LMFDB - Embedded newform 6031.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59785 q^{2} -1.74392 q^{3} +4.74884 q^{4} +1.33654 q^{5} +4.53044 q^{6} -2.87132 q^{7} -7.14109 q^{8} +0.0412485 q^{9} +O(q^{10})$	\(q-2.59785 q^{2} -1.74392 q^{3} +4.74884 q^{4} +1.33654 q^{5} +4.53044 q^{6} -2.87132 q^{7} -7.14109 q^{8} +0.0412485 q^{9} -3.47214 q^{10} -1.41423 q^{11} -8.28159 q^{12} -4.06879 q^{13} +7.45926 q^{14} -2.33082 q^{15} +9.05381 q^{16} -6.44793 q^{17} -0.107158 q^{18} +5.30377 q^{19} +6.34702 q^{20} +5.00734 q^{21} +3.67396 q^{22} -2.36987 q^{23} +12.4535 q^{24} -3.21366 q^{25} +10.5701 q^{26} +5.15982 q^{27} -13.6354 q^{28} +1.20354 q^{29} +6.05512 q^{30} -2.97149 q^{31} -9.23831 q^{32} +2.46630 q^{33} +16.7508 q^{34} -3.83763 q^{35} +0.195883 q^{36} -1.00000 q^{37} -13.7784 q^{38} +7.09564 q^{39} -9.54435 q^{40} +5.31462 q^{41} -13.0083 q^{42} -9.58580 q^{43} -6.71595 q^{44} +0.0551303 q^{45} +6.15656 q^{46} -7.64293 q^{47} -15.7891 q^{48} +1.24446 q^{49} +8.34862 q^{50} +11.2447 q^{51} -19.3220 q^{52} -11.4761 q^{53} -13.4045 q^{54} -1.89017 q^{55} +20.5043 q^{56} -9.24933 q^{57} -3.12663 q^{58} +8.53408 q^{59} -11.0687 q^{60} -12.8869 q^{61} +7.71951 q^{62} -0.118438 q^{63} +5.89214 q^{64} -5.43810 q^{65} -6.40708 q^{66} -6.67124 q^{67} -30.6202 q^{68} +4.13285 q^{69} +9.96960 q^{70} -6.68727 q^{71} -0.294559 q^{72} +2.60336 q^{73} +2.59785 q^{74} +5.60436 q^{75} +25.1867 q^{76} +4.06070 q^{77} -18.4334 q^{78} -8.95578 q^{79} +12.1008 q^{80} -9.12204 q^{81} -13.8066 q^{82} -4.15588 q^{83} +23.7791 q^{84} -8.61792 q^{85} +24.9025 q^{86} -2.09888 q^{87} +10.0991 q^{88} +6.08923 q^{89} -0.143220 q^{90} +11.6828 q^{91} -11.2541 q^{92} +5.18204 q^{93} +19.8552 q^{94} +7.08870 q^{95} +16.1108 q^{96} -0.291118 q^{97} -3.23291 q^{98} -0.0583349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * 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 $

$2$	−2.59785	−1.83696	−0.918480	−	0.395468i	$-0.870582\pi$
$2$	−2.59785	−1.83696	−0.918480	+	0.395468i	$0.870582\pi$
$3$	−1.74392	−1.00685	−0.503426	−	0.864039i	$-0.667927\pi$
$3$	−1.74392	−1.00685	−0.503426	+	0.864039i	$0.667927\pi$
$4$	4.74884	2.37442
$5$	1.33654	0.597719	0.298860	−	0.954297i	$-0.403394\pi$
$5$	1.33654	0.597719	0.298860	+	0.954297i	$0.403394\pi$
$6$	4.53044	1.84955
$7$	−2.87132	−1.08526	−0.542628	−	0.839973i	$-0.682571\pi$
$7$	−2.87132	−1.08526	−0.542628	+	0.839973i	$0.682571\pi$
$8$	−7.14109	−2.52476
$9$	0.0412485	0.0137495
$10$	−3.47214	−1.09799
$11$	−1.41423	−0.426406	−0.213203	−	0.977008i	$-0.568390\pi$
$11$	−1.41423	−0.426406	−0.213203	+	0.977008i	$0.568390\pi$
$12$	−8.28159	−2.39069
$13$	−4.06879	−1.12848	−0.564240	−	0.825611i	$-0.690831\pi$
$13$	−4.06879	−1.12848	−0.564240	+	0.825611i	$0.690831\pi$
$14$	7.45926	1.99357
$15$	−2.33082	−0.601814
$16$	9.05381	2.26345
$17$	−6.44793	−1.56385	−0.781927	−	0.623371i	$-0.785763\pi$
$17$	−6.44793	−1.56385	−0.781927	+	0.623371i	$0.785763\pi$
$18$	−0.107158	−0.0252573
$19$	5.30377	1.21677	0.608384	−	0.793643i	$-0.291818\pi$
$19$	5.30377	1.21677	0.608384	+	0.793643i	$0.291818\pi$
$20$	6.34702	1.41924
$21$	5.00734	1.09269
$22$	3.67396	0.783291
$23$	−2.36987	−0.494151	−0.247076	−	0.968996i	$-0.579470\pi$
$23$	−2.36987	−0.494151	−0.247076	+	0.968996i	$0.579470\pi$
$24$	12.4535	2.54205
$25$	−3.21366	−0.642732
$26$	10.5701	2.07297
$27$	5.15982	0.993008
$28$	−13.6354	−2.57685
$29$	1.20354	0.223492	0.111746	−	0.993737i	$-0.464356\pi$
$29$	1.20354	0.223492	0.111746	+	0.993737i	$0.464356\pi$
$30$	6.05512	1.10551
$31$	−2.97149	−0.533696	−0.266848	−	0.963739i	$-0.585982\pi$
$31$	−2.97149	−0.533696	−0.266848	+	0.963739i	$0.585982\pi$
$32$	−9.23831	−1.63312
$33$	2.46630	0.429328
$34$	16.7508	2.87274
$35$	−3.83763	−0.648678
$36$	0.195883	0.0326471
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−13.7784	−2.23515
$39$	7.09564	1.13621
$40$	−9.54435	−1.50909
$41$	5.31462	0.830005	0.415002	−	0.909820i	$-0.363781\pi$
$41$	5.31462	0.830005	0.415002	+	0.909820i	$0.363781\pi$
$42$	−13.0083	−2.00723
$43$	−9.58580	−1.46182	−0.730910	−	0.682473i	$-0.760904\pi$
$43$	−9.58580	−1.46182	−0.730910	+	0.682473i	$0.760904\pi$
$44$	−6.71595	−1.01247
$45$	0.0551303	0.00821834
$46$	6.15656	0.907736
$47$	−7.64293	−1.11484	−0.557418	−	0.830232i	$-0.688208\pi$
$47$	−7.64293	−1.11484	−0.557418	+	0.830232i	$0.688208\pi$
$48$	−15.7891	−2.27896
$49$	1.24446	0.177779
$50$	8.34862	1.18067
$51$	11.2447	1.57457
$52$	−19.3220	−2.67949
$53$	−11.4761	−1.57637	−0.788185	−	0.615439i	$-0.788979\pi$
$53$	−11.4761	−1.57637	−0.788185	+	0.615439i	$0.788979\pi$
$54$	−13.4045	−1.82411
$55$	−1.89017	−0.254871
$56$	20.5043	2.74000
$57$	−9.24933	−1.22510
$58$	−3.12663	−0.410547
$59$	8.53408	1.11104	0.555522	−	0.831502i	$-0.312519\pi$
$59$	8.53408	1.11104	0.555522	+	0.831502i	$0.312519\pi$
$60$	−11.0687	−1.42896
$61$	−12.8869	−1.64999	−0.824997	−	0.565138i	$-0.808823\pi$
$61$	−12.8869	−1.64999	−0.824997	+	0.565138i	$0.808823\pi$
$62$	7.71951	0.980378
$63$	−0.118438	−0.0149217
$64$	5.89214	0.736517
$65$	−5.43810	−0.674514
$66$	−6.40708	−0.788657
$67$	−6.67124	−0.815022	−0.407511	−	0.913200i	$-0.633603\pi$
$67$	−6.67124	−0.815022	−0.407511	+	0.913200i	$0.633603\pi$
$68$	−30.6202	−3.71325
$69$	4.13285	0.497537
$70$	9.96960	1.19160
$71$	−6.68727	−0.793633	−0.396817	−	0.917898i	$-0.629885\pi$
$71$	−6.68727	−0.793633	−0.396817	+	0.917898i	$0.629885\pi$
$72$	−0.294559	−0.0347141
$73$	2.60336	0.304700	0.152350	−	0.988327i	$-0.451316\pi$
$73$	2.60336	0.304700	0.152350	+	0.988327i	$0.451316\pi$
