LMFDB - Embedded newform 6031.2.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.20055 q^{2} -1.32438 q^{3} +2.84242 q^{4} -2.94026 q^{5} +2.91437 q^{6} -4.27239 q^{7} -1.85380 q^{8} -1.24601 q^{9} +O(q^{10})$	\(q-2.20055 q^{2} -1.32438 q^{3} +2.84242 q^{4} -2.94026 q^{5} +2.91437 q^{6} -4.27239 q^{7} -1.85380 q^{8} -1.24601 q^{9} +6.47020 q^{10} -4.67147 q^{11} -3.76446 q^{12} +5.54416 q^{13} +9.40160 q^{14} +3.89403 q^{15} -1.60548 q^{16} -0.0257115 q^{17} +2.74191 q^{18} +2.68252 q^{19} -8.35747 q^{20} +5.65828 q^{21} +10.2798 q^{22} +6.64765 q^{23} +2.45514 q^{24} +3.64514 q^{25} -12.2002 q^{26} +5.62334 q^{27} -12.1439 q^{28} +2.20822 q^{29} -8.56902 q^{30} -8.63062 q^{31} +7.24052 q^{32} +6.18681 q^{33} +0.0565796 q^{34} +12.5619 q^{35} -3.54169 q^{36} -1.00000 q^{37} -5.90301 q^{38} -7.34260 q^{39} +5.45065 q^{40} +4.71030 q^{41} -12.4513 q^{42} -8.70576 q^{43} -13.2783 q^{44} +3.66359 q^{45} -14.6285 q^{46} -5.79314 q^{47} +2.12626 q^{48} +11.2533 q^{49} -8.02132 q^{50} +0.0340519 q^{51} +15.7589 q^{52} +4.51270 q^{53} -12.3745 q^{54} +13.7353 q^{55} +7.92013 q^{56} -3.55268 q^{57} -4.85929 q^{58} -0.800227 q^{59} +11.0685 q^{60} -3.63802 q^{61} +18.9921 q^{62} +5.32343 q^{63} -12.7222 q^{64} -16.3013 q^{65} -13.6144 q^{66} -9.65981 q^{67} -0.0730831 q^{68} -8.80403 q^{69} -27.6432 q^{70} -14.9617 q^{71} +2.30985 q^{72} -10.0495 q^{73} +2.20055 q^{74} -4.82757 q^{75} +7.62485 q^{76} +19.9583 q^{77} +16.1578 q^{78} -10.8789 q^{79} +4.72052 q^{80} -3.70943 q^{81} -10.3653 q^{82} -12.8362 q^{83} +16.0832 q^{84} +0.0755987 q^{85} +19.1575 q^{86} -2.92452 q^{87} +8.65994 q^{88} -11.3862 q^{89} -8.06193 q^{90} -23.6868 q^{91} +18.8954 q^{92} +11.4302 q^{93} +12.7481 q^{94} -7.88730 q^{95} -9.58923 q^{96} -6.84985 q^{97} -24.7634 q^{98} +5.82069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.20055	−1.55602	−0.778012	−	0.628249i	$-0.783772\pi$
$2$	−2.20055	−1.55602	−0.778012	+	0.628249i	$0.783772\pi$
$3$	−1.32438	−0.764633	−0.382316	−	0.924031i	$-0.624874\pi$
$3$	−1.32438	−0.764633	−0.382316	+	0.924031i	$0.624874\pi$
$4$	2.84242	1.42121
$5$	−2.94026	−1.31493	−0.657463	−	0.753487i	$-0.728370\pi$
$5$	−2.94026	−1.31493	−0.657463	+	0.753487i	$0.728370\pi$
$6$	2.91437	1.18979
$7$	−4.27239	−1.61481	−0.807405	−	0.589998i	$-0.799129\pi$
$7$	−4.27239	−1.61481	−0.807405	+	0.589998i	$0.799129\pi$
$8$	−1.85380	−0.655416
$9$	−1.24601	−0.415336
$10$	6.47020	2.04606
$11$	−4.67147	−1.40850	−0.704250	−	0.709952i	$-0.748717\pi$
$11$	−4.67147	−1.40850	−0.704250	+	0.709952i	$0.748717\pi$
$12$	−3.76446	−1.08671
$13$	5.54416	1.53767	0.768837	−	0.639445i	$-0.220836\pi$
$13$	5.54416	1.53767	0.768837	+	0.639445i	$0.220836\pi$
$14$	9.40160	2.51268
$15$	3.89403	1.00544
$16$	−1.60548	−0.401369
$17$	−0.0257115	−0.00623597	−0.00311798	−	0.999995i	$-0.500992\pi$
$17$	−0.0257115	−0.00623597	−0.00311798	+	0.999995i	$0.500992\pi$
$18$	2.74191	0.646274
$19$	2.68252	0.615411	0.307706	−	0.951482i	$-0.400439\pi$
$19$	2.68252	0.615411	0.307706	+	0.951482i	$0.400439\pi$
$20$	−8.35747	−1.86879
$21$	5.65828	1.23474
$22$	10.2798	2.19166
$23$	6.64765	1.38613	0.693065	−	0.720875i	$-0.256260\pi$
$23$	6.64765	1.38613	0.693065	+	0.720875i	$0.256260\pi$
$24$	2.45514	0.501152
$25$	3.64514	0.729029
$26$	−12.2002	−2.39266
$27$	5.62334	1.08221
$28$	−12.1439	−2.29499
$29$	2.20822	0.410055	0.205028	−	0.978756i	$-0.434272\pi$
$29$	2.20822	0.410055	0.205028	+	0.978756i	$0.434272\pi$
$30$	−8.56902	−1.56448
$31$	−8.63062	−1.55010	−0.775052	−	0.631897i	$-0.782277\pi$
$31$	−8.63062	−1.55010	−0.775052	+	0.631897i	$0.782277\pi$
$32$	7.24052	1.27996
$33$	6.18681	1.07699
$34$	0.0565796	0.00970331
$35$	12.5619	2.12335
$36$	−3.54169	−0.590281
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.90301	−0.957595
$39$	−7.34260	−1.17576
$40$	5.45065	0.861823
$41$	4.71030	0.735625	0.367813	−	0.929900i	$-0.380107\pi$
$41$	4.71030	0.735625	0.367813	+	0.929900i	$0.380107\pi$
$42$	−12.4513	−1.92128
$43$	−8.70576	−1.32762	−0.663808	−	0.747903i	$-0.731061\pi$
$43$	−8.70576	−1.32762	−0.663808	+	0.747903i	$0.731061\pi$
$44$	−13.2783	−2.00178
$45$	3.66359	0.546136
$46$	−14.6285	−2.15685
$47$	−5.79314	−0.845017	−0.422508	−	0.906359i	$-0.638850\pi$
$47$	−5.79314	−0.845017	−0.422508	+	0.906359i	$0.638850\pi$
$48$	2.12626	0.306900
$49$	11.2533	1.60761
$50$	−8.02132	−1.13439
$51$	0.0340519	0.00476822
$52$	15.7589	2.18536
$53$	4.51270	0.619867	0.309934	−	0.950758i	$-0.399693\pi$
$53$	4.51270	0.619867	0.309934	+	0.950758i	$0.399693\pi$
$54$	−12.3745	−1.68395
$55$	13.7353	1.85207
$56$	7.92013	1.05837
$57$	−3.55268	−0.470564
$58$	−4.85929	−0.638056
$59$	−0.800227	−0.104181	−0.0520904	−	0.998642i	$-0.516588\pi$
$59$	−0.800227	−0.104181	−0.0520904	+	0.998642i	$0.516588\pi$
$60$	11.0685	1.42894
$61$	−3.63802	−0.465801	−0.232900	−	0.972501i	$-0.574822\pi$
$61$	−3.63802	−0.465801	−0.232900	+	0.972501i	$0.574822\pi$
$62$	18.9921	2.41200
$63$	5.32343	0.670689
$64$	−12.7222	−1.59027
$65$	−16.3013	−2.02193
$66$	−13.6144	−1.67582
$67$	−9.65981	−1.18013	−0.590067	−	0.807354i	$-0.700899\pi$
$67$	−9.65981	−1.18013	−0.590067	+	0.807354i	$0.700899\pi$
$68$	−0.0730831	−0.00886263
$69$	−8.80403	−1.05988
$70$	−27.6432	−3.30399
$71$	−14.9617	−1.77563	−0.887815	−	0.460201i	$-0.847777\pi$
$71$	−14.9617	−1.77563	−0.887815	+	0.460201i	$0.847777\pi$
$72$	2.30985	0.272218
$73$	−10.0495	−1.17620	−0.588102	−	0.808787i	$-0.700125\pi$
$73$	−10.0495	−1.17620	−0.588102	+	0.808787i	$0.700125\pi$
$74$	2.20055	0.255809
