LMFDB - Embedded newform 6011.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71378 q^{2} -2.39167 q^{3} +5.36460 q^{4} -2.12248 q^{5} +6.49047 q^{6} +2.98262 q^{7} -9.13079 q^{8} +2.72010 q^{9} +O(q^{10})$	\(q-2.71378 q^{2} -2.39167 q^{3} +5.36460 q^{4} -2.12248 q^{5} +6.49047 q^{6} +2.98262 q^{7} -9.13079 q^{8} +2.72010 q^{9} +5.75996 q^{10} +0.769140 q^{11} -12.8304 q^{12} -5.61673 q^{13} -8.09418 q^{14} +5.07629 q^{15} +14.0498 q^{16} +0.0488202 q^{17} -7.38175 q^{18} -0.775402 q^{19} -11.3863 q^{20} -7.13346 q^{21} -2.08728 q^{22} -9.04016 q^{23} +21.8379 q^{24} -0.495062 q^{25} +15.2426 q^{26} +0.669433 q^{27} +16.0006 q^{28} -1.67998 q^{29} -13.7759 q^{30} -4.32319 q^{31} -19.8664 q^{32} -1.83953 q^{33} -0.132487 q^{34} -6.33057 q^{35} +14.5922 q^{36} +1.04760 q^{37} +2.10427 q^{38} +13.4334 q^{39} +19.3800 q^{40} -10.6200 q^{41} +19.3586 q^{42} -5.56581 q^{43} +4.12613 q^{44} -5.77337 q^{45} +24.5330 q^{46} -12.9172 q^{47} -33.6024 q^{48} +1.89604 q^{49} +1.34349 q^{50} -0.116762 q^{51} -30.1315 q^{52} -12.1699 q^{53} -1.81670 q^{54} -1.63249 q^{55} -27.2337 q^{56} +1.85451 q^{57} +4.55910 q^{58} +2.56463 q^{59} +27.2323 q^{60} -1.56199 q^{61} +11.7322 q^{62} +8.11303 q^{63} +25.8134 q^{64} +11.9214 q^{65} +4.99208 q^{66} +8.13414 q^{67} +0.261901 q^{68} +21.6211 q^{69} +17.1798 q^{70} +9.38993 q^{71} -24.8367 q^{72} -6.65088 q^{73} -2.84294 q^{74} +1.18403 q^{75} -4.15973 q^{76} +2.29405 q^{77} -36.4552 q^{78} +11.5955 q^{79} -29.8204 q^{80} -9.76136 q^{81} +28.8203 q^{82} +3.09039 q^{83} -38.2682 q^{84} -0.103620 q^{85} +15.1044 q^{86} +4.01796 q^{87} -7.02286 q^{88} -9.65668 q^{89} +15.6676 q^{90} -16.7526 q^{91} -48.4969 q^{92} +10.3397 q^{93} +35.0544 q^{94} +1.64578 q^{95} +47.5139 q^{96} +3.42475 q^{97} -5.14543 q^{98} +2.09214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.71378	−1.91893	−0.959466	−	0.281824i	$-0.909061\pi$
$2$	−2.71378	−1.91893	−0.959466	+	0.281824i	$0.909061\pi$
$3$	−2.39167	−1.38083	−0.690416	−	0.723412i	$-0.742573\pi$
$3$	−2.39167	−1.38083	−0.690416	+	0.723412i	$0.742573\pi$
$4$	5.36460	2.68230
$5$	−2.12248	−0.949204	−0.474602	−	0.880201i	$-0.657408\pi$
$5$	−2.12248	−0.949204	−0.474602	+	0.880201i	$0.657408\pi$
$6$	6.49047	2.64972
$7$	2.98262	1.12733	0.563663	−	0.826005i	$-0.309392\pi$
$7$	2.98262	1.12733	0.563663	+	0.826005i	$0.309392\pi$
$8$	−9.13079	−3.22822
$9$	2.72010	0.906699
$10$	5.75996	1.82146
$11$	0.769140	0.231904	0.115952	−	0.993255i	$-0.463008\pi$
$11$	0.769140	0.231904	0.115952	+	0.993255i	$0.463008\pi$
$12$	−12.8304	−3.70381
$13$	−5.61673	−1.55780	−0.778900	−	0.627148i	$-0.784222\pi$
$13$	−5.61673	−1.55780	−0.778900	+	0.627148i	$0.784222\pi$
$14$	−8.09418	−2.16326
$15$	5.07629	1.31069
$16$	14.0498	3.51244
$17$	0.0488202	0.0118406	0.00592032	−	0.999982i	$-0.498115\pi$
$17$	0.0488202	0.0118406	0.00592032	+	0.999982i	$0.498115\pi$
$18$	−7.38175	−1.73989
$19$	−0.775402	−0.177889	−0.0889447	−	0.996037i	$-0.528349\pi$
$19$	−0.775402	−0.177889	−0.0889447	+	0.996037i	$0.528349\pi$
$20$	−11.3863	−2.54605
$21$	−7.13346	−1.55665
$22$	−2.08728	−0.445009
$23$	−9.04016	−1.88500	−0.942501	−	0.334202i	$-0.891533\pi$
$23$	−9.04016	−1.88500	−0.942501	+	0.334202i	$0.891533\pi$
$24$	21.8379	4.45764
$25$	−0.495062	−0.0990123
$26$	15.2426	2.98931
$27$	0.669433	0.128833
$28$	16.0006	3.02383
$29$	−1.67998	−0.311965	−0.155982	−	0.987760i	$-0.549854\pi$
$29$	−1.67998	−0.311965	−0.155982	+	0.987760i	$0.549854\pi$
$30$	−13.7759	−2.51513
$31$	−4.32319	−0.776468	−0.388234	−	0.921561i	$-0.626915\pi$
$31$	−4.32319	−0.776468	−0.388234	+	0.921561i	$0.626915\pi$
$32$	−19.8664	−3.51191
$33$	−1.83953	−0.320221
$34$	−0.132487	−0.0227214
$35$	−6.33057	−1.07006
$36$	14.5922	2.43204
$37$	1.04760	0.172224	0.0861118	−	0.996285i	$-0.472556\pi$
$37$	1.04760	0.172224	0.0861118	+	0.996285i	$0.472556\pi$
$38$	2.10427	0.341358
$39$	13.4334	2.15106
$40$	19.3800	3.06424
$41$	−10.6200	−1.65856	−0.829281	−	0.558832i	$-0.811250\pi$
$41$	−10.6200	−1.65856	−0.829281	+	0.558832i	$0.811250\pi$
$42$	19.3586	2.98710
$43$	−5.56581	−0.848779	−0.424389	−	0.905480i	$-0.639511\pi$
$43$	−5.56581	−0.848779	−0.424389	+	0.905480i	$0.639511\pi$
$44$	4.12613	0.622038
$45$	−5.77337	−0.860642
$46$	24.5330	3.61719
$47$	−12.9172	−1.88417	−0.942084	−	0.335378i	$-0.891136\pi$
$47$	−12.9172	−1.88417	−0.942084	+	0.335378i	$0.891136\pi$
$48$	−33.6024	−4.85009
$49$	1.89604	0.270863
$50$	1.34349	0.189998
$51$	−0.116762	−0.0163499
$52$	−30.1315	−4.17849
$53$	−12.1699	−1.67167	−0.835833	−	0.548984i	$-0.815015\pi$
$53$	−12.1699	−1.67167	−0.835833	+	0.548984i	$0.815015\pi$
$54$	−1.81670	−0.247221
$55$	−1.63249	−0.220125
$56$	−27.2337	−3.63926
$57$	1.85451	0.245636
$58$	4.55910	0.598639
$59$	2.56463	0.333886	0.166943	−	0.985967i	$-0.446610\pi$
$59$	2.56463	0.333886	0.166943	+	0.985967i	$0.446610\pi$
$60$	27.2323	3.51567
$61$	−1.56199	−0.199993	−0.0999964	−	0.994988i	$-0.531883\pi$
$61$	−1.56199	−0.199993	−0.0999964	+	0.994988i	$0.531883\pi$
$62$	11.7322	1.48999
$63$	8.11303	1.02215
$64$	25.8134	3.22668
$65$	11.9214	1.47867
$66$	4.99208	0.614483
$67$	8.13414	0.993743	0.496871	−	0.867824i	$-0.334482\pi$
$67$	8.13414	0.993743	0.496871	+	0.867824i	$0.334482\pi$
$68$	0.261901	0.0317602
$69$	21.6211	2.60287
$70$	17.1798	2.05338
$71$	9.38993	1.11438	0.557190	−	0.830385i	$-0.311880\pi$
$71$	9.38993	1.11438	0.557190	+	0.830385i	$0.311880\pi$
$72$	−24.8367	−2.92703
$73$	−6.65088	−0.778426	−0.389213	−	0.921148i	$-0.627253\pi$
$73$	−6.65088	−0.778426	−0.389213	+	0.921148i	$0.627253\pi$