$74$	2.59785	0.301994
$75$	5.60436	0.647135
$76$	25.1867	2.88912
$77$	4.06070	0.462760
$78$	−18.4334	−2.08717
$79$	−8.95578	−1.00760	−0.503802	−	0.863819i	$-0.668066\pi$
$79$	−8.95578	−1.00760	−0.503802	+	0.863819i	$0.668066\pi$
$80$	12.1008	1.35291
$81$	−9.12204	−1.01356
$82$	−13.8066	−1.52469
$83$	−4.15588	−0.456167	−0.228084	−	0.973642i	$-0.573246\pi$
$83$	−4.15588	−0.456167	−0.228084	+	0.973642i	$0.573246\pi$
$84$	23.7791	2.59451
$85$	−8.61792	−0.934745
$86$	24.9025	2.68531
$87$	−2.09888	−0.225024
$88$	10.0991	1.07657
$89$	6.08923	0.645457	0.322728	−	0.946492i	$-0.395400\pi$
$89$	6.08923	0.645457	0.322728	+	0.946492i	$0.395400\pi$
$90$	−0.143220	−0.0150968
$91$	11.6828	1.22469
$92$	−11.2541	−1.17332
$93$	5.18204	0.537353
$94$	19.8552	2.04791
$95$	7.08870	0.727285
$96$	16.1108	1.64431
$97$	−0.291118	−0.0295586	−0.0147793	−	0.999891i	$-0.504705\pi$
$97$	−0.291118	−0.0295586	−0.0147793	+	0.999891i	$0.504705\pi$
$98$	−3.23291	−0.326573
$99$	−0.0583349	−0.00586287
$100$	−15.2612	−1.52612
$101$	−9.32055	−0.927430	−0.463715	−	0.885985i	$-0.653484\pi$
$101$	−9.32055	−0.927430	−0.463715	+	0.885985i	$0.653484\pi$
$102$	−29.2120	−2.89242
$103$	−9.49254	−0.935328	−0.467664	−	0.883906i	$-0.654904\pi$
$103$	−9.49254	−0.935328	−0.467664	+	0.883906i	$0.654904\pi$
$104$	29.0556	2.84914
$105$	6.69251	0.653122
$106$	29.8133	2.89573
$107$	7.96164	0.769681	0.384840	−	0.922983i	$-0.374256\pi$
$107$	7.96164	0.769681	0.384840	+	0.922983i	$0.374256\pi$
$108$	24.5032	2.35782
$109$	−1.11646	−0.106938	−0.0534688	−	0.998570i	$-0.517028\pi$
$109$	−1.11646	−0.106938	−0.0534688	+	0.998570i	$0.517028\pi$
$110$	4.91040	0.468188
$111$	1.74392	0.165525
$112$	−25.9964	−2.45643
$113$	7.46360	0.702116	0.351058	−	0.936354i	$-0.385822\pi$
$113$	7.46360	0.702116	0.351058	+	0.936354i	$0.385822\pi$
$114$	24.0284	2.25047
$115$	−3.16742	−0.295364
$116$	5.71544	0.530665
$117$	−0.167832	−0.0155160
$118$	−22.1703	−2.04094
$119$	18.5140	1.69718
$120$	16.6446	1.51943
$121$	−8.99996	−0.818178
$122$	33.4782	3.03097
$123$	−9.26827	−0.835691
$124$	−14.1112	−1.26722
$125$	−10.9779	−0.981892
$126$	0.307683	0.0274106
$127$	0.312114	0.0276956	0.0138478	−	0.999904i	$-0.495592\pi$
$127$	0.312114	0.0276956	0.0138478	+	0.999904i	$0.495592\pi$
$128$	3.16971	0.280165
$129$	16.7168	1.47184
$130$	14.1274	1.23905
$131$	−18.6011	−1.62518	−0.812592	−	0.582833i	$-0.801944\pi$
$131$	−18.6011	−1.62518	−0.812592	+	0.582833i	$0.801944\pi$
$132$	11.7121	1.01940
$133$	−15.2288	−1.32050
$134$	17.3309	1.49716
$135$	6.89631	0.593540
$136$	46.0452	3.94835
$137$	−9.05862	−0.773930	−0.386965	−	0.922094i	$-0.626477\pi$
$137$	−9.05862	−0.773930	−0.386965	+	0.922094i	$0.626477\pi$
$138$	−10.7365	−0.913955
$139$	12.4298	1.05428	0.527140	−	0.849779i	$-0.323264\pi$
$139$	12.4298	1.05428	0.527140	+	0.849779i	$0.323264\pi$
$140$	−18.2243	−1.54023
$141$	13.3286	1.12247
$142$	17.3726	1.45787
$143$	5.75420	0.481191
$144$	0.373456	0.0311214
$145$	1.60858	0.133586
$146$	−6.76315	−0.559722
$147$	−2.17023	−0.178997
$148$	−4.74884	−0.390352
$149$	−10.6838	−0.875249	−0.437624	−	0.899158i	$-0.644180\pi$
$149$	−10.6838	−0.875249	−0.437624	+	0.899158i	$0.644180\pi$
$150$	−14.5593	−1.18876
$151$	−6.19923	−0.504486	−0.252243	−	0.967664i	$-0.581168\pi$
$151$	−6.19923	−0.504486	−0.252243	+	0.967664i	$0.581168\pi$
$152$	−37.8747	−3.07204
$153$	−0.265968	−0.0215022
$154$	−10.5491	−0.850071
$155$	−3.97152	−0.319000
$156$	33.6961	2.69784
$157$	14.8162	1.18246	0.591232	−	0.806501i	$-0.298642\pi$
$157$	14.8162	1.18246	0.591232	+	0.806501i	$0.298642\pi$
$158$	23.2658	1.85093
$159$	20.0134	1.58717
$160$	−12.3474	−0.976145
$161$	6.80463	0.536280
$162$	23.6977	1.86187
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	25.2383	1.97078
$165$	3.29631	0.256617
$166$	10.7964	0.837961
$167$	−20.1324	−1.55789	−0.778946	−	0.627091i	$-0.784245\pi$
$167$	−20.1324	−1.55789	−0.778946	+	0.627091i	$0.784245\pi$
$168$	−35.7578	−2.75878
$169$	3.55506	0.273466
$170$	22.3881	1.71709
$171$	0.218772	0.0167299
$172$	−45.5215	−3.47098
$173$	20.1573	1.53253	0.766264	−	0.642526i	$-0.222114\pi$
$173$	20.1573	1.53253	0.766264	+	0.642526i	$0.222114\pi$
$174$	5.45258	0.413359
$175$	9.22743	0.697528
$176$	−12.8042	−0.965151
$177$	−14.8827	−1.11866
$178$	−15.8189	−1.18568
$179$	−1.83781	−0.137365	−0.0686823	−	0.997639i	$-0.521879\pi$
$179$	−1.83781	−0.137365	−0.0686823	+	0.997639i	$0.521879\pi$
$180$	0.261805	0.0195138
$181$	−2.22064	−0.165059	−0.0825294	−	0.996589i	$-0.526300\pi$
$181$	−2.22064	−0.165059	−0.0825294	+	0.996589i	$0.526300\pi$
$182$	−30.3502	−2.24970
$183$	22.4736	1.66130
$184$	16.9234	1.24761
$185$	−1.33654	−0.0982644
$186$	−13.4622	−0.987095
$187$	9.11885	0.666837
$188$	−36.2951	−2.64709
$189$	−14.8155	−1.07767
$190$	−18.4154	−1.33599
$191$	−21.7065	−1.57062	−0.785312	−	0.619100i	$-0.787498\pi$
$191$	−21.7065	−1.57062	−0.785312	+	0.619100i	$0.787498\pi$
$192$	−10.2754	−0.741563
$193$	23.8558	1.71718	0.858589	−	0.512665i	$-0.171342\pi$
$193$	23.8558	1.71718	0.858589	+	0.512665i	$0.171342\pi$
$194$	0.756283	0.0542979
$195$	9.48361	0.679135
$196$	5.90972	0.422123
$197$	15.0736	1.07395	0.536976	−	0.843597i	$-0.319567\pi$
$197$	15.0736	1.07395	0.536976	+	0.843597i	$0.319567\pi$
$198$	0.151545	0.0107699
$199$	−3.12985	−0.221869	−0.110934	−	0.993828i	$-0.535384\pi$
$199$	−3.12985	−0.221869	−0.110934	+	0.993828i	$0.535384\pi$
$200$	22.9490	1.62274
$201$	11.6341	0.820606
$202$	24.2134	1.70365
$203$	−3.45575	−0.242546
$204$	53.3991	3.73869
