LMFDB - Embedded newform 6031.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58445 q^{2} +2.91776 q^{3} +4.67939 q^{4} +3.62109 q^{5} -7.54082 q^{6} +1.31660 q^{7} -6.92475 q^{8} +5.51335 q^{9} +O(q^{10})$	\(q-2.58445 q^{2} +2.91776 q^{3} +4.67939 q^{4} +3.62109 q^{5} -7.54082 q^{6} +1.31660 q^{7} -6.92475 q^{8} +5.51335 q^{9} -9.35852 q^{10} -1.80609 q^{11} +13.6534 q^{12} +0.943093 q^{13} -3.40270 q^{14} +10.5655 q^{15} +8.53790 q^{16} +7.39596 q^{17} -14.2490 q^{18} +0.202791 q^{19} +16.9445 q^{20} +3.84154 q^{21} +4.66776 q^{22} -7.05323 q^{23} -20.2048 q^{24} +8.11227 q^{25} -2.43738 q^{26} +7.33336 q^{27} +6.16090 q^{28} +2.41670 q^{29} -27.3060 q^{30} +2.60666 q^{31} -8.21628 q^{32} -5.26976 q^{33} -19.1145 q^{34} +4.76753 q^{35} +25.7991 q^{36} -1.00000 q^{37} -0.524103 q^{38} +2.75172 q^{39} -25.0751 q^{40} +6.74242 q^{41} -9.92826 q^{42} +7.86203 q^{43} -8.45141 q^{44} +19.9643 q^{45} +18.2287 q^{46} +12.3621 q^{47} +24.9116 q^{48} -5.26656 q^{49} -20.9658 q^{50} +21.5797 q^{51} +4.41310 q^{52} +11.8592 q^{53} -18.9527 q^{54} -6.54002 q^{55} -9.11714 q^{56} +0.591696 q^{57} -6.24585 q^{58} -9.96109 q^{59} +49.4400 q^{60} -4.89839 q^{61} -6.73679 q^{62} +7.25889 q^{63} +4.15879 q^{64} +3.41502 q^{65} +13.6194 q^{66} -7.41467 q^{67} +34.6086 q^{68} -20.5797 q^{69} -12.3215 q^{70} -14.3751 q^{71} -38.1786 q^{72} -11.3261 q^{73} +2.58445 q^{74} +23.6697 q^{75} +0.948938 q^{76} -2.37791 q^{77} -7.11169 q^{78} +15.6886 q^{79} +30.9165 q^{80} +4.85697 q^{81} -17.4255 q^{82} -12.2577 q^{83} +17.9760 q^{84} +26.7814 q^{85} -20.3190 q^{86} +7.05137 q^{87} +12.5067 q^{88} -13.7550 q^{89} -51.5968 q^{90} +1.24168 q^{91} -33.0048 q^{92} +7.60563 q^{93} -31.9493 q^{94} +0.734324 q^{95} -23.9732 q^{96} -14.2318 q^{97} +13.6112 q^{98} -9.95762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58445	−1.82748	−0.913741	−	0.406296i	$-0.866820\pi$
$2$	−2.58445	−1.82748	−0.913741	+	0.406296i	$0.866820\pi$
$3$	2.91776	1.68457	0.842286	−	0.539031i	$-0.181209\pi$
$3$	2.91776	1.68457	0.842286	+	0.539031i	$0.181209\pi$
$4$	4.67939	2.33969
$5$	3.62109	1.61940	0.809700	−	0.586844i	$-0.199630\pi$
$5$	3.62109	1.61940	0.809700	+	0.586844i	$0.199630\pi$
$6$	−7.54082	−3.07853
$7$	1.31660	0.497629	0.248815	−	0.968551i	$-0.419959\pi$
$7$	1.31660	0.497629	0.248815	+	0.968551i	$0.419959\pi$
$8$	−6.92475	−2.44827
$9$	5.51335	1.83778
$10$	−9.35852	−2.95943
$11$	−1.80609	−0.544558	−0.272279	−	0.962218i	$-0.587777\pi$
$11$	−1.80609	−0.544558	−0.272279	+	0.962218i	$0.587777\pi$
$12$	13.6534	3.94138
$13$	0.943093	0.261567	0.130783	−	0.991411i	$-0.458251\pi$
$13$	0.943093	0.261567	0.130783	+	0.991411i	$0.458251\pi$
$14$	−3.40270	−0.909409
$15$	10.5655	2.72800
$16$	8.53790	2.13447
$17$	7.39596	1.79378	0.896892	−	0.442249i	$-0.145819\pi$
$17$	7.39596	1.79378	0.896892	+	0.442249i	$0.145819\pi$
$18$	−14.2490	−3.35852
$19$	0.202791	0.0465234	0.0232617	−	0.999729i	$-0.492595\pi$
$19$	0.202791	0.0465234	0.0232617	+	0.999729i	$0.492595\pi$
$20$	16.9445	3.78890
$21$	3.84154	0.838292
$22$	4.66776	0.995170
$23$	−7.05323	−1.47070	−0.735350	−	0.677688i	$-0.762982\pi$
$23$	−7.05323	−1.47070	−0.735350	+	0.677688i	$0.762982\pi$
$24$	−20.2048	−4.12428
$25$	8.11227	1.62245
$26$	−2.43738	−0.478009
$27$	7.33336	1.41131
$28$	6.16090	1.16430
$29$	2.41670	0.448770	0.224385	−	0.974501i	$-0.427963\pi$
$29$	2.41670	0.448770	0.224385	+	0.974501i	$0.427963\pi$
$30$	−27.3060	−4.98536
$31$	2.60666	0.468171	0.234085	−	0.972216i	$-0.424791\pi$
$31$	2.60666	0.468171	0.234085	+	0.972216i	$0.424791\pi$
$32$	−8.21628	−1.45245
$33$	−5.26976	−0.917347
$34$	−19.1145	−3.27811
$35$	4.76753	0.805860
$36$	25.7991	4.29985
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−0.524103	−0.0850208
$39$	2.75172	0.440628
$40$	−25.0751	−3.96472
$41$	6.74242	1.05299	0.526495	−	0.850178i	$-0.323506\pi$
$41$	6.74242	1.05299	0.526495	+	0.850178i	$0.323506\pi$
$42$	−9.92826	−1.53196
$43$	7.86203	1.19895	0.599474	−	0.800394i	$-0.295376\pi$
$43$	7.86203	1.19895	0.599474	+	0.800394i	$0.295376\pi$
$44$	−8.45141	−1.27410
$45$	19.9643	2.97610
$46$	18.2287	2.68768
$47$	12.3621	1.80320	0.901601	−	0.432568i	$-0.142393\pi$
$47$	12.3621	1.80320	0.901601	+	0.432568i	$0.142393\pi$
$48$	24.9116	3.59568
$49$	−5.26656	−0.752365
$50$	−20.9658	−2.96501
$51$	21.5797	3.02176
$52$	4.41310	0.611986
$53$	11.8592	1.62899	0.814493	−	0.580174i	$-0.197015\pi$
$53$	11.8592	1.62899	0.814493	+	0.580174i	$0.197015\pi$
$54$	−18.9527	−2.57914
$55$	−6.54002	−0.881856
$56$	−9.11714	−1.21833
$57$	0.591696	0.0783721
$58$	−6.24585	−0.820120
$59$	−9.96109	−1.29682	−0.648411	−	0.761290i	$-0.724566\pi$
$59$	−9.96109	−1.29682	−0.648411	+	0.761290i	$0.724566\pi$
$60$	49.4400	6.38267
$61$	−4.89839	−0.627175	−0.313587	−	0.949559i	$-0.601531\pi$
$61$	−4.89839	−0.627175	−0.313587	+	0.949559i	$0.601531\pi$
$62$	−6.73679	−0.855574
$63$	7.25889	0.914534
$64$	4.15879	0.519848
$65$	3.41502	0.423581
$66$	13.6194	1.67644
$67$	−7.41467	−0.905847	−0.452923	−	0.891549i	$-0.649619\pi$
$67$	−7.41467	−0.905847	−0.452923	+	0.891549i	$0.649619\pi$
$68$	34.6086	4.19691
$69$	−20.5797	−2.47750
$70$	−12.3215	−1.47270
$71$	−14.3751	−1.70601	−0.853003	−	0.521907i	$-0.825221\pi$
$71$	−14.3751	−1.70601	−0.853003	+	0.521907i	$0.825221\pi$
$72$	−38.1786	−4.49939
$73$	−11.3261	−1.32562	−0.662811	−	0.748787i	$-0.730637\pi$
$73$	−11.3261	−1.32562	−0.662811	+	0.748787i	$0.730637\pi$
$74$	2.58445	0.300436
$75$	23.6697	2.73314
$76$	0.948938	0.108851