$74$	−2.84294	−0.330486
$75$	1.18403	0.136719
$76$	−4.15973	−0.477153
$77$	2.29405	0.261432
$78$	−36.4552	−4.12774
$79$	11.5955	1.30460	0.652299	−	0.757962i	$-0.273805\pi$
$79$	11.5955	1.30460	0.652299	+	0.757962i	$0.273805\pi$
$80$	−29.8204	−3.33402
$81$	−9.76136	−1.08460
$82$	28.8203	3.18267
$83$	3.09039	0.339215	0.169607	−	0.985512i	$-0.445750\pi$
$83$	3.09039	0.339215	0.169607	+	0.985512i	$0.445750\pi$
$84$	−38.2682	−4.17540
$85$	−0.103620	−0.0112392
$86$	15.1044	1.62875
$87$	4.01796	0.430771
$88$	−7.02286	−0.748639
$89$	−9.65668	−1.02361	−0.511803	−	0.859103i	$-0.671022\pi$
$89$	−9.65668	−1.02361	−0.511803	+	0.859103i	$0.671022\pi$
$90$	15.6676	1.65151
$91$	−16.7526	−1.75615
$92$	−48.4969	−5.05615
$93$	10.3397	1.07217
$94$	35.0544	3.61559
$95$	1.64578	0.168853
$96$	47.5139	4.84936
$97$	3.42475	0.347730	0.173865	−	0.984769i	$-0.444374\pi$
$97$	3.42475	0.347730	0.173865	+	0.984769i	$0.444374\pi$
$98$	−5.14543	−0.519767
$99$	2.09214	0.210268
$100$	−2.65581	−0.265581
$101$	−0.998417	−0.0993463	−0.0496731	−	0.998766i	$-0.515818\pi$
$101$	−0.998417	−0.0993463	−0.0496731	+	0.998766i	$0.515818\pi$
$102$	0.316866	0.0313744
$103$	−9.59730	−0.945650	−0.472825	−	0.881156i	$-0.656766\pi$
$103$	−9.59730	−0.945650	−0.472825	+	0.881156i	$0.656766\pi$
$104$	51.2852	5.02893
$105$	15.1406	1.47758
$106$	33.0265	3.20781
$107$	−15.6568	−1.51360	−0.756802	−	0.653644i	$-0.773239\pi$
$107$	−15.6568	−1.51360	−0.756802	+	0.653644i	$0.773239\pi$
$108$	3.59124	0.345568
$109$	10.0922	0.966655	0.483327	−	0.875440i	$-0.339428\pi$
$109$	10.0922	0.966655	0.483327	+	0.875440i	$0.339428\pi$
$110$	4.43021	0.422404
$111$	−2.50551	−0.237812
$112$	41.9051	3.95966
$113$	17.0829	1.60702	0.803512	−	0.595289i	$-0.202962\pi$
$113$	17.0829	1.60702	0.803512	+	0.595289i	$0.202962\pi$
$114$	−5.03273	−0.471358
$115$	19.1876	1.78925
$116$	−9.01243	−0.836783
$117$	−15.2781	−1.41246
$118$	−6.95983	−0.640705
$119$	0.145612	0.0133483
$120$	−46.3505	−4.23120
$121$	−10.4084	−0.946220
$122$	4.23891	0.383772
$123$	25.3995	2.29020
$124$	−23.1922	−2.08272
$125$	11.6632	1.04319
$126$	−22.0170	−1.96143
$127$	13.0466	1.15770	0.578848	−	0.815436i	$-0.303503\pi$
$127$	13.0466	1.15770	0.578848	+	0.815436i	$0.303503\pi$
$128$	−30.3193	−2.67987
$129$	13.3116	1.17202
$130$	−32.3521	−2.83747
$131$	1.37506	0.120139	0.0600696	−	0.998194i	$-0.480868\pi$
$131$	1.37506	0.120139	0.0600696	+	0.998194i	$0.480868\pi$
$132$	−9.86835	−0.858930
$133$	−2.31273	−0.200539
$134$	−22.0743	−1.90693
$135$	−1.42086	−0.122288
$136$	−0.445767	−0.0382242
$137$	−16.1210	−1.37731	−0.688655	−	0.725089i	$-0.741799\pi$
$137$	−16.1210	−1.37731	−0.688655	+	0.725089i	$0.741799\pi$
$138$	−58.6749	−4.99474
$139$	−14.1452	−1.19978	−0.599891	−	0.800082i	$-0.704789\pi$
$139$	−14.1452	−1.19978	−0.599891	+	0.800082i	$0.704789\pi$
$140$	−33.9610	−2.87023
$141$	30.8937	2.60172
$142$	−25.4822	−2.13842
$143$	−4.32005	−0.361261
$144$	38.2167	3.18473
$145$	3.56573	0.296118
$146$	18.0490	1.49375
$147$	−4.53470	−0.374016
$148$	5.61994	0.461956
$149$	−0.902821	−0.0739620	−0.0369810	−	0.999316i	$-0.511774\pi$
$149$	−0.902821	−0.0739620	−0.0369810	+	0.999316i	$0.511774\pi$
$150$	−3.21318	−0.262355
$151$	−9.88529	−0.804454	−0.402227	−	0.915540i	$-0.631764\pi$
$151$	−9.88529	−0.804454	−0.402227	+	0.915540i	$0.631764\pi$
$152$	7.08004	0.574267
$153$	0.132796	0.0107359
$154$	−6.22556	−0.501670
$155$	9.17590	0.737026
$156$	72.0647	5.76980
$157$	−13.6066	−1.08593	−0.542963	−	0.839757i	$-0.682697\pi$
$157$	−13.6066	−1.08593	−0.542963	+	0.839757i	$0.682697\pi$
$158$	−31.4677	−2.50344
$159$	29.1064	2.30829
$160$	42.1661	3.33352
$161$	−26.9634	−2.12501
$162$	26.4902	2.08127
$163$	−8.08603	−0.633346	−0.316673	−	0.948535i	$-0.602566\pi$
$163$	−8.08603	−0.633346	−0.316673	+	0.948535i	$0.602566\pi$
$164$	−56.9720	−4.44876
$165$	3.90438	0.303955
$166$	−8.38665	−0.650930
$167$	−3.70086	−0.286381	−0.143190	−	0.989695i	$-0.545736\pi$
$167$	−3.70086	−0.286381	−0.143190	+	0.989695i	$0.545736\pi$
$168$	65.1341	5.02521
$169$	18.5476	1.42674
$170$	0.281202	0.0215672
$171$	−2.10917	−0.161292
$172$	−29.8584	−2.27668
$173$	3.27099	0.248689	0.124345	−	0.992239i	$-0.460317\pi$
$173$	3.27099	0.248689	0.124345	+	0.992239i	$0.460317\pi$
$174$	−10.9039	−0.826620
$175$	−1.47658	−0.111619
$176$	10.8062	0.814550
$177$	−6.13375	−0.461041
$178$	26.2061	1.96423
$179$	15.6873	1.17252	0.586261	−	0.810123i	$-0.300599\pi$
$179$	15.6873	1.17252	0.586261	+	0.810123i	$0.300599\pi$
$180$	−30.9718	−2.30850
$181$	−13.6816	−1.01695	−0.508473	−	0.861078i	$-0.669790\pi$
$181$	−13.6816	−1.01695	−0.508473	+	0.861078i	$0.669790\pi$
$182$	45.4628	3.36993
$183$	3.73578	0.276157
$184$	82.5438	6.08521
$185$	−2.22351	−0.163475
$186$	−28.0595	−2.05743
$187$	0.0375496	0.00274590
$188$	−69.2957	−5.05390
$189$	1.99667	0.145236
$190$	−4.46628	−0.324018
$191$	4.89061	0.353872	0.176936	−	0.984222i	$-0.443381\pi$
$191$	4.89061	0.353872	0.176936	+	0.984222i	$0.443381\pi$
$192$	−61.7373	−4.45551
$193$	−18.2359	−1.31265	−0.656323	−	0.754480i	$-0.727889\pi$
$193$	−18.2359	−1.31265	−0.656323	+	0.754480i	$0.727889\pi$
$194$	−9.29401	−0.667271
$195$	−28.5121	−2.04180
$196$	10.1715	0.726535
$197$	−14.0634	−1.00198	−0.500989	−	0.865453i	$-0.667030\pi$
$197$	−14.0634	−1.00198	−0.500989	+	0.865453i	$0.667030\pi$
$198$	−5.67760	−0.403489
$199$	−10.9965	−0.779522	−0.389761	−	0.920916i	$-0.627442\pi$
$199$	−10.9965	−0.779522	−0.389761	+	0.920916i	$0.627442\pi$
$200$	4.52031	0.319634
$201$	−19.4542	−1.37219