$205$	7.10321	0.496110
$206$	24.6602	1.71816
$207$	−0.0977534	−0.00679433
$208$	−36.8381	−2.55426
$209$	−7.50074	−0.518837
$210$	−17.3862	−1.19976
$211$	−12.9301	−0.890142	−0.445071	−	0.895495i	$-0.646822\pi$
$211$	−12.9301	−0.890142	−0.445071	+	0.895495i	$0.646822\pi$
$212$	−54.4984	−3.74296
$213$	11.6621	0.799071
$214$	−20.6832	−1.41387
$215$	−12.8118	−0.873758
$216$	−36.8467	−2.50710
$217$	8.53210	0.579197
$218$	2.90040	0.196440
$219$	−4.54005	−0.306788
$220$	−8.97614	−0.605171
$221$	26.2353	1.76478
$222$	−4.53044	−0.304063
$223$	−26.6335	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$223$	−26.6335	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$224$	26.5261	1.77235
$225$	−0.132559	−0.00883724
$226$	−19.3893	−1.28976
$227$	14.1302	0.937855	0.468927	−	0.883237i	$-0.344641\pi$
$227$	14.1302	0.937855	0.468927	+	0.883237i	$0.344641\pi$
$228$	−43.9236	−2.90891
$229$	−27.0244	−1.78582	−0.892911	−	0.450232i	$-0.851341\pi$
$229$	−27.0244	−1.78582	−0.892911	+	0.450232i	$0.851341\pi$
$230$	8.22850	0.542571
$231$	−7.08152	−0.465930
$232$	−8.59461	−0.564264
$233$	24.7386	1.62068	0.810341	−	0.585958i	$-0.199282\pi$
$233$	24.7386	1.62068	0.810341	+	0.585958i	$0.199282\pi$
$234$	0.436002	0.0285023
$235$	−10.2151	−0.666359
$236$	40.5270	2.63808
$237$	15.6181	1.01451
$238$	−48.0968	−3.11765
$239$	13.0406	0.843524	0.421762	−	0.906707i	$-0.361412\pi$
$239$	13.0406	0.843524	0.421762	+	0.906707i	$0.361412\pi$
$240$	−21.1028	−1.36218
$241$	−15.2859	−0.984649	−0.492324	−	0.870412i	$-0.663853\pi$
$241$	−15.2859	−0.984649	−0.492324	+	0.870412i	$0.663853\pi$
$242$	23.3806	1.50296
$243$	0.428637	0.0274971
$244$	−61.1977	−3.91778
$245$	1.66326	0.106262
$246$	24.0776	1.53513
$247$	−21.5799	−1.37310
$248$	21.2197	1.34745
$249$	7.24751	0.459292
$250$	28.5189	1.80370
$251$	4.58474	0.289386	0.144693	−	0.989477i	$-0.453781\pi$
$251$	4.58474	0.289386	0.144693	+	0.989477i	$0.453781\pi$
$252$	−0.562441	−0.0354305
$253$	3.35153	0.210709
$254$	−0.810827	−0.0508758
$255$	15.0289	0.941149
$256$	−20.0187	−1.25117
$257$	−28.8004	−1.79652	−0.898258	−	0.439468i	$-0.855167\pi$
$257$	−28.8004	−1.79652	−0.898258	+	0.439468i	$0.855167\pi$
$258$	−43.4279	−2.70370
$259$	2.87132	0.178415
$260$	−25.8247	−1.60158
$261$	0.0496444	0.00307291
$262$	48.3229	2.98540
$263$	−24.6464	−1.51976	−0.759881	−	0.650062i	$-0.774743\pi$
$263$	−24.6464	−1.51976	−0.759881	+	0.650062i	$0.774743\pi$
$264$	−17.6121	−1.08395
$265$	−15.3383	−0.942226
$266$	39.5622	2.42571
$267$	−10.6191	−0.649879
$268$	−31.6807	−1.93520
$269$	−13.5627	−0.826935	−0.413467	−	0.910519i	$-0.635682\pi$
$269$	−13.5627	−0.826935	−0.413467	+	0.910519i	$0.635682\pi$
$270$	−17.9156	−1.09031
$271$	−30.0457	−1.82515	−0.912573	−	0.408914i	$-0.865908\pi$
$271$	−30.0457	−1.82515	−0.912573	+	0.408914i	$0.865908\pi$
$272$	−58.3784	−3.53971
$273$	−20.3738	−1.23308
$274$	23.5330	1.42168
$275$	4.54485	0.274065
$276$	19.6263	1.18136
$277$	4.14799	0.249228	0.124614	−	0.992205i	$-0.460231\pi$
$277$	4.14799	0.249228	0.124614	+	0.992205i	$0.460231\pi$
$278$	−32.2907	−1.93667
$279$	−0.122570	−0.00733806
$280$	27.4049	1.63775
$281$	7.59951	0.453349	0.226674	−	0.973971i	$-0.427215\pi$
$281$	7.59951	0.453349	0.226674	+	0.973971i	$0.427215\pi$
$282$	−34.6258	−2.06194
$283$	−9.58056	−0.569505	−0.284753	−	0.958601i	$-0.591911\pi$
$283$	−9.58056	−0.569505	−0.284753	+	0.958601i	$0.591911\pi$
$284$	−31.7568	−1.88442
$285$	−12.3621	−0.732268
$286$	−14.9486	−0.883928
$287$	−15.2600	−0.900767
$288$	−0.381066	−0.0224546
$289$	24.5758	1.44564
$290$	−4.17887	−0.245392
$291$	0.507686	0.0297611
$292$	12.3629	0.723487
$293$	30.4254	1.77747	0.888736	−	0.458419i	$-0.151584\pi$
$293$	30.4254	1.77747	0.888736	+	0.458419i	$0.151584\pi$
$294$	5.63793	0.328811
$295$	11.4061	0.664092
$296$	7.14109	0.415067
$297$	−7.29717	−0.423425
$298$	27.7549	1.60780
$299$	9.64249	0.557640
$300$	26.6142	1.53657
$301$	27.5239	1.58645
$302$	16.1047	0.926721
$303$	16.2543	0.933784
$304$	48.0193	2.75410
$305$	−17.2238	−0.986232
$306$	0.690945	0.0394987
$307$	8.91438	0.508770	0.254385	−	0.967103i	$-0.418127\pi$
$307$	8.91438	0.508770	0.254385	+	0.967103i	$0.418127\pi$
$308$	19.2836	1.09879
$309$	16.5542	0.941736
$310$	10.3174	0.585991
$311$	−1.94791	−0.110456	−0.0552278	−	0.998474i	$-0.517589\pi$
$311$	−1.94791	−0.110456	−0.0552278	+	0.998474i	$0.517589\pi$
$312$	−50.6706	−2.86866
$313$	−6.73160	−0.380493	−0.190246	−	0.981736i	$-0.560929\pi$
$313$	−6.73160	−0.380493	−0.190246	+	0.981736i	$0.560929\pi$
$314$	−38.4904	−2.17214
$315$	−0.158297	−0.00891900
$316$	−42.5296	−2.39247
$317$	−15.8815	−0.891996	−0.445998	−	0.895034i	$-0.647151\pi$
$317$	−15.8815	−0.891996	−0.445998	+	0.895034i	$0.647151\pi$
$318$	−51.9920	−2.91557
$319$	−1.70209	−0.0952986
$320$	7.87508	0.440230
$321$	−13.8844	−0.774954
$322$	−17.6774	−0.985125
$323$	−34.1983	−1.90285
$324$	−43.3191	−2.40662
$325$	13.0757	0.725310
$326$	−2.59785	−0.143882
$327$	1.94702	0.107670
$328$	−37.9522	−2.09556
$329$	21.9453	1.20988
$330$	−8.56333	−0.471396
$331$	−10.1982	−0.560546	−0.280273	−	0.959920i	$-0.590425\pi$
$331$	−10.1982	−0.560546	−0.280273	+	0.959920i	$0.590425\pi$
$332$	−19.7356	−1.08313
$333$	−0.0412485	−0.00226040
$334$	52.3010	2.86178
$335$	−8.91638	−0.487154
$336$	45.3355	2.47325
$337$	13.0323	0.709915	0.354957	−	0.934883i	$-0.384495\pi$
$337$	13.0323	0.709915	0.354957	+	0.934883i	$0.384495\pi$
$338$	−9.23554	−0.502347
$339$	−13.0159	−0.706927
$340$	−40.9251	−2.21948
$341$	4.20237	0.227571
$342$	−0.568339	−0.0307322
