LMFDB - Embedded newform 6031.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.24334 q^{2} -3.44407 q^{3} +3.03258 q^{4} -0.143577 q^{5} +7.72622 q^{6} +5.03410 q^{7} -2.31642 q^{8} +8.86161 q^{9} +O(q^{10})$	\(q-2.24334 q^{2} -3.44407 q^{3} +3.03258 q^{4} -0.143577 q^{5} +7.72622 q^{6} +5.03410 q^{7} -2.31642 q^{8} +8.86161 q^{9} +0.322092 q^{10} -2.30080 q^{11} -10.4444 q^{12} +5.44857 q^{13} -11.2932 q^{14} +0.494490 q^{15} -0.868634 q^{16} +7.85393 q^{17} -19.8796 q^{18} -5.83852 q^{19} -0.435409 q^{20} -17.3378 q^{21} +5.16147 q^{22} +4.00564 q^{23} +7.97791 q^{24} -4.97939 q^{25} -12.2230 q^{26} -20.1878 q^{27} +15.2663 q^{28} +3.52500 q^{29} -1.10931 q^{30} -4.27799 q^{31} +6.58148 q^{32} +7.92410 q^{33} -17.6190 q^{34} -0.722782 q^{35} +26.8735 q^{36} -1.00000 q^{37} +13.0978 q^{38} -18.7652 q^{39} +0.332585 q^{40} +1.49938 q^{41} +38.8946 q^{42} -5.75470 q^{43} -6.97734 q^{44} -1.27232 q^{45} -8.98601 q^{46} +8.27858 q^{47} +2.99164 q^{48} +18.3422 q^{49} +11.1705 q^{50} -27.0495 q^{51} +16.5232 q^{52} +0.578900 q^{53} +45.2881 q^{54} +0.330342 q^{55} -11.6611 q^{56} +20.1083 q^{57} -7.90777 q^{58} +0.800272 q^{59} +1.49958 q^{60} +12.1913 q^{61} +9.59698 q^{62} +44.6102 q^{63} -13.0272 q^{64} -0.782290 q^{65} -17.7765 q^{66} -2.07025 q^{67} +23.8177 q^{68} -13.7957 q^{69} +1.62145 q^{70} +8.26221 q^{71} -20.5272 q^{72} +5.25576 q^{73} +2.24334 q^{74} +17.1493 q^{75} -17.7057 q^{76} -11.5824 q^{77} +42.0968 q^{78} -8.04741 q^{79} +0.124716 q^{80} +42.9433 q^{81} -3.36363 q^{82} -6.69854 q^{83} -52.5782 q^{84} -1.12765 q^{85} +12.9098 q^{86} -12.1403 q^{87} +5.32961 q^{88} -5.91434 q^{89} +2.85426 q^{90} +27.4286 q^{91} +12.1474 q^{92} +14.7337 q^{93} -18.5717 q^{94} +0.838278 q^{95} -22.6671 q^{96} -2.77038 q^{97} -41.1478 q^{98} -20.3888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.24334	−1.58628	−0.793141	−	0.609039i	$-0.791555\pi$
$2$	−2.24334	−1.58628	−0.793141	+	0.609039i	$0.791555\pi$
$3$	−3.44407	−1.98843	−0.994217	−	0.107390i	$-0.965751\pi$
$3$	−3.44407	−1.98843	−0.994217	+	0.107390i	$0.965751\pi$
$4$	3.03258	1.51629
$5$	−0.143577	−0.0642097	−0.0321048	−	0.999485i	$-0.510221\pi$
$5$	−0.143577	−0.0642097	−0.0321048	+	0.999485i	$0.510221\pi$
$6$	7.72622	3.15422
$7$	5.03410	1.90271	0.951356	−	0.308094i	$-0.0996911\pi$
$7$	5.03410	1.90271	0.951356	+	0.308094i	$0.0996911\pi$
$8$	−2.31642	−0.818978
$9$	8.86161	2.95387
$10$	0.322092	0.101855
$11$	−2.30080	−0.693716	−0.346858	−	0.937918i	$-0.612751\pi$
$11$	−2.30080	−0.693716	−0.346858	+	0.937918i	$0.612751\pi$
$12$	−10.4444	−3.01504
$13$	5.44857	1.51116	0.755580	−	0.655056i	$-0.227355\pi$
$13$	5.44857	1.51116	0.755580	+	0.655056i	$0.227355\pi$
$14$	−11.2932	−3.01824
$15$	0.494490	0.127677
$16$	−0.868634	−0.217159
$17$	7.85393	1.90486	0.952429	−	0.304760i	$-0.0985761\pi$
$17$	7.85393	1.90486	0.952429	+	0.304760i	$0.0985761\pi$
$18$	−19.8796	−4.68567
$19$	−5.83852	−1.33945	−0.669724	−	0.742610i	$-0.733588\pi$
$19$	−5.83852	−1.33945	−0.669724	+	0.742610i	$0.733588\pi$
$20$	−0.435409	−0.0973603
$21$	−17.3378	−3.78342
$22$	5.16147	1.10043
$23$	4.00564	0.835233	0.417617	−	0.908623i	$-0.362866\pi$
$23$	4.00564	0.835233	0.417617	+	0.908623i	$0.362866\pi$
$24$	7.97791	1.62848
$25$	−4.97939	−0.995877
$26$	−12.2230	−2.39713
$27$	−20.1878	−3.88514
$28$	15.2663	2.88506
$29$	3.52500	0.654576	0.327288	−	0.944925i	$-0.393865\pi$
$29$	3.52500	0.654576	0.327288	+	0.944925i	$0.393865\pi$
$30$	−1.10931	−0.202531
$31$	−4.27799	−0.768349	−0.384174	−	0.923261i	$-0.625514\pi$
$31$	−4.27799	−0.768349	−0.384174	+	0.923261i	$0.625514\pi$
$32$	6.58148	1.16345
$33$	7.92410	1.37941
$34$	−17.6190	−3.02164
$35$	−0.722782	−0.122172
$36$	26.8735	4.47892
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	13.0978	2.12474
$39$	−18.7652	−3.00484
$40$	0.332585	0.0525863
$41$	1.49938	0.234164	0.117082	−	0.993122i	$-0.462646\pi$
$41$	1.49938	0.234164	0.117082	+	0.993122i	$0.462646\pi$
$42$	38.8946	6.00156
$43$	−5.75470	−0.877584	−0.438792	−	0.898589i	$-0.644593\pi$
$43$	−5.75470	−0.877584	−0.438792	+	0.898589i	$0.644593\pi$
$44$	−6.97734	−1.05187
$45$	−1.27232	−0.189667
$46$	−8.98601	−1.32491
$47$	8.27858	1.20755	0.603777	−	0.797153i	$-0.293662\pi$
$47$	8.27858	1.20755	0.603777	+	0.797153i	$0.293662\pi$
$48$	2.99164	0.431805
$49$	18.3422	2.62031
$50$	11.1705	1.57974
$51$	−27.0495	−3.78769
$52$	16.5232	2.29135
$53$	0.578900	0.0795180	0.0397590	−	0.999209i	$-0.487341\pi$
$53$	0.578900	0.0795180	0.0397590	+	0.999209i	$0.487341\pi$
$54$	45.2881	6.16293
$55$	0.330342	0.0445433
$56$	−11.6611	−1.55828
$57$	20.1083	2.66340
$58$	−7.90777	−1.03834
$59$	0.800272	0.104187	0.0520933	−	0.998642i	$-0.483411\pi$
$59$	0.800272	0.104187	0.0520933	+	0.998642i	$0.483411\pi$
$60$	1.49958	0.193595
$61$	12.1913	1.56094	0.780469	−	0.625195i	$-0.214981\pi$
$61$	12.1913	1.56094	0.780469	+	0.625195i	$0.214981\pi$
$62$	9.59698	1.21882
$63$	44.6102	5.62036
$64$	−13.0272	−1.62840
$65$	−0.782290	−0.0970311
$66$	−17.7765	−2.18813
$67$	−2.07025	−0.252921	−0.126460	−	0.991972i	$-0.540362\pi$
$67$	−2.07025	−0.252921	−0.126460	+	0.991972i	$0.540362\pi$
$68$	23.8177	2.88831
$69$	−13.7957	−1.66081
$70$	1.62145	0.193800
$71$	8.26221	0.980544	0.490272	−	0.871570i	$-0.336897\pi$
$71$	8.26221	0.980544	0.490272	+	0.871570i	$0.336897\pi$
$72$	−20.5272	−2.41915
$73$	5.25576	0.615140	0.307570	−	0.951525i	$-0.400484\pi$
$73$	5.25576	0.615140	0.307570	+	0.951525i	$0.400484\pi$
$74$	2.24334	0.260783
$75$	17.1493	1.98024
$76$	−17.7057	−2.03099