$77$	−2.37791	−0.270988
$78$	−7.11169	−0.805241
$79$	15.6886	1.76510	0.882551	−	0.470216i	$-0.155824\pi$
$79$	15.6886	1.76510	0.882551	+	0.470216i	$0.155824\pi$
$80$	30.9165	3.45657
$81$	4.85697	0.539663
$82$	−17.4255	−1.92432
$83$	−12.2577	−1.34546	−0.672731	−	0.739887i	$-0.734879\pi$
$83$	−12.2577	−1.34546	−0.672731	+	0.739887i	$0.734879\pi$
$84$	17.9760	1.96135
$85$	26.7814	2.90485
$86$	−20.3190	−2.19106
$87$	7.05137	0.755986
$88$	12.5067	1.33322
$89$	−13.7550	−1.45802	−0.729012	−	0.684501i	$-0.760020\pi$
$89$	−13.7550	−1.45802	−0.729012	+	0.684501i	$0.760020\pi$
$90$	−51.5968	−5.43878
$91$	1.24168	0.130163
$92$	−33.0048	−3.44099
$93$	7.60563	0.788667
$94$	−31.9493	−3.29532
$95$	0.734324	0.0753400
$96$	−23.9732	−2.44675
$97$	−14.2318	−1.44502	−0.722512	−	0.691359i	$-0.757012\pi$
$97$	−14.2318	−1.44502	−0.722512	+	0.691359i	$0.757012\pi$
$98$	13.6112	1.37493
$99$	−9.95762	−1.00078
$100$	37.9605	3.79605
$101$	0.282074	0.0280674	0.0140337	−	0.999902i	$-0.495533\pi$
$101$	0.282074	0.0280674	0.0140337	+	0.999902i	$0.495533\pi$
$102$	−55.7716	−5.52221
$103$	1.37418	0.135402	0.0677008	−	0.997706i	$-0.478434\pi$
$103$	1.37418	0.135402	0.0677008	+	0.997706i	$0.478434\pi$
$104$	−6.53068	−0.640386
$105$	13.9105	1.35753
$106$	−30.6495	−2.97694
$107$	−17.2785	−1.67037	−0.835185	−	0.549968i	$-0.814640\pi$
$107$	−17.2785	−1.67037	−0.835185	+	0.549968i	$0.814640\pi$
$108$	34.3156	3.30202
$109$	−14.6567	−1.40386	−0.701930	−	0.712246i	$-0.747678\pi$
$109$	−14.6567	−1.40386	−0.701930	+	0.712246i	$0.747678\pi$
$110$	16.9024	1.61158
$111$	−2.91776	−0.276942
$112$	11.2410	1.06218
$113$	17.3516	1.63230	0.816151	−	0.577838i	$-0.196104\pi$
$113$	17.3516	1.63230	0.816151	+	0.577838i	$0.196104\pi$
$114$	−1.52921	−0.143224
$115$	−25.5403	−2.38165
$116$	11.3087	1.04999
$117$	5.19960	0.480703
$118$	25.7439	2.36992
$119$	9.73754	0.892639
$120$	−73.1633	−6.67886
$121$	−7.73803	−0.703457
$122$	12.6597	1.14615
$123$	19.6728	1.77384
$124$	12.1976	1.09538
$125$	11.2698	1.00800
$126$	−18.7602	−1.67130
$127$	4.22559	0.374960	0.187480	−	0.982268i	$-0.439968\pi$
$127$	4.22559	0.374960	0.187480	+	0.982268i	$0.439968\pi$
$128$	5.68438	0.502433
$129$	22.9395	2.01971
$130$	−8.82596	−0.774088
$131$	8.70414	0.760485	0.380242	−	0.924887i	$-0.375841\pi$
$131$	8.70414	0.760485	0.380242	+	0.924887i	$0.375841\pi$
$132$	−24.6592	−2.14631
$133$	0.266995	0.0231514
$134$	19.1629	1.65542
$135$	26.5547	2.28547
$136$	−51.2152	−4.39166
$137$	13.5842	1.16058	0.580290	−	0.814410i	$-0.302939\pi$
$137$	13.5842	1.16058	0.580290	+	0.814410i	$0.302939\pi$
$138$	53.1871	4.52759
$139$	5.43183	0.460722	0.230361	−	0.973105i	$-0.426009\pi$
$139$	5.43183	0.460722	0.230361	+	0.973105i	$0.426009\pi$
$140$	22.3091	1.88547
$141$	36.0698	3.03762
$142$	37.1516	3.11770
$143$	−1.70331	−0.142438
$144$	47.0724	3.92270
$145$	8.75109	0.726739
$146$	29.2718	2.42255
$147$	−15.3666	−1.26741
$148$	−4.67939	−0.384643
$149$	−5.78497	−0.473923	−0.236961	−	0.971519i	$-0.576152\pi$
$149$	−5.78497	−0.473923	−0.236961	+	0.971519i	$0.576152\pi$
$150$	−61.1732	−4.99477
$151$	11.2624	0.916525	0.458262	−	0.888817i	$-0.348472\pi$
$151$	11.2624	0.916525	0.458262	+	0.888817i	$0.348472\pi$
$152$	−1.40428	−0.113902
$153$	40.7765	3.29659
$154$	6.14559	0.495225
$155$	9.43895	0.758155
$156$	12.8764	1.03094
$157$	−17.2892	−1.37982	−0.689912	−	0.723893i	$-0.742351\pi$
$157$	−17.2892	−1.37982	−0.689912	+	0.723893i	$0.742351\pi$
$158$	−40.5464	−3.22570
$159$	34.6023	2.74414
$160$	−29.7519	−2.35209
$161$	−9.28630	−0.731863
$162$	−12.5526	−0.986225
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	31.5504	2.46367
$165$	−19.0822	−1.48555
$166$	31.6795	2.45881
$167$	−5.19498	−0.401999	−0.201000	−	0.979591i	$-0.564419\pi$
$167$	−5.19498	−0.401999	−0.201000	+	0.979591i	$0.564419\pi$
$168$	−26.6017	−2.05236
$169$	−12.1106	−0.931583
$170$	−69.2153	−5.30857
$171$	1.11806	0.0855000
$172$	36.7895	2.80517
$173$	−10.4075	−0.791270	−0.395635	−	0.918408i	$-0.629476\pi$
$173$	−10.4075	−0.791270	−0.395635	+	0.918408i	$0.629476\pi$
$174$	−18.2239	−1.38155
$175$	10.6806	0.807381
$176$	−15.4202	−1.16234
$177$	−29.0641	−2.18459
$178$	35.5491	2.66451
$179$	3.37968	0.252609	0.126305	−	0.991992i	$-0.459688\pi$
$179$	3.37968	0.252609	0.126305	+	0.991992i	$0.459688\pi$
$180$	93.4208	6.96317
$181$	0.450321	0.0334721	0.0167361	−	0.999860i	$-0.494672\pi$
$181$	0.450321	0.0334721	0.0167361	+	0.999860i	$0.494672\pi$
$182$	−3.20906	−0.237871
$183$	−14.2924	−1.05652
$184$	48.8418	3.60067
$185$	−3.62109	−0.266228
$186$	−19.6564	−1.44128
$187$	−13.3578	−0.976819
$188$	57.8472	4.21894
$189$	9.65512	0.702307
$190$	−1.89782	−0.137683
$191$	−3.57695	−0.258819	−0.129410	−	0.991591i	$-0.541308\pi$
$191$	−3.57695	−0.258819	−0.129410	+	0.991591i	$0.541308\pi$
$192$	12.1344	0.875722
$193$	9.74379	0.701374	0.350687	−	0.936493i	$-0.385948\pi$
$193$	9.74379	0.701374	0.350687	+	0.936493i	$0.385948\pi$
$194$	36.7815	2.64076
$195$	9.96423	0.713553
$196$	−24.6443	−1.76030
$197$	26.4071	1.88143	0.940715	−	0.339198i	$-0.110156\pi$
$197$	26.4071	1.88143	0.940715	+	0.339198i	$0.110156\pi$
$198$	25.7350	1.82891
$199$	−21.4688	−1.52188	−0.760942	−	0.648820i	$-0.775263\pi$
$199$	−21.4688	−1.52188	−0.760942	+	0.648820i	$0.775263\pi$
$200$	−56.1754	−3.97220
$201$	−21.6343	−1.52596
$202$	−0.729007	−0.0512927
$203$	3.18184	0.223321
$204$	100.980	7.06999
$205$	24.4149	1.70521
$206$	−3.55149	−0.247444
$207$	−38.8869	−2.70283
$208$	8.05203	0.558308