$75$	−4.82757	−0.557439
$76$	7.62485	0.874630
$77$	19.9583	2.27446
$78$	16.1578	1.82951
$79$	−10.8789	−1.22397	−0.611983	−	0.790871i	$-0.709628\pi$
$79$	−10.8789	−1.22397	−0.611983	+	0.790871i	$0.709628\pi$
$80$	4.72052	0.527770
$81$	−3.70943	−0.412159
$82$	−10.3653	−1.14465
$83$	−12.8362	−1.40896	−0.704478	−	0.709726i	$-0.748819\pi$
$83$	−12.8362	−1.40896	−0.704478	+	0.709726i	$0.748819\pi$
$84$	16.0832	1.75482
$85$	0.0755987	0.00819983
$86$	19.1575	2.06580
$87$	−2.92452	−0.313542
$88$	8.65994	0.923153
$89$	−11.3862	−1.20694	−0.603469	−	0.797387i	$-0.706215\pi$
$89$	−11.3862	−1.20694	−0.603469	+	0.797387i	$0.706215\pi$
$90$	−8.06193	−0.849802
$91$	−23.6868	−2.48305
$92$	18.8954	1.96998
$93$	11.4302	1.18526
$94$	12.7481	1.31487
$95$	−7.88730	−0.809220
$96$	−9.58923	−0.978696
$97$	−6.84985	−0.695497	−0.347749	−	0.937588i	$-0.613054\pi$
$97$	−6.84985	−0.695497	−0.347749	+	0.937588i	$0.613054\pi$
$98$	−24.7634	−2.50148
$99$	5.82069	0.585001
$100$	10.3610	1.03610
$101$	11.2653	1.12094	0.560471	−	0.828174i	$-0.310620\pi$
$101$	11.2653	1.12094	0.560471	+	0.828174i	$0.310620\pi$
$102$	−0.0749330	−0.00741947
$103$	−18.3442	−1.80751	−0.903753	−	0.428054i	$-0.859199\pi$
$103$	−18.3442	−1.80751	−0.903753	+	0.428054i	$0.859199\pi$
$104$	−10.2777	−1.00782
$105$	−16.6368	−1.62359
$106$	−9.93043	−0.964528
$107$	8.53346	0.824961	0.412481	−	0.910966i	$-0.364662\pi$
$107$	8.53346	0.824961	0.412481	+	0.910966i	$0.364662\pi$
$108$	15.9839	1.53805
$109$	−17.2598	−1.65319	−0.826593	−	0.562800i	$-0.809724\pi$
$109$	−17.2598	−1.65319	−0.826593	+	0.562800i	$0.809724\pi$
$110$	−30.2253	−2.88187
$111$	1.32438	0.125705
$112$	6.85921	0.648135
$113$	10.5511	0.992569	0.496284	−	0.868160i	$-0.334697\pi$
$113$	10.5511	0.992569	0.496284	+	0.868160i	$0.334697\pi$
$114$	7.81785	0.732209
$115$	−19.5458	−1.82266
$116$	6.27668	0.582776
$117$	−6.90808	−0.638652
$118$	1.76094	0.162108
$119$	0.109850	0.0100699
$120$	−7.21874	−0.658978
$121$	10.8226	0.983873
$122$	8.00565	0.724797
$123$	−6.23824	−0.562483
$124$	−24.5319	−2.20303
$125$	3.98364	0.356307
$126$	−11.7145	−1.04361
$127$	7.36280	0.653343	0.326671	−	0.945138i	$-0.394073\pi$
$127$	7.36280	0.653343	0.326671	+	0.945138i	$0.394073\pi$
$128$	13.5148	1.19455
$129$	11.5298	1.01514
$130$	35.8718	3.14617
$131$	17.0736	1.49173	0.745865	−	0.666098i	$-0.232037\pi$
$131$	17.0736	1.49173	0.745865	+	0.666098i	$0.232037\pi$
$132$	17.5855	1.53062
$133$	−11.4607	−0.993772
$134$	21.2569	1.83632
$135$	−16.5341	−1.42303
$136$	0.0476639	0.00408715
$137$	−2.43280	−0.207848	−0.103924	−	0.994585i	$-0.533140\pi$
$137$	−2.43280	−0.207848	−0.103924	+	0.994585i	$0.533140\pi$
$138$	19.3737	1.64920
$139$	10.6303	0.901652	0.450826	−	0.892612i	$-0.351129\pi$
$139$	10.6303	0.901652	0.450826	+	0.892612i	$0.351129\pi$
$140$	35.7063	3.01774
$141$	7.67234	0.646127
$142$	32.9240	2.76292
$143$	−25.8994	−2.16581
$144$	2.00044	0.166703
$145$	−6.49273	−0.539192
$146$	22.1144	1.83020
$147$	−14.9037	−1.22923
$148$	−2.84242	−0.233646
$149$	21.0050	1.72080	0.860400	−	0.509620i	$-0.170214\pi$
$149$	21.0050	1.72080	0.860400	+	0.509620i	$0.170214\pi$
$150$	10.6233	0.867389
$151$	−14.0497	−1.14335	−0.571673	−	0.820482i	$-0.693705\pi$
$151$	−14.0497	−1.14335	−0.571673	+	0.820482i	$0.693705\pi$
$152$	−4.97284	−0.403350
$153$	0.0320368	0.00259002
$154$	−43.9193	−3.53912
$155$	25.3763	2.03827
$156$	−20.8708	−1.67100
$157$	−9.84323	−0.785575	−0.392788	−	0.919629i	$-0.628489\pi$
$157$	−9.84323	−0.785575	−0.392788	+	0.919629i	$0.628489\pi$
$158$	23.9395	1.90452
$159$	−5.97654	−0.473971
$160$	−21.2890	−1.68305
$161$	−28.4013	−2.23834
$162$	8.16279	0.641330
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	13.3887	1.04548
$165$	−18.1908	−1.41616
$166$	28.2467	2.19237
$167$	10.3593	0.801626	0.400813	−	0.916160i	$-0.368728\pi$
$167$	10.3593	0.801626	0.400813	+	0.916160i	$0.368728\pi$
$168$	−10.4893	−0.809266
$169$	17.7377	1.36444
$170$	−0.166359	−0.0127591
$171$	−3.34244	−0.255603
$172$	−24.7455	−1.88682
$173$	−24.3077	−1.84808	−0.924038	−	0.382300i	$-0.875132\pi$
$173$	−24.3077	−1.84808	−0.924038	+	0.382300i	$0.875132\pi$
$174$	6.43556	0.487879
$175$	−15.5735	−1.17724
$176$	7.49993	0.565328
$177$	1.05981	0.0796600
$178$	25.0560	1.87802
$179$	−18.1528	−1.35680	−0.678401	−	0.734692i	$-0.737327\pi$
$179$	−18.1528	−1.35680	−0.678401	+	0.734692i	$0.737327\pi$
$180$	10.4135	0.776175
$181$	8.56263	0.636455	0.318228	−	0.948014i	$-0.396912\pi$
$181$	8.56263	0.636455	0.318228	+	0.948014i	$0.396912\pi$
$182$	52.1240	3.86369
$183$	4.81813	0.356167
$184$	−12.3234	−0.908492
$185$	2.94026	0.216172
$186$	−25.1528	−1.84430
$187$	0.120111	0.00878336
$188$	−16.4666	−1.20095
$189$	−24.0251	−1.74757
$190$	17.3564	1.25917
$191$	9.19156	0.665078	0.332539	−	0.943090i	$-0.392095\pi$
$191$	9.19156	0.665078	0.332539	+	0.943090i	$0.392095\pi$
$192$	16.8490	1.21598
$193$	−0.738780	−0.0531785	−0.0265893	−	0.999646i	$-0.508465\pi$
$193$	−0.738780	−0.0531785	−0.0265893	+	0.999646i	$0.508465\pi$
$194$	15.0734	1.08221
$195$	21.5892	1.54603
$196$	31.9866	2.28476
$197$	−16.5278	−1.17756	−0.588780	−	0.808294i	$-0.700391\pi$
$197$	−16.5278	−1.17756	−0.588780	+	0.808294i	$0.700391\pi$
$198$	−12.8087	−0.910277
$199$	−3.51059	−0.248859	−0.124430	−	0.992228i	$-0.539710\pi$
$199$	−3.51059	−0.248859	−0.124430	+	0.992228i	$0.539710\pi$
$200$	−6.75735	−0.477817
$201$	12.7933	0.902369
$202$	−24.7899	−1.74421
$203$	−9.43435	−0.662162
$204$	0.0967900	0.00677666
$205$	−13.8495	−0.967292
$206$	40.3673	2.81252