$77$	−11.5824	−1.31994
$78$	42.0968	4.76653
$79$	−8.04741	−0.905404	−0.452702	−	0.891662i	$-0.649540\pi$
$79$	−8.04741	−0.905404	−0.452702	+	0.891662i	$0.649540\pi$
$80$	0.124716	0.0139437
$81$	42.9433	4.77148
$82$	−3.36363	−0.371450
$83$	−6.69854	−0.735260	−0.367630	−	0.929972i	$-0.619831\pi$
$83$	−6.69854	−0.735260	−0.367630	+	0.929972i	$0.619831\pi$
$84$	−52.5782	−5.73675
$85$	−1.12765	−0.122310
$86$	12.9098	1.39209
$87$	−12.1403	−1.30158
$88$	5.32961	0.568138
$89$	−5.91434	−0.626919	−0.313460	−	0.949602i	$-0.601488\pi$
$89$	−5.91434	−0.626919	−0.313460	+	0.949602i	$0.601488\pi$
$90$	2.85426	0.300865
$91$	27.4286	2.87530
$92$	12.1474	1.26645
$93$	14.7337	1.52781
$94$	−18.5717	−1.91552
$95$	0.838278	0.0860055
$96$	−22.6671	−2.31345
$97$	−2.77038	−0.281290	−0.140645	−	0.990060i	$-0.544918\pi$
$97$	−2.77038	−0.281290	−0.140645	+	0.990060i	$0.544918\pi$
$98$	−41.1478	−4.15655
$99$	−20.3888	−2.04915
$100$	−15.1004	−1.51004
$101$	6.33954	0.630808	0.315404	−	0.948957i	$-0.397860\pi$
$101$	6.33954	0.630808	0.315404	+	0.948957i	$0.397860\pi$
$102$	60.6812	6.00833
$103$	−16.8213	−1.65746	−0.828728	−	0.559651i	$-0.810935\pi$
$103$	−16.8213	−1.65746	−0.828728	+	0.559651i	$0.810935\pi$
$104$	−12.6212	−1.23761
$105$	2.48931	0.242932
$106$	−1.29867	−0.126138
$107$	0.0416869	0.00403003	0.00201501	−	0.999998i	$-0.499359\pi$
$107$	0.0416869	0.00403003	0.00201501	+	0.999998i	$0.499359\pi$
$108$	−61.2210	−5.89099
$109$	11.8409	1.13415	0.567076	−	0.823665i	$-0.308074\pi$
$109$	11.8409	1.13415	0.567076	+	0.823665i	$0.308074\pi$
$110$	−0.741069	−0.0706582
$111$	3.44407	0.326897
$112$	−4.37279	−0.413190
$113$	10.0230	0.942886	0.471443	−	0.881897i	$-0.343733\pi$
$113$	10.0230	0.942886	0.471443	+	0.881897i	$0.343733\pi$
$114$	−45.1097	−4.22491
$115$	−0.575118	−0.0536300
$116$	10.6898	0.992525
$117$	48.2831	4.46377
$118$	−1.79528	−0.165269
$119$	39.5375	3.62440
$120$	−1.14545	−0.104564
$121$	−5.70634	−0.518758
$122$	−27.3493	−2.47609
$123$	−5.16398	−0.465620
$124$	−12.9733	−1.16504
$125$	1.43281	0.128155
$126$	−100.076	−8.91548
$127$	4.09680	0.363533	0.181766	−	0.983342i	$-0.441819\pi$
$127$	4.09680	0.363533	0.181766	+	0.983342i	$0.441819\pi$
$128$	16.0616	1.41965
$129$	19.8196	1.74502
$130$	1.75494	0.153919
$131$	4.04064	0.353033	0.176516	−	0.984298i	$-0.443517\pi$
$131$	4.04064	0.353033	0.176516	+	0.984298i	$0.443517\pi$
$132$	24.0304	2.09158
$133$	−29.3917	−2.54858
$134$	4.64427	0.401203
$135$	2.89850	0.249464
$136$	−18.1930	−1.56004
$137$	17.2520	1.47394	0.736970	−	0.675926i	$-0.236256\pi$
$137$	17.2520	1.47394	0.736970	+	0.675926i	$0.236256\pi$
$138$	30.9484	2.63451
$139$	16.1144	1.36680	0.683402	−	0.730043i	$-0.260500\pi$
$139$	16.1144	1.36680	0.683402	+	0.730043i	$0.260500\pi$
$140$	−2.19189	−0.185249
$141$	−28.5120	−2.40114
$142$	−18.5349	−1.55542
$143$	−12.5360	−1.04832
$144$	−7.69750	−0.641458
$145$	−0.506109	−0.0420301
$146$	−11.7905	−0.975785
$147$	−63.1717	−5.21032
$148$	−3.03258	−0.249276
$149$	−3.63512	−0.297801	−0.148900	−	0.988852i	$-0.547573\pi$
$149$	−3.63512	−0.297801	−0.148900	+	0.988852i	$0.547573\pi$
$150$	−38.4718	−3.14121
$151$	16.0085	1.30275	0.651375	−	0.758756i	$-0.274193\pi$
$151$	16.0085	1.30275	0.651375	+	0.758756i	$0.274193\pi$
$152$	13.5245	1.09698
$153$	69.5985	5.62670
$154$	25.9834	2.09380
$155$	0.614221	0.0493354
$156$	−56.9070	−4.55621
$157$	3.15309	0.251644	0.125822	−	0.992053i	$-0.459843\pi$
$157$	3.15309	0.251644	0.125822	+	0.992053i	$0.459843\pi$
$158$	18.0531	1.43623
$159$	−1.99377	−0.158116
$160$	−0.944950	−0.0747049
$161$	20.1648	1.58921
$162$	−96.3364	−7.56890
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	4.54699	0.355060
$165$	−1.13772	−0.0885714
$166$	15.0271	1.16633
$167$	9.97021	0.771518	0.385759	−	0.922600i	$-0.373940\pi$
$167$	9.97021	0.771518	0.385759	+	0.922600i	$0.373940\pi$
$168$	40.1616	3.09854
$169$	16.6869	1.28361
$170$	2.52969	0.194019
$171$	−51.7387	−3.95655
$172$	−17.4516	−1.33067
$173$	−17.7634	−1.35052	−0.675262	−	0.737578i	$-0.735970\pi$
$173$	−17.7634	−1.35052	−0.675262	+	0.737578i	$0.735970\pi$
$174$	27.2349	2.06467
$175$	−25.0667	−1.89487
$176$	1.99855	0.150646
$177$	−2.75619	−0.207168
$178$	13.2679	0.994470
$179$	15.3814	1.14966	0.574829	−	0.818273i	$-0.305069\pi$
$179$	15.3814	1.14966	0.574829	+	0.818273i	$0.305069\pi$
$180$	−3.85842	−0.287590
$181$	−17.9238	−1.33227	−0.666134	−	0.745832i	$-0.732052\pi$
$181$	−17.9238	−1.33227	−0.666134	+	0.745832i	$0.732052\pi$
$182$	−61.5318	−4.56104
$183$	−41.9877	−3.10382
$184$	−9.27874	−0.684038
$185$	0.143577	0.0105560
$186$	−33.0527	−2.42354
$187$	−18.0703	−1.32143
$188$	25.1054	1.83100
$189$	−101.627	−7.39230
$190$	−1.88054	−0.136429
$191$	−20.7503	−1.50144	−0.750719	−	0.660622i	$-0.770293\pi$
$191$	−20.7503	−1.50144	−0.750719	+	0.660622i	$0.770293\pi$
$192$	44.8667	3.23797
$193$	−15.6852	−1.12905	−0.564523	−	0.825417i	$-0.690940\pi$
$193$	−15.6852	−1.12905	−0.564523	+	0.825417i	$0.690940\pi$
$194$	6.21491	0.446205
$195$	2.69426	0.192940
$196$	55.6241	3.97315
$197$	−6.93234	−0.493908	−0.246954	−	0.969027i	$-0.579430\pi$
$197$	−6.93234	−0.493908	−0.246954	+	0.969027i	$0.579430\pi$
$198$	45.7389	3.25052
$199$	7.13986	0.506132	0.253066	−	0.967449i	$-0.418561\pi$
$199$	7.13986	0.506132	0.253066	+	0.967449i	$0.418561\pi$
$200$	11.5343	0.815602
$201$	7.13007	0.502916
$202$	−14.2218	−1.00064
$203$	17.7452	1.24547
$204$	−82.0296	−5.74322
$205$	−0.215277	−0.0150356
$206$	37.7360	2.62919
$207$	35.4964	2.46717
$208$	−4.73281	−0.328161