$209$	−0.366260	−0.0253347
$210$	−35.9511	−2.48086
$211$	−5.89314	−0.405701	−0.202850	−	0.979210i	$-0.565020\pi$
$211$	−5.89314	−0.405701	−0.202850	+	0.979210i	$0.565020\pi$
$212$	55.4938	3.81133
$213$	−41.9430	−2.87389
$214$	44.6553	3.05257
$215$	28.4691	1.94158
$216$	−50.7817	−3.45525
$217$	3.43194	0.232975
$218$	37.8796	2.56553
$219$	−33.0470	−2.23311
$220$	−30.6033	−2.06327
$221$	6.97508	0.469195
$222$	7.54082	0.506107
$223$	−2.03909	−0.136548	−0.0682738	−	0.997667i	$-0.521749\pi$
$223$	−2.03909	−0.136548	−0.0682738	+	0.997667i	$0.521749\pi$
$224$	−10.8176	−0.722780
$225$	44.7258	2.98172
$226$	−44.8444	−2.98300
$227$	−6.38094	−0.423518	−0.211759	−	0.977322i	$-0.567919\pi$
$227$	−6.38094	−0.423518	−0.211759	+	0.977322i	$0.567919\pi$
$228$	2.76878	0.183367
$229$	−8.82679	−0.583291	−0.291645	−	0.956527i	$-0.594203\pi$
$229$	−8.82679	−0.583291	−0.291645	+	0.956527i	$0.594203\pi$
$230$	66.0078	4.35242
$231$	−6.93817	−0.456498
$232$	−16.7351	−1.09871
$233$	4.50807	0.295334	0.147667	−	0.989037i	$-0.452824\pi$
$233$	4.50807	0.295334	0.147667	+	0.989037i	$0.452824\pi$
$234$	−13.4381	−0.878477
$235$	44.7644	2.92011
$236$	−46.6118	−3.03417
$237$	45.7756	2.97344
$238$	−25.1662	−1.63128
$239$	17.4181	1.12668	0.563340	−	0.826225i	$-0.309516\pi$
$239$	17.4181	1.12668	0.563340	+	0.826225i	$0.309516\pi$
$240$	90.2070	5.82284
$241$	8.13346	0.523922	0.261961	−	0.965078i	$-0.415631\pi$
$241$	8.13346	0.523922	0.261961	+	0.965078i	$0.415631\pi$
$242$	19.9986	1.28556
$243$	−7.82859	−0.502204
$244$	−22.9215	−1.46740
$245$	−19.0707	−1.21838
$246$	−50.8434	−3.24166
$247$	0.191251	0.0121690
$248$	−18.0505	−1.14621
$249$	−35.7652	−2.26653
$250$	−29.1263	−1.84211
$251$	17.3342	1.09413	0.547063	−	0.837092i	$-0.315746\pi$
$251$	17.3342	1.09413	0.547063	+	0.837092i	$0.315746\pi$
$252$	33.9672	2.13973
$253$	12.7388	0.800881
$254$	−10.9208	−0.685234
$255$	78.1419	4.89343
$256$	−23.0086	−1.43804
$257$	7.98510	0.498097	0.249048	−	0.968491i	$-0.419882\pi$
$257$	7.98510	0.498097	0.249048	+	0.968491i	$0.419882\pi$
$258$	−59.2861	−3.69099
$259$	−1.31660	−0.0818097
$260$	15.9802	0.991051
$261$	13.3241	0.824743
$262$	−22.4954	−1.38977
$263$	−13.4299	−0.828120	−0.414060	−	0.910249i	$-0.635890\pi$
$263$	−13.4299	−0.828120	−0.414060	+	0.910249i	$0.635890\pi$
$264$	36.4917	2.24591
$265$	42.9432	2.63798
$266$	−0.690036	−0.0423088
$267$	−40.1338	−2.45615
$268$	−34.6961	−2.11940
$269$	23.8439	1.45379	0.726893	−	0.686751i	$-0.240964\pi$
$269$	23.8439	1.45379	0.726893	+	0.686751i	$0.240964\pi$
$270$	−68.6294	−4.17665
$271$	−1.81973	−0.110541	−0.0552703	−	0.998471i	$-0.517602\pi$
$271$	−1.81973	−0.110541	−0.0552703	+	0.998471i	$0.517602\pi$
$272$	63.1460	3.82879
$273$	3.62293	0.219269
$274$	−35.1078	−2.12094
$275$	−14.6515	−0.883520
$276$	−96.3002	−5.79659
$277$	5.32602	0.320010	0.160005	−	0.987116i	$-0.448849\pi$
$277$	5.32602	0.320010	0.160005	+	0.987116i	$0.448849\pi$
$278$	−14.0383	−0.841961
$279$	14.3714	0.860396
$280$	−33.0140	−1.97296
$281$	10.6870	0.637532	0.318766	−	0.947833i	$-0.396732\pi$
$281$	10.6870	0.637532	0.318766	+	0.947833i	$0.396732\pi$
$282$	−93.2206	−5.55121
$283$	−7.60395	−0.452008	−0.226004	−	0.974126i	$-0.572566\pi$
$283$	−7.60395	−0.452008	−0.226004	+	0.974126i	$0.572566\pi$
$284$	−67.2665	−3.99153
$285$	2.14258	0.126916
$286$	4.40213	0.260303
$287$	8.87709	0.523998
$288$	−45.2992	−2.66928
$289$	37.7003	2.21766
$290$	−22.6168	−1.32810
$291$	−41.5251	−2.43425
$292$	−52.9993	−3.10155
$293$	−1.33773	−0.0781512	−0.0390756	−	0.999236i	$-0.512441\pi$
$293$	−1.33773	−0.0781512	−0.0390756	+	0.999236i	$0.512441\pi$
$294$	39.7142	2.31618
$295$	−36.0700	−2.10007
$296$	6.92475	0.402493
$297$	−13.2447	−0.768537
$298$	14.9510	0.866086
$299$	−6.65185	−0.384686
$300$	110.760	6.39472
$301$	10.3512	0.596631
$302$	−29.1072	−1.67493
$303$	0.823026	0.0472816
$304$	1.73141	0.0993031
$305$	−17.7375	−1.01565
$306$	−105.385	−6.02445
$307$	7.36800	0.420514	0.210257	−	0.977646i	$-0.432570\pi$
$307$	7.36800	0.420514	0.210257	+	0.977646i	$0.432570\pi$
$308$	−11.1272	−0.634028
$309$	4.00952	0.228094
$310$	−24.3945	−1.38552
$311$	30.5618	1.73300	0.866501	−	0.499175i	$-0.166363\pi$
$311$	30.5618	1.73300	0.866501	+	0.499175i	$0.166363\pi$
$312$	−19.0550	−1.07878
$313$	6.02230	0.340400	0.170200	−	0.985410i	$-0.445559\pi$
$313$	6.02230	0.340400	0.170200	+	0.985410i	$0.445559\pi$
$314$	44.6830	2.52161
$315$	26.2851	1.48100
$316$	73.4129	4.12980
$317$	−11.3592	−0.637995	−0.318998	−	0.947756i	$-0.603346\pi$
$317$	−11.3592	−0.637995	−0.318998	+	0.947756i	$0.603346\pi$
$318$	−89.4281	−5.01488
$319$	−4.36479	−0.244381
$320$	15.0593	0.841842
$321$	−50.4144	−2.81386
$322$	24.0000	1.33747
$323$	1.49983	0.0834530
$324$	22.7276	1.26265
$325$	7.65063	0.424380
$326$	−2.58445	−0.143140
$327$	−42.7649	−2.36490
$328$	−46.6896	−2.57800
$329$	16.2760	0.897326
$330$	49.3171	2.71482
$331$	12.9173	0.710000	0.355000	−	0.934866i	$-0.384481\pi$
$331$	12.9173	0.710000	0.355000	+	0.934866i	$0.384481\pi$
$332$	−57.3587	−3.14797
$333$	−5.51335	−0.302130
$334$	13.4262	0.734647
$335$	−26.8492	−1.46693
$336$	32.7986	1.78931
$337$	−3.05560	−0.166449	−0.0832245	−	0.996531i	$-0.526522\pi$
$337$	−3.05560	−0.166449	−0.0832245	+	0.996531i	$0.526522\pi$
$338$	31.2992	1.70245
$339$	50.6279	2.74973
$340$	125.321	6.79647
$341$	−4.70788	−0.254946
$342$	−2.88957	−0.156250
$343$	−16.1502	−0.872028
$344$	−54.4426	−2.93535
$345$	−74.5207	−4.01206
$346$	26.8978	1.44603