$343$	16.5260	0.892319
$344$	68.4530	3.69074
$345$	5.52372	0.297387
$346$	−52.3656	−2.81519
$347$	35.2256	1.89101	0.945506	−	0.325605i	$-0.105568\pi$
$347$	35.2256	1.89101	0.945506	+	0.325605i	$0.105568\pi$
$348$	−9.96725	−0.534301
$349$	−15.1228	−0.809502	−0.404751	−	0.914427i	$-0.632642\pi$
$349$	−15.1228	−0.809502	−0.404751	+	0.914427i	$0.632642\pi$
$350$	−23.9715	−1.28133
$351$	−20.9942	−1.12059
$352$	13.0651	0.696371
$353$	21.5127	1.14500	0.572502	−	0.819903i	$-0.305973\pi$
$353$	21.5127	1.14500	0.572502	+	0.819903i	$0.305973\pi$
$354$	38.6632	2.05492
$355$	−8.93781	−0.474370
$356$	28.9168	1.53259
$357$	−32.2870	−1.70881
$358$	4.77437	0.252333
$359$	19.3898	1.02335	0.511677	−	0.859178i	$-0.329024\pi$
$359$	19.3898	1.02335	0.511677	+	0.859178i	$0.329024\pi$
$360$	−0.393690	−0.0207493
$361$	9.12993	0.480523
$362$	5.76889	0.303206
$363$	15.6952	0.823783
$364$	55.4797	2.90793
$365$	3.47950	0.182125
$366$	−58.3832	−3.05174
$367$	−22.4358	−1.17114	−0.585570	−	0.810622i	$-0.699129\pi$
$367$	−22.4358	−1.17114	−0.585570	+	0.810622i	$0.699129\pi$
$368$	−21.4563	−1.11849
$369$	0.219220	0.0114122
$370$	3.47214	0.180508
$371$	32.9516	1.71076
$372$	24.6087	1.27590
$373$	−19.1373	−0.990890	−0.495445	−	0.868639i	$-0.664995\pi$
$373$	−19.1373	−0.990890	−0.495445	+	0.868639i	$0.664995\pi$
$374$	−23.6894	−1.22495
$375$	19.1445	0.988619
$376$	54.5788	2.81469
$377$	−4.89697	−0.252207
$378$	38.4884	1.97963
$379$	30.7199	1.57798	0.788988	−	0.614408i	$-0.210605\pi$
$379$	30.7199	1.57798	0.788988	+	0.614408i	$0.210605\pi$
$380$	33.6631	1.72688
$381$	−0.544301	−0.0278854
$382$	56.3902	2.88517
$383$	−36.1416	−1.84675	−0.923374	−	0.383901i	$-0.874581\pi$
$383$	−36.1416	−1.84675	−0.923374	+	0.383901i	$0.874581\pi$
$384$	−5.52771	−0.282085
$385$	5.42729	0.276600
$386$	−61.9738	−3.15439
$387$	−0.395400	−0.0200993
$388$	−1.38247	−0.0701845
$389$	−12.3255	−0.624928	−0.312464	−	0.949930i	$-0.601154\pi$
$389$	−12.3255	−0.624928	−0.312464	+	0.949930i	$0.601154\pi$
$390$	−24.6370	−1.24754
$391$	15.2807	0.772780
$392$	−8.88676	−0.448849
$393$	32.4387	1.63632
$394$	−39.1591	−1.97281
$395$	−11.9698	−0.602264
$396$	−0.277023	−0.0139209
$397$	−12.8123	−0.643031	−0.321515	−	0.946904i	$-0.604192\pi$
$397$	−12.8123	−0.643031	−0.321515	+	0.946904i	$0.604192\pi$
$398$	8.13088	0.407564
$399$	26.5577	1.32955
$400$	−29.0959	−1.45479
$401$	−13.6019	−0.679247	−0.339623	−	0.940562i	$-0.610300\pi$
$401$	−13.6019	−0.679247	−0.339623	+	0.940562i	$0.610300\pi$
$402$	−30.2237	−1.50742
$403$	12.0904	0.602265
$404$	−44.2618	−2.20211
$405$	−12.1920	−0.605824
$406$	8.97754	0.445548
$407$	1.41423	0.0701007
$408$	−80.2991	−3.97540
$409$	7.92603	0.391917	0.195959	−	0.980612i	$-0.437218\pi$
$409$	7.92603	0.391917	0.195959	+	0.980612i	$0.437218\pi$
$410$	−18.4531	−0.911333
$411$	15.7975	0.779232
$412$	−45.0786	−2.22086
$413$	−24.5041	−1.20577
$414$	0.253949	0.0124809
$415$	−5.55450	−0.272660
$416$	37.5887	1.84294
$417$	−21.6765	−1.06150
$418$	19.4858	0.953083
$419$	−17.5971	−0.859673	−0.429836	−	0.902907i	$-0.641429\pi$
$419$	−17.5971	−0.859673	−0.429836	+	0.902907i	$0.641429\pi$
$420$	31.7817	1.55079
$421$	21.9824	1.07136	0.535678	−	0.844422i	$-0.320056\pi$
$421$	21.9824	1.07136	0.535678	+	0.844422i	$0.320056\pi$
$422$	33.5904	1.63516
$423$	−0.315259	−0.0153284
$424$	81.9521	3.97995
$425$	20.7215	1.00514
$426$	−30.2963	−1.46786
$427$	37.0022	1.79066
$428$	37.8086	1.82755
$429$	−10.0349	−0.484487
$430$	33.2832	1.60506
$431$	17.9673	0.865454	0.432727	−	0.901525i	$-0.357551\pi$
$431$	17.9673	0.865454	0.432727	+	0.901525i	$0.357551\pi$
$432$	46.7160	2.24763
$433$	1.50235	0.0721985	0.0360992	−	0.999348i	$-0.488507\pi$
$433$	1.50235	0.0721985	0.0360992	+	0.999348i	$0.488507\pi$
$434$	−22.1651	−1.06396
$435$	−2.80524	−0.134501
$436$	−5.30190	−0.253915
$437$	−12.5692	−0.601267
$438$	11.7944	0.563557
$439$	−41.1847	−1.96564	−0.982820	−	0.184567i	$-0.940912\pi$
$439$	−41.1847	−1.96564	−0.982820	+	0.184567i	$0.940912\pi$
$440$	13.4979	0.643487
$441$	0.0513319	0.00244438
$442$	−68.1554	−3.24182
$443$	20.6308	0.980197	0.490098	−	0.871667i	$-0.336961\pi$
$443$	20.6308	0.980197	0.490098	+	0.871667i	$0.336961\pi$
$444$	8.28159	0.393027
$445$	8.13850	0.385802
$446$	69.1899	3.27624
$447$	18.6316	0.881245
$448$	−16.9182	−0.799309
$449$	17.5393	0.827732	0.413866	−	0.910338i	$-0.364178\pi$
$449$	17.5393	0.827732	0.413866	+	0.910338i	$0.364178\pi$
$450$	0.344368	0.0162337
$451$	−7.51610	−0.353919
$452$	35.4434	1.66712
$453$	10.8109	0.507943
$454$	−36.7082	−1.72280
$455$	15.6145	0.732020
$456$	66.0503	3.09309
$457$	4.29312	0.200824	0.100412	−	0.994946i	$-0.467984\pi$
$457$	4.29312	0.200824	0.100412	+	0.994946i	$0.467984\pi$
$458$	70.2054	3.28048
$459$	−33.2702	−1.55292
$460$	−15.0416	−0.701318
$461$	−22.6565	−1.05522	−0.527608	−	0.849488i	$-0.676911\pi$
$461$	−22.6565	−1.05522	−0.527608	+	0.849488i	$0.676911\pi$
$462$	18.3968	0.855895
$463$	−34.8910	−1.62152	−0.810760	−	0.585378i	$-0.800946\pi$
$463$	−34.8910	−1.62152	−0.810760	+	0.585378i	$0.800946\pi$
$464$	10.8967	0.505865
$465$	6.92601	0.321186
$466$	−64.2674	−2.97713
$467$	15.5493	0.719534	0.359767	−	0.933042i	$-0.382856\pi$
$467$	15.5493	0.719534	0.359767	+	0.933042i	$0.382856\pi$
$468$	−0.797006	−0.0368416
$469$	19.1552	0.884507
$470$	26.5373	1.22407
$471$	−25.8383	−1.19057
$472$	−60.9426	−2.80511
$473$	13.5565	0.623329
$474$	−40.5736	−1.86361
$475$	−17.0445	−0.782055
$476$	87.9203	4.02982
$477$	−0.473374	−0.0216743
$478$	−33.8775	−1.54952