$209$	13.4332	0.929197
$210$	−5.58437	−0.385358
$211$	5.88157	0.404904	0.202452	−	0.979292i	$-0.435109\pi$
$211$	5.88157	0.404904	0.202452	+	0.979292i	$0.435109\pi$
$212$	1.75556	0.120572
$213$	−28.4556	−1.94975
$214$	−0.0935180	−0.00639276
$215$	0.826243	0.0563493
$216$	46.7634	3.18185
$217$	−21.5358	−1.46195
$218$	−26.5632	−1.79908
$219$	−18.1012	−1.22317
$220$	1.00179	0.0675404
$221$	42.7927	2.87855
$222$	−7.72622	−0.518550
$223$	−14.0136	−0.938423	−0.469211	−	0.883086i	$-0.655462\pi$
$223$	−14.0136	−0.938423	−0.469211	+	0.883086i	$0.655462\pi$
$224$	33.1319	2.21372
$225$	−44.1254	−2.94169
$226$	−22.4850	−1.49568
$227$	29.8227	1.97940	0.989702	−	0.143142i	$-0.0457205\pi$
$227$	29.8227	1.97940	0.989702	+	0.143142i	$0.0457205\pi$
$228$	60.9798	4.03849
$229$	−11.4955	−0.759642	−0.379821	−	0.925060i	$-0.624014\pi$
$229$	−11.4955	−0.759642	−0.379821	+	0.925060i	$0.624014\pi$
$230$	1.29019	0.0850723
$231$	39.8907	2.62462
$232$	−8.16537	−0.536083
$233$	−1.93792	−0.126957	−0.0634787	−	0.997983i	$-0.520219\pi$
$233$	−1.93792	−0.126957	−0.0634787	+	0.997983i	$0.520219\pi$
$234$	−108.315	−7.08080
$235$	−1.18861	−0.0775366
$236$	2.42689	0.157977
$237$	27.7158	1.80034
$238$	−88.6961	−5.74931
$239$	18.1691	1.17526	0.587629	−	0.809130i	$-0.300061\pi$
$239$	18.1691	1.17526	0.587629	+	0.809130i	$0.300061\pi$
$240$	−0.429531	−0.0277261
$241$	−5.94375	−0.382871	−0.191435	−	0.981505i	$-0.561314\pi$
$241$	−5.94375	−0.382871	−0.191435	+	0.981505i	$0.561314\pi$
$242$	12.8013	0.822896
$243$	−87.3363	−5.60262
$244$	36.9711	2.36683
$245$	−2.63352	−0.168249
$246$	11.5846	0.738604
$247$	−31.8116	−2.02412
$248$	9.90961	0.629261
$249$	23.0702	1.46202
$250$	−3.21428	−0.203289
$251$	−20.1486	−1.27177	−0.635883	−	0.771786i	$-0.719364\pi$
$251$	−20.1486	−1.27177	−0.635883	+	0.771786i	$0.719364\pi$
$252$	135.284	8.52209
$253$	−9.21615	−0.579415
$254$	−9.19053	−0.576665
$255$	3.88369	0.243206
$256$	−9.97708	−0.623567
$257$	−15.1639	−0.945897	−0.472949	−	0.881090i	$-0.656810\pi$
$257$	−15.1639	−0.945897	−0.472949	+	0.881090i	$0.656810\pi$
$258$	−44.4621	−2.76809
$259$	−5.03410	−0.312804
$260$	−2.37235	−0.147127
$261$	31.2371	1.93353
$262$	−9.06454	−0.560009
$263$	−4.43372	−0.273395	−0.136697	−	0.990613i	$-0.543649\pi$
$263$	−4.43372	−0.273395	−0.136697	+	0.990613i	$0.543649\pi$
$264$	−18.3555	−1.12971
$265$	−0.0831168	−0.00510583
$266$	65.9356	4.04277
$267$	20.3694	1.24659
$268$	−6.27818	−0.383501
$269$	−6.94879	−0.423675	−0.211838	−	0.977305i	$-0.567945\pi$
$269$	−6.94879	−0.423675	−0.211838	+	0.977305i	$0.567945\pi$
$270$	−6.50233	−0.395719
$271$	16.3464	0.992975	0.496487	−	0.868044i	$-0.334623\pi$
$271$	16.3464	0.992975	0.496487	+	0.868044i	$0.334623\pi$
$272$	−6.82219	−0.413656
$273$	−94.4661	−5.71735
$274$	−38.7022	−2.33808
$275$	11.4566	0.690856
$276$	−41.8365	−2.51826
$277$	−6.20555	−0.372856	−0.186428	−	0.982469i	$-0.559691\pi$
$277$	−6.20555	−0.372856	−0.186428	+	0.982469i	$0.559691\pi$
$278$	−36.1500	−2.16813
$279$	−37.9098	−2.26960
$280$	1.67427	0.100057
$281$	3.66224	0.218471	0.109235	−	0.994016i	$-0.465160\pi$
$281$	3.66224	0.218471	0.109235	+	0.994016i	$0.465160\pi$
$282$	63.9621	3.80889
$283$	13.5874	0.807688	0.403844	−	0.914828i	$-0.367674\pi$
$283$	13.5874	0.807688	0.403844	+	0.914828i	$0.367674\pi$
$284$	25.0558	1.48679
$285$	−2.88709	−0.171016
$286$	28.1226	1.66292
$287$	7.54805	0.445547
$288$	58.3225	3.43669
$289$	44.6843	2.62849
$290$	1.13537	0.0666715
$291$	9.54139	0.559326
$292$	15.9385	0.932729
$293$	31.1631	1.82057	0.910283	−	0.413986i	$-0.135864\pi$
$293$	31.1631	1.82057	0.910283	+	0.413986i	$0.135864\pi$
$294$	141.716	8.26503
$295$	−0.114901	−0.00668978
$296$	2.31642	0.134639
$297$	46.4480	2.69518
$298$	8.15481	0.472396
$299$	21.8250	1.26217
$300$	52.0067	3.00261
$301$	−28.9698	−1.66979
$302$	−35.9124	−2.06653
$303$	−21.8338	−1.25432
$304$	5.07154	0.290873
$305$	−1.75039	−0.100227
$306$	−156.133	−8.92553
$307$	−3.44443	−0.196584	−0.0982920	−	0.995158i	$-0.531338\pi$
$307$	−3.44443	−0.196584	−0.0982920	+	0.995158i	$0.531338\pi$
$308$	−35.1246	−2.00141
$309$	57.9339	3.29574
$310$	−1.37791	−0.0782598
$311$	−14.4815	−0.821168	−0.410584	−	0.911823i	$-0.634675\pi$
$311$	−14.4815	−0.821168	−0.410584	+	0.911823i	$0.634675\pi$
$312$	43.4682	2.46090
$313$	−2.16590	−0.122424	−0.0612120	−	0.998125i	$-0.519497\pi$
$313$	−2.16590	−0.122424	−0.0612120	+	0.998125i	$0.519497\pi$
$314$	−7.07346	−0.399178
$315$	−6.40501	−0.360882
$316$	−24.4044	−1.37285
$317$	27.8423	1.56378	0.781889	−	0.623418i	$-0.214257\pi$
$317$	27.8423	1.56378	0.781889	+	0.623418i	$0.214257\pi$
$318$	4.47271	0.250817
$319$	−8.11030	−0.454090
$320$	1.87041	0.104559
$321$	−0.143573	−0.00801344
$322$	−45.2365	−2.52093
$323$	−45.8553	−2.55146
$324$	130.229	7.23493
$325$	−27.1305	−1.50493
$326$	−2.24334	−0.124247
$327$	−40.7809	−2.25519
$328$	−3.47320	−0.191775
$329$	41.6752	2.29763
$330$	2.55229	0.140499
$331$	−14.2677	−0.784225	−0.392113	−	0.919917i	$-0.628256\pi$
$331$	−14.2677	−0.784225	−0.392113	+	0.919917i	$0.628256\pi$
$332$	−20.3138	−1.11487
$333$	−8.86161	−0.485613
$334$	−22.3666	−1.22384
$335$	0.297240	0.0162400
$336$	15.0602	0.821601
$337$	−1.30129	−0.0708856	−0.0354428	−	0.999372i	$-0.511284\pi$
$337$	−1.30129	−0.0708856	−0.0354428	+	0.999372i	$0.511284\pi$
$338$	−37.4344	−2.03616
$339$	−34.5199	−1.87487
$340$	−3.41967	−0.185458
$341$	9.84277	0.533016
$342$	116.067	6.27621
$343$	57.0977	3.08299
$344$	13.3303	0.718722
$345$	1.98075	0.106640
$346$	39.8493	2.14231