$347$	16.3177	0.875981	0.437991	−	0.898980i	$-0.355690\pi$
$347$	16.3177	0.875981	0.437991	+	0.898980i	$0.355690\pi$
$348$	32.9961	1.76878
$349$	29.3796	1.57266	0.786328	−	0.617810i	$-0.211980\pi$
$349$	29.3796	1.57266	0.786328	+	0.617810i	$0.211980\pi$
$350$	−27.6036	−1.47547
$351$	6.91604	0.369151
$352$	14.8394	0.790941
$353$	6.19054	0.329489	0.164745	−	0.986336i	$-0.447320\pi$
$353$	6.19054	0.329489	0.164745	+	0.986336i	$0.447320\pi$
$354$	75.1147	3.99230
$355$	−52.0533	−2.76270
$356$	−64.3648	−3.41133
$357$	28.4119	1.50371
$358$	−8.73462	−0.461639
$359$	−6.17866	−0.326097	−0.163049	−	0.986618i	$-0.552133\pi$
$359$	−6.17866	−0.326097	−0.163049	+	0.986618i	$0.552133\pi$
$360$	−138.248	−7.28630
$361$	−18.9589	−0.997836
$362$	−1.16383	−0.0611697
$363$	−22.5777	−1.18502
$364$	5.81030	0.304542
$365$	−41.0129	−2.14671
$366$	36.9379	1.93077
$367$	−35.2881	−1.84203	−0.921013	−	0.389532i	$-0.872637\pi$
$367$	−35.2881	−1.84203	−0.921013	+	0.389532i	$0.872637\pi$
$368$	−60.2197	−3.13917
$369$	37.1733	1.93517
$370$	9.35852	0.486526
$371$	15.6138	0.810631
$372$	35.5897	1.84524
$373$	−19.4822	−1.00875	−0.504375	−	0.863485i	$-0.668277\pi$
$373$	−19.4822	−1.00875	−0.504375	+	0.863485i	$0.668277\pi$
$374$	34.5226	1.78512
$375$	32.8827	1.69805
$376$	−85.6047	−4.41472
$377$	2.27917	0.117383
$378$	−24.9532	−1.28345
$379$	−25.9773	−1.33436	−0.667182	−	0.744895i	$-0.732500\pi$
$379$	−25.9773	−1.33436	−0.667182	+	0.744895i	$0.732500\pi$
$380$	3.43619	0.176273
$381$	12.3293	0.631648
$382$	9.24445	0.472987
$383$	−33.1266	−1.69269	−0.846344	−	0.532636i	$-0.821201\pi$
$383$	−33.1266	−1.69269	−0.846344	+	0.532636i	$0.821201\pi$
$384$	16.5857	0.846385
$385$	−8.61061	−0.438837
$386$	−25.1824	−1.28175
$387$	43.3461	2.20341
$388$	−66.5962	−3.38091
$389$	−9.50314	−0.481828	−0.240914	−	0.970546i	$-0.577447\pi$
$389$	−9.50314	−0.481828	−0.240914	+	0.970546i	$0.577447\pi$
$390$	−25.7521	−1.30401
$391$	−52.1654	−2.63812
$392$	36.4696	1.84199
$393$	25.3966	1.28109
$394$	−68.2479	−3.43828
$395$	56.8097	2.85841
$396$	−46.5956	−2.34152
$397$	31.3085	1.57133	0.785664	−	0.618654i	$-0.212322\pi$
$397$	31.3085	1.57133	0.785664	+	0.618654i	$0.212322\pi$
$398$	55.4851	2.78122
$399$	0.779029	0.0390002
$400$	69.2618	3.46309
$401$	−28.8380	−1.44010	−0.720051	−	0.693921i	$-0.755882\pi$
$401$	−28.8380	−1.44010	−0.720051	+	0.693921i	$0.755882\pi$
$402$	55.9127	2.78867
$403$	2.45833	0.122458
$404$	1.31993	0.0656692
$405$	17.5875	0.873930
$406$	−8.22330	−0.408116
$407$	1.80609	0.0895247
$408$	−149.434	−7.39808
$409$	32.7162	1.61771	0.808855	−	0.588008i	$-0.200088\pi$
$409$	32.7162	1.61771	0.808855	+	0.588008i	$0.200088\pi$
$410$	−63.0991	−3.11624
$411$	39.6356	1.95508
$412$	6.43031	0.316798
$413$	−13.1148	−0.645337
$414$	100.501	4.93937
$415$	−44.3864	−2.17884
$416$	−7.74872	−0.379912
$417$	15.8488	0.776119
$418$	0.946580	0.0462987
$419$	−20.7473	−1.01357	−0.506787	−	0.862071i	$-0.669167\pi$
$419$	−20.7473	−1.01357	−0.506787	+	0.862071i	$0.669167\pi$
$420$	65.0928	3.17620
$421$	−17.8509	−0.870000	−0.435000	−	0.900430i	$-0.643252\pi$
$421$	−17.8509	−0.870000	−0.435000	+	0.900430i	$0.643252\pi$
$422$	15.2305	0.741411
$423$	68.1568	3.31389
$424$	−82.1219	−3.98819
$425$	59.9981	2.91033
$426$	108.400	5.25198
$427$	−6.44924	−0.312100
$428$	−80.8526	−3.90816
$429$	−4.96987	−0.239947
$430$	−73.5770	−3.54820
$431$	17.3491	0.835675	0.417838	−	0.908522i	$-0.362788\pi$
$431$	17.3491	0.835675	0.417838	+	0.908522i	$0.362788\pi$
$432$	62.6115	3.01240
$433$	12.8795	0.618949	0.309475	−	0.950908i	$-0.399847\pi$
$433$	12.8795	0.618949	0.309475	+	0.950908i	$0.399847\pi$
$434$	−8.86968	−0.425758
$435$	25.5336	1.22424
$436$	−68.5845	−3.28460
$437$	−1.43033	−0.0684220
$438$	85.4082	4.08096
$439$	−16.9506	−0.809009	−0.404505	−	0.914536i	$-0.632556\pi$
$439$	−16.9506	−0.809009	−0.404505	+	0.914536i	$0.632556\pi$
$440$	45.2880	2.15902
$441$	−29.0364	−1.38268
$442$	−18.0267	−0.857445
$443$	6.56490	0.311908	0.155954	−	0.987764i	$-0.450155\pi$
$443$	6.56490	0.311908	0.155954	+	0.987764i	$0.450155\pi$
$444$	−13.6534	−0.647959
$445$	−49.8080	−2.36112
$446$	5.26993	0.249539
$447$	−16.8792	−0.798357
$448$	5.47547	0.258692
$449$	11.9318	0.563096	0.281548	−	0.959547i	$-0.409152\pi$
$449$	11.9318	0.563096	0.281548	+	0.959547i	$0.409152\pi$
$450$	−115.592	−5.44904
$451$	−12.1774	−0.573414
$452$	81.1949	3.81909
$453$	32.8612	1.54395
$454$	16.4912	0.773971
$455$	4.49623	0.210786
$456$	−4.09735	−0.191876
$457$	15.8624	0.742013	0.371007	−	0.928630i	$-0.379013\pi$
$457$	15.8624	0.742013	0.371007	+	0.928630i	$0.379013\pi$
$458$	22.8124	1.06595
$459$	54.2372	2.53158
$460$	−119.513	−5.57233
$461$	10.1753	0.473912	0.236956	−	0.971520i	$-0.423850\pi$
$461$	10.1753	0.473912	0.236956	+	0.971520i	$0.423850\pi$
$462$	17.9314	0.834243
$463$	4.65879	0.216512	0.108256	−	0.994123i	$-0.465473\pi$
$463$	4.65879	0.216512	0.108256	+	0.994123i	$0.465473\pi$
$464$	20.6336	0.957889
$465$	27.5406	1.27717
$466$	−11.6509	−0.539717
$467$	37.7667	1.74764	0.873818	−	0.486253i	$-0.161637\pi$
$467$	37.7667	1.74764	0.873818	+	0.486253i	$0.161637\pi$
$468$	24.3309	1.12470
$469$	−9.76218	−0.450776
$470$	−115.691	−5.33644
$471$	−50.4457	−2.32441
$472$	68.9780	3.17497
$473$	−14.1996	−0.652896
$474$	−118.305	−5.43392
$475$	1.64510	0.0754822
$476$	45.5657	2.08850
$477$	65.3839	2.99372
$478$	−45.0161	−2.05899
$479$	−4.23438	−0.193474	−0.0967370	−	0.995310i	$-0.530841\pi$
$479$	−4.23438	−0.193474	−0.0967370	+	0.995310i	$0.530841\pi$