$479$	36.3175	1.65939	0.829694	−	0.558218i	$-0.188515\pi$
$479$	36.3175	1.65939	0.829694	+	0.558218i	$0.188515\pi$
$480$	21.5328	0.982833
$481$	4.06879	0.185521
$482$	39.7104	1.80876
$483$	−11.8667	−0.539955
$484$	−42.7394	−1.94270
$485$	−0.389091	−0.0176677
$486$	−1.11354	−0.0505110
$487$	−1.10831	−0.0502224	−0.0251112	−	0.999685i	$-0.507994\pi$
$487$	−1.10831	−0.0502224	−0.0251112	+	0.999685i	$0.507994\pi$
$488$	92.0262	4.16583
$489$	−1.74392	−0.0788627
$490$	−4.32092	−0.195199
$491$	−9.84580	−0.444335	−0.222167	−	0.975009i	$-0.571313\pi$
$491$	−9.84580	−0.444335	−0.222167	+	0.975009i	$0.571313\pi$
$492$	−44.0135	−1.98428
$493$	−7.76037	−0.349509
$494$	56.0615	2.52232
$495$	−0.0779669	−0.00350435
$496$	−26.9034	−1.20800
$497$	19.2013	0.861295
$498$	−18.8280	−0.843702
$499$	1.58502	0.0709554	0.0354777	−	0.999370i	$-0.488705\pi$
$499$	1.58502	0.0709554	0.0354777	+	0.999370i	$0.488705\pi$
$500$	−52.1323	−2.33143
$501$	35.1092	1.56856
$502$	−11.9105	−0.531591
$503$	6.45529	0.287827	0.143914	−	0.989590i	$-0.454031\pi$
$503$	6.45529	0.287827	0.143914	+	0.989590i	$0.454031\pi$
$504$	0.845773	0.0376737
$505$	−12.4573	−0.554342
$506$	−8.70679	−0.387064
$507$	−6.19974	−0.275340
$508$	1.48218	0.0657611
$509$	29.1931	1.29396	0.646980	−	0.762507i	$-0.276032\pi$
$509$	29.1931	1.29396	0.646980	+	0.762507i	$0.276032\pi$
$510$	−39.0430	−1.72885
$511$	−7.47507	−0.330678
$512$	45.6663	2.01818
$513$	27.3665	1.20826
$514$	74.8191	3.30013
$515$	−12.6872	−0.559064
$516$	79.3857	3.49476
$517$	10.8089	0.475373
$518$	−7.45926	−0.327741
$519$	−35.1526	−1.54303
$520$	38.8340	1.70298
$521$	10.3727	0.454435	0.227217	−	0.973844i	$-0.427037\pi$
$521$	10.3727	0.454435	0.227217	+	0.973844i	$0.427037\pi$
$522$	−0.128969	−0.00564481
$523$	−15.7108	−0.686986	−0.343493	−	0.939155i	$-0.611610\pi$
$523$	−15.7108	−0.686986	−0.343493	+	0.939155i	$0.611610\pi$
$524$	−88.3336	−3.85887
$525$	−16.0919	−0.702307
$526$	64.0277	2.79174
$527$	19.1600	0.834622
$528$	22.3294	0.971763
$529$	−17.3837	−0.755815
$530$	39.8467	1.73083
$531$	0.352018	0.0152763
$532$	−72.3191	−3.13543
$533$	−21.6241	−0.936644
$534$	27.5869	1.19380
$535$	10.6411	0.460053
$536$	47.6399	2.05773
$537$	3.20499	0.138306
$538$	35.2340	1.51905
$539$	−1.75994	−0.0758062
$540$	32.7495	1.40931
$541$	37.6195	1.61739	0.808695	−	0.588228i	$-0.200174\pi$
$541$	37.6195	1.61739	0.808695	+	0.588228i	$0.200174\pi$
$542$	78.0543	3.35272
$543$	3.87261	0.166190
$544$	59.5680	2.55396
$545$	−1.49220	−0.0639186
$546$	52.9282	2.26512
$547$	−9.10710	−0.389392	−0.194696	−	0.980864i	$-0.562372\pi$
$547$	−9.10710	−0.389392	−0.194696	+	0.980864i	$0.562372\pi$
$548$	−43.0179	−1.83763
$549$	−0.531564	−0.0226866
$550$	−11.8069	−0.503446
$551$	6.38331	0.271938
$552$	−29.5131	−1.25616
$553$	25.7149	1.09351
$554$	−10.7759	−0.457822
$555$	2.33082	0.0989376
$556$	59.0270	2.50330
$557$	38.2673	1.62144	0.810718	−	0.585437i	$-0.199077\pi$
$557$	38.2673	1.62144	0.810718	+	0.585437i	$0.199077\pi$
$558$	0.318418	0.0134797
$559$	39.0026	1.64964
$560$	−34.7452	−1.46825
$561$	−15.9025	−0.671405
$562$	−19.7424	−0.832783
$563$	8.30646	0.350076	0.175038	−	0.984562i	$-0.443995\pi$
$563$	8.30646	0.350076	0.175038	+	0.984562i	$0.443995\pi$
$564$	63.2956	2.66523
$565$	9.97540	0.419668
$566$	24.8889	1.04616
$567$	26.1923	1.09997
$568$	47.7544	2.00373
$569$	−27.4618	−1.15126	−0.575630	−	0.817710i	$-0.695243\pi$
$569$	−27.4618	−1.15126	−0.575630	+	0.817710i	$0.695243\pi$
$570$	32.1149	1.34515
$571$	23.9128	1.00072	0.500359	−	0.865818i	$-0.333201\pi$
$571$	23.9128	1.00072	0.500359	+	0.865818i	$0.333201\pi$
$572$	27.3258	1.14255
$573$	37.8543	1.58139
$574$	39.6431	1.65467
$575$	7.61594	0.317607
$576$	0.243042	0.0101267
$577$	−6.90592	−0.287497	−0.143749	−	0.989614i	$-0.545916\pi$
$577$	−6.90592	−0.287497	−0.143749	+	0.989614i	$0.545916\pi$
$578$	−63.8444	−2.65558
$579$	−41.6025	−1.72894
$580$	7.63891	0.317189
$581$	11.9328	0.495058
$582$	−1.31889	−0.0546699
$583$	16.2299	0.672174
$584$	−18.5908	−0.769294
$585$	−0.224314	−0.00927423
$586$	−79.0408	−3.26515
$587$	34.0508	1.40543	0.702714	−	0.711472i	$-0.251971\pi$
$587$	34.0508	1.40543	0.702714	+	0.711472i	$0.251971\pi$
$588$	−10.3061	−0.425015
$589$	−15.7601	−0.649384
$590$	−29.6315	−1.21991
$591$	−26.2872	−1.08131
$592$	−9.05381	−0.372109
$593$	15.3148	0.628905	0.314453	−	0.949273i	$-0.398179\pi$
$593$	15.3148	0.628905	0.314453	+	0.949273i	$0.398179\pi$
$594$	18.9570	0.777814
$595$	24.7448	1.01444
$596$	−50.7356	−2.07821
$597$	5.45820	0.223389
$598$	−25.0498	−1.02436
$599$	−41.4411	−1.69324	−0.846619	−	0.532199i	$-0.821366\pi$
$599$	−41.4411	−1.69324	−0.846619	+	0.532199i	$0.821366\pi$
$600$	−40.0212	−1.63386
$601$	−19.1958	−0.783013	−0.391507	−	0.920175i	$-0.628046\pi$
$601$	−19.1958	−0.783013	−0.391507	+	0.920175i	$0.628046\pi$
$602$	−71.5030	−2.91424
$603$	−0.275179	−0.0112061
$604$	−29.4392	−1.19786
$605$	−12.0288	−0.489040
$606$	−42.2262	−1.71532
$607$	−31.4369	−1.27598	−0.637992	−	0.770043i	$-0.720235\pi$
$607$	−31.4369	−1.27598	−0.637992	+	0.770043i	$0.720235\pi$
$608$	−48.9978	−1.98712
$609$	6.02655	0.244208
$610$	44.7449	1.81167
$611$	31.0975	1.25807
$612$	−1.26304	−0.0510553
$613$	−20.6616	−0.834512	−0.417256	−	0.908789i	$-0.637008\pi$
$613$	−20.6616	−0.834512	−0.417256	+	0.908789i	$0.637008\pi$
$614$	−23.1582	−0.934591
$615$	−12.3874	−0.499509
$616$	−28.9978	−1.16835
$617$	43.1021	1.73522	0.867612	−	0.497242i	$-0.165654\pi$
$617$	43.1021	1.73522	0.867612	+	0.497242i	$0.165654\pi$
$618$	−43.0054	−1.72993