$347$	8.53709	0.458295	0.229147	−	0.973392i	$-0.426406\pi$
$347$	8.53709	0.458295	0.229147	+	0.973392i	$0.426406\pi$
$348$	−36.8165	−1.97357
$349$	25.0908	1.34308	0.671541	−	0.740967i	$-0.265633\pi$
$349$	25.0908	1.34308	0.671541	+	0.740967i	$0.265633\pi$
$350$	56.2332	3.00579
$351$	−109.994	−5.87107
$352$	−15.1426	−0.807106
$353$	−17.1315	−0.911819	−0.455909	−	0.890026i	$-0.650686\pi$
$353$	−17.1315	−0.911819	−0.455909	+	0.890026i	$0.650686\pi$
$354$	6.18308	0.328627
$355$	−1.18626	−0.0629604
$356$	−17.9357	−0.950590
$357$	−136.170	−7.20687
$358$	−34.5057	−1.82368
$359$	6.52326	0.344284	0.172142	−	0.985072i	$-0.444931\pi$
$359$	6.52326	0.344284	0.172142	+	0.985072i	$0.444931\pi$
$360$	2.94724	0.155333
$361$	15.0883	0.794120
$362$	40.2093	2.11335
$363$	19.6530	1.03152
$364$	83.1795	4.35979
$365$	−0.754607	−0.0394979
$366$	94.1927	4.92353
$367$	−3.04271	−0.158828	−0.0794142	−	0.996842i	$-0.525305\pi$
$367$	−3.04271	−0.158828	−0.0794142	+	0.996842i	$0.525305\pi$
$368$	−3.47943	−0.181378
$369$	13.2869	0.691691
$370$	−0.322092	−0.0167448
$371$	2.91424	0.151300
$372$	44.6810	2.31660
$373$	−12.6115	−0.652998	−0.326499	−	0.945197i	$-0.605869\pi$
$373$	−12.6115	−0.652998	−0.326499	+	0.945197i	$0.605869\pi$
$374$	40.5378	2.09616
$375$	−4.93470	−0.254827
$376$	−19.1767	−0.988961
$377$	19.2062	0.989169
$378$	227.985	11.7263
$379$	−25.5722	−1.31355	−0.656777	−	0.754085i	$-0.728081\pi$
$379$	−25.5722	−1.31355	−0.656777	+	0.754085i	$0.728081\pi$
$380$	2.54214	0.130409
$381$	−14.1097	−0.722860
$382$	46.5499	2.38170
$383$	15.4947	0.791742	0.395871	−	0.918306i	$-0.370443\pi$
$383$	15.4947	0.791742	0.395871	+	0.918306i	$0.370443\pi$
$384$	−55.3171	−2.82289
$385$	1.66297	0.0847530
$386$	35.1873	1.79098
$387$	−50.9959	−2.59227
$388$	−8.40140	−0.426516
$389$	−20.5455	−1.04170	−0.520850	−	0.853648i	$-0.674385\pi$
$389$	−20.5455	−1.04170	−0.520850	+	0.853648i	$0.674385\pi$
$390$	−6.04414	−0.306057
$391$	31.4600	1.59100
$392$	−42.4882	−2.14598
$393$	−13.9163	−0.701982
$394$	15.5516	0.783478
$395$	1.15542	0.0581357
$396$	−61.8305	−3.10710
$397$	6.86859	0.344724	0.172362	−	0.985034i	$-0.444860\pi$
$397$	6.86859	0.344724	0.172362	+	0.985034i	$0.444860\pi$
$398$	−16.0171	−0.802867
$399$	101.227	5.06769
$400$	4.32526	0.216263
$401$	11.5335	0.575957	0.287978	−	0.957637i	$-0.407017\pi$
$401$	11.5335	0.575957	0.287978	+	0.957637i	$0.407017\pi$
$402$	−15.9952	−0.797767
$403$	−23.3089	−1.16110
$404$	19.2251	0.956487
$405$	−6.16567	−0.306375
$406$	−39.8085	−1.97566
$407$	2.30080	0.114046
$408$	62.6580	3.10203
$409$	20.0183	0.989839	0.494920	−	0.868939i	$-0.335197\pi$
$409$	20.0183	0.989839	0.494920	+	0.868939i	$0.335197\pi$
$410$	0.482940	0.0238507
$411$	−59.4172	−2.93083
$412$	−51.0120	−2.51318
$413$	4.02865	0.198237
$414$	−79.6305	−3.91362
$415$	0.961757	0.0472108
$416$	35.8596	1.75816
$417$	−55.4990	−2.71780
$418$	−30.1353	−1.47397
$419$	−6.91624	−0.337881	−0.168940	−	0.985626i	$-0.554035\pi$
$419$	−6.91624	−0.337881	−0.168940	+	0.985626i	$0.554035\pi$
$420$	7.54903	0.368355
$421$	−12.1093	−0.590171	−0.295085	−	0.955471i	$-0.595348\pi$
$421$	−12.1093	−0.590171	−0.295085	+	0.955471i	$0.595348\pi$
$422$	−13.1944	−0.642292
$423$	73.3615	3.56696
$424$	−1.34098	−0.0651235
$425$	−39.1078	−1.89701
$426$	63.8356	3.09285
$427$	61.3723	2.97001
$428$	0.126419	0.00611068
$429$	43.1750	2.08451
$430$	−1.85355	−0.0893859
$431$	−6.17575	−0.297476	−0.148738	−	0.988877i	$-0.547521\pi$
$431$	−6.17575	−0.297476	−0.148738	+	0.988877i	$0.547521\pi$
$432$	17.5358	0.843692
$433$	3.60087	0.173047	0.0865234	−	0.996250i	$-0.472424\pi$
$433$	3.60087	0.173047	0.0865234	+	0.996250i	$0.472424\pi$
$434$	48.3122	2.31906
$435$	1.74307	0.0835740
$436$	35.9084	1.71970
$437$	−23.3870	−1.11875
$438$	40.6071	1.94028
$439$	8.42020	0.401874	0.200937	−	0.979604i	$-0.435601\pi$
$439$	8.42020	0.401874	0.200937	+	0.979604i	$0.435601\pi$
$440$	−0.765210	−0.0364800
$441$	162.541	7.74006
$442$	−95.9986	−4.56619
$443$	−6.47498	−0.307636	−0.153818	−	0.988099i	$-0.549157\pi$
$443$	−6.47498	−0.307636	−0.153818	+	0.988099i	$0.549157\pi$
$444$	10.4444	0.495669
$445$	0.849165	0.0402543
$446$	31.4374	1.48860
$447$	12.5196	0.592157
$448$	−65.5804	−3.09838
$449$	−6.54609	−0.308929	−0.154464	−	0.987998i	$-0.549365\pi$
$449$	−6.54609	−0.308929	−0.154464	+	0.987998i	$0.549365\pi$
$450$	98.9882	4.66635
$451$	−3.44977	−0.162444
$452$	30.3955	1.42969
$453$	−55.1342	−2.59043
$454$	−66.9025	−3.13989
$455$	−3.93813	−0.184622
$456$	−46.5792	−2.18127
$457$	−31.1036	−1.45496	−0.727482	−	0.686127i	$-0.759309\pi$
$457$	−31.1036	−1.45496	−0.727482	+	0.686127i	$0.759309\pi$
$458$	25.7882	1.20501
$459$	−158.553	−7.40064
$460$	−1.74409	−0.0813186
$461$	16.8874	0.786524	0.393262	−	0.919427i	$-0.371347\pi$
$461$	16.8874	0.786524	0.393262	+	0.919427i	$0.371347\pi$
$462$	−89.4885	−4.16338
$463$	36.9285	1.71621	0.858106	−	0.513473i	$-0.171641\pi$
$463$	36.9285	1.71621	0.858106	+	0.513473i	$0.171641\pi$
$464$	−3.06193	−0.142147
$465$	−2.11542	−0.0981002
$466$	4.34741	0.201390
$467$	−7.49038	−0.346613	−0.173307	−	0.984868i	$-0.555445\pi$
$467$	−7.49038	−0.346613	−0.173307	+	0.984868i	$0.555445\pi$
$468$	146.422	6.76836
$469$	−10.4218	−0.481235
$470$	2.66647	0.122995
$471$	−10.8595	−0.500378
$472$	−1.85377	−0.0853265
$473$	13.2404	0.608794
$474$	−62.1760	−2.85584
$475$	29.0722	1.33393
$476$	119.900	5.49563
$477$	5.12999	0.234886
$478$	−40.7594	−1.86429
$479$	−16.3019	−0.744854	−0.372427	−	0.928061i	$-0.621474\pi$
$479$	−16.3019	−0.744854	−0.372427	+	0.928061i	$0.621474\pi$