$480$	−86.8090	−3.96227
$481$	−0.943093	−0.0430013
$482$	−21.0205	−0.957459
$483$	−27.0952	−1.23288
$484$	−36.2092	−1.64587
$485$	−51.5347	−2.34007
$486$	20.2326	0.917769
$487$	−4.62844	−0.209735	−0.104867	−	0.994486i	$-0.533442\pi$
$487$	−4.62844	−0.209735	−0.104867	+	0.994486i	$0.533442\pi$
$488$	33.9201	1.53549
$489$	2.91776	0.131946
$490$	49.2872	2.22657
$491$	−27.4202	−1.23746	−0.618729	−	0.785604i	$-0.712352\pi$
$491$	−27.4202	−1.23746	−0.618729	+	0.785604i	$0.712352\pi$
$492$	92.0567	4.15024
$493$	17.8738	0.804997
$494$	−0.494278	−0.0222386
$495$	−36.0574	−1.62066
$496$	22.2554	0.999298
$497$	−18.9262	−0.848958
$498$	92.4334	4.14204
$499$	7.17159	0.321044	0.160522	−	0.987032i	$-0.448682\pi$
$499$	7.17159	0.321044	0.160522	+	0.987032i	$0.448682\pi$
$500$	52.7358	2.35842
$501$	−15.1577	−0.677197
$502$	−44.7994	−1.99950
$503$	−26.5742	−1.18489	−0.592443	−	0.805613i	$-0.701836\pi$
$503$	−26.5742	−1.18489	−0.592443	+	0.805613i	$0.701836\pi$
$504$	−50.2660	−2.23902
$505$	1.02141	0.0454524
$506$	−32.9228	−1.46360
$507$	−35.3358	−1.56932
$508$	19.7732	0.877292
$509$	37.0845	1.64374	0.821871	−	0.569673i	$-0.192930\pi$
$509$	37.0845	1.64374	0.821871	+	0.569673i	$0.192930\pi$
$510$	−201.954	−8.94267
$511$	−14.9120	−0.659668
$512$	48.0958	2.12555
$513$	1.48714	0.0656588
$514$	−20.6371	−0.910263
$515$	4.97601	0.219269
$516$	107.343	4.72551
$517$	−22.3272	−0.981948
$518$	3.40270	0.149506
$519$	−30.3667	−1.33295
$520$	−23.6482	−1.03704
$521$	−2.61167	−0.114419	−0.0572096	−	0.998362i	$-0.518220\pi$
$521$	−2.61167	−0.114419	−0.0572096	+	0.998362i	$0.518220\pi$
$522$	−34.4355	−1.50720
$523$	0.911181	0.0398432	0.0199216	−	0.999802i	$-0.493658\pi$
$523$	0.911181	0.0398432	0.0199216	+	0.999802i	$0.493658\pi$
$524$	40.7301	1.77930
$525$	31.1636	1.36009
$526$	34.7088	1.51338
$527$	19.2788	0.839797
$528$	−44.9926	−1.95805
$529$	26.7480	1.16296
$530$	−110.985	−4.82086
$531$	−54.9189	−2.38328
$532$	1.24937	0.0541672
$533$	6.35873	0.275427
$534$	103.724	4.48857
$535$	−62.5668	−2.70500
$536$	51.3447	2.21776
$537$	9.86111	0.425538
$538$	−61.6233	−2.65677
$539$	9.51189	0.409706
$540$	124.260	5.34730
$541$	21.6341	0.930123	0.465062	−	0.885278i	$-0.346032\pi$
$541$	21.6341	0.930123	0.465062	+	0.885278i	$0.346032\pi$
$542$	4.70300	0.202011
$543$	1.31393	0.0563862
$544$	−60.7673	−2.60538
$545$	−53.0733	−2.27341
$546$	−9.36327	−0.400711
$547$	−17.2702	−0.738419	−0.369210	−	0.929346i	$-0.620372\pi$
$547$	−17.2702	−0.738419	−0.369210	+	0.929346i	$0.620372\pi$
$548$	63.5659	2.71540
$549$	−27.0065	−1.15261
$550$	37.8661	1.61462
$551$	0.490086	0.0208783
$552$	142.509	6.06558
$553$	20.6556	0.878366
$554$	−13.7648	−0.584812
$555$	−10.5655	−0.448480
$556$	25.4176	1.07795
$557$	7.44791	0.315578	0.157789	−	0.987473i	$-0.449563\pi$
$557$	7.44791	0.315578	0.157789	+	0.987473i	$0.449563\pi$
$558$	−37.1423	−1.57236
$559$	7.41462	0.313605
$560$	40.7047	1.72009
$561$	−38.9749	−1.64552
$562$	−27.6200	−1.16508
$563$	38.4487	1.62042	0.810211	−	0.586139i	$-0.199353\pi$
$563$	38.4487	1.62042	0.810211	+	0.586139i	$0.199353\pi$
$564$	168.785	7.10711
$565$	62.8317	2.64335
$566$	19.6520	0.826036
$567$	6.39470	0.268552
$568$	99.5436	4.17676
$569$	−24.5679	−1.02994	−0.514970	−	0.857208i	$-0.672197\pi$
$569$	−24.5679	−1.02994	−0.514970	+	0.857208i	$0.672197\pi$
$570$	−5.53740	−0.231936
$571$	−2.46209	−0.103035	−0.0515176	−	0.998672i	$-0.516406\pi$
$571$	−2.46209	−0.103035	−0.0515176	+	0.998672i	$0.516406\pi$
$572$	−7.97047	−0.333262
$573$	−10.4367	−0.435999
$574$	−22.9424	−0.957598
$575$	−57.2177	−2.38614
$576$	22.9288	0.955368
$577$	−8.48004	−0.353029	−0.176514	−	0.984298i	$-0.556482\pi$
$577$	−8.48004	−0.353029	−0.176514	+	0.984298i	$0.556482\pi$
$578$	−97.4345	−4.05274
$579$	28.4301	1.18151
$580$	40.9498	1.70035
$581$	−16.1386	−0.669541
$582$	107.320	4.44854
$583$	−21.4188	−0.887077
$584$	78.4305	3.24548
$585$	18.8282	0.778450
$586$	3.45731	0.142820
$587$	−7.09627	−0.292894	−0.146447	−	0.989219i	$-0.546784\pi$
$587$	−7.09627	−0.292894	−0.146447	+	0.989219i	$0.546784\pi$
$588$	−71.9062	−2.96536
$589$	0.528608	0.0217809
$590$	93.2211	3.83785
$591$	77.0498	3.16940
$592$	−8.53790	−0.350905
$593$	20.3275	0.834749	0.417375	−	0.908735i	$-0.362950\pi$
$593$	20.3275	0.834749	0.417375	+	0.908735i	$0.362950\pi$
$594$	34.2304	1.40449
$595$	35.2605	1.44554
$596$	−27.0701	−1.10883
$597$	−62.6410	−2.56372
$598$	17.1914	0.703008
$599$	−17.7867	−0.726746	−0.363373	−	0.931644i	$-0.618375\pi$
$599$	−17.7867	−0.726746	−0.363373	+	0.931644i	$0.618375\pi$
$600$	−163.907	−6.69146
$601$	−5.46951	−0.223106	−0.111553	−	0.993758i	$-0.535582\pi$
$601$	−5.46951	−0.223106	−0.111553	+	0.993758i	$0.535582\pi$
$602$	−26.7521	−1.09033
$603$	−40.8797	−1.66475
$604$	52.7013	2.14439
$605$	−28.0201	−1.13918
$606$	−2.12707	−0.0864063
$607$	44.6009	1.81030	0.905148	−	0.425097i	$-0.139760\pi$
$607$	44.6009	1.81030	0.905148	+	0.425097i	$0.139760\pi$
$608$	−1.66619	−0.0675729
$609$	9.28385	0.376201
$610$	45.8417	1.85608
$611$	11.6586	0.471658
$612$	190.809	7.71300
$613$	−17.0322	−0.687925	−0.343962	−	0.938983i	$-0.611769\pi$
$613$	−17.0322	−0.687925	−0.343962	+	0.938983i	$0.611769\pi$
$614$	−19.0422	−0.768482
$615$	71.2370	2.87255
$616$	16.4664	0.663451
$617$	−2.77751	−0.111818	−0.0559091	−	0.998436i	$-0.517806\pi$
$617$	−2.77751	−0.111818	−0.0559091	+	0.998436i	$0.517806\pi$
$618$	−10.3624	−0.416838
$619$	−9.15230	−0.367862	−0.183931	−	0.982939i	$-0.558882\pi$