$202$	2.70949	0.190639
$203$	−5.01075	−0.351686
$204$	−0.626382	−0.0438555
$205$	22.5407	1.57431
$206$	26.0450	1.81464
$207$	−24.5901	−1.70913
$208$	−78.9137	−5.47168
$209$	−0.596393	−0.0412534
$210$	−41.0884	−2.83537
$211$	18.1533	1.24973	0.624864	−	0.780734i	$-0.285155\pi$
$211$	18.1533	1.24973	0.624864	+	0.780734i	$0.285155\pi$
$212$	−65.2867	−4.48391
$213$	−22.4576	−1.53877
$214$	42.4892	2.90451
$215$	11.8134	0.805664
$216$	−6.11246	−0.415900
$217$	−12.8944	−0.875332
$218$	−27.3879	−1.85495
$219$	15.9067	1.07488
$220$	−8.75765	−0.590440
$221$	−0.274210	−0.0184454
$222$	6.79939	0.456345
$223$	16.2472	1.08799	0.543996	−	0.839088i	$-0.316911\pi$
$223$	16.2472	1.08799	0.543996	+	0.839088i	$0.316911\pi$
$224$	−59.2539	−3.95907
$225$	−1.34662	−0.0897744
$226$	−46.3592	−3.08377
$227$	−0.178775	−0.0118657	−0.00593286	−	0.999982i	$-0.501888\pi$
$227$	−0.178775	−0.0118657	−0.00593286	+	0.999982i	$0.501888\pi$
$228$	9.94870	0.658869
$229$	−15.9152	−1.05171	−0.525853	−	0.850576i	$-0.676254\pi$
$229$	−15.9152	−1.05171	−0.525853	+	0.850576i	$0.676254\pi$
$230$	−52.0709	−3.43345
$231$	−5.48663	−0.360994
$232$	15.3396	1.00709
$233$	−2.23891	−0.146676	−0.0733378	−	0.997307i	$-0.523365\pi$
$233$	−2.23891	−0.146676	−0.0733378	+	0.997307i	$0.523365\pi$
$234$	41.4613	2.71041
$235$	27.4166	1.78846
$236$	13.7582	0.895583
$237$	−27.7327	−1.80143
$238$	−0.395160	−0.0256144
$239$	−23.9404	−1.54857	−0.774287	−	0.632835i	$-0.781891\pi$
$239$	−23.9404	−1.54857	−0.774287	+	0.632835i	$0.781891\pi$
$240$	71.3206	4.60373
$241$	−16.7767	−1.08068	−0.540342	−	0.841445i	$-0.681705\pi$
$241$	−16.7767	−1.08068	−0.540342	+	0.841445i	$0.681705\pi$
$242$	28.2462	1.81573
$243$	21.3377	1.36881
$244$	−8.37947	−0.536441
$245$	−4.02431	−0.257104
$246$	−68.9287	−4.39473
$247$	4.35522	0.277116
$248$	39.4741	2.50661
$249$	−7.39121	−0.468399
$250$	−31.6513	−2.00180
$251$	18.0788	1.14112	0.570560	−	0.821256i	$-0.306726\pi$
$251$	18.0788	1.14112	0.570560	+	0.821256i	$0.306726\pi$
$252$	43.5232	2.74170
$253$	−6.95315	−0.437141
$254$	−35.4055	−2.22154
$255$	0.247825	0.0155194
$256$	30.6530	1.91581
$257$	15.2641	0.952147	0.476073	−	0.879406i	$-0.342060\pi$
$257$	15.2641	0.952147	0.476073	+	0.879406i	$0.342060\pi$
$258$	−36.1248	−2.24903
$259$	3.12458	0.194152
$260$	63.9537	3.96624
$261$	−4.56971	−0.282858
$262$	−3.73160	−0.230539
$263$	−10.8512	−0.669111	−0.334556	−	0.942376i	$-0.608586\pi$
$263$	−10.8512	−0.669111	−0.334556	+	0.942376i	$0.608586\pi$
$264$	16.7964	1.03375
$265$	25.8304	1.58675
$266$	6.27625	0.384821
$267$	23.0956	1.41343
$268$	43.6364	2.66552
$269$	−27.7856	−1.69412	−0.847058	−	0.531501i	$-0.821628\pi$
$269$	−27.7856	−1.69412	−0.847058	+	0.531501i	$0.821628\pi$
$270$	3.85591	0.234663
$271$	−20.2639	−1.23095	−0.615473	−	0.788158i	$-0.711035\pi$
$271$	−20.2639	−1.23095	−0.615473	+	0.788158i	$0.711035\pi$
$272$	0.685912	0.0415895
$273$	40.0667	2.42495
$274$	43.7489	2.64297
$275$	−0.380772	−0.0229614
$276$	115.989	6.98169
$277$	22.0111	1.32252	0.661260	−	0.750157i	$-0.270022\pi$
$277$	22.0111	1.32252	0.661260	+	0.750157i	$0.270022\pi$
$278$	38.3870	2.30230
$279$	−11.7595	−0.704023
$280$	57.8031	3.45440
$281$	−1.32437	−0.0790055	−0.0395027	−	0.999219i	$-0.512577\pi$
$281$	−1.32437	−0.0790055	−0.0395027	+	0.999219i	$0.512577\pi$
$282$	−83.8388	−4.99253
$283$	21.9031	1.30200	0.651001	−	0.759077i	$-0.274349\pi$
$283$	21.9031	1.30200	0.651001	+	0.759077i	$0.274349\pi$
$284$	50.3732	2.98910
$285$	−3.93616	−0.233158
$286$	11.7237	0.693235
$287$	−31.6754	−1.86974
$288$	−54.0385	−3.18425
$289$	−16.9976	−0.999860
$290$	−9.67661	−0.568230
$291$	−8.19087	−0.480158
$292$	−35.6793	−2.08797
$293$	23.7582	1.38797	0.693984	−	0.719990i	$-0.255854\pi$
$293$	23.7582	1.38797	0.693984	+	0.719990i	$0.255854\pi$
$294$	12.3062	0.717711
$295$	−5.44338	−0.316926
$296$	−9.56538	−0.555976
$297$	0.514888	0.0298768
$298$	2.45006	0.141928
$299$	50.7761	2.93646
$300$	6.35183	0.366723
$301$	−16.6007	−0.956850
$302$	26.8265	1.54369
$303$	2.38789	0.137181
$304$	−10.8942	−0.624826
$305$	3.31531	0.189834
$306$	−0.360379	−0.0206015
$307$	−33.3505	−1.90341	−0.951707	−	0.307009i	$-0.900672\pi$
$307$	−33.3505	−1.90341	−0.951707	+	0.307009i	$0.900672\pi$
$308$	12.3067	0.701239
$309$	22.9536	1.30578
$310$	−24.9014	−1.41430
$311$	−16.7426	−0.949386	−0.474693	−	0.880152i	$-0.657441\pi$
$311$	−16.7426	−0.949386	−0.474693	+	0.880152i	$0.657441\pi$
$312$	−122.657	−6.94411
$313$	−0.969220	−0.0547836	−0.0273918	−	0.999625i	$-0.508720\pi$
$313$	−0.969220	−0.0547836	−0.0273918	+	0.999625i	$0.508720\pi$
$314$	36.9253	2.08382
$315$	−17.2198	−0.970224
$316$	62.2054	3.49933
$317$	−26.4631	−1.48631	−0.743157	−	0.669117i	$-0.766673\pi$
$317$	−26.4631	−1.48631	−0.743157	+	0.669117i	$0.766673\pi$
$318$	−78.9885	−4.42945
$319$	−1.29214	−0.0723460
$320$	−54.7886	−3.06278
$321$	37.4461	2.09004
$322$	73.1727	4.07775
$323$	−0.0378553	−0.00210633
$324$	−52.3658	−2.90921
$325$	2.78063	0.154241
$326$	21.9437	1.21535
$327$	−24.1372	−1.33479
$328$	96.9688	5.35421
$329$	−38.5271	−2.12407
$330$	−10.5956	−0.583269
$331$	24.3571	1.33879	0.669395	−	0.742907i	$-0.266553\pi$
$331$	24.3571	1.33879	0.669395	+	0.742907i	$0.266553\pi$
$332$	16.5787	0.909876
$333$	2.84956	0.156155
$334$	10.0433	0.549546
$335$	−17.2646	−0.943265
$336$	−100.223	−5.46763
$337$	−26.9949	−1.47051	−0.735254	−	0.677792i	$-0.762937\pi$
$337$	−26.9949	−1.47051	−0.735254	+	0.677792i	$0.762937\pi$
$338$	−50.3342	−2.73782
$339$	−40.8567	−2.21903
$340$	−0.555881	−0.0301469