$480$	3.25447	0.148546
$481$	−5.44857	−0.248433
$482$	13.3339	0.607340
$483$	−69.4489	−3.16004
$484$	−17.3049	−0.786587
$485$	0.397764	0.0180615
$486$	195.925	8.88734
$487$	41.5582	1.88318	0.941591	−	0.336760i	$-0.109331\pi$
$487$	41.5582	1.88318	0.941591	+	0.336760i	$0.109331\pi$
$488$	−28.2402	−1.27837
$489$	−3.44407	−0.155746
$490$	5.90788	0.266891
$491$	42.1113	1.90046	0.950228	−	0.311555i	$-0.100850\pi$
$491$	42.1113	1.90046	0.950228	+	0.311555i	$0.100850\pi$
$492$	−15.6602	−0.706014
$493$	27.6851	1.24687
$494$	71.3642	3.21082
$495$	2.92736	0.131575
$496$	3.71600	0.166854
$497$	41.5928	1.86569
$498$	−51.7544	−2.31917
$499$	−0.0272978	−0.00122202	−0.000611009	−	1.00000i	$-0.500194\pi$
$499$	−0.0272978	−0.00122202	−0.000611009		1.00000i	$0.500194\pi$
$500$	4.34511	0.194319
$501$	−34.3381	−1.53411
$502$	45.2001	2.01738
$503$	11.3366	0.505474	0.252737	−	0.967535i	$-0.418669\pi$
$503$	11.3366	0.505474	0.252737	+	0.967535i	$0.418669\pi$
$504$	−103.336	−4.60295
$505$	−0.910213	−0.0405040
$506$	20.6750	0.919115
$507$	−57.4708	−2.55237
$508$	12.4239	0.551220
$509$	33.8314	1.49955	0.749775	−	0.661693i	$-0.230162\pi$
$509$	33.8314	1.49955	0.749775	+	0.661693i	$0.230162\pi$
$510$	−8.71243	−0.385793
$511$	26.4580	1.17043
$512$	−9.74114	−0.430502
$513$	117.867	5.20394
$514$	34.0178	1.50046
$515$	2.41516	0.106425
$516$	60.1044	2.64595
$517$	−19.0473	−0.837700
$518$	11.2932	0.496195
$519$	61.1783	2.68543
$520$	1.81211	0.0794663
$521$	−0.373606	−0.0163680	−0.00818399	−	0.999967i	$-0.502605\pi$
$521$	−0.373606	−0.0163680	−0.00818399	+	0.999967i	$0.502605\pi$
$522$	−70.0756	−3.06712
$523$	−27.7313	−1.21260	−0.606302	−	0.795235i	$-0.707348\pi$
$523$	−27.7313	−1.21260	−0.606302	+	0.795235i	$0.707348\pi$
$524$	12.2536	0.535299
$525$	86.3316	3.76782
$526$	9.94635	0.433681
$527$	−33.5990	−1.46360
$528$	−6.88314	−0.299550
$529$	−6.95487	−0.302386
$530$	0.186459	0.00809928
$531$	7.09170	0.307753
$532$	−89.1326	−3.86439
$533$	8.16949	0.353860
$534$	−45.6955	−1.97744
$535$	−0.00598529	−0.000258767 0
$536$	4.79556	0.207137
$537$	−52.9745	−2.28602
$538$	15.5885	0.672068
$539$	−42.2016	−1.81775
$540$	8.78994	0.378259
$541$	−30.1271	−1.29527	−0.647633	−	0.761953i	$-0.724241\pi$
$541$	−30.1271	−1.29527	−0.647633	+	0.761953i	$0.724241\pi$
$542$	−36.6706	−1.57514
$543$	61.7309	2.64913
$544$	51.6905	2.21621
$545$	−1.70008	−0.0728235
$546$	211.920	9.06933
$547$	29.5834	1.26490	0.632448	−	0.774602i	$-0.282050\pi$
$547$	29.5834	1.26490	0.632448	+	0.774602i	$0.282050\pi$
$548$	52.3181	2.23492
$549$	108.035	4.61081
$550$	−25.7009	−1.09589
$551$	−20.5808	−0.876770
$552$	31.9566	1.36016
$553$	−40.5115	−1.72272
$554$	13.9212	0.591454
$555$	−0.494490	−0.0209899
$556$	48.8681	2.07247
$557$	2.77022	0.117378	0.0586889	−	0.998276i	$-0.481308\pi$
$557$	2.77022	0.117378	0.0586889	+	0.998276i	$0.481308\pi$
$558$	85.0447	3.60023
$559$	−31.3549	−1.32617
$560$	0.627833	0.0265308
$561$	62.2353	2.62758
$562$	−8.21565	−0.346556
$563$	−23.2392	−0.979417	−0.489708	−	0.871886i	$-0.662897\pi$
$563$	−23.2392	−0.979417	−0.489708	+	0.871886i	$0.662897\pi$
$564$	−86.4648	−3.64082
$565$	−1.43908	−0.0605424
$566$	−30.4812	−1.28122
$567$	216.181	9.07874
$568$	−19.1387	−0.803044
$569$	−3.85121	−0.161451	−0.0807256	−	0.996736i	$-0.525724\pi$
$569$	−3.85121	−0.161451	−0.0807256	+	0.996736i	$0.525724\pi$
$570$	6.47672	0.271280
$571$	8.11658	0.339668	0.169834	−	0.985473i	$-0.445677\pi$
$571$	8.11658	0.339668	0.169834	+	0.985473i	$0.445677\pi$
$572$	−38.0165	−1.58955
$573$	71.4654	2.98551
$574$	−16.9328	−0.706763
$575$	−19.9456	−0.831790
$576$	−115.442	−4.81009
$577$	4.95417	0.206245	0.103122	−	0.994669i	$-0.467117\pi$
$577$	4.95417	0.206245	0.103122	+	0.994669i	$0.467117\pi$
$578$	−100.242	−4.16952
$579$	54.0209	2.24503
$580$	−1.53481	−0.0637297
$581$	−33.7211	−1.39899
$582$	−21.4046	−0.887249
$583$	−1.33193	−0.0551629
$584$	−12.1745	−0.503786
$585$	−6.93235	−0.286617
$586$	−69.9094	−2.88793
$587$	27.5838	1.13851	0.569253	−	0.822162i	$-0.307232\pi$
$587$	27.5838	1.13851	0.569253	+	0.822162i	$0.307232\pi$
$588$	−191.573	−7.90034
$589$	24.9771	1.02916
$590$	0.257762	0.0106119
$591$	23.8754	0.982104
$592$	0.868634	0.0357006
$593$	−13.4142	−0.550854	−0.275427	−	0.961322i	$-0.588819\pi$
$593$	−13.4142	−0.550854	−0.275427	+	0.961322i	$0.588819\pi$
$594$	−104.199	−4.27532
$595$	−5.67668	−0.232721
$596$	−11.0238	−0.451552
$597$	−24.5902	−1.00641
$598$	−48.9609	−2.00216
$599$	−25.1103	−1.02598	−0.512990	−	0.858395i	$-0.671462\pi$
$599$	−25.1103	−1.02598	−0.512990	+	0.858395i	$0.671462\pi$
$600$	−39.7251	−1.62177
$601$	−42.6365	−1.73918	−0.869590	−	0.493775i	$-0.835617\pi$
$601$	−42.6365	−1.73918	−0.869590	+	0.493775i	$0.835617\pi$
$602$	64.9890	2.64875
$603$	−18.3457	−0.747095
$604$	48.5469	1.97534
$605$	0.819300	0.0333093
$606$	48.9807	1.98970
$607$	4.77945	0.193992	0.0969960	−	0.995285i	$-0.469077\pi$
$607$	4.77945	0.193992	0.0969960	+	0.995285i	$0.469077\pi$
$608$	−38.4261	−1.55838
$609$	−61.1157	−2.47653
$610$	3.92673	0.158989
$611$	45.1064	1.82481
$612$	211.063	8.53170
$613$	−2.44998	−0.0989537	−0.0494769	−	0.998775i	$-0.515755\pi$
$613$	−2.44998	−0.0989537	−0.0494769	+	0.998775i	$0.515755\pi$
$614$	7.72703	0.311837
$615$	0.741429	0.0298973
$616$	26.8298	1.08100
$617$	−20.9211	−0.842251	−0.421125	−	0.907002i	$-0.638365\pi$
$617$	−20.9211	−0.842251	−0.421125	+	0.907002i	$0.638365\pi$
$618$	−129.965	−5.22797
$619$	22.1011	0.888317	0.444159	−	0.895948i	$-0.353503\pi$