$619$	−9.15230	−0.367862	−0.183931	+	0.982939i	$0.558882\pi$
$620$	44.1685	1.77385
$621$	−51.7238	−2.07561
$622$	−78.9856	−3.16703
$623$	−18.1098	−0.725555
$624$	23.4939	0.940510
$625$	0.247616	0.00990465
$626$	−15.5643	−0.622076
$627$	−1.06866	−0.0426781
$628$	−80.9027	−3.22837
$629$	−7.39596	−0.294896
$630$	−67.9325	−2.70650
$631$	−50.0686	−1.99320	−0.996599	−	0.0824069i	$-0.973739\pi$
$631$	−50.0686	−1.99320	−0.996599	+	0.0824069i	$0.973739\pi$
$632$	−108.639	−4.32144
$633$	−17.1948	−0.683432
$634$	29.3572	1.16593
$635$	15.3012	0.607210
$636$	161.918	6.42046
$637$	−4.96685	−0.196794
$638$	11.2806	0.446603
$639$	−79.2547	−3.13527
$640$	20.5836	0.813640
$641$	5.71703	0.225809	0.112905	−	0.993606i	$-0.463985\pi$
$641$	5.71703	0.225809	0.112905	+	0.993606i	$0.463985\pi$
$642$	130.294	5.14228
$643$	5.41799	0.213665	0.106832	−	0.994277i	$-0.465929\pi$
$643$	5.41799	0.213665	0.106832	+	0.994277i	$0.465929\pi$
$644$	−43.4542	−1.71233
$645$	83.0661	3.27072
$646$	−3.87625	−0.152509
$647$	12.1064	0.475951	0.237975	−	0.971271i	$-0.423516\pi$
$647$	12.1064	0.475951	0.237975	+	0.971271i	$0.423516\pi$
$648$	−33.6333	−1.32124
$649$	17.9907	0.706195
$650$	−19.7727	−0.775548
$651$	10.0136	0.392464
$652$	4.67939	0.183259
$653$	12.4620	0.487676	0.243838	−	0.969816i	$-0.421593\pi$
$653$	12.4620	0.487676	0.243838	+	0.969816i	$0.421593\pi$
$654$	110.524	4.32182
$655$	31.5185	1.23153
$656$	57.5661	2.24758
$657$	−62.4449	−2.43621
$658$	−42.0646	−1.63985
$659$	−31.8398	−1.24030	−0.620150	−	0.784483i	$-0.712928\pi$
$659$	−31.8398	−1.24030	−0.620150	+	0.784483i	$0.712928\pi$
$660$	−89.2932	−3.47573
$661$	−5.94250	−0.231136	−0.115568	−	0.993300i	$-0.536869\pi$
$661$	−5.94250	−0.231136	−0.115568	+	0.993300i	$0.536869\pi$
$662$	−33.3842	−1.29751
$663$	20.3516	0.790392
$664$	84.8818	3.29405
$665$	0.966813	0.0374914
$666$	14.2490	0.552137
$667$	−17.0455	−0.660006
$668$	−24.3093	−0.940556
$669$	−5.94959	−0.230024
$670$	69.3904	2.68078
$671$	8.84695	0.341533
$672$	−31.5631	−1.21757
$673$	39.5195	1.52336	0.761681	−	0.647952i	$-0.224374\pi$
$673$	39.5195	1.52336	0.761681	+	0.647952i	$0.224374\pi$
$674$	7.89704	0.304183
$675$	59.4902	2.28978
$676$	−56.6701	−2.17962
$677$	−29.4438	−1.13162	−0.565808	−	0.824537i	$-0.691436\pi$
$677$	−29.4438	−1.13162	−0.565808	+	0.824537i	$0.691436\pi$
$678$	−130.845	−5.02509
$679$	−18.7377	−0.719085
$680$	−185.455	−7.11186
$681$	−18.6181	−0.713446
$682$	12.1673	0.465909
$683$	−13.9032	−0.531993	−0.265997	−	0.963974i	$-0.585701\pi$
$683$	−13.9032	−0.531993	−0.265997	+	0.963974i	$0.585701\pi$
$684$	5.23183	0.200044
$685$	49.1897	1.87944
$686$	41.7394	1.59362
$687$	−25.7545	−0.982595
$688$	67.1252	2.55912
$689$	11.1843	0.426089
$690$	192.595	7.33197
$691$	−29.6903	−1.12947	−0.564735	−	0.825272i	$-0.691022\pi$
$691$	−29.6903	−1.12947	−0.564735	+	0.825272i	$0.691022\pi$
$692$	−48.7009	−1.85133
$693$	−13.1102	−0.498017
$694$	−42.1723	−1.60084
$695$	19.6691	0.746092
$696$	−48.8289	−1.85086
$697$	49.8667	1.88884
$698$	−75.9302	−2.87400
$699$	13.1535	0.497511
$700$	49.9789	1.88902
$701$	11.9761	0.452333	0.226166	−	0.974089i	$-0.427381\pi$
$701$	11.9761	0.452333	0.226166	+	0.974089i	$0.427381\pi$
$702$	−17.8742	−0.674617
$703$	−0.202791	−0.00764841
$704$	−7.51116	−0.283087
$705$	130.612	4.91913
$706$	−15.9991	−0.602136
$707$	0.371380	0.0139672
$708$	−136.002	−5.11128
$709$	−27.8289	−1.04514	−0.522569	−	0.852597i	$-0.675026\pi$
$709$	−27.8289	−1.04514	−0.522569	+	0.852597i	$0.675026\pi$
$710$	134.529	5.04879
$711$	86.4966	3.24388
$712$	95.2497	3.56963
$713$	−18.3854	−0.688538
$714$	−73.4291	−2.74801
$715$	−6.16785	−0.230664
$716$	15.8148	0.591028
$717$	50.8218	1.89797
$718$	15.9685	0.595938
$719$	14.2978	0.533219	0.266609	−	0.963805i	$-0.414097\pi$
$719$	14.2978	0.533219	0.266609	+	0.963805i	$0.414097\pi$
$720$	170.453	6.35242
$721$	1.80924	0.0673798
$722$	48.9983	1.82353
$723$	23.7315	0.882585
$724$	2.10723	0.0783145
$725$	19.6050	0.728110
$726$	58.3511	2.16561
$727$	25.8612	0.959141	0.479570	−	0.877503i	$-0.340793\pi$
$727$	25.8612	0.959141	0.479570	+	0.877503i	$0.340793\pi$
$728$	−8.59831	−0.318675
$729$	−37.4129	−1.38566
$730$	105.996	3.92308
$731$	58.1473	2.15065
$732$	−66.8795	−2.47194
$733$	−22.9506	−0.847699	−0.423850	−	0.905733i	$-0.639321\pi$
$733$	−22.9506	−0.847699	−0.423850	+	0.905733i	$0.639321\pi$
$734$	91.2005	3.36627
$735$	−55.6437	−2.05245
$736$	57.9513	2.13611
$737$	13.3916	0.493286
$738$	−96.0727	−3.53648
$739$	−12.3619	−0.454738	−0.227369	−	0.973809i	$-0.573012\pi$
$739$	−12.3619	−0.454738	−0.227369	+	0.973809i	$0.573012\pi$
$740$	−16.9445	−0.622891
$741$	0.558025	0.0204995
$742$	−40.3532	−1.48141
$743$	22.6832	0.832168	0.416084	−	0.909326i	$-0.363402\pi$
$743$	22.6832	0.832168	0.416084	+	0.909326i	$0.363402\pi$
$744$	−52.6671	−1.93087
$745$	−20.9479	−0.767470
$746$	50.3508	1.84347
$747$	−67.5812	−2.47267
$748$	−62.5063	−2.28546
$749$	−22.7489	−0.831225
$750$	−84.9836	−3.10316
$751$	5.99954	0.218926	0.109463	−	0.993991i	$-0.465087\pi$
$751$	5.99954	0.218926	0.109463	+	0.993991i	$0.465087\pi$
$752$	105.547	3.84889
$753$	50.5771	1.84313
$754$	−5.89042	−0.214516
$755$	40.7823	1.48422
$756$	45.1801	1.64318
$757$	−23.9553	−0.870671	−0.435335	−	0.900268i	$-0.643370\pi$
$757$	−23.9553	−0.870671	−0.435335	+	0.900268i	$0.643370\pi$
$758$	67.1371	2.43853
$759$	37.1688	1.34914
$760$	−5.08501	−0.184453
$761$	28.6075	1.03702	0.518510	−	0.855071i	$-0.326487\pi$