$341$	−3.32514	−0.180066
$342$	5.72382	0.309509
$343$	−15.2232	−0.821975
$344$	50.8203	2.74005
$345$	−45.8904	−2.47066
$346$	−8.87676	−0.477218
$347$	−29.5092	−1.58414	−0.792068	−	0.610433i	$-0.790995\pi$
$347$	−29.5092	−1.58414	−0.792068	+	0.610433i	$0.790995\pi$
$348$	21.5548	1.15546
$349$	0.338389	0.0181135	0.00905676	−	0.999959i	$-0.497117\pi$
$349$	0.338389	0.0181135	0.00905676	+	0.999959i	$0.497117\pi$
$350$	4.00712	0.214190
$351$	−3.76003	−0.200695
$352$	−15.2800	−0.814428
$353$	−26.3430	−1.40210	−0.701048	−	0.713114i	$-0.747284\pi$
$353$	−26.3430	−1.40210	−0.701048	+	0.713114i	$0.747284\pi$
$354$	16.6456	0.884706
$355$	−19.9300	−1.05777
$356$	−51.8043	−2.74562
$357$	−0.348257	−0.0184317
$358$	−42.5718	−2.24999
$359$	7.98268	0.421310	0.210655	−	0.977560i	$-0.432440\pi$
$359$	7.98268	0.421310	0.210655	+	0.977560i	$0.432440\pi$
$360$	52.7154	2.77835
$361$	−18.3988	−0.968355
$362$	37.1289	1.95145
$363$	24.8935	1.30657
$364$	−89.8709	−4.71052
$365$	14.1164	0.738885
$366$	−10.1381	−0.529926
$367$	13.3365	0.696158	0.348079	−	0.937465i	$-0.386834\pi$
$367$	13.3365	0.696158	0.348079	+	0.937465i	$0.386834\pi$
$368$	−127.012	−6.62096
$369$	−28.8874	−1.50382
$370$	6.03410	0.313698
$371$	−36.2982	−1.88451
$372$	55.4681	2.87589
$373$	−10.9786	−0.568451	−0.284225	−	0.958757i	$-0.591736\pi$
$373$	−10.9786	−0.568451	−0.284225	+	0.958757i	$0.591736\pi$
$374$	−0.101901	−0.00526919
$375$	−27.8945	−1.44047
$376$	117.944	6.08251
$377$	9.43599	0.485978
$378$	−5.41852	−0.278698
$379$	8.77788	0.450889	0.225445	−	0.974256i	$-0.427617\pi$
$379$	8.77788	0.450889	0.225445	+	0.974256i	$0.427617\pi$
$380$	8.82895	0.452916
$381$	−31.2031	−1.59858
$382$	−13.2720	−0.679056
$383$	−2.60171	−0.132941	−0.0664707	−	0.997788i	$-0.521174\pi$
$383$	−2.60171	−0.132941	−0.0664707	+	0.997788i	$0.521174\pi$
$384$	72.5138	3.70045
$385$	−4.86909	−0.248152
$386$	49.4882	2.51888
$387$	−15.1396	−0.769587
$388$	18.3724	0.932718
$389$	7.34378	0.372345	0.186172	−	0.982517i	$-0.440392\pi$
$389$	7.34378	0.372345	0.186172	+	0.982517i	$0.440392\pi$
$390$	77.3756	3.91807
$391$	−0.441342	−0.0223196
$392$	−17.3123	−0.874405
$393$	−3.28868	−0.165892
$394$	38.1651	1.92273
$395$	−24.6113	−1.23833
$396$	11.2235	0.564001
$397$	10.7079	0.537414	0.268707	−	0.963222i	$-0.413404\pi$
$397$	10.7079	0.537414	0.268707	+	0.963222i	$0.413404\pi$
$398$	29.8421	1.49585
$399$	5.53130	0.276911
$400$	−6.95550	−0.347775
$401$	5.62667	0.280982	0.140491	−	0.990082i	$-0.455132\pi$
$401$	5.62667	0.280982	0.140491	+	0.990082i	$0.455132\pi$
$402$	52.7944	2.63315
$403$	24.2822	1.20958
$404$	−5.35611	−0.266477
$405$	20.7183	1.02950
$406$	13.5981	0.674861
$407$	0.805748	0.0399394
$408$	1.06613	0.0527813
$409$	0.140358	0.00694024	0.00347012	−	0.999994i	$-0.498895\pi$
$409$	0.140358	0.00694024	0.00347012	+	0.999994i	$0.498895\pi$
$410$	−61.1706	−3.02100
$411$	38.5562	1.90184
$412$	−51.4857	−2.53652
$413$	7.64931	0.376398
$414$	66.7322	3.27971
$415$	−6.55931	−0.321984
$416$	111.584	5.47086
$417$	33.8307	1.65670
$418$	1.61848	0.0791624
$419$	17.5993	0.859781	0.429890	−	0.902881i	$-0.358552\pi$
$419$	17.5993	0.859781	0.429890	+	0.902881i	$0.358552\pi$
$420$	81.2236	3.96330
$421$	5.75912	0.280682	0.140341	−	0.990103i	$-0.455180\pi$
$421$	5.75912	0.280682	0.140341	+	0.990103i	$0.455180\pi$
$422$	−49.2642	−2.39814
$423$	−35.1361	−1.70837
$424$	111.121	5.39651
$425$	−0.0241690	−0.00117237
$426$	60.9451	2.95280
$427$	−4.65884	−0.225457
$428$	−83.9928	−4.05994
$429$	10.3321	0.498841
$430$	−32.0588	−1.54601
$431$	−9.49228	−0.457227	−0.228614	−	0.973517i	$-0.573419\pi$
$431$	−9.49228	−0.457227	−0.228614	+	0.973517i	$0.573419\pi$
$432$	9.40538	0.452516
$433$	39.4143	1.89413	0.947065	−	0.321042i	$-0.104033\pi$
$433$	39.4143	1.89413	0.947065	+	0.321042i	$0.104033\pi$
$434$	34.9927	1.67970
$435$	−8.52806	−0.408889
$436$	54.1405	2.59286
$437$	7.00976	0.335322
$438$	−43.1673	−2.06261
$439$	7.00341	0.334255	0.167127	−	0.985935i	$-0.446551\pi$
$439$	7.00341	0.334255	0.167127	+	0.985935i	$0.446551\pi$
$440$	14.9059	0.710611
$441$	5.15741	0.245591
$442$	0.744145	0.0353954
$443$	6.57392	0.312336	0.156168	−	0.987730i	$-0.450086\pi$
$443$	6.57392	0.312336	0.156168	+	0.987730i	$0.450086\pi$
$444$	−13.4410	−0.637884
$445$	20.4962	0.971611
$446$	−44.0913	−2.08778
$447$	2.15925	0.102129
$448$	76.9918	3.63752
$449$	−10.1676	−0.479841	−0.239920	−	0.970793i	$-0.577121\pi$
$449$	−10.1676	−0.479841	−0.239920	+	0.970793i	$0.577121\pi$
$450$	3.65442	0.172271
$451$	−8.16825	−0.384628
$452$	91.6429	4.31052
$453$	23.6424	1.11082
$454$	0.485156	0.0227695
$455$	35.5571	1.66694
$456$	−16.9331	−0.792967
$457$	1.03315	0.0483286	0.0241643	−	0.999708i	$-0.492308\pi$
$457$	1.03315	0.0483286	0.0241643	+	0.999708i	$0.492308\pi$
$458$	43.1903	2.01815
$459$	0.0326819	0.00152546
$460$	102.934	4.79931
$461$	29.5797	1.37766	0.688832	−	0.724921i	$-0.258124\pi$
$461$	29.5797	1.37766	0.688832	+	0.724921i	$0.258124\pi$
$462$	14.8895	0.692722
$463$	28.7532	1.33628	0.668138	−	0.744037i	$-0.267091\pi$
$463$	28.7532	1.33628	0.668138	+	0.744037i	$0.267091\pi$
$464$	−23.6033	−1.09576
$465$	−21.9457	−1.01771
$466$	6.07590	0.281461
$467$	−38.6558	−1.78878	−0.894389	−	0.447291i	$-0.852389\pi$
$467$	−38.6558	−1.78878	−0.894389	+	0.447291i	$0.852389\pi$
$468$	−81.9607	−3.78863
$469$	24.2611	1.12027
$470$	−74.4025	−3.43193
$471$	32.5425	1.49948
$472$	−23.4171	−1.07786
$473$	−4.28089	−0.196836
$474$	75.2604	3.45683
$475$	0.383872	0.0176133
$476$	0.781152	0.0358040
$477$	−33.1033	−1.51570
