LMFDB - Embedded newform 6031.2.a.e.1.7

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:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.54672 q^{2} -0.772659 q^{3} +4.48577 q^{4} +3.37038 q^{5} +1.96774 q^{6} +0.335508 q^{7} -6.33055 q^{8} -2.40300 q^{9} +O(q^{10})$	\(q-2.54672 q^{2} -0.772659 q^{3} +4.48577 q^{4} +3.37038 q^{5} +1.96774 q^{6} +0.335508 q^{7} -6.33055 q^{8} -2.40300 q^{9} -8.58341 q^{10} -5.47110 q^{11} -3.46597 q^{12} +6.30370 q^{13} -0.854443 q^{14} -2.60416 q^{15} +7.15058 q^{16} -2.93966 q^{17} +6.11975 q^{18} -7.52962 q^{19} +15.1188 q^{20} -0.259233 q^{21} +13.9333 q^{22} -2.67796 q^{23} +4.89136 q^{24} +6.35948 q^{25} -16.0537 q^{26} +4.17468 q^{27} +1.50501 q^{28} +6.45716 q^{29} +6.63205 q^{30} -10.7000 q^{31} -5.54940 q^{32} +4.22730 q^{33} +7.48649 q^{34} +1.13079 q^{35} -10.7793 q^{36} +1.00000 q^{37} +19.1758 q^{38} -4.87061 q^{39} -21.3364 q^{40} -0.232344 q^{41} +0.660193 q^{42} +3.89768 q^{43} -24.5421 q^{44} -8.09902 q^{45} +6.82000 q^{46} +1.76102 q^{47} -5.52496 q^{48} -6.88743 q^{49} -16.1958 q^{50} +2.27136 q^{51} +28.2769 q^{52} +5.31955 q^{53} -10.6317 q^{54} -18.4397 q^{55} -2.12395 q^{56} +5.81783 q^{57} -16.4446 q^{58} +2.20357 q^{59} -11.6816 q^{60} -12.5706 q^{61} +27.2498 q^{62} -0.806224 q^{63} -0.168393 q^{64} +21.2459 q^{65} -10.7657 q^{66} -7.58107 q^{67} -13.1866 q^{68} +2.06915 q^{69} -2.87980 q^{70} +1.88840 q^{71} +15.2123 q^{72} -6.90246 q^{73} -2.54672 q^{74} -4.91371 q^{75} -33.7761 q^{76} -1.83560 q^{77} +12.4041 q^{78} -0.0721463 q^{79} +24.1002 q^{80} +3.98339 q^{81} +0.591715 q^{82} -1.51389 q^{83} -1.16286 q^{84} -9.90779 q^{85} -9.92628 q^{86} -4.98918 q^{87} +34.6351 q^{88} +16.2499 q^{89} +20.6259 q^{90} +2.11494 q^{91} -12.0127 q^{92} +8.26744 q^{93} -4.48483 q^{94} -25.3777 q^{95} +4.28780 q^{96} +7.90960 q^{97} +17.5403 q^{98} +13.1470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.54672	−1.80080	−0.900400	−	0.435062i	$-0.856726\pi$
$2$	−2.54672	−1.80080	−0.900400	+	0.435062i	$0.856726\pi$
$3$	−0.772659	−0.446095	−0.223048	−	0.974808i	$-0.571601\pi$
$3$	−0.772659	−0.446095	−0.223048	+	0.974808i	$0.571601\pi$
$4$	4.48577	2.24288
$5$	3.37038	1.50728	0.753640	−	0.657287i	$-0.228296\pi$
$5$	3.37038	1.50728	0.753640	+	0.657287i	$0.228296\pi$
$6$	1.96774	0.803329
$7$	0.335508	0.126810	0.0634050	−	0.997988i	$-0.479804\pi$
$7$	0.335508	0.126810	0.0634050	+	0.997988i	$0.479804\pi$
$8$	−6.33055	−2.23819
$9$	−2.40300	−0.800999
$10$	−8.58341	−2.71431
$11$	−5.47110	−1.64960	−0.824799	−	0.565425i	$-0.808712\pi$
$11$	−5.47110	−1.64960	−0.824799	+	0.565425i	$0.808712\pi$
$12$	−3.46597	−1.00054
$13$	6.30370	1.74833	0.874166	−	0.485628i	$-0.161409\pi$
$13$	6.30370	1.74833	0.874166	+	0.485628i	$0.161409\pi$
$14$	−0.854443	−0.228359
$15$	−2.60416	−0.672391
$16$	7.15058	1.78764
$17$	−2.93966	−0.712973	−0.356487	−	0.934300i	$-0.616025\pi$
$17$	−2.93966	−0.712973	−0.356487	+	0.934300i	$0.616025\pi$
$18$	6.11975	1.44244
$19$	−7.52962	−1.72741	−0.863707	−	0.503995i	$-0.831863\pi$
$19$	−7.52962	−1.72741	−0.863707	+	0.503995i	$0.831863\pi$
$20$	15.1188	3.38066
$21$	−0.259233	−0.0565693
$22$	13.9333	2.97060
$23$	−2.67796	−0.558393	−0.279196	−	0.960234i	$-0.590068\pi$
$23$	−2.67796	−0.558393	−0.279196	+	0.960234i	$0.590068\pi$
$24$	4.89136	0.998444
$25$	6.35948	1.27190
$26$	−16.0537	−3.14840
$27$	4.17468	0.803417
$28$	1.50501	0.284420
$29$	6.45716	1.19906	0.599532	−	0.800351i	$-0.295353\pi$
$29$	6.45716	1.19906	0.599532	+	0.800351i	$0.295353\pi$
$30$	6.63205	1.21084
$31$	−10.7000	−1.92177	−0.960887	−	0.276941i	$-0.910679\pi$
$31$	−10.7000	−1.92177	−0.960887	+	0.276941i	$0.910679\pi$
$32$	−5.54940	−0.981005
$33$	4.22730	0.735878
$34$	7.48649	1.28392
$35$	1.13079	0.191138
$36$	−10.7793	−1.79655
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	19.1758	3.11073
$39$	−4.87061	−0.779922
$40$	−21.3364	−3.37358
$41$	−0.232344	−0.0362860	−0.0181430	−	0.999835i	$-0.505775\pi$
$41$	−0.232344	−0.0362860	−0.0181430	+	0.999835i	$0.505775\pi$
$42$	0.660193	0.101870
$43$	3.89768	0.594390	0.297195	−	0.954817i	$-0.403949\pi$
$43$	3.89768	0.594390	0.297195	+	0.954817i	$0.403949\pi$
$44$	−24.5421	−3.69986
$45$	−8.09902	−1.20733
$46$	6.82000	1.00555
$47$	1.76102	0.256872	0.128436	−	0.991718i	$-0.459004\pi$
$47$	1.76102	0.256872	0.128436	+	0.991718i	$0.459004\pi$
$48$	−5.52496	−0.797460
$49$	−6.88743	−0.983919
$50$	−16.1958	−2.29043
$51$	2.27136	0.318054
$52$	28.2769	3.92131
$53$	5.31955	0.730697	0.365348	−	0.930871i	$-0.380950\pi$
$53$	5.31955	0.730697	0.365348	+	0.930871i	$0.380950\pi$
$54$	−10.6317	−1.44679
$55$	−18.4397	−2.48641
$56$	−2.12395	−0.283824
$57$	5.81783	0.770591
$58$	−16.4446	−2.15928
$59$	2.20357	0.286880	0.143440	−	0.989659i	$-0.454184\pi$
$59$	2.20357	0.286880	0.143440	+	0.989659i	$0.454184\pi$
$60$	−11.6816	−1.50809
$61$	−12.5706	−1.60951	−0.804753	−	0.593609i	$-0.797702\pi$
$61$	−12.5706	−1.60951	−0.804753	+	0.593609i	$0.797702\pi$
$62$	27.2498	3.46073
$63$	−0.806224	−0.101575
$64$	−0.168393	−0.0210491
$65$	21.2459	2.63523
$66$	−10.7657	−1.32517
$67$	−7.58107	−0.926175	−0.463087	−	0.886313i	$-0.653258\pi$
$67$	−7.58107	−0.926175	−0.463087	+	0.886313i	$0.653258\pi$
$68$	−13.1866	−1.59912
$69$	2.06915	0.249096
$70$	−2.87980	−0.344202
$71$	1.88840	0.224112	0.112056	−	0.993702i	$-0.464256\pi$
$71$	1.88840	0.224112	0.112056	+	0.993702i	$0.464256\pi$
$72$	15.2123	1.79279
$73$	−6.90246	−0.807871	−0.403936	−	0.914787i	$-0.632358\pi$
$73$	−6.90246	−0.807871	−0.403936	+	0.914787i	$0.632358\pi$