$761$	28.6075	1.03702	0.518510	+	0.855071i	$0.326487\pi$
$762$	−31.8644	−1.15433
$763$	−19.2971	−0.698602
$764$	−16.7379	−0.605557
$765$	147.655	5.33849
$766$	85.6140	3.09336
$767$	−9.39423	−0.339206
$768$	−67.1336	−2.42248
$769$	4.82450	0.173976	0.0869880	−	0.996209i	$-0.472276\pi$
$769$	4.82450	0.173976	0.0869880	+	0.996209i	$0.472276\pi$
$770$	22.2537	0.801968
$771$	23.2986	0.839080
$772$	45.5950	1.64100
$773$	1.99467	0.0717434	0.0358717	−	0.999356i	$-0.488579\pi$
$773$	1.99467	0.0717434	0.0358717	+	0.999356i	$0.488579\pi$
$774$	−112.026	−4.02669
$775$	21.1460	0.759585
$776$	98.5518	3.53780
$777$	−3.84154	−0.137814
$778$	24.5604	0.880533
$779$	1.36730	0.0489887
$780$	46.6265	1.66950
$781$	25.9627	0.929018
$782$	134.819	4.82111
$783$	17.7225	0.633352
$784$	−44.9653	−1.60590
$785$	−62.6055	−2.23449
$786$	−65.6364	−2.34117
$787$	−31.6729	−1.12902	−0.564509	−	0.825427i	$-0.690935\pi$
$787$	−31.6729	−1.12902	−0.564509	+	0.825427i	$0.690935\pi$
$788$	123.569	4.40197
$789$	−39.1852	−1.39503
$790$	−146.822	−5.22369
$791$	22.8452	0.812281
$792$	68.9540	2.45017
$793$	−4.61964	−0.164048
$794$	−80.9152	−2.87157
$795$	125.298	4.44387
$796$	−100.461	−3.56074
$797$	23.5583	0.834477	0.417238	−	0.908797i	$-0.362998\pi$
$797$	23.5583	0.834477	0.417238	+	0.908797i	$0.362998\pi$
$798$	−2.01336	−0.0712723
$799$	91.4299	3.23456
$800$	−66.6527	−2.35653
$801$	−75.8360	−2.67953
$802$	74.5305	2.63176
$803$	20.4560	0.721878
$804$	−101.235	−3.57029
$805$	−33.6265	−1.18518
$806$	−6.35342	−0.223790
$807$	69.5708	2.44901
$808$	−1.95329	−0.0687166
$809$	13.2221	0.464863	0.232431	−	0.972613i	$-0.425332\pi$
$809$	13.2221	0.464863	0.232431	+	0.972613i	$0.425332\pi$
$810$	−45.4541	−1.59709
$811$	−44.0482	−1.54674	−0.773370	−	0.633955i	$-0.781431\pi$
$811$	−44.0482	−1.54674	−0.773370	+	0.633955i	$0.781431\pi$
$812$	14.8891	0.522503
$813$	−5.30954	−0.186214
$814$	−4.66776	−0.163605
$815$	3.62109	0.126841
$816$	184.245	6.44987
$817$	1.59435	0.0557792
$818$	−84.5534	−2.95634
$819$	6.84581	0.239212
$820$	114.247	3.98967
$821$	23.4795	0.819442	0.409721	−	0.912211i	$-0.365626\pi$
$821$	23.4795	0.819442	0.409721	+	0.912211i	$0.365626\pi$
$822$	−102.436	−3.57288
$823$	−5.32655	−0.185672	−0.0928359	−	0.995681i	$-0.529593\pi$
$823$	−5.32655	−0.185672	−0.0928359	+	0.995681i	$0.529593\pi$
$824$	−9.51583	−0.331500
$825$	−42.7497	−1.48835
$826$	33.8945	1.17934
$827$	−24.6599	−0.857509	−0.428754	−	0.903421i	$-0.641047\pi$
$827$	−24.6599	−0.857509	−0.428754	+	0.903421i	$0.641047\pi$
$828$	−181.967	−6.32379
$829$	39.0722	1.35703	0.678517	−	0.734585i	$-0.262623\pi$
$829$	39.0722	1.35703	0.678517	+	0.734585i	$0.262623\pi$
$830$	114.714	3.98179
$831$	15.5401	0.539079
$832$	3.92212	0.135975
$833$	−38.9513	−1.34958
$834$	−40.9604	−1.41834
$835$	−18.8115	−0.650998
$836$	−1.71387	−0.0592754
$837$	19.1156	0.660732
$838$	53.6205	1.85229
$839$	−49.6621	−1.71453	−0.857263	−	0.514879i	$-0.827837\pi$
$839$	−49.6621	−1.71453	−0.857263	+	0.514879i	$0.827837\pi$
$840$	−96.3270	−3.32360
$841$	−23.1595	−0.798605
$842$	46.1348	1.58991
$843$	31.1821	1.07397
$844$	−27.5763	−0.949215
$845$	−43.8535	−1.50860
$846$	−176.148	−6.05609
$847$	−10.1879	−0.350061
$848$	101.253	3.47703
$849$	−22.1865	−0.761439
$850$	−155.062	−5.31859
$851$	7.05323	0.241781
$852$	−196.268	−6.72402
$853$	−24.1764	−0.827786	−0.413893	−	0.910326i	$-0.635831\pi$
$853$	−24.1764	−0.827786	−0.413893	+	0.910326i	$0.635831\pi$
$854$	16.6677	0.570358
$855$	4.04858	0.138459
$856$	119.649	4.08952
$857$	−6.46112	−0.220708	−0.110354	−	0.993892i	$-0.535198\pi$
$857$	−6.46112	−0.220708	−0.110354	+	0.993892i	$0.535198\pi$
$858$	12.8444	0.438500
$859$	7.31828	0.249697	0.124848	−	0.992176i	$-0.460156\pi$
$859$	7.31828	0.249697	0.124848	+	0.992176i	$0.460156\pi$
$860$	133.218	4.54269
$861$	25.9013	0.882713
$862$	−44.8378	−1.52718
$863$	14.7170	0.500974	0.250487	−	0.968120i	$-0.419409\pi$
$863$	14.7170	0.500974	0.250487	+	0.968120i	$0.419409\pi$
$864$	−60.2530	−2.04985
$865$	−37.6866	−1.28138
$866$	−33.2864	−1.13112
$867$	110.000	3.73581
$868$	16.0594	0.545091
$869$	−28.3350	−0.961200
$870$	−65.9904	−2.23728
$871$	−6.99273	−0.236939
$872$	101.494	3.43703
$873$	−78.4650	−2.65564
$874$	3.69662	0.125040
$875$	14.8379	0.501612
$876$	−154.640	−5.22479
$877$	−25.8533	−0.873004	−0.436502	−	0.899703i	$-0.643783\pi$
$877$	−25.8533	−0.873004	−0.436502	+	0.899703i	$0.643783\pi$
$878$	43.8081	1.47845
$879$	−3.90319	−0.131651
$880$	−55.8380	−1.88230
$881$	47.8766	1.61300	0.806502	−	0.591231i	$-0.201358\pi$
$881$	47.8766	1.61300	0.806502	+	0.591231i	$0.201358\pi$
$882$	75.0431	2.52683
$883$	40.1990	1.35280	0.676402	−	0.736533i	$-0.263538\pi$
$883$	40.1990	1.35280	0.676402	+	0.736533i	$0.263538\pi$
$884$	32.6391	1.09777
$885$	−105.244	−3.53773
$886$	−16.9667	−0.570006
$887$	3.78693	0.127153	0.0635764	−	0.997977i	$-0.479749\pi$
$887$	3.78693	0.127153	0.0635764	+	0.997977i	$0.479749\pi$
$888$	20.2048	0.678028
$889$	5.56342	0.186591
$890$	128.726	4.31491
$891$	−8.77214	−0.293878
$892$	−9.54170	−0.319480
$893$	2.50693	0.0838912
$894$	43.6234	1.45898
$895$	12.2381	0.409075
$896$	7.48407	0.250025
$897$	−19.4085	−0.648032
$898$	−30.8371	−1.02905
$899$	6.29953	0.210101
$900$	209.289	6.97631
$901$	87.7102	2.92205
$902$	31.4720	1.04790
$903$	30.2023	1.00507
$904$	−120.156	−3.99631
$905$	1.63065	0.0542047
$906$	−84.9280	−2.82155
$907$	22.8149	0.757556	0.378778	−	0.925488i	$-0.376344\pi$
$907$	22.8149	0.757556	0.378778	+	0.925488i	$0.376344\pi$