$207$	−8.28303	−0.575710
$208$	−8.90102	−0.617175
$209$	−12.5313	−0.866807
$210$	36.6102	2.52634
$211$	12.0009	0.826173	0.413086	−	0.910692i	$-0.364451\pi$
$211$	12.0009	0.826173	0.413086	+	0.910692i	$0.364451\pi$
$212$	12.8270	0.880962
$213$	19.8150	1.35770
$214$	−18.7783	−1.28366
$215$	25.5972	1.74572
$216$	−10.4245	−0.709299
$217$	36.8733	2.50312
$218$	37.9810	2.57240
$219$	13.3094	0.899364
$220$	39.0416	2.63219
$221$	−0.142549	−0.00958888
$222$	−2.91437	−0.195600
$223$	15.4348	1.03359	0.516797	−	0.856108i	$-0.327124\pi$
$223$	15.4348	1.03359	0.516797	+	0.856108i	$0.327124\pi$
$224$	−30.9343	−2.06688
$225$	−4.54188	−0.302792
$226$	−23.2183	−1.54446
$227$	−28.8654	−1.91587	−0.957933	−	0.286993i	$-0.907344\pi$
$227$	−28.8654	−1.91587	−0.957933	+	0.286993i	$0.907344\pi$
$228$	−10.0982	−0.668771
$229$	16.0174	1.05846	0.529230	−	0.848479i	$-0.322481\pi$
$229$	16.0174	1.05846	0.529230	+	0.848479i	$0.322481\pi$
$230$	43.0116	2.83610
$231$	−26.4324	−1.73913
$232$	−4.09358	−0.268757
$233$	−25.7576	−1.68744	−0.843718	−	0.536787i	$-0.819638\pi$
$233$	−25.7576	−1.68744	−0.843718	+	0.536787i	$0.819638\pi$
$234$	15.2016	0.993758
$235$	17.0334	1.11113
$236$	−2.27458	−0.148063
$237$	14.4078	0.935885
$238$	−0.241730	−0.0156690
$239$	−22.8787	−1.47990	−0.739950	−	0.672662i	$-0.765151\pi$
$239$	−22.8787	−1.47990	−0.739950	+	0.672662i	$0.765151\pi$
$240$	−6.25178	−0.403550
$241$	−21.7618	−1.40180	−0.700902	−	0.713258i	$-0.747219\pi$
$241$	−21.7618	−1.40180	−0.700902	+	0.713258i	$0.747219\pi$
$242$	−23.8157	−1.53093
$243$	−11.9573	−0.767062
$244$	−10.3408	−0.662001
$245$	−33.0876	−2.11389
$246$	13.7276	0.875238
$247$	14.8723	0.946302
$248$	15.9994	1.01596
$249$	17.0000	1.07733
$250$	−8.76619	−0.554423
$251$	4.65243	0.293659	0.146829	−	0.989162i	$-0.453093\pi$
$251$	4.65243	0.293659	0.146829	+	0.989162i	$0.453093\pi$
$252$	15.1314	0.953192
$253$	−31.0543	−1.95237
$254$	−16.2022	−1.01662
$255$	−0.100122	−0.00626986
$256$	−4.29556	−0.268473
$257$	3.74825	0.233809	0.116905	−	0.993143i	$-0.462703\pi$
$257$	3.74825	0.233809	0.116905	+	0.993143i	$0.462703\pi$
$258$	−25.3718	−1.57958
$259$	4.27239	0.265473
$260$	−46.3352	−2.87359
$261$	−2.75146	−0.170311
$262$	−37.5714	−2.32117
$263$	0.151340	0.00933203	0.00466601	−	0.999989i	$-0.498515\pi$
$263$	0.151340	0.00933203	0.00466601	+	0.999989i	$0.498515\pi$
$264$	−11.4691	−0.705873
$265$	−13.2685	−0.815079
$266$	25.2199	1.54633
$267$	15.0797	0.922864
$268$	−27.4573	−1.67722
$269$	24.1758	1.47402	0.737012	−	0.675880i	$-0.236236\pi$
$269$	24.1758	1.47402	0.737012	+	0.675880i	$0.236236\pi$
$270$	36.3841	2.21427
$271$	11.1430	0.676890	0.338445	−	0.940986i	$-0.390099\pi$
$271$	11.1430	0.676890	0.338445	+	0.940986i	$0.390099\pi$
$272$	0.0412793	0.00250292
$273$	31.3704	1.89862
$274$	5.35350	0.323417
$275$	−17.0282	−1.02684
$276$	−25.0248	−1.50632
$277$	−13.8987	−0.835089	−0.417545	−	0.908656i	$-0.637109\pi$
$277$	−13.8987	−0.835089	−0.417545	+	0.908656i	$0.637109\pi$
$278$	−23.3926	−1.40299
$279$	10.7538	0.643815
$280$	−23.2873	−1.39168
$281$	19.4018	1.15742	0.578708	−	0.815535i	$-0.303557\pi$
$281$	19.4018	1.15742	0.578708	+	0.815535i	$0.303557\pi$
$282$	−16.8834	−1.00539
$283$	−10.0100	−0.595035	−0.297518	−	0.954716i	$-0.596159\pi$
$283$	−10.0100	−0.595035	−0.297518	+	0.954716i	$0.596159\pi$
$284$	−42.5275	−2.52355
$285$	10.4458	0.618756
$286$	56.9929	3.37006
$287$	−20.1242	−1.18789
$288$	−9.02176	−0.531612
$289$	−16.9993	−0.999961
$290$	14.2876	0.838996
$291$	9.07183	0.531800
$292$	−28.5649	−1.67163
$293$	−18.3173	−1.07011	−0.535053	−	0.844818i	$-0.679708\pi$
$293$	−18.3173	−1.07011	−0.535053	+	0.844818i	$0.679708\pi$
$294$	32.7962	1.91272
$295$	2.35288	0.136990
$296$	1.85380	0.107750
$297$	−26.2693	−1.52430
$298$	−46.2226	−2.67761
$299$	36.8556	2.13142
$300$	−13.7220	−0.792239
$301$	37.1944	2.14385
$302$	30.9170	1.77907
$303$	−14.9196	−0.857109
$304$	−4.30671	−0.247007
$305$	10.6967	0.612493
$306$	−0.0704987	−0.00403014
$307$	1.19003	0.0679186	0.0339593	−	0.999423i	$-0.489188\pi$
$307$	1.19003	0.0679186	0.0339593	+	0.999423i	$0.489188\pi$
$308$	56.7300	3.23249
$309$	24.2947	1.38208
$310$	−55.8418	−3.17160
$311$	−27.1436	−1.53918	−0.769588	−	0.638541i	$-0.779538\pi$
$311$	−27.1436	−1.53918	−0.769588	+	0.638541i	$0.779538\pi$
$312$	13.6117	0.770609
$313$	25.0777	1.41748	0.708738	−	0.705472i	$-0.249265\pi$
$313$	25.0777	1.41748	0.708738	+	0.705472i	$0.249265\pi$
$314$	21.6605	1.22237
$315$	−15.6523	−0.881906
$316$	−30.9223	−1.73952
$317$	20.9369	1.17593	0.587966	−	0.808886i	$-0.299929\pi$
$317$	20.9369	1.17593	0.587966	+	0.808886i	$0.299929\pi$
$318$	13.1517	0.737510
$319$	−10.3156	−0.577563
$320$	37.4066	2.09109
$321$	−11.3016	−0.630792
$322$	62.4985	3.48291
$323$	−0.0689716	−0.00383768
$324$	−10.5438	−0.585765
$325$	20.2093	1.12101
$326$	−2.20055	−0.121877
$327$	22.8585	1.26408
$328$	−8.73193	−0.482140
$329$	24.7505	1.36454
$330$	40.0299	2.20357
$331$	15.5628	0.855410	0.427705	−	0.903918i	$-0.359322\pi$
$331$	15.5628	0.855410	0.427705	+	0.903918i	$0.359322\pi$
$332$	−36.4859	−2.00242
$333$	1.24601	0.0682809
$334$	−22.7962	−1.24735
$335$	28.4024	1.55179
$336$	−9.08422	−0.495585
$337$	−25.8350	−1.40732	−0.703660	−	0.710537i	$-0.748452\pi$
$337$	−25.8350	−1.40732	−0.703660	+	0.710537i	$0.748452\pi$
$338$	−39.0328	−2.12310
$339$	−13.9738	−0.758951
$340$	0.214883	0.0116537
$341$	40.3177	2.18332
$342$	7.35521	0.397724
$343$	−18.1716	−0.981176
$344$	16.1387	0.870141
$345$	25.8862	1.39366