$478$	64.9689	2.97161
$479$	30.2809	1.38357	0.691785	−	0.722103i	$-0.256824\pi$
$479$	30.2809	1.38357	0.691785	+	0.722103i	$0.256824\pi$
$480$	−100.847	−4.60303
$481$	−5.88406	−0.268290
$482$	45.5284	2.07376
$483$	64.4876	2.93429
$484$	−55.8371	−2.53805
$485$	−7.26897	−0.330067
$486$	−57.9058	−2.62666
$487$	−30.3120	−1.37357	−0.686784	−	0.726861i	$-0.740978\pi$
$487$	−30.3120	−1.37357	−0.686784	+	0.726861i	$0.740978\pi$
$488$	14.2622	0.645621
$489$	19.3391	0.874546
$490$	10.9211	0.493365
$491$	19.1111	0.862471	0.431235	−	0.902239i	$-0.358078\pi$
$491$	19.1111	0.862471	0.431235	+	0.902239i	$0.358078\pi$
$492$	136.258	6.14300
$493$	−0.0820170	−0.00369386
$494$	−11.8191	−0.531767
$495$	−4.44053	−0.199587
$496$	−60.7398	−2.72730
$497$	28.0066	1.25627
$498$	20.0581	0.898826
$499$	−19.8538	−0.888780	−0.444390	−	0.895833i	$-0.646580\pi$
$499$	−19.8538	−0.888780	−0.444390	+	0.895833i	$0.646580\pi$
$500$	62.5683	2.79814
$501$	8.85124	0.395444
$502$	−49.0618	−2.18973
$503$	−4.72840	−0.210829	−0.105414	−	0.994428i	$-0.533617\pi$
$503$	−4.72840	−0.210829	−0.105414	+	0.994428i	$0.533617\pi$
$504$	−74.0784	−3.29971
$505$	2.11913	0.0942998
$506$	18.8693	0.838843
$507$	−44.3599	−1.97009
$508$	69.9896	3.10529
$509$	3.04554	0.134991	0.0674957	−	0.997720i	$-0.478499\pi$
$509$	3.04554	0.134991	0.0674957	+	0.997720i	$0.478499\pi$
$510$	−0.672544	−0.0297807
$511$	−19.8371	−0.877539
$512$	−22.5468	−0.996439
$513$	−0.519080	−0.0229179
$514$	−41.4233	−1.82710
$515$	20.3701	0.897615
$516$	71.4115	3.14371
$517$	−9.93514	−0.436947
$518$	−8.47943	−0.372565
$519$	−7.82315	−0.343398
$520$	−108.852	−4.77347
$521$	−21.4552	−0.939971	−0.469986	−	0.882674i	$-0.655741\pi$
$521$	−21.4552	−0.939971	−0.469986	+	0.882674i	$0.655741\pi$
$522$	12.4012	0.542786
$523$	18.0425	0.788944	0.394472	−	0.918908i	$-0.370928\pi$
$523$	18.0425	0.788944	0.394472	+	0.918908i	$0.370928\pi$
$524$	7.37663	0.322249
$525$	3.53150	0.154127
$526$	29.4477	1.28398
$527$	−0.211059	−0.00919387
$528$	−25.8450	−1.12476
$529$	58.7244	2.55324
$530$	−70.0981	−3.04487
$531$	6.97604	0.302734
$532$	−12.4069	−0.537907
$533$	59.6495	2.58371
$534$	−62.6765	−2.71228
$535$	33.2314	1.43672
$536$	−74.2711	−3.20802
$537$	−37.5188	−1.61906
$538$	75.4039	3.25089
$539$	1.45832	0.0628142
$540$	−7.62236	−0.328014
$541$	40.8272	1.75530	0.877648	−	0.479305i	$-0.159111\pi$
$541$	40.8272	1.75530	0.877648	+	0.479305i	$0.159111\pi$
$542$	54.9919	2.36210
$543$	32.7219	1.40423
$544$	−0.969881	−0.0415833
$545$	−21.4205	−0.917552
$546$	−108.732	−4.65331
$547$	−6.93821	−0.296657	−0.148328	−	0.988938i	$-0.547389\pi$
$547$	−6.93821	−0.296657	−0.148328	+	0.988938i	$0.547389\pi$
$548$	−86.4828	−3.69436
$549$	−4.24877	−0.181333
$550$	1.03333	0.0440614
$551$	1.30266	0.0554952
$552$	−197.418	−8.40266
$553$	34.5851	1.47071
$554$	−59.7333	−2.53783
$555$	5.31790	0.225732
$556$	−75.8835	−3.21818
$557$	18.6068	0.788395	0.394198	−	0.919026i	$-0.371023\pi$
$557$	18.6068	0.788395	0.394198	+	0.919026i	$0.371023\pi$
$558$	31.9127	1.35097
$559$	31.2617	1.32223
$560$	−88.9430	−3.75853
$561$	−0.0898063	−0.00379163
$562$	3.59406	0.151606
$563$	−28.9097	−1.21840	−0.609199	−	0.793017i	$-0.708509\pi$
$563$	−28.9097	−1.21840	−0.609199	+	0.793017i	$0.708509\pi$
$564$	165.733	6.97860
$565$	−36.2582	−1.52539
$566$	−59.4401	−2.49845
$567$	−29.1145	−1.22269
$568$	−85.7375	−3.59746
$569$	24.0351	1.00760	0.503802	−	0.863819i	$-0.331934\pi$
$569$	24.0351	1.00760	0.503802	+	0.863819i	$0.331934\pi$
$570$	10.6819	0.447415
$571$	23.8364	0.997524	0.498762	−	0.866739i	$-0.333788\pi$
$571$	23.8364	0.997524	0.498762	+	0.866739i	$0.333788\pi$
$572$	−23.1754	−0.969010
$573$	−11.6967	−0.488638
$574$	85.9600	3.58790
$575$	4.47543	0.186639
$576$	70.2151	2.92563
$577$	−31.2631	−1.30150	−0.650750	−	0.759292i	$-0.725545\pi$
$577$	−31.2631	−1.30150	−0.650750	+	0.759292i	$0.725545\pi$
$578$	46.1278	1.91866
$579$	43.6142	1.81255
$580$	19.1287	0.794278
$581$	9.21748	0.382405
$582$	22.2282	0.921390
$583$	−9.36036	−0.387667
$584$	60.7278	2.51293
$585$	32.4274	1.34071
$586$	−64.4745	−2.66342
$587$	−25.4229	−1.04931	−0.524657	−	0.851314i	$-0.675806\pi$
$587$	−25.4229	−1.04931	−0.524657	+	0.851314i	$0.675806\pi$
$588$	−24.3269	−1.00322
$589$	3.35221	0.138125
$590$	14.7721	0.608159
$591$	33.6352	1.38357
$592$	14.7185	0.604925
$593$	−31.8551	−1.30813	−0.654067	−	0.756437i	$-0.726938\pi$
$593$	−31.8551	−1.30813	−0.654067	+	0.756437i	$0.726938\pi$
$594$	−1.39729	−0.0573316
$595$	−0.309060	−0.0126702
$596$	−4.84328	−0.198388
$597$	26.3001	1.07639
$598$	−137.795	−5.63486
$599$	25.5654	1.04458	0.522288	−	0.852769i	$-0.325079\pi$
$599$	25.5654	1.04458	0.522288	+	0.852769i	$0.325079\pi$
$600$	−10.8111	−0.441361
$601$	−2.11701	−0.0863546	−0.0431773	−	0.999067i	$-0.513748\pi$
$601$	−2.11701	−0.0863546	−0.0431773	+	0.999067i	$0.513748\pi$
$602$	45.0507	1.83613
$603$	22.1257	0.901026
$604$	−53.0307	−2.15779
$605$	22.0917	0.898156
$606$	−6.48020	−0.263240
$607$	−38.3551	−1.55678	−0.778392	−	0.627779i	$-0.783964\pi$
$607$	−38.3551	−1.55678	−0.778392	+	0.627779i	$0.783964\pi$
$608$	15.4044	0.624732
$609$	11.9841	0.485619
$610$	−8.99701	−0.364278
$611$	72.5524	2.93516
$612$	0.712397	0.0287969
$613$	23.9347	0.966713	0.483356	−	0.875424i	$-0.339418\pi$
$613$	23.9347	0.966713	0.483356	+	0.875424i	$0.339418\pi$
$614$	90.5059	3.65252
$615$	−53.9101	−2.17386
$616$	−20.9465	−0.843960
$617$	−11.5577	−0.465297	−0.232649	−	0.972561i	$-0.574739\pi$
$617$	−11.5577	−0.465297	−0.232649	+	0.972561i	$0.574739\pi$