$619$	22.1011	0.888317	0.444159	+	0.895948i	$0.353503\pi$
$620$	1.86267	0.0748067
$621$	−80.8649	−3.24500
$622$	32.4868	1.30260
$623$	−29.7734	−1.19285
$624$	16.3001	0.652527
$625$	24.6912	0.987648
$626$	4.85885	0.194199
$627$	−46.2650	−1.84765
$628$	9.56199	0.381565
$629$	−7.85393	−0.313157
$630$	14.3686	0.572460
$631$	−13.1502	−0.523502	−0.261751	−	0.965135i	$-0.584300\pi$
$631$	−13.1502	−0.523502	−0.261751	+	0.965135i	$0.584300\pi$
$632$	18.6412	0.741506
$633$	−20.2565	−0.805125
$634$	−62.4597	−2.48059
$635$	−0.588207	−0.0233423
$636$	−6.04626	−0.239750
$637$	99.9386	3.95971
$638$	18.1942	0.720314
$639$	73.2165	2.89640
$640$	−2.30607	−0.0911555
$641$	−4.83846	−0.191108	−0.0955538	−	0.995424i	$-0.530462\pi$
$641$	−4.83846	−0.191108	−0.0955538	+	0.995424i	$0.530462\pi$
$642$	0.322082	0.0127116
$643$	43.3184	1.70831	0.854155	−	0.520019i	$-0.174075\pi$
$643$	43.3184	1.70831	0.854155	+	0.520019i	$0.174075\pi$
$644$	61.1513	2.40970
$645$	−2.84564	−0.112047
$646$	102.869	4.04733
$647$	−27.4116	−1.07766	−0.538831	−	0.842414i	$-0.681134\pi$
$647$	−27.4116	−1.07766	−0.538831	+	0.842414i	$0.681134\pi$
$648$	−99.4747	−3.90773
$649$	−1.84126	−0.0722759
$650$	60.8630	2.38724
$651$	74.1708	2.90698
$652$	3.03258	0.118765
$653$	−30.4140	−1.19019	−0.595095	−	0.803655i	$-0.702886\pi$
$653$	−30.4140	−1.19019	−0.595095	+	0.803655i	$0.702886\pi$
$654$	91.4854	3.57736
$655$	−0.580144	−0.0226681
$656$	−1.30242	−0.0508508
$657$	46.5745	1.81704
$658$	−93.4917	−3.64468
$659$	2.54358	0.0990840	0.0495420	−	0.998772i	$-0.484224\pi$
$659$	2.54358	0.0990840	0.0495420	+	0.998772i	$0.484224\pi$
$660$	−3.45022	−0.134300
$661$	−32.6349	−1.26935	−0.634676	−	0.772778i	$-0.718867\pi$
$661$	−32.6349	−1.26935	−0.634676	+	0.772778i	$0.718867\pi$
$662$	32.0074	1.24400
$663$	−147.381	−5.72380
$664$	15.5166	0.602162
$665$	4.21998	0.163644
$666$	19.8796	0.770319
$667$	14.1199	0.546723
$668$	30.2354	1.16984
$669$	48.2639	1.86599
$670$	−0.666810	−0.0257611
$671$	−28.0497	−1.08285
$672$	−114.108	−4.40183
$673$	−17.3690	−0.669528	−0.334764	−	0.942302i	$-0.608657\pi$
$673$	−17.3690	−0.669528	−0.334764	+	0.942302i	$0.608657\pi$
$674$	2.91923	0.112444
$675$	100.523	3.86912
$676$	50.6043	1.94632
$677$	−15.7609	−0.605740	−0.302870	−	0.953032i	$-0.597945\pi$
$677$	−15.7609	−0.605740	−0.302870	+	0.953032i	$0.597945\pi$
$678$	77.4400	2.97406
$679$	−13.9464	−0.535214
$680$	2.61210	0.100169
$681$	−102.712	−3.93591
$682$	−22.0807	−0.845513
$683$	32.7857	1.25451	0.627255	−	0.778814i	$-0.284178\pi$
$683$	32.7857	1.25451	0.627255	+	0.778814i	$0.284178\pi$
$684$	−156.901	−5.99928
$685$	−2.47700	−0.0946412
$686$	−128.090	−4.89049
$687$	39.5912	1.51050
$688$	4.99873	0.190575
$689$	3.15418	0.120165
$690$	−4.44349	−0.169161
$691$	−4.30440	−0.163747	−0.0818735	−	0.996643i	$-0.526090\pi$
$691$	−4.30440	−0.163747	−0.0818735	+	0.996643i	$0.526090\pi$
$692$	−53.8688	−2.04778
$693$	−102.639	−3.89894
$694$	−19.1516	−0.726985
$695$	−2.31366	−0.0877620
$696$	28.1221	1.06597
$697$	11.7761	0.446050
$698$	−56.2873	−2.13051
$699$	6.67433	0.252446
$700$	−76.0168	−2.87316
$701$	0.0486365	0.00183697	0.000918487	−	1.00000i	$-0.499708\pi$
$701$	0.0486365	0.00183697	0.000918487		1.00000i	$0.499708\pi$
$702$	246.755	9.31317
$703$	5.83852	0.220204
$704$	29.9730	1.12965
$705$	4.09367	0.154177
$706$	38.4318	1.44640
$707$	31.9139	1.20025
$708$	−8.35836	−0.314126
$709$	−31.2394	−1.17322	−0.586610	−	0.809869i	$-0.699538\pi$
$709$	−31.2394	−1.17322	−0.586610	+	0.809869i	$0.699538\pi$
$710$	2.66119	0.0998729
$711$	−71.3130	−2.67445
$712$	13.7001	0.513433
$713$	−17.1361	−0.641750
$714$	305.475	11.4321
$715$	1.79989	0.0673120
$716$	46.6452	1.74321
$717$	−62.5755	−2.33692
$718$	−14.6339	−0.546132
$719$	32.8278	1.22427	0.612136	−	0.790753i	$-0.290311\pi$
$719$	32.8278	1.22427	0.612136	+	0.790753i	$0.290311\pi$
$720$	1.10518	0.0411878
$721$	−84.6804	−3.15366
$722$	−33.8482	−1.25970
$723$	20.4707	0.761313
$724$	−54.3554	−2.02010
$725$	−17.5523	−0.651877
$726$	−44.0884	−1.63627
$727$	−13.4653	−0.499402	−0.249701	−	0.968323i	$-0.580332\pi$
$727$	−13.4653	−0.499402	−0.249701	+	0.968323i	$0.580332\pi$
$728$	−63.5363	−2.35481
$729$	171.962	6.36897
$730$	1.69284	0.0626548
$731$	−45.1970	−1.67167
$732$	−127.331	−4.70629
$733$	−15.5334	−0.573739	−0.286869	−	0.957970i	$-0.592615\pi$
$733$	−15.5334	−0.573739	−0.286869	+	0.957970i	$0.592615\pi$
$734$	6.82584	0.251946
$735$	9.07002	0.334553
$736$	26.3630	0.971754
$737$	4.76321	0.175455
$738$	−29.8071	−1.09722
$739$	−26.2775	−0.966632	−0.483316	−	0.875446i	$-0.660568\pi$
$739$	−26.2775	−0.966632	−0.483316	+	0.875446i	$0.660568\pi$
$740$	0.435409	0.0160059
$741$	109.561	4.02483
$742$	−6.53764	−0.240004
$743$	3.79158	0.139099	0.0695497	−	0.997578i	$-0.477844\pi$
$743$	3.79158	0.139099	0.0695497	+	0.997578i	$0.477844\pi$
$744$	−34.1294	−1.25124
$745$	0.521920	0.0191217
$746$	28.2919	1.03584
$747$	−59.3598	−2.17186
$748$	−54.7996	−2.00367
$749$	0.209856	0.00766798
$750$	11.0702	0.404227
$751$	35.0205	1.27792	0.638958	−	0.769242i	$-0.279366\pi$
$751$	35.0205	1.27792	0.638958	+	0.769242i	$0.279366\pi$
$752$	−7.19105	−0.262231
$753$	69.3930	2.52882
$754$	−43.0860	−1.56910
$755$	−2.29845	−0.0836491
$756$	−308.193	−11.2089
$757$	39.3868	1.43154	0.715769	−	0.698337i	$-0.246076\pi$
$757$	39.3868	1.43154	0.715769	+	0.698337i	$0.246076\pi$
$758$	57.3671	2.08367
$759$	31.7411	1.15213
$760$	−1.94180	−0.0704366
$761$	10.5254	0.381545	0.190772	−	0.981634i	$-0.438901\pi$
$761$	10.5254	0.381545	0.190772	+	0.981634i	$0.438901\pi$