$346$	53.4902	2.87565
$347$	−10.0177	−0.537777	−0.268888	−	0.963171i	$-0.586656\pi$
$347$	−10.0177	−0.537777	−0.268888	+	0.963171i	$0.586656\pi$
$348$	−8.31274	−0.445609
$349$	−9.24271	−0.494751	−0.247375	−	0.968920i	$-0.579568\pi$
$349$	−9.24271	−0.494751	−0.247375	+	0.968920i	$0.579568\pi$
$350$	34.2702	1.83182
$351$	31.1767	1.66409
$352$	−33.8239	−1.80282
$353$	−4.60799	−0.245258	−0.122629	−	0.992453i	$-0.539133\pi$
$353$	−4.60799	−0.245258	−0.122629	+	0.992453i	$0.539133\pi$
$354$	−2.33216	−0.123953
$355$	43.9914	2.33482
$356$	−32.3645	−1.71531
$357$	−0.145483	−0.00769978
$358$	39.9461	2.11122
$359$	26.2776	1.38688	0.693440	−	0.720514i	$-0.256094\pi$
$359$	26.2776	1.38688	0.693440	+	0.720514i	$0.256094\pi$
$360$	−6.79155	−0.357946
$361$	−11.8041	−0.621269
$362$	−18.8425	−0.990340
$363$	−14.3333	−0.752302
$364$	−67.3279	−3.52894
$365$	29.5481	1.54662
$366$	−10.6025	−0.554204
$367$	24.7958	1.29433	0.647165	−	0.762350i	$-0.275954\pi$
$367$	24.7958	1.29433	0.647165	+	0.762350i	$0.275954\pi$
$368$	−10.6726	−0.556350
$369$	−5.86908	−0.305532
$370$	−6.47020	−0.336369
$371$	−19.2800	−1.00097
$372$	32.4896	1.68451
$373$	−30.7427	−1.59180	−0.795899	−	0.605429i	$-0.793001\pi$
$373$	−30.7427	−1.59180	−0.795899	+	0.605429i	$0.793001\pi$
$374$	−0.264310	−0.0136671
$375$	−5.27586	−0.272444
$376$	10.7393	0.553837
$377$	12.2427	0.630532
$378$	52.8684	2.71926
$379$	−21.0416	−1.08083	−0.540416	−	0.841398i	$-0.681733\pi$
$379$	−21.0416	−1.08083	−0.540416	+	0.841398i	$0.681733\pi$
$380$	−22.4190	−1.15007
$381$	−9.75117	−0.499567
$382$	−20.2265	−1.03488
$383$	−34.8856	−1.78257	−0.891285	−	0.453443i	$-0.850196\pi$
$383$	−34.8856	−1.78257	−0.891285	+	0.453443i	$0.850196\pi$
$384$	−17.8987	−0.913391
$385$	−58.6827	−2.99075
$386$	1.62572	0.0827471
$387$	10.8475	0.551408
$388$	−19.4702	−0.988449
$389$	11.2580	0.570803	0.285402	−	0.958408i	$-0.407873\pi$
$389$	11.2580	0.570803	0.285402	+	0.958408i	$0.407873\pi$
$390$	−47.5080	−2.40566
$391$	−0.170921	−0.00864386
$392$	−20.8613	−1.05365
$393$	−22.6120	−1.14063
$394$	36.3703	1.83231
$395$	31.9867	1.60942
$396$	16.5449	0.831411
$397$	−30.6839	−1.53998	−0.769989	−	0.638057i	$-0.779739\pi$
$397$	−30.6839	−1.53998	−0.769989	+	0.638057i	$0.779739\pi$
$398$	7.72524	0.387231
$399$	15.1784	0.759871
$400$	−5.85219	−0.292609
$401$	17.8140	0.889591	0.444795	−	0.895632i	$-0.353276\pi$
$401$	17.8140	0.889591	0.444795	+	0.895632i	$0.353276\pi$
$402$	−28.1523	−1.40411
$403$	−47.8496	−2.38356
$404$	32.0208	1.59310
$405$	10.9067	0.541959
$406$	20.7608	1.03034
$407$	4.67147	0.231556
$408$	−0.0631253	−0.00312517
$409$	−26.0690	−1.28903	−0.644516	−	0.764591i	$-0.722941\pi$
$409$	−26.0690	−1.28903	−0.644516	+	0.764591i	$0.722941\pi$
$410$	30.4766	1.50513
$411$	3.22196	0.158927
$412$	−52.1419	−2.56885
$413$	3.41888	0.168232
$414$	18.2272	0.895819
$415$	37.7418	1.85267
$416$	40.1426	1.96815
$417$	−14.0786	−0.689433
$418$	27.5757	1.34877
$419$	−30.3318	−1.48181	−0.740903	−	0.671612i	$-0.765602\pi$
$419$	−30.3318	−1.48181	−0.740903	+	0.671612i	$0.765602\pi$
$420$	−47.2889	−2.30746
$421$	1.07240	0.0522656	0.0261328	−	0.999658i	$-0.491681\pi$
$421$	1.07240	0.0522656	0.0261328	+	0.999658i	$0.491681\pi$
$422$	−26.4085	−1.28555
$423$	7.21831	0.350966
$424$	−8.36562	−0.406271
$425$	−0.0937222	−0.00454620
$426$	−43.6040	−2.11262
$427$	15.5430	0.752180
$428$	24.2557	1.17244
$429$	34.3007	1.65605
$430$	−56.3280	−2.71638
$431$	−26.1805	−1.26107	−0.630535	−	0.776160i	$-0.717165\pi$
$431$	−26.1805	−1.26107	−0.630535	+	0.776160i	$0.717165\pi$
$432$	−9.02814	−0.434367
$433$	3.17177	0.152425	0.0762127	−	0.997092i	$-0.475717\pi$
$433$	3.17177	0.152425	0.0762127	+	0.997092i	$0.475717\pi$
$434$	−81.1416	−3.89492
$435$	8.59887	0.412284
$436$	−49.0596	−2.34953
$437$	17.8324	0.853040
$438$	−29.2880	−1.39943
$439$	−8.96458	−0.427856	−0.213928	−	0.976849i	$-0.568626\pi$
$439$	−8.96458	−0.427856	−0.213928	+	0.976849i	$0.568626\pi$
$440$	−25.4625	−1.21388
$441$	−14.0217	−0.667699
$442$	0.313686	0.0149205
$443$	−13.8165	−0.656440	−0.328220	−	0.944601i	$-0.606449\pi$
$443$	−13.8165	−0.656440	−0.328220	+	0.944601i	$0.606449\pi$
$444$	3.76446	0.178653
$445$	33.4785	1.58703
$446$	−33.9651	−1.60830
$447$	−27.8187	−1.31578
$448$	54.3541	2.56799
$449$	−13.2520	−0.625402	−0.312701	−	0.949852i	$-0.601234\pi$
$449$	−13.2520	−0.625402	−0.312701	+	0.949852i	$0.601234\pi$
$450$	9.99464	0.471152
$451$	−22.0040	−1.03613
$452$	29.9908	1.41065
$453$	18.6071	0.874240
$454$	63.5198	2.98113
$455$	69.6454	3.26503
$456$	6.58594	0.308415
$457$	−0.461246	−0.0215762	−0.0107881	−	0.999942i	$-0.503434\pi$
$457$	−0.461246	−0.0215762	−0.0107881	+	0.999942i	$0.503434\pi$
$458$	−35.2471	−1.64699
$459$	−0.144585	−0.00674864
$460$	−55.5575	−2.59038
$461$	4.49530	0.209367	0.104684	−	0.994506i	$-0.466617\pi$
$461$	4.49530	0.209367	0.104684	+	0.994506i	$0.466617\pi$
$462$	58.1659	2.70612
$463$	−9.23708	−0.429283	−0.214642	−	0.976693i	$-0.568858\pi$
$463$	−9.23708	−0.429283	−0.214642	+	0.976693i	$0.568858\pi$
$464$	−3.54524	−0.164583
$465$	−33.6079	−1.55853
$466$	56.6809	2.62569
$467$	−18.9552	−0.877144	−0.438572	−	0.898696i	$-0.644516\pi$
$467$	−18.9552	−0.877144	−0.438572	+	0.898696i	$0.644516\pi$
$468$	−19.6357	−0.907660
$469$	41.2704	1.90569
$470$	−37.4828	−1.72895
$471$	13.0362	0.600677
$472$	1.48346	0.0682817
$473$	40.6687	1.86995
$474$	−31.7050	−1.45626
$475$	9.77815	0.448652
$476$	0.312239	0.0143115
$477$	−5.62287	−0.257453
$478$	50.3457	2.30276