$618$	−62.2910	−2.50571
$619$	12.9985	0.522453	0.261226	−	0.965278i	$-0.415873\pi$
$619$	12.9985	0.522453	0.261226	+	0.965278i	$0.415873\pi$
$620$	49.2251	1.97693
$621$	−6.05178	−0.242850
$622$	45.4357	1.82181
$623$	−28.8022	−1.15394
$624$	188.736	7.55547
$625$	−22.2796	−0.891184
$626$	2.63025	0.105126
$627$	1.42638	0.0569640
$628$	−72.9940	−2.91278
$629$	0.0511439	0.00203924
$630$	46.7307	1.86179
$631$	0.873071	0.0347564	0.0173782	−	0.999849i	$-0.494468\pi$
$631$	0.873071	0.0347564	0.0173782	+	0.999849i	$0.494468\pi$
$632$	−105.876	−4.21153
$633$	−43.4168	−1.72566
$634$	71.8150	2.85214
$635$	−27.6911	−1.09889
$636$	156.144	6.19153
$637$	−10.6495	−0.421950
$638$	3.50658	0.138827
$639$	25.5415	1.01041
$640$	64.3522	2.54374
$641$	27.5976	1.09004	0.545020	−	0.838423i	$-0.316522\pi$
$641$	27.5976	1.09004	0.545020	+	0.838423i	$0.316522\pi$
$642$	−101.620	−4.01064
$643$	−8.09283	−0.319150	−0.159575	−	0.987186i	$-0.551012\pi$
$643$	−8.09283	−0.319150	−0.159575	+	0.987186i	$0.551012\pi$
$644$	−144.648	−5.69992
$645$	−28.2537	−1.11249
$646$	0.102731	0.00404190
$647$	25.3616	0.997068	0.498534	−	0.866870i	$-0.333872\pi$
$647$	25.3616	0.997068	0.498534	+	0.866870i	$0.333872\pi$
$648$	89.1290	3.50132
$649$	1.97256	0.0774296
$650$	−7.54601	−0.295979
$651$	30.8393	1.20869
$652$	−43.3783	−1.69883
$653$	22.9315	0.897379	0.448689	−	0.893688i	$-0.351891\pi$
$653$	22.9315	0.897379	0.448689	+	0.893688i	$0.351891\pi$
$654$	65.5030	2.56137
$655$	−2.91853	−0.114037
$656$	−149.208	−5.82560
$657$	−18.0910	−0.705798
$658$	104.554	4.07595
$659$	−26.4249	−1.02937	−0.514684	−	0.857380i	$-0.672091\pi$
$659$	−26.4249	−1.02937	−0.514684	+	0.857380i	$0.672091\pi$
$660$	20.9454	0.815300
$661$	9.11163	0.354401	0.177201	−	0.984175i	$-0.443296\pi$
$661$	9.11163	0.354401	0.177201	+	0.984175i	$0.443296\pi$
$662$	−66.0999	−2.56905
$663$	0.655820	0.0254699
$664$	−28.2177	−1.09506
$665$	4.90874	0.190353
$666$	−7.73309	−0.299651
$667$	15.1873	0.588054
$668$	−19.8536	−0.768160
$669$	−38.8580	−1.50234
$670$	46.8523	1.81006
$671$	−1.20139	−0.0463792
$672$	141.716	5.46681
$673$	12.2551	0.472398	0.236199	−	0.971705i	$-0.424098\pi$
$673$	12.2551	0.472398	0.236199	+	0.971705i	$0.424098\pi$
$674$	73.2583	2.82180
$675$	−0.331411	−0.0127560
$676$	99.5007	3.82695
$677$	−26.7466	−1.02796	−0.513978	−	0.857804i	$-0.671829\pi$
$677$	−26.7466	−1.02796	−0.513978	+	0.857804i	$0.671829\pi$
$678$	110.876	4.25817
$679$	10.2147	0.392005
$680$	0.946134	0.0362826
$681$	0.427571	0.0163846
$682$	9.02369	0.345535
$683$	−16.1030	−0.616165	−0.308083	−	0.951360i	$-0.599687\pi$
$683$	−16.1030	−0.616165	−0.308083	+	0.951360i	$0.599687\pi$
$684$	−11.3149	−0.432635
$685$	34.2166	1.30735
$686$	41.3124	1.57731
$687$	38.0639	1.45223
$688$	−78.1983	−2.98128
$689$	68.3551	2.60412
$690$	124.537	4.74103
$691$	−43.6617	−1.66097	−0.830484	−	0.557043i	$-0.811936\pi$
$691$	−43.6617	−1.66097	−0.830484	+	0.557043i	$0.811936\pi$
$692$	17.5476	0.667059
$693$	6.24005	0.237040
$694$	80.0814	3.03985
$695$	30.0230	1.13884
$696$	−36.6872	−1.39062
$697$	−0.518470	−0.0196384
$698$	−0.918312	−0.0347586
$699$	5.35473	0.202535
$700$	−7.92128	−0.299396
$701$	−33.2194	−1.25468	−0.627340	−	0.778745i	$-0.715856\pi$
$701$	−33.2194	−1.25468	−0.627340	+	0.778745i	$0.715856\pi$
$702$	10.2039	0.385121
$703$	−0.812308	−0.0306368
$704$	19.8542	0.748282
$705$	−65.5714	−2.46956
$706$	71.4891	2.69053
$707$	−2.97790	−0.111996
$708$	−32.9051	−1.23665
$709$	24.5552	0.922192	0.461096	−	0.887350i	$-0.347456\pi$
$709$	24.5552	0.922192	0.461096	+	0.887350i	$0.347456\pi$
$710$	54.0856	2.02979
$711$	31.5410	1.18288
$712$	88.1732	3.30443
$713$	39.0823	1.46364
$714$	0.945093	0.0353692
$715$	9.16924	0.342910
$716$	84.1559	3.14506
$717$	57.2575	2.13832
$718$	−21.6632	−0.808465
$719$	10.5228	0.392434	0.196217	−	0.980560i	$-0.437134\pi$
$719$	10.5228	0.392434	0.196217	+	0.980560i	$0.437134\pi$
$720$	−81.1144	−3.02295
$721$	−28.6251	−1.06606
$722$	49.9302	1.85821
$723$	40.1245	1.49224
$724$	−73.3964	−2.72775
$725$	0.831694	0.0308883
$726$	−67.5556	−2.50722
$727$	44.6126	1.65459	0.827294	−	0.561769i	$-0.189879\pi$
$727$	44.6126	1.65459	0.827294	+	0.561769i	$0.189879\pi$
$728$	152.964	5.66924
$729$	−21.7487	−0.805506
$730$	−38.3087	−1.41787
$731$	−0.271724	−0.0100501
$732$	20.0410	0.740735
$733$	5.75338	0.212506	0.106253	−	0.994339i	$-0.466115\pi$
$733$	5.75338	0.212506	0.106253	+	0.994339i	$0.466115\pi$
$734$	−36.1922	−1.33588
$735$	9.62483	0.355017
$736$	179.595	6.61996
$737$	6.25629	0.230453
$738$	78.3940	2.88572
$739$	−50.3291	−1.85138	−0.925692	−	0.378277i	$-0.876517\pi$
$739$	−50.3291	−1.85138	−0.925692	+	0.378277i	$0.876517\pi$
$740$	−11.9282	−0.438490
$741$	−10.4163	−0.382651
$742$	98.5054	3.61625
$743$	24.4111	0.895556	0.447778	−	0.894145i	$-0.352215\pi$
$743$	24.4111	0.895556	0.447778	+	0.894145i	$0.352215\pi$
$744$	−94.4092	−3.46121
$745$	1.91622	0.0702050
$746$	29.7935	1.09082
$747$	8.40617	0.307566
$748$	0.201439	0.00736532
$749$	−46.6985	−1.70633
$750$	75.6996	2.76416
$751$	−33.4064	−1.21902	−0.609508	−	0.792780i	$-0.708633\pi$
$751$	−33.4064	−1.21902	−0.609508	+	0.792780i	$0.708633\pi$
$752$	−181.484	−6.61802
$753$	−43.2385	−1.57570
$754$	−25.6072	−0.932560
$755$	20.9814	0.763591
$756$	10.7113	0.389567
$757$	−5.45962	−0.198433	−0.0992167	−	0.995066i	$-0.531634\pi$
$757$	−5.45962	−0.198433	−0.0992167	+	0.995066i	$0.531634\pi$
$758$	−23.8212	−0.865226
$759$	16.6296	0.603618
$760$	−15.0273	−0.545096
$761$	−34.6357	−1.25554	−0.627772	−	0.778397i	$-0.716033\pi$