$74$	−2.54672	−0.296050
$75$	−4.91371	−0.567386
$76$	−33.7761	−3.87439
$77$	−1.83560	−0.209185
$78$	12.4041	1.40448
$79$	−0.0721463	−0.00811710	−0.00405855	−	0.999992i	$-0.501292\pi$
$79$	−0.0721463	−0.00811710	−0.00405855	+	0.999992i	$0.501292\pi$
$80$	24.1002	2.69448
$81$	3.98339	0.442599
$82$	0.591715	0.0653439
$83$	−1.51389	−0.166171	−0.0830855	−	0.996542i	$-0.526477\pi$
$83$	−1.51389	−0.166171	−0.0830855	+	0.996542i	$0.526477\pi$
$84$	−1.16286	−0.126878
$85$	−9.90779	−1.07465
$86$	−9.92628	−1.07038
$87$	−4.98918	−0.534897
$88$	34.6351	3.69211
$89$	16.2499	1.72249	0.861243	−	0.508193i	$-0.169686\pi$
$89$	16.2499	1.72249	0.861243	+	0.508193i	$0.169686\pi$
$90$	20.6259	2.17416
$91$	2.11494	0.221706
$92$	−12.0127	−1.25241
$93$	8.26744	0.857294
$94$	−4.48483	−0.462575
$95$	−25.3777	−2.60370
$96$	4.28780	0.437622
$97$	7.90960	0.803098	0.401549	−	0.915838i	$-0.368472\pi$
$97$	7.90960	0.803098	0.401549	+	0.915838i	$0.368472\pi$
$98$	17.5403	1.77184
$99$	13.1470	1.32133
$100$	28.5271	2.85271
$101$	10.6810	1.06279	0.531397	−	0.847123i	$-0.321667\pi$
$101$	10.6810	1.06279	0.531397	+	0.847123i	$0.321667\pi$
$102$	−5.78451	−0.572752
$103$	4.49925	0.443324	0.221662	−	0.975124i	$-0.428852\pi$
$103$	4.49925	0.443324	0.221662	+	0.975124i	$0.428852\pi$
$104$	−39.9059	−3.91309
$105$	−0.873714	−0.0852658
$106$	−13.5474	−1.31584
$107$	11.5981	1.12123	0.560617	−	0.828075i	$-0.310564\pi$
$107$	11.5981	1.12123	0.560617	+	0.828075i	$0.310564\pi$
$108$	18.7266	1.80197
$109$	−0.754615	−0.0722790	−0.0361395	−	0.999347i	$-0.511506\pi$
$109$	−0.754615	−0.0722790	−0.0361395	+	0.999347i	$0.511506\pi$
$110$	46.9607	4.47753
$111$	−0.772659	−0.0733376
$112$	2.39907	0.226691
$113$	17.4681	1.64326	0.821628	−	0.570024i	$-0.193066\pi$
$113$	17.4681	1.64326	0.821628	+	0.570024i	$0.193066\pi$
$114$	−14.8164	−1.38768
$115$	−9.02574	−0.841655
$116$	28.9653	2.68936
$117$	−15.1478	−1.40041
$118$	−5.61187	−0.516615
$119$	−0.986279	−0.0904121
$120$	16.4857	1.50494
$121$	18.9329	1.72118
$122$	32.0139	2.89840
$123$	0.179523	0.0161870
$124$	−47.9976	−4.31032
$125$	4.58196	0.409823
$126$	2.05322	0.182916
$127$	13.2155	1.17268	0.586341	−	0.810064i	$-0.300568\pi$
$127$	13.2155	1.17268	0.586341	+	0.810064i	$0.300568\pi$
$128$	11.5277	1.01891
$129$	−3.01158	−0.265154
$130$	−54.1072	−4.74552
$131$	−0.743240	−0.0649371	−0.0324686	−	0.999473i	$-0.510337\pi$
$131$	−0.743240	−0.0649371	−0.0324686	+	0.999473i	$0.510337\pi$
$132$	18.9627	1.65049
$133$	−2.52624	−0.219053
$134$	19.3068	1.66786
$135$	14.0703	1.21097
$136$	18.6097	1.59577
$137$	1.85448	0.158439	0.0792196	−	0.996857i	$-0.474757\pi$
$137$	1.85448	0.158439	0.0792196	+	0.996857i	$0.474757\pi$
$138$	−5.26954	−0.448573
$139$	1.67371	0.141962	0.0709812	−	0.997478i	$-0.477387\pi$
$139$	1.67371	0.141962	0.0709812	+	0.997478i	$0.477387\pi$
$140$	5.07246	0.428701
$141$	−1.36067	−0.114589
$142$	−4.80922	−0.403581
$143$	−34.4882	−2.88405
$144$	−17.1828	−1.43190
$145$	21.7631	1.80733
$146$	17.5786	1.45482
$147$	5.32164	0.438922
$148$	4.48577	0.368728
$149$	13.6589	1.11898	0.559492	−	0.828836i	$-0.310996\pi$
$149$	13.6589	1.11898	0.559492	+	0.828836i	$0.310996\pi$
$150$	12.5138	1.02175
$151$	2.74494	0.223380	0.111690	−	0.993743i	$-0.464374\pi$
$151$	2.74494	0.223380	0.111690	+	0.993743i	$0.464374\pi$
$152$	47.6666	3.86627
$153$	7.06400	0.571091
$154$	4.67474	0.376701
$155$	−36.0630	−2.89665
$156$	−21.8484	−1.74928
$157$	10.0831	0.804717	0.402358	−	0.915482i	$-0.368191\pi$
$157$	10.0831	0.804717	0.402358	+	0.915482i	$0.368191\pi$
$158$	0.183736	0.0146173
$159$	−4.11020	−0.325960
$160$	−18.7036	−1.47865
$161$	−0.898475	−0.0708097
$162$	−10.1446	−0.797032
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−1.04224	−0.0813854
$165$	14.2476	1.10917
$166$	3.85545	0.299241
$167$	7.88115	0.609862	0.304931	−	0.952375i	$-0.401367\pi$
$167$	7.88115	0.609862	0.304931	+	0.952375i	$0.401367\pi$
$168$	1.64109	0.126613
$169$	26.7366	2.05666
$170$	25.2323	1.93523
$171$	18.0937	1.38366
$172$	17.4841	1.33315
$173$	−10.2014	−0.775602	−0.387801	−	0.921743i	$-0.626765\pi$
$173$	−10.2014	−0.775602	−0.387801	+	0.921743i	$0.626765\pi$
$174$	12.7060	0.963242
$175$	2.13365	0.161289
$176$	−39.1215	−2.94890
$177$	−1.70261	−0.127976
$178$	−41.3839	−3.10186
$179$	23.0826	1.72528	0.862638	−	0.505821i	$-0.168810\pi$
$179$	23.0826	1.72528	0.862638	+	0.505821i	$0.168810\pi$
$180$	−36.3303	−2.70790
$181$	6.39875	0.475615	0.237808	−	0.971312i	$-0.423571\pi$
$181$	6.39875	0.475615	0.237808	+	0.971312i	$0.423571\pi$
$182$	−5.38615	−0.399248
$183$	9.71283	0.717993
$184$	16.9529	1.24979
$185$	3.37038	0.247795
$186$	−21.0548	−1.54382
$187$	16.0832	1.17612
$188$	7.89955	0.576134
$189$	1.40064	0.101881
$190$	64.6298	4.68874
$191$	−4.45446	−0.322314	−0.161157	−	0.986929i	$-0.551523\pi$
$191$	−4.45446	−0.322314	−0.161157	+	0.986929i	$0.551523\pi$
$192$	0.130110	0.00938991
$193$	−9.65744	−0.695158	−0.347579	−	0.937651i	$-0.612996\pi$
$193$	−9.65744	−0.695158	−0.347579	+	0.937651i	$0.612996\pi$
$194$	−20.1435	−1.44622
$195$	−16.4158	−1.17556
$196$	−30.8954	−2.20682
$197$	−8.91686	−0.635300	−0.317650	−	0.948208i	$-0.602894\pi$
$197$	−8.91686	−0.635300	−0.317650	+	0.948208i	$0.602894\pi$
$198$	−33.4818	−2.37945
$199$	22.5220	1.59655	0.798273	−	0.602296i	$-0.205747\pi$
$199$	22.5220	1.59655	0.798273	+	0.602296i	$0.205747\pi$
$200$	−40.2590	−2.84674
$201$	5.85758	0.413162
$202$	−27.2014	−1.91388
$203$	2.16642	0.152053
$204$	10.1888	0.713358
$205$	−0.783088	−0.0546933
