
$924$	0.870558	0.0286392
$925$	5.60876	0.184415
$926$	7.41188	0.243569
$927$	14.3130	0.470101
$928$	−2.37332	−0.0779079
$929$	−45.2642	−1.48507	−0.742535	−	0.669807i	$-0.766377\pi$
$929$	−45.2642	−1.48507	−0.742535	+	0.669807i	$0.766377\pi$
$930$	−18.0807	−0.592891
$931$	−14.9006	−0.488348
$932$	3.39484	0.111202
$933$	19.0572	0.623904
$934$	−9.18352	−0.300494
$935$	−10.9475	−0.358021
$936$	8.06611	0.263649
$937$	1.03817	0.0339157	0.0169578	−	0.999856i	$-0.494602\pi$
$937$	1.03817	0.0339157	0.0169578	+	0.999856i	$0.494602\pi$
$938$	4.48813	0.146543
$939$	−3.61316	−0.117911
$940$	−22.2893	−0.726997
$941$	−48.5849	−1.58382	−0.791911	−	0.610636i	$-0.790914\pi$
$941$	−48.5849	−1.58382	−0.791911	+	0.610636i	$0.790914\pi$
$942$	−15.1923	−0.494993
$943$	−16.5443	−0.538756
$944$	−0.507851	−0.0165292
$945$	−1.94032	−0.0631186
$946$	14.9979	0.487624
$947$	12.4397	0.404236	0.202118	−	0.979361i	$-0.435217\pi$
$947$	12.4397	0.404236	0.202118	+	0.979361i	$0.435217\pi$
$948$	20.9358	0.679963
$949$	−8.72434	−0.283204
$950$	5.01401	0.162676
$951$	33.6296	1.09051
$952$	1.99069	0.0645187
$953$	−15.1401	−0.490437	−0.245219	−	0.969468i	$-0.578860\pi$
$953$	−15.1401	−0.490437	−0.245219	+	0.969468i	$0.578860\pi$
$954$	1.31986	0.0427321
$955$	−19.3579	−0.626406
$956$	20.8642	0.674796
$957$	5.87300	0.189847
$958$	−22.5962	−0.730051
$959$	2.31553	0.0747723
$960$	3.43584	0.110891
$961$	−3.30722	−0.106684
$962$	−14.0187	−0.451981
$963$	−4.33405	−0.139663
$964$	−11.7101	−0.377156
$965$	31.4895	1.01368
$966$	3.66724	0.117992
$967$	−60.0122	−1.92986	−0.964932	−	0.262502i	$-0.915453\pi$
$967$	−60.0122	−1.92986	−0.964932	+	0.262502i	$0.915453\pi$
$968$	9.60660	0.308768
$969$	25.7057	0.825787
$970$	−25.7970	−0.828291
$971$	−37.2587	−1.19569	−0.597845	−	0.801612i	$-0.703976\pi$
$971$	−37.2587	−1.19569	−0.597845	+	0.801612i	$0.703976\pi$
$972$	13.4652	0.431896
$973$	5.88909	0.188795
$974$	−2.49179	−0.0798421
$975$	−28.0525	−0.898398
$976$	2.88543	0.0923603
$977$	−21.2895	−0.681112	−0.340556	−	0.940224i	$-0.610615\pi$
$977$	−21.2895	−0.681112	−0.340556	+	0.940224i	$0.610615\pi$
$978$	−27.3750	−0.875356
$979$	−6.42878	−0.205465
$980$	11.2698	0.360002
$981$	21.1821	0.676291
$982$	7.12504	0.227369
$983$	−44.4932	−1.41911	−0.709557	−	0.704648i	$-0.751105\pi$
$983$	−44.4932	−1.41911	−0.709557	+	0.704648i	$0.751105\pi$
$984$	−6.97484	−0.222350
$985$	28.8567	0.919452
$986$	13.4297	0.427688
$987$	−10.0297	−0.319250
$988$	−12.5322	−0.398701
$989$	63.1789	2.00897
$990$	−2.69833	−0.0857587
$991$	47.2108	1.49970	0.749850	−	0.661608i	$-0.230126\pi$
$991$	47.2108	1.49970	0.749850	+	0.661608i	$0.230126\pi$
$992$	−5.26239	−0.167081
$993$	−15.2367	−0.483522
$994$	1.27908	0.0405700
$995$	−8.74871	−0.277353
$996$	−24.7519	−0.784295
$997$	32.7330	1.03666	0.518332	−	0.855179i	$-0.326553\pi$
$997$	32.7330	1.03666	0.518332	+	0.855179i	$0.326553\pi$
$998$	−6.77556	−0.214477
$999$	−8.15733	−0.258086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.14	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.14	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.09636 q^{3} +1.00000 q^{4} -1.63895 q^{5} +2.09636 q^{6} +0.351798 q^{7} -1.00000 q^{8} +1.39473 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.09636 q^{3} +1.00000 q^{4} -1.63895 q^{5} +2.09636 q^{6} +0.351798 q^{7} -1.00000 q^{8} +1.39473 q^{9} +1.63895 q^{10} -1.18042 q^{11} -2.09636 q^{12} -5.78326 q^{13} -0.351798 q^{14} +3.43584 q^{15} +1.00000 q^{16} -5.65862 q^{17} -1.39473 q^{18} +2.16697 q^{19} -1.63895 q^{20} -0.737496 q^{21} +1.18042 q^{22} +4.97255 q^{23} +2.09636 q^{24} -2.31383 q^{25} +5.78326 q^{26} +3.36522 q^{27} +0.351798 q^{28} +2.37332 q^{29} -3.43584 q^{30} +5.26239 q^{31} -1.00000 q^{32} +2.47459 q^{33} +5.65862 q^{34} -0.576581 q^{35} +1.39473 q^{36} -2.42401 q^{37} -2.16697 q^{38} +12.1238 q^{39} +1.63895 q^{40} -3.32712 q^{41} +0.737496 q^{42} +12.7055 q^{43} -1.18042 q^{44} -2.28590 q^{45} -4.97255 q^{46} +13.5997 q^{47} -2.09636 q^{48} -6.87624 q^{49} +2.31383 q^{50} +11.8625 q^{51} -5.78326 q^{52} -0.946318 q^{53} -3.36522 q^{54} +1.93466 q^{55} -0.351798 q^{56} -4.54276 q^{57} -2.37332 q^{58} -0.507851 q^{59} +3.43584 q^{60} +2.88543 q^{61} -5.26239 q^{62} +0.490665 q^{63} +1.00000 q^{64} +9.47849 q^{65} -2.47459 q^{66} -12.7577 q^{67} -5.65862 q^{68} -10.4243 q^{69} +0.576581 q^{70} -3.63583 q^{71} -1.39473 q^{72} +1.50855 q^{73} +2.42401 q^{74} +4.85063 q^{75} +2.16697 q^{76} -0.415271 q^{77} -12.1238 q^{78} -9.98672 q^{79} -1.63895 q^{80} -11.2389 q^{81} +3.32712 q^{82} +11.8071 q^{83} -0.737496 q^{84} +9.27421 q^{85} -12.7055 q^{86} -4.97533 q^{87} +1.18042 q^{88} +5.44617 q^{89} +2.28590 q^{90} -2.03454 q^{91} +4.97255 q^{92} -11.0319 q^{93} -13.5997 q^{94} -3.55157 q^{95} +2.09636 q^{96} -15.7399 q^{97} +6.87624 q^{98} -1.64638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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