$619$	11.0017	0.442198	0.221099	−	0.975251i	$-0.429036\pi$
$619$	11.0017	0.442198	0.221099	+	0.975251i	$0.429036\pi$
$620$	−18.8601	−0.757441
$621$	−12.2281	−0.490696
$622$	5.06038	0.202903
$623$	−17.4841	−0.700485
$624$	64.2426	2.57176
$625$	1.39591	0.0558362
$626$	17.4877	0.698950
$627$	13.0807	0.522392
$628$	70.3600	2.80767
$629$	6.44793	0.257096
$630$	0.411231	0.0163838
$631$	15.4958	0.616878	0.308439	−	0.951244i	$-0.400193\pi$
$631$	15.4958	0.616878	0.308439	+	0.951244i	$0.400193\pi$
$632$	63.9540	2.54395
$633$	22.5490	0.896241
$634$	41.2579	1.63856
$635$	0.417153	0.0165542
$636$	95.0407	3.76861
$637$	−5.06343	−0.200620
$638$	4.42177	0.175060
$639$	−0.275840	−0.0109121
$640$	4.23644	0.167460
$641$	9.28907	0.366896	0.183448	−	0.983029i	$-0.441274\pi$
$641$	9.28907	0.366896	0.183448	+	0.983029i	$0.441274\pi$
$642$	36.0697	1.42356
$643$	−13.3577	−0.526775	−0.263388	−	0.964690i	$-0.584840\pi$
$643$	−13.3577	−0.526775	−0.263388	+	0.964690i	$0.584840\pi$
$644$	32.3141	1.27336
$645$	22.3427	0.879745
$646$	88.8422	3.49545
$647$	−33.7727	−1.32774	−0.663871	−	0.747847i	$-0.731088\pi$
$647$	−33.7727	−1.32774	−0.663871	+	0.747847i	$0.731088\pi$
$648$	65.1413	2.55899
$649$	−12.0692	−0.473756
$650$	−33.9688	−1.33237
$651$	−14.8793	−0.583165
$652$	4.74884	0.185979
$653$	37.3573	1.46190	0.730952	−	0.682428i	$-0.239076\pi$
$653$	37.3573	1.46190	0.730952	+	0.682428i	$0.239076\pi$
$654$	−5.05806	−0.197786
$655$	−24.8611	−0.971403
$656$	48.1176	1.87868
$657$	0.107385	0.00418948
$658$	−57.0106	−2.22250
$659$	46.0440	1.79362	0.896809	−	0.442418i	$-0.145879\pi$
$659$	46.0440	1.79362	0.896809	+	0.442418i	$0.145879\pi$
$660$	15.6536	0.609317
$661$	40.0584	1.55809	0.779046	−	0.626967i	$-0.215704\pi$
$661$	40.0584	1.55809	0.779046	+	0.626967i	$0.215704\pi$
$662$	26.4935	1.02970
$663$	−45.7522	−1.77687
$664$	29.6775	1.15171
$665$	−20.3539	−0.789290
$666$	0.107158	0.00415227
$667$	−2.85224	−0.110439
$668$	−95.6055	−3.69909
$669$	46.4466	1.79573
$670$	23.1635	0.894882
$671$	18.2250	0.703567
$672$	−46.2593	−1.78449
$673$	−18.5350	−0.714472	−0.357236	−	0.934014i	$-0.616281\pi$
$673$	−18.5350	−0.714472	−0.357236	+	0.934014i	$0.616281\pi$
$674$	−33.8560	−1.30408
$675$	−16.5819	−0.638238
$676$	16.8824	0.649325
$677$	−16.0250	−0.615892	−0.307946	−	0.951404i	$-0.599642\pi$
$677$	−16.0250	−0.615892	−0.307946	+	0.951404i	$0.599642\pi$
$678$	33.8134	1.29860
$679$	0.835893	0.0320786
$680$	61.5413	2.36000
$681$	−24.6419	−0.944280
$682$	−10.9171	−0.418039
$683$	18.9703	0.725877	0.362938	−	0.931813i	$-0.381774\pi$
$683$	18.9703	0.725877	0.362938	+	0.931813i	$0.381774\pi$
$684$	1.03892	0.0397239
$685$	−12.1072	−0.462593
$686$	−42.9321	−1.63915
$687$	47.1283	1.79806
$688$	−86.7881	−3.30876
$689$	46.6940	1.77890
$690$	−14.3498	−0.546288
$691$	−9.50747	−0.361681	−0.180841	−	0.983512i	$-0.557882\pi$
$691$	−9.50747	−0.361681	−0.180841	+	0.983512i	$0.557882\pi$
$692$	95.7236	3.63887
$693$	0.167498	0.00636271
$694$	−91.5111	−3.47371
$695$	16.6129	0.630163
$696$	14.9883	0.568130
$697$	−34.2683	−1.29801
$698$	39.2867	1.48702
$699$	−43.1422	−1.63179
$700$	43.8196	1.65623
$701$	24.2026	0.914120	0.457060	−	0.889436i	$-0.348902\pi$
$701$	24.2026	0.914120	0.457060	+	0.889436i	$0.348902\pi$
$702$	54.5399	2.05848
$703$	−5.30377	−0.200035
$704$	−8.33283	−0.314055
$705$	17.8143	0.670924
$706$	−55.8867	−2.10333
$707$	26.7622	1.00650
$708$	−70.6758	−2.65616
$709$	5.54185	0.208128	0.104064	−	0.994571i	$-0.466815\pi$
$709$	5.54185	0.208128	0.104064	+	0.994571i	$0.466815\pi$
$710$	23.2191	0.871398
$711$	−0.369412	−0.0138540
$712$	−43.4837	−1.62962
$713$	7.04204	0.263727
$714$	83.8768	3.13901
$715$	7.69073	0.287617
$716$	−8.72748	−0.326161
$717$	−22.7417	−0.849303
$718$	−50.3718	−1.87986
$719$	−3.89434	−0.145234	−0.0726172	−	0.997360i	$-0.523135\pi$
$719$	−3.89434	−0.145234	−0.0726172	+	0.997360i	$0.523135\pi$
$720$	0.499140	0.0186018
$721$	27.2561	1.01507
$722$	−23.7182	−0.882701
$723$	26.6573	0.991395
$724$	−10.5455	−0.391919
$725$	−3.86778	−0.143646
$726$	−40.7738	−1.51326
$727$	−25.7546	−0.955187	−0.477593	−	0.878581i	$-0.658491\pi$
$727$	−25.7546	−0.955187	−0.477593	+	0.878581i	$0.658491\pi$
$728$	−83.4278	−3.09204
$729$	26.6186	0.985875
$730$	−9.03922	−0.334557
$731$	61.8086	2.28607
$732$	106.724	3.94462
$733$	28.0066	1.03445	0.517224	−	0.855850i	$-0.326965\pi$
$733$	28.0066	1.03445	0.517224	+	0.855850i	$0.326965\pi$
$734$	58.2849	2.15134
$735$	−2.90060	−0.106990
$736$	21.8935	0.807007
$737$	9.43466	0.347530
$738$	−0.569502	−0.0209637
$739$	6.34376	0.233359	0.116680	−	0.993170i	$-0.462775\pi$
$739$	6.34376	0.233359	0.116680	+	0.993170i	$0.462775\pi$
$740$	−6.34702	−0.233321
$741$	37.6336	1.38250
$742$	−85.6035	−3.14260
$743$	−29.7096	−1.08994	−0.544970	−	0.838456i	$-0.683459\pi$
$743$	−29.7096	−1.08994	−0.544970	+	0.838456i	$0.683459\pi$
$744$	−37.0054	−1.35668
$745$	−14.2793	−0.523153
$746$	49.7158	1.82022
$747$	−0.171424	−0.00627207
$748$	43.3040	1.58335
$749$	−22.8604	−0.835300
$750$	−49.7347	−1.81605
$751$	30.3449	1.10730	0.553651	−	0.832749i	$-0.313234\pi$
$751$	30.3449	1.10730	0.553651	+	0.832749i	$0.313234\pi$
$752$	−69.1977	−2.52338
$753$	−7.99541	−0.291369
$754$	12.7216	0.463294
$755$	−8.28552	−0.301541
$756$	−70.3563	−2.55883
$757$	−47.9766	−1.74374	−0.871869	−	0.489739i	$-0.837092\pi$
$757$	−47.9766	−1.74374	−0.871869	+	0.489739i	$0.837092\pi$
$758$	−79.8059	−2.89868
$759$	−5.84480	−0.212153
$760$	−50.6210	−1.83622
$761$	0.973903	0.0353039	0.0176520	−	0.999844i	$-0.494381\pi$