$206$	−11.4583	−0.798338
$207$	6.43512	0.447272
$208$	45.0751	3.12540
$209$	41.1953	2.84954
$210$	2.22510	0.153547
$211$	−11.1175	−0.765359	−0.382680	−	0.923881i	$-0.624999\pi$
$211$	−11.1175	−0.765359	−0.382680	+	0.923881i	$0.624999\pi$
$212$	23.8623	1.63887
$213$	−1.45909	−0.0999752
$214$	−29.5372	−2.01912
$215$	13.1367	0.895913
$216$	−26.4280	−1.79820
$217$	−3.58992	−0.243700
$218$	1.92179	0.130160
$219$	5.33325	0.360387
$220$	−82.7162	−5.57673
$221$	−18.5308	−1.24651
$222$	1.96774	0.132066
$223$	−20.0816	−1.34477	−0.672383	−	0.740204i	$-0.734729\pi$
$223$	−20.0816	−1.34477	−0.672383	+	0.740204i	$0.734729\pi$
$224$	−1.86187	−0.124401
$225$	−15.2818	−1.01879
$226$	−44.4862	−2.95918
$227$	17.7368	1.17723	0.588616	−	0.808413i	$-0.299673\pi$
$227$	17.7368	1.17723	0.588616	+	0.808413i	$0.299673\pi$
$228$	26.0974	1.72835
$229$	−15.0331	−0.993413	−0.496706	−	0.867919i	$-0.665457\pi$
$229$	−15.0331	−0.993413	−0.496706	+	0.867919i	$0.665457\pi$
$230$	22.9860	1.51565
$231$	1.41829	0.0933166
$232$	−40.8773	−2.68373
$233$	7.15272	0.468590	0.234295	−	0.972166i	$-0.424722\pi$
$233$	7.15272	0.468590	0.234295	+	0.972166i	$0.424722\pi$
$234$	38.5771	2.52186
$235$	5.93533	0.387178
$236$	9.88471	0.643439
$237$	0.0557446	0.00362100
$238$	2.51177	0.162814
$239$	6.85975	0.443720	0.221860	−	0.975078i	$-0.428787\pi$
$239$	6.85975	0.443720	0.221860	+	0.975078i	$0.428787\pi$
$240$	−18.6212	−1.20200
$241$	12.1497	0.782630	0.391315	−	0.920257i	$-0.372020\pi$
$241$	12.1497	0.782630	0.391315	+	0.920257i	$0.372020\pi$
$242$	−48.2168	−3.09950
$243$	−15.6018	−1.00086
$244$	−56.3890	−3.60994
$245$	−23.2133	−1.48304
$246$	−0.457194	−0.0291496
$247$	−47.4645	−3.02009
$248$	67.7368	4.30129
$249$	1.16972	0.0741280
$250$	−11.6690	−0.738009
$251$	29.9205	1.88856	0.944282	−	0.329136i	$-0.106758\pi$
$251$	29.9205	1.88856	0.944282	+	0.329136i	$0.106758\pi$
$252$	−3.61653	−0.227820
$253$	14.6514	0.921124
$254$	−33.6561	−2.11177
$255$	7.65535	0.479396
$256$	−29.0209	−1.81381
$257$	−21.9630	−1.37002	−0.685008	−	0.728535i	$-0.740201\pi$
$257$	−21.9630	−1.37002	−0.685008	+	0.728535i	$0.740201\pi$
$258$	7.66963	0.477490
$259$	0.335508	0.0208474
$260$	95.3041	5.91051
$261$	−15.5165	−0.960449
$262$	1.89282	0.116939
$263$	−26.6410	−1.64275	−0.821377	−	0.570385i	$-0.806794\pi$
$263$	−26.6410	−1.64275	−0.821377	+	0.570385i	$0.806794\pi$
$264$	−26.7611	−1.64703
$265$	17.9289	1.10137
$266$	6.43363	0.394471
$267$	−12.5556	−0.768393
$268$	−34.0069	−2.07730
$269$	−0.331388	−0.0202051	−0.0101025	−	0.999949i	$-0.503216\pi$
$269$	−0.331388	−0.0202051	−0.0101025	+	0.999949i	$0.503216\pi$
$270$	−35.8330	−2.18072
$271$	−29.0315	−1.76354	−0.881769	−	0.471681i	$-0.843647\pi$
$271$	−29.0315	−1.76354	−0.881769	+	0.471681i	$0.843647\pi$
$272$	−21.0203	−1.27454
$273$	−1.63413	−0.0989019
$274$	−4.72284	−0.285317
$275$	−34.7933	−2.09812
$276$	9.28172	0.558694
$277$	−6.55483	−0.393842	−0.196921	−	0.980419i	$-0.563094\pi$
$277$	−6.55483	−0.393842	−0.196921	+	0.980419i	$0.563094\pi$
$278$	−4.26247	−0.255646
$279$	25.7120	1.53934
$280$	−7.15851	−0.427803
$281$	18.4764	1.10221	0.551104	−	0.834437i	$-0.314207\pi$
$281$	18.4764	1.10221	0.551104	+	0.834437i	$0.314207\pi$
$282$	3.46525	0.206352
$283$	30.2925	1.80070	0.900350	−	0.435167i	$-0.143311\pi$
$283$	30.2925	1.80070	0.900350	+	0.435167i	$0.143311\pi$
$284$	8.47093	0.502657
$285$	19.6083	1.16150
$286$	87.8316	5.19359
$287$	−0.0779532	−0.00460143
$288$	13.3352	0.785785
$289$	−8.35838	−0.491669
$290$	−55.4244	−3.25463
$291$	−6.11142	−0.358258
$292$	−30.9628	−1.81196
$293$	−3.95361	−0.230972	−0.115486	−	0.993309i	$-0.536843\pi$
$293$	−3.95361	−0.230972	−0.115486	+	0.993309i	$0.536843\pi$
$294$	−13.5527	−0.790410
$295$	7.42687	0.432409
$296$	−6.33055	−0.367956
$297$	−22.8401	−1.32532
$298$	−34.7855	−2.01507
$299$	−16.8810	−0.976256
$300$	−22.0418	−1.27258
$301$	1.30770	0.0753745
$302$	−6.99058	−0.402262
$303$	−8.25274	−0.474107
$304$	−53.8411	−3.08800
$305$	−42.3679	−2.42598
$306$	−17.9900	−1.02842
$307$	26.3786	1.50551	0.752754	−	0.658302i	$-0.228725\pi$
$307$	26.3786	1.50551	0.752754	+	0.658302i	$0.228725\pi$
$308$	−8.23405	−0.469179
$309$	−3.47639	−0.197765
$310$	91.8424	5.21630
$311$	−1.10834	−0.0628479	−0.0314240	−	0.999506i	$-0.510004\pi$
$311$	−1.10834	−0.0628479	−0.0314240	+	0.999506i	$0.510004\pi$
$312$	30.8336	1.74561
$313$	18.6458	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$313$	18.6458	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$314$	−25.6787	−1.44913
$315$	−2.71728	−0.153102
$316$	−0.323632	−0.0182057
$317$	8.50689	0.477794	0.238897	−	0.971045i	$-0.423214\pi$
$317$	8.50689	0.477794	0.238897	+	0.971045i	$0.423214\pi$
$318$	10.4675	0.586990
$319$	−35.3278	−1.97797
$320$	−0.567549	−0.0317269
$321$	−8.96141	−0.500177
$322$	2.28816	0.127514
$323$	22.1346	1.23160
$324$	17.8686	0.992698
$325$	40.0882	2.22370
$326$	2.54672	0.141050
$327$	0.583060	0.0322433
$328$	1.47087	0.0812149
$329$	0.590837	0.0325739
$330$	−36.2846	−1.99740
$331$	14.1628	0.778457	0.389229	−	0.921141i	$-0.372742\pi$
$331$	14.1628	0.778457	0.389229	+	0.921141i	$0.372742\pi$
$332$	−6.79095	−0.372702
$333$	−2.40300	−0.131683
$334$	−20.0711	−1.09824
$335$	−25.5511	−1.39601
$336$	−1.85367	−0.101126
$337$	22.0076	1.19883	0.599415	−	0.800439i	$-0.295400\pi$
$337$	22.0076	1.19883	0.599415	+	0.800439i	$0.295400\pi$
$338$	−68.0906	−3.70364
$339$	−13.4969	−0.733049
$340$	−44.4441	−2.41032
$341$	58.5407	3.17016
$342$	−46.0794	−2.49169
$343$	−4.65934	−0.251581
$344$	−24.6744	−1.33036