$479$	−19.9123	−0.909816	−0.454908	−	0.890538i	$-0.650328\pi$
$479$	−19.9123	−0.909816	−0.454908	+	0.890538i	$0.650328\pi$
$480$	28.1948	1.28691
$481$	−5.54416	−0.252792
$482$	47.8880	2.18124
$483$	37.6142	1.71151
$484$	30.7624	1.39829
$485$	20.1404	0.914527
$486$	26.3127	1.19357
$487$	9.35910	0.424101	0.212051	−	0.977259i	$-0.431986\pi$
$487$	9.35910	0.424101	0.212051	+	0.977259i	$0.431986\pi$
$488$	6.74415	0.305293
$489$	−1.32438	−0.0598907
$490$	72.8109	3.28926
$491$	−2.42476	−0.109428	−0.0547139	−	0.998502i	$-0.517425\pi$
$491$	−2.42476	−0.109428	−0.0547139	+	0.998502i	$0.517425\pi$
$492$	−17.7317	−0.799408
$493$	−0.0567766	−0.00255709
$494$	−32.7273	−1.47247
$495$	−17.1144	−0.769233
$496$	13.8562	0.622164
$497$	63.9222	2.86730
$498$	−37.4095	−1.67636
$499$	−26.7868	−1.19914	−0.599570	−	0.800322i	$-0.704662\pi$
$499$	−26.7868	−1.19914	−0.599570	+	0.800322i	$0.704662\pi$
$500$	11.3232	0.506388
$501$	−13.7197	−0.612950
$502$	−10.2379	−0.456940
$503$	−32.1567	−1.43380	−0.716899	−	0.697177i	$-0.754439\pi$
$503$	−32.1567	−1.43380	−0.716899	+	0.697177i	$0.754439\pi$
$504$	−9.86855	−0.439580
$505$	−33.1230	−1.47395
$506$	68.3365	3.03793
$507$	−23.4916	−1.04330
$508$	20.9282	0.928538
$509$	−20.9167	−0.927117	−0.463558	−	0.886066i	$-0.653428\pi$
$509$	−20.9167	−0.927117	−0.463558	+	0.886066i	$0.653428\pi$
$510$	0.220323	0.00975605
$511$	42.9353	1.89935
$512$	−17.5769	−0.776798
$513$	15.0847	0.666006
$514$	−8.24822	−0.363813
$515$	53.9367	2.37674
$516$	32.7725	1.44273
$517$	27.0625	1.19021
$518$	−9.40160	−0.413083
$519$	32.1926	1.41310
$520$	30.2193	1.32520
$521$	1.82187	0.0798178	0.0399089	−	0.999203i	$-0.487293\pi$
$521$	1.82187	0.0798178	0.0399089	+	0.999203i	$0.487293\pi$
$522$	6.05472	0.265008
$523$	−15.8770	−0.694253	−0.347126	−	0.937818i	$-0.612843\pi$
$523$	−15.8770	−0.694253	−0.347126	+	0.937818i	$0.612843\pi$
$524$	48.5305	2.12006
$525$	20.6252	0.900158
$526$	−0.333031	−0.0145209
$527$	0.221907	0.00966640
$528$	−9.93278	−0.432269
$529$	21.1912	0.921357
$530$	29.1981	1.26828
$531$	0.997091	0.0432701
$532$	−32.5763	−1.41236
$533$	26.1147	1.13115
$534$	−33.1837	−1.43600
$535$	−25.0906	−1.08476
$536$	17.9073	0.773478
$537$	24.0412	1.03746
$538$	−53.2000	−2.29362
$539$	−52.5693	−2.26432
$540$	−46.9969	−2.02243
$541$	26.2674	1.12932	0.564661	−	0.825323i	$-0.309007\pi$
$541$	26.2674	1.12932	0.564661	+	0.825323i	$0.309007\pi$
$542$	−24.5208	−1.05326
$543$	−11.3402	−0.486655
$544$	−0.186165	−0.00798176
$545$	50.7482	2.17382
$546$	−69.0322	−2.95430
$547$	14.3644	0.614176	0.307088	−	0.951681i	$-0.400645\pi$
$547$	14.3644	0.614176	0.307088	+	0.951681i	$0.400645\pi$
$548$	−6.91505	−0.295396
$549$	4.53301	0.193464
$550$	37.4713	1.59778
$551$	5.92357	0.252353
$552$	16.3209	0.694663
$553$	46.4787	1.97647
$554$	30.5847	1.29942
$555$	−3.89403	−0.165293
$556$	30.2159	1.28144
$557$	37.0855	1.57137	0.785683	−	0.618630i	$-0.212312\pi$
$557$	37.0855	1.57137	0.785683	+	0.618630i	$0.212312\pi$
$558$	−23.6644	−1.00179
$559$	−48.2662	−2.04144
$560$	−20.1679	−0.852248
$561$	−0.159072	−0.00671605
$562$	−42.6947	−1.80097
$563$	−5.92600	−0.249751	−0.124876	−	0.992172i	$-0.539853\pi$
$563$	−5.92600	−0.249751	−0.124876	+	0.992172i	$0.539853\pi$
$564$	21.8080	0.918284
$565$	−31.0231	−1.30515
$566$	22.0276	0.925890
$567$	15.8481	0.665559
$568$	27.7360	1.16378
$569$	16.7060	0.700352	0.350176	−	0.936684i	$-0.386122\pi$
$569$	16.7060	0.700352	0.350176	+	0.936684i	$0.386122\pi$
$570$	−22.9865	−0.962800
$571$	32.0004	1.33918	0.669588	−	0.742733i	$-0.266471\pi$
$571$	32.0004	1.33918	0.669588	+	0.742733i	$0.266471\pi$
$572$	−73.6170	−3.07808
$573$	−12.1731	−0.508540
$574$	44.2844	1.84839
$575$	24.2316	1.01053
$576$	15.8520	0.660498
$577$	18.4348	0.767451	0.383725	−	0.923447i	$-0.374641\pi$
$577$	18.4348	0.767451	0.383725	+	0.923447i	$0.374641\pi$
$578$	37.4079	1.55596
$579$	0.978427	0.0406620
$580$	−18.4551	−0.766306
$581$	54.8412	2.27520
$582$	−19.9630	−0.827494
$583$	−21.0809	−0.873083
$584$	18.6297	0.770902
$585$	20.3116	0.839780
$586$	40.3081	1.66511
$587$	24.4307	1.00836	0.504182	−	0.863597i	$-0.331794\pi$
$587$	24.4307	1.00836	0.504182	+	0.863597i	$0.331794\pi$
$588$	−42.3625	−1.74700
$589$	−23.1518	−0.953952
$590$	−5.17763	−0.213160
$591$	21.8892	0.900401
$592$	1.60548	0.0659846
$593$	20.8021	0.854240	0.427120	−	0.904195i	$-0.359528\pi$
$593$	20.8021	0.854240	0.427120	+	0.904195i	$0.359528\pi$
$594$	57.8068	2.37184
$595$	−0.322987	−0.0132412
$596$	59.7052	2.44562
$597$	4.64937	0.190286
$598$	−81.1027	−3.31654
$599$	16.8630	0.689005	0.344502	−	0.938785i	$-0.388048\pi$
$599$	16.8630	0.689005	0.344502	+	0.938785i	$0.388048\pi$
$600$	8.94932	0.365354
$601$	−28.2142	−1.15088	−0.575441	−	0.817843i	$-0.695170\pi$
$601$	−28.2142	−1.15088	−0.575441	+	0.817843i	$0.695170\pi$
$602$	−81.8481	−3.33588
$603$	12.0362	0.490152
$604$	−39.9351	−1.62494
$605$	−31.8213	−1.29372
$606$	32.8314	1.33368
$607$	27.0622	1.09842	0.549211	−	0.835683i	$-0.314928\pi$
$607$	27.0622	1.09842	0.549211	+	0.835683i	$0.314928\pi$
$608$	19.4228	0.787699
$609$	12.4947	0.506311
$610$	−23.5387	−0.953054
$611$	−32.1181	−1.29936
$612$	0.0910622	0.00368097
$613$	−10.0533	−0.406050	−0.203025	−	0.979174i	$-0.565077\pi$
$613$	−10.0533	−0.406050	−0.203025	+	0.979174i	$0.565077\pi$
$614$	−2.61872	−0.105683
$615$	18.3421	0.739623
$616$	−36.9986	−1.49072
$617$	−33.5643	−1.35125	−0.675624	−	0.737247i	$-0.736126\pi$
$617$	−33.5643	−1.35125	−0.675624	+	0.737247i	$0.736126\pi$
$618$	−53.4618	−2.15055