$761$	0.973903	0.0353039	0.0176520	+	0.999844i	$0.494381\pi$
$762$	1.41401	0.0512244
$763$	3.20571	0.116055
$764$	−103.081	−3.72932
$765$	−0.355476	−0.0128523
$766$	93.8905	3.39240
$767$	−34.7234	−1.25379
$768$	34.9110	1.25974
$769$	−45.5610	−1.64297	−0.821486	−	0.570228i	$-0.806855\pi$
$769$	−45.5610	−1.64297	−0.821486	+	0.570228i	$0.806855\pi$
$770$	−14.0993	−0.508103
$771$	50.2254	1.80882
$772$	113.287	4.07730
$773$	18.3909	0.661476	0.330738	−	0.943723i	$-0.392702\pi$
$773$	18.3909	0.661476	0.330738	+	0.943723i	$0.392702\pi$
$774$	1.02719	0.0369216
$775$	9.54937	0.343023
$776$	2.07890	0.0746282
$777$	−5.00734	−0.179637
$778$	32.0199	1.14797
$779$	28.1875	1.00992
$780$	45.0361	1.61255
$781$	9.45734	0.338410
$782$	−39.6971	−1.41957
$783$	6.21007	0.221930
$784$	11.2671	0.402395
$785$	19.8025	0.706782
$786$	−84.2711	−3.00585
$787$	−9.77927	−0.348593	−0.174297	−	0.984693i	$-0.555765\pi$
$787$	−9.77927	−0.348593	−0.174297	+	0.984693i	$0.555765\pi$
$788$	71.5823	2.55001
$789$	42.9813	1.53017
$790$	31.0957	1.10633
$791$	−21.4303	−0.761975
$792$	0.416574	0.0148023
$793$	52.4339	1.86198
$794$	33.2845	1.18122
$795$	26.7488	0.948682
$796$	−14.8631	−0.526810
$797$	40.4453	1.43265	0.716323	−	0.697769i	$-0.245824\pi$
$797$	40.4453	1.43265	0.716323	+	0.697769i	$0.245824\pi$
$798$	−68.9931	−2.44233
$799$	49.2811	1.74344
$800$	29.6888	1.04966
$801$	0.251172	0.00887471
$802$	35.3357	1.24775
$803$	−3.68175	−0.129926
$804$	55.2485	1.94846
$805$	9.09467	0.320545
$806$	−31.4091	−1.10634
$807$	23.6523	0.832600
$808$	66.5589	2.34153
$809$	−20.4690	−0.719653	−0.359827	−	0.933019i	$-0.617164\pi$
$809$	−20.4690	−0.719653	−0.359827	+	0.933019i	$0.617164\pi$
$810$	31.6730	1.11288
$811$	14.8728	0.522254	0.261127	−	0.965305i	$-0.415906\pi$
$811$	14.8728	0.522254	0.261127	+	0.965305i	$0.415906\pi$
$812$	−16.4108	−0.575907
$813$	52.3972	1.83765
$814$	−3.67396	−0.128772
$815$	1.33654	0.0468170
$816$	101.807	3.56396
$817$	−50.8408	−1.77870
$818$	−20.5907	−0.719936
$819$	0.481898	0.0168389
$820$	33.7320	1.17797
$821$	5.40692	0.188703	0.0943515	−	0.995539i	$-0.469922\pi$
$821$	5.40692	0.188703	0.0943515	+	0.995539i	$0.469922\pi$
$822$	−41.0395	−1.43142
$823$	−17.3050	−0.603213	−0.301607	−	0.953432i	$-0.597523\pi$
$823$	−17.3050	−0.603213	−0.301607	+	0.953432i	$0.597523\pi$
$824$	67.7871	2.36148
$825$	−7.92585	−0.275943
$826$	63.6579	2.21494
$827$	−16.8090	−0.584506	−0.292253	−	0.956341i	$-0.594405\pi$
$827$	−16.8090	−0.584506	−0.292253	+	0.956341i	$0.594405\pi$
$828$	−0.464216	−0.0161326
$829$	9.29397	0.322793	0.161397	−	0.986890i	$-0.448400\pi$
$829$	9.29397	0.322793	0.161397	+	0.986890i	$0.448400\pi$
$830$	14.4298	0.500865
$831$	−7.23374	−0.250936
$832$	−23.9739	−0.831144
$833$	−8.02416	−0.278021
$834$	56.3124	1.94994
$835$	−26.9078	−0.931181
$836$	−35.6198	−1.23194
$837$	−15.3324	−0.529964
$838$	45.7146	1.57918
$839$	−13.3716	−0.461639	−0.230820	−	0.972997i	$-0.574141\pi$
$839$	−13.3716	−0.461639	−0.230820	+	0.972997i	$0.574141\pi$
$840$	−47.7918	−1.64897
$841$	−27.5515	−0.950051
$842$	−57.1070	−1.96804
$843$	−13.2529	−0.456455
$844$	−61.4028	−2.11357
$845$	4.75149	0.163456
$846$	0.818998	0.0281577
$847$	25.8417	0.887932
$848$	−103.903	−3.56804
$849$	16.7077	0.573407
$850$	−53.8313	−1.84640
$851$	2.36987	0.0812380
$852$	55.3813	1.89733
$853$	16.7290	0.572792	0.286396	−	0.958111i	$-0.407543\pi$
$853$	16.7290	0.572792	0.286396	+	0.958111i	$0.407543\pi$
$854$	−96.1264	−3.28938
$855$	0.292398	0.00999981
$856$	−56.8548	−1.94326
$857$	−12.6425	−0.431859	−0.215930	−	0.976409i	$-0.569278\pi$
$857$	−12.6425	−0.431859	−0.215930	+	0.976409i	$0.569278\pi$
$858$	26.0691	0.889984
$859$	26.8700	0.916793	0.458397	−	0.888748i	$-0.348424\pi$
$859$	26.8700	0.916793	0.458397	+	0.888748i	$0.348424\pi$
$860$	−60.8413	−2.07467
$861$	26.6121	0.906939
$862$	−46.6764	−1.58980
$863$	26.5082	0.902348	0.451174	−	0.892436i	$-0.351005\pi$
$863$	26.5082	0.902348	0.451174	+	0.892436i	$0.351005\pi$
$864$	−47.6680	−1.62170
$865$	26.9410	0.916021
$866$	−3.90289	−0.132626
$867$	−42.8582	−1.45554
$868$	40.5176	1.37526
$869$	12.6655	0.429648
$870$	7.28760	0.247073
$871$	27.1439	0.919735
$872$	7.97275	0.269991
$873$	−0.0120082	−0.000406416 0
$874$	32.6530	1.10450
$875$	31.5210	1.06560
$876$	−21.5600	−0.728444
$877$	17.3255	0.585041	0.292520	−	0.956259i	$-0.405506\pi$
$877$	17.3255	0.585041	0.292520	+	0.956259i	$0.405506\pi$
$878$	106.992	3.61080
$879$	−53.0594	−1.78965
$880$	−17.1133	−0.576889
$881$	20.1875	0.680133	0.340066	−	0.940401i	$-0.389550\pi$
$881$	20.1875	0.680133	0.340066	+	0.940401i	$0.389550\pi$
$882$	−0.133353	−0.00449022
$883$	−24.2922	−0.817499	−0.408749	−	0.912647i	$-0.634035\pi$
$883$	−24.2922	−0.817499	−0.408749	+	0.912647i	$0.634035\pi$
$884$	124.587	4.19032
$885$	−19.8914	−0.668642
$886$	−53.5957	−1.80058
$887$	−30.9161	−1.03806	−0.519030	−	0.854756i	$-0.673707\pi$
$887$	−30.9161	−1.03806	−0.519030	+	0.854756i	$0.673707\pi$
$888$	−12.4535	−0.417911
$889$	−0.896178	−0.0300569
$890$	−21.1426	−0.708702
$891$	12.9007	0.432188
$892$	−126.478	−4.23481
$893$	−40.5363	−1.35650
$894$	−48.4022	−1.61881
$895$	−2.45631	−0.0821054
$896$	−9.10124	−0.304051
$897$	−16.8157	−0.561460
$898$	−45.5646	−1.52051
$899$	−3.57632	−0.119277
$900$	−0.629500	−0.0209833
$901$	73.9974	2.46521
$902$	19.5257	0.650135
$903$	−47.9993	−1.59732
$904$	−53.2982	−1.77267
$905$	−2.96797	−0.0986588
$906$	−28.0853	−0.933070
$907$	−42.7552	−1.41966	−0.709831	−	0.704372i	$-0.751229\pi$