$762$	31.6528	1.14666
$763$	59.6083	2.15797
$764$	−62.9268	−2.27661
$765$	−9.99275	−0.361289
$766$	−34.7599	−1.25593
$767$	4.36034	0.157443
$768$	34.3617	1.23992
$769$	52.7129	1.90088	0.950438	−	0.310916i	$-0.100636\pi$
$769$	52.7129	1.90088	0.950438	+	0.310916i	$0.100636\pi$
$770$	−3.73062	−0.134442
$771$	52.2255	1.88085
$772$	−47.5666	−1.71196
$773$	−21.0196	−0.756024	−0.378012	−	0.925801i	$-0.623392\pi$
$773$	−21.0196	−0.756024	−0.378012	+	0.925801i	$0.623392\pi$
$774$	114.401	4.11207
$775$	21.3017	0.765181
$776$	6.41737	0.230370
$777$	17.3378	0.621990
$778$	46.0906	1.65243
$779$	−8.75417	−0.313651
$780$	8.17055	0.292553
$781$	−19.0097	−0.680219
$782$	−70.5755	−2.52377
$783$	−71.1619	−2.54312
$784$	−15.9327	−0.569023
$785$	−0.452712	−0.0161580
$786$	31.2189	1.11354
$787$	−40.7500	−1.45258	−0.726290	−	0.687389i	$-0.758757\pi$
$787$	−40.7500	−1.45258	−0.726290	+	0.687389i	$0.758757\pi$
$788$	−21.0228	−0.748908
$789$	15.2700	0.543628
$790$	−2.59201	−0.0922195
$791$	50.4569	1.79404
$792$	47.2289	1.67821
$793$	66.4252	2.35883
$794$	−15.4086	−0.546830
$795$	0.286260	0.0101526
$796$	21.6522	0.767441
$797$	−25.3723	−0.898733	−0.449366	−	0.893348i	$-0.648350\pi$
$797$	−25.3723	−0.898733	−0.449366	+	0.893348i	$0.648350\pi$
$798$	−227.087	−8.03878
$799$	65.0194	2.30022
$800$	−32.7717	−1.15866
$801$	−52.4106	−1.85184
$802$	−25.8736	−0.913629
$803$	−12.0924	−0.426732
$804$	21.6225	0.762566
$805$	−2.89520	−0.102042
$806$	52.2898	1.84183
$807$	23.9321	0.842450
$808$	−14.6850	−0.516618
$809$	−13.6932	−0.481429	−0.240714	−	0.970596i	$-0.577382\pi$
$809$	−13.6932	−0.481429	−0.240714	+	0.970596i	$0.577382\pi$
$810$	13.8317	0.485997
$811$	−29.2877	−1.02843	−0.514215	−	0.857661i	$-0.671917\pi$
$811$	−29.2877	−1.02843	−0.514215	+	0.857661i	$0.671917\pi$
$812$	53.8137	1.88849
$813$	−56.2982	−1.97447
$814$	−5.16147	−0.180909
$815$	−0.143577	−0.00502929
$816$	23.4961	0.822528
$817$	33.5989	1.17548
$818$	−44.9078	−1.57016
$819$	243.062	8.49327
$820$	−0.652844	−0.0227983
$821$	−40.3679	−1.40885	−0.704425	−	0.709779i	$-0.748795\pi$
$821$	−40.3679	−1.40885	−0.704425	+	0.709779i	$0.748795\pi$
$822$	133.293	4.64912
$823$	−3.38236	−0.117902	−0.0589509	−	0.998261i	$-0.518776\pi$
$823$	−3.38236	−0.117902	−0.0589509	+	0.998261i	$0.518776\pi$
$824$	38.9653	1.35742
$825$	−39.4571	−1.37372
$826$	−9.03764	−0.314460
$827$	−10.5244	−0.365970	−0.182985	−	0.983116i	$-0.558576\pi$
$827$	−10.5244	−0.365970	−0.182985	+	0.983116i	$0.558576\pi$
$828$	107.646	3.74094
$829$	21.8274	0.758096	0.379048	−	0.925377i	$-0.376251\pi$
$829$	21.8274	0.758096	0.379048	+	0.925377i	$0.376251\pi$
$830$	−2.15755	−0.0748896
$831$	21.3724	0.741399
$832$	−70.9798	−2.46078
$833$	144.058	4.99132
$834$	124.503	4.31119
$835$	−1.43149	−0.0495389
$836$	40.7373	1.40893
$837$	86.3630	2.98514
$838$	15.5155	0.535974
$839$	−10.3136	−0.356067	−0.178033	−	0.984024i	$-0.556973\pi$
$839$	−10.3136	−0.356067	−0.178033	+	0.984024i	$0.556973\pi$
$840$	−5.76629	−0.198956
$841$	−16.5744	−0.571531
$842$	27.1653	0.936177
$843$	−12.6130	−0.434415
$844$	17.8363	0.613952
$845$	−2.39586	−0.0824199
$846$	−164.575	−5.65820
$847$	−28.7263	−0.987047
$848$	−0.502852	−0.0172680
$849$	−46.7960	−1.60603
$850$	87.7320	3.00918
$851$	−4.00564	−0.137311
$852$	−86.2938	−2.95638
$853$	−55.8921	−1.91371	−0.956855	−	0.290567i	$-0.906156\pi$
$853$	−55.8921	−1.91371	−0.956855	+	0.290567i	$0.906156\pi$
$854$	−137.679	−4.71128
$855$	7.42849	0.254049
$856$	−0.0965644	−0.00330050
$857$	−12.5352	−0.428194	−0.214097	−	0.976812i	$-0.568681\pi$
$857$	−12.5352	−0.428194	−0.214097	+	0.976812i	$0.568681\pi$
$858$	−96.8562	−3.30662
$859$	33.2583	1.13476	0.567378	−	0.823457i	$-0.307958\pi$
$859$	33.2583	1.13476	0.567378	+	0.823457i	$0.307958\pi$
$860$	2.50565	0.0854418
$861$	−25.9960	−0.885941
$862$	13.8543	0.471880
$863$	−3.45333	−0.117553	−0.0587763	−	0.998271i	$-0.518720\pi$
$863$	−3.45333	−0.117553	−0.0587763	+	0.998271i	$0.518720\pi$
$864$	−132.866	−4.52018
$865$	2.55042	0.0867167
$866$	−8.07798	−0.274501
$867$	−153.896	−5.22657
$868$	−65.3090	−2.21673
$869$	18.5154	0.628093
$870$	−3.91031	−0.132572
$871$	−11.2799	−0.382204
$872$	−27.4285	−0.928846
$873$	−24.5501	−0.830894
$874$	52.4650	1.77465
$875$	7.21292	0.243841
$876$	−54.8932	−1.85467
$877$	−1.20627	−0.0407330	−0.0203665	−	0.999793i	$-0.506483\pi$
$877$	−1.20627	−0.0407330	−0.0203665	+	0.999793i	$0.506483\pi$
$878$	−18.8894	−0.637485
$879$	−107.328	−3.62008
$880$	−0.286946	−0.00967295
$881$	31.9542	1.07656	0.538281	−	0.842765i	$-0.319074\pi$
$881$	31.9542	1.07656	0.538281	+	0.842765i	$0.319074\pi$
$882$	−364.635	−12.2779
$883$	−12.1965	−0.410443	−0.205222	−	0.978716i	$-0.565792\pi$
$883$	−12.1965	−0.410443	−0.205222	+	0.978716i	$0.565792\pi$
$884$	129.772	4.36471
$885$	0.395726	0.0133022
$886$	14.5256	0.487997
$887$	−45.8038	−1.53794	−0.768971	−	0.639283i	$-0.779231\pi$
$887$	−45.8038	−1.53794	−0.768971	+	0.639283i	$0.779231\pi$
$888$	−7.97791	−0.267721
$889$	20.6237	0.691698
$890$	−1.90497	−0.0638546
$891$	−98.8037	−3.31005
$892$	−42.4974	−1.42292
$893$	−48.3346	−1.61746
$894$	−28.0857	−0.939327
$895$	−2.20841	−0.0738192
$896$	80.8555	2.70119
$897$	−75.1667	−2.50974
$898$	14.6851	0.490048
$899$	−15.0799	−0.502942
$900$	−133.814	−4.46045
$901$	4.54664	0.151471
$902$	7.73902	0.257681
$903$	99.7738	3.32026
$904$	−23.2175	−0.772203
$905$	2.57345	0.0855445
$906$	123.685	4.10915
$907$	45.3459	1.50569	0.752844	−	0.658199i	$-0.228682\pi$
$907$	45.3459	1.50569	0.752844	+	0.658199i	$0.228682\pi$