$345$	6.97382	0.375458
$346$	25.9802	1.39670
$347$	−19.0612	−1.02326	−0.511630	−	0.859206i	$-0.670958\pi$
$347$	−19.0612	−1.02326	−0.511630	+	0.859206i	$0.670958\pi$
$348$	−22.3803	−1.19971
$349$	5.02302	0.268876	0.134438	−	0.990922i	$-0.457077\pi$
$349$	5.02302	0.268876	0.134438	+	0.990922i	$0.457077\pi$
$350$	−5.43381	−0.290449
$351$	26.3159	1.40464
$352$	30.3613	1.61827
$353$	−33.7964	−1.79880	−0.899400	−	0.437128i	$-0.855996\pi$
$353$	−33.7964	−1.79880	−0.899400	+	0.437128i	$0.855996\pi$
$354$	4.33606	0.230459
$355$	6.36463	0.337800
$356$	72.8933	3.86334
$357$	0.762058	0.0403324
$358$	−58.7849	−3.10688
$359$	−24.2576	−1.28027	−0.640134	−	0.768263i	$-0.721121\pi$
$359$	−24.2576	−1.28027	−0.640134	+	0.768263i	$0.721121\pi$
$360$	51.2712	2.70223
$361$	37.6952	1.98396
$362$	−16.2958	−0.856489
$363$	−14.6287	−0.767808
$364$	9.48712	0.497260
$365$	−23.2639	−1.21769
$366$	−24.7358	−1.29296
$367$	−25.9860	−1.35646	−0.678229	−	0.734850i	$-0.737252\pi$
$367$	−25.9860	−1.35646	−0.678229	+	0.734850i	$0.737252\pi$
$368$	−19.1489	−0.998208
$369$	0.558322	0.0290651
$370$	−8.58341	−0.446230
$371$	1.78475	0.0926596
$372$	37.0858	1.92281
$373$	26.5147	1.37288	0.686439	−	0.727187i	$-0.259173\pi$
$373$	26.5147	1.37288	0.686439	+	0.727187i	$0.259173\pi$
$374$	−40.9593	−2.11796
$375$	−3.54029	−0.182820
$376$	−11.1483	−0.574927
$377$	40.7040	2.09636
$378$	−3.56702	−0.183468
$379$	−6.90573	−0.354724	−0.177362	−	0.984146i	$-0.556756\pi$
$379$	−6.90573	−0.354724	−0.177362	+	0.984146i	$0.556756\pi$
$380$	−113.838	−5.83979
$381$	−10.2111	−0.523128
$382$	11.3443	0.580423
$383$	29.0357	1.48366	0.741829	−	0.670589i	$-0.233959\pi$
$383$	29.0357	1.48366	0.741829	+	0.670589i	$0.233959\pi$
$384$	−8.90695	−0.454531
$385$	−6.18666	−0.315301
$386$	24.5948	1.25184
$387$	−9.36610	−0.476106
$388$	35.4806	1.80126
$389$	−13.6760	−0.693403	−0.346702	−	0.937975i	$-0.612698\pi$
$389$	−13.6760	−0.693403	−0.346702	+	0.937975i	$0.612698\pi$
$390$	41.8065	2.11695
$391$	7.87229	0.398119
$392$	43.6012	2.20219
$393$	0.574271	0.0289681
$394$	22.7087	1.14405
$395$	−0.243161	−0.0122347
$396$	58.9746	2.96358
$397$	3.82381	0.191912	0.0959559	−	0.995386i	$-0.469409\pi$
$397$	3.82381	0.191912	0.0959559	+	0.995386i	$0.469409\pi$
$398$	−57.3573	−2.87506
$399$	1.95193	0.0977185
$400$	45.4739	2.27370
$401$	−9.40367	−0.469597	−0.234798	−	0.972044i	$-0.575443\pi$
$401$	−9.40367	−0.469597	−0.234798	+	0.972044i	$0.575443\pi$
$402$	−14.9176	−0.744023
$403$	−67.4495	−3.35990
$404$	47.9123	2.38373
$405$	13.4255	0.667121
$406$	−5.51727	−0.273818
$407$	−5.47110	−0.271192
$408$	−14.3789	−0.711864
$409$	−4.53696	−0.224338	−0.112169	−	0.993689i	$-0.535780\pi$
$409$	−4.53696	−0.224338	−0.112169	+	0.993689i	$0.535780\pi$
$410$	1.99430	0.0984917
$411$	−1.43288	−0.0706789
$412$	20.1826	0.994324
$413$	0.739314	0.0363793
$414$	−16.3884	−0.805448
$415$	−5.10238	−0.250466
$416$	−34.9818	−1.71512
$417$	−1.29321	−0.0633287
$418$	−104.913	−5.13145
$419$	8.74396	0.427170	0.213585	−	0.976924i	$-0.431486\pi$
$419$	8.74396	0.427170	0.213585	+	0.976924i	$0.431486\pi$
$420$	−3.91928	−0.191241
$421$	22.6841	1.10556	0.552778	−	0.833329i	$-0.313568\pi$
$421$	22.6841	1.10556	0.552778	+	0.833329i	$0.313568\pi$
$422$	28.3131	1.37826
$423$	−4.23174	−0.205754
$424$	−33.6757	−1.63544
$425$	−18.6947	−0.906827
$426$	3.71589	0.180035
$427$	−4.21755	−0.204101
$428$	52.0266	2.51480
$429$	26.6476	1.28656
$430$	−33.4553	−1.61336
$431$	−11.2792	−0.543301	−0.271651	−	0.962396i	$-0.587569\pi$
$431$	−11.2792	−0.543301	−0.271651	+	0.962396i	$0.587569\pi$
$432$	29.8514	1.43622
$433$	4.75846	0.228677	0.114339	−	0.993442i	$-0.463525\pi$
$433$	4.75846	0.228677	0.114339	+	0.993442i	$0.463525\pi$
$434$	9.14252	0.438855
$435$	−16.8155	−0.806239
$436$	−3.38503	−0.162113
$437$	20.1640	0.964575
$438$	−13.5823	−0.648986
$439$	4.21471	0.201157	0.100578	−	0.994929i	$-0.467931\pi$
$439$	4.21471	0.201157	0.100578	+	0.994929i	$0.467931\pi$
$440$	116.733	5.56505
$441$	16.5505	0.788118
$442$	47.1926	2.24472
$443$	−3.27965	−0.155821	−0.0779104	−	0.996960i	$-0.524825\pi$
$443$	−3.27965	−0.155821	−0.0779104	+	0.996960i	$0.524825\pi$
$444$	−3.46597	−0.164488
$445$	54.7684	2.59627
$446$	51.1422	2.42165
$447$	−10.5537	−0.499173
$448$	−0.0564971	−0.00266924
$449$	−36.2502	−1.71075	−0.855377	−	0.518006i	$-0.826674\pi$
$449$	−36.2502	−1.71075	−0.855377	+	0.518006i	$0.826674\pi$
$450$	38.9184	1.83463
$451$	1.27118	0.0598574
$452$	78.3576	3.68563
$453$	−2.12090	−0.0996486
$454$	−45.1706	−2.11996
$455$	7.12815	0.334173
$456$	−36.8301	−1.72473
$457$	−26.9588	−1.26108	−0.630540	−	0.776157i	$-0.717167\pi$
$457$	−26.9588	−1.26108	−0.630540	+	0.776157i	$0.717167\pi$
$458$	38.2850	1.78894
$459$	−12.2721	−0.572815
$460$	−40.4874	−1.88773
$461$	23.9636	1.11610	0.558049	−	0.829808i	$-0.311550\pi$
$461$	23.9636	1.11610	0.558049	+	0.829808i	$0.311550\pi$
$462$	−3.61198	−0.168045
$463$	−5.63324	−0.261799	−0.130899	−	0.991396i	$-0.541786\pi$
$463$	−5.63324	−0.261799	−0.130899	+	0.991396i	$0.541786\pi$
$464$	46.1724	2.14350
$465$	27.8644	1.29218
$466$	−18.2160	−0.843838
$467$	3.63939	0.168411	0.0842055	−	0.996448i	$-0.473165\pi$
$467$	3.63939	0.168411	0.0842055	+	0.996448i	$0.473165\pi$
$468$	−67.9494	−3.14096
$469$	−2.54351	−0.117448
$470$	−15.1156	−0.697231
$471$	−7.79078	−0.358980
$472$	−13.9498	−0.642092
$473$	−21.3246	−0.980505
$474$	−0.141966	−0.00652070
$475$	−47.8845	−2.19709
$476$	−4.42422	−0.202784
$477$	−12.7829	−0.585288
$478$	−17.4698	−0.799052