$761$	−34.6357	−1.25554	−0.627772	+	0.778397i	$0.716033\pi$
$762$	84.6784	3.06757
$763$	30.1011	1.08973
$764$	26.2362	0.949191
$765$	−0.281857	−0.0101906
$766$	7.06048	0.255105
$767$	−14.4048	−0.520128
$768$	−73.3119	−2.64541
$769$	−15.2285	−0.549152	−0.274576	−	0.961565i	$-0.588538\pi$
$769$	−15.2285	−0.549152	−0.274576	+	0.961565i	$0.588538\pi$
$770$	13.2136	0.476187
$771$	−36.5067	−1.31476
$772$	−97.8282	−3.52091
$773$	38.7436	1.39351	0.696755	−	0.717309i	$-0.254626\pi$
$773$	38.7436	1.39351	0.696755	+	0.717309i	$0.254626\pi$
$774$	41.0854	1.47679
$775$	2.14024	0.0768799
$776$	−31.2707	−1.12255
$777$	−7.47298	−0.268092
$778$	−19.9294	−0.714504
$779$	8.23475	0.295041
$780$	−152.956	−5.47671
$781$	7.22217	0.258430
$782$	1.19771	0.0428299
$783$	−1.12464	−0.0401912
$784$	26.6389	0.951388
$785$	28.8798	1.03076
$786$	8.92476	0.318336
$787$	40.0202	1.42657	0.713284	−	0.700875i	$-0.247207\pi$
$787$	40.0202	1.42657	0.713284	+	0.700875i	$0.247207\pi$
$788$	−75.4448	−2.68761
$789$	25.9524	0.923931
$790$	66.7897	2.37627
$791$	50.9518	1.81164
$792$	−19.1029	−0.678791
$793$	8.77329	0.311549
$794$	−29.0589	−1.03126
$795$	−61.7779	−2.19104
$796$	−58.9919	−2.09091
$797$	19.8744	0.703986	0.351993	−	0.936003i	$-0.385504\pi$
$797$	19.8744	0.703986	0.351993	+	0.936003i	$0.385504\pi$
$798$	−15.0107	−0.531374
$799$	−0.630621	−0.0223098
$800$	9.83508	0.347723
$801$	−26.2671	−0.928103
$802$	−15.2695	−0.539186
$803$	−5.11545	−0.180520
$804$	−104.364	−3.68064
$805$	57.2293	2.01707
$806$	−65.8965	−2.32110
$807$	66.4540	2.33929
$808$	9.11634	0.320712
$809$	5.53026	0.194433	0.0972167	−	0.995263i	$-0.469006\pi$
$809$	5.53026	0.194433	0.0972167	+	0.995263i	$0.469006\pi$
$810$	−56.2250	−1.97554
$811$	16.4519	0.577706	0.288853	−	0.957373i	$-0.406726\pi$
$811$	16.4519	0.577706	0.288853	+	0.957373i	$0.406726\pi$
$812$	−26.8807	−0.943327
$813$	48.4647	1.69973
$814$	−2.18662	−0.0766411
$815$	17.1625	0.601175
$816$	−1.64048	−0.0574282
$817$	4.31574	0.150989
$818$	−0.380900	−0.0133178
$819$	−45.5687	−1.59230
$820$	120.922	4.22278
$821$	−7.42216	−0.259035	−0.129518	−	0.991577i	$-0.541343\pi$
$821$	−7.42216	−0.259035	−0.129518	+	0.991577i	$0.541343\pi$
$822$	−104.633	−3.64949
$823$	−27.2862	−0.951137	−0.475569	−	0.879679i	$-0.657758\pi$
$823$	−27.2862	−0.951137	−0.475569	+	0.879679i	$0.657758\pi$
$824$	87.6310	3.05277
$825$	0.910681	0.0317059
$826$	−20.7586	−0.722283
$827$	−6.30199	−0.219142	−0.109571	−	0.993979i	$-0.534948\pi$
$827$	−6.30199	−0.219142	−0.109571	+	0.993979i	$0.534948\pi$
$828$	−131.916	−4.58440
$829$	18.8539	0.654822	0.327411	−	0.944882i	$-0.393824\pi$
$829$	18.8539	0.654822	0.327411	+	0.944882i	$0.393824\pi$
$830$	17.8005	0.617865
$831$	−52.6434	−1.82618
$832$	−144.987	−5.02652
$833$	0.0925650	0.00320719
$834$	−91.8092	−3.17909
$835$	7.85501	0.271834
$836$	−3.19941	−0.110654
$837$	−2.89409	−0.100034
$838$	−47.7606	−1.64986
$839$	−39.4170	−1.36083	−0.680413	−	0.732829i	$-0.738199\pi$
$839$	−39.4170	−1.36083	−0.680413	+	0.732829i	$0.738199\pi$
$840$	−138.246	−4.76994
$841$	−26.1777	−0.902678
$842$	−15.6290	−0.538610
$843$	3.16747	0.109093
$844$	97.3854	3.35215
$845$	−39.3671	−1.35427
$846$	95.3515	3.27825
$847$	−31.0444	−1.06670
$848$	−170.984	−5.87162
$849$	−52.3850	−1.79785
$850$	0.0655894	0.00224970
$851$	−9.47043	−0.324642
$852$	−120.476	−4.12745
$853$	26.1436	0.895140	0.447570	−	0.894249i	$-0.352290\pi$
$853$	26.1436	0.895140	0.447570	+	0.894249i	$0.352290\pi$
$854$	12.6431	0.432636
$855$	4.47668	0.153099
$856$	142.959	4.88625
$857$	11.7958	0.402938	0.201469	−	0.979495i	$-0.435429\pi$
$857$	11.7958	0.402938	0.201469	+	0.979495i	$0.435429\pi$
$858$	−28.0392	−0.957242
$859$	−13.9363	−0.475499	−0.237749	−	0.971327i	$-0.576410\pi$
$859$	−13.9363	−0.475499	−0.237749	+	0.971327i	$0.576410\pi$
$860$	63.3739	2.16103
$861$	75.7572	2.58180
$862$	25.7600	0.877388
$863$	26.4111	0.899044	0.449522	−	0.893269i	$-0.351594\pi$
$863$	26.4111	0.899044	0.449522	+	0.893269i	$0.351594\pi$
$864$	−13.2992	−0.452448
$865$	−6.94263	−0.236057
$866$	−106.962	−3.63471
$867$	40.6527	1.38064
$868$	−69.1735	−2.34790
$869$	8.91858	0.302542
$870$	23.1433	0.784631
$871$	−45.6872	−1.54805
$872$	−92.1495	−3.12058
$873$	9.31565	0.315287
$874$	−19.0229	−0.643461
$875$	34.7869	1.17601
$876$	85.3332	2.88314
$877$	2.87087	0.0969426	0.0484713	−	0.998825i	$-0.484565\pi$
$877$	2.87087	0.0969426	0.0484713	+	0.998825i	$0.484565\pi$
$878$	−19.0057	−0.641412
$879$	−56.8218	−1.91655
$880$	−22.9361	−0.773174
$881$	−13.4940	−0.454626	−0.227313	−	0.973822i	$-0.572994\pi$
$881$	−13.4940	−0.454626	−0.227313	+	0.973822i	$0.572994\pi$
$882$	−13.9961	−0.471272
$883$	21.4175	0.720755	0.360378	−	0.932806i	$-0.382648\pi$
$883$	21.4175	0.720755	0.360378	+	0.932806i	$0.382648\pi$
$884$	−1.47103	−0.0494760
$885$	13.0188	0.437622
$886$	−17.8402	−0.599352
$887$	14.6444	0.491711	0.245855	−	0.969306i	$-0.420931\pi$
$887$	14.6444	0.491711	0.245855	+	0.969306i	$0.420931\pi$
$888$	22.8773	0.767711
$889$	38.9130	1.30510
$890$	−55.6221	−1.86446
$891$	−7.50785	−0.251523
$892$	87.1597	2.91832
$893$	10.0160	0.335174
$894$	−5.85974	−0.195979
$895$	−33.2960	−1.11296
$896$	−90.4310	−3.02109
$897$	−121.440	−4.05476
$898$	27.5927	0.920782
$899$	7.26287	0.242230
$900$	−7.22406	−0.240802
$901$	−0.594137	−0.0197936
$902$	22.1668	0.738075
$903$	39.7035	1.32125
$904$	−155.980	−5.18783
$905$	29.0390	0.965288
$906$	−64.1602	−2.13158
$907$	−5.63816	−0.187212	−0.0936061	−	0.995609i	$-0.529839\pi$
$907$	−5.63816	−0.187212	−0.0936061	+	0.995609i	$0.529839\pi$