$619$	3.73866	0.150269	0.0751347	−	0.997173i	$-0.476061\pi$
$619$	3.73866	0.150269	0.0751347	+	0.997173i	$0.476061\pi$
$620$	72.1301	2.89682
$621$	37.3820	1.50009
$622$	59.7310	2.39499
$623$	48.6464	1.94898
$624$	11.7884	0.471912
$625$	−29.9386	−1.19755
$626$	−55.1847	−2.20563
$627$	16.5962	0.662789
$628$	−27.9786	−1.11647
$629$	0.0257115	0.00102519
$630$	34.4437	1.37227
$631$	41.1235	1.63710	0.818550	−	0.574435i	$-0.194778\pi$
$631$	41.1235	1.63710	0.818550	+	0.574435i	$0.194778\pi$
$632$	20.1672	0.802207
$633$	−15.8937	−0.631719
$634$	−46.0727	−1.82978
$635$	−21.6486	−0.859097
$636$	−16.9879	−0.673613
$637$	62.3900	2.47198
$638$	22.7000	0.898702
$639$	18.6424	0.737484
$640$	−39.7370	−1.57074
$641$	−3.66060	−0.144585	−0.0722925	−	0.997383i	$-0.523032\pi$
$641$	−3.66060	−0.144585	−0.0722925	+	0.997383i	$0.523032\pi$
$642$	24.8697	0.981528
$643$	6.89720	0.271999	0.136000	−	0.990709i	$-0.456575\pi$
$643$	6.89720	0.271999	0.136000	+	0.990709i	$0.456575\pi$
$644$	−80.7286	−3.18115
$645$	−33.9005	−1.33483
$646$	0.151776	0.00597153
$647$	22.4991	0.884532	0.442266	−	0.896884i	$-0.354175\pi$
$647$	22.4991	0.884532	0.442266	+	0.896884i	$0.354175\pi$
$648$	6.87653	0.270136
$649$	3.73824	0.146739
$650$	−44.4715	−1.74432
$651$	−48.8344	−1.91397
$652$	2.84242	0.111318
$653$	−13.7811	−0.539297	−0.269649	−	0.962959i	$-0.586908\pi$
$653$	−13.7811	−0.539297	−0.269649	+	0.962959i	$0.586908\pi$
$654$	−50.3014	−1.96694
$655$	−50.2009	−1.96151
$656$	−7.56227	−0.295257
$657$	12.5218	0.488520
$658$	−54.4648	−2.12326
$659$	35.4063	1.37923	0.689617	−	0.724174i	$-0.257779\pi$
$659$	35.4063	1.37923	0.689617	+	0.724174i	$0.257779\pi$
$660$	−51.7061	−2.01266
$661$	−3.44990	−0.134186	−0.0670928	−	0.997747i	$-0.521372\pi$
$661$	−3.44990	−0.134186	−0.0670928	+	0.997747i	$0.521372\pi$
$662$	−34.2468	−1.33104
$663$	0.188789	0.00733198
$664$	23.7957	0.923452
$665$	33.6976	1.30674
$666$	−2.74191	−0.106247
$667$	14.6794	0.568390
$668$	29.4455	1.13928
$669$	−20.4416	−0.790320
$670$	−62.5009	−2.41462
$671$	16.9949	0.656080
$672$	40.9689	1.58041
$673$	−29.2129	−1.12608	−0.563038	−	0.826431i	$-0.690367\pi$
$673$	−29.2129	−1.12608	−0.563038	+	0.826431i	$0.690367\pi$
$674$	56.8511	2.18982
$675$	20.4979	0.788964
$676$	50.4182	1.93916
$677$	−41.6462	−1.60059	−0.800296	−	0.599605i	$-0.795324\pi$
$677$	−41.6462	−1.60059	−0.800296	+	0.599605i	$0.795324\pi$
$678$	30.7500	1.18095
$679$	29.2652	1.12310
$680$	−0.140145	−0.00537430
$681$	38.2289	1.46493
$682$	−88.7210	−3.39730
$683$	7.26397	0.277948	0.138974	−	0.990296i	$-0.455620\pi$
$683$	7.26397	0.277948	0.138974	+	0.990296i	$0.455620\pi$
$684$	−9.50063	−0.363266
$685$	7.15307	0.273305
$686$	39.9876	1.52673
$687$	−21.2132	−0.809333
$688$	13.9769	0.532864
$689$	25.0191	0.953154
$690$	−56.9638	−2.16858
$691$	−43.5495	−1.65670	−0.828351	−	0.560209i	$-0.810721\pi$
$691$	−43.5495	−1.65670	−0.828351	+	0.560209i	$0.810721\pi$
$692$	−69.0926	−2.62651
$693$	−24.8682	−0.944666
$694$	22.0444	0.836793
$695$	−31.2559	−1.18561
$696$	5.42147	0.205500
$697$	−0.121109	−0.00458733
$698$	20.3390	0.769844
$699$	34.1129	1.29027
$700$	−44.2664	−1.67311
$701$	−28.9863	−1.09480	−0.547398	−	0.836872i	$-0.684382\pi$
$701$	−28.9863	−1.09480	−0.547398	+	0.836872i	$0.684382\pi$
$702$	−68.6060	−2.58937
$703$	−2.68252	−0.101173
$704$	59.4313	2.23990
$705$	−22.5587	−0.849609
$706$	10.1401	0.381628
$707$	−48.1298	−1.81011
$708$	3.01242	0.113214
$709$	13.2705	0.498383	0.249191	−	0.968454i	$-0.419835\pi$
$709$	13.2705	0.498383	0.249191	+	0.968454i	$0.419835\pi$
$710$	−96.8053	−3.63304
$711$	13.5552	0.508358
$712$	21.1077	0.791046
$713$	−57.3733	−2.14865
$714$	0.320143	0.0119810
$715$	76.1510	2.84788
$716$	−51.5979	−1.92830
$717$	30.3002	1.13158
$718$	−57.8252	−2.15802
$719$	15.4779	0.577227	0.288614	−	0.957446i	$-0.406806\pi$
$719$	15.4779	0.577227	0.288614	+	0.957446i	$0.406806\pi$
$720$	−5.88181	−0.219202
$721$	78.3734	2.91878
$722$	25.9755	0.966710
$723$	28.8210	1.07187
$724$	24.3386	0.904538
$725$	8.04926	0.298942
$726$	31.5411	1.17060
$727$	−23.0827	−0.856090	−0.428045	−	0.903757i	$-0.640798\pi$
$727$	−23.0827	−0.856090	−0.428045	+	0.903757i	$0.640798\pi$
$728$	43.9105	1.62743
$729$	26.9644	0.998680
$730$	−65.0222	−2.40658
$731$	0.223839	0.00827897
$732$	13.6952	0.506188
$733$	31.7449	1.17253	0.586263	−	0.810121i	$-0.300599\pi$
$733$	31.7449	1.17253	0.586263	+	0.810121i	$0.300599\pi$
$734$	−54.5644	−2.01401
$735$	43.8206	1.61635
$736$	48.1324	1.77419
$737$	45.1255	1.66222
$738$	12.9152	0.475415
$739$	30.8262	1.13396	0.566981	−	0.823731i	$-0.308111\pi$
$739$	30.8262	1.13396	0.566981	+	0.823731i	$0.308111\pi$
$740$	8.35747	0.307227
$741$	−19.6966	−0.723574
$742$	42.4266	1.55753
$743$	−21.8132	−0.800249	−0.400125	−	0.916461i	$-0.631033\pi$
$743$	−21.8132	−0.800249	−0.400125	+	0.916461i	$0.631033\pi$
$744$	−21.1893	−0.776839
$745$	−61.7603	−2.26272
$746$	67.6509	2.47688
$747$	15.9940	0.585191
$748$	0.341405	0.0124830
$749$	−36.4582	−1.33216
$750$	11.6098	0.423930
$751$	9.23918	0.337142	0.168571	−	0.985689i	$-0.446085\pi$
$751$	9.23918	0.337142	0.168571	+	0.985689i	$0.446085\pi$
$752$	9.30075	0.339163
$753$	−6.16160	−0.224541
$754$	−26.9407	−0.981122
$755$	41.3097	1.50341
$756$	−68.2895	−2.48366
$757$	13.6481	0.496049	0.248024	−	0.968754i	$-0.420219\pi$
$757$	13.6481	0.496049	0.248024	+	0.968754i	$0.420219\pi$
$758$	46.3030	1.68180
$759$	41.1277	1.49284
$760$	14.6214	0.530375
$761$	38.8719	1.40911	0.704553	−	0.709652i	$-0.251148\pi$