$907$	−42.7552	−1.41966	−0.709831	+	0.704372i	$0.751229\pi$
$908$	67.1021	2.22686
$909$	−0.384459	−0.0127517
$910$	−40.5642	−1.34469
$911$	−11.6791	−0.386946	−0.193473	−	0.981106i	$-0.561975\pi$
$911$	−11.6791	−0.386946	−0.193473	+	0.981106i	$0.561975\pi$
$912$	−83.7417	−2.77297
$913$	5.87737	0.194512
$914$	−11.1529	−0.368905
$915$	30.0369	0.992989
$916$	−128.335	−4.24029
$917$	53.4096	1.76374
$918$	86.4310	2.85265
$919$	−40.8628	−1.34794	−0.673970	−	0.738759i	$-0.735412\pi$
$919$	−40.8628	−1.34794	−0.673970	+	0.738759i	$0.735412\pi$
$920$	22.6188	0.745721
$921$	−15.5459	−0.512256
$922$	58.8582	1.93839
$923$	27.2091	0.895599
$924$	−33.6290	−1.10631
$925$	3.21366	0.105664
$926$	90.6416	2.97867
$927$	−0.391553	−0.0128603
$928$	−11.1187	−0.364989
$929$	6.16386	0.202230	0.101115	−	0.994875i	$-0.467759\pi$
$929$	6.16386	0.202230	0.101115	+	0.994875i	$0.467759\pi$
$930$	−17.9927	−0.590005
$931$	6.60030	0.216316
$932$	117.480	3.84818
$933$	3.39699	0.111212
$934$	−40.3947	−1.32175
$935$	12.1877	0.398581
$936$	1.19850	0.0391742
$937$	31.5906	1.03202	0.516009	−	0.856583i	$-0.327417\pi$
$937$	31.5906	1.03202	0.516009	+	0.856583i	$0.327417\pi$
$938$	−49.7625	−1.62480
$939$	11.7394	0.383100
$940$	−48.5098	−1.58222
$941$	−52.8307	−1.72223	−0.861116	−	0.508408i	$-0.830234\pi$
$941$	−52.8307	−1.72223	−0.861116	+	0.508408i	$0.830234\pi$
$942$	67.1241	2.18702
$943$	−12.5949	−0.410148
$944$	77.2660	2.51479
$945$	−19.8015	−0.644142
$946$	−35.2179	−1.14503
$947$	−27.5892	−0.896527	−0.448264	−	0.893901i	$-0.647957\pi$
$947$	−27.5892	−0.896527	−0.448264	+	0.893901i	$0.647957\pi$
$948$	74.1681	2.40887
$949$	−10.5925	−0.343848
$950$	44.2791	1.43660
$951$	27.6961	0.898107
$952$	−132.210	−4.28496
$953$	−47.4894	−1.53833	−0.769166	−	0.639049i	$-0.779328\pi$
$953$	−47.4894	−1.53833	−0.769166	+	0.639049i	$0.779328\pi$
$954$	1.22976	0.0398148
$955$	−29.0116	−0.938792
$956$	61.9276	2.00288
$957$	2.96830	0.0959515
$958$	−94.3475	−3.04823
$959$	26.0101	0.839911
$960$	−13.7335	−0.443246
$961$	−22.1702	−0.715169
$962$	−10.5701	−0.340794
$963$	0.328406	0.0105827
$964$	−72.5901	−2.33797
$965$	31.8842	1.02639
$966$	30.8280	0.991875
$967$	13.0896	0.420935	0.210467	−	0.977601i	$-0.432501\pi$
$967$	13.0896	0.420935	0.210467	+	0.977601i	$0.432501\pi$
$968$	64.2695	2.06570
$969$	59.6390	1.91588
$970$	1.01080	0.0324549
$971$	12.6968	0.407460	0.203730	−	0.979027i	$-0.434694\pi$
$971$	12.6968	0.407460	0.203730	+	0.979027i	$0.434694\pi$
$972$	2.03553	0.0652896
$973$	−35.6898	−1.14416
$974$	2.87923	0.0922565
$975$	−22.8030	−0.730279
$976$	−116.675	−3.73468
$977$	−44.6450	−1.42832	−0.714161	−	0.699982i	$-0.753191\pi$
$977$	−44.6450	−1.42832	−0.714161	+	0.699982i	$0.753191\pi$
$978$	4.53044	0.144868
$979$	−8.61156	−0.275227
$980$	7.89858	0.252311
$981$	−0.0460524	−0.00147034
$982$	25.5779	0.816225
$983$	23.4417	0.747675	0.373838	−	0.927494i	$-0.378042\pi$
$983$	23.4417	0.747675	0.373838	+	0.927494i	$0.378042\pi$
$984$	66.1855	2.10992
$985$	20.1465	0.641922
$986$	20.1603	0.642035
$987$	−38.2707	−1.21817
$988$	−102.480	−3.26031
$989$	22.7171	0.722361
$990$	0.202547	0.00643735
$991$	37.9574	1.20576	0.602878	−	0.797833i	$-0.294021\pi$
$991$	37.9574	1.20576	0.602878	+	0.797833i	$0.294021\pi$
$992$	27.4516	0.871588
$993$	17.7849	0.564386
$994$	−49.8821	−1.58216
$995$	−4.18317	−0.132615
$996$	34.4173	1.09055
$997$	25.7420	0.815256	0.407628	−	0.913148i	$-0.366356\pi$
$997$	25.7420	0.815256	0.407628	+	0.913148i	$0.366356\pi$
$998$	−4.11766	−0.130342
$999$	−5.15982	−0.163249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.6	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.6	✓	133	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59785 q^{2} -1.74392 q^{3} +4.74884 q^{4} +1.33654 q^{5} +4.53044 q^{6} -2.87132 q^{7} -7.14109 q^{8} +0.0412485 q^{9} +O(q^{10})\)	\(q-2.59785 q^{2} -1.74392 q^{3} +4.74884 q^{4} +1.33654 q^{5} +4.53044 q^{6} -2.87132 q^{7} -7.14109 q^{8} +0.0412485 q^{9} -3.47214 q^{10} -1.41423 q^{11} -8.28159 q^{12} -4.06879 q^{13} +7.45926 q^{14} -2.33082 q^{15} +9.05381 q^{16} -6.44793 q^{17} -0.107158 q^{18} +5.30377 q^{19} +6.34702 q^{20} +5.00734 q^{21} +3.67396 q^{22} -2.36987 q^{23} +12.4535 q^{24} -3.21366 q^{25} +10.5701 q^{26} +5.15982 q^{27} -13.6354 q^{28} +1.20354 q^{29} +6.05512 q^{30} -2.97149 q^{31} -9.23831 q^{32} +2.46630 q^{33} +16.7508 q^{34} -3.83763 q^{35} +0.195883 q^{36} -1.00000 q^{37} -13.7784 q^{38} +7.09564 q^{39} -9.54435 q^{40} +5.31462 q^{41} -13.0083 q^{42} -9.58580 q^{43} -6.71595 q^{44} +0.0551303 q^{45} +6.15656 q^{46} -7.64293 q^{47} -15.7891 q^{48} +1.24446 q^{49} +8.34862 q^{50} +11.2447 q^{51} -19.3220 q^{52} -11.4761 q^{53} -13.4045 q^{54} -1.89017 q^{55} +20.5043 q^{56} -9.24933 q^{57} -3.12663 q^{58} +8.53408 q^{59} -11.0687 q^{60} -12.8869 q^{61} +7.71951 q^{62} -0.118438 q^{63} +5.89214 q^{64} -5.43810 q^{65} -6.40708 q^{66} -6.67124 q^{67} -30.6202 q^{68} +4.13285 q^{69} +9.96960 q^{70} -6.68727 q^{71} -0.294559 q^{72} +2.60336 q^{73} +2.59785 q^{74} +5.60436 q^{75} +25.1867 q^{76} +4.06070 q^{77} -18.4334 q^{78} -8.95578 q^{79} +12.1008 q^{80} -9.12204 q^{81} -13.8066 q^{82} -4.15588 q^{83} +23.7791 q^{84} -8.61792 q^{85} +24.9025 q^{86} -2.09888 q^{87} +10.0991 q^{88} +6.08923 q^{89} -0.143220 q^{90} +11.6828 q^{91} -11.2541 q^{92} +5.18204 q^{93} +19.8552 q^{94} +7.08870 q^{95} +16.1108 q^{96} -0.291118 q^{97} -3.23291 q^{98} -0.0583349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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