$908$	−0.959057	−0.0318274
$909$	−2.71579	−0.0900772
$910$	−96.4941	−3.19875
$911$	5.38321	0.178354	0.0891769	−	0.996016i	$-0.471576\pi$
$911$	5.38321	0.178354	0.0891769	+	0.996016i	$0.471576\pi$
$912$	26.0554	0.862780
$913$	2.37694	0.0786654
$914$	−2.80374	−0.0927394
$915$	−7.92912	−0.262129
$916$	−85.3787	−2.82099
$917$	4.10127	0.135436
$918$	−0.0886914	−0.00292725
$919$	33.5369	1.10628	0.553141	−	0.833088i	$-0.313429\pi$
$919$	33.5369	1.10628	0.553141	+	0.833088i	$0.313429\pi$
$920$	−175.198	−5.77610
$921$	79.7635	2.62830
$922$	−80.2729	−2.64365
$923$	−52.7407	−1.73598
$924$	−29.4336	−0.968294
$925$	−0.518624	−0.0170523
$926$	−78.0300	−2.56422
$927$	−26.1056	−0.857420
$928$	33.3751	1.09559
$929$	28.9318	0.949221	0.474611	−	0.880196i	$-0.342589\pi$
$929$	28.9318	0.949221	0.474611	+	0.880196i	$0.342589\pi$
$930$	59.5559	1.95292
$931$	−1.47019	−0.0481836
$932$	−12.0108	−0.393428
$933$	40.0428	1.31094
$934$	104.903	3.43254
$935$	−0.0796984	−0.00260642
$936$	139.501	4.55972
$937$	−19.9834	−0.652830	−0.326415	−	0.945227i	$-0.605841\pi$
$937$	−19.9834	−0.652830	−0.326415	+	0.945227i	$0.605841\pi$
$938$	−65.8392	−2.14973
$939$	2.31806	0.0756470
$940$	147.079	4.79719
$941$	−8.15856	−0.265961	−0.132981	−	0.991119i	$-0.542455\pi$
$941$	−8.15856	−0.265961	−0.132981	+	0.991119i	$0.542455\pi$
$942$	−88.3133	−2.87740
$943$	96.0063	3.12639
$944$	36.0324	1.17275
$945$	−4.23789	−0.137859
$946$	11.6174	0.377714
$947$	0.264395	0.00859168	0.00429584	−	0.999991i	$-0.498633\pi$
$947$	0.264395	0.00859168	0.00429584	+	0.999991i	$0.498633\pi$
$948$	−148.775	−4.83198
$949$	37.3562	1.21263
$950$	−1.04174	−0.0337986
$951$	63.2910	2.05235
$952$	−1.32956	−0.0430911
$953$	50.7637	1.64440	0.822199	−	0.569200i	$-0.192747\pi$
$953$	50.7637	1.64440	0.822199	+	0.569200i	$0.192747\pi$
$954$	89.8352	2.90852
$955$	−10.3802	−0.335896
$956$	−128.431	−4.15374
$957$	3.09038	0.0998977
$958$	−82.1758	−2.65498
$959$	−48.0829	−1.55268
$960$	131.036	4.22918
$961$	−12.3100	−0.397098
$962$	15.9680	0.514830
$963$	−42.5882	−1.37238
$964$	−90.0005	−2.89872
$965$	38.7053	1.24597
$966$	−175.005	−5.63070
$967$	57.1268	1.83707	0.918537	−	0.395335i	$-0.129372\pi$
$967$	57.1268	1.83707	0.918537	+	0.395335i	$0.129372\pi$
$968$	95.0372	3.05461
$969$	0.0905375	0.00290848
$970$	19.7264	0.633376
$971$	1.07578	0.0345234	0.0172617	−	0.999851i	$-0.494505\pi$
$971$	1.07578	0.0345234	0.0172617	+	0.999851i	$0.494505\pi$
$972$	114.468	3.67157
$973$	−42.1899	−1.35254
$974$	82.2601	2.63578
$975$	−6.65035	−0.212982
$976$	−21.9456	−0.702462
$977$	20.5186	0.656449	0.328224	−	0.944600i	$-0.393550\pi$
$977$	20.5186	0.656449	0.328224	+	0.944600i	$0.393550\pi$
$978$	−52.4821	−1.67819
$979$	−7.42734	−0.237379
$980$	−21.5888	−0.689630
$981$	27.4517	0.876465
$982$	−51.8633	−1.65502
$983$	0.977262	0.0311698	0.0155849	−	0.999879i	$-0.495039\pi$
$983$	0.977262	0.0311698	0.0155849	+	0.999879i	$0.495039\pi$
$984$	−231.918	−7.39327
$985$	29.8494	0.951082
$986$	0.222576	0.00708827
$987$	92.1443	2.93299
$988$	23.3640	0.743309
$989$	50.3158	1.59995
$990$	12.0506	0.382994
$991$	11.2276	0.356656	0.178328	−	0.983971i	$-0.442931\pi$
$991$	11.2276	0.356656	0.178328	+	0.983971i	$0.442931\pi$
$992$	85.8861	2.72689
$993$	−58.2543	−1.84865
$994$	−76.0038	−2.41069
$995$	23.3399	0.739925
$996$	−39.6509	−1.25639
$997$	−22.6674	−0.717885	−0.358942	−	0.933360i	$-0.616863\pi$
$997$	−22.6674	−0.717885	−0.358942	+	0.933360i	$0.616863\pi$
$998$	53.8789	1.70551
$999$	0.701296	0.0221880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.6	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.6	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71378 q^{2} -2.39167 q^{3} +5.36460 q^{4} -2.12248 q^{5} +6.49047 q^{6} +2.98262 q^{7} -9.13079 q^{8} +2.72010 q^{9} +O(q^{10})\)	\(q-2.71378 q^{2} -2.39167 q^{3} +5.36460 q^{4} -2.12248 q^{5} +6.49047 q^{6} +2.98262 q^{7} -9.13079 q^{8} +2.72010 q^{9} +5.75996 q^{10} +0.769140 q^{11} -12.8304 q^{12} -5.61673 q^{13} -8.09418 q^{14} +5.07629 q^{15} +14.0498 q^{16} +0.0488202 q^{17} -7.38175 q^{18} -0.775402 q^{19} -11.3863 q^{20} -7.13346 q^{21} -2.08728 q^{22} -9.04016 q^{23} +21.8379 q^{24} -0.495062 q^{25} +15.2426 q^{26} +0.669433 q^{27} +16.0006 q^{28} -1.67998 q^{29} -13.7759 q^{30} -4.32319 q^{31} -19.8664 q^{32} -1.83953 q^{33} -0.132487 q^{34} -6.33057 q^{35} +14.5922 q^{36} +1.04760 q^{37} +2.10427 q^{38} +13.4334 q^{39} +19.3800 q^{40} -10.6200 q^{41} +19.3586 q^{42} -5.56581 q^{43} +4.12613 q^{44} -5.77337 q^{45} +24.5330 q^{46} -12.9172 q^{47} -33.6024 q^{48} +1.89604 q^{49} +1.34349 q^{50} -0.116762 q^{51} -30.1315 q^{52} -12.1699 q^{53} -1.81670 q^{54} -1.63249 q^{55} -27.2337 q^{56} +1.85451 q^{57} +4.55910 q^{58} +2.56463 q^{59} +27.2323 q^{60} -1.56199 q^{61} +11.7322 q^{62} +8.11303 q^{63} +25.8134 q^{64} +11.9214 q^{65} +4.99208 q^{66} +8.13414 q^{67} +0.261901 q^{68} +21.6211 q^{69} +17.1798 q^{70} +9.38993 q^{71} -24.8367 q^{72} -6.65088 q^{73} -2.84294 q^{74} +1.18403 q^{75} -4.15973 q^{76} +2.29405 q^{77} -36.4552 q^{78} +11.5955 q^{79} -29.8204 q^{80} -9.76136 q^{81} +28.8203 q^{82} +3.09039 q^{83} -38.2682 q^{84} -0.103620 q^{85} +15.1044 q^{86} +4.01796 q^{87} -7.02286 q^{88} -9.65668 q^{89} +15.6676 q^{90} -16.7526 q^{91} -48.4969 q^{92} +10.3397 q^{93} +35.0544 q^{94} +1.64578 q^{95} +47.5139 q^{96} +3.42475 q^{97} -5.14543 q^{98} +2.09214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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