$479$	9.86925	0.450938	0.225469	−	0.974250i	$-0.427609\pi$
$479$	9.86925	0.450938	0.225469	+	0.974250i	$0.427609\pi$
$480$	14.4515	0.659619
$481$	6.30370	0.287424
$482$	−30.9418	−1.40936
$483$	0.694215	0.0315879
$484$	84.9288	3.86040
$485$	26.6584	1.21049
$486$	39.7335	1.80235
$487$	−3.16888	−0.143596	−0.0717978	−	0.997419i	$-0.522874\pi$
$487$	−3.16888	−0.143596	−0.0717978	+	0.997419i	$0.522874\pi$
$488$	79.5791	3.60238
$489$	0.772659	0.0349409
$490$	59.1177	2.67066
$491$	10.0170	0.452059	0.226030	−	0.974120i	$-0.427425\pi$
$491$	10.0170	0.452059	0.226030	+	0.974120i	$0.427425\pi$
$492$	0.805298	0.0363056
$493$	−18.9819	−0.854900
$494$	120.879	5.43858
$495$	44.3106	1.99161
$496$	−76.5111	−3.43545
$497$	0.633573	0.0284196
$498$	−2.97895	−0.133490
$499$	43.0576	1.92752	0.963761	−	0.266766i	$-0.0859549\pi$
$499$	43.0576	1.92752	0.963761	+	0.266766i	$0.0859549\pi$
$500$	20.5536	0.919185
$501$	−6.08944	−0.272056
$502$	−76.1990	−3.40093
$503$	27.4357	1.22330	0.611649	−	0.791129i	$-0.290506\pi$
$503$	27.4357	1.22330	0.611649	+	0.791129i	$0.290506\pi$
$504$	5.10384	0.227343
$505$	35.9989	1.60193
$506$	−37.3129	−1.65876
$507$	−20.6583	−0.917468
$508$	59.2815	2.63019
$509$	−14.8402	−0.657780	−0.328890	−	0.944368i	$-0.606675\pi$
$509$	−14.8402	−0.657780	−0.328890	+	0.944368i	$0.606675\pi$
$510$	−19.4960	−0.863298
$511$	−2.31583	−0.102446
$512$	50.8527	2.24739
$513$	−31.4337	−1.38783
$514$	55.9336	2.46713
$515$	15.1642	0.668214
$516$	−13.5092	−0.594711
$517$	−9.63474	−0.423736
$518$	−0.854443	−0.0375421
$519$	7.88224	0.345992
$520$	−134.498	−5.89813
$521$	35.3721	1.54968	0.774841	−	0.632156i	$-0.217830\pi$
$521$	35.3721	1.54968	0.774841	+	0.632156i	$0.217830\pi$
$522$	39.5162	1.72958
$523$	26.3087	1.15040	0.575199	−	0.818014i	$-0.304925\pi$
$523$	26.3087	1.15040	0.575199	+	0.818014i	$0.304925\pi$
$524$	−3.33400	−0.145646
$525$	−1.64859	−0.0719502
$526$	67.8471	2.95827
$527$	31.4544	1.37017
$528$	30.2276	1.31549
$529$	−15.8285	−0.688198
$530$	−45.6599	−1.98334
$531$	−5.29517	−0.229791
$532$	−11.3321	−0.491311
$533$	−1.46463	−0.0634400
$534$	31.9757	1.38372
$535$	39.0902	1.69002
$536$	47.9923	2.07295
$537$	−17.8350	−0.769638
$538$	0.843952	0.0363854
$539$	37.6818	1.62307
$540$	63.1159	2.71608
$541$	16.2031	0.696624	0.348312	−	0.937379i	$-0.386755\pi$
$541$	16.2031	0.696624	0.348312	+	0.937379i	$0.386755\pi$
$542$	73.9350	3.17578
$543$	−4.94406	−0.212170
$544$	16.3134	0.699431
$545$	−2.54334	−0.108945
$546$	4.16166	0.178103
$547$	46.4842	1.98752	0.993760	−	0.111537i	$-0.0355772\pi$
$547$	46.4842	1.98752	0.993760	+	0.111537i	$0.0355772\pi$
$548$	8.31878	0.355361
$549$	30.2072	1.28921
$550$	88.6088	3.77829
$551$	−48.6199	−2.07128
$552$	−13.0988	−0.557524
$553$	−0.0242056	−0.00102933
$554$	16.6933	0.709230
$555$	−2.60416	−0.110540
$556$	7.50789	0.318405
$557$	−15.8926	−0.673389	−0.336695	−	0.941614i	$-0.609309\pi$
$557$	−15.8926	−0.673389	−0.336695	+	0.941614i	$0.609309\pi$
$558$	−65.4813	−2.77204
$559$	24.5698	1.03919
$560$	8.08579	0.341687
$561$	−12.4268	−0.524661
$562$	−47.0541	−1.98486
$563$	−15.1903	−0.640194	−0.320097	−	0.947385i	$-0.603715\pi$
$563$	−15.1903	−0.640194	−0.320097	+	0.947385i	$0.603715\pi$
$564$	−6.10366	−0.257010
$565$	58.8740	2.47685
$566$	−77.1463	−3.24270
$567$	1.33646	0.0561259
$568$	−11.9546	−0.501604
$569$	−25.7341	−1.07883	−0.539414	−	0.842040i	$-0.681354\pi$
$569$	−25.7341	−1.07883	−0.539414	+	0.842040i	$0.681354\pi$
$570$	−49.9368	−2.09162
$571$	−0.291344	−0.0121924	−0.00609619	−	0.999981i	$-0.501940\pi$
$571$	−0.291344	−0.0121924	−0.00609619	+	0.999981i	$0.501940\pi$
$572$	−154.706	−6.46858
$573$	3.44178	0.143783
$574$	0.198525	0.00828626
$575$	−17.0304	−0.710217
$576$	0.404648	0.0168603
$577$	−4.07574	−0.169675	−0.0848377	−	0.996395i	$-0.527037\pi$
$577$	−4.07574	−0.169675	−0.0848377	+	0.996395i	$0.527037\pi$
$578$	21.2864	0.885398
$579$	7.46191	0.310106
$580$	97.6242	4.05362
$581$	−0.507921	−0.0210721
$582$	15.5641	0.645151
$583$	−29.1038	−1.20536
$584$	43.6963	1.80817
$585$	−51.0538	−2.11081
$586$	10.0687	0.415935
$587$	0.462879	0.0191051	0.00955254	−	0.999954i	$-0.496959\pi$
$587$	0.462879	0.0191051	0.00955254	+	0.999954i	$0.496959\pi$
$588$	23.8716	0.984450
$589$	80.5668	3.31970
$590$	−18.9141	−0.778683
$591$	6.88970	0.283404
$592$	7.15058	0.293887
$593$	1.62726	0.0668236	0.0334118	−	0.999442i	$-0.489363\pi$
$593$	1.62726	0.0668236	0.0334118	+	0.999442i	$0.489363\pi$
$594$	58.1672	2.38663
$595$	−3.32414	−0.136276
$596$	61.2709	2.50975
$597$	−17.4019	−0.712211
$598$	42.9912	1.75804
$599$	−8.82570	−0.360608	−0.180304	−	0.983611i	$-0.557708\pi$
$599$	−8.82570	−0.360608	−0.180304	+	0.983611i	$0.557708\pi$
$600$	31.1065	1.26992
$601$	10.4839	0.427646	0.213823	−	0.976872i	$-0.431408\pi$
$601$	10.4839	0.427646	0.213823	+	0.976872i	$0.431408\pi$
$602$	−3.33034	−0.135735
$603$	18.2173	0.741865
$604$	12.3131	0.501015
$605$	63.8112	2.59430
$606$	21.0174	0.853773
$607$	−21.7021	−0.880863	−0.440431	−	0.897786i	$-0.645174\pi$
$607$	−21.7021	−0.880863	−0.440431	+	0.897786i	$0.645174\pi$
$608$	41.7849	1.69460
$609$	−1.67391	−0.0678302
$610$	107.899	4.36870
$611$	11.1010	0.449097
$612$	31.6875	1.28089
$613$	38.9330	1.57249	0.786245	−	0.617915i	$-0.212022\pi$
$613$	38.9330	1.57249	0.786245	+	0.617915i	$0.212022\pi$
$614$	−67.1789	−2.71112
$615$	0.605061	0.0243984
$616$	11.6203	0.468196
$617$	31.8301	1.28143	0.640716	−	0.767778i	$-0.278638\pi$
$617$	31.8301	1.28143	0.640716	+	0.767778i	$0.278638\pi$
$618$	8.85337	0.356135
$619$	35.2812	1.41807	0.709035	−	0.705173i	$-0.249131\pi$