$908$	−29.8589	−0.990901
$909$	1.55517	0.0515818
$910$	−11.6203	−0.385208
$911$	−27.6178	−0.915017	−0.457509	−	0.889205i	$-0.651258\pi$
$911$	−27.6178	−0.915017	−0.457509	+	0.889205i	$0.651258\pi$
$912$	5.05184	0.167283
$913$	22.1386	0.732682
$914$	−40.9957	−1.35602
$915$	−51.7539	−1.71093
$916$	−41.3040	−1.36472
$917$	11.4599	0.378439
$918$	−140.174	−4.62642
$919$	38.4917	1.26972	0.634862	−	0.772626i	$-0.281057\pi$
$919$	38.4917	1.26972	0.634862	+	0.772626i	$0.281057\pi$
$920$	176.860	5.83092
$921$	21.4981	0.708386
$922$	−26.2976	−0.866066
$923$	−13.5570	−0.446234
$924$	−32.4664	−1.06807
$925$	−8.11227	−0.266730
$926$	−12.0404	−0.395672
$927$	7.57632	0.248839
$928$	−19.8563	−0.651815
$929$	55.7115	1.82784	0.913918	−	0.405900i	$-0.133042\pi$
$929$	55.7115	1.82784	0.913918	+	0.405900i	$0.133042\pi$
$930$	−71.1775	−2.33400
$931$	−1.06801	−0.0350026
$932$	21.0950	0.690990
$933$	89.1722	2.91937
$934$	−97.6063	−3.19378
$935$	−48.3698	−1.58186
$936$	−36.0059	−1.17689
$937$	−32.7789	−1.07084	−0.535421	−	0.844586i	$-0.679847\pi$
$937$	−32.7789	−1.07084	−0.535421	+	0.844586i	$0.679847\pi$
$938$	25.2299	0.823785
$939$	17.5716	0.573429
$940$	209.470	6.83215
$941$	9.70939	0.316517	0.158258	−	0.987398i	$-0.449412\pi$
$941$	9.70939	0.316517	0.158258	+	0.987398i	$0.449412\pi$
$942$	130.374	4.24783
$943$	−47.5558	−1.54863
$944$	−85.0467	−2.76803
$945$	34.9620	1.13732
$946$	36.6981	1.19316
$947$	−32.9974	−1.07227	−0.536136	−	0.844132i	$-0.680116\pi$
$947$	−32.9974	−1.07227	−0.536136	+	0.844132i	$0.680116\pi$
$948$	214.202	6.95695
$949$	−10.6816	−0.346739
$950$	−4.25167	−0.137942
$951$	−33.1434	−1.07475
$952$	−67.4300	−2.18542
$953$	49.6398	1.60799	0.803995	−	0.594636i	$-0.202704\pi$
$953$	49.6398	1.60799	0.803995	+	0.594636i	$0.202704\pi$
$954$	−168.981	−5.47098
$955$	−12.9524	−0.419131
$956$	81.5058	2.63609
$957$	−12.7354	−0.411678
$958$	10.9436	0.353570
$959$	17.8850	0.577538
$960$	43.9396	1.41814
$961$	−24.2053	−0.780816
$962$	2.43738	0.0785842
$963$	−95.2621	−3.06978
$964$	38.0596	1.22582
$965$	35.2831	1.13580
$966$	70.0263	2.25306
$967$	3.47021	0.111594	0.0557972	−	0.998442i	$-0.482230\pi$
$967$	3.47021	0.111594	0.0557972	+	0.998442i	$0.482230\pi$
$968$	53.5839	1.72225
$969$	4.37616	0.140583
$970$	133.189	4.27644
$971$	−9.13637	−0.293200	−0.146600	−	0.989196i	$-0.546833\pi$
$971$	−9.13637	−0.293200	−0.146600	+	0.989196i	$0.546833\pi$
$972$	−36.6330	−1.17500
$973$	7.15156	0.229268
$974$	11.9620	0.383287
$975$	22.3227	0.714899
$976$	−41.8220	−1.33869
$977$	−50.7924	−1.62499	−0.812497	−	0.582966i	$-0.801892\pi$
$977$	−50.7924	−1.62499	−0.812497	+	0.582966i	$0.801892\pi$
$978$	−7.54082	−0.241129
$979$	24.8428	0.793978
$980$	−89.2390	−2.85064
$981$	−80.8077	−2.57999
$982$	70.8663	2.26143
$983$	11.0378	0.352050	0.176025	−	0.984386i	$-0.443676\pi$
$983$	11.0378	0.352050	0.176025	+	0.984386i	$0.443676\pi$
$984$	−136.229	−4.34283
$985$	95.6225	3.04679
$986$	−46.1941	−1.47112
$987$	47.4896	1.51161
$988$	0.894936	0.0284717
$989$	−55.4527	−1.76329
$990$	93.1887	2.96173
$991$	20.7713	0.659821	0.329910	−	0.944012i	$-0.392981\pi$
$991$	20.7713	0.659821	0.329910	+	0.944012i	$0.392981\pi$
$992$	−21.4171	−0.679993
$993$	37.6897	1.19605
$994$	48.9139	1.55146
$995$	−77.7405	−2.46454
$996$	−167.359	−5.30298
$997$	−29.2640	−0.926801	−0.463401	−	0.886149i	$-0.653371\pi$
$997$	−29.2640	−0.926801	−0.463401	+	0.886149i	$0.653371\pi$
$998$	−18.5346	−0.586703
$999$	−7.33336	−0.232017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.7	✓	133

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

\(f(q)\)	\(=\)	\(q-2.58445 q^{2} +2.91776 q^{3} +4.67939 q^{4} +3.62109 q^{5} -7.54082 q^{6} +1.31660 q^{7} -6.92475 q^{8} +5.51335 q^{9} +O(q^{10})\)	\(q-2.58445 q^{2} +2.91776 q^{3} +4.67939 q^{4} +3.62109 q^{5} -7.54082 q^{6} +1.31660 q^{7} -6.92475 q^{8} +5.51335 q^{9} -9.35852 q^{10} -1.80609 q^{11} +13.6534 q^{12} +0.943093 q^{13} -3.40270 q^{14} +10.5655 q^{15} +8.53790 q^{16} +7.39596 q^{17} -14.2490 q^{18} +0.202791 q^{19} +16.9445 q^{20} +3.84154 q^{21} +4.66776 q^{22} -7.05323 q^{23} -20.2048 q^{24} +8.11227 q^{25} -2.43738 q^{26} +7.33336 q^{27} +6.16090 q^{28} +2.41670 q^{29} -27.3060 q^{30} +2.60666 q^{31} -8.21628 q^{32} -5.26976 q^{33} -19.1145 q^{34} +4.76753 q^{35} +25.7991 q^{36} -1.00000 q^{37} -0.524103 q^{38} +2.75172 q^{39} -25.0751 q^{40} +6.74242 q^{41} -9.92826 q^{42} +7.86203 q^{43} -8.45141 q^{44} +19.9643 q^{45} +18.2287 q^{46} +12.3621 q^{47} +24.9116 q^{48} -5.26656 q^{49} -20.9658 q^{50} +21.5797 q^{51} +4.41310 q^{52} +11.8592 q^{53} -18.9527 q^{54} -6.54002 q^{55} -9.11714 q^{56} +0.591696 q^{57} -6.24585 q^{58} -9.96109 q^{59} +49.4400 q^{60} -4.89839 q^{61} -6.73679 q^{62} +7.25889 q^{63} +4.15879 q^{64} +3.41502 q^{65} +13.6194 q^{66} -7.41467 q^{67} +34.6086 q^{68} -20.5797 q^{69} -12.3215 q^{70} -14.3751 q^{71} -38.1786 q^{72} -11.3261 q^{73} +2.58445 q^{74} +23.6697 q^{75} +0.948938 q^{76} -2.37791 q^{77} -7.11169 q^{78} +15.6886 q^{79} +30.9165 q^{80} +4.85697 q^{81} -17.4255 q^{82} -12.2577 q^{83} +17.9760 q^{84} +26.7814 q^{85} -20.3190 q^{86} +7.05137 q^{87} +12.5067 q^{88} -13.7550 q^{89} -51.5968 q^{90} +1.24168 q^{91} -33.0048 q^{92} +7.60563 q^{93} -31.9493 q^{94} +0.734324 q^{95} -23.9732 q^{96} -14.2318 q^{97} +13.6112 q^{98} -9.95762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 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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