$761$	38.8719	1.40911	0.704553	+	0.709652i	$0.251148\pi$
$762$	21.4579	0.777339
$763$	73.7404	2.66958
$764$	26.1263	0.945217
$765$	−0.0941967	−0.00340569
$766$	76.7675	2.77372
$767$	−4.43659	−0.160196
$768$	5.68897	0.205283
$769$	−8.73046	−0.314828	−0.157414	−	0.987533i	$-0.550316\pi$
$769$	−8.73046	−0.314828	−0.157414	+	0.987533i	$0.550316\pi$
$770$	129.134	4.65367
$771$	−4.96412	−0.178778
$772$	−2.09992	−0.0755779
$773$	5.64673	0.203099	0.101549	−	0.994830i	$-0.467620\pi$
$773$	5.64673	0.203099	0.101549	+	0.994830i	$0.467620\pi$
$774$	−23.8704	−0.858004
$775$	−31.4598	−1.13007
$776$	12.6982	0.455840
$777$	−5.65828	−0.202989
$778$	−24.7738	−0.888184
$779$	12.6355	0.452712
$780$	61.3655	2.19724
$781$	69.8932	2.50097
$782$	0.376121	0.0134501
$783$	12.4176	0.443767
$784$	−18.0669	−0.645245
$785$	28.9417	1.03297
$786$	49.7589	1.77484
$787$	36.7421	1.30971	0.654856	−	0.755753i	$-0.272729\pi$
$787$	36.7421	1.30971	0.654856	+	0.755753i	$0.272729\pi$
$788$	−46.9791	−1.67356
$789$	−0.200432	−0.00713557
$790$	−70.3883	−2.50430
$791$	−45.0786	−1.60281
$792$	−10.7904	−0.383419
$793$	−20.1698	−0.716250
$794$	67.5214	2.39624
$795$	17.5726	0.623236
$796$	−9.97860	−0.353682
$797$	35.9414	1.27311	0.636555	−	0.771231i	$-0.280359\pi$
$797$	35.9414	1.27311	0.636555	+	0.771231i	$0.280359\pi$
$798$	−33.4009	−1.18238
$799$	0.148951	0.00526949
$800$	26.3927	0.933124
$801$	14.1873	0.501285
$802$	−39.2007	−1.38422
$803$	46.9459	1.65668
$804$	36.3639	1.28246
$805$	83.5073	2.94325
$806$	105.295	3.70887
$807$	−32.0180	−1.12709
$808$	−20.8836	−0.734683
$809$	23.1271	0.813104	0.406552	−	0.913628i	$-0.366731\pi$
$809$	23.1271	0.813104	0.406552	+	0.913628i	$0.366731\pi$
$810$	−24.0008	−0.843301
$811$	29.9175	1.05055	0.525273	−	0.850934i	$-0.323963\pi$
$811$	29.9175	1.05055	0.525273	+	0.850934i	$0.323963\pi$
$812$	−26.8164	−0.941072
$813$	−14.7576	−0.517572
$814$	−10.2798	−0.360307
$815$	−2.94026	−0.102993
$816$	−0.0546696	−0.00191382
$817$	−23.3534	−0.817030
$818$	57.3662	2.00576
$819$	29.5140	1.03130
$820$	−39.3662	−1.37473
$821$	14.1731	0.494645	0.247323	−	0.968933i	$-0.420449\pi$
$821$	14.1731	0.494645	0.247323	+	0.968933i	$0.420449\pi$
$822$	−7.09008	−0.247295
$823$	−25.3692	−0.884315	−0.442157	−	0.896937i	$-0.645787\pi$
$823$	−25.3692	−0.884315	−0.442157	+	0.896937i	$0.645787\pi$
$824$	34.0064	1.18467
$825$	22.5518	0.785153
$826$	−7.52342	−0.261773
$827$	19.7643	0.687273	0.343636	−	0.939103i	$-0.388341\pi$
$827$	19.7643	0.687273	0.343636	+	0.939103i	$0.388341\pi$
$828$	−23.5439	−0.818206
$829$	−29.5423	−1.02605	−0.513023	−	0.858375i	$-0.671475\pi$
$829$	−29.5423	−1.02605	−0.513023	+	0.858375i	$0.671475\pi$
$830$	−83.0527	−2.88280
$831$	18.4071	0.638537
$832$	−70.5339	−2.44532
$833$	−0.289339	−0.0100250
$834$	30.9807	1.07277
$835$	−30.4590	−1.05408
$836$	−35.6192	−1.23192
$837$	−48.5329	−1.67754
$838$	66.7467	2.30573
$839$	−50.2913	−1.73625	−0.868124	−	0.496347i	$-0.834674\pi$
$839$	−50.2913	−1.73625	−0.868124	+	0.496347i	$0.834674\pi$
$840$	30.8413	1.06412
$841$	−24.1238	−0.831855
$842$	−2.35987	−0.0813265
$843$	−25.6955	−0.884999
$844$	34.1115	1.17417
$845$	−52.1536	−1.79414
$846$	−15.8843	−0.546112
$847$	−46.2383	−1.58877
$848$	−7.24503	−0.248795
$849$	13.2571	0.454984
$850$	0.206241	0.00707399
$851$	−6.64765	−0.227878
$852$	56.3228	1.92959
$853$	−36.5964	−1.25304	−0.626519	−	0.779406i	$-0.715521\pi$
$853$	−36.5964	−1.25304	−0.626519	+	0.779406i	$0.715521\pi$
$854$	−34.2032	−1.17041
$855$	9.82765	0.336099
$856$	−15.8193	−0.540692
$857$	18.3118	0.625520	0.312760	−	0.949832i	$-0.398746\pi$
$857$	18.3118	0.625520	0.312760	+	0.949832i	$0.398746\pi$
$858$	−75.4804	−2.57686
$859$	−14.2640	−0.486681	−0.243341	−	0.969941i	$-0.578243\pi$
$859$	−14.2640	−0.486681	−0.243341	+	0.969941i	$0.578243\pi$
$860$	72.7582	2.48103
$861$	26.6522	0.908304
$862$	57.6115	1.96226
$863$	7.51358	0.255765	0.127883	−	0.991789i	$-0.459182\pi$
$863$	7.51358	0.255765	0.127883	+	0.991789i	$0.459182\pi$
$864$	40.7159	1.38518
$865$	71.4709	2.43008
$866$	−6.97963	−0.237178
$867$	22.5136	0.764603
$868$	104.810	3.55747
$869$	50.8202	1.72396
$870$	−18.9222	−0.641524
$871$	−53.5556	−1.81466
$872$	31.9961	1.08352
$873$	8.53498	0.288865
$874$	−39.2411	−1.32735
$875$	−17.0196	−0.575369
$876$	37.8309	1.27819
$877$	−7.85275	−0.265169	−0.132584	−	0.991172i	$-0.542328\pi$
$877$	−7.85275	−0.265169	−0.132584	+	0.991172i	$0.542328\pi$
$878$	19.7270	0.665754
$879$	24.2591	0.818239
$880$	−22.0518	−0.743364
$881$	−4.72470	−0.159179	−0.0795897	−	0.996828i	$-0.525361\pi$
$881$	−4.72470	−0.159179	−0.0795897	+	0.996828i	$0.525361\pi$
$882$	30.8554	1.03896
$883$	−4.44832	−0.149698	−0.0748490	−	0.997195i	$-0.523847\pi$
$883$	−4.44832	−0.149698	−0.0748490	+	0.997195i	$0.523847\pi$
$884$	−0.405185	−0.0136278
$885$	−3.11611	−0.104747
$886$	30.4038	1.02144
$887$	−2.32136	−0.0779435	−0.0389718	−	0.999240i	$-0.512408\pi$
$887$	−2.32136	−0.0779435	−0.0389718	+	0.999240i	$0.512408\pi$
$888$	−2.45514	−0.0823890
$889$	−31.4567	−1.05502
$890$	−73.6711	−2.46946
$891$	17.3285	0.580526
$892$	43.8724	1.46895
$893$	−15.5402	−0.520033
$894$	61.2165	2.04739
$895$	53.3739	1.78409
$896$	−57.7403	−1.92897
$897$	−48.8110	−1.62975
$898$	29.1618	0.973141
$899$	−19.0583	−0.635629
$900$	−12.9100	−0.430332
$901$	−0.116028	−0.00386547
$902$	48.4209	1.61224
$903$	−49.2596	−1.63926
$904$	−19.5597	−0.650545
$905$	−25.1764	−0.836891
$906$	−40.9460	−1.36034
$907$	−45.6373	−1.51536	−0.757681	−	0.652625i	$-0.773668\pi$
$907$	−45.6373	−1.51536	−0.757681	+	0.652625i	$0.773668\pi$