$619$	35.2812	1.41807	0.709035	+	0.705173i	$0.249131\pi$
$620$	−161.770	−6.49686
$621$	−11.1796	−0.448622
$622$	2.82262	0.113177
$623$	5.45196	0.218428
$624$	−34.8277	−1.39422
$625$	−16.3544	−0.654177
$626$	−47.4856	−1.89791
$627$	−31.8299	−1.27117
$628$	45.2303	1.80489
$629$	−2.93966	−0.117212
$630$	6.92015	0.275705
$631$	−33.9823	−1.35281	−0.676407	−	0.736528i	$-0.736464\pi$
$631$	−33.9823	−1.35281	−0.676407	+	0.736528i	$0.736464\pi$
$632$	0.456726	0.0181676
$633$	8.59003	0.341423
$634$	−21.6646	−0.860412
$635$	44.5412	1.76756
$636$	−18.4374	−0.731091
$637$	−43.4163	−1.72022
$638$	89.9698	3.56194
$639$	−4.53782	−0.179513
$640$	38.8526	1.53578
$641$	−17.7244	−0.700073	−0.350037	−	0.936736i	$-0.613831\pi$
$641$	−17.7244	−0.700073	−0.350037	+	0.936736i	$0.613831\pi$
$642$	22.8222	0.900720
$643$	−48.0778	−1.89600	−0.948001	−	0.318267i	$-0.896899\pi$
$643$	−48.0778	−1.89600	−0.948001	+	0.318267i	$0.896899\pi$
$644$	−4.03035	−0.158818
$645$	−10.1502	−0.399662
$646$	−56.3704	−2.21787
$647$	−8.54228	−0.335832	−0.167916	−	0.985801i	$-0.553704\pi$
$647$	−8.54228	−0.335832	−0.167916	+	0.985801i	$0.553704\pi$
$648$	−25.2170	−0.990619
$649$	−12.0560	−0.473238
$650$	−102.093	−4.00443
$651$	2.77379	0.108713
$652$	−4.48577	−0.175676
$653$	−14.8611	−0.581561	−0.290780	−	0.956790i	$-0.593915\pi$
$653$	−14.8611	−0.581561	−0.290780	+	0.956790i	$0.593915\pi$
$654$	−1.48489	−0.0580638
$655$	−2.50500	−0.0978785
$656$	−1.66139	−0.0648666
$657$	16.5866	0.647104
$658$	−1.50469	−0.0586591
$659$	36.7403	1.43120	0.715599	−	0.698511i	$-0.246154\pi$
$659$	36.7403	1.43120	0.715599	+	0.698511i	$0.246154\pi$
$660$	63.9115	2.48775
$661$	−29.3670	−1.14224	−0.571122	−	0.820865i	$-0.693492\pi$
$661$	−29.3670	−1.14224	−0.571122	+	0.820865i	$0.693492\pi$
$662$	−36.0686	−1.40185
$663$	14.3180	0.556064
$664$	9.58375	0.371922
$665$	−8.51441	−0.330175
$666$	6.11975	0.237136
$667$	−17.2920	−0.669549
$668$	35.3530	1.36785
$669$	15.5163	0.599893
$670$	65.0714	2.51393
$671$	68.7753	2.65504
$672$	1.43859	0.0554948
$673$	−30.7429	−1.18505	−0.592526	−	0.805551i	$-0.701869\pi$
$673$	−30.7429	−1.18505	−0.592526	+	0.805551i	$0.701869\pi$
$674$	−56.0471	−2.15885
$675$	26.5488	1.02186
$676$	119.934	4.61286
$677$	25.6735	0.986714	0.493357	−	0.869827i	$-0.335770\pi$
$677$	25.6735	0.986714	0.493357	+	0.869827i	$0.335770\pi$
$678$	34.3727	1.32007
$679$	2.65373	0.101841
$680$	62.7217	2.40527
$681$	−13.7045	−0.525158
$682$	−149.087	−5.70882
$683$	35.8366	1.37125	0.685625	−	0.727955i	$-0.259529\pi$
$683$	35.8366	1.37125	0.685625	+	0.727955i	$0.259529\pi$
$684$	81.1640	3.10338
$685$	6.25032	0.238812
$686$	11.8660	0.453047
$687$	11.6154	0.443157
$688$	27.8706	1.06256
$689$	33.5329	1.27750
$690$	−17.7604	−0.676125
$691$	−32.5978	−1.24008	−0.620040	−	0.784570i	$-0.712884\pi$
$691$	−32.5978	−1.24008	−0.620040	+	0.784570i	$0.712884\pi$
$692$	−45.7613	−1.73958
$693$	4.41093	0.167557
$694$	48.5435	1.84269
$695$	5.64105	0.213977
$696$	31.5843	1.19720
$697$	0.683013	0.0258710
$698$	−12.7922	−0.484192
$699$	−5.52662	−0.209036
$700$	9.57107	0.361752
$701$	−35.0454	−1.32365	−0.661823	−	0.749660i	$-0.730217\pi$
$701$	−35.0454	−1.32365	−0.661823	+	0.749660i	$0.730217\pi$
$702$	−67.0192	−2.52948
$703$	−7.52962	−0.283985
$704$	0.921295	0.0347226
$705$	−4.58599	−0.172718
$706$	86.0698	3.23928
$707$	3.58354	0.134773
$708$	−7.63751	−0.287035
$709$	−37.7020	−1.41593	−0.707964	−	0.706249i	$-0.750386\pi$
$709$	−37.7020	−1.41593	−0.707964	+	0.706249i	$0.750386\pi$
$710$	−16.2089	−0.608310
$711$	0.173367	0.00650179
$712$	−102.871	−3.85525
$713$	28.6541	1.07310
$714$	−1.94075	−0.0726306
$715$	−116.238	−4.34707
$716$	103.543	3.86960
$717$	−5.30025	−0.197942
$718$	61.7773	2.30551
$719$	8.84463	0.329849	0.164925	−	0.986306i	$-0.447262\pi$
$719$	8.84463	0.329849	0.164925	+	0.986306i	$0.447262\pi$
$720$	−57.9127	−2.15828
$721$	1.50953	0.0562179
$722$	−95.9990	−3.57271
$723$	−9.38756	−0.349127
$724$	28.7033	1.06675
$725$	41.0641	1.52508
$726$	37.2552	1.38267
$727$	−8.35217	−0.309765	−0.154882	−	0.987933i	$-0.549500\pi$
$727$	−8.35217	−0.309765	−0.154882	+	0.987933i	$0.549500\pi$
$728$	−13.3887	−0.496219
$729$	0.104737	0.00387915
$730$	59.2466	2.19282
$731$	−11.4579	−0.423784
$732$	43.5695	1.61038
$733$	−48.4177	−1.78835	−0.894175	−	0.447718i	$-0.852237\pi$
$733$	−48.4177	−1.78835	−0.894175	+	0.447718i	$0.852237\pi$
$734$	66.1790	2.44271
$735$	17.9360	0.661578
$736$	14.8611	0.547786
$737$	41.4768	1.52782
$738$	−1.42189	−0.0523404
$739$	52.4041	1.92772	0.963858	−	0.266417i	$-0.0858399\pi$
$739$	52.4041	1.92772	0.963858	+	0.266417i	$0.0858399\pi$
$740$	15.1188	0.555776
$741$	36.6739	1.34725
$742$	−4.54525	−0.166862
$743$	−0.409528	−0.0150241	−0.00751207	−	0.999972i	$-0.502391\pi$
$743$	−0.409528	−0.0150241	−0.00751207	+	0.999972i	$0.502391\pi$
$744$	−52.3374	−1.91878
$745$	46.0359	1.68662
$746$	−67.5254	−2.47228
$747$	3.63787	0.133103
$748$	72.1455	2.63790
$749$	3.89126	0.142184
$750$	9.01613	0.329222
$751$	−29.0708	−1.06081	−0.530404	−	0.847745i	$-0.677960\pi$
$751$	−29.0708	−1.06081	−0.530404	+	0.847745i	$0.677960\pi$
$752$	12.5923	0.459196
$753$	−23.1184	−0.842480
$754$	−103.662	−3.77513
$755$	9.25148	0.336696
$756$	6.28293	0.228508
$757$	4.27846	0.155503	0.0777515	−	0.996973i	$-0.475226\pi$
$757$	4.27846	0.155503	0.0777515	+	0.996973i	$0.475226\pi$
$758$	17.5869	0.638787
$759$	−11.3205	−0.410909
$760$	160.655	5.82756
$761$	21.9463	0.795554	0.397777	−	0.917482i	$-0.369782\pi$