$908$	90.4397	3.00135
$909$	56.1785	1.86332
$910$	8.83456	0.292863
$911$	−16.8200	−0.557272	−0.278636	−	0.960397i	$-0.589882\pi$
$911$	−16.8200	−0.557272	−0.278636	+	0.960397i	$0.589882\pi$
$912$	−17.4667	−0.578381
$913$	15.4120	0.510062
$914$	69.7759	2.30798
$915$	6.02848	0.199295
$916$	−34.8609	−1.15184
$917$	20.3410	0.671719
$918$	355.689	11.7395
$919$	−27.5315	−0.908180	−0.454090	−	0.890956i	$-0.650035\pi$
$919$	−27.5315	−0.908180	−0.454090	+	0.890956i	$0.650035\pi$
$920$	1.33221	0.0439218
$921$	11.8628	0.390894
$922$	−37.8841	−1.24765
$923$	45.0172	1.48176
$924$	120.972	3.97968
$925$	4.97939	0.163721
$926$	−82.8431	−2.72239
$927$	−149.064	−4.89591
$928$	23.1997	0.761568
$929$	22.3740	0.734068	0.367034	−	0.930207i	$-0.380373\pi$
$929$	22.3740	0.734068	0.367034	+	0.930207i	$0.380373\pi$
$930$	4.74561	0.155615
$931$	−107.091	−3.50977
$932$	−5.87689	−0.192504
$933$	49.8751	1.63284
$934$	16.8035	0.549826
$935$	2.59448	0.0848486
$936$	−111.844	−3.65573
$937$	−34.9239	−1.14091	−0.570457	−	0.821327i	$-0.693234\pi$
$937$	−34.9239	−1.14091	−0.570457	+	0.821327i	$0.693234\pi$
$938$	23.3797	0.763375
$939$	7.45951	0.243432
$940$	−3.60456	−0.117568
$941$	15.2397	0.496799	0.248399	−	0.968658i	$-0.420095\pi$
$941$	15.2397	0.496799	0.248399	+	0.968658i	$0.420095\pi$
$942$	24.3615	0.793739
$943$	6.00598	0.195582
$944$	−0.695144	−0.0226250
$945$	14.5914	0.474657
$946$	−29.7027	−0.965718
$947$	−23.3210	−0.757832	−0.378916	−	0.925431i	$-0.623703\pi$
$947$	−23.3210	−0.757832	−0.378916	+	0.925431i	$0.623703\pi$
$948$	84.0503	2.72983
$949$	28.6364	0.929575
$950$	−65.2189	−2.11598
$951$	−95.8907	−3.10947
$952$	−91.5855	−2.96830
$953$	−38.5348	−1.24826	−0.624132	−	0.781319i	$-0.714547\pi$
$953$	−38.5348	−1.24826	−0.624132	+	0.781319i	$0.714547\pi$
$954$	−11.5083	−0.372595
$955$	2.97927	0.0964068
$956$	55.0991	1.78203
$957$	27.9324	0.902927
$958$	36.5708	1.18155
$959$	86.8485	2.80448
$960$	−6.44183	−0.207909
$961$	−12.6988	−0.409640
$962$	12.2230	0.394085
$963$	0.369413	0.0119042
$964$	−18.0249	−0.580542
$965$	2.25204	0.0724957
$966$	155.798	5.01270
$967$	−41.9839	−1.35011	−0.675056	−	0.737767i	$-0.735880\pi$
$967$	−41.9839	−1.35011	−0.675056	+	0.737767i	$0.735880\pi$
$968$	13.2183	0.424851
$969$	157.929	5.07341
$970$	−0.892320	−0.0286507
$971$	−24.4354	−0.784171	−0.392085	−	0.919929i	$-0.628246\pi$
$971$	−24.4354	−0.784171	−0.392085	+	0.919929i	$0.628246\pi$
$972$	−264.854	−8.49519
$973$	81.1214	2.60063
$974$	−93.2292	−2.98725
$975$	93.4394	2.99245
$976$	−10.5898	−0.338971
$977$	−3.98891	−0.127617	−0.0638083	−	0.997962i	$-0.520325\pi$
$977$	−3.98891	−0.127617	−0.0638083	+	0.997962i	$0.520325\pi$
$978$	7.72622	0.247057
$979$	13.6077	0.434904
$980$	−7.98635	−0.255114
$981$	104.929	3.35014
$982$	−94.4700	−3.01466
$983$	−23.2667	−0.742092	−0.371046	−	0.928614i	$-0.621001\pi$
$983$	−23.2667	−0.742092	−0.371046	+	0.928614i	$0.621001\pi$
$984$	11.9619	0.381333
$985$	0.995325	0.0317137
$986$	−62.1071	−1.97789
$987$	−143.532	−4.56868
$988$	−96.4710	−3.06915
$989$	−23.0512	−0.732987
$990$	−6.56706	−0.208715
$991$	25.5440	0.811432	0.405716	−	0.913999i	$-0.367022\pi$
$991$	25.5440	0.811432	0.405716	+	0.913999i	$0.367022\pi$
$992$	−28.1555	−0.893938
$993$	49.1390	1.55938
$994$	−93.3068	−2.95951
$995$	−1.02512	−0.0324985
$996$	69.9622	2.21684
$997$	41.7387	1.32188	0.660939	−	0.750440i	$-0.270158\pi$
$997$	41.7387	1.32188	0.660939	+	0.750440i	$0.270158\pi$
$998$	0.0612383	0.00193847
$999$	20.1878	0.638713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.18	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.24334 q^{2} -3.44407 q^{3} +3.03258 q^{4} -0.143577 q^{5} +7.72622 q^{6} +5.03410 q^{7} -2.31642 q^{8} +8.86161 q^{9} +O(q^{10})\)	\(q-2.24334 q^{2} -3.44407 q^{3} +3.03258 q^{4} -0.143577 q^{5} +7.72622 q^{6} +5.03410 q^{7} -2.31642 q^{8} +8.86161 q^{9} +0.322092 q^{10} -2.30080 q^{11} -10.4444 q^{12} +5.44857 q^{13} -11.2932 q^{14} +0.494490 q^{15} -0.868634 q^{16} +7.85393 q^{17} -19.8796 q^{18} -5.83852 q^{19} -0.435409 q^{20} -17.3378 q^{21} +5.16147 q^{22} +4.00564 q^{23} +7.97791 q^{24} -4.97939 q^{25} -12.2230 q^{26} -20.1878 q^{27} +15.2663 q^{28} +3.52500 q^{29} -1.10931 q^{30} -4.27799 q^{31} +6.58148 q^{32} +7.92410 q^{33} -17.6190 q^{34} -0.722782 q^{35} +26.8735 q^{36} -1.00000 q^{37} +13.0978 q^{38} -18.7652 q^{39} +0.332585 q^{40} +1.49938 q^{41} +38.8946 q^{42} -5.75470 q^{43} -6.97734 q^{44} -1.27232 q^{45} -8.98601 q^{46} +8.27858 q^{47} +2.99164 q^{48} +18.3422 q^{49} +11.1705 q^{50} -27.0495 q^{51} +16.5232 q^{52} +0.578900 q^{53} +45.2881 q^{54} +0.330342 q^{55} -11.6611 q^{56} +20.1083 q^{57} -7.90777 q^{58} +0.800272 q^{59} +1.49958 q^{60} +12.1913 q^{61} +9.59698 q^{62} +44.6102 q^{63} -13.0272 q^{64} -0.782290 q^{65} -17.7765 q^{66} -2.07025 q^{67} +23.8177 q^{68} -13.7957 q^{69} +1.62145 q^{70} +8.26221 q^{71} -20.5272 q^{72} +5.25576 q^{73} +2.24334 q^{74} +17.1493 q^{75} -17.7057 q^{76} -11.5824 q^{77} +42.0968 q^{78} -8.04741 q^{79} +0.124716 q^{80} +42.9433 q^{81} -3.36363 q^{82} -6.69854 q^{83} -52.5782 q^{84} -1.12765 q^{85} +12.9098 q^{86} -12.1403 q^{87} +5.32961 q^{88} -5.91434 q^{89} +2.85426 q^{90} +27.4286 q^{91} +12.1474 q^{92} +14.7337 q^{93} -18.5717 q^{94} +0.838278 q^{95} -22.6671 q^{96} -2.77038 q^{97} -41.1478 q^{98} -20.3888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 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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