$908$	−82.0477	−2.72285
$909$	−14.0367	−0.465568
$910$	−153.258	−5.08046
$911$	17.8228	0.590495	0.295248	−	0.955421i	$-0.404598\pi$
$911$	17.8228	0.590495	0.295248	+	0.955421i	$0.404598\pi$
$912$	5.70374	0.188870
$913$	59.9639	1.98451
$914$	1.01500	0.0335731
$915$	−14.1666	−0.468332
$916$	45.5282	1.50429
$917$	−72.9451	−2.40886
$918$	0.318166	0.0105011
$919$	24.3023	0.801658	0.400829	−	0.916153i	$-0.368722\pi$
$919$	24.3023	0.801658	0.400829	+	0.916153i	$0.368722\pi$
$920$	36.2340	1.19460
$921$	−1.57606	−0.0519328
$922$	−9.89214	−0.325780
$923$	−82.9502	−2.73034
$924$	−75.1322	−2.47167
$925$	−3.64514	−0.119852
$926$	20.3267	0.667975
$927$	22.8570	0.750723
$928$	15.9886	0.524853
$929$	4.45540	0.146177	0.0730885	−	0.997325i	$-0.476714\pi$
$929$	4.45540	0.146177	0.0730885	+	0.997325i	$0.476714\pi$
$930$	73.9559	2.42511
$931$	30.1871	0.989342
$932$	−73.2140	−2.39820
$933$	35.9486	1.17690
$934$	41.7120	1.36486
$935$	−0.353157	−0.0115495
$936$	12.8062	0.418583
$937$	−43.6743	−1.42678	−0.713389	−	0.700768i	$-0.752841\pi$
$937$	−43.6743	−1.42678	−0.713389	+	0.700768i	$0.752841\pi$
$938$	−90.8177	−2.96530
$939$	−33.2125	−1.08385
$940$	48.4160	1.57916
$941$	−39.0072	−1.27160	−0.635799	−	0.771855i	$-0.719329\pi$
$941$	−39.0072	−1.27160	−0.635799	+	0.771855i	$0.719329\pi$
$942$	−28.6868	−0.934667
$943$	31.3124	1.01967
$944$	1.28475	0.0418149
$945$	70.6401	2.29792
$946$	−89.4935	−2.90969
$947$	31.7451	1.03158	0.515788	−	0.856716i	$-0.327499\pi$
$947$	31.7451	1.03158	0.515788	+	0.856716i	$0.327499\pi$
$948$	40.9530	1.33009
$949$	−55.7160	−1.80862
$950$	−21.5173	−0.698114
$951$	−27.7284	−0.899156
$952$	−0.203639	−0.00659997
$953$	58.9315	1.90898	0.954489	−	0.298246i	$-0.0964016\pi$
$953$	58.9315	1.90898	0.954489	+	0.298246i	$0.0964016\pi$
$954$	12.3734	0.400604
$955$	−27.0256	−0.874528
$956$	−65.0310	−2.10325
$957$	13.6618	0.441624
$958$	43.8180	1.41570
$959$	10.3939	0.335635
$960$	−49.5406	−1.59892
$961$	43.4876	1.40283
$962$	12.2002	0.393351
$963$	−10.6328	−0.342636
$964$	−61.8564	−1.99226
$965$	2.17221	0.0699258
$966$	−82.7720	−2.66315
$967$	−20.9148	−0.672574	−0.336287	−	0.941760i	$-0.609171\pi$
$967$	−20.9148	−0.672574	−0.336287	+	0.941760i	$0.609171\pi$
$968$	−20.0629	−0.644846
$969$	0.0913449	0.00293442
$970$	−44.3199	−1.42303
$971$	−59.5684	−1.91164	−0.955821	−	0.293949i	$-0.905030\pi$
$971$	−59.5684	−1.91164	−0.955821	+	0.293949i	$0.905030\pi$
$972$	−33.9878	−1.09016
$973$	−45.4168	−1.45600
$974$	−20.5952	−0.659912
$975$	−26.7648	−0.857160
$976$	5.84075	0.186958
$977$	19.7104	0.630591	0.315295	−	0.948994i	$-0.397896\pi$
$977$	19.7104	0.630591	0.315295	+	0.948994i	$0.397896\pi$
$978$	2.91437	0.0931913
$979$	53.1904	1.69997
$980$	−94.0489	−3.00428
$981$	21.5058	0.686628
$982$	5.33581	0.170272
$983$	23.3003	0.743165	0.371583	−	0.928400i	$-0.378815\pi$
$983$	23.3003	0.743165	0.371583	+	0.928400i	$0.378815\pi$
$984$	11.5644	0.368660
$985$	48.5962	1.54840
$986$	0.124940	0.00397890
$987$	−32.7792	−1.04337
$988$	42.2734	1.34490
$989$	−57.8729	−1.84025
$990$	37.6610	1.19695
$991$	26.1874	0.831870	0.415935	−	0.909394i	$-0.363454\pi$
$991$	26.1874	0.831870	0.415935	+	0.909394i	$0.363454\pi$
$992$	−62.4902	−1.98407
$993$	−20.6111	−0.654075
$994$	−140.664	−4.46159
$995$	10.3221	0.327232
$996$	48.3213	1.53112
$997$	−20.1612	−0.638513	−0.319257	−	0.947668i	$-0.603433\pi$
$997$	−20.1612	−0.638513	−0.319257	+	0.947668i	$0.603433\pi$
$998$	58.9456	1.86589
$999$	−5.62334	−0.177915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.20	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.20055 q^{2} -1.32438 q^{3} +2.84242 q^{4} -2.94026 q^{5} +2.91437 q^{6} -4.27239 q^{7} -1.85380 q^{8} -1.24601 q^{9} +O(q^{10})\)	\(q-2.20055 q^{2} -1.32438 q^{3} +2.84242 q^{4} -2.94026 q^{5} +2.91437 q^{6} -4.27239 q^{7} -1.85380 q^{8} -1.24601 q^{9} +6.47020 q^{10} -4.67147 q^{11} -3.76446 q^{12} +5.54416 q^{13} +9.40160 q^{14} +3.89403 q^{15} -1.60548 q^{16} -0.0257115 q^{17} +2.74191 q^{18} +2.68252 q^{19} -8.35747 q^{20} +5.65828 q^{21} +10.2798 q^{22} +6.64765 q^{23} +2.45514 q^{24} +3.64514 q^{25} -12.2002 q^{26} +5.62334 q^{27} -12.1439 q^{28} +2.20822 q^{29} -8.56902 q^{30} -8.63062 q^{31} +7.24052 q^{32} +6.18681 q^{33} +0.0565796 q^{34} +12.5619 q^{35} -3.54169 q^{36} -1.00000 q^{37} -5.90301 q^{38} -7.34260 q^{39} +5.45065 q^{40} +4.71030 q^{41} -12.4513 q^{42} -8.70576 q^{43} -13.2783 q^{44} +3.66359 q^{45} -14.6285 q^{46} -5.79314 q^{47} +2.12626 q^{48} +11.2533 q^{49} -8.02132 q^{50} +0.0340519 q^{51} +15.7589 q^{52} +4.51270 q^{53} -12.3745 q^{54} +13.7353 q^{55} +7.92013 q^{56} -3.55268 q^{57} -4.85929 q^{58} -0.800227 q^{59} +11.0685 q^{60} -3.63802 q^{61} +18.9921 q^{62} +5.32343 q^{63} -12.7222 q^{64} -16.3013 q^{65} -13.6144 q^{66} -9.65981 q^{67} -0.0730831 q^{68} -8.80403 q^{69} -27.6432 q^{70} -14.9617 q^{71} +2.30985 q^{72} -10.0495 q^{73} +2.20055 q^{74} -4.82757 q^{75} +7.62485 q^{76} +19.9583 q^{77} +16.1578 q^{78} -10.8789 q^{79} +4.72052 q^{80} -3.70943 q^{81} -10.3653 q^{82} -12.8362 q^{83} +16.0832 q^{84} +0.0755987 q^{85} +19.1575 q^{86} -2.92452 q^{87} +8.65994 q^{88} -11.3862 q^{89} -8.06193 q^{90} -23.6868 q^{91} +18.8954 q^{92} +11.4302 q^{93} +12.7481 q^{94} -7.88730 q^{95} -9.58923 q^{96} -6.84985 q^{97} -24.7634 q^{98} +5.82069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 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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