$761$	21.9463	0.795554	0.397777	+	0.917482i	$0.369782\pi$
$762$	26.0047	0.942050
$763$	−0.253179	−0.00916569
$764$	−19.9817	−0.722912
$765$	23.8084	0.860794
$766$	−73.9458	−2.67177
$767$	13.8906	0.501562
$768$	22.4233	0.809130
$769$	−7.90737	−0.285147	−0.142574	−	0.989784i	$-0.545538\pi$
$769$	−7.90737	−0.285147	−0.142574	+	0.989784i	$0.545538\pi$
$770$	15.7557	0.567795
$771$	16.9699	0.611158
$772$	−43.3210	−1.55916
$773$	14.1968	0.510622	0.255311	−	0.966859i	$-0.417822\pi$
$773$	14.1968	0.510622	0.255311	+	0.966859i	$0.417822\pi$
$774$	23.8528	0.857372
$775$	−68.0463	−2.44430
$776$	−50.0721	−1.79748
$777$	−0.259233	−0.00929993
$778$	34.8290	1.24868
$779$	1.74946	0.0626810
$780$	−73.6376	−2.63665
$781$	−10.3316	−0.369695
$782$	−20.0485	−0.716933
$783$	26.9565	0.963348
$784$	−49.2491	−1.75890
$785$	33.9838	1.21293
$786$	−1.46251	−0.0521659
$787$	34.3906	1.22589	0.612946	−	0.790125i	$-0.289984\pi$
$787$	34.3906	1.22589	0.612946	+	0.790125i	$0.289984\pi$
$788$	−39.9990	−1.42490
$789$	20.5844	0.732825
$790$	0.619262	0.0220323
$791$	5.86066	0.208381
$792$	−83.2280	−2.95738
$793$	−79.2416	−2.81395
$794$	−9.73817	−0.345595
$795$	−13.8530	−0.491314
$796$	101.029	3.58087
$797$	−5.64374	−0.199911	−0.0999557	−	0.994992i	$-0.531870\pi$
$797$	−5.64374	−0.199911	−0.0999557	+	0.994992i	$0.531870\pi$
$798$	−4.97100	−0.175972
$799$	−5.17682	−0.183143
$800$	−35.2913	−1.24774
$801$	−39.0485	−1.37971
$802$	23.9485	0.845650
$803$	37.7640	1.33266
$804$	26.2758	0.926675
$805$	−3.02820	−0.106730
$806$	171.775	6.05051
$807$	0.256050	0.00901340
$808$	−67.6163	−2.37873
$809$	−0.245375	−0.00862694	−0.00431347	−	0.999991i	$-0.501373\pi$
$809$	−0.245375	−0.00862694	−0.00431347	+	0.999991i	$0.501373\pi$
$810$	−34.1911	−1.20135
$811$	−29.8051	−1.04660	−0.523298	−	0.852149i	$-0.675299\pi$
$811$	−29.8051	−1.04660	−0.523298	+	0.852149i	$0.675299\pi$
$812$	9.71808	0.341038
$813$	22.4315	0.786706
$814$	13.9333	0.488363
$815$	−3.37038	−0.118059
$816$	16.2415	0.568567
$817$	−29.3480	−1.02676
$818$	11.5544	0.403989
$819$	−5.08219	−0.177586
$820$	−3.51275	−0.122671
$821$	−42.2654	−1.47507	−0.737536	−	0.675308i	$-0.764011\pi$
$821$	−42.2654	−1.47507	−0.737536	+	0.675308i	$0.764011\pi$
$822$	3.64915	0.127279
$823$	−36.2204	−1.26256	−0.631282	−	0.775553i	$-0.717471\pi$
$823$	−36.2204	−1.26256	−0.631282	+	0.775553i	$0.717471\pi$
$824$	−28.4827	−0.992242
$825$	26.8834	0.935960
$826$	−1.88282	−0.0655118
$827$	−20.5131	−0.713311	−0.356655	−	0.934236i	$-0.616083\pi$
$827$	−20.5131	−0.713311	−0.356655	+	0.934236i	$0.616083\pi$
$828$	28.8665	1.00318
$829$	−50.4478	−1.75212	−0.876062	−	0.482199i	$-0.839838\pi$
$829$	−50.4478	−1.75212	−0.876062	+	0.482199i	$0.839838\pi$
$830$	12.9943	0.451040
$831$	5.06465	0.175691
$832$	−1.06150	−0.0368008
$833$	20.2467	0.701508
$834$	3.29344	0.114042
$835$	26.5625	0.919233
$836$	184.793	6.39119
$837$	−44.6690	−1.54399
$838$	−22.2684	−0.769249
$839$	−48.5786	−1.67712	−0.838559	−	0.544810i	$-0.816602\pi$
$839$	−48.5786	−1.67712	−0.838559	+	0.544810i	$0.816602\pi$
$840$	5.53109	0.190841
$841$	12.6949	0.437754
$842$	−57.7700	−1.99089
$843$	−14.2759	−0.491689
$844$	−49.8705	−1.71661
$845$	90.1127	3.09997
$846$	10.7770	0.370522
$847$	6.35214	0.218262
$848$	38.0379	1.30623
$849$	−23.4057	−0.803283
$850$	47.6102	1.63302
$851$	−2.67796	−0.0917992
$852$	−6.54514	−0.224233
$853$	12.5718	0.430451	0.215226	−	0.976564i	$-0.430951\pi$
$853$	12.5718	0.430451	0.215226	+	0.976564i	$0.430951\pi$
$854$	10.7409	0.367546
$855$	60.9825	2.08556
$856$	−73.4226	−2.50953
$857$	32.1975	1.09985	0.549923	−	0.835216i	$-0.314657\pi$
$857$	32.1975	1.09985	0.549923	+	0.835216i	$0.314657\pi$
$858$	−67.8639	−2.31684
$859$	30.1710	1.02942	0.514711	−	0.857364i	$-0.327899\pi$
$859$	30.1710	1.02942	0.514711	+	0.857364i	$0.327899\pi$
$860$	58.9280	2.00943
$861$	0.0602313	0.00205268
$862$	28.7250	0.978377
$863$	−27.0136	−0.919553	−0.459777	−	0.888035i	$-0.652071\pi$
$863$	−27.0136	−0.919553	−0.459777	+	0.888035i	$0.652071\pi$
$864$	−23.1670	−0.788156
$865$	−34.3828	−1.16905
$866$	−12.1185	−0.411802
$867$	6.45818	0.219331
$868$	−16.1036	−0.546591
$869$	0.394720	0.0133900
$870$	42.8242	1.45188
$871$	−47.7888	−1.61926
$872$	4.77713	0.161774
$873$	−19.0067	−0.643281
$874$	−51.3520	−1.73701
$875$	1.53728	0.0519696
$876$	23.9237	0.808307
$877$	41.1839	1.39068	0.695342	−	0.718679i	$-0.255253\pi$
$877$	41.1839	1.39068	0.695342	+	0.718679i	$0.255253\pi$
$878$	−10.7337	−0.362244
$879$	3.05479	0.103036
$880$	−131.855	−4.44482
$881$	22.5946	0.761232	0.380616	−	0.924733i	$-0.375712\pi$
$881$	22.5946	0.761232	0.380616	+	0.924733i	$0.375712\pi$
$882$	−42.1494	−1.41924
$883$	−17.9833	−0.605188	−0.302594	−	0.953120i	$-0.597853\pi$
$883$	−17.9833	−0.605188	−0.302594	+	0.953120i	$0.597853\pi$
$884$	−83.1247	−2.79579
$885$	−5.73844	−0.192896
$886$	8.35234	0.280602
$887$	22.2838	0.748217	0.374109	−	0.927385i	$-0.377949\pi$
$887$	22.2838	0.748217	0.374109	+	0.927385i	$0.377949\pi$
$888$	4.89136	0.164143
$889$	4.43389	0.148708
$890$	−139.480	−4.67537
$891$	−21.7935	−0.730110
$892$	−90.0815	−3.01615
$893$	−13.2598	−0.443724
$894$	26.8773	0.898912
$895$	77.7973	2.60048
$896$	3.86762	0.129208
$897$	13.0433	0.435503
$898$	92.3191	3.08073
$899$	−69.0915	−2.30433
$900$	−68.5506	−2.28502
$901$	−15.6377	−0.520967
$902$	−3.23733	−0.107791
$903$	−1.01041	−0.0336242
$904$	−110.582	−3.67791
$905$	21.5662	0.716886
$906$	5.40133	0.179447
$907$	44.1651	1.46648	0.733239	−	0.679971i	$-0.238008\pi$
$907$	44.1651	1.46648	0.733239	+	0.679971i	$0.238008\pi$
$908$	79.5631	2.64040
$909$	−25.6663	−0.851298
$910$	−18.1534	−0.601779
$911$	−3.62911	−0.120238	−0.0601189	−	0.998191i	$-0.519148\pi$
$911$	−3.62911	−0.120238	−0.0601189	+	0.998191i	$0.519148\pi$
$912$	41.6009	1.37754
$913$	8.28264	0.274115
$914$	68.6565	2.27096
$915$	32.7360	1.08222
$916$	−67.4348	−2.22811
$917$	−0.249362	−0.00823467
$918$	31.2537	1.03153
$919$	26.0285	0.858602	0.429301	−	0.903162i	$-0.358760\pi$
$919$	26.0285	0.858602	0.429301	+	0.903162i	$0.358760\pi$
$920$	57.1379	1.88378
$921$	−20.3817	−0.671600
$922$	−61.0286	−2.00987
$923$	11.9039	0.391822
$924$	6.36212	0.209298
$925$	6.35948	0.209098
$926$	14.3463	0.471447
$927$	−10.8117	−0.355102
$928$	−35.8334	−1.17629
$929$	−2.67762	−0.0878499	−0.0439249	−	0.999035i	$-0.513986\pi$
$929$	−2.67762	−0.0878499	−0.0439249	+	0.999035i	$0.513986\pi$
$930$	−70.9629	−2.32696
$931$	51.8598	1.69964
$932$	32.0854	1.05099
$933$	0.856366	0.0280362
$934$	−9.26850	−0.303275
$935$	54.2065	1.77274
$936$	95.8937	3.13438
$937$	−35.4533	−1.15821	−0.579105	−	0.815253i	$-0.696598\pi$
$937$	−35.4533	−1.15821	−0.579105	+	0.815253i	$0.696598\pi$
$938$	6.47759	0.211501
$939$	−14.4069	−0.470150
$940$	26.6245	0.868395
$941$	18.9788	0.618693	0.309346	−	0.950949i	$-0.399890\pi$
$941$	18.9788	0.618693	0.309346	+	0.950949i	$0.399890\pi$
$942$	19.8409	0.646452
$943$	0.622207	0.0202619
$944$	15.7568	0.512840
$945$	4.72068	0.153564
$946$	54.3077	1.76569
$947$	−17.2637	−0.560994	−0.280497	−	0.959855i	$-0.590499\pi$
$947$	−17.2637	−0.560994	−0.280497	+	0.959855i	$0.590499\pi$
$948$	0.250057	0.00812148
$949$	−43.5110	−1.41243
$950$	121.948	3.95652
$951$	−6.57292	−0.213142
$952$	6.24369	0.202359
$953$	52.9422	1.71496	0.857482	−	0.514513i	$-0.172027\pi$
$953$	52.9422	1.71496	0.857482	+	0.514513i	$0.172027\pi$
$954$	32.5544	1.05399
$955$	−15.0133	−0.485817
$956$	30.7713	0.995213
$957$	27.2963	0.882365
$958$	−25.1342	−0.812049
$959$	0.622193	0.0200917
$960$	0.438522	0.0141532
$961$	83.4897	2.69321
$962$	−16.0537	−0.517593
$963$	−27.8703	−0.898108
$964$	54.5006	1.75535
$965$	−32.5493	−1.04780
$966$	−1.76797	−0.0568835
$967$	51.5486	1.65769	0.828846	−	0.559477i	$-0.188998\pi$
$967$	51.5486	1.65769	0.828846	+	0.559477i	$0.188998\pi$
$968$	−119.856	−3.85231
$969$	−17.1025	−0.549410
$970$	−67.8913	−2.17986
$971$	40.2768	1.29254	0.646272	−	0.763107i	$-0.276327\pi$
$971$	40.2768	1.29254	0.646272	+	0.763107i	$0.276327\pi$
$972$	−69.9862	−2.24481
$973$	0.561543	0.0180022
$974$	8.07024	0.258587
$975$	−30.9746	−0.991980
$976$	−89.8874	−2.87723
$977$	−34.4240	−1.10132	−0.550661	−	0.834729i	$-0.685624\pi$
$977$	−34.4240	−1.10132	−0.550661	+	0.834729i	$0.685624\pi$
$978$	−1.96774	−0.0629215
$979$	−88.9049	−2.84141
$980$	−104.129	−3.32629
$981$	1.81334	0.0578954
$982$	−25.5104	−0.814068
$983$	40.0303	1.27677	0.638385	−	0.769717i	$-0.279603\pi$
$983$	40.0303	1.27677	0.638385	+	0.769717i	$0.279603\pi$
$984$	−1.13648	−0.0362296
$985$	−30.0532	−0.957576
$986$	48.3415	1.53951
$987$	−0.456516	−0.0145311
$988$	−212.915	−6.77371
$989$	−10.4378	−0.331903
$990$	−112.846	−3.58650
$991$	12.7550	0.405176	0.202588	−	0.979264i	$-0.435065\pi$
$991$	12.7550	0.405176	0.202588	+	0.979264i	$0.435065\pi$
$992$	59.3785	1.88527
$993$	−10.9430	−0.347266
$994$	−1.61353	−0.0511781
$995$	75.9079	2.40644
$996$	5.24710	0.166261
$997$	33.2564	1.05324	0.526620	−	0.850101i	$-0.323459\pi$
$997$	33.2564	1.05324	0.526620	+	0.850101i	$0.323459\pi$
$998$	−109.656	−3.47109
$999$	4.17468	0.132081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.7	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.7	✓	134	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)

\(f(q)\)	\(=\)	\(q-2.54672 q^{2} -0.772659 q^{3} +4.48577 q^{4} +3.37038 q^{5} +1.96774 q^{6} +0.335508 q^{7} -6.33055 q^{8} -2.40300 q^{9} +O(q^{10})\)	\(q-2.54672 q^{2} -0.772659 q^{3} +4.48577 q^{4} +3.37038 q^{5} +1.96774 q^{6} +0.335508 q^{7} -6.33055 q^{8} -2.40300 q^{9} -8.58341 q^{10} -5.47110 q^{11} -3.46597 q^{12} +6.30370 q^{13} -0.854443 q^{14} -2.60416 q^{15} +7.15058 q^{16} -2.93966 q^{17} +6.11975 q^{18} -7.52962 q^{19} +15.1188 q^{20} -0.259233 q^{21} +13.9333 q^{22} -2.67796 q^{23} +4.89136 q^{24} +6.35948 q^{25} -16.0537 q^{26} +4.17468 q^{27} +1.50501 q^{28} +6.45716 q^{29} +6.63205 q^{30} -10.7000 q^{31} -5.54940 q^{32} +4.22730 q^{33} +7.48649 q^{34} +1.13079 q^{35} -10.7793 q^{36} +1.00000 q^{37} +19.1758 q^{38} -4.87061 q^{39} -21.3364 q^{40} -0.232344 q^{41} +0.660193 q^{42} +3.89768 q^{43} -24.5421 q^{44} -8.09902 q^{45} +6.82000 q^{46} +1.76102 q^{47} -5.52496 q^{48} -6.88743 q^{49} -16.1958 q^{50} +2.27136 q^{51} +28.2769 q^{52} +5.31955 q^{53} -10.6317 q^{54} -18.4397 q^{55} -2.12395 q^{56} +5.81783 q^{57} -16.4446 q^{58} +2.20357 q^{59} -11.6816 q^{60} -12.5706 q^{61} +27.2498 q^{62} -0.806224 q^{63} -0.168393 q^{64} +21.2459 q^{65} -10.7657 q^{66} -7.58107 q^{67} -13.1866 q^{68} +2.06915 q^{69} -2.87980 q^{70} +1.88840 q^{71} +15.2123 q^{72} -6.90246 q^{73} -2.54672 q^{74} -4.91371 q^{75} -33.7761 q^{76} -1.83560 q^{77} +12.4041 q^{78} -0.0721463 q^{79} +24.1002 q^{80} +3.98339 q^{81} +0.591715 q^{82} -1.51389 q^{83} -1.16286 q^{84} -9.90779 q^{85} -9.92628 q^{86} -4.98918 q^{87} +34.6351 q^{88} +16.2499 q^{89} +20.6259 q^{90} +2.11494 q^{91} -12.0127 q^{92} +8.26744 q^{93} -4.48483 q^{94} -25.3777 q^{95} +4.28780 q^{96} +7.90960 q^{97} +17.5403 q^{98} +13.1470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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